Measurement device and measurement method

Abstract

To provide a measurement device and a measurement method with which it is possible to model the three-dimensional shape of a deep hole having a complex cross sectional shape with good accuracy while reducing the number of parameters.SOLUTION: The measurement device comprises an X-ray irradiation unit 21, an X-ray detection unit 23 for detecting a scattered X-ray generated from a specimen 7, and an analysis unit 24 for analyzing the diffraction image obtained by photoelectrically converting the scattered X-ray and estimating the three-dimensional shape of the specimen 7. The analysis unit 24 extracts a feature quantity from known shape information and determines a plurality of shape parameters that express a three-dimensional shape, and calculates the theoretical scattering intensity of the scattered X-ray when the values of the shape parameters are changed. The analysis unit 24 also creates a regression model of a relationship between the difference between measured and theoretical scattering intensities and the shape parameters. Furthermore, the analysis unit 24 estimates, while repeatedly changing shape parameter candidate values, the values of shape parameters with which the difference between the measured and theoretical scattering intensities is minimum.SELECTED DRAWING: Figure 5

Description

[Technical field]

[0001] The present embodiment relates to a measurement apparatus and a measurement method. [Background technology]

[0002] Measurement devices that use the Transmission Small Angle X-ray Scattering (T-SAXS) technique are known as devices for measuring the depth and three-dimensional shape of the sidewalls of deep holes and trenches formed in film formation sites on semiconductor substrates. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] JP 2020-176988 A Summary of the Invention [Problem to be solved by the invention]

[0004] An object of the present embodiment is to provide a measuring device and a measuring method that can accurately model the three-dimensional shape of a deep hole having a complex cross-sectional shape while reducing the number of parameters. [Means for solving the problem]

[0005] The measurement device of this embodiment includes an X-ray irradiation unit that irradiates an object with X-rays, an X-ray detection unit that detects scattered X-rays emitted from the object by the irradiation of the X-rays, and an analysis unit that analyzes a diffraction image obtained by photoelectrically converting the scattered X-rays, and estimates the surface contour shape of a measurement region in the object that is irradiated with the X-rays.

[0006] The analysis unit extracts features from known shape information to determine a plurality of shape parameters used to express the surface contour shape, and calculates the theoretical scattering intensity of the scattered X-rays when values ​​of the plurality of shape parameters are changed. The analysis unit also calculates a difference between a measured scattering intensity, which is the intensity of the scattered X-rays detected by the X-ray detection unit, and the theoretical scattering intensity, and creates a regression model of the relationship between the value of the shape parameter and the difference for each of the shape parameters. Furthermore, the analysis unit extracts at least one shape parameter candidate value that reduces the difference from the regression model, calculates the theoretical scattering intensity for the shape parameter candidate value, and estimates the value of the shape parameter that minimizes the difference between the measured scattering intensity and the theoretical scattering intensity while repeatedly changing the shape parameter candidate value. [Brief description of the drawings]

[0007] [Figure 1] FIG. 1 is a schematic diagram illustrating an example of the configuration of a T-SAXS measurement apparatus. [Diagram 2] FIG. 1 is a schematic diagram illustrating an example of the configuration of a T-SAXS measurement apparatus. [Diagram 3] FIG. 1 is a schematic diagram illustrating an example of the configuration of a T-SAXS measurement apparatus. [Figure 4] FIG. 2 is a diagram illustrating the relationship between the angle of incidence of X-rays and diffraction patterns. [Diagram 5] FIG. 1 is a block diagram illustrating an example of the configuration of a measurement apparatus according to an embodiment. [Figure 6] 1 is a cross-sectional view of a partial area of ​​a semiconductor memory device having a memory cell array of a NAND memory having a three-dimensional structure. [Figure 7] 1A to 1C are schematic cross-sectional views illustrating a step of forming a memory hole. [Figure 8] 11 is a flowchart illustrating an example of a procedure for forming a memory hole. [Figure 9] FIG. 13 is a diagram for explaining shape parameters in a comparative example. [Figure 10] 11 is a flowchart illustrating an example of a measurement method in a comparative example. [Figure 11] FIG. 11 is a diagram for explaining an example of a measurement result in a comparative example. [Figure 12] 6A and 6B are diagrams illustrating the relationship between the difference between the theoretical value and the measured value and the value of the shape parameter. [Figure 13] 13A and 13B are diagrams for explaining the difference between the measurement results and the shape of a machined hole in a comparative example. [Figure 14A] 4 is a flowchart illustrating an example of a measurement method according to the embodiment. [Figure 14B] 10 is a flowchart illustrating another example of a measurement method according to the embodiment. [Figure 15] FIG. 1 is a diagram for explaining principal component analysis. [Figure 16A] FIG. 11 is a diagram for explaining an example of a difference calculation result between a measured value and a theoretical value. [Figure 16B] FIG. 11 is a diagram for explaining an example of a difference calculation result between a measured value and a theoretical value. [Figure 17] FIG. 13 is a diagram for explaining a regression model that estimates a difference from values ​​of shape parameters. [Figure 18] 5A and 5B are diagrams for explaining shape parameter value candidates; [Figure 19] FIG. 13 is a diagram illustrating an example of an updated regression model. [Figure 20] 13A to 13C are diagrams illustrating shape representation in the second embodiment. [Figure 21] A comparison of the geometric representation of a machined hole before and after conversion to a polar coordinate system. [Figure 22] FIG. 13 is a diagram showing an example of the relationship between the distance r of a processed hole and processing time. [Diagram 23] 11A and 11B are diagrams for explaining the relationship between the difference in remaining film thickness of a mask material and the difference in depth of a memory hole. [Figure 24] 13 is a flowchart illustrating an example of a measurement method according to the fourth embodiment. [Diagram 25] 13A to 13C are views for explaining an example of a measurement result obtained by a measurement method according to a fourth embodiment. [Figure 26] FIG. 13 is a diagram for explaining rank calculation. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0008] Hereinafter, an embodiment will be described with reference to the drawings. (First embodiment) The measuring device of the embodiment is, for example, a measuring device (T-SAXS measuring device) that measures the three-dimensional shape of a deep hole having a complex cross-sectional shape from the X-ray diffraction scattering intensity by transmission small-angle X-ray scattering.

[0009] The T-SAXS measurement device 2 is a device that measures the three-dimensional shape of a periodic pattern formed on the surface of a specimen using transmitted X-rays. Using multiple diffraction images (SAXS image group) acquired by changing the angle of incidence of X-rays on the specimen, the average three-dimensional shape of the periodic pattern formed within a spot size (for example, about 50 to 1000 μm square) can be measured.

[0010] 1 to 3 are schematic diagrams for explaining an example of the configuration of a T-SAXS measurement device. As shown in Fig. 1, in the T-SAXS measurement device 2, X-rays emitted from an X-ray source 211 are converged to a beam spot by an X-ray converging mechanism 213, and the beam spot is irradiated onto a surface of a specimen (a semiconductor substrate having a periodic pattern such as holes and grooves formed on its surface) 7 held on a measurement stage 22.

[0011] 2, the X-rays irradiated to the subject 7 are scattered by a pattern formed on the surface of the subject 7. The scattered X-rays are converted by the detector 232 into a signal (diffraction image) indicating the characteristics of the subject 7.

[0012] As shown in FIG. 3, the specimen 7 is set so as to be rotatable about either one or both of two orthogonal directions (x direction, y direction) parallel to the surface of the specimen 7 as a rotation axis. The surface of the specimen 7 refers to the surface of a semiconductor substrate constituting the specimen 7. By irradiating the specimen 7 with X-rays while rotating the specimen 7 about the set rotation axis, the incident angle θi of the X-rays on the specimen 7 can be adjusted. The T-SAXS measurement device 2 acquires multiple diffraction images (diffraction image group) while gradually changing the incident angle θi. FIG. 4 is a diagram for explaining the relationship between the X-ray incident angle and the diffraction image. The acquired diffraction image group is compared with multiple diffraction image groups calculated by simulating the intensity distribution of X-ray diffraction light corresponding to various three-dimensional shape patterns. A diffraction image group with a high degree of coincidence is extracted from the multiple diffraction image groups, and the three-dimensional shape pattern corresponding to this diffraction image group is estimated to be a pattern formed on the surface of the specimen 7.

