A simulation method for micro-nano metal sintering connection layer mesostructure evolution and stress migration behavior

Abstract

The application relates to a micro-nano metal sintering connection layer mesostructure evolution and stress migration behavior simulation method, which comprises the following steps: establishing a chip-sintering connection layer-substrate simulation model, and establishing a second layer unit model of the sintering connection layer for phase field simulation; using a random number generation and Gaussian filtering method, a binary matrix representing a porous structure is generated, and initial values of the phase field are obtained; a first control equation of the phase field describing pore evolution is established, and then the second control equation is obtained by considering the atom migration driven by the hydrostatic stress gradient; thermal coupling simulation is carried out, the node hydrostatic stress is calculated from the simulation result and input into the second layer unit model; phase field simulation is carried out, the second control equation is iteratively solved, and the evolution and migration results of the sintering connection layer mesostructure are obtained. The application can establish a micro-nano metal sintering connection layer mesostructure evolution and stress migration behavior simulation method, and provide support for studying the evolution of the mechanical and heat transfer characteristics of the sintering connection layer.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of numerical simulation, in particular, the present application relates to a micro-nano metal sintering connection layer mesoscopic structure evolution and stress migration behavior simulation method, which is mainly based on phase field theory and finite element technology. BACKGROUND

[0002] The rapid development of power device materials and technology makes its heat dissipation also higher and higher. At present, the device chip working temperature based on the third generation power semiconductor material is more than 250 DEG C, which puts forward severe challenge to the traditional chip bonding material. Micro-nano metal sintering connection provides a chip bonding solution for the device with high power dissipation. The small size particles of micro-nano metal have high surface activation energy, which can be sintered at a lower temperature, and the melting point of the sintered bonding layer can be close to the melting point of the corresponding bulk metal, so that it can still work reliably at high temperature. The commonly used sintered micro-nano metal is copper and silver.

[0003] The sintered metal micro-nano particles present a porous structure, and this porous structure will continue to evolve under high temperature and stress conditions. High temperature will lead to the decrease of the number of pores and the continuous increase of the size, and the evolution towards the direction of lower system surface energy. The thermal mismatch stress caused by temperature will also lead to the migration of atoms to the direction of high hydrostatic stress and the migration of pores to the direction of low hydrostatic stress. The evolution and migration behavior of this porous structure will affect the mechanical and heat transfer characteristics of the sintered connection layer, so it is necessary to establish a simulation method for the evolution and migration behavior of the mesoscopic structure of the sintered connection layer of micro-nano metal, to provide support for the research on the evolution of the mechanical and heat transfer characteristics of the sintered connection layer. SUMMARY

[0004] The present application proposes a method for simulating the mesoscopic structure evolution and migration behavior of micro-nano metal sintered connection layer. The method considers the continuous fusion of micro-nano metal particles and the increase of average pore size caused by high temperature environment, as well as the stress gradient driven material migration and pore segregation caused by thermal mismatch.

[0005] Step one: in the finite element software, a simulation model 100 of chip-micro-nano metal sintered connection layer-substrate sandwich structure is established; for the micro-nano metal sintered connection layer, a second layer unit model 200 is also established for phase field simulation;

[0006] Step two: for the micro-nano metal sintered connection layer, a binary matrix representing the structure of the sintered connection layer is generated by using random number generation and Gaussian filtering method;

[0007] Step three: according to the binary matrix of step two, form the input of phase field simulation, that is, for the nodes of the second layer unit model 200: set the initial value of the node to 0 to represent the pore region, and set the initial value of the node to 1 to represent the solid region;

[0008] Step four: taking the minimization of surface energy as the evolution driving force, a first control equation describing the evolution of the phase field is established;

[0009] Step five: modify the first control equation to consider the material migration caused by the hydrostatic stress gradient, obtain the second control equation; and weakly form the control equation to facilitate finite element implementation;

[0010] Step six: use the simulation model 100 to carry out thermal-mechanical coupling simulation, and extract the hydrostatic stress from the simulation results to calculate the hydrostatic stress gradient;

[0011] Step seven: based on the simulation model 100, the second layer unit model 200 of the micro-nano metal sintering connection layer and the second control equation, the Newton-Raphson algorithm is used to iteratively solve the second control equation in the finite element framework, and the node phase field value is output to obtain the pore evolution and migration results of the micro-nano metal sintering connection layer.

