System and method for adjusting kinetic models of surface reactions during plasma processing - Patents.com

Abstract

A system according to one or more embodiments of the present disclosure is disclosed. The system includes a metrology tool configured to obtain one or more measurements of a portion of a specimen. The system includes a controller including one or more processors configured to execute program instructions that cause the one or more processors to generate a surface kinetic model output based on the surface kinetic model, determine an expected response of the surface kinetic model output to excitation by polarized light, compare the determined expected response to one or more measured values, generate one or more metrics based on a comparison of the determined expected response to the one or more measured values ​​of the specimen, adjust one or more parameters of the surface kinetic model to generate an adjusted surface kinetic model, and apply the adjusted surface kinetic model to simulate performance on the specimen during a plasma process.

Description

[Technical field]

[0001] The present invention relates generally to the field of plasma processing, and more particularly to a system and method for adjusting a surface dynamics model to simulate performance on a specimen during a plasma process. [Background technology]

[0002] (CROSS REFERENCE TO RELATED APPLICATIONS) This application claims the benefit under 35 U.S.C. §119(e) of U.S. Provisional Application No. 62 / 889,949, filed August 21, 2019, and entitled “METHOD TO OPTIMIZE MODEL OF KINETICS OF SURFACE REACTIONS DURING PLASMA PROCESSING” to Ankur Agarwal, Chad Huard, Yiting Zhang, Haifeng Pu, Xin Li, Premkumar Panneerchelvam, and Fiddle Han as inventors, the disclosures of which are incorporated herein by reference in their entireties.

[0003] Microelectronics manufacturing involves a variety of plasma process steps. For example, a specimen may undergo hundreds of plasma processes (e.g., etching, deposition, ion implantation, etc.) during manufacturing. During these processes, the specimen is periodically measured using a variety of techniques to characterize the specimen's features, uniformity, and specifications. Characterization of such parameters is difficult due to the changing conditions (e.g., temperature, power, and gas composition) of each plasma process. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] US Patent Application Publication No. 2019 / 0049937 Summary of the Invention [Problem to be solved by the invention]

[0005] As critical dimensions of features in microelectronics manufacturing continue to decrease, the challenges in developing processes that allow for the continued shrinking of critical dimensions of features increase, for example, the time to develop a process that can be manufactured on a large scale increases along with the associated research and development costs.

[0006] It would therefore be desirable to provide a system and method that addresses the deficiencies of previous approaches identified above. [Means for solving the problem]

[0007] A system is disclosed according to one or more embodiments of the present disclosure. In one embodiment, the system includes a metrology tool configured to obtain one or more measurements of a portion of a specimen. In another embodiment, the system includes a controller communicatively coupled to the metrology tool, the controller including one or more processors configured to execute program instructions, the program instructions causing the one or more processors to generate a surface kinetic model output based on the surface kinetic model, the surface kinetic model being executed based on an initial estimate of one or more parameters of the surface kinetic model, determine an expected response of the surface kinetic model output to excitation by polarized light, compare the determined expected response to one or more measurements of the specimen received from the metrology tool, generate one or more metrics based on a comparison of the determined expected response to the one or more measurements of the specimen, adjust one or more parameters of the surface kinetic model based on the one or more metrics to generate an adjusted surface kinetic model, and apply the adjusted surface kinetic model to simulate performance on the specimen during a plasma process of the specimen.

[0008] A method is disclosed according to one or more embodiments of the present disclosure. In one embodiment, the method includes generating a surface kinetic model output using a surface kinetic model, where the surface kinetic model is performed based on an initial estimate of one or more parameters of the surface kinetic model. In another embodiment, the method includes determining an expected response of the surface kinetic model output to excitation by polarized light. In another embodiment, the method includes comparing the determined expected response to one or more measurements of the specimen received from a metrology tool. In another embodiment, the method includes generating one or more metrics based on a comparison between the determined expected response and the one or more measurements of the specimen. In another embodiment, the method includes tuning one or more parameters of the surface kinetic model based on the one or more metrics to generate an tuned surface kinetic model. In another embodiment, the method includes applying the tuned surface kinetic model to simulate performance on the specimen during a plasma process of the specimen.

[0009] A system is disclosed according to one or more embodiments of the present disclosure. In one embodiment, the system includes a metrology tool configured to obtain one or more measurements of a portion of a specimen. In another embodiment, the system includes a controller communicatively coupled to the metrology tool, the controller including one or more processors configured to execute program instructions, the processor instructions causing the one or more processors to generate a surface kinetic model output based on the surface kinetic model, the surface kinetic model being executed based on an initial estimate of one or more parameters of the surface kinetic model, determine an expected response of the surface kinetic model output to excitation with polarized light, compare the determined expected response to one or more measurements of the specimen received from the metrology tool, generate one or more metrics based on a comparison of the determined expected response to the one or more measurements of the specimen, generate a machine learning model, train the machine learning model, tune one or more parameters of the surface kinetic model based on the one or more metrics using the machine learning model to generate an tuned surface kinetic model, and apply the tuned surface kinetic model to simulate performance on the specimen during a plasma process of the specimen.

[0010] A method is disclosed according to one or more embodiments of the present disclosure. In one embodiment, the method includes generating a surface kinetic model output using a surface kinetic model, where the surface kinetic model is performed based on an initial estimate of one or more parameters of the surface kinetic model. In another embodiment, the method includes determining an expected response of the surface kinetic model output to excitation by polarized light. In another embodiment, the method includes comparing the determined expected response to one or more measurements of the specimen received from a metrology tool. In another embodiment, the method includes generating one or more metrics based on a comparison between the determined expected response and the one or more measurements of the specimen. In another embodiment, the method includes generating a machine learning model. In another embodiment, the method includes training the machine learning model. In another embodiment, the method includes tuning one or more parameters of the surface kinetic model based on the one or more metrics with the machine learning model to generate a tuned surface kinetic model. In another embodiment, the method includes applying the tuned surface kinetic model to simulate performance on the specimen during a plasma process of the specimen.