[0013] Fig. 5 is a schematic block diagram for explaining an example of the configuration of a measurement device of an embodiment. The measurement device of the embodiment, i.e., a T-SAXS measurement device 2, includes an X-ray irradiation unit 21, a measurement stage 22, an X-ray detection unit 23, and an analysis unit 24. The T-SAXS measurement device 2 also includes a transport unit 25, a position measurement unit 26, and an operation control unit 27. In Fig. 5, the thick lines indicate the transport path of the specimen 7. The dotted lines indicate the optical paths of the irradiated light and the diffracted light. The solid lines indicate signal transmission paths for transmitting data and information (electrical signals).

[0014] The X-ray irradiation unit 21 is mainly composed of an X-ray source 211, a shutter 212, and an X-ray focusing mechanism 213. The X-ray source 211 is a part that generates X-rays having a predetermined wavelength and energy. The X-ray source 211 is configured, for example, as an electron beam source configured to excite X-rays by irradiating a solid or liquid target with particles. The shutter 212 is installed between the measurement stage 22 and the X-ray source 211. The shutter 212 can be opened and closed, and is controlled by the operation control unit 27. When the shutter 212 is in an open state, the measurement stage 22 is irradiated with X-rays emitted from the X-ray source 211. When the shutter 212 is in a closed state, the optical path of the X-rays is blocked, so that the measurement stage 22 is not irradiated with X-rays.

[0015] The X-ray converging mechanism 213 is mainly composed of a first slit 213a, a mirror 213b, and a second slit 213c. The X-ray converging mechanism 213 is installed between the shutter 212 and the measurement stage 22. The first slit 213a is used to limit the angular spread of the emitted X-rays. The mirror 213b converges the emitted X-rays and suppresses the beam size. The second slit 213c is arranged close to the measurement stage 22 and further narrows the beam size of the emitted X-rays. That is, the X-ray converging mechanism 213 is provided to prevent the scattered rays of the emitted X-rays from being irradiated to the subject and to narrow the irradiation range of the X-rays on the subject 7. The X-rays narrowed by the X-ray converging mechanism 213 are irradiated to the imaging area of ​​the subject 7 installed on the measurement stage 22.

[0016] The measurement stage 22 is a member that supports the specimen 7 rotatably around a rotation axis in the x direction and / or the y direction. The measurement stage 22 is composed of, for example, a support shaft made of a cylindrical or rod-shaped member, and a chuck that is a hollow ring-shaped member. The chuck is rotatably engaged with one end of the support shaft.

[0017] The measurement stage 22 can be moved in the x-direction and / or y-direction and in a direction perpendicular to the x-direction and y-direction (z-direction) by a driving means such as a motor (not shown). By moving the measurement stage 22 in the x-direction and / or y-direction, it is possible to move the imaging region 7a, which is the range of the specimen 7 irradiated with X-rays. By moving the measurement stage 22 in the z-direction, it is possible to change the focus of the diffraction image of the specimen 7 detected by the X-ray detection unit 23. With the specimen 7 held by the chuck, the support shaft and the measurement stage are configured to be operable by a driving means such as a motor (not shown) so that the center of rotation of the specimen 7 coincides with an axis perpendicular to the wafer surface at the measurement point.

[0018] The X-ray detection unit 23 is mainly composed of a vacuum pipe 231 and a detector 232. The vacuum pipe 231 is a columnar member with the inside kept in a vacuum state, and is disposed between the measurement stage 22 and the detector 232. Diffracted X-rays generated from the specimen 7 placed on the measurement stage 22 enter the vacuum pipe 231 from one end face thereof, pass through the vacuum pipe 231, and are emitted from the other end face thereof toward the detector 232. The vacuum pipe 231 is provided to prevent the diffracted X-rays from being affected by disturbances due to the environment (such as air disturbances), and to prevent noise from being superimposed on the diffraction image.

[0019] The detector 232 receives the diffracted X-rays generated from the subject 7 and generates a diffraction image. The detector 232 is composed of, for example, a plurality of semiconductor detection elements (such as solid-state imaging elements) arranged in a two-dimensional array. As the semiconductor detection elements, for example, a CCD (charge-coupled device) or a CMOS image sensor is used. The diffracted X-rays generated by the irradiated X-rays in the imaging region of the subject 7 are photoelectrically converted by the semiconductor detection elements arranged in the projection region of the detector 232 and output as an imaging signal (diffraction image).

[0020] The analysis unit 24 compares the diffraction image group (a plurality of diffraction images obtained by changing the rotation angle of the object 7) output from the detector 232 with a diffraction image group calculated in advance by simulating the intensity distribution of X-ray diffracted light corresponding to various three-dimensional shape patterns. A diffraction image group having a high degree of agreement is extracted from the plurality of diffraction image groups, and the three-dimensional shape pattern corresponding to this diffraction image group is estimated to be a pattern formed on the surface of the subject 7. The analysis unit 24 includes a central processing unit (CPU) 241 and a memory (RAM) 242. The operation of estimating the three-dimensional shape pattern is performed in software, for example, by storing the program in advance in the memory 242 and executing it in the CPU. Furthermore, the operation of generating the three-dimensional shape pattern may be performed by one or more processors configured as hardware. For example, the processor may be a processor configured as an electronic circuit, or may be a processor configured as an integrated circuit such as an FPGA (Field Programmable Gate Array). Furthermore, the analysis unit 24 may include a database 243 that stores a diffraction image group calculated in advance by simulating the intensity distribution of X-ray diffracted light corresponding to various three-dimensional shape patterns.

[0021] The transport section 25 includes a load port 251, a transport unit 252, and a pre-aligner 253. The load port 251 is an entrance provided for inserting the specimen 7 into the T-SAXS measurement apparatus 2. The transport unit 252 is a part that automatically transports the specimen 7 to each part in the T-SAXS measurement apparatus 2. The pre-aligner 253 aligns a reference position (e.g., a notch, an orientation flat, etc.) provided on the specimen 7 to a desired position when the specimen 7 is placed on the measurement stage 22.

[0022] When the specimen 7 is set on the measurement stage 22 of the T-SAXS measurement instrument 2, the transport unit 25 operates as follows. When a container containing the specimen 7 is placed on the load port 251, the transport unit 252 picks up the specimen 7 from the container and moves it to the pre-aligner 253. In the pre-aligner 253, the specimen 7 is aligned in the x and y directions and in the rotation direction about the center of the specimen 7 in the xy plane, and then the transport unit 252 picks up the specimen 7 again and places it on the measurement stage 22. When the acquisition of the diffraction image group is completed and the specimen 7 is to be removed from the T-SAXS measurement instrument 2, the transport unit 252 picks up the specimen 7 from the measurement stage 22 and moves it into the container placed on the load port 251. The above-mentioned operation of the transport unit 25 is controlled by the operation control unit 27.

[0023] The position measurement unit 26 has an alignment camera 261 and a subject tilt measurement unit 262. The alignment camera 261 detects the amount of deviation (amount of deviation in the xy plane) between the irradiation position on the measurement stage 22 of the X-rays irradiated from the X-ray irradiation unit 21 and the measurement target position on the subject 7. The detected amount of deviation is output to the operation control unit 27. The subject tilt measurement unit 262 measures the angle of the surface of the subject 7 placed on the measurement stage 22 at the measurement position.

[0024] The operation control unit 27 controls the operation of each part of the T-SAXS measurement apparatus 2. For example, the operation control unit 27 instructs parameters of the X-ray irradiation unit 21 and the X-ray detection unit 23, instructs the rotation angle and rotation direction of the measurement stage 22, and instructs the operation of the transport unit 25.

[0025] The T-SAXS measurement apparatus 2 of the embodiment described above is used, for example, in an etching process for forming memory holes in a semiconductor memory device having a memory cell array with a three-dimensional structure. Here, a semiconductor memory device having a memory cell array with a three-dimensional structure will be described with reference to FIG.

[0026] FIG. 6 is a cross-sectional view of a part of a semiconductor memory device having a memory cell array of a three-dimensional NAND memory. For example, the semiconductor memory device functions as the test object 7. More specifically, for example, a semiconductor wafer for manufacturing the semiconductor memory device functions as the test object 7. FIG. 6 illustrates a part of a memory cell array and a peripheral circuit region. In the following description, the direction in which the bit line BL extends in a plane parallel to the surface of the semiconductor substrate 71 is defined as the x direction. The direction parallel to the surface of the semiconductor substrate 71 and perpendicular to the x direction is defined as the y direction. The direction perpendicular to the surface of the semiconductor substrate 71 is defined as the z direction. In this embodiment, a memory region 600 in which a memory circuit is formed is provided on a semiconductor substrate, and a peripheral circuit region 500 in which a peripheral circuit is formed is provided on the semiconductor substrate 71 around the memory region 600. That is, when viewed from the Z direction, the memory region 600 and the peripheral circuit region 500 are arranged so as not to overlap each other.

