System and method for semiconductor profile measurement

Abstract

This paper describes a method and system for measuring semiconductor structures based on a trained scan-conditional measurement model. A scan-conditional model is trained based on design-of-experiment (DOE) measurement data associated with known values ​​of one or more parameters of interest and a perturbation set of one or more parameters of interest. The trained scan-conditional model minimizes the output of an error function that characterizes the error between the known values ​​of the perturbation values ​​of the one or more parameters of interest from the given DOE measurement data. During inference, an error value associated with each candidate value of the one or more parameters of interest is determined by the trained scan-conditional measurement model. The estimated value of the parameter of interest is the candidate value of the parameter of interest associated with the minimum error value.

Description

Semiconductor Shape Measurement Based on Scan Condition Model The embodiments described relate to measurement systems and methods, and more specifically to methods and systems for modified measurements of semiconductor structures. Semiconductor devices (such as logic and memory devices) are typically manufactured by a series of processing steps applied to a sample. These processing steps form the various features and multiple structural levels of the semiconductor device. For example, lithography is a semiconductor manufacturing process that involves creating a pattern on a semiconductor wafer. Additional examples of semiconductor manufacturing 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 divided into individual semiconductor devices. Metrics procedures are used at various stages of a semiconductor manufacturing process to detect defects on wafers to promote higher yields. Optical and X-ray-based metrology techniques offer the possibility of high throughput without the risk of sample destruction. Several metrology-based techniques, including scatterometry, reflectometry, and ellipsometry implementations, along with correlation analysis algorithms, are typically used to characterize the critical dimensions, film thickness, composition, stacking, and other parameters of nanoscale structures. Many metrology techniques are indirect methods for measuring the physical properties of a sample. In most cases, the raw measurement signal cannot be used to directly determine the physical properties of the sample. Instead, a measurement model is used to estimate the values ​​of one or more parameters of interest based on the raw measurement signal. For example, ellipsometric measurement is one indirect method for measuring the physical properties of a sample. Generally, a physics-based measurement model or a machine learning-based measurement model is needed to estimate the values ​​of one or more parameters of interest based on the raw measurement signal (e.g., α). meas and β meas To determine the physical properties of the sample. In some instances, a model is established that attempts to predict the original measured signal based on assumed values ​​of one or more model parameters (e.g., α). meas and β meas One of the measurement models is based on physics. As illustrated in equations (1) and (2), the measurement model includes parameters associated with the measuring instrument itself (e.g., machine parameters (P)). machine And parameters associated with the measured sample. When solving for the parameters of interest, some sample parameters are treated as fixed values ​​(P). spec-fixed And cause other parameters of interest to fluctuate (P) spec-float That is, analysis is performed based on the original measurement signal. (1) (2) Machine parameters are parameters used to characterize measuring instruments (e.g., ellipsometry 101). Illustrative machine parameters include the angle of incidence (AOI), analyzer angle (A...). 0), Polarizer angle (P) 0) Illumination wavelength, numerical aperture (NA), compensator or waveplate (if present), etc. Sample parameters are parameters used to characterize the sample (e.g., characterizing the material and geometric parameters of (some) of the measured structure). For a thin film sample, exemplary sample parameters include refractive index, dielectric tensor, nominal layer thickness of all layers, layer sequence, etc. For a CD sample, exemplary sample parameters include geometric parameter values ​​associated with different layers, refractive index associated with different layers, etc. For measurement purposes, machine parameters and many sample parameters are considered as known fixed values. However, the value of one or more sample parameters is considered as an unknown floating parameter of interest. In some instances, the value of the floating parameter of interest is analyzed using an iterative procedure (e.g., regression) that generates a best fit between theoretical predictions and experimental data. The value of the unknown floating parameter of interest is changed, and the model output (e.g., α) is calculated iteratively. model and β model And compare these model output values ​​with the original measurement data until it is determined that the model output value is inconsistent with the experimental measurement value (e.g., α). meas and β meas A set of sample parameter values ​​that are sufficiently closely matched between ( ). In some other instances, floating parameters are resolved by searching through a pre-computed library of solutions to find the closest match. Implementing a physics-based measurement model to predict the values ​​of one or more parameters characteristic of a measured structure from measured signals (e.g., spectra, X-ray diffraction images, etc.) has several drawbacks. In practice, developing a physics-based model is costly in terms of time, effort, and computational workload. In many cases, the trade-offs necessary to implement a computationally tractable physics-based model have an undesirable impact on measurement accuracy. Furthermore, a physics-based measurement model can lead to misleading results when multiple solutions exist (i.e., when the same set of measured signals has more than one solution for a parameter of interest). In such instances, the regression procedures used in implementing a physics-based measurement model attempt to find a single solution among multiple solutions, resulting in a loss of measurement integrity. In some other instances, a machine learning-based measurement model is used to directly estimate the value of the parameter of interest based on the raw measurement data. In these instances, a machine learning-based measurement model takes the raw measurement signal as its input and produces the value of the parameter of interest as its output. A machine learning-based measurement model must be trained to produce estimates of the parameters of interest that are useful for a specific measurement application. Generally, model training is based on raw measurement signals collected from a sample that has known values ​​of the parameters of interest (i.e., Design of Experiments (DOE) data). A machine learning-based measurement model is parameterized by several weight parameters. Typically, a machine learning-based measurement model is trained using a regression procedure that minimizes the total output error (e.g., ordinary least squares regression). The values ​​of the weight parameters are iteratively adjusted to minimize the difference between a known reference value of the parameter of interest and the value of the parameter of interest estimated by the machine learning-based measurement model based on the measured original measurement signal. Traditional methods for training a machine learning-based measurement model to predict the values ​​of one or more parameters characteristic of a measured structure from self-measured signals (e.g., spectra, X-ray diffraction images, etc.) have several drawbacks. In practice, model training requires a large number of DOE measurement samples, which are