Microwave electromagnetic pole ultraviolet topography inversion method, device and electronic equipment

Abstract

The application belongs to the technical field of semiconductor manufacturing, extreme ultraviolet scatterometry and nanostructure topography parameter measurement, and specifically discloses a differentiable electromagnetic extreme ultraviolet topography inversion method, device and electronic equipment, which comprises the following steps: obtaining initial estimation of a nanostructure topography parameter to be measured by initializing a model in advance according to physical conditions; calling a differentiable electromagnetic forward model to obtain a theoretical diffraction response by taking the initial estimation of the topography parameter as an initial point; constructing an inversion objective function based on the difference between the theoretical diffraction response and a measured diffraction response, and obtaining an analytical gradient of the inversion objective function with respect to the topography parameter along a differentiable computational graph corresponding to the differentiable electromagnetic forward model; and iteratively refining the topography parameter based on the analytical gradient and outputting a physically consistent topography parameter inversion result. The application combines the global positioning capability of deep learning with the physical consistency of a strict electromagnetic forward model, so that the inversion accuracy, system deviation, stability and calculation efficiency are considered.

Description

Technical Field

[0001] This application belongs to the fields of semiconductor manufacturing, extreme ultraviolet scattering metrology, and nanostructure morphology parameter measurement technology. More specifically, it relates to a method, apparatus, and electronic device for microscopic electromagnetic extreme ultraviolet morphology inversion. Background Technology

[0002] As integrated circuit manufacturing processes continue to advance towards advanced nodes, device feature sizes are shrinking and structural morphologies are becoming increasingly complex. Even minute deviations in critical dimensions, structural height, sidewall corners, left and right sidewall corners, fillets, trench depth, film thickness, and asymmetric morphology parameters can affect device electrical performance, process windows, and product yield. Therefore, developing rapid, accurate, non-destructive, and in-line integration-suitable nanostructure morphology parameter measurement techniques is a crucial aspect of advanced semiconductor manufacturing process control.

[0003] Optical scattering metrology, with its advantages of being non-contact, non-destructive, and high-throughput, has been widely applied in semiconductor critical dimension measurement and process monitoring. Its basic principle is to measure the far-field scattering or diffraction signals generated by the nanostructure under test under specific illumination conditions, and then extract structural morphology parameters by combining electromagnetic forward models and parameter inversion algorithms. As the size of the structure under test further decreases, visible light scattering metrology and deep ultraviolet scattering metrology are limited by the operating wavelength and higher-order diffraction information, gradually reducing their sensitivity to nanoscale morphology perturbations. Furthermore, in complex three-dimensional structures, parameter coupling, multiple inversion solutions, and non-convex optimization issues easily arise. Extreme ultraviolet scattering metrology, utilizing a shorter operating wavelength and richer higher-order diffraction responses, provides a new technical approach for high-precision metrology of advanced node nanostructures.

[0004] The inversion of morphological parameters in extreme ultraviolet (EUV) scatterometrics still faces significant challenges. On one hand, there are often strong coupling relationships between critical dimensions, structural height, sidewall angles, and asymmetric morphological parameters of the measured structure. Different combinations of morphological parameters may produce similar diffraction intensity distributions, making the inversion problem significantly ill-conditioned and prone to multiple solutions. On the other hand, EUV light sources have limited flux, low optical system transmission efficiency, and strong absorption by samples and materials, limiting the number of effective photons received by the detector. Actual measurement signals often contain interference such as photon shot noise, dark current noise, readout noise, background noise, and light source intensity fluctuations. These noises and disturbances further exacerbate the instability of the inversion.

[0005] In extreme ultraviolet (EUV) scattering metrology, the dependence of electromagnetic response on structural parameters is highly nonlinear, and the inversion objective function often exhibits non-convex, multi-valley, and locally flat characteristics. When the initial parameters deviate significantly from the actual structure, local optimization algorithms are prone to converge to erroneous solutions. Furthermore, when using derivative-free global optimization methods such as genetic algorithms and particle swarm optimization, a large amount of forward electromagnetic computation is required, placing high demands on the computational efficiency of online metrology. Therefore, for the nonlinear, multi-parameter, and strongly coupled topographic parameter inversion scenarios in EUV scattering metrology, how to combine the global localization capabilities of deep learning with the physical consistency of a rigorous electromagnetic forward model, thereby balancing inversion accuracy, system bias, stability, and computational efficiency, is a pressing technical problem to be solved in this field. Summary of the Invention

[0006] To address the shortcomings of existing technologies, the purpose of this application is to combine the global localization capabilities of deep learning with the physical consistency of a rigorous electromagnetic forward model, thereby balancing inversion accuracy, system bias, stability, and computational efficiency.

[0007] To achieve the above objectives, in a first aspect, this application provides a method for microscopic electromagnetic extreme ultraviolet morphology inversion, comprising: The intensity-normalized multi-channel extreme ultraviolet diffraction measurement data are input into the physical prior depth initialization model to obtain the initial estimate of the morphology parameters of the nanostructure to be measured. Starting with the initial estimation of morphological parameters, based on the morphological parameters of the nanostructure to be measured and the measurement configuration, a differentiable electromagnetic forward model is invoked to obtain the theoretical diffraction response; Based on the difference between the theoretical diffraction response and the measured diffraction response, an inversion objective function is constructed, and the analytical gradient of the inversion objective function with respect to the topographic parameters is obtained by automatic differentiation, adjoint differentiation or analytical differentiation along the differentiable computation graph corresponding to the differentiable electromagnetic forward model. Based on analytical gradient, a gradient optimization algorithm is used to iteratively refine the topography parameters until a preset stopping condition is met, and outputs physically consistent topography parameter inversion results.

[0008] It is understandable that the differentiable electromagnetic extreme ultraviolet morphology inversion method provided in this application divides the inversion process into two interconnected stages: physical prior depth initialization and differentiable electromagnetic model constraint refinement, in order to achieve a combination of deep learning global localization capability and strict electromagnetic forward model physical consistency.

[0009] In the initialization phase, intensity-normalized multi-channel extreme ultraviolet diffraction measurement data are input into the physical prior depth initialization model. This intensity normalization process makes the input data approximately insensitive to overall scale factors such as light source power drift, exposure time fluctuation, and detector gain variation. Based on this, the initialization model extracts the relative spatial frequency features and diffraction order distribution features related to the morphology of the nanostructure under test, and outputs an initial estimate of the morphology parameters that is close to the real physical state. In this way, the global localization capability of the deep learning model is used to make the initial point fall into the convergence region near the real parameters, while avoiding the systematic bias caused by the pure data-driven method directly outputting the final measurement results.

