HAR microstructure morphology restoration method based on modulation aberration data model

Abstract

The invention discloses an HAR microstructure morphology restoration method based on a modulation aberration data model, which avoids using expensive devices such as a deformable mirror to compensate aberration in the process of measuring a microstructure by near-infrared microscopic interferometry, avoids an aberration detection link, achieves transient response and accelerates the characterization process of a sample to be detected. On the basis of a BP neural network, a modulation aberration data network is constructed, errors are transmitted layer by layer through training, so that network parameters are corrected, a modulation aberration data model is constructed and optimized, required modulation aberration data are obtained through prediction according to characteristic parameters of a sample to be tested, a virtual phase filter is constructed, and accordingly aberration of an HAR microstructure interferogram is corrected. And finishing the morphology restoration of the HAR microstructure. The modulation aberration data model is continuously iterated and updated, accidental errors are avoided, and the robustness of the correction algorithm is higher.

Description

Technical Field

[0001] This invention relates to the field of precision optical measurement engineering technology, specifically to a HAR microstructure morphology restoration method based on modulation aberration data model, which predicts modulation aberration data of trench structures in silicon-based MEMS devices, and is particularly suitable for deep trench structures with high aspect ratios. Background Technology

[0002] In the semiconductor industry, as large-scale integrated circuits and micro / nano integrated optical systems develop towards three-dimensionality and with increasing layers, there is a need to fabricate deep vias (TSV-through silicon vias) for electrical signal transmission leads. On the other hand, various silicon-based MEMS sensors require increasing the response area of ​​the sensing structure to continuously improve sensor sensitivity, resulting in increasingly deeper trench structures without increasing the linewidth (CD dimension), or even decreasing it. These types of microstructures are characterized by high aspect ratios, typically greater than 10:1. Currently, the trench width of high aspect ratio MEMS microstructures ranges from 3 to 30 μm, and the depth ranges from 30 to 300 μm. The development of such high aspect ratio microstructures will play a crucial role in driving the application of microelectromechanical systems (MEMS) technology in many fields such as aerospace, electronics, biology, and medicine.

[0003] Chinese patent CN200710053292.5, entitled "A Measurement Method and Device for Micro / Nano Deep Trench Structures," describes a method that projects an infrared beam onto the surface of a silicon wafer containing a deep trench structure. The method analyzes the interference light reflected from the interfaces of the trench structure to obtain the measured reflection spectrum. It then constructs a theoretical reflection spectrum using equivalent medium theory to model an equivalent multilayer thin film stack optical model of the trench structure. Simulated annealing and gradient-based optimization algorithms are used to fit the measured reflection spectrum to the theoretical reflection spectrum, thereby extracting ensemble characteristic parameters such as trench depth and width. This achieves accurate measurement of the width and depth of high aspect ratio deep trenches. However, this method requires pre-modeling the trench structure of the sample to be tested and calculating the theoretical reflection spectrum. The measurement results are obtained by fitting the theoretical spectrum to the measured spectrum. The accuracy of the measurement results is affected by the pre-established theoretical model. Modeling complex or unknown structures is difficult, making it hard to guarantee the accuracy of the measurement results.

[0004] Chinese patent: "High aspect ratio microstructure transmission interferometric microscopic non-destructive measurement device and method"

[0005] (CN2022112135W) describes a method that uses a microscope objective exit pupil aberration monitoring optical path and an active aberration compensation system. To address the problem of excessive aberrations in reflective structures, a transmission structure is employed to reduce aberrations and improve measurement accuracy. This patented method overcomes the difficulty of non-destructive measurement of high aspect ratio trench structures in silicon-based MEMS devices, but requires expensive hardware instruments such as deformable mirrors. Summary of the Invention

[0006] The purpose of this invention is to provide a method for restoring the morphology of HAR microstructures based on a modulation aberration data model, in order to solve the problem of random errors in existing interferometric microscopy nondestructive measurement methods when performing aberration correction, as well as the problem of high costs caused by the use of expensive hardware.

