Modeling method and system for semiconductor device model

Abstract

The application provides a modeling method and system of a semiconductor device model, and relates to the technical field of semiconductor modeling. The application obtains an initial process cross-sectional image of a semiconductor device, divides the image into a conductive channel region, a source-drain region and a gate dielectric layer region based on a gray scale distribution peak value; then extracts an initial boundary line between the channel and the source-drain, obtains a corrected boundary point, fits a channel-source-drain contour line after removing outliers; determines an offset amount by using the average thickness of the gate dielectric layer, generates two offset contour lines and intercepts a coupling transition region, generates a grid node in the coupling transition region; finally, performs a Boolean intersection operation on each grid node, performs weighted average assignment on the material property parameters of each node according to the area proportion of each region in the neighborhood, and completes the construction of a simulation model. The application effectively suppresses the interference of image noise and interface blur on modeling, and improves the representation accuracy of the device model and the reliability of subsequent electrical simulation convergence.

Description

Technical Field

[0001] This invention relates to the field of semiconductor modeling technology, specifically to a modeling method and system for semiconductor device models. Background Technology

[0002] In the field of semiconductor device design and process development, building accurate device simulation models based on process cross-sectional images is an important means of evaluating device electrical performance and optimizing process parameters. As the feature size of semiconductor devices continues to shrink and their structures become increasingly complex, the industry commonly uses image segmentation techniques to process scanning electron microscope (SEM) or transmission electron microscope (TEM) images of the device's process cross-section. Through methods such as grayscale thresholding, edge detection operators, or region growing, the contour boundaries of key structures such as conductive channels, source / drain regions, and gate dielectric layers are extracted. Based on the extracted contours, a mesh is generated in simulation software, and corresponding material properties are assigned to the mesh nodes, ultimately constructing a device model that can be used for electrical simulation.

[0003] However, the aforementioned existing technologies still have many limitations: On the one hand, due to the interface roughness and local structural deformation caused by semiconductor process technology, as well as the noise from electron microscope image acquisition, the grayscale distribution of device images is uneven, and the material boundaries exhibit blurred and gradual characteristics. Traditional single global threshold segmentation is difficult to accurately distinguish different material regions, and edge detection algorithms are easily interfered with by noise. The extracted structural contours often exhibit defects such as jagged edges, breaks, and boundary distortion, making it impossible to accurately restore the fine interface morphology of core structures such as channels, source drains, and gate dielectrics, ultimately resulting in distortion of the device physical structure modeling. On the other hand, traditional solutions do not consider the actual situation of the distribution of mesh nodes across material boundaries and assign values ​​to mesh nodes using a single solidified material parameter, leading to non-physical step changes in parameters at the material interface. This problem not only reduces the accuracy of the device model in representing the real structure and material properties, but also generates numerical oscillations in electrical simulations, seriously affecting the accuracy and reliability of simulation results, while reducing the convergence of simulation calculations, which is not conducive to device process optimization and accurate performance evaluation.

[0004] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0005] The purpose of this invention is to provide a modeling method and system for semiconductor devices to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A modeling method for semiconductor devices, comprising the following steps: Step 1: Obtain an electron microscope cross-sectional image of the semiconductor device and perform grayscale statistics on the image. Based on the grayscale distribution peak, the image is divided into conductive channel region, source / drain region, and gate dielectric layer region. Step 2: Based on the spatial relationship between the conductive channel region and the source / drain region, extract the initial boundary line between the conductive channel region and the source / drain region, and sample each initial boundary line at equal intervals along the length direction perpendicular to the extension of the channel to obtain several initial boundary points. Combine the image grayscale features to perform grayscale correction processing on all initial boundary points to obtain corrected boundary points. Step 3: Filter effective correction boundary points by calculating the Euclidean distance between adjacent correction boundary points, and fit the channel-source-drain profile to determine the upper and lower interfaces of the gate dielectric layer region. Extract the interface response points from the upper and lower interfaces respectively, and calculate the normal distance between them to obtain the width of the interface transition region. Determine the curvature adjustment factor and gray level adjustment factor according to the local radius of curvature of each contour point on the profile line and the gray level standard deviation of the corresponding region, and according to the preset mapping relationship. Step 4: Determine the offset of each contour point based on the width of the interface transition zone, the curvature adjustment factor, and the grayscale adjustment factor. Offset the channel-source-drain contour line equidistantly in the inward and outward normal directions according to the offset, generating two parallel offset contour lines. Extract the area between the two offset contour lines as the coupling transition area of ​​each material region, and generate the simulation mesh nodes in the coupling transition area. Step 5: For each mesh node in the coupling transition region, perform Boolean intersection operation between the node coordinates and each material region to obtain the area ratio of all material regions within the preset neighborhood window of the mesh node. Assign a weighted average value to the material property parameters of each mesh node based on the area ratio of each material region. Match the material property parameters of each mesh node with the standard material property parameters of each material region to determine the material region to which each mesh node belongs, thus completing the construction of the semiconductor device simulation model.

[0007] Furthermore, based on the grayscale distribution peaks, the image is divided into conductive channel region, source / drain region, and gate dielectric layer region. The specific steps are as follows: In the electron microscope cross-sectional image, the gray value of each pixel is quantized into gray levels in the range of 0 to 255. The entire electron microscope cross-sectional image is traversed pixel by pixel, and the number of pixels appearing at each gray level is counted to generate a gray level histogram. Perform a first-order difference operation on the grayscale histogram to determine all the inflection points where the frequency changes from increasing to decreasing, and extract the gray levels corresponding to the three inflection points with the largest frequency values, which are marked as the first peak gray level, the second peak gray level, and the third peak gray level, respectively. The midpoint gray value between the first peak gray level and the second peak gray level is taken as the first segmentation threshold, and the midpoint gray value between the second peak gray level and the third peak gray level is taken as the second segmentation threshold. Pixels with gray values ​​less than the first segmentation threshold are classified as conductive channel regions, pixels with gray values ​​greater than or equal to the first segmentation threshold and less than the second segmentation threshold are classified as source-drain regions, and pixels with gray values ​​greater than or equal to the second segmentation threshold are classified as gate dielectric layer regions.

[0008] Furthermore, based on the spatial relationship between the conductive channel region and the source / drain region, the initial boundary line between the conductive channel region and the source / drain region is extracted. The specific steps are as follows: The boundary between the conductive channel region and the source / drain region is traversed pixel by pixel. Pixels that satisfy the condition of belonging to the conductive channel region and having a source / drain region pixel in their four-connected neighborhood are marked as first boundary points. Pixels that satisfy the condition of belonging to the source / drain region and having a conductive channel region pixel in their four-connected neighborhood are marked as second boundary points. Pixels that simultaneously satisfy the condition of belonging to the conductive channel region and having at least one source / drain region pixel in their eight-connected neighborhood are marked as candidate boundary pixels. The first and second boundary points are merged to obtain a set of boundary pixels. An 8-connected neighborhood connection operation is performed on all pixels in this set. Specifically, any unclassified pixel is selected from the set of boundary pixels. If there are candidate boundary pixels in the adjacent positions of the pixel in the four diagonal directions, these candidate boundary pixels are grouped with the unclassified pixels into the same boundary pixel cluster. The classification process of boundary pixels is repeated. All candidate boundary pixels are grouped into one boundary pixel cluster, and each boundary pixel cluster corresponds to an initial boundary line.

[0009] Furthermore, grayscale correction is performed on all initial boundary points based on image grayscale features to obtain corrected boundary points. The specific steps are as follows: For each initial boundary pixel, a local image window is extracted from the electron microscope cross-sectional image with the initial boundary pixel as the center. Within the local image window, the first-order gray-level gradient values ​​along the horizontal and vertical directions at the location of the initial boundary pixel are calculated to generate the gradient magnitude of the initial boundary pixel. Starting from the initial boundary pixel, search line segments are generated by extending along the positive and negative normal directions of the boundary line of the initial boundary pixel. The gradient magnitude of each pixel on the search line segment is calculated, and the position of the pixel with the largest gradient magnitude is selected as the correction boundary point of the initial boundary point.