[0012] In step one, the finite element software is used to establish the simulation model 100 of the chip-micro-nano metal sintering connection layer-substrate sandwich structure, and generate the corresponding simulation input file 500, which includes: description of node coordinates, description of unit type and unit composition, material thermal and mechanical performance parameters, boundary conditions, solver settings, output settings; for the micro-nano metal sintering connection layer, according to the nodes in the simulation model 100, a second layer unit model 200 is established, and the description of the unit type and unit composition of the second layer unit is written into the simulation input file 500; Since the second layer unit model 200 is used for phase field calculation, and the control equation of the phase field has two coupled variables c and μ, the second layer unit model needs to be assigned two degrees of freedom.

[0013] In step two, the random number generation is performed according to the micro-nano metal sintering connection layer in the simulation model 100 to generate a random number matrix X with the same number of elements as the micro-nano metal sintering connection layer, and the distribution of the random number is [0, 1] uniform distribution; then Gaussian filtering is performed on the random number matrix, and normal-uniform distribution transformation is performed on the data after Gaussian filtering:

[0014]

[0015]

[0016] In the formula, x is the data in the matrix X, and x" is the transformed data; is the average value of the data in matrix X, σ(X) is the standard deviation of the data in matrix X, X min , X max are the minimum and maximum values of the data in matrix X, respectively; erfc(x) is the complementary error function:

[0017]

[0018] The transformed data has a value range of [0, 1], and then a threshold p is given, and the numbers greater than or equal to p in the data are set to 1, and the numbers less than p are set to 0, and the binary matrix obtained can represent the micro-nano metal sintering connection layer structure; the size of the generated pores is controlled by setting the σ value of the Gaussian filter, and the porosity is controlled by p.

[0019] In step three, the binary matrix is converted into the input of phase field simulation, and the implementation method is as follows: each value 0 or 1 in the binary matrix represents that the corresponding unit in the second layer unit model 200 of the micro-nano metal sintering connection layer should be a pore or a solid. The representation of the pore or the solid in the second layer unit model 200 is that the phase field initial value of the node of the unit corresponding to the pore is 0, and the phase field initial value of the node of the unit corresponding to the solid is 1. For two adjacent units, that is, units sharing a node, the unit value is preferentially taken as 1.

[0020] In step four, the first control equation of phase field evolution established is:

[0021]

[0022]

[0023]

[0024] In the formula, c ∈ [0, 1] is the phase field value, c = 0 represents the solid phase, and c = 1 represents the pore phase; t is time; M is the diffusion coefficient; κ is the concentration gradient energy coefficient; n is the normal vector perpendicular to the surface ; is the Hamiltonian operator; f is the free energy density function of the system, which in this paper is:

[0025] f(c) = Ac 2 (1-c) 2

[0026] is used to determine the equilibrium phase as the solid phase c = 0 and the pore phase c = 1. In the formula, A is a normal number, which controls the energy barrier size between the two equilibrium phases.

[0027] In step five, the second control equation considering the material migration caused by the hydrostatic stress gradient is:

[0028]

[0029] wherein,

[0030]

[0031] wherein, J s represents the diffusion flux of stress migration; D is the mobility coefficient; k is the Boltzmann constant; T is the temperature; σ H is the hydrostatic stress.

[0032] The weak form of the second control equation is:

[0033]

[0034]

[0035] wherein, η and ξ are the trial functions corresponding to c and μ respectively.

