Detection-assisted two-step phase unwrapping for patterned wafer shape metrology

Abstract

Receive a wrapped phase map associated with an interferometric measurement of a sample including patterned features; Remove gradients from the wrapped phase map; Generate a background; Detect features in the wrapped phase map, where the features in the wrapped phase map correspond to at least some of the patterned features of the sample; Replace phases of the features with the background at corresponding locations in the wrapped phase map to generate a modified wrapped phase map; Unwrap the modified wrapped phase map using global phase unwrapping to generate a temporary unwrapped phase map; Apply local phase unwrapping to restore phases of features in the temporary unwrapped phase map at corresponding locations; Reapply gradients to the temporary unwrapped phase map to generate an output unwrapped phase map.

Description

[Technical field]

[0001] REFERENCE TO RELATED APPLICATIONS This application claims the benefit under 35 U.S.C. §119(e) of U.S. Provisional Application No. 63 / 195,716 (filed June 2, 2021), which is incorporated by reference herein in its entirety.

[0002] The present disclosure relates generally to phase unwrapping of patterned semiconductor device metrology, and more particularly to a system and method for detection-assisted two-stage phase unwrapping of patterned semiconductor device metrology. [Background technology]

[0003] Metrology processes are used at various steps during semiconductor manufacturing processes to monitor and control one or more semiconductor layer processes. Some of these characteristics include the flatness and thickness uniformity of a sample (e.g., a wafer). Interferometric measurement tools can be used to generate wrapped phase maps of the sample with high accuracy. For example, a patterned wafer geometry (PWG) tool may be used in-process.

[0004] Interferometry is a technique that uses interference of superimposed electromagnetic waves to extract information (e.g., interference patterns) that can correspond to extremely accurate measurements of the surface topology of a sample. However, such information (e.g., phase data, interferograms, wrapped phase maps, etc.) obtained using interferometric tools may span multiple phase cycles. For example, as the height of the surface topology changes, the measured interference pattern values ​​may span multiple phase cycles, with each cycle ranging between -pi and pi, such that the value at any given point on the wrapped phase map does not map uniquely to an absolute height value. In this regard, values ​​across an increasing / decreasing surface topology may be repeated periodically over multiple phase cycles, and the repeated values ​​of different phase cycles are identical with respect to the ambiguity prior to phase unwrapping as to which phase cycle a particular value belongs to and how many phase cycles there are. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] U.S. Patent No. 11,035,665 Summary of the Invention [Problem to be solved by the invention]

[0006] Phase unwrapping can be utilized in an attempt to resolve these phase ambiguities in the wrapped phase map. However, in general, as the complexity and magnitude of the variations in the surface topology increase, it becomes increasingly difficult to accurately resolve the phase ambiguities. [Means for solving the problem]

[0007] A metrology system is disclosed according to one or more embodiments of the present disclosure. In an exemplary embodiment, the system includes a controller communicatively coupled to an interferometric measurement tool. In another exemplary embodiment, the controller includes one or more processors and a memory. In another exemplary embodiment, the memory is configured to store a set of program instructions. In another exemplary embodiment, the one or more processors are configured to execute program instructions that cause the one or more processors to receive a wrapped phase map associated with an interferometric measurement of a sample including a patterned feature. In another exemplary embodiment, the one or more processors are configured to execute program instructions that cause the one or more processors to remove a gradient from the wrapped phase map. In another exemplary embodiment, the one or more processors are configured to execute program instructions that cause the one or more processors to generate a background. In another exemplary embodiment, the one or more processors are configured to execute program instructions that cause the one or more processors to detect features in the wrapped phase map, the features in the wrapped phase map corresponding to at least some of the patterned features of the sample. In another exemplary embodiment, the one or more processors are configured to execute program instructions that cause the one or more processors to replace the phase of the features with the background at a corresponding location in the wrapped phase map to generate a modified wrapped phase map. In another exemplary embodiment, the one or more processors are configured to execute program instructions that cause the one or more processors to unwrap the modified wrapped phase map using global phase unwrapping to generate a temporarily unwrapped phase map. In another exemplary embodiment, the one or more processors are configured to execute program instructions that cause the one or more processors to apply local phase unwrapping to restore phases of features of the temporarily unwrapped phase map at corresponding locations.In another exemplary embodiment, the one or more processors are configured to execute program instructions that cause the one or more processors to re-apply a gradient to the temporary unwrapped phase map to generate the output unwrapped phase map.

[0008] A metrology method is disclosed according to one or more embodiments of the present disclosure. In one exemplary embodiment, the method may include, but is not limited to, receiving a wrapped phase map associated with an interferometric measurement of a sample including a patterned feature. In one exemplary embodiment, the method may include removing a gradient from the wrapped phase map. In one exemplary embodiment, the method may include generating a background. In one exemplary embodiment, the method may include detecting features in the wrapped phase map, where the features in the wrapped phase map correspond to at least some of the patterned features of the sample. In one exemplary embodiment, the method may include replacing the phase of the features with the background at corresponding locations in the wrapped phase map to generate a modified wrapped phase map. In one exemplary embodiment, the method may include unwrapping the modified wrapped phase map using global phase unwrapping to generate a temporary unwrapped phase map. In one exemplary embodiment, the method may include applying local phase unwrapping to restore the phase of the features of the temporary unwrapped phase map at corresponding locations. In one exemplary embodiment, the method may include reapplying a gradient to the temporary unwrapped phase map to generate an output unwrapped phase map. Effect of the Invention

[0009] It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not necessarily restrictive of the invention as claimed. The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate embodiments of the invention and, together with the general description, serve to explain the principles of the invention. [Brief description of the drawings]

