Non-destructive measurement of semiconductor buried layer structures by cd-saxs discretization inversion method

Abstract

The application provides a CD-SAXS discretization inversion method for non-destructive measurement of a semiconductor buried layer structure, comprising: selecting a cross-section reconstruction area of a sample and discretizing the cross-section reconstruction area into a first grid matrix; constructing an electron density matrix according to a composition distribution of the sample; calculating a theoretical scattering form factor and a theoretical scattering intensity according to the electron density matrix based on an X-ray scattering physical model; obtaining experimental data of the sample to obtain an experimental scattering intensity; adjusting parameters of the electron density matrix through an iterative optimization algorithm to make a residual error of the theoretical scattering intensity and the experimental scattering intensity converge, and obtaining the electron density matrix at the time of convergence; and outputting the converged electron density matrix to reconstruct the cross-section structure of the sample. The method breaks the dependence of a traditional parameterized model on regular geometric shapes, can accurately reconstruct a complex buried layer structure containing irregular defects and voids, and improves the accuracy of electron density boundaries and defect distribution in the reconstructed result to a sub-angstrom level.

Description

Technical Field

[0001] This invention relates to semiconductor nanometrology, and more specifically to a non-destructive CD-SAXS discretization inversion method for measuring semiconductor buried layer structures, which is suitable for non-destructively measuring complex three-dimensional nanostructures covered with opaque coatings and internal buried layer defects. Background Technology

[0002] As integrated circuit manufacturing processes continue to shrink, transistor structures have evolved from planar MOSFETs to complex three-dimensional structures such as FinFETs, GAA FETs, and complementary field-effect transistors (CFETs). These devices typically involve multilayer stacks of heterogeneous materials and often require metal filling or coating deposition within high aspect ratio structures. Existing metrology techniques face significant challenges: Scanning electron microscopy (SEM) and atomic force microscopy (AFM) can only detect surface morphology and cannot penetrate opaque metal overlays to detect internal "buried structures"; Optical critical dimension measurement (OCD) is limited by skin depth and diffraction limits, making it difficult to resolve deep subwavelength features. While transmission electron microscopy (TEM) and focused ion beam (FIB) can provide cross-sectional images with atomic resolution, they are destructive and extremely time-consuming, failing to meet the high throughput demands of in-line metrology in industry.

[0003] Critical-size small-angle X-ray scattering (CD-SAXS), as a non-destructive technique, is considered ideal for measuring buried structures due to the strong penetrating power of X-rays. However, traditional CD-SAXS data processing methods rely on modeling regular geometries, assuming the sample cross-section is a trapezoidal, rectangular, or other regular geometric shape. This method has the following drawbacks:

[0004] (1) Poor versatility: When irregular shapes appear in actual processes (such as bottom voids caused by CVD deposition, irregular shape coverage), regular geometric models cannot describe them, resulting in fitting failure or a significant decrease in accuracy.

[0005] (2) High computational complexity: For multi-layered complex structures, the analytical form factor derivation is extremely difficult.

[0006] (3) Unable to adapt: ​​It is difficult to “discover” unknown defects without knowing the shape in advance.

[0007] Therefore, there is an urgent need for a CD-SAXS data processing method that does not rely on regular geometric assumptions, can flexibly describe arbitrarily complex cross-sectional distributions, and has efficient computational capabilities. Summary of the Invention

[0008] The purpose of this invention is to provide a non-destructive CD-SAXS discretization inversion method for measuring semiconductor buried layer structures, in order to solve the problem that traditional parametric models cannot accurately characterize irregular buried layer structures and defects, and improve the computational accuracy of CD-SAXS data processing.

[0009] To achieve the above objectives, the present invention provides a non-destructive CD-SAXS discretization inversion method for measuring semiconductor buried layer structures, comprising:

[0010] S1: Select the cross-sectional reconstruction region of the sample and discretize the cross-sectional reconstruction region into a first grid matrix;

[0011] S2: Construct the electron density matrix based on the composition distribution of the sample;

[0012] S3: Based on the X-ray scattering physical model, calculate the theoretical scattering form factor F(q) and the theoretical scattering intensity I(q) according to the electron density matrix;

[0013] S4: Obtain the CD-SAXS experimental data of the sample to obtain the experimental scattering intensity;

[0014] S5: Adjust the parameters of the electron density matrix through an iterative optimization algorithm so that the residual between the theoretical scattering intensity and the experimental scattering intensity converges, and obtain the electron density matrix at the convergence point.