[0010] Further, the Euclidean distance between adjacent correction boundary points is calculated to screen effective correction boundary points, and the channel-source-drain profile is fitted. The specific steps are as follows: All correction boundary points are sorted according to the sampling order of their corresponding initial boundary points to generate an ordered point sequence distributed along the channel length. For each correction boundary point in the ordered point sequence, the first Euclidean distance with the previous adjacent correction boundary point, the second Euclidean distance with the next adjacent correction boundary point, and the third Euclidean distance between the previous adjacent correction boundary point and the next adjacent correction boundary point are calculated. The arithmetic mean of the above three Euclidean distances is calculated. If the first Euclidean distance or the second Euclidean distance is greater than three times the arithmetic mean, then the correction boundary point is determined to be an outlier. After removing outliers, control points are selected at equal intervals from the remaining effective correction boundary points to construct cubic B-spline curves. The coordinates of the control points are solved by the least squares method to minimize the sum of squares of the deviations between the cubic B-spline curves and the control points, thereby obtaining the channel-source-drain profile.

[0011] Furthermore, the channel-source-drain profile is offset equidistantly in the inward and outward normal directions according to the offset amount, generating two parallel offset profiles. The specific steps are as follows: Obtain the normal vector of each pixel on the channel-source-drain contour line. The normal vector points to the normal direction of the channel-source-drain contour line. The two sides of the channel-source-drain contour line are the outer side and the inner side, respectively. The outer side points to the side where the source-drain region and the gate dielectric layer region are located, and the inner side points to the side where the conductive channel region is located. For each contour point on the channel-source-drain contour line, starting from the coordinates of the contour point, move outward and inward along the normal direction of the contour point according to the offset amount to generate an outer offset point and an inner offset point respectively. Connect the outer offset points corresponding to all contour points in the order of arrangement to generate an outer offset contour line. Connect the inner offset points corresponding to all contour points in the order of arrangement to generate an inner offset contour line.

[0012] Furthermore, for each contour point on the channel-source-drain contour line, a grayscale sampling line segment is extracted along its normal direction with the contour point as the center, passing through the conductive channel region, the source-drain region and the gate dielectric layer region, and the two endpoints of the grayscale sampling line segment are located inside the conductive channel region and inside the gate dielectric layer region, respectively. Calculate the gray-level gradient magnitude of each pixel on the gray-level sampling line segment, detect the local maxima of the gray-level gradient magnitude of all pixels on the gray-level sampling line segment, and select the two maxima with the largest gray-level gradient magnitudes, which are denoted as the first interface response point and the second interface response point, respectively. Calculate the normal distance between the two response points, which is denoted as the width of the interface transition area. Take k points before and after the contour point to form a local point set. Perform least squares fitting on the local point set to obtain the local parameter curve. Calculate the first and second derivatives of the parameters corresponding to the contour points. Based on the first and second derivatives, calculate the radius of curvature using the plane curve curvature formula. The offset of the contour points is calculated based on the width of the interface transition area, the radius of curvature of the contour points, and the standard deviation of the gray values ​​of all pixels on the gray sampling line segment. The calculation logic is as follows: take 1 / 2 of the width of the interface transition area as the basic adjustment component, obtain the curvature adjustment factor based on the radius of curvature, generate the gray adjustment factor based on the standard deviation of the gray values, and multiply the basic adjustment component, the curvature adjustment factor and the gray adjustment factor in sequence to obtain the offset.

[0013] Furthermore, Boolean intersection operations are performed between the node coordinates and each material region to obtain the area percentage of all material regions within the preset neighborhood window of the grid nodes. The specific steps are as follows: For each grid node, a square neighborhood window with a side length of L pixels is set with the grid node position as the center point. Within the square neighborhood window, Boolean intersection is performed pixel by pixel, and the number of pixels belonging to each region is counted. The number of pixels belonging to the conductive channel region is recorded as the first pixel count, the number of pixels belonging to the source / drain region is recorded as the second pixel count, and the number of pixels belonging to the gate dielectric layer region is recorded as the third pixel count. Divide the count of the first pixel, the count of the second pixel, and the count of the third pixel by L respectively. 2 The area ratios of the conductive channel region, source / drain region, and gate dielectric layer region were obtained respectively.

[0014] Furthermore, the material property parameters of each mesh node are weighted and averaged based on the area proportion of each material region. The material property parameters of each mesh node are then matched with the standard material property parameters of each material region to determine the material region to which each mesh node belongs, thus completing the construction of the semiconductor device simulation model. The specific steps are as follows: The material properties of the grid nodes include carrier mobility and relative permittivity; The standard carrier mobility and standard relative permittivity of the conductive channel region, source / drain region, and gate dielectric layer region are obtained in advance. For each grid node, the standard carrier mobility and standard relative permittivity of the conductive channel region, source / drain region, and gate dielectric layer region are weighted and combined according to the area ratio of the conductive channel region, source / drain region, and gate dielectric layer region of its neighboring window to obtain the effective carrier mobility and effective relative permittivity. The effective carrier mobility and effective relative permittivity are then assigned to the corresponding grid node. For each grid node, the effective carrier mobility is subtracted from the standard carrier mobility of each material region, and the effective relative permittivity is subtracted from the standard relative permittivity of each material region. The results of the subtraction are normalized, and then the normalized results for the same material region are added together to obtain the material property deviation of the grid node relative to the material region. The grid node is then assigned to the material region with the smallest deviation of its material properties.

[0015] The present invention also provides a modeling system for semiconductor device models, the system being used to implement the modeling method for semiconductor device models described in any of the above claims, specifically including: The image acquisition and processing module is used to acquire cross-sectional images of semiconductor devices using electron microscopes, and to perform gray-level statistics on the images. Based on the peak values ​​of the gray-level distribution, the images are divided into conductive channel regions, source / drain regions, and gate dielectric layer regions. The boundary calculation module is used to extract the initial boundary line between the conductive channel region and the source / drain region based on the spatial relationship between the conductive channel region and the source / drain region. It then samples each initial boundary line at equal intervals along the length direction perpendicular to the extension of the channel to obtain several initial boundary points. Finally, it performs grayscale correction processing on all initial boundary points in combination with image grayscale features to obtain corrected boundary points. The contour fitting module is used to filter effective correction boundary points by calculating the Euclidean distance between adjacent correction boundary points, and fit the channel-source-drain contour line to determine the upper and lower interfaces of the gate dielectric layer region. Interface response points are extracted from the upper and lower interfaces respectively, and the normal distance between them is calculated to obtain the width of the interface transition region. The curvature adjustment factor and gray level adjustment factor are determined according to the local radius of curvature of each contour point on the contour line and the gray level standard deviation of the corresponding region, and according to the preset mapping relationship. The region coupling module is used to determine the offset of each contour point based on the width of the interface transition zone, the curvature adjustment factor and the grayscale adjustment factor. The channel-source-drain contour line is offset equidistantly in the inward and outward normal directions according to the offset, generating two parallel offset contour lines. The area between the two offset contour lines is selected as the coupling transition area of ​​each material region, and the simulation mesh nodes are generated in the coupling transition area. The model building module is used to perform Boolean intersection operations on the node coordinates and material regions for each mesh node in the coupling transition region, so as to obtain the area ratio of all material regions within the preset neighborhood window of the mesh node. The material property parameters of each mesh node are weighted and averaged based on the area ratio of each material region. The material property parameters of each mesh node are matched with the standard material property parameters of each material region to determine the material region to which each mesh node belongs, thus completing the construction of the semiconductor device simulation model.