[0010] Many advantages of the present disclosure may be better understood by those skilled in the art by reference to the following drawings. [Figure 1A] FIG. 1A shows a process diagram for generating an unwrapped phase map in accordance with one or more embodiments of the present disclosure. [Figure 1B] FIG. 1B shows a partially failed unwrapped phase wrap diagram. [Figure 1C] FIG. 1C illustrates an unwrapped phase wrap diagram in accordance with one or more embodiments of the present disclosure. [Diagram 2] FIG. 2 illustrates a schematic block diagram of a system in accordance with one or more embodiments of the present disclosure. [Diagram 3] FIG. 3 is a flow diagram of a method for unwrapping a phase map in accordance with one or more embodiments of the present disclosure. [Figure 4A] FIG. 4A shows a cross-sectional view of a schematic of a sample according to one or more embodiments of the present disclosure. [Figure 4B] FIG. 4B shows a flow chart including schematics of steps of a method for unwrapping a phase map in accordance with one or more embodiments of the present disclosure. [Figure 4C] FIG. 4C shows a flow chart including schematics of steps of a method for unwrapping a phase map in accordance with one or more embodiments of the present disclosure. [Figure 5A] FIG. 5A shows a flow diagram including a phase map of method steps for unwrapping a phase map in accordance with one or more embodiments of the present disclosure. [Figure 5B] FIG. 5B shows a flow diagram including more phase maps of more steps of the method of FIG. 5A in accordance with one or more embodiments of the present disclosure. [Figure 6A] FIG. 6A shows a flow diagram including another example of a phase map of the step of FIG. 5A, in accordance with one or more embodiments of the present disclosure. [Figure 6B] FIG. 6B shows a flow diagram including another example of a phase map of the step of FIG. 5B, in accordance with one or more embodiments of the present disclosure. [Figure 7A] FIG. 7A shows the unwrapped phase map of the sample. [Figure 7B] FIG. 7B illustrates a different unwrapped phase map of the sample of FIG. 7A, in accordance with one or more embodiments of the present disclosure. [Figure 8A] FIG. 8A shows the unwrapped phase map of the sample. [Figure 8B] FIG. 8B illustrates a different unwrapped phase map of the sample of FIG. 8A, in accordance with one or more embodiments of the present disclosure. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0011] Reference will now be made in detail to the disclosed subject matter, which is illustrated in the accompanying drawings. The present disclosure has been specifically shown and described with respect to certain embodiments and certain features thereof. The embodiments described herein are to be construed as illustrative and not restrictive. It will be readily apparent to those skilled in the art that various changes and modifications in form and detail may be made therein without departing from the spirit and scope of the present disclosure.

[0012] Some embodiments of the present disclosure are directed to systems and methods for two-stage phase unwrapping of a wrapped phase map in the presence of features with sharp and rapidly varying profiles. For example, a two-stage phase unwrapping technique may identify a smoothly varying background signal based on prior knowledge of the sample, temporarily remove detected features with sharp profiles, replace the removed features with the background signal, perform a first phase unwrapping step on the wrapped phase map with the replaced features, and then restore the features in a second phase unwrapping step. In this manner, any suitable phase unwrapping technique may be used in the first phase unwrapping step to accurately perform global phase unwrapping across the sample based on the background signal without inducing errors from the features. The second phase unwrapping step can then restore information content associated with the features through a local phase unwrapping technique without the risk of propagating errors through other areas already unwrapped in the first phase unwrapping step.

[0013] Resolving patterned samples (e.g., wafers) is difficult using conventional techniques, as patterned samples, especially with the increasing use of relatively high 3D NAND stacked memory features, may have many ambiguities that are difficult to resolve. Ambiguous values ​​in a wrapped phase map may repeat periodically. The values ​​in a wrapped phase map represent the intensity between light and dark values ​​as the optical path difference between the two arms of an interferometric tool, and such intensity values ​​may be represented by colored pixels for illustrative purposes. For example, the value at a given point in a wrapped phase map may be the same as the value at a different point, even if those points on the sample have different heights. In a sense, this may mean that any given value may be "ambiguous." Such values ​​may be "unwrapped" in some embodiments so that the data covers a single range. For example, unwrapped data may mean data that does not repeat periodically.

[0014] It should be noted that a "patterned sample," a "sample having patterned features," and the like, refers to a sample that is not a "blank" wafer that does not yet have a layer of a patterned device (e.g., a 3D NAND device). Also, it should be noted that the terms "feature," "feature 402," "sharp feature," "high feature," and the like, as used in this disclosure, are not meant to have exactly the same meaning as a "patterned feature." However, it should be noted that a "feature 402," and the like, may include features that are a subset of a patterned feature. In some embodiments, a "feature 402" includes defects (e.g., particles, unexpected raised defects that cause discontinuities in measurements) that are not a subset of a patterned feature.

[0015] When the surface topology of a sample changes rapidly, it is difficult to accurately resolve ambiguities in values ​​of a wrapped phase map by unwrapping using methods other than the embodiments of the present disclosure. For example, phase unwrapping techniques using conventional path tracing throughout the phase map may partially fail when attempting to resolve rapidly changing surface topology height ambiguities if the values ​​result from incorrect phase cycles. For example, if such an incorrect assignment is made, that error in the assignment may propagate through the sample during the unwrapping process, increasing the size of the error.

[0016] In a general sense, path tracing is a phase unwrapping technique that makes assumptions such as that values ​​at one end of a phase cycle happen to be close to values ​​at the other end of the phase cycle. Such assumptions may be true for smoothly varying wrapped phase maps, but not necessarily for abruptly varying wrapped phase maps. For example, if the height difference between adjacent values ​​in a wrapped phase map varies by more than a threshold (e.g., one half phase cycle, one full phase cycle, etc.), there is a high probability of errors in attributing values ​​to the wrong phase cycle when unwrapping the phase map.

