Method, device and equipment for extracting morphology parameters and readable storage medium

Abstract

The invention discloses a morphology parameter extraction method, device and equipment and a readable storage medium, and can be applied to the technical field of semiconductors, and the method comprises the steps: obtaining an actual measurement scattering spectrum of a to-be-measured nanostructure; determining a to-be-measured morphology parameter corresponding to the to-be-measured nanostructure; based on the to-be-measured morphology parameters, determining a theoretical scattering spectrum corresponding to the to-be-measured nanostructure; constructing an evaluation function based on the theoretical scattering spectrum and the actually measured scattering spectrum; based on the evaluation function and a non-gradient optimization algorithm, determining an initial parameter value corresponding to the to-be-measured morphology parameter; and optimizing the initial parameter value based on the evaluation function and a gradient optimization algorithm to obtain a target parameter value corresponding to the to-be-measured morphology parameter. Thus, the gradient optimization algorithm and the non-gradient optimization algorithm are combined, the relative position of the parameter solution is searched firstly, then the morphology parameter value of the to-be-measured nanostructure is finely solved, and therefore the accuracy of morphology parameter calculation is improved.

Description

Technical Field

[0001] The present application relates to the field of semiconductor technology, and in particular to a method, device, equipment and readable storage medium for extracting morphological parameters. Background Art

[0002] With the rapid development of semiconductor manufacturing technology, the structural design of integrated circuit devices has gradually shifted from two-dimensional planar structures to three-dimensional structures with higher complexity, smaller eigenvalue sizes and more stacked layers.

[0003] Among three-dimensional structures, the etching process of high aspect ratio structures is particularly critical and challenging in modern storage technology. Since the increase in the number of layers and stress in the oxide / nitride stack will cause the wafer to bend and deform, it is necessary to introduce nano-measurement technology to accurately characterize its etching process and its quality, and monitor it in real time during the manufacturing process. However, the optimization algorithm used in the inverse problem solving process of existing measurement technology cannot balance the global optimization well, resulting in the problem of low accuracy in the calculation of the morphological parameters of the nanostructure to be measured.

[0004] Therefore, how to improve the accuracy of morphology parameter calculation is a problem that technical personnel in this field need to solve urgently. Summary of the invention

[0005] Based on the above problems, the present application provides a method, device, equipment and readable storage medium for extracting morphology parameters, which improves the accuracy of morphology parameter calculation by first finding the relative position of the parameter solution and then finely solving the morphology parameter value of the nanostructure to be measured.

[0006] In a first aspect, an embodiment of the present application provides a method for extracting morphological parameters, comprising:

[0007] Obtaining a measured scattering spectrum of the nanostructure to be measured;

[0008] Determining the morphological parameters to be measured corresponding to the nanostructure to be measured;

[0009] Based on the measured morphological parameters, determining a theoretical scattering spectrum corresponding to the measured nanostructure;

[0010] Constructing an evaluation function based on the theoretical scattering spectrum and the measured scattering spectrum;

[0011] Determine the initial parameter value corresponding to the measured morphological parameter based on the evaluation function and the non-gradient optimization algorithm;

[0012] The initial parameter value is optimized based on the evaluation function and the gradient optimization algorithm to obtain a target parameter value corresponding to the measured morphological parameter.

[0013] Optionally, the method further includes:

[0014] The uncertainty of the target parameter value is determined based on error propagation theory, and the uncertainty is used to evaluate whether the target parameter value is credible.

[0015] Optionally, the determining of the measured morphological parameters corresponding to the measured nanostructure includes:

[0016] Determining a parameterized model based on the nanostructure to be measured;

[0017] Based on the parameterized model, the morphological parameters to be measured corresponding to the nanostructure to be measured are determined.

[0018] Optionally, determining a theoretical scattering spectrum corresponding to the nanostructure to be measured based on the morphological parameters to be measured includes:

[0019] Determining a theoretical scattering spectrum based on the measured morphological parameters and the scattering formula;

[0020] Wherein, the expression of the scattering formula is:

[0021]

[0022] Among them I sim (q, x) is the theoretical scattering spectrum, I0 is the intensity scaling factor, G(q) is the instrument factor, F(q, x) is the shape factor, S(q) is the structure factor, is the roughness factor, I bk is the background scattering intensity, and x is the morphological parameter to be measured.

[0023] Optionally, the evaluation function includes: 2 Evaluation function, log absolute error evaluation function and absolute error evaluation function.

[0024] Optionally, determining the initial parameter value corresponding to the measured morphological parameter based on the evaluation function and the non-gradient optimization algorithm includes:

[0025] Determine a preset parameter initial value and a preset parameter search interval corresponding to the morphological parameter to be measured;

[0026] The evaluation function is used as the optimization target, based on the preset parameter initial value and the preset parameter search interval, a non-gradient optimization algorithm is used to iterate, and when it iterates to a first preset termination condition, an initial parameter value corresponding to the measured morphological parameter is obtained.