[0010] In the refinement stage, starting from the initial estimate, a differentiable electromagnetic forward model is invoked based on the morphology parameters of the nanostructure to be measured and the measurement configuration to obtain the theoretical diffraction response. This forward model constructs differentiable operations for physical processes such as structural parameterization, dielectric constant distribution construction, Fourier expansion, eigenmode solving, interlayer field propagation, far-field diffraction transformation, tilt projection, detector sampling, and intensity normalization, forming a complete differentiable computational graph. After constructing the inversion objective function based on the difference between the theoretical and measured diffraction responses, the analytical gradient of the inversion objective function with respect to the morphology parameters is obtained along the differentiable computational graph through automatic differentiation, adjoint differentiation, or analytical differentiation, thereby avoiding the perturbation step size and the truncation error and step size sensitivity problems that finite difference differentiation relies on. Furthermore, based on this physically consistent analytical gradient, a gradient optimization algorithm is used to iteratively refine the morphology parameters until a preset stopping condition is met, outputting a physically consistent morphology parameter inversion result.

[0011] Therefore, this application provides global localization capability by initializing the model, reducing dependence on artificial initial values ​​and avoiding local optima traps; it replaces the finite difference gradient with the analytical gradient of the differentiable electromagnetic forward model, reducing the number of forward model calls and eliminating step size dependence, ultimately balancing inversion accuracy, system bias, stability and computational efficiency.

[0012] In one possible implementation, the physical prior deep initialization model is obtained by introducing dynamic noise enhancement training; Dynamic noise enhancement involves generating diffraction data corresponding to different structural parameters using a differentiable electromagnetic forward model, and randomly adding one or more of the following: photon shot noise, dark current noise, readout noise, background noise, gain fluctuation, and exposure perturbation. It also involves randomly setting different photon counts, full-well capacity, exposure time, or noise intensity for different training batches.

[0013] In one possible implementation, a differentiable electromagnetic forward model is invoked to obtain the theoretical diffraction response, including: The structure under test is discretized into multiple sub-layers along the height direction, and the dielectric constant of each sub-layer is Fourier expanded along the periodic direction to obtain the Toplitz dielectric constant matrix of each sub-layer. Based on the expression of Maxwell's equations in Fourier space, the characteristic modes and propagation constants of each sublayer are solved, and the scattering matrix, transmission matrix or enhanced transmission matrix is ​​used to complete the interlayer electromagnetic field continuity matching and field propagation to obtain the near-field electromagnetic field. Based on the near-field electromagnetic field, far-field propagation, tilt projection, detector sampling, and intensity normalization are performed to obtain the theoretical diffraction response. Among them, structural parameterization, dielectric constant distribution construction, Fourier expansion, characteristic mode solution, interlayer field propagation, far-field transformation, tilt projection, detector sampling and intensity normalization are all constructed into differentiable operations.

[0014] In one possible implementation, the inversion objective function is constructed by obtaining it based on the following formula: ; in, Represent the inversion objective function; A vector representing the morphological parameters of the nanostructure to be measured; Indicates the number of measurement channels; Indicates the first Theoretical diffraction response under each measurement channel; Indicates the first Measured diffraction response under each measurement channel; Indicates the first Noise weighting matrix for each measurement channel; Indicates the measurement configuration; Represents physical prior constraints; This represents the weight of the physical prior constraint term.

[0015] In one possible implementation, the noise weight matrix is ​​taken as the reciprocal of the total noise variance for each pixel or diffraction order, and the total noise variance is obtained based on the following formula: ; in, Indicates the first The first channel The total noise variance of each pixel or diffraction order; This represents the variance of photon shot noise; Indicates the variance of dark current noise; Indicates the readout noise variance; This represents the variance of the background noise.

[0016] In one possible implementation, the analytical gradient of the inverted objective function with respect to the topographic parameters is obtained by backpropagating the gradient along a differentiable electromagnetic computation graph using inverse automatic differentiation, and obtaining the analytical gradient based on the following formula: ; in, This represents the gradient of the inversion objective function with respect to the topographic parameters; Indicates the first Jacobian matrix of theoretical diffraction response with respect to topographic parameters under each measurement channel; This represents the gradient of the physical prior constraint term with respect to the topographic parameters.

[0017] In one possible implementation, the topography parameters are iteratively refined using a gradient optimization algorithm based on analytical gradients, including obtaining the iteratively updated topography parameters based on the following formula: ; in, Indicates the first The morphological parameters of the next iteration; Indicates the first The morphological parameters of the next iteration; This represents the gradient optimization operator.

[0018] In one possible implementation, the preset stopping conditions include the loss function change being less than the corresponding threshold, the parameter change being less than the corresponding threshold, the gradient norm being less than the corresponding threshold, and the number of iterations reaching the maximum number of iterations; when any of the stopping conditions is met, the iterative refinement is terminated.

[0019] Secondly, this application provides a micro-electromagnetic extreme ultraviolet morphology inversion device, comprising: The initialization module is used to input the intensity-normalized multi-channel extreme ultraviolet diffraction measurement data into the physical prior depth initialization model to obtain the initial estimate of the morphology parameters of the nanostructure to be measured. The forward calculation module is used to obtain the theoretical diffraction response by calling a differentiable electromagnetic forward model based on the initial estimate of the morphology parameters and the morphology parameters and measurement configuration of the nanostructure to be measured, starting from the initial estimate of the morphology parameters. The gradient calculation module is used to construct the inversion objective function based on the difference between the theoretical diffraction response and the measured diffraction response, and obtain the analytical gradient of the inversion objective function with respect to the topographic parameters by automatic differentiation, adjoint differentiation or analytical differentiation along the differentiable computation graph corresponding to the differentiable electromagnetic forward model. The refinement output module is used to iteratively refine the topography parameters based on analytical gradients using gradient optimization algorithms until a preset stopping condition is met, and outputs physically consistent topography parameter inversion results.