[0007] The technical solution to achieve the purpose of this invention is as follows: a method for restoring the morphology of HAR microstructures based on a modulation aberration data model, comprising the following steps:

[0008] Step 1: A series of HAR microstructures with different parameters and the corresponding modulation aberration coefficients of the HAR microstructures are obtained through FDTD simulation calculation, thereby forming a modulation aberration dataset. The modulation aberration dataset is divided into a training set and a test set. The HAR microstructure parameters include line width and depth. The line width ranges from 2 to 30 micrometers, and the depth ranges from 30 to 300 micrometers.

[0009] Step 2, construct the modulation aberration data network:

[0010] A three-layer BP neural network was used as the modulation aberration data network. The linewidth and depth of the HAR microstructure were used as input layer neurons, and the Zernike fitting coefficient of the modulation aberration was used as output layer neurons. The network parameters were initialized and the number of hidden layer neurons was set to 7.

[0011] Step 3: Initialize network parameters and use stochastic gradient descent to train the modulation aberration data network using the training set to obtain a trained modulation aberration data model.

[0012] A single sample from the training set is randomly selected in a single pass, and the output of the output layer is obtained through forward propagation. The output of the output layer is compared with the actual output of the sample in the training set, the loss function is calculated, the loss function is backpropagated, the gradient of each network parameter is calculated, and the network parameters are updated to obtain the trained modulation aberration data model.

[0013] Step 4: Test the modulation aberration data model using the test set, output the prediction results corresponding to each HAR microstructure in the modulation aberration data model, test the accuracy of the trained modulation aberration data model, and obtain the optimal modulation aberration data model.

[0014] Step 5: Using an interferometer, acquire the top and bottom interferograms of the HAR microstructure under test. Perform EMD preprocessing on both, extracting the initial depth and initial linewidth of the HAR microstructure as initial structural parameters. Input the initial structural parameters into the optimal modulation aberration data model to obtain the modulation aberration coefficients. Construct a virtual phase filter using the aforementioned modulation aberration coefficients to correct aberrations in the bottom interferogram of the HAR microstructure under test. Merge the corrected bottom interferogram with the top interferogram after EMD preprocessing, and complete the structural morphology reconstruction based on the HDVSI morphology restoration algorithm.

[0015] Compared with the prior art, the significant advantages of this invention are:

[0016] (1) The modulation aberration data model predicts the corresponding results by matching the characteristic parameters of the HAR microstructure with the modulation aberration coefficients, avoiding repeated calculations, and can respond instantly, effectively improving the compensation speed.

[0017] (2) To address the problem of random errors in the method of establishing a simulation model based on the characteristic parameters of microstructures with high aspect ratio, deriving the modulation aberration coefficients and compensating for them, the aberration data model can avoid random errors through continuous iteration and updating, and its robustness is greatly improved. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the HAR microstructure morphology restoration method based on a modulation aberration data model.

[0019] Figure 2 The diagram shows the principle of simulation modeling for modulation aberrations caused by HAR grooves. Figure (a) is a three-dimensional view of a single HAR groove, and Figure (b) is a cross-section of the far-field propagation model.

[0020] Figure 3 This is a diagram of the BP neural network structure.

[0021] Figure 4 Schematic diagram for extracting the initial linewidth and initial depth of HAR samples. Detailed Implementation

[0022] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0023] Combination Figure 1 A method for reconstructing the microstructure morphology of HAR based on a modulation aberration data model, comprising the following steps:

[0024] Step 1: A series of HAR microstructures with different parameters and the corresponding modulation aberration coefficients of the HAR microstructures are obtained through FDTD simulation calculation, thereby forming a modulation aberration dataset. The modulation aberration dataset is divided into a training set and a test set. The HAR microstructure parameters include line width and depth. The line width ranges from 2 to 30 micrometers, and the depth ranges from 30 to 300 micrometers.