[0011] 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 this 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]

[0012] Many advantages of the present disclosure may be better understood, by those skilled in the art, by reference to the following accompanying drawings. [Figure 1A] FIG. 1 illustrates a simplified block diagram of a system for adjusting a surface dynamics model in accordance with one or more embodiments of the present disclosure. [Figure 1B] FIG. 1 shows a simplified schematic diagram of a system for adjusting a surface dynamics model in accordance with one or more embodiments of the present disclosure. [Diagram 2]1 shows a flowchart illustrating a method for adjusting a surface dynamics model in accordance with one or more embodiments of the present disclosure. [Figure 3A] 1 illustrates an example output of a surface dynamics model, in accordance with one or more embodiments of the present disclosure. [Figure 3B] 1 illustrates an example output of a surface dynamics model, in accordance with one or more embodiments of the present disclosure. [Figure 3C] 1 illustrates an example output of a surface dynamics model, in accordance with one or more embodiments of the present disclosure. [Figure 3D] 1 illustrates an example output of a surface dynamics model, in accordance with one or more embodiments of the present disclosure. [Figure 4] 1 is a plot showing rigorous coupled wave theory (RCWA) iteration results in accordance with one or more embodiments of the present disclosure. [Diagram 5] 1 is a plot illustrating a comparison of a measured response and a determined expected response in accordance with one or more embodiments of the present disclosure. [Figure 6] 1 shows a flowchart illustrating a method for adjusting a surface dynamics model in accordance with one or more embodiments of the present disclosure. [Figure 7] 1 shows a flowchart illustrating a method for adjusting a surface dynamics model in accordance with one or more embodiments of the present disclosure. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0013] The present disclosure has been particularly shown and described with respect to certain embodiments and certain features thereof. The embodiments described herein are to be construed as illustrative and not limiting. It will be readily apparent to those skilled in the art that various changes and modifications in form and details may be made therein without departing from the spirit and scope of the present disclosure.

[0014] Reference will now be made in detail to the disclosed subject matter, which is illustrated in the accompanying drawings.

[0015] Specimen processing includes various plasma process steps. For example, a specimen may undergo hundreds of plasma processes (e.g., etching, deposition, ion implantation, etc.) during manufacturing. Surface kinetic models may be utilized to simulate performance on a specimen during such plasma processes. However, surface kinetic models are not predictive unless the parameters of the model are adjusted. Adjusting the parameters is difficult due to the changing conditions (e.g., temperature, power, gas composition, etc.) of the numerous plasma processes required during manufacturing. Determining the parameters of the surface kinetic model may require manually adjusting the parameters using cross-sectional images of the plasma processes performance on the specimen. Additionally, the parameters may be determined by programmatic methods. These conventional methods require metrology techniques to cross-section the specimen, which leads to specimen waste. Thus, the obtained parameters are not predictive.

[0016] Furthermore, as critical dimensions of features in microelectronics manufacturing continue to decrease, the challenges in developing processes that allow for continued shrinkage of critical dimensions of features increase, e.g., the time to develop a process that can be manufactured on a large scale increases along with the associated research and development costs.

[0017] Accordingly, embodiments of the present disclosure relate to systems and methods for tuning a surface kinetic model. In particular, embodiments of the present disclosure relate to systems and methods for tuning a surface kinetic model based on one or more measurements obtained from a metrology subsystem. In particular, embodiments of the present disclosure relate to systems and methods that combine physical modeling forces with non-destructive measurements of features on a specimen to reduce development time and R&D costs associated with tuning a process. Additionally, embodiments of the present disclosure relate to systems and methods for using physical models to guide the development of optical critical dimension models (compared to purely statistical approaches).

[0018] It is noted herein that one or more embodiments of the present disclosure may have many advantages over conventional methods. For example, one or more embodiments of the present disclosure may allow for reuse of specimens, allowing for building an integrated model by using the same specimen and processing multiple layers. As another example, one or more embodiments of the present disclosure may prevent the need to build optical critical dimension models that typically require long time to fit spectra. Furthermore, one or more embodiments of the present disclosure may provide for fast and automated generation of tailored surface dynamics models. Furthermore, one or more embodiments of the present disclosure may allow for the generation of accurate and predictable surface dynamics models. Furthermore, one or more embodiments of the present disclosure may allow for accelerated research and development of plasma processes.

[0019] 1A shows a simplified block diagram of a system for adjusting a surface dynamics model in accordance with one or more embodiments of the present disclosure. In one embodiment, the system 100 includes a metrology subsystem 102. In another embodiment, the system 100 includes a controller 104, which includes one or more processors 106 and a memory 108. The controller 104 may include or be communicatively coupled to a user interface 110.

[0020] It is noted herein that the metrology subsystem 102 may include any metrology subsystem 102 known in the art, including, but not limited to, optical metrology systems, charged particle based metrology systems, etc. For example, the metrology subsystem may include, but is not limited to, optical critical dimension (OCD) tools, critical dimension scanning electron microscope (CD-SEM) tools, transmission electron microscope (TEM) tools, cross-sectional scanning electron microscope (X-SEM) tools, etc.

[0021] In another embodiment, the controller 104 is communicatively coupled to the metrology subsystem 102. In this regard, the one or more processors 106 of the controller 104 may be configured to receive one or more measurement signals 132 from the metrology subsystem 102. This collected data 132 may be used to adjust the surface dynamics model, as further described herein. Additionally, the one or more processors 106 of the controller 104 may be configured to generate one or more control signals to adjust one or more properties / parameters of the metrology subsystem 102.

[0022] In another embodiment, the system 100 may further include one or more process tools communicatively coupled to the controller 104. The one or more process tools may include any process tools known in the art, including, but not limited to, a lithography tool, an etch tool, a deposition tool, a polishing tool, a scanner, etc. For example, the controller 104 may be configured to generate one or more control signals, where the control signals are configured to adjust one or more characteristics of the one or more process tools in a feedforward or feedback loop based on the adjusted surface dynamics model. For example, the one or more processors 106 of the controller 104 may be configured to generate one or more control signals to a downstream process tool. In another example, the one or more processors 106 of the controller 104 may be configured to generate one or more control signals to an upstream process tool.

[0023] FIG. 1B illustrates a simplified schematic diagram of a metrology subsystem 102 arranged in a reflectometry and / or ellipsometry configuration in accordance with one or more embodiments of the present disclosure.

[0024] In one embodiment, the metrology subsystem 102 includes an illumination source 112, an illumination arm 114, a collection arm 116, and a detector assembly 118. Illumination 101 from the illumination source 112 may be directed to a specimen 120 via the illumination arm 114.

[0025] The metrology subsystem 102 may be configured to collect illumination emanating from the sample via a collection arm 116. The path of the illumination arm 114 may include one or more optical elements 122 suitable for modifying and / or conditioning the illumination 101. For example, the one or more optical elements 122 may include, without limitation, one or more polarizers, one or more filters, one or more beam splitters, one or more diffusers, one or more homogenizers, one or more apodizers, one or more beam shapers, one or more lenses, or any combination thereof.