[0017] Furthermore, phase unwrapping techniques using filtering and 2D optimization (e.g., 2D weighted least squares), such as preconditioned conjugate gradient (PCG) techniques, may be less accurate and / or efficient than embodiments of the present disclosure. For example, 2D optimization approaches may not distinguish areas with sharp features from non-difficult areas, which may lead to introducing errors far from the difficult areas. For example, errors may propagate from areas with sharp features to non-difficult areas when using path-following unwrapping techniques. Such far-away errors may be difficult to identify and therefore difficult to resolve. Furthermore, such techniques often use pseudo-thickness maps to determine the surface gradient (slope) of the sample, and the pseudo-thickness may introduce errors from the back to the front side of the sample. Furthermore, as the techniques become more robust (e.g., less prone to errors), processing times may increase and efficiency may decrease.

[0018] There is a need for a robust, accurate and efficient method for resolving phase ambiguities during phase unwrapping.

[0019] The present disclosure, in at least some embodiments, addresses at least some of the shortcomings of previous phase unwrapping techniques, such as those mentioned above. For example, as shown in Figures 1B and 1C, a more accurate unwrapped phase map 122 of Figure 1C may be obtained using at least some embodiments of the present disclosure, as compared to the partially failed phase map 120 of Figure 1B using other techniques. In another example, some embodiments of the present disclosure enable reduced surface topology-height measurement errors and more wafer coverage on challenging layers with complex height discontinuities. In another example, some embodiments enable reduced measurement errors on samples with non-uniform film thickness.

[0020] FIG. 1A shows a process flow diagram illustrating a method 100 for generating an unwrapped phase map in accordance with one or more embodiments of the present disclosure.

[0021] 1A includes two examples of the unwrapping method 100 (Examples 1-114, and Example 2-116) shown in an interferogram (interferometric pattern) array 102, a wrapped phase map (wrapped phase array) 104, and an unwrapped phase array 106. The first example, Example 1-114, may be an example of a zoomed-in example 114 of a zoomed-in portion of an interferogram, and the second example, Example 2-116, may be an example wafer 116 of an unpatterned wafer sample in an unpatterned wafer array 112. Interferogram array 102 includes interferograms of interferogram data that may be interferometric measurements of the sample.

[0022] Note that the line plot rows 110 may show plots of the corresponding phase map rows 108. For example, each plot in the line plot rows 110 may correspond to the phase map above it. For example, each line plot in the line plot rows 110 may represent a one-dimensional cross section of a horizontal line at the center of the phase map above each line plot. Note that unlike the data in the wrapped wrapped phase column 104, the data in the unwrapped phase map (unwrapped phase column) 106 is not circularly wrapped, so there are no discontinuities in the line plots of the unwrapped phase column 106.

[0023] It should be noted that in some embodiments, the step of calculating the phase is performed to determine / generate a wrapped phase map based on an interferogram, as shown. For example, raw sensor data obtained from the interferometric measurement tool 214 may be represented by an interferogram. Such data may need to be processed to obtain a wrapped phase map.

[0024] It should be noted that in some embodiments, an unwrapping step is performed to determine / generate an unwrapped phase map 106 based on the wrapped phase map 104 as shown.

[0025] FIG. 2 illustrates a simplified schematic diagram of a system 200 for unwrapping the wrapped phase map 104 in accordance with one or more embodiments of the present disclosure.

[0026] The system 200 may be any system, such as a metrology system, for determining an unwrapped phase map 106 of the sample 202. Note that throughout this disclosure, "system" refers to, but is not required to refer to, a "metrology system," and any description, element, method, etc., of the system 200 may be applicable to one or more embodiments of the metrology system 200. Note that the metrology system 200 may, but does not necessarily, include a tool for measuring a property of the sample 202. Such a tool may be an inspection tool, an interferometric measurement tool 214, etc. The system 200 may include, but is not limited to, an imaging system 204. The imaging system 204 may include, but is not limited to, one or more metrology tools (e.g., the interferometric measurement tool 214). The system 200 may further include a controller 206 including one or more processors 210 and a memory 212. In one embodiment, the controller 206 is communicatively coupled to the imaging system 204. In this regard, the one or more processors 210 of the controller 206 may be configured to generate one or more control signals configured to adjust one or more characteristics of the imaging system 204 according to a recipe. Additionally, the controller 206 may be configured to receive data, including but not limited to, interferometric data related to the sample 202, from an interferometric measurement tool 214.

[0027] Additionally, the system 200 may include a sample stage 208 for positioning the sample 202 within the field of view of the imaging system 204 for determination of measurements. The sample stage 208 may include any system suitable for positioning the sample 202 within the system 200. For example, the sample stage 208 may include any combination of linear translation stages, rotational stages, tip / tilt stages, etc.

[0028] It is contemplated that the interferometric measurement tool 214 may include, but is not limited to, any tool that uses interferometric principles. For example, such a tool 214 may be any wafer geometry measurement system that can measure the geometry of a semiconductor wafer using interferometry. It is noted that the term wafer geometry may include wafer front height, back height, thickness variation, flatness, and all resulting derivatives such as shape, shape difference, nanotopography, etc. In some embodiments, a WaferSight Patterned Wafer Geometry (PWG) system from KLA Corporation may be utilized as the interferometric measurement tool 214. Further examples include multiple interferometric measurement tools 214, Michelson interferometers, Linnick interferometers, double-sided phase-shifting Fizeau interferometers, surface topology interferometers, etc. However, it should be understood that other types of interferometric measurement tools 214 may also be utilized without departing from the spirit and scope of the present disclosure.

[0029] In some embodiments, the interferometric measurement tool 214 generates the wrapped phase map 104 based on interference between the reference beam and light reflected from the surface of the sample 202 .

[0030] 3 shows a process flow diagram of a method 300 for unwrapping a phase map, according to one or more embodiments of the present disclosure. Any system or combination of systems disclosed herein may perform the steps of method 300. For example, one or more components of system 200 may perform one or more of the steps of method 300, as well as one or more additional steps.

