An adaptive optimization method for optical scatterometry

Abstract

This invention discloses an adaptive optimization method for optical scattering measurement. It involves parametrically modeling the nanostructure to be measured and building a basic coarse-grained sample library. A coarse-grained surrogate model is then trained based on this sample library, enabling rapid identification of multiple key regions. Adaptive sampling is then performed based on these key regions to build a fine-grained sample library. A fine-grained surrogate model is further trained based on this library, and this model performs fine-grained search optimization within the key regions to find the optimal values ​​within these regions. These optimal values ​​represent the relevant parameters of the sample to be measured. This invention can narrow the search range and rapidly build the library using a variable-grained surrogate model, and improve optimization efficiency through an adaptive optimization strategy, thereby achieving accurate and efficient solution for the relevant parameters of the sample to be measured.

Description

Technical Field

[0001] This invention belongs to the field of computational optical measurement technology, and relates to a method for rapidly inversely calculating the parameters to be measured and rapidly optimizing the configuration of optical scattering measurements. It can be applied to the rapid measurement of geometric and physical quantities of semiconductor nanostructures based on optical scattering. Background Technology

[0002] Semiconductor and integrated circuit manufacturing inevitably requires metrological inspection during the manufacturing process. Currently, semiconductor front-end metrology technologies mainly include scanning electron microscopy (SEM), atomic force microscopy (AFM), transmission electron microscopy (TEM), and optical scattering measurement. Optical scattering measurement involves projecting a beam of polarized light onto the surface of a sample and measuring the change in polarization state before and after reflection to determine the relevant dimensional parameters of the sample. Due to its advantages of speed and non-destructive nature, optical scattering measurement is currently the mainstream technology for online optical measurement (especially in the field of optical critical dimension measurement). Spectral ellipsometric measurement is not limited by the optical diffraction limit and is a spectral, computational, model-based indirect measurement method. Therefore, it has been widely used in predictive approximation and optimization design in the field of computational optical measurement technology.

[0003] Currently, optical scattering measurement mainly involves two key technologies: forward modeling and inverse solving. Forward modeling of the optical response of nanostructures is primarily achieved through methods such as rigorous coupled wave analysis (RCWA), finite element analysis (FEA), and finite difference time domain (FDTD). Inverse solving mainly includes two methods: library search matching and direct fitting optimization. While library search matching is simple and easy to implement, it requires establishing a simulation sample library of ellipsometric response based on the variation range of input parameters, necessitating extensive offline modeling and simulation computation. Furthermore, the performance of library search matching largely depends on the network granularity of the ellipsometric simulation sample library and its corresponding interpolation algorithm. Direct fitting optimization does not require a pre-established simulation sample library, but each iteration requires calling forward modeling for calculation, leading to repeated calls and solutions, resulting in low simulation efficiency and high computational costs. Therefore, the current simulation performance and efficiency of optical scattering measurement of semiconductor nanostructures are one of the main reasons limiting rapid fitting optimization techniques.

[0004] CN102798342B proposes a library matching method for optical scattering measurements based on fitting error interpolation. This method utilizes a pre-established spectral library and the measured spectral responses to construct an interpolation function for the fitting error, thus transforming the inverse problem of solving the structure of the sample in optical scattering measurements into solving the problem of finding the optimal value of the fitting error interpolation objective function. The optimal value of the objective function represents the geometric parameters of the sample. However, this method still requires the establishment of a complete spectral response library before measurement, necessitating extensive preliminary simulation work. Furthermore, the final measurement accuracy depends not only on the granularity of the established spectral response library but also on the performance of the interpolation algorithm used.

[0005] CN103559329B proposes a method for extracting characteristic parameters of rough nanostructures in optical scattering measurements. This method determines the mapping relationship between the extracted parameters and the measured parameters of the rough nanostructure through simulation calculations, and optimizes the measurement configuration and equivalent medium model. Then, based on the simulation results, the measured parameters are corrected using the parameter mapping relationship to obtain rough nanostructure characteristic parameters that are closer to the true values. However, this method requires the use of the optimal measurement configuration and optimal equivalent medium model for subsequent calculations, which poses a significant challenge to the optimization process. Avoiding getting trapped in local optima becomes the key issue.

[0006] Currently, although relevant patents have proposed methods for solving and calculating the parameters of semiconductor nanostructures in optical scattering measurements, the problem of rapid optimization has not yet been solved, especially in terms of solution accuracy and efficiency, which still need to be improved. Summary of the Invention

[0007] The purpose of this invention is to provide an adaptive optimization method for optical scattering measurement, comprising the following steps:

[0008] Step 1: Perform parametric modeling for specific types of semiconductor nanostructures according to process requirements to generate a coarse-grained optical scattering response sample library α.