[0027] Optionally, the iterating using the non-gradient optimization algorithm to obtain an initial parameter value corresponding to the measured morphological parameter when iterating to a first preset termination condition includes:

[0028] Determining an initial population from the preset parameter search interval;

[0029] Based on the evaluation function, a non-gradient optimization algorithm is used to iterate the fitness of each individual in the initial population, and a first iteration result is obtained;

[0030] The parameter value corresponding to the first iteration result when the first preset termination condition is reached is used as the initial parameter value corresponding to the morphological parameter to be measured.

[0031] Optionally, the optimizing the initial parameter value based on the evaluation function and the gradient optimization algorithm to obtain a target parameter value corresponding to the measured morphological parameter includes:

[0032] Based on the initial parameter value, determining an optimization interval, wherein the optimization interval is an upper and lower limit of the parameter value determined based on the initial parameter value;

[0033] The evaluation function is used as the optimization target, and based on the initial parameter value and the optimization interval, a gradient optimization algorithm is used to iterate, and when it iterates to a second preset termination condition, a target parameter value corresponding to the measured morphological parameter is obtained.

[0034] Optionally, the iterating using the gradient optimization algorithm to obtain a target parameter value corresponding to the measured morphological parameter when iterating to a second preset termination condition includes:

[0035] Determining a gradient corresponding to the initial parameter value using a gradient optimization algorithm;

[0036] Iterating along the reverse direction of the gradient and obtaining a second iteration result;

[0037] The parameter value corresponding to the second iteration result when the second preset termination condition is reached is used as the target parameter value corresponding to the morphological parameter to be measured.

[0038] In a second aspect, an embodiment of the present application provides a device for extracting morphological parameters, comprising:

[0039] An acquisition module, used to acquire a measured scattering spectrum of the nanostructure to be measured;

[0040] A determination module, used to determine the morphological parameters to be measured corresponding to the nanostructure to be measured;

[0041] A first calculation module is used to determine a theoretical scattering spectrum corresponding to the nanostructure to be measured based on the morphological parameters to be measured;

[0042] A construction module, used for constructing an evaluation function based on the theoretical scattering spectrum and the measured scattering spectrum;

[0043] A second calculation module is used to determine the initial parameter value corresponding to the measured morphological parameter based on the evaluation function and the non-gradient optimization algorithm;

[0044] The third calculation module is used to optimize the initial parameter value based on the evaluation function and the gradient optimization algorithm to obtain the target parameter value corresponding to the measured morphological parameter.

[0045] In a third aspect, an embodiment of the present application provides a device for extracting morphological parameters, including:

[0046] Memory for storing computer programs;

[0047] A processor is used to implement the steps of the above-mentioned method for extracting morphological parameters when executing the computer program.

[0048] In a fourth aspect, an embodiment of the present application provides a readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the steps of the method for extracting morphological parameters as described above are implemented.

[0049] It can be seen from the above technical solutions that compared with the prior art, the present application has the following advantages:

[0050] The present application first obtains the measured scattering spectrum of the nanostructure to be measured, and determines the measured morphological parameters corresponding to the nanostructure to be measured. Then, based on the measured morphological parameters, the theoretical scattering spectrum corresponding to the nanostructure to be measured is determined, and an evaluation function is constructed based on the theoretical scattering spectrum and the measured scattering spectrum. Finally, based on the evaluation function and the non-gradient optimization algorithm, the initial parameter values ​​corresponding to the measured morphological parameters are determined, and the initial parameter values ​​are optimized based on the evaluation function and the gradient optimization algorithm to obtain the target parameter values ​​corresponding to the measured morphological parameters. In this way, in combination with the gradient optimization algorithm and the non-gradient optimization algorithm, the relative position of the parameter solution is first found and then the morphological parameter values ​​of the nanostructure to be measured are precisely solved, thereby improving the accuracy of the morphological parameter calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 A flow chart of a method for extracting morphological parameters provided in an embodiment of the present application;

[0052] Figure 2 A schematic diagram of a small-angle X-ray scattering measurement provided in an embodiment of the present application;

[0053] Figure 3 A flow chart of morphological parameter extraction from small-angle X-ray scattering measurement based on a parameterized model provided in an embodiment of the present application;

[0054] Figure 4 A schematic diagram of the structure of a morphology parameter extraction device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0055] As mentioned above, the accuracy of existing morphological parameter calculations is low. Specifically, critical dimension small angle X-ray scattering measurement technology (CD-SAXS) has become one of the main means of online measurement of integrated circuit devices due to its ability to measure high-density, high aspect ratio structures and buried layer structures. However, the existing CD-SAXS inverse problem solution process usually uses a gradient-based optimization algorithm or a non-gradient optimization algorithm alone. Since the optimization algorithm used cannot balance the global optimal problem and the uncertainty evaluation of traceability well, the accuracy of the morphological parameter calculation of the nanostructure to be measured is low.