[0026] The illumination arm 114 can utilize a first focusing element 124 to focus and / or direct the illumination 101 (e.g., a beam) onto the specimen 120. In some embodiments, the specimen 120 is disposed on a stage assembly 126 to facilitate movement of the specimen 120. In some embodiments, the stage assembly 126 is an actuatable stage. For example, the stage assembly 126 can include, but is not limited to, one or more translation stages adapted to selectively translate the specimen 120 along one or more linear directions (e.g., x-direction, y-direction, and / or z-direction). As another example, the stage assembly 126 can include, but is not limited to, one or more rotation stages adapted to selectively rotate the specimen 120 along a rotational direction. As another example, the stage assembly 126 can include, but is not limited to, a rotational stage and a translation stage adapted to selectively translate the specimen 120 along a linear direction and / or rotate the specimen 120 along a rotational direction. It is noted herein that the system 100 may operate in any scanning mode known in the art.

[0027] The collection arm 116 may include a second focusing element 128 to collect illumination from the specimen 120. In another embodiment, the detector assembly 118 is configured to capture illumination emanating from the specimen 120 via the collection arm 116. For example, the detector assembly 118 may receive illumination reflected or scattered from the specimen 120 (e.g., via specular reflection, diffuse reflection, etc.). As another example, the detector assembly 118 may receive illumination generated by the specimen 120 (e.g., emission associated with absorption of the illumination 101, etc.). It is noted that the detector assembly 118 may include any sensor and detector assembly known in the art. The sensor may include, but is not limited to, a charge-coupled device (CCD detector), a complementary metal-oxide semiconductor (CMOS) detector, a time-delay integration (TDI) detector, a photomultiplier tube (PMT), an avalanche photodiode (APD), etc.

[0028] In another embodiment, the controller 104 may obtain one or more measurements of the specimen 120. For example, the controller 104 may be configured to collect metrology measurements of the specimen 120.

[0029] The collection arm 116 may further include collection optics 130 for directing and / or modifying the illumination collected by the second focusing element 128, including, but not limited to, one or more lenses, one or more filters, one or more polarizers, or one or more phase plates.

[0030] As used throughout this disclosure, the term "specimen" generally refers to a substrate formed of a semiconductor or non-semiconductor material (e.g., wafer, reticle, etc.). For example, the semiconductor or non-semiconductor material may include, but is not limited to, monocrystalline silicon, gallium arsenide, and indium phosphide. The specimen may include one or more layers. For example, such layers may include, but are not limited to, resist, dielectric material, conductive material, and semiconductive material. Many different types of such layers are known in the art, and the term specimen, as used herein, is intended to encompass specimens upon which all types of such layers may be formed. The one or more layers formed on the specimen may be patterned or unpatterned. For example, the specimen may include multiple dies, each having repeatable patterned features. The formation and processing of such layers of material may ultimately result in a completed device. Many different types of devices may be formed on the specimen, and the term specimen, as used herein, is intended to encompass specimens upon which any type of device known in the art may be fabricated. Furthermore, for purposes of this disclosure, the terms specimen and wafer should be construed as interchangeable.

[0031] 2 shows a flowchart illustrating a method 200 of adjusting a surface kinetic model in accordance with one or more embodiments of the present disclosure. In particular, FIG. 2 shows a flowchart 200 for adjusting a surface kinetic model using one or more measurements from a metrology tool (e.g., the metrology subsystem 102 shown in FIGS. 1A-1B). In this regard, the flowchart 200 may be considered a conceptual flowchart illustrating steps performed by / within the one or more processors 106 of the controller 104.

[0032] In step 202, the system 100 determines one or more parameters (p n) based on an initial estimate of the surface dynamics model. For example, one or more processors 106 of the controller 104 may be configured to execute the surface dynamics model. In one embodiment, the system 100 calculates a surface dynamics model output (CD n、i ) based on one or more parameters used in step 202. For example, the one or more processors 106 of the controller 104 may be configured to generate a surface dynamics model output.

[0033] In one embodiment, as shown in Figures 3A-3D, the surface kinetics model performed in step 202 may generate a profile describing the shape of a feature created during one or more plasma processes. In another embodiment, the surface kinetics model performed in step 202 may generate one or more critical shape parameters configured to enable reconstruction of the shape of a feature on a specimen. It is noted herein that although Figures 3A-3D show a one-dimensional profile, the shape of a feature may be a two-dimensional or three-dimensional shape. Thus, the above description should not be considered as limiting the scope of the present disclosure, but merely exemplary.

[0034] In step 204, the system 100 calculates the surface dynamics model output (CD n、i ) to determine an expected response of the surface dynamics model output to excitation by polarized light. For example, one or more processors 106 of the controller 104 are configured to determine the expected response. In one embodiment, the determined expected response may be determined using a Fourier space method. For example, the determined expected response may be determined using rigorous coupled wave theory (RCWA). In this regard, the determined expected response of a Fourier space method (e.g., RCWA) may be expressed as a sum of spatial harmonics as a function of the wavelength of the light utilized. In another embodiment, the determined expected response may be determined using a finite element method. In another embodiment, the determined expected response may be determined using a boundary element method.

[0035] In another embodiment, the determined expected response may be determined using small angle X-ray scattering. For example, the determined expected response may be determined by generating one or more scattering images at one or more specimen rotation angles. For example, the one or more scattering images may be generated using x-rays, thereby generating one or more small angle X-ray scattering images. The one or more small angle X-ray scattering images may be generated using any method known in the art, including, but not limited to, grazing incidence small angle X-ray scattering, critical dimension small angle X-ray scattering, grazing incidence transmission small angle X-ray scattering, soft X-ray scattering, etc. It is noted herein that the one or more scattering images may be generated at any specimen rotation angle known in the art.

[0036] It is noted herein that the determined predicted response of the surface dynamics model to excitation by polarized light can be configured in a reflective or transmissive configuration.

[0037] In another embodiment, the system 100 is configured to use an illumination source of a metrology tool (e.g., illumination source 112 of the metrology subsystem 102 shown in FIG. 1B) to excite the specimen with polarized light. In another embodiment, the system 100 is configured to collect a measured response of the specimen to excitation with polarized light. For example, the controller 104 may be configured to collect the measured response of the specimen obtained by the metrology subsystem 102.

[0038] In step 206, the system 100 is configured to compare the determined expected response, determined in step 204, to a measured response of the specimen received from the metrology tool. For example, the one or more processors 106 of the controller 104 may be configured to compare the determined expected response to the measured response obtained from the metrology tool.

[0039] In another embodiment, the system 100 is configured to generate one or more metrics based on a comparison between the determined expected response and the measured response. For example, the one or more processors 106 of the controller 104 may be configured to generate one or more metrics based on a comparison between the determined expected response and the measured response. In another embodiment, the one or more metrics are configured to account for the deviation of the determined expected response from the measured response. For example, the one or more metrics may include a normalized sum of squared deviations between the measured response and the determined expected response. For example, the one or more metrics may include a goodness of fit to account for the discrepancy between the measured response and the determined expected response. In another example, the one or more metrics may include a least squares sum of the deviations between the measured response and the determined expected response. The discrepancy between the measured response and the determined expected response may be accounted for utilizing any statistical metric known in the art, and thus the above discussion should not be construed as limiting the scope of the present disclosure.