[0009] Step 2: Train and construct a coarse-grained surrogate model S1 based on the optical scattering response sample library α;

[0010] Step 3: Perform a global coarse search based on the coarse-grained proxy model S1 to quickly identify multiple key areas;

[0011] Step 4: Based on the variation range of the parameters to be measured in the key areas mentioned above, perform fine-grained rapid library construction to generate the optical scattering response sample library β;

[0012] Step 5: Train and construct a fine-grained surrogate model S2 based on the optical scattering response sample library β;

[0013] Step 6: Based on the surrogate model S2, perform a fine search on the key areas. At this point, the optimal value among multiple key areas is the final output parameter to be tested.

[0014] (1) Based on actual process requirements, an optical scattering response sample library α is constructed for a certain type of semiconductor nanostructure to be tested. This sample library is a basic coarse-grained sample library, which is used to sample and generate a training set to construct a coarse-grained surrogate model for approximate calculation.

[0015] (2) Using the coarse-grained optical scattering response sample library α in (1) as the sampling space, the sampling points are input to generate a basic training set; and based on this training set, a coarse-grained surrogate model S1 is trained and constructed.

[0016] (3) Use the surrogate model S1 trained and constructed in (2) to complete the coarse-grained stage of search optimization and rapid database construction in key regions. The sample database generated in this stage is the fine-grained optical scattering response sample database β, thus providing a training and construction foundation for the subsequent fine-grained stage of search optimization. The specific content is as follows:

[0017] (3.1) The above-described surrogate model is used to complete the adaptive search optimization in the coarse-grained stage. First, the approximate calculation model is used to perform a global search, thereby completing the adaptive and rapid identification of multiple key regions (regions of interest). Then, the current local optimum is broken, and a global search is performed again based on the spatial distribution distance standard to find whether there are any undiscovered key regions.

[0018] (3.2) Rapidly build a library for the key regions identified in (3.1). After the search and optimization of the coarse-grained surrogate model S1 in the early stage, the range of parameter variation of the test sample is narrowed and limited to the key regions. Then, a library is built for the region and a fine-grained optical scattering response sample library β is generated.

[0019] (4) Using the optical scattering response sample library β from (3) as the sampling space, sampling is performed, and then a training set is generated. This training set is then used to construct a fine-grained surrogate model S2. To ensure the accuracy of the surrogate model S2, an adaptive sampling method is used here, and a multi-objective dual-space performance evaluation system is introduced. This evaluation system mainly includes:

[0020] (4.1) Establish a multi-objective optimization model for the local and global performance of the sampling points. The local performance mainly includes: ① the change in the model's prediction variance after the addition of the sampling point; ② the change in neighborhood sensitivity after the addition of the sampling point, i.e., the change in the perturbation effect of the sampling point on the response output within its neighborhood. The global performance mainly includes: ① the spatial distance of the sampling distribution; ② the distribution properties in the sampling space.

[0021] (4.2) Evaluation of sampling points in dual spaces. That is, the performance and contribution of sampling points are evaluated in multiple dimensions in both the measurement input space and the response output space.

[0022] (4.3) Considering the trade-off between global search and local optimization, such as... Figure 4 As shown, constructing an adaptive weighted scoring system mainly addresses two issues: ① designing a suitable and effective development standard to identify key areas; ② moving beyond the current local optimum to search for key areas that were not discovered in the previous round of development.

[0023] (5) Use the surrogate model S2 from (4) to perform fine-grained search optimization on the multiple key regions identified in (3.1). At this time, the optimal value of the search output is the parameter to be measured of the semiconductor nanostructure.

[0024] Preferably, in step 1, the parametric modeling method is the strictly coupled wave analysis (RCWA), the finite-time difference method (FDTD), or the finite element method (FEA).

[0025] Preferably, in step 1, the input parameters of the coarse-grained optical scattering response sample library include: nanostructure, material parameters, process node, and measurement configuration parameters; the output scattering response of the coarse-grained optical scattering response sample library includes the reflectivity, diffraction efficiency, Jones matrix, and Mueller matrix of the structure under test.

[0026] The nanostructure includes linewidth, lineheight, and sidewall angle; material parameters include refractive index n and extinction coefficient k; measurement configuration parameters include measurement incident angle, measurement azimuth angle, and incident light wavelength.

[0027] Preferably, in steps 2 and 5, the method for training and constructing the surrogate model is: Kriging model (KRG), polynomial regression (PRS), radial basis function (RBF), or deep neural network (DNN).