[0027] As shown in Fig. 6, a plurality of NAND strings NS are formed on a p-type well region (P-well). That is, a plurality of wiring layers 633 functioning as select gate lines SGS, a plurality of wiring layers 632 functioning as word lines WLi, and a plurality of wiring layers 631 functioning as select gate lines SGD are stacked on the p-type well region. Note that, although Fig. 6 shows a structure in which eight wiring layers 632 functioning as word lines WLi are stacked, in the memory cell array of the semiconductor memory device, more wiring layers 632 may be stacked, such as 48 layers, 64 layers, or 96 layers.

[0028] A memory hole 634 is formed penetrating these wiring layers 633, 632, 631 to reach the p-type well region. A block insulating film 635, a charge storage film 636, and a gate insulating film 637 are sequentially formed on the side surface of the memory hole 634, and further a conductor pillar 638 is embedded in the memory hole 634. The conductor pillar 638 is made of, for example, polysilicon, and functions as a region where a channel is formed during operation of the memory cell transistor MT and the select transistors ST1 and ST2 included in the NAND string NS.

[0029] In each NAND string NS, a select transistor ST2, a plurality of memory cell transistors MT, and a select transistor ST1 are formed on a p-type well region. A wiring layer functioning as a bit line BL is formed above the conductor pillar 638. A contact plug 639 that connects the conductor pillar 638 to the bit line BL is formed at the upper end of the conductor pillar 638.

[0030] Furthermore, an n+ type impurity diffusion layer and a p+ type impurity diffusion layer are formed in the surface of the p-type well region. A contact plug 640 is formed on the n+ type impurity diffusion layer, and a wiring layer that functions as a source line SL is formed on the contact plug 640.

[0031] A plurality of the configurations shown in FIG. 6 are arranged in the depth direction (y direction) of the paper surface of FIG. 6, and a set of a plurality of NAND strings aligned in a row in the depth direction forms one string unit SU.

[0032] On the other hand, in the peripheral circuit region 500, various circuits included in the peripheral circuit, such as an input / output circuit, are formed. For example, the above-mentioned input / output circuit is configured by combining logic gates, such as inverters, in multiple stages. Therefore, in the peripheral circuit region 500, a large number of MOS transistors constituting the logic gates are formed. These many MOS transistors are formed on a semiconductor substrate 71 in the peripheral circuit region 500. FIG. 6 shows one of these MOS transistors. Note that FIG. 6 is a schematic diagram showing the cross-sectional structure of a non-volatile memory, and the size of the MOS transistor 100 shown in FIG. 6 and the ratio between the elements constituting the MOS transistor 101 are different from the actual size and ratio.

[0033] The MOS transistor 100 constituting the peripheral circuit has a gate wiring 110 formed on a semiconductor substrate 71 via a gate insulating film. The gate wiring 110 is, for example, a polysilicon film into which an impurity suitable for the operation of the MOS transistor is implanted. A drain region 120 and a source region 130 are formed in the semiconductor substrate on the right and left sides in the X direction of the gate wiring 110. For example, when the MOS transistor 100 is an n-type MOS transistor (NMOS transistor), impurities such as arsenic (As) or phosphorus (P) are implanted into the semiconductor substrate 71 and diffused to a predetermined depth in the drain region 120 and the source region 130.

[0034] A metal wiring 113 for supplying a potential to the gate wiring 110 via an insulating layer is formed above the gate wiring 110. A gate electrode 111 is formed as a contact region on the gate wiring 110. A contact plug 112 for electrically connecting the metal wiring 113 and the gate electrode 110 is formed above the gate electrode 111. That is, the potential of the metal wiring 113 is supplied from the gate electrode 111 to the gate wiring 110 via the contact plug 112.

[0035] A metal wiring 123 for supplying a potential to the drain region 120 via an insulating layer is formed above the drain region 120. A drain electrode 121 is formed as a contact region on the drain region 120. A contact plug 122 for electrically connecting the metal wiring 123 and the drain electrode 121 is formed above the drain electrode 121. That is, the potential of the metal wiring 123 is supplied from the drain electrode 121 to the drain region 120 via the contact plug 122.

[0036] A metal wiring 133 is formed above the source region 130 to supply a potential to the source region 130 via an insulating layer. A source electrode 131 is formed on the source region 130 as a contact region. A contact plug 132 is formed above the source electrode 131 to electrically connect the metal wiring 133 and the source electrode 131. That is, the potential of the metal wiring 133 is supplied from the source electrode 131 to the source region 130 via the contact plug 132.

[0037] Wiring layers made of metal materials, such as the bit lines BL, source lines SL, and metal wirings 131-133, are formed above the NAND strings NS after they are formed. Usually, wiring layers made of metal materials are formed in multiple layers with insulating films sandwiched between them. The example of FIG. 6 shows a case where three wiring layers ML1, ML2, and ML3 are provided. The bit lines BL, source lines SL, and metal wirings 131-133 are formed in one or more layers of these wiring layers. For example, FIG. 6 shows a case where the metal wirings 131-133 and the source lines SL are formed in the wiring layer ML1, which is the first layer from the bottom, and the bit lines BL are formed in the wiring layer ML2, which is the second layer from the bottom. In addition, the uppermost wiring layer ML3 has wirings, for example, for transmitting a power supply voltage, formed therein.

[0038] Next, a method for forming a memory hole 634 in a semiconductor memory device having a structure as shown in Fig. 6 will be described with reference to Fig. 7. Fig. 7 is a schematic cross-sectional view illustrating a process for forming a memory hole. The memory hole 634 is formed through, for example, a plurality of processes. Fig. 7 shows cross-sectional views of a plurality of processes for forming the memory hole 634 arranged from left to right in chronological order.

[0039] First, in the first step (step 1), silicon oxide films and silicon nitride films are alternately deposited on a semiconductor substrate 71, and an ON stacked film 72 is formed on the entire surface of the semiconductor substrate 71. In Fig. 7, the solid lines correspond to the silicon nitride films, and the spaces adjacent to the solid lines correspond to the silicon oxide films. The silicon nitride films in the ON stacked film 72 are replaced with conductive films (e.g., tungsten films) in later steps, and become wiring layers 631, 632, and 633. The silicon oxide films in the ON stacked film 72 become insulating films between the above-mentioned wiring layers.

[0040] In the subsequent step (step 2), an etching mask film 73 is deposited on the surface of the ON stacked film 72. The etching mask film 73 may be, for example, an amorphous carbon film. Then, in the next step (step 3), the etching mask film 73 located in an area where a memory hole is to be formed is removed, and an opening is formed in the etching mask film 73.

[0041] In the subsequent steps (steps 4 to 6), the ON laminated film 72 formed under the opening of the etching mask film 73 is removed by dry etching using the etching mask film 73 as a mask. The memory hole 634 is a hole with a high aspect ratio, for example, a diameter of about 100 nm and a depth of several μm. Therefore, the optimal etching conditions may change in the process of forming the memory hole 634. Therefore, the etching conditions are changed in multiple stages in the process of forming the memory hole 634. For example, when each predetermined stage is completed, the etching is temporarily stopped and the processed state of the hole (the remaining film thickness of the etching mask film 73, the etching depth of the ON laminated film 72, and the cross-sectional shape, etc.) are measured. Then, the etching conditions are adjusted according to the measured processed state, and the etching of the next stage is performed. In FIG. 7, a cross section at the end of a certain stage is shown as step 4, and a cross section at the end of a stage after step 4 is shown as step 5. Note that more "stages" for measuring the processed state and adjusting the etching conditions may be defined in the etching for forming the memory hole. After each step, the processing state is measured and the results are fed back to adjust the etching conditions for the next step. Depending on the results of the processing state measurement, the etching conditions for the next step may not be changed.

