System and method for adjusting a kinetic model of surface reactions during plasma processing

Abstract

According to one or more embodiments of the present disclosure, a system is disclosed. The system includes a metrology tool configured to acquire one or more measurements of a portion of a sample. 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 kinetics model output based on a surface kinetics model, determine an expected response of the surface kinetics model output to excitation by polarized light, compare the determined expected response to the one or more measurements, generate one or more metrics based on the comparison between the determined expected response and the one or more measurements of the sample, adjust one or more parameters of the surface kinetics model to generate an adjusted surface kinetics model, and apply the adjusted surface kinetics model to simulate performance on a sample during a plasma process.

Description

[0001] Cross-reference to related applications

[0002] This application claims the benefit under 35 U.S.C. §119(e) of U.S. Provisional Application Serial No. 62 / 889,949, filed on August 21, 2019, entitled “METHOD TO OPTIMIZE MODEL OF KINETICS OF SURFACE REACTIONS DURING PLASMA PROCESSING,” by inventors Ankur Agarwal, Chad Huard, Yiting Zhang, Haifeng Pu, Xin Li, Premkumar Panneerchelvam, and Fiddle Han, the entirety of which is incorporated herein by reference. Technical Field

[0003] 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 properties on a sample during plasma processing. Background Art

[0004] Microelectronics manufacturing involves a variety of plasma process steps. For example, a sample may be exposed to hundreds of plasma processes (e.g., etching, deposition, ion implantation, or the like) during manufacturing. During these processes, the sample is periodically measured using various techniques to characterize its characteristics, uniformity, and specifications. Characterizing these parameters is challenging due to the varying conditions of each plasma process (e.g., temperature, power, and gas composition).

[0005] As the critical dimensions of features in microelectronics manufacturing continue to decrease, the challenges of developing processes that achieve the ever-shrinking critical dimensions of features increase. For example, the time to develop a process that can be mass-manufactured increases along with the associated research and development costs.

[0006] Therefore, it would be desirable to provide a system and method that addresses the shortcomings of previous approaches identified above. Summary of the Invention

[0007] According to one or more embodiments of the present disclosure, a system is disclosed. In one embodiment, the system includes a metrology tool configured to obtain one or more measurements of a portion of a sample. 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 dynamic model output based on a surface dynamic model, the surface dynamic model being run based on an initial guess of one or more parameters of the surface dynamic model; determine an expected response of the surface dynamic model output to excitation by polarized light; compare the determined expected response with the one or more measurements of the sample received from the metrology tool; generate one or more metrics based on the comparison between the determined expected response and the one or more measurements of the sample; adjust the one or more parameters of the surface dynamic model based on the one or more metrics to generate an adjusted surface dynamic model; and apply the adjusted surface dynamic model to simulate on-sample performance during plasma processing of the sample.

[0008] According to one or more embodiments of the present disclosure, a method is disclosed. In one embodiment, the method includes generating a surface dynamic model output using a surface dynamic model, the surface dynamic model being run based on an initial guess of one or more parameters of the surface dynamic model. In another embodiment, the method includes determining an expected response of the surface dynamic model output to excitation by polarized light. In another embodiment, the method includes comparing the determined expected response with one or more measurements of a sample received from a metrology tool. In another embodiment, the method includes generating one or more metrics based on the comparison between the determined expected response and the one or more measurements of the sample. In another embodiment, the method includes adjusting the one or more parameters of the surface dynamic model based on the one or more metrics to generate an adjusted surface dynamic model. In another embodiment, the method includes applying the adjusted surface dynamic model to simulate on-sample performance during plasma processing of the sample.

[0009] According to one or more embodiments of the present disclosure, a system is disclosed. In one embodiment, the system includes a metrology tool configured to obtain one or more measurements of a portion of a sample. 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 dynamic model output based on a surface dynamic model, the surface dynamic model being run based on an initial guess of one or more parameters of the surface dynamic model; determine an expected response of the surface dynamic model output to excitation by polarized light; compare the determined expected response with the one or more measurements of the sample received from the metrology tool; generate one or more metrics based on the comparison between the determined expected response and the one or more measurements of the sample; generate a machine learning model; train the machine learning model; use the machine learning model to adjust the one or more parameters of the surface dynamic model based on the one or more metrics to generate an adjusted surface dynamic model; and apply the adjusted surface dynamic model to simulate on-sample performance during plasma processing of the sample.

[0010] According to one or more embodiments of the present disclosure, a method is disclosed. In one embodiment, the method includes generating a surface dynamic model output using a surface dynamic model, the surface dynamic model being run based on an initial guess of one or more parameters of the surface dynamic model. In another embodiment, the method includes determining an expected response of the surface dynamic model output to excitation by polarized light. In another embodiment, the method includes comparing the determined expected response with one or more measurements of a sample received from a metrology tool. In another embodiment, the method includes generating one or more metrics based on the comparison between the determined expected response and the one or more measurements of the sample. 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 using the machine learning model to adjust the one or more parameters of the surface dynamic model based on the one or more metrics to generate an adjusted surface dynamic model. In another embodiment, the method includes applying the adjusted surface dynamic model to simulate on-sample performance during plasma processing of the sample.

[0011] It should be understood that both the foregoing general description and the following detailed description are exemplary and illustrative only and do not necessarily limit 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] By referring to the accompanying drawings, those skilled in the art can better understand the advantages of the present disclosure, wherein:

[0013] Figure 1A A simplified block diagram illustrating a system for adjusting a surface dynamic model in accordance with one or more embodiments of the present disclosure.

[0014] Figure 1B A simplified schematic diagram illustrating a system for adjusting a surface dynamic model in accordance with one or more embodiments of the present disclosure.

[0015] Figure 2 A flowchart is illustrated depicting a method of adjusting a surface dynamic model according to one or more embodiments of the present disclosure.