[0025] The method for obtaining the one-to-one correspondence between depth, linewidth parameters and aberrations is as follows:

[0026] Combination Figure 2 To simulate sample-induced aberrations, a silicon-based trench with a depth of 100 μm, a width of 10 μm, and an aspect ratio of 10:1 was selected. The incident light wavelength was 1.32 μm, and the numerical aperture (NA) was 0.5. The reverse propagation process was simulated using the principle of optical path reversibility. The light started from the bottom of the HAR trench, propagated along the optical axis (z-axis), passed through the trench, and reached near the top. The FDTD method was used to solve for the surface light distribution modulated by the trench, and ASM was combined for far-field propagation to determine the modulation aberrations caused by the HAR trench. The wavefront distribution was simulated using Zernike polynomial fitting to describe the wavefront characteristics.

[0027] Using the same method, simulations were performed on HAR microstructures with different morphological parameters. These simulation models had linewidths ranging from 2 to 30 micrometers and depths ranging from 30 to 300 micrometers. The Zernike fitting coefficients for modulation aberrations were then calculated. Utilizing the symmetry properties of the HAR microstructures, symmetric terms were selected from the Zernike polynomials, and 37 sets of Zernike fitting coefficients were extracted for each HAR microstructure.

[0028] Proceed to step 2.

[0029] Step 2, construct the modulation aberration data network:

[0030] A three-layer backpropagation neural network is used as the modulation aberration data network. The linewidth and depth of the HAR microstructure are used as input layer neurons, and the Zernike fitting coefficients of the modulation aberration are used as output layer neurons. The network parameters are initialized, and the number of hidden layer neurons is set as follows:

[0031] S2.1 Backpropagation (BP) neural networks are a type of multilayer feedforward neural network that utilizes error backpropagation techniques. This type of network belongs to supervised learning algorithms. Its core idea is to predict values ​​through forward propagation and then use the backpropagation algorithm to pass the error layer by layer, thereby correcting the network parameters (including weights and biases) to optimize the objective function.

[0032] Combination Figure 3A three-layer backpropagation (BP) neural network is used as the modulation aberration data network. The connection weights w and bias b are initialized, and the number of hidden layer neurons is set to 7. The input received by the hidden layer neurons is calculated as follows:

[0033]

[0034] Where, x i For the i-th neuron in the input layer, w is the input received by the j-th neuron in the hidden layer. ij b represents the connection weight between the i-th neuron in the input layer and the j-th neuron in the hidden layer. j represents the bias of the j-th neuron in the hidden layer, and n represents the total number of neurons in the input layer.

[0035] The output h of the hidden layer neurons is calculated using the activation function f(·). j :

[0036]

[0037] S2.2, Output h of hidden layer neurons j As the input to the output layer, the input received by the output layer neurons is obtained through weighted summation during this process:

[0038]

[0039] in, w represents the input received by the k-th neuron in the output layer. jk b represents the connection weight between the j-th neuron in the hidden layer and the k-th neuron in the output layer. k represents the bias of the k-th neuron in the output layer, and p represents the number of neurons in the hidden layer.

[0040] The output y of the output layer neuron is calculated using the activation function f(·). k :

[0041]

[0042] This process corresponds to the modulation aberrations introduced by grooves with different characteristic parameters.

[0043] Proceed to step 3.

[0044] Step 3: Initialize network parameters (including weights and biases), and use stochastic gradient descent to train the modulation aberration data network using the training set to obtain the trained modulation aberration data model.

[0045] A single sample is randomly selected from the training set, and the output of the output layer is obtained through forward propagation. The output of the output layer is compared with the actual output of the samples in the training set, the loss function is calculated, the loss function is backpropagated, the gradient of each network parameter is calculated, and the network parameters are updated to obtain the trained modulation aberration data model, as follows:

[0046] S3.1 Set the training target to 0.01 and the learning rate to 0.005, and use the modulation aberration data network to predict the modulation aberration caused by HAR microstructures with random shape parameters.

