Methods and systems for data driven parameterization and measurement of semiconductor structures

Abstract

Methods and systems for generating optimized geometric models of semiconductor structures parameterized by a set of variables in a latent mathematical space are presented herein. Reference shape profiles characterize the shape of a semiconductor structure of interest over a process space. A set of observable geometric variables describing the reference shape profiles is transformed to a set of latent variables. The number of latent variables is smaller than the number of observable geometric variables, thus the dimension of the parameter space employed to characterize the structure of interest is reduced. This dramatically reduces the mathematical dimension of the measurement problem to be solved. As a result, measurement model solutions involving regression are more robust, and training of machine learning based measurement models is simplified. Geometric models parameterized by a set of latent variables are useful for generating measurement models for optical metrology, x-ray metrology, and electron beam based metrology.

Description

[Technical Field]

[0001] The embodiments described relate to measurement systems and methods, and more specifically, the embodiments described relate to methods and systems for improving measurement accuracy. [Previous Technology]

[0002] Semiconductor devices, such as logic and memory devices, are typically manufactured by a sequence of processing steps applied to a sample. Various features and multiple structural layers of a semiconductor device are formed by these processing steps. For example, lithography involves a semiconductor process that creates a pattern on a semiconductor wafer. Additional examples of semiconductor processes include (but are not limited to) chemical mechanical polishing, etching, deposition, and ion implantation. Multiple semiconductor devices can be manufactured on a single semiconductor wafer and then discretely separated into individual semiconductor devices.

[0003] Metrology procedures are used at various stages of a semiconductor manufacturing process to detect defects on wafers to achieve higher yields. Optical, electron beam, and X-ray-based metrology techniques offer the potential for high throughput with no risk of sample damage. Numerous techniques, including scattering and reflection measurement implementations and associated analytical algorithms, are commonly used to characterize the critical dimensions, film thickness, composition, and other parameters of nanoscale structures.

[0004] As devices (such as logic and memory devices) move towards smaller nanometer-scale dimensions, characterization becomes more difficult. Devices incorporating complex three-dimensional geometries and materials with diverse physical properties increase the difficulty of characterization. The shape and profile of the device change significantly. In one instance, recently conceived semiconductor devices incorporate new complex three-dimensional geometries and materials with diverse orientations and physical properties, which are particularly difficult to characterize, especially using optical metrology.

[0005] In response to these challenges, more sophisticated metrology tools have been developed. Measurements are performed over a wide range of machine parameters (such as wavelength, azimuth, and angle of incidence, etc.) and often simultaneously. As a result, the measurement time, computation time, and total time to produce reliable results (including the measurement scheme and accurate measurement model) have increased significantly.

[0006] Existing model-based metrology methods typically involve a series of steps for modeling and then measuring structural parameters. Typically, measurement data (e.g., DOE spectra) are collected from a set of samples or wafers, a specific metrological target, a test critical size target, an actual device target within a cell, an SRAM memory target, etc. An accurate model of the optical response from such complex structures includes a model of geometric features, a model of dispersion parameters, and a metrology system is defined. Typically, a regression is performed to improve the geometric model. Additionally, simulation approximations (e.g., rough rolling, rigorous coupled-wave analysis (RCWA), etc.) are performed to avoid introducing excessive errors. Discretization and RCWA parameters are defined. A series of simulations, analyses, and regressions are performed to improve the geometric model and determine which model parameters are fluctuating. A synthetic spectral library is generated. Finally, measurements are performed in real-time using the library or regression with the geometric model.

[0007] The geometric model of the measured device structure is usually parameterized using a general family of functions that characterizes any shape with arbitrary accuracy, or it is parameterized by a user based on a specific understanding of the expected model variation.

[0008] In some instances, the geometric model of the measured device structure is assembled by a user from primitive building blocks within a measurement modeling tool. These primitive building blocks are simple geometries (e.g., square frustums) that are assembled together to approximate more complex structures. The primitive building blocks are sized by the user and sometimes customized based on user input to specify the shape details of each primitive building block. In one instance, each primitive building block includes an integrated customization control panel where the user inputs specific parameters to determine shape details to match an actual entity structure being modeled. Similarly, primitive building blocks are joined together by constraints also manually input by the user. For example, the user inputs a constraint connecting a vertex of one primitive building block to a vertex of another building block. This allows the user to build models representing a range of actual device geometries as the size of a building block changes. User-defined constraints between primitive building blocks enable extensive modeling flexibility. For example, in multi-object measurement applications, the thickness or height of different primitive building blocks can be constrained by a single parameter. Furthermore, the building blocks of the primitive structure have simple geometric parameterization, which users can constrain to specific application parameters. For example, the sidewall angle of a photoresist line can be manually constrained to parameters representing the focus and dosage of a lithography process.

[0009] Although models built from primitive structure building blocks offer a wide range of modeling flexibility and user control, the modeling process becomes very complex and error-prone when modeling complex semiconductor structures.

[0010] In many instances, the number of parameters required to describe a complex shape is relatively large. This increases the mathematical dimension of the measurement problem to be solved. As a result, solutions to measurement models involving regression often encounter multiple minima, and measurement models based on machine learning are often difficult to train due to high parameter correlation and low sensitivity.

[0011] In summary, modeling complex semiconductor structures using existing geometric modeling tools requires specifying a large number of structural primitives, constraints, and independent parameters, which introduces computational problems and limits the achievable accuracy. As complex semiconductor structures become more prevalent, there is a need to improve modeling methods and tools. [Summary of the Invention]

[0012] This paper presents a method and system for generating optimized geometric models of semiconductor structures parameterized by a set of variables in a latent mathematical space. Parameterizing a measured structure by a set of latent variables rather than observable geometric variables significantly reduces the number of parameters required to describe a complex shape. This significantly reduces the mathematical dimensionality of the measurement problem to be solved. Therefore, measurement model solutions involving regression are more robust, and training machine learning-based measurement models is simplified. Geometric models parameterized by a set of latent variables of the semiconductor structure are used to generate measurement models for optical metrology, X-ray metrology, and electron beam metrology.

[0013] Reference shape profile characterization is of interest to the shape of a semiconductor structure. The reference shape profile is parameterized by a set of observable geometric variables, such as critical dimensions, height, ellipticity, tilt, etc.

[0014] In a given state, the observable geometric variables are transformed into a set of latent variables. The latent variables characterizing the reference shape profile define the geometry of the structure of interest in an alternative mathematical space. Changes in the values ​​of the latent variables represent changes in the geometry of the structure of interest. The number of latent variables is less than the number of observable geometric variables, thus reducing the dimensionality of the parameter space used to characterize the structure of interest.

[0015] In some instances, transforming observable geometric variables into latent variables involves principal component analysis (PCA), weighted PCA, or a trained autoencoder. In some instances, transforming observable geometric variables into latent variables involves a hybrid parameterization that includes one of the latent spatial parameterizations described above and a function fit of the difference between the reference shape profile and the reconstructed profile derived from the values ​​of the latent variables. The sum of the latent spatial parameterization and the function fit provides a more accurate representation of the reference shape profile using a relatively small number of independent variables.

[0016] In general, any program-driven parameterization or combination of different parameterizations can be used to reduce the dimensionality of the parameter space used for characterizing the structure of interest.

[0017] In another further state, a set of reconstructed shape profiles is determined based on sampling one of the values ​​of the latent variables. In one instance, the reconstructed shape profiles are generated by random sampling from the range of latent variables. For comparison, the sampled values ​​of the latent variables are transformed back to the values ​​of the observable geometric variables by an inverse transformation from the latent space to the observable geometric space.

[0018] In another further state, the latent variable array is truncated into a reduced set of latent variables based on the difference between the first set of reconstructed shape profiles and the reference shape profile. The difference between the profile reconstructed from the sampled values ​​of the latent variables and the reference shape profile provides one of the quantifiable measures of the accuracy of the representation of the reference shape profile in the latent mathematical space.

[0019] In another further state, a set of reconstructed shape profiles is generated based on sampling one of the values ​​of the latent variables, and additionally, a mathematical function is fitted to the difference between the reference shape profile and the reconstructed shape profile. Subsequently, another set of reconstructed shape profiles is generated based on the sum of the reconstructed shape profiles derived from the values ​​of the latent variables and the fitted curve. The resulting reconstructed shape profiles can be used to train a measurement model.

[0020] In another further state, the range of values ​​for one or more of the observable geometric variables is expanded to effectively extend the range of the training set of the reference shape profile. The expanded training set of the reference shape profile is then used as the basis for generating transformations to the latent space, for example, through PCA, a trained autoencoder, etc.

[0021] In another further state, the reconstructed shape contours are eliminated by generating a non-solid shape contour free latent variable array before the reconstructed contour data set is used to train a measurement model.

[0022] In another further embodiment, a measurement model is trained at least in part on reconstructed shape profiles derived from an optimized geometric model of the self-measured structure. A large number of reconstructed shape profiles across relevant procedural variations are efficiently generated based on the optimized geometric model. A measurement simulation tool is used to generate synthetic measurement data associated with each different reconstructed shape profile, such as spectra, images, electron density maps, etc. The reconstructed shape profiles and corresponding measurement data sets include a training data set used to train the measurement model.

[0023] In another further example, a modeling tool uses a trained measurement model to estimate the values ​​of observable geometric parameters of interest associated with a measured structure.

[0024] The foregoing is an overview and therefore necessarily contains simplifications, generalizations and omissions of details; therefore, those skilled in the art will understand that the overview is for illustrative purposes only and is by no means limiting. Other forms, inventive features and advantages of the apparatus and / or process described herein will become clear from the non-limiting detailed description set forth herein.

Implementation Method

[0041] Cross-Reference to Related Applications This patent application claims priority to U.S. Provisional Patent Application No. 63 / 284,645, filed December 1, 2021, entitled “Method for Data Driven Parameterization and Measurement,” under 35 USC §119, the entire contents of which are incorporated herein by reference.

[0042] Detailed reference will now be made to the background examples and some embodiments of the present invention, examples of which are illustrated in the accompanying drawings.