[0016] Figure 3A Exemplary output of a surface dynamics model according to one or more embodiments of the present disclosure is illustrated.

[0017] Figure 3B Exemplary output of a surface dynamics model according to one or more embodiments of the present disclosure is illustrated.

[0018] Figure 3C Exemplary output of a surface dynamics model according to one or more embodiments of the present disclosure is illustrated.

[0019] Figure 3D Exemplary output of a surface dynamics model according to one or more embodiments of the present disclosure is illustrated.

[0020] Figure 4 is a graph illustrating iterative results of a rigorous coupled wave analysis (RCWA) according to one or more embodiments of the present disclosure.

[0021] Figure 5 is a graph illustrating a comparison of a measured response to a determined expected response according to one or more embodiments of the present disclosure.

[0022] Figure 6 A flowchart depicting a method for adjusting a surface dynamic model is described in accordance with one or more embodiments of the present disclosure.

[0023] Figure 7 A flowchart depicting a method for adjusting a surface dynamic model is described in accordance with one or more embodiments of the present disclosure. DETAILED DESCRIPTION

[0024] The present disclosure has been particularly shown and described with respect to specific embodiments and specific features thereof. The embodiments set forth herein are to be considered illustrative rather than restrictive. It will be readily apparent to those skilled in the art that various changes and modifications in form and details may be made without departing from the spirit and scope of the present disclosure.

[0025] Reference will now be made in detail to the disclosed subject matter, which is illustrated in the accompanying drawings.

[0026] Sample processing involves various plasma process steps. For example, a sample may be exposed to hundreds of plasma processes (e.g., etching, deposition, ion implantation, or the like) during manufacturing. Surface dynamics models can be used to simulate properties on a sample during such plasma processing. However, surface dynamics models are not predictive unless the parameters of the model are adjusted. Due to the varying conditions (e.g., temperature, power, gas composition, or the like) required for many plasma processes during manufacturing, parameter adjustment is a challenge. Determining the parameters of the surface dynamics model may require manual adjustment of the parameters using cross-sectional images of properties on the plasma-treated sample. Alternatively, the parameters can be determined programmatically. These conventional methods require metrology techniques that require cross-sectioning of the sample, resulting in sample rejection. Therefore, the parameters obtained are not predictive.

[0027] Furthermore, as the critical dimensions of features in microelectronics fabrication continue to decrease, the challenges of developing processes that achieve the ever-shrinking critical dimensions of features increase. For example, the time to develop a process that can be mass-produced increases, along with the research and development costs associated therewith.

[0028] Thus, embodiments of the present disclosure relate to a system and method for adjusting a surface dynamics model. More particularly, embodiments of the present disclosure relate to a system and method for adjusting a surface dynamics model based on one or more measurements acquired from a metrology subsystem. Specifically, embodiments of the present disclosure relate to a system and method for combining the power of physical modeling with non-destructive measurement of features on a sample to shrink development time and reduce the research and development costs associated with the adjustment process. Furthermore, embodiments of the present disclosure relate to a system and method for using a physical model to guide optical critical dimension model development (as opposed to purely statistical methods).

[0029] It should be noted herein that one or more embodiments of the present disclosure may have several advantages over conventional methods. For example, one or more embodiments of the present disclosure allow for sample reuse and the creation of a consolidated model by using the same sample and processing multiple layers. By way of another example, one or more embodiments of the present disclosure prevent the necessity of creating an optical critical dimension model, which typically takes a long time to fit the spectrum. Furthermore, one or more embodiments of the present disclosure provide for the rapid and automatic generation of an adjusted surface dynamics model. Furthermore, one or more embodiments of the present disclosure enable the generation of an accurate and predictive surface dynamics model. Furthermore, one or more embodiments of the present disclosure enable accelerated research and development of plasma processes.

[0030] Figure 1AA simplified block diagram illustrating a system for adjusting a surface dynamic model according to one or more embodiments of the present disclosure. In one embodiment, system 100 includes a metrology subsystem 102. In another embodiment, system 100 includes a controller 104 including one or more processors 106 and a memory 108. Controller 104 may include or be communicatively coupled to a user interface 110.

[0031] It should be noted herein that the metrology subsystem 102 may include any metrology subsystem 102 known in the art, including but not limited to an optical metrology system, a charged particle-based metrology system, or the like. For example, the metrology subsystem may include 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, or the like.

[0032] 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 can be configured to receive one or more measurement signals 132 from the metrology subsystem 102. This collected data 132 can be used to adjust the surface dynamics model, as will be discussed further herein. Additionally, the one or more processors 106 of the controller 104 can be configured to generate one or more control signals to adjust one or more characteristics / parameters of the metrology subsystem 102.

[0033] 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, photolithography tools, etching tools, deposition tools, polishing tools, scanners, and the like. For example, the controller 104 may be configured to generate one or more control signals configured to adjust one or more characteristics of the one or more process tools based on the adjusted surface dynamics model in a feedforward or feedback loop. 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.

[0034] Figure 1B A simplified schematic diagram illustrating a metrology subsystem 102 arranged in a reflectometer and / or ellipsometer configuration in accordance with one or more embodiments of the present disclosure.

[0035] In one embodiment, metrology subsystem 102 includes an illumination source 112, an illumination arm 114, a light collecting arm 116, and a detector assembly 118. Illumination 101 from illumination source 112 may be directed to sample 120 via illumination arm 114.

[0036] The metrology subsystem 102 can be configured to collect illumination emitted from the sample via a light collecting arm 116. The illumination arm 114 path can include one or more optical elements 122 suitable for modifying and / or adjusting the illumination 101. For example, the one or more optical elements 122 can include, but are not limited to, 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.

