Grid reconstruction method and device and electronic equipment

Abstract

The invention relates to the technical field of grid reconstruction, and provides a grid reconstruction method and device and electronic equipment, and the method comprises the steps: carrying out the refining of a new grid through employing a quartering method according to a node coordinate in a gradient large region and a material boundary node coordinate in the pre-constructed new grid; extracting an old boundary of the old grid to be reconstructed, and screening reconstruction target nodes located in the old boundary in the refined new grid; and on the basis of the old boundary and the reconstruction target node, performing grid division and physical quantity data recovery operation on the refined new grid, and performing conformal stitching on the divided new grid and the old grid. Through cooperation of the steps, on the premise that the core structure and the physical characteristics of the device are not changed, the accuracy of the simulation result can be remarkably improved, the reasonability of the grid structure can be optimized, redundant calculation is reduced, the simulation solving speed is increased, the stability of the simulation process is ensured, and the method is suitable for large-scale popularization and application. And solving interruption or result deviation caused by a grid problem is avoided.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of mesh reconstruction, in particular to a mesh reconstruction method, device and electronic equipment. BACKGROUND

[0002] In the field of semiconductor industry, process simulation software has become a key supporting tool for shortening the process design and development cycle of semiconductor devices and reducing production costs. In the process of process simulation, the calculation of core physical processes such as drift-diffusion equation solving and doping concentration change is based on mesh nodes, and the rationality of the mesh structure is directly related to the accuracy of the simulation results, the speed and stability of the solving process, and is a basic prerequisite for ensuring efficient process simulation.

[0003] In current semiconductor process simulation, the mesh structure is usually generated directly through process simulation instructions to adapt to the initial structure of the device and the process requirements. However, in actual process steps such as oxidation, etching, and deposition, the device structure will change dynamically, and these process operations will directly affect the initial mesh, resulting in the formation of an undesirable mesh shape in local areas. At the same time, the existing mesh construction method is prone to density mutations between sparse and dense areas when dealing with differences in physical quantities in different areas, which can adversely affect the accuracy of the simulation solution. In addition, during the process of adjusting and optimizing the mesh, the stability of the overall doping distribution and physical distribution of the device will also be reduced due to changes in the mesh structure. The above problems all restrict the effectiveness of semiconductor process simulation. SUMMARY

[0004] The present application aims to solve at least one of the above technical problems.

[0005] To solve the above problems, the present application provides a mesh reconstruction method, device and electronic equipment.

[0006] In a first aspect, the present application provides a mesh reconstruction method, comprising: refining the new mesh according to the node coordinates and material boundary node coordinates in the large gradient area of the pre-constructed new mesh using the quartering method; extracting the old boundary of the old mesh to be reconstructed, and screening out the reconstruction target nodes in the refined new mesh located in the old boundary; performing mesh division and physical quantity data recovery operations on the refined new mesh based on the old boundary and the reconstruction target nodes, and performing conformal suture on the divided new mesh and the old mesh.

[0007] Optionally, before the step of refining the new mesh according to the node coordinates and material boundary node coordinates in the large gradient area of the pre-constructed new mesh, the method further comprises: Traverse all the old edges of the old grid and extract the physical quantity values ​​corresponding to the two endpoints, point 1 and point 2, of each old edge; The arcsinh function is used to convert the physical quantity values ​​corresponding to point 1 and point 2 to obtain physical quantity 1 and physical quantity 2; If the difference between physical quantity 1 and physical quantity 2 is greater than a preset physical quantity, then the coordinates of point 1 and point 2 are recorded in the gradient-sensitive region node coordinate set to obtain the node coordinates within the gradient region.

[0008] Optionally, before the step of determining the node coordinates and material boundary node coordinates within the gradient region in the pre-constructed new mesh, the following steps are included: Iterate through the material information of all mesh cells in the old mesh and determine whether the boundary surface of each mesh cell is a shared surface; If the boundary surface belongs to mesh cells of two different materials at the same time, it is determined to be a material-material boundary; If the boundary surface belongs to only one material grid cell, it is determined to be a material-vacuum boundary; Extract the coordinates of all nodes on the boundary to form a set of material boundary node coordinates, and obtain the material boundary node coordinates.

[0009] Optionally, the step of refining the new mesh using a quartering method based on the node coordinates within the gradient region and the material boundary node coordinates in the pre-constructed new mesh includes: Determine whether the cells in the new mesh contain coordinates from the set of node coordinates of the gradient large region or the set of node coordinates of the material boundary; If it is included, a refinement operation is performed, dividing the unit into a preset number of sub-units along the central axis; Repeat the operation of determining whether the cells in the new mesh contain the coordinates of the gradient large region node coordinate set or the coordinates of the material boundary node coordinate set until the spacing of the sub-cells is less than or equal to the preset minimum mesh spacing, or the sub-cells do not contain the coordinates of the gradient large region node coordinate set or the coordinates of the material boundary node coordinate set and the spacing is less than or equal to the preset maximum mesh spacing. Traverse the spacing difference between adjacent sub-units after refinement. If the spacing difference is greater than or equal to a preset multiple, then perform semi-refinement segmentation on the sub-unit with large spacing according to the preset semi-refinement side length.

[0010] Optionally, the step of filtering out the reconstruction target nodes located within the old boundary in the refined new mesh includes: The ray method is used to determine all the grid nodes of the refined new grid. A ray with a preset horizontal direction is emitted from the grid node, and the number of intersections between the ray and the old boundary is counted. If the number of intersection points is odd, then the grid node is determined to be located within the old boundary, and the coordinates of the grid node are recorded in the set of reconstruction target nodes, where the coordinates in the set of reconstruction target nodes are the reconstruction target nodes.

[0011] Optionally, the conformal stitching of the newly divided mesh with the old mesh includes: Extract the new boundary nodes of the newly divided mesh and the old boundary nodes of the old mesh respectively; The kd-tree algorithm is used to quickly find matching node pairs between the new boundary node and the old boundary node whose distance is less than or equal to a preset distance, and the coordinates of the new boundary node in the matching node pair are corrected to the coordinates of the corresponding node of the old boundary node; The boundary cells of the revised new mesh are reconstructed so that the boundary cells of the new mesh and the boundary cells of the old mesh form a shared boundary. Update the topology table of the new grid, including node-cell associations and cell-cell adjacency relationships.