[0031] It should be noted that the method 300 may be better understood, but is not limited to, by referring to three exemplary flow diagrams of steps 302-312 illustrated by the schematic diagrams of Figures 4A-4C, the phase maps of Figures 5A-5B, and the phase maps of Figures 6A-6B. These three examples may illustrate various embodiments and examples of phase unwrapping.

[0032] FIG. 4A shows a schematic cross-sectional view of a wrapped phase map 104 of a sample 202, according to one or more embodiments of the present disclosure. FIGs. 4B-4C show a flow diagram including an outline of steps of a method 300 for unwrapping a phase map, according to one or more embodiments of the present disclosure. FIGs. 4B-4C can be better understood by referring to the exemplary representation of an interferometer of the labeled feature 402 in FIG. 4A. In general, the phase unwrapping steps 302-312 of the present disclosure can be better understood by looking at the three examples of phase unwrapping shown in FIGs. 4A-6B.

[0033] In step 302, a wrapped phase map 104, 502 is received, as shown in Figure 5A. Note that wrapped phase map 602 is also an example of a wrapped phase map 104, 502 that may be received in step 302, and generally Figures 6A-6B provide alternative exemplary phase maps to those shown in Figures 5A-5B for the same step. Note that Figure 4B does not show a schematic diagram of step 302 or wrapped phase maps 502, 602, rather step 302 may still be present for Figure 4B, but is simply not shown.

[0034] In an embodiment, the wrapped phase map 502 received in step 302 may include features 402. For example, the features 402 may be sharp / low features, defined as those associated with a discontinuity of at least half a phase cycle (or more) from adjacent / nearby phase data, features that create ambiguous discontinuities in the wrapped phase map data, NAND features, and / or the like. For example, a wrapped phase map 502 may be received that is associated with an interferometric measurement of a sample 202 that includes patterned features.

[0035] For simplicity, the schematic diagrams of Figures 4A-4C may be referred to as "phase maps" or similar language such as "phase maps 504, 412, 604," although it should be noted that such schematic diagrams are two-dimensional.

[0036] In step 304, tilt is removed from the wrapped phase map 502, 602. Such removal may be illustrated by diagram 412 in Figure 4B, wrapped phase map 504 in Figure 5A, and wrapped phase map 604 in Figure 6A. For example, the sample 202 may be tilted such that the received wrapped phase map 502, 412, 602 exists with multiple phase cycles across the wrapped phase map 502, 412, 602 due to tilt of the sample 202 relative to the imaging system 204 of the system 200.

[0037] In some embodiments, removing the tilt (i.e., removing linear components, linear signals, dominant linear components, etc.) may be any step that removes linear components of the surface topology of the sample 202. For example, such removal may be performed mathematically and / or mechanically by sample rotation. In some embodiments, the tilt may be the overall tilt of the entire sample 202. For example, the tilt may be a single angle measured from the highest point on the outer edge of the sample 202 to a point opposite the highest point on the opposite edge of the sample 202, which is measured relative to a direction that the imaging system 204 considers to be "level", e.g., parallel to gravity, the optical axis of the imaging system 204, etc. For example, the overall tilt is illustrated by the angled schematic 426 compared to the level diagram 424.

[0038] In at least some embodiments, the tilt is determined and removed based on a directional tilt technique. For example, the tilt difference in the Y direction is Dz / Dy, and the tilt difference in the X direction is Dz / Dx. Dz / Dy can be the change in surface height in the z direction from pixel (i) to pixel (i+N), where "i" is an arbitrary pixel and N is the number of pixels. Then, the median values ​​of Dz / Dx and Dz / Dy are determined from the values ​​across the X and Y directions of the sample / wafer 202, respectively. Such median values ​​represent the tilt estimates of the sample 202 in the X and Y directions. Such median values ​​can then be used to remove the tilt of the wrapped phase map 502.

[0039] Note that the Z direction in the above examples is the direction perpendicular to the surface of the wafer such that the wafer shown in Example 2-116 of FIG. 1A lies in the XY plane.

[0040] In some embodiments, the slope may be more than a simple gradient. For example, the slope may be a varying slope, an average height map, a surface topology, a surface slope, a pseudo-thickness, a bow, etc. For example, the slope may be measured across the entire sample 202 or a portion of the sample 202. Such slopes may be mathematically smoothed, flattened, averaged, or fitted to a mathematical function / curve in some embodiments. In this regard, the slope may be used to remove one or more "bows" / warps from the sample measurements.

[0041] In one example, the pseudo-thickness may be a thickness determined by calculating the difference between the front and back topologies of the sample 202. Note that while pseudo-thickness may be used, it is not required in at least some embodiments of the present disclosure. In general, at least one drawback of using pseudo-thickness is that it may introduce inaccuracies due to artifacts from the back surface being transferred to the calculated surface topology of the front surface.

[0042] At least one benefit of some embodiments of the present disclosure is that no pseudo-thickness is required during the tilt removal step 304, thereby potentially allowing for avoidance of transfer of inaccuracies from the back surface.

[0043] In an optional step (not shown), removing the tilt from the wrapped phase map 502 includes extracting 502 a surface profile measurement from the wrapped phase map, removing a linear signal from the surface profile measurement. For example, the tilt may be measured by the imaging system 204 by any technique, and the wrapped phase map 502 may be mathematically adjusted to remove the tilt.

[0044] In an optional step (not shown), removing the gradient from the wrapped phase map 502 includes: extracting 502 a surface gradient measurement from the wrapped phase map; and removing the linear signal from the surface gradient measurement.

[0045] In an optional step (not shown), removing the gradient from the wrapped phase map 502 includes: extracting 502 a thickness measurement from the wrapped phase map; and removing the linear signal from the thickness measurement.

[0046] In step 306, features 402 in the wrapped phase map 504 are detected and smoothed. For example, smoothing the features 402 may include replacing the features 402 with the background 506.