[0016] Compared with the prior art, the beneficial effects of the present invention are: This invention acquires an initial process cross-sectional image and performs grayscale statistics. Based on the peak values ​​of the grayscale distribution, the image is divided into conductive channel regions, source / drain regions, and gate dielectric layer regions. This multi-threshold segmentation method can adapt to the actual situation of uneven grayscale in the image, avoiding regional misclassification caused by a single global threshold, and providing an accurate partitioning basis for subsequent boundary extraction. The initial boundary line between the conductive channel and the source / drain is extracted based on the spatial position relationship, and the initial boundary points are obtained by sampling at equal intervals. Then, grayscale correction is performed on the boundary points to generate corrected boundary points, which can guide the boundary points to the real interface position with the largest grayscale gradient, effectively correcting the boundary point offset caused by image blurring or noise, and improving the spatial accuracy of boundary positioning. By calculating the Euclidean distance between adjacent corrected boundary points and removing outliers, the remaining points are fitted to obtain the channel-source / drain contour line, which effectively eliminates the interference of abnormal noise points on the contour morphology, making the fitted contour line smoother and more continuous, and truly reflecting the actual geometric morphology of the device interface.

[0017] This invention also generates two offset contour lines by equidistantly offsetting the channel-source-drain contour lines inward and outward normal directions, respectively, thereby extracting the coupling transition region and generating mesh nodes. The coupling transition region is generated using the average thickness of the dielectric layer, which can accurately locate the boundary transition zone between different material regions and avoid the loss of region division caused by a single boundary. Boolean intersection operation is performed on the coordinates of each mesh node in the coupling transition region with each region, and the area ratio of each mesh node in each region is calculated within a set neighborhood window. The material property parameters of each node are weighted and assigned a weighted average value based on this ratio. This avoids the non-physical step change of node material parameters at the interface in traditional hard classification methods, and makes the material properties of nodes near the interface change continuously with the proportion of region composition, so that the material parameter distribution in the simulation model is smoother in space and more physically reasonable. Attached Figure Description

[0018] Figure 1 This is a flowchart illustrating the modeling method for the semiconductor device model of the present invention; Figure 2 This invention is based on the grayscale histogram of the cross-sectional image of a semiconductor device obtained by electron microscopy. Figure 3 This is a schematic diagram of the module composition of the modeling system for the semiconductor device model of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0020] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0021] Example: Please see Figures 1 to 2 The present invention provides a technical solution: A modeling method for semiconductor devices, comprising the following steps: Step 1: Obtain an electron microscope cross-sectional image of the semiconductor device and perform grayscale statistics on the image. Based on the grayscale distribution peak, the image is divided into conductive channel region, source / drain region, and gate dielectric layer region. In this embodiment, the image is divided into a conductive channel region, a source / drain region, and a gate dielectric layer region based on the grayscale distribution peak value. The specific steps are as follows: In the electron microscope cross-sectional image, the gray value of each pixel is quantized into gray levels in the range of 0 to 255. The entire electron microscope cross-sectional image is traversed pixel by pixel, and the number of pixels appearing at each gray level is counted to generate a gray level histogram. Perform a first-order difference operation on the grayscale histogram to determine all the inflection points where the frequency changes from increasing to decreasing, and extract the gray levels corresponding to the three inflection points with the largest frequency values, which are marked as the first peak gray level, the second peak gray level, and the third peak gray level, respectively. The midpoint gray value between the first peak gray level and the second peak gray level is taken as the first segmentation threshold, and the midpoint gray value between the second peak gray level and the third peak gray level is taken as the second segmentation threshold. Pixels with gray values ​​less than the first segmentation threshold are classified as conductive channel regions, pixels with gray values ​​greater than or equal to the first segmentation threshold and less than the second segmentation threshold are classified as source-drain regions, and pixels with gray values ​​greater than or equal to the second segmentation threshold are classified as gate dielectric layer regions.

[0022] Semiconductor devices are observed using a scanning electron microscope (SEM) to obtain cross-sectional images. The conductive channel region is a thin layer on the surface of the semiconductor substrate, appearing as horizontal or arc-shaped stripes in the cross-sectional image. Due to differences in doping concentration or materials, its grayscale value is usually low. The source / drain region is a semiconductor region with a high doping concentration, and its grayscale value is between that of the channel and the gate dielectric layer. The gate dielectric layer region appears as a thin layer covering the conductive channel, and its material is usually a high-dielectric-constant insulator such as silicon oxide, with the highest grayscale value. In the cross-sectional image, the distribution of the conductive channel region, source / drain region, and gate dielectric layer region has a clear spatial stacking structure, with the gate dielectric layer region, conductive channel region, and source / drain region arranged sequentially from top to bottom.

[0023] It should be noted that in the electron microscope cross-sectional image, due to the differences in the atomic number, density, and doping concentration of the materials in the conductive channel region, source / drain region, and gate dielectric layer region, different and stable grayscale ranges are represented in the image. Grayscale statistics of the entire electron microscope cross-sectional image yield a grayscale histogram containing three frequency peaks, corresponding to the pixel cluster grayscale bands in the three regions. The inflection point where the frequency changes from increasing to decreasing corresponds to the peak apex. These inflection points are extracted to identify the grayscale levels of the three peaks, representing the grayscale centers of the conductive channel region, source / drain region, and gate dielectric layer region, respectively. The first peak grayscale level represents the grayscale center of the conductive channel region, and the second peak grayscale level represents the grayscale center of the source / drain region. Since the grayscale distribution of these two types of regions approximately follows a normal distribution and forms two independent peaks on the grayscale axis, the grayscale distribution of these two types of regions in the electron microscope image is approximately normally distributed. Within the grayscale interval between the two peaks, the probability density curves of the two types of regions overlap. Taking the midpoint grayscale value of the two peaks as the segmentation threshold is the equilibrium position where the total risk of misclassification of the two types of pixels in the overlapping region is minimized. This position makes the probability of a conductive channel pixel being misclassified as a source / drain region equal to the probability of a source / drain pixel being misclassified as a conductive channel region, and the overall probability is minimized. Similarly, the grayscale levels of the second and third peaks correspond to the grayscale centers of the source / drain region and the gate dielectric layer region, respectively. The midpoint grayscale value of the two peaks is the optimal threshold for separating the source / drain region and the gate dielectric layer region. Since the three peaks correspond to the main grayscale aggregation bands of the three material regions, taking the midpoint of adjacent peaks as the segmentation boundary actually divides the entire grayscale range into three continuous intervals on the grayscale axis. Each interval belongs to the material category that is closest to its grayscale center, thereby achieving optimal segmentation based on three regions in the entire grayscale space.

[0024] To illustrate the frequency distribution of each gray level in the electron microscope cross-sectional image, Table 1 is provided, as follows: Table 1. Grayscale level-pixel frequency distribution of electron microscope cross-sectional images of semiconductor devices. Table 1 shows the grayscale distribution characteristics and distinguishability of three key material regions in the electron microscope cross-sectional images of semiconductor devices. From the overall data structure, the frequencies reach local maxima at grayscale levels 45, 145, and 230, corresponding to the first, second, and third peak grayscale levels, respectively. Using the midpoint of adjacent peak grayscale levels as the segmentation threshold, the first segmentation threshold is the midpoint between grayscale levels 45 and 145, corresponding to grayscale level 95; the second segmentation threshold is the midpoint between grayscale levels 145 and 230, 187.5, which, after rounding, corresponds to grayscale level 188. The grayscale range is... The pixels correspond to the conductive channel region, with a grayscale range of [missing information]. The pixels correspond to the source / drain regions, with a grayscale range of [value missing]. The pixels correspond to the gate dielectric layer region, where the conductive channel region corresponds to the darkest pixel group in the image, the source / drain region corresponds to the medium brightness pixel group, and the gate dielectric layer region corresponds to the brightest pixel group. Each region is separated by a segmentation threshold to ensure that different material regions form their own stable clustering ranges on the grayscale axis, with low overlap and a low probability of pixels being misclassified.

[0025] Figure 2 Based on the grayscale histogram drawn in Table 1, by Figure 2 As can be seen, the trend of its data changes is consistent with that in Table 1.