[0043] This paper presents a method and system for generating optimized geometric models of semiconductor structures parameterized by a set of variables in a latent mathematical space. Measurements of critical dimensions (CD), film thickness, optical properties and composition, overlap, lithography focus / dosage, etc., often require a geometric model of the structure of interest. Parameterizing a measured structure by a set of latent variables rather than observable geometric variables significantly reduces the number of parameters required to describe a complex shape. This significantly reduces the mathematical dimensionality of the measurement problem to be solved. Therefore, measurement model solutions involving regression are more robust, and training machine learning-based measurement models is simplified.

[0044] The optimization of a geometric model is based on the expected geometry of the measured structure. The expected geometry is provided by program data, user expectations of the shape geometry, program simulation data, or any combination thereof. The optimization parameterization of the geometric model rigorously defines the parameter space of feasible shape profiles and effectively constrains the geometric model.

[0045] In some instances, metrology systems employ geometric models parameterized by a set of latent variables to measure structural and material properties associated with semiconductor processes (e.g., material composition, structure, and film dimensional properties). Geometric models parameterized by a set of latent variables of the semiconductor structure generate substantially simpler, less error-prone, and more accurate measurement models. Therefore, the time to obtain useful measurement results is significantly reduced, especially when modeling complex structures. Geometric models parameterized by a set of latent variables of the semiconductor structure are used to generate measurement models for optical metrology, X-ray metrology, and electron beam-based metrology.

[0046] Figure 1 illustrates a system 100 for measuring the characteristics of a semiconductor wafer. As shown in Figure 1, system 100 can be used to perform elliptic polarization spectroscopy measurements on one or more structures 114 of a semiconductor wafer 112 mounted on a wafer positioning system 110. In this configuration, system 100 may include a spectroellipsometer equipped with an illuminator 102 and a spectrometer 104. The illuminator 102 of system 100 is configured to generate and guide illumination of a selected wavelength range (e.g., 150 nm to 4500 nm) onto the structures 114 mounted on the surface of the semiconductor wafer 112. The spectrometer 104 is then configured to receive the light from the surface of the semiconductor wafer 112. It should be further noted that the light emitted from the illuminator 102 is polarized using a polarization state generator 107 to generate a polarized illumination beam 106. Radiation reflected by structure 114 mounted on wafer 112 passes through a polarization state analyzer 109 and reaches spectrometer 104. Polarization state analysis is performed on the radiation received by a detector in the collection beam 108 by the spectrometer 104 to allow spectral analysis of the radiation passing through the analyzer. These spectra 111 are then transmitted to a computing system 116 for analysis of structure 114.

[0047] In a further embodiment, the metrology system 100 is a measurement system 100 that includes one or more computing systems 116 configured to perform modeling and analysis tools 130 according to the description provided herein. In a preferred embodiment, the modeling and analysis tools 130 are a set of program instructions 120 stored on a carrier medium 118. The program instructions 120 stored on the carrier medium 118 are read and executed by the computing system 116 to implement the modeling and analysis functions described herein. One or more computing systems 116 are communicatively coupled to the spectrometer 104. In one state, one or more computing systems 116 are configured to receive measurement data 111 associated with a measurement (e.g., critical dimensions, film thickness, composition, program, etc.) of the structure 114 of the sample 112. In one example, the measurement data 111 includes an indication by the measurement system 100 based on the measurement spectral response (e.g., measurement intensity varying according to wavelength) of the sample from one or more sampling procedures of the spectrometer 104. In some embodiments, one or more computing systems 116 are further configured to determine the sample parameter values ​​of structure 114 using autometric data 111.

[0048] In some instances, metrology based on optical scattering measurements involves determining the size of a sample by inversely solving a predetermined measurement model using measurement data. The measurement model contains several (approximately 10) adjustable parameters and represents the geometric and optical properties of the sample and the optical properties of the measurement system. Inverse solution methods include (but are not limited to) model-based regression, tomography, machine learning, or any combination thereof. In this manner, target profile parameters are estimated by solving for the value of a parameterized measurement model that minimizes the error between the measured optical intensity and the modeled result.

[0049] In a further embodiment, the computing system 116 is configured to generate a structural model (e.g., a geometric model, a material model, or a combined geometric and material model) of a measurement structure of a sample, generate an optical response model from the structural model containing at least one geometric parameter, and resolve at least one sample parameter value by performing a fitting analysis on the optical measurement data using the optical response model. An analysis engine is used to compare the simulated optical response signal with the measurement data, thereby allowing the determination of the sample's geometric and material properties. In the embodiment depicted in Figure 1, the computing system 116 is configured as a modeling and analysis engine 130, which is configured to implement the modeling and analysis functions described herein.

[0050] Figure 2 is a diagram illustrating an exemplary modeling and analysis engine 130 implemented by the computing system 116. As depicted in Figure 2, the modeling and analysis engine 130 includes a structural modeling module 131, which generates a structural model 132 of a measured semiconductor structure disposed on a sample, based in part on expected profile data 113. In some embodiments, the structural model 132 also includes the material properties of the sample. The structural model 132 is received as input to an optical response function (OPF) construction module 133. The ORF construction module 133 generates an ORF model 135 based at least in part on the structural model 132.

[0051] The optical response function model 135 is received as input to the fitting analysis module 137. The fitting analysis module 137 compares the modeled optical response with the corresponding measurement data 111 to determine the geometry and material properties of the sample.

[0052] In some instances, the fitting analysis module 137 resolves at least one sample parameter value by performing a fitting analysis on the optical measurement data 111 using the optical response model 135.

[0053] Fitting optical metrology data is beneficial for any type of optical metrology technique that provides sensitivity to geometric and / or material parameters of interest. The sample parameters can be decisional (e.g., CD, SWA, etc.) or statistical (e.g., RMS height of sidewall roughness, roughness correlation length, etc.), as long as an appropriate model describing the interaction between light and the sample is used.

[0054] Generally, the computing system 116 is configured to access model parameters in real-time using the Real-Time Critical Size Method (RTCD), or an accessible pre-computed model library, for determining one of the values ​​of at least one sample parameter associated with sample 114. Generally, some form of CD engine can be used to evaluate the difference between a specified CD parameter of a sample and a CD parameter associated with a measurement sample. An illustrative method and system for computing sample parameter values ​​is described in U.S. Patent No. 7,826,071, issued by KLA-Tencor Corporation on November 2, 2010, the entire contents of which are incorporated herein by reference.

[0055] Additionally, in some embodiments, one or more computing systems 116 are further configured to receive expected profile data 113 from an expected profile data source 103, such as a program tool, a drawing tool operated by a user, a program simulation tool, etc. One or more computer systems are further configured to configure the structural model described herein (e.g., structural model 132).

[0056] In some embodiments, the measurement system 100 is further configured to store one or more optimized structural models 115 in a memory (e.g., carrier media 118).

[0057] In one state, a modeling tool (e.g., a modeling and analysis engine 130 and 350) generates an optimized geometric model of a semiconductor structure parameterized by a set of variables in a latent mathematical space. As described above, the optimization of a geometric model is informed by expected profile data, i.e., an expected shape of the structure of interest in one or more steps of a process flow.

[0058] In some embodiments, the modeling tool receives from a source of expected contour data a plurality of reference shape profiles characterizing the shape of a semiconductor structure of interest. The reference shape profiles are parameterized by a set of observable geometric variables, such as critical dimensions, height, ellipticity, tilt, etc. The modeling tool transforms the observable geometric variables into a set of latent variables. The latent variables characterizing the reference shape profiles define the geometry of the structure of interest in an alternative mathematical space. Changes in the values ​​of the latent variables represent changes in the geometry of the structure of interest.

[0059] Generally, many different sources of expected profile data can be considered within the scope of this patent document. In some instances, a source of expected profile data is a trusted metrology system. In such instances, the reference shape profile is generated by a trusted metrology system (e.g., a scanning electron microscope, a tunneling electron microscope, a focused ion beam metrology system, an atomic force microscope, etc.) through measurements of several different examples of a structure of interest.

[0060] In some instances, a source of expected profile data is a semiconductor process simulation tool, such as ProETCH® etching simulation software or ProLITH® lithography and patterning simulation software, available from KLA Corporation (Miltitas, California, USA). In these instances, the reference shape profile is simulated by a semiconductor process simulator. Generally, the reference profile set is simulated by randomly sampling relevant process variables within a predefined range. In this way, the reference shape profile data set captures the expected changes in relevant process variables.

[0061] In some instances, a source of expected profile data is a user-generated specification of a reference shape profile. In some instances, a user uses an interactive software tool (e.g., a mechanical drawing software tool) to generate the reference shape profile. In this way, the user defines the reference shape profile based on their process experience.

[0062] Figure 3 is a plot 140 illustrating reference shape profiles generated by several users associated with a particular semiconductor structure of interest. The reference shape profile is parameterized by a critical dimension drawn along the horizontal axis of plot 140 and a height dimension drawn along the vertical axis. In the example depicted in Figure 3, the reference shape profile is defined by a user based on user experience.

[0063] As shown in Figure 3, the reference shape profile is parameterized by a set of observable geometric variables, such as height, critical dimension (CD), tilt, ellipticity, etc. The observable geometric variables can be directly observed from one of the geometric representations of the structure of interest (e.g., a shape profile).

[0064] In a further step, a modeling tool transforms the observable geometric variables into a set of latent variables. The number of latent variables is less than the number of observable geometric variables, thus reducing the dimensionality of the parameter space used to characterize the structure of interest. Generally, any program-driven parameterization or combination of different parameterizations can be used to reduce the dimensionality of the parameter space used to characterize the structure of interest.

[0065] In some instances, transforming an observable geometric variable into a latent variable involves principal component analysis (PCA). PCA is a linear transformation from observable geometric variables to one of a set of principal components. In these instances, the principal components are latent variables.

[0066] In another further state, a modeling tool generates a first set of reconstructed shape profiles based on sampling one of the values ​​of the latent variable array. After transforming the observable geometric variable array into the latent variable array, a new shape profile belonging to the reference shape profile family is generated. The new shape profile is generated by randomly sampling from the range of the latent variables. For comparison, the sampled values ​​of the latent variables are transformed back to the values ​​of the observable geometric variables by an inverse transformation from the latent space to the observable geometric space.