typically costly to generate. Furthermore, the existence of multiple solutions (i.e., when the same set of measurement signals has more than one solution for a parameter of interest) usually compromises the stability of model training. In these instances, traditional methods for training a machine learning-based measurement model attempt to find a middle ground between multiple solutions, leading to a loss of measurement accuracy. The increasing demands for lower resolution, multi-parameter correlations, more complex geometries, and the growing use of opaque materials pose challenges to future applications of measurement. Therefore, methods and systems for improving measurement model training and parametric inference are desired. This paper describes a method and system for measuring semiconductor structures based on a trained scan-conditional measurement model. A scan-conditional model is trained based on design-of-experiment (DOE) measurement data associated with known values ​​of one or more parameters of interest and a perturbation set of one or more parameters of interest. The trained conditional model minimizes the output of an error function characterized by the error between the known values ​​of the one or more parameters of interest and the perturbation values ​​of the one or more parameters of interest in the given DOE measurement data. Furthermore, a trained scan-conditional measurement model estimates the values ​​of one or more parameters of interest based on actual measurement data collected from a measured semiconductor structure. The values ​​of the one or more parameters of interest are determined by scanning over a range of candidate values ​​for one or more parameters of interest. The trained scan-conditional measurement model determines an error value associated with each candidate value of the one or more parameters of interest. The estimated value of the parameter of interest is the candidate value of the parameter of interest associated with the minimum error value. In a sample, a geometric model of a measured structure is determined. The geometric model characterizes the geometry of the structure with respect to one or more parameters of interest. In this way, the values ​​of the one or more parameters of interest define the shape of the measured structure. In some embodiments, a geometric model defines the shape of a structure in two dimensions. In some other embodiments, a geometric model defines the shape of a structure in three dimensions. In another sample, a DOE training dataset is generated based on one of the DOE sets of geometric model parameter values. In another sample, a one-sweep conditional model is trained using a training dataset of measurement data corresponding to the DOE set of geometric model parameter values ​​and a perturbed value set of the DOE set of geometric model parameters. In another scenario, a trained scan-conditional measurement model is used to estimate the values ​​of the parameters of interest based on actual measurements of a structure with unknown values ​​for one or more parameters of interest. Measurement data and a set of candidate values ​​associated with each parameter of interest are provided as input to the trained scan-conditional measurement model. The trained scan-conditional measurement model generates an error value associated with each candidate value. The estimated value of each parameter of interest is selected as the candidate value with the minimum error value. Generally, any number of geometric parameters can be used as input to train and use a scan-condition measurement model. Similarly, any combination of measurement signals can be used as input to train and use a scan-condition measurement model (e.g., signals from one or more optical metrology systems, one or more X-ray metrology systems, or a combination thereof). The foregoing is an overview and therefore necessarily contains simplifications, generalizations, and omissions of details; thus, those skilled in the art will understand that the overview is merely illustrative and not in any way limiting. Other forms, inventive features, and advantages of the apparatus and / or procedures described herein will become apparent from the non-limiting [implementations] set forth herein. The background examples and some embodiments of the present invention will now be described in detail with reference to the accompanying drawings. This paper describes a method and system for measuring semiconductor structures based on a trained scan condition measurement model. A scan conditional model is trained based on Design of Experiments (DOE) measurements associated with known values ​​of one or more parameters of interest and a perturbation set of one or more of those parameters. The trained conditional model minimizes the output of an error function. The error function characterizes the error between one or more of the parameters of interest given in the DOE measurements and the known values ​​of the perturbation values ​​of one or more of those parameters. The values ​​of one or more parameters of interest are estimated based on actual measurement data collected from a measured semiconductor structure using a trained scan-conditional measurement model. The values ​​of one or more parameters of interest are determined by scanning over a range of candidate values. An error value associated with each candidate value of the one or more parameters of interest is determined using the trained scan-conditional measurement model. The estimated value of the parameter of interest is the candidate value of the parameter of interest associated with the minimum error value. As described in this paper, one type of scan-conditional measurement model enables the training of a machine learning-based measurement model with a smaller number of DOE measurement samples. This is because the error is learned based on numerous perturbations in each DOE dataset. Therefore, for a given number of DOE measurement samples, the total number of training samples increases significantly. Furthermore, the scan-conditional modeling technique's scan nature allows the trained model to accurately predict multiple solutions for a parameter of interest. Additionally, as described in this paper, one type of scan-conditional measurement model enables the trained model to reconstruct a two-dimensional or three-dimensional image of the measured model. Figure 1 illustrates a system 100 for measuring the properties of a sample according to the exemplary methods presented herein. As shown in Figure 1, system 100 can be used to perform a spectral ellipsometric measurement of the structure 101 depicted in Figure 1. 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 illumination within a selected wavelength range (e.g., 100 nm to 2500 nm) and directs this illumination over a measurement point 110 of the structure disposed on the surface of the sample. The spectrometer 104 is then configured to receive the illumination reflected from the structure 101. It should be further noted that a polarization state generator 107 is used to polarize the light emitted from the illuminator 102 to generate a polarized illumination beam 106. The radiation reflected from the structure 101 travels through a polarization state analyzer 109 and to the spectrometer 104. The polarization state analysis collects the radiation in the beam 108 received by the spectrometer 104, allowing spectral analysis of the radiation transmitted by the analyzer. These spectra 111 are then transmitted to the computing system 130 for analysis of the structure as described herein. As depicted in Figure 1, system 100 includes a single measurement technique (i.e., SE). However, in general, system 100 may include any number of different measurement techniques. By way of non-limiting examples, system 100 may be configured as a spectroscopic ellipsometer (including a Mueller matrix ellipsometer), a spectroscopic reflectometer, a spectroscopic scatterometer, a superimposed scatterometer, an angle-resolved beam profile reflectometer, a polarization-resolved