[0028] Preferably, the mapping strategy of the surrogate model includes: multi-model single-output form, single-model multi-output form, or a hybrid of multi-model single-output form and single-model multi-output form, with the model parameters to be determined as input and the optical response characterization quantity of scattering measurement as output.

[0029] Preferably, the sampling strategy of the surrogate model includes: Latin hypercube sampling (LHD) and uniform design (UD) with single sampling as the main method in the coarse search stage; and adaptive sampling methods based on variance, cross-validation error, and local gradient in the fine search stage.

[0030] Preferably, in step 4, the data sources used in the fine-grained optical scattering response sample library β to ensure its accuracy are: high-fidelity simulation modeling data and measured data from high-precision scattering measurement instruments.

[0031] Preferably, in step 6, the method used in the fine search stage is: if the granularity of the sample library β is sufficiently fine, a search optimization method of library matching and direct fitting optimization is adopted.

[0032] Preferably, the scattering instrument includes a reflectometer, an ellipsometer, a Fourier scatterer, an angle-resolved scatterer, and an instrument based on spectral measurement data.

[0033] This invention provides an optimization method for rapidly solving for measured parameters online in optical scattering measurements. This method combines a variable-granularity surrogate model with an adaptive optimization strategy to achieve an iterative optimization process of coarse and fine searches. First, based on parametric simulation modeling, the method performs electromagnetic field simulation modeling on the measured sample to obtain a basic optical scattering response sample library. Then, a coarse-granular surrogate model is constructed using the basic sample library. Next, this surrogate model is used for rapid identification of multiple key regions and rapid library construction within these key regions, thereby constructing a fine-granular surrogate model. Finally, the fine-granular surrogate model is combined with an adaptive optimization strategy to perform optimization approximation in the key regions, and the final optimal value output is the measured parameter.

[0034] In summary, the rapid online optimization method for optical scattering measurement proposed in this invention has the following advantages compared with existing technologies:

[0035] 1. This invention uses a coarse-grained surrogate model to search for key regions and narrow down the range of relevant parameter variations in the test samples, thereby enabling the rapid construction of a fine-grained optical scattering response sample library. Compared with traditional methods, this saves a significant amount of time in the initial offline library construction, thus making rapid online optimization possible.

[0036] 2. This invention addresses the problem that traditional methods require continuous iteration of forward modeling in search optimization, which consumes a lot of solution time. It can accelerate or replace the forward modeling process by using a variable-granularity surrogate model, thereby improving search optimization efficiency and saving expensive simulation calculation costs.

[0037] 3. This invention employs a search optimization method combining a variable-granularity surrogate model and an adaptive optimization strategy. A low-cost, coarse-grained surrogate model performs a global search and identifies key regions, while a high-cost, fine-grained surrogate model performs optimization within those key regions, thus achieving a combined coarse- and fine-grained adaptive search strategy. Compared to traditional methods, this method can accurately and efficiently solve for the relevant parameters of the sample under test, and is expected to be widely used in optical scattering measurements. Attached Figure Description

[0038] Figure 1 This is a flowchart of a rapid online optimization method for optical scattering measurement according to the present invention;

[0039] Figure 2 This is a schematic diagram of the parameter range and key regions of the coarse and fine-grained optical scattering response sample library established according to the present invention;

[0040] Figure 3 This is a schematic diagram of a fully connected deep neural network (DNN) with multiple hidden layers according to the present invention;

[0041] Figure 4This is a schematic diagram illustrating the trade-off between global search and local optimization as described in this invention. Detailed Implementation

[0042] To more clearly explain the purpose, technical solution, and advantages of this invention, further explanation will be provided below with reference to specific embodiments and related drawings. This invention provides a rapid online optimization method for optical scattering measurement, specifically comprising:

[0043] (1) Figure 1 This is a flowchart of a rapid online optimization method for optical scattering measurement according to the present invention. Figure 1 As shown, firstly, based on actual process requirements, an optical scattering response sample library α is constructed for a certain type of semiconductor nanostructure under test. For example, the test parameters of the semiconductor nanostructure and the relevant measurement configuration parameters are labeled as an n-dimensional column vector. The sample library α is constructed using the input parameters; then, the sample library α is constructed using simulation modeling methods such as rigorous coupled-wave analysis (RCWA).