[0067] Figure 4 is a plot 165 illustrating several different reference shape profiles 166 and reconstructed shape profiles 167. The reference shape profile 166 is the same as depicted in Figure 3. Additionally, Figure 4 illustrates a large number of reconstructed profiles 167. The reconstructed profiles 167 are generated by random sampling from the range of latent variables. The sampled values ​​of the latent variables are transformed back to the values ​​of the observable geometric variables by an inverse transformation from the latent space to the observable geometric space. The resulting values ​​of the observable geometric variables are plotted as the reconstructed profiles 167. In this example, the latent variables (i.e., principal components) simultaneously capture CD and height variations.

[0068] In another further embodiment, a modeling tool truncates the latent variable set into a reduced set of latent variables based on the difference between the first set of reconstructed shape profiles and the reference shape profile. The difference between the profile reconstructed from the sampled values ​​of the latent variables and the reference shape profile provides one quantifiable measure of the accuracy of the representation of the reference shape profile in the latent mathematical space. In this way, a modeling tool determines the number of latent variables required to represent the reference shape profile at a desired accuracy level.

[0069] Figure 5 is a plot of the root mean square error (CD-RMSE) measurement of the difference between critical dimensions associated with a set of reference shape profiles and the corresponding critical dimensions associated with the reconstructed profiles predicted by an optimized geometric model. As depicted in Figure 5, plot line 171 shows the maximum value of the CD-RMSE value set varying with the number of latent variables in the optimized geometric model. Plot line 172 shows the average value of the CD-RMSE value set varying with the number of latent variables in the optimized geometric model. Plot line 173 shows the minimum value of the CD-RMSE value set varying with the number of latent variables in the optimized geometric model. As depicted in Figure 5, the CD-RMSE value decreases significantly with increasing number of latent variables. Therefore, an optimized geometric model can represent the geometry of a structure of interest with relatively few latent variables (e.g., less than 10 latent variables).

[0070] Figure 6 is a plot of the root mean square error (CD-RMSE) measurement of the difference between critical dimensions associated with a set of reference shape profiles and the corresponding values ​​of the critical dimensions associated with the reconstructed profiles predicted by an optimized geometric model at different heights. As depicted in Figure 6, the plot lines 175A to 175I represent the error varying according to the height of an optimized geometric model parameterized by 1 to 9 latent variables. As depicted in Figure 6, the height is expressed as a ratio of the total height of the structure of interest. Furthermore, the reconstruction error decreases significantly as the number of latent variables increases from 1 to 9. In addition, an optimized geometric model can represent the geometry of a structure of interest with a relatively small number of latent variables (e.g., less than 10 latent variables).

[0071] Figure 7 is a plot illustrating several reference shape profiles and several reconstructed shape profiles captured at different etch depths. Each reference shape profile specifies a CD value at one of 50 different height values ​​in the hard mask layer and a CD value at one of 50 different height values ​​in the ON stack layer. Reference shape profile 151 is characterized as a shallow etch profile, i.e., the expected shape profile after a relatively short etch time. Within this time, the etch penetrates the hard mask layer but does not significantly penetrate the ON stack layer. Reference shape profile 152 is characterized as a medium etch profile, i.e., the expected shape profile after an etch time longer than the shallow etch. Within this time, the etch penetrates both the hard mask layer and the ON stack layer. Reference shape profile 153 is characterized as a deep etch profile, i.e., the expected shape profile after an etch time longer than the medium etch. Within this time, the etch penetrates the hard mask layer and deeply penetrates the ON stack layer. As depicted in Figure 7, as the etch depth increases, more of the hard mask layer is etched away, i.e., the CD value increases. Additionally, Figure 7 illustrates a large number of reconstructed profiles 154. The reconstructed profiles 154 are generated by random sampling from the range of latent variables, as described above.

[0072] Figures 8A to 8C depict both reference shape profiles and reconstructed profiles associated with the shallow, medium, and deep etched structures depicted in Figure 7. In the examples depicted in Figures 8A to 8C, a conventional PCA is used to define the potential variables and truncate the number of potential variables into two principal components. Observable geometric variables (i.e., 50 critical dimensions in the hard mask region, 50 critical dimensions in the ON stack region, the height of both the hard mask region and the ON stack region, and the height ratio of both the hard mask region and the ON stack region) are equally weighted. Reconstructed profiles 155, 156, and 157 are derived from the two principal components. The principal components describe the variations in the height and CD of the hard mask and ON stack.

[0073] In some instances, a weighted PCA is used to transform the observable geometric variables into a set of latent variables. Weighting the observable geometric parameters improves the accuracy of latent parameterization with a smaller number of variables. Weighted PCA parameterization increases the weighting of one of the observable geometric variables that has relatively low sensitivity, more challenging accuracy requirements, or both.

[0074] In one example, a weighted PCA is used to improve the accuracy of parameterization of a portion of the etched structure depicted in the partial etched reference shape outlines shown in Figures 7 and 8A to 8C.

[0075] Figures 9A to 9C depict both reference shape profiles and reconstructed profiles associated with the shallow, medium, and deep etched structures depicted in Figure 7. In the examples depicted in Figures 9A to 9C, a weighted PCA is used to define the latent variables and truncate the number of latent variables into two principal components. In the examples depicted in Figures 9A to 9C, the height variable is weighted by a factor of 10 and the critical size is weighted by a factor of 1. Weighting the height variable more than the critical size variable improves the accuracy of the height in the reconstructed profiles. As depicted in Figures 9A to 9C, the reconstructed profiles 158, 159, and 160 are derived from the two principal components of the weighted PCA, and their fit with the reference shape profiles 151, 152, and 153 is better than that of the reconstructed profiles 155, 156, and 157 derived from the unweighted PCA, respectively.

[0076] In some instances, transforming observable geometric variables into latent variables involves a trained autoencoder. The trained autoencoder includes an encoder that transforms the observable geometric variables into latent variables and a decoder that transforms the latent variables back into observable geometric variables. Generally, a trained autoencoder is a nonlinear transformation that models a more complex latent space, which models the reference shape profile more accurately with fewer latent variables than a linear transformation such as PCA. In this way, a trained autoencoder can be more efficient and accurate than a PCA operation, especially when the reference profile geometry is more complex.

[0077] In some embodiments, the trained autoencoder includes a neural network (i.e., an encoder) trained to transform a reference shape profile parameterized by a relatively large number of observable geometric variables into a latent space parameterized by a relatively small number of latent variables, and a neural network (i.e., a decoder) trained to transform the values ​​of the latent variables back to the values ​​of the observable geometric variables. The profile can be generated using random values ​​of the latent variables within the constraints of the latent space. In some instances, an autoencoder is a variational autoencoder. In these instances, the latent space is trained to have a unit normal distribution and the random profile can be generated using a normal distribution.

[0078] In some instances, transforming observable geometric variables into latent variables involves a hybrid parameterization that includes a latent space parameterization as described above and a function fit of the difference between the reference shape profile and the reconstructed profile derived from the values ​​of the latent variables. The sum of the latent space parameterization and the function fit provides a more accurate representation of the reference shape profile using a relatively small number of independent variables. In general, any suitable mathematical function can serve as the basis for the function fit, including (but not limited to) a linear function, a Chebyshev polynomial function, a fast Fourier transform function, a discrete cosine transform function, a user-defined parameterization, and so on.

[0079] Generally, a latent space parameterization accurately captures the contours present in the training set of the reference shape contour. However, there may be additional contour variations induced by procedural changes, which are not captured in the training set of the reference shape contour and therefore not captured by the latent space parameterization. In such instances, contour variations can be more accurately characterized by a combination of the latent space parameterization and one or more general mathematical functions (e.g., Chebyshev polynomial curves). In this way, hybrid parameterization effectively expands the scope of the program by introducing a general parameterization into the program-based latent space parameterization.

[0080] In another further embodiment, a modeling tool generates a set of reconstructed shape profiles based on sampling one of the values ​​of the latent variables described above. Additionally, the modeling tool fits a mathematical function (e.g., a curve) to the difference between the reference shape profile and the reconstructed shape profile. Then, the modeling tool generates another set of reconstructed shape profiles based on the sum of the reconstructed shape profiles derived from the values ​​of the latent variables and the fitted curve. The resulting reconstructed shape profiles can be used to train a measurement model.

[0081] In another further embodiment, a modeling tool expands the range of values ​​for one or more of the observable geometric variables to effectively extend the range of the training set of the reference shape profile. The expanded training set of the reference shape profile is then used as the basis for generating transformations to the latent space, for example, through PCA, a trained autoencoder, etc. Expanding the range of observable geometric variables used as the basis for generating transformations to the latent space effectively extends the range of program variations considered within the program space. This enhances the robustness of the latent space to program variations, but generally at the cost of a larger number of latent variables required to accurately represent the expanded range of the reference shape profile.

[0082] Figure 10 is a plot 180 illustrating an expanded training group of one of several reference shape contours by scaling the reference contour height value by 20%.

[0083] Figure 11 is a diagram 181 illustrating an expanded training group of reference shape profiles containing several reference shape profiles by shifting the critical size range by 20%.

[0084] Figure 12 is a plot of an expanded training group of one of several reference shape profiles, which is expanded by scaling the critical size range by 20%.

[0085] As illustrated in Figures 10 to 12, the range of values ​​of observable geometric variables can be expanded by scaling their values, shifting their values, or any combination thereof. However, in general, any number of different expansions of any combination of training sets of reference shape profiles can be considered within the scope of this patent document.

[0086] In another further state, a modeling tool generates a reconstructed shape profile by a free potential variable array to eliminate non-solid shape profiles.

[0087] As described above, the reconstructed shape profile is generated by sampling latent variables. When latent variables are trained on a finite set of reference shape profiles, non-solid shape profiles that can be caused by random combinations of latent variables can be generated. The presence of non-solid profiles in the reconstructed profile data can be problematic when training a measurement model to fit the measurement spectrum to the shape profile. To mitigate this risk, a modeling tool eliminates non-solid profiles from the reconstructed profile data used to train a measurement model.

[0088] In some instances, non-solid profiles are identified based on the values ​​of one or more derivatives of the reconstructed shape profile. Each derivative value is compared to an acceptable value within a corresponding predetermined range, and if the calculated derivative value is outside the acceptable range, the reconstructed shape profile is eliminated. In one instance, a reconstructed shape profile is generated in a latent space and transformed back to the space of observable geometric variables. In one instance, a critical dimension of a reconstructed shape profile is expressed as a function of height. In this instance, one or more derivatives of CD with respect to height are calculated, such as dCD / dH, d²CD / dH², etc. If the value of any of the derivatives is outside the corresponding acceptable range of the critical value, the reconstructed shape profile is eliminated.