[0056] To solve the above problems, the embodiment of the present application provides a method for extracting morphological parameters, firstly obtaining the measured scattering spectrum of the nanostructure to be measured, and determining the morphological parameters to be measured corresponding to the nanostructure to be measured. Then, based on the morphological parameters to be measured, the theoretical scattering spectrum corresponding to the nanostructure to be measured is determined, and an evaluation function is constructed based on the theoretical scattering spectrum and the measured scattering spectrum. Finally, based on the evaluation function and the non-gradient optimization algorithm, the initial parameter value corresponding to the morphological parameter to be measured is determined, and the initial parameter value is optimized based on the evaluation function and the gradient optimization algorithm to obtain the target parameter value corresponding to the morphological parameter to be measured.

[0057] In this way, by combining the gradient optimization algorithm and the non-gradient optimization algorithm, the relative position of the parameter solution is first found and then the morphological parameter values ​​of the nanostructure to be measured are precisely solved, thereby improving the accuracy of the morphological parameter calculation.

[0058] It should be noted that the method, device, equipment and readable storage medium for extracting morphological parameters provided by the present application can be applied to the field of semiconductor devices. The above is only an example and does not limit the application field of the method, device, equipment and readable storage medium for extracting morphological parameters provided by the present application.

[0059] In order to make the purpose, technical solution and advantages of the embodiments of the present application clearer, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0060] Figure 1 A flow chart of a method for extracting morphological parameters provided in an embodiment of the present application. Figure 1 As shown, a method for extracting morphological parameters provided in an embodiment of the present application may include:

[0061] S101: Obtaining a measured scattering spectrum of the nanostructure to be measured.

[0062] In practical applications, a scattering map is a graphical representation of the scattering phenomenon. Figure 2 A schematic diagram of a small-angle X-ray scattering measurement provided in an embodiment of the present application. Figure 2 As shown in the figure, in order to meet the measurement requirements of complex integrated circuit nanostructures at advanced technology nodes of 7nm and below, a shorter X-ray band is used for scattering measurement. In addition, in order to obtain richer scattering information, the nanostructure (sample) to be measured can be placed on a rotatable sample stage for rotation, and based on automated optical inspection (AOI), the sample is irradiated with X-rays at a scattering angle of 2θ, so that scattering data at different rotation angles can be obtained through the detector. Then, the collected scattering data is processed, including background correction, normalization, and angle conversion, and then combined with a suitable coordinate system to obtain the measured scattering map corresponding to the nanostructure to be measured.

[0063] S102: Determine the morphological parameters to be measured corresponding to the nanostructure to be measured.

[0064] In practical applications, different nanostructures to be tested have different corresponding morphological parameters to be tested. For example, the morphological parameters of a circular hole may include diameter or radius, roundness, and surface roughness, while the morphological parameters of a square hole may include side length, angle, surface roughness, and aspect ratio. Therefore, before calculating the morphological parameter values ​​corresponding to the nanostructure to be tested, it is necessary to first determine the specific morphological parameters to be tested.

[0065] In addition, since the methods for determining the morphological parameters to be measured are not the same, the embodiments of the present application can illustrate a possible determination method.

[0066] In one case, S102: determining the morphological parameters to be measured corresponding to the nanostructure to be measured, specifically includes:

[0067] Determining a parameterized model based on the nanostructure to be measured;

[0068] Based on the parameterized model, the morphological parameters to be measured corresponding to the nanostructure to be measured are determined.

[0069] Figure 3 A flow chart of extracting morphological parameters from small-angle X-ray scattering measurements based on a parameterized model is provided in an embodiment of the present application. Figure 3As shown, a corresponding parameterized model can be pre-built for each different nanostructure, and the parameterized model is used to reasonably describe each nanostructure. These parameterized models can be associated with the respective corresponding nanostructures and stored in the memory together. After determining the nanostructure to be measured, the corresponding parameterized model is retrieved from the memory, and then the morphological parameter x to be measured is determined from the parameterized model, and the simulation data and measurement data corresponding to the parameterized model are determined, so as to determine the evaluation function to be adopted in the follow-up. In combination with the evaluation function, when the goodness of fit (GOF) is less than the preset value, the value corresponding to the morphological parameter to be measured is obtained by repeatedly iterating and solving through the optimization algorithm. It is understandable that the morphological parameters to be measured may include but are not limited to the electron density, film thickness, line width, line height, side wall angle, aperture size, inclination, ellipticity and torsion of the nanostructure to be measured.

[0070] S103: Determine a theoretical scattering spectrum corresponding to the nanostructure to be measured based on the morphological parameters to be measured.

[0071] In practical applications, the measured morphological parameter h can be substituted into the expression used to calculate the theoretical scattering spectrum, thereby determining the theoretical scattering spectrum corresponding to the measured nanostructure.

