Modeling method for polycrystalline porous microstructure of sintered nano-silver material

Abstract

The invention belongs to the technical field of electronic packaging material analysis, and discloses a modeling method for a polycrystalline porous microstructure of a sintered nano-silver material, and the method comprises the steps: firstly carrying out the binarization processing of an SEM image of sintered nano-silver, and separating out a pore region and a solid-phase region; then extracting the contour of the pore region to obtain a discrete point set on the contour; based on the discrete point set, constructing geometric constraint conditions representing pore boundaries; then, by taking the geometric constraint condition as a boundary which cannot be invaded, performing constrained Delaunay triangulation in the solid-phase region, and generating a constrained Delaunay triangulation network; and finally, extracting a geometric dual graph of the constrained Delaunay triangulation network, and generating a Voronoi graph. According to the method, the limitation of simplifying pore morphology or neglecting solid-phase anisotropy in a traditional method is overcome, and a real and reliable geometric model basis is provided for high-precision finite element simulation.

Description

Technical Field

[0001] This application belongs to the field of electronic packaging material analysis technology, specifically relating to a method for modeling the polycrystalline porous microstructure of sintered nanosilver materials. Background Technology

[0002] As high-power electronic devices continue to evolve towards higher integration, their service temperatures have generally exceeded 175℃, placing more stringent demands on the thermal conductivity and long-term high-temperature stability of electronic packaging materials. Sintered silver nanomaterials, with their excellent thermal conductivity and stable performance under high-temperature environments, have become one of the key materials for high-power device packaging. At the microstructural level, sintered silver nanomaterials exhibit typical polycrystalline and porous characteristics: the solid phase region consists of a dense three-dimensional network metal framework formed by the aggregation of numerous grains, while the porous phase region exhibits a large number of irregularly shaped and randomly distributed pores.

[0003] Existing modeling methods mainly fall into two categories. The first simplifies irregularly shaped pores into regular geometric shapes like circles and polygons, reducing modeling complexity but severely sacrificing the true morphological characteristics of the pores. The second, while capable of constructing irregular pore morphologies, treats the material as an isotropic homogeneous body when dealing with the solid phase, neglecting the significant influence of grain orientation on the anisotropy of material properties. Research shows that under high-temperature service conditions, the microstructure of sintered silver undergoes significant evolution: on the one hand, atomic diffusion accelerates, promoting grain growth and grain boundary migration; on the other hand, pores also undergo morphological changes and repositioning. Crucially, pores naturally constitute the physical boundaries for grain growth within the structure, their spatial distribution directly constraining the grain growth direction and final morphology, while the evolution of the grain structure, in turn, influences the migration and merging of pores. This mutually constraining and co-evolving coupling relationship between pores and grains requires modeling methods to collaboratively characterize the geometric features of both.

[0004] However, existing technologies have failed to effectively address the problem of co-generating the true morphology of pores and the polycrystalline structure of the solid phase: either sacrificing the geometric fidelity of the pore morphology during modeling or ignoring the material anisotropy of the solid phase. This makes it difficult for the established models to accurately predict the structural evolution behavior of materials under high-temperature environments, thus limiting the prediction accuracy of numerical simulation analysis. Therefore, developing a novel modeling method that can simultaneously and accurately characterize the true morphology of pores and the polycrystalline structure of the solid phase has become a key technical problem that urgently needs to be solved in this field. Summary of the Invention

[0005] To address the technical problem that existing modeling methods cannot achieve polycrystalline segmentation of the solid phase region while preserving the true morphology of pores, this application provides a modeling method for the polycrystalline porous microstructure of sintered nanosilver materials. This method introduces pore boundaries as geometric constraints to collaboratively generate high-fidelity pore morphology and polycrystalline structures that conform to real physical characteristics, thereby accurately characterizing the anisotropy of the solid phase region and providing a reliable geometric model basis for subsequent accurate finite element analysis.

[0006] To achieve the above technical objectives, this application specifically adopts the following technical solution: In one aspect of this application, a method for modeling the polycrystalline porous microstructure of sintered nanosilver materials is provided, comprising the following steps: S1. The SEM image of sintered silver nanoparticles is binarized to separate the porous region and the solid phase region. S2. Extract the contour of the pore region to obtain a set of discrete points on the contour; S3. Based on the set of discrete points, construct geometric constraint conditions that characterize the pore boundary; S4. Using the geometric constraints as inviolable boundaries, perform constrained Delaunay triangulation within the solid region to generate a constrained Delaunay triangulation network. S5. Extract the geometric dual diagram of the constrained Delaunay triangulation and generate a Voronoi diagram, which is the polycrystalline microstructure of the solid-phase region obtained by dividing it.