[0020] Thirdly, this application provides an electronic device, including: a memory and one or more processors; The memory is coupled to one or more processors and is used to store computer program code, which includes computer instructions. One or more processors invoke computer instructions to cause an electronic device to perform the method described in the first aspect or any possible implementation thereof.

[0021] Overall, the technical solutions conceived in this application have the following beneficial effects compared with the prior art.

[0022] (1) This application can combine the global localization capability of deep learning with the physical consistency of a strict electromagnetic model, so that the initialization model is only used to provide a global initial point close to the real physical state, rather than directly used as the final measurement result, and the forward model is used to provide a physically consistent analytical gradient for closed-loop refinement, thereby reducing the system bias of data-driven inversion.

[0023] (2) This application introduces intensity normalization at the input end and dynamic noise enhancement during training, so that the input features of the initialization model are insensitive to light source power drift, exposure time fluctuation and detector gain change, and the initialization model outputs stable initial values ​​of morphology parameters under different photon numbers and detector noise conditions, thereby improving the robustness of the initialization model under actual measurement conditions.

[0024] (3) This application constructs a differentiable computational graph by constructing physical processes such as structural parameterization, dielectric constant distribution construction, Fourier expansion, characteristic mode solution, interlayer field propagation, far-field diffraction transformation, tilt projection and intensity normalization. It can obtain the analytical gradient of the diffraction response with respect to the morphological parameters through automatic differentiation, adjoint differentiation or analytical differentiation, avoid the step size dependence and truncation error of finite difference differentiation, and reduce the dependence of traditional physical optimization on artificial initial values ​​and finite difference gradients. Attached Figure Description

[0025] Figure 1 This is a schematic flowchart of the method for microscopic electromagnetic extreme ultraviolet morphology inversion provided in the embodiments of this application; Figure 2 This is a schematic diagram showing the comparison of computation time for different morphological parameter inversion methods provided in the embodiments of this application; Figure 3 This is a schematic diagram showing the comparison of the systematic bias and three-times-standard-deviation accuracy of different morphological parameter inversion methods provided in the embodiments of this application; Figure 4 This is a schematic diagram of the topography parameter inversion results under different multi-channel data input formats provided in the embodiments of this application; Figure 5This is a schematic diagram of the micro-electromagnetic extreme ultraviolet morphology inversion device provided in the embodiments of this application; Figure 6 This is a schematic diagram of the structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0026] To facilitate a clearer understanding of the various embodiments of this application, some relevant background knowledge will be introduced as follows.

[0027] (I) Common methods for inverting topographic parameters and their limitations.

[0028] Topography parameter inversion methods can be broadly classified into two categories: purely data-driven methods and physical optimization methods based on electromagnetic models. Purely data-driven methods typically utilize neural networks to directly establish the mapping relationship between diffraction images and topography parameters, resulting in relatively fast inference speeds. However, their outputs are easily affected by factors such as training sample distribution, light source power drift, exposure time variations, and detector gain changes, and they lack strict electromagnetic physical consistency constraints, which may lead to uncontrollable system biases.

[0029] Physical optimization methods based on electromagnetic models (hereinafter referred to as physical optimization methods) typically use rigorous coupled-wave analysis, the finite element method, the finite-difference time-domain method, or other Maxwell equation solution methods as forward models. They invert structural parameters by minimizing the error between the measured diffraction response and the theoretical diffraction response. These methods have strong physical interpretability; however, their optimization process usually relies on artificial initial values, global search, or finite-difference gradients, resulting in drawbacks such as high computational cost, slow convergence speed, susceptibility to local minima, and sensitivity to finite-difference step size.

[0030] In extreme ultraviolet (EUV) scattering metrology scenarios, the shortcomings of the aforementioned two types of methods are further amplified. For purely data-driven methods, due to the strong intensity scale perturbations and noise perturbations in EUV measurement data, the morphological parameters output by the model will drift with the measurement conditions, making them unreliable final measurement results. For physical optimization methods, because the inversion objective function exhibits obvious non-convex and multi-valley characteristics, optimization is prone to falling into erroneous convergence basins when the artificial initial values ​​deviate significantly from the real structure. Furthermore, finite difference gradients introduce error sources such as truncation errors, rounding errors, and step size sensitivity. In analyzing the above shortcomings, the inventors of this application noted that relying solely on purely data-driven methods or solely on physical optimization methods is insufficient to simultaneously meet the requirements of EUV scattering metrology for high precision, low system bias, high stability, and high efficiency. This constitutes the starting point of the technical solution of this application.

[0031] (ii) Key technology concepts.

[0032] Intensity scale normalization (hereinafter referred to as intensity normalization) refers to the process of removing the mean, dividing by the standard deviation, and applying an affine transformation to the input diffraction measurement data. This is used to suppress the influence of light source power drift, exposure time fluctuation, detector gain change, and overall system intensity scaling on subsequent processing, so that the processing result is approximately insensitive to the overall scale factor of the input data.

[0033] A differentiable electromagnetic forward model (hereinafter referred to as the forward model) is an electromagnetic model that constructs a differentiable computational graph from the physical processes of nanostructure parameterization, dielectric constant distribution construction, Fourier expansion, characteristic mode solution, interlayer field propagation, far-field diffraction transformation, tilt projection, detector sampling, and intensity normalization. Since each step in this computational graph is differentiable, the derivative of the theoretical diffraction response with respect to the morphology parameters can be obtained through automatic differentiation, adjoint differentiation, or analytical differentiation, thereby avoiding the perturbation step size and the truncation error that finite difference differentiation depends on.

[0034] The physical prior deep initialization model (hereinafter referred to as the initialization model) is a deep learning model that introduces intensity normalization at the input and dynamic noise enhancement during training. The output of the initialization model is constrained to provide only a global initial point that approximates the real physical state, rather than being used directly as the final measurement result. This avoids the systematic bias caused by directly outputting measurement results in pure data-driven methods while utilizing the global localization capabilities of deep learning.

[0035] It is understandable that the Jacobian matrix of the theoretical diffraction response output by the forward model with respect to the topography parameters characterizes the sensitivity of the diffraction response to changes in the topography parameters. When this Jacobian matrix can be obtained analytically, it can provide a physically consistent and step-size-independent descent direction for subsequent gradient optimization. This is the technical basis for the initialization model and the forward model to form a closed-loop refinement.

[0036] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0037] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0038] In the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more, for example, multiple processing units means two or more processing units, multiple elements means two or more elements, etc.

