Method, device and computer equipment for detecting sidewall roughness of dense trench array material

Abstract

The application relates to a sidewall roughness detection method, device and computer equipment of a dense groove array material. The method comprises the following steps: collecting a secondary electron image of a material sample with a dense groove array structure based on a preset tilt angle through a scanning electron microscope; determining a target image from the secondary electron image, and determining the profile angle of the target image through a boundary detection algorithm; determining the image ridge line of the target image based on the profile angle; determining the sidewall region of the material sample based on the image ridge line, and determining a correction strip according to the sidewall region; determining the target sidewall depth map of the material sample based on the correction strip; and performing sidewall roughness analysis on the sidewall region of the material sample based on the target sidewall depth map, and determining the sidewall roughness parameter of the material sample. The above scheme can realize complete reconstruction of the three-dimensional morphology of the groove sidewall and automatic and accurate quantitative detection of the surface roughness.

Description

Technical Field

[0001] This application relates to the field of material roughness detection technology, and in particular to a method, apparatus and computer equipment for detecting the sidewall roughness of a densely grooved array material. Background Technology

[0002] Currently, SEM (Scanning Electron Microscope) has become the mainstream tool for critical dimension measurement due to its high resolution and large depth of field. However, for materials with high aspect ratio trench structures, especially dense trench arrays, the top edge of the trench can cause shading on the sidewalls when the electron beam is incident perpendicularly, making it impossible to directly measure the sidewall roughness. This shading effect is particularly significant in trenches with an aspect ratio exceeding 5:1, limiting the application of traditional SEM in material process quality control. Current technical solutions for sidewall roughness detection in dense trench array materials struggle to avoid the shading effect of the trench top edge on the sidewalls at the imaging source, lack standardized imaging schemes for systematic, multi-angle simultaneous observation of complete trench arrays, struggle to accurately extract industry-standard quantitative parameters for sidewall roughness based on the three-dimensional morphology of the sidewalls, and lack unified standard specifications for the detection process, resulting in poor consistency of measurement results and failing to support stable process quality control in semiconductor production lines. Therefore, the problems that need to be solved are how to eliminate the imaging obstruction of the trench top to the sidewall, build a systematic multi-angle observation system for the trench array, accurately extract the roughness parameters of the trench sidewall, and establish a standardized measurement process to support process quality control. Summary of the Invention

[0003] Based on this, it is necessary to provide a method, device, and computer equipment for sidewall roughness detection that eliminates the imaging obstruction of the top of the trench on the sidewall when detecting the sidewall roughness of a dense trench array material, establishes a systematic multi-angle observation system for the trench array, and realizes accurate extraction of trench sidewall roughness parameters.

[0004] In a first aspect, this application provides a method for detecting the sidewall roughness of a dense trench array material, the method comprising:

[0005] Secondary electron images of a material sample with a dense groove array structure are acquired using a scanning electron microscope based on a preset tilt angle; the material sample is fixed on a nano-positioning stage with tilt and rotation degrees of freedom, and the direction of the groove array of the material sample is perpendicular to the electron beam incident plane of the scanning electron microscope.

[0006] The target image is determined from the secondary electronic image, and the contour angle of the target image is determined by the boundary detection algorithm. Based on the contour angle, the ridge line is detected in the target image to determine the image ridge line of the target image.

[0007] Based on the image ridges, the sidewall region of the material sample is determined, and the correction strip is determined according to the sidewall region;

[0008] Based on the correction strip, the sidewall region of the material sample is reconstructed in three dimensions to determine the target sidewall depth map of the material sample;

[0009] Based on the target sidewall depth map, sidewall roughness analysis is performed on the sidewall region of the material sample to determine the sidewall roughness parameters of the material sample.

[0010] In one embodiment, the contour angle of the target image is determined using a boundary detection algorithm, including:

[0011] The image gradient magnitude of each target image is determined by the boundary detection algorithm based on the horizontal and vertical gradient components of the target image.

[0012] The angle to be tested is determined based on the preset angle step size and the preset tilt angle range of the groove boundary slope.

[0013] The image gradient magnitude is projected onto a direction perpendicular to the angle to be tested to determine a first projection curve;

[0014] Gaussian smoothing is applied to the first projection curve to determine the two peak values ​​of the first projection curve after Gaussian smoothing.

[0015] The peak values ​​of the two first curves corresponding to the first projection curve are summed to determine the total peak value of each first projection curve.

[0016] The maximum value among the sum of the peak values ​​is determined, and the angle to be tested corresponding to the maximum value is taken as the contour angle of the target image.

[0017] In one embodiment, based on the contour angle, ridge detection is performed on the target image to determine the image ridges of the target image, including:

[0018] The target image is subjected to Gaussian smoothing to determine the smoothed grayscale image, and the image grayscale function is determined based on the grayscale value and pixel coordinates of each pixel in the smoothed grayscale image.

[0019] The normal component is calculated based on the contour angle, and the second directional derivative of the smoothed grayscale image along the normal direction is determined based on the normal component and the image grayscale function.

[0020] The ridge response intensity is determined based on the second-order directional derivative.

[0021] The ridge response intensity is projected along the normal direction to determine the second projection curve; the peak value of the second projection curve corresponds to the center position of the ridge.

[0022] The continuous pixel lines corresponding to the peak of the second curve are used as candidate boundary lines;

[0023] Based on the candidate boundary lines, the image ridge lines of the target image are determined.

[0024] In one embodiment, determining the image ridge line of the target image based on the candidate boundary line includes:

[0025] Obtain the pre-built top projection width model and side projection height model;

[0026] Based on candidate boundary lines, multiple sets of boundary line combinations are constructed; the boundary line combinations include the upper edge boundary of the background, the top sidewall boundary, and the lower edge boundary of the sidewall.

[0027] Based on the ridge response intensity, the peak response intensity at the upper edge of the background boundary, the peak response intensity at the top sidewall boundary, and the peak response intensity at the lower edge of the sidewall boundary are determined.

[0028] Based on the top surface projection width model, the side surface projection height model, and the tilt angle of the nano-positioning stage, the predicted ordinate of the top surface sidewall boundary and the predicted ordinate of the lower edge boundary of the sidewall corresponding to each boundary line combination are determined.

[0029] Based on the peak response intensity of the upper boundary of the background, the peak response intensity of the top sidewall boundary, the peak response intensity of the lower boundary of the sidewall, the predicted ordinate of the top sidewall boundary, the predicted ordinate of the lower boundary of the sidewall, the actual ordinate of the top sidewall boundary, and the actual ordinate of the lower boundary of the sidewall, the three-line combination comprehensive matching score of each boundary line combination is determined respectively.

[0030] Based on the comprehensive matching score of the three-line combination, the target combination is determined from the boundary line combination, and the background upper edge boundary, top side wall boundary and side wall lower edge boundary corresponding to the target combination are taken as the image ridge line of the target image.

[0031] In one embodiment, determining the corrective strip based on the sidewall region includes:

[0032] A first preset number of sampling points are uniformly selected along the direction of the image ridge line as the first sampling points;

[0033] A second preset number of sampling points are taken along the direction perpendicular to the ridge line of the image as the second sampling points; the sampling range of the second sampling points is limited to the boundary between the top sidewall and the lower edge of the sidewall corresponding to the sidewall region;

[0034] The gray values ​​of the first and second sampling points are determined by bilinear interpolation, and the standard rectangular sidewall strip is determined based on the gray values ​​of the sampling points.

[0035] The standard rectangular sidewall strips are cut according to a preset cutting ratio to determine the correction strips.

[0036] In one embodiment, based on the correction strip, a three-dimensional reconstruction of the sidewall region of the material sample is performed to determine the target sidewall depth map of the material sample, including:

[0037] The correction strip is subjected to high-pass filtering to determine the high-pass filtered output image, and a slope field is constructed based on the high-pass filtered output image.

[0038] The initial height field is determined based on the slope field using the frequency domain integration method, and the initial height field is then subjected to Gaussian smoothing, zero-mean normalization, and linear scaling in sequence to determine the target height field.

[0039] Based on the cotangent difference between tilt angles, the effective angle combination is determined, and the correction strip is subjected to adaptive histogram equalization to determine the enhanced strip image.

[0040] The parallax field between two sets of enhanced strip images corresponding to the effective angle combination of each sidewall protrusion of the material sample is determined by the dense optical flow algorithm, and the initial depth of each sidewall protrusion in the material sample is determined according to the parallax field and the two tilt angles in the effective angle combination.

[0041] The initial depth is fused and processed to determine the mean depth, and the mean depth is then smoothed by Gaussian and pruned to determine the predicted sidewall depth.

[0042] Based on the target height field and the predicted sidewall depth, the target sidewall depth map of the material sample is determined.

[0043] In one embodiment, based on the target sidewall depth map, sidewall roughness analysis is performed on the sidewall region of the material sample to determine the sidewall roughness parameters of the material sample, including:

[0044] Determine the target area for roughness analysis from the sidewall region of the material sample;

[0045] Based on the sidewall depth sampling values ​​of the target region in the target sidewall depth map, determine the average depth of the target region;

[0046] Based on the target sidewall depth map, average depth, and normalized standard deviation of depth, roughness analysis is performed on the target area to determine the sidewall roughness parameters of the target area of ​​the material sample.

[0047] Secondly, this application also provides a sidewall roughness detection device for a dense trench array material, the device comprising:

[0048] The image acquisition module is used to acquire secondary electron images of a material sample with a dense groove array structure using a scanning electron microscope based on a preset tilt angle; the material sample is fixed on a nano-positioning stage with tilt and rotation degrees of freedom, and the direction of the groove array of the material sample is perpendicular to the electron beam incident plane of the scanning electron microscope.

[0049] The image ridgeline determination module is used to determine the target image from the secondary electronic image, and to determine the contour angle of the target image through a boundary detection algorithm, and to perform ridgeline detection on the target image based on the contour angle to determine the image ridgeline of the target image;

[0050] The correction strip determination module is used to determine the sidewall region of the material sample based on the image ridge line, and to determine the correction strip according to the sidewall region;

[0051] A three-dimensional reconstruction module is used to perform three-dimensional reconstruction of the sidewall region of the material sample based on the correction strip, and to determine the target sidewall depth map of the material sample.

[0052] The sidewall roughness analysis module is used to perform sidewall roughness analysis on the sidewall region of the material sample based on the target sidewall depth map, and to determine the sidewall roughness parameters of the material sample.