[0042] 7, the cross section at the end of a stage after step 5 is shown as step 6. In step 6, the ON stacked film 72 formed under the opening of the etching mask film 73 is entirely removed, completing the formation of the memory hole. In addition, in FIG. 7, the remaining film thickness of the etching mask film 73 is shown as Tm, the etching depth of the ON stacked film 72 is shown as Th, and the depth from the surface of the etching mask film 73 to the bottom of the processed hole is shown as Ta. In other words, there is a relationship of Tm+Th=Ta.

[0043] The measuring device of the embodiment can be applied to measure the three-dimensional shape of the memory hole 634 at the time when each of the above-mentioned steps is completed. Fig. 8 is a flowchart for explaining an example of a procedure for forming a memory hole.

[0044] First, a silicon oxide film and a silicon nitride film are alternately deposited on a semiconductor substrate 71 to form an ON laminated film 72 (S1). Next, amorphous carbon is deposited as a hard mask material on the surface of the ON laminated film 72 to form an etching mask film 73 (S2). Next, the etching mask film 73 is removed from an area where a memory hole is to be formed, and an opening (memory hole pattern) is formed in the etching mask film 73 (S3).

[0045] Next, the ON laminated film 72 is dry-etched (anisotropic etched) (S4). As described above, the ON laminated film 72 is thick and the diameter of the memory hole is small, so a hole with a high aspect ratio must be formed. Therefore, the etching is performed in a plurality of stages. During the etching, in order to determine the end of the etching, it is detected whether the semiconductor substrate 71 is exposed at the bottom of the opening (end point detection) (S5). If the semiconductor substrate 71 is detected (S5, YES), it is assumed that the hole formed by the etching has penetrated the ON laminated film 72, and the etching is stopped. Next, the processed shape of the hole is measured by the measuring device of the embodiment (S7), and the formation of the memory hole is completed.

[0046] On the other hand, when the first etching stage is completed, if the semiconductor substrate 71 is not detected in the end point detection (S5, NO), the etching is temporarily stopped and the processed shape of the hole is measured by the measuring device of the embodiment (S6). Based on the measurement result in S6, the parameters of the next etching stage are adjusted as necessary. Then, the process returns to S4, and the next etching stage of the ON stacked film 72 is performed. The series of steps from S4 to S6 are repeatedly executed until the end point is detected in S5.

[0047] Next, a method for measuring a deep hole having a complicated cross-sectional shape, such as the processed hole of the above-mentioned memory hole, will be described. Prior to the measurement method of the embodiment, a measurement method of a comparative example will be described. FIG. 9 is a diagram for explaining shape parameters in the comparative example. FIG. 10 is a flow chart for explaining an example of the measurement method in the comparative example. Furthermore, FIG. 11 is a diagram for explaining an example of the measurement result in the comparative example.

[0048] In the comparative example shown in FIG. 9, the processed hole to be measured is sliced ​​finely in the depth direction, and the diameter and position fluctuations are given as shape parameters at each depth. For example, if the processed hole is divided into 25 equal layers in the depth direction and four parameters, diameter parameters (Dx, Dy) and position deviation parameters (Δx, Δy), are set at each depth, a total of 25×4=100 shape parameters must be set. In the case of a complex shape such as a memory hole, if it is necessary to express the shape by slicing it finely in the depth direction, the number of shape parameters will increase even more. The shape parameters in the comparative example may be called grid parameters.

[0049] In the comparative example, the optimal solution for each shape parameter is calculated using the procedure shown in FIG. 10. That is, the object is placed in the measurement device (S101), and the scattering intensity is measured to obtain a group of diffraction images (S102). Meanwhile, under specific conditions such as the conditions of a specific shape model or slice layer, initial values ​​are given to the shape parameters to theoretically calculate a group of diffraction images (S103). The theoretical value calculated in S103 is fitted to the measured value obtained in S102 (S104), and if it is not optimal (S104, NO), the value of the shape parameter is changed (S106), and the process returns to the theoretical calculation in S103. If it is optimal (S104, YES), the value used in the theoretical calculation at that time is set as the value of the shape parameter. That is, in the comparative example, the group of diffraction images is analyzed by shape parameter fitting using theoretical calculation to measure the shape of the processed hole. By expressing the shape by slicing it finely in the depth direction, a smooth cross-sectional shape is obtained as shown in FIG. 11.

[0050] However, in the comparative example, if the initial value given when theoretically calculating the group of diffraction images is not appropriate, the local optimum solution may be used as the value of the shape parameter. FIG. 12 is a diagram for explaining the relationship between the difference between the theoretical value and the measured value and the value of the shape parameter. As shown in FIG. 12, the difference between the theoretical value and the measured value varies depending on the value of the shape parameter. For example, when a value (initial value 2) shown in the double circle in FIG. 12 is given as the initial value for a certain shape parameter and a numerical search is started, a value (minimum value, global optimum solution) shown in the diagonal line circle in FIG. 12 is calculated as the value of the shape parameter. However, when a value (initial value 1) shown in the white circle in FIG. 12 is given as the initial value and a numerical search is started, according to the method of the comparative example, a value (local minimum value, local optimum solution) shown in the black circle in FIG. 12 is calculated as the value of the shape parameter. That is, according to the method of the comparative example, depending on how the initial value is given, there may be a case where the value (minimum value, global optimum solution) at which the difference between the theoretical value and the measured value is the smallest cannot be calculated as the value of the shape parameter. In addition, the greater the number of shape parameters, the greater the number of shape parameters for which non-optimal values ​​are calculated. Therefore, as shown in Fig. 13, in the comparative example, the measurement results may deviate from the actual shape of the processed hole (reference in Fig. 13), which may result in a decrease in the accuracy of the analysis. Fig. 13 is a diagram for explaining the difference between the measurement results and the shape of the processed hole in the comparative example.

[0051] Next, the measurement method of the embodiment will be described with reference to FIG. 14A. FIG. 14A is a flow chart for explaining an example of the measurement method of the embodiment. That is, the series of steps shown in FIG. 14A can be applied to the measurement of the processed shape in S6 and S7 of FIG. 8. Hereinafter, the measurement method of the embodiment will be described with the processed hole shown in step 6 of FIG. 7 as an example.

[0052] The measurement method of the embodiment is composed of three phases. The first phase is a procedure (S11 to S12) performed before measuring the X-ray diffraction scattering intensity of the machined hole, which is the measurement target. The second phase is a procedure (S13) for measuring the X-ray diffraction scattering intensity of the machined hole. The third phase is a procedure (S14 to S20) performed after measuring the X-ray diffraction scattering intensity of the machined hole. Hereinafter, the first phase will be referred to as the measurement preparation phase, the second phase as the measurement phase, and the third phase as the shape measurement phase.

[0053] First, the measurement preparation phase will be described. As shown in FIG. 14A, the measurement preparation phase is composed of two procedures: dimensionality reduction of shape parameters (S11) and creation of a database of theoretical scattering intensity (S12). In dimensionality reduction of shape parameters (S11), feature values ​​are extracted from known shape information to reduce the number of shape parameters. As a specific method of dimensionality reduction, for example, principal component analysis can be used. FIG. 15 is a diagram for explaining principal component analysis. First, feature values ​​are extracted from the shapes of multiple known processed holes by principal component analysis and decomposed into principal components. Principal component 1, principal component 2, principal component 3, ..., principal component n shown in FIG. 15 correspond to the extracted feature values. The shape of the processed hole is expressed by combining these feature values ​​at a predetermined ratio. At this time, the degree of contribution of principal component 1, principal component 2, principal component 3, ..., principal component n to the processed hole shape is set as t1, t2, t3, ..., tn. A specific shape can be expressed by substituting specific values ​​for t1, t2, t3, ..., tn. That is, n variables t1, t2, t3, ..., tn are shape parameters in the measurement method of the embodiment. In this embodiment, for example, the shape parameters are decomposed into about 5 to 7 principal components. This makes it possible to reduce the number of shape parameters compared to the comparative example.

[0054] The method of extracting features from a known shape is not limited to the above-mentioned principal component analysis. For example, other dimensionality reduction methods such as independent component analysis, singular value analysis, eigenvalue analysis, factor analysis, non-negative matrix factor analysis, neural network, Auto Encoder, Variational Auto Encoder, and UMAP (Uniform Manifold Approximation and Projection) may be used.

