Multi-layer Moiré targets and method of use thereof in measuring offsets in semiconductor devices

Abstract

The present invention relates to a multi-layer Moiré target for calculating offsets between at least a first layer, a second layer, and a third layer formed on a semiconductor device wafer, and includes at least one group of stacked periodic structures, each of the at least one group including: a first stack including a first stack first periodic structure (S1P1) having an S1P1 pitch along a first axis; a second stack including a second stack first periodic structure (S2P1) having an S2P1 pitch along a second axis; and a third stack including a third stack first periodic structure (S3P1) having an S3P1 pitch along a third axis; the first axis being parallel to the x-axis or the y-axis, and at least one of the stacks including a second periodic structure having a second periodic structure pitch along at least a fourth axis, the at least one fourth axis being parallel to the first axis and coaxial with one of the axes.

Description

[0001] References to Related Applications

[0002] Reference is made to U.S. Provisional Patent Application No. 62 / 872,422, filed Jul. 10, 2019, and U.S. Provisional Patent Application No. 62 / 829,839, filed Apr. 5, 2019, the disclosures of which are hereby incorporated by reference and for which priority is claimed herein.

[0003] Reference is also made to the following patents and patent applications of the applicant related to the subject matter of the present application, the disclosures of which are hereby incorporated by reference:

[0004] U.S. Patent No. 7,440,105, titled "CONTINUOUSLY VARYING OFFSET MARK AND METHODS OF DETERMINING OVERLAY";

[0005] U.S. Published Patent Application No. 2018 / 0188663, titled "DEVICE-LIKE METROLOGY TARGETS"; and

[0006] U.S. Provisional Patent Application No. 62 / 898,980, filed Sep. 11, 2019, titled "IMAGING OVERLAY TARGETS INCLUDING MOIRE ELEMENTS AND ROTATIONAL SYMMETRY ARRANGEMENTS". TECHNICAL FIELD

[0007] The present invention generally relates to measuring offsets in semiconductor device manufacturing. BACKGROUND ART

[0008] Various methods and systems are known for measuring offsets in semiconductor device manufacturing. SUMMARY OF THE INVENTION

[0009] The present invention seeks to provide improved methods and systems for measuring offsets in semiconductor device manufacturing.

[0010] Accordingly, according to a preferred embodiment of the present invention, there is provided a multi-layer Moiré target for calculating an offset between at least a first layer, a second layer, and a third layer, the first layer, the second layer, and the third layer being formed on a semiconductor device wafer, the semiconductor device wafer defining an x-y plane, the multi-layer Moiré target comprising: at least one group of stacked periodic structures, each of the at least one group comprising: a first stack of periodic structures, which at least includes a first stack first periodic structure (S1P1), the S1P1 being formed together with at least one of the first layer, the second layer, and the third layer, the S1P1 having an S1P1 pitch along a first axis; a second stack of periodic structures, which at least includes a second stack first periodic structure (S2P1), the S2P1 being formed together with at least one of the first layer, the second layer, and the third layer, the S2P1 having an S2P1 pitch along a second axis; and a third stack of periodic structures, which at least includes a third stack first periodic structure (S3P1), the S3P1 being formed together with at least one of the first layer, the second layer, and the third layer, the S3P1 having an S3P1 pitch along a third axis, when the target is imaged in the x-y plane, the first axis being parallel to the x-axis or the y-axis; when the target is imaged in the x-y plane, the second axis and the third axis being parallel to the first axis, and at least one of the first stack, the second stack, and the third stack includes a second periodic structure, the second periodic structure having a second periodic structure pitch along at least one fourth axis, when the target is imaged in the x-y plane, the at least one fourth axis being parallel to the first axis and coaxial with one of the first axis, the second axis, and the third axis.

[0011] According to a preferred embodiment of the present invention, the first layer defines a first generally planar surface parallel to the x-y plane; the second layer defines a second generally planar surface parallel to the x-y plane; the third layer defines a third generally planar surface parallel to the x-y plane; the first axis is located in a first plane parallel to one of the x-z plane or the y-z plane, one of the x-z plane or the y-z plane and the x-y plane defining a three-dimensional x-y-z coordinate system; the second axis is located in a second plane parallel to the first plane; the third axis is located in a third plane parallel to the first plane; and the at least one fourth axis is located in a respective one of the first plane, the second plane, and the third plane and parallel to a respective one of the first axis, the second axis, or the third axis.

[0012] Preferably, the first stack of the periodic structures includes the S1P1 formed together with the first layer and a first-stack second periodic structure (S1P2) formed together with the second layer, the S1P2 having an S1P2 pitch along a first one of the at least one fourth axis, the first one being coaxial with the first axis when the target is imaged in the x-y plane; the second stack of the periodic structures includes the S2P1 formed together with the second layer and a second-stack second periodic structure (S2P2) formed together with the third layer, the S2P2 having an S2P2 pitch along a second one of the at least one fourth axis, the second one being coaxial with the second axis when the target is imaged in the x-y plane; and the third stack of the periodic structures includes the S3P1 formed together with the first layer and a third-stack second periodic structure (S3P2) formed together with the third layer, the S3P2 having an S3P2 pitch along a third one of the at least one fourth axis when the target is imaged in the x-y plane.

[0013] Preferably, the S2P1 pitch is related to the S1P2 pitch by a second-stack multiplication factor; the S2P2 pitch is related to the S1P1 pitch by the second-stack multiplication factor; the S3P1 pitch is related to the S1P1 pitch by a third-stack multiplication factor; and the S3P2 pitch is related to the S1P2 pitch by the third-stack multiplication factor. According to a preferred embodiment of the present invention, the second-stack multiplication factor is equal to 1 and the third-stack multiplication factor is equal to 1.

[0014] According to a preferred embodiment of the present invention, the first stack of the periodic structures includes the S1P1 formed together with the first layer and a first-stack second periodic structure (S1P2) formed together with the second layer, the S1P2 having an S1P2 pitch along a first one of the at least one fourth axis; the second stack of the periodic structures includes the S2P1 formed together with the first layer and a second-stack second periodic structure (S2P2) formed together with the second layer, the S2P2 having an S2P2 pitch along a second one of the at least one fourth axis; and the third stack of the periodic structures includes the S3P1 formed together with the second layer and a third-stack second periodic structure (S3P2) formed together with the third layer, the S3P2 having an S3P2 pitch along a third one of the at least one fourth axis.

[0015] According to a preferred embodiment of the present invention, the first stack of the periodic structure includes the S1P1 formed together with the first layer and a first-stack second periodic structure (S1P2) formed together with the second layer, and the S1P2 has an S1P2 pitch along a first one of the at least one fourth axis; the second stack of the periodic structure includes the S2P1 formed together with the first layer and a second-stack second periodic structure (S2P2) formed together with the second layer, and the S2P2 has an S2P2 pitch along a second one of the at least one fourth axis; and the third stack of the periodic structure includes the S3P1 formed together with the second layer and a third-stack second periodic structure (S3P2) formed together with the first layer, and the S3P2 has an S3P2 pitch along a third one of the at least one fourth axis.

[0016] Preferably, the S3P1 pitch is related to the S2P2 pitch by a third-stack multiplication factor, and the S3P2 pitch is related to the S2P1 pitch by the third-stack multiplication factor. According to a preferred embodiment of the present invention, the third-stack multiplication factor is equal to 1. According to a preferred embodiment of the present invention, the S1P1 pitch is the same as the S2P2 pitch and the S1P2 pitch is the same as the S2P1 pitch. Alternatively, the S1P1 pitch is the same as the S2P1 pitch; the S1P2 pitch differs from the S1P1 pitch by an additional term; the S2P2 pitch differs from the S1P1 pitch by the additional term; the S3P1 pitch differs from the S1P1 pitch by the additional term; and the S3P2 pitch is the same as the S1P1 pitch.

[0017] According to a preferred embodiment of the present invention, the first stack of the periodic structure includes the S1P1 formed together with the second layer; the second stack of the periodic structure includes the S2P1 formed together with the first layer and a second-stack second periodic structure (S2P2) formed together with the second layer, and the S2P2 has an S2P2 pitch along a second one of the at least one fourth axis; and the third stack of the periodic structure includes the S3P1 formed together with the second layer and a third-stack second periodic structure (S3P2) formed together with the third layer, and the S3P2 has an S3P2 pitch along a third one of the at least one fourth axis. According to a preferred embodiment of the present invention, the S2P1 pitch is the same as the S3P2 pitch, and the S2P2 pitch is the same as the S3P1 pitch.

[0018] According to a preferred embodiment of the present invention, the first stack of the periodic structure includes the S1P1 formed together with the second layer; the second stack of the periodic structure includes the S2P1 formed together with the first layer; and the third stack of the periodic structure includes the S3P1 formed together with the second layer and a third stack second periodic structure (S3P2) formed together with the third layer, and the S3P2 has an S3P2 pitch along the at least one fourth axis.

[0019] According to a preferred embodiment of the present invention, the first stack of the periodic structure includes the S1P1 formed together with the first layer; the second stack of the periodic structure includes the S2P1 formed together with the first layer; and the third stack of the periodic structure includes the S3P1 formed together with the first layer and a third stack second periodic structure (S3P2) formed together with the third layer, and the S3P2 has an S3P2 pitch along the at least one fourth axis.

[0020] According to a preferred embodiment of the present invention, the first stack of the periodic structure includes the S1P1 formed together with the second layer; the second stack of the periodic structure includes the S2P1 formed together with the first layer; and the third stack of the periodic structure includes the S3P1 formed together with the second layer and a third stack second periodic structure (S3P2) formed together with the first layer, and the S3P2 has an S3P2 pitch along the at least one fourth axis.

[0021] According to a preferred embodiment of the present invention, the first stack of the periodic structure includes the S1P1 formed together with the first layer; the second stack of the periodic structure includes the S2P1 formed together with the first layer and a second stack second periodic structure (S2P2) formed together with the second layer, and the S2P2 has an S2P2 pitch along the first one of the at least one fourth axis; and the third stack of the periodic structure includes the S3P1 formed together with the second layer and a third stack second periodic structure (S3P2) formed together with the third layer, and the S3P2 has an S3P2 pitch along the second one of the at least one fourth axis.

[0022] Preferably, the at least one group of the periodic structure stacks includes: at least one first group of periodic stacks, wherein when the target is imaged in the x-y plane, the first axis is parallel to the x-axis; and at least one second group of periodic stacks, wherein when the target is imaged in the x-y plane, the first axis is parallel to the y-axis. Additionally, the at least one first group of periodic stacks and the at least one second group of periodic stacks are identical except for their orientations.

[0023] According to a preferred embodiment of the present invention, the target is characterized by mirror symmetry. According to a preferred embodiment of the present invention, the target is characterized by rotational symmetry.

[0024] According to another preferred embodiment of the present invention, there is also provided a multi-layer Moiré target for calculating the offset between at least a first layer, a second layer, a third layer, and a fourth layer, the first layer, the second layer, the third layer, and the fourth layer being formed on a semiconductor device wafer that defines an x-y plane, the multi-layer Moiré target including: at least one group of stacked periodic structures, each of the at least one group including: a first stack of periodic structures that includes at least a first stacked first periodic structure (S1P1) formed together with at least one of the first layer, the second layer, the third layer, and the fourth layer, the S1P1 having an S1P1 pitch along a first axis; a second stack of periodic structures that includes at least a second stacked first periodic structure (S2P1) formed together with at least one of the first layer, the second layer, the third layer, and the fourth layer, the S2P1 having an S2P1 pitch along a second axis; a third stack of periodic structures that includes at least a third stacked first periodic structure (S3P1) formed together with at least one of the first layer, the second layer, the third layer, and the fourth layer, the S3P1 having an S3P1 pitch along a third axis; and a fourth stack of periodic structures that includes at least a fourth stacked first periodic structure (S4P1) formed together with at least one of the first layer, the second layer, the third layer, and the fourth layer, the S4P1 having an S4P1 pitch along a fourth axis, when the target is imaged in the x-y plane, the first axis being parallel to the x-axis or the y-axis; when the target is imaged in the x-y plane, the second axis, the third axis, and the fourth axis being parallel to the first axis, and at least one of the first stack, the second stack, the third stack, and the fourth stack including a second periodic structure having a second periodic structure pitch along at least a fifth axis, when the target is imaged in the x-y plane, the at least a fifth axis being parallel to the first axis and coaxial with one of the first axis, the second axis, the third axis, and the fourth axis.

[0025] According to a preferred embodiment of the present invention, the first layer defines a first generally planar surface parallel to the x-y plane; the second layer defines a second generally planar surface parallel to the x-y plane; the third layer defines a third generally planar surface parallel to the x-y plane; the fourth layer defines a first generally planar surface parallel to the x-y plane; the first axis lies in a first plane parallel to one of the x-z plane or the y-z plane, and the one of the x-z plane or the y-z plane together with the x-y plane defines a three-dimensional x-y-z coordinate system; the second axis lies in a second plane parallel to the first plane; the third axis lies in a third plane parallel to the first plane; the fourth axis lies in a third plane parallel to the first plane; and the at least one fifth axis lies in a respective one of the first plane, the second plane, the third plane, and the fourth plane and is parallel to a respective one of the first axis, the second axis, the third axis, or the fourth axis.

[0026] According to a preferred embodiment of the present invention, the first stack of periodic structures includes the S1P1 formed with the first layer and a first stack second periodic structure (S1P2) formed with the second layer, the S1P2 having an S1P2 pitch along a first one of the at least one fifth axis, the first one being coaxial with the first axis when the target is imaged in the x-y plane; the second stack of periodic structures includes the S2P1 formed with the first layer and a second stack second periodic structure (S2P2) formed with the second layer, the S2P2 having an S2P2 pitch along a second one of the at least one fifth axis, the second one being coaxial with the second axis when the target is imaged in the x-y plane; the third stack of periodic structures includes the S3P1 formed with the second layer and a third stack second periodic structure (S3P2) formed with the third layer, the S3P2 having an S3P2 pitch along a third one of the at least one fifth axis, the third one being coaxial with the third axis when the target is imaged in the x-y plane; and the fourth stack of periodic structures includes the S4P1 formed with the third layer and a fourth stack second periodic structure (S4P2) formed with the fourth layer, the S4P2 having an S4P2 pitch along a fourth one of the at least one fifth axis, the fourth one being coaxial with the fourth axis when the target is imaged in the x-y plane.

[0027] According to a preferred embodiment of the present invention, the S3P1 pitch is related to the S2P2 pitch by a third stacking multiplication factor; the S3P2 pitch is related to the S2P1 pitch by the third stacking multiplication factor; the S4P1 pitch is related to the S2P1 pitch by a fourth stacking multiplication factor; and the S4P2 pitch is related to the S2P2 pitch by the fourth stacking multiplication factor.

[0028] According to a preferred embodiment of the present invention, the first stack of the periodic structure includes the S1P1 formed together with the first layer and a first stack second periodic structure (S1P2) formed together with the second layer. The S1P2 has an S1P2 pitch along a first one of the at least one fifth axis, and when the target is imaged in the x-y plane, the first one is coaxial with the first axis; the second stack of the periodic structure includes the S2P1 formed together with the second layer; the third stack of the periodic structure includes the S3P1 formed together with the second layer and a third stack second periodic structure (S3P2) formed together with the third layer. The S3P2 has an S3P2 pitch along a second one of the at least one fifth axis, and when the target is imaged in the x-y plane, the second one is coaxial with the third axis; and the fourth stack of the periodic structure includes the S4P1 formed together with the third layer and a fourth stack second periodic structure (S4P2) formed together with the fourth layer. The S4P2 has an S4P2 pitch along a third one of the at least one fifth axis, and when the target is imaged in the x-y plane, the third one is coaxial with the fourth axis.

[0029] Preferably, the S4P1 pitch is related to the S3P2 pitch by a fourth stacking multiplication factor, and the S4P2 pitch is related to the S3P1 pitch by the fourth stacking multiplication factor.

[0030] According to a preferred embodiment of the present invention, the first stack of the periodic structures includes the S1P1 formed together with the first layer and a second periodic structure of the first stack (S1P2) formed together with the second layer, the S1P2 having an S1P2 pitch along a first one of the at least one fifth axis, the first one being coaxial with the first axis when the target is imaged in the x-y plane; the second stack of the periodic structures includes the S2P1 formed together with the second layer and a second periodic structure of the second stack (S2P2) formed together with the third layer, the S2P2 having an S2P2 pitch along a second one of the at least one fifth axis, the second one being coaxial with the second axis when the target is imaged in the x-y plane; the third stack of the periodic structures includes the S3P1 formed together with the first layer and a second periodic structure of the third stack (S3P2) formed together with the third layer, the S3P2 having an S3P2 pitch along a third one of the at least one fifth axis, the third one being coaxial with the third axis when the target is imaged in the x-y plane; and the fourth stack of the periodic structures includes the S4P1 formed together with the third layer and a second periodic structure of the fourth stack (S4P2) formed together with the fourth layer, the S4P2 having an S4P2 pitch along a fourth one of the at least one fifth axis, the fourth one being coaxial with the fourth axis when the target is imaged in the x-y plane.

[0031] Preferably, the S2P1 pitch is related to the S1P2 pitch by a second stack multiplication factor; the S2P2 pitch is related to the S1P1 pitch by the second stack multiplication factor; the S3P1 pitch is related to the S1P1 pitch by a third stack multiplication factor; the S3P2 pitch is related to the S1P2 pitch by the third stack multiplication factor; the S4P1 pitch is related to the S1P2 pitch by a fourth stack multiplication factor; and the S4P2 pitch is related to the S1P1 pitch by the fourth stack multiplication factor.

[0032] According to a preferred embodiment of the present invention, the first stack of the periodic structures includes the S1P1 formed together with the first layer and a second periodic structure of the first stack (S1P2) formed together with the second layer, the S1P2 having an S1P2 pitch along a first one of the at least one fifth axis, the first one being coaxial with the first axis when the target is imaged in the x-y plane; the second stack of the periodic structures includes the S2P1 formed together with the second layer; the third stack of the periodic structures includes the S3P1 formed together with the third layer; and the fourth stack of the periodic structures includes the S4P1 formed together with the fourth layer.

[0033] According to a preferred embodiment of the present invention, the first stack of the periodic structures includes the S1P1 formed together with the first layer and a second periodic structure of the first stack (S1P2) formed together with the second layer, the S1P2 having an S1P2 pitch along a first one of the at least one fifth axis, which is coaxial with the first axis when the target is imaged in the x-y plane; the second stack of the periodic structures includes the S2P1 formed together with the second layer; the third stack of the periodic structures includes the S3P1 formed together with the third layer; and the fourth stack of the periodic structures includes the S4P1 formed together with the fourth layer.

[0034] According to a preferred embodiment of the present invention, the first stack of the periodic structures includes the S1P1 formed together with the first layer and a second periodic structure of the first stack (S1P2) formed together with the second layer, the S1P2 having an S1P2 pitch along a first one of the at least one fifth axis, which is coaxial with the first axis when the target is imaged in the x-y plane; the second stack of the periodic structures includes the S2P1 formed together with the second layer; the third stack of the periodic structures includes the S3P1 formed together with the third layer; and the fourth stack of the periodic structures includes the S4P1 formed together with the second layer.

[0035] According to a preferred embodiment of the present invention, the first stack of the periodic structures includes the S1P1 formed together with the first layer and a second periodic structure of the first stack (S1P2) formed together with the second layer, the S1P2 having an S1P2 pitch along a first one of the at least one fifth axis, which is coaxial with the first axis when the target is imaged in the x-y plane; the second stack of the periodic structures includes the S2P1 formed together with the second layer; the third stack of the periodic structures includes the S3P1 formed together with the third layer; and the fourth stack of the periodic structures includes the S4P1 formed together with the third layer.

[0036] According to a preferred embodiment of the present invention, the at least one group of the periodic structure stacks includes: at least one first group of periodic stacks, wherein the first axis is parallel to the x-axis when the target is imaged in the x-y plane; and at least one second group of periodic stacks, wherein the first axis is parallel to the y-axis when the target is imaged in the x-y plane. Additionally, the at least one first group of periodic stacks and the at least one second group of periodic stacks are identical except for their orientations.

[0037] Preferably, the target is characterized by mirror symmetry. According to a preferred embodiment of the present invention, the target is characterized by rotational symmetry.

[0038] According to yet another preferred embodiment of the present invention, there is further provided a multi-layer Moiré target for calculating an offset between at least a first layer, a second layer, a third layer, and a fourth layer, the first layer, the second layer, the third layer, and the fourth layer being formed on a semiconductor device wafer, the semiconductor device wafer defining an x-y plane, the multi-layer Moiré target comprising: at least one group of stacked periodic structures, each of the at least one group comprising: a first stack of periodic structures, which at least comprises a first stack first periodic structure (S1P1), the S1P1 being formed together with at least one of the first layer, the second layer, the third layer, and the fourth layer, the S1P1 having an S1P1 pitch along a first axis; a second stack of periodic structures, which at least comprises a second stack first periodic structure (S2P1), the S2P1 being formed together with at least one of the first layer, the second layer, the third layer, and the fourth layer, the S2P1 having an S2P1 pitch along a second axis; and a third stack of periodic structures, which at least comprises a third stack first periodic structure (S3P1), the S3P1 being formed together with at least one of the first layer, the second layer, the third layer, and the fourth layer, the S3P1 having an S3P1 pitch along a third axis; when the target is imaged in the x-y plane, the first axis is parallel to the x-axis or the y-axis; when the target is imaged in the x-y plane, the second axis and the third axis are parallel to the first axis, and at least one of the first stack, the second stack, and the third stack comprises a second periodic structure, the second periodic structure having a second periodic structure pitch along at least a fourth axis, when the target is imaged in the x-y plane, the at least one fourth axis is parallel to the first axis and coaxial with one of the first axis, the second axis, and the third axis.

[0039] According to a preferred embodiment of the present invention, the first stack of the periodic structures includes the S1P1 formed together with the first layer and a first-stack second periodic structure (S1P2) formed together with the second layer, and the S1P2 has an S1P2 pitch along a first one of the at least one fourth axis; the second stack of the periodic structures includes the S2P1 formed together with the first layer and a second-stack second periodic structure (S2P2) formed together with the third layer, and the S2P2 has an S2P2 pitch along a second one of the at least one fourth axis; and the third stack of the periodic structures includes the S3P1 formed together with the first layer and a third-stack second periodic structure (S3P2) formed together with the fourth layer, and the S3P2 has an S3P2 pitch along a third one of the at least one fourth axis.

[0040] According to a preferred embodiment of the present invention, the at least one group of stacks of periodic structures includes: at least one first group of periodic stacks, wherein when the target is imaged in the x-y plane, the first axis is parallel to the x axis; and at least one second group of periodic stacks, wherein when the target is imaged in the x-y plane, the first axis is parallel to the y axis. Additionally, the at least one first group of periodic stacks and the at least one second group of periodic stacks are identical except for their orientation. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] The present invention will be more fully understood and appreciated in conjunction with the drawings, in which:

[0042] Figure 1 is a simplified illustrative view of a first embodiment of a multi-layer Moiré target of the present invention;

[0043] Figure 2A 、 2B 、2C, and 2D are simplified corresponding top view, first cross-sectional side view, second cross-sectional side view, and third cross-sectional side view illustrative views of another embodiment of a multi-layer Moiré target of the present invention, Figure 2B 、 2C and 2D are taken along lines B–B, C–C, and D–D in Figure 2A respectively;

[0044] Figure 3A is a simplified flow chart illustrating a preferred method for calculating the offset between layers, Figure 1 or Figures 2A to 2D a multi-layer Moiré target of is formed on the layer;

[0045] Figure 3B and 3C are respectively Figure 3ASimplified illustrations of the first and second embodiments of parts of the method are illustrated;

[0046] Figure 4 Is a simplified illustration of another embodiment of the multi-layer Moiré target of the present invention;

[0047] Figure 5A 、 5B 、5C and 5D are simplified illustrations of the corresponding top view, first cross-sectional side view, second cross-sectional side view, and third cross-sectional side view of another embodiment of the multi-layer Moiré target of the present invention, Figure 5B 、 5C and 5D are taken along the lines B–B, C–C, and D–D in Figure 5A respectively;

[0048] Figure 6A Is a simplified flowchart illustrating a preferred method for calculating the offset between layers, Figure 4 or Figures 5A to 5D The multi-layer Moiré target ofis formed on the layer;

[0049] Figure 6B and 6C are respectively Figure 6A Simplified illustrations of the first and second embodiments of parts of the method;

[0050] Figure 7 Is a simplified illustration of another embodiment of the multi-layer Moiré target of the present invention;

[0051] Figure 8A 、 8B 、8C and 8D are simplified illustrations of the corresponding top view, first cross-sectional side view, second cross-sectional side view, and third cross-sectional side view of another embodiment of the multi-layer Moiré target of the present invention, Figure 8B 、 8C and 8D are taken along the lines B–B, C–C, and D–D in Figure 8A respectively;

[0052] Figure 9A Is a simplified flowchart illustrating a preferred method for calculating the offset between layers, Figure 7 or Figures 8A to 8D The multi-layer Moiré target ofis formed on the layer;

[0053] Figure 9B and 9C are respectively Figure 9A Simplified illustrations of the first and second embodiments of parts of the method;

[0054] Figure 10 Is a simplified illustration of another embodiment of the multi-layer Moiré target of the present invention;

[0055] Figure 11A 、 11B Figures 11C and 11D are simplified corresponding top views, first cross-sectional side views, second cross-sectional side views, and third cross-sectional side views of another embodiment of the multi-layer Moiré target of the present invention, Figure 11B 、 Figure 11C and 11D are taken along lines B–B, C–C, and D–D in Figure 11A respectively;

[0056] Figure 12A is a simplified flowchart illustrating a preferred method for calculating the offset between layers, Figure 10 or Figures 11A to 11D A multi-layer Moiré target is formed on the layer;

[0057] Figure 12B and 12C are respectively simplified illustrated diagrams of a first embodiment and a second embodiment of parts of the method of Figure 12A ;

[0058] Figure 13 is a simplified illustration of another embodiment of the multi-layer Moiré target of the present invention;

[0059] Figure 14A 、 14B Figures 14C and 14D are simplified corresponding top views, first cross-sectional side views, second cross-sectional side views, and third cross-sectional side views of another embodiment of the multi-layer Moiré target of the present invention, Figure 14B 、 14C and 14D are taken along lines B–B, C–C, and D–D in Figure 14A respectively;

[0060] Figure 15A is a simplified flowchart illustrating a preferred method for calculating the offset between layers, Figure 13 or Figures 14A to 14D A multi-layer Moiré target is formed on the layer;

[0061] Figure 15B and 15C are respectively simplified illustrated diagrams of a first embodiment and a second embodiment of parts of the method of Figure 15A ;

[0062] Figure 16 is a simplified illustration of another embodiment of the multi-layer Moiré target of the present invention;

[0063] Figure 17A 、 17B, 17C and 17D are simplified corresponding top views, first cross-sectional side views, second cross-sectional side views, and third cross-sectional side views of another embodiment of the multi-layer Moiré target of the present invention, Figure 17B , 17C and 17D are respectively taken along Figure 17A the lines B–B, C–C, and D–D in

[0064] Figure 18A is a simplified flowchart illustrating a preferred method for calculating the offset between layers, Figure 16 or Figures 17A to 17D a multi-layer Moiré target is formed on the layer;

[0065] Figure 18B and 18C are respectively simplified illustrated diagrams of a first embodiment and a second embodiment of parts of the Figure 18A method;

[0066] Figure 19A , 19B , 19C and 19D are simplified corresponding top views, first cross-sectional side views, second cross-sectional side views, and third cross-sectional side views of another embodiment of the multi-layer Moiré target of the present invention, Figure 19B , 19C and 19D are respectively taken along Figure 19A the lines B–B, C–C, and D–D in

[0067] Figure 20A , 20B , 20C and 20D are simplified corresponding top views, first cross-sectional side views, second cross-sectional side views, and third cross-sectional side views of another embodiment of the multi-layer Moiré target of the present invention, Figure 20B , 20C and 20D are respectively taken along Figure 20A the lines B–B, C–C, and D–D in

[0068] Figure 21A is a simplified flowchart illustrating a preferred method for calculating the offset between layers, Figures 19A to 19D or Figures 20A to 20D a multi-layer Moiré target is formed on the layer;

[0069] Figure 21B and 21C are respectively Figure 21A simplified illustrated diagrams of a first embodiment and a second embodiment of parts of the

[0070] Figure 22A , 22B, 22C, 22D, and 22E are simplified corresponding top view, first cross-sectional side view, second cross-sectional side view, third cross-sectional side view, and fourth cross-sectional side view illustrations of another embodiment of the multi-layer Moiré target of the present invention. Figure 22B , 22C , 22D, and 22E are taken along lines B–B, C–C, D–D, and E–E in Figure 22A respectively;

[0071] Figure 23A , 23B , 23C, 23D, and 23E are simplified corresponding top view, first cross-sectional side view, second cross-sectional side view, third cross-sectional side view, and fourth cross-sectional side view illustrations of another embodiment of the multi-layer Moiré target of the present invention. Figure 23B , 23C , 23D, and 23E are taken along lines B–B, C–C, D–D, and E–E in Figure 23A respectively;

[0072] Figure 24A and 24B together are a simplified flowchart illustrating a preferred method for calculating the offset between layers. Figures 22A to 22E or Figures 23A to 23E of the multi-layer Moiré target is formed on the layer;

[0073] Figure 24C and 24D are respectively simplified illustrated diagrams of the first embodiment and the second embodiment of parts of the method of Figure 24A and 24B ;

[0074] Figure 25A , 25B , 25C, 25D, and 25E are simplified corresponding top view, first cross-sectional side view, second cross-sectional side view, third cross-sectional side view, and fourth cross-sectional side view illustrations of another embodiment of the multi-layer Moiré target of the present invention. Figure 25B , 25C , 25D, and 25E are taken along lines B–B, C–C, D–D, and E–E in Figure 25A respectively;

[0075] Figure 26A , 26B , 26C, 26D, and 26E are simplified corresponding top view, first cross-sectional side view, second cross-sectional side view, third cross-sectional side view, and fourth cross-sectional side view illustrations of another embodiment of the multi-layer Moiré target of the present invention. Figure 26B , 26C , 26D, and 26E are taken along lines B–B, C–C, D–D, and E–E in Figure 26A respectively;

[0076] Figure 27A Together with 27B is a simplified flowchart illustrating a preferred method for calculating the offset between calculation layers, Figures 25A to 25E or Figures 26A to 26E a multi-layer Moiré target is formed on the layer;

[0077] Figure 27C and 27D are respectively Figure 27A and 27B simplified illustrations of the first and second embodiments of parts of the methods of

[0078] Figure 28A , 28B , 28C, 28D and 28E are simplified corresponding top views, first cross-sectional side views, second cross-sectional side views, third cross-sectional side views and fourth cross-sectional side views of another embodiment of the multi-layer Moiré target of the present invention, Figure 28B , 28C , 28D and 28E are respectively taken along Figure 28A the lines B–B, C–C, D–D and E–E in

[0079] Figure 29A , 29B , 29C, 29D and 29E are simplified corresponding top views, first cross-sectional side views, second cross-sectional side views, third cross-sectional side views and fourth cross-sectional side views of another embodiment of the multi-layer Moiré target of the present invention, Figure 29B , 29C , 29D and 29E are respectively taken along Figure 29A the lines B–B, C–C, D–D and E–E in

[0080] Figure 30A Together with 30B is a simplified flowchart illustrating a preferred method for calculating the offset between calculation layers, Figures 28A to 28E or Figures 29A to 29E a multi-layer Moiré target is formed on the layer;

[0081] Figure 30C and 30D are respectively Figure 30A and 30B simplified illustrations of the first and second embodiments of parts of the methods of

[0082] Figure 31A , 31B, 31C, 31D, and 31E are simplified corresponding top view, first cross-sectional side view, second cross-sectional side view, third cross-sectional side view, and fourth cross-sectional side view illustrations of another embodiment of the multi-layer Moiré target of the present invention. Figure 31B , 31C , 31D, and 31E are taken along lines B–B, C–C, D–D, and E–E in Figure 31A respectively;

[0083] Figure 32A , 32B , 32C, 32D, and 32E are simplified corresponding top view, first cross-sectional side view, second cross-sectional side view, third cross-sectional side view, and fourth cross-sectional side view illustrations of another embodiment of the multi-layer Moiré target of the present invention. Figure 32B , 32C , 32D, and 32E are taken along lines B–B, C–C, D–D, and E–E in Figure 32A respectively;

[0084] Figure 33A and 33B together are a simplified flowchart illustrating a preferred method for calculating the offset between layers, Figures 31A to 31E or Figures 32A to 32E of the multi-layer Moiré target is formed on the layer;

[0085] Figure 33C and 33D are respectively Figure 33A and 33B of the first embodiment and the second embodiment of the part of the method are simplified illustrated diagrams;

[0086] Figure 34 is a simplified illustration of another embodiment of the multi-layer Moiré target of the present invention;

[0087] Figure 35 is a simplified illustration of another embodiment of the multi-layer Moiré target of the present invention;

[0088] Figure 36 is a simplified illustration of another embodiment of the multi-layer Moiré target of the present invention;

[0089] Figure 37 is a simplified illustration of another embodiment of the multi-layer Moiré target of the present invention;

[0090] Figure 38 is a simplified illustration of another embodiment of the multi-layer Moiré target of the present invention; and

[0091] Figure 39 is a simplified illustration of another embodiment of the multi-layer Moiré target of the present invention. Detailed Description

[0092] It should be understood that the objectives and methods described hereinafter form part of the manufacturing process for semiconductor devices, and the offsets measured using the objectives and methods described hereinafter are used to adjust the manufacturing process of semiconductor devices to more closely align the various layers of the semiconductor device being fabricated. Figures 1 to 39 It should be understood that the objectives and methods described hereinafter form part of the manufacturing process for semiconductor devices, and the offsets measured using the objectives and methods described hereinafter are used to adjust the manufacturing process of semiconductor devices to more closely align the various layers of the semiconductor device being fabricated. Figures 1 to 39 It should be understood that the objectives described hereinafter include at least one group of periodic structure stacks, where each stack contains one or more periodic structures, and each periodic structure has a pitch. It should be understood that in the embodiments described hereinafter, all the periodic structures within a single stack have different pitches.