[0089] In some instances, the reconstructed shape profile is generated by sampling a subspace of the latent space spanned by the latent variable array. In one instance, the sampled values ​​of the latent variable array are selected from a hypersphere rather than a hypercube in the latent space. In other words, the reconstructed shape profile is generated by selecting only the values ​​of the latent variable array within a fixed distance from the center of the latent space, rather than the extreme values ​​of the latent variable array.

[0090] In some instances, the values ​​of observable geometric variables associated with each reconstructed shape profile are compared to a predetermined acceptable range for the values ​​of each of the observable geometric variables, and if any of the values ​​of the observable geometric variables associated with a particular reconstructed shape profile are outside the acceptable range, the reconstructed shape profile is eliminated. In one instance, acceptable ranges for CD and height are established, and the values ​​of CD and height associated with each reconstructed shape profile are compared to the acceptable range. If the value of CD or height associated with a particular reconstructed shape profile is outside the acceptable range, the reconstructed shape profile is eliminated.

[0091] In another further embodiment, a modeling tool trains a measurement model based at least in part on reconstructed shape profiles derived from an optimized geometric model of the self-measured structure. A large number of reconstructed shape profiles across relevant procedural variations are efficiently generated based on the optimized geometric model. A measurement simulation tool is used to generate synthetic measurement data associated with each different reconstructed shape profile, such as spectra, images, electron density maps, etc. The reconstructed shape profiles and corresponding measurement data sets include a training data set for training a measurement model, such as the optical response function model 135 depicted in Figure 2, the X-ray scattering measurement response model 355, or a machine learning-based measurement model.

[0092] In another further example, a modeling tool uses a trained measurement model to estimate the values ​​of observable geometric parameters of interest associated with a measured structure.

[0093] In these examples, the measurements are performed by a metrology system, such as metrology systems 100, 300, and 500 depicted in Figures 1, 13, and 15, respectively. Generally, an example of a semiconductor structure of interest is irradiated with a certain amount of energy. A quantity of measurement data is detected in response to the amount of energy. The values ​​of the latent variables of the semiconductor structure of interest are estimated based on a fitting of a trained measurement model with the quantity of measurement data. Finally, the estimated values ​​of the latent variables are transformed into the values ​​of the observable geometric variables of the structure of interest. The estimated values ​​of the latent variables are transformed back to the values ​​of the observable geometric variables by an inverse transformation from the latent space to the observable geometric space. The inverse transformation is the inverse of the transformation used to determine the latent variables from the observable geometric variables (e.g., the inverse of a forward PCA transformation), a trained decoder, etc.

[0094] Measurements employing an optimized geometric model can be performed by a variety of different semiconductor measurement systems. By way of non-limiting examples, a rotating polarizer ellipsometer, a rotating polarizer, a rotating compensator ellipsometer, a rotating compensator, a rotating compensator ellipsometer, a soft X-ray-based reflectometer, a small-angle X-ray scatterometer, or any combination thereof can employ one of the optimized geometric models described herein.

[0095] By way of example, Figure 13 illustrates an embodiment of an x-ray metrology tool 300 that uses an optimized geometric model to measure the characteristics of a sample according to the exemplary method presented herein. As shown in Figure 13, the system 300 can be used to perform x-ray scattering measurements on a detection area 302 of a sample 301 placed on a sample positioning system 340.

[0096] In the depicted embodiment, the metrology tool 300 includes an X-ray illumination source 310 configured to generate X-ray radiation suitable for X-ray scattering measurement. In some embodiments, the X-ray illumination system 310 is configured to generate wavelengths between 0.01 nanometers and 1 nanometer. The X-ray illumination source 310 generates an X-ray beam 317 incident on a detection region 302 of the sample 301.

[0097] Generally, any suitable high-brightness x-ray illumination source capable of producing high-brightness x-rays at a flux level sufficient to achieve high-flux measurement can be considered to supply x-ray illumination for x-ray scattering measurements. In some embodiments, an x-ray source includes a tunable monochromator that enables the x-ray source to deliver x-ray radiation at different selectable wavelengths.

[0098] In some embodiments, one or more x-ray sources emitting radiation with photon energies greater than 15 keV are used to ensure that the x-ray source supplies light at a wavelength that allows sufficient transmission through the entire device and the wafer substrate. By way of non-limiting examples, any of a particle accelerator source, a liquid anode source, a rotating anode source, a fixed solid anode source, a microjoule source, a microjoule rotating anode source, and an inverse Compton source may be used as x-ray source 310. In one example, an inverse Compton source purchased from Lyncean Technologies (Palo Alto, California, USA) may be considered. The inverse Compton source has the additional advantage of being able to generate x-rays in a range of photon energies, thereby enabling the x-ray source to deliver x-ray radiation at different selectable wavelengths. In some embodiments, an x-ray source includes an electron beam source configured to bombard a solid or liquid target to excite x-ray radiation.

[0099] In some embodiments, the profile of the incident X-ray beam is controlled by one or more apertures, slits, or combinations thereof. In a further embodiment, the aperture, slit, or both are configured to rotate in coordination with the orientation of the sample to optimize the profile of the incident beam for each incident angle, azimuth angle, or both.

[0100] As depicted in Figure 13, the x-ray optics 315 shapes and guides the incident x-ray beam 317 to the sample 301. In some instances, the x-ray optics 315 includes an x-ray monochromator for monochromating the x-ray beam incident on the sample 301. In one instance, a crystal monochromator (such as a Loxley-Tanner-Bowen monochromator) is used to monochromate the x-ray radiation beam. In some instances, the x-ray optics 315 uses multilayer x-ray optics to collimate or focus the x-ray beam 317 onto the detection region 302 of the sample 301 with a divergence of less than 1 milliradian. In some embodiments, the x-ray optics 315 includes one or more x-ray collimators, x-ray apertures, x-ray beam stops, refractive x-ray optics, diffractive optics such as zone plates, mirror x-ray optics such as grazing-incidence ellipsoidal mirrors, multicapillary optics such as hollow capillary x-ray waveguides, multilayer optics or systems, or any combination thereof. Further details are described in U.S. Patent Publication No. 2015 / 0110249, the entire contents of which are incorporated herein by reference.

[0101] Generally, the focal plane of an illumination optics system is optimized for various measurement applications. In this way, the system 300 is configured to position the focal plane at different depths within the sample depending on the measurement application.

[0102] The X-ray detector 316 collects the X-ray radiation 325 scattered from the sample 301 and generates an output signal 326 indicating one of the properties of the sample 301 that is sensitive to the incident X-ray radiation, based on an X-ray scattering measurement mode. In some embodiments, the scattered X-rays 325 are collected by the X-ray detector 316 when the sample positioning system 340 positions and orients the sample 301 to generate angle-resolved scattered X-rays.

[0103] In some embodiments, an X-ray scattering measurement system includes one or more photon counting detectors having a high dynamic range (e.g., greater than 10⁵) and a thick, highly absorptive crystal substrate that absorbs the direct beam (i.e., the zero-order beam) without damage and has minimal parasitic backscattering. In some embodiments, a single photon counting detector detects the position and number of the detected photons.

[0104] In some embodiments, the x-ray detector analyzes one or more x-ray photon energies and generates signals indicating the properties of a sample for each x-ray energy component. In some embodiments, the x-ray detector 316 includes any of a CCD array, a microchannel plate, a photodiode array, a microstrip proportional counter, a gas proportional counter, a scintillator, or a fluorescent material.

[0105] In this manner, in addition to pixel position and count, the X-ray photon interactions within the detector are also distinguished by energy. In some embodiments, X-ray photon interactions are distinguished by comparing the energy of the X-ray photon interactions with a predetermined upper threshold and a predetermined lower threshold. In one embodiment, this information is transmitted to the computing system 330 via output signal 326 for further processing and storage.

[0106] In a further embodiment, the X-ray scattering measurement system 300 is used to determine the properties of a sample (e.g., structural parameter values) based on one or more measurement intensities. As depicted in FIG13, the measurement system 300 includes a computational system 330 for acquiring a signal 326 generated by the detector 316 and determining the properties of the sample based at least in part on the acquired signal.

[0107] In some embodiments, it is desirable to perform measurements with different orientations described by rotations around the x-axis and y-axis indicated by the coordinate system 346 depicted in FIG. 13. This improves the precision and accuracy of the measurement parameters and reduces the correlation between parameters by expanding the number and diversity of data sets available for analysis to include a variety of large-angle out-of-plane orientations. Measuring sample parameters with a deeper and more diverse data set also reduces the correlation between parameters and improves measurement accuracy. For example, in a normal orientation, X-ray scattering measurements can resolve the critical dimensions of a feature, but are essentially insensitive to the sidewall angles and height of a feature. However, the sidewall angles and height of a feature can be resolved by collecting measurement data over a wide range at out-of-plane angular locations.

[0108] As illustrated in FIG. 13, the metrology tool 300 includes a sample positioning system 340 configured to align and orient the sample 301 over a large angular range relative to a scatterometer in exterior angular orientation. In other words, the sample positioning system 340 is configured to rotate the sample 301 over a large angular range about one or more axes of rotation coplanar with the surface of the sample 301. In some embodiments, the sample positioning system is configured to rotate the sample 301 over a range of at least 120 degrees about one or more axes of rotation coplanar with the surface of the sample 301. In this manner, angular resolution measurements of the sample 301 are collected by the metrology system 300 at any number of locations on the surface of the sample 301. In one example, the computational system 330 transmits a command signal indicating the desired position of the sample 301 to the motion controller 345 of the sample positioning system 340. In response, the motion controller 345 generates command signals to various actuators of the sample positioning system 340 to achieve the desired positioning of the sample 301.