[0055] In the theoretical scattering intensity database creation (S12), the theoretical scattering intensity when at least one set of shape parameters is changed is calculated, and a database of the theoretical scattering intensity is created. In other words, various shape patterns are assumed by changing the shape parameters, and the intensity distribution of X-ray diffracted light corresponding to these shape patterns is calculated by simulation and stored in a database. For example, M (e.g., 1000) different shape patterns are set by changing the shape parameters, and the intensity distribution of X-ray diffracted light is calculated for each shape pattern by simulation. That is, a group of diffraction images is theoretically calculated for each of the M shape patterns, and stored in a database.

[0056] Next, the measurement phase will be described. As shown in Fig. 14A, the measurement phase is a procedure (S13) for measuring the diffraction scattering intensity of the drilled hole. In S13, X-rays are irradiated into the drilled hole while gradually changing the incident angle, and multiple diffraction images (diffraction image group) are obtained.

[0057] Next, the shape measurement phase will be described. In the difference calculation (S14) between the measured value and the theoretical value in the database, the group of diffraction images (measured value) acquired in S13 is compared with the group of diffraction images (theoretical value) stored in the database created in S12, and the difference is calculated. FIGS. 16A and 16B are diagrams for explaining an example of the calculation result of the difference between the measured value and the theoretical value. In the table of FIG. 16A, the leftmost column indicates the identification number of the shape pattern stored in the database. The second to sixth columns from the left indicate the value of the shape parameter in each shape pattern. The rightmost column indicates the difference between the theoretical scattering intensity of the shape pattern and the measured scattering intensity. As a specific difference calculation method, the index representing each data element (for example, pixel of a picture element) of the diffraction scattering intensity is i, the diffraction scattering intensity of each data element of the diffraction image group of the measured value is Iexp,i, the diffraction scattering intensity of each data element of the diffraction image group of the theoretical value is Ical,i, and the weighting coefficient of each data element is wi,j, and the calculation is performed, for example, by fj in the following formula (1). TIFF0007672903000001.tif21120

[0058] In formula (1), N is the total number of diffraction scattering intensity data, j is a weighting coefficient, and wi,j are data sets, and multiple data sets can be taken depending on which data among the data elements is emphasized. Therefore, multiple values ​​representing the difference fj can also be taken depending on j. FIG. 16A is an example of the difference result when there is one type of difference, and FIG. 16B is an example of the difference result when there are two types. In S14, the difference from the measured value is calculated for all shape patterns registered in the database.

[0059] In the subsequent calculation of the regression model (S15), a regression model that estimates the difference from the shape parameter value is calculated based on the difference calculated in S14. Specifically, for each shape parameter, a relationship between the shape parameter value and the difference between the theoretical scattering intensity and the measured value is extracted. Then, a regression model that estimates the difference between the theoretical scattering intensity and the measured value for the shape parameter value is created. FIG. 17 is a diagram explaining a regression model that estimates the difference from the shape parameter value when the difference is one type of f1 as shown in FIG. 16A. The horizontal axis of FIG. 17 indicates the shape parameter value, and the vertical axis indicates the difference between the theoretical scattering intensity and the measured value. First, from the difference calculated in S14, a relationship between the shape parameter value and the difference is extracted for each shape parameter. For example, for the shape parameter t1, M pieces of data are extracted, such as (shape parameter value, difference)=(0.542, 0.679), (0.387, 0.742).... A regression model that estimates the difference from the shape parameter is calculated using the extracted M pieces of data for each shape parameter. For example, Gaussian process regression is used as the regression model. For example, as shown in FIG. 17, in the regression model calculated in S15, a curve (difference estimation curve) is calculated that passes through the calculation points corresponding to the extracted data and passes through the point (estimated value) with the highest probability of existence in the area where no calculation points exist. At this time, in the area where no calculation points exist, an area (probability density area) having a probability that a difference exists is also calculated. That is, the estimated value is a value that exists in the probability density area and is an undetermined value. For example, in FIG. 17, when the value of the shape parameter is V1, there is no corresponding calculation value. According to the estimated regression model, when the value of the shape parameter is V1, it is estimated that the difference between the theoretical value and the actual value exists between D1 and D2. Note that a regression model is created for each of all the set shape parameters. That is, n regression models are created.

[0060] The regression model used in S15 is not limited to the Gaussian process regression described above. For example, other regression models such as neural network, principal component regression, multiple regression, Lasso regression, Ridge regression, convolutional neural network, Pays regression, and PLS regression may be used.

[0061] When the calculation of the regression model is completed and the difference estimation curve is acquired, the process proceeds to S16, where shape parameter value candidates are calculated. Specifically, the value of the shape parameter that is estimated to reduce the difference in the difference estimation curve is calculated. FIG. 18 is a diagram for explaining shape parameter value candidates. In the case of the difference estimation curve shown in FIG. 18, the probability that the difference will be the minimum value when the value of the shape parameter is V1 is high, and the difference at this time is estimated to be D3. Therefore, for the shape parameter, the candidate for the shape parameter value is V1. The calculation of the shape parameter value candidates is performed for all the set shape parameters. That is, for each of the n shape parameters, a shape parameter value candidate is calculated. Note that, if there are multiple other minimum points in the difference estimation curve where the difference may be the minimum value, multiple parameter value candidates are also calculated. The parameter value candidates calculated for each shape parameter are combined to generate a parameter value candidate set. For example, in the case where n=5, i.e., the number of shape parameters is five, and 0.766 and 0.312 are calculated as candidates for parameter t1, 0.678 as a candidate for parameter t2, 0.560 as a candidate for parameter t3, 0.808 as a candidate for parameter t4, and 0.815 as a candidate for parameter t5, two sets of parameter value candidate sets are generated: (t1, t2, t3, t4, t5)=(0.766, 0.678, 0.560, 0.808, 0.815)(0.312, 0.678, 0.560, 0.808, 0.815). The parameter value candidate set generated in S16 may be generated by selecting parameter values ​​that are estimated to have a small difference from the difference results between the measured values ​​and theoretical values ​​for all shape patterns registered in the database calculated in S14.

[0062] Next, the X-ray scattering intensity is theoretically calculated for the shape represented by the shape parameter value candidate set calculated in S16, and a group of diffraction images is obtained (S17). The theoretical value calculated in S17 is compared with the actual measurement value acquired in S13, and a difference is calculated (S18). A calculation point is added to the difference estimation curve using the calculated difference, and the regression model is updated. FIG. 19 is a diagram for explaining an example of an updated regression model. When it is calculated that the difference between the actual measurement value and the theoretical value of V1, which is a shape parameter value candidate, is D4, (V1, D4) is added to the regression model as a new calculation value. Then, the regression model is updated together with the calculation point that has already been set. As shown in FIG. 19, it can be seen that the probability density region of the updated regression model is reduced, the uncertain region is reduced, and the accuracy of the difference estimation curve is improved.

[0063] It is determined whether the shape parameter value candidate is a value that minimizes the difference according to a predetermined convergence condition (S19), and if the convergence condition is not satisfied (S19, NO), the value of the shape parameter candidate is changed using an optimization algorithm that obtains a minimum value (S20). As the optimization algorithm that obtains the minimum value, for example, Bayesian optimization can be used. S17 to S20 are repeated while changing the value of the shape parameter candidate. If the predetermined convergence condition is satisfied (S19, YES), the value of the shape parameter candidate at that time is determined as the value of the shape parameter. The shape expressed using the determined values ​​of the n shape parameters is determined as the shape of the machined hole, and a series of procedures related to the measurement method of the embodiment is completed.

[0064] The optimization algorithm for finding the minimum value is not limited to the Bayesian optimization described above. For example, other numerical optimization methods such as a genetic algorithm, a simulated annealing method, a gradient method, a simplex method, a differential evolution method, a multi-objective genetic algorithm, and a multi-objective simulated annealing method may be used.

[0065] In this way, the measurement device and the measurement method of the embodiment can reduce the number of shape parameters that represent the shape of the deep hole to be measured. Also, by using a small number of shape parameters and analyzing the shape using a regression model such as Gaussian feedback regression and a global optimization method such as Bayesian optimization, the influence of the initial values ​​given during the analysis on the analysis results can be reduced, and a global optimum solution, i.e., parameter values ​​that minimize the difference between the measured value and the theoretical value, can be obtained. This allows the shape of the measurement object to be modeled with high accuracy. Second embodiment Next, a second embodiment will be described. The measurement method of this embodiment differs from the first embodiment in the method of dimensional compression of shape parameters. The configuration of the measurement device and the structure of the object 7 to be measured are the same as those of the first embodiment, so the description will be omitted, and only the differences from the first embodiment will be described below.