[0012] Optionally, before refining the new mesh using the quartering method based on the node coordinates within the gradient region and the material boundary node coordinates in the pre-constructed new mesh, the method further includes: Traverse all grid nodes of the new grid and calculate the shortest distance between each grid node and the old boundary; If the shortest distance is less than the preset minimum grid spacing, then delete the grid node and the grid cell with the grid node as the vertex.

[0013] Optionally, before the step of determining the node coordinates and material boundary node coordinates within the gradient region in the pre-constructed new mesh, the following steps are included: Traverse all old grid nodes in the region to be rebuilt, and record the coordinates of the minimum and maximum nodes; The new mesh is established with the minimum node coordinates and the maximum node coordinates as diagonal points respectively, and the material of the new mesh is configured to be a universal material.

[0014] In a second aspect, the present invention provides a mesh reconstruction apparatus, comprising: The refinement module is used to refine the new mesh using a quartering method based on the node coordinates of the large gradient region and the material boundary node coordinates in the pre-constructed new mesh. The filtering module is used to extract the old boundary of the old mesh to be reconstructed and filter out the reconstruction target nodes located within the old boundary in the refined new mesh; The stitching module is used to perform mesh generation and physical quantity data recovery operations on the refined new mesh based on the old boundary and the reconstruction target node, and to conformally stitch the new mesh with the old mesh.

[0015] Thirdly, the present invention provides an electronic device, including a memory and a processor; The memory is used to store computer programs; The processor is configured to implement the mesh reconstruction method as described in the first aspect when executing the computer program.

[0016] The beneficial effects of mesh reconstruction in this invention are as follows: By using the node coordinates in regions with large gradients and the coordinates of material boundary nodes, key regions requiring optimization, such as areas with drastic changes in physical quantities and material interface regions, are accurately located. A four-part method is used to refine the new mesh in a targeted manner, forming a dense mesh in key regions to ensure simulation accuracy, while maintaining a relatively sparse mesh in non-critical regions. Simultaneously, a smooth density transition zone is naturally formed, completely avoiding the adverse effects of sudden changes in mesh density on simulation accuracy. This achieves intelligent and accurate differentiation between dense and sparse mesh regions, fundamentally improving the local suboptimal mesh morphology and laying the foundation for improved simulation accuracy. By extracting the old boundaries of the old mesh to be reconstructed, the range constraints of mesh reconstruction are clarified, ensuring that the new mesh always conforms to the original structural boundaries of the device. Screening the reconstruction target nodes within the old boundaries further limits the effective reconstruction area, preventing the new mesh from exceeding the core structural range of the device or deviating from the actual shape. This provides a precise geometric benchmark for subsequent mesh generation and data recovery, ensuring the consistency between mesh reconstruction and device structure. The mesh generation operation is based on the old boundary and the reconstructed target node, ensuring the structural rationality of the new mesh. The physical quantity data recovery operation reuses the core physical quantity information of the old mesh, effectively avoiding the distortion of the overall doping distribution and physical quantity distribution of the device during the mesh adjustment process, and solving the problem of reduced stability of physical quantity distribution in existing mesh optimization. The conformal stitching realizes the seamless connection between the new mesh and the old mesh after generation, eliminating problems such as mesh gaps and overlaps, ensuring the overall continuity of the mesh, and further improving the stability and accuracy of the simulation solution.

[0017] This invention, through the synergistic cooperation of the above steps, comprehensively solves the problems of local mesh imperfections, abrupt density changes in sparse and dense regions, and insufficient stability of physical quantity distribution in existing semiconductor process simulations, without altering the core structure and physical characteristics of the device. In practical applications, this invention not only significantly improves the accuracy of simulation results but also optimizes the rationality of the mesh structure, reduces redundant calculations, and increases the simulation solution speed. Simultaneously, the combination of conformal stitching and physical quantity data recovery ensures the stability of the simulation process and avoids solution interruptions or result deviations caused by mesh issues. Attached Figure Description

[0018] Figure 1 This is a schematic flowchart of the mesh reconstruction method according to an embodiment of the present invention; Figure 2 This is a schematic diagram comparing the mesh reconstruction method of this invention with the mesh reconstruction results of existing technologies; Figure 3 This is a schematic diagram of the structure of the grid reconstruction device according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the structure of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0019] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Although some embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of the present invention. It should be understood that the accompanying drawings and embodiments of the present invention are for illustrative purposes only and are not intended to limit the scope of protection of the present invention.

[0020] It should be understood that the various steps described in the method embodiments of the present invention may be performed in different orders and / or in parallel. Furthermore, the method embodiments may include additional steps and / or omit the steps shown. The scope of the present invention is not limited in this respect.

[0021] The term "comprising" and its variations as used herein are open-ended, meaning "including but not limited to"; the term "based on" means "at least partially based on"; the term "one embodiment" means "at least one embodiment"; the term "another embodiment" means "at least one additional embodiment"; the term "some embodiments" means "at least some embodiments"; and the term "optionally" means "optional embodiments". Definitions of other terms will be given in the following description. It should be noted that the concepts of "first," "second," etc., mentioned in this invention are used only to distinguish different devices, modules, or units, and are not intended to limit the order of functions performed by these devices, modules, or units or their interdependencies.

[0022] It should be noted that the terms "a" and "a plurality of" used in this invention are illustrative rather than restrictive. Those skilled in the art should understand that, unless otherwise expressly indicated in the context, they should be understood as "one or more".

[0023] The names of the messages or information exchanged between the multiple devices in the embodiments of the present invention are for illustrative purposes only and are not intended to limit the scope of these messages or information.

[0024] like Figure 1 As shown, an embodiment of the present invention provides a mesh reconstruction method, comprising: Step S1: Based on the node coordinates of the large gradient region and the material boundary node coordinates in the pre-constructed new mesh, refine the new mesh using the quartering method.

[0025] Before performing step S1, an initial new grid, such as a rectangular grid, needs to be constructed to cover the area to be reconstructed.