[0036] wherein, step six extracts the hydrostatic stress from the thermal-mechanical coupling simulation result of the simulation model 100, and calculates the hydrostatic stress gradient Generally, the hydrostatic stress value output by the finite element is the average value of the stress of the element, which is the same everywhere in the element, so in order to calculate the gradient, the hydrostatic stress value at the node of the element must be recalculated, and the following method is adopted:

[0037] For a four-node quadrilateral element, the hydrostatic stress value at the node is the average value of the hydrostatic stresses of the four elements sharing the node, as shown in Figure 2 that is, the hydrostatic stress at node 1 is calculated as:

[0038]

[0039] wherein, is the hydrostatic stress at node N1, respectively, are the hydrostatic stresses of elements E1, E2, E4 and E5 in the thermal-mechanical coupling simulation result.

[0040] wherein, in step seven, a fully coupled thermal-mechanical solver should be used for solving in the finite element framework. The thermal-mechanical coupling field and the phase field are solved in a semi-staggered manner, that is, in the n+1 increment step, the hydrostatic stress σ H as shown in Figure 6 .

[0041] The technical scheme provided by the embodiments of the present application has the beneficial technical effects including:

[0042] The porous structure evolution and stress migration simulation method of the embodiment of the application establishes a simulation model 100 of a chip-micro-nano metal sintering connection layer-substrate sandwich structure, establishes a second layer unit model 200 for phase field simulation for the micro-nano metal sintering connection layer, and generates a simulation input file 500; a binary matrix representing the porous structure of the sintering connection layer is generated by using a random number generation and Gaussian filtering method, then the initial value of the phase field is generated according to the binary matrix, and is written into the simulation input file 500; the thermal force coupling simulation uses a simulation module provided by the finite element software, and the phase field simulation uses the control equation established by the method; the first control equation describing the evolution of the phase field is established by taking the minimization of the surface energy as the driving force of the evolution of the pores, then the second control equation is derived on the basis of the first control equation by considering the atomic migration driven by the hydrostatic stress gradient of the thermal field, and is weakly formed; the thermal force coupling simulation is carried out for the simulation model 100, the unit hydrostatic stress is extracted from the simulation result, the node hydrostatic stress is calculated, and the gradient value of the hydrostatic stress is input into the second layer unit model 200 for phase field simulation; the phase field simulation is realized by using the Newton-Raphson algorithm to iteratively solve the second control equation in the finite element framework, and the phase field cloud chart is output, that is, the evolution and migration results of the porous structure of the micro-nano metal sintering connection layer at different time points can be obtained. The embodiment of the application can establish a simulation method of the mesostructure evolution and stress migration behavior of the micro-nano metal sintering connection layer, and provide support for studying the evolution of the mechanical and heat transfer characteristics of the sintering connection layer.

[0043] Additional aspects and advantages of the application will be set forth in part in the description which follows, and in part will become apparent to those skilled in the art upon examination of the following and / or can be learned by practice of the application. BRIEF DESCRIPTION OF DRAWINGS

[0044] The above and / or additional aspects and advantages of the application will become apparent and be readily appreciated from the following description, taken in conjunction with the accompanying drawings, in which:

[0045] Figure 1 A flowchart of a simulation method of mesostructure evolution and stress migration behavior of a micro-nano metal sintering connection layer provided by the embodiment of the application is shown in FIG. 1;

[0046] Figure 2 A schematic diagram of a calculation method of the hydrostatic stress value at the node of a four-side element provided by the embodiment of the application is shown in FIG. 2;

[0047] Figure 3 A schematic diagram of a two-dimensional simulation model of a chip-micro-nano metal sintering connection layer-substrate sandwich structure provided by the embodiment of the application is shown in FIG. 3;

[0048] Figure 4 An image form of a binary matrix of a nano-silver sintering connection layer structure provided by the embodiment of the application is shown in FIG. 4;

[0049] Figure 5 An initial phase field value diagram of a chip-micro-nano metal sintering connection layer-substrate sandwich structure provided by an embodiment of the present application;

