Complex electronic device-oriented thermal-mechanical coupling transient simulation method and system

Abstract

The invention discloses a thermodynamic coupling transient simulation method and system for a complex electronic device, and relates to the technical field of thermodynamic coupling transient simulation. The method comprises the following steps of: discretizing an interpolation approximation equation on a non-equidistant GLL spectrum interpolation node based on an orthogonal basis function to obtain an interpolation function; then a Galerkin method is used, the thermodynamic equation and the solid mechanical equation are weakened through an interpolation function, and a thermodynamic weakening equation and a solid mechanical weakening equation are obtained respectively; and finally, a Newmark-beta implicit iteration method is used to carry out iterative solution on the thermal-mechanical coupling system equation to be solved based on the solved thermodynamic weakening equation and the solid mechanical weakening equation, and a transient temperature field and a stress field are obtained. According to the method, the implicit Newmark-beta method is adopted to support transient simulation of any time step length, so that the transient thermal coupling behavior of a complex electronic device can be accurately simulated, and the calculation efficiency and stability are remarkably improved.

Description

Technical Field

[0001] The present invention relates to the technical field of thermodynamically coupled transient simulation, and particularly to a thermo-mechanical coupled transient simulation method and system for complex electronic devices. Background Art

[0002] With the reduction of the size and the increase of the integration degree of electronic devices, the power consumption and the heat density per unit area increase significantly, resulting in local overheating becoming a serious problem. High temperature not only accelerates material aging, but also triggers a series of heat-related failure modes, such as electromigration, thermal oxidation, solder joint fatigue, etc., thereby reducing the performance, stability and lifespan of the device. Therefore, carrying out thermo-mechanical co-simulation of electronic devices is crucial for the design and application of modern high-performance electronic devices and integrated circuits.

[0003] The implementation of steady-state thermo-mechanical co-analysis is simple, but it cannot provide the transient response of multi-physical field coupling. Transient thermo-mechanical coupling simulation can provide comprehensive and accurate spatio-temporal information of multi-physical fields, but spatio-temporal difference requires huge computing resources. The finite difference time domain method is simple to implement and has high efficiency, but there are staircase errors, making it difficult to accurately depict the complex geometries of electronic devices. The FEM has strong geometric adaptability and a solid theoretical foundation, can adapt to any complex geometric model and minimize model errors. However, the FEM using high-order interpolation has the Runge phenomenon, and using Gaussian integral interpolation has numerical dissipation and numerical dispersion. The spectral element method combines the flexibility of the FEM and the high-order accuracy of the spectral method, and satisfies the exponential convergence property. However, the construction of GLL basis functions depends on hexahedral mesh elements, which significantly reduces the computational efficiency and stability of the algorithm and is difficult to apply to the field of electronic devices with complex geometric features. Summary of the Invention

[0004] The object of the present invention is to provide a thermo-mechanical coupled transient simulation method and system for complex electronic devices, which can not only accurately simulate the transient thermo-mechanical coupling behavior of complex electronic devices, but also significantly improve the computational efficiency and stability.

[0005] To achieve the above object, the present invention provides a thermo-mechanical coupled transient simulation method for complex electronic devices, the method comprising:

[0006] Constructing a thermodynamic equation and a solid mechanics equation;

[0007] Applying the GLL polynomial in the hexahedron to the tetrahedron element through a mathematical transformation to construct an orthogonal basis function of any order;

[0008] Generating non-uniform GLL spectral interpolation nodes of the tetrahedron by using triangle construction transformation;

[0009] On the non-uniform GLL spectral interpolation nodes, discretize the interpolation approximation equation based on the orthogonal basis functions to obtain an interpolation function;

[0010] Using the Galerkin method, weaken the thermodynamic equation and the solid mechanics equation respectively by using the interpolation function, and obtain the weakened thermodynamic equation and the weakened solid mechanics equation respectively;

[0011] Construct the thermo-mechanical coupling system equation to be solved based on the mass matrix, stiffness matrix, damping matrix and thermal stress matrix in different fields;

[0012] Using the Newmark-beta implicit iteration method, iteratively solve the thermo-mechanical coupling system equation to be solved based on the solved weakened thermodynamic equation and the weakened solid mechanics equation, and obtain the transient temperature field and stress field.