[0047] In some embodiments, the feature 402 may be illustrated by the feature 402 in FIG. 4A, although it should be noted that FIG. 4A may be an exaggerated view for illustrative purposes and the feature 402 may be of any shape or height. In embodiments, such feature 402 corresponds to at least some of the patterned features of the sample 202. For example, a physical patterned NAND feature of the sample 202 may correspond to the detected feature 402. For example, since the feature 402 may represent (e.g., correspond to or be associated with) a physical patterned NAND feature, the data / region of the phase map associated with the feature 402 may be associated with the physical patterned NAND feature. In embodiments, the feature 402 may be a sharp / low feature, a feature that causes a difficult-to-resolve phase ambiguity, etc. For example, the feature 402 may be associated with a gradual phase change in the wrapped phase map 504. For example, detecting the feature 402 in the wrapped phase map 504 may include detecting a gradual phase change in the wrapped phase map 504 that is greater than a selected threshold (as shown in FIG. 4B). Such features 402 may be detected using various techniques such as outlier detection combined with outlier low-pass filtering, including median filtering, local averaging, and / or the like. Other techniques include local polynomial fitting, and the like. Further techniques include pattern-based outlier search based on prior knowledge, such as pre-patterned wafer topology measurements, prior knowledge of wafer designs, die layouts, and / or the like. For example, the wafer sample 202 may be designed to have sharp features 402, and such detection of features 402 may be based on prior knowledge. For example, a height threshold may be set, and features 402 of the wafer / die design that meet / exceed such threshold may be identified, and their corresponding locations may be identified.

[0048] In some embodiments, step 306 may include sub-steps 306 illustrated by schematic diagrams 414-418, phase maps 506-512, and phase maps 606-612. For example, such sub-step 306 is labeled 306 in Figures 4B, 5A, and 6A and may include at least the following sub-steps: background generating sub-step 306, difference calculating sub-step 306, feature removing sub-step 306, and / or background filling sub-step 306.

[0049] In the background generation sub-step 306, a background 506, 414, 606, sometimes referred to as a background signal or the like, is generated. The background 506, 414, 606 may be relatively smooth relative to the wrapped phase map 504, 412, 604. In one example, the background 506, 414, 606 is generated based on a priori design knowledge of the sample 202. In this regard, the background 506, 414, 606 may be the expected shape / topology of the sample 202 without unexpected sharp discontinuities.

[0050] In another example, the background 506, 414, 606 may correspond to the surface topology of the sample 202 when the sample has no or minimal features 402. For example, the background 506, 414, 606 may be limited to spatial frequencies below a threshold selected to exclude features 402. For example, the background 506, 414, 606 may represent a slowly changing topology of the sample 202 based on one or more measured layer heights of the sample 202. For example, such a topology may be estimated based on measured heights of die edges / streets / cut lines in some embodiments. In this regard, specific background topology information such as one or more arcs may be generated, each arc spanning one or more dies of the sample 202. For example, in an embodiment, the background signal 506, 414, 606 is generated based on the wrapped phase map 504, 412, 604. In some embodiments, the background 506, 414, 606 is in a wrapped state. It should be noted that the background 506, 414, 606 (or portions thereof) may be referred to interchangeably as the "background" and other similar terms for purposes of this disclosure.

[0051] In the subtraction sub-step 306, a subtraction 508, 416, 608 is generated based on a computable difference between the wrapped phase map 504, 412, 604 and the generated background 506, 414, 606. The subtraction 508, 416, 608 may be a flat (or nearly flat) phase map, where certain background topology information, e.g., curvature of the wrapped phase map 504, 412, 604, is corrected, but the features 402 are still represented.

[0052] In some embodiments, the difference 508, 416, 608 is used to perform detection of the feature 402. For example, as shown in FIG. 4B, a threshold may be set and used to determine a corresponding location of the sample 202 where the feature 402 is located. The corresponding location may also be determined using any other method for determining the feature 402. For example, the feature 402 may be determined based on the chip design of the sample 202. In one example, the feature 402 is detected using a classical adaptive threshold technique. For example, the threshold may vary as a function of the background topology 414.

[0053] In the feature removal sub-step 306, a pre-corrected wrapped phase map 510, 610 may be determined / calculated using the corresponding positions of the features 402. For example, the features 402 at the corresponding positions may be removed as indicated by white pixels in the pre-corrected wrapped phase map 510, 610.

[0054] In the background fill sub-step 306, the background 506, 414, 606 is used to fill / replace corresponding locations to generate a modified wrapped phase map 512, 418, 612. In this regard, sharp features 402 that may cause a failure of the overall unwrapping of the phase map may be removed and replaced with portions of the background 506, 414, 606 at corresponding locations that closely match the surrounding phase map data. In this regard, step 306 may be referred to as "flattening", "detecting and flattening", etc.

[0055] In step 308, a global phase unwrapping technique is applied to the modified wrapped phase map 512, 418, 612. For example, the phase of the modified wrapped phase map 512, 418, 612 may be unwrapped. In an embodiment, such global phase unwrapping produces a temporary unwrapped phase map 514, 422, 614. Note that step 308 may continue (directly and / or indirectly) from step 306, and that step 308 is only shown in a separate figure for purposes of clarity and lack of space.

[0056] In this regard, the modified wrapped phase map 512, 418, 612 may be unwrapped to generate such a temporary unwrapped phase map 514, 422, 614. Any unwrapping technique may be used, such as, for example, but not limited to, path finding techniques, preconditioned conjugate gradient techniques, region growing algorithms, discontinuity minimization algorithms, minimum Lp-norm and least squares algorithms, quality-guided and network flow algorithms, branch-cut algorithms, flood-fill algorithms, and the like. In this regard, a (more accurate) temporary unwrapped phase map 514, 422, 614 may be generated and "failures" (e.g., failure 124 shown in FIG. 1B) caused by ambiguity in the features 402 may be prevented.