[0007] In one embodiment, the binarization processing of the SEM image of sintered silver nanoparticles in step S1 includes: Using a two-dimensional matrix Describe the SEM image, wherein, For pixel coordinates, This is the grayscale value of that pixel; By threshold Binarization is performed to obtain a two-dimensional matrix. :

[0008] Among them, threshold Porosity determination based on sintered nanosilver; two-dimensional matrix In the diagram, 0 represents pores and 1 represents the solid phase.

[0009] In one implementation, step S2 involves extracting the contour of the pore region to obtain a set of discrete points on the contour, including: Define the set of all aperture pixels. ; Based on connectivity Divided into multiple non-interconnected pore regions ; For each pore region Detect all pixels on its boundary to form the discrete point set. .

[0010] In one implementation, step S3, based on the set of discrete points, constructs the geometric constraints characterizing the pore boundary, including: By fitting the discrete point set with a B-spline curve, a continuous pore profile curve function is obtained. ; The B-spline curve is discretized into equally spaced polygonal line segments, and the set of endpoints of these polygonal line segments is... Sum of edges Together they constitute the geometric constraints.

[0011] In one implementation, fitting using B-spline curves includes: use k The function expression for an order B spline curve is:

[0012] in, P i To control the vertices, For node vectors, These are the basis functions calculated using the DeBoor-Cox recurrence relation; According to the set of discrete points C The control vertex is obtained by inverse calculation. P i With node vectors U .

[0013] In one implementation, discretizing the B-spline curve into equally spaced line segments includes: Determine the length of the broken line segment based on the target grain size. L ; The total arc length of the B-spline curve is calculated by numerical integration. B total ; Calculate the number of vertices of a polyline segment ; Vertices are obtained by sampling at equal parameter intervals: ; From continuous vertices Constructing the set of constraint edges for a polyline segment .

[0014] In one implementation, the constrained Delaunay triangulation described in step S4 satisfies: All the boundaries in the geometric constraints become edges in the constrained Delaunay triangulation. In the triangulation, all edges except the constraint edges satisfy the Delaunay empty circumcircle property and the minimum angle maximum property.

[0015] In one implementation, step S5, extracting the geometric dual graph of the constrained Delaunay triangulation and generating the Voronoi diagram, includes: Calculate the constrained Delaunay triangulation circumcenter of each triangle ; The nodes of the Voronoi diagram are the set of all circumcenters of triangles; Connect any two adjacent triangles and outer core and To form Voronoi edges, where and public side e The boundary is not included in the geometric constraints.

[0016] The beneficial effects of this application are as follows: This application introduces pore boundaries as geometric constraints to collaboratively generate high-fidelity pore morphologies and physically realistic polycrystalline structures during the microstructure modeling process. The method in this application effectively overcomes the inherent limitations of traditional modeling methods that simplify pore morphology or neglect solid-phase anisotropy, achieving accurate reconstruction of the polycrystalline porous microstructure of sintered silver materials. The constructed model significantly improves the predictive accuracy of finite element simulation analysis, providing a reliable geometric model foundation for studying the structural evolution behavior of materials under high-temperature environments. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the process for modeling the polycrystalline porous microstructure of sintered nanosilver materials according to an embodiment of this application; Figure 2 These are SEM images of sintered nanosilver from embodiments of this application; Figure 3 This is the image after binarization processing according to the embodiments of this application; Figure 4 It is the pore outline composed of discrete pixels on the boundary of the pore region in the embodiments of this application; Figure 5 In this embodiment of the application, B-spline curves are used to fit discrete pore contour pixels; Figure 6 In this embodiment of the application, the B-spline curve is divided into equally spaced broken line segments; Figure 7 This is a Delaunay triangulation constructed according to an embodiment of this application; Figure 8 This application embodiment extracts the dual Voronoi diagram of the Delaunay triangular network; Figure 9 This is the polycrystalline porous microstructure of the sintered nanosilver material in the embodiments of this application. Detailed Implementation