[0026] Optionally, before the step of determining the node coordinates and material boundary node coordinates within the gradient region in the pre-constructed new mesh, the following steps are included: Traverse all old grid nodes in the region to be rebuilt, and record the coordinates of the minimum and maximum nodes; The new mesh is established with the minimum node coordinates and the maximum node coordinates as diagonal points respectively, and the material of the new mesh is configured to be a universal material.

[0027] Specifically, a specific region (i.e., the region to be reconstructed) that needs mesh optimization in semiconductor process simulation is determined. This region is defined by the range of materials to be optimized specified by the user. The old mesh nodes within the region to be reconstructed are mesh vertices that naturally formed in previous process simulations, carrying physical quantity data such as doping concentration, and do not require additional construction. A region-by-region traversal method is adopted, traversing all old mesh nodes within the region block by block in xyz coordinate order, avoiding the inefficiency waste caused by traditional global traversal. During the traversal, the x, y, and z coordinate values ​​of each node are compared in real time, and the minimum coordinate values ​​(i.e., minimum node coordinates, which are the set of minimum values ​​in the x, y, and z directions) and maximum coordinate values ​​(i.e., maximum node coordinates, which are the set of maximum values ​​in the x, y, and z directions) in each direction are dynamically selected, ultimately forming complete coordinate extreme value data, minimum node coordinates (minx, miny, minz) and maximum node coordinates (maxx, maxy, maxz). Precisely defining the spatial extent of the region to be reconstructed provides a clear geometric boundary reference for the subsequent construction of a new mesh, ensuring that the new mesh completely covers the region to be optimized, without omitting key areas or exceeding the necessary range. This lays the foundation for subsequent mesh refinement and optimization, while reducing the computational load in invalid regions. A rectangular (in 2D scenes) or cuboid (in 3D scenes) spatial framework enclosing the region to be reconstructed is constructed using the smallest node coordinates as the lower left diagonal and the largest node coordinates as the upper right diagonal. Based on the user-specified or software-calculated mesh spacing (e.g., a maximum spacing of 5nm and a minimum spacing of 1nm), uniformly arranged mesh cells are generated within this framework to form a new mesh. This new mesh serves as a temporary mesh carrier for subsequent refinement and optimization and does not directly participate in the initial simulation calculations. In the property configuration of the new mesh, the material type is set to a software-preset universal material. Universal materials are virtual materials without actual physical properties (such as dielectric constant or doping characteristics), serving only as a mesh carrier. Configuration is completed by specifying a unique material ID, avoiding property conflicts with physical materials such as silicon and silicon oxide in the old mesh. A temporary mesh framework covering the area to be reconstructed is constructed to provide a basic carrier for subsequent refinement operations based on gradient large areas and material boundaries. The configuration of universal materials avoids property conflicts between the new mesh and the existing materials in the old mesh, while facilitating the subsequent screening and trimming of effective areas, ensuring the consistency and accuracy of material properties during the mesh reconstruction process.

[0028] Specifically, a semiconductor device comprising a silicon (Si) substrate and a silicon oxide (SiO2) dielectric layer is used as the simulation object. An old mesh is set up accordingly. After process simulation (including oxidation, deposition, etc.), the old mesh exhibits uneven density and local node distortion at the Si-SiO2 interface and in the highly doped region of the Si substrate, resulting in slow simulation speed and insufficient accuracy. This mesh reconstruction method is needed for optimization. After constructing a uniform rectangular new mesh covering the Si substrate and SiO2 dielectric layer, step S1 is executed. The region with a large gradient refers to a region where the spatial rate of change of physical quantities is significantly higher than the surrounding area. Here, doping concentration is used as the determining physical quantity, determined by calculating the difference in doping concentration between adjacent nodes in the new mesh. The corresponding node coordinates are recorded, corresponding to the region where the boron (B) doping concentration abruptly changes in the Si substrate. The material boundary node coordinates are the node position information at the interface between different materials. By traversing the new mesh cells, the material properties of adjacent cells (such as Si and SiO2) are detected. The nodes at the points of abrupt property change are the material boundary nodes, and their coordinates are recorded, such as the boundary node between the upper surface of the Si substrate and the lower surface of the SiO2 substrate. Subsequently, a four-part method, an adaptive mesh refinement algorithm derived from the spatial divide-and-conquer concept, is adopted. Compared with the existing binary method, the segmentation efficiency is doubled. It is applicable to 2D / 3D meshes. For the refinement of the new mesh, each cell of the new mesh is taken as the initial cell to be refined and placed in a queue for sequential processing. For nodes that meet the requirements, sub-cells are recursively segmented, ultimately forming a smooth transition mesh with dense mesh (1nm side length) at the high-doped region and material boundary, and sparse mesh (5nm side length) far away from the critical region.

[0029] Optionally, before the step of determining the node coordinates and material boundary node coordinates within the gradient region in the pre-constructed new mesh, the following steps are included: Traverse all the old edges of the old mesh and extract the physical quantity values ​​corresponding to the two endpoints, point 1 and point 2, of each old edge. Specifically, an old edge refers to a line segment in the old mesh to be reconstructed that connects two adjacent nodes. It is a fundamental component of the old mesh topology, naturally formed by the node connections of the old mesh. Each node is connected to surrounding nodes through old edges, constituting a complete mesh structure. During implementation, a mesh traversal algorithm scans each old edge of the old mesh one by one. For each old edge, its two endpoints, point 1 and point 2, are extracted, along with their corresponding doping concentration values. For example, an old edge connects node 1 (coordinates x=20nm, y=15nm) and node 2 (coordinates x=25nm, y=15nm). The physical quantity database of the old mesh shows that the doping concentration of node A is 1.2 × 10⁻⁶. 17 atoms / cm 3 The doping concentration of node B is 3.5 × 10⁻⁶. 19 atoms / cm 3This step obtains the raw physical quantity data of adjacent nodes in the old mesh, providing a basic data source for subsequent gradient determination.

[0030] The arcsinh function is used to convert the physical quantity values ​​corresponding to point 1 and point 2 to obtain physical quantity 1 and physical quantity 2.