[0057] In step 310, a local phase unwrapping technique is applied to restore the phase of the feature 402 at the corresponding location of the temporary unwrapped phase map 514, 422, 614. Step 310 results in the phase map 516, 424, 616. In an embodiment, in a sense, the feature 402 can be "added back" (replacing the background) to the temporary unwrapped phase map 514, 422, 614 at the corresponding location, and a local phase unwrapping technique (e.g., phase unwrapping is applied individually at each corresponding location and / or multiple corresponding locations) can be applied to the wrapped feature 402 (the previously removed feature 402) to generate a fully unwrapped feature-accurate version of the phase map of the sample 202. For example, applying local phase unwrapping to restore the data of the detected feature 402 removed in step 306 may include replacing the background 506, 414, 606 with the feature 402 at the corresponding location. In this regard, the risk of areas not associated with features 402 not being properly unwrapped may be reduced since they have already been unwrapped in global unwrapping step 308. For example, method 300 may be configured in step 310 to keep regions other than the corresponding location intact.

[0058] Any local phase unwrapping technique may be utilized in step 310. For example, local phase unwrapping techniques such as those disclosed in U.S. Patent 11,035,665 (June 15, 2021), which is incorporated by reference in its entirety, may be utilized. For example, selection and unwrapping of a subset of pixels and associated steps, as disclosed in U.S. Patent 11,035,665, may be utilized herein to unwrap various corresponding locations of the phase map to achieve "local unwrapping."

[0059] In step 312 , the gradient is reapplied to the temporary unwrapped phase map 514 , 422 , 614 to generate the output unwrapped phase map 518 , 426 , 618 .

[0060] In an optional step (not shown), a height map (not shown) is generated based on the output unwrapped phase map 518, 426, 618. For example, the height map may be used in a metrology analysis process.

[0061] Figure 7A illustrates an unwrapped phase map 700 of a sample 202 in accordance with one or more embodiments of the present disclosure, and Figure 7B illustrates a different unwrapped phase map 702 of the sample 202 of Figure 7A. For example, the unwrapped phase map 702 of Figure 7B may be obtained using at least some embodiments of the present disclosure as compared to the partially failed unwrapped phase map 700 of Figure 7A using other techniques. For example, regions of failed unwrap 704 of phase ambiguity are shown.

[0062] Figure 8A illustrates a sample unwrapped phase map 800, and Figure 8B illustrates a different unwrapped phase map 802 of the sample of Figure 8A, in accordance with one or more embodiments of the present disclosure. For example, the unwrapped phase map 802 of Figure 8B may be obtained using at least some embodiments of the present disclosure, as compared to the partially failed phase map 800 of Figure 8A using other techniques. For example, regions of failed unwrap 804 of phase ambiguity are shown.

[0063] Referring again to FIG. 2, embodiments of various components are described in further detail.

[0064] As previously described herein, the controller 206 of the system 200 may include one or more processors 210 and a memory 212. The memory 212 may include program instructions configured to cause the one or more processors 210 to perform various steps of the present disclosure.

[0065] In another embodiment, the display of the user interface 216 may be configured to display data of the system 200 to a user.

[0066] As previously described herein, the one or more processors 210 of the controller 206 may be communicatively coupled to the memory 212, and the one or more processors 210 may be configured to execute a set of program instructions maintained in the memory 212, which may be configured to cause the one or more processors 210 to perform various functions and steps of the present disclosure.

[0067] It is noted herein that one or more components of system 200 may be communicatively coupled to various other components of system 200 in any manner known in the art. For example, one or more processors 210 may be communicatively coupled to each other and the other components via wireline (e.g., copper wire, fiber optic cable, etc.) or wireless connections (e.g., RF coupling, IR coupling, WiMax, Bluetooth, 3G, 4G, 4G LTE, 5G, etc.). As another example, controller 206 may be communicatively coupled to one or more components of system 200 via any wired or wireless connection known in the art.

[0068] In one embodiment, the one or more processors 210 may include any one or more processing elements known in the art. In this sense, the one or more processors 210 may include any microprocessor-type device configured to execute software algorithms and / or instructions. In one embodiment, the one or more processors 210 may be comprised of a desktop computer, a mainframe computer system, a workstation, an image computer, a parallel processor, or other computer system (e.g., a networked computer) configured to execute programs configured to operate the system 200 as described throughout this disclosure. It should be appreciated that the steps described throughout this disclosure may be performed by a single computer system, or alternatively, by multiple computer systems. Furthermore, it should be appreciated that the steps described throughout this disclosure may be performed in any one or more of the one or more processors 210. In general, the term "processor" may be broadly defined to encompass any device having one or more processing elements that execute program instructions from memory 212. Additionally, different subsystems of system 200 (e.g., interferometric measurement tool 214, controller 206, user interface 216, etc.) may include processors or logic elements suitable for performing at least some of the steps described throughout this disclosure. Thus, the above description should not be construed as a limitation on the present disclosure, but merely as an example.

[0069] The memory 212 may include any storage medium known in the art suitable for storing program instructions executable by the associated processor(s) 210 and data received from the system 200. For example, the memory 212 may include a non-transitory storage medium. For example, the memory 212 may include, but is not limited to, a read-only memory (ROM), a random access memory (RAM), a magnetic or optical memory device (e.g., disk), a magnetic tape, a solid-state drive, and the like. Furthermore, it should be noted that the memory 212 may be housed in a common controller housing with the processor(s) 210. In alternative embodiments, the memory 212 may be located remotely relative to the physical locations of the processors 210, the controller 206, and the like. In another embodiment, the memory 212 holds program instructions for causing the processor(s) 210 to perform various steps described throughout this disclosure.

[0070] In one embodiment, the user interface 216 is communicatively coupled to the controller 206. The user interface 216 may include, but is not limited to, one or more desktops, tablets, smartphones, smart watches, etc. In another embodiment, the user interface 216 includes a display used to display data of the system 200 to a user. The display of the user interface 216 may include any display known in the art. For example, the display may include, but is not limited to, a liquid crystal display (LCD), an organic light emitting diode (OLED)-based display, or a CRT display. Those skilled in the art should recognize that any display device capable of integration with the user interface 216 is suitable for implementation in the present disclosure. In another embodiment, a user may input selections and / or commands in response to data displayed to the user via a user input device of the user interface 216.