[0040] In step 208, the system 100 calculates one or more parameters of the surface dynamics model (P n ) based on one or more metrics to generate an adjusted surface dynamics model. For example, the system 100 may be configured to adjust a first parameter P1 of the surface dynamics model based on one or more metrics. As another example, the system 100 may be configured to adjust a second parameter P2 of the surface dynamics model based on one or more metrics. As used herein, the system 100 may be configured to adjust up to N parameters P n It is noted that the present invention may be configured to adjust the number of parameters. For example, the number of parameters to be adjusted may range from 1 to 1000. Therefore, the above description should not be construed as limiting the scope of the present disclosure.

[0041] In another embodiment, the system 100 is configured to generate an adjusted surface dynamics model based on one or more adjusted parameters. For example, one or more parameters of the surface dynamics model may be adjusted until convergence is achieved. For example, convergence may be defined based on one or more metrics being lower than a threshold tolerance. In this regard, the threshold tolerance may be 1×10 -10 ~5000. In this example, the surface kinetic model is configured such that one or more metrics exceed a threshold (e.g., 1 × 10 -10 .about.5000). It is noted herein that the tolerance level of the threshold may be adjusted based on the complexity of the process being characterized.

[0042] In step 210, the system 100 is configured to apply the adjusted surface kinetics model to simulate performance on the specimen during plasma processing of the specimen. For example, the one or more processors 106 of the controller 104 may be configured to apply the adjusted surface kinetics model to simulate performance on the specimen during plasma processing of the specimen 120.

[0043] 3A-3D show example outputs of a surface dynamics model in accordance with one or more embodiments of the present disclosure. Fig. 3A shows output 300. Fig. 3B shows output 310. Fig. 3C shows output 320. Fig. 3D shows output 330.

[0044] One or more outputs 300, 310, 320, 330 may include one or more shape description parameters (CD n、i For example, one or more of the outputs 300, 310, 320, 330 may include a first shape describing parameter CD 1、i As another example, one or more of the outputs 300, 310, 320, 330 may include a second shape-descriptive parameter CD 2、i One or more outputs 300, 310, 320, 330 may include up to N shape description parameters CD n、i may include.

[0045] It is further noted herein that the output of the surface dynamics model may not be the profile itself, but may be a list of shape describing parameters that allow reconstruction, and thus the outputs 300, 310, 320, 330 shown in Figures 3A-3D should not be construed as limiting the scope of the present disclosure, but are provided for illustrative purposes.

[0046] 4 is a plot 400 illustrating the results of a Rigorous Coupled Wave Theory (RCWA) iteration, in accordance with one or more embodiments of the present disclosure. In particular, FIG. 4 illustrates a plot 400 including the results of an iteration of the RCWA response of step 202 compared to a measured response 402 of the specimen received from a metrology tool (e.g., metrology subsystem 102 as shown in FIGS. 1A-1B). The model parameter P n As varies, the RCWA response evolves from modeling at iteration 1 404 (modeled response 404) to modeling at iteration n 406 (modeled response 406), where the model is deemed to have converged based on a comparison of the measured response 402 and the modeled response 406.

[0047] 5 is a plot 500 illustrating a comparison between a measured response and a determined modeled response, in accordance with one or more embodiments of the present disclosure. In particular, FIG. 5 illustrates a plot 500 illustrating the deviation of the modeled response from the measured metric below a threshold 506. The model parameter P n As varies, the deviation between the modeled responses 404, 406 and the measured response 402 is quantified as deviation 502. At iteration n 504, deviation 502 is less than threshold 506 and the iterative process is considered to have converged.

[0048] In another embodiment, step 208 (shown in FIG. 2) may be performed before iteration n 504. For example, the system 100 may adjust one or more parameters P nIn another embodiment, at iteration n 504, step 210 (shown in FIG. 2 ) may be performed. For example, system 100 may be configured to apply the adjusted surface dynamics model to simulate performance on the specimen during plasma processing of the specimen.

[0049] FIG. 6 shows a flowchart illustrating a method 600 for adjusting a surface dynamics model, according to one or more embodiments of the present disclosure. It is noted that the embodiments and implementations described herein above in the context of the system 100 should be construed to extend to the method 600. In this regard, the steps of the method 600 may be performed by the system 100, and the method 600 may further include one or more steps that are required or implied by the architecture of the system 100. However, it is recognized that the method 600 is not limited to the architecture of the system 100, and one or more steps of the method 600, or portions thereof, may be performed using alternative system components and / or architectures. Furthermore, the steps of the method 600 may be performed in any order, unless otherwise specified herein.

[0050] In step 602, a surface kinetic model output is generated using the surface kinetic model. For example, the surface kinetic model output may be generated by one or more processors 106 of the controller 104. As another example, the surface kinetic model may be executed based on an initial estimate of one or more parameters of the surface kinetic model. For example, the surface kinetic model based on the initial estimate of the one or more parameters may be executed on one or more processors 106 of the controller 104. In one embodiment, the surface kinetic model output includes a profile configured to describe a shape of a feature of the specimen. In another embodiment, the surface kinetic model output includes one or more critical shape parameters configured to enable reconstruction of the shape of the feature of the specimen.

[0051] It is noted herein that the surface kinetic model may be run simultaneously at one or more sites across the specimen. For example, the surface kinetic model may be run at one or more sites across the specimen for each feature of one or more features on the specimen. The one or more sites may be determined individually. Additionally, the one or more sites may be determined using an algorithm configured to guide the determination.

[0052] It is further noted herein that one or more of the initial estimated parameters may be altered based on one or more features on the specimen, for example, one or more shape parameters of the one or more parameters may be altered based on one or more features on the specimen.

[0053] In step 604, a predicted response of the surface dynamics model output to excitation with polarized light is determined. The excitation with polarized light may be configured in a reflection or transmission configuration. In one embodiment, the predicted response is determined using a Fourier space method. For example, a rigorous coupled wave theory (RCWA) may be implemented, so that the determined predicted response is expressed as a sum of spatial harmonics.

[0054] In another embodiment, the one or more small angle x-ray scattering images are generated at one or more specimen rotation angles. For example, the one or more small angle x-ray images are generated using grazing incidence small angle x-ray scattering, critical dimension small angle x-ray scattering, grazing incidence transmission small angle x-ray scattering, soft x-ray scattering, etc.