[0015] S6: Output the converged electron density matrix to reconstruct the sample cross-sectional structure.

[0016] In step S5, after obtaining the convergent electron density matrix, the method further includes: discretizing the cross-sectional reconstruction region into a second grid matrix with a resolution higher than the first grid matrix, and constructing a new electron density matrix by combining it with the convergent electron density matrix; then adjusting the parameters of the new electron density matrix again through an iterative optimization algorithm so that the residual between the theoretical scattering intensity and the experimental scattering intensity converges, resulting in a more optimized convergent electron density matrix.

[0017] When the parameters of the electron density matrix are adjusted again through the iterative optimization algorithm, the parameters of the electron density matrix are only locally adjusted at the grid cells of the second grid matrix corresponding to the specific selected region or the high-frequency variation region of the cross-section reconstruction region.

[0018] The first grid matrix has a resolution of 1nm-3nm, and the second grid matrix has a resolution of 0.1nm.

[0019] Step S2 specifically includes: based on the composition distribution of the sample and a shape segmentation strategy, by determining the position coordinates of each grid cell in the first grid cell, assigning the electron density value of the material corresponding to the position coordinates to each grid cell in the first grid matrix, thereby constructing an electron density matrix.

[0020] Based on the first Born approximation, the theoretical scattering shape factor F(q) and structure factor S(q) are calculated using the discretization summation formula. The formulas for calculating the theoretical scattering shape factor F(q) and structure factor S(q) are as follows:

[0021] ,

[0022] ,

[0023] in, Let be the electron density of the k-th grid cell, (y k , x k Let q be the center coordinate of the k-th grid cell, n be the total number of grid cells, w and h be the width and height of the grid cell, respectively. y and q x denoted by , where is the component of the scattering vector in the y and x directions; the structure factor S(q) is the spatial distribution characteristic of the periodic structure corresponding to the entire cross-sectional reconstruction region; m is the diffraction order; and L is the period length of the sample in the y direction.

[0024] The formula for calculating the theoretical scattering intensity I(q) is as follows:

[0025] ,

[0026] Where F(q) is the scattering form factor and S(q) is the structure factor. DWF Here, q is the roughness factor, and q is the scattering vector value. This represents the initial light intensity influence coefficient.

[0027] The calculation process is achieved by using the GPU to perform parallel operations on the calculation formulas for the theoretical scattering form factor F(q) and the theoretical scattering intensity I(q).

[0028] In step S4, CD-SAXS experimental data of the sample are obtained using a CD-SAXS experimental apparatus. The CD-SAXS experimental apparatus, in transmission mode, includes a slit, a filter, a sample, and a detector arranged sequentially along the propagation direction of the beamline. The sample is mounted on a rotatable sample stage, allowing the sample to rotate around the z-axis.

[0029] Obtain the CD-SAXS experimental data of the sample to obtain the experimental scattering intensity, specifically including:

[0030] S41: The sample was rotated around the z-axis using the transmission mode of the CD-SAXS experimental setup to collect scattering patterns of the sample at different angles.

[0031] S42: Scatter the scattering patterns from different angles in reciprocal space to construct q. x -q z Two-dimensional scattering intensity spectrum;

[0032] S43: From the q x -q z Slice data are extracted from the two-dimensional scattering intensity spectrum to serve as the experimental scattering intensity I', i.e., as the fitting target.

[0033] The sample is a semiconductor device with a periodic structure and identical cross-sections in the thickness direction; the method is used for online measurement in semiconductor processes to quickly obtain the electron density distribution of the cross-section; or, the method is used for online detection of deposition defects to obtain the real-time deposition layer thickness and deposition quality based on the reconstructed sample cross-sectional structure.