[0109] By a non-limiting example, as illustrated in FIG13, the sample positioning system 340 includes an edge clamping chuck 341 for securing a sample 301 to an edge clamping chuck 341 of the sample positioning system 340. A rotary actuator 342 is configured to rotate the edge clamping chuck 341 and the attached sample 301 relative to a peripheral frame 343. In the depicted embodiment, the rotary actuator 342 is configured to rotate the sample 301 about the x-axis of the coordinate system 346 illustrated in FIG13. As depicted in FIG13, the sample 301 rotates in a plane of a rotational system about the z-axis. The out-of-plane rotation of the sample 301 about the x-axis and y-axis (not shown) effectively tilts the surface of the sample relative to the measuring element of the measuring system 300. Although not illustrated, a second rotary actuator is configured to rotate the sample 301 about the y-axis. A linear actuator 344 is configured to translate the peripheral frame 343 in the x-direction. Another linear actuator (not shown) is configured to translate the peripheral frame 343 in the y-direction. In this way, each position on the surface of sample 301 can be measured within a range of exterior angular positions. For example, in one embodiment, a position of sample 301 is measured in angular increments within a range of -45 degrees to +45 degrees relative to the normal orientation of sample 301.

[0110] Generally speaking, the sample positioning system 340 may include any suitable combination of mechanical elements for achieving the desired linear and angular positioning performance, including (but not limited to) a goniometer, a hexapod, an angle stage, and a linear stage.

[0111] In some instances, metrology based on X-ray scattering measurements involves determining the size of a sample by inversely solving a predetermined measurement model using measurement data. The measurement model contains several (approximately 10) adjustable parameters and represents the geometric and optical properties of the sample and the optical properties of the measurement system. Inverse solution methods include (but are not limited to) model-based regression, tomography, machine learning, or any combination thereof. In this manner, target profile parameters are estimated by solving for values ​​in a parameterized measurement model that minimize the error between the measured scattered X-ray intensity and the modeled result.

[0112] In a further embodiment, the computing system 330 is configured to generate a structural model (e.g., a geometric model, a material model, or a combined geometric and material model) of a measurement structure of a sample, generate an X-ray scattering measurement response model from the structural model containing at least one geometric parameter, and resolve at least one sample parameter value by performing a fitting analysis of the X-ray scattering measurement data using the X-ray scattering measurement response model. The analysis engine is used to compare the simulated X-ray scattering measurement signal with the measurement data, thereby allowing the determination of geometric and material properties, such as the electron density of the sample. In the embodiment depicted in Figure 13, the computing system 330 is configured as a modeling and analysis engine 350 configured to implement the modeling and analysis functions described herein.

[0113] Figure 14 is a diagram illustrating an exemplary modeling and analysis engine 350 implemented by the computing system 330. As depicted in Figure 14, the modeling and analysis engine 350 includes a structure modeling module 351, which generates a structural model 352 of a measurement semiconductor structure disposed on a sample, based in part on a reference shape profile 313 received from a expected profile data source 303 described herein. In some embodiments, the structural model 352 also includes the material properties of the sample. The structural model 352 is received as input to an x-ray scattering measurement response function construction module 353. The x-ray scattering measurement response function construction module 353 generates an x-ray scattering measurement response function model 355 based at least in part on the structural model 352. The x-ray scattering measurement response function model 355 is received as input to a fitting analysis module 357. The fitting analysis module 357 compares the modeled X-ray scattering measurement response with the corresponding measurement data 326 to determine the properties 370 (e.g., the geometry and material properties of the sample) stored in memory (e.g., memory 380).

[0114] Figure 15 illustrates one embodiment of a soft X-ray reflectance (SXR) metrology tool 500 used for measuring the characteristics of a sample. In some embodiments, SXR measurements of a semiconductor wafer are performed using a small spot size (e.g., less than 50 micrometers across the effective illumination spot) within a range of wavelength, angle of incidence, and azimuth. In one embodiment, SXR measurements are performed using X-ray radiation in a soft X-ray region (i.e., 30 eV to 3000 eV) at a grazing angle of incidence ranging from 5 degrees to 20 degrees. The grazing angle for a particular metrology application is selected to achieve the desired penetration into the measured structure and maximize the measurement information content using a small spot size (e.g., less than 50 micrometers).

[0115] As shown in Figure 15, the system 500 performs SXR measurement on a measurement area 502 of a sample 501 illuminated by an incident illumination spot.

[0116] In the depicted embodiment, the metrology tool 500 includes an x-ray illumination source 510, focusing optics 511, a beam divergence control slit 512, and a slit 513. The x-ray illumination source 510 is configured to generate soft X-ray radiation suitable for SXR measurement. The x-ray illumination source 510 is a multicolor, high-brightness, large-spread source. In some embodiments, the x-ray illumination source 510 is configured to generate x-ray radiation in the range of 30 electron volts to 3000 electron volts. Generally, any suitable high-brightness x-ray illumination source capable of generating high-brightness soft X-rays at a flux level sufficient to achieve high-throughput, in-line metrology can be considered for supplying x-ray illumination for SXR measurement.

[0117] In some embodiments, an x-ray source includes a tunable monochromator that enables the x-ray source to deliver x-ray radiation at different selectable wavelengths. In some embodiments, one or more x-ray sources are used to ensure that the x-ray source supplies light at a wavelength that allows sufficient penetration into the measured sample.

[0118] In some embodiments, the illumination source 510 is a high-order harmonic generation (HHG) x-ray source. In some other embodiments, the illumination source 510 is a oscillator / waver synchrotron radiation source (SRS). An exemplary oscillator / waver SRS is described in U.S. Patent Nos. 8,941,336 and 8,749,179, the entire contents of which are incorporated herein by reference.

[0119] In some other embodiments, the illumination source 110 is a laser-generated plasma (LPP) source. In some of these embodiments, the LPP source comprises any of xenon, krypton, argon, neon, and nitrogen emitting materials. Generally, a suitable choice of LPP target material is chosen for brightness optimization in the resonant soft X-ray region. For example, krypton-emitted plasma provides high brightness at the silicon-K edge. In another example, xenon-emitted plasma provides high brightness throughout the soft X-ray region (80 eV to 3000 eV). Thus, xenon-based emitting materials are a good choice when broadband soft X-ray illumination is desired.

[0120] The selection of LPP target materials can also be optimized for reliable and long-life light source operation. Inert gas target materials such as xenon, krypton, and argon are inert and can be reused in a closed-loop operation with little or no need for decontamination. An exemplary soft X-ray illumination source is described in U.S. Patent Application No. 15 / 867,633, the entire contents of which are incorporated herein by reference.

[0121] In a further embodiment, the wavelength emitted by the illumination source (e.g., illumination source 510) is selectable. In some embodiments, illumination source 510 is an LPP light source controlled by computing system 530 to maximize flux in one or more selected spectral regions. The peak laser intensity at the target material controls the plasma temperature and thus the spectral region of the emitted radiation. The peak laser intensity is varied by adjusting the pulse energy, pulse width, or both. In one example, a 100 picosecond pulse width is suitable for generating soft X-ray radiation. As depicted in FIG15, computing system 530 transmits a command signal 536 to illumination source 510 causing it to adjust the spectral range of wavelengths emitted from illumination source 510. In one example, illumination source 510 is an LPP light source, and the LPP light source adjusts any of the pulse duration, pulse frequency, and target material composition to achieve a desired spectral range of wavelengths emitted from the LPP light source.

[0122] By way of non-limiting examples, any of a particle accelerator source, a liquid anode source, a rotating anode source, a fixed solid anode source, a microjoule source, a microjoule rotating anode source, a plasma-based source, and an inverse Compton source can be used as an X-ray illumination source 510.

[0123] An exemplary X-ray source includes an electron beam source configured to bombard a solid or liquid target to excite X-ray radiation. Methods and systems for generating high-brightness liquid metal X-ray illumination are described in U.S. Patent No. 7,929,667, issued by KLA-Tencor Corporation on April 19, 2011, the entire contents of which are incorporated herein by reference.

[0124] The X-ray illumination source 510 generates X-ray emission in a source region having a finite lateral dimension (i.e., a non-zero dimension orthogonal to the beam axis). In one sample, the source region of the illumination source 510 is characterized by a lateral dimension of less than 20 micrometers. In some embodiments, the source region is characterized by a lateral dimension of 10 micrometers or less. The small source size enables high brightness illumination of a small target area on the sample, thus improving measurement accuracy, precision, and throughput.

[0125] Generally, X-ray optics shape and guide X-ray radiation onto sample 501. In some instances, multilayer X-ray optics collimate or focus the X-ray beam onto the measurement region 502 of sample 501 with a divergence of less than 1 milliradian. In some embodiments, X-ray optics include one or more X-ray collimators, X-ray apertures, X-ray beam stops, refractive X-ray optics, diffractive optics (such as zone plates), Schwarzschild optics, Kirkpatrick-Baez optics, Montel optics, Wolter optics, mirror X-ray optics (such as ellipsoidal mirrors), multicapillary optics (such as hollow capillary X-ray waveguides), multilayer optics or systems, or any combination thereof. Further details are described in U.S. Patent Publication No. 2015 / 0110249, the entire contents of which are incorporated herein by reference.

[0126] As depicted in Figure 15, the focusing optics 511 focuses the source radiation onto a metrological target located on the sample 501. The finite lateral source size results in a finite spot size 502 on the target defined by rays 516 from the edge of the source and any beam shaping provided by beam slits 512 and 513.

[0127] In some embodiments, the focusing optics 511 comprises an elliptical focusing optics element. In the embodiment depicted in FIG15, the magnification of the focusing optics 511 at the center of the ellipse is approximately 1. Therefore, the size of the illumination spot projected onto the surface of the sample 501 is approximately the same as the size of the illumination source, due to the adjustment for beam spread at the nominal grazing incidence angle (e.g., 5 to 20 degrees).

[0128] In a further state, the focusing optics 511 collects the source emission and selects one or more discrete wavelengths or spectral bands, and focuses the selected light onto the sample 501 at a grazing incidence angle in the range of 5 degrees to 20 degrees.

[0129] The nominal grazing incidence angle is selected to achieve one of the metrological objectives: desired penetration to maximize signal information content while remaining within the metrological target boundaries. The critical angle for hard X-rays is very small, but the critical angle for soft X-rays is significantly larger. Due to this additional metrological flexibility, SXR measurements can probe deeper into structures and are less sensitive to the precise value of the grazing incidence angle.

[0130] In some embodiments, the focusing optics 511 includes a hierarchical multilayer structure (e.g., a layer or coating) that selects a desired wavelength or wavelength range for projection onto the sample 501. In some instances, the focusing optics 511 includes a hierarchical multilayer structure (e.g., a layer or coating) that selects a wavelength and projects the selected wavelength onto the sample 501 within an incident angle range. In some instances, the focusing optics 511 includes a hierarchical multilayer structure that selects a wavelength range and projects the selected wavelength onto the sample 501 within an incident angle range.