[0026] Step 2: Based on the spatial relationship between the conductive channel region and the source / drain region, extract the initial boundary line between the conductive channel region and the source / drain region, and sample each initial boundary line at equal intervals along the length direction perpendicular to the extension of the channel to obtain several initial boundary points. Combine the image grayscale features to perform grayscale correction processing on all initial boundary points to obtain corrected boundary points. In this embodiment, based on the spatial relationship between the conductive channel region and the source / drain region, the initial boundary line between the conductive channel region and the source / drain region is extracted. The specific steps are as follows: The boundary between the conductive channel region and the source / drain region is traversed pixel by pixel. Pixels that satisfy the condition of belonging to the conductive channel region and having a source / drain region pixel in their four-connected neighborhood are marked as first boundary points. Pixels that satisfy the condition of belonging to the source / drain region and having a conductive channel region pixel in their four-connected neighborhood are marked as second boundary points. Pixels that simultaneously satisfy the condition of belonging to the conductive channel region and having at least one source / drain region pixel in their eight-connected neighborhood are marked as candidate boundary pixels. The first and second boundary points are merged to obtain a set of boundary pixels. An 8-connected neighborhood connection operation is performed on all pixels in this set. Specifically, any unclassified pixel is selected from the set of boundary pixels. If there are candidate boundary pixels in the adjacent positions of the pixel in the four diagonal directions, these candidate boundary pixels are grouped with the unclassified pixels into the same boundary pixel cluster. The classification process of boundary pixels is repeated. All candidate boundary pixels are grouped into one boundary pixel cluster, and each boundary pixel cluster corresponds to an initial boundary line.

[0027] It should be noted that in the cross-sectional images of semiconductor devices obtained by electron microscopy, the material cross-section between the conductive channel region and the source / drain region is not an ideal geometric line, but a grayscale transition band with a certain width. Due to image noise, local doping fluctuations, and the influence of electron microscopy sampling, relying solely on a single rule to extract boundary points can easily lead to boundary breakage. The first boundary point is defined as a pixel belonging to the conductive channel region and containing a pixel from the source / drain region within its four-connected neighborhood. The principle behind this selection method is that the four-connected neighborhood reflects the most direct and closest spatial contact relationship in a digital image. Only when two regions have continuous edge-to-edge contact at the actual physical interface will an adjacency response occur at the four-connected level. Therefore, pixels that meet this condition must be located at the outermost edge of the channel region facing the source / drain side, rather than inside the channel or far from the interface, thus providing high-confidence boundary localization seed points. This stringent condition effectively eliminates false boundary responses caused by image noise or grayscale transition bands, ensuring the geometric accuracy of the initial boundary extraction. The selection of the second boundary point is a symmetrical complement to the first boundary point. Its criteria are that the pixel itself belongs to the source / drain region, and at least one pixel in its four-connected neighborhood belongs to the conductive channel region. The principle behind this selection method is that there are clear material boundaries on both sides of the interface of a real semiconductor device. Extracting boundary points from only one side is prone to bias due to region segmentation errors or interface tilt, introducing system bias. By using the same four-connected neighborhood condition on one side of the source / drain region for screening, a boundary seed point with the same confidence level as the first boundary point is obtained from the other side of the interface. The two are spatially mirror constraints, jointly limiting the true range of the interface. This bidirectional constraint mechanism ensures that the position of the initial boundary line will not significantly shift due to small fluctuations in the one-sided region segmentation threshold, thereby improving the robustness and symmetry of boundary extraction. The criteria for determining candidate boundary pixels are that the pixel itself belongs to the conductive channel region, and at least one pixel in its eight-connected neighborhood belongs to the source / drain region. The principle behind this selection method is that in actual device cross-sections, material interfaces are not always aligned with the direction of the image pixel grid. Especially at locations with curved channels, tilted interfaces, or irregular morphologies caused by the manufacturing process, interfaces often only demonstrate regional adjacency through diagonal pixel contact. If only the four-connectivity condition is relied upon, such oblique or highly curved interface locations cannot be marked as boundary points, resulting in broken or jagged edges in the extracted boundary lines. The eight-connectivity neighborhood introduces diagonal tolerance on top of the four-connectivity condition, allowing interfaces to be effectively captured as candidate boundary pixels even at arbitrary angles to the pixel grid. Because this condition is relatively lenient, it may introduce some boundary noise; therefore, it is set as a candidate boundary pixel rather than a final boundary point.

[0028] The first and second boundary points are merged into a single boundary pixel set, where each pixel has the highest boundary confidence. From this merged set, any unclassified pixel is selected as the starting seed point for the boundary cluster. This seed point is then expanded and clustered using an 8-connected neighborhood-based region growing algorithm. If a candidate boundary pixel has no pixels already included in the boundary pixel set within its 8-connected neighborhood, it is considered an isolated noise point and not included in the boundary cluster. After the search and clustering, each complete boundary pixel cluster corresponds to an initial boundary curve. The pixels within the boundary cluster are then sorted according to their 8-connected adjacency order in space, forming a continuous chain of points.

[0029] In this embodiment, grayscale correction processing is performed on all initial boundary points based on image grayscale features to obtain corrected boundary points. The specific steps are as follows: For each initial boundary pixel, a local image window is extracted from the electron microscope cross-sectional image with the initial boundary pixel as the center. Within the local image window, the first-order gray-level gradient values ​​along the horizontal and vertical directions at the location of the initial boundary pixel are calculated to generate the gradient magnitude of the initial boundary pixel. Starting from the initial boundary pixel, search line segments are generated by extending along the positive and negative normal directions of the boundary line of the initial boundary pixel. The gradient magnitude of each pixel on the search line segment is calculated, and the position of the pixel with the largest gradient magnitude is selected as the correction boundary point of the initial boundary point.

[0030] It should be noted that the local image window is square, and each local image window contains an initial boundary pixel and surrounding neighboring pixels. The horizontal and vertical first-order gray-level gradient values ​​of the initial boundary pixel are calculated using the Sobel operator. The squares of the two values ​​are added together and the square root is taken to obtain the gradient magnitude of the initial boundary pixel. The gradient magnitude reflects the degree of gray-level change at the initial pixel. A search line segment is set along the normal direction of the initial boundary point because the normal direction is the direction of the fastest interface change. In the normal direction perpendicular to the interface direction, the gray-level profile usually presents an S-shaped or sloping transition, and the first derivative of this profile reaches its peak at the center of the interface. Since different semiconductor materials have different atomic numbers, densities, and doping concentrations, their scattering ability for incident electrons is different, resulting in different gray-level levels in the image. When crossing from one material to another, the gray-level value will change significantly. The spatial location where this change is most drastic is the physical boundary between the two materials. Therefore, the pixel with the largest gradient magnitude on the search line segment is used as the correction boundary point.

[0031] Step 3: Filter effective correction boundary points by calculating the Euclidean distance between adjacent correction boundary points, and fit the channel-source-drain profile. In this embodiment, the Euclidean distance between adjacent correction boundary points is calculated to screen effective correction boundary points, and the channel-source-drain profile is fitted. The specific steps are as follows: All correction boundary points are sorted according to the sampling order of their corresponding initial boundary points to generate an ordered point sequence distributed along the channel length. For each correction boundary point in the ordered point sequence, the first Euclidean distance with the previous adjacent correction boundary point, the second Euclidean distance with the next adjacent correction boundary point, and the third Euclidean distance between the previous adjacent correction boundary point and the next adjacent correction boundary point are calculated. The arithmetic mean of the above three Euclidean distances is calculated. If the first Euclidean distance or the second Euclidean distance is greater than three times the arithmetic mean, then the correction boundary point is determined to be an outlier. After removing outliers, control points are selected at equal intervals from the remaining effective correction boundary points to construct cubic B-spline curves. The coordinates of the control points are solved by the least squares method to minimize the sum of squares of the deviations between the cubic B-spline curves and the control points, thereby obtaining the channel-source-drain profile.