[0034] In summary, this invention transforms the continuous integral of the sample into discrete summation, enabling the model to handle electron density distributions of arbitrary shapes. This breaks the dependence of traditional parametric models on regular geometric shapes and allows for accurate reconstruction of complex buried structures containing irregular defects and voids. Since adjusting the parameters in the electron density matrix affects the scattering intensity, the method of this invention discretizes complex structures with different electron density distributions and adjusts the parameters of the electron density matrix, resulting in higher accuracy of the material boundary positions and defect distributions in the reconstruction results. Furthermore, because fine-tuning is performed only in local areas, computational efficiency is significantly improved.

[0035] Furthermore, this invention utilizes GPU acceleration to significantly improve computational efficiency, enabling non-destructive, high-precision measurement of the buried structure inside three-dimensional semiconductor devices. Attached Figure Description

[0036] Figure 1 This is a flowchart of a non-destructive CD-SAXS discretization inversion method for measuring semiconductor buried layer structures according to the present invention.

[0037] Figure 2 This is a schematic diagram of the CD-SAXS experimental setup used in the non-destructive CD-SAXS discretization inversion method for measuring semiconductor buried layer structures according to the present invention.

[0038] Figure 3 This is a schematic diagram of the sample and its cross-sectional reconstruction region used in the CD-SAXS discretization inversion method for non-destructive measurement of semiconductor buried layer structures according to the present invention.

[0039] Figure 4 This is a schematic diagram illustrating the principle of discretization grid generation and electron density matrix construction in the CD-SAXS discretization inversion method for non-destructive measurement of semiconductor buried layer structures according to the present invention.

[0040] Figure 5 This is a schematic diagram of the parameters of the sample used in the CD-SAXS discretization inversion method for non-destructive measurement of semiconductor buried layer structures according to the present invention. Detailed Implementation

[0041] The present invention will be further described in detail below with reference to specific embodiments and accompanying drawings. It should be understood that the following embodiments are for illustrative purposes only and are not intended to limit the scope of the invention.

[0042] Example 1: A non-destructive CD-SAXS discretization inversion method for measuring semiconductor buried layer structures

[0043] According to Example 1, the present invention provides a non-destructive CD-SAXS discretization inversion method for measuring semiconductor buried layer structures, which is suitable for measuring the size of samples and can then be used for online measurement in semiconductor processes to detect deposition defects generated after chemical vapor deposition (CVD) or electroplating processes.

[0044] like Figure 2 As shown, when the sample is mounted on the experimental setup, the Z-direction is the direction of the sample's rotation axis (i.e., the vertical direction), and the X-direction is the opposite direction of the X-ray incident direction. The sample is a semiconductor device with a periodic structure and every cross-section in the thickness direction (i.e., the Z-direction) is identical. Therefore, the length and material of the thickness direction (i.e., the Z-direction) at every point on the cross-section are the same.

[0045] In one embodiment, the sample is a semiconductor device with a metal layer covering its surface, such as... Figures 3-5 The silicon nanograting sample shown has a silver (Ag) coating deposited on its surface. The X-ray incident direction of the silicon nanograting sample is the opposite direction to the X-ray direction, i.e. Figure 3 In the top-to-bottom direction, the rotation axis of the silicon nanograting sample is in the Z direction. In other embodiments, the semiconductor device includes, but is not limited to, FinFET, GAA FET, CFET, or nanograting structures with high aspect ratio trenches. The method of the present invention can penetrate the surface metal capping layer to reconstruct the buried silicon-based structure and the bottom voids generated during metal deposition, thus improving the computational accuracy of CD-SAXS data processing.

[0046] like Figure 1 As shown, the present invention provides a non-destructive CD-SAXS discretization inversion method for measuring semiconductor buried layer structures, comprising:

[0047] Step S1: Select the cross-sectional reconstruction region Ω of the sample and discretize the cross-sectional reconstruction region into a first grid matrix; thus, model initialization and grid discretization are realized.

[0048] like Figures 3-5 As shown, in this embodiment, the sample is a nanograting sample with a physical period of approximately 140 nm and a height of approximately 150 nm.