[0055] In another embodiment, the determined expected response is determined by utilizing one or more additional parameters of the surface kinetic model. For example, the one or more additional parameters may be related to the dispersion (n, k) or thickness of the layer. For example, the dispersion or thickness of the layer may be related to the primary material and / or the material below the primary material. Furthermore, the one or more additional parameters may be additional shape parameters. For the purposes of this disclosure, the term "additional parameters" refers to parameters not previously used by the surface kinetic model (e.g., not used during the initial estimation of step 602). In this embodiment, an iterative optimization may be used to derive the best combination of optical critical dimension (OCD) parameters to minimize the deviation between the determined expected response and the measured response.

[0056] In step 606, the determined expected response is compared to one or more measurements of the specimen received from a metrology tool. For example, a metrology subsystem (e.g., metrology subsystem 102 shown in FIGS. 1A-1B) may be configured to obtain one or more measurements of the specimen. In this regard, the one or more measurements of the specimen may be obtained from the controller 104 of the system 100. In this example, the one or more metrology subsystems may be configured to obtain one or more measurements of the specimen. In particular, a first metrology subsystem may be used to obtain a first measurement, and a second metrology subsystem may be used to obtain a second measurement. In particular, one or more optical critical dimension measurements from an OCD metrology tool may be used in combination with one or more CD-SEM measurements from a critical dimension scanning electron microscope (CD-SEM) tool. It is noted that the one or more metrology tools may include any metrology tool known in the art, including, but not limited to, optical critical dimension (OCD) tools, critical dimension scanning electron microscope (CD-SEM) tools, transmission electron microscope (TEM) tools, cross-sectional scanning electron microscope (X-SEM) tools, etc. configured to obtain up to N measurements.

[0057] In step 608, one or more metrics are generated based on the comparison between the determined expected response and the one or more measurements of the specimen. For example, the one or more processors 106 of the controller 104 may be configured to generate the one or more metrics. For example, a normalized sum of squared deviations between the one or more measurements of the specimen and the determined expected response may be generated. In another example, a fit may be generated to explain the discrepancy between the one or more measurements of the specimen and the determined expected response. In a further example, a least squared sum of deviations between the one or more measurements of the specimen and the determined expected response may be generated.

[0058] At step 610, one or more parameters of the surface dynamics model are adjusted based on the one or more metrics of step 608 to generate an adjusted surface dynamics model. The adjusted surface dynamics model may be configured to generate an adjusted surface dynamics model output. For example, the one or more processors 106 of the controller 104 may be configured to generate the adjusted surface dynamics model based on the adjusted one or more parameters.

[0059] In another embodiment, one or more parameters of the surface dynamics model are adjusted until convergence is achieved. For example, convergence may be defined based on one or more metrics being lower than a threshold tolerance. In this regard, the threshold tolerance may be 1×10 -10 ~5000. In this example, the surface kinetic model is configured such that one or more metrics exceed a threshold (e.g., 1 × 10 -10 .about.5000). It is noted herein that the tolerance level of the threshold may be adjusted based on the complexity of the process being characterized.

[0060] In another embodiment, an iterative optimization algorithm is used to tune one or more parameters of the surface dynamics model. For example, a steepest descent method may be configured to find the minimum of one or more metrics. In another embodiment, a stochastic gradient descent method is used to tune the steepest descent method. The stochastic gradient descent method may be configured to randomly select samples to evaluate the gradient.

[0061] In step 612, the adjusted surface kinetics model is applied to simulate performance on the specimen during plasma processing of the specimen. For example, the one or more processors 106 of the controller 104 are configured to apply the adjusted surface kinetics model to simulate performance on the specimen during plasma processing of the specimen 120.

[0062] In an optional step, the one or more control signals are configured to selectively adjust one or more characteristics of the one or more process tools based on the adjusted surface dynamics model. For example, the system 100 may further include one or more process tools communicatively coupled to the controller 104. The one or more process tools may include any process tool known in the art, including, but not limited to, a lithography tool, an etch tool, a deposition tool, a polishing tool, a scanner, etc. Continuing with the same example, the controller 104 may be configured to generate one or more control signals, the control signals configured to adjust one or more characteristics of the one or more process tools in a feedforward or feedback loop based on the adjusted surface dynamics model.

[0063] In an optional step, the one or more control signals are configured to selectively adjust one or more characteristics of the metrology subsystem 102 based on the adjusted surface dynamics model.

[0064] 7 illustrates a flowchart of a method 700 for adjusting a surface dynamics model, according to one or more embodiments of the present disclosure. It is noted that the embodiments and enabling techniques described herein above in the context of the system 100 should be construed to extend to the method 700. In this regard, the steps of the method 700 may be performed by the system 100, and the method 700 may further include one or more steps required or implied by the architecture of the system 100. However, it is recognized that the method 700 is not limited to the architecture of the system 100, and one or more steps of the method 700, or portions thereof, may be performed using alternative system components and / or architectures. Furthermore, the steps of the method 700 may be performed in any order, unless otherwise specified herein.

[0065] In step 702, a surface kinetic model output is generated using the surface kinetic model. For example, one or more processors 106 of the controller 104 may be configured to generate the surface kinetic model output using the surface kinetic model. For example, the surface kinetic model may be performed based on an initial estimate of one or more parameters of the surface kinetic model. In one embodiment, the surface kinetic model output includes a profile configured to describe a shape of a feature of the specimen. In another embodiment, the surface kinetic model output includes one or more critical shape parameters configured to enable reconstruction of the shape of the feature of the specimen.

[0066] In step 704, a predicted response of the surface dynamics model output to excitation with polarized light is determined. The excitation with polarized light may be configured in a reflection or transmission configuration. In one embodiment, the predicted response is determined using a Fourier space method. For example, a rigorous coupled wave theory (RCWA) may be implemented, so that the determined predicted response is expressed as a sum of spatial harmonics.

[0067] In another embodiment, the one or more small angle x-ray scattering images are generated at one or more specimen rotation angles. For example, the one or more small angle x-ray images are generated using grazing incidence small angle x-ray scattering, critical dimension small angle x-ray scattering, grazing incidence transmission small angle x-ray scattering, soft x-ray scattering, etc.

[0068] In step 706, the determined expected response is compared to one or more measurements of the specimen received from a metrology tool. For example, a metrology subsystem (e.g., metrology subsystem 102 shown in FIGS. 1A-1B) may be configured to obtain one or more measurements of the specimen. In this regard, the one or more measurements of the specimen may be obtained from the controller 104 of the system 100. The metrology tool may include any metrology tool known in the art, including, but not limited to, an optical critical dimension (OCD) tool, a critical dimension scanning electron microscope (CD-SEM) tool, a transmission electron microscope (TEM) tool, a cross-sectional scanning electron microscope (X-SEM) tool, etc.

[0069] In step 708, one or more metrics are generated based on a comparison between the determined expected response and the one or more measurements of the specimen. For example, a normalized sum of squared deviation between the one or more measurements of the specimen and the determined expected response may be generated.