[0047] Using stochastic gradient descent, a single sample is randomly selected from the training set in a single pass to complete the forward propagation of the modulated aberration data network, obtaining the output y of the output layer neurons. k The predicted value is used as the target value. The root mean square error is used as the loss function to calculate the predicted value y. k Compared with the actual output Y of the training set samples k Variance between:

[0048]

[0049] Where m represents the number of neurons in the output layer, and L represents the loss function.

[0050] S3.2. Backpropagate the loss function and use the chain rule to calculate the gradient of the loss function L with respect to each connection weight. gradient of bias

[0051] Calculate the gradient of the loss function L with respect to the connection weights from the hidden layer to the output layer. gradient of bias

[0052]

[0053] in, This represents the error of the k-th neuron in the output layer.

[0054] Calculate the gradient of the loss function with respect to the connection weights from the input layer to the hidden layer. gradient of bias

[0055]

[0056] in, This represents the error of the j-th neuron in the hidden layer.

[0057] Calculate the gradient of the loss function with respect to the bias from the input layer to the hidden layer.

[0058]

[0059] Gradient descent is used to adjust the connection weights and biases to minimize the loss function.

[0060]

[0061] Among them, w new w represents the updated connection weights. old b represents the connection weights before the update. new Represents the updated bias, b old η represents the bias before the update, and η represents the learning rate, which is used to adjust the update step size.

[0062] S3.3 Repeat the above training process until the change in the loss function before and after the update is no greater than the training target of 0.01, and obtain the trained modulation aberration data model, then proceed to step 4.

[0063] Step 4: Test the modulation aberration data model using the test set, output the prediction results corresponding to each HAR microstructure in the modulation aberration data model, test the accuracy of the trained modulation aberration data model, obtain the optimal modulation aberration data model, and proceed to Step 5.

[0064] Step 5: Acquire the top and bottom interferograms of the HAR microstructure under test using an interferometer. Perform EMD preprocessing on both images to extract the initial depth and initial linewidth of the HAR microstructure as initial structural parameters. Input these initial structural parameters into the optimal modulation aberration data model to obtain the modulation aberration coefficients. Construct a virtual phase filter using these modulation aberration coefficients to correct aberrations in the bottom interferogram of the HAR microstructure. Merge the corrected bottom interferogram with the top interferogram after EMD preprocessing. Based on the HDVSI morphology restoration algorithm, complete the structural morphology reconstruction, as detailed below:

[0065] S5.1. Use an interferometer to acquire the top and bottom interferograms of the HAR microstructure under test. Perform Empirical Mode Decomposition (EMD) on the top and bottom interferograms of the HAR microstructure under test to remove background light intensity and highlight the main features. Obtain the top and bottom interferograms of the HAR microstructure under test after EMD preprocessing, so as to extract the initial depth and initial linewidth of the HAR microstructure under test and use them as the initial structural parameters.

[0066] S5.2, Combination Figure 4The initial linewidth of the HAR microstructure under test is directly read from the top interferogram. After EMD processing of the top and bottom interferograms, the initial depth of the HAR microstructure is obtained by solving the envelope of the coherent signal. The initial depth and initial linewidth of the HAR microstructure are used as structural parameters of the optimal modulation aberration data model. The optimal modulation aberration data model is then used for calculation and matching to obtain the modulation aberration of the matched HAR microstructure. The modulation aberration of the HAR microstructure obtained by calculation and matching using the optimal modulation aberration data model is less prone to random errors, exhibits better robustness, and has higher computational efficiency.

[0067] S5.3. The aberration wavefront of the HAR microstructure under test is generated by fitting the Zernike polynomial to the modulation aberration of the matched HAR microstructure under test.