[0066] In the above-mentioned first embodiment, the feature amount is extracted from a known shape, decomposed into principal components, and a specific value is estimated for the degree of contribution of each principal component to the machining shape (shape parameter), thereby expressing the shape of the machined hole. In contrast, in this embodiment, the shape of the machined hole is expressed by a distance r from a set origin and an angle θ with respect to an xy plane passing through the origin using polar coordinate conversion. FIG. 20 is a diagram for explaining the shape expression in the second embodiment, and FIG. 20(a) is a diagram for explaining the method of expressing the shape of the machined hole in the second embodiment. Also, FIG. 20(b) is a diagram for explaining the shape expression of a machined hole according to a comparative example, and FIG. 20(c) is a diagram in which the machined hole having the shape shown in FIG. 20(b) is expressed by the method of the second embodiment.

[0067] As shown in FIG. 20(a), for example, the center of a processing hole at the interface between a mask material (etching mask film 73) and a processing target film (ON laminated film 72) is taken as the origin O, and an arbitrary position P (position where measurement is performed) on the surface of the processing hole is converted into polar coordinates using the distance r from the origin O and the angle θ of a line segment OP with respect to the interface between the mask material and the processing target film. Furthermore, the angle θ is cubed and converted into a θ^3-r plane. By cubing the angle θ, the curve obtained by the conversion becomes smooth. Note that the degree to which the angle θ is raised to a power may be any odd number, and may be a higher power such as the fifth or seventh power.

[0068] In this way, the complexity of the machined shape is reduced by expressing the shape of the machined hole by converting it into the θ^3-r plane after the polar coordinate conversion. For example, the shape of the machined hole with a complex uneven shape as shown in Fig. 20(b) can be expressed as a downward convex parabola with the origin as a vertex as shown in Fig. 20(c).

[0069] FIG. 21 is a diagram comparing the shape representation of the processed hole before and after conversion to a polar coordinate system. FIG. 21 shows, as an example, four processed holes corresponding to steps 3, 4, 5, and 6 in FIG. 7. The four diagrams shown in the upper part of FIG. 21 are the shapes of the processed holes represented by the representation method according to the comparative example. In the four diagrams shown in the upper part, the dotted lines indicate the position of the interface between the mask material and the film to be processed. The four diagrams shown in the lower part are the shapes of the processed holes represented by the representation method in this embodiment, that is, after conversion to polar coordinates, they are further converted to the θ^3-r plane. In the four diagrams shown in the lower part, the dashed line indicates the position of the interface between the mask material and the film to be processed. Two diagrams shown vertically in the same row represent the same processed hole, and represent processed holes corresponding to steps 3, 4, 5, and 6 from left to right.

[0070] As shown in FIG. 21, in the representation method according to the comparative example, the curve changes as the process proceeds, and the positions and number of the unevenness change in a complex manner. In contrast, in the representation method according to the present embodiment, in every process, it is represented by a downwardly convex smooth parabola with the origin (the interface between the mask material and the film to be processed) as the apex. That is, the shape of the processing hole can be represented by estimating the end point of the curve in the θ^3-r plane. The right end point of the curve in the θ^3-r plane is estimated from the remaining film thickness of the mask material. In addition, the left end point is estimated from the depth of the processing hole (memory hole) formed in the film to be processed. As a result, in the second embodiment, the shape of the processing hole can be represented by using two shape parameters, the remaining film thickness Tm of the mask material and the depth of the memory hole (=etching depth Th of the ON stacked film 72).

[0071] The measurement method in this embodiment differs from that in the first embodiment in that the above-mentioned two variables (residual film thickness Tm of the mask material, depth Th of the memory hole) are used as shape parameters in S11 (dimensionality reduction of shape parameters) in Fig. 14A. Also, it differs from the first embodiment in that candidates for shape parameters (range of values ​​that the shape parameters can take) are estimated in S14 in Fig. 14A, and a set of theoretical values ​​for which difference calculation is performed with measured values ​​is limited to the estimated range.

[0072] FIG. 22 is a diagram showing an example of the relationship between the distance r of the processing hole and the processing time. In FIG. 22, the horizontal axis is the processing time tp, and the vertical axis is r×sgn(θ). sgn(θ) is a sign function of θ, and returns a value of 1 when θ>0, 0 when θ=0, and -1 when θ<0. That is, r×sgn(θ)=0 indicates the interface between the mask material and the film to be processed, the region of r×sgn(θ)>0 indicates the mask material, and the region of r×sgn(θ)<0 indicates the film to be processed. In FIG. 22, the white circle plotted in the region of r×sgn(θ)>0 indicates the maximum value of the distance r in the mask material (the distance from the contour of the processing hole on the surface of the mask material to the origin O). In addition, the black diamond plotted in the region of r×sgn(θ)<0 indicates the maximum value of the distance r in the film to be processed (the distance from the contour of the processing hole on the bottom surface of the memory hole to the origin O). That is, it can be said that the white circles represent the relationship between the remaining film thickness Tm of the mask material and the processing time tp, and the black diamonds represent the relationship between the depth Th of the memory hole and the processing time tp.

[0073] Prior to measurement, by acquiring the relationship between the distance r of the processed hole and the processing time as shown in FIG. 22, the remaining film thickness Tm of the mask material and the depth Th of the memory hole can be estimated according to the processing time of the processed hole to be measured. Taking the relationship in FIG. 22 as an example, when the processing time is t1, it can be estimated that the distance from the contour of the processed hole on the surface of the mask material to the origin O is r2, and the distance from the contour of the processed hole on the bottom surface of the memory hole to the origin O is r1. Therefore, the candidates of the shape parameters in S14 (the range of values ​​that the shape parameters can take) can be limited to values ​​near r2·sinθ for the remaining film thickness Tm of the mask material, and to values ​​near r1·sin(-θ) for the depth Th of the memory hole. In other words, the amount of calculation of the difference between the measured value and the theoretical value can be reduced, and the measurement cost can be reduced.

[0074] In the memory hole formation procedure shown in FIG. 8, when performing step trace measurement in which the processed shape is measured step by step (in time series) while etching is proceeding, if the measurement method of this embodiment is applied to the measurement of the processed shape (S6), the following method can also be applied as a method of estimating a set of theoretical values ​​for performing difference calculations with the measured values ​​in S14 of FIG. 14A and limiting the range.

[0075] FIG. 23 is a diagram for explaining the relationship between the difference in the remaining film thickness of the mask material and the difference in the depth of the memory hole. The vertical axis of FIG. 23 is the difference in the remaining film thickness of the mask material (the value obtained by subtracting the remaining film thickness of the mask material estimated in the previous measurement from the remaining film thickness of the mask material in the current measurement target). The horizontal axis is the difference in the memory hole (the value obtained by subtracting the depth of the memory hole estimated in the previous measurement from the depth of the memory hole in the current measurement target). When etching of the mask material and the processing target film proceeds, the remaining film thickness of the mask material decreases and the depth of the memory hole increases as the processing time increases. That is, the two shape parameters of this time can be limited to those existing in the region (the region indicated by the diagonal lines in FIG. 23) where the horizontal axis is positive and the vertical axis is negative in the diagram of FIG. 23. Furthermore, when the etching rates of the mask material and the processing target film can be estimated based on the analysis of the measurement results or known knowledge, the region where the shape parameters exist can be further limited. For example, it can be limited to the region indicated by the black shading in FIG. 23.

[0076] That is, when measuring the processed shape several times while etching is proceeding, the range of values ​​that the shape parameters can take this time can be limited using the results of the previous measurement (residual film thickness of mask material, depth of memory hole). That is, by eliminating obviously erroneous values, the shape parameters can be estimated with higher accuracy. In addition, the amount of calculation of the difference between the measured value and the theoretical value can be reduced, and the measurement cost can be reduced.

[0077] In this way, according to the measurement method of the embodiment, the number of shape parameters expressing the shape of the deep hole to be measured can be further reduced. Also, the existing range of the values ​​of the shape parameters can be estimated using known measurement results and etching rates. This allows the shape of the measurement object to be modeled with high accuracy while reducing the measurement cost. Third embodiment Next, a third embodiment will be described. The measurement method of this embodiment differs from the first and second embodiments in the method of dimensional compression of shape parameters. The configuration of the measurement device and the structure of the object 7 to be measured are the same as those of the first embodiment, so the description will be omitted, and only the differences from the first and second embodiments will be described below.