[0093] It should be understood that the objectives described hereinafter include at least one group of periodic structure stacks, where each stack contains one or more periodic structures, and each periodic structure has a pitch. It should be understood that in the embodiments described hereinafter, all the periodic structures within a single stack have different pitches.

[0094] Now referring to Figure 1 , which is a simplified graphical illustration of a first embodiment of the multi-layer Moiré target 100 of the present invention. Figure 1 The illustration includes three different dimensions indicated by the x-axis, y-axis, and z-axis, which are hereinafter referred to as the x-y plane, x-z plane, and y-z plane, respectively. It should be noted that Figure 1 generally illustrates the x-y plane, while Figure 1 the enlarged views A, B, and C of illustrate a plane parallel to the x-z plane.

[0095] The target 100 is preferably formed on a semiconductor device wafer, on which at least a first layer 102, a second layer 104, and a third layer 106 are preferably formed. It should be understood that each of the first layer 102, the second layer 104, and the third layer 106 defines a generally planar surface parallel to the x-y plane. The first layer 102, the second layer 104, and the third layer 106 may be adjacent layers but need not be. Preferably, any material between the first layer 102, the second layer 104, and the third layer 106 is at least partially transparent to electromagnetic radiation. In the embodiment illustrated in Figure 1 , the first layer 102 is located below the second layer 104 and the third layer 106, and the third layer 106 is located above the first layer 102 and the second layer 104. However, it should be understood that the layers 102, 104, and 106 may be arranged in any suitable order relative to each other along the z-axis.

[0096] It should be understood that Figure 1 illustrates one possible layout of the target 100, and in other embodiments of the present invention, the target 100 may include additional structures. For example, as described hereinafter with reference to Figures 2A to 2D and 34 to 39, suitable targets may include Figure 1 multiple examples of the structures shown in , and those multiple examples can be arranged in various ways.

[0097] Preferably, the target 100 includes a first stack 122 of periodic structures, a second stack 124 of periodic structures, and a third stack 126 of periodic structures. Each of the first stack 122, the second stack 124, and the third stack 126 includes one or more periodic structures, and each periodic structure has a pitch. Preferably, none of the first stack 122, the second stack 124, and the third stack 126 overlap with each other.

[0098] It should be understood that although in Figure 1 , each of the periodic structures of the first stack 122, the second stack 124, and the third stack 126 is shown as being formed by a plurality of lines and spaces, in other embodiments of the present invention, the periodic structures of the first stack 122, the second stack 124, and the third stack 126 may be formed by any suitable periodic features. It should be further understood that the periodic features forming the periodic structures included in the first stack 122, the second stack 124, and the third stack 126 may be formed by sub-structures. The pitch of each of the periodic structures of the first stack 122, the second stack 124, and the third stack 126 is preferably between 10 nm and 3000 nm, and more preferably between 200 nm and 800 nm.

[0099] The first x-z plane 131 intersects the first stack 122. A plurality of first axes 132 are located in the first x-z plane 131 and parallel to the x-axis. The second x-z plane 133 intersects the second stack 124. A plurality of second axes 134 are located in the second x-z plane 133 and parallel to the x-axis. The third x-z plane 135 intersects the third stack 126. A plurality of third axes 136 are located in the third x-z plane 135 and parallel to the x-axis.

[0100] As specifically seen in magnification A, the first stack 122 includes a first-stack first periodic structure (S1P1) 142, which is formed together with the first layer 102 and has an S1P1 pitch designated as A along one of the first axes 132. The first stack 122 further includes a first-stack second periodic structure (S1P2) 144, which is formed together with the second layer 104 and has an S1P2 pitch designated as B along the other of the first axes 132.

[0101] It should be understood that S1P1 142 and S1P2 144 at least partially overlap each other, and a first-stack moiré pattern 150 is visible immediately after imaging the first stack 122. As is known in the art, the first-stack moiré pattern 150 is characterized by a pitch C1, which is a function of pitches A and B, as shown in Equation 1:

[0102]

[0103] Preferably, the first stack 122 does not include a periodic structure that forms with the third layer 106 and affects the periodicity of the Moiré pattern 150. However, the first stack 122 may include a periodic structure that forms with the third layer 106 and does not affect the periodicity of the Moiré pattern 150, such as a periodic structure that is periodic along an axis parallel to the y-axis or has a pitch size that does not affect the Moiré pattern 150.

[0104] As specifically seen in magnification B, the second stack 124 includes a second-stack first periodic structure (S2P1) 152 that forms with the second layer 104 and has an S2P1 pitch designated as dB along one of the second axes 134. Preferably, the S2P1 pitch dB is related to the S1P2 pitch B by a second-stack multiplication factor designated as d. The second-stack multiplication factor d can be any positive number. The second stack 124 further includes a second-stack second periodic structure (S2P2) 154 that forms with the third layer 106 and has an S2P2 pitch designated as dA along the other of the second axes 134. Preferably, the S2P2 pitch dA is related to the S1P1 pitch A by the second-stack multiplication factor d. It should be understood that the second-stack multiplication factor d that relates the S2P2 pitch dA to the S1P1 pitch A has the same value as the second-stack multiplication factor d that relates the S2P1 pitch dB to the S1P2 pitch B. In an embodiment of the present invention, the value of d is 1 and thus the S2P1 pitch dB is the same as the S1P2 pitch B and the S2P2 pitch dA is the same as the S1P1 pitch A.

[0105] It should be understood that S2P1 152 and S2P2 154 at least partially overlap each other, and a second-stack Moiré pattern 160 is visible immediately after imaging the second stack 124. As is known in the art, the second-stack Moiré pattern 160 is characterized by a pitch C2 that is a function of the second-stack multiplication factor d, the pitch A, and the pitch B, as shown in Equation 2:

[0106]

[0107] Preferably, the second stack 124 does not include a periodic structure that forms with the first layer 102 and affects the periodicity of the Moiré pattern 160. However, the second stack 124 may include a periodic structure that forms with the first layer 102 and does not affect the periodicity of the Moiré pattern 160, such as a periodic structure that is periodic along an axis parallel to the y-axis or has a pitch size that does not affect the Moiré pattern 160.

[0108] As specifically seen in magnification C, the third stack 126 includes a third stack first periodic structure (S3P1) 162, the S3P1 being formed with the first layer 102 and having an S3P1 pitch designated as eA along one of the third axes 136. Preferably, the S3P1 pitch eA is related to the S1P1 pitch A by a third stack multiplication factor designated as e. The third stack multiplication factor e can be any positive number. The third stack 126 further includes a third stack second periodic structure (S3P2) 164, the S3P2 being formed with the third layer 106 and having an S3P2 pitch designated as eB along the other of the third axes 136. Preferably, the S3P2 pitch eB is related to the S1P2 pitch B by the third stack multiplication factor e. It should be understood that the third stack multiplication factor e that relates the S3P2 pitch eB to the S1P2 pitch B has the same value as the third stack multiplication factor e that relates the S3P1 pitch eA to the S1P1 pitch A. In an embodiment of the present invention, the value of e is 1 and thus the S3P1 pitch eA is the same as the S1P1 pitch A and the S3P2 pitch eB is the same as the S1P2 pitch B.

[0109] It should be understood that the S3P1 162 and the S3P2 164 at least partially overlap each other, and a third stack moiré pattern 170 is visible immediately after imaging the third stack 126. As is known in the art, the third stack moiré pattern 170 is characterized by a pitch C3, the pitch C3 being a function of the third stack multiplication factor e, the pitch A, and the pitch B, as shown in Equation 3:

[0110]

[0111] Preferably, the third stack 126 does not include a periodic structure that forms with the second layer 104 and affects the moiré pattern 170. However, the third stack 126 can include a periodic structure that forms with the second layer 104 and does not affect the moiré pattern 170, such as a periodic structure that is periodic along an axis parallel to the y-axis or has a pitch size that does not affect the moiré pattern 170.

[0112] Preferably, an imaging offset metrology tool with adjustable polarization, wavelength, and numerical aperture settings is used to measure the offset between any two of the layers 102, 104, and 106. An example of a suitable imaging offset metrology tool is the Archer available commercially from KLA Corporation, Milpitas, California, USA TM 700. The pitches A, B, dA, dB, eA, and eB do not need to be optically resolvable by the offset metrology tool used to generate the image of the target 100. However, preferably, each of the pitches C1, C2, and C3 is optically resolvable by the offset metrology tool used to generate the image of the target 100.

[0113] Now referring toFigures 2A to 2D , which is a simplified illustrative diagram of another embodiment of the multi-layer Moiré target 200 of the present invention. Figures 2A to 2D An illustrative diagram in three different dimensions indicated by the x-axis, y-axis, and z-axis, which three dimensions are hereinafter referred to as the x-y plane, x-z plane, and y-z plane respectively. It should be noted that Figure 2A generally illustrates the x-y plane, while Figure 2B , 2C and the 2D illustrates a plane parallel to the x-z plane.

[0114] It should be noted that the target 200 is an example of an alternative layout of the target 100 described above with reference to Figure 1 and additional layouts are described hereinafter with reference to Figures 34 to 39 . The target 200 is preferably formed on a semiconductor device wafer, on which at least a first layer 202, a second layer 204, and a third layer 206 are preferably formed. It should be understood that each of the first layer 202, the second layer 204, and the third layer 206 defines a generally planar surface parallel to the x-y plane. The first layer 202, the second layer 204, and the third layer 206 may be adjacent layers but need not be so. Preferably, any material between the first layer 202, the second layer 204, and the third layer 206 is at least partially transparent to electromagnetic radiation. In the embodiment illustrated in Figures 2A to 2D , the first layer 202 is located below the second layer 204 and the third layer 206, and the third layer 206 is located above the first layer 202 and the second layer 204. However, it should be understood that the layers 202, 204, and 206 may be arranged in any suitable order relative to each other along the z-axis.

[0115] As specifically seen in Figure 2A , the target 200 includes four target quadrants 212, 214, 216, and 218. In the embodiment shown in Figure 2A , the rotational orientation in the x-y plane of each of the target quadrants 212, 214, 216, and 218 preferably differs by an integer multiple of 90° from the rotational orientation in the x-y plane of each of the other target quadrants 212, 214, 216, and 218. Additionally, the target 200 is preferably characterized by rotational symmetry in the x direction or the y direction or both. In a preferred embodiment of the present invention, the target 200 is designed such that when in an aligned state, the whole of the target 200 is characterized by a single symmetry point in the x direction and a single symmetry point in the y direction. However, even in this embodiment, when in an offset state, the various elements of the target 200 will be characterized by unique symmetry points.

[0116] Each of the target quadrants 212, 214, 216, and 218 includes a first stack 222 of periodic structures, a second stack 224 of periodic structures, and a third stack 226 of periodic structures. Each of the first stack 222, the second stack 224, and the third stack 226 includes one or more periodic structures, and each periodic structure has a pitch. Preferably, none of the first stack 222, the second stack 224, and the third stack 226 overlap each other. In Figures 2A to 2D , the first stack 222 is illustrated as being located closer to the center of the target 200 than the second stack 224 and the third stack 226, and the third stack 226 is illustrated as being located closer to the edge of the target 200 than the first stack 222 and the second stack 224. However, the first stack 222, the second stack 224, and the third stack 226 can be arranged relative to each other in any suitable arrangement with respect to the x-y plane.

[0117] It should be understood that although in the embodiment illustrated in Figures 2A to 2D , each of the periodic structures of the first stack 222, the second stack 224, and the third stack 226 is illustrated as being formed by a plurality of lines and spaces, in other embodiments of the present invention, the periodic structures of the first stack 222, the second stack 224, and the third stack 226 can be formed by any suitable periodic features. It should be further understood that the periodic features forming the periodic structures included in the first stack 222, the second stack 224, and the third stack 226 can be formed by sub-structures. The pitch of each of the periodic structures of the first stack 222, the second stack 224, and the third stack 226 is preferably between 10 nm and 3000 nm, and more preferably between 200 nm and 800 nm.

[0118] As Figure 2A seen, in each of the quadrants 212, 214, 216, and 218, a first plane 231 that intersects the first stack 222 and includes a plurality of first axes 232 located therein, a second plane 233 that intersects the second stack 224 and includes a plurality of second axes 234 located therein, and a third plane 235 that intersects the third stack 226 and includes a plurality of third axes 236 located therein are defined. Depending on the orientation of the first stack 222, the second stack 224, and the third stack 226 within each of the quadrants 212, 214, 216, and 218, each of the first plane 231, the second plane 233, and the third plane 235 is the x-z plane or the y-z plane, and the first axes 232, the second axes 234, and the third axes 236 are parallel to the corresponding x-axis or y-axis. It should be understood that in each of the quadrants 212, 214, 216, and 218, the first plane 231, the second plane 233, and the third plane 235 are all parallel to each other.

[0119] Specifically, in Figure 2B as seen, the first stack 222 includes a first stack first periodic structure (S1P1) 242, the S1P1 is formed together with the first layer 202 and has an S1P1 pitch designated as D along one of the first axes 232. The first stack 222 further includes a first stack second periodic structure (S1P2) 244, the S1P2 is formed together with the second layer 204 and has an S1P2 pitch designated as E along the other of the first axes 232.

[0120] It should be understood that the S1P1 242 and the S1P2 244 at least partially overlap each other, and the first stack moiré pattern 250 is visible immediately after imaging the first stack 222. As is known in the art, the first stack moiré pattern 250 is characterized by a pitch F1, and the pitch F1 is a function of the pitches D and E, as shown in Equation 4:

[0121]

[0122] Preferably, the first stack 222 does not include a periodic structure that forms together with the third layer 206 and affects the moiré pattern 250. However, the first stack 222 may include a periodic structure that forms together with the third layer 206 and does not affect the moiré pattern 250, such as a periodic structure that is periodic in a plane parallel to the x - y plane along an axis perpendicular to the first axis 232 or a periodic structure having a pitch size that does not affect the moiré pattern 250.

[0123] Specifically, in Figure 2C as seen, the second stack 224 includes a second stack first periodic structure (S2P1) 252, the S2P1 is formed together with the second layer 204 and has an S2P1 pitch designated as fE along one of the second axes 234. Preferably, the S2P1 pitch fE is related to the S1P2 pitch E by a second stack multiplication factor designated as f. The second stack multiplication factor f can be any positive number. The second stack 224 further includes a second stack second periodic structure (S2P2) 254, the S2P2 is formed together with the third layer 206 and has an S2P2 pitch designated as fD along the other of the second axes 234. Preferably, the S2P2 pitch fD is related to the S1P1 pitch D by the second stack multiplication factor f. It should be understood that the second stack multiplication factor f that relates the S2P2 pitch fD to the S1P1 pitch D has the same value as the second stack multiplication factor f that relates the S2P1 pitch fE to the S1P2 pitch E. In an embodiment of the present invention, the value of f is 1 and thus the S2P1 pitch fE is the same as the S1P2 pitch E and the S2P2 pitch fD is the same as the S1P1 pitch D.

[0124] It should be understood that S2P1 252 and S2P2 254 at least partially overlap each other, and the second stack Moiré pattern 260 is visible immediately after imaging the second stack 224. As is known in the art, the second stack Moiré pattern 260 is characterized by a pitch F2, which is a function of the second stack multiplication factor f, the pitch D, and the pitch E, as shown in Equation 5:

[0125]

[0126] Preferably, the second stack 224 does not include a periodic structure that forms with the first layer 202 and affects the periodicity of the Moiré pattern 260. However, the second stack 224 may include a periodic structure that forms with the first layer 202 and does not affect the periodicity of the Moiré pattern 260, such as a periodic structure that is periodic in a plane parallel to the x-y plane along an axis perpendicular to the second axis 234 or a periodic structure having a pitch size that does not affect the Moiré pattern 260.

[0127] As specifically seen in Figure 2D the third stack 226 includes a third stack first periodic structure (S3P1) 262, which forms with the first layer 202 and has an S3P1 pitch designated as gD along one of the third axes 236. Preferably, the S3P1 pitch gD is related to the S1P1 pitch D by a third stack multiplication factor designated as g. The third stack multiplication factor g can be any positive number. The third stack 226 further includes a third stack second periodic structure (S3P2) 264, which forms with the third layer 206 and has an S3P2 pitch designated as gE along the other of the third axes 236. Preferably, the S3P2 pitch gE is related to the S1P2 pitch E by the third stack multiplication factor g. It should be understood that the third stack multiplication factor g that relates the S3P2 pitch gE to the S1P2 pitch E has the same value as the third stack multiplication factor g that relates the S3P1 pitch gD to the S1P1 pitch D. In an embodiment of the present invention, the value of g is 1 and thus the S3P1 pitch gD is the same as the S1P1 pitch D and the S3P2 pitch gE is the same as the S1P2 pitch E.

[0128] It should be understood that S3P1 262 and S3P2 264 at least partially overlap each other, and the third stack Moiré pattern 270 is visible immediately after imaging the third stack 226. As is known in the art, the third stack Moiré pattern 270 is characterized by a pitch F3, which is a function of the third stack multiplication factor g, the pitch D, and the pitch E, as shown in Equation 6:

[0129]

[0130] Preferably, the third stack 226 does not include a periodic structure formed with the second layer 204 that affects the periodicity of the Moiré pattern 270. However, the third stack 226 may include a periodic structure formed with the second layer 204 that does not affect the periodicity of the Moiré pattern 270, such as a periodic structure that is periodic in a plane parallel to the x-y plane along an axis perpendicular to the third axis 236 or a periodic structure having a pitch size that does not affect the Moiré pattern 270.

[0131] Preferably, an imaging offset metrology tool with adjustable polarization, wavelength, and numerical aperture settings is used to measure the offset between any two of the layers 202, 204, and 206. An example of a suitable imaging offset metrology tool is the Archer commercially available from KLA Corporation, Milpitas, California, USA TM 700. The pitches D, E, fD, fE, gD, and gE do not need to be optically resolvable by the offset metrology tool used to generate the image of the target 200. However, preferably, each of the pitches F1, F2, and F3 is optically resolvable by the offset metrology tool used to generate the image of the target 200.

[0132] Now refer to Figure 3A , which is a simplified flowchart that illustrates a preferred method of calculating the offset between a first layer 302, a second layer 304, and a third layer 306 (such as layers 102, 104, and 106 ( Figure 1 ) or 202, 204, and 206 ( Figures 2A to 2D )) of a multi-layer semiconductor device wafer on which the target 300 (such as target 100 ( Figure 1 ) or target 200 ( Figures 2A to 2D )) is formed in a direction parallel to the x-direction or the y-direction. Further refer to Figure 3B and 3C , which are simplified illustrations of a first embodiment and a second embodiment of parts of the method of Figure 3A .

[0133] Although it should be understood that when using the target 200 ( Figures 2A to 2D ), the method described with reference to Figures 3A to 3C may be performed only once to calculate the offset in the x-direction or the y-direction, but typically Figures 3A to 3C the method described in Figure 1 will be performed twice to calculate the offset in each of the x-direction and the y-direction. It should also be understood that when using the target 100 (

[0134] ), the offset can be calculated in only one direction parallel to the first axis 132, the second axis 134, and the third axis 136. Figure 3A and3B When using the target 100 in the method of, the direction of the measurement offset is automatically selected as the direction parallel to the first axis 132, the second axis 134, and the third axis 136. When in Figure 3A and 3B When using the target 200 in the method of, the structures of the quadrants 214 and 218 are utilized to measure the offset in the direction parallel to the x-axis, and the structures of the quadrants 212 and 216 are utilized to measure the offset in the direction parallel to the y-axis.

[0135] Preferably, at the next step 309, an imaging offset metrology tool with adjustable polarization, wavelength, and numerical aperture settings is used to generate an image of the target 300. An example of a suitable imaging offset metrology tool is the Archer TM 700 available commercially from KLA Corporation, Milpitas, California, USA. It should be noted that the spacings A, B, dA, dB, eA, eB, D, E, fD, fE, gD, and gE do not need to be optically resolvable by the offset metrology tool used to generate the image of the target 300. However, preferably, each of the spacings C1, C2, C3, F1, F2, and F3 is optically resolvable by the offset metrology tool used to generate the image of the target 300.

[0136] In the next step 311 and as Figure 3B and 3C seen in, for each of the corresponding first stack 322, second stack 324, and third stack 326 (such as the first stack 122, second stack 124, and third stack 126 ( Figure 1 )) or the first stack 222, second stack 224, and third stack 226 ( Figures 2A to 2D )) in the quadrant selected in step 307, the first region of interest 312, the second region of interest 314, and the third region of interest 316 are selected. It should be understood that as seen in the illustrated embodiments of Figure 3B and 3C , although the first region of interest 312, the second region of interest 314, and the third region of interest 316 are preferably completely located within each of the corresponding first stack 322, second stack 324, and third stack 326 (as illustrated for the first region of interest 312 completely located within the first stack 322), the first region of interest 312, the second region of interest 314, and the third region of interest 316 may extend beyond the corresponding first stack 322, second stack 324, and third stack 326, as illustrated for the regions of interest 314 and 316 extending beyond the corresponding second stack 324 and third stack 326. It should be further understood that Figure 3B and 3CThe regions of interest 312, 314, and 316 shown are representative regions of interest, and other suitable regions of interest can be selected at step 311.

[0137] In the next step 331 and as Figure 3B and 3C seen in, calculate the position of the symmetry points 332 between all examples of the first region of interest 312 selected in step 311. In the next step 333 and as Figure 3B and 3C seen in, calculate the position of the symmetry points 334 between all examples of the second region of interest 314 selected in step 311. In the next step 335 and as Figure 3B and 3C seen in, calculate the position of the symmetry points 336 between all examples of the third region of interest 316 selected in step 311.

[0138] In the next step 337, calculate the distance in the direction selected at step 307 between the positions of the symmetry points 332 of one or more first regions of interest 312 identified at step 331 and the positions of the symmetry points 334 of one or more second regions of interest 314 identified at step 333. The distance found at step 337 is divided by the gain G1, which is a function of the spacings A and B for target 100, as shown in Equation 7a:

[0139]

[0140] and is a function of the spacings D and E for target 200, as shown in Equation 7b:

[0141]

[0142] And report the result as the offset between the first layer 302 and the third layer 306 in the direction selected at step 307. It should be understood that in addition to the distance calculated at step 337, the method further calculates an adjustment direction, such as right, left, up, or down. The adjustment direction varies with the relative values of the spacings A and B or the spacings D and E and which of the adjustment layers 302 and 306 will be adjusted.

[0143] In the next step 339, calculate the distance in the direction selected at step 307 between the positions of the symmetry points 332 of one or more first regions of interest 312 identified at step 331 and the positions of the symmetry points 336 of one or more third regions of interest 316 identified at step 335. The distance found at step 339 is divided by the gain G2, which is a function of the spacings A and B for target 100, as shown in Equation 8a:

[0144]

[0145] and is a function of spacings D and E for target 200, as shown in Equation 8b:

[0146]

[0147] And report the result as an offset between the second layer 304 and the third layer 306 in the direction selected at step 307. It should be understood that, in addition to the distance calculated at step 339, the method further calculates an adjustment direction, such as right, left, up, or down. The adjustment direction varies with the relative values of spacings A and B or spacings D and E and which of the adjustment layers 304 and 306 is to be adjusted.

[0148] In the next step 341, calculate the difference between the offset value reported at step 337 and the offset value reported at step 339. Report the difference calculated at step 341 as an offset between the first layer 302 and the second layer 304 in the direction selected at step 307. It should be understood that, in addition to the distance calculated at step 341, the method further calculates an adjustment direction, such as right, left, up, or down. The adjustment direction varies with the relative values of spacings A and B or spacings D and E and which of the adjustment layers 302 and 304 is to be adjusted.

[0149] Now refer to Figure 4 , which is a simplified graphical illustration of another embodiment of the multi-layer moiré target 400 of the present invention. Figure 4 A graphical illustration is included in three different dimensions indicated by the x-axis, y-axis, and z-axis, which three dimensions are hereinafter referred to as the x-y plane, the x-z plane, and the y-z plane, respectively. It should be noted that Figure 4 generally illustrates the x-y plane, while Figure 4 the magnified views A, B, and C illustrate planes parallel to the x-z plane.

[0150] The target 400 is preferably formed on a semiconductor device wafer, on which at least a first layer 402, a second layer 404, and a third layer 406 are preferably formed. It should be understood that each of the first layer 402, the second layer 404, and the third layer 406 defines a generally planar surface parallel to the x-y plane. The first layer 402, the second layer 404, and the third layer 406 may be adjacent layers but need not be. Preferably, any material between the first layer 402, the second layer 404, and the third layer 406 is at least partially transparent to electromagnetic radiation. In Figure 4In the illustrated embodiment, the first layer 402 is located below the second layer 404 and the third layer 406, and the third layer 406 is located above the first layer 402 and the second layer 404. However, it should be understood that the layers 402, 404, and 406 may be arranged in any suitable order relative to each other along the z-axis.

[0151] It should be understood that Figure 4 illustrates a possible layout of the target 400, and in other embodiments of the present invention, the target 400 may include additional structures. For example, as described hereinafter with reference to Figures 5A to 5D and 34 to 39, suitable targets may include Figure 4 multiple examples of the structures shown in, and those multiple examples may be arranged in various ways.

[0152] Preferably, the target 400 includes a first stack 422 of periodic structures, a second stack 424 of periodic structures, and a third stack 426 of periodic structures. Each of the first stack 422, the second stack 424, and the third stack 426 includes one or more periodic structures, and each periodic structure has a pitch. Preferably, none of the first stack 422, the second stack 424, and the third stack 426 overlap each other.

[0153] It should be understood that although in Figure 4 each of the periodic structures of the first stack 422, the second stack 424, and the third stack 426 is shown as being formed by a plurality of lines and spaces, in other embodiments of the present invention, the periodic structures of the first stack 422, the second stack 424, and the third stack 426 may be formed by any suitable periodic features. It should be further understood that the periodic features forming the periodic structures included in the first stack 422, the second stack 424, and the third stack 426 may be formed by sub-structures. The pitch of each of the periodic structures of the first stack 422, the second stack 424, and the third stack 426 is preferably between 10 nm and 3000 nm, and more preferably between 200 nm and 800 nm.

[0154] The first x-z plane 431 intersects the first stack 422. A plurality of first axes 432 are located in the first x-z plane 431 and parallel to the x-axis. The second x-z plane 433 intersects the second stack 424. A plurality of second axes 434 are located in the second x-z plane 433 and parallel to the x-axis. The third x-z plane 435 intersects the third stack 426. A plurality of third axes 436 are located in the third x-z plane 435 and parallel to the x-axis.

[0155] As specifically seen in magnification A, the first stack 422 includes a first stack first periodic structure (S1P1) 442, which is formed together with the first layer 402 and has an S1P1 pitch designated as H along one of the first axes 432. The first stack 422 further includes a first stack second periodic structure (S1P2) 444, which is formed together with the second layer 404 and has an S1P2 pitch designated as I along the other of the first axes 432.

[0156] It should be understood that S1P1 442 and S1P2 444 at least partially overlap each other, and a first stack moiré pattern 450 is visible immediately after imaging the first stack 422. As is known in the art, the first stack moiré pattern 450 is characterized by a pitch J1, which is a function of the pitches H and I, as shown in Equation 9:

[0157]

[0158] Preferably, the first stack 422 does not include a periodic structure that forms together with the third layer 406 and affects the moiré pattern 450. However, the first stack 422 may include a periodic structure that forms together with the third layer 406 and does not affect the moiré pattern 450, such as a periodic structure that is periodic along an axis parallel to the y-axis or has a pitch size that does not affect the moiré pattern 450.

[0159] As seen in magnification B, the second stack 424 includes a second stack first periodic structure (S2P1) 452, which is formed together with the first layer 402 and has an S2P1 pitch designated as K along one of the second axes 434. The second stack 424 further includes a second stack second periodic structure (S2P2) 454, which is formed together with the second layer 404 and has an S2P2 pitch designated as L along the other of the second axes 434.

[0160] It should be understood that S2P1 452 and S2P2 454 at least partially overlap each other, and a second stack moiré pattern 460 is visible immediately after imaging the second stack 424. The second stack moiré pattern 460 is characterized by a pitch J2, which is a function of the pitches K and L, as shown in Equation 10:

[0161]

[0162] Preferably, the second stack 424 does not include a periodic structure that forms with the third layer 406 and affects the periodicity of the Moiré pattern 460. However, the second stack 424 may include a periodic structure that forms with the third layer 406 and does not affect the periodicity of the Moiré pattern 460, such as a periodic structure that is periodic along an axis parallel to the y-axis or has a pitch size that does not affect the Moiré pattern 460.

[0163] As specifically seen in magnification C, the third stack 426 includes a third-stack first periodic structure (S3P1) 462 that forms with the second layer 404 and has an S3P1 pitch designated as hL along one of the third axes 436. Preferably, the S3P1 pitch hL is related to the S2P2 pitch L by a third-stack multiplication factor designated as h. The third-stack multiplication factor h can be any positive number. The third stack 426 further includes a third-stack second periodic structure (S3P2) 464 that forms with the third layer 406 and has an S3P2 pitch designated as hK along the other of the third axes 436. Preferably, the S3P2 pitch hK is related to the S2P1 pitch K by the third-stack multiplication factor h. It should be understood that the third-stack multiplication factor h that relates the S3P2 pitch hK to the S2P1 pitch K has the same value as the third-stack multiplication factor h that relates the S3P1 pitch hL to the S2P2 pitch L. In an embodiment of the present invention, the value of h is 1 and thus the S3P1 pitch hL is the same as the S2P2 pitch L and the S3P2 pitch hK is the same as the S2P1 pitch K.

[0164] It should be understood that S3P1 462 and S3P2 464 at least partially overlap each other, and thus the third-stack Moiré pattern 470 is visible immediately after imaging the third stack 426. As is known in the art, the third-stack Moiré pattern 470 is characterized by a pitch J3 that is a function of the third-stack multiplication factor h, the pitch K, and the pitch L, as shown in Equation 11:

[0165]

[0166] Preferably, the third stack 426 does not include a periodic structure that forms with the first layer 402 and affects the periodicity of the Moiré pattern 470. However, the third stack 426 may include a periodic structure that forms with the first layer 402 and does not affect the periodicity of the Moiré pattern 470, such as a periodic structure that is periodic along an axis parallel to the y-axis or has a pitch size that does not affect the Moiré pattern 470.

[0167] An imaging offset metrology tool with adjustable polarization, wavelength, and numerical aperture settings is preferably used to measure the offset between any two of the layers 402, 404, and 406. An example of a suitable imaging offset metrology tool is the Archer 1000, commercially available from KLA Corporation of Milpitas, California, USA. TM 700. Spacings I, H, K, L, hK, and hL need not be optically resolvable by an offset metrology tool used to generate an image of target 400. However, preferably, each of spacings J1, J2, and J3 is optically resolvable by an offset metrology tool used to generate an image of target 400.

[0168] Now refer to Figures 5A to 5D , which is a simplified diagrammatic illustration of another embodiment of a multi-layer moiré target 500 of the present invention. Figures 5A to 5D The diagrams are illustrated in three different dimensions indicated by the x-axis, y-axis, and z-axis, which are hereinafter referred to as the xy plane, xz plane, and yz plane, respectively. Figure 5A Generally, the diagram illustrates the xy plane, while Figure 5B 、 5C and 5D diagram illustrating a plane parallel to the xz plane.

[0169] It should be noted that target 500 is the reference above Figure 4 An example of an alternative layout of the target 400 is described and referred to below. Figures 34 to 39 Additional layouts are described. The target 500 is preferably formed on a semiconductor device wafer on which at least a first layer 502, a second layer 504, and a third layer 506 are preferably formed. It should be understood that each of the first layer 502, the second layer 504, and the third layer 506 defines a substantially planar surface parallel to the xy plane. The first layer 502, the second layer 504, and the third layer 506 can be adjacent layers but need not be. Preferably, any material between the first layer 502, the second layer 504, and the third layer 506 is at least partially transparent to electromagnetic radiation. Figures 5A to 5D , the first layer 502 is below the second layer 504 and the third layer 506, and the third layer 506 is above the first layer 502 and the second layer 504. However, it should be understood that the layers 502, 504, and 506 can be arranged in any suitable order relative to each other along the z-axis.