beam profile reflectometer, a beam profile reflectometer, a beam profile ellipsometer, any single or multi-wavelength ellipsometer, or any combination thereof. Furthermore, in general, measurement data collected by different measurement techniques and analyzed according to the methods described herein can be collected from multiple tools, a single tool integrating multiple techniques, or a combination thereof (by way of non-limiting examples, including soft X-ray reflectance measurement, small-angle X-ray scattering measurement, an imaging-based metrology system, a hyperspectral imaging-based metrology system, a scattering measurement superimposed metrology system, etc.). In another embodiment, system 100 may include one or more computing systems 130 for performing measurements of a structure based on a measurement model developed according to the methods described herein. The one or more computing systems 130 may be communicatively coupled to spectrometer 104. In one configuration, the one or more computing systems 130 are configured to receive measurement data 111 associated with a measurement of a measured structure (e.g., structure 101). In some embodiments, the computing system 130 is configured to develop and train a scan conditional measurement model and execute the trained scan conditional model to estimate the values ​​of one or more parameters of interest, as described herein. In a sample, a geometric model of a measured structure is determined. The geometric model characterizes the geometry of the structure with respect to one or more parameters of interest. In this way, the values ​​of the one or more parameters of interest define the shape of the measured structure. In some embodiments, a geometric model defines the shape of a structure in two dimensions. In some other embodiments, a geometric model defines the shape of a structure in three dimensions. In some instances, a geometric model is developed based on geometric primitives (e.g., trapezoids) and parameterized based on knowledge of semiconductor programs used to manufacture the structure. In some instances, a geometric model is developed based on geometric primitives (e.g., trapezoids) and parameterized using reference measurements provided by a trusted reference metrology system. In one instance, scanning electron microscope (SEM) images are used to directly measure the shape of a semiconductor structure, and the measured shape is used to parameterize the geometric model. In some instances, a geometric model is developed based on a series of reference shapes. In other instances, the reference shapes are determined by measurements of a semiconductor structure manufactured by a DOE based on one of the program parameters. In some instances, a geometric model is developed using simulation (e.g., a procedural simulation tool that predicts the shape of a structure manufactured based on a series of manufacturing steps such as etching and lithography). In some of these instances, the geometric model comprises a dataset of shape profiles synthesized based on a DOE (Design of Engineering) parameter. In some embodiments, a geometric model of a measured structure is characterized as a monolithic voxel grid array spanning a three-dimensional volume encapsulating the measured structure. The size and spacing of the voxels in the array are known prior. Each voxel of the voxel model is parameterized by a value of a property associated with that voxel (e.g., transparency, electron density, etc.). In this way, the parameter values ​​of the voxel model define a three-dimensional image of the geometry of the measured structure. In typical semiconductor metrology applications, a voxel model of a measured structure contains a large number of voxels (e.g., one million or more voxels) to provide sufficient resolution for accurately estimating parameters of interest (e.g., critical dimensions, height, sidewall angles, etc.). In another state, based on one of the geometric model parameter values, the DOE set (P) i DOE One of the measurement data generated is the DOE training dataset (S). i DOE ). In some embodiments, the DOE training dataset is derived from the DOE set (P) based on one of the parameter values. i DOE Measurement data collected from the structure being measured. In some embodiments, the values ​​of each DOE parameter associated with each of the measured structures are measured by a trusted reference measurement system (e.g., SEM). In some embodiments, the values ​​of each DOE parameter associated with each of the measured structures are programmed values ​​known to be generated from one of the measured structures. In some other embodiments, the DOE set of geometric model parameter values ​​is a known set of programmed parameter values, and the corresponding training dataset (S) of the measurement data is used. i DOE The DOE (P) is generated by metrology simulation. In these examples, a metrology simulation tool simulates the response of the metrology tool to a DOE (P) with characteristic parameter values. i DOEA training dataset (S) of measurement data generated from the measurement of a known structure with a standardized shape. i DOE In some embodiments, the analog metrology tool is the same metrology tool used to ultimately measure structures with unknown values ​​of one or more parameters of interest. In some embodiments, a set of Design of Elements (DOEs) for geometric model parameter values ​​is generated by program simulation. In these embodiments, a program simulator is used to generate a set of DOEs (Programmable Parameters) based on one of the known, programmable parameters. i To generate a product with known geometric parameter values ​​(P) i DOE A dataset of geometric models of ) is used. Then, a metrology simulator is employed to generate a training dataset (S) of measurement data corresponding to known geometric parameter values. i DOE ). In another state, based on the DOE set (P) corresponding to the geometric model parameter values... i DOE The training data set of measurement data of the DOE set of geometric model parameters and the perturbation value set (S) i DOE Training a one-scan conditional model. Figure 2 illustrates one embodiment of a scan-conditional measurement model training engine 200. As depicted in Figure 2, the scan-conditional measurement model training engine 200 includes a machine learning module 201, an error evaluation module 203, and a perturbation generator module 204. A training dataset (S) of measurement data is used... i DOE ) 205 is provided as an input to the machine learning module 201. In some instances, the scan conditional measurement model is a neural network model. As depicted in Figure 2, the machine learning module 201 evaluates the dataset (S). i DOE ) 205 and the disturbance parameter value (P) ij DOE + dP k The neural network model 210 represents an index for each measurement sample, an index for each individual parameter, and an index for each error sample. The output of the neural network model is transmitted to the error evaluation module 203, which provides the error value (ERR). ijk 207. Error Evaluation Module 203 compares the error value (ERR) determined by the neural network model. ijk ) 207 and associated with each error sample and each disturbed parameter value (P) ij DOE + dP k ) 210 One of the known error values ​​(ERR) ijk *) 208. The loss assessment module 203 updates the neural network weights 211 to minimize a function (e.g., a quadratic error function, a linear error function, or any other suitable difference function) between the characterized determined error value and the known error value. The updated neural network weights 211 are passed to the machine learning module 201. The machine learning module 201 updates the neural network model with the updated neural network weights for the next iteration of the training procedure. Iteration continues until a function (e.g., a function) between the characterized determined error value and the known error value is minimized. The resulting trained scan-conditional measurement model 