[0049] The selected cross-sectional reconstruction region Ω is a single-period cross-sectional region of the sample, that is, the smallest repeatable cross-sectional unit. The length and material of each point on the cross-section are the same in the thickness direction (i.e., the Z direction). Therefore, each cross-sectional reconstruction region Ω corresponds to the periodic structure of the semiconductor buried layer structure. The advantage of CD-SAXS technology is that it can quickly obtain the average information of multiple periods, that is, it obtains the average value of periodically repeating cross-sectional units.

[0050] It should be noted that in this invention, only one layer is needed to reconstruct the cross-section region Ω of the sample. One layer is sufficient to fit the cross-section, calculate the scattering intensity, and complete the CD-SAXS data processing.

[0051] In this embodiment, the first grid matrix is ​​composed of It consists of numerous tiny grid cells. In the coarse fitting stage of this embodiment, the first grid matrix uses a 250×250 grid, meaning the spatial resolution of the grid is approximately 0.5-1 nm. For boundary resolution requiring higher precision, the second grid matrix described below can further refine the grid to 2500×1400 or use a step size of 0.1 nm.

[0052] Step S2: Construct the electron density matrix based on the composition distribution of the sample;

[0053] The construction of the electron density matrix is ​​a crucial step in transforming the physical geometry and material distribution of a sample cross-section into a digital two-dimensional matrix ρ(i,j). The core of this strategy lies in the shape segmentation strategy, which, based on the sample's compositional distribution and spatial geometric features, assigns an electron density value corresponding to the position coordinates of each grid cell in the first grid unit, thereby achieving accurate digital characterization of complex multilayer structures. Therefore, step S2 specifically includes: based on the sample's compositional distribution and the shape segmentation strategy, assigning the electron density value of the material (such as the electron density values ​​of silicon, metals, air, etc.) corresponding to the position coordinates of each grid cell in the first grid matrix to each grid cell in the first grid matrix, thereby constructing the electron density matrix.

[0054] In this embodiment, each grid cell in the first grid cell is assigned a corresponding electron density value to construct an electron density matrix:

[0055] Silicon substrate region (Si): Assigned a correspondingly lower density value (e.g., 6.9 × 10⁻⁶). 23 e•cm -3 etc);

[0056] Silver coating region (Ag): Due to the high atomic number of silver, it is assigned a corresponding high density value;

[0057] Void or background region: assigned a value of 0. That is, for samples containing coatings or defects, the grid cells in the electron density matrix are assigned the electron density of the corresponding material or the zero electron density of air / vacuum, respectively, based on the spatial coordinates of the grid cells.

[0058] Thus, the geometry and material distribution of the sample are transformed into a digital two-dimensional electron density matrix in the form of ρ(i, j), which can flexibly describe any irregular shape, including deposition defects (such as bottom voids) generated in the CVD process.

[0059] Figure 4 This is a schematic diagram of discretization mesh generation and electron density matrix construction, showing the cross-section of the sample, the first discretized mesh matrix, and the constructed electron density matrix (used to represent shape, structure, and corresponding material). Gray represents the deposited silver layer, black represents silicon, and in the electron density matrix, number 1 corresponds to silicon, number 2 corresponds to the deposited silver layer, and 0 corresponds to air.

[0060] Step S3: Based on the X-ray scattering physical model, calculate the theoretical scattering form factor F(q) and the theoretical scattering intensity I(q) according to the electron density matrix;

[0061] In step S3, based on the first Born approximation, the theoretical scattering shape factor F(q) and structure factor S(q) are calculated using the discretization summation formula. The formulas for calculating the theoretical scattering shape factor F(q) and structure factor S(q) are as follows:

[0062] ,

[0063] ,

[0064] in, Let be the electron density of the k-th grid cell, (y k , x k) represents the center coordinates of the k-th grid cell, n is the total number of grid cells, w and h are the width (y-axis length) and height (x-axis length) of the grid cell, respectively, and q y and q x y represents the components of the scattering vector in the y and x directions; the structure factor S(q) represents the spatial distribution characteristics of the periodic structure corresponding to the entire cross-sectional reconstruction region, which is used to quantify the contribution of the periodic structure in the sample to the scattering intensity; m represents the diffraction order; and L represents the period length of the sample in the y direction.