[0170] Specifically, in Figure 5A As seen in FIG, target 500 includes four target quadrants 512, 514, 516, and 518. Figure 5AIn the embodiments shown, the rotational orientation in the x-y plane of each of the target quadrants 512, 514, 516, and 518 preferably differs from the rotational orientation in the x-y plane of each of the other target quadrants 512, 514, 516, and 518 by an integer multiple of 90°. Additionally, the target 500 is preferably characterized by rotational symmetry in the x direction or the y direction or both. In a preferred embodiment of the present invention, the target 500 is designed such that when in the aligned state, the whole of the target 500 is characterized by a single symmetry point in the x direction and a single symmetry point in the y direction. However, even in this embodiment, when in the offset state, the various elements of the target 500 will be characterized by unique symmetry points.

[0171] Each of the target quadrants 512, 514, 516, and 518 includes a first stack 522 of periodic structures, a second stack 524 of periodic structures, and a third stack 526 of periodic structures. Each of the first stack 522, the second stack 524, and the third stack 526 includes one or more periodic structures, each periodic structure having a pitch. Preferably, none of the first stack 522, the second stack 524, and the third stack 526 overlap each other. In Figures 5A to 5D FIG., the first stack 522 is illustrated as being located closer to the center of the target 500 than the second stack 524 and the third stack 526, and the third stack 526 is illustrated as being located closer to the edge of the target 500 than the first stack 522 and the second stack 524. However, the first stack 522, the second stack 524, and the third stack 526 may actually be arranged relative to each other in any suitable arrangement with respect to the x-y plane.

[0172] It should be understood that although in the embodiment illustrated in Figures 5A to 5D FIG., each of the periodic structures of the first stack 522, the second stack 524, and the third stack 526 is illustrated as being formed by a plurality of lines and spaces, in other embodiments of the present invention, the periodic structures of the first stack 522, the second stack 524, and the third stack 526 may be formed by any suitable periodic features. It should be further understood that the periodic features forming the periodic structures included in the first stack 522, the second stack 524, and the third stack 526 may be formed by sub-structures. The pitch of each of the periodic structures of the first stack 522, the second stack 524, and the third stack 526 is preferably between 10 nm and 3000 nm, and more preferably between 200 nm and 800 nm.

[0173] As Figure 5AAs seen, in each of quadrants 512, 514, 516, and 518, a first plane 531 is defined that intersects the first stack 522 and includes a plurality of first axes 532 therein, a second plane 533 that intersects the second stack 524 and includes a plurality of second axes 534 therein, and a third plane 535 that intersects the third stack 526 and includes a plurality of third axes 536 therein. Depending on the orientation of the first stack 522, second stack 524, and third stack 526 within each of quadrants 512, 514, 516, and 518, each of the first plane 531, second plane 533, and third plane 535 is an x-z plane or a y-z plane, and the first axes 532, second axes 534, and third axes 536 are parallel to the corresponding x-axis or y-axis. It should be understood that in each of quadrants 512, 514, 516, and 518, the first plane 531, second plane 533, and third plane 535 are all parallel to each other.

[0174] As specifically seen in Figure 5B As seen, the first stack 522 includes a first stack first periodic structure (S1P1) 542 that is formed with the first layer 502 and has an S1P1 pitch designated as M along one of the first axes 532. The first stack 522 further includes a first stack second periodic structure (S1P2) 544 that is formed with the second layer 504 and has an S1P2 pitch designated as N along the other of the first axes 532.

[0175] It should be understood that S1P1 542 and S1P2 544 at least partially overlap each other, and thus a first stack moiré pattern 550 is immediately visible after imaging the first stack 522. As is known in the art, the first stack moiré pattern 550 is characterized by a pitch O1 that is a function of pitches M and N, as shown in Equation 12:

[0176]

[0177] Preferably, the first stack 522 does not include a periodic structure that is formed with the third layer 506 and affects the moiré pattern 550. However, the first stack 522 may include a periodic structure that is formed with the third layer 506 and does not affect the moiré pattern 550, such as a periodic structure that is periodic in a plane parallel to the x-y plane along an axis perpendicular to the first axes 532 or a periodic structure having a pitch size that does not affect the moiré pattern 550.

[0178] As specifically seen in Figure 5CAs seen, the second stack 524 includes a second-stack first periodic structure (S2P1) 552, which is formed with the first layer 502 and has an S2P1 pitch designated as P along one of the second axes 534. The second stack 524 further includes a second-stack second periodic structure (S2P2) 554, which is formed with the second layer 504 and has an S1P2 pitch designated as Q along the other of the second axes 534.

[0179] It should be understood that S2P1 552 and S2P2 554 at least partially overlap each other, and thus a second-stack moiré pattern 560 is visible immediately after imaging the second stack 524. As is known in the art, the second-stack moiré pattern 560 is characterized by a pitch O2, which is a function of pitches P and Q, as shown in Equation 13:

[0180]

[0181] Preferably, the second stack 524 does not include a periodic structure that forms with the third layer 506 and affects the moiré pattern 560. However, the second stack 524 may include a periodic structure that forms with the third layer 506 and does not affect the moiré pattern 560, such as a periodic structure that is periodic in a plane parallel to the x-y plane along an axis perpendicular to the second axis 534 or a periodic structure having a pitch size that does not affect the moiré pattern 560.

[0182] As specifically seen in Figure 5D the third stack 526 includes a third-stack first periodic structure (S3P1) 562, which is formed with the second layer 504 and has an S3P1 pitch designated as kQ along one of the third axes 536. Preferably, the S3P1 pitch kQ is related to the S2P2 pitch Q by a third-stack multiplication factor designated as k. The third-stack multiplication factor k can be any positive number. The third stack 526 further includes a third-stack second periodic structure (S3P2) 564, which is formed with the third layer 506 and has an S3P2 pitch designated as kP along the other of the third axes 536. Preferably, the S3P2 pitch kP is related to the S2P1 pitch P by the third-stack multiplication factor k. It should be understood that the third-stack multiplication factor k that relates the S3P2 pitch kP to the S2P1 pitch P has the same value as the third-stack multiplication factor k that relates the S3P1 pitch kQ to the S2P2 pitch Q. In an embodiment of the present invention, the value of k is 1 and thus the S3P1 pitch kQ is the same as the S2P2 pitch Q and the S3P2 pitch kP is the same as the S2P1 pitch P.

[0183] It should be understood that S3P1 562 and S3P2 564 at least partially overlap each other, and thus the third stack Moiré pattern 570 is visible immediately after imaging the third stack 526. As is known in the art, the third stack Moiré pattern 570 is characterized by a pitch O3, which is a function of the third stack multiplication factor k, pitch P, and pitch Q, as shown in Equation 14:

[0184]

[0185] Preferably, the third stack 526 does not include a periodic structure that forms with the first layer 502 and affects the Moiré pattern 570. However, the third stack 526 may include a periodic structure that forms with the first layer 502 and does not affect the Moiré pattern 570, such as a periodic structure that is periodic in a plane parallel to the x-y plane along an axis perpendicular to the third axis 536 or a periodic structure having a pitch size that does not affect the Moiré pattern 570.

[0186] An imaging offset metrology tool with adjustable polarization, wavelength, and numerical aperture settings is preferably used to measure the offset between any two of the layers 502, 504, and 506. An example of a suitable imaging offset metrology tool is the Archer commercially available from KLA Corporation, Milpitas, California, USA TM 700. The pitches M, N, P, Q, kP, and kQ do not need to be optically resolvable by the offset metrology tool used to generate the image of the target 500. However, preferably, each of the pitches O1, O2, and O3 is optically resolvable by the offset metrology tool used to generate the image of the target 500.

[0187] Now refer to Figure 6A , which is a simplified flowchart that illustrates a preferred method for calculating the offset between the first layer 602, the second layer 604, and the third layer 606 (such as layers 402, 404, and 406 ( Figure 4 ) or 502, 504, and 506 ( Figures 5A to 5D )) of a multi-layer semiconductor device wafer formed with the target 600 in a direction parallel to the x-direction or the y-direction using a multi-layer Moiré target 600 (such as the target 400 ( Figure 4 ) or the target 500 ( Figures 5A to 5D )). Further refer to Figure 6B and 6C , which are simplified illustrations of the first embodiment and the second embodiment of parts of the method of Figure 6A , respectively.

[0188] Although it should be understood that when using the target 500 ( Figures 5A to 5D ), refer to Figures 6A to 6CThe method described may be performed only once to calculate the offset in the x or y direction, but typically Figures 6A to 6C the method described in Figure 4 will be performed twice to calculate the offset in each of the x and y directions. It should also be understood that when using the target 400 (

[0189] ), the offset may be calculated only in one direction parallel to the first axis 432, the second axis 434, and the third axis 436. Figure 6A and 6B ), the direction for measuring the offset is automatically selected as the direction parallel to the first axis 432, the second axis 434, and the third axis 436. When using the target 500 in the method of Figure 6A and 6B ), the structures of the quadrants 514 and 518 are used to measure the offset in a direction parallel to the x-axis, and the structures of the quadrants 512 and 516 are used to measure the offset in a direction parallel to the y-axis.

[0190] Preferably, in the next step 609, an imaging offset metrology tool with adjustable polarization, wavelength, and numerical aperture settings is used to generate an image of the target 600. An example of a suitable imaging offset metrology tool is the Archer TM 700 commercially available from KLA Corporation, Milpitas, California, USA. It should be noted that the spacings I, H, L, K, hK, hL, M, N, P, Q, kP, kQ need not be optically resolvable by the offset metrology tool used to generate the image of the target 600. However, preferably, each of the spacings J1, J2, J3, O1, O2, and O3 is optically resolvable by the offset metrology tool used to generate the image of the target 600.

[0191] In the next step 611 and as seen in Figure 6B and 6C ), for each of the corresponding first stack 622, second stack 624, and third stack 626 (such as the first stack 422, second stack 424, and third stack 426 ( [[ID= )) or the first stack 522, second stack 524, and third stack 526 ( ​ )) in the quadrant selected in step 607, the first region of interest 612, the second region of interest 614, and the third region of interest 616 are selected. It should be understood that as in ​ and 6CAs seen in the illustrated embodiments, although the first region of interest 612, the second region of interest 614, and the third region of interest 616 are preferably entirely located within each of the respective first stack 622, second stack 624, and third stack 626 (as illustrated for the first region of interest 612 that is entirely located within the first stack 622), the first region of interest 612, the second region of interest 614, and the third region of interest 616 may extend beyond the respective first stack 622, second stack 624, and third stack 626, as illustrated by the regions of interest 614 and 616 that extend beyond the respective second stack 624 and third stack 626. It should be further understood that ​ and 6C the regions of interest 612, 614, and 616 shown in are representative regions of interest, and other suitable regions of interest may be selected at step 611.

[0192] In the next step 631 and as ​ and 6C seen in, the position of the symmetry point 632 is calculated between all examples of the first region of interest 612 selected in step 611. In the next step 633 and as ​ and 6C seen in, the position of the symmetry point 634 is calculated between all examples of the second region of interest 614 selected in step 611. In the next step 635 and as ​ and 6C seen in, the position of the symmetry point 636 is calculated between all examples of the third region of interest 616 selected in step 611.

[0193] In the next step 637, the distance in the direction selected at step 607 is calculated between the position of the symmetry point 632 of one or more first regions of interest 612 identified at step 631 and the position of the symmetry point 634 of one or more second regions of interest 614 identified at step 633. The distance found at step 637 is divided by the gain R1, which is a function of the spacings H, I, K, and L for the target 400, as shown in Equation 15a:

[0194]

[0195] and is a function of the spacings M, N, P, and Q for the target 500, as shown in Equation 15b:

[0196]

[0197] And report the result as the offset between the first layer 602 and the second layer 604 in the direction selected at step 607. It should be understood that in addition to the distance calculated at step 637, the method further calculates an adjustment direction, such as right, left, up, or down. The adjustment direction varies with the relative values of the spacings H and I and the spacings K and L or the spacings M and N and the spacings P and Q and which of the layers 602 and 604 is to be adjusted.

[0198] In the next step 639, calculate the distance in the direction selected at step 607 between the position of the symmetry point 634 of one or more second regions of interest 614 identified at step 633 and the position of the symmetry point 636 of one or more third regions of interest 616 identified at step 635. The distance found at step 639 is divided by a gain R2, which is a function of the spacings K and L for the target 400, as shown in Equation 16a:

[0199]

[0200] and is a function of the spacings P and Q for the target 500, as shown in Equation 16b:

[0201]

[0202] And report the result as the offset between the first layer 602 and the third layer 606 in the direction selected at step 607. It should be understood that in addition to the distance calculated at step 639, the method further calculates an adjustment direction, such as right, left, up, or down. The adjustment direction varies with the relative values of the spacings H and I and the spacings K and L or the spacings M and N and the spacings P and Q and which of the layers 602 and 606 is to be adjusted.

[0203] In the next step 641, calculate the difference between the offset value reported at step 637 and the offset value reported at step 639. Report the difference calculated at step 641 as the offset between the first layer 602 and the third layer 606 in the direction selected at step 607. It should be understood that in addition to the distance calculated at step 641, the method further calculates an adjustment direction, such as right, left, up, or down. The adjustment direction varies with the relative values of the spacings H and I and the spacings K and L or the spacings M and N and the spacings P and Q and which of the layers 602 and 606 is to be adjusted.

[0204] It should be understood that only the first two previously formed layers among the layers 602, 604, and 606 that will form the third layer among those layers can be used to perform the above reference ​The relevant part of the described method. As described above, layers 602, 604, and 606 can be formed in any suitable order relative to each other.

[0205] Now refer to ​ , which is a simplified illustration of another embodiment of the multi-layer Moiré target 700 of the present invention. ​ An illustration including three different dimensions indicated by the x-axis, y-axis, and z-axis, which are hereinafter referred to as the x-y plane, x-z plane, and y-z plane, respectively. It should be noted that ​ generally illustrates the x-y plane, while ​ the enlarged views A, B, and C of

[0206] illustrate a plane parallel to the x-z plane. The target 700 is preferably formed on a semiconductor device wafer, on which at least a first layer 702, a second layer 704, and a third layer 706 are preferably formed. It should be understood that each of the first layer 702, the second layer 704, and the third layer 706 defines a generally planar surface parallel to the x-y plane. The first layer 702, the second layer 704, and the third layer 706 may be adjacent layers but need not be. Preferably, any material between the first layer 702, the second layer 704, and the third layer 706 is at least partially transparent to electromagnetic radiation. In the embodiment illustrated in ​ , the first layer 702 is located below the second layer 704 and the third layer 706, and the third layer 706 is located above the first layer 702 and the second layer 704. However, it should be understood that the layers 702, 704, and 706 can be arranged in any suitable order relative to each other along the z-axis.

[0207] It should be understood that ​ illustrates one possible layout of the target 700, and in other embodiments of the present invention, the target 700 may include additional structures. For example, as described hereinafter with reference to ​ and 34 to 39, suitable targets can include ​ multiple examples of the structures shown in

[0208] and those multiple examples can be arranged in various ways. Preferably, the target 700 includes a first stack 722 of periodic structures, a second stack 724 of periodic structures, and a third stack 726 of periodic structures. Each of the first stack 722, the second stack 724, and the third stack 726 includes one or more periodic structures, each periodic structure having a pitch. Preferably, the first stack 722, the second stack 724, and the third stack 726 do not overlap each other.

[0209] It should be understood that although in ​In [the figure], each of the periodic structures of the first stack 722, the second stack 724, and the third stack 726 is shown as being formed by a plurality of lines and spaces. However, in other embodiments of the present invention, the periodic structures of the first stack 722, the second stack 724, and the third stack 726 may be formed by any suitable periodic features. It should be further understood that the periodic features forming the periodic structures included in the first stack 722, the second stack 724, and the third stack 726 may be formed by sub-structures. The pitch of each of the periodic structures of the first stack 722, the second stack 724, and the third stack 726 is preferably between 10 nm and 3000 nm, and more preferably between 200 nm and 800 nm.

[0210] The first x-z plane 731 intersects the first stack 722. A plurality of first axes 732 are located within the first x-z plane 731 and parallel to the x-axis. The second x-z plane 733 intersects the second stack 724. A plurality of second axes 734 are located within the second x-z plane 733 and parallel to the x-axis. The third x-z plane 735 intersects the third stack 726. A plurality of third axes 736 are located within the third x-z plane 735 and parallel to the x-axis.

[0211] As specifically seen in magnification A, the first stack 722 includes a first stack first periodic structure (S1P1) 742, which is formed together with the first layer 702 and has an S1P1 pitch designated as S along one of the first axes 732. Preferably, the first stack 722 does not include a periodic structure formed together with either the second layer 704 or the third layer 706, which, after imaging the first stack 722, would immediately produce a moiré pattern together with the S1P1 742. However, the first stack 722 may include a periodic structure formed together with the second layer 704 or the third layer 706, which does not produce a moiré pattern after imaging the first stack 722, such as a periodic structure that is periodic along an axis parallel to the y-axis or a periodic structure having a pitch size that does not produce a moiré pattern after imaging the first stack 722.

[0212] As specifically seen in magnification B, the second stack 724 includes a second stack first periodic structure (S2P1) 752, which is formed together with the first layer 702 and has an S2P1 pitch designated as T along one of the second axes 734. The second stack 724 further includes a second stack second periodic structure (S2P2) 754, which is formed together with the second layer 704 and has an S2P2 pitch designated as U along the other of the second axes 734.

[0213] It should be understood that S2P1 752 and S2P2 754 at least partially overlap each other, and thus the second stack Moiré pattern 760 is visible immediately after imaging the second stack 724. As is known in the art, the second stack Moiré pattern 760 is characterized by a pitch V2, which is a function of the pitch T and the pitch U, as shown in Equation 17:

[0214]

[0215] Preferably, the second stack 724 does not include a periodic structure that forms with the third layer 706 and affects the periodicity of the Moiré pattern 760. However, the second stack 724 may include a periodic structure that forms with the third layer 706 and does not affect the Moiré pattern 760, such as a periodic structure that is periodic along an axis parallel to the y-axis or a periodic structure having a pitch size that does not affect the Moiré pattern 760.

[0216] As specifically seen in magnification C, the third stack 726 includes a first periodic structure of the third stack (S3P1) 762, which is formed with the second layer 704 and has an S3P1 pitch designated as lU along one of the third axes 736. Preferably, the S3P1 pitch lU is related to the S2P2 pitch U by a third stack multiplication factor designated as l. The third stack multiplication factor l can be any positive number. The third stack 726 further includes a second periodic structure of the third stack (S3P2) 764, which is formed with the third layer 706 and has an S3P2 pitch designated as lT along the other of the third axes 736. Preferably, the S3P2 pitch lT is related to the S1P1 pitch T by the third stack multiplication factor l. It should be understood that the third stack multiplication factor l that relates the S3P2 pitch lT to the S2P1 pitch T has the same value as the third stack multiplication factor l that relates the S3P1 pitch lU to the S2P2 pitch U. In an embodiment of the present invention, the value of l is 1 and thus the S3P1 pitch lU is the same as the S2P2 pitch U and the S3P2 pitch lT is the same as the S2P1 pitch T.

[0217] It should be understood that S3P1 762 and S3P2 764 at least partially overlap each other, and thus the third stack Moiré pattern 770 is visible immediately after imaging the third stack 726. As is known in the art, the third stack Moiré pattern 770 is characterized by a pitch V3, which is a function of the third stack multiplication factor l, the pitch U, and the pitch T, as shown in Equation 18:

[0218]

[0219] Preferably, the third stack 726 does not include a periodic structure formed with the first layer 702 that affects the periodicity of the Moiré pattern 770. However, the third stack 726 may include a periodic structure formed with the first layer 702 that does not affect the periodicity of the Moiré pattern 770, such as a periodic structure that is periodic along an axis parallel to the y-axis or a periodic structure having a pitch size that does not affect the Moiré pattern 770.

[0220] Preferably, an imaging offset metrology tool with adjustable polarization, wavelength, and numerical aperture settings is used to measure the offset between any two of the layers 702, 704, and 706. An example of a suitable imaging offset metrology tool is the Archer commercially available from KLA Corporation of Milpitas, California, USA TM 700. The pitches T, U, lU, and lT need not be optically resolvable by the offset metrology tool used to generate an image of the target 700. However, preferably, each of the pitches S, V2, and V3 is optically resolvable by the offset metrology tool used to generate an image of the target 700.

[0221] Now refer ​ to, which is a simplified graphical illustration of another embodiment of the multi-layer Moiré target 800 of the present invention. ​ A graphical illustration is included in three different dimensions indicated by the x-axis, y-axis, and z-axis, which are hereinafter referred to as the x-y plane, x-z plane, and y-z plane, respectively. It should be noted that ​ generally illustrates the x-y plane, while ​ , 8C and 8D illustrate planes parallel to the x-z plane.

[0222] It should be noted that the target 800 is an example of an alternative layout of the target 700 described above with reference to ​ and additional layouts are described below with reference to ​ The target 800 is preferably formed on a semiconductor device wafer on which at least a first layer 802, a second layer 804, and a third layer 806 are preferably formed. It should be understood that each of the first layer 802, the second layer 804, and the third layer 806 defines a generally planar surface parallel to the x-y plane. The first layer 802, the second layer 804, and the third layer 806 may be adjacent layers but need not be. Preferably, any material between the first layer 802, the second layer 804, and the third layer 806 is at least partially transparent to electromagnetic radiation. In ​ the illustrated embodiment, the first layer 802 is located below the second layer 804 and the third layer 806, and the third layer 806 is located above the first layer 802 and the second layer 804. However, it should be understood that the layers 802, 804, and 806 may be arranged in any suitable order relative to each other along the z-axis.

[0223] Specifically, in ​ as seen, the target 800 includes four target quadrants 812, 814, 816, and 818. In the embodiment shown in ​ , the rotational orientation in the x-y plane of each of the target quadrants 812, 814, 816, and 818 preferably differs by an integer multiple of 90° from the rotational orientation in the x-y plane of each of the other target quadrants 812, 814, 816, and 818. Additionally, the target 800 is preferably characterized by rotational symmetry in the x direction or the y direction or both. In a preferred embodiment of the present invention, the target 800 is designed such that when in the aligned state, the overall target 800 is characterized by a single symmetry point in the x direction and a single symmetry point in the y direction. However, even in this embodiment, when in the offset state, the various elements of the target 800 will be characterized by unique symmetry points.

[0224] Each of the target quadrants 812, 814, 816, and 818 includes a first stack 822 of periodic structures, a second stack 824 of periodic structures, and a third stack 826 of periodic structures. Each of the first stack 822, the second stack 824, and the third stack 826 includes one or more periodic structures, each periodic structure having a pitch. Preferably, none of the first stack 822, the second stack 824, and the third stack 826 overlap each other. In ​ , the first stack 822 is illustrated as being located closer to the center of the target 800 than the second stack 824 and the third stack 826, and the third stack 826 is illustrated as being located closer to the edge of the target 800 than the first stack 822 and the second stack 824. However, the first stack 822, the second stack 824, and the third stack 826 can be arranged relative to each other in any suitable arrangement with respect to the x-y plane.

[0225] It should be understood that although in the embodiment illustrated in ​ , each of the periodic structures of the first stack 822, the second stack 824, and the third stack 826 is illustrated as being formed by a plurality of lines and spaces, in other embodiments of the present invention, the periodic structures of the first stack 822, the second stack 824, and the third stack 826 can be formed by any suitable periodic features. It should be further understood that the periodic features forming the periodic structures included in the first stack 822, the second stack 824, and the third stack 826 can be formed by substructures. The pitch of each of the periodic structures of the first stack 822, the second stack 824, and the third stack 826 is preferably between 10 nm and 3000 nm, and more preferably between 200 nm and 800 nm.

[0226] As ​As seen in, in each of quadrants 812, 814, 816, and 818, a first plane 831 is defined that intersects the first stack 822 and includes a plurality of first axes 832 therein, a second plane 833 that intersects the second stack 824 and includes a plurality of second axes 834 therein, and a third plane 835 that intersects the third stack 826 and includes a plurality of third axes 836 therein. Depending on the orientation of the first stack 822, second stack 824, and third stack 826 within each of quadrants 812, 814, 816, and 818, each of the first plane 831, second plane 833, and third plane 835 is an x-z plane or a y-z plane, and the first axes 832, second axes 834, and third axes 836 are parallel to the corresponding x-axis or y-axis. It should be understood that in each of quadrants 812, 814, 816, and 818, the first plane 831, second plane 833, and third plane 835 are all parallel to each other.

[0227] As specifically seen in ​ the first stack 822 includes a first stack first periodic structure (S1P1) 842 that is formed with the first layer 802 and has an S1P1 pitch designated as W along one of the first axes 832. Preferably, the first stack 822 does not include a periodic structure formed with either the second layer 804 or the third layer 806 that would immediately produce a moiré pattern with the S1P1 842 after imaging the first stack 822. However, the first stack 822 may include a periodic structure formed with the second layer 804 or the third layer 806 that does not produce a moiré pattern after imaging the first stack 822, such as a periodic structure that is periodic in a plane parallel to the x-y plane along an axis perpendicular to the first axes 832 or a periodic structure having a pitch size that does not produce a moiré pattern after imaging the first stack 822.

[0228] As specifically seen in ​ the second stack 824 includes a second stack first periodic structure (S2P1) 852 that is formed with the first layer 802 and has an S2P1 pitch designated as X along one of the second axes 834. The second stack 824 further includes a second stack second periodic structure (S2P2) 854 that is formed with the second layer 804 and has an S2P2 pitch designated as Y along the other of the second axes 834.

[0229] It should be understood that S2P1 852 and S2P2 854 at least partially overlap each other, and thus the second stack Moiré pattern 860 is visible immediately after imaging the second stack 824. As is known in the art, the second stack Moiré pattern 860 is characterized by a pitch Z2, which is a function of the pitches X and Y, as shown in Equation 19:

[0230]

[0231] Preferably, the second stack 824 does not include a periodic structure that forms with the third layer 806 and affects the periodicity of the Moiré pattern 860. However, the second stack 824 may include a periodic structure that forms with the third layer 806 and does not affect the Moiré pattern 860, such as a periodic structure that is periodic in a plane parallel to the x-y plane along an axis perpendicular to the second axis 834 or a periodic structure having a pitch size that does not affect the Moiré pattern 860.

[0232] As specifically seen in ​ the third stack 826 includes a first periodic structure of the third stack (S3P1) 862, which is formed with the second layer 804 and has an S3P1 pitch designated as mY along one of the third axes 836. Preferably, the S3P1 pitch mY is related to the S2P2 pitch Y by a third stack multiplication factor designated as m. The third stack multiplication factor m can be any positive number. The third stack 826 further includes a second periodic structure of the third stack (S3P2) 864, which is formed with the third layer 806 and has an S3P2 pitch designated as mX along the other of the third axes 836. Preferably, the S3P2 pitch mX is related to the S2P1 pitch X by the third stack multiplication factor m. It should be understood that the third stack multiplication factor m that relates the S3P2 pitch mX to the S2P1 pitch X has the same value as the third stack multiplication factor m that relates the S3P1 pitch mY to the S2P2 pitch Y. In an embodiment of the present invention, the value of m is 1 and thus the S3P1 pitch mY is the same as the S2P2 pitch Y and the S3P2 pitch mX is the same as the S2P1 pitch X.

[0233] It should be understood that S3P1 862 and S3P2 864 at least partially overlap each other, and thus the third stack Moiré pattern 870 is visible immediately after imaging the third stack 826. As is known in the art, the third stack Moiré pattern 870 is characterized by a pitch Z3, which is a function of the third stack multiplication factor m, the pitch Y, and the pitch X, as shown in Equation 20:

[0234]

[0235] Preferably, the third stack 826 does not include a periodic structure that forms with the first layer 802 and affects the periodicity of the Moiré pattern 870. However, the third stack 826 may include a periodic structure that forms with the first layer 802 and does not affect the periodicity of the Moiré pattern 870, such as a periodic structure that is periodic in a plane parallel to the x-y plane along an axis perpendicular to the third axis 836 or has a pitch size that does not affect the Moiré pattern 870.

[0236] Preferably, an imaging offset metrology tool with adjustable polarization, wavelength, and numerical aperture settings is used to measure the offset between any two of the layers 802, 804, and 806. An example of a suitable imaging offset metrology tool is the Archer commercially available from KLA Corporation, Milpitas, California, USA TM The pitches X, Y, mY, and mX do not need to be optically resolvable by the offset metrology tool used to generate the image of the target 800. However, preferably, each of the pitches W, Z2, and Z3 is optically resolvable by the offset metrology tool used to generate the image of the target 800.

[0237] Now refer to ​ , which is a simplified flowchart that illustrates a preferred method for calculating the offset between a first layer 902, a second layer 904, and a third layer 906 (such as layers 702, 704, and 706 ( ​ ) or 802, 804, and 806 ( ​ )) of a multi-layer semiconductor device wafer on which the target 900 (such as target 700 ( ​ ) or target 800 ( ​ )) is formed in a direction parallel to the x-direction or the y-direction. Further refer to ​ and 9C , which are simplified illustrations of a first embodiment and a second embodiment of parts of the method of ​ .

[0238] Although it should be understood that when using the target 800 ( ​ ), the method described with reference to ​ may be performed only once to calculate the offset in the x-direction or the y-direction, but generally ​ the method described in ​ will be performed twice to calculate the offset in each of the x-direction and the y-direction. It should also be understood that when using the target 700 ( ), the offset may be calculated only in one direction parallel to the first axis 732, the second axis 734, and the third axis 736.

[0239] ​ and 9BWhen using the target 700 in the method, the direction of the measurement offset is automatically selected to be parallel to the first axis 732, the second axis 734, and the third axis 736. When in ​ and 9B When using the target 800 in the method, the structures of the quadrants 814 and 818 are utilized to measure the offset in a direction parallel to the x-axis, and the structures of the quadrants 812 and 816 are utilized to measure the offset in a direction parallel to the y-axis.

[0240] Preferably, in the next step 909, an imaging offset metrology tool with adjustable polarization, wavelength, and numerical aperture settings is used to generate an image of the target 900. An example of a suitable imaging offset metrology tool is the Archer TM 700 available commercially from KLA Corporation, Milpitas, California, USA. It should be noted that the spacings T, U, lU, lT, X, Y, mY, and mX do not need to be optically resolvable by the offset metrology tool used to generate the image of the target 900. However, preferably, each of the spacings S, W, V2, V3, Z2, and Z3 is optically resolvable by the offset metrology tool used to generate the image of the target 900.

[0241] In the next step 911 and as ​ and 9C seen in, for each of the corresponding first stack 922, second stack 924, and third stack 926 (such as the first stack 722, second stack 724, and third stack 726 ( ​ )) or the first stack 822, second stack 824, and third stack 826 ( ​ )) in the quadrants selected in step 907, the first region of interest 912, the second region of interest 914, and the third region of interest 916 are selected. It should be understood that as seen in the illustrated embodiments of ​ and 9C , although the first region of interest 912, the second region of interest 914, and the third region of interest 916 are preferably entirely located within each of the corresponding first stack 922, second stack 924, and third stack 926 (as illustrated for the first region of interest 912 entirely located within the first stack 922), the first region of interest 912, the second region of interest 914, and the third region of interest 916 may extend beyond the corresponding first stack 922, second stack 924, and third stack 926, as illustrated for the regions of interest 914 and 916 extending beyond the corresponding second stack 924 and third stack 926. It should be further understood that ​ and 9C the regions of interest 912, 914, and 916 shown in are representative regions of interest, and other suitable regions of interest may be selected at step 911.

[0242] In the next step 931 and as ​ and 9C seen in, calculate the position of the symmetry points 932 between all examples of the first region of interest 912 selected in step 911. In the next step 933 and as ​ and 9C seen in, calculate the position of the symmetry points 934 between all examples of the second region of interest 914 selected in step 911. In the next step 935 and as ​ and 9C seen in, calculate the position of the symmetry points 936 between all examples of the third region of interest 916 selected in step 911.

[0243] In the next step 937, calculate the distance in the direction selected in step 907 between the positions of the symmetry points 932 of one or more first regions of interest 912 identified in step 931 and the positions of the symmetry points 934 of one or more second regions of interest 914 identified in step 933. The distance found in step 937 is divided by the gain α1, which is a function of the spacings T and U for target 700, as shown in Equation 21a:

[0244]

[0245] and is a function of the spacings X and Y for target 800, as shown in Equation 21b:

[0246]

[0247] And report the result as the offset between the first layer 902 and the second layer 904 in the direction selected in step 907. It should be understood that in addition to the distance calculated in step 937, the method further calculates an adjustment direction, such as right, left, up, or down. The adjustment direction varies with the relative values of the spacings T and U or the spacings X and Y and which of the adjustment layers 902 and 904.