[0131] Hierarchical multilayer optics better minimize optical loss when the single-layer grating structure is too deep. Generally, multilayer optics select the reflection wavelength. Optimization of the spectral bandwidth of the selected wavelength provides the flux to sample 501, measures the information content in the diffraction order, and prevents signal degradation due to angular divergence and overlapping diffraction peaks at the detector. In addition, hierarchical multilayer optics are used to control divergence. Angular divergence at each wavelength is optimized for minimum spatial overlap at the flux and detector.

[0132] In some examples, hierarchical multilayer optics select wavelengths to enhance the contrast and information content of diffracted signals from specific material interfaces or structural dimensions. For example, the selected wavelength can be chosen to span specific resonant regions of elements (e.g., silicon K-edges, nitrogen K-edges, oxygen K-edges, etc.). Additionally, in these examples, the illumination source can also be tuned to maximize flux in selected spectral regions (e.g., HHG spectral tuning, LPP laser tuning, etc.).

[0133] In some embodiments, the focusing optics 511 includes a plurality of reflective optical elements, each having an elliptical surface shape. Each reflective optical element includes a substrate and a multilayer coating tuned to reflect a different wavelength or wavelength range. In some embodiments, the plurality of reflective optical elements reflecting a different wavelength or wavelength range (e.g., one to five) are arranged at various angles of incidence. In a further embodiment, multiple groups (e.g., two to five groups) of reflective optical elements reflecting a different wavelength or wavelength range are arranged at different angles of incidence. In some embodiments, the multiple groups of reflective optical elements simultaneously project illumination light onto the sample 501 during measurement. In some other embodiments, the multiple groups of reflective optical elements sequentially project illumination light onto the sample 501 during measurement. In these embodiments, an active shutter or aperture is used to control the illumination light projected onto the sample 501.

[0134] In some embodiments, the focusing optics 511 focuses light of multiple wavelengths, azimuth angles and AOIs onto the same measurement target area.

[0135] In a further embodiment, the range of wavelengths, AOIs, azimuth angles, or any combination thereof projected onto the same measurement area is adjusted by one or more mirror elements of the active positioning focusing optics. As depicted in FIG15, the computing system 530 transmits a command signal 537 to the actuator system 515, which causes the actuator system 515 to adjust the position, alignment, or both of one or more optical elements of the focusing optics 511 to achieve the desired range of wavelengths, AOIs, azimuth angles, or any combination thereof projected onto the sample 501.

[0136] Generally, the incident angle is selected for each wavelength to optimize the penetration and absorption of the illumination light by the target being measured. In many cases, multilayer structures are measured, and the incident angle is selected to maximize the signal information associated with the desired layer. In cases of overlay metrology, several wavelengths and several incident angles are selected to maximize the signal information resulting from the interference between scattering from the previous and current layers. Additionally, an azimuth angle is selected to optimize the signal information content. Furthermore, an azimuth angle is selected to ensure angular separation of diffraction peaks at the detector.

[0137] In a further embodiment, an SXR metrology system (e.g., metrology tool 500) includes one or more beam slits or apertures to shape an illumination beam 514 incident on the sample 501 and selectively block a portion of the illumination light that would otherwise illuminate a measured target. The one or more beam slits define the beam size and shape such that the X-ray illumination spot is suited to the area of ​​the measured target. Additionally, the one or more beam slits define the illumination beam divergence to minimize the overlap of diffraction orders on the detector.

[0138] In another further embodiment, an SXR metrology system (e.g., metrology tool 500) includes one or more beam slits or apertures for selecting one or more of a set of illumination wavelengths to simultaneously illuminate a metrology target being measured. In some embodiments, illumination comprising multiple wavelengths is simultaneously incident on a metrology target being measured. In these embodiments, one or more slits are configured to transmit illumination comprising multiple illumination wavelengths. Generally, simultaneous illumination of a metrology target being measured preferably increases signal information and throughput. However, in practice, the overlap of diffraction stages at the detector limits the range of illumination wavelengths. In some embodiments, one or more slits are configured to sequentially transmit different illumination wavelengths. In some instances, sequential illumination at larger angular divergences provides higher throughput because the signal-to-noise ratio of sequential illumination can be higher than that of simultaneous illumination when the beam divergence is large. When measurements are performed sequentially, the problem of diffraction stage overlap is not an issue. This increases measurement flexibility and improves the signal-to-noise ratio.

[0139] Figure 15 depicts a beam divergence control slit 512 located in the beam path between the focusing optics 511 and the beam shaping slit 513. The beam divergence control slit 512 limits the divergence of illumination provided to the measured sample. The beam shaping slit 513 is located in the beam path between the beam divergence control slit 512 and the sample 501. The beam shaping slit 513 further shapes the incident beam 514 and selects several illumination wavelengths of the incident beam 514. The beam shaping slit 513 is located in the beam path directly before the sample 501. In one configuration, the slit of the beam shaping slit 513 is positioned close to the sample 501 to minimize the incident spot size due to the expansion of beam divergence defined by the finite source size.

[0140] In some embodiments, the beam shaping slit 513 includes a plurality of independently actuated beam shaping slits. In one embodiment, the beam shaping slit 513 includes four independently actuated beam shaping slits. These four beam shaping slits effectively block a portion of the incident beam and produce an illumination beam 514 having one of the box-shaped illumination cross sections.

[0141] The slit of the beam-shaping slit 513 is made of a material that minimizes scattering and effectively blocks incident radiation. Exemplary materials include single-crystal materials such as germanium, gallium arsenide, indium phosphide, etc. Typically, the slit material is cleaved along a single crystal direction rather than sawed to minimize scattering across structural boundaries. Furthermore, the slit is oriented relative to the incident beam so that the interaction between the incident radiation and the internal structure of the slit material produces a minimum amount of scattering. Crystals are attached to slit holders made of a high-density material (e.g., tungsten) to completely block the X-ray beam on one side of the slit.

[0142] The X-ray detector 519 collects the X-ray radiation 518 scattered from the sample 501 and generates an output signal 535 indicating the properties of the sample 501 that are sensitive to the incident X-ray radiation, according to an SXR measurement mode. In some embodiments, the scattered X-rays 518 are collected by the X-ray detector 519 when the sample positioning system 540 positions and orients the sample 501 to generate angle-resolved scattered X-rays.

[0143] In some embodiments, an SXR system includes one or more photon counting detectors having a high dynamic range (e.g., greater than 10⁵). In some embodiments, a single photon counting detector detects the position and number of detected photons.

[0144] In some embodiments, the x-ray detector analyzes one or more x-ray photon energies and generates signals indicating the properties of a sample for each x-ray energy component. In some embodiments, the x-ray detector 519 includes any of a CCD array, a microchannel plate, a photodiode array, a microstrip proportional counter, a gas proportional counter, a scintillator, or a fluorescent material.

[0145] In this manner, in addition to pixel position and count, the X-ray photon interactions within the detector are also distinguished by energy. In some embodiments, X-ray photon interactions are distinguished by comparing the energy of the X-ray photon interactions with a predetermined upper threshold and a predetermined lower threshold. In one embodiment, this information is transmitted to the computing system 530 via an output signal 535 for further processing and storage.

[0146] Due to diffraction, the diffraction pattern caused by the simultaneous illumination of a periodic target with multiple illumination wavelengths separates at the detector plane. In these embodiments, an integral detector is employed. The diffraction pattern is measured using a region detector (e.g., a vacuum-compatible back-side CCD or a hybrid pixel array detector). Angular sampling is optimized for Bragg peak integration. If a pixel-level model fitting is used, angular sampling is optimized for signal information content. The sampling rate is selected to prevent zero-order signal saturation.

[0147] In a further embodiment, an SXR system is used to determine the properties (e.g., structural parameter values) of a sample based on one or more diffraction orders of the scattered light. As depicted in Figure 15, the metrology tool 500 includes a computational system 530 for acquiring a signal 535 generated by the detector 519 and determining the properties of the sample based at least in part on the acquired signal using one of the optimized geometric models described herein.

[0148] It is desirable to perform measurements over a wide range of wavelengths, incident angles, and azimuth angles to improve the precision and accuracy of measurement parameter values. This method reduces the correlation between parameters by increasing the number and diversity of data sets available for analysis.

[0149] Measurements of the intensity of diffracted radiation, which varies with the illumination wavelength and the X-ray incident angle relative to the wafer surface normal, are collected. Information contained in multiple diffraction levels is generally unique among the model parameters under consideration. Therefore, X-ray scattering produces estimates of the parameters of interest with small errors and reduced parameter correlation.

[0150] In one configuration, the metrology tool 500 includes a wafer chuck 503 that holds a fixed support wafer 501 and is coupled to a sample positioning system 540. The sample positioning system 540 is configured to actively position the sample 501 in six degrees of freedom relative to an illumination beam 514. In one example, the computing system 530 transmits a command signal (not shown) indicating the desired position of the sample 501 to the sample positioning system 540. In response, the sample positioning system 540 generates command signals to various actuators of the sample positioning system 540 to achieve the desired positioning of the sample 501.

[0151] In a further embodiment, the focusing optics of an SXR system projects an image of an illumination source onto the sample being measured at a reduction factor of at least 5 times (i.e., a magnification factor of 0.2 or less). One SXR system described herein employs a soft X-ray illumination source having a source region characterized by a lateral dimension of 20 micrometers or less (i.e., a source size of 20 micrometers or less). In some embodiments, a focusing optics having a reduction factor of at least 5 (i.e., projecting an image of the source that is 5 times smaller than the source size onto the wafer) is used to project illumination having an incident illumination spot size of 4 micrometers or less onto the sample.

[0152] In some instances, SXR-based metrology involves determining sample size by inversely solving a predetermined measurement model using measurement data. The measurement model contains several (approximately 10) adjustable parameters and represents the geometric and optical properties of the sample and the optical properties of the measurement system. Inverse solution methods include (but are not limited to) model-based regression, tomography, machine learning, or any combination thereof. In this manner, target profile parameters are estimated by solving for values ​​of a parameterized measurement model that minimizes the error between the measured scattered X-ray intensity and the modeled result.

[0153] Further description of the metrology system based on soft X-rays is provided in U.S. Patent Publication No. 2019 / 0017946, the entire contents of which are incorporated herein by reference.