[0037] The illumination arm 114 can utilize a first focusing element 124 to focus and / or direct the illumination 101 (e.g., a light beam) onto the sample 120. In some embodiments, the sample 120 is disposed on a stage assembly 126 to facilitate movement of the sample 120. In some embodiments, the stage assembly 126 is an actuatable stage. For example, the stage assembly 126 may include, but is not limited to, one or more translation stages adapted to selectively translate the sample 120 along one or more linear directions (e.g., the x-direction, the y-direction, and / or the z-direction). By way of another example, the stage assembly 126 may include, but is not limited to, one or more rotation stages adapted to selectively rotate the sample 120 along a rotational direction. By way of another example, the stage assembly 126 may include, but is not limited to, a rotation stage and a translation stage adapted to selectively translate the sample 120 along a linear direction and / or rotate along a rotational direction. It should be noted herein that the system 100 can operate in any scanning mode known in the art.

[0038] The collecting arm 116 may include a second focusing element 128 for collecting illumination from the sample 120. In another embodiment, the detector assembly 118 is configured to capture illumination emitted from the sample 120 through the collecting arm 116. For example, the detector assembly 118 may receive illumination reflected or scattered from the sample 120 (e.g., via specular reflection, diffuse reflection, and the like). By way of another example, the detector assembly 118 may receive illumination generated by the sample 120 (e.g., luminescence associated with absorption of the illumination 101, and the like). It should be noted that the detector assembly 118 may include any sensor and detector assembly known in the art. Sensors may include, but are not limited to, charge coupled devices (CCD detectors), complementary metal oxide semiconductor (CMOS) detectors, time delay integration (TDI) detectors, photomultiplier tubes (PMTs), avalanche photodiodes (APDs), and the like.

[0039] In another embodiment, the controller 104 may obtain one or more measurements of the sample 120. For example, the controller 104 may be configured to collect metrology measurements of the sample 120.

[0040] The collecting arm 116 may further include collecting 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.

[0041] As used throughout this disclosure, the term "sample" generally refers to a substrate (e.g., a wafer, a reticle, or the like) formed from semiconductor or non-semiconductor materials. For example, semiconductor or non-semiconductor materials may include, but are not limited to, single crystal silicon, gallium arsenide, and indium phosphide. A sample may include one or more layers. For example, such layers may include, but are not limited to, resists, dielectric materials, conductive materials, and semiconducting materials. Many different types of such layers are known in the art, and the term sample, as used herein, is intended to encompass samples on which all types of such layers may be formed. The one or more layers formed on a sample may be patterned or unpatterned. For example, a sample may include a plurality of dies, each having repeatable patterned features. The formation and processing of such material layers may ultimately result in a completed device. Many different types of devices may be formed on a sample, and the term, as used herein, is intended to encompass samples on which any type of device known in the art is fabricated. Furthermore, for the purposes of this disclosure, the terms sample and wafer should be interpreted as interchangeable.

[0042] Figure 2 A flow chart depicting a method 200 for adjusting a surface dynamic model according to one or more embodiments of the present disclosure is described. Specifically, Figure 2 Instructions for using data from metrology tools (e.g. Figures 1A to 1B 1. In this regard, the flowchart 200 may be viewed as a conceptual flowchart illustrating steps performed by or within the one or more processors 106 of the controller 104.

[0043] In step 202, the system 100 is configured to generate a signal based on one or more parameters (p n ) is run on an initial guess of the surface dynamics model. For example, the one or more processors 106 of the controller 104 may be configured to run the surface dynamics model. In one embodiment, the system 100 is configured to generate a surface dynamics model output (CD) for each of the one or more features (i) based on the one or more parameters used in step 202. n,i For example, the one or more processors 106 of the controller 104 may be configured to generate a surface dynamic model output.

[0044] In one embodiment, Figures 3A to 3DAs shown in FIG, the surface dynamics model run 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 dynamics model run in step 202 may generate one or more critical shape parameters configured to allow reconstruction of the shape of a feature on the sample. Figures 3A to 3D A one-dimensional profile is described, but it should be noted herein that the shape of the features may be two-dimensional or three-dimensional. Therefore, the above description should not be considered as limiting the scope of the present disclosure, but is merely illustrative.

[0045] In step 204, the system 100 is configured to utilize the surface dynamics model output (CD n,i ) to determine an expected response of the surface dynamic model output to excitation by polarized light. For example, the 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 analysis (RCWA). In this regard, the determined expected response of a Fourier space method (e.g., RCWA) may be represented as a sum of spatial harmonics that vary depending on 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.

[0046] In another embodiment, the determined expected response may be determined using a small-angle x-ray scattering technique. For example, the determined expected response may be determined by generating one or more scattering images at one or more sample rotation angles. For example, x-rays may be used to generate the one or more scattering images, such that one or more small-angle x-ray scattering images are generated. 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, or the like. It should be noted herein that the one or more scattering images may be generated at any sample rotation angle known in the art.

[0047] It is noted herein that the determined expected response of the surface dynamics model to excitation by polarized light may be configured as either a reflective configuration or a transmissive configuration.

[0048] In another embodiment, the system 100 is configured to use a metrology tool illumination source (e.g., Figure 1B 1 (illumination source 112 of metrology subsystem 102 shown in FIG) to excite the sample with polarized light. In another embodiment, system 100 is configured to collect a measured response of the sample to the excitation with polarized light. For example, controller 104 can be configured to collect a measured response of the sample acquired by metrology subsystem 102.

[0049] In step 206, the system 100 is configured to compare the determined expected response determined in step 204 with the measured response of the sample 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 with the measured response obtained from the metrology tool.

[0050] 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 describe the deviation of the determined expected response from the measured response. For example, the one or more metrics may include a normalized sum of squares of the deviations between the measured response and the determined expected response. For example, the one or more metrics may include a goodness of fit for describing the difference between the measured response and the determined expected response. In another example, the one or more metrics may include a minimum sum of squares of the deviations between the measured response and the determined expected response. Any statistical metric known in the art may be used to describe the difference between the measured response and the determined expected response, and therefore, the above discussion should not be construed as limiting the scope of the present disclosure.