[0053] Thirdly, this application also provides a computer device, the computer device including a memory and a processor, the memory storing a computer program, and the processor executing the computer program to perform the following steps:

[0054] Secondary electron images of a material sample with a dense groove array structure are acquired using a scanning electron microscope based on a preset tilt angle; the material sample is fixed on a nano-positioning stage with tilt and rotation degrees of freedom, and the direction of the groove array of the material sample is perpendicular to the electron beam incident plane of the scanning electron microscope.

[0055] The target image is determined from the secondary electronic image, and the contour angle of the target image is determined by the boundary detection algorithm. Based on the contour angle, the ridge line is detected in the target image to determine the image ridge line of the target image.

[0056] Based on the image ridges, the sidewall region of the material sample is determined, and the correction strip is determined according to the sidewall region;

[0057] Based on the correction strip, the sidewall region of the material sample is reconstructed in three dimensions to determine the target sidewall depth map of the material sample;

[0058] Based on the target sidewall depth map, sidewall roughness analysis is performed on the sidewall region of the material sample to determine the sidewall roughness parameters of the material sample.

[0059] Fourthly, this application also provides a computer-readable storage medium having a computer program stored thereon, the computer program performing the following steps when executed by a processor:

[0060] Secondary electron images of a material sample with a dense groove array structure are acquired using a scanning electron microscope based on a preset tilt angle; the material sample is fixed on a nano-positioning stage with tilt and rotation degrees of freedom, and the direction of the groove array of the material sample is perpendicular to the electron beam incident plane of the scanning electron microscope.

[0061] The target image is determined from the secondary electronic image, and the contour angle of the target image is determined by the boundary detection algorithm. Based on the contour angle, the ridge line is detected in the target image to determine the image ridge line of the target image.

[0062] Based on the image ridges, the sidewall region of the material sample is determined, and the correction strip is determined according to the sidewall region;

[0063] Based on the correction strip, the sidewall region of the material sample is reconstructed in three dimensions to determine the target sidewall depth map of the material sample;

[0064] Based on the target sidewall depth map, sidewall roughness analysis is performed on the sidewall region of the material sample to determine the sidewall roughness parameters of the material sample.

[0065] The aforementioned method, apparatus, and computer equipment for detecting the sidewall roughness of densely grooved array materials utilize a scanning electron microscope to acquire secondary electron images of a material sample with a densely grooved array structure based on a preset tilt angle. The material sample is fixed on a nano-positioning stage with tilt and rotation degrees of freedom, and the direction of the groove array of the material sample is perpendicular to the electron beam incident plane of the scanning electron microscope. A target image is determined from the secondary electron image, and the contour angle of the target image is determined using a boundary detection algorithm. Based on the contour angle, ridge line detection is performed on the target image to determine the image ridge line. Based on the image ridge line, the sidewall region of the material sample is determined, and a correction strip is determined according to the sidewall region. Based on the correction strip, a three-dimensional reconstruction of the sidewall region of the material sample is performed to determine the target sidewall depth map of the material sample. Based on the target sidewall depth map, sidewall roughness analysis is performed on the sidewall region of the material sample to determine the sidewall roughness parameters of the material sample. This solution addresses the shortcomings of current techniques for sidewall roughness detection in dense trench array materials. These limitations include the difficulty in mitigating the occlusion effect of the trench top edge on the sidewall from the imaging source, the challenge in accurately extracting industry-standard quantitative parameters for sidewall roughness based on the three-dimensional morphology of the sidewall, and the lack of standardized testing procedures leading to inconsistent measurement results and inability to support stable process quality control in semiconductor production lines. The proposed solution utilizes a nano-positioning stage with tilt and rotation degrees of freedom to fix the sample, ensuring the trench array is perpendicular to the electron beam incident plane. Secondary electron images are acquired using a scanning electron microscope at a preset tilt angle, ensuring regular imaging geometry. Boundary detection is then used to obtain contour angles, and ridge detection extracts image ridges, precisely segmenting the trench sidewall region and generating correction strips. Based on these correction strips, three-dimensional reconstruction of the sidewall is performed to obtain a depth map of the target sidewall. Finally, quantitative roughness analysis is conducted based on the depth map to output standard roughness parameters. This approach accurately separates the effective observation area of ​​the trench sidewall, avoids interference from irrelevant areas, and achieves complete three-dimensional morphology reconstruction of the trench sidewall and automated, precise quantitative detection of surface roughness. Attached Figure Description

[0066] Figure 1 This is an application environment diagram of a sidewall roughness detection method for a dense trench array material in one embodiment.

[0067] Figure 2 This is a flowchart illustrating a method for detecting the sidewall roughness of a dense trench array material in one embodiment;

[0068] Figure 3 This is a structural block diagram of a sidewall roughness detection device for a dense trench array material in one embodiment;

[0069] Figure 4 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0070] 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.

[0071] The sidewall roughness detection method for densely grooved array materials provided in this application embodiment can be applied to, for example... Figure 1 In the application environment shown, terminal 102 communicates with server 104 via a network. A data storage system can store the data that server 104 needs to process. The data storage system can be integrated onto server 104, or it can be located in the cloud or on another network server. Server 104 acquires secondary electron images of a material sample with a dense groove array structure using a scanning electron microscope at a preset tilt angle. The material sample is fixed on a nano-positioning stage with tilt and rotation degrees of freedom, and the direction of the groove array of the material sample is perpendicular to the electron beam incident plane of the scanning electron microscope. A target image is determined from the secondary electron images, and the contour angle of the target image is determined using a boundary detection algorithm. Based on the contour angle, ridge line detection is performed on the target image to determine the image ridge line. Based on the image ridge line, the sidewall region of the material sample is determined, and a correction strip is determined according to the sidewall region. Based on the correction strip, the sidewall region of the material sample is reconstructed in three dimensions to determine the target sidewall depth map of the material sample. Based on the target sidewall depth map, the sidewall roughness of the sidewall region of the material sample is analyzed to determine the sidewall roughness parameters of the material sample. The sidewall roughness parameters of the material sample are sent to terminal 102 via a communication network. The terminal 102 can be, but is not limited to, various personal computers, laptops, smartphones, tablets, IoT devices, and portable wearable devices. IoT devices can include smart speakers, smart TVs, smart air conditioners, and smart in-vehicle systems. Portable wearable devices can include smartwatches, smart bracelets, and head-mounted devices. The server 104 can be implemented using a standalone server or a server cluster consisting of multiple servers.

[0072] In one embodiment, such as Figure 2 As shown, a method for detecting the sidewall roughness of a dense trench array material is provided. This embodiment illustrates the application of this method to a terminal. It is understood that this method can also be applied to a server, and further to a system including both a terminal and a server, and implemented through interaction between the terminal and the server. In this embodiment, the method includes the following steps:

[0073] S210. Secondary electron images of material samples with dense groove array structures are acquired using a scanning electron microscope based on a preset tilt angle.

[0074] The material sample is fixed on a nanostage with tilt and rotation degrees of freedom, and the direction of the groove array of the material sample is perpendicular to the electron beam incident plane of the scanning electron microscope.

[0075] Scanning electron microscopy (SEM) is a precision characterization instrument that uses a focused high-energy electron beam to scan the surface of a sample, collecting signals generated by the interaction between electrons and the sample to image and observe the microscopic morphology of the sample. When the electron beam of the scanning electron microscope bombards the surface of a material sample, the surface atoms of the sample are struck and release low-energy electrons, which are called secondary electrons. The detector collects the secondary electron signals and converts them into grayscale images according to the scanning position, which are the target images. The preset tilt angles can include 0°, 5°, 10°, 15°, 20°, 25°, 30°, 35°, 40°, 45°, 50°, 55°, 60°, and 65°.

[0076] Specifically, a material sample with a high aspect ratio dense trench array structure is fixed on a nanostage with tilt and rotation degrees of freedom, ensuring the trench array direction is perpendicular to the electron beam incident plane. The stage possesses nanometer-level positioning accuracy, with a tilt angle range of -4° to 70° and a rotation angle range of 0° to 360°. The sample is secured by clamps to ensure the trench array direction remains stable during tilting and rotation. Secondary electron images of the trench array of the material sample with the dense trench array structure are acquired at multiple set tilt angles. Exemplary image parameters of the secondary electron images are shown in Table 1.

[0077] Table 1

[0078]

[0079] S220. Determine the target image from the secondary electronic image, and determine the contour angle of the target image through a boundary detection algorithm. Based on the contour angle, perform ridge line detection on the target image to determine the image ridge line of the target image.

[0080] Among them, the overall tilt angle of the complete outline of the groove or sidewall structure in the target image is the tilt angle of the long boundary line formed by the top surface, sidewall, and bottom of the groove in the target image relative to the horizontal or vertical coordinate axis of the image. The image ridge line refers to the linear feature formed by the extreme values ​​of gray-level gradients in the target image, which is the center line of the abrupt change in brightness of the groove structure.

[0081] For example, the target image may include secondary electronic images acquired at six tilt angles: 30°, 35°, 40°, 45°, 50°, and 55°. The secondary electronic images acquired at these six tilt angles have a moderate visible area on the sides, providing sufficient parallax signal without excessive tilt causing the sides to be obscured by the top surface. The file numbers and uses of the target images corresponding to each tilt angle are shown in Table 2.

[0082] Table 2

[0083]

[0084] Among them, the FC (Frangi Curve / Frangi Ridge Filter) texture source is a Hessian multi-scale filtering operator in the image domain for extracting linear ridges and groove boundaries.

[0085] For example, determining the contour angle of a target image using a boundary detection algorithm includes:

[0086] S2211. Using a boundary detection algorithm, determine the image gradient magnitude of each target image based on the horizontal and vertical gradient components of the target image.

[0087] The horizontal gradient component describes the difference in grayscale brightness between the left and right sides of a pixel; when there is a change in brightness between the left and right sides of the groove diagonal line, the value of the horizontal gradient component increases. The vertical gradient component describes the difference in grayscale brightness between the top and bottom of a pixel; when there is a change in brightness between the top and bottom of the groove diagonal line, the value of the vertical gradient component increases.

[0088] It should be noted that the material sample in the target image is a rectangular cross-section beam. When viewed at an angle, three regions, A', B', and C', are visible. The locations and characteristics of these three regions are shown in Table 3.

[0089] Table 3

[0090]

[0091] Specifically, using a boundary detection algorithm and a 5×5 Sobel operator, the image gradient magnitude is determined based on the horizontal and vertical gradient components of the secondary electronic image. For example, the formula for calculating the image gradient magnitude is shown in formula (1).