[0031] Specifically, the arcsinh function (inverse hyperbolic sine function) is a commonly used function in mathematics for data normalization, and its expression is arcsinh(x) = ln(x + √(x)). 2 +1)), derived mathematically, its core feature is its ability to map data of vastly different orders of magnitude to a similar numerical range. In implementation, the extracted doping concentration values ​​at the two endpoints, point 1 and point 2, are substituted into this function for conversion. For example, the doping concentration at node 1 is 1.2 × 10⁻⁶. 17 After substituting the values, we calculate that physical quantity 1 ≈ 39.3; the doping concentration of node 2 is 3.5 × 10⁻⁶. 19 After substituting, the calculated physical quantity 2 ≈ 45.1. This step solves the problem of huge differences in the order of magnitude between different physical quantities (or different regions of the same physical quantity), avoids gradient judgment bias caused by direct comparison of the original data, and ensures the fairness and accuracy of subsequent gradient identification.

[0032] If the difference between physical quantity 1 and physical quantity 2 is greater than a preset physical quantity, then the coordinates of point 1 and point 2 are recorded in the gradient-sensitive region node coordinate set to obtain the node coordinates within the gradient region.

[0033] Specifically, the preset physical quantity is a gradient judgment threshold set according to the accuracy requirements of semiconductor process simulation. Here, it is set to 1, obtained through extensive simulation experiments to ensure accurate differentiation between the boundaries of gradual and drastic changes in physical quantities. The gradient-sensitive region node coordinate set is a dataset used to store the coordinates of nodes that meet the large gradient condition. It is organized into an array of node coordinates that meet the judgment condition. During implementation, the absolute value of the difference between the transformed physical quantity 1 and physical quantity 2 is first calculated, i.e., |45.1-39.3|=5.8. Then, this absolute value is compared with the preset physical quantity 1. Since 5.8>1, the old edge region where node A and node B are located is determined to be a large gradient region. The coordinates of the two nodes, point 1 (20nm, 15nm) and point 1 (25nm, 15nm), are recorded one by one into the gradient-sensitive region node coordinate set. This operation is repeated, and after traversing all old edges, a gradient-sensitive region node coordinate set containing multiple node coordinates is finally obtained. Precisely identifying nodes in regions with drastic changes in physical quantities provides a clear target for subsequent mesh refinement based on these coordinates, ensuring that mesh optimization can be applied specifically to key areas.

[0034] Optionally, before the step of determining the node coordinates and material boundary node coordinates within the gradient region in the pre-constructed new mesh, the following steps are included: Iterate through the material information of all grid cells in the old grid and determine whether the boundary surface of each grid cell is a shared surface.

[0035] Specifically, a grid cell is the basic building block of the old grid, formed by connecting multiple nodes. It is the core carrier of material information and physical quantity data, naturally formed by the topological division of the old grid. A boundary surface refers to the surface of a single grid cell, serving as the interface between the grid cell and the external environment or other cells, existing as the grid cell is formed. A shared surface is a boundary surface belonging to two adjacent grid cells simultaneously, obtained by detecting the adjacency relationship of grid cells (if a boundary surface is shared by two cells, it is a shared surface). In implementation, a region-based block traversal algorithm is used, dividing the old grid into multiple blocks according to the XY coordinates, and scanning the grid cells within each block one by one. For each grid cell, its material ID is extracted from the old grid's material property database, such as 1 for Si, 2 for SiO2, and 3 for Si3N4, and all boundary surfaces of that cell are traversed. By querying the grid cell adjacency table, it is determined whether each boundary surface has adjacent grid cells. If adjacent cells exist, the boundary surface is a shared surface; if no adjacent cells exist, and only the current cell possesses the boundary surface, it is a non-shared surface. For example, if an edge of a Si material unit (ID=1) is adjacent to a SiO2 material unit (ID=2), then that edge is a shared surface; while an edge on the outermost layer of the Si substrate has no adjacent units, then it is a non-shared surface. Identifying shared and non-shared surfaces provides a basis for subsequent boundary type determination, ensuring the comprehensiveness of boundary identification.

[0036] If the boundary surface belongs to mesh cells of two different materials, it is determined to be a material-material boundary.

[0037] If the boundary surface belongs to only one material grid cell, it is determined to be a material-vacuum boundary.

[0038] Specifically, a material-material boundary is the contact interface between two different material mesh elements, determined by the difference in material IDs between the elements on both sides of a shared surface. A material-vacuum boundary is the interface where a single material mesh element is exposed to the vacuum or gas environment of the simulation, directly determined by non-shared surfaces; the absence of adjacent elements indicates contact with the vacuum. During implementation, for identified shared surfaces, the material IDs of the adjacent mesh elements on both sides are extracted and compared. If the material IDs on both sides are different, such as one side being 1 (Si) and the other side being 2 (SiO2), or one side being 2 (SiO2) and the other side being 3 (Si3N4), then the shared surface is determined to be a material-material boundary, corresponding to the contact interface between Si and SiO2, or the contact interface between SiO2 and Si3N4. For identified non-shared surfaces, they are directly determined to be material-vacuum boundaries, corresponding to exposed areas such as the lower surface of the Si substrate, the upper surface of the Si3N4 mask layer, etc. Accurately distinguishing different types of material boundaries meets the differentiated processing requirements of subsequent mesh refinement, avoiding mesh optimization errors caused by boundary type confusion.

[0039] Extract the coordinates of all nodes on the boundary to form a set of material boundary node coordinates, and obtain the material boundary node coordinates.

[0040] Specifically, the material boundary node coordinate set is a dataset storing the coordinates of all nodes on the material boundaries. It consists of deduplicated node coordinates from all material-material boundaries and material-vacuum boundaries, stored in an array structure for later retrieval. During implementation, for each determined material-material boundary and material-vacuum boundary, all node coordinates are extracted. For material-material boundaries, the coordinates of the two endpoints are extracted; for complex polygonal material boundaries, all vertex coordinates are extracted. For example, for a polygonal boundary where Si meets SiO2, the coordinates of its five vertices (x1, y1), (x2, y2), ..., (x5, y5) are extracted. All extracted coordinates are stored in a temporary array, and deduplication is performed using coordinate hashing to avoid duplicate recording of the same node belonging to multiple boundaries, ultimately forming a material boundary node coordinate set containing unique node coordinates. This centralized organization of node position information for all material boundaries provides a clear and accurate boundary reference for subsequent mesh refinement based on these coordinates, ensuring that the new mesh closely matches the actual material boundaries of the device.