[0013] Optionally, the generation of non-uniform GLL spectral interpolation nodes of a tetrahedron by using triangular construction transformation specifically includes:

[0014] Mix the triangular construction transformation into the interior of the tetrahedron to obtain the vector distortion functions of the four faces;

[0015] Construct four scalar surface mixing functions;

[0016] Combine and deform the vector distortion functions of the four faces and the four scalar surface mixing functions to obtain the Warp&Blend transformation;

[0017] Generate non-uniform GLL spectral interpolation nodes of a tetrahedron through the Warp&Blend transformation.

[0018] Optionally, apply the GLL polynomials in a hexahedron to a tetrahedron element through a mathematical transformation to construct orthogonal basis functions of any order. The specific formula is:

[0019]

[0020]

[0021] where r represents the reference coordinate system corresponding to the x-axis, s represents the reference coordinate system corresponding to the y-axis, t represents the reference coordinate system corresponding to the z-axis, i, j and k respectively represent integers, and P i (a) represents the i-th Jacobi polynomial, and ψ m (r, s, t) represents the expression of the basis function on the reference coordinate system, and N represents the order of the basis function.

[0022] Optionally, the thermo-mechanical coupling system equation to be solved is constructed based on the mass matrix, stiffness matrix, damping matrix, and thermal stress matrix in different fields. The specific formula is as follows:

[0023]

[0024] where M T represents the mass matrix in the thermal field, K T represents the stiffness matrix in the thermal field, Q T represents the load matrix in the thermal field, K TS represents the thermal stress matrix in the field of elasticity, K S represents the stiffness matrix in the field of elasticity, N S represents the damping matrix in the field of elasticity, M S represents the mass matrix in the field of elasticity. ns represents the ns-th moment, x = [u T], x represents the unknown quantity to be solved, u represents the stress field, T represents the transient temperature field, the superscript S represents the field of elasticity, and the superscript T represents the thermal field.

[0025] Optionally, the Newmark-beta implicit iteration method is used to iteratively solve the thermo-mechanical coupling system equation to be solved based on the solved thermodynamic weakening equation and the solid mechanics weakening equation, and the transient temperature field and stress field are obtained. The specific formula is as follows:

[0026]

[0027] where Δt represents the time interval, β represents the constant in the implicit iteration method, which is taken as 0.25 here, and K represents the stiffness matrix.

[0028] Optionally, the thermodynamic weakening equation is expressed as:

[0029]

[0030] where ρ represents the density of the medium, represents the partial derivative of temperature with respect to time, T represents the transient temperature field, κ represents the thermal conductivity of the medium, ▽ represents the differential operator, ▽T represents the differential with respect to time, Q represents the externally applied heat source, h represents the heat transfer coefficient, Γ represents the surface integral, T a represents the external reference temperature, Γ q represents the surface integral of the heat dissipation surface, n represents the unit normal vector, L k represents the k-th basis function, V represents the volume integral, and c represents the specific heat capacity.

[0031] Optionally, the solid mechanics weakening equation is expressed as:

[0032]

[0033] Among them, \(u\) represents the displacement vector, \(C\) ij represents the elastic tensor, \(\varepsilon\) ij represents the strain tensor, \(\tau\) represents the stress tensor, \(n\) represents the unit normal vector, \(\alpha\) ij represents the coefficient of thermal expansion, where the subscripts \(i\) and \(j\) take the values 1, 2, and 3 corresponding to the \(x\), \(y\), and \(z\) directions respectively.

[0034] The present invention also provides a thermo-mechanical coupling transient simulation system for complex electronic devices, and the system includes:

[0035] A mechanical equation construction module for constructing thermodynamic equations and solid mechanics equations;

[0036] An orthogonal basis function construction module for applying GLL polynomials in a hexahedron to a tetrahedron element through a mathematical transformation to construct orthogonal basis functions of any order;

[0037] An interpolation node construction module for generating non-uniform GLL spectral interpolation nodes of a tetrahedron by using a triangular construction transformation;

[0038] An interpolation function construction module for discretizing an interpolation approximation equation based on the orthogonal basis functions at the non-uniform GLL spectral interpolation nodes to obtain an interpolation function;

[0039] A weakening equation construction module for using the Galerkin method to weaken the thermodynamic equation and the solid mechanics equation respectively by using the interpolation function to obtain a thermodynamic weakening equation and a solid mechanics weakening equation;

[0040] A thermo-mechanical coupling system equation construction module for constructing a thermo-mechanical coupling system equation to be solved based on mass matrices, stiffness matrices, damping matrices, and thermal stress matrices in different fields;

[0041] An iterative solution module for using the Newmark-beta implicit iterative method to iteratively solve the thermo-mechanical coupling system equation to be solved based on the solved thermodynamic weakening equation and solid mechanics weakening equation to obtain a transient temperature field and a stress field.