[0092] (1).

[0093] Where G is the image gradient magnitude, G x G represents the horizontal gradient component of the target image. y This represents the vertical gradient component of the target image.

[0094] Understandably, the 5th-order Sobel operator has stronger noise resistance and can stably capture the gray-scale changes of the long oblique line boundary of the groove, reducing spurious gradient interference.

[0095] S2212. Determine the angle to be tested based on the preset angle step size and the preset tilt angle range of the groove boundary slope.

[0096] The preset angle step size and the preset tilt angle range of the trench boundary slope can both be set according to actual needs. For example, the preset angle step size can be 0.5°, and the preset tilt angle range of the trench boundary slope can be... ,in, This indicates the inclination angle of the groove boundary slope. The angle to be tested characterizes the degree of inclination of the groove edge line relative to the image coordinate axes.

[0097] Specifically, by using a step size of 0.5°, the inclination angle range of the groove boundary slope is traversed to determine the angle to be tested.

[0098] S2213. Project the image gradient magnitude based on a direction perpendicular to the angle to be tested to determine the first projection curve.

[0099] Specifically, for each angle to be tested, the image gradient magnitude is projected onto a coordinate axis perpendicular to the angle to be tested, generating the gradient accumulation projection curve corresponding to each angle to be tested, i.e., the first projection curve.

[0100] For example, the expression for the first projection curve is shown in formula (2).

[0101] (2).

[0102] in, d represents the first projection curve; d represents the discrete distance grid number, i.e., the discrete projection distance index; (x,y) represents the pixel coordinates of the target image; G(x,y) represents the image gradient magnitude at (x,y); This indicates the angle to be tested. This represents the pixel coordinates (x, y) projected onto a surface perpendicular to the x-axis. The signed distance on the direction axis is obtained by mapping each pixel (x,y) onto the coordinate axis perpendicular to the angle to be tested, thus obtaining the signed projection distance of the pixel. This indicates rounding down, and its function is to discretize a continuous distance into integer bins; This represents the minimum projection distance of all pixels, and its function is to shift the distance to start from 0. This represents the Kronecker delta function, which states that if the current pixel's discrete grid number equals the target distance grid d, then... =1; if the current pixel discrete grid number is not equal to the target distance grid d, then =0.

[0103] S2214. Perform Gaussian smoothing on the first projection curve and determine the two peak values ​​of the first projection curve after Gaussian smoothing.

[0104] Among them, the peak values ​​of the first curve are the two largest values ​​corresponding to the first projection curve after Gaussian smoothing.

[0105] Specifically, Gaussian smoothing is applied to each first projection curve, and the two highest peaks of each first projection curve are determined from the Gaussian smoothed first projection curves as the two first curve peaks.

[0106] S2215. Sum the peak values ​​of the two first curves corresponding to the first projection curve to determine the total sum of the peak values ​​corresponding to each first projection curve.

[0107] S2216. Determine the maximum value in the sum of peak values, and take the angle to be tested corresponding to the maximum value as the contour angle of the target image.

[0108] The above scheme, by selecting the optimal angle through multi-angle gradient projection, Gaussian smoothing and peak summation, can accurately solve the contour tilt angle of the groove image and improve the accuracy of subsequent ridge detection.

[0109] For example, based on contour angles, ridge detection is performed on the target image to determine the image ridges, including:

[0110] The target image is Gaussian smoothed to determine the smoothed grayscale image. Based on the grayscale values ​​and coordinates of each pixel in the smoothed grayscale image, the image grayscale function is determined. Normal components are calculated based on the contour angle, and the second directional derivative of the smoothed grayscale image along the normal direction is determined based on the normal components and the image grayscale function. The ridge response intensity is determined based on the second directional derivative. The ridge response intensity is projected along the normal direction to determine the second projection curve. The peak value of the second projection curve corresponds to the ridge center position. The continuous pixel lines corresponding to the peak value of the second curve are used as candidate boundary lines. Based on the candidate boundary lines, the image ridges of the target image are determined.

[0111] Specifically, the target image is Gaussian smoothed to determine the smoothed grayscale image. Based on the coordinates and corresponding grayscale values ​​of each pixel in the image, an image grayscale function I that characterizes the grayscale distribution of the entire image is constructed. The normal direction of the groove boundary of the material sample is determined based on the contour angle. The second-order partial derivative I of the image grayscale function is determined. xx The second-order partial derivative I of the image grayscale function on the ordinate yyAnd the mixed second-order partial derivative I of the image grayscale function after taking the first-order partial derivative with respect to the horizontal axis and then the first-order partial derivative with respect to the vertical axis. xy Calculate the normal component n based on the contour angle. x and n y Based on the normal components and the image grayscale function, the second-order directional derivative of the smoothed grayscale image along the normal direction is determined. xx I yy and I xy All are Gaussian smoothed =5 and then calculate.

[0112] The expression for the second directional derivative of the smoothed grayscale image along the normal direction is shown in formula (3).

[0113] (3).

[0114] in, Let be the second directional derivative of the grayscale value along the normal direction n.

[0115] The ridge response intensity is determined based on the second directional derivative. The expression for the ridge response intensity is shown in formula (4).

[0116] (4).

[0117] Where R is the ridge response intensity, that is, the larger value between the negative of the second derivative and 0 is taken as the ridge response intensity R. The second derivative of the normal at the bright ridge position of the trench is negative, and the value is positive after taking the negative. Regions without ridges are directly truncated to 0, and only the effective ridge response is retained.

[0118] The ridge response intensity is projected along the normal direction to determine the second projection curve. The peak positions on the second projection curve are extracted, and the coordinates of all peaks are summarized to obtain the candidate boundary lines to be screened. Based on the candidate boundary lines, the image ridge lines of the target image are determined.

[0119] The above scheme first eliminates image noise through Gaussian smoothing, obtains the normal direction based on the contour angle, solves the second-order directional derivative of the normal by combining the image grayscale function and calculates the ridge response intensity, then projects the response intensity onto the normal to generate a projection curve, accurately locates the ridge center based on the curve peak to determine the candidate boundary line, and determines the image ridge line based on the candidate boundary line, which can improve the accuracy of ridge line extraction and anti-interference ability.

[0120] For example, determining the image ridge line of a target image based on candidate boundary lines includes:

[0121] Obtain pre-built top projection width model and side projection height model; construct multiple boundary line combinations based on candidate boundary lines; the boundary line combinations include the upper edge boundary of the background, the upper side wall boundary of the top surface, and the lower edge boundary of the side wall; determine the peak response intensity of the upper edge boundary of the background, the upper side wall boundary of the top surface, and the lower edge boundary of the side wall based on the ridge response intensity; determine the predicted ordinate of the upper side wall boundary and the lower edge boundary of the side wall corresponding to each boundary line combination based on the top projection width model, the side projection height model, and the tilt angle. Based on the peak response intensity of the upper edge boundary of the background, the peak response intensity of the upper sidewall boundary, the peak response intensity of the lower sidewall boundary, the predicted ordinate of the upper sidewall boundary, the predicted ordinate of the lower sidewall boundary, the actual ordinate of the upper sidewall boundary, and the actual ordinate of the lower sidewall boundary, the three-line combination comprehensive matching score of each boundary line combination is determined. Based on the three-line combination comprehensive matching score, the target combination is determined from the boundary line combinations, and the upper edge boundary of the background, the upper sidewall boundary, and the lower sidewall boundary corresponding to the target combination are taken as the image ridge lines of the target image.

[0122] Specifically, construct the top surface projection width model d AB and side projection height model d BC .in, , . , . d AB d is the width of the projection of the top surface in the image, i.e., the distance from line A to line B; BC D is the projection height of the side view in the image, i.e., the distance from line B to line C; top H is the calibrated value of the actual width of the top surface. side The calibrated value representing the actual side height; The tilt angle is px; the pixel represents a pixel; the calibration value is calculated from the detection result of the 45° image, that is, the boundary detection is completed in advance using the standard groove SEM image of the nano-positioning stage at 45°, and the pixel reference value corresponding to the standard physical size is calculated in reverse as a globally fixed prior parameter.

[0123] Based on candidate boundary lines, multiple boundary line combinations are constructed. Each combination includes a background upper edge boundary (A), a top sidewall boundary (B), and a sidewall lower edge boundary (C). Response regions corresponding to the upper edge boundary (A), top sidewall boundary (B), and sidewall lower edge boundary (C) are extracted from the ridge response intensity map. For each response region, the ridge response intensity is projected onto a line to generate a projection curve. The maximum peak value of each projection curve is extracted. The maximum peak value corresponding to the extracted upper edge boundary (A) can be used as the peak response intensity of the background upper edge boundary (A). The maximum peak value corresponding to the extracted top sidewall boundary B can be used as the peak response intensity of the top sidewall boundary B. The maximum peak value corresponding to the extracted lower edge boundary C of the sidewall can be used as the peak response intensity of the lower edge boundary C of the sidewall. Based on the top projection width model, the side projection height model, and the tilt angle of the fixed material sample, the predicted ordinate of the top sidewall boundary corresponding to each boundary line combination is determined. The predicted ordinate of the boundary with the lower edge of the sidewall Based on the peak response intensity of the background upper boundary A, the peak response intensity of the top sidewall boundary B, the peak response intensity of the sidewall lower boundary C, the predicted ordinate of the top sidewall boundary, the predicted ordinate of the sidewall lower boundary, and the actual ordinate y of the top sidewall boundary. B The actual ordinate y of the boundary between the sidewall and the lower edge C The three-line combination comprehensive matching score of each boundary line combination is determined. The boundary line combination with the highest three-line combination comprehensive matching score is determined as the target combination, and the background upper edge boundary A, top side wall boundary B, and side wall lower edge boundary C corresponding to the target combination are taken as the image ridge lines of the target image.

[0124] For example, the formula for calculating the comprehensive matching score of the three-line combination is shown in formula (5):

[0125] (5).

[0126] Where S is the three-line combination comprehensive matching score; 0.5 represents the peak response intensity at the boundary A along the background. The weight, 0.3, represents the peak response intensity at the top sidewall boundary B. The weight is 0.2, which represents the peak response intensity at the lower edge boundary C of the sidewall. The weights. , y A This represents the actual ordinate of the upper boundary A.

[0127] For example, the ridge parameters of the top sidewall boundary B and the lower sidewall boundary C corresponding to the target combination are shown in Table 4.