212 is passed to memory (e.g., memory 132). The trained scan-conditional measurement model 212 predicts the error between a parameter value provided by a measurement signal (e.g., a spectrum) and the true parameter value. As depicted in Figure 2, the scan conditional measurement model training engine 200 receives DOE geometric model parameter values ​​(P) from a reference source 202. ij DOE ) 206. Reference source 202 is a trusted measurement system, a simulator, or a set of DOEs used to generate geometric model parameter values ​​(P ij DOE Any combination of the geometric model parameter values, as described above. The DOE set (P) of the geometric model parameter values. ij DOE ) 206 is transmitted to the disturbance generator module 204. The disturbance generator module 204 generates geometric model parameter values ​​(P) ij DOE ) 206, one of the perturbation sets. In some embodiments, a perturbation set includes the nominal geometric model parameter values ​​(P ij DOE Several values ​​within + / -30% of each of the parameters. In some embodiments, the number of perturbations associated with each parameter is 10 or more. The perturbation set (dP) k Each perturbation of 209 is added to the corresponding geometric model parameter value (P). ij DOE ) 206, and the sum (P) ij DOE + dP k ) 210 is provided as input to the machine learning module 201. Additionally, the perturbation generator module 204 determines the values ​​of each error sample and each perturbed parameter (P) ij DOE + dP k ) 210 Associated Known Error Value (ERR) ijk *) 208, and provides the known error value to the error evaluation module 203. Generally, the known error value associated with each sample, each individual parameter, and each error sample in the parameter space is calculated as a distance between the known DOE parameter value and the disturbed parameter value. In this way, for each measurement sample (S) i ), operations and parameters (P) ij +dP k ) and the corresponding parameter specific error (Err) ijk Multiple parameter perturbations associated with it. In another scenario, the values ​​of the parameters of interest are estimated based on a trained scan-conditional measurement model. Measurement data and a set of candidate values ​​associated with each parameter of interest are provided as input to the trained scan-conditional measurement model. The trained scan-conditional measurement model generates an error value associated with each candidate value. The estimated value of each parameter of interest is selected as the candidate value with the minimum error value. Figure 3 illustrates one embodiment of a trained scan-conditional measurement model inference engine 220. As depicted in Figure 3, the trained scan-conditional measurement model inference engine 220 includes a trained scan-conditional measurement module 221 and a candidate selection module 225. In the embodiment depicted in Figure 3, measured data (S) collected by a measurement system or a combination of measurement systems are... MEAS ) 222 and one or more parameters of interest (P) TEST A set of candidate values ​​223 is provided as input to the trained scan conditional measurement module 221. The trained scan conditional measurement module 221 uses a trained scan conditional measurement model to determine an error value associated with each candidate value of each parameter of interest. The error value (E) associated with each parameter of interest is then used to determine the error value associated with each candidate value of each parameter of interest. TEST ) 224 is provided to candidate selection module 225. Candidate selection module 225 selects the candidate value with the smallest error associated with each parameter of interest. The selected candidate value corresponds to the parameter of interest (POI). MEAS The estimated value of 226. Figure 4 illustrates an error value trajectory 231 associated with the range of candidate values ​​for one of the parameters of interest. As depicted in Figure 4, the candidate value with the smallest error is selected as the estimated value of the parameter of interest. As shown in Figure 4, the scanning properties of the trained scanning conditional model enable the trained model to predict two distinct values ​​(POI) of one parameter of interest. 1 MEAS and POI 2 MEAS In one instance, measuring the pitch walk requires extracting two different values ​​for a parameter of interest from the same set of measurement signals. In some measurement applications, determining the two-dimensional shape of a measured structure is important (e.g., memory measurement applications). In some of these applications, two parameters are used as inputs to a trained scan-conditional measurement model. Figure 5 illustrates one of the aperture structures 240 parameterized by two geometric parameters. As depicted in Figure 5, the shape 241 of the aperture structure 240 is described by a critical dimension parameter (CD) and a height parameter (H). In this example, the CD and H parameters describe the shape of the aperture structure and are used as input to a trained scan-conditional measurement model. Figure 6 illustrates an error value plot 245 associated with the range of candidate values ​​for CD and H. Point 247 on the error value plot corresponds to a specific combination of candidate values ​​(CD). CAND H CAND Related to this, line 246 marks a trajectory of points with a minimum error value within the height range. The trajectory of the minimum value represents the point on Figure 245 with the highest probability of alignment with the shape of the measured hole structure. In this way, line 246 depicts an image of the shape 241 of the hole structure 240. Figures 7A to 7F depict error values ​​associated with candidate ranges of CD and H values ​​for different examples of measurements related to a single-hole structure. Figures 7A to 7F depict trajectories 251 to 256 of points with a minimum error value within the height range. The trajectory of the minimum value represents the point on the graph with the highest probability of alignment with the shape of the measured hole structure. In this way, lines 251 to 256 depict images 251 to 256 of the shape of each of the measured hole structures. Figures 8A to 8F depict an error value plot that is associated with the asymmetry (ASYM) of measurements for different examples of a single-hole structure and the range of candidate values ​​for H. Figures 8A to 8F depict trajectories 261 to 266 of points with a minimum error value within the height range. The trajectory of the minimum value represents the point on the graph with the highest probability of alignment with the shape of the measured hole structure. In this way, lines 261 to 266 depict images 261 to 266 of the shape of each of the measured hole structures. In general, one of the trained scan-conditional measurement models described herein can be applied to estimate the values ​​of any parameters of interest (e.g., critical dimensions, height, tilt, asymmetry, ellipticity, helix, etc.) used to characterize the geometry of a measured structure. In some measurement applications, determining the three-dimensional shape of a measured structure is important. In some of these applications, a monolithic model is used to characterize the measured structure. Figure 9 illustrates a voxel model of a channel aperture structure 271. The geometric model of the channel aperture structure 271 is characterized as a voxel grid array spanning a three-dimensional volume of the encapsulated measurement structure. The size and spacing of the voxels in the array are known prior. As shown in Figure 9, the nth voxel 272 is located at coordinates {X} in three-dimensional space. n ,Y n Z n The size of the nth voxel is known. Each voxel is parameterized by a value of one of its properties (e.g., transparency, electron density, etc.). In this way, the values ​​associated with each voxel define a three-dimensional image of the geometry of the measured channel aperture structure 271. Based on the geometric model parameter values ​​(P) of a DOE set ij DOE The disturbance values ​​and corresponding DOE datasets (S) i DOE This is used to train a scanning condition measurement model for the channel aperture structure 271. In this example, the geometric model parameter values ​​are the positions of voxels with specific values ​​(e.g., a minimum) of properties associated with each voxel. In this example, a perturbation set of each geometric model parameter value is generated for training purposes, namely, a perturbation set (dP) of the three-dimensional positions of each voxel. k =(ΔX k , ΔY k , ΔZ k The perturbation set (dP) k Each perturbation is added to the corresponding model parameter value (P). ij DOE =(X ij DOE Y ij DOE Z ij DOE ), and the sum (P) ij DOE + dP k This is provided as input to the machine learning module 201. Additionally, for example, for each error sample, the known error value (ERR) associated with that error sample is... ijk *) is determined as the distance between the nominal voxel position and the perturbed voxel position. Known error values ​​are calculated for each DOE measurement sample, each individual voxel, and each error sample. In this way, for each measurement sample (S) i The specific error (Err) between the calculation and each voxel and its corresponding parameter ijk Multiple parameters associated with the perturbation are used to train a scanning condition measurement model for one of the channel aperture structures 271, as described with respect to Figure 2. A trained scanning condition measurement model of channel aperture structure 271 is used to collect measurement data (S) based on a channel aperture structure with an unknown shape. MEAS Estimate the three-dimensional image of one of the channel aperture structures once measured. As described with respect to Figure 3, the measurement data (S) MEAS ) and the set of integral element locations (P) TEST The voxel position set is provided as input to the trained scan conditional measurement model. The voxel position set is scanned by the three-dimensional space occupied by the measurement channel aperture. The trained scan conditional measurement model determines an error value associated with each voxel position. The error value (E) associated with each voxel position is evaluated. TEST The surface shape of the channel hole is depicted using voxel positions with minimal error. Figures 10A to 10F each depict a cross-sectional view of a three-dimensional image of an error value associated with the voxel position range of different measured examples of a channel hole structure. Bright lines 281A to 286A and 281B to 286B respectively plot the trajectory of the point with the minimum error across the cross-section of each measured channel hole structure. In this manner, bright lines 281A to 286A plot the left side of the shape of each measured channel hole structure, and bright lines 281B to 286B plot the right side of the shape of each measured channel hole structure. Generally speaking, once a three-dimensional image of a structure is measured, the tilt, asymmetry, ellipticity, helix, critical dimensions, sidewall angles, etc., can be evaluated from the same three-dimensional image. In some embodiments, a trained scan conditional model is used to reconstruct a three-dimensional image of a measured structure by evaluating voxels in a sequential manner. In these embodiments, errors associated with each voxel are determined sequentially. The smaller the error, the closer the predicted voxel value is to the true voxel value. In some other embodiments, a three-dimensional image of a measured structure is reconstructed by replicating a trained scan condition model for each voxel and evaluating all voxels in parallel. Generally, any number of geometric parameters can be used as input to train and use a scan-condition measurement model. Similarly, any combination of measurement signals can be used as input to train and use a scan-condition measurement model (e.g., signals from one or more optical metrology systems, one or more X-ray metrology systems, or a combination thereof). In another further embodiment, a trained scan-conditional measurement model is employed to estimate the value of the parameter of interest based on actual measurements of a structure having unknown values ​​for one or more parameters of interest. The actual measurement data (e.g., measured spectra) is collected by a measurement system (e.g., metrology system 100). In some embodiments, the measurement system is the same system used to collect DOE measurement data. In other embodiments, the measurement system is a system that is simulated to synthetically generate DOE measurement data. In one instance, the actual measurement data comprises measured spectra 111 collected by metrology system 100 from one or more metrology targets having unknown values ​​for one or more parameters of interest. Generally, a trained scanning conditional measurement model can be used to estimate the value of the parameter of interest based on a single measured spectrum, or simultaneously based on multiple spectra. In some instances, simulations are generated from measurement data associated with multiple instances of one or more Design of Experiments (DOE) measurement objectives measured by a measurement system. The simulated data are produced from a parameterized model measuring one or more DOE measurement structures by the measurement system. In some other instances, measurement data associated with multiple instances of one or more Design of Experiments (DOE) measurement objectives are actual measurement data collected by a measurement system or multiple instances of a measurement system. In some embodiments, actual measurement data is collected from instances of a measurement objective having unknown values ​​for one or more parameters of interest using the same measurement system or multiple instances of the same measurement system. In some embodiments, actual measurement data is collected from instances of a measurement objective having unknown values ​​for one or more parameters of interest using different instances of one measurement system or multiple different instances of the same measurement system. In some embodiments, values ​​of parameters of interest for training a scan-conditional measurement model are derived from measurements of the DOE wafer using a reference metrology system. The reference metrology system is a trusted measurement system that produces sufficiently accurate measurement results. In some instances, the reference metrology system is too slow to be used for online wafer measurements as part of the wafer fabrication process, but is suitable for offline use for purposes such as model training. By way of non-limiting examples, a reference metrology system may include a stand-alone optical metrology system, such as a spectroscopic ellipsometer (SE), an SE with multiple illumination angles, an SE that measures Mueller matrix elements, a single-wavelength ellipsometer, a beam profile ellipsometer, a beam profile reflectometer, a broadband reflectometer, a single-wavelength reflectometer, an angle-resolving reflectometer, an imaging system, a scatterometer (such as a spot analyzer), or an X-ray-based metrology system (such as a small-angle X-ray scatterometer (SAXS) operating in a transmission or grazing incidence mode). An X-ray diffraction (XRD) system, an X-ray fluorescence (XRF) system, an X-ray photoelectron spectroscopy (XPS) system, an X-ray reflectometer (XRR) system, a Raman spectroscopy system, an atomic force microscope (AFM) system, a transmission electron microscope system, a scanning electron microscope system, a soft X-ray reflectance measurement system, an imaging-based metrology system, a hyperspectral imaging-based metrology system, a scattering measurement superposition metrology system, or other techniques capable of determining the geometry of the device. In some embodiments, a measurement model trained as described herein is implemented as a neural network model. In other instances, a measurement model may be implemented as a