[0072] In addition, since there are different ways to determine the theoretical scattering spectrum, the embodiment of the present application can illustrate a possible determination method.

[0073] In one case, S103: determining a theoretical scattering spectrum corresponding to the nanostructure to be measured based on the morphological parameters to be measured, specifically includes:

[0074] Determining a theoretical scattering spectrum based on the measured morphological parameters and the scattering formula;

[0075] Wherein, the expression of the scattering formula is:

[0076]

[0077] Among them I sim (q, x) is the theoretical scattering spectrum, I0 is the intensity scaling factor, G(q) is the instrument factor, F(q, x) is the shape factor, S(q) is the structure factor, is the roughness factor, I bk is the background scattering intensity, and x is the morphological parameter to be measured.

[0078] In practical applications, in small-angle X-ray scattering measurement technology, the theoretical scattering spectrum can help understand the information such as the voids and particle distribution inside the nanostructure to be measured. Specifically, in the embodiment of the present application, the theoretical scattering spectrum can be determined by substituting the measured morphological parameter x into the scattering formula. The expression of the scattering formula after substitution is shown in the following formula (1):

[0079]

[0080] In the formula, I sim (q, x) is the theoretical scattering spectrum, I0 is the intensity scale factor, which is used to adjust or scale the intensity value and analyze the structure and performance of the material. G(q) is the instrument coefficient. Different instruments may have different structures, working principles and performance characteristics, so their corresponding instrument coefficients will also be different. F(q, x) is the shape factor, S(q) is the structure factor, is the roughness factor, I bk is the background scattering intensity, and x is the morphological parameter to be measured.

[0081] S104: constructing an evaluation function based on the theoretical scattering spectrum and the measured scattering spectrum.

[0082] In practical applications, there is an error between the measured scattering spectrum and the theoretical scattering spectrum corresponding to the nanostructure to be tested. Therefore, the extraction of morphological parameters requires the further construction of an evaluation function for measuring the fitting error between the theoretical scattering spectrum and the measured scattering spectrum.

[0083] In addition, since the evaluation functions are not the same, the embodiment of the present application can illustrate a possible evaluation function.

[0084] In one embodiment, the evaluation function includes: 2 Evaluation function, log absolute error evaluation function and absolute error evaluation function.

[0085] In practical applications, the evaluation function may include but is not limited to x 2 There are differences between the evaluation functions, such as logarithmic absolute error evaluation function and absolute error evaluation function. 2 The evaluation function mainly emphasizes the impact of the error size on the result. The logarithmic absolute error evaluation function is mainly used in situations where a wide range of error values ​​need to be processed and the impact of extreme values ​​is expected to be reduced. The absolute error evaluation function is used in situations where the error size needs to be directly measured. In the embodiment of the present application, any of the above evaluation functions can be used, with x 2 Taking the evaluation function as an example, the evaluation function expression is shown in the following formula (2):

[0086]

[0087] In the formula, and are the values ​​of the kth data point in the measured scattering spectrum and theoretical scattering spectrum corresponding to the nanostructure to be measured, ω k is the weight factor.

[0088] S105: Based on the evaluation function and the non-gradient optimization algorithm, determine the initial parameter value corresponding to the measured morphological parameter.

[0089] In practical applications, the non-gradient optimization algorithm can effectively avoid the situation of local optimal solution that may be trapped when the gradient optimization algorithm is used directly because of its global search capability, thereby avoiding the problem of long calculation time. In the embodiment of the present application, the non-gradient optimization algorithm can use but is not limited to genetic algorithm, particle swarm algorithm, simulated annealing method, differential evolution algorithm, covariance matrix adaptive evolution strategy and Markov chain-Monte Carlo algorithm. The extraction of morphological parameters takes the above-constructed evaluation function as the optimization target, and uses the non-gradient optimization algorithm to find the parameter solution that can make this optimization target smaller, that is, to obtain the initial parameter value corresponding to the morphological parameter to be measured.

[0090] In addition, since there are different ways to determine the initial parameter value, the embodiment of the present application can illustrate a possible determination method.

[0091] In one case, S105: determining the initial parameter value corresponding to the measured morphological parameter based on the evaluation function and the non-gradient optimization algorithm, specifically includes:

[0092] Determine a preset parameter initial value and a preset parameter search interval corresponding to the morphological parameter to be measured;

[0093] The evaluation function is used as the optimization target, based on the preset parameter initial value and the preset parameter search interval, a non-gradient optimization algorithm is used to iterate, and when it iterates to a first preset termination condition, an initial parameter value corresponding to the measured morphological parameter is obtained.