[0018] The technical solution of this application will be clearly and completely described below with reference to specific embodiments. However, those skilled in the art will understand that the embodiments described below are only some embodiments of this application, not all embodiments, and are only used to illustrate this application, and should not be regarded as limiting the scope of this application. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0019] This application establishes a microstructure modeling method based on geometric constraint transfer. It drives the generation of polycrystalline structures in the solid phase region by transforming the real pore morphology into inviolable geometric constraints. First, the SEM image is binarized to accurately separate the solid phase and pores. Then, discrete points at the pore boundaries are extracted and fitted using B-spline curves to obtain a continuous and smooth mathematical representation of the pore contour. Subsequently, the curve is discretized into equidistant polygonal segments based on the target grain size, serving as rigid boundary constraints for subsequent triangulation. By performing constrained Delaunay triangulation, the pore boundaries are strictly preserved as triangle sides, thereby generating a triangular mesh conforming to the Delaunay criterion within the solid phase region. Finally, by extracting the geometric dual Voronoi diagram of the triangular mesh, a polycrystalline structure constrained by the pore boundaries is naturally formed. This application achieves an organic unity between the real pore morphology and grain structure generation through a continuous geometric transformation of pore boundary – polygonal constraint – constrained triangulation – Voronoi duality, preserving the complex geometric features of the pores while reflecting the physical constraint mechanism of grain growth.

[0020] In one specific embodiment, a method for modeling the polycrystalline porous microstructure of sintered nanosilver materials is provided, including the following steps: S1. The SEM image of sintered silver nanoparticles is binarized to separate the porous region and the solid phase region.

[0021] Specifically, using a two-dimensional matrix SEM images describing sintered silver nanoparticles, where These are the coordinates of pixels in the image. This represents the grayscale value of that pixel. For the two-dimensional matrix output after binarization... It meets the following conditions:

[0022] in, The binarization threshold was selected based on the porosity of sintered nanosilver. Two-dimensional matrix Positions with a median value of 0 represent pores, while positions with a median value of 1 represent the solid phase.

[0023] S2. Extract discrete pixels on the boundary of the pore region to obtain the pore contour.

[0024] definition Two-dimensional matrix The set of all pixels in the pore region, i.e. Based on the connectivity of the pore regions, the set Divided into k A series of unconnected pore regions For the first The set of all pixels within a pore region ,set up and It is a porous region A point in the middle, as long as there exists a point that is parallel to... Adjacent points Not in the area Inside, then point That is, the porous region Points on the boundary. The final set of discrete points on the boundaries of all porous regions. .

[0025] S3. Use B-spline curves to fit the set of discrete points on the boundary of the pore region to obtain the functional expression of the pore profile curve.

[0026] No. The boundary of each pore region Rank ( The function expression for the (second degree) B-spline curve is:

[0027] in, It is a B-spline curve One control vertex, vector It is the node vector of the B-spline curve, which will be in the parameter domain. u Divide into several non-decreasing sequences of real numbers Interval. yes Rank ( The basis functions of the (b)-spline curve are obtained from the De Boor-Cox recursive formula:

[0028]

[0029] B-spline curves are controlled by vertices. Node vectors With basis functions This is jointly determined, and therefore based on the set of points on the boundary of the pore region. Inversely calculate the control vertices of the corresponding B-spline curve. With node vectors This gives the B-spline curve function expression for the pore profile.

[0030] S4. Discretize the B-spline curve into equally spaced broken line segments.

[0031] The length of the broken line segment is determined based on the target grain size. The B-spline curve is divided into equally spaced broken line segments. Since the arc length of the B-spline curve has no analytical solution, the total arc length of the B-spline curve is approximated using numerical integration:

[0032] Number of vertices of a polyline segment Then the set of vertices of the broken line segment The expression:

[0033] in, These are the parameter values ​​for equally spaced sampling.

[0034] S5. Construct a Delaunay triangle network using the endpoints and segments of the polyline as constraint points and constraint edges.

[0035] It is a B-spline curve Polyline transformation yields an ordered set of vertices for the polyline segment, where, The constraint edges formed by the polyline segments are denoted as... Based on the set of constrained vertices With constraint boundary set Delaunay triangulation is performed to obtain a constrained Delaunay triangulation:

[0036] in, For the constrained Delaunay triangulation obtained by triangulation, The set of all triangle vertices is denoted as ,but The CDT process must satisfy the following condition: all constraint edges All became The sides of the middle triangle, and All unconstrained edges in the array satisfy the empty circle property and the minimum angle maximum property. That is... The circumcircle of any triangle in the set does not contain the set. Among the other points in the triangle, the sum of the smallest interior angles of the convex quadrilateral formed by two adjacent triangles is always greater than the smallest interior angle of the two triangles formed by exchanging the diagonals of the convex quadrilateral.

[0037] S6. Extract the geometric dual diagram of the constrained Delaunay triangulation and generate a Voronoi diagram, which is the polycrystalline microstructure of the solid-phase region obtained by dividing it.