[0051] In step 208, the system 100 is configured to adjust one or more parameters (P n ) to generate an adjusted surface dynamic model. For example, the system 100 may be configured to adjust a first parameter P1 of the surface dynamic model based on one or more metrics. By way of another example, the system 100 may be configured to adjust a second parameter P2 of the surface dynamic model based on one or more metrics. It should be noted herein that the system 100 may be configured to adjust up to N parameters P n 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.

[0052] 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 below a threshold tolerance value. In this regard, the threshold tolerance value may be within 1x10 -10 In this example, the surface dynamics model can be adjusted until one or more metrics are below a threshold (e.g., 1x10 -10 and 5000). It should be noted herein that the threshold tolerance level may be adjusted based on the complexity of the process being characterized.

[0053] In step 210, the system 100 is configured to apply the adjusted surface dynamics model to simulate on-sample properties during plasma processing of the sample. For example, the one or more processors 106 of the controller 104 may be configured to apply the adjusted surface dynamics model to simulate on-sample properties during plasma processing of the sample 120.

[0054] Figures 3A to 3D Exemplary output of a surface dynamics model according to one or more embodiments of the present disclosure is illustrated. Figure 3A The output is 300. Figure 3B Description output 310. Figure 3C The output is 320. Figure 3D The output is 330.

[0055] One or more outputs 300, 310, 320, 330 may include one or more shape description parameters (CD n,i For example, one or more outputs 300, 310, 320, 330 may include a first shape description parameter CD 1,i By way of another example, one or more outputs 300, 310, 320, 330 may include a second shape description parameter CD 2,i One or more outputs 300, 310, 320, 330 may include up to N shape description parameters CD n,i .

[0056] Furthermore, it should be noted in this context that the output of the surface dynamics model may not be the contour itself, but rather a list of parameters describing the shape that can be used to achieve reconstruction, thus, Figures 3A to 3D The outputs 300 , 310 , 320 , 330 shown in should not be construed as limiting the scope of the present disclosure, but are provided for illustrative purposes.

[0057] Figure 4 is a graph 400 illustrating iterative results of a rigorous coupled wave analysis (RCWA) according to one or more embodiments of the present disclosure. In particular, Figure 4 Graph 400 is illustrated, which includes a graph comparing the measured values ​​from a metrology tool (e.g., Figures 1A to 1B The iterative result of the RCWA response of step 202 is the measured response 402 of the sample received by the metrology subsystem 102 shown in FIG. n The RCWA response evolves from being modeled at iteration 1 404 (modeled response 404 ) to being modeled at iteration n 406 (modeled response 406 ), at which point the model is deemed to have converged based on a comparison of the measured response 402 to the modeled response 406 .

[0058] Figure 5is a graph 500 illustrating a comparison of a measured response and a determined modeled response according to one or more embodiments of the present disclosure. In particular, Figure 5 A graph 500 is illustrated which illustrates the deviation of the modeled response from the measured metric below a threshold 506. As the model parameter P n The deviation between the modeled responses 404, 406 and the measured response 402 is quantified as a deviation 502. At iteration n 504, the deviation 502 is below a threshold 506 and the iterative process is deemed to have converged.

[0059] In another embodiment, before iteration n 504, step 208 (e.g. Figure 2 For example, the system 100 may be configured to adjust one or more parameters P of the surface dynamics model. n In another embodiment, at iteration n504, step 210 (e.g. Figure 2 For example, the system 100 can be configured to apply the adjusted surface dynamics model to simulate on-sample properties during plasma processing of the sample.

[0060] Figure 6 A flow chart depicting a method 600 for adjusting a surface dynamic model according to one or more embodiments of the present disclosure is described. It should be noted that the embodiments and implementation techniques previously described herein in the context of system 100 should be interpreted as extending to method 600. In this regard, the steps of method 600 may be implemented by system 100, and method 600 may further include one or more steps required or implied by the architecture of system 100. However, method 600 is not limited to the architecture of system 100, and it should be recognized that one or more steps of method 600, or portions thereof, may be implemented using alternative system components and / or architectures. Furthermore, the steps of method 600 may be implemented in any order unless otherwise specified herein.

[0061] In step 602, a surface dynamic model output is generated using the surface dynamic model. For example, the surface dynamic model output may be generated by one or more processors 106 of the controller 104. By way of another example, the surface dynamic model may be run based on an initial guess of one or more parameters of the surface dynamic model. For example, the surface dynamic model based on the initial guess of the one or more parameters may be run on the one or more processors 106 of the controller 104. In one embodiment, the surface dynamic model output includes a profile configured to describe the shape of a feature of the sample. In another embodiment, the surface dynamic model output includes one or more critical shape parameters configured to allow reconstruction of the shape of the feature of the sample.

[0062] It should be noted herein that a surface dynamics model can be run simultaneously at one or more sites across a sample. For example, a surface dynamics model can be run at one or more sites across a sample for each of one or more features on the sample. The one or more sites can be determined discretely. Furthermore, the one or more sites can be determined using an algorithm configured to guide the determination.

[0063] Furthermore, it should be noted herein that one or more initial guess parameters may vary based on one or more features of the sample. For example, one or more shape parameters of one or more parameters may vary based on one or more features of the sample.

[0064] In step 604, the expected response of the surface dynamic model output to excitation by polarized light is determined. Excitation by polarized light can be configured in a reflective or transmissive configuration. In one embodiment, a Fourier space method is used to determine the expected response. For example, rigorous coupled wave analysis (RCWA) can be performed to express the determined expected response as a sum of spatial harmonics.

[0065] In another embodiment, one or more small-angle x-ray scattering images are generated at one or more sample rotation angles, for example, 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, or the like.