[0094] In practical applications, the calculation process of the non-gradient optimization algorithm listed above is basically the same, and it is first necessary to determine the preset parameter initial value and preset parameter search interval corresponding to the measured morphology parameter. Reasonable starting value (preset parameter initial value) can accelerate the convergence speed for continuous optimization problems. The preset parameter initial value provided in the embodiment of the present application needs to be set according to the actual nanostructure to be measured, and the starting value setting corresponding to different nanostructures is generally different. The preset parameter search interval refers to the search range (upper and lower limits) of the initial parameter value. The reasonable setting search interval can avoid the algorithm from performing unnecessary searches in irrelevant areas, thereby improving the efficiency of the algorithm. Then, the evaluation function constructed above is used as the optimization target, the preset parameter initial value is used as the initial value of the iterative calculation, and the non-gradient optimization algorithm is used to perform iterative calculation in the preset parameter search interval, so as to find the parameter solution when this optimization target meets the requirements as the initial parameter value corresponding to the measured morphology parameter. It can be understood that the optimization target meets the requirements and reaches the first preset termination condition, and the specific first preset termination condition can be set to the difference between the measured signal and the theoretical signal is less than the threshold value or reaches the maximum number of iterations.

[0095] In addition, since the iterative calculation methods are not the same, the embodiments of the present application can illustrate a possible iterative calculation method.

[0096] In one case, the non-gradient optimization algorithm is used to iterate, and when it iterates to a first preset termination condition, an initial parameter value corresponding to the measured morphological parameter is obtained, specifically including:

[0097] Determining an initial population from the preset parameter search interval;

[0098] Based on the evaluation function, a non-gradient optimization algorithm is used to iterate the fitness of each individual in the initial population, and a first iteration result is obtained;

[0099] The parameter value corresponding to the first iteration result when the first preset termination condition is reached is used as the initial parameter value corresponding to the morphological parameter to be measured.

[0100] Specifically, taking the genetic algorithm as an example, we first need to determine the initial population from the preset parameter search interval. The initial population is a group of randomly generated individuals that represent potential solutions in the problem space, that is, possible initial parameter values. Then, the fitness of each individual in the initial population is iteratively calculated, the best individual is selected to replace the worst individual, and the first iteration result is obtained. 2 Evaluation function, the first iteration result can be expressed by min{x 2}, when the first iteration result reaches the first preset termination condition (the difference is less than the threshold or the maximum number of iterations is reached), the iterative calculation is terminated, and the parameter value corresponding to the first iteration result is used as the initial parameter value corresponding to the measured morphological parameter. If the first preset termination condition is not reached, a loop is performed, and mutation, crossover, selection and other operations are performed in sequence until the first preset termination condition is met and the corresponding parameter value is output.

[0101] S106: Optimizing the initial parameter value based on the evaluation function and the gradient optimization algorithm to obtain a target parameter value corresponding to the measured morphological parameter.

[0102] In practical applications, the initial parameter values ​​calculated above are still used as initial values, and the evaluation function constructed above is still used as the optimization target. The gradient optimization algorithm is used to find the parameter solution that makes this optimization target smaller, so as to optimize the initial parameter values, and the parameter solution that meets the requirements is output as the target parameter value corresponding to the measured morphology parameter. In this way, by combining the gradient optimization algorithm and the non-gradient optimization algorithm, the relative position of the parameter solution is first found and then the morphology parameter value of the nanostructure to be measured is precisely solved. The hybrid optimization strategy can effectively avoid the problem of local optimal solutions, thereby improving the accuracy and reliability of the morphology parameter calculation.

[0103] In addition, since there are different ways to determine the target parameter value, the embodiment of the present application can illustrate a possible determination method.

[0104] In one case, S106: optimizing the initial parameter value based on the evaluation function and the gradient optimization algorithm to obtain a target parameter value corresponding to the measured morphological parameter, specifically includes:

[0105] Based on the initial parameter value, determining an optimization interval, wherein the optimization interval is an upper and lower limit of the parameter value determined based on the initial parameter value;

[0106] The evaluation function is used as the optimization target, and based on the initial parameter value and the optimization interval, a gradient optimization algorithm is used to iterate, and when it iterates to a second preset termination condition, a target parameter value corresponding to the measured morphological parameter is obtained.

[0107] In practical applications, the non-gradient optimization algorithm in the embodiment of the present application can use but is not limited to the gradient descent method, the optimal gradient method, the conjugate gradient method and the Newton method. The calculation process of the non-gradient optimization algorithm listed above is basically the same, and the optimization interval needs to be re-determined first. Specifically, the optimization interval is determined based on the initial parameter value, and the upper and lower limits of the parameter value are determined based on the initial parameter value. In addition, the upper and lower limits of the optimization interval are generally smaller than the above-mentioned preset parameter search interval. In this way, the evaluation function constructed above is used as the optimization target by the extraction device of the morphology parameter, and the initial parameter value is used as the initial value of the iterative calculation, and the gradient optimization algorithm is used to perform iterative calculations within the optimization interval, so as to find the parameter solution when this optimization target meets the requirements as the target parameter value corresponding to the morphology parameter to be measured. It can be understood that the optimization target meets the requirements, that is, the second preset termination condition is reached, and the specific second preset termination condition can be set to the gradient being small enough or reaching the maximum number of iterations.