[0071] All of the methods described herein may include storing results of one or more steps of the method embodiments in memory 212. The results may include any of the results described herein and may be stored in any manner known in the art. Memory 212 may include any memory described herein, or any other suitable storage medium known in the art. After the results are stored, they can be accessed in memory 212, used by any of the method or system embodiments described herein, formatted for display to a user, used by another software module, method, or system, etc. Additionally, the results may be stored "permanently," "semi-permanently," "temporarily," or for a period of time. For example, memory 212 may be a random access memory (RAM), and the results may not necessarily persist in memory indefinitely.

[0072] It is further contemplated that each of the method embodiments described above may include any other step(s) of any other method described herein. In addition, each of the method embodiments described above may be performed by any of the systems described herein.

[0073] Those skilled in the art will recognize that the component operations, devices, objects, and their accompanying discussion described herein are used as examples for conceptual clarity, and that various configuration modifications are contemplated. Thus, as used herein, the specific examples described and the accompanying discussion are intended to be representative of their more general classes. In general, the use of any specific example is intended to represent its class, and non-inclusion of specific components, operations, devices, and objects should not be construed as limiting.

[0074] As used herein, directional terms such as "top", "bottom", "over", "under", "upper", "upward", "lower", "down", "downward", and the like are intended to provide relative positions for purposes of description and are not intended to indicate an absolute frame of reference. Various modifications to the described embodiments will be apparent to those skilled in the art, and the general principles defined herein may be applied to other embodiments.

[0075] With respect to the use of virtually any plural and / or singular term herein, those of skill in the art can convert from plural to singular and / or from singular to plural as appropriate to the context and / or application. The various singular / plural permutations are not expressly set forth herein for ease of understanding.

[0076] The subject matter described herein illustrates different components that are sometimes included within or connected to other components. It should be understood that such depicted architectures are merely exemplary, and that in fact many other architectures that achieve the same functionality may be implemented. In a conceptual sense, any arrangement of components to achieve the same functionality is effectively "associated" such that the desired functionality is achieved. Thus, any two components herein that are combined to achieve a particular functionality can be considered to be "associated" with each other such that the desired functionality is achieved, regardless of the architecture or intermediate components. Similarly, any two components so associated can also be considered to be "connected" or "coupled" with each other to achieve the desired functionality, and any two components capable of being so associated can also be considered to be "couplable" with each other to achieve the desired functionality. Specific examples of what can be coupled include, but are not limited to, physically coupleable and / or physically interacting components and / or wirelessly interactable and / or wirelessly interacting components and / or logically interacting and / or logically interacting components.

[0077] It should further be understood that the present invention is defined by the appended claims. In general, those skilled in the art will understand that the terms used in this specification and in particular in the appended claims (e.g., the body of the appended claims) are generally intended as "open" terms (e.g., the term "including" should be interpreted as "including but not limited to", the term "having" should be interpreted as "having at least", the term "includes" should be interpreted as "includes but not limited to", etc.). Those skilled in the art will further understand that if a specific number of claim recitations introduced are intended, such intention will be explicitly stated in the claim, and in the absence of such recitation, no such intention exists. For example, as an aid to understanding, the following appended claims can include the use of the introductory phrases "at least one" and "one or more" to introduce the claim recitation. However, the use of such phrases should not be interpreted as meaning that the introduction of a claim recitation with the indefinite article "a" or "an" limits any particular claim that includes such an introduced claim recitation to an invention that includes only one such recitation. The same applies to the use of clear articles used to introduce claim recitations, even when the same claim includes the introductory phrase "one or more" or "at least one" and an indefinite article such as "a" or "an" (e.g., "a" and / or "an" should typically be interpreted to mean "at least one" or "one or more"). Also, those skilled in the art will recognize that even when a specific number of introduced claim recitations is explicitly recited, such recitation should typically be interpreted to mean at least the recited number (e.g., a bare recitation of "two recitations" without other modifiers typically means at least two recitations, or two or more recitations).Furthermore, in instances where a conventional expression similar to "such as at least one of A, B, and C" is used, such a configuration is generally intended in the sense that one of ordinary skill in the art would understand the conventional expression (e.g., "a system having at least one of A, B, and C" includes, but is not limited to, systems having only A, only B, only C, A and B together, A and C together, B and C together, and / or A, B, and C together). In instances where a conventional expression similar to "such as at least one of A, B, or C" is used, such a configuration is generally intended in the sense that one of ordinary skill in the art would understand the conventional expression (e.g., "a system having at least one of A, B, or C" includes, but is not limited to, systems having only A, only B, only C, A and B together, A and C together, B and C together, and / or A, B, and C together). Those skilled in the art will further appreciate that virtually any disjunctive word and / or phrase presenting two or more alternative terms, wherever in the description, claims, or drawings, should be understood to contemplate the possibility of including one of the terms, either of the terms, or both terms. For example, the phrase "A or B" will be understood to include the possibilities of "A" or "B" or "A and B."

[0078] It is believed that the present disclosure and many of its attendant advantages will be understood from the foregoing description, and it will be apparent that various changes can be made in the form, construction and arrangement of the elements without departing from the disclosed subject matter or sacrificing all of its material advantages. The forms described are merely illustrative, and it is the intent of the following claims to embrace and include such modifications. It is to be understood, further, that the invention is defined by the appended claims.