[0039] The embodiments of this application are described below with reference to the accompanying drawings.

[0040] Example 1: Morphological parameter inversion method.

[0041] Example 1 provides a method for inverting morphological parameters in extreme ultraviolet (EUV) scatterometrics based on a differentiable electromagnetic model and physical prior deep initialization (hereinafter referred to as a differentiable electromagnetic EUV morphological inversion method). Example 1 addresses the nonlinear, multi-parameter, and strongly coupled morphological inversion scenarios in EUV scatterometrics. The inversion process is divided into two interconnected stages: physical prior deep initialization and differentiable electromagnetic model constraint refinement. In the first stage, the initial model is used to quickly predict the initial estimates of the morphological parameters (measured structure parameters) of the nanostructure under test based on multi-channel EUV diffraction measurement data. In the second stage, starting from this initial estimate, the forward model is invoked to calculate the theoretical diffraction response. The gradient of the inversion objective function with respect to the morphological parameters is obtained through automatic differentiation, adjoint differentiation, or analytical differentiation. Then, a gradient optimization algorithm is used to iteratively refine the morphological parameters, ultimately outputting physically consistent morphological parameter inversion results.

[0042] like Figure 1 As shown, the method in Example 1 includes steps such as parameterized modeling of the structure under test, acquisition of extreme ultraviolet diffraction measurement data, intensity normalization, physical prior depth initialization, differentiable electromagnetic forward modeling, construction of physical constraint objective function, gradient-driven parameter refinement, and output of morphological parameters. The output of the previous step serves as the input of the next step, and the steps are interconnected to form a complete inversion process.

[0043] Step 1: Establish a parameterized morphology model of the nanostructure to be tested.

[0044] First, a parameterized morphology model of the nanostructure to be tested is established, and the morphology parameter vector to be inverted is defined: ; Parameter explanation: : Represents the morphological parameter vector of the nanostructure to be tested; : indicates the first One topographic parameter to be inverted; : Indicates the number of topographic parameters to be inverted.

[0045] Example 1 applies to periodic nanostructures in extreme ultraviolet scattering metrology, including one-dimensional periodic gratings, two-dimensional periodic structures, symmetric trapezoidal gratings, asymmetric trapezoidal gratings, multilayer periodic structures, and other nanostructures that can be described by a parameterized model. The morphological parameters to be inverted include one or more of the following: top critical dimension, bottom critical dimension, structure height, sidewall corners, left sidewall corner, right sidewall corner, fillet radius, trench depth, film thickness, edge roughness characterization parameters, or material optical constant correction parameters.

[0046] In one implementation, the nanostructure to be tested is a one-dimensional asymmetric trapezoidal grating, whose morphological parameter vector is represented as follows: ; Parameter explanation: : Represents a vector of topographic parameters; : Indicates the top key dimension; : Indicates the structural height; : Indicates the left corner; : Indicates the right corner of the wall.

[0047] In another implementation, when the nanostructure under test is approximately bilaterally symmetrical, the left and right sidewall corners can be combined into an average sidewall corner. The topographic parameter vector is represented as: ; Parameter explanation: : Represents a vector of topographic parameters; : Indicates the top key dimension; : Indicates the structural height; : Indicates the average sidewall angle.

[0048] Step 2: Collect far-field diffraction intensity data of the nanostructure to be tested.

[0049] In a given measurement configuration Below, far-field diffraction intensity data of the nanostructure under test were acquired using an extreme ultraviolet scattering metrology system. Measurement configuration. This includes one or more of the following: incident wavelength, incident angle, azimuth angle set, polarization state, diffraction order acquisition range, exposure time, detector distance, detector pixel size, and detector gain.

[0050] In one implementation, extreme ultraviolet incident light irradiates the periodic nanostructure in a grazing incidence manner, and a detector acquires discrete diffraction order intensities or two-dimensional diffraction intensity images at different azimuth angles. Measurement data corresponding to multiple azimuth angles, multiple diffraction orders, multiple polarization states, or multiple detection regions collectively constitute a multi-channel diffraction measurement tensor. ; Parameter explanation: : Represents the multichannel diffraction measurement tensor; : indicates the first Diffraction intensity data for each measurement channel; : Indicates the number of measurement channels.

[0051] The measurement channel can correspond to different azimuth angles, different diffraction orders, different detector regions, different polarization states, or combinations thereof.

[0052] Step 3: Normalize the intensity of the diffraction measurement data.

[0053] To reduce the impact of light source power drift, exposure time variations, detector gain fluctuations, and overall system intensity scaling on the inversion results, intensity normalization is applied to the diffraction measurement data at the input of the initialization model. For any input channel... The intensity normalization is expressed as: ; Parameter explanation: : Indicates the input channel Output after intensity normalization; : Represents the input channel to be normalized; : Indicates the input channel The mean; : Indicates the input channel The variance; : Represents the stability constant to prevent division by zero; : Indicates learnable or preset affine scaling parameters; : Indicates a learnable or preset affine bias parameter.

[0054] When the input diffraction intensity is affected by the global scale factor When the influence occurs, the input before intensity normalization becomes Since the mean and variance satisfy: ; ; Parameter explanation: : Represents the overall scale factor acting on the input diffraction intensity; : Indicates the mean value of the input channel after applying the scaling factor; : Represents the variance of the input channel after the scaling factor is applied.

[0055] Therefore: .

[0056] Therefore, the subsequent initialization model mainly extracts the relative spatial frequency features, diffraction order distribution features, and multi-channel response difference features related to the morphology of the structure under test, rather than the absolute intensity features that are sensitive to changes in overall light intensity.

[0057] In one implementation, intensity normalization is instance normalization. Other implementations may employ channel normalization, intra-sample normalization, total intensity normalization, logarithmic intensity normalization, or a combination thereof. For measurement data with detector bias, dark background, or local anomalous pixels, background subtraction, bad pixel correction, intensity clipping, dynamic range compression, or noise filtering can be performed before intensity normalization.

[0058] Step 4: Initialize the topographic parameters from the initialization model.

[0059] The intensity-normalized multichannel diffraction measurement tensor is input into the initialization model to obtain initial estimates of the morphology parameters of the nanostructure to be measured: ; Parameter explanation: : Indicates the initial estimate of topographic parameters; : Represents the physical prior depth initialization model; : Indicates the model parameters for initializing the model; : Represents the intensity-normalized diffraction measurement tensor; : Indicates the measurement configuration code.