[0068]

[0069] Where (u,v) represents the coordinates of the pupil plane, C is the coefficient matrix of the modulation aberration, Z represents the Zernike polynomial, and M is the number of Zernike terms. M is consistent with the number of neurons in the output layer, m, i.e., M = m.

[0070] aberration wavefront of the HAR microstructure under test Obtain the virtual phase filter I represents the imaginary part.

[0071] S5.4. Perform a Fourier transform on the bottom interferogram of the HAR microstructure under test, convert it to the frequency domain, and obtain the Fourier transformed bottom interferogram G of the HAR microstructure under test. a (u,v).

[0072] The interferogram can be viewed as the convolution result of the objective function o(x,y) and the system point spread function (PSF). Based on coherent imaging theory, the interferogram g(x,y) within the coherence length range can be expressed as:

[0073]

[0074] In the formula, o(x,y) is the objective function, h(x,y) is the point spread function of the system, and (x,y) are the image plane coordinates. Based on the convolution theorem, the pupil plane can be rewritten as:

[0075] G(u,v)=O(u,v)H(u,v) (13)

[0076] Where G(u,v) and O(u,v) are the Fourier transforms of g(x,y) and o(x,y), respectively. H(u,v) is the system coherent transfer function (CTF), and (u,v) are the pupil plane coordinates. For an ideal system, the system point spread function h(x,y) and the pupil function p(u,v) are a pair of Fourier transforms. Therefore, the system CTF can be described as:

[0077]

[0078] For a system with aberrations, assuming the phase difference between the actual wavefront and the ideal wavefront at the pupil plane is... Then the generalized pupil function is represented as P(u,v), and the system CTF with aberrations...

[0079] H a (u,v) can be represented as:

[0080]

[0081] Compared to an ideal system, phase distortion is introduced into the frequency passband due to aberrations, resulting in decreased system resolution, reduced imaging quality, and lower interference fringe contrast. Combining equations (13) and (15), the aberration map G of the pupil plane... a (u,v) can be represented as:

[0082]

[0083] Based on the principle of phase conjugation, if it is possible to obtain This allows for the correction of aberrations in the interferogram, resulting in the bottom interferogram g of the HAR microstructure under test on the image plane after aberration correction. c (x,y) can be represented as:

[0084]

[0085] in, This represents the inverse Fourier transform. This is a virtual phase filter. This process simplifies the original hardware-based front-end optical design to back-end numerical processing, eliminating the high cost of hardware-based aberration correction while achieving the same aberration correction effect.

[0086] S5.5 To more accurately correct aberrations, adjust the structural parameters of the input optimal modulation aberration data model according to the initial depth and initial linewidth of the HAR microstructure under test, rematch the modulation aberrations of the HAR microstructure under test, and repeat the above steps until the number of cycles is reached; evaluate the contrast of the interference fringes of each aberration-corrected bottom interferogram of the HAR microstructure under test, and select the one with the maximum contrast of interference fringes as the accurately corrected bottom interferogram of the HAR microstructure under test.

[0087] S5.6. Merge the bottom interferogram of the HAR microstructure under test after accurate correction and the top interferogram of the HAR microstructure under test after EMD preprocessing, and complete the morphological restoration of the HAR microstructure based on the HDVSI morphological restoration algorithm.

[0088] Example 1

[0089] Combination Figure 1 , Figure 2 , Figure 3 and Figure 4 A method for reconstructing the microstructure morphology of HAR based on a modulation aberration data model includes the following steps:

[0090] Step 1: 155 sets of HAR microstructures with different parameters and the corresponding modulation aberration coefficients of the HAR microstructures are obtained through FDTD simulation calculation, thereby forming a modulation aberration dataset. The modulation aberration dataset is divided into 115 training sets and 40 test sets. The HAR microstructure parameters include linewidth and depth. The linewidth ranges from 2 to 30 micrometers, and the depth ranges from 30 to 300 micrometers. Proceed to Step 2.