[0070] In another example, a fit may be generated to explain the discrepancy between one or more measurements of the specimen and the determined expected response. In a further example, a least squares sum of deviations between one or more measurements of the specimen and the determined expected response may be generated.

[0071] At step 710, a machine learning model is generated. In one embodiment, the controller 104 may be configured to generate the machine learning model and use the machine learning model to adjust the surface dynamics model. The controller 104 may be configured to generate the machine learning model via any technique known in the art, including, but not limited to, supervised learning, unsupervised learning, etc.

[0072] It is noted herein that the machine learning model generated in step 710 may include any type of machine learning algorithm and / or deep learning technique known in the art, including, but not limited to, convolutional neural networks (CNNs), artificial neural networks (ANNs), generative adversarial networks (GANs), and the like. As another example, the machine learning model may include deep convolutional neural networks. For example, in some embodiments, the machine learning may include ALEXNET and / or GOOGLENET. In this regard, the machine learning algorithm, classifier, or predictive model is configured to adjust the surface dynamics model.

[0073] In step 712, the machine learning model generated in step 710 is trained. For example, the machine learning model may be trained using pre-generated synthetic data from the surface dynamics model and RCWA responses to the generated outputs. Other training techniques such as pre-labeling, feature extraction, etc. may be applied as well.

[0074] In step 714, one or more parameters of the surface kinetic model are tuned using the machine learning model based on the one or more metrics to generate an tuned surface kinetic model.

[0075] In step 716, the tuned surface dynamics model is applied to simulate performance on the specimen during plasma processing of the specimen.

[0076] It is noted herein that the use of machine learning models to tune the surface dynamics model may enable faster generation of tuned parameters.

[0077] It is further noted herein that a machine learning model may be used in step 704. For example, a machine learning model may be used to determine an expected response to excitation with polarized light. In this regard, the machine learning model may substitute for Fourier space methods (e.g., RCWA) or SAXS to calibrate the measured structure of the specimen.

[0078] It is noted herein that one or more components of system 100 may be communicatively coupled to various other components of system 100 in any manner known in the art. For example, one or more processors 106 may be communicatively coupled to each other and to the other components via wired (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 104 may be communicatively coupled to one or more components of metrology subsystem 102 via any wired or wireless connection known in the art.

[0079] In one embodiment, the one or more processors 106 may include any one or more processing elements known in the art. In this sense, the one or more processors 106 may include any microprocessor-type device configured to execute software algorithms and / or instructions. In one embodiment, the one or more processors 106 may comprise 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 100 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, multiple computer systems. Furthermore, it should be appreciated that the steps described throughout this disclosure may be performed by any one or more of the one or more processors 106. In general, the term "processor" may be broadly defined to encompass any device having one or more processing elements to execute program instructions from memory 108. Additionally, different subsystems of system 100 (e.g., illumination source 112, detector assembly 118, controller 104, user interface 110, etc.) may include processors or logic elements suitable for performing at least a portion of the steps described throughout this disclosure. Thus, the above description should not be construed as a limitation of the present disclosure, but merely as an example.

[0080] The memory 108 may include any storage medium known in the art suitable for storing program instructions executable by the associated one or more processors 106 and data received from the metrology subsystem 102. For example, the memory 108 may include a non-transitory memory medium. For example, the memory 108 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. It is further noted that the memory 108 may be housed in a common controller housing along with the one or more processors 106. In alternative embodiments, the memory 108 may be located remotely with respect to the physical location of the processors 106, the controller 104, and the like. In another embodiment, the memory 108 maintains program instructions for causing the one or more processors 106 to perform various steps described throughout this disclosure.

[0081] In one embodiment, the user interface 110 is communicatively coupled to the controller 104. In one embodiment, the user interface 110 may include, but is not limited to, one or more desktops, tablets, smartphones, smart watches, etc. In another embodiment, the user interface 110 includes a display used to display data of the system 100 to a user. The display of the user interface 110 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 that can be integrated with the user interface 110 is suitable for implementation in the present disclosure. In another embodiment, a user may input selections and / or commands responsive to data displayed to the user via a user input device of the user interface 110.

[0082] Those skilled in the art will recognize that the components (e.g., operations), devices, objects, and their accompanying descriptions described herein are used as examples for conceptual clarity, and that various configuration modifications are contemplated. Thus, as used herein, the specific embodiments described and the accompanying descriptions are intended to represent their more general classes. In general, the use of a specific embodiment is intended to represent the class, and the inclusion of the specific components (e.g., operations), devices, and objects should not be considered limiting.

[0083] Those skilled in the art will appreciate that there are a variety of vehicles (e.g., hardware, software, and / or firmware) in which the processes and / or systems and / or other techniques described herein may be implemented, and that the preferred vehicle will vary depending on the context in which the processes and / or systems and / or other techniques are deployed. For example, if the implementer determines that speed and accuracy are paramount, the implementer may select a primarily hardware and / or firmware vehicle; alternatively, if flexibility is paramount, the implementer may select a primarily software implementation, or again alternatively, the implementer may select some combination of hardware, software, and / or firmware. Thus, there are several possible vehicles in which the processes and / or devices and / or other techniques described herein may be implemented, and any vehicle utilized is a choice depending on the context in which the vehicle is deployed and the particular interests of the implementer (e.g., speed, flexibility, or predictability), none of which is inherently better than another, in that any of which may be subject to change.

[0084] The preceding description is presented to enable one skilled in the art to make and use the invention as provided in the context of a particular application and its requirements. As used herein, directional terms such as "top", "bottom", "over", "under", "upper", "upward", "lower", "down" and "downward" are intended to provide relative positions for purposes of description and are not intended to specify 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. Thus, the present invention is not intended to be limited to the specific embodiments shown and described, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

[0085] With respect to the use of substantially any plural and / or singular term herein, those of skill in the art may interpret from the plural to the singular and / or from the singular to the plural as appropriate to the context and / or application. The various singular / plural permutations have not been explicitly set forth herein for the sake of clarity.

[0086] All methods described herein may include storing results of one or more steps of the method embodiments in memory. The results may include any of the results described herein and may be stored in any manner known in the art. The memory may include any of the memories described herein, or any other suitable storage medium known in the art. After storing the results, the results may be accessed in the memory and 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. Furthermore, the results may be stored "permanently," "semi-permanently," "temporarily," or for a period of time. For example, the memory may be a random access memory (RAM), and the results may not necessarily persist in memory indefinitely.

[0087] It is further contemplated that each of the method embodiments described above may include any other step(s) of any other method(s) described herein. In addition, each of the method embodiments described above may be performed by any of the systems described herein.