[0050] Figure 6 A hydrostatic stress gradient extraction and input to the phase field process diagram provided by an embodiment of the present application;

[0051] Figure 7 A Mises stress nephogram of a chip-micro-nano metal sintering connection layer-substrate sandwich structure provided by an embodiment of the present application at 300°C;

[0052] Figure 8 A hydrostatic stress nephogram of a chip-micro-nano metal sintering connection layer-substrate sandwich structure provided by an embodiment of the present application at 300°C;

[0053] Figure 9 A porous structure diagram of a chip-micro-nano metal sintering connection layer-substrate sandwich structure provided by an embodiment of the present application at dimensionless time 1;

[0054] Figure 10 A porous structure diagram of a chip-micro-nano metal sintering connection layer-substrate sandwich structure provided by an embodiment of the present application at dimensionless time 25;

[0055] Figure 11 A porous structure diagram of a chip-micro-nano metal sintering connection layer-substrate sandwich structure provided by an embodiment of the present application at dimensionless time 75;

[0056] Figure 12 A porous structure diagram of a chip-micro-nano metal sintering connection layer-substrate sandwich structure provided by an embodiment of the present application at dimensionless time 150;

[0057] Figure 13 A porous structure diagram of a chip-micro-nano metal sintering connection layer-substrate sandwich structure provided by an embodiment of the present application at dimensionless time 300;

[0058] Figure 14 A porous structure diagram of a chip-micro-nano metal sintering connection layer-substrate sandwich structure provided by an embodiment of the present application at dimensionless time 600; DETAILED DESCRIPTION

[0059] Embodiments of the present application are described below by referring to the accompanying drawings. The embodiments described below by referring to the accompanying drawings are exemplary, and are intended to explain the embodiments of the present application, and cannot be understood as a limitation of the embodiments of the present application.

[0060] The chip-micro / nano metal sintered bonding layer-substrate sandwich structure provided in this case has a thickness of 1.5 mm and a length of 3 mm. The materials are: chip-silicon (Si), micro / nano metal sintered bonding layer-silver (Ag), and substrate-copper (Cu). The chip-micro / nano metal sintered bonding layer-substrate sandwich structure is subjected to a temperature of 300℃.

[0061] Step 1: Constructing the sandwich structure model and the second-layer unit model

[0062] A sandwich structure model of chip-micro / nano metal sintering connection layer-substrate was established using ABAQUS software, such as... Figure 3 As shown. From top to bottom, the first layer is a silicon chip with dimensions of 3mm x 0.25mm; the second layer is a nano-silver sintered layer with dimensions of 3mm x 1mm; and the third layer is a copper substrate with dimensions of 3mm x 1mm. The model is meshed using quadrilaterals with a mesh size of 0.01mm to obtain the model's nodes and elements, including 300x100 nano-silver sintered layer elements. For the nodes of the nano-silver sintered layer, another layer of elements is created for phase-field simulation.

[0063] The corresponding cell in the silicon chip is endowed with the material properties of silicon: thermal conductivity of 130 mW / (mm×K); density of 2.33×10⁻⁹ T / mm². 3 Young's modulus is 162000 MPa, Poisson's ratio is 0.28, and coefficient of thermal expansion is 3.00 × 10⁻⁶. -6 / K; Specific heat capacity 7x10 8 mJ / (T×K).

[0064] The unit cells corresponding to the sintered nano-silver layer were endowed with the material properties of silver: thermal conductivity of 418 mW / (mm×K); density of 1.04 x 10⁻⁶. -8 T / mm 3 Young's modulus is 81500 MPa, Poisson's ratio is 0.38, and coefficient of thermal expansion is 1.89 x 10⁻⁶. -5 / K; specific heat capacity 1.7x10 8 mJ / (T×K).

[0065] The cell corresponding to the copper substrate is endowed with the material properties of copper: thermal conductivity of 400 mW / (mm×K); density of 8.96×10⁻⁶. -9 T / mm 3 Young's modulus is 110,000 MPa, Poisson's ratio is 0.35, and coefficient of thermal expansion is 1.70 × 10⁻⁶. -5 / K; specific heat capacity 3.85×10 8 mJ / (T×K).