[0078] In the first embodiment described above, feature amounts are extracted from a known shape, decomposed into principal components, and a specific value is estimated for the degree of contribution of each principal component to the processed shape (shape parameter), to represent the shape of the machined hole. In contrast, in this embodiment, the shape is represented by process simulation.

[0079] In general, an etching process simulator outputs the shape of a processed hole to be generated when parameters related to the apparatus, parameters related to process conditions, and parameters related to the workpiece are input. The parameters related to process conditions include, for example, 20 to 30 types of parameters such as processing time, etching gas pressure, etching gas flow rate (when multiple etching gases are used, each gas flow rate), and RF power. In other words, when the set values ​​of the parameters related to the apparatus and the parameters related to the workpiece are known (fixed), various processed shapes can be obtained by changing the values ​​of the parameters related to the process conditions.

[0080] The measurement method in this embodiment differs from the first and second embodiments in that the parameters related to the process conditions described above are used as shape parameters in S11 (dimensionality reduction of shape parameters) in Fig. 14A. Note that it is possible to extract parameters that have a particular effect on the processed shape and use them as shape parameters, rather than using all parameters related to the process conditions as shape parameters. For example, when 30 types of parameters related to the process conditions are set, five parameters may be extracted from these and used as shape parameters.

[0081] In addition, in S12 (creation of a database of theoretical scattering intensity), an etching process simulator is used when estimating the shape of a processed hole generated when the shape parameters are changed, which is also different from the first and second embodiments. Furthermore, in this embodiment, the shape used in the theoretical calculation in S17 is also the shape obtained by inputting the shape parameter value candidate set calculated in S16 into the etching process simulator.

[0082] In this way, according to the measurement method of the embodiment, the number of shape parameters expressing the shape of the deep hole to be measured can be reduced compared to the comparative example. Furthermore, since parameters related to the etching process conditions are used as the shape parameters and the processed shape is estimated by an etching process simulator, a physically appropriate shape can be estimated. Furthermore, the search range for the values ​​of the shape parameters can be limited to a range that is feasible as an etching process, so that the shape of the measurement object can be modeled with high accuracy while reducing the measurement cost.

[0083] In the memory hole formation procedure shown in FIG. 8, when performing step trace measurement in which the processed shape is measured step by step (in time series) while proceeding with etching, a high dimensionality reduction effect is obtained when the measurement method of this embodiment is applied to the measurement of the processed shape (S6). For example, when measuring the shapes of four processed holes corresponding to steps 3, 4, 5, and 6 in FIG. 7, according to the comparative example, it is necessary to calculate the values ​​of shape parameters for each of the four processed holes. For example, if 100 shape parameters are required to express the shape of one processed hole, it is necessary to calculate 100×4=400 values ​​to express the shapes of the above-mentioned four processed holes. In contrast, in this embodiment, the values ​​of the process parameters other than the processing time are basically not changed in the four steps. In other words, the values ​​of the shape parameters other than the processing time can be calculated by the value calculated in the measurement of the processed hole in step 3. For example, if the number of shape parameters required to express the shape of one processed hole is 30, it is sufficient to calculate 30+3=33 values ​​to express the shapes of the above-mentioned four processed holes. In this way, when the measurement method of the embodiment is used to measure a plurality of processed holes in which it is known that the values ​​of specific process parameters will not change, such as in step trace measurement, the measurement costs can be further reduced. (Fourth embodiment) Next, a fourth embodiment will be described. The measurement method of this embodiment differs from the first to third embodiments in that a plurality of different shape parameter sets are used. The shape parameter set refers to a set of a plurality of shape parameters used to express the shape of a processed hole. The configuration of the measurement device and the structure of the object 7 to be measured are the same as those of the first embodiment, so their explanations are omitted, and only the differences from the first to third embodiments will be described below.

[0084] In the measurement method of this embodiment, the processed shape is measured multiple times using several different shape parameter sets among shape parameters such as shape parameters dimensionally compressed by principal component analysis, shape parameters dimensionally compressed using polar coordinate transformation, shape parameters dimensionally compressed using process parameters used in process simulation, and grid parameters used in the comparative example. FIG. 24 is a flowchart for explaining an example of the measurement method in the fourth embodiment. FIG. 24 shows a procedure for performing measurement using three different shape parameter sets. S21 to S30 in FIG. 24 are a first-stage measurement procedure using a first shape parameter set, S31 to S35 are a second-stage measurement procedure using a second shape parameter set, and S41 to S45 are a third-stage measurement procedure using a third shape parameter set.

[0085] The first to third shape parameter sets are selected so that the number of shape parameters increases as the stage proceeds. For example, the first shape parameter set uses shape parameters (number of shape parameters=5) that are dimension-reduced using process parameters used in process simulation, the second shape parameter set uses shape parameters (number of shape parameters=10) that are dimension-reduced by principal component analysis, and the third shape parameter set uses grid parameters (number of shape parameters=100).

[0086] The procedure in the first stage, i.e., S21 to S30 in FIG. 24, is the same as the measurement procedure shown in FIG. 14A. By executing S21 to S30, the shape of the machined hole measured using the first shape parameter set is output. In the subsequent second stage, first, the shape parameter set is switched (S31). Specifically, the shape parameters used in the procedures from S32 onwards are switched from the first shape parameter set to the second shape parameter set. In addition, if a regression model corresponding to the shape parameter set used in the second stage has not been created, a regression model is created that estimates the difference between the theoretical scattering intensity and the measured value for the value of the shape parameters.

[0087] Next, the X-ray scattering intensity is theoretically calculated for the processed shape output as the measurement result of the first stage, and a group of diffraction images is obtained (S32). The theoretical value calculated in S32 is compared with the actual measurement value acquired in S23, and the difference is calculated (S33). Then, a calculation point is added to the difference estimation curve using the calculated difference, and the regression model is updated. It is determined whether the shape parameter value candidate is a value that minimizes the difference according to a predetermined convergence condition (S34), and if the convergence condition is not satisfied (S34, NO), the value of the shape parameter candidate is changed using an optimization algorithm that obtains the minimum value (S35). S32 to S35 are repeated while changing the value of the shape parameter candidate. If the predetermined convergence condition is satisfied (S34, YES), a shape expressed by using the value of the shape parameter candidate at that time using the value of the shape parameter is output as the measurement result by the second shape parameter set. That is, S32 to S35 are the same procedures as S17 to S20 in FIG. 14A.

[0088] In the third stage, first, the shape parameter set is switched (S41). Specifically, the shape parameters used in the procedure from S42 onwards are switched from the second shape parameter set to the third shape parameter set. If a regression model corresponding to the shape parameter set used in the third stage has not been created, a regression model is created that estimates the difference between the theoretical scattering intensity and the measured value for the value of the shape parameter.

[0089] Next, the X-ray scattering intensity is theoretically calculated for the processed shape output as the measurement result of the second stage, and a group of diffraction images is obtained (S42). The theoretical value calculated in S42 is compared with the actual measurement value acquired in S23, and the difference is calculated (S43). Then, a calculation point is added to the difference estimation curve using the calculated difference, and the regression model is updated. It is determined whether the shape parameter value candidate is a value that minimizes the difference according to a predetermined convergence condition (S44), and if the convergence condition is not satisfied (S44, NO), the value of the shape parameter candidate is changed using an optimization algorithm that obtains the minimum value (S45). S42 to S45 are repeated while changing the value of the shape parameter candidate. If the predetermined convergence condition is satisfied (S44, YES), a shape expressed by using the value of the shape parameter candidate at that time is output as the final measurement result. That is, S42 to S45 are the same procedures as S17 to S20 in FIG. 14A.

[0090] FIG. 25 is a diagram for explaining an example of a measurement result by the measurement method of the fourth embodiment. Of the three diagrams shown in FIG. 25, the left diagram shows the measurement result at the end of the first stage, the center diagram shows the measurement result at the end of the second stage, and the right diagram shows the measurement result at the end of the third stage. In each diagram, the curve connecting the black circles shows the actual processed shape (reference), and the curve connecting the white squares shows the output shape at each stage. As shown in FIG. 25, as the stage progresses, the difference between the shape obtained as a result of the measurement and the actual shape becomes smaller. In this way, by using multiple shape parameter sets and fitting the shape parameters in order from the smallest number of dimensions, global analysis becomes possible, and the measurement accuracy is further improved.