[0042] Optionally, the interpolation node construction module specifically includes:

[0043] A vector distortion function generation unit for mixing a triangular construction transformation into the interior of a tetrahedron to obtain vector distortion functions of the four faces;

[0044] A scalar surface mixing function construction unit for constructing four scalar surface mixing functions;

[0045] The Warp&Blend transformation generation unit is used to combine and deform the vector distortion functions of the four faces and the four scalar face blending functions to obtain the Warp&Blend transformation;

[0046] The interpolation node generation unit is used to generate non-uniform GLL spectral interpolation nodes of a tetrahedron through the Warp&Blend transformation.

[0047] The present invention also provides an electronic device, including a storage medium, a processor, and a computer program stored on the storage medium and executable on the processor. When the processor executes the computer program, the above method is implemented.

[0048] According to the specific embodiments provided by the present invention, the following technical effects are disclosed:

[0049] The present invention discloses a thermo-mechanical coupling transient simulation method and system for complex electronic devices. First, on non-uniform GLL spectral interpolation nodes, the interpolation approximation equation is discretized based on orthogonal basis functions to obtain an interpolation function; then the Galerkin method is used to weaken the thermodynamic equation and the solid mechanics equation respectively using the interpolation function to obtain a thermodynamic weakening equation and a solid mechanics weakening equation; finally, the Newmark-beta implicit iteration method is used to iteratively solve the heat-mechanical coupling system equation to be solved based on the solved thermodynamic weakening equation and the solid mechanics weakening equation to obtain a transient temperature field and a stress field. The present invention adopts the implicit Newmark-beta method to support transient simulation with any time step, which can not only accurately simulate the transient thermo-mechanical coupling behavior of complex electronic devices, but also significantly improve the calculation efficiency and stability. In addition, the present invention adopts a collapse transformation method to transform the orthogonal GLL basis functions in a hexahedron reference element into a tetrahedron reference element to achieve the numerical accuracy and stability of arbitrary high-order interpolation. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or in the prior art, the following will briefly introduce the drawings required in the embodiments. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0051] Figure 1 It is a flowchart of the thermo-mechanical coupling transient simulation method for complex electronic devices according to the embodiments of the present invention;

[0052] Figure 2 It is a model diagram of Case 1 of the present invention.

[0053] Figure 3It is a comparison chart of temperature data at the receiving point in Case 1 of the present invention.

[0054] Figure 4 It is a comparison chart of displacement data at the receiving point in Case 1 of the present invention.

[0055] Figure 5 It is a model diagram of Case 2 of the present invention.

[0056] Figure 6 It is a stress distribution diagram of Case 2 of the present invention.

[0057] Figure 7 It is a model diagram of Case 3 of the present invention.

[0058] Figure 8 It is a stress distribution diagram of Case 3 of the present invention. Detailed implementation manners

[0059] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0060] The purpose of the present invention is to provide a thermo-mechanical coupling transient simulation method and system for complex electronic devices, which can not only accurately simulate the transient thermo-mechanical coupling behavior of complex electronic devices, but also significantly improve the calculation efficiency and stability.

[0061] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0062] As Figure 1 shown, the present invention discloses a thermo-mechanical coupling transient simulation method for complex electronic devices. The method includes:

[0063] Step S1: Construct thermodynamic equations and solid mechanics equations.

[0064] Step S2: Apply the GLL polynomial in the hexahedron to the tetrahedron element through mathematical transformation to construct orthogonal basis functions of any order.

[0065] Step S3: Use the triangle construction transformation to generate non-uniform GLL spectral interpolation nodes of the tetrahedron.

[0066] Step S4: Discretize the interpolation approximation equation based on the orthogonal basis functions at the non-uniform GLL spectral interpolation nodes to obtain an interpolation function.

[0067] Step S5: Using the Galerkin method, the thermodynamic equation and the solid mechanics equation are weakened respectively by using the interpolation function to obtain the thermodynamic weakened equation and the solid mechanics weakened equation.