[0065] The electron density matrix not only describes the geometry but also the sidewall roughness or interfacial diffusion effect through the Debye-Waller factor. Therefore, the theoretical scattering intensity I(q) is calculated as follows:

[0066] ,

[0067] Where F(q) is the scattering form factor and S(q) is the structure factor. DWF Here, q is the roughness factor, and q is the scattering vector value. This represents the initial light intensity influence coefficient.

[0068] Preferably, the calculation process utilizes a GPU (such as an NVIDIA GPU) to perform parallel computations on the formulas for calculating the theoretical scattering form factor F(q) and the theoretical scattering intensity I(q). Specifically, the GPU parallel computation in step S3 includes: loading the constructed electron density matrix into the GPU; decomposing the calculation tasks of the theoretical scattering form factor F(q) and the theoretical scattering intensity I(q) of the electron density matrix into multiple parallel thread blocks; and simultaneously calculating the scattering intensities under different scattering vectors q and different rotation angles using the GPU's CUDA cores. Compared to traditional CPU serial computation, the computation time is reduced from approximately 6 minutes and 40 seconds to approximately 14.2 seconds, achieving a computational speedup of approximately 28 times, thus enabling real-time iteration of high-dimensional matrix models.

[0069] Step S4: Obtain the CD-SAXS experimental data of the sample to obtain the experimental scattering intensity;

[0070] In step S4, the CD-SAXS experimental setup is used to obtain CD-SAXS experimental data for the sample. For example... Figure 2 As shown, the CD-SAXS experimental setup, in transmission mode, includes a slit 10, a filter 20, a sample 30, and a detector 40 arranged sequentially along the beamline propagation direction. The sample 30 is mounted on a rotatable sample stage 31, allowing the sample 30 to rotate around the z-axis. The beamline originates from a synchrotron radiation source (such as the SSRF scattering beamline station at the Shanghai Synchrotron Radiation Facility).

[0071] In step S4, the CD-SAXS experimental data of the sample are obtained to obtain the experimental scattering intensity, specifically including:

[0072] Step S41: Use the transmission mode of the CD-SAXS experimental setup to perform a rotational scan of the sample around the z-axis and collect the scattering patterns of the sample at different angles.

[0073] The experimental conditions for the CD-SAXS setup were: X-ray energy of 12 keV and spot size of 50 ± 5 μm. m. Due to the use of high-energy X-rays and transmission mode, the phase shift when 12 keV X-rays penetrate the 95 nm silver layer of the sample is much less than 1, approximately Δ. ≈ 0.072 rad, which satisfies the physical premise of the first Born approximation.

[0074] The preferred scanning method for rotational scanning is as follows: the sample is rotated around the z-axis in the range of -25° to 25°, with a step size of 1°.

[0075] Step S42: Scatter the scattering patterns from different angles in reciprocal space to construct q x -q z Two-dimensional scattering intensity spectrum;

[0076] The scattering patterns at different angles (i.e., the raw data acquired by the detector) are directly processed by preprocessing software such as sgtool and fit2d to provide the required reciprocal lattice space coordinates q. x q z In one embodiment, q is constructed based on the scattering patterns at different angles. x -q z Two-dimensional scattering intensity spectrum, specifically including:

[0077] Step S421: Determine detector parameters;

[0078] Experimental parameters include, for example, X-ray energy (12 keV, corresponding to wavelength λ≈0.103 nm), detector-to-sample distance L, and detector pixel size (e.g., how many micrometers per pixel).

[0079] Step S422: Calculate the scattering angle and scattering vector: For each pixel in the scattering image, calculate the scattering angle θ using geometric relationships, and calculate the scattering vector q based on the scattering angle θ. xz ;

[0080] Scattering vector q xz The formula for calculating q is xz =4πsinθ / λ.