[0091] Step 2, construct the modulation aberration data network:

[0092] A three-layer BP neural network is used as the modulation aberration data network. The linewidth and depth of the HAR microstructure are used as input layer neurons, and the Zernike fitting coefficient of the modulation aberration is used as output layer neurons. The network parameters are initialized, and the number of hidden layer neurons is set to 7. Proceed to step 3.

[0093] Step 3: Initialize network parameters (including weights and biases), set the training target to 0.01, the learning rate to 0.005, and use stochastic gradient descent to train the modulation aberration data network using the training set to obtain the trained modulation aberration data model.

[0094] A single sample from the training set is randomly selected in a single pass, and the output of the output layer is obtained through forward propagation. The output of the output layer is compared with the actual output of the sample in the training set, the loss function is calculated, the loss function is backpropagated, the gradient of each network parameter is calculated, and the network parameters are updated to obtain the trained modulation aberration data model.

[0095] Proceed to step 4.

[0096] Step 4: Test the modulation aberration data model using the test set, output the prediction results corresponding to each HAR microstructure in the modulation aberration data model, test the accuracy of the trained modulation aberration data model, obtain the optimal modulation aberration data model, and proceed to Step 5.

[0097] Step 5: Use an interferometer to acquire 200 top and 200 bottom interferograms of the HAR microstructure under test. Perform EMD preprocessing on these images to extract the initial depth (100 μm) and initial linewidth (10 μm) of the HAR microstructure under test as initial structural parameters. Input the initial structural parameters into the optimal modulation aberration data model to obtain the modulation aberration coefficients under test. Construct a virtual phase filter using the modulation aberration coefficients under test to correct aberrations in the bottom interferogram of the HAR microstructure under test. Merge the corrected bottom interferogram with the top interferogram after EMD preprocessing and complete the structural morphology reconstruction based on the HDVSI morphology restoration algorithm.

Claims

1. A method for reconstructing the microstructure morphology of HAR based on a modulation aberration data model, characterized in that: The steps are as follows: Step 1: A series of HAR microstructures with different parameters and the corresponding modulation aberration coefficients of the HAR microstructures are obtained through FDTD simulation calculation, thereby forming a modulation aberration dataset. The modulation aberration dataset is divided into a training set and a test set. The HAR microstructure parameters include line width and depth. The line width ranges from 2 to 30 micrometers, and the depth ranges from 30 to 300 micrometers. Proceed to Step 2. Step 2, construct the modulation aberration data network: A three-layer BP neural network was used as the modulation aberration data network. The linewidth and depth of the HAR microstructure were used as input layer neurons, and the Zernike fitting coefficient of the modulation aberration was used as output layer neurons. The network parameters were initialized and the number of hidden layer neurons was set to 7. Proceed to step 3; Step 3: Initialize network parameters and use stochastic gradient descent to train the modulation aberration data network using the training set to obtain a trained modulation aberration data model. A single sample is randomly selected from the training set in a single pass, and the output of the output layer is obtained through forward propagation. The output of the output layer is compared with the actual output of the sample in the training set, the loss function is calculated, the loss function is backpropagated, the gradient of each network parameter is calculated, and the network parameters are updated to obtain the trained modulation aberration data model. Proceed to step 4; Step 4: Test the modulation aberration data model using the test set, output the prediction results corresponding to each HAR microstructure in the modulation aberration data model, test the accuracy of the trained modulation aberration data model, obtain the optimal modulation aberration data model, and proceed to step 5. Step 5: Use an interferometer to acquire the top and bottom interferograms of the HAR microstructure under test, and perform EMD preprocessing on them respectively. Extract the initial depth and initial linewidth of the HAR microstructure under test as initial structural parameters. Input the initial structural parameters into the optimal modulation aberration data model to obtain the modulation aberration coefficients under test. Use the above modulation aberration coefficients to construct a virtual phase filter and perform aberration correction on the bottom interferogram of the HAR microstructure under test. Merge the corrected bottom interferogram and the top interferogram after EMD preprocessing, and complete the structural morphology construction based on the HDVSI morphology restoration algorithm.