[0068] Step S6: Based on the mass matrix, stiffness matrix, damping matrix and thermal stress matrix in different fields, the thermo-mechanical coupling system equation to be solved is constructed.

[0069] Step S7: Using the Newmark-beta implicit iteration method, the thermo-mechanical coupling system equation to be solved is iteratively solved based on the solved thermodynamic weakened equation and solid mechanics weakened equation to obtain the transient temperature field and stress field.

[0070] The following is a detailed discussion of each step:

[0071] To achieve thermo-mechanical coupling transient simulation, it is necessary to solve the thermodynamic equation and the solid mechanics equation.

[0072] Step S1: Construct the thermodynamic equation and the solid mechanics equation, specifically including:

[0073] Step S11: Based on the principle of heat conservation, the thermodynamic equation is constructed. The thermodynamic equation is:

[0074]

[0075] where ρ represents the density of the medium, c p represents the specific heat capacity of the medium, T represents the temperature to be solved, κ represents the thermal conductivity of the medium, Q represents the externally applied heat source, represents the partial derivative of temperature with respect to time, ▽ represents the differential operator, and ▽T represents the differential with respect to time.

[0076] In the thermodynamics part, the calculation of the thermodynamic equation needs to be completed in cooperation with the convective heat flux equation. The convective heat flux equation is:

[0077] -n·q = h(T ext -T) (2)

[0078] where n represents the unit normal vector, q represents the heat flux vector, h represents the heat transfer coefficient, and T ext represents the temperature of the external fluid far from the boundary.

[0079] Step S12: Based on the principle of kinetic energy conservation, the solid mechanics equation is constructed. The specific formula is:

[0080]

[0081] The constitutive relation in formula (3) is

[0082]

[0083] Among them, (i, j, k, l) represents the subscript of the tensor, indicating the direction in three-dimensional space. In the Cartesian coordinate system, (i, j, k, l = 1, 2, 3) respectively correspond to the directions of the (x, y, z) axes. Therefore, x i represents the i-th spatial coordinate, and u i is the i-th component of the displacement vector u. c ijkl is the fourth-order elastic tensor, ε ij and τ ij are the strain and stress tensors respectively, and are the elastic tensor component and the thermal strain tensor component respectively, and α ij represents the coefficient of thermal expansion.

[0084] In mechanical analysis, it is necessary to cooperate with boundary conditions to complete the calculation. Therefore, the present invention uses the absorbing boundary condition (ABC) to simulate the unbounded region. The specific formula of the absorbing boundary condition is

[0085]

[0086] Among them, V n and V t respectively represent the normal component and the tangential component of the elastic wave velocity along the absorbing boundary, V p represents the P-wave velocity, V s represents the S-wave velocity, λ and μ respectively represent the Lamé parameters, n represents the unit normal vector, ρ represents the density of the medium, τ represents the stress tensor, represents the time partial derivative of the displacement.

[0087] Step S2: Apply the GLL polynomial in the hexahedron to the tetrahedron element through mathematical transformation to construct the orthogonal basis function of any order. The specific formula is:

[0088]

[0089] Among them, N is the order of the basis function, and the total number of nodes on a tetrahedron satisfies

[0090] N p = ((N + 1)(N + 2)(N + 3)) / 6 (8)

[0091] is the n-th order Jacobi polynomial, defined

[0092]

[0093] When both α and β are 0, the Jacobi polynomial degenerates into the Legendre polynomial; (a, b, c) ∈ [-1, 1] 3, a, b, c are the coordinates in the hexahedron; (r, s, t) ∈ T 3 , T 3 = {(r, s, t)|r, s, t ≥ -1; r + s + t ≤ -1}, r, s, t are the coordinates in the tetrahedron; the coordinates in the tetrahedron and the coordinates in the hexahedron can be transformed through formula (7).

[0094] The present invention adopts a collapse transformation method to convert the orthogonal GLL basis functions in the hexahedron reference element into the tetrahedron reference element to achieve the numerical accuracy and stability of arbitrary high-order interpolation.

[0095] Step S3: Generate non-uniform GLL spectral interpolation nodes of the tetrahedron by using triangle construction transformation. The specific formula is as follows:

[0096] Step S31: Mix the triangle construction transformation into the interior of the tetrahedron to obtain the vector distortion functions of these four faces. The specific formula is as follows:

[0097]

[0098] Among them, g1 and g2 respectively represent the vectors calculated by the barycentric coordinates, t f,1 , t f,2 respectively represent the two vectors forming an orthogonal coordinate system on the plane of face f; w 1 , w 2 , w 3 , w 4 respectively represent the distortion functions of each face on the tetrahedron, λ 1 , λ 2 , λ 3 , λ 4 respectively represent the four centroids on the equilateral tetrahedron.