[0081] Step S423: Decompose to obtain the reciprocal space coordinates q x q z Based on the sample's rotation angle α, the scattering vector q is... xz Transformed into reciprocal space coordinates q x q z .

[0082] Wherein, the reciprocal space coordinates q x q z The formula for calculating q is x =qcosα,q z = qsinα.

[0083] Step S43: From the q x -q z Slice data are extracted from the two-dimensional scattering intensity spectrum to serve as the experimental scattering intensity I', i.e., as the fitting target.

[0084] Slice data refers to the q x -q z A two-dimensional scattering intensity spectrum with scattering intensity curves at specified x- or y-axis points. The number of slices can be multiple, corresponding to multiple different x- and / or y-axis points.

[0085] Step S5: Adjust the parameters of the electron density matrix through an iterative optimization algorithm so that the residual between the theoretical scattering intensity and the experimental scattering intensity converges, and obtain the electron density matrix at the convergence point.

[0086] Therefore, this invention transforms the continuous integral of the sample into discrete summation, enabling the model to handle electron density distributions of arbitrary shapes. Since adjusting the parameters in the electron density matrix affects the scattering intensity, the method of this invention discretizes complex structures with different electron density distributions and adjusts the parameters of the electron density matrix, resulting in higher accuracy of the material boundary positions and defect distributions in the reconstruction results.

[0087] Step S5 specifically includes:

[0088] Step S51: Calculate the theoretical scattering intensity The mean square error (MSE) between the experimental scattering intensity I' and the scattering intensity is used as the objective function.

[0089] As mentioned above, the experimental scattering intensity I' is from the q x -q z Slice data extracted from a two-dimensional scattering intensity spectrum; when there are multiple slices, the theoretical scattering intensity... The mean square error (MSE) between the experimental scattering intensity I' and the average square error is the sum of the mean square errors corresponding to multiple slice data.

[0090] Step S52: Iteratively adjust the parameters in the electron density matrix using an iterative optimization algorithm until the objective function converges.

[0091] Iterative optimization algorithms can be, for example, differential evolution algorithms.

[0092] After obtaining the electron density matrix at convergence, it can also include:

[0093] The reconstructed cross-section region is discretized into a second grid matrix with a higher resolution than the first grid matrix, and a new electron density matrix is ​​constructed by combining it with the electron density matrix at convergence. Subsequently, the parameters of the electron density matrix are adjusted again using an iterative optimization algorithm to ensure that the residual between the theoretical and experimental scattering intensities converges, resulting in a more optimized electron density matrix at convergence. This achieves a coarse-to-fine dynamic grid adjustment strategy, allowing subsequent electron density matrices to utilize the more optimized electron density matrix at convergence.

[0094] When the parameters of the electron density matrix are adjusted again using the iterative optimization algorithm, the parameters are only locally adjusted at the grid cells of the second grid matrix corresponding to the specific selected region or the high-frequency variation region of the cross-section reconstruction region. In this embodiment, the resolution of the first grid matrix is ​​1nm-3nm, and the resolution of the second grid matrix is ​​0.1nm.

[0095] Therefore, this invention transforms the continuous integral of the sample into discrete summation, enabling the model to handle electron density distributions of arbitrary shapes. Since adjusting the parameters in the electron density matrix affects the scattering intensity, the method of this invention discretizes complex structures with different electron density distributions and adjusts the parameters of the electron density matrix, resulting in higher accuracy of the material boundary positions and defect distributions in the reconstruction results.

[0096] Step S6: Output the converged electron density matrix and reconstruct the sample cross-sectional structure.

[0097] Reconstruction was achieved using a material density segmentation method. For example... Figure 5 As shown, the reconstructed sample cross-sectional structure includes various materials and shapes of the cross-section. The shape structure of the cross-section includes key dimension (CD) parameters (Pitch, Linewidth, Height, Sidewall Angle (SWA)), shape and shape defects, as well as the size and location of buried voids.