[0088] The subject matter described herein may depict different components contained 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" to achieve the desired functionality. Thus, any two components herein that are combined to achieve a particular functionality may be considered to be "associated" with one another, such that the desired functionality is achieved without regard to the architecture or intermediate components. Similarly, any two components so associated may also be considered to be "connected" or "coupled" with one another to achieve the desired functionality, and any two components capable of being so associated may be considered to be "coupleable" with one another to achieve the desired functionality. Specific examples of components that may be coupled include, but are not limited to, components that are physically matable and / or physically interacting, and / or components that are wirelessly interacting and / or wirelessly interacting, and / or components that are logically interacting and / or logically interacting.

[0089] It should further be understood that the present invention is defined by the appended claims. In general, it will be understood by those skilled in the art that the terms used herein, particularly 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 "including but not limited to," etc.). If a specific number of introduced claim recitations are intended, such intent will be explicitly set forth in the claims, and it will be further understood by those skilled in the art that, in the absence of such recitation, no such intent exists. For example, to aid in understanding, the following appended claims may include the use of the introductory phrases "at least one" and "one or more" to introduce the claim recitations. However, the use of such phrases should not be construed to mean that the introduction of a claim recitation with the indefinite article "a" or "an" limits the scope of any particular claim containing the claim recitation so introduced to inventions containing only one such recitation, even if the same claim includes the introductory phrase "one or more" or "at least one" and the indefinite article "a" or "an" (e.g., "a" and / or "an" should generally be interpreted to mean "at least one" or "one or more"), and the same applies to the use of definite articles used to introduce claim recitations. In addition, even if a specific number of introduced claim recitations is explicitly recited, one of ordinary skill in the art will recognize that such a recitation should generally be interpreted to mean at least the recited number (e.g., a recitation of only "two recitations" without any other modifier generally means at least two recitations, or more than two recitations).Further, in instances where a phrase similar to "at least one of A, B, and C, etc." is used, such a configuration is generally intended to have the meaning as one of ordinary skill in the art would understand the phrase (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, etc.). In instances where a phrase similar to "at least one of A, B, or C, etc." is used, such a configuration is generally intended to have the meaning as one of ordinary skill in the art would understand the phrase (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, etc.). It will be further understood by those skilled in the art that virtually any disjunction and / or phrase expressing two or more alternative terms, whether in the specification, 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."

[0090] It will be apparent that the present disclosure and many of its attendant advantages will be understood from the foregoing description, and that various changes in the form, construction and arrangement of the elements may be made without departing from the disclosed subject matter or sacrificing all of its important advantages. The forms described are merely illustrative, and it is the intent of the following claims to encompass and include such modifications. It is to be understood, further, that the invention is defined by the appended claims.

Claims

1. a metrology tool configured to obtain one or more measurements of a portion of the specimen; and a controller communicatively coupled to the metrology tool, the controller comprising one or more processors configured to execute program instructions, the program instructions causing the one or more processors to: generating a surface kinetic model output based on a surface kinetic model, where the surface kinetic model is run based on an initial estimate of one or more parameters of the surface kinetic model; determining a predicted response of the surface kinetic model output to excitation by polarized light using one or more additional parameters of the surface kinetic model, the one or more additional parameters including one or more parameters not used in an initial estimate of the one or more parameters of the surface kinetic model; comparing the determined expected response to the one or more measurements of the sample received from the metrology tool; generating one or more metrics based on the comparison between the determined expected response and the one or more measurements of the specimen; adjusting the one or more parameters of the surface kinetic model based on the one or more metrics to generate an adjusted surface kinetic model; applying the tuned surface dynamics model to simulate performance on a specimen during plasma processing of the specimen; generating one or more control signals configured to selectively adjust one or more characteristics of one or more process tools based on the adjusted surface dynamics model; A controller, system.

2. Said generation of the adjusted surface dynamics model comprises: generating an adjusted surface dynamics model output based on the one or more adjusted parameters until convergence is achieved, wherein the convergence is defined based on the one or more metrics being below a threshold tolerance. The system of claim 1 .

3. The system of claim 2 , wherein the threshold tolerance is between 1×10 −10 and 5000.

4. The metrology tool includes: an optical critical dimension (OCD) tool, a critical dimension scanning electron microscope (CD-SEM) tool, a transmission electron microscope (TEM) tool, or a cross-sectional scanning electron microscope (X-SEM) tool; The system of claim 1 , comprising at least one of:

5. The system of claim 1 , wherein the surface dynamics model output comprises a profile configured to describe a shape of a feature of the specimen.

6. The system of claim 1 , wherein the surface dynamics model output includes one or more critical shape parameters configured to enable reconstruction of a shape of a feature on the specimen.

7. The system of claim 1 , wherein the excitation with the polarized light is configured in at least one of a reflective configuration or a transmissive configuration.

8. The determining of the expected response of the surface dynamics model output to excitation by polarized light comprises: Implementing Fourier space methods; The system of claim 1 , comprising:

9. The determining of the expected response of the surface dynamics model output to excitation by polarized light comprises: Implementing rigorous coupled wave theory; The system of claim 8 , comprising:

10. The system of claim 9 , wherein the determined expected response is expressed as a sum of spatial harmonics as a function of wavelength of the polarization utilized.

11. The one or more metrics may be: a normalized sum of squared deviations between the one or more measurements of the sample and the determined expected response; a goodness of fit to explain the discrepancy between the one or more measurements of the sample and the determined expected response; or a least squared sum of deviations between the one or more measurements of the sample and the determined expected response. The system of claim 1 , comprising at least one of:

12. adjusting the one or more parameters of the surface kinetic model based on the one or more metrics to generate an adjusted surface kinetic model, adjusting said one or more parameters using an optimization algorithm; The system of claim 1 , comprising:

13. The optimization algorithm comprises: a gradient descent method, wherein the gradient descent method is configured to find a minimum of the one or more metrics. The system of claim 12.

14. and further comprising adjusting the steepest descent method using a stochastic gradient descent method, where the stochastic gradient descent method is configured to randomly select examples and evaluate gradients. The system of claim 13.

15. The system of claim 1 , wherein the surface dynamics model is run simultaneously at one or more sites across the specimen.

16. The system of claim 1 , wherein one or more shape parameters of the one or more parameters of the initial guess are varied based on one or more features on the specimen.

17. The system of claim 1 , wherein the one or more additional parameters include at least one of dispersion or thickness.