[0032] It should be noted that the channel-source-drain boundary of a semiconductor device is a continuous and smooth curve at the microscale. The Euclidean distance between adjacent correction boundary points should be kept within a certain range and there should be no jumps that are much larger than the local average spacing. If such a jump occurs, the correction boundary point will be identified as an outlier and removed. Using three times the arithmetic mean of the Euclidean distance as the judgment threshold, ideally, the Euclidean distance between adjacent correction boundary points is stable near the average sampling step size. For any correction boundary point, calculate its distance to the two points before and after it, as well as the distance between the two points before and after it. Take the average of the three as the expected estimate of the distance between adjacent points in the local neighborhood of the correction boundary point, which reflects the distribution density of boundary points in the local area. For normal continuous boundaries, the fluctuation of the distance between adjacent points usually does not exceed twice the local average distance. However, outliers caused by noise, gray-scale anomalies, or tracking errors have a higher distance from their neighbors. Setting the threshold to three times can reliably capture most outliers while also preserving sufficient margin for normal local curvature changes.

[0033] Step 4: Determine the upper and lower interfaces of the gate dielectric layer region. Extract the interface response points from the upper and lower interfaces respectively, and calculate the normal distance between them to obtain the width of the interface transition region. Determine the curvature adjustment factor and gray level adjustment factor according to the local radius of curvature of each contour point on the contour line and the gray level standard deviation of the corresponding region, and according to the preset mapping relationship. Determine the offset of each contour point according to the width of the interface transition region, the curvature adjustment factor and the gray level adjustment factor. Offset the channel-source-drain contour line equidistantly in the inward and outward normal directions according to the offset, and generate two parallel offset contour lines. Extract the area between the two offset contour lines as the coupling transition region of each material region, and generate the simulation mesh nodes in the coupling transition region. In this embodiment, the channel-source-drain profile is offset equidistantly in the inward and outward normal directions according to the offset amount, generating two parallel offset profiles. The specific steps are as follows: Obtain the normal vector of each pixel on the channel-source-drain contour line. The normal vector points to the normal direction of the channel-source-drain contour line. The two sides of the channel-source-drain contour line are the outer side and the inner side, respectively. The outer side points to the side where the source-drain region and the gate dielectric layer region are located, and the inner side points to the side where the conductive channel region is located. For each contour point on the channel-source-drain contour line, starting from the coordinates of the contour point, move outward and inward along the normal direction of the contour point according to the offset amount to generate an outer offset point and an inner offset point respectively. Connect the outer offset points corresponding to all contour points in the order of arrangement to generate an outer offset contour line. Connect the inner offset points corresponding to all contour points in the order of arrangement to generate an inner offset contour line.

[0034] For each contour point on the channel-source-drain contour line, take the contour point as the center and cut a gray-scale sampling line segment along its normal direction that runs through the conductive channel region, the source-drain region and the gate dielectric layer region, and the two endpoints of the gray-scale sampling line segment are located inside the conductive channel region and inside the gate dielectric layer region, respectively. It should be noted that the interface grayscale changes the fastest in the normal direction. Sampling along this direction can capture the most complete grayscale transition information with the shortest line segment. If the grayscale sampling line segment is intercepted along the tangential or oblique direction, the grayscale sampling line segment extends along the interface direction, mixing the curved or jagged grayscale changes of the interface into the profile, causing the estimated width of the transition area to be too large and the gradient peak to be weakened, affecting the accuracy of the offset calculation.

[0035] Calculate the gray-level gradient magnitude of each pixel on the gray-level sampling line segment, detect the local maxima of the gray-level gradient magnitude of all pixels on the gray-level sampling line segment, select the two maxima with the largest gray-level gradient magnitude, and record them as the first interface response point and the second interface response point respectively. Calculate the normal distance between the two response points and record it as the width of the interface transition area. Specifically, the interface transition zone represents a band-shaped area where the grayscale value changes continuously and gradually between two different material regions. The spatial span of this band-shaped area in the normal direction, that is, the distance from the position where the grayscale value begins to deviate significantly from the typical value of the first material to the position where the grayscale value reaches the typical value of the second material, is the width of the interface transition zone.

[0036] Take k points before and after the contour point to form a local point set. Perform least squares fitting on the local point set to obtain the local parameter curve. Calculate the first and second derivatives of the parameters corresponding to the contour points. Based on the first and second derivatives, calculate the radius of curvature using the plane curve curvature formula. Specifically, the channel-source-drain profile of a semiconductor device is not a flat straight line; it may have bends, corners, sharp points, or local undulations. In these areas, relying solely on grayscale distribution will lead to geometric distortion due to deviations in the profile. This geometric distortion is corrected by using the radius of curvature. For any point on the profile, a larger radius of curvature indicates a straighter profile and less curvature near that point, while a smaller radius of curvature indicates more severe curvature near that point. The radius of curvature quantifies the local steepness or smoothness of the channel-source-drain boundary. The calculation process for the radius of curvature is as follows: take the profile point... The local point set consists of the points before and after it, and the k points before and after it. Specifically: in, Represents a local point set, Indicates the first One contour point, Represents the index of the contour point, and , Indicates the number of contour points. Represents contour points The number of points before and after, express The previous chapter One point, express The later One point; Cubic B-spline interpolation is used to perform least-squares fitting on the local point set to obtain the local parameter curve. ,and ,in, Indicates the arc length parameter. This represents the x-coordinate of a point on the channel-source-drain profile when the arc length parameter is t. This represents the ordinate of a point on the channel-source-drain profile when the arc length parameter is t. Let the contour points The corresponding arc length parameter is ,beg The first-order derivative vector and the second-order derivative vector are respectively: , ; Arc length parameter The formula for calculating curvature is: in, The arc length parameter is Curvature at time; Taking the reciprocal of the curvature gives the radius of curvature. ,and .

[0037] The offset of the contour points is calculated based on the width of the interface transition area, the radius of curvature of the contour points, and the standard deviation of the gray values ​​of all pixels on the gray sampling line segment. The calculation logic is as follows: take 1 / 2 of the width of the interface transition area as the basic adjustment component, obtain the curvature adjustment factor based on the radius of curvature, obtain the gray adjustment factor based on the standard deviation of the gray values, and multiply the basic adjustment component, the curvature adjustment factor and the gray adjustment factor in sequence to obtain the offset.

[0038] It should be noted that the basic adjustment component is half the width of the interface transition zone, which represents the spatial span of the transition from one material to another in terms of grayscale. The geometric center of this transition zone is located at the point where the grayscale change is most dramatic. The distance from the geometric center to the edge of this transition zone is approximately half the width of the interface transition zone. This distance is used as the baseline value for the offset, representing the average distance from the boundary of the real material to the boundary of the transition zone. Based on the basic adjustment component, the effects of curvature and grayscale are considered sequentially. Where the contour is sharply curved, the radius of curvature is small. If the offset is too large, the offset contour line will self-intersect or twist. Where it is straight, the radius of curvature is larger, allowing for a larger offset. The curvature adjustment factor is used to prevent the offset contour from shifting. Line distortion is addressed by calculating the curvature adjustment factor using the formula: the radius of curvature at the contour point divided by the sum of the radius of curvature at the contour point and the width of the interface transition zone. A larger radius of curvature indicates a contour closer to a straight line, allowing for greater offset, and the curvature adjustment factor approaches 1. Conversely, a smaller radius of curvature indicates more severe contour bending, requiring compression of the offset, and the curvature adjustment factor approaches 0. In the formula for calculating the curvature adjustment factor, the width of the interface transition zone controls the compression sensitivity, determining how small the radius of curvature will be significantly compressed. The width of the interface transition zone is a geometric feature scale at the interface, used to control compression sensitivity. This indicates that when the radius of curvature is smaller than the width of the interface transition zone, geometric deformation is significant, and offset must be limited. The standard deviation of the grayscale values ​​is normalized, and the grayscale adjustment factor is calculated using the following formula: in, This represents the grayscale adjustment factor. This represents the standard deviation of the normalized gray values. Represents the grayscale sensitivity coefficient; The standard deviation of the grayscale values ​​is mapped to a normalized value. The range ensures that the grayscale adjustment factor is independent of the overall grayscale scale of the image. A larger standard deviation of the normalized grayscale value indicates more drastic fluctuations in grayscale values ​​along the sampling line segment, corresponding to a more blurred or noisy interface and higher uncertainty in the interface position. If the contour is still extrapolated based on the basic adjustment components, this uncertainty will be carried into subsequent steps, causing model distortion. Therefore, reducing the offset caused by grayscale values ​​at this point reduces distortion. Conversely, a smaller standard deviation of the normalized grayscale value indicates smoother fluctuations in grayscale values ​​along the sampling line segment, with less blur or noise interference. The main influencing factor of the offset is not image grayscale but geometric curvature. At this point, the grayscale adjustment factor is close to 1, avoiding over-correction. Grayscale sensitivity coefficient... Used to control the sensitivity of the grayscale adjustment factor to changes in the standard deviation of the normalized grayscale value. The larger, the more it means Follow The faster the increase and decrease, the more significant the compression of the offset will be, even if there is a slight fluctuation in gray level. The offset is highly sensitive to gray level noise in the image. The smaller, the better. Follow The smoother the decrease, the more likely the offset is to be compressed only when grayscale fluctuations are severe, meaning the offset is less sensitive to image grayscale noise; this is determined by calculating the half-compression point. The range of values ​​for , when When the standard deviation of the normalized gray value is at the half-compression point, then when At that time, the half-compression point was set at 0.693, meaning that the standard deviation had to reach 0.693 before halving the compression based on the baseline adjustment component. This was overly conservative. At this point, the half-compression point is 0.347, meaning that when the standard deviation reaches 0.347, the compression is halved based on the baseline adjustment component. At this point, the half-compression point is 0.231, meaning that when the standard deviation reaches 0.231, the compression is halved based on the baseline adjustment component. When the standard deviation reaches 0.173, the half-compression point is 0.173, which means that when the standard deviation reaches 0.173, the component is compressed by half based on the baseline adjustment component, indicating that it is relatively sensitive. As one implementation method, The range of values ​​is The specific value is set by those skilled in the art based on the actual situation, and is not limited here.