[0098] If this invention is used for in-line metrology in semiconductor processes, the method can quickly obtain the electron density distribution of a cross-section, thereby determining the presence of defects based on the reconstructed sample cross-sectional structure. If the method is used for in-line detection of deposition defects, the real-time deposition layer thickness, deposition quality, etc., can be obtained based on the reconstructed sample cross-sectional structure. Therefore, the method of this invention can be used for in-line metrology in semiconductor processes to detect deposition defects generated after chemical vapor deposition (CVD) or electroplating processes.

[0099] In this embodiment, the inversion results successfully reconstructed the silver coating and the silicon grating structure buried by the silver coating, and detected a tiny gap at the bottom of the grating, a feature that is difficult to describe by traditional trapezoidal geometry models.

[0100] The non-destructive CD-SAXS discretization inversion method for measuring semiconductor buried layer structures of the present invention has the following advantages:

[0101] 1. Strong topological adaptability: It abandons the simple geometric parameter model and can adaptively reconstruct buried structures of arbitrary shapes through the "pixelated / voxelated" electron density matrix, including random voids caused by process defects.

[0102] 2. Non-destructive deep-layer detection: Utilizing the penetrating power of X-rays, it can accurately measure the internal silicon structure through thick metal layers (such as 95nm Ag), with extremely high agreement with the results of destructive SEM cross-sectional tests.

[0103] 3. High computational efficiency: By combining discretization algorithms with GPU parallel computing, the computation time of high-dimensional matrix models is significantly shortened, meeting the requirements of semiconductor production lines for detection speed.

[0104] Implementation effect verification:

[0105] To verify the accuracy of this invention, the CD-SAXS data processing results obtained by the method of this invention were compared with the cross-sectional measurement results of destructive scanning electron microscopy (SEM). The results are shown in the table below:

[0106] Comparative results show that the key dimensional parameters measured by the method of this invention are highly consistent with the SEM results, and the error range is smaller (sub-nanometer precision). More importantly, this invention achieves non-destructive measurement of buried structures, avoiding the physical damage to the sample caused by SEM sample preparation (FIB cutting).

[0107] Table 1: CD values ​​of uncoated gratings obtained by different methods

[0108] method Height (nm) Period (nm) Top linewidth (nm) Bottom line width (nm) Silicon bottom radius (nm) SEM 143 ± 1 139 ± 2 63 ± 3 76 ± 2 2 ± 1 CD-SAXS 145.8 ± 0.6 137.5 ± 0.3 63.4 ± 0.5 74.3 ± 0.7 3.0 ± 0.5

[0109] Table 2: CD values ​​of coated samples obtained by different methods

[0110] method Silicon height (nm) Period (nm) Coating thickness (nm) Top linewidth (nm) Bottom line width (nm) Silicon bottom radius (nm) Silver top radius (nm) SEM 143 ± 2 138 ± 3 92 ± 4 65 ± 4 76 ± 2 2 ± 2 13.0 ± 5 CD-SAXS 140.8± 0.4 138.3±0.6 95.4 ± 0.8 67.1 ± 0.6 74.2 ± 0.3 3.5 ± 0.7 15.0 ± 1.6

[0111] In summary, this invention utilizes discretized matrix inversion combined with GPU acceleration technology to overcome the problem of poor adaptability of traditional parametric models to complex geometries, enabling rapid and accurate reconstruction of buried nanostructures containing defects.

[0112] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of the invention. Various variations can be made to the above embodiments of the present invention. All simple and equivalent changes and modifications made in accordance with the claims and description of this application fall within the protection scope of the claims of this patent. All aspects not described in detail in this invention are conventional technical content.

Claims

1. A non-destructive CD-SAXS discretization inversion method for measuring semiconductor buried layer structures, characterized in that, include: Step S1: Select the cross-sectional reconstruction region of the sample and discretize the cross-sectional reconstruction region into a first grid matrix; Step S2: Construct the electron density matrix based on the composition distribution of the sample; Step S3: Based on the X-ray scattering physical model, calculate the theoretical scattering form factor F(q) and the theoretical scattering intensity I(q) according to the electron density matrix; Step S4: Obtain the CD-SAXS experimental data of the sample to obtain the experimental scattering intensity; Step S5: Adjust the parameters of the electron density matrix through an iterative optimization algorithm so that the residual between the theoretical scattering intensity and the experimental scattering intensity converges, and obtain the electron density matrix at the convergence point. Step S6: Output the converged electron density matrix and reconstruct the sample cross-sectional structure.