[0154] In another further embodiment, the computing system 530 is configured to generate an optimized geometric model of a measurement structure of one of the samples described herein, generate an SXR response model from the structural model containing at least one latent parameter, and resolve the at least one latent parameter value by performing a fitting analysis of the SXR measurement data using the SXR response model. The analysis engine is used to compare the simulated SXR signal with the measurement data, thereby allowing the determination of latent parameter values ​​and material properties, such as the electron density of the sample. In the embodiment depicted in FIG15, the computing system 530 is configured as a modeling and analysis engine (e.g., modeling and analysis engine 350), which is configured to implement the modeling and analysis functions described with reference to FIG14.

[0155] In some instances, modeling and analysis engines 130 and 350 improve the accuracy of measurement parameters through any combination of lateral feedforward analysis, feedforward analysis, and parallel analysis. Lateral feedforward analysis refers to obtaining multiple datasets from different regions of the same sample and transferring common parameters determined from the first dataset to the second dataset for analysis. Feedforward analysis refers to obtaining datasets from different samples and using a progressively replicating accurate parameter feedforward method to forward common parameters to subsequent analyses. Parallel analysis refers to a nonlinear fitting method applied in parallel or simultaneously to multiple datasets, wherein at least one common parameter is coupled during fitting.

[0156] Multi-tool and structural analysis refers to feedforward, lateral, or parallel analysis based on regression, a lookup table (i.e., "library" matching), or another fitting procedure for multiple data sets. Illustrative methods and systems for multi-tool and structural analysis are described in U.S. Patent No. 7,478,019, issued by KLA-Tencor Corporation on January 13, 2009, the entire contents of which are incorporated herein by reference.

[0157] Although reference systems 100, 300, and 500 explain the methods discussed herein, any optical, X-ray, or electron beam-based measurement system configured to irradiate a sample with a certain amount of energy (e.g., electromagnetic radiation, electron beam energy, etc.) and detect the energy reflected, transmitted, or diffracted from the sample can be used to implement the exemplary methods described herein. Exemplary systems include an angle resolving reflectometer, a scatterometer, a reflectometer, an ellipsometer, a spectroreflectometer or ellipsometer, a beam profile reflectometer, a multi-wavelength two-dimensional beam profile reflectometer, a multi-wavelength two-dimensional beam profile ellipsometer, a rotating compensator spectroreflectometer, a transmission X-ray scatterometer, a reflection X-ray scatterometer, etc. By way of non-limiting examples, an ellipsometer may include a single rotating compensator, multiple rotating compensators, a rotating polarizer, a rotating analyzer, a modulation element, multiple modulation elements, or no modulation element.

[0158] It should be noted that the output from a source and / or target measurement system can be configured in a way that allows the measurement system to use more than one technology. In fact, an application can be configured to use any combination of available metrology subsystems within a single tool or across several different tools.

[0159] A system implementing one of the methods described herein can also be configured in several different ways. For example, a wide range of wavelengths (including visible light, ultraviolet light, infrared light, and X-rays), incident angles, polarization states, and coherence states can be considered. In another instance, the system may include any of several different light sources (e.g., a direct-coupled light source, a laser continuous plasma light source, etc.). In yet another instance, the system may include elements for regulating the light directed to or collected from the sample (e.g., apodizers, filters, etc.).

[0160] FIG16 illustrates a method 200 suitable for implementation by the metrology systems 100, 300, and 500 of the present invention. In one embodiment, it should be appreciated that the data processing blocks of method 200 may be implemented via a pre-programmed algorithm executed by one or more processors of computing systems 116, 330, or 530. Although the following description is presented in the context of metrology systems 100, 300, and 500, it should be understood that the specific structural embodiments of metrology systems 100, 300, and 500 are not intended to be limiting but should be interpreted as illustrative only.

[0161] In block 201, for example, a modeling tool receives a plurality of reference shape profiles characterizing a semiconductor structure of interest. Each of the reference shape profiles is parameterized by a set of observable geometric variables.

[0162] In block 202, the observable geometric variables are transformed into a set of latent variables. The latent variables characterize a reference shape profile in an alternative mathematical space.

[0163] In block 203, a first set of reconstructed shape profiles is generated by sampling one of the values ​​of the potential variable array.

[0164] In block 204, the potential variable array is truncated into a reduced set of potential variables based on the difference between the first set of reconstructed shape profiles and the reference shape profiles.

[0165] In block 205, a measurement model is trained at least in part based on sampling one of the values ​​of a reduced potential variable array.

[0166] It should be understood that the various steps described throughout this invention can be implemented by a single computer system 116, 330, and 530, or alternatively, by multiple computer systems 116, 330, and 530. Furthermore, different subsystems of systems 100, 300, and 500 (such as the spectroscopic ellipsometry 101) may include one of the computer systems suitable for implementing at least a portion of the steps described herein. Therefore, the above description should not be construed as a limitation of the invention, but is merely illustrative. Additionally, one or more computing systems 116 can be configured to perform any of any of the other steps of any of the method embodiments described herein.

[0167] Computing systems 116, 330, and 530 may include (but are not limited to) personal computer systems, mainframe computer systems, workstations, video computers, parallel processors, or any other devices known in the art. Generally, the term "computing system" may be broadly defined to encompass any device having one or more processors that execute instructions from a memory medium. Generally, computing systems 116, 330, and 530 may be integrated with or alternatively separated from any measurement system, such as measurement systems 100, 300, and 500. In this sense, computing systems 116, 330, and 530 may be remotely located and receive measurement data and user input from any measurement source and user input source, respectively.

[0168] The program instructions 120 of the implementation method (such as the method described herein) may be transmitted or stored on the carrier medium 118. The carrier medium may be a transmission medium, such as a wire, cable or wireless transmission link. The carrier medium may also include a computer-readable medium, such as a read-only memory, a random access memory, a magnetic disk or optical disk or a magnetic tape.

[0169] Similarly, program instructions 334 implementing the method (such as those described herein) can be transmitted via a transmission medium, such as a wire, cable, or wireless transmission link. For example, as illustrated in FIG13, program instructions stored in memory 332 are transmitted to processor 331 via bus 333. Program instructions 334 are stored in a computer-readable medium (e.g., memory 332). Exemplary computer-readable media include read-only memory, random access memory, a magnetic disk or optical disk, or a magnetic tape.

[0170] Similarly, program instructions 534 implementing the method (such as those described herein) can be transmitted via a transmission medium, such as a wire, cable, or wireless transmission link. For example, as illustrated in FIG15, program instructions stored in memory 532 are transmitted to processor 531 via bus 533. Program instructions 534 are stored in a computer-readable medium (e.g., memory 532). Exemplary computer-readable media include read-only memory, random access memory, a magnetic disk or optical disk, or a magnetic tape.

[0171] As described herein, the term "critical dimension" includes any critical dimension of a structure (e.g., bottom critical dimension, middle critical dimension, top critical dimension, sidewall angle, grating height, etc.), a critical dimension between any two or more structures (e.g., the distance between two structures), a displacement between two or more structures (e.g., the overlap displacement between overlapping grating structures, etc.), and a dispersion property value for a material in the structure or a part of the structure. Structures may include three-dimensional structures, patterned structures, overlapping structures, etc.

[0172] As described herein, the terms “critical size application” or “critical size measurement application” include any critical size measurement.

[0173] As described herein, the term "metrology system" includes any system used at least in part to characterize a sample in any state. However, these technical terms do not limit the scope of the term "metrology system" as described herein. Additionally, the metrology system 100 can be configured to measure patterned wafers and / or unpatterned wafers. The metrology system can be configured as an LED inspection tool, edge inspection tool, backside inspection tool, macroscopic inspection tool, or multi-mode inspection tool (involving data from one or more platforms simultaneously), and any other metrology or inspection tool that benefits from calibration of system parameters based on critical dimension data.

[0174] Various embodiments of a semiconductor processing system (e.g., a detection system or a lithography system) that can be used to process a sample are described herein. The term "sample" is used herein to refer to one or more sites on a wafer, a photomask, or any other sample that can be processed (e.g., printed or inspected for defects) by means of components known in the art. In some instances, a sample comprises a single site having one or more measurement targets, the simultaneous combined measurement of which is regarded as a single sample measurement or reference measurement. In some other instances, a sample is a set of sites, wherein the measurement data associated with the set of measurement sites is a statistical set of data associated with each of the multiple sites. Furthermore, each of these multiple sites may contain one or more measurement targets associated with a sample or reference measurement.

[0175] As used herein, the term "wafer" generally refers to a substrate formed of a semiconductor or non-semiconductor material. Examples include (but are not limited to) single-crystal silicon, gallium arsenide, and indium phosphide. Such substrates are typically found and / or processed in semiconductor manufacturing facilities. In some cases, a wafer may contain only a substrate (i.e., a bare wafer). Alternatively, a wafer may contain one or more layers of different materials formed on a substrate. The one or more layers formed on a wafer may be "patterned" or "unpatterned." For example, a wafer may contain a plurality of dies having repeatable pattern features.

[0176] A "reduction mask" may be a reduction mask at any stage of a reduction mask manufacturing process, or a complete reduction mask that may or may not be released for use in a semiconductor manufacturing facility. A reduction mask or a "mask" is generally defined as a substantially transparent substrate on which substantially opaque areas are formed and patterned. The substrate may comprise, for example, a glass material, such as amorphous SiO2. A reduction mask may be placed over a photoresist-coated wafer during an exposure step in a lithography process, such that the pattern on the reduction mask can be transferred to the photoresist.

[0177] One or more layers formed on a wafer may be patterned or unpatterned. For example, a wafer may contain a plurality of grains, each having repeatable pattern features. The formation and processing of these material layers can ultimately result in a complete device. Many different types of devices can be formed on a wafer, and the term "wafer" as used herein is intended to cover a wafer on which any type of device known in the art is fabricated.