[0066] In another embodiment, the determined expected response is determined by utilizing one or more additional parameters of the surface dynamics 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 that were not previously used by the surface dynamics model (e.g., not used during the initial guessing in step 602). In this embodiment, iterative optimization may be used to derive an optimal combination of optical critical dimension (OCD) parameters to minimize the deviation between the determined estimated response and the measured response.

[0067] In step 606, the determined expected response is compared to one or more measurements of the sample received from the metrology tool. For example, a metrology subsystem (e.g., Figures 1A to 1B1 ) can be configured to acquire one or more measurements of a sample. In this regard, the one or more measurements of the sample can be acquired from the controller 104 of the system 100. In this example, the one or more metrology subsystems can be configured to acquire one or more measurements on the sample. More specifically, a first metrology subsystem can be used to acquire a first measurement and a second metrology subsystem can be used to acquire a second measurement. Specifically, one or more optical critical dimension measurements from an OCD metrology tool can be used in combination with one or more CD-SEM measurements from a critical dimension scanning electron microscope (CD-SEM) tool. It should be noted here that the one or more metrology tools can 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, or the like configured to acquire up to N measurements.

[0068] 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 sample. 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 squares of the deviations between the one or more measurements of the sample and the determined expected response may be generated. In another example, a goodness of fit metric describing the difference between the one or more measurements of the sample and the determined expected response may be generated. In yet another example, a minimum sum of squares of the deviations between the one or more measurements of the sample and the determined expected response may be generated.

[0069] In step 610, one or more parameters of the surface dynamic model are adjusted based on the one or more metrics of step 608 to generate an adjusted surface dynamic model. The adjusted surface dynamic model may be configured to generate an adjusted surface dynamic model output. For example, one or more processors 106 of the controller 104 may be configured to generate the adjusted surface dynamic model based on the one or more adjusted parameters.

[0070] In another embodiment, one or more parameters of the surface dynamics model are adjusted until convergence is achieved. For example, convergence can be defined based on one or more metrics being below a threshold tolerance value. In this regard, the threshold tolerance value can be within 1x10 -10 In this example, the surface dynamics model can be adjusted until one or more metrics are below a threshold (e.g., 1x10 -10 and 5000). It should be noted herein that the threshold tolerance level may be adjusted based on the complexity of the process being characterized.

[0071] In another embodiment, an iterative optimization algorithm is used to adjust one or more parameters of the surface dynamics model. For example, a gradient descent method can be configured to find the minimum of one or more metrics. In another embodiment, a stochastic gradient descent method is used to adjust the gradient descent method. The stochastic gradient descent method can be configured to randomly select samples to evaluate the gradient.

[0072] In step 612, the adjusted surface dynamics model is applied during plasma processing of the sample to simulate on-sample properties. For example, the one or more processors 106 of the controller 104 may be configured to apply the adjusted surface dynamics model during plasma processing of the sample 120 to simulate on-sample properties.

[0073] In an optional step, one or more control signals are configured to selectively adjust one or more characteristics of 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 tools known in the art, including but not limited to lithography tools, etching tools, deposition tools, polishing tools, scanners, and the like. Continuing with the same example, the controller 104 may be configured to generate one or more control signals configured to adjust one or more characteristics of the one or more process tools based on the adjusted surface dynamics model in a feedforward or feedback loop.

[0074] In an optional step, one or more control signals are configured to selectively adjust one or more characteristics of the metrology subsystem 102 based on the adjusted surface dynamic model.

[0075] Figure 7 A flow chart illustrating a method 700 for adjusting a surface dynamic model according to one or more embodiments of the present disclosure. It should be noted that the embodiments and implementation techniques previously described herein in the context of system 100 should be interpreted as extending to method 700. In this regard, the steps of method 700 may be implemented by system 100, and method 700 may further include one or more steps required or implied by the architecture of system 100. However, method 700 is not limited to the architecture of system 100, and it should be recognized that one or more steps of method 700, or portions thereof, may be implemented using alternative system components and / or architectures. Furthermore, the steps of method 700 may be implemented in any order unless otherwise specified herein.

[0076] In step 702, a surface dynamic model output is generated using the surface dynamic model. For example, one or more processors 106 of the controller 104 may be configured to generate the surface dynamic model output using the surface dynamic model. For example, the surface dynamic model may be run based on an initial guess of one or more parameters of the surface dynamic model. In one embodiment, the surface dynamic model output includes a profile configured to describe the shape of a feature of the sample. In another embodiment, the surface dynamic model output includes one or more critical shape parameters configured to allow reconstruction of the shape of the feature of the sample.

[0077] In step 704, the expected response of the surface dynamic model output to excitation by polarized light is determined. Excitation by polarized light can be configured in a reflective or transmissive configuration. In one embodiment, a Fourier space method is used to determine the expected response. For example, rigorous coupled wave analysis (RCWA) can be performed to express the determined expected response as a sum of spatial harmonics.

[0078] In another embodiment, one or more small-angle x-ray scattering images are generated at one or more sample rotation angles, for example, 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, or the like.

[0079] In step 706, the determined expected response is compared to one or more measurements of the sample received from the metrology tool. For example, the metrology subsystem (e.g., Figures 1A to 1B ) can be configured to acquire one or more measurements of a sample. In this regard, the one or more measurements of the sample can be acquired from a controller 104 of the system 100. The metrology tool can 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, or the like.

[0080] In step 708, one or more metrics are generated based on a comparison between the determined expected response and one or more measurements of the sample. For example, a normalized sum of squares of deviations between one or more measurements of the sample and the determined expected response may be generated.

[0081] By another example, a goodness of fit describing the difference between one or more measurements of a sample and the determined expected response can be generated. By another example, a minimum sum of squares of deviations between one or more measurements of a sample and the determined expected response can be generated.