[0041] Optionally, the step of refining the new mesh using a quartering method based on the node coordinates within the gradient region and the material boundary node coordinates in the pre-constructed new mesh includes: Determine whether the cells in the new mesh contain coordinates from the set of node coordinates of the gradient large region or the set of node coordinates of the material boundary.

[0042] Specifically, all elements in the new mesh are stored in a queue as elements to be refined. For each element, a coordinate matching algorithm is used to determine whether it intersects with the coordinate set of nodes in the gradient region or with the coordinate set of nodes in the material boundary. If an element has coordinates from either set, a refinement operation is performed, dividing the element into multiple equally sized sub-elements along the central axis according to a preset refinement amount. The initial side length of the sub-elements can be 2.5 nm.

[0043] If it is included, a refinement operation is performed, dividing the unit into a preset number of sub-units along the central axis.

[0044] Repeat the operation of determining whether the cells in the new mesh contain the coordinates of the gradient large region node coordinate set or the coordinates of the material boundary node coordinate set until the spacing of the sub-cells is less than or equal to the preset minimum mesh spacing, or the sub-cells do not contain the coordinates of the gradient large region node coordinate set or the coordinates of the material boundary node coordinate set and the spacing is less than or equal to the preset maximum mesh spacing. Specifically, the preset minimum mesh spacing is the critical spacing to ensure simulation accuracy in key areas, determined by the process node size and sensitivity to changes in physical quantities; for example, 1nm is the default for 7nm processes. The preset maximum mesh spacing is the critical spacing to control the computational load in non-critical areas, automatically allocated by user requirements or software based on device geometry, and can be 5nm. During implementation, the sub-units obtained from the segmentation are used as new units to be judged, and coordinate inclusion checks are repeatedly performed. If the side length of the sub-unit is less than or equal to the preset minimum mesh spacing, refinement stops regardless of whether it contains the target coordinates, ensuring that the mesh in key areas is sufficiently dense. If the sub-unit does not contain regions with large gradients or material boundary coordinate sets, and its side length is less than or equal to the preset maximum mesh spacing, refinement also stops to avoid excessive densification in non-critical areas leading to computational redundancy. This achieves adaptive termination of mesh refinement, balancing simulation accuracy and computational efficiency.

[0045] Traverse the spacing difference between adjacent sub-units after refinement. If the spacing difference is greater than or equal to a preset multiple, then perform semi-refinement segmentation on the sub-unit with large spacing according to the preset semi-refinement side length.

[0046] Specifically, the preset multiplier is a critical value for judging whether the transition between mesh density and sparseness is smooth. It is determined through simulation stability testing and can be 3 times. Semi-refinement refers to a refinement method that divides an element into two sub-elements along a single axis, unlike the four sub-elements in the quartering method. This is determined by the smoothness requirements of the transition zone mesh density. During implementation, all refined sub-elements are traversed, and the difference in side length between adjacent sub-elements is calculated. For example, if a sub-element located at the material boundary has a side length of 1nm, and an adjacent non-critical region sub-elements have a side length of 5nm, the spacing difference is 5 times or greater than the preset multiplier of 3 times. In this case, semi-refinement is performed on the 5nm sub-elements, dividing them into two 2.5nm sub-elements along the central axis. The spacing difference is checked again (1nm vs. 2.5nm, difference 2.5 times < 3 times), and processing stops. This avoids abrupt changes in mesh density, forming a smooth density transition zone and preventing simulation errors caused by abrupt mesh changes.

[0047] Optionally, before refining the new mesh using the quartering method based on the mesh node coordinates within the gradient region and the material boundary mesh node coordinates in the pre-constructed new mesh, the method further includes: Traverse all grid nodes of the new grid and calculate the shortest distance between each grid node and the old boundary.

[0048] Specifically, a point-to-line segment shortest distance algorithm (corresponding to 2D) or a point-to-surface shortest distance algorithm (corresponding to 3D) is adopted to avoid distance calculation errors caused by the boundary being a polyline / curved surface. Taking the point-to-line segment shortest distance algorithm in the 2D perspective as an example, for a grid node P and a boundary line segment AB, the dot product of vectors PA, PB, and AB is calculated to determine whether P is outside the extension line of AB, on the line segment, or inside the line segment. The shortest distance for different scenarios is calculated respectively. If it is inside the line segment, the perpendicular distance is calculated. If it is outside the extension line, the distance from P to A or B is calculated to obtain the shortest distance between each grid node and the old boundary.

[0049] If the shortest distance is less than the preset minimum grid spacing, then delete the grid node and the grid cell with the grid node as the vertex.

[0050] Specifically, the minimum grid spacing is preset to half of the minimum grid spacing. For example, if the minimum spacing is 1 nm, the preset minimum grid spacing is 0.5 nm. If the distance from a grid node to the original grid boundary is less than a threshold, it is considered a redundant point. Redundant points are deleted, along with the grid cells with that node as a vertex. For incomplete cells resulting from deleted grid nodes, such as quadrilateral cells missing a vertex, the cells are reconstructed using interpolation with neighboring grid nodes. For example, the midpoint of two adjacent grid nodes is used to replace the deleted grid node, ensuring the integrity of the grid. After deletion, the continuity of the new grid boundary is checked. If gaps exist, such as gaps formed after deleting grid nodes, supplementary grid nodes are automatically added, which can be generated according to the threshold distance.

[0051] Step S2: Extract the old boundary of the old mesh to be reconstructed, and select the reconstruction target nodes located within the old boundary in the refined new mesh.

[0052] Optionally, the step of filtering out the reconstruction target nodes located within the old boundary in the refined new mesh includes: The ray method is used to determine all the grid nodes of the refined new grid. A ray with a preset horizontal direction is emitted from the grid node, and the number of intersections between the ray and the old boundary is counted. If the number of intersection points is odd, then the grid node is determined to be located within the old boundary, and the coordinates of the grid node are recorded in the set of reconstruction target nodes, where the coordinates in the set of reconstruction target nodes are the reconstruction target nodes.