[0128] Table 4

[0129]

[0130] The above scheme not only makes full use of the grayscale texture features of the image to ensure clear and distinguishable boundaries, but also uses the groove imaging geometric and physical model to constrain the position of the ridge line, which can improve the accuracy of the extracted image ridge line.

[0131] S230. Based on the image ridge line, determine the sidewall region of the material sample, and determine the correction strip according to the sidewall region.

[0132] The sidewall region of the material sample is the pixel region between the two ridge lines, namely the top sidewall boundary B and the lower sidewall boundary C.

[0133] Specifically, based on the top sidewall boundary B and the lower sidewall boundary C corresponding to the ridge lines in each group of images, the sidewall region of the material sample corresponding to the ridge lines in each group of images is determined. Correction strips are then determined based on the sidewall regions.

[0134] For example, determining the corrective strip based on the sidewall region includes:

[0135] A first preset number of sampling points are uniformly selected along the direction of the image ridge line as the first sampling points; a second preset number of sampling points are selected along the direction perpendicular to the image ridge line as the second sampling points; the sampling range of the second sampling points is limited to the boundary between the top sidewall and the bottom edge of the sidewall corresponding to the sidewall region; the gray values ​​of the sampling points of the first and second sampling points are determined by bilinear interpolation, and a standard rectangular sidewall strip is determined based on the gray values ​​of the sampling points; the standard rectangular sidewall strip is cropped according to a preset cropping ratio to determine the correction strip.

[0136] The first and second preset quantities can be set according to actual needs. For example, the first preset quantity can be 400 and the second preset quantity can be 250. The preset cropping ratio can be 12% cropping on the left side of the image, 8% cropping on the right side of the image, 5% cropping on the top side of the image, and 5% cropping on the bottom side of the image.

[0137] Specifically, 400 sampling points are uniformly selected along the image ridge line as the first sampling points, and 250 sampling points are selected perpendicular to the image ridge line as the second sampling points. The gray values ​​of the first and second sampling points are determined using bilinear interpolation, and a standard rectangular sidewall strip is determined based on these gray values. The standard rectangular sidewall strip is then cropped by 12% on the left, 8% on the right, 5% on the top, and 5% on the bottom. This cropped standard rectangular sidewall strip is used as the correction strip.

[0138] For example, after determining the correction strips, the height of the correction strips can be corrected to determine the physical wall height corresponding to each correction strip. The expression for the physical wall height is shown in formula (6).

[0139] (6).

[0140] in, The corrected true physical wall height is expressed in pixels (px). Multiplying this pixel height by the pixel-nanometer conversion factor corresponding to the image scale will give you the actual nanometer physical height of the wall. , which is the vertical pixel width of the strip, representing the pixel distance along the normal direction of the groove ridge line between the boundary B of the top sidewall and the boundary C of the lower edge of the sidewall inside the correction strip, that is, the pixel height of the sidewall image after tilted geometric projection by the nano-positioning stage. The angle is the tilt angle. Since the side projection height = actual height × sinθ, dividing by sinθ can restore the actual height.

[0141] For example, the physical wall height related parameters for each target image are shown in Table 5.

[0142] Table 5

[0143]

[0144] The above scheme can obtain corrected stripes with uniform size, complete texture and no boundary noise, providing standardized image input for subsequent sidewall-related feature calculation.

[0145] S240. Based on the correction strip, perform three-dimensional reconstruction of the sidewall region of the material sample to determine the target sidewall depth map of the material sample.

[0146] Specifically, the sidewall morphology of the material sample is reconstructed in three dimensions based on the physical wall height corresponding to the corrected strip and the effective sidewall image using the multi-angle parallax method and gradient integral method, thereby determining the target sidewall depth map of the material sample.

[0147] It should be noted that the intensity of the SEM secondary electron signal is related to the normal direction of the material sample surface. For surfaces with a small slope, the expression for the gray level of the secondary electron signal is shown in formula (7).

[0148] (7)

[0149] Where I(x,y) is the gray level of the secondary electronic signal of pixel (x,y); I0 is the average brightness of the substrate; α is the sensitivity coefficient of brightness to slope; and z is the surface height function. Let be the slope of the surface along the x-direction. Let be the slope of the surface along the y-direction. The grayscale value after high-pass filtering is approximately proportional to the surface slope along the detector direction, representing the projection components of the detector direction in the x and y directions.

[0150] The pixel secondary electronic grayscale refers to the original imaging brightness (x, y) in the correction strip, which is an image observation value that the algorithm can directly read; the substrate average brightness refers to the global average grayscale of the entire sidewall correction strip, representing the basic background brightness when there are no small morphological undulations, and is used to eliminate the constant brightness shift caused by uneven overall illumination; the brightness sensitivity coefficient to slope refers to the inherent proportionality constant of the imaging system, characterizing how much grayscale change will be caused by a small surface tilt; the surface height function is used to describe the true three-dimensional height and undulation distribution of each part of the trench sidewall; the slope of the surface along the x direction and the slope of the surface along the y direction represent the degree of tilt of the local sidewall on the two coordinate axes of the image; the projection components of the detector direction on x and y represent the weighting coefficients that decompose the signal receiving sensitive direction of the secondary electron detector onto the x and y coordinate axes of the image, respectively.

[0151] For example, based on the correction strips, a three-dimensional reconstruction of the sidewall region of the material sample is performed to determine the target sidewall depth map of the material sample, including:

[0152] S2401. Perform high-pass filtering on the correction strip, determine the high-pass filtered output image, and construct a slope field based on the high-pass filtered output image.

[0153] Among them, the slope field is the local texture tilt slope distribution map corresponding to each pixel point of the entire correction strip, which is used to characterize the texture direction of the trench sidewall. It is divided into two sets of slope components in the x and y directions, which are adapted to the detector's main imaging coordinate system.

[0154] Specifically, the correction strip is subjected to high-pass filtering to remove large-scale illumination gradients. The expression for high-pass filtering of the correction strip is shown in Equation (8).

[0155] (8).

[0156] Among them, I hp This represents the high-pass filtered output image; Standard deviation =50 Gaussian kernel; For convolution operation; I' represents the correction strip.

[0157] For example, the slope field and the expressions for its construction are shown in Equations (9) and (10).

[0158] (9).

[0159] (10).

[0160] Where p represents the slope in the x-direction, with the main imaging direction of the detector as the x-axis reference, the local tilt slope of the texture along the x-axis at each pixel is calculated, and the texture change information in the x-direction is completely preserved without attenuation; q represents the slope in the y-direction: the local tilt slope of the pixel along the y-axis is calculated, and a weighting factor of 0.3 is introduced to reduce the weight of the y-direction component.

[0161] S2402. The initial height field is determined based on the slope field by frequency domain integration, and the initial height field is then subjected to Gaussian smoothing, zero-mean processing and linear scaling in sequence to determine the standard height field.

[0162] For example, the expression for the initial height field is shown in Equation (11).

[0163] (11).

[0164] in, This represents the two-dimensional inverse Fourier transform. The symbol z(x,y) represents the two-dimensional Fourier transform of the height field. The capped symbol indicates that the quantity is in the frequency domain and is no longer the pixel value in the spatial domain of the original image. z(x,y) represents the surface height function of the trench sidewall.

[0165] The expression is shown in formula (12).

[0166] (12).

[0167] in, and ω and y are the angular frequencies in the x and y directions, respectively, and are coordinates in the frequency domain coordinate system, corresponding to texture undulations at different scales in the spatial domain; j is the imaginary unit, i.e. ; and For slope field Fourier transform; The sum of squared frequencies corresponds to the Laplacian operator in the frequency domain, and the slope field is derived from the local surface tilt information obtained by converting the SEM grayscale imaging model.

[0168] The initial height field is filtered using Gaussian smoothing with a standard deviation of σ=2 to weaken the slight height fluctuations caused by slope field noise. Then, zero-mean scaling is applied to the Gaussian smoothed height field to eliminate the overall height offset. Finally, linear scaling is used to constrain the overall height fluctuation range of the above-processed height field to 6% of the total wall height, thereby eliminating global height deviations and abnormal extreme values ​​generated during reconstruction, and obtaining a standard height field with fluctuation amplitude that closely matches the micro-morphology of the real sidewall and with lower noise.

[0169] It should be noted that the above scheme can select a single image with the tilt angle of the nano-positioning stage closest to 45° to extract the correction strip as the input for 3D reconstruction. At this angle, the visible range of the trench sidewall and the imaging resolution achieve the optimal balance. The advantage of the above 3D reconstruction scheme is that it can completely capture the high-frequency fine concave and convex texture of the sidewall, and the reconstructed height field is complete without missing holes. However, there are two limitations: first, the calculated absolute depth value depends on the theoretical assumption of the orientation of the secondary electron detector; second, the scaling factor used for grayscale and morphology conversion is a calibration empirical parameter, which has a certain systematic bias.

[0170] S2403. Based on the cotangent difference between tilt angles, determine the effective angle combination and perform adaptive histogram equalization on the correction strip to determine the enhanced strip image.

[0171] It should be noted that the apparent location of the lateral protrusion within each orthodontic strip is... The expression is: ;in, y represents the position of the lateral protrusion, and y represents the depth of the lateral protrusion; the apparent displacement between every two tilt angles. The calculation formula is θ1 and θ2 represent two paired tilt angles, which are the two tilt angles in the effective angle combinations described later. Let be the cotangent difference between the two angles. From the above formula, we can derive the expression for the depth of the side protrusion: .

[0172] Specifically, priority is given to pairing two groups of tilt angles with large differences in tilt angles as angle combinations. This involves first randomly combining tilt angles in pairs to determine candidate angle combinations. The absolute value of the cotangent difference between the two tilt angles in each candidate angle combination is determined, and candidate angle combinations with an absolute value greater than a threshold are selected as valid angle combinations. The CLAHE (Contrast Limited Adaptive Histogram Equalization) method is used to adaptively equalize the corrected strips, determining the enhanced strip image. When using the CLAHE method for adaptive histogram equalization of the corrected strips, a clipping threshold of clipLimit=2.0 and a tileGridSize=8×8 are set. Applying this processing to each group of corrected strips can improve local grayscale contrast, enhance the difference in brightness and darkness of subtle sidewall textures, and eliminate uneven imaging brightness.

[0173] S2404. Using a dense optical flow algorithm, determine the parallax field between two sets of enhanced strip images corresponding to the effective angle combination for each sidewall protrusion of the material sample, and determine the initial depth of each sidewall protrusion in the material sample based on the parallax field and the two tilt angles in the effective angle combination.