2. The method according to claim 1, characterized in that, In step S5, after obtaining the electron density matrix at convergence, the following steps are also included: The reconstructed cross-section region is discretized into a second grid matrix with a resolution higher than that of the first grid matrix, and a new electron density matrix is ​​constructed by combining it with the electron density matrix at convergence. Then, the parameters of the new electron density matrix are adjusted again by an iterative optimization algorithm so that the residual between the theoretical scattering intensity and the experimental scattering intensity converges, resulting in a more optimized electron density matrix at convergence.

3. The method according to claim 2, characterized in that, When the parameters of the electron density matrix are adjusted again through the iterative optimization algorithm, the parameters of the electron density matrix are only locally adjusted at the grid cells of the second grid matrix corresponding to the specific selected region or the high-frequency variation region of the cross-section reconstruction region.

4. The method according to claim 2, characterized in that, The first grid matrix has a resolution of 1nm-3nm, and the second grid matrix has a resolution of 0.1nm.

5. The method according to claim 1, characterized in that, Step S2 specifically includes: based on the composition distribution of the sample and a shape segmentation strategy, by determining the position coordinates of each grid cell in the first grid cell, assigning the electron density value of the material corresponding to the position coordinates to each grid cell in the first grid matrix, thereby constructing an electron density matrix.

6. The method according to claim 1, characterized in that, Based on the first Born approximation, the theoretical scattering shape factor F(q) and structure factor S(q) are calculated using the discretization summation formula. The formulas for calculating the theoretical scattering shape factor F(q) and structure factor S(q) are as follows: ， ， in, Let be the electron density of the k-th grid cell, (y k , x k Let q be the center coordinate of the k-th grid cell, n be the total number of grid cells, w and h be the width and height of the grid cell, respectively. y and q x denoted by , where is the component of the scattering vector in the y and x directions; the structure factor S(q) is the spatial distribution characteristic of the periodic structure corresponding to the entire cross-sectional reconstruction region; m is the diffraction order; and L is the period length of the sample in the y direction.

7. The method according to claim 6, characterized in that, The formula for calculating the theoretical scattering intensity I(q) is as follows: ， Where F(q) is the scattering form factor and S(q) is the structure factor. DWF Here, q is the roughness factor, and q is the scattering vector value. This represents the initial light intensity influence coefficient.

8. The method according to claim 1, characterized in that, The calculation process is achieved by using the GPU to perform parallel operations on the calculation formulas for the theoretical scattering form factor F(q) and the theoretical scattering intensity I(q).

9. The method according to claim 1, characterized in that, In step S4, CD-SAXS experimental data of the sample are obtained using a CD-SAXS experimental apparatus. The CD-SAXS experimental apparatus, in transmission mode, includes a slit, a filter, a sample, and a detector arranged sequentially along the propagation direction of the beamline. The sample is mounted on a rotatable sample stage, allowing the sample to rotate around the z-axis. Obtain the CD-SAXS experimental data of the sample to obtain the experimental scattering intensity, specifically including: Step S41: Use the transmission mode of the CD-SAXS experimental setup to perform a rotational scan of the sample around the z-axis and collect the scattering patterns of the sample at different angles. Step S42: Scatter the scattering patterns from different angles in reciprocal space to construct q x -q z Two-dimensional scattering intensity spectrum; Step S43: From the q x -q z Slice data are extracted from the two-dimensional scattering intensity spectrum to serve as the experimental scattering intensity I', i.e., as the fitting target.

10. The method according to claim 1, characterized in that, The sample is a semiconductor device with a periodic structure and identical cross-sections in the thickness direction; The method is used for online measurement in semiconductor processes to quickly obtain the electron density distribution of a cross section; or, the method is used for online detection of deposition defects to obtain the real-time deposition layer thickness and deposition quality based on the reconstructed sample cross-sectional structure.

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