[0248] In the next step 939, calculate the distance in the direction selected in step 907 between the positions of the symmetry points 934 of one or more second regions of interest 914 identified in step 933 and the positions of the symmetry points 936 of one or more third regions of interest 916 identified in step 935. The distance found in step 939 is divided by the gain α2, which is a function of the spacings T and U for target 700, as shown in Equation 22a:

[0249]

[0250] And the target 800 is a function of pitch X and pitch Y, as shown in Equation 22b:

[0251]

[0252] And report the result as the offset between the first layer 902 and the third layer 906 in the direction selected at step 907. It should be understood that in addition to the distance calculated at step 939, the method further calculates an adjustment direction, such as right, left, up, or down. The adjustment direction varies with the relative values of pitches T and U or pitches X and Y and which of the layers 902 and 906 are to be adjusted.

[0253] In the next step 941, calculate the difference between the offset value reported at step 937 and the offset value reported at step 939. Report the difference calculated at step 941 as the offset between the second layer 904 and the third layer 906 in the direction selected at step 907. It should be understood that in addition to the distance calculated at step 941, the method further calculates an adjustment direction, such as right, left, up, or down. The adjustment direction varies with the relative values of pitches T and U or pitches X and Y and which of the layers 904 and 906 are to be adjusted.

[0254] It should be understood that in an embodiment of the present invention, only the first two previously formed layers among the layers 902, 904, and 906 that will form the third layer among those layers can be used to perform the relevant part of the method described above ​ as described above. As described above, the layers 902, 904, and 906 can be formed in any suitable order relative to each other.

[0255] Now refer to ​ , which is a simplified illustrative diagram of another embodiment of the multi-layer Moiré target 1000 of the present invention. ​ An illustration including three different dimensions indicated by the x-axis, y-axis, and z-axis, which are hereinafter referred to as the x-y plane, the x-z plane, and the y-z plane respectively. It should be noted that Figure 10 generally illustrates the x-y plane, while Figure 10 the magnified A, B, and C illustrate planes parallel to the x-z plane.

[0256] The target 1000 is preferably formed on a semiconductor device wafer, on which at least a first layer 1002, a second layer 1004, and a third layer 1006 are preferably formed. It should be understood that each of the first layer 1002, the second layer 1004, and the third layer 1006 defines a generally planar surface parallel to the x-y plane. The first layer 1002, the second layer 1004, and the third layer 1006 may be adjacent layers but need not be. Preferably, any material between the first layer 1002, the second layer 1004, and the third layer 1006 is at least partially transparent to electromagnetic radiation. In Figure 10 In the illustrated embodiment, the first layer 1002 is located below the second layer 1004 and the third layer 1006, and the third layer 1006 is located above the first layer 1002 and the second layer 1004. However, it should be understood that the layers 1002, 1004, and 1006 may be arranged in any suitable order relative to each other along the z-axis.

[0257] Additionally, in an embodiment of the present invention, the structure shown as being formed with the first layer 1002 and the third layer 1006 may all be formed with the layer 1002. In this embodiment, no part of the target 1000 is formed with the layer 1006. This embodiment is particularly useful for calibration, as described below with reference to Figures 12A to 12C described.

[0258] It should be understood that Figure 10 illustrates one possible layout of the target 1000, and in other embodiments of the present invention, the target 1000 may include additional structures. For example, as described below with reference to Figures 11A to 11D and 34 to 39, suitable targets may include Figure 10 multiple examples of the structures shown in, and those multiple examples may be arranged in various ways.

[0259] Preferably, the target 1000 includes a first stack 1022 of periodic structures, a second stack 1024 of periodic structures, and a third stack 1026 of periodic structures. Each of the first stack 1022, the second stack 1024, and the third stack 1026 includes one or more periodic structures, each periodic structure having a pitch. Preferably, the first stack 1022, the second stack 1024, and the third stack 1026 do not overlap each other.

[0260] It should be understood that although in Figure 10In [the figure], each of the periodic structures of the first stack 1022, the second stack 1024, and the third stack 1026 is shown as being formed by a plurality of lines and spaces. However, in other embodiments of the present invention, the periodic structures of the first stack 1022, the second stack 1024, and the third stack 1026 can be formed by any suitable periodic features. It should be further understood that the periodic features forming the periodic structures included in the first stack 1022, the second stack 1024, and the third stack 1026 can be formed by sub-structures. The pitch of each of the periodic structures of the first stack 1022, the second stack 1024, and the third stack 1026 is preferably between 10 nm and 3000 nm, and more preferably between 200 nm and 800 nm.

[0261] The first x-z plane 1031 intersects the first stack 1022. A plurality of first axes 1032 are located in the first x-z plane 1031 and parallel to the x-axis. The second x-z plane 1033 intersects the second stack 1024. A plurality of second axes 1034 are located in the second x-z plane 1033 and parallel to the x-axis. The third x-z plane 1035 intersects the third stack 1026. A plurality of third axes 1036 are located in the third x-z plane 1035 and parallel to the x-axis.

[0262] As specifically seen in magnification A, the first stack 1022 includes a first stack first periodic structure (S1P1) 1042, which is formed together with the first layer 1002 and has an S1P1 pitch designated as β along one of the first axes 1032. The first stack 1022 further includes a first stack second periodic structure (S1P2) 1044, which is formed together with the second layer 1004 and has an S1P2 pitch designated as β - n along the other of the first axes 1032. Preferably, the S1P2 pitch β - n differs from the S1P1 pitch β by a first stack addition designated as n. The first stack addition n can have any non-zero value.

[0263] It should be understood that S1P1 1042 and S1P2 1044 at least partially overlap each other, and thus the first stack Moiré pattern 1050 is immediately visible after imaging the first stack 1022. As is known in the art, the first stack Moiré pattern 1050 is characterized by a pitch γ1, which is a function of the addition n, the pitch β, and the pitch β - n, as shown in Equation 23:

[0264]

[0265] Preferably, the first stack 1022 does not include a periodic structure that forms with the third layer 1006 and affects the periodicity of the Moiré pattern 1050. However, the first stack 1022 may include a periodic structure that forms with the third layer 1006 and does not affect the periodicity of the Moiré pattern 1050, such as a periodic structure that is periodic along an axis parallel to the y-axis or a periodic structure having a pitch size that does not affect the Moiré pattern 1050.

[0266] As specifically seen in magnification B, the second stack 1024 includes a second-stack first periodic structure (S2P1) 1052 that forms with the first layer 1002 and has an S2P1 pitch designated as β along one of the second axes 1034. It should be understood that the S2P1 pitch β has the same value as the S1P1 pitch β. The second stack 1024 further includes a second-stack second periodic structure (S2P2) 1054 that forms with the second layer 1004 and has an S2P2 pitch designated as β + n along the other of the second axes 1034. Preferably, the S2P2 pitch β + n differs from the S2P1 pitch β by a second-stack additional term designated as n. It should be understood that the second-stack additional term n has the same value as the first-stack additional term n.

[0267] It should be understood that the S2P1 1052 and the S2P2 1054 at least partially overlap each other, and thus the second-stack Moiré pattern 1060 is visible immediately after imaging the second stack 1024. As is known in the art, the second-stack Moiré pattern 1060 is characterized by a pitch γ2 that is a function of the additional term n, the pitch β, and the pitch β + n, as shown in Equation 24:

[0268]

[0269] Preferably, the second stack 1024 does not include a periodic structure that forms with the third layer 1006 and affects the periodicity of the Moiré pattern 1060. However, the second stack 1024 may include a periodic structure that forms with the third layer 1006 and does not affect the periodicity of the Moiré pattern 1060, such as a periodic structure that is periodic along an axis parallel to the y-axis or a periodic structure having a pitch size that does not affect the Moiré pattern 1060.

[0270] As specifically seen in magnification C, the third stack 1026 includes a third stack first periodic structure (S3P1) 1062, which is formed with the second layer 1004 and has an S3P1 pitch designated as β + n along one of the third axes 1036. It should be understood that the S3P1 pitch β + n has the same value as the S2P2 pitch β + n. The third stack 1026 further includes a third stack second periodic structure (S3P2) 1064, which is formed with the third layer 1006 and has an S3P2 pitch designated as β along the other of the third axes 1036. It should be understood that the S3P2 pitch β has the same value as the S1P1 pitch β.

[0271] It should be understood that S3P1 1062 and S3P2 1064 at least partially overlap each other, and thus the third stack moiré pattern 1070 is visible immediately after imaging the third stack 1026. As is known in the art, the third stack moiré pattern 1070 is characterized by a pitch γ3, which is a function of the additional term n, the pitch β, and the pitch β + n, as shown in Equation 25:

[0272]

[0273] Preferably, the third stack 1026 does not include a periodic structure that forms with the first layer 1002 and affects the moiré pattern 1070. However, the third stack 1026 may include a periodic structure that forms with the first layer 1002 and does not affect the moiré pattern 1070, such as a periodic structure that is periodic along an axis parallel to the y-axis or a periodic structure having a pitch size that does not affect the moiré pattern 1070.

[0274] Preferably, an imaging offset metrology tool with adjustable polarization, wavelength, and numerical aperture settings is used to measure the offset between any two of the layers 1002, 1004, and 1006. An example of a suitable imaging offset metrology tool is the Archer TM 700, which is commercially available from KLA Corporation, Milpitas, California, USA. The pitches β, β - n, and β + n do not need to be optically resolvable by the offset metrology tool used to generate the image of the target 1000. However, preferably, each of the pitches γ1, γ2, and γ3 is optically resolvable by the offset metrology tool used to generate the image of the target 1000.

[0275] Now refer to Figures 11A to 11D , which is a simplified graphical illustration of another embodiment of the multi-layer moiré target 1100 of the present invention. Figures 11A to 11D A graphical illustration is included in three different dimensions indicated by the x-axis, y-axis, and z-axis, which are hereinafter referred to as the x-y plane, the x-z plane, and the y-z plane, respectively. It should be noted that Figure 11AThe general illustration shows the x-y plane, while Figure 11B , 11C and 11D illustrations show planes parallel to the x-z plane.

[0276] It should be noted that the target 1100 is an example of an alternative layout of the target 1000 described above with reference to Figure 10 and additional layouts are described below with reference to Figures 34 to 39 . The target 1100 is preferably formed on a semiconductor device wafer, on which at least a first layer 1102, a second layer 1104, and a third layer 1106 are preferably formed. It should be understood that each of the first layer 1102, the second layer 1104, and the third layer 1106 defines a substantially planar surface parallel to the x-y plane. The first layer 1102, the second layer 1104, and the third layer 1106 may be adjacent layers but need not be. Preferably, any material between the first layer 1102, the second layer 1104, and the third layer 1106 is at least partially transparent to electromagnetic radiation. In the embodiment illustrated in Figures 11A to 11D , the first layer 1102 is located below the second layer 1104 and the third layer 1106, and the third layer 1106 is located above the first layer 1102 and the second layer 1104. However, it should be understood that the layers 1102, 1104, and 1106 may be arranged in any suitable order relative to each other along the z-axis.

[0277] In addition, in an embodiment of the present invention, the structure shown as being formed together with the first layer 1102 and the third layer 1106 may all be formed together with the layer 1102. In this embodiment, no part of the target 1100 is formed together with the layer 1106. This embodiment is particularly useful for calibration, as described below with reference to Figures 12A to 12C .

[0278] As specifically seen in Figure 11A , the target 1100 includes four target quadrants 1112, 1114, 1116, and 1118. In the embodiment shown in Figure 11A , the rotational orientation in the x-y plane of each of the target quadrants 1112, 1114, 1116, and 1118 preferably differs by an integer multiple of 90° from the rotational orientation in the x-y plane of each of the other target quadrants 1112, 1114, 1116, and 1118. In addition, the target 1100 is preferably characterized by rotational symmetry in the x direction or the y direction or both. In a preferred embodiment of the present invention, the target 1100 is designed such that when in the aligned state, the whole of the target 1100 is characterized by a single symmetry point in the x direction and a single symmetry point in the y direction. However, even in this embodiment, when in the offset state, the various elements of the target 1100 will be characterized by unique symmetry points.

[0279] Each of the target quadrants 1112, 1114, 1116, and 1118 includes a first stack 1122 of periodic structures, a second stack 1124 of periodic structures, and a third stack 1126 of periodic structures. Each of the first stack 1122, the second stack 1124, and the third stack 1126 includes one or more periodic structures, each periodic structure having a pitch. Preferably, the first stack 1122, the second stack 1124, and the third stack 1126 do not overlap with each other. In Figures 11A to 11D FIG. 1, the first stack 1122 is illustrated as being located closer to the center of the target 1100 than the second stack 1124 and the third stack 1126, and the third stack 1126 is illustrated as being located closer to the edge of the target 1100 than the first stack 1122 and the second stack 1124. However, the first stack 1122, the second stack 1124, and the third stack 1126 may be arranged relative to each other in any suitable arrangement with respect to the x-y plane.

[0280] It should be understood that although in the embodiment illustrated in Figures 11A to 11D FIG. 1, each of the periodic structures of the first stack 1122, the second stack 1124, and the third stack 1126 is illustrated as being formed by a plurality of lines and spaces, in other embodiments of the present invention, the periodic structures of the first stack 1122, the second stack 1124, and the third stack 1126 may be formed by any suitable periodic features. It should be further understood that the periodic features forming the periodic structures included in the first stack 1122, the second stack 1124, and the third stack 1126 may be formed by sub-structures. The pitch of each of the periodic structures of the first stack 1122, the second stack 1124, and the third stack 1126 is preferably between 10 nm and 3000 nm, and more preferably between 200 nm and 800 nm.

[0281] As Figure 11AAs seen in, in each of quadrants 1112, 1114, 1116, and 1118, a first plane 1131 is defined that intersects the first stack 1122 and includes a plurality of first axes 1132 located therein, a second plane 1133 that intersects the second stack 1124 and includes a plurality of second axes 1134 located therein, and a third plane 1135 that intersects the third stack 1126 and includes a plurality of third axes 1136 located therein. Depending on the orientation of the first stack 1122, the second stack 1124, and the third stack 1126 within each of quadrants 1112, 1114, 1116, and 1118, each of the first plane 1131, the second plane 1133, and the third plane 1135 is an x-z plane or a y-z plane, and the first axes 1132, the second axes 1134, and the third axes 1136 are parallel to the respective x-axis or y-axis. It should be understood that in each of quadrants 1112, 1114, 1116, and 1118, the first plane 1131, the second plane 1133, and the third plane 1135 are all parallel to each other.

[0282] As specifically seen in Figure 11B the first stack 1122 includes a first stack first periodic structure (S1P1) 1142 that is formed with the first layer 1102 and has an S1P1 pitch designated as δ along one of the first axes 1132. The first stack 1122 further includes a first stack second periodic structure (S1P2) 1144 that is formed with the second layer 1104 and has an S1P2 pitch designated as δ-p along the other of the first axes 1132. Preferably, the S1P2 pitch δ-p differs from the S1P1 pitch δ by a first stack additive designated as p. The first stack additive p can have any non-zero value.

[0283] It should be understood that the S1P1 1142 and the S1P2 1144 at least partially overlap each other, and thus a first stack moiré pattern 1150 is visible immediately after imaging the first stack 1122. As is known in the art, the first stack moiré pattern 1150 is characterized by a pitch ε1 that is a function of the additive p, the pitch δ, and the pitch δ-p, as shown in Equation 26:

[0284]

[0285] Preferably, the first stack 1122 does not include a periodic structure that is formed with the third layer 1106 and affects the moiré pattern 1150. However, the first stack 1122 can include a periodic structure that is formed with the third layer 1106 and does not affect the moiré pattern 1150, such as a periodic structure that is periodic in a plane parallel to the x-y plane along an axis perpendicular to the first axes 1132 or a periodic structure having a pitch magnitude that does not affect the moiré pattern 1150.

[0286] As specifically seen in Figure 11C the second stack 1124 includes a second-stack first periodic structure (S2P1) 1152, the S2P1 being formed with the first layer 1102 and having an S2P1 pitch designated as δ along one of the second axes 1134. It should be understood that the S2P1 pitch δ has the same value as the S1P1 pitch δ. The second stack 1124 further includes a second-stack second periodic structure (S2P2) 1154, the S2P2 being formed with the second layer 1104 and having an S2P2 pitch designated as δ + p along the other of the second axes 1134. Preferably, the S2P2 pitch δ + p differs from the S2P1 pitch δ by a second-stack additional term designated as p. It should be understood that the second-stack additional term p has the same value as the first-stack additional term p.

[0287] It should be understood that the S2P1 1152 and the S2P2 1154 at least partially overlap each other, and thus a second-stack moiré pattern 1160 is visible immediately after imaging the second stack 1124. As is known in the art, the second-stack moiré pattern 1160 is characterized by a pitch ε2, the pitch ε2 being a function of the additional term p, the pitch δ, and the pitch δ + p, as shown in Equation 27:

[0288]

[0289] Preferably, the second stack 1124 does not include a periodic structure that forms with the third layer 1106 and affects the moiré pattern 1160. However, the second stack 1124 may include a periodic structure that forms with the third layer 1106 and does not affect the moiré pattern 1160, such as a periodic structure that is periodic in a plane parallel to the x-y plane along an axis perpendicular to the second axis 1134 or a periodic structure having a pitch magnitude that does not affect the moiré pattern 1160.

[0290] As specifically seen in Figure 11D the third stack 1126 includes a third-stack first periodic structure (S3P1) 1162, the S3P1 being formed with the second layer 1104 and having an S3P1 pitch designated as δ + p along one of the third axes 1136. It should be understood that the S3P1 pitch δ + p has the same value as the S2P2 pitch δ + p. The third stack 1126 further includes a third-stack second periodic structure (S3P2) 1164, the S3P2 being formed with the third layer 1106 and having an S3P2 pitch designated as δ along the other of the third axes 1136. It should be understood that the S3P2 pitch δ has the same value as the S1P1 pitch δ.

[0291] It should be understood that S3P1 1162 and S3P2 1164 at least partially overlap each other, and thus the third stack Moiré pattern 1170 is visible immediately after imaging the third stack 1126. As is known in the art, the third stack Moiré pattern 1170 is characterized by a pitch ε3, which is a function of the additional term p, the pitch δ, and the pitch δ + p, as shown in Equation 28:

[0292]

[0293] Preferably, the third stack 1126 does not include a periodic structure that forms with the first layer 1102 and affects the periodicity of the Moiré pattern 1170. However, the third stack 1126 may include a periodic structure that forms with the first layer 1102 and does not affect the Moiré pattern 1170, such as a periodic structure that is periodic in a plane parallel to the x-y plane along an axis perpendicular to the third axis 1136 or a periodic structure having a pitch size that does not affect the Moiré pattern 1170.

[0294] Preferably, an imaging offset metrology tool with adjustable polarization, wavelength, and numerical aperture settings is used to measure the offset between any two of the layers 1102, 1104, and 1106. An example of a suitable imaging offset metrology tool is the Archer commercially available from KLA Corporation, Milpitas, California, USA TM 700. The pitches δ, δ - p, and δ + p do not need to be optically resolvable by the offset metrology tool used to generate the image of the target 1100. However, preferably, each of the pitches ε1, ε2, and ε3 is optically resolvable by the offset metrology tool used to generate the image of the target 1100.

[0295] Now refer to Figure 12A , which is a simplified flowchart that illustrates a preferred method for calculating the offset between the first layer 1202, the second layer 1204, and the third layer 1206 (such as the layers 1002, 1004, and 1006 ( Figure 10 ) or 1102, 1104, and 1106 ( Figures 11A to 11D )) of a multi-layer semiconductor device wafer on which the target 1200 is formed (such as the target 1000 ( Figure 10 ) or the target 1100 ( Figures 11A to 11D )) in a direction parallel to the x direction or the y direction. Further refer to Figure 12B and 12C , which are simplified illustrations of the first embodiment and the second embodiment of parts of the method of Figure 12A respectively.

[0296] Although it should be understood that when using the target 1100 ( Figures 11A to 11D ), refer to Figures 12A to 12CThe described method may be performed only once to calculate the offset in the x or y direction, but typically Figures 12A to 12C the method described in Figure 10 will be performed twice to calculate the offset in each of the x and y directions. It should also be understood that when using the target 1000 (

[0297] ), the offset may be calculated only in one direction parallel to the first axis 1032, the second axis 1034, and the third axis 1036. Figure 12A and 12B ), the direction for measuring the offset is automatically selected as the direction parallel to the first axis 1032, the second axis 1034, and the third axis 1036. When using the target 1100 in the method of Figure 12A and 12B ), the structures of the quadrants 1114 and 1118 are used to measure the offset in a direction parallel to the x-axis, and the structures of the quadrants 1112 and 1116 are used to measure the offset in a direction parallel to the y-axis.

[0298] Preferably, in the next step 1209, an imaging offset metrology tool with adjustable polarization, wavelength, and numerical aperture settings is used to generate an image of the target 1200. An example of a suitable imaging offset metrology tool is the Archer TM 700 commercially available from KLA Corporation, Milpitas, California, USA. It should be noted that the spacings β, β - n, β + n, δ, δ - p, and δ + p do not need to be optically resolvable by the offset metrology tool used to generate the image of the target 1200. However, preferably, each of the spacings γ1, γ2, γ3, ε1, ε2, and ε3 is optically resolvable by the offset metrology tool used to generate the image of the target 1200.

[0299] In the next step 1211 and as seen in Figure 12B and 12C ), for each of the corresponding first stack 1222, second stack 1224, and third stack 1226 (such as the first stack 1022, second stack 1024, and third stack 1026 ( Figure 10 )) or the first stack 1122, second stack 1124, and third stack 1126 ( Figures 11A to 11D )) in the quadrant selected in step 1207, the first region of interest 1212, the second region of interest 1214, and the third region of interest 1216 are selected. It should be understood that as in Figure 12B and 12CAs seen in the illustrated embodiments, although the first region of interest 1212, the second region of interest 1214, and the third region of interest 1216 are preferably entirely located within each of the respective first stack 1222, second stack 1224, and third stack 1226 (as illustrated for the first region of interest 1212 entirely located within the first stack 1222), the first region of interest 1212, the second region of interest 1214, and the third region of interest 1216 may extend beyond the respective first stack 1222, second stack 1224, and third stack 1226, as illustrated for the regions of interest 1214 and 1216 that extend beyond the respective second stack 1224 and third stack 1226. It should be further understood that Figure 12B and 12C the regions of interest 1212, 1214, and 1216 shown in are representative regions of interest, and other suitable regions of interest may be selected at step 1211.

[0300] In the next step 1231 and as Figure 12B and 12C seen in, the position of the symmetry point 1232 between all examples of the first region of interest 1212 selected in step 1211 is calculated. In the next step 1233 and as Figure 12B and 12C seen in, the position of the symmetry point 1234 between all examples of the second region of interest 1214 selected in step 1211 is calculated. In the next step 1235 and as Figure 12B and 12C seen in, the position of the symmetry point 1236 between all examples of the third region of interest 1216 selected in step 1211 is calculated.

[0301] At the next step 1237, the distance in the direction selected at step 1207 between the position of the symmetry point 1232 of one or more first regions of interest 1212 identified at step 1231 and the position of the symmetry point 1234 of one or more second regions of interest 1214 identified at step 1233 is calculated. The distance found at step 1237 is divided by the gain ζ1, which is a function of the pitch β and an additional term n for the target 1000, as shown in Equation 29a:

[0302]

[0303] and is a function of the pitch δ and an additional term p for the target 1100, as shown in Equation 29b:

[0304]

[0305] And report the result as the offset between the first layer 1202 and the second layer 1204 in the direction selected at step 1207. It should be understood that in addition to the distance calculated at step 1237, the method further calculates an adjustment direction, such as right, left, up, or down. The adjustment direction varies with the value of the spacing β and the additional term n or the spacing δ and the additional term p, and which of the adjustment layers 1202 and 1204.

[0306] In the next step 1239, calculate the distance in the direction selected at step 1207 between the position of the symmetric point 1234 of one or more second regions of interest 1214 identified at step 1233 and the position of the symmetric point 1236 of one or more third regions of interest 1216 identified at step 1235. The distance found at step 1239 is divided by a gain ζ2, which is a function of the spacing β and the additional term n for the target 1000, as shown in Equation 30a:

[0307]

[0308] And is a function of the spacing δ and the additional term p for the target 1100, as shown in Equation 30b:

[0309]

[0310] And report the result as the offset between the first layer 1202 and the third layer 1206 in the direction selected at step 1207. It should be understood that in addition to the distance calculated at step 1239, the method further calculates an adjustment direction, such as right, left, up, or down. The adjustment direction varies with the value of the spacing β and the additional term n or the spacing δ and the additional term p, and which of the adjustment layers 1202 and 1206.

[0311] In the next step 1241, calculate the difference between the offset value reported at step 1237 and the offset value reported at step 1239. Report the difference calculated at step 1241 as the offset between the second layer 1204 and the third layer 1206 in the direction selected at step 1207. It should be understood that in addition to the distance calculated at step 1241, the method further calculates an adjustment direction, such as right, left, up, or down. The adjustment direction varies with the value of the spacing β and the additional term n or the spacing δ and the additional term p, and which of the adjustment layers 1204 and 1206.

[0312] Preferably, in the embodiments described above, where the structure shown as formed together with the first layer 1202 and the third layer 1206 is all formed together with the layer 1202, as referred to above Figures 12A to 12CThe described method continues to calculate and report the difference between the offset value reported at step 1237 and the offset value reported at step 1241. The difference between the offset values reported at steps 1237 and 1241 is useful in calibrating the offset metrology tool in the method for Figures 12A to 12C .

[0313] It should be understood that, in an embodiment of the present invention, only layers 1202 and 1204 may be used to perform the relevant part of the method described above prior to forming layer 1206. Figures 12A to 12C .

[0314] Now referring to Figure 13 , which is a simplified graphical illustration of another embodiment of the multi-layer moiré target 1300 of the present invention. Figure 13 The illustration includes three different dimensions indicated by the x-axis, y-axis, and z-axis, which are hereinafter referred to as the x-y plane, x-z plane, and y-z plane, respectively. It should be noted that Figure 13 generally illustrates the x-y plane, while Figure 13 the magnified illustrations A, B, and C illustrate planes parallel to the x-z plane.

[0315] The target 1300 is preferably formed on a semiconductor device wafer, on which at least a first layer 1302, a second layer 1304, and a third layer 1306 are preferably formed. It should be understood that each of the first layer 1302, the second layer 1304, and the third layer 1306 defines a generally planar surface parallel to the x-y plane. The first layer 1302, the second layer 1304, and the third layer 1306 may be adjacent layers but need not be. Preferably, any material between the first layer 1302, the second layer 1304, and the third layer 1306 is at least partially transparent to electromagnetic radiation. In the embodiment illustrated in Figure 13 , the first layer 1302 is located below the second layer 1304 and the third layer 1306, and the third layer 1306 is located above the first layer 1302 and the second layer 1304. However, it should be understood that the layers 1302, 1304, and 1306 may be arranged in any suitable order relative to each other along the z-axis.

[0316] Additionally, in an embodiment of the present invention, the structure shown as being formed with the first layer 1302 and the third layer 1306 may all be formed with the layer 1302. In this embodiment, no part of the target 1300 is formed with the layer 1306. This embodiment is particularly useful for calibration, as described below with reference to Figures 15A to 15C .

[0317] It should be understood that Figure 13The figure illustrates a possible layout of the target 1300, and in other embodiments of the present invention, the target 1300 may include additional structures. For example, as described hereinafter with reference to Figures 14A to 14D and 34 to 39, suitable targets may include Figure 13 multiple examples of the structures shown in, and those multiple examples may be arranged in various ways.

[0318] Preferably, the target 1300 includes a first stack 1322 of periodic structures, a second stack 1324 of periodic structures, and a third stack 1326 of periodic structures. Each of the first stack 1322, the second stack 1324, and the third stack 1326 includes one or more periodic structures, and each periodic structure has a pitch. Preferably, none of the first stack 1322, the second stack 1324, and the third stack 1326 overlap each other.

[0319] It should be understood that although in Figure 13 each of the periodic structures of the first stack 1322, the second stack 1324, and the third stack 1326 is shown as being formed by a plurality of lines and spaces, in other embodiments of the present invention, the periodic structures of the first stack 1322, the second stack 1324, and the third stack 1326 may be formed by any suitable periodic features. It should be further understood that the periodic features forming the periodic structures included in the first stack 1322, the second stack 1324, and the third stack 1326 may be formed by sub-structures. The pitch of each of the periodic structures of the first stack 1322, the second stack 1324, and the third stack 1326 is preferably between 10 nm and 3000 nm, and more preferably between 200 nm and 800 nm.

[0320] A first x-z plane 1331 intersects the first stack 1322. A plurality of first axes 1332 are located in the first x-z plane 1331 and are parallel to the x-axis. A second x-z plane 1333 intersects the second stack 1324. A plurality of second axes 1334 are located in the second x-z plane 1333 and are parallel to the x-axis. A third x-z plane 1335 intersects the third stack 1326. A plurality of third axes 1336 are located in the third x-z plane 1335 and are parallel to the x-axis.

[0321] As specifically seen in magnification A, the first stack 1322 includes a first stack first periodic structure (S1P1) 1342, the S1P1 being formed with the second layer 1304 and having an S1P1 pitch designated as η along one of the first axes 1332. Preferably, the first stack 1322 does not include a periodic structure formed with either the first layer 1302 or the third layer 1306, which, after imaging the first stack 1322, would immediately produce a moiré pattern together with the S1P1 1342. However, the first stack 1322 may include a periodic structure formed with the first layer 1302 or the third layer 1306, which, after imaging the first stack 1322, does not produce a moiré pattern, such as a periodic structure that is periodic along an axis parallel to the y-axis or a periodic structure having a pitch size that does not produce a moiré pattern after imaging the first stack 1322.

[0322] As specifically seen in magnification B, the second stack 1324 includes a second stack first periodic structure (S2P1) 1352, the S2P1 being formed with the first layer 1302 and having an S2P1 pitch designated as θ along one of the second axes 1334. The second stack 1324 further includes a second stack second periodic structure (S2P2) 1354, the S2P2 being formed with the second layer 1304 and having an S2P2 pitch designated as ι along the other of the second axes 1334.

[0323] It should be understood that the S2P1 1352 and the S2P2 1354 at least partially overlap each other, and thus the second stack moiré pattern 1360 is immediately visible after imaging the second stack 1324. As is known in the art, the second stack moiré pattern 1360 is characterized by a pitch κ2, which is a function of the pitch θ and the pitch ι, as shown in Equation 31:

[0324]

[0325] Preferably, the second stack 1324 does not include a periodic structure formed with the third layer 1306 that affects the moiré pattern 1360. However, the second stack 1324 may include a periodic structure formed with the third layer 1306 that does not affect the moiré pattern 1360, such as a periodic structure that is periodic along an axis parallel to the y-axis or a periodic structure having a pitch size that does not affect the moiré pattern 1360.

[0326] As specifically seen in magnification C, the third stack 1326 includes a third stack first periodic structure (S3P1) 1362, the S3P1 being formed with the second layer 1304 and having an S3P1 pitch designated as λ along one of the third axes 1336. The third stack 1326 further includes a third stack second periodic structure (S3P2) 1364, the S3P2 being formed with the third layer 1306 and having an S3P2 pitch designated as μ along another of the third axes 1336. In an embodiment of the present invention, the value of the S3P1 pitch λ and the S2P2 pitch ι are the same and the value of the S3P2 pitch μ and the S2P1 pitch θ are the same.

[0327] It should be understood that the S3P1 1362 and the S3P2 1364 at least partially overlap each other, and thus the third stack moiré pattern 1370 is visible immediately after imaging the third stack 1326. As is known in the art, the third stack moiré pattern 1370 is characterized by a pitch κ3, the pitch κ3 being a function of the pitch λ and the pitch μ, as shown in Equation 32:

[0328]

[0329] Preferably, the third stack 1326 does not include a periodic structure that forms with the first layer 1302 and affects the moiré pattern 1370. However, the third stack 1326 may include a periodic structure that forms with the first layer 1302 and does not affect the moiré pattern 1370, such as a periodic structure that is periodic along an axis parallel to the y-axis or a periodic structure having a pitch size that does not affect the moiré pattern 1370.

[0330] Preferably, an imaging offset metrology tool with adjustable polarization, wavelength, and numerical aperture settings is used to measure the offset between any two of the layers 1302, 1304, and 1306. An example of a suitable imaging offset metrology tool is the Archer commercially available from KLA Corporation, Milpitas, California, USA TM 700. The pitches θ, ι, λ, and μ do not need to be optically resolvable by the offset metrology tool used to generate the image of the target 1300. However, preferably, each of the pitches η, κ2, and κ3 is optically resolvable by the offset metrology tool used to generate the image of the target 1300.

[0331] Now refer Figures 14A to 14D to, which is a simplified graphical illustration of another embodiment of the multi-layer moiré target 1400 of the present invention. Figures 14A to 14D A graphical illustration is included in three different dimensions indicated by the x-axis, y-axis, and z-axis, the three dimensions being hereinafter referred to as the x-y plane, the x-z plane, and the y-z plane, respectively. It should be noted that Figure 14A generally illustrates the x-y plane, whileFigure 14B , 14C and the 14D diagram illustrates a plane parallel to the x-z plane.