linear model, a nonlinear model, a multinomial model, a response surface model, a support vector machine model, a decision tree model, a random forest model, a kernel regression model, a deep network model, a convolutional network model, or other types of models. In a further embodiment, the measurement results described herein can be used to provide active feedback to a program tool (e.g., a lithography tool, an etching tool, a deposition tool, etc.). For example, the value of a measured parameter determined based on the measurement method described herein can be transmitted to an etching tool to adjust the etching time to achieve a desired etching depth. Similarly, etching parameters (e.g., etching time, diffusion rate, etc.) or deposition parameters (e.g., time, concentration, etc.) can be included in a measurement model to provide active feedback to the etching tool or deposition tool, respectively. In some instances, corrections to program parameters determined based on measured device parameter values ​​using a trained scan condition measurement model can be transmitted to the program tool. In one embodiment, the computing system 130 determines the values ​​of one or more parameters of interest during programming based on a measured signal 111 received from a measurement system. Additionally, the computing system 130 transmits control commands to a program controller (not shown) based on the determined values ​​of one or more parameters of interest. Control commands cause the program controller to change the state of a program (e.g., stop the etching process, change the diffusion rate, change the lithography focus, change the lithography dose, etc.). In some embodiments, the methods and systems for metrology of semiconductor devices as described herein are applicable to the measurement of memory structures. These embodiments enable metrology of optical critical dimensions (CD), films, and compositions for periodic and planar structures. In some instances, the measurement model was implemented using SpectraShape, a product of KLA-Tencor, Inc., located in Milpitas, California, USA. ® A component of an optical critical size measurement system. In this way, the model is built and ready for immediate use after the spectrum is collected by the system. In some other instances, the measurement model is implemented, for example, by AcuShape, which is available from KLA-Tencor, Milpitas, California, USA. ® The software's computational system is implemented offline. The resulting trained model can be incorporated into AcuShape, a measurement system accessible by the measurement execution mechanism. ® One of the components of the library. Figure 11 illustrates one method 300 for training a scan conditional measurement model in at least one novel sample. Method 300 is adapted to be implemented by a measurement system (such as the measurement system 100 illustrated in Figure 1 of this invention). In one sample, it should be understood that the data processing blocks of method 300 can be implemented via a pre-programmed algorithm executed by one or more processors of computing system 130 or any other general-purpose computing system. It should be understood herein that the specific structural sample of measurement system 100 is not intended to be limiting and should only be interpreted illustratively. In block 301, a certain amount of measurement data is collected from one or more structures mounted on a first wafer. In block 302, a set of candidate values ​​for one or more parameters of interest is generated, characterized in the shape of one or more structures disposed on the first wafer. In block 303, an error value is determined based on a trained scan conditional measurement model and associated with each candidate value of a candidate value set of one or more parameters of interest. The candidate value set and each of the given amount of measurement data are provided as input to the trained scan conditional measurement model. In block 304, a first estimated value is determined for one or more parameters of interest. The first estimated value is a first candidate value from a set of candidate values ​​for one or more parameters of interest that has a first minimum error value. In another embodiment, system 100 includes one or more computing systems 130 for performing measurements of a semiconductor structure based on a trained scan condition measurement model according to the methods described herein. The one or more computing systems 130 may be communicatively coupled to one or more spectrometers, active optics, programmable controllers, etc. In one configuration, the one or more computing systems 130 are configured to receive measurement data associated with spectral measurements of the structure of wafer 101. It should be understood that one or more steps described throughout this invention may be implemented by a single computer system 130 or alternatively by a multi-computer system 130. Furthermore, different subsystems of system 100 may include computer systems suitable for implementing at least a portion of the steps described herein. Therefore, the foregoing description should not be construed as a limitation of the invention but merely as illustrative. Additionally, computer system 130 may be communicatively coupled to the spectrometer in any manner known in the art. For example, one or more computing systems 130 may be coupled to a computing system associated with the spectrometer. In another example, the spectrometer may be directly controlled by a single computer system coupled to computer system 130. The computer system 130 of system 100 can be configured to receive and / or acquire data or information from a subsystem of the system (e.g., a spectrometer and the like) via a transmission medium that may include wired and / or wireless components. In this manner, the transmission medium can be used as a data link between the computer system 130 and other subsystems of system 100. The computer system 130 of system 100 can be configured to receive and / or acquire data or information (e.g., measurement results, modeling input, modeling results, reference measurement results, etc.) from other systems via a transmission medium that may include wired and / or wireless components. In this manner, the transmission medium can serve as a data link between the computer system 130 and other systems (e.g., system 100 on a memory board, external memory, or other external systems). For example, the computing system 130 can be configured to receive measurement data from a storage medium (i.e., memory 132 or an external memory) via a data link. For example, spectral results obtained using the spectrometer described herein can be stored in a permanent or semi-permanent memory device (e.g., memory 132 or an external memory). In this regard, spectral results can be imported from on-board memory or from an external memory system. Furthermore, the computer system 130 can transmit data to other systems via a transmission medium. For example, a measurement model determined by the computer system 130 or an estimated parameter value can be transmitted and stored in an external memory. In this regard, the measurement results can be exported to another system. The computing system 130 may include, but is not limited to, a personal computer system, a mainframe computer system, a workstation, a video computer, a parallel processor, or any other device known in the art. Generally, the term "computing system" can be broadly defined to encompass any device having one or more processors that execute instructions from a memory medium. Program instructions 134 implementing methods 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 FIG1, program instructions 134 stored in memory 132 are transmitted to processor 131 via bus 133. Program instructions 134 are stored in a computer-readable medium (e.g., memory 132). Exemplary computer-readable media include read-only memory, random access memory, a magnetic disk or optical disk, or a magnetic tape. 