18. The determining of the expected response of the surface dynamics model output to excitation by polarized light comprises: generating one or more small angle x-ray scattering images at one or more specimen rotation angles; The system of claim 1 , comprising:

19. The one or more small angle x-ray scattering images include at least Grazing incidence small angle x-ray scattering, critical dimension small angle x-ray scattering, grazing incidence transmission small angle x-ray scattering, or soft x-ray scattering; The system of claim 18, wherein the signal is generated using one of the following:

20. The controller: Generate a machine learning model, training a machine learning model, where the trained machine learning model is utilized to adjust the one or more parameters of the surface kinetic model based on the one or more metrics to generate an adjusted surface kinetic model. The system of claim 1 further configured to:

21. generating a surface kinetic model output based on a surface kinetic model, wherein the surface kinetic model is run based on an initial estimate of one or more parameters of the surface kinetic model; determining a predicted response of the surface kinetic model output to excitation by polarized light using one or more additional parameters of the surface kinetic model, wherein the one or more additional parameters include one or more parameters not used in an initial estimate of the one or more parameters of the surface kinetic model; comparing the determined expected response to one or more measurements of the sample received from a metrology tool; generating one or more metrics based on the comparison between the determined expected response and the one or more measurements of the specimen; adjusting the one or more parameters of the surface kinetic model based on the one or more metrics to generate an adjusted surface kinetic model; applying the tuned surface dynamics model to simulate performance on a specimen during plasma processing of the specimen; generating one or more control signals configured to selectively adjust one or more characteristics of one or more process tools based on the adjusted surface dynamics model; Including, method.

22. Said generation of the adjusted surface dynamics model comprises: generating an adjusted surface dynamics model output based on the one or more adjusted parameters until convergence is achieved, wherein the convergence is defined based on the one or more metrics being below a threshold tolerance; 22. The method of claim 21 , comprising:

23. The method of claim 22, wherein the threshold tolerance is between 1×10-10 and 5000.

24. 22. The method of claim 21, wherein the surface dynamics model output comprises a profile configured to describe a shape of a feature of the specimen.

25. 22. The method of claim 21, wherein the surface dynamics model output includes one or more critical shape parameters configured to enable reconstruction of a shape of a feature on the specimen.

26. The method of claim 21 , wherein the excitation with the polarized light is configured in at least one of a reflective or transmissive configuration.

27. The determining of the expected response of the surface dynamics model output to excitation by polarized light comprises: Implementing Fourier space methods; 22. The method of claim 21 , comprising:

28. The determining of the expected response of the surface dynamics model output to excitation by polarized light comprises: Implementing rigorous coupled wave theory; 28. The method of claim 27, comprising:

29. 30. The method of claim 28, wherein the determined expected response is expressed as a sum of spatial harmonics as a function of wavelength of the polarization utilized.

30. The one or more metrics may be: a normalized sum of squared deviations between the one or more measurements of the sample and the determined expected response; a goodness of fit to explain the discrepancy between the one or more measurements of the sample and the determined expected response; or a least squared sum of deviations between the one or more measurements of the sample and the determined expected response.

22. The method of claim 21, comprising at least one of:

31. adjusting the one or more parameters of the surface kinetic model based on the one or more metrics to generate an adjusted surface kinetic model, adjusting said one or more parameters using an optimization algorithm; 22. The method of claim 21 , comprising:

32. The optimization algorithm comprises: a gradient descent method, wherein the gradient descent method is configured to find a minimum of the one or more metrics.

32. The method of claim 31 .

33. and further comprising adjusting the steepest descent method using a stochastic gradient descent method, where the stochastic gradient descent method is configured to randomly select examples and evaluate gradients.

33. The method of claim 32.

34. The metrology tool includes: an optical critical dimension (OCD) tool, a critical dimension scanning electron microscope (CD-SEM) tool, a transmission electron microscope (TEM) tool, or a cross-sectional scanning electron microscope (X-SEM) tool; 22. The method of claim 21, comprising at least one of:

35. 22. The method of claim 21, wherein the surface dynamics model is run simultaneously at one or more sites across the specimen.

36. 22. The method of claim 21, wherein one or more shape parameters of the one or more parameters of the initial guess are varied based on one or more features on the specimen.

37. The method of claim 21 , wherein the one or more additional parameters include at least one of dispersion or thickness.

38. The determining of the expected response of the surface dynamics model output to excitation by polarized light comprises: generating one or more scattering images at one or more specimen rotation angles; 22. The method of claim 21 , comprising:

39. 40. The method of claim 38, wherein the one or more scatter images include one or more small angle x-ray images.

40. The one or more small angle x-ray scattering images Grazing incidence small angle x-ray scattering, critical dimension small angle x-ray scattering, grazing incidence transmission small angle x-ray scattering, or soft x-ray scattering; 40. The method of claim 39, wherein the signal is generated using at least one of:

41. Generating a machine learning model; and training the machine learning model, wherein the trained machine learning model is utilized to adjust the one or more parameters of the surface kinetics model based on the one or more metrics to generate an adjusted surface kinetics model; 22. The method of claim 21 further comprising:

42. a metrology tool configured to obtain one or more measurements of a portion of the specimen; and a controller communicatively coupled to the metrology tool, the controller including one or more processors configured to execute program instructions, the program instructions causing the one or more processors to: generating a surface kinetic model output based on a surface kinetic model, where the surface kinetic model is run based on an initial estimate of one or more parameters of the surface kinetic model; determining a predicted response of the surface kinetic model output to excitation by polarized light using one or more additional parameters of the surface kinetic model, the one or more additional parameters including one or more parameters not used in an initial estimate of the one or more parameters of the surface kinetic model; comparing the determined expected response to the one or more measurements of the sample received from the metrology tool; generating one or more metrics based on the comparison between the determined expected response and the one or more measurements of the specimen; Generate a machine learning model, training said machine learning model; tuning the one or more parameters of the surface kinetic model using the machine learning model based on the one or more metrics to generate an adjusted surface kinetic model; applying the tuned surface dynamics model to simulate performance on a specimen during plasma processing of the specimen; generating one or more control signals configured to selectively adjust one or more characteristics of one or more process tools based on the adjusted surface dynamics model; A controller, system.

43. generating a surface kinetic model output using a surface kinetic model, where the surface kinetic model is run based on an initial estimate of one or more parameters of the surface kinetic model; determining a predicted response of the surface kinetic model output to excitation by polarized light using one or more additional parameters of the surface kinetic model, wherein the one or more additional parameters include one or more parameters not used in an initial estimate of the one or more parameters of the surface kinetic model; comparing the determined expected response to the one or more measurements of the specimen from a metrology tool; generating one or more metrics based on the comparison between the determined expected response and the one or more measurements of the specimen; generating a machine learning model; training the machine learning model; tuning the one or more parameters of the surface kinetic model based on the one or more metrics using the machine learning model to generate an adjusted surface kinetic model; applying the tuned surface dynamics model to simulate performance on a specimen during plasma processing of the specimen; generating one or more control signals configured to selectively adjust one or more characteristics of one or more process tools based on the adjusted surface dynamics model; Including, method.

Images