[0332] It should be noted that the target 1400 is an example of an alternative layout of the target 1300 described above with reference to Figure 13 and the additional layouts are described below with reference to Figures 34 to 39 . The target 1400 is preferably formed on a semiconductor device wafer on which at least a first layer 1402, a second layer 1404, and a third layer 1406 are preferably formed. It should be understood that each of the first layer 1402, the second layer 1404, and the third layer 1406 defines a generally planar surface parallel to the x-y plane. The first layer 1402, the second layer 1404, and the third layer 1406 may be adjacent layers but need not be. Preferably, any material between the first layer 1402, the second layer 1404, and the third layer 1406 is at least partially transparent to electromagnetic radiation. In the Figures 14A to 14D illustrated embodiment, the first layer 1402 is located below the second layer 1404 and the third layer 1406, and the third layer 1406 is located above the first layer 1402 and the second layer 1404. However, it should be understood that the layers 1402, 1404, and 1406 may be arranged in any suitable order relative to each other along the z-axis.

[0333] Additionally, in an embodiment of the present invention, the structure shown as being formed with the first layer 1402 and the third layer 1406 may all be formed with the layer 1402. In this embodiment, no part of the target 1400 is formed with the layer 1406. This embodiment is particularly useful for calibration, as described below with reference to Figures 15A to 15C .

[0334] As specifically seen in Figure 14A , the target 1400 includes four target quadrants 1412, 1414, 1416, and 1418. In the Figure 14A illustrated embodiment, the rotational orientation in the x-y plane of each of the target quadrants 1412, 1414, 1416, and 1418 preferably differs by an integer multiple of 90° from the rotational orientation in the x-y plane of each of the other target quadrants 1412, 1414, 1416, and 1418. Additionally, the target 1400 is preferably characterized by rotational symmetry in the x direction or the y direction or both. In a preferred embodiment of the present invention, the target 1400 is designed such that when in an aligned state, the whole of the target 1400 is characterized by a single symmetry point in the x direction and a single symmetry point in the y direction. However, even in this embodiment, when in an offset state, the various elements of the target 1400 will be characterized by unique symmetry points.

[0335] Each of the target quadrants 1412, 1414, 1416, and 1418 includes a first stack 1422 of periodic structures, a second stack 1424 of periodic structures, and a third stack 1426 of periodic structures. Each of the first stack 1422, the second stack 1424, and the third stack 1426 includes one or more periodic structures, each periodic structure having a pitch. Preferably, the first stack 1422, the second stack 1424, and the third stack 1426 do not overlap each other. In Figures 14A to 14D the first stack 1422 is illustrated as being located closer to the center of the target 1400 than the second stack 1424 and the third stack 1426, and the third stack 1426 is illustrated as being located closer to the edge of the target 1400 than the first stack 1422 and the second stack 1424. However, the first stack 1422, the second stack 1424, and the third stack 1426 may be arranged relative to each other in any suitable arrangement relative to the x-y plane.

[0336] It should be understood that although in the embodiment illustrated in Figures 14A to 14D each of the periodic structures of the first stack 1422, the second stack 1424, and the third stack 1426 is illustrated as being formed by a plurality of lines and spaces, in other embodiments of the present invention, the periodic structures of the first stack 1422, the second stack 1424, and the third stack 1426 may be formed by any suitable periodic features. It should be further understood that the periodic features forming the periodic structures included in the first stack 1422, the second stack 1424, and the third stack 1426 may be formed by sub-structures. The pitch of each of the periodic structures of the first stack 1422, the second stack 1424, and the third stack 1426 is preferably between 10 nm and 3000 nm, and more preferably between 200 nm and 800 nm.

[0337] As Figure 14AAs seen, in each of quadrants 1412, 1414, 1416, and 1418, a first plane 1431 that intersects the first stack 1422 and includes a plurality of first axes 1432 therein, a second plane 1433 that intersects the second stack 1424 and includes a plurality of second axes 1434 therein, and a third plane 1435 that intersects the third stack 1426 and includes a plurality of third axes 1436 therein are defined. Depending on the orientation of the first stack 1422, the second stack 1424, and the third stack 1426 within each of quadrants 1412, 1414, 1416, and 1418, each of the first plane 1431, the second plane 1433, and the third plane 1435 is an x-z plane or a y-z plane, and the first axes 1432, the second axes 1434, and the third axes 1436 are parallel to the corresponding x-axis or y-axis. It should be understood that in each of quadrants 1412, 1414, 1416, and 1418, the first plane 1431, the second plane 1433, and the third plane 1435 are all parallel to each other.

[0338] As specifically seen in Figure 14B As seen, the first stack 1422 includes a first stack first periodic structure (S1P1) 1442, which is formed with the second layer 1404 and has an S1P1 pitch designated as ν along one of the first axes 1432. Preferably, the first stack 1422 does not include a periodic structure formed with either the first layer 1402 or the third layer 1406, which would immediately produce a moiré pattern with the S1P1 1442 after imaging the first stack 1422. However, the first stack 1422 may include a periodic structure formed with the first layer 1402 or the third layer 1406, which does not produce a moiré pattern after imaging the first stack 1422, such as a periodic structure that is periodic in a plane parallel to the x-y plane along an axis perpendicular to the first axes 1432 or a periodic structure having a pitch size that does not produce a moiré pattern after imaging the first stack 1422.

[0339] As specifically seen in Figure 14C As seen, the second stack 1424 includes a second stack first periodic structure (S2P1) 1452, which is formed with the first layer 1402 and has an S2P1 pitch designated as ξ along one of the second axes 1434. The second stack 1424 further includes a second stack second periodic structure (S2P2) 1454, which is formed with the second layer 1404 and has an S2P2 pitch designated as π along the other of the second axes 1434.

[0340] It should be understood that S2P1 1452 and S2P2 1454 at least partially overlap each other, and thus the second stack Moiré pattern 1460 is visible immediately after imaging the second stack 1424. As is known in the art, the second stack Moiré pattern 1460 is characterized by a pitch ρ2, which is a function of the pitch ξ and the pitch π, as shown in Equation 33:

[0341]

[0342] Preferably, the second stack 1424 does not include a periodic structure that forms with the third layer 1406 and affects the Moiré pattern 1460. However, the second stack 1424 may include a periodic structure that forms with the third layer 1406 and does not affect the Moiré pattern 1460, such as a periodic structure that is periodic in a plane parallel to the x-y plane along an axis perpendicular to the second axis 1434 or a periodic structure having a pitch size that does not affect the Moiré pattern 1460.

[0343] As specifically seen in Figure 14D the third stack 1426 includes a first periodic structure of the third stack (S3P1) 1462, which forms with the second layer 1404 and has an S3P1 pitch designated as σ along one of the third axes 1436. The third stack 1426 further includes a second periodic structure of the third stack (S3P2) 1464, which forms with the third layer 1406 and has an S3P2 pitch designated as τ along the other of the third axes 1436. In an embodiment of the present invention, the value of the S3P1 pitch σ and the S2P2 pitch π are the same, and the value of the S3P2 pitch τ and the S2P1 pitch ξ are the same.

[0344] It should be understood that S3P1 1462 and S3P2 1464 at least partially overlap each other, and thus the third stack Moiré pattern 1470 is visible immediately after imaging the third stack 1426. As is known in the art, the third stack Moiré pattern 1470 is characterized by a pitch ρ3, which is a function of the pitch σ and the pitch τ, as shown in Equation 34:

[0345]

[0346] Preferably, the third stack 1426 does not include a periodic structure that forms with the first layer 1402 and affects the Moiré pattern 1470. However, the third stack 1426 may include a periodic structure that forms with the first layer 1402 and does not affect the Moiré pattern 1470, such as a periodic structure that is periodic in a plane parallel to the x-y plane along an axis perpendicular to the third axis 1436 or a periodic structure having a pitch size that does not affect the Moiré pattern 1470.

[0347] Preferably, an imaging offset metrology tool with adjustable polarization, wavelength, and numerical aperture settings is used to measure the offset between any two of layers 1402, 1404, and 1406. An example of a suitable imaging offset metrology tool is the Archer, commercially available from KLA Corporation, Milpitas, California, USA. TM 700. The pitches ξ, π, σ, and τ need not be optically resolvable by the offset metrology tool used to generate the image of target 1400. However, preferably, each of the pitches ν, ρ2, and ρ3 is optically resolvable by the offset metrology tool used to generate the image of target 1400.

[0348] Now refer to Figure 15A , which is a simplified flowchart that illustrates a preferred method of calculating the offset between a first layer 1502, a second layer 1504, and a third layer 1506 (such as layers 1302, 1304, and 1306 ( Figure 13 )) or 1402, 1404, and 1406 ( Figures 14A to 14D )) of a multi-layer semiconductor device wafer on which target 1500 (such as target 1300 ( Figure 13 )) or target 1400 ( Figures 14A to 14D )) is formed, in a direction parallel to the x-direction or the y-direction. Further refer to Figure 15B and 15C , which are simplified illustrations of a first embodiment and a second embodiment of parts of the method of Figure 15A respectively.

[0349] Although it should be understood that when using target 1400 ( Figures 14A to 14D ), the method described with reference to Figures 15A to 15C may be performed only once to calculate the offset in the x-direction or the y-direction, but typically Figures 15A to 15C the method described in Figure 13 will be performed twice, once for each of the x-direction and the y-direction, to calculate the offset. It should also be understood that when using target 1300 (

[0350] Figure 15A and 15B ), the offset can be calculated only in one direction parallel to the first axis 1332, the second axis 1334, and the third axis 1336. As seen at the first step 1507, the direction for measuring the offset is selected. When using target 1300 in the methods of Figure 15A and 15BWhen using the target 1400 in the method, the structures of quadrants 1414 and 1418 are utilized to measure the offset in a direction parallel to the x-axis, and the structures of quadrants 1412 and 1416 are utilized to measure the offset in a direction parallel to the y-axis.

[0351] Preferably, at the next step 1509, an imaging offset metrology tool with adjustable polarization, wavelength, and numerical aperture settings is used to generate an image of the target 1500. An example of a suitable imaging offset metrology tool is the Archer commercially available from KLA Corporation, Milpitas, California, USA TM 700. It should be noted that the spacings θ, ι, λ, μ, ξ, π, σ, and τ do not need to be optically resolvable by the offset metrology tool used to generate the image of the target 1500. However, preferably, each of the spacings η, ν, κ2, κ3, ρ2, and ρ3 is optically resolvable by the offset metrology tool used to generate the image of the target 1500.

[0352] At the next step 1511 and as Figure 15B and 15C seen in, for each of the corresponding first stack 1522, second stack 1524, and third stack 1526 (e.g., first stack 1322, second stack 1324, and third stack 1326 ( Figure 13 ) or first stack 1422, second stack 1424, and third stack 1426 ( Figures 14A to 14D )) in the quadrant selected in step 1507, a first region of interest 1512, a second region of interest 1514, and a third region of interest 1516 are selected. It should be understood that as seen in the illustrated embodiments of Figure 15B and 15C , although the first region of interest 1512, the second region of interest 1514, and the third region of interest 1516 are preferably entirely located within each of the corresponding first stack 1522, second stack 1524, and third stack 1526 (as illustrated for the first region of interest 1512 entirely located within the first stack 1522), the first region of interest 1512, the second region of interest 1514, and the third region of interest 1516 may extend beyond the corresponding first stack 1522, second stack 1524, and third stack 1526, as illustrated by the regions of interest 1514 and 1516 extending beyond the corresponding second stack 1524 and third stack 1526. It should be further understood that Figure 15B and 15C the regions of interest 1512, 1514, and 1516 shown in are representative regions of interest, and other suitable regions of interest may be selected at step 1511.

[0353] At the next step 1531 and as Figure 15B and15C As seen in, calculate the position of the symmetry point 1532 between all examples of the first region of interest 1512 selected in step 1511. In the next step 1533 and as Figure 15B and 15C As seen in, calculate the position of the symmetry point 1534 between all examples of the second region of interest 1514 selected in step 1511. In the next step 1535 and as Figure 15B and 15C As seen in, calculate the position of the symmetry point 1536 between all examples of the third region of interest 1516 selected in step 1511.

[0354] In the next step 1537, calculate the distance in the direction selected in step 1507 between the position of the symmetry point 1532 of one or more first regions of interest 1512 identified in step 1531 and the position of the symmetry point 1534 of one or more second regions of interest 1514 identified in step 1533. The distance found in step 1537 is divided by the gain υ1, which is a function of the pitch θ and the pitch ι for the target 1300, as shown in Equation 35a:

[0355]

[0356] and is a function of the pitch π and the pitch ξ for the target 1400, as shown in Equation 35b:

[0357]

[0358] And report the result as the offset between the first layer 1502 and the second layer 1504 in the direction selected in step 1507. It should be understood that in addition to the distance calculated in step 1537, the method further calculates an adjustment direction, such as right, left, up, or down. The adjustment direction varies with the relative values of the pitch θ and the pitch ι or the pitch π and the pitch ξ and which of the adjustment layers 1502 and 1504 is to be adjusted.

[0359] In the next step 1539, calculate the distance in the direction selected in step 1507 between the position of the symmetry point 1532 of one or more first regions of interest 1512 identified in step 1531 and the position of the symmetry point 1536 of one or more third regions of interest 1516 identified in step 1535. The distance found in step 1539 is divided by the gain υ2, which is a function of the pitch λ and the pitch μ for the target 1300, as shown in Equation 36a:

[0360]

[0361] and is a function of the spacings σ and τ for target 1400, as shown in Equation 36b:

[0362]

[0363] And report the result as the offset between the second layer 1504 and the third layer 1506 in the direction selected at step 1507. It should be understood that in addition to the distance calculated at step 1539, the method further calculates an adjustment direction, such as right, left, up, or down. The adjustment direction varies with the relative values of the spacings θ and ι or the spacings π and ξ and which of the layers 1504 and 1506 is to be adjusted.

[0364] In the next step 1541, calculate an offset value between the first layer 1502 and the third layer 1506. In the embodiment described above, where the S3P1 spacing does not have the same value as the S2P2 spacing and the S3P2 spacing does not have the same value as the S2P1 spacing, at step 1541, calculate the difference between the offset value reported at step 1537 and the offset value reported at step 1539. Report the difference calculated at step 1541 as the offset between the first layer 1502 and the third layer 1506 in the direction selected at step 1507. It should be understood that in addition to the distance calculated at step 1541, the method further calculates an adjustment direction, such as right, left, up, or down. The adjustment direction varies with the relative values of the spacings θ and ι or the spacings π and ξ and which of the layers 1502 and 1506 is to be adjusted.

[0365] In the embodiment described above, where the S3P1 spacing has the same value as the S2P2 spacing and the S3P2 spacing has the same value as the S2P1 spacing, at step 1541, calculate the distance in the direction selected at step 1507 between the position of the symmetric point 1534 of one or more second regions of interest 1514 identified at step 1533 and the position of the symmetric point 1536 of one or more third regions of interest 1516 identified at step 1535. The distance found at step 1541 is divided by the gain υ3, which is a function of the spacings θ and ι for target 1300, as shown in Equation 37a:

[0366]

[0367] and is a function of the spacings π and ξ for target 1400, as shown in Equation 37b:

[0368]

[0369] And report the result as the offset between the first layer 1502 and the third layer 1506 in the direction selected at step 1507. It should be understood that in addition to the distance calculated at step 1541, the method further calculates an adjustment direction, such as right, left, up, or down. The adjustment direction varies with the relative values of the pitch θ and the pitch ι or the pitch π and the pitch ξ and which of the layers 1502 and 1506 is to be adjusted.

[0370] Preferably, in the embodiments described above, where the structure shown as formed with the first layer 1502 and the third layer 1506 can all be formed with the layer 1502, referring above to Figures 15A to 15C the method described continues to calculate and report the difference between the offset value reported at step 1537 and the offset value reported at step 1539. The difference between the offset values reported at steps 1537 and 1539 is useful in calibrating the offset measuring tool in the method for Figures 15A to 15C use.

[0371] It should be understood that in an embodiment of the present invention, only the layers 1502 and 1504 can be used to perform the relevant part of the method described above before forming the layer 1506. Similarly, in an embodiment of the present invention where the layer 1506 is located below the layer 1502, only the layers 1504 and 1506 can be used to perform the relevant part of the method described above before forming the layer 1502. Figures 15A to 15C referring above to Figures 15A to 15C use.

[0372] Now refer to Figure 16 which is a simplified graphical illustration of another embodiment of the multi-layer Moiré target 1600 of the present invention. Figure 16 The illustration includes three different dimensions indicated by the x-axis, y-axis, and z-axis, which are hereinafter referred to as the x-y plane, the x-z plane, and the y-z plane, respectively. It should be noted that Figure 16 generally illustrates the x-y plane, while Figure 16 the magnified views A, B, and C illustrate planes parallel to the x-z plane.

[0373] The target 1600 is preferably formed on a semiconductor device wafer, on which at least a first layer 1602, a second layer 1604, and a third layer 1606 are preferably formed. It should be understood that each of the first layer 1602, the second layer 1604, and the third layer 1606 defines a generally planar surface parallel to the x-y plane. The first layer 1602, the second layer 1604, and the third layer 1606 may be adjacent layers but need not be. Preferably, any material between the first layer 1602, the second layer 1604, and the third layer 1606 is at least partially transparent to electromagnetic radiation. In Figure 16In the illustrated embodiment, the first layer 1602 is located below the second layer 1604 and the third layer 1606, and the third layer 1606 is located above the first layer 1602 and the second layer 1604. However, it should be understood that the layers 1602, 1604, and 1606 may be arranged in any suitable order relative to each other along the z-axis.

[0374] In addition, in an embodiment of the present invention, the structure shown as being formed with the first layer 1602 and the second layer 1604 may all be formed with the layer 1602. In this embodiment, no part of the target 1600 is formed with the layer 1604. This embodiment is particularly useful for calibration, as described below with reference to Figures 18A to 18C In addition, in another embodiment of the present invention, the structure shown as being formed with the first layer 1602 and the third layer 1606 may all be formed with the layer 1602. In this embodiment, no part of the target 1600 is formed with the layer 1606. This embodiment is particularly useful for calibration, as described below with reference to Figures 18A to 18C as described.

[0375] It should be understood that Figure 16 illustrates a possible layout of the target 1600, and in other embodiments of the present invention, the target 1600 may include additional structures. For example, as described below with reference to Figures 17A to 17D and 34 to 39, suitable targets may include Figure 16 multiple examples of the structures shown in, and those multiple examples may be arranged in various ways.

[0376] Preferably, the target 1600 includes a first stack 1622 of periodic structures, a second stack 1624 of periodic structures, and a third stack 1626 of periodic structures. Each of the first stack 1622, the second stack 1624, and the third stack 1626 includes one or more periodic structures, each periodic structure having a pitch. Preferably, the first stack 1622, the second stack 1624, and the third stack 1626 do not overlap each other.

[0377] It should be understood that although in Figure 16In [the figure], each of the periodic structures of the first stack 1622, the second stack 1624, and the third stack 1626 is shown as being formed by a plurality of lines and spaces. However, in other embodiments of the present invention, the periodic structures of the first stack 1622, the second stack 1624, and the third stack 1626 may be formed by any suitable periodic features. It should be further understood that the periodic features forming the periodic structures included in the first stack 1622, the second stack 1624, and the third stack 1626 may be formed by sub-structures. The pitch of each of the periodic structures of the first stack 1622, the second stack 1624, and the third stack 1626 is preferably between 10 nm and 3000 nm, and more preferably between 200 nm and 800 nm.

[0378] The first x-z plane 1631 intersects the first stack 1622. A plurality of first axes 1632 are located in the first x-z plane 1631 and parallel to the x-axis. The second x-z plane 1633 intersects the second stack 1624. A plurality of second axes 1634 are located in the second x-z plane 1633 and parallel to the x-axis. The third x-z plane 1635 intersects the third stack 1626. A plurality of third axes 1636 are located in the third x-z plane 1635 and parallel to the x-axis.

[0379] As specifically seen in magnification A, the first stack 1622 includes a first stack first periodic structure (S1P1) 1642, which is formed with the second layer 1604 and has a pitch designated as for the S1P1 along one of the first axes 1632. Preferably, the first stack 1622 does not include a periodic structure formed with either the first layer 1602 or the third layer 1606, which would immediately produce a moiré pattern with the S1P1 1642 after imaging the first stack 1622. However, the first stack 1622 may include a periodic structure formed with the first layer 1602 or the third layer 1606, which does not produce a moiré pattern after imaging the first stack 1622, such as a periodic structure that is periodic along an axis parallel to the y-axis or a periodic structure with a pitch size that does not produce a moiré pattern after imaging the first stack 1622.

[0380] As specifically seen in magnification B, the second stack 1624 includes a second stack first periodic structure (S2P1) 1652, the S2P1 being formed with the first layer 1602 and having an S2P1 pitch designated as χ along one of the second axes 1634. Preferably, the second stack 1624 does not include a periodic structure formed with either the second layer 1604 or the third layer 1606, which, after imaging the second stack 1624, would immediately produce a moiré pattern together with the S2P1 1652. However, the second stack 1624 may include a periodic structure formed with the second layer 1604 or the third layer 1606, which, after imaging the second stack 1624, does not produce a moiré pattern, such as a periodic structure that is periodic along an axis parallel to the y-axis or a periodic structure having a pitch size that does not produce a moiré pattern after imaging the second stack 1624.

[0381] As specifically seen in magnification C, the third stack 1626 includes a third stack first periodic structure (S3P1) 1662, the S3P1 being formed with the second layer 1604 and having an S3P1 pitch designated as ψ along one of the third axes 1636. The third stack 1626 further includes a third stack second periodic structure (S3P2) 1664, the S3P2 being formed with the third layer 1606 and having an S3P2 pitch designated as ω along the other of the third axes 1636.

[0382] It should be understood that the S3P1 1662 and the S3P2 1664 at least partially overlap each other, and thus a third stack moiré pattern 1670 is immediately visible after imaging the third stack 1626. As is known in the art, the third stack moiré pattern 1670 is characterized by a pitch which is a function of the pitch ψ and the pitch ω, as shown in Equation 38:

[0383]

[0384] Preferably, the third stack 1626 does not include a periodic structure formed with the first layer 1602 that affects the moiré pattern 1670. However, the third stack 1626 may include a periodic structure formed with the first layer 1602 that does not affect the moiré pattern 1670, such as a periodic structure that is periodic along an axis parallel to the y-axis or a periodic structure having a pitch size that does not affect the moiré pattern 1670.

[0385] Preferably, an imaging offset metrology tool with adjustable polarization, wavelength, and numerical aperture settings is used to measure the offset between any two of layers 1602, 1604, and 1606. An example of a suitable imaging offset metrology tool is the Archer commercially available from KLA Corporation, Milpitas, California, USA TM 700. The pitches ψ and ω need not be optically resolvable by the offset metrology tool used to generate the image of target 1600. However, preferably, each of the pitches , χ, and is optically resolvable by the offset metrology tool used to generate the image of target 1600.

[0386] Now refer to Figures 17A to 17D , which is a simplified graphical illustration of another embodiment of the multi-layer Moiré target 1700 of the present invention. Figures 17A to 17D A graphical illustration is included in three different dimensions indicated by the x-axis, y-axis, and z-axis, which three dimensions are hereinafter referred to as the x-y plane, the x-z plane, and the y-z plane, respectively. It should be noted that Figure 17A generally illustrates the x-y plane, while Figure 17B , 17C and 17D illustrate planes parallel to the x-z plane.

[0387] It should be noted that target 1700 is an example of an alternative layout of target 1600 described above with reference to Figure 16 and additional layouts are described below with reference to Figures 34 to 39 . Target 1700 is preferably formed on a semiconductor device wafer, on which at least a first layer 1702, a second layer 1704, and a third layer 1706 are preferably formed. It should be understood that each of the first layer 1702, the second layer 1704, and the third layer 1706 defines a generally planar surface parallel to the x-y plane. The first layer 1702, the second layer 1704, and the third layer 1706 may be adjacent layers but need not be. Preferably, any material between the first layer 1702, the second layer 1704, and the third layer 1706 is at least partially transparent to electromagnetic radiation. In the embodiment illustrated in Figures 17A to 17D , the first layer 1702 is located below the second layer 1704 and the third layer 1706, and the third layer 1706 is located above the first layer 1702 and the second layer 1704. However, it should be understood that the layers 1702, 1704, and 1706 may be arranged in any suitable order relative to each other along the z-axis.

[0388] In addition, in an embodiment of the present invention, the structure shown as being formed with the first layer 1702 and the second layer 1704 may all be formed with the layer 1702. In this embodiment, no part of target 1700 is formed with the layer 1704. This embodiment is particularly useful for calibration, as described below with reference toFigures 18A to 18C as described. Additionally, in another embodiment of the present invention, the structure shown as being formed with the first layer 1702 and the third layer 1706 may all be formed with layer 1702. In this embodiment, no part of the target 1700 is formed with layer 1706. This embodiment is particularly useful for calibration, as described below with reference to Figures 18A to 18C as described.

[0389] As specifically seen in Figure 17A , the target 1700 includes four target quadrants 1712, 1714, 1716, and 1718. In the embodiment shown in Figure 17A , the rotational orientation in the x-y plane of each of the target quadrants 1712, 1714, 1716, and 1718 is preferably an integer multiple of 90° different from the rotational orientation in the x-y plane of each of the other target quadrants 1712, 1714, 1716, and 1718. Additionally, the target 1700 is preferably characterized by rotational symmetry in the x direction or the y direction or both. In a preferred embodiment of the present invention, the target 1700 is designed such that when in the aligned state, the whole of the target 1700 is characterized by a single symmetry point in the x direction and a single symmetry point in the y direction. However, even in this embodiment, when in the offset state, the various elements of the target 1700 will be characterized by unique symmetry points.

[0390] Each of the target quadrants 1712, 1714, 1716, and 1718 includes a first stack 1722 of periodic structures, a second stack 1724 of periodic structures, and a third stack 1726 of periodic structures. Each of the first stack 1722, the second stack 1724, and the third stack 1726 includes one or more periodic structures, each periodic structure having a pitch. Preferably, the first stack 1722, the second stack 1724, and the third stack 1726 do not overlap each other. In Figures 17A to 17D , the first stack 1722 is illustrated as being located closer to the center of the target 1700 than the second stack 1724 and the third stack 1726, and the third stack 1726 is illustrated as being located closer to the edge of the target 1700 than the first stack 1722 and the second stack 1724. However, the first stack 1722, the second stack 1724, and the third stack 1726 may be arranged relative to each other in any suitable arrangement with respect to the x-y plane.

[0391] It should be understood that although in Figures 17A to 17DIn the illustrated embodiment, each of the periodic structures of the first stack 1722, the second stack 1724, and the third stack 1726 is illustrated as being formed by a plurality of lines and spaces, but in other embodiments of the present invention, the periodic structures of the first stack 1722, the second stack 1724, and the third stack 1726 may be formed by any suitable periodic features. It should be further understood that the periodic features forming the periodic structures included in the first stack 1722, the second stack 1724, and the third stack 1726 may be formed by sub-structures. The pitch of each of the periodic structures of the first stack 1722, the second stack 1724, and the third stack 1726 is preferably between 10 nm and 3000 nm, and more preferably between 200 nm and 800 nm.

[0392] As Figure 17A As seen, in each of the quadrants 1712, 1714, 1716, and 1718, a first plane 1731 intersecting the first stack 1722 and including a plurality of first axes 1732 located therein, a second plane 1733 intersecting the second stack 1724 and including a plurality of second axes 1734 located therein, and a third plane 1735 intersecting the third stack 1726 and including a plurality of third axes 1736 located therein are defined. Depending on the orientation of the first stack 1722, the second stack 1724, and the third stack 1726 within each of the quadrants 1712, 1714, 1716, and 1718, each of the first plane 1731, the second plane 1733, and the third plane 1735 is an x-z plane or a y-z plane, and the first axis 1732, the second axis 1734, and the third axis 1736 are parallel to the corresponding x-axis or y-axis. It should be understood that in each of the quadrants 1712, 1714, 1716, and 1718, the first plane 1731, the second plane 1733, and the third plane 1735 are all parallel to each other.

[0393] As specifically in Figure 17BAs can be seen, for example, in

[0394] As specifically seen in Figure 17C the first stack 1722 includes a first stack first periodic structure (S1P1) 1742 that is formed with the second layer 1704 and has an S1P1 pitch designated as Γ along one of the first axes 1732. Preferably, the first stack 1722 does not include a periodic structure formed with either the first layer 1702 or the third layer 1706 that, upon imaging the first stack 1722, would immediately produce a moiré pattern with the S1P1 1742. However, the first stack 1722 can include a periodic structure formed with the first layer 1702 or the third layer 1706 that does not produce a moiré pattern upon imaging the first stack 1722, such as a periodic structure that is periodic in a plane parallel to the x - y plane along an axis perpendicular to the first axis 1732 or has a pitch size that does not produce a moiré pattern upon imaging the first stack 1722.

[0395] As specifically seen in Figure 17D the second stack 1724 includes a second stack first periodic structure (S2P1) 1752 that is formed with the first layer 1702 and has an S2P1 pitch designated as Θ along one of the second axes 1734. Preferably, the second stack 1724 does not include a periodic structure formed with either the second layer 1704 or the third layer 1706 that, upon imaging the second stack 1724, would immediately produce a moiré pattern with the S2P1 1752. However, the second stack 1724 can include a periodic structure formed with the second layer 1704 or the third layer 1706 that does not produce a moiré pattern upon imaging the second stack 1724, such as a periodic structure that is periodic in a plane parallel to the x - y plane along an axis perpendicular to the second axis 1734 or has a pitch size that does not produce a moiré pattern upon imaging the second stack 1724.

[0396] It should be understood that S3P1 1762 and S3P2 1764 at least partially overlap each other, and thus the third stack Moiré pattern 1770 is visible immediately after imaging the third stack 1726. As is known in the art, the third stack Moiré pattern 1770 is characterized by a pitch Π3, which is a function of the pitch Λ and the pitch Ξ, as shown in Equation 39:

[0397]

[0398] Preferably, the third stack 1726 does not include a periodic structure that forms with the first layer 1702 and affects the periodicity of the Moiré pattern 1770. However, the third stack 1726 may include a periodic structure that forms with the first layer 1702 and does not affect the Moiré pattern 1770, such as a periodic structure that is periodic in a plane parallel to the x-y plane along an axis perpendicular to the third axis 1736 or a periodic structure having a pitch size that does not affect the Moiré pattern 1770.

[0399] Preferably, an imaging offset metrology tool with adjustable polarization, wavelength, and numerical aperture settings is used to measure the offset between any two of the layers 1702, 1704, and 1706. An example of a suitable imaging offset metrology tool is the Archer commercially available from KLA Corporation, Milpitas, California, USA TM 700. The pitches Λ and Ξ do not need to be optically resolvable by the offset metrology tool used to generate the image of the target 1700. However, preferably, each of the pitches Γ, Θ, and Π3 is optically resolvable by the offset metrology tool used to generate the image of the target 1700.

[0400] Now refer to Figure 18A , which is a simplified flowchart that illustrates a preferred method for calculating the offset between the first layer 1802, the second layer 1804, and the third layer 1806 (such as the layers 1602, 1604, and 1606( Figure 16 ) or 1702, 1704, and 1706( Figures 17A to 17D )) of a multi-layer semiconductor device wafer on which the target 1800 (such as the target 1600( Figure 16 ) or the target 1700( Figures 17A to 17D )) is formed in a direction parallel to the x direction or the y direction. Further refer to Figure 18B and 18C , which are simplified illustrations of the first embodiment and the second embodiment of parts of the method of Figure 18A respectively.

[0401] Although it should be understood that when using the target 1700( Figures 17A to 17D ), refer to Figures 18A to 18CThe described method may be performed only once to calculate the offset in the x or y direction, but typically Figures 18A to 18C the method described in Figure 16 will be performed twice to calculate the offset in each of the x and y directions. It should also be understood that when using the target 1600 (

[0402] ) the offset may be calculated only in one direction parallel to the first axis 1632, the second axis 1634, and the third axis 1636. Figure 18A and 18B When using the target 1600 in the method of Figure 18A and 18B , the direction in which the offset is measured is automatically selected as the direction parallel to the first axis 1632, the second axis 1634, and the third axis 1636. When using the target 1700 in the method of

[0403] the structure of quadrants 1714 and 1718 is used to measure the offset in a direction parallel to the x-axis, and the structure of quadrants 1712 and 1716 is used to measure the offset in a direction parallel to the y-axis. TM Preferably, in the next step 1809, an imaging offset metrology tool with adjustable polarization, wavelength, and numerical aperture settings is used to generate an image of the target 1800. An example of a suitable imaging offset metrology tool is the Archer χ, Γ, Θ, and Π3 can each be optically resolved by the offset metrology tool used to generate the image of the target 1800.