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.), any critical dimension between any two or more structures (e.g., distance between two structures), and any displacement between two or more structures (e.g., overlap displacement between stacked grating structures, etc.). Structures may include three-dimensional structures, patterned structures, stacked structures, etc. As described herein, the terms "critical size application" or "critical size measurement application" encompass any critical size measurement. As described herein, the term "metric system" includes at least part of any system used to characterize a sample in any state of matter (including measurement applications such as critical size metrics, stacking metrics, focus / dose metrics, and composition metrics). However, these technical terms do not limit the scope of the term "metric system" as described herein. Additionally, system 100 can be configured for measurements on patterned and / or unpatterned wafers. The metric system can be configured as an LED inspection tool, edge inspection tool, backside inspection tool, macroscopic inspection tool, or multi-mode inspection tool (which involves data simultaneously from one or more platforms) and any other metric or inspection tool that benefits from the techniques described herein. This document describes various embodiments of a semiconductor measurement system that can be used to measure a sample within any semiconductor processing tool (e.g., an inspection system or a lithography system). The term "sample" is used herein to refer to a wafer, a photomask, or any other sample that can be processed by means known in this art (e.g., printing or defect detection). 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 can be commonly found and / or processed in semiconductor manufacturing facilities. In some cases, a wafer may consist only of a substrate (i.e., a bare wafer). Alternatively, a wafer may contain one or more different material layers 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. A "reduced mask" can be a reduced mask at any stage of a reduced mask manufacturing process, or a completed reduced mask that may or may not be released for use in a semiconductor manufacturing facility. A reduced mask or a "mask" is generally defined as a substantially transparent substrate having substantially opaque areas formed thereon in a patterned configuration. The substrate may comprise, for example, a glass material, such as amorphous SiO2. 2. A photomask can be placed over a resist-coated wafer during an exposure step in a lithography process, allowing the pattern on the photomask to be transferred to the resist. 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 completed device. Many different types of devices can be formed on a wafer, and the term wafer, as used herein, is intended to encompass a wafer on which any type of device known in this art is manufactured. In one or more exemplary embodiments, the 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 program code 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 without 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 components 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 a coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL), or wireless technology (such as infrared, radio, and microwave), then the coaxial cable, fiber optic cable, twisted pair, DSL, or wireless technology (such as infrared, radio, and microwave) are included in the definition of media. As used herein, magnetic disks and optical disks include optical discs (CDs), laser discs, optical discs, digital versatile discs (DVDs), floppy disks, and Blu-ray discs, wherein magnetic disks typically reproduce data magnetically while optical discs reproduce data optically using lasers. Combinations of the above should also be included within the scope of computer-readable media. While certain specific embodiments have been described above for guiding 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 features of the described embodiments can be practiced without departing from the scope of the invention as set forth in the claims. 100: Measurement system / system / system on memory board 101: Ellipsometry / structure / wafer 102: Illuminator 104: Spectrometer 106: Polarized illumination beam 107: Polarization state generator 108: Beam collection 109: Polarization state analyzer 110: Measurement point 111: Spectrum / Measurement data / Measured spectrum 130: Computing system / Single-computer system / Multi-computer system / Computer system 131: Processor 132: Memory 133: Bus 134: Program instructions 200: Scan conditional measurement model training engine 201: Machine learning module 202: Reference source 203: Error assessment module / Loss assessment module 204: Perturbation generator module 205: Training subset of measurement data (S i DOE ) / Data set (S i DOE ) 206: Design of Experiments (DOE) Geometric Model Parameter Values ​​(P ij DOE 207: Error Value (ERR) ijk 208: Known error value (ERR) ijk *) 209: Perturbation set (dP) k ) 210: Disturbance parameter value (P) ij DOE + dP k ) / Sum of (P) ij DOE + dP k 211: Neural network weighting; 212: Trained scan-conditional measurement model; 220: Trained scan-conditional measurement model inference engine; 221: Trained scan-conditional measurement module; 222: Measurement data (S) MEAS ) 223: Parameter of interest (P) TEST 224: Error value (E) TEST 225: Candidate Selection Module 226: Parameters of Interest (POI) MEAS 231: Error value trajectory 240: Hole structure 241: Shape 245: Error value diagram 246: Line 247: Point 251 to 256: Image of point trajectory / line / shape 261 to 266: Image of point trajectory / line / shape 271: Channel hole structure 272: nth voxel 281A to 286A: Bright line 281B to 286B: Bright line 300: Method 301: Block 302: Block 303: Block 304: Block CD: Critical size parameter H: Height parameter Figure 1 illustrates one of a measurement system 100 used to measure the characteristics of a semiconductor structure according to the exemplary methods presented herein. Figure 2 is a diagram illustrating one example of a scan condition measurement model training engine 200 in one embodiment. Figure 3 illustrates one embodiment of a trained scan conditional measurement model inference engine 220. Figure 4 depicts a curve illustrating the trajectory of an error value associated with the range of candidate values ​​for one of the parameters of interest. Figure 5 illustrates a single-hole structure parameterized by two geometric parameters. Figure 6 is one of the graphs showing an error value associated with a range of candidate values ​​for a critical dimension (CD) and height (H). Figures 7A to 7F are graphs showing the error values ​​associated with a range of candidate values ​​for CD and H for different examples of measurements related to a single hole structure. Figures 8A to 8F are graphs showing the error values ​​associated with the asymmetry (ASYM) and the range of candidate values ​​of H for different examples of measurements related to a single hole structure. Figure 9 shows a voxel model of a channel hole structure. Figures 10A to 10F are cross-sectional views of a three-dimensional image showing the error values ​​associated with the voxel position ranges of different measured examples of a channel hole structure. Figure 11 illustrates a flowchart of a method 300 for training a scan conditional measurement model for estimating the values ​​of parameters of interest. 132: Memory 200: Scan Conditional Measurement Model Training Engine 201: Machine Learning Module 202: Reference Source 203: Error Assessment Module / Loss Assessment Module 204: Disturbance Generator Module 205: Training subset of measurement data (S) i DOE ) / Data set (S i DOE ) 206: Design of Experiments (DOE) Geometric Model Parameter Values ​​(P) ij DOE ) 207: Error Value (ERR) ijk ) 208: Known Error Value (ERR) ijk *) 209: Perturbation set (dP) k ) 210: Disturbance parameter value (P) ij DOE +dP k ) / Sum of (P) ij DOE +dP k ) 211: Neural Network Weighting 212: Trained scanning conditional measurement model