[0039] The base adjustment component, curvature adjustment factor, and grayscale adjustment factor correspond to different independent physical extrema, and their influence on the offset is modulated step by step. The base adjustment component represents the average distance from the geometric center of the grayscale transition zone to the boundary of the transition zone. It is the initial reference value of the offset and is completely determined by the grayscale profile of the image. First, geometric correction is performed through the curvature adjustment factor. If the contour is severely curved, the offset contour line will self-intersect or twist. This factor is independent of grayscale information and depends only on the geometric shape of the contour line itself. Its purpose is to compress the offset proportionally based on the base adjustment component, and the degree of compression is only related to the degree of local curvature. After geometric adjustment, grayscale adjustment is performed. If the local grayscale fluctuation is large, it indicates that the interface is blurred or the noise is strong. This factor is independent of the contour geometry and depends only on the grayscale statistical characteristics of the local image. Its function is to compress the offset proportionally again based on the geometric correction, and the degree of compression is related to the grayscale value of the image. The three are in a series correction relationship. The subsequent correction only acts on the result of the previous correction, rather than independently affecting the original reference value. This is consistent with the actual physical process—geometric distortion risk and grayscale ambiguity risk are two different factors that exist independently and can be superimposed to constrain each other.

[0040] Step 5: For each mesh node in the coupling transition region, perform Boolean intersection operation between the node coordinates and each material region to obtain the area ratio of all material regions within the preset neighborhood window of the mesh node. Assign a weighted average value to the material property parameters of each mesh node based on the area ratio of each material region. Match the material property parameters of each mesh node with the standard material property parameters of each material region to determine the material region to which each mesh node belongs, thus completing the construction of the semiconductor device simulation model.

[0041] In this embodiment, Boolean intersection operations are performed between the node coordinates and each material region to obtain the area ratio of all material regions within the preset neighborhood window of the grid node. The specific steps are as follows: For each grid node, a square neighborhood window with a side length of L pixels is set with the grid node position as the center point. Within the square neighborhood window, Boolean intersection is performed pixel by pixel, and the number of pixels belonging to each region is counted. The number of pixels belonging to the conductive channel region is recorded as the first pixel count, the number of pixels belonging to the source / drain region is recorded as the second pixel count, and the number of pixels belonging to the gate dielectric layer region is recorded as the third pixel count. Divide the count of the first pixel, the count of the second pixel, and the count of the third pixel by L respectively. 2 The area ratios of the conductive channel region, source / drain region, and gate dielectric layer region were obtained respectively.

[0042] It should be noted that in the actual physical structure of semiconductor devices, a grid node is a geometric point and cannot be directly identified as belonging to any material region. By dividing a neighborhood window around it, the grid node is expanded into a region with an area, thereby allowing the material composition ratio within that region to be statistically analyzed. L should not be less than the width of the interface transition area in the image to ensure that the neighborhood window contains representative pixels of the materials on both sides, and L should not be greater than the critical structure of the device (such as the length of the conductive channel) to avoid excessive smoothing that could lead to structural distortion.

[0043] The material property parameters of each mesh node are weighted and averaged based on the area proportion of each material region. The material property parameters of each mesh node are then matched with the standard material property parameters of each material region to determine the material region to which each mesh node belongs. This completes the construction of the semiconductor device simulation model. The specific steps are as follows: The material properties of the grid nodes include carrier mobility and relative permittivity; The standard carrier mobility and standard relative permittivity of the conductive channel region, source / drain region, and gate dielectric layer region are obtained in advance. For each grid node, the standard carrier mobility and standard relative permittivity of the conductive channel region, source / drain region, and gate dielectric layer region are weighted and combined according to the area ratio of the conductive channel region, source / drain region, and gate dielectric layer region of its neighboring window to obtain the effective carrier mobility and effective relative permittivity. The effective carrier mobility and effective relative permittivity are then assigned to the corresponding grid node. It should be noted that the Hall voltage perpendicular to the current direction is measured in advance in the conductive channel region, source / drain region, and gate dielectric layer region to obtain the carrier mobility; the materials in the conductive channel region, source / drain region, and gate dielectric layer region are used to prepare parallel plate capacitor samples, and the capacitance and loss factor are measured by an impedance analyzer, and the relative permittivity is calculated by combining the sample thickness and electrode area. Weighted by area percentage, in the cross-section of a semiconductor device, the channel and source / drain regions are directly adjacent and occupy the majority of the area, while the gate dielectric layer only covers the channel and is a very thin insulating layer. For mesh nodes located in the coupling transition region, their neighborhood window falls into both the channel and source / drain regions, and their area percentages are usually similar; while the gate dielectric layer is far from this boundary and only enters the window when the node is very close to the gate side. Therefore, in transition region nodes, the area percentage of the conductive channel region is usually greater than that of the gate dielectric layer region, the area percentage of the source / drain region is greater than that of the gate dielectric layer region, and the area percentages of the conductive channel region and the source / drain region are approximately equal. Under the electrostatic field approximation, for a mixed region composed of multiple media, its equivalent dielectric constant is obtained by area-weighted averaging. This is because the electric field lines satisfy the tangential continuity condition at the interface. When the material delamination direction is parallel or approximately parallel to the electric field direction, area-weighted averaging can better approximate the macroscopic dielectric response of the composite region. Mobility is a transport parameter. Near the interface, the transport characteristics actually experienced by charge carriers are the spatial average effect of the transport capabilities of multiple materials. Using area weighting is equivalent to linearly mixing the transport contributions of multiple materials at the nodal scale.

[0044] For each grid node, the effective carrier mobility is subtracted from the standard carrier mobility of each material region, and the effective relative permittivity is subtracted from the standard relative permittivity of each material region. The results of the subtraction are normalized, and then the normalized results for the same material region are added together to obtain the material property deviation of the grid node relative to the material region. The grid node is then assigned to the material region with the smallest deviation of its material properties.