[0082] In step 710, a machine learning model is generated. In one embodiment, the controller 104 may be configured to generate a machine learning model that can be used 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, and the like.

[0083] It should be 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. By way of another example, the machine learning model may include a deep convolutional neural network. 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.

[0084] In step 712, the machine learning model generated in step 710 is trained. For example, the machine learning model can be trained using previously generated synthetic data from the surface dynamics model and the RCWA response to the generated output. Other training techniques (such as pre-labeling, feature extraction, and the like) are also applicable.

[0085] In step 714 , one or more parameters of the surface dynamics model are adjusted based on the one or more metrics using the machine learning model to generate an adjusted surface dynamics model.

[0086] In step 716, the adjusted surface dynamics model is applied during plasma processing of the sample to simulate on-sample properties.

[0087] It should be noted herein that using a machine learning model to tune the surface dynamics model may allow for faster generation of tuned parameters.

[0088] Furthermore, it should be noted herein that a machine learning model can be used in step 704. For example, a machine learning model can be used to determine the expected response to excitation by polarized light. In this regard, the machine learning model can replace Fourier space methods (e.g., RCWA) or SAXS to calibrate the measured structure on the sample.

[0089] It is noted herein that one or more components of system 100 can be communicatively coupled to various other components of system 100 in any manner known in the art. For example, one or more processors 106 can be communicatively coupled to one another and to other components via wired connections (e.g., copper wires, fiber optic cables, and the like) or wireless connections (e.g., RF coupling, IR coupling, WiMax, Bluetooth, 3G, 4G, 4G LTE, 5G, and the like). By way of another example, controller 104 can be communicatively coupled to one or more components of metrology subsystem 102 via any wired or wireless connection known in the art.

[0090] In one embodiment, one or more processors 106 can include any one or more processing elements known in the art. In this sense, one or more processors 106 can include any microprocessor-type device configured to execute software algorithms and / or instructions. In one embodiment, one or more processors 106 can be comprised of a desktop computer, a mainframe computer system, a workstation, a graphics computer, a parallel processor, or other computer system (e.g., networked computer) configured to execute a program (which is configured to operate system 100, as described throughout the present disclosure). It is recognized that the steps described throughout the present disclosure can be carried out by a single computer system or, alternatively, multiple computer systems. Further, it is recognized that the steps described throughout the present disclosure can be carried out on any one or more of one or more processors 106. Generally, the term “processor” can be broadly defined to encompass any device having one or more processing elements, which execute program instructions from memory 108. Further, different subsystems of system 100 (e.g., illumination source 112, detector assembly 118, controller 104, user interface 110, and the like) can include processors or logic elements suitable for carrying out at least a portion of the steps described throughout the present disclosure. Accordingly, the above description should not be interpreted as a limitation on the present disclosure but merely an illustration.

[0091] Memory 108 can include any storage media suitable for storing program instructions executable by one or more associated processors 106 and data received from metrology subsystem 102 known in the art. For example, memory 108 can include non-transitory storage media. For example, memory 108 can include, but is not limited to, read-only memory (ROM), random access memory (RAM), magnetic or optical storage devices (e.g., magnetic diskette, magnetic tape), solid state drives, and the like. It is further noted that memory 108 can be housed in a common controller housing with one or more processors 106. In alternative embodiments, memory 108 can be remotely located with respect to the physical location of processors 106, controller 104, and the like. In another embodiment, memory 108 maintains program instructions for causing one or more processors 106 to carry out the various steps described throughout the present disclosure.

[0092] In one embodiment, the user interface 110 is communicatively coupled to the controller 104. In one embodiment, the user interface 110 can include, but is not limited to, one or more desktop computers, tablet computers, smart phones, smart watches, or the like. In another embodiment, the user interface 110 includes a display for displaying data of the system 100 to a user. The display of the user interface 110 can include any display known in the art. For example, the display can 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 will recognize that any display device capable of integration with the user interface 110 is suitable for use in the implementations in the present disclosure. In another embodiment, a user can input selections and / or instructions via a user input device of the user interface 110 in response to data displayed to the user.

[0093] Those skilled in the art will recognize that, for clarity, the components (e.g., operations), devices, objects, and the discussion accompanying them have been presented in a particular order and in a particular arrangement. However, it should be recognized that the components (e.g., operations), devices, and objects can be combined in other orders, arranged differently, or omitted, and still be considered within the scope of the present disclosure.

[0094] Those skilled in the art will appreciate that there are various vehicles by which processes and / or systems and / or other technologies described herein can be implemented, and that the preferred vehicle will vary with the context in which the processes and / or systems and / or other technologies are deployed. For example, if speed and accuracy is paramount, then an implementer can opt for hard-wired device or system; alternatively, if flexibility is paramount, then an implementer can opt for a softer- wired device or system. Or, in yet another scenario, if interactivity is paramount, then an implementer can opt for a completely software implementation. Accordingly, there are a number of possible vehicles by which the processes and / or devices and / or other technologies described herein can be implemented, and any such implementation is contemplated to be within the scope of the present disclosure.

[0095] The foregoing description is presented to enable one of ordinary skill in the art to make and use the present invention as provided in the context of a particular application and its requirements. As used herein, directional terms such as "top," "bottom," "above," "below," "up," "upward," "down," "downward," and "downwardly" are intended to provide relative positions for descriptive purposes and are not intended to specify an absolute reference system. 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. Therefore, the present invention is not intended to be limited to the particular embodiments shown and described, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

[0096] With respect to the use of substantially any plural and / or singular terms herein, those skilled in the art can translate from the plural to the singular and / or from the singular to the plural as the context and / or application permits. For clarity, the various singular / plural permutations are not explicitly stated herein.