Claims

1. A system for measuring the shape of a semiconductor, comprising: One or more measurement systems, each comprising an illumination source and a detector, each illumination source configured to generate a quantitative illumination light characterized by one or more physical properties, each detector configured to collect a quantitative amount of measurement data from one or more structures mounted on a first wafer, the quantitative measurement data depending on the one or more physical properties of the quantitative illumination light and one or more physical features of the one or more structures mounted on the first wafer; and a computing system configured to: generate a set of candidate values ​​for one or more parameters of interest characterized by a shape of one or more structures mounted on the first wafer; and determine an error value associated with each candidate value of the candidate value set of the one or more parameters of interest based on a trained scan-conditional measurement model, wherein the candidate value set and each of the quantitative measurement data are provided as input to the trained scan-conditional measurement model; Determine a first estimated value for one or more parameters of interest, wherein the first estimated value is a first candidate value of the candidate value set of one or more parameters of interest having a first minimum error value; and transmit an indication of one of the first estimated values ​​for one or more parameters of interest to a semiconductor manufacturing tool, causing the semiconductor manufacturing tool to adjust one or more parameters of one of its manufacturing processes to achieve the desired output from one of the semiconductor manufacturing tools.

2. The system of claim 1, wherein the computing system is further configured to: receive a set of DOE data associated with measurement data of a plurality of DOE structures characterized as a set of Design of Experiments (DOE) parameter values; and train the scan-conditional measurement model based on the set of DOE data of measurement data corresponding to the set of DOE parameter values ​​and a set of perturbed values ​​of each DOE parameter value of the set of DOE parameter values.

3. The system of claim 2, wherein the DOE dataset of the measurement data is actual measurement data collected from the plurality of DOE structures manufactured based on the DOE parameter value set.

4. The system as requested in item 3, wherein the set of DOE parameter values ​​is measured by a trusted reference measurement system.

5. The system of request item 3, wherein the set of DOE parameter values ​​is used to generate known, programmed values ​​for the plurality of DOE structures.

6. The system of claim 2, wherein the DOE data set is used to simulate measurement data based on the DOE parameter value set, wherein the DOE parameter value set consists of known values ​​associated with the simulation.

7. The system of request item 2, wherein the DOE parameter value set is simulated based on one of the DOE parameter value sets, and wherein the DOE data set of measurement data is simulated based on the DOE parameter value set.

8. The system as requested in item 2, wherein the scan condition measurement model is a machine learning-based model.

9. The system of request item 1, wherein the computing system is further configured to: determine a second estimated value of one or more parameters of interest, wherein the second estimated value is a second candidate value of the candidate value set of one or more parameters of interest having a second minimum error value.

10. The system of claim 1, wherein the one or more parameters of interest are characterized in a two-dimensional shape of one or more structures disposed on the first wafer.

11. The system of claim 1, wherein the one or more parameters of interest are characterized in a three-dimensional shape of one or more structures disposed on the first wafer.

12. The system of claim 1, wherein the quantity of measurement data comprises measurements of the one or more structures by at least one optical-based metrology system, at least one X-ray-based metrology system, or any combination thereof.

13. A method for measuring the shape of a semiconductor, comprising: A certain amount of measurement data is collected from one or more structures mounted on a first wafer. This collection of quantitative measurement data involves an illumination source and a detector. The illumination source is configured to generate a quantitative illumination light characterized by one or more physical properties. The detector is configured to collect the quantitative measurement data, which is dependent on the one or more physical properties of the quantitative illumination light and one or more physical features of the one or more structures mounted on the first wafer. A candidate set of one or more parameters of interest is generated, characterizing the shape of one or more structures mounted on the first wafer. Based on an error value determined by a trained scanning conditional measurement model and associated with each candidate value of the candidate value set of one or more parameters of interest, wherein the candidate value set and each of the certain amount of measurement data are provided as input to the trained scanning conditional measurement model to determine a first estimated value of each of the one or more parameters of interest, wherein the first estimated value is a first candidate value of the candidate value set of one or more parameters of interest having a first minimum error value; and one of the first estimated values ​​of the one or more parameters of interest is transmitted to a semiconductor manufacturing tool, causing the semiconductor manufacturing tool to adjust one or more parameters of one of its manufacturing processes to achieve the desired output from one of the semiconductor manufacturing tools.

14. The method of claim 13, further comprising: The scan-conditional measurement model is trained using the DOE dataset, which is a set of measurement data associated with a plurality of DOE structures characterized as a set of Design of Experiments (DOE) parameter values, and the DOE dataset, which is a set of measurement data corresponding to the set of DOE parameter values ​​and a set of perturbed values ​​of each DOE parameter value in the set of DOE parameter values.

15. The method of claim 14, wherein the DOE dataset of the measurement data is actual measurement data collected from the plurality of DOE structures manufactured based on the DOE parameter value set.

16. The method of claim 14, wherein the DOE data set of the measurement data is simulated based on the DOE parameter value set, wherein the DOE parameter value set consists of known values ​​associated with the simulation.

17. The method of claim 14, wherein the DOE parameter value set is simulated based on one of the DOE parameter value sets, and wherein the DOE data set of measurement data is simulated based on the DOE parameter value set.

18. The method of request item 14, wherein the scan condition measurement model is a machine learning-based model.

19. The method of claim 13, further comprising: Determine a second estimated value for one of the one or more parameters of interest, wherein the second estimated value is a second candidate value of the candidate value set of the one or more parameters of interest having a second minimum error value.

20. The method of claim 13, wherein the one or more parameters of interest are characterized in a two-dimensional shape or a three-dimensional shape of the one or more structures disposed on the first wafer.

21. The method of claim 13, wherein the quantity of measurement data comprises measurements of the one or more structures by at least one optical-based measurement system, at least one X-ray-based measurement system, or any combination thereof.

22. A system for measuring the shape of a semiconductor, comprising: One or more measurement systems, each comprising an illumination source and a detector, each illumination source configured to generate a quantitative illumination light characterized by one or more physical properties, each detector configured to collect a quantitative amount of measurement data from one or more structures mounted on a first wafer, the quantitative measurement data depending on the one or more physical properties of the quantitative illumination light and one or more physical features of the one or more structures mounted on the first wafer; and a non-transitory computer-readable medium comprising instructions that, when executed by one or more processors of a computing system, cause the computing system to: generate a candidate set of one or more parameters of interest characterized by a shape of one or more structures mounted on the first wafer; and determine an error value associated with each candidate value of the candidate set of the one or more parameters of interest based on a trained scan-conditional measurement model, wherein the candidate set of values ​​and each of the quantitative measurement data are provided as input to the trained scan-conditional measurement model; Determine a first estimated value for one or more parameters of interest, wherein the first estimated value is a first candidate value of the candidate value set of one or more parameters of interest having a first minimum error value; and transmit an indication of one of the first estimated values ​​for one or more parameters of interest to a semiconductor manufacturing tool, causing the semiconductor manufacturing tool to adjust one or more parameters of one of its manufacturing processes to achieve the desired output from one of the semiconductor manufacturing tools.

23. The system of claim 22, wherein the non-transitory computer-readable medium further includes instructions that, when executed by the one or more processors of the computing system, cause the computing system to: receive a set of DOE data relating to measurements of a plurality of DOE structures characterized as a set of Design of Experiments (DOE) parameter values; and train the scan-conditional measurement model based on the set of DOE data relating to measurement data of a perturbed set of DOE parameter values ​​corresponding to the set of DOE parameter values ​​and the set of DOE parameter values ​​of each of the DOE parameter values.

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