[0108] In addition, since the iterative calculation methods are not the same, the embodiments of the present application can illustrate a possible iterative calculation method.

[0109] In one case, the iterating using the gradient optimization algorithm, when iterating to the second preset termination condition, obtains a target parameter value corresponding to the measured morphological parameter, including:

[0110] Determining a gradient corresponding to the initial parameter value using a gradient optimization algorithm;

[0111] Iterating along the reverse direction of the gradient and obtaining a second iteration result;

[0112] The parameter value corresponding to the second iteration result when the second preset termination condition is reached is used as the target parameter value corresponding to the morphological parameter to be measured.

[0113] Specifically, taking the gradient descent method as an example, we first need to calculate the gradient of the current initial parameter value based on the optimization interval. The expression can be Then, the initial parameter value is used as the initial value of the gradient optimization algorithm, and a certain step length is moved in the opposite direction of the gradient within the optimization interval to perform iterative calculations, and the initial parameter value is updated to obtain the second iterative result. When the second iterative result reaches the second preset termination condition (the gradient is small enough or the maximum number of iterations is reached), the iterative calculation is terminated, and the parameter value corresponding to the second iterative result is output as the target parameter value corresponding to the measured morphological parameter.

[0114] In addition, since the methods for determining the credibility of the target parameter value are different, the embodiment of the present application can illustrate a possible determination method.

[0115] In one embodiment, the method further comprises:

[0116] The uncertainty of the target parameter value is determined based on error propagation theory, and the uncertainty is used to evaluate whether the target parameter value is credible.

[0117] In practical applications, in order to better understand the credibility of the calculation results for the measured morphological parameters, it is necessary not only to give the calculated values ​​of these measured morphological parameters (target parameter values), but also to give the uncertainty of each target parameter value to ensure the credibility and comparability of the measurement results. Specifically, the theoretical scattering signal can be expanded by a first-order Taylor near the target parameter value according to the error propagation theory. The theoretical scattering signal is the signal value corresponding to the theoretical scattering spectrum. Then, based on the gradient information, the Jacobian matrix of the target parameter is calculated. Furthermore, using the corresponding error propagation formula, a linear error transfer formula for the deviation of the measured parameter caused by the measurement signal deviation can be obtained, and then a traceable uncertainty assessment corresponding to the target parameter value can be calculated.

[0118] In summary, the present application first obtains the measured scattering spectrum of the nanostructure to be measured, and determines the measured morphology parameters corresponding to the nanostructure to be measured. Then, based on the measured morphology parameters, the theoretical scattering spectrum corresponding to the nanostructure to be measured is determined, and an evaluation function is constructed based on the theoretical scattering spectrum and the measured scattering spectrum. Finally, based on the evaluation function and the non-gradient optimization algorithm, the initial parameter values ​​corresponding to the measured morphology parameters are determined, and the initial parameter values ​​are optimized based on the evaluation function and the gradient optimization algorithm to obtain the target parameter values ​​corresponding to the measured morphology parameters. In this way, in combination with the gradient optimization algorithm and the non-gradient optimization algorithm, the relative position of the parameter solution is first found and then the morphology parameter values ​​of the nanostructure to be measured are precisely solved, thereby improving the accuracy of the morphology parameter calculation.

[0119] Based on the method for extracting morphological parameters provided in the above embodiment, the present application also provides a device for extracting morphological parameters. The device for extracting morphological parameters is described below in conjunction with the embodiments and drawings.

[0120] Figure 4 A schematic diagram of a device for extracting morphological parameters provided in an embodiment of the present application. Figure 4 As shown, the device 400 for extracting morphological parameters provided in the embodiment of the present application includes:

[0121] An acquisition module 401 is used to acquire a measured scattering spectrum of the nanostructure to be measured;

[0122] A determination module 402 is used to determine the morphological parameters to be measured corresponding to the nanostructure to be measured;

[0123] A first calculation module 403 is used to determine a theoretical scattering spectrum corresponding to the nanostructure to be measured based on the morphological parameters to be measured;

[0124] A construction module 404 is used to construct an evaluation function based on the theoretical scattering spectrum and the measured scattering spectrum;

[0125] A second calculation module 405 is used to determine the initial parameter value corresponding to the measured morphological parameter based on the evaluation function and the non-gradient optimization algorithm;

[0126] The third calculation module 406 is used to optimize the initial parameter value based on the evaluation function and the gradient optimization algorithm to obtain the target parameter value corresponding to the measured morphological parameter.

[0127] As an implementation manner, with respect to how to determine whether the target parameter value is credible, the above-mentioned morphological parameter extraction device 400 further includes: a credibility calculation module;

[0128] The credibility calculation module is used to determine the uncertainty of the target parameter value based on the error propagation theory, and the uncertainty is used to evaluate whether the target parameter value is credible.