[0060] Measurement configuration code It includes one or more of the following: normalized incident wavelength, normalized incident angle, azimuth encoding, polarization state encoding, diffraction order marking, exposure time encoding, detector parameter encoding, and effective measurement channel marking.

[0061] In one implementation, the initialization model uses a residual neural network. Its input is a multi-channel tensor formed by stacking multi-azimuth diffraction images. An intensity normalization layer is set at the network front end, followed by convolutional layers, residual modules, global average pooling layers, and fully connected layers to output initial values ​​for the topographic parameters. In other implementations, the initialization model can also use convolutional neural networks, Transformer networks, multilayer perceptrons, graph neural networks, hybrid convolutional attention networks, lookup table regression models, or combinations thereof.

[0062] To improve the robustness of the initialization model under actual low photon count and detector noise conditions, dynamic noise enhancement is introduced during training. Specifically, the forward model generates ideal diffraction data corresponding to different structural parameters, and photon shot noise, dark current noise, readout noise, background noise, gain fluctuations, or exposure perturbations are randomly added. For each training batch, different photon counts, full-well capacity, exposure times, or noise intensities are randomly set, enabling the initialization model to learn to extract stable morphological features from the diffraction distribution under different signal-to-noise ratio conditions.

[0063] It should be noted that the output of the initialization model is not used as the final topographic measurement result, but only as the initial point for subsequent refinement of the physical constraints of the differentiable electromagnetic model. This setting leverages the global localization capability of the deep learning model to ensure the initial point falls within the convergence region near the true parameters, while avoiding the systematic biases introduced by purely data-driven methods that directly output the final measurement result.

[0064] Step 5: Establish a differentiable electromagnetic forward model and calculate the theoretical diffraction response.

[0065] Based on the structural parameters under test and measurement configuration Establish a differentiable electromagnetic forward model for extreme ultraviolet scattering metrology: ; Parameter explanation: : Indicates the current structure parameters The predicted theoretical diffraction response; : Represents a differentiable electromagnetic forward model; : Indicates the structural parameters to be measured; : Indicates the measurement configuration.

[0066] In one implementation, the forward model is a differentiable, rigorously coupled-wave analysis model. For trapezoidal or non-rectangular structures, the structure is first discretized along the height direction. Sub-layers (structural parameterization): ; Parameter explanation: : Indicates the composition of topographic parameters The spatial dielectric constant distribution is determined; : indicates the first Dielectric constant distribution within each sublayer; : Indicates the number of sub-layers obtained by discretization along the height direction.

[0067] Fourier expansion of the dielectric constant of each sublayer along the periodic direction: ; Parameter explanation: : indicates the first The first sub-layer Fourier coefficients; : Indicates the order index of the Fourier expansion; : Indicates the truncation diffraction order; : Represents the imaginary unit; : Indicates the structural period.

[0068] Construct the dielectric constant matrix in Toeplitz form based on the Fourier coefficients: ; Parameter explanation: : indicates the first The Toplitz dielectric constant matrix of each sublayer; : indicates that by the first The matrix elements are composed of Fourier coefficients of order 1; : Represents the row index of the matrix; : Represents the column index of the matrix.

[0069] Based on the expression of Maxwell's equations in Fourier space, the characteristic modulus and propagation constant within each layer are solved: ; Parameter explanation: : indicates the first The electromagnetic eigenvalue matrix corresponding to the layer; : indicates the first The first layer One eigenvalue; : indicates the first The eigenvectors corresponding to each eigenvalue; : Indicates the index of the intrinsic modulus.

[0070] Then, using the scattering matrix, transmission matrix, or enhanced transmission matrix methods, the interlayer electromagnetic field continuity matching and field propagation calculations are performed to obtain the electromagnetic field at the exit surface or near-surface of the structure: ; Parameter explanation: : Represents the electromagnetic field at the exit surface or near-surface of the structure; : Represents the interlayer field propagation and boundary continuity matching operator.

[0071] Finally, the near-field distribution is propagated to the far-field observation plane, and the theoretical diffraction intensity is obtained by combining tilt projection, detector sampling, and intensity normalization: ; ; Parameter explanation: : Represents the electromagnetic field at the far-field observation plane; : Represents the far-field propagation or Fourier transform operator; : Indicates theoretical diffraction intensity; : Represents the tilt projection operator; : Represents the detector sampling and intensity normalization operator.

[0072] In the forward model, structural parameterization, dielectric constant distribution construction, Fourier expansion, eigenmode solving, interlayer field propagation, far-field transformation, tilt projection, detector sampling, and intensity normalization are all constructed as differentiable operations, allowing the derivative of the theoretical diffraction response with respect to the topographic parameters to be obtained through automatic differentiation, adjoint differentiation, or analytical differentiation. ; Parameter explanation: : Represents the Jacobian matrix of the theoretical diffraction response with respect to the topography parameters.

[0073] In other implementations, the forward model can also employ differentiable finite element method, differentiable finite difference time-domain method, differentiable boundary element method, differentiable integral equation method, differentiable multilayer thin film model, differentiable surrogate electromagnetic model, or a combination thereof.

[0074] Step 6: Construct the multi-channel joint inversion objective function.

[0075] Based on the difference between the measured diffraction response and the theoretical diffraction response, a multi-channel joint inversion objective function is constructed: ; Parameter explanation: : Represents the inversion objective function; : indicates the first Theoretical diffraction response under each measurement channel; : indicates the first Measured diffraction response under each measurement channel; : indicates the first The noise weight matrix or inverse noise covariance matrix of each measurement channel; : Represents a priori physical constraints; : Represents the weight of the physical prior constraint term.

[0076] Noise weight matrix Determined based on the detector noise model. In one implementation, the first... The first channel The noise variance of a pixel or diffraction order can be expressed as: ; Parameter explanation: : indicates the first The first channel The total noise variance of each pixel or diffraction order; : Represents the variance of photon shot noise; : Represents the variance of dark current noise; : Indicates the variance of readout noise; : Represents the variance of background noise.

[0077] Correspondingly, the noise weight matrix can be expressed as: ; Parameter explanation: : indicates the first Noise weighting matrix for each measurement channel; : indicates the first The number of pixels or diffraction orders involved in the inversion in each measurement channel.