[0174] Among them, the dense optical flow algorithm is the Farneback algorithm.

[0175] Specifically, the dense optical flow algorithm is used to determine the apparent displacement of each sidewall protrusion of the material sample between two sets of enhanced strip images corresponding to the effective angle combination, thereby determining the disparity field between the two sets of enhanced strip images corresponding to the effective angle combination. The Farneback dense optical flow algorithm employs a five-layer image pyramid structure, a 21×21 computation window, and iterates 7 times per block. The initial depth of each sidewall protrusion in the material sample is determined based on the disparity field and the cotangent values ​​of the two tilt angles in the effective angle combination.

[0176] For example, the initial depth of each sidewall protrusion in the material sample can be calculated with reference to formula (13).

[0177] (13).

[0178] Where y' represents the initial depth of the sidewall protrusion, θ1 and θ2 represent the two tilt angles in the effective angle combination, and v flow This represents the apparent displacement of the sidewall protrusion being calculated in the parallax field between two sets of enhanced strip images corresponding to the effective angle combination.

[0179] S2405. Perform mean fusion and processing on the initial depth to determine the mean depth, and perform Gaussian smoothing and outlier pruning on the mean depth to determine the predicted sidewall depth.

[0180] It should be noted that the above scheme can obtain the initial depth corresponding to multiple effective angle combinations. It requires that each pixel position in the enhanced strip image has at least two calculated initial depths. The initial depths corresponding to each pixel position are then mean-fused and processed to determine the mean depth corresponding to each pixel position in the enhanced strip image. The mean depth is then Gaussian smoothed, and outlier clipping is performed on the smoothed mean depth to remove abnormal depth points below 2% and above 98% of the depth distribution. This results in a predicted sidewall depth with lower noise and a reasonable numerical range, which is used as the predicted depth field.

[0181] S2406. Based on the standard height field and the predicted sidewall depth, determine the target sidewall depth map of the material sample.

[0182] Specifically, the standard height field and the predicted sidewall depth are fused to determine the target sidewall depth map of the material sample.

[0183] For example, Table 6 shows the optional strategies for fusing the standard height field and the predicted sidewall depth, the corresponding formulas for the optional strategies, and the applicable scenarios for the optional strategies.

[0184] Table 6

[0185]

[0186] Among these, "Manual" refers to the manual calibration method, where feature points are manually selected and contours are manually fitted to calculate the sidewall depth as a benchmark. "SNR Weighted" refers to the signal-to-noise ratio weighted fusion method, which assigns weights based on the image's signal-to-noise ratio for each pixel location; pixels with higher signal-to-noise ratios and clearer images receive greater weights. Multiple depth results are weighted and averaged to reduce invalid data in noisy areas. "Frequency Split" refers to the frequency domain decomposition and fusion method, which splits the reconstructed height field into two parts: low-frequency large-amplitude topography and high-frequency fine texture. These are solved separately using an adaptation algorithm and then merged. "FC Only" refers to Frankot-Chellappa frequency domain integral reconstruction, relying solely on the slope field of a single tilted image to reconstruct the height field through frequency domain Poisson integrals, without involving stereo dual-angle optical flow parallax. "Stereo Only" refers to stereo optical flow parallax reconstruction, using only two sets of images with different tilt angles and the Farneback dense optical flow algorithm to calculate parallax and geometrically transformed depth, without introducing FC slope integrals. This represents the target sidewall height corresponding to the target sidewall depth map of the material sample, that is, the height corresponding to each pixel in the target sidewall depth map, i.e., the concavity and convexity depth of the sidewall of the material sample relative to the reference plane; z ST Indicates the predicted sidewall depth, z FC This represents the standard depth value in the standard height field. and Manual weights for the two methods; Automatic weights for a method weighted by SNR (Signal-to-Noise Ratio). The signal-to-noise ratio of the selected strategy. The signal-to-noise ratio of the gradient integral method is... The signal-to-noise ratio of the two-angle parallax method; For low-pass filtering, For high-pass filtering; SNR is defined as the ratio of signal standard deviation to noise standard deviation. The original height field is smoothed by Gaussian with σ=3 to obtain the base morphology. The difference between the original data and the smoothed result is the residual used to characterize the noise.

[0187] For example, a frequency domain segmentation and fusion strategy can also be used to fuse the standard height field and the predicted sidewall depth to generate a target sidewall depth map of the material sample. The expression for the frequency domain segmentation and fusion strategy is shown in formula (14).

[0188] (14).

[0189] in, For the frequency domain fusion result, according to The depth map of the target sidewall can be determined; This is the low-pass portion of the stereo parallax result, which preserves the large-scale structure. To determine the high-pass portion of the standard height field results using the gradient integration method, i.e., to preserve details; for =15 Gaussian kernel, This represents convolution.

[0190] The above scheme first extracts subtle textures from the corrected strips using high-pass filtering to construct a slope field. This is followed by Gaussian smoothing, zero-mean normalization, and linear scaling to obtain a standard height field. Next, it selects geometrically consistent combinations of tilt angles, enhances image texture features using CLAHE to improve optical flow matching accuracy, calculates parallax using dense optical flow, and combines this with bi-angle cotangent geometry to calculate the initial depth. Finally, it obtains a precisely scaled predicted sidewall depth through multi-pixel mean fusion, Gaussian smoothing, and outlier clipping. The scheme then merges the standard height field, which contains both microscopic high-frequency details, and the predicted sidewall depth, which possesses a reliable absolute depth scale, to generate a target sidewall depth map. This approach suppresses morphological distortion caused by imaging noise and matching errors while simultaneously preserving the overall macroscopic contour and nanoscale micro-texture of the trench sidewall, thus improving the accuracy, stability, and numerical reliability of the sidewall 3D depth reconstruction.

[0191] S250. Based on the target sidewall depth map, perform sidewall roughness analysis on the sidewall region of the material sample to determine the sidewall roughness parameters of the material sample.

[0192] For example, sidewall roughness analysis is performed on the sidewall region of a material sample to determine the sidewall roughness parameters of the material sample, including:

[0193] The target area for roughness analysis is determined from the sidewall region of the material sample; the average depth of the target area is determined based on the sidewall depth sampling value of the target area in the target sidewall depth map; and the roughness analysis of the target area is performed based on the target sidewall depth map, the average depth, and the normalized standard deviation of the depth to determine the sidewall roughness parameters of the target area of ​​the material sample.

[0194] For example, the sidewall roughness parameter includes the arithmetic mean roughness R. a Root mean square roughness R qMaximum peak-valley height R z Maximum peak height R p Maximum valley depth R v skewness R sk and kurtosis R ku The target region can be represented as The calculation formulas and physical meanings of the sidewall roughness parameters are shown in Table 7.

[0195] Table 7

[0196]

[0197] Among them, z i Let N be the depth value of the i-th sampling point, and N be the total number of sampling points. , R represents the depth mean (referencing the mean surface). q It is used as the normalized standard deviation in the formulas for calculating skewness and kurtosis.

[0198] The above scheme provides two roughness calculation modes: full surface mode and custom region mode. The full surface mode directly uses all pixel data of the reconstructed sidewall depth map to calculate the roughness parameters; the custom region mode can select a local target area and calculate only the depth data within the target area, which can be used to specifically analyze the local trench sidewall morphology.

[0199] It should be noted that the system has a preset pixel scale of s=3.846nm / px, which will automatically convert the image pixel distance into a nanometer physical length; at the same time, a custom scale function is available, and users can modify the actual nanometer length and pixel number corresponding to the scale on the user interface. After modification, all depth and roughness values ​​in the interface will be automatically updated with the unit conversion results.

[0200] In the above-mentioned method for detecting the sidewall roughness of a densely grooved array material, a secondary electron image of a material sample with a densely grooved array structure is acquired using a scanning electron microscope (SEM) at a preset tilt angle. The material sample is fixed on a nano-positioning stage with tilt and rotation degrees of freedom, and the direction of the groove array of the material sample is perpendicular to the electron beam incident plane of the SEM. A target image is determined from the secondary electron image, and the contour angle of the target image is determined using a boundary detection algorithm. Based on the contour angle, ridge line detection is performed on the target image to determine the image ridge line. Based on the image ridge line, the sidewall region of the material sample is determined, and a correction strip is determined according to the sidewall region. Based on the correction strip, a three-dimensional reconstruction of the sidewall region of the material sample is performed to determine the target sidewall depth map of the material sample. Based on the target sidewall depth map, sidewall roughness analysis is performed on the sidewall region of the material sample to determine the sidewall roughness parameters of the material sample. This solution addresses the shortcomings of current techniques for sidewall roughness detection in dense trench array materials. These limitations include the difficulty in mitigating the occlusion effect of the trench top edge on the sidewall from the imaging source, the challenge in accurately extracting industry-standard quantitative parameters for sidewall roughness based on the three-dimensional morphology of the sidewall, and the lack of standardized testing procedures leading to inconsistent measurement results and inability to support stable process quality control in semiconductor production lines. The proposed solution utilizes a nano-positioning stage with tilt and rotation degrees of freedom to fix the sample, ensuring the trench array is perpendicular to the electron beam incident plane. Secondary electron images are acquired using a scanning electron microscope at a preset tilt angle, ensuring regular imaging geometry. Boundary detection is then used to obtain contour angles, and ridge detection extracts image ridges, precisely segmenting the trench sidewall region and generating correction strips. Based on these correction strips, three-dimensional reconstruction of the sidewall is performed to obtain a depth map of the target sidewall. Finally, quantitative roughness analysis is conducted based on the depth map to output standard roughness parameters. This approach accurately separates the effective observation area of ​​the trench sidewall, avoids interference from irrelevant areas, and achieves complete three-dimensional morphology reconstruction of the trench sidewall and automated, precise quantitative detection of surface roughness.

[0201] For example, based on the above embodiments, the method for detecting the sidewall roughness of dense trench array materials further includes:

[0202] A material sample with a high aspect ratio, densely packed trench array structure was fixed on a nanostage with tilt and rotation degrees of freedom, ensuring the trench array direction was perpendicular to the electron beam incident plane. The stage possessed nanometer-level positioning accuracy, with a tilt angle range of -4° to 70° and a rotation angle range of 0° to 360°. The sample was secured with clamps to ensure the trench array direction remained stable during tilting and rotation. Secondary electron images of the trench array of the material sample with the densely packed trench array structure were acquired at multiple set tilt angles.