[0404] In the next step 1811 and as seen in Figure 18B and 18C the first region of interest 1812, the second region of interest 1814, and the third region of interest 1816 are selected for each of the corresponding first stack 1822, second stack 1824, and third stack 1826 (e.g., the first stack 1622, the second stack 1624, and the third stack 1626 ( Figure 16 ) or the first stack 1722, the second stack 1724, and the third stack 1726 ( Figures 17A to 17D )) in the quadrant selected in step 1807. It should be understood that as in Figure 18B and 18CAs seen in the illustrated embodiments, although the first region of interest 1812, the second region of interest 1814, and the third region of interest 1816 are preferably completely located within each of the corresponding first stack 1822, second stack 1824, and third stack 1826 (as illustrated for the first region of interest 1812 completely located within the first stack 1822), the first region of interest 1812, the second region of interest 1814, and the third region of interest 1816 may extend beyond the corresponding first stack 1822, second stack 1824, and third stack 1826, as illustrated for the regions of interest 1814 and 1816 that extend beyond the corresponding second stack 1824 and third stack 1826. It should be further understood that Figure 18B and 18C the regions of interest 1812, 1814, and 1816 shown in are representative regions of interest, and other suitable regions of interest may be selected at step 1811.

[0405] In the next step 1831 and as Figure 18B and 18C seen in, the position of the symmetry point 1832 between all examples of the first region of interest 1812 selected in step 1811 is calculated. In the next step 1833 and as Figure 18B and 18C seen in, the position of the symmetry point 1834 between all examples of the second region of interest 1814 selected in step 1811 is calculated. In the next step 1835 and as Figure 18B and 18C seen in, the position of the symmetry point 1836 between all examples of the third region of interest 1816 selected in step 1811 is calculated.

[0406] In the next step 1837, the distance in the direction selected at step 1807 between the position of the symmetry point 1832 of one or more first regions of interest 1812 identified at step 1831 and the position of the symmetry point 1834 of one or more second regions of interest 1814 identified at step 1833 is calculated. The distance found at step 1837 is reported as the offset between the first layer 1802 and the second layer 1804 in the direction selected at step 1807. It should be understood that in addition to the distance calculated at step 1837, the method further calculates an adjustment direction, such as right, left, up, or down. The adjustment direction varies with the positions of the symmetry points 1832 and 1834 and which of the adjustment layers 1802 and 1806.

[0407] At the next step 1839, calculate the distance in the direction selected at step 1807 between the positions of the symmetry points 1832 of one or more first regions of interest 1812 identified at step 1831 and the positions of the symmetry points 1836 of one or more third regions of interest 1816 identified at step 1835. Divide the distance found at step 1839 by the gain Ω1, where the gain is a function of the spacings ψ and ω for the target 1600, as shown in Equation 40a:

[0408]

[0409] and is a function of the spacings Λ and Ξ for the target 1700, as shown in Equation 40b:

[0410]

[0411] And report the result as the offset between the second layer 1804 and the third layer 1806 in the direction selected at step 1807. It should be understood that, in addition to the distance calculated at step 1839, the method further calculates an adjustment direction, such as right, left, up, or down. The adjustment direction varies with the relative values of the spacings ψ and ω or the spacings Λ and Ξ and which of the layers 1804 and 1806 is to be adjusted.

[0412] At the next step 1841, calculate the difference between the offset value reported at step 1837 and the offset value reported at step 1839. Report the difference calculated at step 1841 as the offset between the first layer 1802 and the third layer 1806 in the direction selected at step 1807. It should be understood that, in addition to the distance calculated at step 1841, the method further calculates an adjustment direction, such as right, left, up, or down. The adjustment direction varies with the relative values of the spacings ψ and ω or the spacings Λ and Ξ and which of the layers 1802 and 1806 is to be adjusted.

[0413] Preferably, in the embodiments described above, where the structure shown as being formed with the first layer 1802 and the second layer 1804 can all be formed with the layer 1802, the method described above with reference to Figures 18A to 18C continues to calculate and report the difference between the offset value reported at step 1839 and the offset value reported at step 1841. The difference between the offset values reported at steps 1839 and 1841 is useful in calibrating the offset measurement tool used in the Figures 18A to 18C method.

[0414] Preferably, in the embodiments described above, the structure shown as being formed with the first layer 1802 and the third layer 1806 may all be formed with the layer 1802. Continuing with the method described with reference to Figures 18A to 18C calculate and report the difference between the offset value reported at step 1837 and the offset value reported at step 1839. The difference between the offset values reported at steps 1837 and 1839 is useful in calibrating the offset metrology tool in the method for Figures 18A to 18C .

[0415] It should be understood that in an embodiment of the present invention, only the layers 1802 and 1804 may be used to perform the relevant part of the method described above prior to forming the layer 1806. Similarly, in an embodiment of the present invention where the layer 1806 is located below the layer 1802, only the layers 1804 and 1806 may be used to perform the relevant part of the method described above prior to forming the layer 1802. Figures 18A to 18C Prior to forming the layer 1802, only the layers 1804 and 1806 may be used to perform the relevant part of the method described above. Figures 18A to 18C

[0416] Now referring to Figures 19A to 19D , which is a simplified graphical illustration of another embodiment of the multi-layer moiré target 1900 of the present invention. Figures 19A to 19D The illustration includes three different dimensions indicated by the x-axis, y-axis, and z-axis, which are hereinafter referred to as the x-y plane, x-z plane, and y-z plane, respectively. It should be noted that Figure 19A generally illustrates the x-y plane, while Figure 19B , 19C and 19D illustrate planes parallel to the x-z plane.

[0417] The target 1900 is preferably formed on a semiconductor device wafer, on which at least a first layer 1902, a second layer 1904, a third layer 1906, and a fourth layer 1908 are preferably formed. It should be understood that each of the first layer 1902, the second layer 1904, the third layer 1906, and the fourth layer 1908 defines a generally planar surface parallel to the x-y plane. The first layer 1902, the second layer 1904, the third layer 1906, and the fourth layer 1908 may be adjacent layers but need not be. Preferably, any material between the first layer 1902, the second layer 1904, the third layer 1906, and the fourth layer 1908 is at least partially transparent to electromagnetic radiation. In Figures 19A to 19D ​In the illustrated embodiment, the first layer 1902 is located below the second layer 1904, the third layer 1906, and the fourth layer 1908, the second layer 1904 is located below the third layer 1906 and the fourth layer 1908, and the fourth layer 1908 is located above the first layer 1902, the second layer 1904, and the third layer 1906. However, it should be understood that the layers 1902, 1904, 1906, and 1908 may be arranged in any suitable order relative to each other along the z-axis.

[0418] In addition, in an embodiment of the present invention, the structure shown as being formed with the second layer 1904 and the third layer 1906 may all be formed with the layer 1904. In this embodiment, no part of the target 1900 is formed with the layer 1906. This embodiment is particularly useful for calibration, as described below with reference to Figures 21A to 21C In addition, in another embodiment of the present invention, the structure shown as being formed with the second layer 1904 and the fourth layer 1908 may all be formed with the layer 1904. In this embodiment, no part of the target 1900 is formed with the layer 1908. This embodiment is particularly useful for calibration, as described below with reference to Figures 21A to 21C In addition, in another embodiment of the present invention, the structure shown as being formed with the third layer 1906 and the fourth layer 1908 may all be formed with the layer 1906. In this embodiment, no part of the target 1900 is formed with the layer 1908. This embodiment is particularly useful for calibration, as described below with reference to Figures 21A to 21C as described.

[0419] It should be understood that Figures 19A to 19D illustrates a possible layout of the target 1900, and in other embodiments of the present invention, the target 1900 may include additional structures. For example, as described below with reference to Figures 20A to 20D and 34 to 39, suitable targets may include Figures 19A to 19D multiple examples of the structures shown in, and those multiple examples may be arranged in various ways.

[0420] Preferably, the target 1900 includes a first stack 1922 of periodic structures, a second stack 1924 of periodic structures, and a third stack 1926 of periodic structures. Each of the first stack 1922, the second stack 1924, and the third stack 1926 includes one or more periodic structures, and each periodic structure has a pitch. Preferably, the first stack 1922, the second stack 1924, and the third stack 1926 do not overlap each other.

[0421] It should be understood that although in Figures 19A to 19DIn [the figure], each of the periodic structures of the first stack 1922, the second stack 1924, and the third stack 1926 is shown as being formed by a plurality of lines and spaces. However, in other embodiments of the present invention, the periodic structures of the first stack 1922, the second stack 1924, and the third stack 1926 may be formed by any suitable periodic features. It should be further understood that the periodic features forming the periodic structures included in the first stack 1922, the second stack 1924, and the third stack 1926 may be formed by sub-structures. The pitch of each of the periodic structures of the first stack 1922, the second stack 1924, and the third stack 1926 is preferably between 10 nm and 3000 nm, and more preferably between 200 nm and 800 nm.

[0422] The first x-z plane 1931 intersects the first stack 1922. A plurality of first axes 1932 are located in the first x-z plane 1931 and parallel to the x-axis. The second x-z plane 1933 intersects the second stack 1924. A plurality of second axes 1934 are located in the second x-z plane 1933 and parallel to the x-axis. The third x-z plane 1935 intersects the third stack 1926. A plurality of third axes 1936 are located in the third x-z plane 1935 and parallel to the x-axis.

[0423] As specifically seen in Figure 19B the first stack 1922 includes a first stack first periodic structure (S1P1) 1942, which is formed together with the first layer 1902 and has a pitch designated as along one of the first axes 1932. The first stack 1922 further includes a first stack second periodic structure (S1P2) 1944, which is formed together with the second layer 1904 and has a pitch designated as along another of the first axes 1932.

[0424] It should be understood that S1P1 1942 and S1P2 1944 at least partially overlap each other, and thus a first stack Moiré pattern 1950 is immediately visible after imaging the first stack 1922. As is known in the art, the first stack Moiré pattern 1950 is characterized by a pitch The pitch is a function of the pitches and as shown in Equation 41:

[0425]

[0426] Preferably, the first stack 1922 does not include a periodic structure that forms with the third layer 1906 or the fourth layer 1908 and affects the periodicity of the Moiré pattern 1950. However, the first stack 1922 may include a periodic structure that forms with the third layer 1906 or the fourth layer 1908 and does not affect the periodicity of the Moiré pattern 1950, such as a periodic structure that is periodic along an axis parallel to the y-axis or a periodic structure having a pitch size that does not affect the Moiré pattern 1950.

[0427] As specifically seen in Figure 19C , the second stack 1924 includes a second-stack first periodic structure (S2P1) 1952 that forms with the first layer 1902 and has a pitch designated as along one of the second axes 1934. Preferably, the S2P1 pitch is related to the S1P1 pitch by a second-stack multiplication factor designated as q. The second-stack multiplication factor q can be any positive number. The second stack 1924 further includes a second-stack second periodic structure (S2P2) 1954 that forms with the third layer 1906 and has a pitch designated as along the other of the second axes 1934. Preferably, the S2P2 pitch is related to the S1P2 pitch by the second-stack multiplication factor q. It should be understood that the second-stack multiplication factor q that relates the S2P2 pitch to the S1P2 pitch has the same value as the second-stack multiplication factor q that relates the S2P1 pitch to the S1P1 pitch . In an embodiment of the present invention, the value of q is 1 and thus the S2P1 pitch is the same as the S1P1 pitch and the S2P2 pitch is the same as the S1P2 pitch .

[0428] It should be understood that the S2P1 1952 and the S2P2 1954 at least partially overlap each other, and thus the second-stack Moiré pattern 1960 is visible immediately after imaging the second stack 1924. As is known in the art, the second-stack Moiré pattern 1960 is characterized by a pitch that is a function of the second-stack multiplication factor q, the pitch , and the pitch , as shown in Equation 42:

[0429] ​

[0430] Preferably, the second stack 1924 does not include a periodic structure that forms with the second layer 1904 or the fourth layer 1908 and affects the periodicity of the Moiré pattern 1960. However, the second stack 1924 may include a periodic structure that forms with the second layer 1904 or the fourth layer 1908 and does not affect the periodicity of the Moiré pattern 1960, such as a periodic structure that is periodic along an axis parallel to the y-axis or has a periodicity size that does not affect the Moiré pattern 1960.

[0431] As specifically seen in Figure 19D the third stack 1926 includes a third-stack first periodic structure (S3P1) 1962, which forms with the first layer 1902 and has a pitch designated as along one of the third axes 1936. Preferably, the S3P1 pitch is related to the S1P1 pitch by a third-stack multiplication factor designated as r. The third-stack multiplication factor r can be any positive number. The third stack 1926 further includes a third-stack second periodic structure (S3P2) 1964, which forms with the fourth layer 1908 and has a pitch designated as along the other of the third axes 1936. Preferably, the S3P2 pitch is related to the S1P2 pitch by the third-stack multiplication factor r. It should be understood that the third-stack multiplication factor r that relates the S3P2 pitch to the S1P2 pitch has the same value as the third-stack multiplication factor r that relates the S3P1 pitch to the S1P1 pitch In an embodiment of the present invention, the value of r is 1 and thus the S3P1 pitch is the same as the S1P1 pitch and the S3P2 pitch is the same as the S1P2 pitch

[0432] It should be understood that S3P1 1962 and S3P2 1964 at least partially overlap each other, and thus the third-stack Moiré pattern 1970 is visible immediately after imaging the third stack 1926. As is known in the art, the third-stack Moiré pattern 1970 is characterized by a pitch which is a function of the third-stack multiplication factor r, the pitch and the pitch as shown in Equation 43:

[0433] ​​

[0434] Preferably, the third stack 1926 does not include a periodic structure that forms, together with the second layer 1904 or the third layer 1906, an affected Moiré pattern 1970. However, the third stack 1926 may include a periodic structure that forms, together with the second layer 1904 or the third layer 1906, a periodic structure that does not affect the Moiré pattern 1970, such as a periodic structure that is periodic along an axis parallel to the y-axis or a periodic structure having a pitch size that does not affect the Moiré pattern 1970.

[0435] Preferably, an imaging offset metrology tool having adjustable polarization, wavelength, and numerical aperture settings is used to measure the offset between any two of the layers 1904, 1906, and 1908. An example of a suitable imaging offset metrology tool is the Archer commercially available from KLA Corporation, Milpitas, California, USA TM 700. Pitch and need not be optically resolvable by the offset metrology tool used to generate an image of the target 1900. However, preferably, each of the pitch and is optically resolvable by the offset metrology tool used to generate an image of the target 1900.

[0436] Now refer to Figures 20A to 20D , which is a simplified graphical illustration of another embodiment of the multi-layer Moiré target 2000 of the present invention. Figures 20A to 20D A graphical illustration is included in three different dimensions indicated by the x-axis, y-axis, and z-axis, which three dimensions are hereinafter referred to as the x-y plane, the x-z plane, and the y-z plane, respectively. It should be noted that Figure 20A generally graphically illustrates the x-y plane, while Figure 20B , 20C and 20D graphically illustrate a plane parallel to the x-z plane.

[0437] It should be noted that the target 2000 is an example of an alternative layout of the target 1900 described above with reference to Figures 19A to 19D , and is hereinafter referred to with reference to Figures 34 to 39Describe the additional layout. The target 2000 is preferably formed on a semiconductor device wafer, on which at least a first layer 2002, a second layer 2004, a third layer 2006, and a fourth layer 2008 are preferably formed. It should be understood that each of the first layer 2002, the second layer 2004, the third layer 2006, and the fourth layer 2008 defines a substantially planar surface parallel to the x-y plane. The first layer 2002, the second layer 2004, the third layer 2006, and the fourth layer 2008 may be adjacent layers but need not be so. Preferably, any material between the first layer 2002, the second layer 2004, the third layer 2006, and the fourth layer 2008 is at least partially transparent to electromagnetic radiation. In Figures 20A to 20D In the illustrated embodiment, the first layer 2002 is located below the second layer 2004, the third layer 2006, and the fourth layer 2008, the second layer 2004 is located below the third layer 2006 and the fourth layer 2008, and the fourth layer 2008 is located above the first layer 2002, the second layer 2004, and the third layer 2006. However, it should be understood that the layers 2002, 2004, 2006, and 2008 may be arranged in any suitable order relative to each other along the z-axis.

[0438] In addition, in an embodiment of the present invention, the structure shown as being formed with the second layer 2004 and the third layer 2006 may all be formed with the layer 2004. In this embodiment, no part of the target 2000 is formed with the layer 2006. This embodiment is particularly useful for calibration, as described below with reference to Figures 21A to 21C In addition, in another embodiment of the present invention, the structure shown as being formed with the second layer 2004 and the fourth layer 2008 may all be formed with the layer 2004. In this embodiment, no part of the target 2000 is formed with the layer 2008. This embodiment is particularly useful for calibration, as described below with reference to Figures 21A to 21C In addition, in another embodiment of the present invention, the structure shown as being formed with the third layer 2006 and the fourth layer 2008 may all be formed with the layer 2006. In this embodiment, no part of the target 2000 is formed with the layer 2008. This embodiment is particularly useful for calibration, as described below with reference to Figures 21A to 21C In addition, in another embodiment of the present invention, the structure shown as being formed with the third layer 2006 and the fourth layer 2008 may all be formed with the layer 2006. In this embodiment, no part of the target 2000 is formed with the layer 2008. This embodiment is particularly useful for calibration, as described below with reference to

[0439] As specifically seen in Figure 20A the target 2000 includes four target quadrants 2012, 2014, 2016, and 2018. In Figure 20AIn the embodiments shown, the rotational orientation in the x-y plane of each of the target quadrants 2012, 2014, 2016, and 2018 preferably differs from the rotational orientation in the x-y plane of each of the other target quadrants 2012, 2014, 2016, and 2018 by an integer multiple of 90°. Additionally, the target 2000 is preferably characterized by rotational symmetry in the x direction or the y direction or both. In a preferred embodiment of the present invention, the target 2000 is designed such that when in the aligned state, the entirety of the target 2000 is characterized by a single symmetry point in the x direction and a single symmetry point in the y direction. However, even in this embodiment, when in the offset state, the various elements of the target 2000 will be characterized by unique symmetry points.

[0440] Each of the target quadrants 2012, 2014, 2016, and 2018 includes a first stack 2022 of periodic structures, a second stack 2024 of periodic structures, and a third stack 2026 of periodic structures. Each of the first stack 2022, the second stack 2024, and the third stack 2026 includes one or more periodic structures, each periodic structure having a pitch. Preferably, none of the first stack 2022, the second stack 2024, and the third stack 2026 overlap each other. In Figures 20A to 20D it, the first stack 2022 is illustrated as being located closer to the center of the target 2000 than the second stack 2024 and the third stack 2026, and the third stack 2026 is illustrated as being located closer to the edge of the target 2000 than the first stack 2022 and the second stack 2024. However, the first stack 2022, the second stack 2024, and the third stack 2026 can be arranged relative to each other in any suitable arrangement with respect to the x-y plane.

[0441] It should be understood that although in the embodiment illustrated in Figures 20A to 20D each of the periodic structures of the first stack 2022, the second stack 2024, and the third stack 2026 is illustrated as being formed by a plurality of lines and spaces, in other embodiments of the present invention, the periodic structures of the first stack 2022, the second stack 2024, and the third stack 2026 can be formed by any suitable periodic features. It should be further understood that the periodic features forming the periodic structures included in the first stack 2022, the second stack 2024, and the third stack 2026 can be formed by substructures. The pitch of each of the periodic structures of the first stack 2022, the second stack 2024, and the third stack 2026 is preferably between 10 nm and 3000 nm, and more preferably between 200 nm and 800 nm.

[0442] As Figure 20AAs seen, in each of quadrants 2012, 2014, 2016, and 2018, a first plane 2031 that defines and intersects the first stack 2022 and includes a plurality of first axes 2032 therein, a second plane 2033 that intersects the second stack 2024 and includes a plurality of second axes 2034 therein, and a third plane 2035 that intersects the third stack 2026 and includes a plurality of third axes 2036 therein are defined. Depending on the orientation of the first stack 2022, the second stack 2024, and the third stack 2026 within each of quadrants 2012, 2014, 2016, and 2018, each of the first plane 2031, the second plane 2033, and the third plane 2035 is an x-z plane or a y-z plane, and the first axes 2032, the second axes 2034, and the third axes 2036 are parallel to the corresponding x-axis or y-axis. It should be understood that in each of quadrants 2012, 2014, 2016, and 2018, the first plane 2031, the second plane 2033, and the third plane 2035 are all parallel to each other.

[0443] As specifically seen in Figure 20B the first stack 2022 includes a first stack first periodic structure (S1P1) 2042, the S1P1 is formed together with the first layer 2002 and has a pitch designated as along one of the first axes 2032. The first stack 2022 further includes a first stack second periodic structure (S1P2) 2044, the S1P2 is formed together with the second layer 2004 and has a pitch designated as along the other of the first axes 2032.

[0444] It should be understood that the S1P1 2042 and the S1P2 2044 at least partially overlap each other, and thus a first stack moiré pattern 2050 is visible immediately after imaging the first stack 2022. As is known in the art, the first stack moiré pattern 2050 is characterized by a pitch the pitch is a function of the pitches and as shown in Equation 44:

[0445]

[0446] Preferably, the first stack 2022 does not include a periodic structure that forms with the third layer 2006 or the fourth layer 2008 and affects the periodicity of the Moiré pattern 2050. However, the first stack 2022 may include a periodic structure that forms with the third layer 2006 or the fourth layer 2008 and does not affect the periodicity of the Moiré pattern 2050, such as a periodic structure that is periodic in a plane parallel to the x-y plane along an axis perpendicular to the first axis 2032 or a periodic structure having a pitch size that does not affect the Moiré pattern 2050.

[0447] As specifically seen in Figure 20C , the second stack 2024 includes a second-stack first periodic structure (S2P1) 2052 that is formed with the first layer 2002 and has a pitch designated as along one of the second axes 2034. Preferably, the S2P1 pitch is related to the S1P1 pitch by a second-stack multiplication factor designated as s. The second-stack multiplication factor s can be any positive number. The second stack 2024 further includes a second-stack second periodic structure (S2P2) 2054 that is formed with the third layer 2006 and has a pitch designated as along the other of the second axes 2034. Preferably, the S2P2 pitch is related to the S1P2 pitch by the second-stack multiplication factor s. It should be understood that the second-stack multiplication factor s that relates the S2P2 pitch to the S1P2 pitch has the same value as the second-stack multiplication factor s that relates the S2P1 pitch to the S1P1 pitch . In an embodiment of the present invention, the value of s is 1 and thus the S2P1 pitch is the same as the S1P1 pitch and the S2P2 pitch is the same as the S1P2 pitch .

[0448] It should be understood that S2P1 2052 and S2P2 2054 at least partially overlap each other, and thus the second-stack Moiré pattern 2060 is visible immediately after imaging the second stack 2024. As is known in the art, the second-stack Moiré pattern 2060 is characterized by a pitch that is a function of the second-stack multiplication factor s, the pitch , and the pitch as shown in Equation 45:

[0449]

[0450] Preferably, the second stack 2024 does not include a periodic structure that forms with the second layer 2004 or the fourth layer 2008 and affects the periodicity of the Moiré pattern 2060. However, the second stack 2024 may include a periodic structure that forms with the second layer 2004 or the fourth layer 2008 and does not affect the periodicity of the Moiré pattern 2060, such as a periodic structure that is periodic in a plane parallel to the x-y plane along an axis perpendicular to the second axis 2034 or a periodic structure having a pitch size that does not affect the Moiré pattern 2060.

[0451] As specifically seen in Figure 20D the third stack 2026 includes a third stack first periodic structure (S3P1) 2062 that forms with the first layer 2002 and has a pitch designated as along one of the third axes 2036. Preferably, the S3P1 pitch is related to the S1P1 pitch by a third stack multiplication factor designated as t. The third stack multiplication factor t can be any positive number. The third stack 2026 further includes a third stack second periodic structure (S3P2) 2064 that forms with the fourth layer 2008 and has a pitch designated as along the other of the third axes 2036. Preferably, the S3P2 pitch is related to the S1P2 pitch by the third stack multiplication factor t. It should be understood that the third stack multiplication factor t that relates the S3P2 pitch to the S1P2 pitch has the same value as the third stack multiplication factor t that relates the S3P1 pitch to the S1P1 pitch In an embodiment of the present invention, the value of t is 1 and thus the S3P1 pitch is the same as the S1P1 pitch and the S3P2 pitch is the same as the S1P2 pitch

[0452] It should be understood that S3P1 2062 and S3P2 2064 at least partially overlap each other, and thus the third stack Moiré pattern 2070 is visible immediately after imaging the third stack 2026. As is known in the art, the third stack Moiré pattern 2070 is characterized by a pitch where the pitch is the third stack multiplication factor t, the pitch and the pitch ​functions, as shown in Equation 46:

[0453]

[0454] Preferably, the third stack 2026 does not include a periodic structure that forms a Moiré pattern 2070 together with the second layer 2004 or the third layer 2006. However, the third stack 2026 may include a periodic structure that forms together with the second layer 2004 or the third layer 2006 and does not affect the periodicity of the Moiré pattern 2070, such as a periodic structure that is periodic in a plane parallel to the x-y plane along an axis perpendicular to the third axis 2036 or a periodic structure having a pitch size that does not affect the Moiré pattern 2070.

[0455] Preferably, an imaging offset metrology tool with adjustable polarization, wavelength, and numerical aperture settings is used to measure the offset between any two of the layers 2004, 2006, and 2008. An example of a suitable imaging offset metrology tool is the Archer commercially available from KLA Corporation, Milpitas, California, USA TM 700. Pitch and need not be optically resolvable by the offset metrology tool used to generate the image of the target 2000. However, preferably, each of the pitches and is optically resolvable by the offset metrology tool used to generate the image of the target 2000.

[0456] Now refer to Figure 21A , which is a simplified flowchart that illustrates a preferred method of calculating the offset between the second layer 2104, the third layer 2106, and the fourth layer 2108 (such as layers 1904, 1906, and 1908 Figures 19A to 19D ) or 2004, 2006, and 2008 Figures 20A to 20D ) of a multi-layer semiconductor device wafer on which the target 2100 (such as the target 1900 including the first layer 1902 Figures 19A to 19D ) or the target 2000 including the first layer 2002 Figures 20A to 20D ) is formed in a direction parallel to the x-direction or the y-direction. Further refer to Figure 21B and 21C , which are simplified illustrations of the first embodiment and the second embodiment of parts of the method of Figure 21A .

[0457] Although it should be understood that when using the target 2000 Figures 20A to 20D ), the method described with reference to Figures 21A to 21C may be performed only once to calculate the offset in the x-direction or the y-direction, but generallyFigures 21A to 21C The method described in Figures 19A to 19D will be performed twice to calculate the offsets in each of the x and y directions. It should also be understood that when using the target 1900 (

[0458] ), the offset can be calculated only in one direction parallel to the first axis 1932, the second axis 1934, and the third axis 1936. Figure 21A and 21B As seen at the first step 2109, the direction for measuring the offset is selected. When using the target 1900 in the method of Figure 21A and 21B , the direction for measuring the offset is automatically selected as the direction parallel to the first axis 1932, the second axis 1934, and the third axis 1936. When using the target 2000 in the method of

[0459] Preferably, at the next step 2110, an imaging offset metrology tool with adjustable polarization, wavelength, and numerical aperture settings is used to generate an image of the target 2100. An example of a suitable imaging offset metrology tool is the Archer TM 700 commercially available from KLA Corporation, Milpitas, California, USA. It should be noted that the spacings and do not need to be optically resolved by the offset metrology tool used to generate the image of the target 2100. However, preferably, each of the spacings and can be optically resolved by the offset metrology tool used to generate the image of the target 2100.

[0460] In the next step 2111 and as seen in Figure 21B and 21C , for each of the corresponding first stack 2122, second stack 2124, and third stack 2126 (such as the first stack 1922, second stack 1924, and third stack 1926 ( Figures 19A to 19D )) or the first stack 2022, second stack 2024, and third stack 2026 ( Figures 20A to 20D )) in the quadrant selected in step 2109, the first region of interest 2112, the second region of interest 2114, and the third region of interest 2116 are selected. It should be understood that as in Figure 21B and 21CAs seen in the illustrated embodiments, although the first region of interest 2112, the second region of interest 2114, and the third region of interest 2116 are preferably entirely located within each of the respective first stack 2122, second stack 2124, and third stack 2126 (as illustrated for the first region of interest 2112 entirely located within the first stack 2122), the first region of interest 2112, the second region of interest 2114, and the third region of interest 2116 may extend beyond the respective first stack 2122, second stack 2124, and third stack 2126, as illustrated for the regions of interest 2114 and 2116 extending beyond the respective second stack 2124 and third stack 2126. It should be further understood that Figure 21B and 21C the regions of interest 2112, 2114, and 2116 shown in are representative regions of interest, and other suitable regions of interest may be selected at step 2111.

[0461] In the next step 2131 and as Figure 21B and 21C seen in, the positions of the symmetry points 2132 between all examples of the first region of interest 2112 selected in step 2111 are calculated. In the next step 2133 and as Figure 21B and 21C seen in, the positions of the symmetry points 2134 between all examples of the second region of interest 2114 selected in step 2111 are calculated. In the next step 2135 and as Figure 21B and 21C seen in, the positions of the symmetry points 2136 between all examples of the third region of interest 2116 selected in step 2111 are calculated.

[0462] In the next step 2137, the distance in the direction selected at step 2109 between the positions of the symmetry points 2132 of one or more first regions of interest 2112 identified at step 2131 and the positions of the symmetry points 2134 of one or more second regions of interest 2114 identified at step 2133 is calculated. The distance found at step 2137 is divided by the gain The gain is a function of the pitch and the pitch as shown in Equation 47a:

[0463]

[0464] and for target 2000 is a function of the pitch and the pitch as shown in Equation 47b:

[0465]

[0466] and report the result as the offset between the second layer 2104 and the third layer 2106 in the direction selected at step 2109. It should be understood that in addition to the distance calculated at step 2137, the method further calculates an adjustment direction, such as right, left, up, or down. The adjustment direction varies with the pitch and the pitch or the pitch and the pitch and which of the adjustment layers 2104 and 2106 will be adjusted based on their relative values.

[0467] In the next step 2139, calculate the distance in the direction selected at step 2109 between the positions of the symmetry points 2134 of one or more second regions of interest 2114 identified at step 2133 and the positions of the symmetry points 2136 of one or more third regions of interest 2116 identified at step 2135. The distance found at step 2139 is divided by the gain The gain is a function of the pitch and the pitch as shown in Equation 48a:

[0468]

[0469] and for target 2000 is a function of the pitch and the pitch as shown in Equation 48b:

[0470]

[0471] and report the result as the offset between the third layer 2106 and the fourth layer 2108 in the direction selected at step 2109. It should be understood that in addition to the distance calculated at step 2139, the method further calculates an adjustment direction, such as right, left, up, or down. The adjustment direction varies with the pitch and the pitch or the pitch and the pitch and which of the adjustment layers 2106 and 2108 will be adjusted based on their relative values.

[0472] In the next step 2141, calculate the distance in the direction selected at step 2109 between the positions of the symmetry points 2132 of one or more first regions of interest 2112 identified at step 2131 and the positions of the symmetry points 2136 of one or more third regions of interest 2116 identified at step 2135. The distance found at step 2141 is divided by the gain The gain is a function of the pitch for target 1900, as shown in Equation 49a: and the pitch as shown in Equation 49a:

[0473]

[0474] and is a function of the pitch for target 2000, as shown in Equation 49b: and the pitch as shown in Equation 49b:

[0475]

[0476] And report the result as the offset between the second layer 2104 and the fourth layer 2108 in the direction selected at step 2109. It should be understood that in addition to the distance calculated at step 2141, the method further calculates an adjustment direction, such as right, left, up, or down. The adjustment direction varies with the pitch and the pitch or the pitch and the pitch and which of the adjustment layers 2104 and 2108 to adjust.

[0477] Preferably, in the embodiments described above, the structure shown as formed with the second layer 2104 and the third layer 2106 can all be formed with the layer 2104. The method described above with reference to Figures 21A to 21C continues to calculate and report the difference between the offset value reported at step 2139 and the offset value reported at step 2141. The difference between the offset values reported at steps 2139 and 2141 is useful in calibrating the offset measurement tool used in the Figures 21A to 21C method.

[0478] Additionally, in the embodiments described above, the structure shown as formed with the second layer 2104 and the fourth layer 2108 can all be formed with the layer 2104. The method described above with reference to Figures 21A to 21C continues to calculate and report the difference between the offset value reported at step 2137 and the offset value reported at step 2139. The difference between the offset values reported at steps 2137 and 2139 is useful in calibrating the offset measurement tool used in the Figures 21A to 21C method.

[0479] Furthermore, the structure shown as formed with the third layer 2106 and the fourth layer 2108 can all be formed with the layer 2106. The method described above with reference to Figures 21A to 21CThe described method continues to calculate and report the difference between the offset value reported at step 2137 and the offset value reported at step 2141. The difference between the offset values reported at steps 2137 and 2141 is useful in calibrating the offset metrology tool in the method for Figures 21A to 21C which.