[0129] As an implementation manner, with respect to how to determine the morphological parameters to be measured corresponding to the nanostructure to be measured, the determination module 402 is specifically used to:

[0130] Determining a parameterized model based on the nanostructure to be measured;

[0131] Based on the parameterized model, the morphological parameters to be measured corresponding to the nanostructure to be measured are determined.

[0132] As an implementation manner, with respect to how to determine a theoretical scattering spectrum corresponding to the nanostructure to be measured based on the measured morphological parameters, the first calculation module 403 is specifically used to:

[0133] Determining a theoretical scattering spectrum based on the measured morphological parameters and the scattering formula;

[0134] Wherein, the expression of the scattering formula is:

[0135]

[0136] Among them I sim (q, x) is the theoretical scattering spectrum, I0 is the intensity scaling factor, G(q) is the instrument factor, F(q, x) is the shape factor, S(q) is the structure factor, is the roughness factor, I bk is the background scattering intensity, and x is the morphological parameter to be measured.

[0137] As an implementation method, the above evaluation function includes: 2 Evaluation function, log absolute error evaluation function and absolute error evaluation function.

[0138] As an implementation method, with respect to how to determine the initial parameter value corresponding to the measured morphological parameter based on the evaluation function and the non-gradient optimization algorithm, the second calculation module 405 specifically includes: a first determination submodule and a first iterative calculation module;

[0139] A first determination submodule is used to determine a preset parameter initial value and a preset parameter search interval corresponding to the measured morphological parameter;

[0140] The first iterative calculation module is used to use the evaluation function as the optimization target, iterate based on the preset parameter initial value and the preset parameter search interval, and obtain the initial parameter value corresponding to the measured morphological parameter when iterating to the first preset termination condition.

[0141] As an implementation mode, regarding how to use the non-gradient optimization algorithm to iterate, when iterating to the first preset termination condition, an initial parameter value corresponding to the measured morphological parameter is obtained, the first iterative calculation module is specifically used for:

[0142] Determining an initial population from the preset parameter search interval;

[0143] Based on the evaluation function, a non-gradient optimization algorithm is used to iterate the fitness of each individual in the initial population, and a first iteration result is obtained;

[0144] The parameter value corresponding to the first iteration result when the first preset termination condition is reached is used as the initial parameter value corresponding to the morphological parameter to be measured.

[0145] As an implementation method, with respect to how to optimize the initial parameter value based on the evaluation function and the gradient optimization algorithm to obtain the target parameter value corresponding to the measured morphological parameter, the third calculation module 406 specifically includes: a second determination submodule and a second iterative calculation module;

[0146] A second determination submodule is used to determine an optimization interval based on the initial parameter value, where the optimization interval is an upper and lower limit of a parameter value determined based on the initial parameter value;

[0147] The second iterative calculation module is used to use the evaluation function as the optimization target, iterate based on the initial parameter value and the optimization interval, and use the gradient optimization algorithm to obtain the target parameter value corresponding to the measured morphological parameter when iterating to the second preset termination condition.

[0148] As an implementation mode, with respect to how to use the gradient optimization algorithm to iterate, when iterating to the second preset termination condition, a target parameter value corresponding to the measured morphological parameter is obtained, the second iterative calculation module is specifically used for:

[0149] Determining a gradient corresponding to the initial parameter value using a gradient optimization algorithm;

[0150] Iterating along the reverse direction of the gradient and obtaining a second iteration result;

[0151] The parameter value corresponding to the second iteration result when the second preset termination condition is reached is used as the target parameter value corresponding to the morphological parameter to be measured.

[0152] In summary, the present application first obtains the measured scattering spectrum of the nanostructure to be measured, and determines the measured morphology parameters corresponding to the nanostructure to be measured. Then, based on the measured morphology parameters, the theoretical scattering spectrum corresponding to the nanostructure to be measured is determined, and an evaluation function is constructed based on the theoretical scattering spectrum and the measured scattering spectrum. Finally, based on the evaluation function and the non-gradient optimization algorithm, the initial parameter values ​​corresponding to the measured morphology parameters are determined, and the initial parameter values ​​are optimized based on the evaluation function and the gradient optimization algorithm to obtain the target parameter values ​​corresponding to the measured morphology parameters. In this way, in combination with the gradient optimization algorithm and the non-gradient optimization algorithm, the relative position of the parameter solution is first found and then the morphology parameter values ​​of the nanostructure to be measured are precisely solved, thereby improving the accuracy of the morphology parameter calculation.

[0153] In addition, the present application also provides a device for extracting morphological parameters, including: a memory for storing a computer program; and a processor for implementing the steps of the method for extracting morphological parameters as described above when executing the computer program.

[0154] In addition, the present application also provides a readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of the method for extracting morphological parameters as described above are implemented.