[0045] It should be noted that mobility and dielectric constant are the two most core material properties in device simulation. Mobility determines the current driving capability, and dielectric constant determines the electric field distribution. Near the interface, the effective properties of a node are a mixed average of multiple material properties. The mobility and dielectric constant of a node are independent physical parameters, and there is no mutual constraint or product relationship between them. Essentially, they should be determined by both of these simultaneously. The carrier mobility and relative dielectric constant of the three material regions each have standard values, which are the values ​​corresponding to the ideal pure material. By subtracting these values, we can determine which material's inherent properties the actual effective properties of the node are closer to. To standardize the dimensions of the effective carrier mobility and effective relative dielectric constant, normalization is first performed. The two are complementary rather than redundant in indicating the material type. Therefore, the normalized mobility deviation and dielectric constant deviation are summed to form the material property deviation. The material property deviation reflects the physical similarity between the mesh node and the material region. The smaller the material property deviation, the closer the effective properties of the mesh node are to that standard material.

[0046] Please see Figure 3The present invention also provides a modeling system for semiconductor device models, the system being used to implement the modeling method for semiconductor device models described in any of the above claims, specifically including: The image acquisition and processing module is used to acquire cross-sectional images of semiconductor devices using electron microscopes, and to perform grayscale statistics on the images. Based on the grayscale distribution peak values, the images are divided into conductive channel regions, source / drain regions, and gate dielectric layer regions. The boundary calculation module is used to extract the initial boundary line between the conductive channel region and the source / drain region based on the spatial relationship between the conductive channel region and the source / drain region. It then samples each initial boundary line at equal intervals along the length direction perpendicular to the extension of the channel to obtain several initial boundary points. Finally, it performs grayscale correction processing on all initial boundary points in combination with image grayscale features to obtain corrected boundary points. The contour fitting module is used to filter effective correction boundary points by calculating the Euclidean distance between adjacent correction boundary points, and fit the channel-source-drain contour line to determine the upper and lower interfaces of the gate dielectric layer region. Interface response points are extracted from the upper and lower interfaces respectively, and the normal distance between them is calculated to obtain the width of the interface transition region. The curvature adjustment factor and gray level adjustment factor are determined according to the local radius of curvature of each contour point on the contour line and the gray level standard deviation of the corresponding region, and according to the preset mapping relationship. The region coupling module is used to determine the offset of each contour point based on the width of the interface transition zone, the curvature adjustment factor and the grayscale adjustment factor. The channel-source-drain contour line is offset equidistantly in the inward and outward normal directions according to the offset, generating two parallel offset contour lines. The area between the two offset contour lines is selected as the coupling transition area of ​​each material region, and the simulation mesh nodes are generated in the coupling transition area. The model building module is used to perform Boolean intersection operations on the node coordinates and material regions for each mesh node in the coupling transition region, so as to obtain the area ratio of all material regions within the preset neighborhood window of the mesh node. The material property parameters of each mesh node are weighted and averaged based on the area ratio of each material region. The material property parameters of each mesh node are matched with the standard material property parameters of each material region to determine the material region to which each mesh node belongs, thus completing the construction of the semiconductor device simulation model.

[0047] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0048] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0049] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0050] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A modeling method for semiconductor device models, characterized in that, include: Obtain cross-sectional images of semiconductor devices using electron microscopes, and perform grayscale statistics on the images. Based on the peak values ​​of the grayscale distribution, the images are divided into conductive channel regions, source / drain regions, and gate dielectric layer regions. Based on the spatial relationship between the conductive channel region and the source / drain region, the initial boundary line between the conductive channel region and the source / drain region is extracted. Along the length direction perpendicular to the extension of the channel, each initial boundary line is sampled at equal intervals to obtain several initial boundary points. Combined with the image grayscale features, all initial boundary points are subjected to grayscale correction processing to obtain corrected boundary points. Effective correction boundary points are selected by calculating the Euclidean distance between adjacent correction boundary points, and the channel-source-drain profile is obtained by fitting. The upper and lower interfaces of the gate dielectric layer region are determined. Interface response points are extracted from the upper and lower interfaces respectively, and the normal distance between them is calculated to obtain the width of the interface transition region. The curvature adjustment factor and gray level adjustment factor are determined according to the local radius of curvature of each profile point on the profile line and the gray level standard deviation of the corresponding region, and according to the preset mapping relationship. The offset of each contour point is determined based on the width of the interface transition zone, the curvature adjustment factor, and the grayscale adjustment factor. The channel-source-drain contour line is offset equidistantly in the inward and outward normal directions according to the offset, generating two parallel offset contour lines. The area between the two offset contour lines is taken as the coupling transition area of ​​each material region, and the simulation mesh nodes are generated in the coupling transition area. For each mesh node in the coupling transition region, Boolean intersection operation is performed between the node coordinates and each material region to obtain the area ratio of all material regions within the preset neighborhood window of the mesh node. The material property parameters of each mesh node are weighted and averaged based on the area ratio of each material region. The material property parameters of each mesh node are matched with the standard material property parameters of each material region to determine the material region to which each mesh node belongs, thus completing the construction of the semiconductor device simulation model.

2. The modeling method for a semiconductor device model according to claim 1, characterized in that: Based on the grayscale distribution peaks, the image is divided into conductive channel region, source / drain region, and gate dielectric layer region. The specific steps are as follows: In the electron microscope cross-sectional image, the gray value of each pixel is quantized into gray levels in the range of 0 to 255. The entire electron microscope cross-sectional image is traversed pixel by pixel, and the number of pixels appearing at each gray level is counted to generate a gray level histogram. Perform a first-order difference operation on the grayscale histogram to determine all the inflection points where the frequency changes from increasing to decreasing, and extract the gray levels corresponding to the three inflection points with the largest frequency values, which are marked as the first peak gray level, the second peak gray level, and the third peak gray level, respectively. The midpoint gray value between the first peak gray level and the second peak gray level is taken as the first segmentation threshold, and the midpoint gray value between the second peak gray level and the third peak gray level is taken as the second segmentation threshold. Pixels with gray values ​​less than the first segmentation threshold are classified as conductive channel regions, pixels with gray values ​​greater than or equal to the first segmentation threshold and less than the second segmentation threshold are classified as source-drain regions, and pixels with gray values ​​greater than or equal to the second segmentation threshold are classified as gate dielectric layer regions.

3. The modeling method for a semiconductor device model according to claim 1, characterized in that: Based on the spatial relationship between the conductive channel region and the source / drain region, the initial boundary line between the conductive channel region and the source / drain region is extracted. The specific steps are as follows: The boundary between the conductive channel region and the source / drain region is traversed pixel by pixel. Pixels that satisfy the condition of belonging to the conductive channel region and having a source / drain region pixel in their four-connected neighborhood are marked as first boundary points. Pixels that satisfy the condition of belonging to the source / drain region and having a conductive channel region pixel in their four-connected neighborhood are marked as second boundary points. Pixels that simultaneously satisfy the condition of belonging to the conductive channel region and having at least one source / drain region pixel in their eight-connected neighborhood are marked as candidate boundary pixels. The first and second boundary points are merged to obtain a set of boundary pixels. An 8-connected neighborhood connection operation is performed on all pixels in this set. Specifically, any unclassified pixel is selected from the set of boundary pixels. If there are candidate boundary pixels in the adjacent positions of the pixel in the four diagonal directions, these candidate boundary pixels are grouped with the unclassified pixels into the same boundary pixel cluster. The classification process of boundary pixels is repeated. All candidate boundary pixels are grouped into one boundary pixel cluster, and each boundary pixel cluster corresponds to an initial boundary line.

4. The modeling method for a semiconductor device model according to claim 1, characterized in that: The grayscale features of the image are combined to perform grayscale correction processing on all initial boundary points to obtain corrected boundary points. The specific steps are as follows: For each initial boundary pixel, a local image window is extracted from the electron microscope cross-sectional image with the initial boundary pixel as the center. Within the local image window, the first-order gray-level gradient values ​​along the horizontal and vertical directions at the location of the initial boundary pixel are calculated to generate the gradient magnitude of the initial boundary pixel. Starting from the initial boundary pixel, search line segments are generated by extending along the positive and negative normal directions of the boundary line of the initial boundary pixel. The gradient magnitude of each pixel on the search line segment is calculated, and the position of the pixel with the largest gradient magnitude is selected as the correction boundary point of the initial boundary point.