[0203] The target image is determined from the secondary electron images, which may include secondary electron images acquired at six tilt angles of 30°, 35°, 40°, 45°, 50° and 55°.

[0204] A boundary detection algorithm using a 5×5 Sobel operator is employed to determine the image gradient magnitude based on the horizontal and vertical gradient components of the secondary electron image. With a step size of 0.5°, the inclination angle range of the trench boundary slope is traversed to determine the angle to be tested. For each angle, the image gradient magnitude is projected onto a coordinate axis perpendicular to the angle, generating a gradient accumulation projection curve (the first projection curve). Gaussian smoothing is applied to each first projection curve, and the two highest peaks of each curve are selected as the two peak values. The two peak values ​​of each first projection curve are summed to determine the total peak value. The maximum value in the total peak value is determined, and the angle corresponding to this maximum value is taken as the contour angle of the target image.

[0205] The target image is Gaussian smoothed to determine the smoothed grayscale image. Based on the coordinates of each pixel and its corresponding grayscale value, an image grayscale function representing the grayscale distribution of the entire image is constructed. The normal direction of the groove boundary of the material sample is determined based on the contour angle. The second-order partial derivatives of the image grayscale function with respect to the x-coordinate and y-coordinate are determined, as well as the mixed second-order partial derivatives obtained by first taking the first-order partial derivatives with respect to the x-coordinate and then the first-order partial derivatives with respect to the y-coordinate. The normal components are calculated based on the contour angle, and the second-order directional derivative of the smoothed grayscale image along the normal direction is determined based on the normal components and the image grayscale function. The ridge response intensity is determined based on the second-order directional derivative. The ridge response intensity is projected along the normal direction to determine the second projection curve. The peak positions on the second projection curve are extracted, and the coordinates of all peaks are summarized to obtain the candidate boundary lines to be screened.

[0206] Construct a top projection width model and a side projection height model. Based on candidate boundary lines, construct multiple sets of boundary line combinations, each including a background upper edge boundary A, a top sidewall boundary B, and a sidewall lower edge boundary C. Extract the response regions corresponding to the upper edge boundary A, top sidewall boundary B, and sidewall lower edge boundary C from the ridge response intensity map. For the ridge response intensity within each response region, generate projection curves using line projection. Extract the maximum peak value of each projection curve. The maximum peak value corresponding to the extracted upper edge boundary A can be used as the peak response intensity of the background upper edge boundary A; the maximum peak value corresponding to the extracted top sidewall boundary B can be used as the peak response intensity of the top sidewall boundary B; and the maximum peak value corresponding to the extracted sidewall lower edge boundary C can be used as the peak response intensity of the sidewall lower edge boundary C. Based on the top projection width model, the side projection height model, and the tilt angle of the fixed material sample, the predicted ordinates of the top sidewall boundary and the lower sidewall boundary corresponding to each boundary line combination are determined. Based on the peak response intensity of the background upper boundary A, the peak response intensity of the top sidewall boundary B, the peak response intensity of the lower sidewall boundary C, the predicted ordinates of the top sidewall boundary and the lower sidewall boundary, the actual ordinates of the top sidewall boundary and the lower sidewall boundary, and the actual ordinates of the lower sidewall boundary, the comprehensive matching score of the three-line combination for each boundary line combination is determined. The boundary line combination with the highest comprehensive matching score is determined as the target combination, and the background upper boundary A, the top sidewall boundary B, and the lower sidewall boundary C corresponding to the target combination are used as the image ridges of the target image.

[0207] Based on the top sidewall boundary B and the lower sidewall boundary C corresponding to the ridge lines of each image group, the sidewall region of the material sample corresponding to each image ridge line is determined. 400 sampling points are uniformly selected along the direction of the image ridge line as the first sampling points, and 250 sampling points are selected along the direction perpendicular to the image ridge line as the second sampling points. The gray values ​​of the first and second sampling points are determined using bilinear interpolation, and a standard rectangular sidewall strip is determined based on these gray values. The standard rectangular sidewall strip is then trimmed by 12% on the left, 8% on the right, 5% on the top, and 5% on the bottom, and the trimmed standard rectangular sidewall strip is used as the correction strip. After determining the correction strip, its height is corrected to determine the physical wall height corresponding to each correction strip.

[0208] High-pass filtering was applied to the correction strips to remove large-scale illumination gradients, resulting in a high-pass filtered output image. A slope field was then constructed based on this image. An initial height field was determined using frequency domain integration based on the slope field. Gaussian smoothing with a standard deviation of σ=2 was applied to the initial height field to reduce minor height fluctuations caused by slope field noise. Zero-mean normalization was then performed on the Gaussian smoothed height field to eliminate overall height offset. Finally, linear scaling constrained the overall height fluctuation range of the processed height field to 6% of the total wall height, thereby eliminating global height deviations and outliers generated during reconstruction. This yielded a standard height field with fluctuation amplitudes closely matching the microstructure of the actual sidewall and lower noise.

[0209] Prioritize pairing two tilt angles with large differences in tilt angles as angle combinations. This involves first randomly combining tilt angles pairwise to determine candidate angle combinations. Then, determine the absolute value of the cotangent difference between the two tilt angles in each candidate angle combination, selecting candidate angle combinations whose absolute value of the cotangent difference is greater than a threshold as valid angle combinations. Finally, apply the CLAHE method to perform adaptive histogram equalization on the corrected strips to determine the enhanced strip image.

[0210] The Farneback dense optical flow algorithm is used to determine the apparent displacement between two sets of enhanced strip images corresponding to the effective angle combination of each sidewall protrusion of the material sample, thereby determining the disparity field between the two sets of enhanced strip images corresponding to the effective angle combination of each sidewall protrusion. The Farneback dense optical flow algorithm employs a five-layer image pyramid structure, a 21×21 computation window, and iterates 7 times per block. The initial depth of each sidewall protrusion in the material sample is determined based on the disparity field and the cotangent values ​​of the two tilt angles in the effective angle combination. The initial depth is then mean-fused and processed to determine the mean depth, and Gaussian smoothing and outlier clipping are applied to the mean depth to determine the predicted sidewall depth. Finally, the standard height field and the predicted sidewall depth are fused to determine the target sidewall depth map of the material sample.

[0211] The target area for roughness analysis is determined from the sidewall region of the material sample; the average depth of the target area is determined based on the sidewall depth sampling value of the target area in the target sidewall depth map; and the roughness analysis of the target area is performed based on the target sidewall depth map, the average depth, and the normalized standard deviation of the depth to determine the sidewall roughness parameters of the target area of ​​the material sample.

[0212] The sidewall roughness detection system for dense trench array materials has a preset pixel scale of s=3.846nm / px, which automatically converts image pixel distance into nanometer physical length. It also features a customizable scale function, allowing users to modify the actual nanometer length and pixel count on the user interface. After modification, all depth and roughness values ​​on the interface are automatically updated with the unit conversion results. The system can automatically read the built-in scale of SEM images to complete the conversion and calibration between pixels and actual nanometer lengths, converting image pixel distance into the true physical size of the sample, providing an accurate dimensional benchmark for subsequent depth and roughness calculations.

[0213] The program can automatically extract the scale bar from the bottom information bar of the SEM image: It limits the scanning range: vertical y-values ​​[715, 748], horizontal x-values ​​[10, 90], and locks the bottom scale bar; it extracts continuous horizontal pixel segments with brightness values ​​greater than 180, filtering out the white scale lines; it identifies the vertical markers at the left and right ends of the scale, corresponding to horizontal coordinates x=22 and x=74; it subtracts the left x-coordinate from the right x-coordinate to obtain a scale occupying 52 pixels; it reads the scale marking value, which represents an actual physical length of 200nm. Based on the scale's physical length and pixel length, it calculates the actual size corresponding to each pixel. .

[0214] Actual size The expression is shown in formula (15).

[0215] (15).

[0216] in, The pixel scale means that each pixel in the image corresponds to an actual length of 3.846 nanometers on the sample surface.

[0217] Scale validity verification: Take the trench sidewall pixel height of 270 px and substitute it into the scale conversion to obtain the physical height of the wall.

[0218] The physical height of the wall surface = 270 px × 3.846 nm / px = 1040 nm ≈ 1.04 μm. This value matches the theoretical expected size of the sample at 30 kX magnification, proving that the automatic scale calibration results are accurate and reliable, and can be used for subsequent quantitative calculations of the three-dimensional morphology and roughness of the sidewall.

[0219] In the above-mentioned method for detecting the sidewall roughness of a densely grooved array material, a secondary electron image of a material sample with a densely grooved array structure is acquired using a scanning electron microscope (SEM) at a preset tilt angle. The material sample is fixed on a nano-positioning stage with tilt and rotation degrees of freedom, and the direction of the groove array of the material sample is perpendicular to the electron beam incident plane of the SEM. A target image is determined from the secondary electron image, and the contour angle of the target image is determined using a boundary detection algorithm. Based on the contour angle, ridge line detection is performed on the target image to determine the image ridge line. Based on the image ridge line, the sidewall region of the material sample is determined, and a correction strip is determined according to the sidewall region. Based on the correction strip, a three-dimensional reconstruction of the sidewall region of the material sample is performed to determine the target sidewall depth map of the material sample. Based on the target sidewall depth map, sidewall roughness analysis is performed on the sidewall region of the material sample to determine the sidewall roughness parameters of the material sample. This solution addresses the shortcomings of current techniques for sidewall roughness detection in dense trench array materials. These limitations include the difficulty in mitigating the occlusion effect of the trench top edge on the sidewall from the imaging source, the challenge in accurately extracting industry-standard quantitative parameters for sidewall roughness based on the three-dimensional morphology of the sidewall, and the lack of standardized testing procedures leading to inconsistent measurement results and inability to support stable process quality control in semiconductor production lines. The proposed solution utilizes a nano-positioning stage with tilt and rotation degrees of freedom to fix the sample, ensuring the trench array is perpendicular to the electron beam incident plane. Secondary electron images are acquired using a scanning electron microscope at a preset tilt angle, ensuring regular imaging geometry. Boundary detection is then used to obtain contour angles, and ridge detection extracts image ridges, precisely segmenting the trench sidewall region and generating correction strips. Based on these correction strips, three-dimensional reconstruction of the sidewall is performed to obtain a depth map of the target sidewall. Finally, quantitative roughness analysis is conducted based on the depth map to output standard roughness parameters. This approach accurately separates the effective observation area of ​​the trench sidewall, avoids interference from irrelevant areas, and achieves complete three-dimensional morphology reconstruction of the trench sidewall and automated, precise quantitative detection of surface roughness.