[0078] Physical prior constraints This is used to constrain structural parameters to be within the allowable range of the process, or to constrain structural height, linewidth, sidewall angle, film thickness, and material parameters to meet preset physical boundaries. In one implementation, the physical feasible space of the topographic parameters is represented as: ; Parameter explanation: : Represents the physical feasible space of topographic parameters; : indicates the first The lower limit of each morphological parameter; : indicates the first The upper limit of each morphological parameter.

[0079] During optimization, parameters can be kept within the physically feasible space through boundary projection, variable transformation, or penalty terms.

[0080] Step 7: Iteratively refine the morphology parameters based on gradients.

[0081] Initial estimation of topography parameters obtained in step four Starting from a point, the gradient of the objective function with respect to the topography parameters is calculated using the forward model: ; Parameter explanation: : Represents the gradient of the inversion objective function with respect to the topographic parameters.

[0082] According to the chain rule, the gradient of the inverted objective function can be further expressed as: ; Parameter explanation: : indicates the first Jacobian matrix of theoretical diffraction response with respect to topographic parameters under each measurement channel; : Represents the gradient of the physical prior constraint term with respect to the topographic parameters.

[0083] Among them, the The Jacobian matrix for each measurement channel is: .

[0084] In one implementation, the analytical gradient of the diffraction error with respect to the structural parameters is obtained by backpropagating the gradient along the differentiable electromagnetic computation diagram using reverse automatic differentiation. This gradient calculation process does not require setting a finite difference perturbation step size for each parameter, thus avoiding the truncation error, rounding error, and step size sensitivity issues caused by finite difference differentiation.

[0085] Subsequently, a gradient optimization algorithm was used to iteratively update the morphology parameters: ; Parameter explanation: : indicates the first The structural parameters for the next iteration; : Represents the gradient optimization operator.

[0086] In one implementation, the gradient optimization algorithm uses the L-BFGS algorithm, and its update direction can be expressed as: ; ; Parameter explanation: : Represents the inverse Hessian matrix obtained by approximation using finite historical gradient information; : indicates the first The search direction for the next iteration; : indicates the first The step size of the next iteration; : Represents the direction to the physical feasible space The projection operator.

[0087] Other implementations may include quasi-Newton methods, Gauss-Newton methods, Levenberg-Marquardt methods, gradient descent methods, Adam optimization algorithms, trust region methods, or combinations thereof.

[0088] During the iteration process, the stopping condition is determined based on the change in the loss function, the change in parameters, the gradient norm, the maximum number of iterations, or physical boundary constraints. The stopping condition can be expressed as: ; ; ; ; Parameter explanation: : Indicates the threshold for the change in the loss function; : Indicates the threshold for parameter variation; : Indicates the gradient norm threshold; : Indicates the maximum number of iterations.

[0089] The optimization will terminate when any of the above-mentioned preset stop conditions are met.

[0090] Step 8: Output the topography parameter inversion results and reliability evaluation indicators.

[0091] After terminating the optimization, the converged parameters are used as the final morphology parameter estimation results: ; Parameter explanation: : Represents the final topographic parameter estimation result vector; : indicates the first Estimates of the topographic parameters.

[0092] In one implementation, when the parameter vector is The final output result is: ; Parameter explanation: : Indicates the estimated value of the critical dimension; : Represents the estimated height of the structure; : Indicates the estimated value of the left side wall corner; : Indicates the estimated value of the right side wall angle.

[0093] In addition to outputting the morphology parameter estimation results, it can also output one or more reliability evaluation indicators among the following: inversion residual, number of convergence iterations, final loss function value, gradient norm, whether the parameters have reached the boundary, noise-weighted residual distribution, and confidence interval.

[0094] In one implementation, a set of multiple inversion results is obtained by repeatedly sampling the measurement noise or performing Monte Carlo verification: ; Parameter explanation: : Represents the set of results from multiple inversions; : indicates the first Morphological parameter inversion results under secondary noise test; : indicates the number of Monte Carlo repetitions.

[0095] For the The systematic deviation of each structural parameter can be expressed as: ; Parameter explanation: : indicates the first Systematic deviations of each structural parameter; : indicates the first The noise test under the first Estimates of the structural parameters; : indicates the first The true values ​​of each structural parameter.

[0096] Its standard deviation can be expressed as: ; Parameter explanation: : indicates the first The standard deviation of the estimated values ​​of each structural parameter under multiple noise tests; : indicates the first The average estimated values ​​of the structural parameters under multiple noise tests.

[0097] The average estimate can be expressed as: .

[0098] Its three-times-standard-deviation precision can be expressed as: ; Parameter explanation: : indicates the first The accuracy of each structural parameter is three times the standard deviation.

[0099] The above reliability evaluation indicators do not change the core inversion process of Example 1, but are only used to characterize the stability and reliability of the output morphology parameters.

[0100] Example 2: Demonstration Case.

[0101] Example 2 uses a one-dimensional asymmetric trapezoidal gold grating as the nanostructure to be tested, with silicon dioxide as the substrate material. The main morphological parameters to be inverted include the critical top dimension, structural height, left side corner, and right side corner, denoted as [reference needed]. , , and In approximately symmetrical analysis, the left and right side wall angles can be combined into an average side wall angle. .

[0102] In Example 2, the grating period is set to 60 nanometers ( The nominal structure parameters are set as follows: ; Parameter explanation: : Represents the nominal structure parameter vector.

[0103] The actual structural parameters for blind testing are set as follows: ; Parameter explanation: : Represents the true structure parameter vector in blind testing.

[0104] The measurement method employed was grazing-incidence extreme ultraviolet cone scattering, with an incident wavelength of 13.5 nm and an incident angle of 70°. The azimuth set is as follows: ; Parameter explanation: : indicates the set of azimuth angles used in Example 2.

[0105] Far-field diffraction intensity data obtained at six azimuth angles were used as multi-channel inputs. First, intensity normalization was performed, and then the data was input into the initialization model to obtain initial estimates of the topographic parameters. Subsequently, using these initial estimates as a starting point, a differentiable strictly coupled-wave analysis model was invoked to calculate the theoretical diffraction response. The gradient of the objective function with respect to the topographic parameters was obtained through automatic differentiation. The L-BFGS algorithm was then used for physical constraint refinement, and finally, the estimated topographic parameters of the structure under test were output.