Claims

1. 1. A weighing system comprising: a controller communicatively coupled to the interferometric measurement tool; the controller includes one or more processors configured to execute program instructions; The one or more processors execute the program instructions to: receiving a wrapped phase map associated with an interferometric measurement of a sample including patterned features; removing gradients from the wrapped phase map; generating a background; detecting features in the wrapped phase map, the features in the wrapped phase map corresponding to at least some of the patterned features of the sample; replacing the phase of the feature with the background at corresponding locations in the wrapped phase map to generate a modified wrapped phase map; unwrapping the modified wrapped phase map using global phase unwrapping to generate a temporary unwrapped phase map; applying a local phase unwrapping to restore the phase of features in the temporary unwrapped phase map at corresponding locations; reapplying the gradient to the temporary unwrapped phase map to generate an output unwrapped phase map; To carry out Weighing system.

2. 2. The weighing system of claim 1, Removing the gradient from the wrapped phase map may include extracting surface profile measurements from the wrapped phase map; removing a linear signal from said surface profile measurements; Including, Weighing system.

3. 2. The weighing system of claim 1, Removing the gradient from the wrapped phase map may include extracting thickness measurements from the wrapped phase map; removing a linear signal from said thickness measurements; Including, Weighing system.

4. 2. The weighing system of claim 1, the background is restricted to spatial frequencies below a selected threshold, the selected threshold being selected to exclude the features; Weighing system.

5. 2. The weighing system of claim 1, The background is based on prior knowledge of the sample. Weighing system.

6. 2. The weighing system of claim 1, Detecting features in the wrapped phase map includes: detecting a gradual phase change in the wrapped phase map that is greater than a selected threshold; Including, Weighing system.

7. 2. The weighing system of claim 1, applying the local phase unwrapping to restore the phase of a feature includes replacing the background at corresponding locations with the feature and unwrapping the feature. Weighing system.

8. 1. A weighing system comprising: An interference measurement tool; a controller communicatively coupled to the interferometry tool, the controller including one or more processors configured to execute program instructions on the one or more processors; Including, The one or more processors execute the program instructions to: receiving a wrapped phase map from the interferometric tool, the wrapped phase map corresponding to an interferometric measurement of a sample including patterned features; removing gradients from the wrapped phase map; Generate the background, Detecting features in the wrapped phase map; replacing the phase of the feature with the background at a corresponding location in the wrapped phase map to generate a modified wrapped phase map; unwrapping the modified wrapped phase map using global phase unwrapping to generate a temporary unwrapped phase map; applying a local phase unwrapping to restore the phase of said feature in the temporary unwrapped phase map at the corresponding location; reapplying the gradient to the temporary unwrapped phase map to generate an output unwrapped phase map. Weighing system.

9. 9. A weighing system according to claim 8, comprising: the interferometry tool generating the wrapped phase map based on interference of a reference beam with light reflected from a surface of the sample. Weighing system.

10. 9. A weighing system according to claim 8, comprising: Removing the gradient from the wrapped phase map may include Extracting surface profile measurements from the wrapped phase map; removing a linear signal from the surface profile measurements; Including, Weighing system.

11. 9. A weighing system according to claim 8, comprising: Removing the gradient from the wrapped phase map may include Extracting a surface slope measurement from the wrapped phase map; removing a linear signal from the surface slope measurements; Including, Weighing system.

12. 9. A weighing system according to claim 8, comprising: Removing the gradient from the wrapped phase map may include Extracting thickness measurements from the wrapped phase map; removing a linear signal from said thickness measurements; Including, Weighing system.

13. 9. A weighing system according to claim 8, comprising: the background is restricted to spatial frequencies below a selected threshold, the selected threshold being selected to exclude the features; Weighing system.

14. 9. A weighing system according to claim 8, comprising: The background is based on prior knowledge of the sample. Weighing system.

15. 9. A weighing system according to claim 8, comprising: Detecting the feature in the wrapped phase map includes: detecting a gradual phase change in the wrapped phase map that is greater than a selected threshold; Including, Weighing system.

16. 9. A weighing system according to claim 8, comprising: Applying the local phase unwrapping to restore the phase of the feature includes: replacing the background at corresponding locations with the features and unwrapping the features. Weighing system.

17. A weighing method comprising the steps of: receiving a wrapped phase map associated with an interferometric measurement of a sample including patterned features; removing gradients from the wrapped phase map; generating a background; detecting features in the wrapped phase map, the features in the wrapped phase map corresponding to at least some of the patterned features of the sample; replacing the phase of the feature with the background at corresponding locations in the wrapped phase map to generate a modified wrapped phase map; unwrapping the modified wrapped phase map using global phase unwrapping to generate a temporary unwrapped phase map; applying local phase unwrapping to restore the phase of features in the temporarily unwrapped phase map at corresponding locations; reapplying a gradient to the temporary unwrapped phase map to generate an output unwrapped phase map; Including, Weighing method.

18. 18. A weighing system according to claim 17, comprising: Removing the gradient from the wrapped phase map extracts a surface profile measurement from the wrapped phase map; removing a linear signal from the surface profile measurements; Including, Weighing method.

19. 18. A weighing system according to claim 17, comprising: Removing the gradient from the wrapped phase map may include Extracting a surface slope measurement from the wrapped phase map; removing a linear signal from the surface slope measurements; Including, Weighing method.

20. 18. A weighing system according to claim 17, comprising: Removing the gradient from the wrapped phase map may include Extracting thickness measurements from the wrapped phase map; removing a linear signal from said thickness measurements; Including, Weighing method.

21. 18. A weighing system according to claim 17, comprising: the background is restricted to spatial frequencies below a selected threshold, the selected threshold being selected to exclude the features; Weighing method.

22. 18. A weighing system according to claim 17, comprising: The background is based on prior knowledge of the sample. Weighing method.

23. 18. A weighing system according to claim 17, comprising: Detecting the feature in the wrapped phase map includes: detecting a gradual phase change in the wrapped phase map that is greater than a selected threshold; Including, Weighing method.

24. 18. A weighing system according to claim 17, comprising: Applying the local phase unwrapping to restore the phase of the feature includes: replacing the background at corresponding locations with the features and unwrapping the features. Weighing method.

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