[0178] In one or more exemplary embodiments, the described functionality may be implemented in hardware, software, firmware, or any combination thereof. If implemented in software, the functionality may be stored as one or more instructions or codes on or transmitted via a computer-readable medium. A computer-readable medium includes both computer storage media and communication media, including any media that facilitates the transfer of a computer program from one location to another. A storage medium may be any available media accessible by a general-purpose or special-purpose computer. By way of example, and not limitation, such computer-readable media may include RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other media that can be used to carry or store desired program code elements in the form of instructions or data structures and is accessible by a general-purpose or special-purpose computer or a general-purpose or special-purpose processor. Furthermore, any connection is appropriately referred to as a computer-readable medium. For example, if software is transmitted from a website, server, or other remote source using coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL), or wireless technologies such as infrared, radio, and microwave, then coaxial cable, fiber optic cable, twisted pair, DSL, or wireless technologies such as infrared, radio, and microwave are included in the definition of media. As used herein, magnetic disks and optical disks include CDs, laser discs, optical discs, digital versatile discs (DVDs), floppy disks, and Blu-ray discs, where magnetic disks typically copy data magnetically, while optical discs copy data optically using lasers. The combination above should also be included within the scope of computer-readable media.

[0179] Although certain specific embodiments have been described above for illustrative purposes, the teachings of this patent document are generally applicable and not limited to the specific embodiments described above. Therefore, various modifications, adaptations, and combinations of the various features of the described embodiments can be practiced without departing from the scope of the invention as set forth in the claims. [Simplified Explanation of the Diagram]

[0025] FIG1 is a diagram illustrating one embodiment of a system 100 for measuring the characteristics of a semiconductor wafer based on an optimized geometric model of the semiconductor structure to be measured as described herein.

[0026] Figure 2 is a diagram illustrating one embodiment of a modeling and analysis engine 130 configured to generate an optimized geometric model of the measured semiconductor structure described herein.

[0027] Figure 3 is a plot of reference shape profiles generated by several users associated with a semiconductor structure of interest.

[0028] Figure 4 is a plot of several reference shape profiles and a reconstructed shape profile generated by an optimized geometric model of one of the semiconductor structures of interest.

[0029] Figure 5 is a plot of the root mean square error (CD-RMSE) measurement of the difference between the values ​​of a critical dimension associated with a set of reference shape profiles and the corresponding values ​​of the critical dimensions associated with the reconstructed profiles predicted by an optimized geometric model.

[0030] Figure 6 is a plot of the root mean square error (CD-RMSE) measurement of the difference between the values ​​of a critical dimension associated with a set of reference shape profiles and the corresponding values ​​of the critical dimensions associated with the reconstructed profiles predicted by an optimized geometric model at different heights.

[0031] Figure 7 is a plot showing several reference shape profiles captured at different etch depths and several reconstructed shape profiles generated by an optimized geometric model.

[0032] Figures 8A to 8C depict reference shape profiles and reconstructed profiles associated with shallow, medium, and deep etched structures, respectively. The reconstructed profiles are generated by an optimized geometric model that defines one of the potential variables derived from principal component analysis.

[0033] Figures 9A to 9C depict both the reference shape profile and the reconstructed profile associated with the shallow, medium, and deep etched structures depicted in Figure 7. The reconstructed profile is generated by an optimized geometric model that defines one of the potential variables from a weighted principal component analysis.

[0034] Figure 10 is a plot of an expanded training group of one of several reference shape contours by scaling the reference contour height value by 20%.

[0035] Figure 11 is a plot of an expanded training group of reference shape profiles containing several reference shape profiles, which is expanded by shifting the critical size range by 20%.

[0036] Figure 12 is a plot of an expanded training group of reference shape profiles containing several reference shape profiles, which is expanded by scaling the critical size range by 20%.

[0037] Figure 13 is a diagram illustrating a system 300 for measuring the characteristics of a semiconductor wafer based on an optimized geometric model of the semiconductor structure to be measured as described herein, in another embodiment.

[0038] Figure 14 is a diagram illustrating one embodiment of a modeling and analysis engine 350 configured to generate an optimized geometric model of the measured semiconductor structure described herein.

[0039] Figure 15 is a diagram illustrating a system 500 for measuring the characteristics of a semiconductor wafer based on an optimized geometric model of the semiconductor structure to be measured as described herein, in another embodiment.

[0040] Figure 16 illustrates one method 200 for training a measurement model for measuring the characteristics of a semiconductor wafer based on an optimized geometric model of the measured semiconductor structure described herein.

Claims

1. A method comprising: The method involves receiving and characterizing a plurality of reference shape profiles of a semiconductor structure of interest, each of which is parameterized by a set of observable geometric variables; transforming the set of observable geometric variables into a set of latent variables that characterize the reference shape profiles in an alternative mathematical space; generating a first set of reconstructed shape profiles based on sampling one of the values ​​of the set of latent variables; truncating the set of latent variables into a set of reduced latent variables based on the difference between the first set of reconstructed shape profiles and the reference shape profiles; and training a measurement model based at least in part on sampling one of the values ​​of the set of reduced latent variables.

2. The method of request item 1, further comprising: Irradiate an example of a semiconductor structure of interest with a certain amount of energy; detect a measurement data quantity associated with a measurement of the semiconductor structure of interest in response to the energy; estimate the value of a set of reduced potential variables characterizing the semiconductor structure of interest based on the fitting of the trained measurement model to the measurement data quantity; and transform the estimated values ​​of the set of reduced potential variables into the values ​​of a set of observable geometric variables.

3. The method of request item 1, further comprising: The plurality of reference shape profiles are generated by a trusted metrology system based on measurements of one of the plurality of instances of the structure of interest.

4. The method of request item 1, further comprising: The plurality of reference shape profiles are generated by a semiconductor process simulator based on one of the plurality of instances of the structure of interest.

5. The method of request item 1, wherein the plurality of reference shape profiles are generated by the user.

6. The method of claim 1, wherein transforming the set of observable geometric parameters into equivalent values ​​of the set of latent variables involves a principal component analysis or a trained autoencoder.

7. The method of claim 1, further comprising: A second set of reconstructed shape profiles is generated by sampling one of the values ​​of the reduced potential variables in this set. Fit a curve to the difference between the reference shape profiles and the second set of reconstructed shape profiles; and generate a third set of reconstructed shape profiles based on the sum of the second set of reconstructed shape profiles and the fitted curve, wherein the training system of the measurement model is based on the third set of reconstructed shape profiles.

8. The method of claim 1, further comprising: Expanding the range of values ​​for one or more of the group of observable variables, wherein the plurality of reference shape profiles characterizing the semiconductor structure of interest include reference shape profiles characterized by the expanded range of values.

9. The method of claim 1, further comprising: A second set of reconstructed shape profiles is generated by sampling one of the values ​​of the reduced potential variables; and the non-solid shape profiles of the second set of reconstructed shape profiles are eliminated.

10. A measurement system comprising: An illumination subsystem configured to irradiate a semiconductor structure with a certain amount of energy at a measurement point; A detector configured to detect a measurement data quantity associated with a measurement of the semiconductor structure in response to the energy; and a computing system configured to: estimate a value of at least one latent variable of a set of latent variables characterizing the semiconductor structure in an unobservable mathematical space based on a fitting of a trained measurement model to the measurement data quantity; and transform the value of the at least one latent variable into a value of at least one observable geometric parameter of interest characterizing the semiconductor structure.

11. The metrology system of claim 10, wherein the computational system is further configured to: receive a plurality of reference shape profiles characterizing the semiconductor structure, each of the reference shape profiles being parameterized by a set of observable geometric variables; transform the set of observable geometric variables into a set of latent variables, the set of latent variables characterizing the reference shape profiles in an unobservable mathematical space; generate a first set of reconstructed shape profiles based on sampling one of the values ​​of the set of latent variables; truncate the set of latent variables into a set of reduced latent variables based on the difference between the first set of reconstructed shape profiles and the reference shape profiles; and train the metrology model at least partially based on sampling one of the values ​​of the set of reduced latent variables.

12. The metrology system of claim 11, wherein the plurality of reference shape profiles are generated by a trusted metrology system by measuring one of the plurality of examples of the semiconductor structure.

13. The metrology system of claim 11, wherein the plurality of reference shape profiles are generated by a semiconductor process simulator by simulating one of the plurality of examples of the structure of interest.

14. The measurement system of claim 11, wherein the plurality of reference shape profiles are generated by the user.

15. The metrology system of claim 11, wherein the transformation of the set of observable geometric parameters into equivalent values ​​of the set of latent variables involves a principal component analysis or a trained autoencoder.

16. The measurement system of claim 11, wherein the computational system is further configured to: generate a second set of reconstructed shape profiles by sampling based on one of the values ​​of the reduced potential variables; fit a curve to the difference between the reference shape profiles and the second set of reconstructed shape profiles; and generate a third set of reconstructed shape profiles based on the sum of the second set of reconstructed shape profiles and the fitted curve, wherein the training of the measurement model is based on the third set of reconstructed shape profiles.

17. The metering system of claim 11, further comprising: Expanding the range of values ​​for one or more of the group of observable variables, wherein the plurality of reference shape profiles characterizing the semiconductor structure include reference shape profiles characterized by the expanded range of values.

18. The metrology system of claim 10, wherein the illumination subsystem and the detector comprise an optical metrology system, an X-ray-based metrology system, or an electron beam-based metrology system.

19. A measurement system comprising: An illumination subsystem configured to irradiate a semiconductor structure with a certain amount of energy at a measurement point; A detector configured to detect a quantity of measurement data associated with a measurement of the semiconductor structure in response to the energy; and a non-transitory computer-readable medium storing instructions that, when executed by one or more processors, cause the one or more processors to: estimate a value of at least one latent variable of a set of latent variables characterizing the semiconductor structure in an unobservable mathematical space based on a fitted fit of a trained measurement model to one of the measurement data; and transform the value of the at least one latent variable into a value of at least one observable geometric parameter of interest characterizing the semiconductor structure.

20. The metrology system of claim 19, wherein the non-transitory computer-readable medium further stores instructions that, when executed by the one or more processors, cause the one or more processors to: receive a plurality of reference shape profiles characterizing the semiconductor structure, each of the reference shape profiles being parameterized by a set of observable geometric variables; transform the set of observable geometric variables into a set of latent variables that characterize the reference shape profiles in an unobservable mathematical space; generate a first set of reconstructed shape profiles based on sampling one of the values ​​of the set of latent variables; truncate the set of latent variables into a set of reduced latent variables based on the difference between the first set of reconstructed shape profiles and the reference shape profiles; and train the metrology model at least partially based on sampling one of the values ​​of the set of reduced latent variables.

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