[0480] It should be understood that in an embodiment of the present invention where layer 2108 is located below layer 2106, only layers 2102, 2104, and 2108 can be used to perform the relevant part of the method described above before forming layer 2106. Figures 21A to 21C which.

[0481] Now referring to Figures 22A to 22E , which is a simplified illustration of another embodiment of the multi-layer Moiré target 2200 of the present invention. Figures 22A to 22E An illustration is included in three different dimensions indicated by the x-axis, y-axis, and z-axis, which are hereinafter referred to as the x-y plane, x-z plane, and y-z plane, respectively. It should be noted that Figure 22A generally illustrates the x-y plane, while Figure 22B , 22C , 22D, and 22E illustrate planes parallel to the x-z plane.

[0482] The target 2200 is preferably formed on a semiconductor device wafer, on which at least a first layer 2202, a second layer 2204, a third layer 2206, and a fourth layer 2208 are preferably formed. It should be understood that each of the first layer 2202, the second layer 2204, the third layer 2206, and the fourth layer 2208 defines a generally planar surface parallel to the x-y plane. The first layer 2202, the second layer 2204, the third layer 2206, and the fourth layer 2208 may be adjacent layers but need not be. Preferably, any material between the first layer 2202, the second layer 2204, the third layer 2206, and the fourth layer 2208 is at least partially transparent to electromagnetic radiation. In the Figures 22A to 22E illustrated embodiment, the first layer 2202 is located below the second layer 2204, the third layer 2206, and the fourth layer 2208, the second layer 2204 is located below the third layer 2206 and the fourth layer 2208, and the fourth layer 2208 is located above the first layer 2202, the second layer 2204, and the third layer 2206. However, it should be understood that the layers 2202, 2204, 2206, and 2208 can be arranged in any suitable order relative to each other along the z-axis.

[0483] Additionally, in embodiments of the present invention, the structure shown as being formed with the first layer 2202 and the third layer 2206 may all be formed with the layer 2202. In this embodiment, no part of the target 2200 is formed with the layer 2206. This embodiment is particularly useful for calibration, as described below with reference to Figures 24A to 24D As described. Additionally, in another embodiment of the present invention, the structure shown as being formed with the first layer 2202 and the fourth layer 2208 may all be formed with the layer 2202. In this embodiment, no part of the target 2200 is formed with the layer 2208. This embodiment is particularly useful for calibration, as described below with reference to Figures 24A to 24D As described. Additionally, in another embodiment of the present invention, the structure shown as being formed with the second layer 2204 and the fourth layer 2208 may all be formed with the layer 2204. In this embodiment, no part of the target 2200 is formed with the layer 2208. This embodiment is particularly useful for calibration, as described below with reference to Figures 24A to 24D As described.

[0484] It should be understood that Figures 22A to 22E FIG. illustrates a possible layout of the target 2200, and in other embodiments of the present invention, the target 2200 may include additional structures. For example, as described below with reference to Figures 23A to 23E and 34 to 39, suitable targets may include Figures 22A to 22E multiple examples of the structures shown in, and those multiple examples may be arranged in various ways.

[0485] Preferably, the target 2200 includes a first stack 2222 of periodic structures, a second stack 2224 of periodic structures, a third stack 2226 of periodic structures, and a fourth stack 2228 of periodic structures. Each of the first stack 2222, the second stack 2224, the third stack 2226, and the fourth stack 2228 includes one or more periodic structures, each periodic structure having a pitch. Preferably, the first stack 2222, the second stack 2224, the third stack 2226, and the fourth stack 2228 do not overlap each other.

[0486] It should be understood that although in Figures 22A to 22EIn [the figure], each of the periodic structures of the first stack 2222, the second stack 2224, the third stack 2226, and the fourth stack 2228 is shown as being formed by a plurality of lines and spaces. However, in other embodiments of the present invention, the periodic structures of the first stack 2222, the second stack 2224, the third stack 2226, and the fourth stack 2228 may be formed by any suitable periodic features. It should be further understood that the periodic features forming the periodic structures included in the first stack 2222, the second stack 2224, the third stack 2226, and the fourth stack 2228 may be formed by sub-structures. The pitch of each of the periodic structures of the first stack 2222, the second stack 2224, the third stack 2226, and the fourth stack 2228 is preferably between 10 nm and 3000 nm, and more preferably between 200 nm and 800 nm.

[0487] The first x-z plane 2231 intersects the first stack 2222. A plurality of first axes 2232 are located in the first x-z plane 2231 and parallel to the x-axis. The second x-z plane 2233 intersects the second stack 2224. A plurality of second axes 2234 are located in the second x-z plane 2233 and parallel to the x-axis. The third x-z plane 2235 intersects the third stack 2226. A plurality of third axes 2236 are located in the third x-z plane 2235 and parallel to the x-axis. The fourth x-z plane 2237 intersects the fourth stack 2228. A plurality of fourth axes 2238 are located in the fourth x-z plane 2237 and parallel to the x-axis.

[0488] As specifically seen in Figure 22B in a preferred embodiment of the present invention, the first stack 2222 includes a first stack first periodic structure (S1P1) 2242, which is formed together with the first layer 2202 and has a pitch designated as along one of the first axes 2232. Preferably, the first stack 2222 further includes a first stack second periodic structure (S1P2) 2244, which is formed together with the second layer 2204 and has a pitch designated as along the other of the first axes 2232.

[0489] It should be understood that S1P1 2242 and S1P2 2244 at least partially overlap each other, and thus a first stack moiré pattern 2250 is immediately visible after imaging the first stack 2222. As is known in the art, the first stack moiré pattern 2250 is characterized by a pitch The pitch is a function of the pitches and as shown in Equation 50:

[0490]

[0491] Preferably, the first stack 2222 does not include a periodic structure that forms with the third layer 2206 or the fourth layer 2208 and affects the periodicity of the Moiré pattern 2250. However, the first stack 2222 may include a periodic structure that forms with the third layer 2206 or the fourth layer 2208 and does not affect the periodicity of the Moiré pattern 2250, such as a periodic structure that is periodic along an axis parallel to the y-axis or a periodic structure having a pitch size that does not affect the Moiré pattern 2250.

[0492] In another embodiment of the present invention, the first stack 2222 includes only one of the periodic structures 2242 and 2244, and no Moiré pattern 2250 is visible after imaging the first stack 2222.

[0493] As specifically seen in Figure 22C In a preferred embodiment of the present invention, the second stack 2224 includes a second-stack first periodic structure (S2P1) 2252 that forms with the first layer 2202 and has a pitch designated as along one of the second axes 2234. Preferably, the second stack 2224 further includes a second-stack second periodic structure (S2P2) 2254 that forms with the second layer 2204 and has a pitch designated as along the other of the second axes 2234.

[0494] It should be understood that the S2P1 2252 and the S2P2 2254 at least partially overlap each other, and thus a second-stack Moiré pattern 2260 is visible immediately after imaging the second stack 2224. As is known in the art, the second-stack Moiré pattern 2260 is characterized by a pitch The pitch is a function of the pitch and the pitch as shown in Equation 51:

[0495]

[0496] Preferably, the second stack 2224 does not include a periodic structure that forms with the third layer 2206 or the fourth layer 2208 and affects the periodicity of the Moiré pattern 2260. However, the second stack 2224 may include a periodic structure that forms with the third layer 2206 or the fourth layer 2208 and does not affect the periodicity of the Moiré pattern 2260, such as a periodic structure that is periodic along an axis parallel to the y-axis or a periodic structure having a pitch size that does not affect the Moiré pattern 2260.

[0497] As specifically seen in Figure 22DAs seen, in a preferred embodiment of the present invention, the third stack 2226 includes a third stack first periodic structure (S3P1) 2262, and the S3P1, together with the second layer 2204, forms and has a spacing designated as for the S3P1 along one of the third axes 2236. Preferably, the S3P1 spacing is related to the S2P2 spacing by a third stack multiplication factor designated as u. The third stack multiplication factor u can be any positive number. Preferably, the third stack 2226 further includes a third stack second periodic structure (S3P2) 2264, and the S3P2, together with the third layer 2206, forms and has a spacing designated as for the S3P2 along the other of the third axes 2236. Preferably, the S3P2 spacing is related to the S2P1 spacing by the third stack multiplication factor u. It should be understood that the third stack multiplication factor u that relates the S3P2 spacing to the S2P1 spacing has the same value as the third stack multiplication factor u that relates the S3P1 spacing to the S2P2 spacing In an embodiment of the present invention, the value of u is 1 and thus the S3P1 spacing is the same as the S2P2 spacing and the S3P2 spacing is the same as the S2P1 spacing

[0498] It should be understood that the S3P1 2262 and the S3P2 2264 at least partially overlap each other, and thus the third stack moiré pattern 2270 is visible immediately after imaging the third stack 2226. As is known in the art, the third stack moiré pattern 2270 is characterized by a spacing The spacing is a function of the third stack multiplication factor u, the spacing and the spacing as shown in Equation 52:

[0499]

[0500] Preferably, the third stack 2226 does not include a periodic structure that forms with the first layer 2202 or the fourth layer 2208 and affects the moiré pattern 2270. However, the third stack 2226 can include a periodic structure that forms with the first layer 2202 or the fourth layer 2208 and does not affect the moiré pattern 2270, such as a periodic structure that is periodic along an axis parallel to the y-axis or a periodic structure having a spacing size that does not affect the moiré pattern 2270. ​

[0501] Specifically, in Figure 22E as seen in the preferred embodiment of the present invention, the fourth stack 2228 includes a fourth stack first periodic structure (S4P1) 2272, and the S4P1, together with the third layer 2206, forms and has a spacing designated as for the S4P1 along one of the fourth axes 2238. Preferably, the S4P1 spacing is related to the S2P1 spacing by a fourth stack multiplication factor designated as v. The fourth stack multiplication factor v can be any positive number. Preferably, the fourth stack 2228 further includes a fourth stack second periodic structure (S4P2) 2274, and the S4P2, together with the fourth layer 2208, forms and has a spacing designated as for the S4P2 along the other of the fourth axes 2238. Preferably, the S4P2 spacing is related to the S2P2 spacing by the fourth stack multiplication factor v. It should be understood that the fourth stack multiplication factor v that relates the S4P2 spacing to the S2P2 spacing has the same value as the fourth stack multiplication factor v that relates the S4P1 spacing to the S2P1 spacing In an embodiment of the present invention, the value of v is 1 and thus the S4P1 spacing is the same as the S2P1 spacing and the S4P2 spacing is the same as the S2P2 spacing

[0502] It should be understood that the S4P1 2272 and the S4P2 2274 at least partially overlap each other, and thus a fourth stack moiré pattern 2280 is visible immediately after imaging the fourth stack 2228. As is known in the art, the fourth stack moiré pattern 2280 is characterized by a spacing and the spacing is a function of the fourth stack multiplication factor v, the spacing and the spacing as shown in Equation 53:

[0503]

[0504] ​Preferably, the fourth stack 2228 does not include a periodic structure that forms with the first layer 2202 or the second layer 2204 and affects the periodicity of the Moiré pattern 2280. However, the fourth stack 2228 may include a periodic structure that forms with the first layer 2202 or the second layer 2204 and does not affect the periodicity of the Moiré pattern 2280, such as a periodic structure that is periodic along an axis parallel to the y-axis or a periodic structure having a pitch size that does not affect the Moiré pattern 2280.

[0505] Preferably, an imaging offset metrology tool with adjustable polarization, wavelength, and numerical aperture settings is used to measure the offset between any two of the layers 2202, 2204, 2206, and 2208. An example of a suitable imaging offset metrology tool is the Archer commercially available from KLA Corporation, Milpitas, California, USA TM 700. Pitch and need not be optically resolvable by the offset metrology tool used to generate an image of the target 2200. However, preferably, each of the pitches and is optically resolvable by the offset metrology tool used to generate an image of the target 2200.

[0506] Now refer to Figures 23A to 23E , which is a simplified graphical illustration of another embodiment of the multi-layer Moiré target 2300 of the present invention. Figures 23A to 23E An illustration is included in three different dimensions indicated by the x-axis, y-axis, and z-axis, which are hereinafter referred to as the x-y plane, the x-z plane, and the y-z plane, respectively. It should be noted that Figure 23A generally illustrates the x-y plane, while Figure 23B , 23C , 23D, and 23E illustrate planes parallel to the x-z plane.

[0507] It should be noted that the target 2300 is an example of an alternative layout of the target 2200 described above with reference to Figures 22A to 22E , and additional layouts are described below with reference to Figures 34 to 39 . The target 2300 is preferably formed on a semiconductor device wafer, and at least a first layer 2302, a second layer 2304, a third layer 2306, and a fourth layer 2308 are preferably formed on the semiconductor device wafer. It should be understood that each of the first layer 2302, the second layer 2304, the third layer 2306, and the fourth layer 2308 defines a generally planar surface parallel to the x-y plane. The first layer 2302, the second layer 2304, the third layer 2306, and the fourth layer 2308 may be adjacent layers but need not be. Preferably, any material between the first layer 2302, the second layer 2304, the third layer 2306, and the fourth layer 2308 is at least partially transparent to electromagnetic radiation. InFigures 23A to 23E In the embodiment illustrated in Figures 23A to 23E , the first layer 2302 is located below the second layer 2304, the third layer 2306, and the fourth layer 2308, the second layer 2304 is located below the third layer 2306 and the fourth layer 2308, and the fourth layer 2308 is located above the first layer 2302, the second layer 2304, and the third layer 2306. However, it should be understood that the layers 2302, 2304, 2306, and 2308 can be arranged in any suitable order relative to each other along the z-axis.

[0508] In addition, in an embodiment of the present invention, the structure shown as being formed together with the first layer 2302 and the third layer 2306 can all be formed together with the layer 2302. In this embodiment, no part of the target 2300 is formed together with the layer 2306. This embodiment is particularly useful for calibration, as described below with reference to Figures 24A to 24D In addition, in another embodiment of the present invention, the structure shown as being formed together with the first layer 2302 and the fourth layer 2308 can all be formed together with the layer 2302. In this embodiment, no part of the target 2300 is formed together with the layer 2308. This embodiment is particularly useful for calibration, as described below with reference to Figures 24A to 24D In addition, in another embodiment of the present invention, the structure shown as being formed together with the second layer 2304 and the fourth layer 2308 can all be formed together with the layer 2304. In this embodiment, no part of the target 2300 is formed together with the layer 2308. This embodiment is particularly useful for calibration, as described below with reference to Figures 24A to 24D as described.

[0509] As specifically seen in Figure 23A Figure 23A , the target 2300 includes four target quadrants 2312, 2314, 2316, and 2318. In the embodiment shown in Figure 23A Figure 23A , the rotational orientation in the x-y plane of each of the target quadrants 2312, 2314, 2316, and 2318 preferably differs by an integer multiple of 90° from the rotational orientation in the x-y plane of each of the other target quadrants 2312, 2314, 2316, and 2318. In addition, the target 2300 is preferably characterized by rotational symmetry in the x direction or the y direction or both. In a preferred embodiment of the present invention, the target 2300 is designed such that when in the aligned state, the overall target 2300 is characterized by a single symmetry point in the x direction and a single symmetry point in the y direction. However, even in this embodiment, when in the offset state, the various elements of the target 2300 will be characterized by unique symmetry points.

[0510] Each of the target quadrants 2312, 2314, 2316, and 2318 includes a first stack 2322 of periodic structures, a second stack 2324 of periodic structures, a third stack 2326 of periodic structures, and a fourth stack 2328 of periodic structures. Each of the first stack 2322, the second stack 2324, the third stack 2326, and the fourth stack 2328 includes one or more periodic structures, each periodic structure having a pitch. Preferably, the first stack 2322, the second stack 2324, the third stack 2326, and the fourth stack 2328 do not overlap with each other. In Figures 23A to 23E FIG. 23, the first stack 2322 is illustrated as being located closer to the center of the target 2300 than the second stack 2324, the third stack 2326, and the fourth stack 2328, the second stack 2324 is illustrated as being located closer to the center of the target 2300 than the third stack 2326 and the fourth stack 2328, the third stack 2326 is illustrated as being located closer to the edge of the target 2300 than the first stack 2322 and the second stack 2324, and the fourth stack 2328 is illustrated as being located closer to the edge of the target 2300 than the third stack 2326. However, the first stack 2322, the second stack 2324, the third stack 2326, and the fourth stack 2328 may be arranged relative to each other in any suitable arrangement with respect to the x-y plane.

[0511] It should be understood that although in Figures 23A to 23E FIG. 23, each of the periodic structures of the first stack 2322, the second stack 2324, the third stack 2326, and the fourth stack 2328 is shown as being formed by a plurality of lines and spaces, in other embodiments of the present invention, the periodic structures of the first stack 2322, the second stack 2324, the third stack 2326, and the fourth stack 2328 may be formed by any suitable periodic features. It should be further understood that the periodic features forming the periodic structures included in the first stack 2322, the second stack 2324, the third stack 2326, and the fourth stack 2328 may be formed by substructures. The pitch of each of the periodic structures of the first stack 2322, the second stack 2324, the third stack 2326, and the fourth stack 2328 is preferably between 10 nm and 3000 nm, and more preferably between 200 nm and 800 nm.

[0512] As Figure 23AAs seen, in each of quadrants 2312, 2314, 2316, and 2318, a first plane 2331 that intersects the first stack 2322 and includes a plurality of first axes 2332 therein, a second plane 2333 that intersects the second stack 2324 and includes a plurality of second axes 2334 therein, a third plane 2335 that intersects the third stack 2326 and includes a plurality of third axes 2336 therein, and a fourth plane 2337 that intersects the fourth stack 2328 and includes a plurality of fourth axes 2338 therein are defined. Depending on the orientation of the first stack 2322, the second stack 2324, the third stack 2326, and the fourth stack 3282 within each of quadrants 2312, 2314, 2316, and 2318, each of the first plane 2331, the second plane 2333, the third plane 2335, and the fourth plane 2337 is an x-z plane or a y-z plane, and the first axis 2332, the second axis 2334, the third axis 2336, and the fourth axis 2338 are parallel to the corresponding x-axis or y-axis. It should be understood that in each of quadrants 2312, 2314, 2316, and 2318, the first plane 2331, the second plane 2333, the third plane 2335, and the fourth plane 2337 are all parallel to each other.

[0513] As specifically seen in Figure 23B In a preferred embodiment of the present invention, the first stack 2322 includes a first stack first periodic structure (S1P1) 2342, which is formed together with the first layer 2302 and has a spacing designated as along one of the first axes 2332. Preferably, the first stack 2322 further includes a first stack second periodic structure (S1P2) 2344, which is formed together with the second layer 2304 and has a spacing designated as along the other of the first axes 2332.

[0514] It should be understood that S1P1 2342 and S1P2 2344 at least partially overlap each other, and thus a first stack moiré pattern 2350 is visible immediately after imaging the first stack 2322. As is known in the art, the first stack moiré pattern 2350 is characterized by a spacing The spacing is a function of the spacings and as shown in Equation 54:

[0515]

[0516] Preferably, the first stack 2322 does not include a periodic structure that forms with the third layer 2306 or the fourth layer 2308 and affects the periodicity of the Moiré pattern 2350. However, the first stack 2322 may include a periodic structure that forms with the third layer 2306 or the fourth layer 2308 and does not affect the periodicity of the Moiré pattern 2350, such as a periodic structure that is periodic in a plane parallel to the x-y plane along an axis perpendicular to the first axis 2332 or a periodic structure having a pitch size that does not affect the Moiré pattern 2350.

[0517] In another embodiment of the present invention, the first stack 2322 includes only one of the periodic structures 2342 and 2344, and no Moiré pattern 2350 is visible after imaging the first stack 2322.

[0518] As specifically seen in Figure 23C in a preferred embodiment of the present invention, the second stack 2324 includes a second-stack first periodic structure (S2P1) 2352 that forms with the first layer 2302 and has a pitch designated as along one of the second axes 2334. Preferably, the second stack 2324 further includes a second-stack second periodic structure (S2P2) 2354 that forms with the second layer 2304 and has a pitch designated as along the other of the second axes 2334.

[0519] It should be understood that the S2P1 2352 and the S2P2 2354 at least partially overlap each other, and thus a second-stack Moiré pattern 2360 is visible immediately after imaging the second stack 2324. As is known in the art, the second-stack Moiré pattern 2360 is characterized by a pitch where the pitch is a function of the pitch and the pitch as shown in Equation 55:

[0520] <0,

[0521] Preferably, the second stack 2324 does not include a periodic structure that forms with the third layer 2306 or the fourth layer 2308 and affects the periodicity of the Moiré pattern 2360. However, the second stack 2324 may include a periodic structure that forms with the third layer 2306 or the fourth layer 2308 and does not affect the periodicity of the Moiré pattern 2360, such as a periodic structure that is periodic in a plane parallel to the x-y plane along an axis perpendicular to the second axis 2334 or a periodic structure having a pitch size that does not affect the Moiré pattern 2360.

[0522] As specifically seen in Figure 23DAs seen, in a preferred embodiment of the present invention, the third stack 2326 includes a third stack first periodic structure (S3P1) 2362, and the S3P1 is formed together with the second layer 2304 and has a spacing designated as for the S3P1 along one of the third axes 2336. Preferably, the S3P1 spacing is related to the S2P2 spacing by a third stack multiplication factor designated as w. The third stack multiplication factor w can be any positive number. Preferably, the third stack 2326 further includes a third stack second periodic structure (S3P2) 2364, and the S3P2 is formed together with the third layer 2306 and has a spacing designated as for the S3P2 along the other of the third axes 2336. Preferably, the S3P2 spacing is related to the S2P1 spacing by the third stack multiplication factor w. It should be understood that the third stack multiplication factor w that relates the S3P2 spacing to the S2P1 spacing has the same value as the third stack multiplication factor w that relates the S3P1 spacing to the S2P2 spacing . In an embodiment of the present invention, the value of w is 1 and thus the S3P1 spacing is the same as the S2P2 spacing and the S3P2 spacing is the same as the S2P1 spacing .

[0523] It should be understood that the S3P1 2362 and the S3P2 2364 at least partially overlap each other, and thus the third stack moiré pattern 2370 is visible immediately after imaging the third stack 2326. As is known in the art, the third stack moiré pattern 2370 is characterized by a spacing , and the spacing is a function of the third stack multiplication factor w, the spacing , and the spacing , as shown in Equation 56:

[0524]

[0525] Preferably, the third stack 2326 does not include a periodic structure that forms with the first layer 2302 or the fourth layer 2308 and affects the periodicity of the Moiré pattern 2370. However, the third stack 2326 may include a periodic structure that forms with the first layer 2302 or the fourth layer 2308 and does not affect the periodicity of the Moiré pattern 2370, such as a periodic structure that is periodic in a plane parallel to the x-y plane along an axis perpendicular to the third axis 2336 or a periodic structure having a pitch size that does not affect the Moiré pattern 2370.

[0526] As specifically seen in Figure 23E , in a preferred embodiment of the present invention, the fourth stack 2328 includes a fourth stack first periodic structure (S4P1) 2372 that forms with the third layer 2306 and has a pitch designated as along one of the fourth axes 2338. Preferably, the S4P1 pitch is related to the S2P1 pitch by a fourth stack multiplication factor designated as x. The fourth stack multiplication factor x can be any positive number. Preferably, the fourth stack 2328 further includes a fourth stack second periodic structure (S4P2) 2374 that forms with the fourth layer 2308 and has a pitch designated as along the other of the fourth axes 2338. Preferably, the S4P2 pitch is related to the S2P2 pitch by the fourth stack multiplication factor x. It should be understood that the fourth stack multiplication factor x that relates the S4P2 pitch to the S2P2 pitch has the same value as the fourth stack multiplication factor x that relates the S4P1 pitch to the S2P1 pitch . In an embodiment of the present invention, the value of x is 1 and thus the S4P1 pitch is the same as the S2P1 pitch and the S4P2 pitch is the same as the S2P2 pitch .

[0527] It should be understood that the S4P1 2372 and the S4P2 2374 at least partially overlap each other, and thus the fourth stack Moiré pattern 2380 is visible immediately after imaging the fourth stack 2328. As is known in the art, the fourth stack Moiré pattern 2380 is characterized by a pitch that is a function of the fourth stack multiplication factor x, the pitch , and the pitch as shown in Equation 57:

[0528]

[0529] Preferably, the fourth stack 2328 does not include a periodic structure that forms with the first layer 2302 or the second layer 2304 and affects the periodicity of the Moiré pattern 2380. However, the fourth stack 2328 may include a periodic structure that forms with the first layer 2302 or the second layer 2304 and does not affect the periodicity of the Moiré pattern 2380, such as a periodic structure that is periodic in a plane parallel to the x-y plane along an axis perpendicular to the fourth axis 2338 or a periodic structure having a pitch size that does not affect the Moiré pattern 2380.

[0530] Preferably, an imaging offset metrology tool with adjustable polarization, wavelength, and numerical aperture settings is used to measure the offset between any two of the layers 2302, 2304, 2306, and 2308. An example of a suitable imaging offset metrology tool is the Archer commercially available from KLA Corporation, Milpitas, California, USA TM 700. Pitch and need not be optically resolvable by the offset metrology tool used to generate an image of the target 2300. However, preferably, each of the pitch and is optically resolvable by the offset metrology tool used to generate an image of the target 2300.

[0531] Now refer to Figure 24A and 24B , which together are a simplified flowchart illustrating a preferred method of calculating the offset between the first layer 2402, the second layer 2404, the third layer 2406, and the fourth layer 2408 (such as the layers 2202, 2204, 2206, and 2208 ( Figures 22A to 22E )) or the layers 2302, 2304, 2306, and 2308 ( Figures 23A to 23E )) of a multi-layer semiconductor device wafer on which the target 2400 is formed in a direction parallel to the x direction or the y direction using a multi-layer Moiré target 2400 (such as the target 2200 ( Figures 22A to 22E )) or the target 2300 ( Figures 23A to 23E ). Further refer to Figure 24C and 24D , which are simplified illustrations of the first embodiment and the second embodiment of parts of the methods of Figure 24A and 24B respectively.

[0532] Although it should be understood that when using the target 2300 ( Figures 23A to 23E ), refer to Figures 24A to 24DThe method described may be performed only once to calculate the offset in the x or y direction, but typically Figures 24A to 24D the method described in Figures 22A to 22E will be performed twice to calculate the offset in each of the x and y directions. It should also be understood that when using the target 2200 (

[0533] ), the offset may be calculated only in one direction parallel to the first axis 2232, the second axis 2234, the third axis 2236, and the fourth axis 2238. Figure 24A and 24B As seen at the first step 2409, the direction for measuring the offset is selected. When using the target 2200 in the methods of Figure 24A and 24B , the direction for measuring the offset is automatically selected as the direction parallel to the first axis 2232, the second axis 2234, the third axis 2236, and the fourth axis 2238. When using the target 2300 in the methods of

[0534] , the structure of the quadrants 2314 and 2318 is used to measure the offset in a direction parallel to the x-axis, and the structure of the quadrants 2312 and 2316 is used to measure the offset in a direction parallel to the y-axis. TM Preferably, at the next step 2410, an imaging offset metrology tool with adjustable polarization, wavelength, and numerical aperture settings is used to generate an image of the target 2400. An example of a suitable imaging offset metrology tool is the Archer and 700 commercially available from KLA Corporation, Milpitas, California, USA. It should be noted that the spacing and need not be optically resolvable by the offset metrology tool used to generate the image of the target 2400. However, preferably, each of the spacings

[0535] In the next step 2411 and as seen in Figure 24C and 24D , for each of the corresponding first stack 2422, second stack 2424, third stack 2426, and fourth stack 2428 (e.g., the first stack 2222, second stack 2224, third stack 2226, and fourth stack 2228 ( Figures 22A to 22E ) or the first stack 2322, second stack 2324, third stack 2326, and fourth stack 2328 ( Figures 23A to 23E )) in the quadrant selected in step 2409, a first region of interest 2412, a second region of interest 2414, a third region of interest 2416, and a fourth region of interest 2418 are selected. It should be understood that as in Figure 24Cand 24D As seen in the illustrated embodiments, although the first region of interest 2412, the second region of interest 2414, the third region of interest 2416, and the fourth region of interest 2418 are preferably entirely located within each of the corresponding first stack 2422, second stack 2424, third stack 2426, and fourth stack 2428 (as illustrated for the first region of interest 2412 and the fourth region of interest 2418 that are entirely located within the corresponding first stack 2422 and fourth stack 2428), the first region of interest 2412, the second region of interest 2414, the third region of interest 2416, and the fourth region of interest 2418 may extend beyond the corresponding first stack 2422, second stack 2424, third stack 2426, and fourth stack 2428, as illustrated for the regions of interest 2414 and 2416 that extend beyond the corresponding second stack 2424 and third stack 2426. It should be further understood that Figure 24C and 24D the regions of interest 2412, 2414, 2416, and 2418 shown in are representative regions of interest, and other suitable regions of interest may be selected at step 2411.

[0536] In the next step 2431 and as Figure 24C and 24D seen in, the position of the symmetry point 2432 between all examples of the first region of interest 2412 selected in step 2411 is calculated. In the next step 2433 and as Figure 24C and 24D seen in, the position of the symmetry point 2434 between all examples of the second region of interest 2414 selected in step 2411 is calculated. In the next step 2435 and as Figure 24C and 24D seen in, the position of the symmetry point 2436 between all examples of the third region of interest 2416 selected in step 2411 is calculated. In the next step 2437 and as Figure 24C and 24D seen in, the position of the symmetry point 2438 between all examples of the fourth region of interest 2418 selected in step 2411 is calculated.

[0537] In the next step 2439, the distance in the direction selected at step 2409 between the position of the symmetry point 2432 of one or more first regions of interest 2412 identified at step 2431 and the position of the symmetry point 2434 of one or more second regions of interest 2414 identified at step 2433 is calculated. The distance found at step 2439 is divided by the gain wherein the gain is the pitch for the target 2200 and function, as shown in Equation 58a:

[0538]

[0539] and is a spacing for target 2300 and function, as shown in Equation 58b:

[0540]

[0541] And report the result as the offset between the first layer 2402 and the second layer 2404 in the direction selected at step 2409. It should be understood that in addition to the distance calculated at step 2439, the method further calculates an adjustment direction, such as right, left, up, or down. The adjustment direction varies with the spacing and or the spacing and and which of the adjustment layers 2402 and 2404 to vary.

[0542] At the next step 2441, calculate the distance in the direction selected at step 2409 between the position of the symmetry point 2434 of one or more second regions of interest 2414 identified at step 2433 and the position of the symmetry point 2436 of one or more third regions of interest 2416 identified at step 2435. The distance found at step 2441 is divided by the gain The gain is a function of the spacing and the spacing as shown in Equation 59a:

[0543]

[0544] and is a spacing for target 2300 and the spacing as shown in Equation 59b:

[0545]

[0546] And report the result as the offset between the first layer 2402 and the third layer 2406 in the direction selected at step 2409. It should be understood that in addition to the distance calculated at step 2441, the method further calculates an adjustment direction, such as right, left, up, or down. The adjustment direction varies with the spacing and or the spacing and and which of the adjustment layers 2402 and 2406 to vary.

[0547] At the next step 2443, calculate the distance in the direction selected at step 2409 between the position of the symmetry point 2436 of one or several third regions of interest 2416 identified at step 2435 and the position of the symmetry point 2438 of one or several fourth regions of interest 2418 identified at step 2437. Divide the distance found at step 2443 by the gain The gain is a function of the pitch and the pitch as shown in Equation 60a:

[0548]

[0549] and for the target 2300 is a function of the pitch and the pitch as shown in Equation 60b:

[0550]

[0551] And report the result as the offset between the second layer 2404 and the fourth layer 2408 in the direction selected at step 2409. It should be understood that in addition to the distance calculated at step 2443, the method further calculates an adjustment direction, such as right, left, up, or down. The adjustment direction varies with the pitch and or the pitch and and which of the adjustment layers 2404 and 2408 will be adjusted.

[0552] At the next step 2445, calculate the difference between the offset value reported at step 2439 and the offset value reported at step 2443. Report the difference calculated at step 2445 as the offset between the first layer 2402 and the fourth layer 2408 in the direction selected at step 2409. It should be understood that in addition to the distance calculated at step 2445, the method further calculates an adjustment direction, such as right, left, up, or down. The adjustment direction varies with the pitch and or the pitch and and which of the adjustment layers 2402 and 2408 will be adjusted.

[0553] At the next step 2447, the difference between the offset value reported at step 2439 and the offset value reported at step 2441 is calculated. The difference calculated at step 2447 is reported as the offset between the second layer 2404 and the third layer 2406 in the direction selected at step 2409. It should be understood that in addition to the distance calculated at step 2447, the method further calculates an adjustment direction, such as right, left, up, or down. The adjustment direction varies with the relative value of the pitch and or with the pitch and and which of the layers 2404 and 2406 will be adjusted.