[0038] Specifically, the process of generating a Voronoi diagram includes the following steps: First, calculate the constrained Delaunay triangulation. Each triangle outer core The circumcenter of a triangle is the intersection of the perpendicular bisectors of its three sides. The nodes of the Voronoi diagram represent the set of all such circumcenters, denoted as... .

[0039] Next, the boundaries of the Voronoi diagram are constructed. For the triangular mesh... Any two adjacent triangles in and If they share a common edge e And the public edge e The set of constraint edges that do not belong to the set defined in the geometric constraints. (i.e., the constraint edge derived from the pore boundary), then the circumcenters of these two triangles are connected. and This connecting line constitutes a Voronoi edge.

[0040] Therefore, the constrained Delaunay triangulation The geometric dual Voronoi diagram can be formally represented as a graph structure. Among them, the node set v As mentioned earlier, this is the set of circumcenters of triangles. Boundary set. ε It consists of all Voronoi edges that satisfy the condition, and its mathematical definition is:

[0041] This definition ensures that the boundaries of the Voronoi diagram do not penetrate the physical contour of the solid region defined by the pore boundaries.

[0042] The Voronoi diagram generated by the above process has each polygonal unit (Voronoi cell) representing a grain, and these units together divide the solid phase region into a polycrystalline microstructure that conforms to crystallographic characteristics.

[0043] Example SEM images of a portion of a sintered silver nanolayer subjected to 1000 hours of high-temperature service at 250°C were obtained. Based on these images, a polycrystalline porous microstructure consistent with the actual pore morphology was constructed. (See also...) Figure 1 As shown, the specific steps are as follows: Step 1: For Figure 2 The actual sintered silver nanoparticle SEM images were binarized to separate the solid phase and the porous phase. A two-dimensional matrix was used. SEM images describing sintered silver nanoparticles, where These are the coordinates of pixels in the image. Using a two-dimensional matrix. Describe the image output after binarization. The following conditions must be met:

[0044] The binarization threshold was selected based on the porosity of sintered nanosilver. Take 0.8. Two-dimensional matrix. The position with a median value of 0 represents pores, and the position with a median value of 1 represents solids. The processed binarized image is as follows: Figure 3 As shown.

[0045] Step 2: Extract discrete pixels on the boundary of the pore region to obtain the pore contour. (Definition) Two-dimensional matrix The set of all pixels in the pore region, i.e. Based on the connectivity of the pore regions, the set Divided into k A series of unconnected pore regions For the first The set of all pixels within a pore region ,set up and It is a porous region A point in the middle, as long as there exists a point that is parallel to... Adjacent points Not in the area Inside, then point That is, the porous region Points on the boundary. The final set of points on the boundaries of all porous regions. The pore profile formed by this set is as follows Figure 4 As shown.

[0046] Step 3: Fit the discrete pore profile points using a B-spline curve to obtain the functional expression of the pore profile curve. The boundary of each pore region Rank ( The function expression for the (second degree) B-spline curve is:

[0047] in, It is a B-spline curve One control vertex, vector It is the node vector of the B-spline curve, which will have the parameter domain Divide into several non-decreasing sequences of real numbers Interval. yes Rank ( The basis functions of the (b)-spline curve. Therefore, based on the set of points on the boundary of the pore region. The B-spline curve function expression of the pore profile is calculated in reverse and plotted as follows: Figure 5 As shown.

[0048] Step 4: Determine the length of the broken line segment based on the size of the target grain. The B-spline curve is divided into equally spaced polygonal segments. The number of vertices in each polygonal segment... set of vertices of a polyline segment The expression:

[0049] in, These are parameter values ​​sampled at equal intervals, and the resulting polyline segments are as follows: Figure 6 As shown.

[0050] Step 5: Construct a Delaunay triangulation using the endpoints and segments of the polyline as constraint points and constraint edges. This is based on the set of constraint vertices. With constraint boundary set The Delaunay triangulation is performed to obtain the Delaunay triangulation network:

[0051] in, For the Delaunay triangulation mesh obtained by triangulation, The set of all triangle vertices is denoted as ,but The CDT process must satisfy the following condition: all constraint edges All became The sides of the middle triangle, and The unconstrained edges in the network satisfy the empty circle property and the minimum angle maximum property. The constructed Delaunay triangulation is as follows: Figure 7 As shown.