[0066] The following boundary conditions are applied to the chip-micro-nano metal sintering connection layer-substrate sandwich structure model: the Y direction displacement of the bottom edge of the model is 0, the displacement of the lower left corner of the model in the X and Y directions is 0, and the temperature of the entire model is 300°C.

[0067] Step two: binary matrix generation of sintering connection layer porous structure

[0068] A random number matrix of size 300x100 is generated using python-numpy.random.random. The random number matrix is filtered using the Gaussian filtering method, and the Gaussian filtering σ value is 5. Then the data after Gaussian filtering is transformed from normal distribution to uniform distribution; the transformed data takes the value interval [0, 1], and then a threshold value 0.2 is given, and the data greater than or equal to 0.2 is set to 1, and the data less than 0.2 is set to 0, to obtain the binary matrix representing the micro-nano metal sintering connection layer structure. The binary matrix image obtained in this case is as shown in Figure 4 , wherein the black part corresponds to the value 1 in the binary matrix, i.e. the solid phase, and the white part corresponds to the value 0 in the binary matrix, i.e. the pore phase.

[0069] Step three: initial value input for phase field simulation according to binary matrix

[0070] The size of the binary matrix generated in step two corresponds to the second layer unit of the nano-silver sintering layer, i.e. both are 300x100. It is necessary to further convert the binary matrix representing the nano-silver sintering layer porous structure into the initial phase field value of the second layer unit node. For example, unit 75000 in the second layer unit is composed of nodes 37624, 37625, 37926, and 37925, and the value of unit 75000 in the binary matrix is 1, so the initial phase field value of nodes 37624, 37625, 37926, and 37925 is set to 1, and other nodes are the same. Thus, the initial value setting for phase field simulation is completed. The initial phase field value cloud chart of the entire chip-micro-nano metal sintering connection layer-substrate structure is as shown in Figure 5 .

[0071] Step four: establish the first control equation of phase field evolution

[0072] The first control equation of phase field evolution is:

[0073]

[0074]

[0075]

[0076] f(c)=Ac 2 (1-c) 2

[0077] In this case, the first control equation of phase field evolution is realized in the Fortran script file corresponding to the UEL user-defined unit of ABAQUS software.

[0078] Wherein the value of the undetermined parameter is: M = 3 x 10 -3 , κ = 8 x 10 -5 , A = 1,

[0079] Step five: derivation of the second control equation

[0080] The second control equation considering migration is

[0081]

[0082] Wherein,

[0083] In this case, the second control equation is realized in the Fortran script file corresponding to the UEL user-defined unit of ABAQUS software.

[0084] Wherein the value of the undetermined parameter is: D / kT = 5 x 10 -5 .

[0085] In this case, the UEL is defined as 4 nodes with X, Y coordinates, occupying 4, 12, 13 degrees of freedom, wherein the 12th degree of freedom is the phase field; the shape function used by the UEL is the first order shape function; according to the second control equation and the shape function, the right-hand side vector and the stiffness matrix are calculated in the UEL, and ABAQUS calculates the right-hand side vector and the stiffness matrix of the UEL to perform iterative solution calculation, and calculates the phase field value of each node at each increment step.

[0086] Step six: calculation of hydrostatic stress gradient of thermal-mechanical coupling field

[0087] The chip-micro-nano metal sintering connection layer-substrate sandwich structure model established in step one is simulated by thermal-mechanical coupling, and the full coupling temperature-displacement solver of ABAQUS is used, the step size is 0.02, and the increment step is 600 steps. At the end of each thermal-mechanical coupling simulation increment step, the USDFLD subroutine is used to extract S11, S22 of each element from the stress output, and S11+S22 is calculated as the element hydrostatic stress value, and the hydrostatic stress value of each node is calculated according to the following formula:

[0088]

[0089] The hydrostatic stress value of each node extracted in the thermal-mechanical coupling simulation will be used as the input of the phase field simulation, and the hydrostatic stress gradient will be calculated in the UEL of step five as input to the second control equation. The whole procedure becomes obvious and easy to understand in Figure 6

[0090] Step seven: simulation calculation of the phase field value of the output node

[0091] The second layer unit model established in step one is simulated by using the full coupling temperature-displacement solver of ABAQUS, with a step length of 0.02 and an increment step of 600 steps. In each increment step, the hydrostatic stress value of each node output in step six is required. The sandwich structure model of the chip-micro-nano metal sintering connection layer-substrate and the second layer unit model are iteratively calculated in the solver of ABAQUS to obtain the thermal-mechanical coupling field and the phase field, respectively. The stress, strain, displacement and phase field values are output in each increment step, and the visualization is performed in ABAQUS / Viewer.

[0092] Figure 7 The Mises stress distribution cloud chart of the chip-micro-nano metal sintering connection layer-substrate sandwich structure at 300°C calculated in this embodiment; Figure 8 The hydrostatic stress distribution cloud chart of the nano-silver sintering connection layer at 300°C calculated in this embodiment, wherein the upper and lower gray areas are the chip and the substrate. Since the evolution and migration of the chip and the substrate do not need to be calculated, the hydrostatic stress of the chip and the substrate is not shown in the figure. It can be seen from Figure 8 that the area with larger hydrostatic stress is the two sides of the nano-silver sintering connection layer, and the area with smaller hydrostatic stress is the upper part, so the gradient direction of the stress is from the two sides to the upper central position, and the migration direction of the pores should be consistent with the gradient direction of the stress. Figures 9 to 13 The phase field distribution cloud charts of the chip-micro-nano metal sintering connection layer-substrate sandwich structure are shown in Figs. 1, 2, 3, 4, 5 and 6, respectively, which are dimensionless time 1, 25, 75, 150, 300 and 600. It can be seen from this series of charts that the evolution and migration of the pores have the following characteristics:

[0093] 1. At the beginning, the size and position of the pores are randomly distributed, and as the evolution proceeds, the average size of the pores is continuously increased, and evolves in the direction of lower surface energy;

[0094] 2. As the migration proceeds, the pores gradually gather in the upper middle region of the nano-silver sintering layer, resulting in a larger pore size in the upper middle region than in other positions, especially the two sides.

[0095] The above characteristics of the evolution and migration of the pores are consistent with the hydrostatic stress distribution and gradient.

[0096] ​Those skilled in the art can understand that the steps, measures, and schemes in various operations, methods, and processes discussed in the present application can be alternated, changed, combined, or deleted. Further, other steps, measures, and schemes in various operations, methods, and processes discussed in the present application can also be alternated, changed, rearranged, decomposed, combined, or deleted. Further, steps, measures, and schemes in various operations, methods, and processes in the prior art can also be alternated, changed, rearranged, decomposed, combined, or deleted.

[0097] In the description of the present application, it should be understood that the terms "center", "upper", "lower", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as limiting the present application.

[0098] The terms "first", "second", are only for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the technical features indicated. Therefore, the features defined with "first", "second" can explicitly or implicitly include one or more of the features. In the description of the present application, unless otherwise stated, the meaning of "a plurality of" is two or more.

[0099] It should be understood that although each step in the flowchart of the drawings is shown in sequence according to the direction of the arrow, these steps are not necessarily executed in sequence according to the direction of the arrow. Unless otherwise stated herein, the execution of these steps is not strictly limited in sequence, and they can be executed in other sequences. Moreover, at least part of the steps in the flowchart of the drawings can include multiple sub-steps or multiple stages, which are not necessarily executed at the same time, but can be executed at different times, and the execution sequence is not necessarily sequential, but can be executed alternately or alternately with at least part of other steps or sub-steps or stages of other steps.