[0554] At the next step 2449, the difference between the offset value reported at step 2441 and the offset value reported at step 2445 is calculated. Alternatively, at the next step 2449, the difference between the offset value reported at step 2447 and the offset value reported at step 2443 is calculated. The difference calculated at step 2449 is reported as the offset between the third layer 2406 and the fourth layer 2408 in the direction selected at step 2409. It should be understood that in addition to the distance calculated at step 2449, the method further calculates an adjustment direction, such as right, left, up, or down. The adjustment direction varies with the pitch and or the pitch and of the relative value and which of the layers 2406 and 2408 will be adjusted.

[0555] Preferably, in the embodiments described above, where the structure shown as formed together with the first layer 2402 and the third layer 2406 can all be formed together with the layer 2402, the method described above with reference to Figures 24A to 24D continues to calculate and report the difference between the offset value reported at step 2439 and the offset value reported at step 2447. The difference between the offset values reported at steps 2439 and 2447 is useful in calibrating the offset measuring tool in the method for Figures 24A to 24D .

[0556] Similarly, in the embodiments described above, where the structure shown as formed together with the first layer 2402 and the third layer 2406 can all be formed together with the layer 2402, the method described above with reference to Figures 24A to 24D continues to calculate and report the difference between the offset value reported at step 2445 and the offset value reported at step 2449. The difference between the offset values reported at steps 2445 and 2449 is useful in calibrating the offset measuring tool in the method for Figures 24A to 24Dis useful in calibrating the offset metrology tool in the method of.

[0557] Preferably, in the embodiment described above, the structure shown as being formed with the first layer 2402 and the fourth layer 2408 can all be formed with the layer 2402. Referring above Figures 24A to 24D the method described continues to calculate and report the difference between the offset value reported at step 2439 and the offset value reported at step 2443. The difference between the offset values reported at steps 2439 and 2443 is useful in calibrating the offset metrology tool for Figures 24A to 24D the method of.

[0558] Similarly, in the embodiment described above, the structure shown as being formed with the first layer 2402 and the fourth layer 2408 can all be formed with the layer 2402. Referring above Figures 24A to 24D the method described continues to calculate and report the difference between the offset value reported at step 2441 and the offset value reported at step 2449. The difference between the offset values reported at steps 2441 and 2449 is useful in calibrating the offset metrology tool for Figures 24A to 24D the method of.

[0559] Preferably, in the embodiment described above, the structure shown as being formed with the second layer 2404 and the fourth layer 2408 can all be formed with the layer 2404. Referring above Figures 24A to 24D the method described continues to calculate and report the difference between the offset value reported at step 2439 and the offset value reported at step 2445. The difference between the offset values reported at steps 2439 and 2445 is useful in calibrating the offset metrology tool for Figures 24A to 24D the method of.

[0560] Similarly, in the embodiment described above, the structure shown as being formed with the second layer 2404 and the fourth layer 2408 can all be formed with the layer 2404. Referring above Figures 24A to 24D the method described continues to calculate and report the difference between the offset value reported at step 2447 and the offset value reported at step 2449. The difference between the offset values reported at steps 2447 and 2449 is useful in calibrating the offset metrology tool for Figures 24A to 24D the method of.

[0561] Now refer to Figures 25A to 25E , which is a simplified graphical illustration of another embodiment of the multi-layer moiré target 2500 of the present invention. Figures 25A to 25EA graphical illustration is included in three different dimensions indicated by the x-axis, y-axis, and z-axis, which are hereinafter referred to as the x-y plane, the x-z plane, and the y-z plane respectively. It should be noted that Figure 25A generally graphically illustrates the x-y plane, while Figure 25B 、 25C 、25D, and 25E graphically illustrate planes parallel to the x-z plane.

[0562] The target 2500 is preferably formed on a semiconductor device wafer, on which at least a first layer 2502, a second layer 2504, a third layer 2506, and a fourth layer 2508 are preferably formed. It should be understood that each of the first layer 2502, the second layer 2504, the third layer 2506, and the fourth layer 2508 defines a generally planar surface parallel to the x-y plane. The first layer 2502, the second layer 2504, the third layer 2506, and the fourth layer 2508 may be adjacent layers but need not be. Preferably, any material between the first layer 2502, the second layer 2504, the third layer 2506, and the fourth layer 2508 is at least partially transparent to electromagnetic radiation. In Figures 25A to 25E the illustrated embodiment, the first layer 2502 is located below the second layer 2504, the third layer 2506, and the fourth layer 2508, the second layer 2504 is located below the third layer 2506 and the fourth layer 2508, and the fourth layer 2508 is located above the first layer 2502, the second layer 2504, and the third layer 2506. However, it should be understood that the layers 2502, 2504, 2506, and 2508 may be arranged in any suitable order relative to each other along the z-axis.

[0563] In addition, in an embodiment of the present invention, the structure shown as being formed together with the first layer 2502 and the third layer 2506 may all be formed together with the layer 2502. In this embodiment, no part of the target 2500 is formed together with the layer 2506. This embodiment is particularly useful for calibration, as described hereinafter with reference to Figures 27A to 27D In addition, in another embodiment of the present invention, the structure shown as being formed together with the first layer 2502 and the fourth layer 2508 may all be formed together with the layer 2502. In this embodiment, no part of the target 2500 is formed together with the layer 2508. This embodiment is particularly useful for calibration, as described hereinafter with reference to Figures 27A to 27D In addition, in another embodiment of the present invention, the structure shown as being formed together with the second layer 2504 and the fourth layer 2508 may all be formed together with the layer 2504. In this embodiment, no part of the target 2500 is formed together with the layer 2508. This embodiment is particularly useful for calibration, as described hereinafter with reference to Figures 27A to 27D described.

[0564] It should be understood thatFigures 25A to 25E The figure illustrates a possible layout of the target 2500, and in other embodiments of the present invention, the target 2500 may include additional structures. For example, as described hereinafter with reference to Figures 26A to 26E and 34 to 39, suitable targets may include Figures 25A to 25E multiple examples of the structures shown in

[0565] Preferably, the target 2500 includes a first stack 2522 of periodic structures, a second stack 2524 of periodic structures, a third stack 2526 of periodic structures, and a fourth stack 2528 of periodic structures. Each of the first stack 2522, the second stack 2524, the third stack 2526, and the fourth stack 2528 includes one or more periodic structures, and each periodic structure has a pitch. Preferably, the first stack 2522, the second stack 2524, the third stack 2526, and the fourth stack 2528 do not overlap each other.

[0566] It should be understood that although in Figures 25A to 25E each of the periodic structures of the first stack 2522, the second stack 2524, the third stack 2526, and the fourth stack 2528 is shown as being formed by a plurality of lines and spaces, in other embodiments of the present invention, the periodic structures of the first stack 2522, the second stack 2524, the third stack 2526, and the fourth stack 2528 may be formed by any suitable periodic features. It should be further understood that the periodic features forming the periodic structures included in the first stack 2522, the second stack 2524, the third stack 2526, and the fourth stack 2528 may be formed by sub-structures. The pitch of each of the periodic structures of the first stack 2522, the second stack 2524, the third stack 2526, and the fourth stack 2528 is preferably between 10 nm and 3000 nm, and more preferably between 200 nm and 800 nm.

[0567] A first x-z plane 2531 intersects the first stack 2522. A plurality of first axes 2532 are located in the first x-z plane 2531 and parallel to the x-axis. A second x-z plane 2533 intersects the second stack 2524. A plurality of second axes 2534 are located in the second x-z plane 2533 and parallel to the x-axis. A third x-z plane 2535 intersects the third stack 2526. A plurality of third axes 2536 are located in the third x-z plane 2535 and parallel to the x-axis. A fourth x-z plane 2537 intersects the fourth stack 2528. A plurality of fourth axes 2538 are located in the fourth x-z plane 2537 and parallel to the x-axis.

[0568] As specifically in Figure 25BAs seen, in a preferred embodiment of the present invention, the first stack 2522 includes a first stack first periodic structure (S1P1) 2542, and the S1P1 is formed together with the first layer 2502 and has a pitch designated as along one of the first axes 2532. Preferably, the first stack 2522 further includes a first stack second periodic structure (S1P2) 2544, and the S1P2 is formed together with the second layer 2504 and has a pitch designated as along the other of the first axes 2532.

[0569] It should be understood that the S1P1 2542 and the S1P2 2544 at least partially overlap each other, and thus a first stack moiré pattern 2550 is visible immediately after imaging the first stack 2522. As is known in the art, the first stack moiré pattern 2550 is characterized by a pitch The pitch is a function of the pitches and as shown in Equation 61:

[0570]

[0571] Preferably, the first stack 2522 does not include a periodic structure that affects the moiré pattern 2550 and is formed together with the third layer 2506 or the fourth layer 2508. However, the first stack 2522 may include a periodic structure that is formed together with the third layer 2506 or the fourth layer 2508 and does not affect the moiré pattern 2250, such as a periodic structure that is periodic along an axis parallel to the y-axis or a periodic structure having a pitch size that does not affect the moiré pattern 2250.

[0572] In another embodiment of the present invention, the first stack 2522 only includes the S1P1 2542 and does not include the S1P2 2544, and no moiré pattern 2550 is visible after imaging the first stack 2522.

[0573] As specifically seen in Figure 25C In a preferred embodiment of the present invention, the second stack 2524 includes a second stack first periodic structure (S2P1) 2552, and the S2P1 is formed together with the first layer 2502 and has a pitch designated as The S2P1 pitch. Preferably, the second stack 2524 does not include a periodic structure formed with any of the first layer 2502, the third layer 2506, or the fourth layer 2508, which would immediately produce a moiré pattern with the S2P1 2552 after imaging the second stack 2524. However, the second stack 2524 may include a periodic structure formed with the first layer 2502, the third layer 2506, or the fourth layer 2508, which does not produce a moiré pattern after imaging the second stack 2524, such as a periodic structure that is periodic along an axis parallel to the y-axis or a periodic structure having a pitch size that does not produce a moiré pattern after imaging the second stack 2524.

[0574] As specifically seen in Figure 25D In a preferred embodiment of the present invention, the third stack 2526 includes a third stack first periodic structure (S3P1) 2562, which is formed with the second layer 2504 and has a pitch designated as along one of the third axes 2536. Preferably, the third stack 2526 further includes a third stack second periodic structure (S3P2) 2564, which is formed with the third layer 2506 and has a pitch designated as along the other of the third axes 2536.

[0575] It should be understood that the S3P1 2562 and the S3P2 2564 at least partially overlap each other, and thus the third stack moiré pattern 2570 is immediately visible after imaging the third stack 2526. As is known in the art, the third stack moiré pattern 2570 is characterized by a pitch The pitch is a function of the pitch and the pitch as shown in Equation 62:

[0576]

[0577] Preferably, the third stack 2526 does not include a periodic structure formed with the first layer 2502 or the fourth layer 2508 that affects the moiré pattern 2570. However, the third stack 2526 may include a periodic structure formed with the first layer 2502 or the fourth layer 2508 that does not affect the moiré pattern 2570, such as a periodic structure that is periodic along an axis parallel to the y-axis or a periodic structure having a pitch size that does not affect the moiré pattern 2570.

[0578] As specifically seen in Figure 25EAs can be seen, in a preferred embodiment of the present invention, the fourth stack 2528 includes a fourth stack first periodic structure (S4P1) 2572, and the S4P1 is formed together with the third layer 2506 and has a spacing designated as for one of the fourth axes 2538. Preferably, the S4P1 spacing is related to the S3P2 spacing by a fourth stack multiplication factor designated as y. The fourth stack multiplication factor y can be any positive number. Preferably, the fourth stack 2528 further includes a fourth stack second periodic structure (S4P2) 2574, and the S4P2 is formed together with the fourth layer 2508 and has a spacing designated as for the other of the fourth axes 2538. Preferably, the S4P2 spacing is related to the S3P1 spacing by the fourth stack multiplication factor y. It should be understood that the fourth stack multiplication factor y that relates the S4P2 spacing to the S3P1 spacing has the same value as the fourth stack multiplication factor y that relates the S4P1 spacing to the S3P2 spacing In an embodiment of the present invention, the value of y is 1 and thus the S4P1 spacing is the same as the S3P2 spacing and the S4P2 spacing is the same as the S3P1 spacing

[0579] It should be understood that the S4P1 2572 and the S4P2 2574 at least partially overlap each other, and thus a fourth stack moiré pattern 2580 is visible ...

Claims

1. A multi-layer Moiré target for calculating offsets between at least a first layer, a second layer, and a third layer, the first layer, the second layer, and the third layer being formed on a semiconductor device wafer that defines an x-y plane, the multi-layer Moiré target comprising: At least one group of stacked periodic structures, each of the at least one group comprising: A first stack of periodic structures that includes at least a first stack first periodic structure (S1P1) formed together with at least one of the first layer, the second layer, and the third layer, the S1P1 having an S1P1 pitch along a first axis; A second stack of periodic structures that includes at least a second stack first periodic structure (S2P1) formed together with at least one of the first layer, the second layer, and the third layer, the S2P1 having an S2P1 pitch along a second axis; and A third stack of periodic structures that includes at least a third stack first periodic structure (S3P1) formed together with at least one of the first layer, the second layer, and the third layer, the S3P1 having an S3P1 pitch along a third axis, When the target is imaged in the x-y plane, the first axis is parallel to the x-axis or the y-axis; When the target is imaged in the x-y plane, the second axis and the third axis are parallel to the first axis, and At least one of the first stack, the second stack, and the third stack includes a second periodic structure having a second periodic structure pitch along at least one fourth axis, When the target is imaged in the x-y plane, the at least one fourth axis is parallel to the first axis and coaxial with one of the first axis, the second axis, and the third axis.

2. The multi-layer Moiré target according to claim 1, and wherein: The first layer defines a first generally planar surface parallel to the x-y plane; The second layer defines a second generally planar surface parallel to the x-y plane; The third layer defines a third generally planar surface parallel to the x-y plane; The first axis lies in a first plane parallel to one of the x-z plane or the y-z plane, and the x-z plane or the y-z plane together with the x-y plane defines a three-dimensional x-y-z coordinate system; The second axis lies in a second plane parallel to the first plane; The third axis lies in a third plane parallel to the first plane; and The at least one fourth axis lies in a respective one of the first plane, the second plane, and the third plane and is parallel to a respective one of the first axis, the second axis, or the third axis.

3. The multi-layer Moiré target according to claim 1, and wherein: The first stack of the periodic structures includes the S1P1 formed together with the first layer and a second periodic structure of the first stack (S1P2) formed together with the second layer. The S1P2 has an S1P2 pitch along a first one of the at least one fourth axis, which is coaxial with the first axis when the target is imaged in the x-y plane; The second stack of the periodic structures includes the S2P1 formed together with the second layer and a second periodic structure of the second stack (S2P2) formed together with the third layer. The S2P2 has an S2P2 pitch along a second one of the at least one fourth axis, which is coaxial with the second axis when the target is imaged in the x-y plane; and The third stack of the periodic structures includes the S3P1 formed together with the first layer and a second periodic structure of the third stack (S3P2) formed together with the third layer. The S3P2 has an S3P2 pitch along a third one of the at least one fourth axis when the target is imaged in the x-y plane.

4. The multi-layer Moiré target according to claim 3, and wherein: The S2P1 pitch is related to the S1P2 pitch by a second stack multiplication factor; The S2P2 pitch is related to the S1P1 pitch by the second stack multiplication factor; The S3P1 pitch is related to the S1P1 pitch by a third stack multiplication factor; and The S3P2 pitch is related to the S1P2 pitch by the third stack multiplication factor, wherein the second stack multiplication factor is equal to 1 and the third stack multiplication factor is equal to 1.

5. The multi-layer Moiré target according to claim 1, and wherein: The first stack of the periodic structures includes the S1P1 formed together with the first layer and a second periodic structure of the first stack (S1P2) formed together with the second layer. The S1P2 has an S1P2 pitch along a first one of the at least one fourth axis; The second stack of the periodic structures includes the S2P1 formed together with the first layer and a second periodic structure of the second stack (S2P2) formed together with the second layer. The S2P2 has an S2P2 pitch along a second one of the at least one fourth axis; and The third stack of the periodic structures includes the S3P1 formed together with the second layer and a second periodic structure of the third stack (S3P2) formed together with the third layer. The S3P2 has an S3P2 pitch along a third one of the at least one fourth axis.

6. The multi-layer Moiré target according to claim 1, and wherein: The first stack of the periodic structures includes the S1P1 formed together with the first layer and a second periodic structure of the first stack (S1P2) formed together with the second layer. The S1P2 has an S1P2 pitch along a first one of the at least one fourth axis; The second stack of the periodic structures includes the S2P1 formed with the first layer and a second stack second periodic structure (S2P2) formed with the second layer, the S2P2 having an S2P2 pitch along a second one of the at least one fourth axis; and The third stack of the periodic structures includes the S3P1 formed with the second layer and a third stack second periodic structure (S3P2) formed with the first layer, the S3P2 having an S3P2 pitch along a third one of the at least one fourth axis.

7. The multi-layer Moiré target according to claim 5, and wherein the S3P1 pitch is related to the S2P2 pitch by a third stack multiplication factor; and the S3P2 pitch is related to the S2P1 pitch by the third stack multiplication factor, wherein the third stack multiplication factor is equal to 1, the S1P1 pitch is the same as the S2P2 pitch, and the S1P2 pitch is the same as the S2P1 pitch.

8. The multi-layer Moiré target according to claim 5, and wherein the S1P1 pitch is the same as the S2P1 pitch; the S1P2 pitch differs from the S1P1 pitch by an additional term; the S2P2 pitch differs from the S1P1 pitch by the additional term; the S3P1 pitch differs from the S1P1 pitch by the additional term; and the S3P2 pitch is the same as the S1P1 pitch.

9. The multi-layer Moiré target according to claim 1, and wherein: the first stack of the periodic structures includes the S1P1 formed with the second layer; the second stack of the periodic structures includes the S2P1 formed with the first layer and a second stack second periodic structure (S2P2) formed with the second layer, the S2P2 having an S2P2 pitch along a second one of the at least one fourth axis; and the third stack of the periodic structures includes the S3P1 formed with the second layer and a third stack second periodic structure (S3P2) formed with the third layer, the S3P2 having an S3P2 pitch along a third one of the at least one fourth axis.

10. The multi-layer Moiré target according to claim 9, and wherein the S2P1 pitch is the same as the S3P2 pitch; and the S2P2 pitch is the same as the S3P1 pitch.

11. The multi-layer Moiré target according to claim 1, and wherein: the first stack of the periodic structures includes the S1P1 formed with the second layer; the second stack of the periodic structures includes the S2P1 formed with the first layer; and the third stack of the periodic structures includes the S3P1 formed with the second layer and a third stack second periodic structure (S3P2) formed with the third layer, the S3P2 having an S3P2 pitch along the at least one fourth axis.

12. The multi-layer Moiré target according to claim 1, and wherein: The first stack of the periodic structure includes the S1P1 formed with the first layer; The second stack of the periodic structure includes the S2P1 formed with the first layer; and The third stack of the periodic structure includes the S3P1 formed with the first layer and a third-stack second periodic structure (S3P2) formed with the third layer, and the S3P2 has an S3P2 pitch along the at least one fourth axis.

13. The multi-layer Moiré target according to claim 1, and wherein: The first stack of the periodic structure includes the S1P1 formed with the second layer; The second stack of the periodic structure includes the S2P1 formed with the first layer; and The third stack of the periodic structure includes the S3P1 formed with the second layer and a third-stack second periodic structure (S3P2) formed with the first layer, and the S3P2 has an S3P2 pitch along the at least one fourth axis.

14. The multi-layer Moiré target according to claim 1, and wherein: The first stack of the periodic structure includes the S1P1 formed with the first layer; The second stack of the periodic structure includes the S2P1 formed with the first layer and a second-stack second periodic structure (S2P2) formed with the second layer, and the S2P2 has an S2P2 pitch along the first one of the at least one fourth axis; and The third stack of the periodic structure includes the S3P1 formed with the second layer and a third-stack second periodic structure (S3P2) formed with the third layer, and the S3P2 has an S3P2 pitch along the second one of the at least one fourth axis.

15. The multi-layer Moiré target according to claim 1, and wherein: The at least one group of the periodic structure stacks includes: At least one first group of periodic stacks, wherein when the target is imaged in the x-y plane, the first axis is parallel to the x axis; And At least one second group of periodic stacks, wherein when the target is imaged in the x-y plane, the first axis is parallel to the y axis.

16. The multi-layer Moiré target according to claim 15, and wherein the at least one first group of periodic stacks is identical to the at least one second group of periodic stacks except for their orientations.

17. The multi-layer Moiré target according to claim 15, and wherein the target is characterized by mirror symmetry, or the target is characterized by rotational symmetry.

18. A multi-layer Moiré target for calculating the offsets between at least a first layer, a second layer, a third layer, and a fourth layer, the first layer, the second layer, the third layer, and the fourth layer being formed on a semiconductor device wafer that defines an x-y plane, the multi-layer Moiré target including: At least one group of periodic structure stacks, each of the at least one group including: A first stack of periodic structures, comprising at least a first periodic structure of the first stack (S1P1), the S1P1 being formed together with at least one of the first layer, the second layer, the third layer, and the fourth layer, the S1P1 having an S1P1 pitch along a first axis; A second stack of periodic structures, comprising at least a first periodic structure of the second stack (S2P1), the S2P1 being formed together with at least one of the first layer, the second layer, the third layer, and the fourth layer, the S2P1 having an S2P1 pitch along a second axis; A third stack of periodic structures, comprising at least a first periodic structure of the third stack (S3P1), the S3P1 being formed together with at least one of the first layer, the second layer, the third layer, and the fourth layer, the S3P1 having an S3P1 pitch along a third axis; and A fourth stack of periodic structures, comprising at least a first periodic structure of the fourth stack (S4P1), the S4P1 being formed together with at least one of the first layer, the second layer, the third layer, and the fourth layer, the S4P1 having an S4P1 pitch along a fourth axis, When the target is imaged in the x-y plane, the first axis is parallel to the x-axis or the y-axis; When the target is imaged in the x-y plane, the second axis, the third axis, and the fourth axis are parallel to the first axis, and At least one of the first stack, the second stack, the third stack, and the fourth stack includes a second periodic structure, the second periodic structure having a second periodic structure pitch along at least one fifth axis, when the target is imaged in the x-y plane, the at least one fifth axis is parallel to the first axis and coaxial with one of the first axis, the second axis, the third axis, and the fourth axis.

19. The multi-layer Moiré target according to claim 18, and wherein: The first layer defines a first generally planar surface parallel to the x-y plane; The second layer defines a second generally planar surface parallel to the x-y plane; The third layer defines a third generally planar surface parallel to the x-y plane; The fourth layer defines a first generally planar surface parallel to the x-y plane; The first axis is located in a first plane parallel to one of the x-z plane or the y-z plane, one of the x-z plane or the y-z plane and the x-y plane define a three-dimensional x-y-z coordinate system; The second axis is located in a second plane parallel to the first plane; The third axis is located in a third plane parallel to the first plane; The fourth axis is located in a fourth plane parallel to the first plane; and The at least one fifth axis is located in a respective one of the first plane, the second plane, the third plane, and the fourth plane and parallel to a respective one of the first axis, the second axis, the third axis, or the fourth axis.

20. The multi-layer Moiré target according to claim 18, and wherein: The first stack of the periodic structures includes the S1P1 formed together with the first layer and a second periodic structure of the first stack (S1P2) formed together with the second layer. The S1P2 has an S1P2 pitch along a first one of the at least one fifth axis, which is coaxial with the first axis when the target is imaged in the x-y plane; The second stack of the periodic structures includes the S2P1 formed together with the first layer and a second periodic structure of the second stack (S2P2) formed together with the second layer. The S2P2 has an S2P2 pitch along a second one of the at least one fifth axis, which is coaxial with the second axis when the target is imaged in the x-y plane; The third stack of the periodic structures includes the S3P1 formed together with the second layer and a second periodic structure of the third stack (S3P2) formed together with the third layer. The S3P2 has an S3P2 pitch along a third one of the at least one fifth axis, which is coaxial with the third axis when the target is imaged in the x-y plane; and The fourth stack of the periodic structures includes the S4P1 formed together with the third layer and a second periodic structure of the fourth stack (S4P2) formed together with the fourth layer. The S4P2 has an S4P2 pitch along a fourth one of the at least one fifth axis, which is coaxial with the fourth axis when the target is imaged in the x-y plane.

21. The multi-layer Moiré target according to claim 20, and wherein: The S3P1 pitch is related to the S2P2 pitch by a third stack multiplication factor; The S3P2 pitch is related to the S2P1 pitch by the third stack multiplication factor; The S4P1 pitch is related to the S2P1 pitch by a fourth stack multiplication factor; and The S4P2 pitch is related to the S2P2 pitch by the fourth stack multiplication factor.

22. The multi-layer Moiré target according to claim 18, and wherein: The first stack of the periodic structures includes the S1P1 formed together with the first layer and a second periodic structure of the first stack (S1P2) formed together with the second layer. The S1P2 has an S1P2 pitch along a first one of the at least one fifth axis, which is coaxial with the first axis when the target is imaged in the x-y plane; The second stack of the periodic structures includes the S2P1 formed together with the second layer; The third stack of the periodic structures includes the S3P1 formed together with the second layer and a second periodic structure of the third stack (S3P2) formed together with the third layer. The S3P2 has an S3P2 pitch along a second one of the at least one fifth axis, which is coaxial with the third axis when the target is imaged in the x-y plane; and The fourth stack of the periodic structures includes the S4P1 formed together with the third layer and a second periodic structure of the fourth stack (S4P2) formed together with the fourth layer. The S4P2 has an S4P2 pitch along a third one of the at least one fifth axis, and when the target is imaged in the x-y plane, the third one is coaxial with the fourth axis.

23. The multi-layer Moiré target according to claim 22, and wherein: The S4P1 pitch is related to the S3P2 pitch by a fourth stack multiplication factor; and The S4P2 pitch is related to the S3P1 pitch by the fourth stack multiplication factor.

24. The multi-layer Moiré target according to claim 18, and wherein: The first stack of the periodic structures includes the S1P1 formed together with the first layer and a second periodic structure of the first stack (S1P2) formed together with the second layer. The S1P2 has an S1P2 pitch along a first one of the at least one fifth axis, and when the target is imaged in the x-y plane, the first one is coaxial with the first axis; The second stack of the periodic structures includes the S2P1 formed together with the second layer and a second periodic structure of the second stack (S2P2) formed together with the third layer. The S2P2 has an S2P2 pitch along a second one of the at least one fifth axis, and when the target is imaged in the x-y plane, the second one is coaxial with the second axis; The third stack of the periodic structures includes the S3P1 formed together with the first layer and a second periodic structure of the third stack (S3P2) formed together with the third layer. The S3P2 has an S3P2 pitch along a third one of the at least one fifth axis, and when the target is imaged in the x-y plane, the third one is coaxial with the third axis; and The fourth stack of the periodic structures includes the S4P1 formed together with the third layer and a second periodic structure of the fourth stack (S4P2) formed together with the fourth layer. The S4P2 has an S4P2 pitch along a fourth one of the at least one fifth axis, and when the target is imaged in the x-y plane, the fourth one is coaxial with the fourth axis.

25. The multi-layer Moiré target according to claim 24, and wherein: The S2P1 pitch is related to the S1P2 pitch by a second stack multiplication factor; The S2P2 pitch is related to the S1P1 pitch by the second stack multiplication factor; The S3P1 pitch is related to the S1P1 pitch by a third stack multiplication factor; The S3P2 pitch is related to the S1P2 pitch by the third stack multiplication factor; The S4P1 pitch is related to the S1P2 pitch by a fourth stack multiplication factor; and The S4P2 pitch is related to the S1P1 pitch by the fourth stack multiplication factor.

26. The multi-layer Moiré target according to claim 18, and wherein: The first stack of the periodic structures includes the S1P1 formed together with the first layer and a second periodic structure of the first stack (S1P2) formed together with the second layer, the S1P2 having an S1P2 pitch along a first one of the at least one fifth axis, the first one being coaxial with the first axis when the target is imaged in the x-y plane; The second stack of the periodic structures includes the S2P1 formed together with the second layer; The third stack of the periodic structures includes the S3P1 formed together with the third layer; and The fourth stack of the periodic structures includes the S4P1 formed together with the fourth layer.

27. The multi-layer Moiré target according to claim 18, and wherein: The first stack of the periodic structures includes the S1P1 formed together with the first layer and a second periodic structure of the first stack (S1P2) formed together with the second layer, the S1P2 having an S1P2 pitch along a first one of the at least one fifth axis, the first one being coaxial with the first axis when the target is imaged in the x-y plane; The second stack of the periodic structures includes the S2P1 formed together with the second layer; The third stack of the periodic structures includes the S3P1 formed together with the second layer; and The fourth stack of the periodic structures includes the S4P1 formed together with the fourth layer.

28. The multi-layer Moiré target according to claim 18, and wherein: The first stack of the periodic structures includes the S1P1 formed together with the first layer and a second periodic structure of the first stack (S1P2) formed together with the second layer, the S1P2 having an S1P2 pitch along a first one of the at least one fifth axis, the first one being coaxial with the first axis when the target is imaged in the x-y plane; The second stack of the periodic structures includes the S2P1 formed together with the second layer; The third stack of the periodic structures includes the S3P1 formed together with the third layer; and The fourth stack of the periodic structures includes the S4P1 formed together with the second layer.

29. The multi-layer Moiré target according to claim 18, and wherein: The first stack of the periodic structures includes the S1P1 formed together with the first layer and a second periodic structure of the first stack (S1P2) formed together with the second layer, the S1P2 having an S1P2 pitch along a first one of the at least one fifth axis, the first one being coaxial with the first axis when the target is imaged in the x-y plane; The second stack of the periodic structures includes the S2P1 formed together with the second layer; The third stack of the periodic structures includes the S3P1 formed together with the third layer; and The fourth stack of the periodic structures includes the S4P1 formed together with the third layer.

30. The multi-layer Moiré target according to claim 18, and wherein: The at least one group of periodically structured stacks comprises: At least one first group of periodic stacks, wherein when the target is imaged in the x-y plane, the first axis is parallel to the x-axis; And At least one second group of periodic stacks, wherein when the target is imaged in the x-y plane, the first axis is parallel to the y-axis.

31. The multi-layer Moiré target according to claim 30, and wherein the at least one first group of periodically stacked structures and the at least one second group of periodically stacked structures are identical except for their orientation.

32. The multi-layer Moiré target according to claim 30, and wherein the target is characterized by mirror symmetry, or the target is characterized by rotational symmetry.

33. A multi-layer Moiré target for calculating the offset between at least a first layer, a second layer, a third layer and a fourth layer, the first layer, the second layer, the third layer and the fourth layer being formed on a semiconductor device wafer defining an x-y plane, the multi-layer Moiré target comprising: At least one group of periodically structured stacks, each of the at least one group comprising: A first stack of periodic structures, which at least includes a first stacked first periodic structure (S1P1), the S1P1 being formed together with at least one of the first layer, the second layer, the third layer and the fourth layer, the S1P1 having an S1P1 pitch along a first axis; A second stack of periodic structures, which at least includes a second stacked first periodic structure (S2P1), the S2P1 being formed together with at least one of the first layer, the second layer, the third layer and the fourth layer, the S2P1 having an S2P1 pitch along a second axis; and A third stack of periodic structures, which at least includes a third stacked first periodic structure (S3P1), the S3P1 being formed together with at least one of the first layer, the second layer, the third layer and the fourth layer, the S3P1 having an S3P1 pitch along a third axis; When the target is imaged in the x-y plane, the first axis is parallel to the x-axis or the y-axis; When the target is imaged in the x-y plane, the second axis and the third axis are parallel to the first axis, and At least one of the first stack, the second stack and the third stack includes a second periodic structure, the second periodic structure having a second periodic structure pitch along at least one fourth axis, When the target is imaged in the x-y plane, the at least one fourth axis is parallel to the first axis and coaxial with one of the first axis, the second axis and the third axis.

34. The multi-layer Moiré target according to claim 33, and wherein: The first stack of periodic structures includes the S1P1 formed together with the first layer and a first stacked second periodic structure (S1P2) formed together with the second layer, the S1P2 having an S1P2 pitch along the first of the at least one fourth axis; The second stack of the periodic structures includes the S2P1 formed with the first layer and a second stack second periodic structure (S2P2) formed with the third layer, the S2P2 having an S2P2 pitch along a second one of the at least one fourth axis; and The third stack of the periodic structures includes the S3P1 formed with the first layer and a third stack second periodic structure (S3P2) formed with the fourth layer, the S3P2 having an S3P2 pitch along a third one of the at least one fourth axis.

35. The multi-layer Moiré target according to claim 33, and wherein: The at least one group of periodic structure stacks comprises: At least one first group of periodic stacks, wherein when the target is imaged in the x-y plane, the first axis is parallel to the x axis; And At least one second group of periodic stacks, wherein when the target is imaged in the x-y plane, the first axis is parallel to the y axis.

36. The multi-layer Moiré target according to claim 35, and wherein the at least one first group of periodic stacks is identical to the at least one second group of periodic stacks except for their orientation.

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