2. The method for HAR microstructure morphology reconstruction based on modulation aberration data model according to claim 1, characterized in that, In step 1, a series of HAR microstructures with different parameters and the corresponding modulation aberration coefficients of the HAR microstructures are obtained through FDTD simulation calculation, thereby forming a modulation aberration dataset, as follows: In order to obtain a one-to-one correspondence between depth, linewidth parameters and aberrations, the structure depth and linewidth will be used as characteristic parameters, and the aberration array corresponding to the structure will be obtained through the HAR sample modulation aberration simulation model. The reverse propagation process is simulated using the principle of optical path reversibility. The light starts from the bottom of the HAR trench, propagates along the optical axis, passes through the trench, and reaches near the top of the trench. The FDTD method is used to solve the surface light distribution modulated by the trench, and ASM is combined to perform far-field propagation to determine the modulation aberration caused by the HAR trench. The wavefront distribution is simulated using Zernike polynomial fitting to describe the wavefront characteristics. Using the same method, simulations were performed on HAR microstructures with different morphological parameters; then the Zernike fitting coefficients of modulation aberrations were calculated, and symmetric terms were selected from the Zernike polynomials using the symmetry properties of the HAR microstructures. 37 sets of Zernike fitting coefficients were extracted for each HAR microstructure.

3. The method for HAR microstructure morphology reconstruction based on modulation aberration data model according to claim 1, characterized in that, In step 2, the modulation aberration data network is constructed as follows: S2.

1. Using a three-layer BP neural network as the modulation aberration data network, initialize the connection weights w and bias b, set the number of hidden layer neurons to 7, and calculate the input received by the hidden layer neurons: Where, x i For the i-th neuron in the input layer, w is the input received by the j-th neuron in the hidden layer. ij b represents the connection weight between the i-th neuron in the input layer and the j-th neuron in the hidden layer. j represents the bias of the j-th neuron in the hidden layer, and n represents the total number of neurons in the input layer; The output h of the hidden layer neurons is calculated using the activation function f(·). j : S2.2, Output h of hidden layer neurons j As the input to the output layer, the input received by the output layer neurons is obtained through weighted summation during this process: in, w represents the input received by the k-th neuron in the output layer. jk b represents the connection weight between the j-th neuron in the hidden layer and the k-th neuron in the output layer. k represents the bias of the k-th neuron in the output layer, and p represents the number of neurons in the hidden layer; The output y of the output layer neuron is calculated using the activation function f(·). k :

4. The method for HAR microstructure morphology reconstruction based on modulation aberration data model according to claim 1, characterized in that, In step 3, the network parameters are initialized, and the stochastic gradient descent method is used to train the modulation aberration data network using the training set, resulting in a trained modulation aberration data model, as detailed below: S3.1 Set the training target to 0.01 and the learning rate to 0.005, and use the modulation aberration data network to predict the modulation aberration caused by HAR microstructures with random shape parameters; Using stochastic gradient descent, a single sample is randomly selected from the training set in a single pass to complete the forward propagation of the modulated aberration data network, obtaining the output y of the output layer neurons. k As the predicted value; using the root mean square error as the loss function, the predicted value y is calculated. k Compared with the actual output Y of the samples in the training set k Variance between: Where m represents the number of neurons in the output layer, and L represents the loss function; S3.