[0044] (2) The global parameter range of the established coarse-grained optical scattering response sample library α is as follows: Figure 2 As shown (for simplicity, only two input parameters are used here), For example, there should actually be n input parameters), and a coarse-grained surrogate model S1 is trained and constructed based on this parameter range. There are various methods for constructing the surrogate model; in this embodiment of the invention, a Kriging model is used as the surrogate model for the coarse search stage. Its representation function is defined as:

[0045]

[0046] in, It is a known basis function. It is an unknown constant that characterizes the global trend. It is a random variable that follows a Gaussian distribution: .

[0047] (3) Based on the proxy model S1 constructed in (2), perform search optimization in the coarse search stage and identify several key regions, such as Figure 2 As shown, the key areas identified here provide the foundation for the subsequent construction of a fine-grained sample library.

[0048] (4) Based on the key regions identified in (3), the range of variation of the parameters to be measured can be narrowed, which can then be used to construct a fine-grained optical scattering response sample library β, such as Figure 2 As shown. For example, to ensure the accuracy of the sample library β, a high-fidelity simulation modeling method such as the finite element method (FEA) is selected here, or a certain amount of measured data from a high-precision scattering instrument is added for data correction.

[0049] (5) Based on the sample library β in (4), a fine-grained proxy model S2 is trained and constructed. To ensure the search accuracy in the fine-grained stage, this embodiment of the invention uses an adaptive sampling method combined with a deep neural network (DNN) to construct the model. There are many types of adaptive sampling methods and DNN architectures. In this embodiment, an adaptive sampling method based on prediction variance is used for sampling design; a fully connected DNN with multiple hidden layers is used for prediction learning. This mainly includes:

[0050] (5.1) The adaptive sampling method based on prediction variance is deeply integrated with the Kriging method, and its output response is regarded as a concrete implementation of the Gaussian process. The prediction variance, as an estimate of the actual prediction error, is used to assist in sampling design and reduce the uncertainty of model construction. Its characterization function is defined as:

[0051]

[0052] Where GP stands for Gaussian process. It is the model's predicted response. It is the prediction variance of the model.

[0053] (5.2) DNN model architecture as follows Figure 3 As shown in the figure, the input is the training points obtained by sampling in the sample library β, and the output is the optical scattering response, which is then used to construct the fine-grained surrogate model S2.

[0054] (6) Using the constructed proxy model S2 in, for example Figure 2 A fine-grained search and optimization is performed on the sample library β shown to find the optimal value within multiple key regions. At this point, the optimal value output by the model is the relevant parameter of the sample to be tested.

[0055] (7) Finally, the final determined parameters of the test sample are output to complete the entire online optimization process.

[0056] Furthermore, the above descriptions are merely embodiments applicable to the present invention and are not intended to limit the present invention. All technical methods and research schemes falling within the scope of the present invention's concept are protected by the present invention. Any modifications, equivalent substitutions, and improvements within the scope of the present invention's concept are included within the protection scope of the present invention.

Claims

1. An adaptive optimization method for optical scattering measurement, characterized in that, Includes the following steps: Step 1: Perform parametric modeling for specific types of semiconductor nanostructures according to process requirements to generate a coarse-grained optical scattering response sample library α. The input parameters of the coarse-grained optical scattering response sample library include: nanostructure, material parameters, process node, and measurement configuration parameters; the output scattering response of the coarse-grained optical scattering response sample library is expressed in the form of reflectivity, diffraction efficiency, Jones matrix, and Mueller matrix of the structure under test. Nanostructures include linewidth, lineheight, and sidewall angles; material parameters include refractive index n and extinction coefficient k; measurement configuration parameters include measurement incident angle, measurement azimuth angle, and incident light wavelength. Step 2: Train and construct a coarse-grained surrogate model S1 based on the optical scattering response sample library α; The sampling design is carried out using the optical scattering response sample library α as the sampling space, and then a training set is generated. A coarse-grained surrogate model S1 is then trained using this training set. The sampling methods used in this step include Latin Hypercube Sampling (LHD) or Uniform Design (UD). Step 3: Perform a global coarse search based on the coarse-grained proxy model S1 to quickly identify multiple key areas; Step 4: Based on the variation range of the parameters to be measured in the key areas mentioned above, perform fine-grained rapid library construction to generate the optical scattering response sample library β; Step 5: Train and construct a fine-grained surrogate model S2 based on the optical scattering response sample library β; The optical scattering response sample library β is used as the sampling space for sampling, and then a training set is generated. A fine-grained surrogate model S2 is then trained and constructed using this set. An adaptive sampling method based on variance, cross-validation error, and local gradient is adopted. Step 6: Based on the surrogate model S2, perform a fine search on the key areas. At this point, the optimal value among multiple key areas is the final output parameter to be tested.

Images