[0100] The above only describes some embodiments of the present application, and it should be pointed out that for those skilled in the art, without departing from the principles of the present application, a number of improvements and refinements can be made, and these improvements and refinements should be considered as the protection scope of the present application.

Claims

1. A method for simulating micro-nano metal sintering connection layer mesostructure evolution and stress migration behavior, characterized in that, A chip-sintering connection layer-substrate simulation model is established, and a second layer unit model is established for the sintering connection layer for phase field simulation; A binary matrix representing the porous structure is generated using a random number generation and Gaussian filtering method to obtain the initial value of the phase field; A first control equation describing the evolution of the pore is established, and then the atomic migration driven by the hydrostatic stress gradient is considered to obtain the second control equation; The thermal coupling simulation is carried out, and the hydrostatic stress of the node is calculated from the simulation results and input into the second layer unit model; the phase field simulation is carried out, and the second control equation is iteratively solved to obtain the evolution and migration results of the sintering connection layer mesostructure, and the specific steps are as follows: Step one: in the finite element software, a simulation model 100 of a chip-micro-nano metal sintering connection layer-substrate sandwich structure is established; for the micro-nano metal sintering connection layer, a second layer unit model 200 is also established for phase field simulation; Step two: for the micro-nano metal sintering connection layer, a binary matrix representing the structure of the sintering connection layer is generated using a random number generation and Gaussian filtering method; Step three: according to the binary matrix of step two, the input of the phase field simulation is formed, that is, the initial value of the node of the second layer unit model 200 is set to 0 to represent the pore region, and the initial value of the node is set to 1 to represent the solid region; Step four: taking the minimization of surface energy as the evolution driving force, a first control equation describing the evolution of the phase field is established; Step five: the first control equation is modified to consider the material migration caused by the hydrostatic stress gradient to obtain the second control equation; And the control equation is weakly formed for easy finite element implementation; Step six: thermal coupling simulation is carried out using the simulation model 100, and the hydrostatic stress gradient is calculated from the simulation results; Step seven: based on the simulation model 100, the second layer unit model 200 of the micro-nano metal sintering connection layer and the second control equation, the Newton-Raphson algorithm is used to iteratively solve the second control equation in the finite element framework, and the node phase field value is output to obtain the pore evolution and migration results of the micro-nano metal sintering connection layer.

2. The micro-nano metal sintering connection layer mesostructure evolution and stress migration behavior simulation method according to claim 1, characterized in that, The process of generating a binary matrix representing the structure of the sintering connection layer is as follows: According to the micro-nano metal sintering connection layer in the simulation model 100, a random number matrix X with the same number of elements as the micro-nano metal sintering connection layer is generated, and the distribution of the random numbers is [0, 1] uniform distribution; then Gaussian filtering is performed on the random number matrix, and normal-uniform distribution transformation is performed on the data after Gaussian filtering: where x is the data in matrix X, is the transformed data; is the mean of the data in matrix X, is the standard deviation of the data in matrix X, X min , X max are the minimum and maximum values of the data in matrix X, respectively; is the complementary error function: The value interval of the transformed data is [0, 1], and then a threshold p is given, the numbers greater than or equal to p in the data are set to 1, and the numbers less than p are set to 0, and the binary matrix obtained can represent the structure of the micro-nano metal sintering connection layer; the size of the generated pores is controlled by setting the value of the Gaussian filter σ, and the porosity is controlled by p.

3. The method of claim 1, wherein, The second control equation and its weak form are as follows: in V wherein ( on ) where J s represents the diffusion flux of stress migration; D is the mobility coefficient; k is the Boltzmann constant; T is the temperature; is the hydrostatic stress, The weak form of the second control equation is: where and are the trial functions corresponding to c and μ, respectively.

4. The method of claim 1, wherein, In the finite element framework, a fully coupled thermal force solver is used for solving: The thermal coupling field and the phase field are solved in a semi-interlaced way, i.e. the hydrostatic stress output of the n-th step is needed for the n+1-th step .

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