[0155] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present application. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for extracting morphological parameters, characterized in that: The method comprises: Obtaining a measured scattering spectrum of the nanostructure to be measured; Determining the morphological parameters to be measured corresponding to the nanostructure to be measured; Based on the measured morphological parameters, determining a theoretical scattering spectrum corresponding to the measured nanostructure; Constructing an evaluation function based on the theoretical scattering spectrum and the measured scattering spectrum; Determine the initial parameter value corresponding to the measured morphological parameter based on the evaluation function and the non-gradient optimization algorithm; The initial parameter value is optimized based on the evaluation function and the gradient optimization algorithm to obtain a target parameter value corresponding to the measured morphological parameter.

2. The method according to claim 1, characterized in that The method further comprises: The uncertainty of the target parameter value is determined based on error propagation theory, and the uncertainty is used to evaluate whether the target parameter value is credible.

3. The method according to claim 1, characterized in that The step of determining the measured morphological parameters corresponding to the measured nanostructure comprises: Determining a parameterized model based on the nanostructure to be measured; Based on the parameterized model, the morphological parameters to be measured corresponding to the nanostructure to be measured are determined.

4. The method according to claim 1, characterized in that The step of determining a theoretical scattering spectrum corresponding to the nanostructure to be measured based on the measured morphological parameters includes: Determining a theoretical scattering spectrum based on the measured morphological parameters and the scattering formula; Wherein, the expression of the scattering formula is: Among them I sim (q, x) is the theoretical scattering spectrum, I0 is the intensity scaling factor, G(q) is the instrument factor, F(q, x) is the shape factor, S(q) is the structure factor, is the roughness factor, I bk is the background scattering intensity, and x is the morphological parameter to be measured.

5. The method according to claim 1, characterized in that The evaluation function includes: 2 Evaluation function, log absolute error evaluation function and absolute error evaluation function.

6. The method according to claim 1, characterized in that Determining the initial parameter value corresponding to the measured morphological parameter based on the evaluation function and the non-gradient optimization algorithm includes: Determine a preset parameter initial value and a preset parameter search interval corresponding to the morphological parameter to be measured; The evaluation function is used as the optimization target, based on the preset parameter initial value and the preset parameter search interval, a non-gradient optimization algorithm is used to iterate, and when it iterates to a first preset termination condition, an initial parameter value corresponding to the measured morphological parameter is obtained.

7. The method according to claim 6, characterized in that The non-gradient optimization algorithm is used to iterate, and when it iterates to a first preset termination condition, an initial parameter value corresponding to the measured morphological parameter is obtained, including: Determining an initial population from the preset parameter search interval; Based on the evaluation function, a non-gradient optimization algorithm is used to iterate the fitness of each individual in the initial population, and a first iteration result is obtained; The parameter value corresponding to the first iteration result when the first preset termination condition is reached is used as the initial parameter value corresponding to the morphological parameter to be measured.

8. The method according to claim 6, characterized in that The step of optimizing the initial parameter value based on the evaluation function and the gradient optimization algorithm to obtain a target parameter value corresponding to the measured morphological parameter includes: Based on the initial parameter value, determining an optimization interval, wherein the optimization interval is an upper and lower limit of the parameter value determined based on the initial parameter value; The evaluation function is used as the optimization target, and based on the initial parameter value and the optimization interval, a gradient optimization algorithm is used to iterate, and when it iterates to a second preset termination condition, a target parameter value corresponding to the measured morphological parameter is obtained.

9. The method according to claim 8, characterized in that The iterating using the gradient optimization algorithm to obtain a target parameter value corresponding to the measured morphological parameter when iterating to the second preset termination condition includes: Determining a gradient corresponding to the initial parameter value using a gradient optimization algorithm; Iterating along the reverse direction of the gradient and obtaining a second iteration result; The parameter value corresponding to the second iteration result when the second preset termination condition is reached is used as the target parameter value corresponding to the morphological parameter to be measured.

10. A device for extracting morphological parameters, characterized in that: include: An acquisition module, used to acquire a measured scattering spectrum of the nanostructure to be measured; A determination module, used to determine the morphological parameters to be measured corresponding to the nanostructure to be measured; A first calculation module is used to determine a theoretical scattering spectrum corresponding to the nanostructure to be measured based on the morphological parameters to be measured; A construction module, used for constructing an evaluation function based on the theoretical scattering spectrum and the measured scattering spectrum; A second calculation module is used to determine the initial parameter value corresponding to the measured morphological parameter based on the evaluation function and the non-gradient optimization algorithm; The third calculation module is used to optimize the initial parameter value based on the evaluation function and the gradient optimization algorithm to obtain the target parameter value corresponding to the measured morphological parameter.

11. A device for extracting morphological parameters, characterized in that: include: Memory for storing computer programs; A processor, configured to implement the steps of the method for extracting morphological parameters as claimed in any one of claims 1 to 9 when executing the computer program.

12. A readable storage medium, characterized in that: The readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the method for extracting morphological parameters as claimed in any one of claims 1 to 9 are implemented.

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