[0053] Specifically, by analyzing the cell topology of the old mesh, edges belonging only to a single cell and edges shared by different material cells are selected. These edges form a closed old boundary in spatial order. Next, target nodes for reconstruction are selected using a ray casting method to determine the nodes of the refined new mesh. A ray is emitted along the positive X-axis for each new mesh node, and the number of intersections between the ray and the old boundary is counted. If the number of intersections is odd, the node is determined to be inside the old boundary, and its coordinates are recorded as the target node for reconstruction. For example, nodes located inside the Si substrate in the new mesh are all determined to be target nodes for reconstruction, while edge nodes outside the Si substrate are excluded. The effective generation range of the new mesh is precisely defined to ensure that the reconstructed mesh is aligned with the actual device structure and to avoid invalid mesh nodes consuming computational resources.

[0054] Step S3: Based on the old boundary and the reconstruction target node, perform mesh generation and physical quantity data recovery operations on the refined new mesh, and conformally stitch the new mesh with the old mesh.

[0055] Specifically, the old boundary serves as a constraint to ensure the new mesh does not exceed the original device's range. The target node is used as the internal seed point, and an open-source meshing tool such as Triangle is called to perform mesh generation. The minimum interior angle of each cell is configured to be ≥30° to avoid generating distorted bad cells, ultimately resulting in a structurally regular new mesh. Subsequently, physical quantity data recovery is performed using the k-nearest neighbor interpolation algorithm to map key physical quantities from the old mesh to the new mesh nodes. First, a spatial index structure of the old mesh is constructed to quickly find the k nearest neighbors (e.g., 6 old mesh nodes) for each new mesh node. The reciprocal of the distance between nodes is used as the weight, with closer nodes having higher weights. Physical quantities such as boron doping concentration and SiO2 dielectric constant of the new nodes are calculated (e.g., doping concentration of a new node = ∑(doping concentration of adjacent old nodes × weight) ÷ ∑weight) to ensure that the overall doping and physical distribution are basically consistent with the old mesh. Finally, conformal stitching is performed.

[0056] Optionally, the conformal stitching of the newly divided mesh with the old mesh includes: Extract the new boundary nodes of the newly divided mesh and the old boundary nodes of the old mesh respectively.

[0057] Specifically, new boundary nodes are the edge nodes of the newly divided mesh, determined by the cell topology of the new mesh. This involves traversing the new mesh cells and selecting endpoints of edges belonging to only a single cell. Old boundary nodes are the edge nodes of the old mesh regions adjacent to the new mesh. They are also extracted by traversing the topology of the old mesh cells, focusing on the old mesh cells surrounding the new mesh, and selecting edge endpoints. In implementation, a region traversal algorithm is used to scan the boundary regions of both the new and old meshes. For the new mesh, all cells are traversed, and each node is determined to belong to only one cell. If so, it is marked as a new boundary node, ultimately extracting multiple new boundary nodes, such as the boundary node between the highly doped region of the Si substrate and the unoptimized region of the old mesh. For the old mesh, the focus is on the old mesh cells surrounding the new mesh, such as within a 5nm range, and old boundary nodes are extracted using the same logic, resulting in multiple old boundary nodes, such as the SiO2 dielectric layer edge nodes in the old mesh close to the new mesh. Clearly defining the connection objects between the new and old meshes lays the foundation for subsequent node matching.

[0058] The kd-tree algorithm is used to quickly find matching node pairs between the new boundary node and the old boundary node whose distance is less than or equal to a preset distance. The coordinates of the new boundary node in the matching node pair are then corrected to the coordinates of the corresponding node in the old boundary node.

[0059] Specifically, the preset distance is the allowable node deviation threshold, determined by the accuracy requirements of the process simulation, used to determine whether a node is matchable (it can be set to 0.1nm to ensure connection accuracy). During implementation, a kd-tree is first constructed from the coordinate data of the old boundary nodes, recursively building a tree index using x and y coordinates as the partition dimensions. Then, each new boundary node is traversed, and its neighboring nodes in the old boundary nodes are quickly found using the kd-tree, calculating the Euclidean distance between them. If the Euclidean distance is ≤ the preset distance of 0.1nm, it is considered a matched node pair. For example, the Euclidean distance between new boundary node A (x=30.2nm, y=15.1nm) and old boundary node B (x=30.25nm, y=15.12nm) is 0.07nm ≤ 0.1nm, forming a matched node pair. The coordinates of new boundary node A are then corrected to the coordinates of node B (30.25nm, 15.12nm). Multiple pairs of nodes are successfully matched; unmatched new boundary nodes will be processed in subsequent cell reconstruction. Ensure that the boundary nodes of the old and new grids are precisely aligned to avoid gaps or overlaps at the junctions.

[0060] The boundary cells of the revised new mesh are reconstructed so that the boundary cells of the new mesh and the boundary cells of the old mesh form a shared boundary.

[0061] Specifically, a shared boundary is an edge (in a 2D scene) or face (in a 3D scene) shared by both new and old mesh boundary cells. It is naturally formed by the coordinate overlap of matching node pairs and is a core indicator of seamless mesh integration. During implementation, for the new boundary nodes after coordinate correction, the boundary cells of the new mesh are traversed, and the cell connections are reconstructed. For example, a new mesh boundary cell originally composed of nodes A, C, D, and E, after node A is corrected, it overlaps with the old boundary node B. This cell is then reconstructed into a quadrilateral cell composed of nodes B, C, D, and E, ensuring that edge BC of this cell completely overlaps with edge BC of a cell in the old mesh, forming a shared boundary. For unmatched new boundary nodes, transition cells are generated. Using adjacent matching nodes and unmatched boundary nodes of the old mesh as vertices, transition cells are constructed to fill the connection gaps and form shared boundaries. This achieves seamless integration of new and old mesh boundary cells, ensuring mesh topology continuity and avoiding numerical abrupt changes during simulation.

[0062] Update the topology table of the new grid, including node-cell associations and cell-cell adjacency relationships.