[0106] To verify the effectiveness of the method in Example 1, it was compared with pure deep learning inversion methods, traditional finite difference Levenberg-Marquardt inversion methods, and genetic algorithm inversion methods. The pure deep learning method directly outputs topographic parameters from the neural network; the traditional finite difference Levenberg-Marquardt method uses finite differences to estimate the Jacobian matrix and performs local optimization; the genetic algorithm uses a derivative-free global search to obtain topographic parameter estimates; and Example 1 uses model initialization to obtain initial values ​​and refines physical constraints using the analytical gradient of the forward model.

[0107] like Figure 2As shown, under different signal-to-noise ratio conditions, the average inversion time of the method in Example 1 (corresponding to the Hybrid curve in the figure) is lower than that of the traditional finite-difference Levenberg-Marquardt method (corresponding to the LM curve in the figure) and the genetic algorithm method (corresponding to the GA curve in the figure). Compared with the Levenberg-Marquardt method, the method in Example 1 achieves approximately 1.5 times the computational speedup; compared with the genetic algorithm, the method in Example 1 achieves approximately 2.6 times the computational speedup. This indicates that the method in Example 1 can reduce computational costs while maintaining the ability to perform physically constrained inversions.

[0108] like Figure 3 As shown, under different signal-to-noise ratio conditions, for , and The systematic bias and accuracy by three standard deviations were statistically analyzed. The results show that while the pure deep learning method (corresponding to the DL curve in the figure) has a faster inference speed, it exhibits significant systematic biases on various morphological parameters; the genetic algorithm shows significant degradation in both bias and accuracy when noise is amplified; the traditional finite difference Levenberg-Marquardt method shows some improvement compared to the genetic algorithm, but it is still affected by initial values ​​and finite difference gradient errors. In contrast, the method in Example 1... , and All of them exhibit low systematic bias and small three-standard-deviation accuracy, and their results are closer to the theoretical accuracy limit characterized by the Cramér-Rao lower bound (corresponding to the CRLB curve in the figure).

[0109] Furthermore, to verify the applicability of the method in Example 1 to different multi-channel extreme ultraviolet scattering data input formats, the same topography parameter inversion process was applied to Baseline, Dual-WL, Dual-Ang, and Spec-Ang data input formats. These data input formats are only used to provide different numbers or sources of diffraction measurement channels. The method in Example 1 employs the same intensity normalization, physical prior depth initialization, differentiable electromagnetic forward calculation, and gradient refinement process for all data input formats, without involving the selection or optimization of measurement configurations.

[0110] like Figure 4 As shown, the method in Example 1 can output values ​​close to the true values ​​under different data input formats. , and The estimation results demonstrate that the inversion process combining deep initialization and differentiable electromagnetic refinement can adapt to different extreme ultraviolet scattering metrology data inputs. The error bar width varies under different data input formats, reflecting the influence of input diffraction information and noise conditions on the inversion uncertainty. However, under all input conditions, the method in Example 1 maintains good inversion stability and physical consistency, thus verifying the versatility and robustness of this topographic parameter inversion method.

[0111] In summary, compared to pure deep learning methods, this application can reduce system bias; compared to traditional finite difference local optimization methods, this application can reduce the dependence on initial values ​​and finite difference step sizes; compared to derivative-free global search methods, this application can reduce the number of forward model calls and improve computational efficiency. Therefore, this application is suitable for high-precision, high-stability, and high-throughput morphology parameter measurement of complex nanostructures in advanced semiconductor manufacturing.

[0112] The following describes the differential electromagnetic extreme ultraviolet (EMI) topography inversion device provided in this application. The differential electromagnetic extreme ultraviolet (EMI) topography inversion device described below can be referred to in correspondence with the differential electromagnetic extreme ultraviolet (EMI) topography inversion method described above.

[0113] like Figure 5 As shown, this application provides a micro-electromagnetic extreme ultraviolet morphology inversion device, which includes: Initialization module 10 is used to input the intensity-normalized multi-channel extreme ultraviolet diffraction measurement data into the physical prior depth initialization model to obtain the initial estimate of the morphology parameters of the nanostructure to be measured. The forward calculation module 20 is used to call the differentiable electromagnetic forward model to obtain the theoretical diffraction response based on the initial estimation of morphology parameters and the morphology parameters and measurement configuration of the nanostructure to be measured, starting from the initial estimate of morphology parameters. The gradient calculation module 30 is used to construct an inversion objective function based on the difference between the theoretical diffraction response and the measured diffraction response, and obtain the analytical gradient of the inversion objective function with respect to the topographic parameters by automatic differentiation, adjoint differentiation or analytical differentiation along the differentiable calculation graph corresponding to the differentiable electromagnetic forward model. The refinement output module 40 is used to iteratively refine the topography parameters based on analytical gradients using gradient optimization algorithms until a preset stopping condition is met, and outputs physically consistent topography parameter inversion results.

[0114] It is understood that the detailed functional implementation of each of the above units / modules can be found in the description in the aforementioned method embodiments, and will not be repeated here.

[0115] It should be understood that the above-described device is used to execute the methods in the above embodiments. The implementation principle and technical effect of the corresponding program modules in the device are similar to those described in the above methods. The working process of the device can be referred to the corresponding process in the above methods, and will not be repeated here.

[0116] Based on the methods in the above embodiments, this application provides an electronic device, such as... Figure 6 As shown, the electronic device may include a processor 810, a communications interface 820, a memory 830, and a communication bus 840, wherein the processor 810, the communications interface 820, and the memory 830 communicate with each other through the communication bus 840. The processor 810 can call logical instructions in the memory 830 to execute the methods in the above embodiments.

[0117] Furthermore, the logical instructions in the aforementioned memory 830 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application.

[0118] Based on the methods in the above embodiments, this application provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0119] Based on the methods in the above embodiments, this application provides a computer program product that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0120] It is understood that the processor in the embodiments of this application can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. A general-purpose processor can be a microprocessor or any conventional processor.

[0121] The method steps in this application embodiment can be implemented in hardware or by a processor executing software instructions. The software instructions can consist of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, portable hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor, enabling the processor to read information from and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can reside in an ASIC.

[0122] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

[0123] It is understood that the various numerical designations used in the embodiments of this application are merely for the convenience of description and are not intended to limit the scope of the embodiments of this application.