2. Backpropagate the loss function and use the chain rule to calculate the gradient of the loss function L with respect to each connection weight. gradient of bias Calculate the gradient of the loss function L with respect to the connection weights from the hidden layer to the output layer. gradient of bias in, This represents the error of the k-th neuron in the output layer; Calculate the gradient of the loss function with respect to the connection weights from the input layer to the hidden layer. gradient of bias in, This represents the error of the j-th neuron in the hidden layer; Calculate the gradient of the loss function with respect to the bias from the input layer to the hidden layer. Gradient descent is used to adjust the connection weights and biases to minimize the loss function. Among them, w new w represents the updated connection weights. old b represents the connection weights before the update. new Represents the updated bias, b old The value represents the bias before the update, and η represents the learning rate, which is used to adjust the update step size. S3.3 Repeat the above training process until the change in the loss function is no greater than the training target of 0.01, and obtain the trained modulation aberration data model.

5. The method for HAR microstructure morphology reconstruction based on a modulation aberration data model according to claim 1, characterized in that, In step 5, the top and bottom interferograms of the HAR microstructure under test are acquired using an interferometer. EMD preprocessing is performed on these interferograms to extract the initial depth and initial linewidth of the HAR microstructure as initial structural parameters. These initial structural parameters are then input into the optimal modulation aberration data model to obtain the modulation aberration coefficients. A virtual phase filter is constructed using these modulation aberration coefficients to correct aberrations in the bottom interferogram of the HAR microstructure. The corrected bottom interferogram is then merged with the top interferogram after EMD preprocessing. Based on the HDVSI morphology restoration algorithm, the structural morphology is constructed, as detailed below: S5.

1. Use an interferometer to acquire the top and bottom interferograms of the HAR microstructure under test. Perform EMD preprocessing on the top and bottom interferograms of the HAR microstructure under test to remove background light intensity and obtain the top and bottom interferograms of the HAR microstructure under test after EMD preprocessing. This will facilitate the extraction of the initial depth and initial linewidth of the HAR microstructure under test, which will be used as the initial structural parameters. S5.

2. The initial linewidth of the HAR microstructure under test is directly read from the top interferogram of the HAR microstructure under test. After EMD processing of the top and bottom interferograms of the HAR microstructure under test, the initial depth of the HAR microstructure under test is obtained by solving the envelope of the coherent signal. The initial depth and initial linewidth of the HAR microstructure under test are used as the structural parameters of the optimal modulation aberration data model. The optimal modulation aberration data model is used to calculate and match to obtain the modulation aberration of the matched HAR microstructure under test. S5.

3. The aberration wavefront of the HAR microstructure under test is generated by fitting the Zernike polynomial to the modulation aberration of the matched HAR microstructure under test. Where (u,v) represents the coordinates of the pupil plane, C is the coefficient matrix of the modulation aberration, Z represents the Zernike polynomial, and M is the number of Zernike terms. M is consistent with the number of neurons in the output layer, m, i.e., M = m. aberration wavefront of the HAR microstructure under test Obtain the virtual phase filter I represents the imaginary part; S5.

4. Perform a Fourier transform on the bottom interferogram of the HAR microstructure under test, convert it to the frequency domain, and obtain the Fourier transformed bottom interferogram G of the HAR microstructure under test. a (u,v); Bottom interferogram g of the HAR microstructure under test after aberration correction on the image plane c (x,y) can be represented as: Where (x, y) represents the coordinates of the image plane. Indicates the inverse Fourier transform; S5.

5. Adjust the structural parameters of the optimal modulation aberration data model based on the initial depth and initial linewidth of the HAR microstructure under test, rematch the modulation aberration of the HAR microstructure under test, and repeat step S5.3 until the number of iterations is reached; evaluate the contrast of the interference fringes for each aberration-corrected bottom interferogram of the HAR microstructure under test, and select the one with the maximum contrast of interference fringes as the accurately corrected bottom interferogram of the HAR microstructure under test. S5.

6. Merge the bottom interferogram of the HAR microstructure under test after accurate correction and the top interferogram of the HAR microstructure under test after EMD preprocessing, and complete the morphology restoration of the HAR microstructure based on the HDVSI morphology restoration algorithm.

Images