[0063] Specifically, the topology table is a data table that records the core association information of the mesh. It includes node-cell associations (which cells each node belongs to) and cell-cell adjacency relationships (the adjacent cells of each cell). It is naturally generated from the cell-node connection relationships of the mesh and serves as the foundational data for numerical solutions in simulation software. During implementation, based on the reconstructed boundary cells of the new mesh and the matched node coordinates, the topology table is updated. First, the node-cell associations are updated, synchronously updating the cells to which the corrected nodes belong. For example, after node A is corrected to B, the association record for A is deleted, and the association between B and the corresponding cell is added. Second, the cell-cell adjacency relationships are updated, adding adjacency records between the new mesh boundary cells and the adjacent cells of the old mesh. For example, the reconstructed new cells BCDE establish an adjacency relationship with the old mesh cell BCFG. Simultaneously, the integrity of the topology is verified to ensure there are no isolated nodes (nodes not associated with any cells) and isolated cells (cells without adjacent cells). This ensures the overall topology structure of the stitched mesh is coherent, providing stable mesh data support for subsequent numerical solutions such as drift and diffusion equations.

[0064] This invention, through the node coordinates within regions of high gradient and the coordinates of material boundary nodes, accurately identifies key areas requiring optimization, such as regions with drastic changes in physical quantities and material interface regions. A four-part method is used to refine the new mesh, creating a dense mesh in key areas to ensure simulation accuracy, while maintaining a relatively sparse mesh in non-critical areas. This naturally forms a smooth density transition zone, completely avoiding the adverse effects of sudden changes in mesh density on simulation accuracy. This achieves intelligent and accurate differentiation between dense and sparse mesh regions, fundamentally improving localized suboptimal mesh morphology and laying the foundation for enhanced simulation accuracy. By extracting the old boundaries of the old mesh to be reconstructed, the scope constraints of mesh reconstruction are clarified, ensuring that the new mesh always conforms to the original structural boundaries of the device. Screening the target nodes within the old boundaries further limits the effective reconstruction area, preventing the new mesh from exceeding the core structural range of the device or deviating from the actual shape. This provides a precise geometric benchmark for subsequent mesh generation and data recovery, ensuring consistency between mesh reconstruction and the device structure. The mesh generation operation is based on the old boundary and the reconstructed target node, ensuring the structural rationality of the new mesh. The physical quantity data recovery operation reuses the core physical quantity information of the old mesh, effectively avoiding the distortion of the overall doping distribution and physical quantity distribution of the device during the mesh adjustment process, and solving the problem of reduced stability of physical quantity distribution in existing mesh optimization. The conformal stitching realizes the seamless connection between the new mesh and the old mesh after generation, eliminating problems such as mesh gaps and overlaps, ensuring the overall continuity of the mesh, and further improving the stability and accuracy of the simulation solution.

[0065] Through the synergistic cooperation of the above steps, this invention comprehensively solves the problems of suboptimal local meshes, abrupt density changes in sparse and dense regions, and insufficient stability of physical quantity distribution in existing semiconductor process simulations, without altering the core structure and physical characteristics of the device. In practical applications, this invention not only significantly improves the accuracy of simulation results but also optimizes the rationality of the mesh structure, reduces redundant calculations, and increases the simulation solution speed. Simultaneously, the combination of conformal stitching and physical quantity data recovery ensures the stability of the simulation process and avoids solution interruptions or result deviations caused by mesh issues.

[0066] To verify the effectiveness of this invention, a device with eighty process steps will be used for comparison. Reconstruction method A reconstructs the entire process based on the original mesh, while reconstruction method B uses the mesh reconstruction method of this invention. Finally, the stability of the simulation process, simulation time, and the obtained process simulation results will be compared. Figure 2 As shown, the morphology and doping distribution of the two process simulation devices remain basically unchanged. It can be seen that the process simulation using mesh adaptive optimization reconstruction is more stable during the simulation process. Compared with using the original mesh throughout, inserting the simulation command of mesh adaptive optimization reconstruction at appropriate places can reduce the simulation time by more than 40%.

[0067] like Figure 3 As shown, an embodiment of the present invention provides a mesh reconstruction device 300, comprising: The refinement module 310 is used to refine the new mesh using a quartering method based on the node coordinates of the gradient large region and the material boundary node coordinates in the pre-constructed new mesh. The filtering module 320 is used to extract the old boundary of the old mesh to be reconstructed and filter out the reconstruction target nodes located within the old boundary in the refined new mesh; The stitching module 330 is used to perform mesh generation and physical quantity data recovery operations on the refined new mesh based on the old boundary and the reconstruction target node, and to conformally stitch the new mesh with the old mesh.

[0068] like Figure 4 As shown, an electronic device 400 provided in this embodiment of the invention includes a memory 410 and a processor 420; the memory 410 is used to store a computer program; the processor 420 is used to implement the mesh reconstruction method as described above when the computer program is executed.

[0069] Alternatively, an electronic device 400 includes a memory 410 and a processor 420 coupled to the memory 410; the memory 410 is configured to store a computer program; and the processor 420 is configured to perform the following operations when the computer program is executed: Based on the node coordinates of the gradient large region and the material boundary node coordinates in the pre-constructed new mesh, the new mesh is refined using the quartering method; Extract the old boundary of the old mesh to be reconstructed, and filter out the reconstruction target nodes located within the old boundary in the refined new mesh; Based on the old boundary and the reconstruction target node, perform mesh generation and physical quantity data recovery operations on the refined new mesh, and conformally stitch the new mesh with the old mesh.

[0070] This invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the mesh reconstruction method described above.

[0071] Alternatively, a non-volatile computer-readable storage medium storing a computer program that, when executed by a processor, causes the processor to perform the following operations: Based on the node coordinates of the gradient large region and the material boundary node coordinates in the pre-constructed new mesh, the new mesh is refined using the quartering method; Extract the old boundary of the old mesh to be reconstructed, and filter out the reconstruction target nodes located within the old boundary in the refined new mesh; Based on the old boundary and the reconstruction target node, mesh generation and physical quantity data recovery operations are performed on the refined new mesh, and the new mesh is conformally stitched with the old mesh. An electronic device 400, which can serve as a server or client of the present invention, will now be described as an example of a hardware device applicable to various aspects of the present invention. Electronic device 400 is intended to represent various forms of digital electronic computer devices, such as laptop computers, desktop computers, workbenches, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. Electronic device 400 can also represent various forms of mobile devices, such as personal digital processors, cellular phones, smartphones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely illustrative and are not intended to limit the implementation of the invention described and / or claimed herein.