[0091] Although an example of performing three-stage measurement using three different shape parameter sets has been described above, any number of stages may be used, including two stages, four stages or more. Also, it is not necessary to use different dimensionality reduction methods in each stage, and for example, shape parameters that have been dimensionally reduced by principal component analysis may be used in both the first and second stages. In this case, the number of shape parameters used in the second stage is set to be greater than the number of shape parameters used in the first stage. Fifth embodiment Next, a fifth embodiment will be described. The measurement method of this embodiment is performed according to the flowchart shown in FIG. 14B. FIG. 14B is a flowchart for explaining another example of the measurement method in the embodiment. The measurement method of this embodiment differs from the measurement method of the first embodiment (FIG. 14A) in that a rank is used instead of a regression model and in the method of calculating shape parameter value candidates. The configuration of the measurement device and the structure of the object 7 to be measured are similar to those of the first embodiment described above, so their explanations are omitted, and only the differences from the first embodiment will be explained below.

[0092] In the first embodiment described above, a regression model is calculated from the difference calculation value between the measured value and the theoretical value. In contrast, in this embodiment, a rank is calculated for each shape parameter from the difference calculation value (S25). A specific rank calculation method in S25 will be described for the case where there are two types of differences f1 and f2 as shown in FIG. 16B. FIG. 26 is a diagram for explaining rank calculation. Since f1 and f2 are both differences, it is desirable that both are small. However, since they are calculated from different weighting coefficients, there are cases where, for example, f1 is small but f2 is large, as shown in FIG. 26. In order to select parameter candidate values ​​that reduce both f1 and f2 in a balanced manner, it is desirable to select data as shown above by the dotted line in FIG. 26. Therefore, a rank is calculated to quantitatively evaluate them.

[0093] Here, the concept of "dominating" is introduced. In the case where data Tn of T1 to T6 exist as shown in FIG. 26, if there exists a Tx' in which all the differences fj (f1, f2) are small for a certain Tx, then Tx is considered to be "dominating" Tx'. For all data Tn, if the number of data that are superior to itself is s, the rank r is calculated as s+1. For example, data in which all the differences f1 and f2 are small for T1 in FIG. 26 exists in area A. Since T2 exists in area A, the rank r is 1+1=2. On the other hand, since there is no data for T2 in area B, the rank r is 0+1=1. In this way, the rank can be calculated for all data. Note that here, the case where there are two types of differences has been described, but the rank can be calculated in the same way when there is one or more types of differences. Next, in S26, candidates for the shape parameter value are calculated by extracting a set of shape parameter values ​​from those with small ranks by a predetermined number of candidates. The steps S21 to S24 are similar to the steps S11 to S14 in Fig. 14A, and the steps S27 to S30 are similar to the steps S17 to S20 in Fig. 14A.

[0094] Thus, according to the fifth embodiment, when there are multiple types of differences, it is possible to examine parameter candidate values ​​that reduce all the difference values ​​in a well-balanced manner. In addition, since the amount of calculation required for rank calculation is small, calculation can be performed in less calculation time than the calculation of the regression model in the first embodiment. Therefore, this embodiment is advantageous when it is desired to reduce the calculation time.

[0095] As described above, according to the measuring device and the measuring method of the embodiment, the three-dimensional shape of a deep hole having a complex cross-sectional shape can be accurately modeled while reducing the number of parameters.

[0096] Although several embodiments of the present invention have been described, these embodiments are presented as examples and are not intended to limit the scope of the invention. These novel embodiments can be implemented in various other forms, and various omissions, substitutions, and modifications can be made without departing from the spirit of the invention. These embodiments and their modifications are included in the scope and spirit of the invention, and are included in the scope of the invention and its equivalents described in the claims. [Explanation of symbols]

[0097] 2...T-SAXS measurement device, 7...object, 21...X-ray irradiation unit, 22...measurement stage, 23...X-ray detection unit, 24...analysis unit, 25...transport unit, 26...position measurement unit, 27...motion control unit, 71...semiconductor substrate, 72...ON laminated film, 73...etching mask film, 91...laser irradiation unit, 211...X-ray source, 212...shutter, 213...X-ray focusing mechanism, 213a...first slit, 213b...mirror, 213c...second slit, 231...vacuum pipe, 232...detector, 241...CPU, 242...RAM, 243...database, 251...load port, 252...transport unit, 253...prealigner, 261...alignment camera, 262...object tilt measurement unit,

Claims

1. an X-ray irradiation unit that irradiates an object with X-rays; an X-ray detection unit that detects scattered X-rays emitted from the subject by the irradiation of the X-rays; an analysis unit that analyzes a diffraction image obtained by photoelectrically converting the scattered X-rays to estimate a surface contour shape of a measurement region in the subject that is irradiated with the X-rays; In a measuring device comprising: The analysis unit is extracting a plurality of principal components by performing principal component analysis on shape information indicating the shape of a known processed hole, and determining variables indicating the respective contributions of the plurality of principal components as a plurality of shape parameters used to express the surface contour shape; Calculating a theoretical scattering intensity of the scattered X-rays when values ​​of the plurality of shape parameters are changed; calculating a difference between a measured scattering intensity, which is the intensity of the scattered X-rays detected by the X-ray detection unit, and the theoretical scattering intensity, and creating a regression model of the relationship between the value of the shape parameter and the difference for each of the shape parameters; extracting at least one shape parameter candidate value that reduces the difference from the regression model, and calculating a theoretical scattering intensity of the shape parameter candidate value; The shape parameter candidate value is repeatedly changed, and the value of the shape parameter that minimizes the difference between the measured scattering intensity and the theoretical scattering intensity is estimated. A measuring device comprising:

2. The regression model uses the measured scattering intensity and 2. The measuring apparatus according to claim 1, wherein recalculation is performed using a difference between the theoretical scattering intensity calculated using the shape parameter candidate value and the theoretical scattering intensity.

3. a first film and a second film made of a material different from that of the first film are laminated in the measurement region of the subject, and a hole penetrating the second film is formed in a part of the measurement region; The measurement device according to claim 1 , characterized in that the analysis unit determines the plurality of shape parameters used to express the surface contour shape using a polar coordinate transformation with the center of the hole at the interface between the first film and the second film as the origin.

4. a first film and a second film made of a material different from that of the first film are laminated in the measurement region of the subject, and a hole penetrating the second film is formed in a part of the measurement region; 2. The measurement device according to claim 1, wherein the analysis unit selects the plurality of shape parameters from process parameters that are set in an etching process for machining the hole.

5. 5. The measurement apparatus according to claim 4, wherein the known shape information is a result of a plurality of process simulations in which the process parameters are changed.

6. 5. The measurement apparatus according to claim 3, wherein the analysis unit limits a search range for the value of the shape parameter based on knowledge of an etching process for processing the hole.

7. 2 . The measurement apparatus according to claim 1 , wherein the analysis unit holds a plurality of sets of the shape parameters and estimates the values ​​of the shape parameters while sequentially switching between the sets of the shape parameters.

8. The measurement apparatus according to claim 7 , wherein each of the plurality of sets of shape parameters is composed of a different number of shape parameters, and values ​​of the shape parameters are estimated in ascending order of the number of shape parameters in the set of shape parameters.

9. The subject is irradiated with X-rays; Detecting scattered X-rays emitted from the subject by the irradiation of the X-rays; a measurement method for estimating a surface contour shape of a measurement region in the subject irradiated with the X-rays by analyzing a diffraction image obtained by photoelectrically converting the scattered X-rays, the method comprising: extracting a plurality of principal components by subjecting shape information indicating the shape of a known processed hole to principal component analysis, and determining variables indicating the respective contributions of the plurality of principal components as a plurality of shape parameters used to express the surface contour shape; Calculating a theoretical scattering intensity of the scattered X-rays when values ​​of the plurality of shape parameters are changed; calculating a difference between a measured scattering intensity, which is the intensity of the scattered X-rays, and the theoretical scattering intensity, and creating a regression model of the relationship between the value of the shape parameter and the difference for each of the shape parameters; extracting at least one shape parameter candidate value that reduces the difference from the regression model and calculating a theoretical scattering intensity of the shape parameter candidate value; While repeatedly changing the candidate value of the shape parameter, a value of the shape parameter that minimizes a difference between the measured scattering intensity and the theoretical scattering intensity is estimated. A measuring method comprising:

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