[0097] All methods described herein may include storing the results of one or more steps of a method embodiment in a memory. The result may include any result described herein and may be stored in any manner known in the art. The memory may include any memory described herein or any other suitable storage medium known in the art. After the results have been stored, the results may be accessed in the memory and used by any method or system embodiment described herein, formatted for display to a user, used by another software module, method or system, and the like. In addition, 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 be stored in the memory indefinitely.

[0098] It is further contemplated that each of the embodiments of the method described above may include any other steps of any other method described herein. Additionally, each of the embodiments of the method described above may be performed by any system described herein.

[0099] The subject matter described herein is sometimes illustrated using different components contained within, or connected with, other components. It is to be understood that such depicted architectures are merely exemplary, and that in fact many other architectures can be implemented which achieve the same functionality. In a conceptual sense, any arrangement of components to achieve the same functionality is effectively "associated" such that the desired functionality is achieved. Hence, any two components herein combined to achieve a particular functionality can be seen as "associated with" each other such that the desired functionality is achieved, irrespective of architectures or intermediate components. Likewise, any two components so associated can also be viewed as being "connected" or "coupled" to each other to achieve the desired functionality, and any two components capable of being so associated can also be viewed as being "couplable" to each other to achieve the desired functionality. Specific examples of couplable include but are not limited to physically mateable and / or physically interacting components and / or wirelessly interactable and / or wirelessly interacting components and / or logically interacting and / or logically interactable components.

[0100] Furthermore, it should be understood that the present invention is defined by the appended claims. Those skilled in the art will understand that, in general, terms used herein, and particularly in the appended claims (e.g., the bodies of the appended claims), are generally intended to be "open-ended" 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.). Those skilled in the art will further understand that if a specific number of claim recitations is intended to be introduced, such intent will be expressly recited in the claim, and in the absence of such recitation, such intent is not present. For example, as an aid to understanding, the following appended claims may contain the use of the introductory phrases "at least one" and "one or more" to introduce claim recitations. However, the use of such phrases should not be construed as implying that introducing a claim recitation with the indefinite article "a" or "an" limits any particular claim containing such introduced claim recitation to inventions containing only one such recitation, even if the same claim contains the introductory phrases "one or more" or "at least one" and an indefinite article such as "a" or "an" (e.g., "a" and / or "an" should generally be construed to mean "at least one" or "one or more"); the foregoing applies equally to the use of definite articles to introduce claim recitations. In addition, even if a specific number of introduced claim recitations is explicitly recited, those skilled in the art will recognize that such recitation should generally be construed to mean at least that number of recitations (e.g., the bare recitation (without other modifiers) of "two recitations" generally means at least two recitations or two or more recitations). Furthermore, in instances where a convention similar to “at least one of A, B, and C, and the like” is used, this construction generally intends that those skilled in the art will understand the meaning of the convention (e.g., “a system having at least one of A, B, and C” will include, but is not limited to, systems having only A, only B, only C, both A and B, both A and C, both B and C, and / or both A, B, and C, etc.). In instances where a convention similar to “at least one of A, B, or C, and the like” is used, this construction generally intends that those skilled in the art will understand the meaning of the convention (e.g., “a system having at least one of A, B, or C” will include, but is not limited to, systems having only A, only B, only C, both A and B, both A and C, both B and C, and / or both A, B, and C, etc.). Those skilled in the art will further understand that virtually any transition word and / or phrase presenting two or more alternative terms, whether in the description, claims, or drawings, should be understood to contemplate the possibility of including: one of the terms, either of the terms, or both of the terms.For example, the phrase "A or B" will generally be understood to include the possibilities of "A" or "B" or "A and B."

[0101] It is believed that the present disclosure and its many attendant advantages will be appreciated from the foregoing description, and it will be understood that various changes may be made to the form, construction, and arrangement of components without departing from the disclosed subject matter or sacrificing all of its material advantages. The forms described are illustrative only, and it is intended that such changes be covered and included by the claims below. Furthermore, it should be understood that the invention is defined by the claims appended hereto.

Claims

1. A system comprising: a metrology tool, wherein the metrology tool is configured to obtain one or more measurements of a portion of a sample; 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 dynamic model output based on a surface dynamic model, wherein the surface dynamic model is run based on an initial guess of one or more parameters of the surface dynamic model; determining an expected response of the surface dynamic model output to excitation by polarized light using one or more additional parameters of the surface dynamic model, wherein the one or more additional parameters include one or more parameters not used during the initial guessing run of the one or more parameters of the surface dynamic 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 sample; adjusting the one or more parameters of the surface dynamic model based on the one or more metrics to produce an adjusted surface dynamic model; applying the adjusted surface dynamics model to simulate on-sample properties during plasma processing of the sample; and 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 are generated.

2. The system of claim 1 , wherein generating the adjusted surface dynamics model comprises: An adjusted surface dynamic model output is generated 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 value.

3. The system according to claim 2, wherein the threshold tolerance value is 1 x 10 -10 to 5000.

4. The system of claim 1 , wherein the metrology tool comprises at least one of: 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.

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 sample.

6. The system of claim 1, wherein the surface dynamics model output comprises one or more critical shape parameters configured to allow reconstruction of a shape of a feature of the sample.

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

8. The system of claim 1 , wherein determining an expected response of the surface dynamics model output to excitation by polarized light comprises: Performs a Fourier space method.

9. The system of claim 8, wherein determining an expected response of the surface dynamics model output to excitation by polarized light comprises: Perform a rigorous coupled-wave analysis.

10. The system of claim 9, wherein the determined expected response is represented as a sum of spatial harmonics that vary as a function of the wavelength of the polarized light utilized.

11. The system of claim 1 , wherein the one or more metrics include at least one of: The normalized sum of squares of the deviations between the one or more measurements of the sample and the determined expected response; a goodness of fit describing the differences between the one or more measurements of the sample and the determined expected response; or the least sum of squares of the deviations between the one or more measurements of the sample and the determined expected response.