[0052] Step 6: Obtain the dual diagram of the Delaunay triangular network; the resulting Voronoi diagram represents the divided polycrystalline microstructure. Let the triangle... The outer center is Then the Delaunay triangle mesh The geometric dual Voronoi diagram can be represented as:

[0053] The nodes of the Voronoi diagram are The set of all circumcenters of triangles The boundaries of the Voronoi diagram Delaunay triangle and The set of circumcentric connecting lines. The dual Voronoi diagram of the Delaunay triangular network is shown below. Figure 8 As shown. The final polycrystalline porous microstructure of the sintered nanosilver material is as follows. Figure 9 As shown.

[0054] Although the embodiments of this application have been described above in conjunction with the accompanying drawings, this application is not limited to the specific embodiments and application fields described above. The specific embodiments described above are merely illustrative and instructive, not restrictive. Those skilled in the art can make many other forms based on the guidance of this specification and without departing from the scope of protection of the claims of this application, and these are all within the scope of protection of this application.

Claims

1. A method of modeling a sintered nanosilver material polycrystalline porous mesostructure, characterized in that, The method comprises the following steps: S1, binarizing an SEM image of sintered nano-silver to separate a pore region and a solid phase region; S2, extracting a contour of the pore region to obtain a discrete point set on the contour; S3, constructing a geometric constraint condition representing a pore boundary based on the discrete point set; S4, performing constrained Delaunay triangulation in the solid phase region with the geometric constraint condition as an inviolable boundary to generate a constrained Delaunay triangular mesh; S5, extracting a geometric dual graph of the constrained Delaunay triangular mesh to generate a Voronoi diagram, wherein the Voronoi diagram is a divided solid phase region polycrystal mesostructure.

2. The modeling method of sintered nanosilver material polycrystalline porous mesostructure according to claim 1, characterized in that, The binarizing of the SEM image of sintered nano-silver in step S1 comprises: Using a two-dimensional matrix The SEM image is described, wherein, is the pixel coordinate, is the gray value of the pixel point; By threshold Binaryzation is performed to obtain a two-dimensional matrix : wherein the threshold value Determination of porosity based on sintered nanosilver; two-dimensional matrix 0 represents a pore, 1 represents a solid phase.

3. The modeling method of sintered nanosilver material polycrystalline porous mesostructure according to claim 1, characterized in that, The extracting of the contour of the pore region in step S2 comprises: define a set of all pore pixels ; According to the connectivity, the plurality of regions are divided into a plurality of regions of pores which are not connected to each other into a plurality of regions of pores which are not connected to each other ; For each pore region , all the pixel points on its boundary are detected to form the discrete point set .

4. The modeling method of sintered nanosilver material polycrystalline porous mesostructure according to claim 1, characterized in that, The constructing of the geometric constraint condition representing the pore boundary based on the discrete point set in step S3 comprises: fitting the set of discrete points using a B-spline curve to obtain a continuous pore profile curve function ; discretizing the B-spline curve into equidistant polyline segments, the endpoint set and the side set together constitute the geometric constraint condition.

5. The modeling method of sintered nanosilver material polycrystalline porous mesostructure according to claim 4, characterized in that, The B-spline curve fitting comprises: The present application relates to a method for producing a semiconductor device, comprising the steps of k a cubic B-spline curve, the function expression of which is wherein, P i for controlling the vertex, for the node vector, for the basis function calculated by the DeBoor-Cox recurrence formula; According to the discrete point set C Back-calculation obtains the control vertex P i With node vector U .

6. The modeling method of sintered nanosilver material polycrystalline porous mesostructure according to claim 4, characterized in that, The discretization of the B-spline curve into equidistant polyline segments comprises: Determining break line segment length according to target grain size L ; calculating the total arc length of the b-spline curve by numerical integration B total ; Counting the number of vertices of a polyline segment ; The vertexes are obtained by equi-parametric interval sampling: ; By consecutive vertices Constructing the set of polyline segment constraints .

7. The modeling method of sintered nanosilver material polycrystalline porous mesostructure according to claim 1, characterized in that, The performing of the constrained Delaunay triangulation in step S4 satisfies: The boundaries in all the geometric constraint conditions become edges in the constrained Delaunay triangular mesh; The edges in the triangular mesh other than the constraint edges satisfy the Delaunay empty circumcircle characteristic and the minimum angle maximum characteristic.

8. The modeling method of sintered nanosilver material polycrystalline porous mesostructure according to claim 1, characterized in that, The extracting of the geometric dual graph of the constrained Delaunay triangular mesh in step S5 comprises: computing the constrained delaunay triangulation circumcenter of each triangle ; The nodes of the Voronoi diagram are a set of all triangle circumcenters; connecting any two adjacent triangles with the circumcenter of with to form a Voronoi edge, wherein with a common edge of e does not belong to the boundary in the geometric constraints.

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