5. The modeling method for a semiconductor device model according to claim 1, characterized in that: The Euclidean distance between adjacent correction boundary points is calculated to screen effective correction boundary points, and the channel-source-drain profile is fitted. The specific steps are as follows: All correction boundary points are sorted according to the sampling order of their corresponding initial boundary points to generate an ordered point sequence distributed along the channel length. For each correction boundary point in the ordered point sequence, the first Euclidean distance with the previous adjacent correction boundary point, the second Euclidean distance with the next adjacent correction boundary point, and the third Euclidean distance between the previous adjacent correction boundary point and the next adjacent correction boundary point are calculated. The arithmetic mean of the above three Euclidean distances is calculated. If the first Euclidean distance or the second Euclidean distance is greater than three times the arithmetic mean, then the correction boundary point is determined to be an outlier. After removing outliers, control points are selected at equal intervals from the remaining effective correction boundary points to construct cubic B-spline curves. The coordinates of the control points are solved by the least squares method to minimize the sum of squares of the deviations between the cubic B-spline curves and the control points, thereby obtaining the channel-source-drain profile.

6. The modeling method for a semiconductor device model according to claim 1, characterized in that: The channel-source-drain profile is offset equidistantly in the inward and outward normal directions according to the offset amount, generating two parallel offset profiles. The specific steps are as follows: Obtain the normal vector of each pixel on the channel-source-drain contour line. The normal vector points to the normal direction of the channel-source-drain contour line. The two sides of the channel-source-drain contour line are the outer side and the inner side, respectively. The outer side points to the side where the source-drain region and the gate dielectric layer region are located, and the inner side points to the side where the conductive channel region is located. For each contour point on the channel-source-drain contour line, starting from the coordinates of the contour point, move outward and inward along the normal direction of the contour point according to the offset amount to generate an outer offset point and an inner offset point respectively. Connect the outer offset points corresponding to all contour points in the order of arrangement to generate an outer offset contour line. Connect the inner offset points corresponding to all contour points in the order of arrangement to generate an inner offset contour line.

7. The modeling method for a semiconductor device model according to claim 6, characterized in that: For each contour point on the channel-source-drain contour line, take the contour point as the center and cut a gray-scale sampling line segment along its normal direction that runs through the conductive channel region, the source-drain region and the gate dielectric layer region, and the two endpoints of the gray-scale sampling line segment are located inside the conductive channel region and inside the gate dielectric layer region, respectively. Calculate the gray-level gradient magnitude of each pixel on the gray-level sampling line segment, detect the local maxima of the gray-level gradient magnitude of all pixels on the gray-level sampling line segment, and select the two maxima with the largest gray-level gradient magnitudes, which are denoted as the first interface response point and the second interface response point, respectively. Calculate the normal distance between the two response points, which is denoted as the width of the interface transition area. Take k points before and after the contour point to form a local point set. Perform least squares fitting on the local point set to obtain the local parameter curve. Calculate the first and second derivatives of the parameters corresponding to the contour points. Based on the first and second derivatives, calculate the radius of curvature using the plane curve curvature formula. The offset of the contour points is calculated based on the width of the interface transition area, the radius of curvature of the contour points, and the standard deviation of the gray values ​​of all pixels on the gray sampling line segment. The calculation logic is as follows: take 1 / 2 of the width of the interface transition area as the basic adjustment component, obtain the curvature adjustment factor based on the radius of curvature, generate the gray adjustment factor based on the standard deviation of the gray values, and multiply the basic adjustment component, the curvature adjustment factor and the gray adjustment factor in sequence to obtain the offset.

8. The modeling method for a semiconductor device model according to claim 1, characterized in that: Perform Boolean intersection operations between the node coordinates and each material region to obtain the area proportion of all material regions within the preset neighborhood window of the grid nodes. The specific steps are as follows: For each grid node, a square neighborhood window with a side length of L pixels is set with the grid node position as the center point. Within the square neighborhood window, Boolean intersection is performed pixel by pixel, and the number of pixels belonging to each region is counted. The number of pixels belonging to the conductive channel region is recorded as the first pixel count, the number of pixels belonging to the source / drain region is recorded as the second pixel count, and the number of pixels belonging to the gate dielectric layer region is recorded as the third pixel count. Divide the count of the first pixel, the count of the second pixel, and the count of the third pixel by L respectively. 2 The area ratios of the conductive channel region, source / drain region, and gate dielectric layer region were obtained respectively.

9. The modeling method for a semiconductor device model according to claim 8, characterized in that: The material property parameters of each mesh node are weighted and averaged based on the area proportion of each material region. The material property parameters of each mesh node are then matched with the standard material property parameters of each material region to determine the material region to which each mesh node belongs. This completes the construction of the semiconductor device simulation model. The specific steps are as follows: The material properties of the grid nodes include carrier mobility and relative permittivity; The standard carrier mobility and standard relative permittivity of the conductive channel region, source / drain region, and gate dielectric layer region are obtained in advance. For each grid node, the standard carrier mobility and standard relative permittivity of the conductive channel region, source / drain region, and gate dielectric layer region are weighted and combined according to the area ratio of the conductive channel region, source / drain region, and gate dielectric layer region of its neighboring window to obtain the effective carrier mobility and effective relative permittivity. The effective carrier mobility and effective relative permittivity are then assigned to the corresponding grid node. For each grid node, the effective carrier mobility is subtracted from the standard carrier mobility of each material region, and the effective relative permittivity is subtracted from the standard relative permittivity of each material region. The results of the subtraction are normalized, and then the normalized results for the same material region are added together to obtain the material property deviation of the grid node relative to the material region. The grid node is then assigned to the material region with the smallest deviation of its material properties.

10. A modeling system for semiconductor device models, characterized in that: The system is used to implement the modeling method for semiconductor device models according to any one of claims 1-9, specifically including: The image acquisition and processing module is used to acquire cross-sectional images of semiconductor devices using electron microscopes, and to perform gray-level statistics on the images. Based on the peak values ​​of the gray-level distribution, the images are divided into conductive channel regions, source / drain regions, and gate dielectric layer regions. The boundary calculation module is used to extract the initial boundary line between the conductive channel region and the source / drain region based on the spatial relationship between the conductive channel region and the source / drain region. It then samples each initial boundary line at equal intervals along the length direction perpendicular to the extension of the channel to obtain several initial boundary points. Finally, it performs grayscale correction processing on all initial boundary points in combination with image grayscale features to obtain corrected boundary points. The contour fitting module is used to filter effective correction boundary points by calculating the Euclidean distance between adjacent correction boundary points, and fit the channel-source-drain contour line to determine the upper and lower interfaces of the gate dielectric layer region. Interface response points are extracted from the upper and lower interfaces respectively, and the normal distance between them is calculated to obtain the width of the interface transition region. The curvature adjustment factor and gray level adjustment factor are determined according to the local radius of curvature of each contour point on the contour line and the gray level standard deviation of the corresponding region, and according to the preset mapping relationship. The region coupling module is used to determine the offset of each contour point based on the width of the interface transition zone, the curvature adjustment factor and the grayscale adjustment factor. The channel-source-drain contour line is offset equidistantly in the inward and outward normal directions according to the offset, generating two parallel offset contour lines. The area between the two offset contour lines is selected as the coupling transition area of ​​each material region, and the simulation mesh nodes are generated in the coupling transition area. The model building module is used to perform Boolean intersection operations on the node coordinates and material regions for each mesh node in the coupling transition region, so as to obtain the area ratio of all material regions within the preset neighborhood window of the mesh node. The material property parameters of each mesh node are weighted and averaged based on the area ratio of each material region. The material property parameters of each mesh node are matched with the standard material property parameters of each material region to determine the material region to which each mesh node belongs, thus completing the construction of the semiconductor device simulation model.

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