12. The system of claim 1 , wherein the adjusting the one or more parameters of the surface dynamics model based on the one or more metrics to generate an adjusted surface dynamics model comprises: The one or more parameters are adjusted using an optimization algorithm.

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

14. The system of claim 13, further comprising: The gradient method is tuned using stochastic gradient descent, where the stochastic gradient descent method is configured to randomly select samples to evaluate the gradient.

15. The system of claim 1, wherein the surface dynamics model is configured to be run simultaneously on one or more sites across the sample.

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

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

18. The system of claim 1 , wherein determining an expected response of the surface dynamics model output to excitation by polarized light comprises: One or more small-angle x-ray scattering images are generated at one or more sample rotation angles.

19. The system of claim 18, wherein the one or more small-angle x-ray images are generated using at least one of: Grazing incidence small angle x-ray scattering, critical size small angle x-ray scattering, grazing incidence transmission small angle x-ray scattering or soft x-ray scattering.

20. The system of claim 1, wherein the controller is further configured to: Generate machine learning models; and A machine learning model is trained, wherein the trained machine learning model is utilized to adjust the one or more parameters of the surface dynamics model based on the one or more metrics to produce an adjusted surface dynamics model.

21. A method comprising: generating a surface dynamic model output using a surface dynamic model, wherein the surface dynamic model is run based on an initial guess of one or more parameters of the surface dynamic model; determining an expected response of the surface dynamic model output to excitation by polarized light using one or more additional parameters of the surface dynamic model, wherein the one or more additional parameters include one or more parameters not used during the initial guessing run of the one or more parameters of the surface dynamic model; comparing the determined expected response to one or more measurements of a 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 sample; adjusting the one or more parameters of the surface dynamic model based on the one or more metrics to produce an adjusted surface dynamic model; applying the adjusted surface dynamics model to simulate on-sample properties during plasma processing of the sample; and 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 are generated.

22. The method of claim 21 , wherein generating the adjusted surface dynamic model comprises: An adjusted surface dynamic model output is generated 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 value.

23. The method according to claim 22, wherein the threshold tolerance value is within 1 x 10 -10 to 5000.

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

25. The method of claim 21, wherein the surface dynamic model output comprises one or more critical shape parameters configured to allow reconstruction of a shape of a feature of the sample.

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

27. The method of claim 21 , wherein determining an expected response of the surface dynamics model output to excitation by polarized light comprises: Performs a Fourier space method.

28. The method of claim 27, wherein determining an expected response of the surface dynamics model output to excitation by polarized light comprises: Perform a rigorous coupled-wave analysis.

29. The method of claim 28, wherein the determined expected response is represented as a sum of spatial harmonics that vary as a function of the wavelength of the polarized light utilized.

30. The method of claim 21, wherein the one or more metrics include at least one of: The normalized sum of squares of the deviations between the one or more measurements of the sample and the determined expected response; a goodness of fit describing the differences between the one or more measurements of the sample and the determined expected response; or the least sum of squares of the deviations between the one or more measurements of the sample and the determined expected response.

31. The method of claim 21 , wherein the adjusting the one or more parameters of the surface dynamic model based on the one or more metrics to produce an adjusted surface dynamic model comprises: The one or more parameters are adjusted using an optimization algorithm.

32. The method of claim 31 , wherein the optimization algorithm comprises: A gradient method, wherein the gradient method is configured to find a minimum in the one or more metrics.

33. The method of claim 32, further comprising: The gradient method is tuned using stochastic gradient descent, where the stochastic gradient descent method is configured to randomly select samples to evaluate the gradient.

34. The method of claim 21, wherein the metrology tool comprises at least one of: 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.

35. The method of claim 21, wherein the surface dynamics model is configured to be run simultaneously on one or more sites across the sample.

36. The method of claim 21, wherein one or more shape parameters of the one or more parameters of the initial guess vary based on one or more features on the sample.

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

38. The method of claim 21, wherein determining an expected response of the surface dynamics model output to excitation by polarized light comprises: One or more scattering images are generated at one or more sample rotation angles.

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

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

41. The method of claim 21, further comprising: Generate machine learning models; and The machine learning model is trained, wherein the trained machine learning model is utilized to adjust the one or more parameters of the surface dynamics model based on the one or more metrics to produce an adjusted surface dynamics model.

42. A system comprising: a metrology tool, wherein the metrology tool is configured to obtain one or more measurements of a portion of a sample; 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 dynamic model output based on a surface dynamic model, wherein the surface dynamic model is run based on an initial guess of one or more parameters of the surface dynamic model; determining an expected response of the surface dynamic model output to excitation by polarized light using one or more additional parameters of the surface dynamic model, wherein the one or more additional parameters include one or more parameters not used during the initial guessing run of the one or more parameters of the surface dynamic 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 sample; Generate machine learning models; training the machine learning model; adjusting the one or more parameters of the surface dynamics model based on the one or more metrics using the machine learning model to produce an adjusted surface dynamics model; applying the adjusted surface dynamics model to simulate on-sample properties during plasma processing of the sample; and 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 are generated.

43. A method comprising: generating a surface dynamic model output using a surface dynamic model, wherein the surface dynamic model is run based on an initial guess of one or more parameters of the surface dynamic model; determining an expected response of the surface dynamic model output to excitation by polarized light using one or more additional parameters of the surface dynamic model, wherein the one or more additional parameters include one or more parameters not used during the initial guessing run of the one or more parameters of the surface dynamic model; comparing the determined expected response to one or more measurements of a sample 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 sample; Generate machine learning models; training the machine learning model; adjusting the one or more parameters of the surface dynamics model based on the one or more metrics using the machine learning model to produce an adjusted surface dynamics model; applying the adjusted surface dynamics model to simulate on-sample properties during plasma processing of the sample; and 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 are generated.

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