[0124] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A method for micro-electromagnetic extreme ultraviolet morphology inversion, characterized in that, include: The intensity-normalized multi-channel extreme ultraviolet diffraction measurement data are input into the physical prior depth initialization model to obtain the initial estimate of the morphology parameters of the nanostructure to be measured. Starting with the initial estimation of morphological parameters, based on the morphological parameters of the nanostructure to be measured and the measurement configuration, a differentiable electromagnetic forward model is invoked to obtain the theoretical diffraction response; Based on the difference between the theoretical diffraction response and the measured diffraction response, an inversion objective function is constructed, and the analytical gradient of the inversion objective function with respect to the topographic parameters is obtained by automatic differentiation, adjoint differentiation or analytical differentiation along the differentiable computation graph corresponding to the differentiable electromagnetic forward model. Based on analytical gradient, a gradient optimization algorithm is used to iteratively refine the topography parameters until a preset stopping condition is met, and outputs physically consistent topography parameter inversion results.

2. The method for inverting the microscopic electromagnetic extreme ultraviolet morphology according to claim 1, characterized in that, The physical prior deep initialization model is obtained by introducing dynamic noise to enhance training; Dynamic noise enhancement involves generating diffraction data corresponding to different structural parameters using a differentiable electromagnetic forward model, and randomly adding one or more of the following: photon shot noise, dark current noise, readout noise, background noise, gain fluctuation, and exposure perturbation. It also involves randomly setting different photon counts, full-well capacity, exposure time, or noise intensity for different training batches.

3. The method for inverting the microscopic electromagnetic extreme ultraviolet morphology according to claim 1, characterized in that, The step of calling a differentiable electromagnetic forward model to obtain the theoretical diffraction response includes: The structure under test is discretized into multiple sub-layers along the height direction, and the dielectric constant of each sub-layer is Fourier expanded along the periodic direction to obtain the Toplitz dielectric constant matrix of each sub-layer. Based on the expression of Maxwell's equations in Fourier space, the characteristic modes and propagation constants of each sublayer are solved, and the scattering matrix, transmission matrix or enhanced transmission matrix is ​​used to complete the interlayer electromagnetic field continuity matching and field propagation to obtain the near-field electromagnetic field. Based on the near-field electromagnetic field, far-field propagation, tilt projection, detector sampling, and intensity normalization are performed to obtain the theoretical diffraction response. Among them, structural parameterization, dielectric constant distribution construction, Fourier expansion, characteristic mode solution, interlayer field propagation, far-field transformation, tilt projection, detector sampling and intensity normalization are all constructed into differentiable operations.

4. The method for inverting the microscopic electromagnetic extreme ultraviolet morphology according to claim 1, characterized in that, The construction of the inversion objective function includes obtaining the inversion objective function based on the following formula: ； in, Represents the inversion objective function; A vector representing the morphological parameters of the nanostructure to be measured; Indicates the number of measurement channels; Indicates the first Theoretical diffraction response under each measurement channel; Indicates the first Measured diffraction response under each measurement channel; Indicates the first Noise weighting matrix for each measurement channel; Indicates the measurement configuration; Represents physical prior constraints; This represents the weight of the physical prior constraint term.

5. The method for inverting the microscopic electromagnetic extreme ultraviolet morphology according to claim 4, characterized in that, The noise weight matrix is ​​the reciprocal of the total noise variance for each pixel or diffraction order. The total noise variance is obtained based on the following formula: ； in, Indicates the first The first channel The total noise variance of each pixel or diffraction order; This represents the variance of photon shot noise; Indicates the variance of dark current noise; Indicates the readout noise variance; This represents the variance of the background noise.

6. The method for inverting the microscopic electromagnetic extreme ultraviolet morphology according to claim 4, characterized in that, The process of obtaining the analytical gradient of the inverted objective function with respect to the topographic parameters includes backpropagating the gradient along a differentiable electromagnetic computation graph using inverse automatic differentiation, and obtaining the analytical gradient based on the following formula: ； in, This represents the gradient of the inversion objective function with respect to the topographic parameters; Indicates the first Jacobian matrix of theoretical diffraction response with respect to topographic parameters under each measurement channel; This represents the gradient of the physical prior constraint term with respect to the topographic parameters.

7. The method for inverting the microscopic electromagnetic extreme ultraviolet morphology according to claim 6, characterized in that, The method of iteratively refining the morphology parameters based on analytical gradient using a gradient optimization algorithm includes obtaining the iteratively updated morphology parameters based on the following formula: ； in, Indicates the first The morphological parameters of the next iteration; Indicates the first The morphological parameters of the next iteration; This represents the gradient optimization operator.

8. The method for inverting the microscopic electromagnetic extreme ultraviolet morphology according to claim 6, characterized in that, The preset stopping conditions include the change in the loss function being less than the corresponding threshold, the change in parameters being less than the corresponding threshold, the gradient norm being less than the corresponding threshold, and the number of iterations reaching the maximum number of iterations; when any of the stopping conditions is met, the iterative refinement is terminated.

9. A micro-electromagnetic extreme ultraviolet morphology inversion device, characterized in that, include: The initialization module is used to input the intensity-normalized multi-channel extreme ultraviolet diffraction measurement data into the physical prior depth initialization model to obtain the initial estimate of the morphology parameters of the nanostructure to be measured. The forward calculation module is used to obtain the theoretical diffraction response by calling a differentiable electromagnetic forward model based on the initial estimate of the morphology parameters and the morphology parameters and measurement configuration of the nanostructure to be measured, starting from the initial estimate of the morphology parameters. The gradient calculation module is used to construct the inversion objective function based on the difference between the theoretical diffraction response and the measured diffraction response, and obtain the analytical gradient of the inversion objective function with respect to the topographic parameters by automatic differentiation, adjoint differentiation or analytical differentiation along the differentiable computation graph corresponding to the differentiable electromagnetic forward model. The refinement output module is used to iteratively refine the topography parameters based on analytical gradients using gradient optimization algorithms until a preset stopping condition is met, and outputs physically consistent topography parameter inversion results.

10. An electronic device, characterized in that, include: Memory and one or more processors; The memory is coupled to the one or more processors, and the memory is used to store computer program code, the computer program code including computer instructions; The one or more processors invoke the computer instructions to cause the electronic device to perform the method as described in any one of claims 1-8.

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