[0220] It should be understood that although the steps in the flowcharts of the embodiments described above are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the embodiments described above may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0221] Based on the same inventive concept, this application also provides a device for detecting the sidewall roughness of densely grooved array materials, used to implement the aforementioned method for detecting the sidewall roughness of densely grooved array materials. The solution provided by this device is similar to the solution described in the above method. Therefore, the specific limitations of one or more embodiments of the device for detecting the sidewall roughness of densely grooved array materials provided below can be found in the limitations of the method for detecting the sidewall roughness of densely grooved array materials described above, and will not be repeated here.

[0222] In one embodiment, such as Figure 3 As shown, a sidewall roughness detection device for a dense trench array material is provided, comprising: an image acquisition module 301, an image ridge determination module 302, a correction strip determination module 303, a three-dimensional reconstruction module 304, and a sidewall roughness analysis module 305, wherein:

[0223] Image acquisition module 301 is used to acquire secondary electron images of a material sample with a dense groove array structure using a scanning electron microscope based on a preset tilt angle; the material sample is fixed on a nano-positioning stage with tilt and rotation degrees of freedom, and the groove array direction of the material sample is perpendicular to the electron beam incident plane of the scanning electron microscope.

[0224] The image ridge determination module 302 is used to determine the target image from the secondary electronic image, and to determine the contour angle of the target image through a boundary detection algorithm, and to perform ridge detection on the target image based on the contour angle to determine the image ridge of the target image;

[0225] The correction strip determination module 303 is used to determine the sidewall region of the material sample based on the image ridge line, and to determine the correction strip according to the sidewall region;

[0226] The three-dimensional reconstruction module 304 is used to perform three-dimensional reconstruction of the sidewall region of the material sample based on the correction strip, and determine the target sidewall depth map of the material sample.

[0227] The sidewall roughness analysis module 305 is used to perform sidewall roughness analysis on the sidewall region of the material sample based on the target sidewall depth map, and to determine the sidewall roughness parameters of the material sample.

[0228] For example, the image ridge determination module 302 is specifically used for:

[0229] The image gradient magnitude of each target image is determined by the boundary detection algorithm based on the horizontal and vertical gradient components of the target image.

[0230] The angle to be tested is determined based on the preset angle step size and the preset tilt angle range of the groove boundary slope.

[0231] The image gradient magnitude is projected onto a direction perpendicular to the angle to be tested to determine a first projection curve;

[0232] Gaussian smoothing is applied to the first projection curve to determine the two peak values ​​of the first projection curve after Gaussian smoothing.

[0233] The peak values ​​of the two first curves corresponding to the first projection curve are summed to determine the total peak value of each first projection curve.

[0234] The maximum value among the sum of the peak values ​​is determined, and the angle to be tested corresponding to the maximum value is taken as the contour angle of the target image.

[0235] For example, the image ridge determination module 302 is also specifically used for:

[0236] The target image is subjected to Gaussian smoothing to determine the smoothed grayscale image, and the image grayscale function is determined based on the grayscale value and pixel coordinates of each pixel in the smoothed grayscale image.

[0237] The normal component is calculated based on the contour angle, and the second directional derivative of the smoothed grayscale image along the normal direction is determined based on the normal component and the image grayscale function.

[0238] The ridge response intensity is determined based on the second-order directional derivative.

[0239] The ridge response intensity is projected along the normal direction to determine the second projection curve; the peak value of the second projection curve corresponds to the center position of the ridge.

[0240] The continuous pixel lines corresponding to the peak of the second curve are used as candidate boundary lines;

[0241] Based on the candidate boundary lines, the image ridge lines of the target image are determined.

[0242] For example, the image ridge determination module 302 is also specifically used for:

[0243] Obtain the pre-built top projection width model and side projection height model;

[0244] Based on candidate boundary lines, multiple sets of boundary line combinations are constructed; the boundary line combinations include the upper edge boundary of the background, the top sidewall boundary, and the lower edge boundary of the sidewall.

[0245] Based on the ridge response intensity, the peak response intensity at the upper edge of the background boundary, the peak response intensity at the top sidewall boundary, and the peak response intensity at the lower edge of the sidewall boundary are determined.

[0246] Based on the top surface projection width model, the side surface projection height model, and the tilt angle of the nano-positioning stage, the predicted ordinate of the top surface sidewall boundary and the predicted ordinate of the lower edge boundary of the sidewall corresponding to each boundary line combination are determined.

[0247] Based on the peak response intensity of the upper boundary of the background, the peak response intensity of the top sidewall boundary, the peak response intensity of the lower boundary of the sidewall, the predicted ordinate of the top sidewall boundary, the predicted ordinate of the lower boundary of the sidewall, the actual ordinate of the top sidewall boundary, and the actual ordinate of the lower boundary of the sidewall, the three-line combination comprehensive matching score of each boundary line combination is determined respectively.

[0248] Based on the comprehensive matching score of the three-line combination, the target combination is determined from the boundary line combination, and the background upper edge boundary, top side wall boundary and side wall lower edge boundary corresponding to the target combination are taken as the image ridge line of the target image.

[0249] For example, the correction strip determination module 303 is specifically used for:

[0250] A first preset number of sampling points are uniformly selected along the direction of the image ridge line as the first sampling points;

[0251] A second preset number of sampling points are taken along the direction perpendicular to the ridge line of the image as the second sampling points; the sampling range of the second sampling points is limited to the boundary between the top sidewall and the lower edge of the sidewall corresponding to the sidewall region;

[0252] The gray values ​​of the first and second sampling points are determined by bilinear interpolation, and the standard rectangular sidewall strip is determined based on the gray values ​​of the sampling points.

[0253] The standard rectangular sidewall strips are cut according to a preset cutting ratio to determine the correction strips.

[0254] For example, the 3D reconstruction module 304 is specifically used for:

[0255] The correction strip is subjected to high-pass filtering to determine the high-pass filtered output image, and a slope field is constructed based on the high-pass filtered output image.

[0256] The initial height field is determined based on the slope field using the frequency domain integration method, and the initial height field is then subjected to Gaussian smoothing, zero-mean normalization, and linear scaling in sequence to determine the target height field.

[0257] Based on the cotangent difference between tilt angles, the effective angle combination is determined, and the correction strip is subjected to adaptive histogram equalization to determine the enhanced strip image.

[0258] The parallax field between two sets of enhanced strip images corresponding to the effective angle combination of each sidewall protrusion of the material sample is determined by the dense optical flow algorithm, and the initial depth of each sidewall protrusion in the material sample is determined according to the parallax field and the two tilt angles in the effective angle combination.

[0259] The initial depth is fused and processed to determine the mean depth, and the mean depth is then smoothed by Gaussian and pruned to determine the predicted sidewall depth.

[0260] Based on the target height field and the predicted sidewall depth, the target sidewall depth map of the material sample is determined.

[0261] For example, the sidewall roughness analysis module 305 is specifically used for:

[0262] Determine the target area for roughness analysis from the sidewall region of the material sample;

[0263] Based on the sidewall depth sampling values ​​of the target region in the target sidewall depth map, determine the average depth of the target region;

[0264] Based on the target sidewall depth map, average depth, and normalized standard deviation of depth, roughness analysis is performed on the target area to determine the sidewall roughness parameters of the target area of ​​the material sample.

[0265] Each module in the aforementioned sidewall roughness detection device for densely grooved array materials can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the corresponding operations of each module.

[0266] In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 4As shown, the computer device includes a processor, memory, input / output interface, communication interface, display unit, and input device. The processor, memory, and input / output interface are connected via a system bus, and the communication interface, display unit, and input device are also connected to the system bus via the input / output interface. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage media. The input / output interface is used for exchanging information between the processor and external devices. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, mobile cellular networks, NFC (Near Field Communication), or other technologies. When executed by the processor, the computer program implements a method for detecting the sidewall roughness of a dense trench array material. The display unit is used to form a visually visible image and can be a display screen, projection device, or virtual reality imaging device. The display screen can be an LCD screen or an e-ink screen. The input device of the computer device can be a touch layer covering the display screen, or a key vector, trackball, or touchpad set on the computer device casing, or an external key vector disk, touchpad, or mouse, etc.

[0267] Those skilled in the art will understand that Figure 4 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0268] In one embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to perform the following steps:

[0269] Step 1: Using a scanning electron microscope, acquire secondary electron images of a material sample with a dense trench array structure based on a preset tilt angle; the material sample is fixed on a nano-positioning stage with tilt and rotation degrees of freedom, and the direction of the trench array of the material sample is perpendicular to the electron beam incident plane of the scanning electron microscope.

[0270] Step 2: Determine the target image from the secondary electronic image, and determine the contour angle of the target image using a boundary detection algorithm. Based on the contour angle, perform ridge line detection on the target image to determine the image ridge line of the target image.

[0271] Step 3: Based on the image ridges, determine the sidewall region of the material sample, and determine the correction strips according to the sidewall region;

[0272] Step 4: Based on the correction strip, perform three-dimensional reconstruction of the sidewall region of the material sample to determine the target sidewall depth map of the material sample;

[0273] Step 5: Based on the target sidewall depth map, perform sidewall roughness analysis on the sidewall region of the material sample to determine the sidewall roughness parameters of the material sample.

[0274] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, the computer program performing the following steps when executed by a processor:

[0275] Step 1: Using a scanning electron microscope, acquire secondary electron images of a material sample with a dense trench array structure based on a preset tilt angle; the material sample is fixed on a nano-positioning stage with tilt and rotation degrees of freedom, and the direction of the trench array of the material sample is perpendicular to the electron beam incident plane of the scanning electron microscope.

[0276] Step 2: Determine the target image from the secondary electronic image, and determine the contour angle of the target image using a boundary detection algorithm. Based on the contour angle, perform ridge line detection on the target image to determine the image ridge line of the target image.

[0277] Step 3: Based on the image ridges, determine the sidewall region of the material sample, and determine the correction strips according to the sidewall region;

[0278] Step 4: Based on the correction strip, perform three-dimensional reconstruction of the sidewall region of the material sample to determine the target sidewall depth map of the material sample;

[0279] Step 5: Based on the target sidewall depth map, perform sidewall roughness analysis on the sidewall region of the material sample to determine the sidewall roughness parameters of the material sample.