[0072] Electronic device 400 includes a computing unit that can perform various appropriate actions and processes based on a computer program stored in read-only memory (ROM) or a computer program loaded from a storage unit into random access memory (RAM). The RAM may also store various programs and data required for device operation. The computing unit, ROM, and RAM are interconnected via a bus. Input / output (I / O) interfaces are also connected to the bus.

[0073] While the present invention has been disclosed above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, and all such changes and modifications will fall within the scope of protection of the present invention.

Claims

1. A mesh reconstruction method, characterized in that, include: Based on the node coordinates of the gradient large region and the material boundary node coordinates in the pre-constructed new mesh, the new mesh is refined using the quartering method; Extract the old boundary of the old mesh to be reconstructed, and filter out the reconstruction target nodes located within the old boundary in the refined new mesh; Based on the old boundary and the reconstruction target node, perform mesh generation and physical quantity data recovery operations on the refined new mesh, and conformally stitch the new mesh with the old mesh.

2. The mesh reconstruction method according to claim 1, characterized in that, Before the node coordinates and material boundary node coordinates within the gradient region in the pre-constructed new mesh, the following is included: Traverse all the old edges of the old grid and extract the physical quantity values ​​corresponding to the two endpoints, point 1 and point 2, of each old edge; The arcsinh function is used to convert the physical quantity values ​​corresponding to point 1 and point 2 to obtain physical quantity 1 and physical quantity 2; If the difference between physical quantity 1 and physical quantity 2 is greater than a preset physical quantity, then the coordinates of point 1 and point 2 are recorded in the gradient-sensitive region node coordinate set to obtain the node coordinates within the gradient region.

3. The mesh reconstruction method according to claim 2, characterized in that, Before the node coordinates and material boundary node coordinates within the gradient region in the pre-constructed new mesh, the following is included: Iterate through the material information of all mesh cells in the old mesh and determine whether the boundary surface of each mesh cell is a shared surface; If the boundary surface belongs to mesh cells of two different materials at the same time, it is determined to be a material-material boundary; If the boundary surface belongs to only one material grid cell, it is determined to be a material-vacuum boundary; Extract the coordinates of all nodes on the boundary to form a set of material boundary node coordinates, and obtain the material boundary node coordinates.

4. The mesh reconstruction method according to claim 3, characterized in that, The refinement of the new mesh using a quartering method, based on the node coordinates within the gradient region and the material boundary node coordinates in the pre-constructed new mesh, includes: Determine whether the cells in the new mesh contain coordinates from the set of node coordinates of the gradient large region or the set of node coordinates of the material boundary; If included, a refinement operation is performed, dividing the unit into a preset number of sub-units along the central axis; Repeat the operation of determining whether the cells in the new mesh contain the coordinates of the gradient large region node coordinate set or the coordinates of the material boundary node coordinate set until the spacing of the sub-cells is less than or equal to the preset minimum mesh spacing, or the sub-cells do not contain the coordinates of the gradient large region node coordinate set or the coordinates of the material boundary node coordinate set and the spacing is less than or equal to the preset maximum mesh spacing. Traverse the spacing difference between adjacent sub-units after refinement. If the spacing difference is greater than or equal to a preset multiple, then perform semi-refinement segmentation on the sub-unit with large spacing according to the preset semi-refinement side length.

5. The mesh reconstruction method according to claim 1, characterized in that, The process of selecting the reconstructed target nodes located within the old boundary in the refined new mesh includes: The ray method is used to determine all the grid nodes of the refined new grid. A ray with a preset horizontal direction is emitted from the grid node, and the number of intersections between the ray and the old boundary is counted. If the number of intersection points is odd, then the grid node is determined to be located within the old boundary, and the coordinates of the grid node are recorded in the set of reconstruction target nodes, where the coordinates in the set of reconstruction target nodes are the reconstruction target nodes.

6. The mesh reconstruction method according to claim 1, characterized in that, The process of conformally stitching the newly divided mesh with the old mesh includes: Extract the new boundary nodes of the newly divided mesh and the old boundary nodes of the old mesh respectively; The kd-tree algorithm is used to quickly find matching node pairs between the new boundary node and the old boundary node whose distance is less than or equal to a preset distance, and the coordinates of the new boundary node in the matching node pair are corrected to the coordinates of the corresponding node of the old boundary node; The boundary cells of the revised new mesh are reconstructed so that the boundary cells of the new mesh and the boundary cells of the old mesh form a shared boundary. Update the topology table of the new grid, including node-cell associations and cell-cell adjacency relationships.

7. The mesh reconstruction method according to claim 1, characterized in that, Before refining the new mesh using the quartering method based on the node coordinates within the gradient region and the material boundary node coordinates in the pre-constructed new mesh, the process further includes: Traverse all grid nodes of the new grid and calculate the shortest distance between each grid node and the old boundary; If the shortest distance is less than the preset minimum grid spacing, then delete the grid node and the grid cell with the grid node as the vertex.

8. The mesh reconstruction method according to claim 1, characterized in that, Before the node coordinates and material boundary node coordinates within the gradient region in the pre-constructed new mesh, the following is included: Traverse all old grid nodes in the region to be rebuilt, and record the coordinates of the minimum and maximum nodes; The new mesh is established with the minimum node coordinates and the maximum node coordinates as diagonal points respectively, and the material of the new mesh is configured to be a universal material.

9. A grid reconstruction device, characterized in that, include: The refinement module is used to refine the new mesh using a quartering method based on the node coordinates of the large gradient region and the material boundary node coordinates in the pre-constructed new mesh. The filtering module is used to extract the old boundary of the old mesh to be reconstructed and filter out the reconstruction target nodes located within the old boundary in the refined new mesh; The stitching module is used to perform mesh generation and physical quantity data recovery operations on the refined new mesh based on the old boundary and the reconstruction target node, and to conformally stitch the new mesh with the old mesh.

10. An electronic device, characterized in that, Including memory and processor; The memory is used to store computer programs; The processor is configured to implement the mesh reconstruction method as described in any one of claims 1 to 7 when executing the computer program.

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