[0280] In one embodiment, a computer program product is provided, including a computer program that, when executed by a processor, performs the following steps:

[0281] Step 1: Using a scanning electron microscope, acquire secondary electron images of a material sample with a dense trench array structure based on a preset tilt angle; the material sample is fixed on a nano-positioning stage with tilt and rotation degrees of freedom, and the direction of the trench array of the material sample is perpendicular to the electron beam incident plane of the scanning electron microscope.

[0282] Step 2: Determine the target image from the secondary electronic image, and determine the contour angle of the target image using a boundary detection algorithm. Based on the contour angle, perform ridge line detection on the target image to determine the image ridge line of the target image.

[0283] Step 3: Based on the image ridges, determine the sidewall region of the material sample, and determine the correction strips according to the sidewall region;

[0284] Step 4: Based on the correction strip, perform three-dimensional reconstruction of the sidewall region of the material sample to determine the target sidewall depth map of the material sample;

[0285] Step 5: Based on the target sidewall depth map, perform sidewall roughness analysis on the sidewall region of the material sample to determine the sidewall roughness parameters of the material sample.

[0286] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of related data must comply with the relevant laws, regulations and standards of the relevant countries and regions.

[0287] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM). The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0288] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0289] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A method for detecting the sidewall roughness of a densely grooved array material, characterized in that, include: Secondary electron images of material samples with dense trench array structures are acquired using a scanning electron microscope based on a preset tilt angle. The material sample is fixed on a nano-positioning stage with tilt and rotation degrees of freedom, and the direction of the groove array of the material sample is perpendicular to the electron beam incident plane of the scanning electron microscope. The target image is determined from the secondary electronic image, and the contour angle of the target image is determined by the boundary detection algorithm. Based on the contour angle, the ridge line is detected in the target image to determine the image ridge line of the target image. Based on the image ridges, the sidewall region of the material sample is determined, and the correction strip is determined according to the sidewall region; Based on the correction strip, the sidewall region of the material sample is reconstructed in three dimensions to determine the target sidewall depth map of the material sample; Based on the target sidewall depth map, sidewall roughness analysis is performed on the sidewall region of the material sample to determine the sidewall roughness parameters of the material sample. Based on the contour angle, ridge line detection is performed on the target image to determine the image ridge lines, including: The target image is subjected to Gaussian smoothing to determine the smoothed grayscale image, and the image grayscale function is determined based on the grayscale value and pixel coordinates of each pixel in the smoothed grayscale image. The normal component is calculated based on the contour angle, and the second directional derivative of the smoothed grayscale image along the normal direction is determined based on the normal component and the image grayscale function. The ridge response intensity is determined based on the second-order directional derivative. The ridge response intensity is projected along the normal direction to determine the second projection curve; the peak value of the second projection curve corresponds to the center position of the ridge. The continuous pixel lines corresponding to the peak of the second curve are used as candidate boundary lines; Based on the candidate boundary lines, the image ridge lines of the target image are determined; Based on the candidate boundary lines, the image ridge lines of the target image are determined, including: Obtain the pre-built top projection width model and side projection height model; Based on candidate boundary lines, multiple sets of boundary line combinations are constructed; the boundary line combinations include the upper edge boundary of the background, the top sidewall boundary, and the lower edge boundary of the sidewall. Based on the ridge response intensity, the peak response intensity at the upper edge of the background boundary, the peak response intensity at the top sidewall boundary, and the peak response intensity at the lower edge of the sidewall boundary are determined. Based on the top surface projection width model, the side surface projection height model, and the tilt angle, the predicted ordinate of the top surface sidewall boundary and the predicted ordinate of the sidewall lower edge boundary corresponding to each boundary line combination are determined. Based on the peak response intensity of the upper boundary of the background, the peak response intensity of the top sidewall boundary, the peak response intensity of the lower boundary of the sidewall, the predicted ordinate of the top sidewall boundary, the predicted ordinate of the lower boundary of the sidewall, the actual ordinate of the top sidewall boundary, and the actual ordinate of the lower boundary of the sidewall, the three-line combination comprehensive matching score of each boundary line combination is determined respectively. Based on the comprehensive matching score of the three-line combination, the target combination is determined from the boundary line combination, and the background upper edge boundary, top side wall boundary and side wall lower edge boundary corresponding to the target combination are taken as the image ridge line of the target image.

2. The method according to claim 1, characterized in that, The contour angle of the target image is determined using a boundary detection algorithm, including: The image gradient magnitude of each target image is determined by the boundary detection algorithm based on the horizontal and vertical gradient components of the target image. The angle to be tested is determined based on the preset angle step size and the preset tilt angle range of the groove boundary slope. The image gradient magnitude is projected onto a direction perpendicular to the angle to be tested to determine a first projection curve; Gaussian smoothing is applied to the first projection curve to determine the two peak values ​​of the first projection curve after Gaussian smoothing. The peak values ​​of the two first curves corresponding to the first projection curve are summed to determine the total peak value of each first projection curve. The maximum value among the sum of the peak values ​​is determined, and the angle to be tested corresponding to the maximum value is taken as the contour angle of the target image.

3. The method according to claim 1, characterized in that, Based on the sidewall region, the corrective strip is determined, including: A first preset number of sampling points are uniformly selected along the direction of the image ridge line as the first sampling points; A second preset number of sampling points are taken along the direction perpendicular to the ridge line of the image as the second sampling points; the sampling range of the second sampling points is limited to the boundary between the top sidewall and the lower edge of the sidewall corresponding to the sidewall region; The gray values ​​of the first and second sampling points are determined by bilinear interpolation, and the standard rectangular sidewall strip is determined based on the gray values ​​of the sampling points. The standard rectangular sidewall strips are cut according to a preset cutting ratio to determine the correction strips.

4. The method according to claim 1, characterized in that, Based on the correction strip, a three-dimensional reconstruction of the sidewall region of the material sample is performed to determine the target sidewall depth map of the material sample, including: The correction strip is subjected to high-pass filtering to determine the high-pass filtered output image, and a slope field is constructed based on the high-pass filtered output image. The initial height field is determined based on the slope field using the frequency domain integration method, and the initial height field is then subjected to Gaussian smoothing, zero-mean normalization, and linear scaling in sequence to determine the standard height field. Based on the cotangent difference between tilt angles, the effective angle combination is determined, and the correction strip is subjected to adaptive histogram equalization to determine the enhanced strip image. The parallax field between two sets of enhanced strip images corresponding to the effective angle combination of each sidewall protrusion of the material sample is determined by the dense optical flow algorithm, and the initial depth of each sidewall protrusion in the material sample is determined according to the parallax field and the two tilt angles in the effective angle combination. The initial depth is fused and processed to determine the mean depth, and the mean depth is then smoothed by Gaussian and pruned to determine the predicted sidewall depth. Based on the standard height field and the predicted sidewall depth, the target sidewall depth map of the material sample is determined.

5. The method according to claim 1, characterized in that, Based on the target sidewall depth map, sidewall roughness analysis is performed on the sidewall region of the material sample to determine the sidewall roughness parameters of the material sample, including: Determine the target area for roughness analysis from the sidewall region of the material sample; Based on the sidewall depth sampling values ​​of the target region in the target sidewall depth map, determine the average depth of the target region; Based on the target sidewall depth map, average depth, and normalized standard deviation of depth, roughness analysis is performed on the target area to determine the sidewall roughness parameters of the target area of ​​the material sample.

6. A device for detecting the sidewall roughness of a densely grooved array material, characterized in that, The sidewall roughness detection device for the dense trench array material includes: The image acquisition module is used to acquire secondary electron images of a material sample with a dense groove array structure using a scanning electron microscope based on a preset tilt angle; the material sample is fixed on a nano-positioning stage with tilt and rotation degrees of freedom, and the direction of the groove array of the material sample is perpendicular to the electron beam incident plane of the scanning electron microscope. The image ridgeline determination module is used to determine the target image from the secondary electronic image, and to determine the contour angle of the target image through a boundary detection algorithm, and to perform ridgeline detection on the target image based on the contour angle to determine the image ridgeline of the target image; The correction strip determination module is used to determine the sidewall region of the material sample based on the image ridge line, and to determine the correction strip according to the sidewall region; A three-dimensional reconstruction module is used to perform three-dimensional reconstruction of the sidewall region of the material sample based on the correction strip, and to determine the target sidewall depth map of the material sample. The sidewall roughness analysis module is used to perform sidewall roughness analysis on the sidewall region of the material sample based on the target sidewall depth map, and to determine the sidewall roughness parameters of the material sample. Based on the contour angle, ridge detection is performed on the target image to determine the image ridge line, including: performing Gaussian smoothing on the target image to determine a smoothed grayscale image, and determining an image grayscale function based on the grayscale value and pixel coordinates of each pixel in the smoothed grayscale image; calculating the normal component based on the contour angle, and determining the second directional derivative of the smoothed grayscale image along the normal direction based on the normal component and the image grayscale function; determining the ridge line response intensity based on the second directional derivative; projecting the ridge line response intensity along the normal direction to determine a second projection curve; the peak value of the second projection curve corresponds to the center position of the ridge line; using the continuous pixel lines corresponding to the peak value of the second curve as candidate boundary lines; and determining the image ridge line of the target image based on the candidate boundary lines. Based on the candidate boundary lines, the image ridge lines of the target image are determined, including: acquiring a pre-constructed top projection width model and a side projection height model; constructing multiple sets of boundary line combinations based on the candidate boundary lines; the boundary line combinations include the background upper edge boundary, the top side wall boundary, and the side wall lower edge boundary; determining the peak response intensity of the background upper edge boundary, the top side wall boundary, and the side wall lower edge boundary based on the ridge line response intensity; and determining the predicted ordinate of the top side wall boundary corresponding to each boundary line combination based on the top projection width model, the side projection height model, and the tilt angle. The predicted ordinate of the boundary line is determined; based on the peak response intensity of the background upper boundary, the peak response intensity of the top sidewall boundary, the peak response intensity of the sidewall lower boundary, the predicted ordinate of the top sidewall boundary, the predicted ordinate of the sidewall lower boundary, the actual ordinate of the top sidewall boundary, and the actual ordinate of the sidewall lower boundary, the three-line combination comprehensive matching score of each boundary line combination is determined; based on the three-line combination comprehensive matching score, the target combination is determined from the boundary line combinations, and the background upper boundary, the top sidewall boundary, and the sidewall lower boundary corresponding to the target combination are taken as the image ridge lines of the target image.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 5.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 5.

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