[0099] The equilateral tetrahedron centered at the origin is specified in the Cartesian coordinate system as:

[0100]

[0101] Step S32: Construct four scalar face mixing functions as follows:

[0102]

[0103] Among them, b 1 , b 2 , b 3 , b 4 respectively represent the four scalar face mixing functions.

[0104] Step S33: Combine and deform the vector distortion functions of the four faces and the four scalar face mixing functions to obtain the Warp&Blend transformation. The specific formula is as follows:

[0105] g(λ 1 ,λ 2 ,λ 3 ,λ 4 ) = b 1 w 1 +b 2 w 2 +b 3 w 3 +b 4 w 4 (13)

[0106] Step S34: Generate non - equidistant GLL spectral interpolation nodes of the tetrahedron through Warp&Blend transformation. Specifically,

[0107] Generate interpolation points on the equilateral tetrahedron through Warp&Blend transformation and then map them to the reference tetrahedron to construct non - equidistant GLL spectral interpolation nodes that form the Vandermonde matrix.

[0108] Generate non - equidistant GLL spectral interpolation nodes of the reference element of the tetrahedron through Warp&Blend transformation. By forming the Vandermonde matrix with the interpolation nodes, the numerical integration calculation of the nodes can be directly realized through the Vandermonde matrix, thereby improving the calculation efficiency of matrix assembly and avoiding numerical dissipation and numerical dispersion that may be caused by Gaussian integration.

[0109] Step S4: Discretize the interpolation approximation equation based on orthogonal basis functions at the non - equidistant GLL spectral interpolation nodes to obtain the interpolation function. The specific formula is as in (17).

[0110] The present invention uses the interpolation approximation equation to discretize the entire region to be calculated into many tetrahedrons, and uses the interpolation approximation unknown u on each tetrahedron. The specific interpolation approximation equation is as follows:

[0111]

[0112] where ξ i represents the nodes on a single tetrahedron, N p represents the total number of nodes on a single tetrahedron, represents the polynomial coefficient, ψ n-1 (ξ i ) represents the value of the (n - 1) - th basis function at the i - th reference node, and u(ξ i ) represents the value of the unknown at the i - th reference node.

[0113] Discretize the interpolation approximation equation based on orthogonal basis functions, and its discrete function is

[0114]

[0115] The relationship between the unknown and the orthogonal basis functions can be obtained:

[0116] V T L = ψ(16)

[0117] From this, the interpolation functions required to construct the weak form of the equation are derived:

[0118] L(r)=(V T ) -1 ψ(r)(17)

[0119] where L(r) represents the interpolation function in the reference coordinate system, V T represents the transpose of the Vandermonde matrix, and ψ(r) represents the basis function in the reference coordinate system.

[0120] Step S5: Using the Galerkin method, the interpolation functions are used to weaken the thermodynamics equation and the solid mechanics equation respectively, and the weakened thermodynamics equation and the weakened solid mechanics equation are obtained respectively; among them, the weakened thermodynamics equation is:

[0121]

[0122] The weakened solid mechanics equation is:

[0123]

[0124] where <.> v and <.> Γ represent volume integral and surface integral respectively, and C ij (i,j = 1,2,3) represents a part of the fourth-order elastic tensor.

[0125] The present invention mainly combines the mass matrix and the stiffness matrix to solve the weakened thermodynamics equation and the weakened solid mechanics equation.

[0126] In the TSEM method, when performing volume integral and surface integral, there is no need to use Gaussian integration points, but the calculation is carried out through the Vandermonde matrix. The following takes the calculation of the mass matrix and the stiffness matrix in the one-dimensional case as an example for illustration:

[0127] The expression of the mass matrix is

[0128]

[0129] The expression of the stiffness matrix

[0130]

[0131] Equations (20) and (21) then give the method for calculating equations (18) and (19). Thus, the present invention can solve equations (18) and (19).

[0132] Step S6: Construct a thermo-mechanical coupling system equation to be solved based on the mass matrix, stiffness matrix, damping matrix, and thermal stress matrix in different fields, specifically including:

[0133] In TSEM, the system matrix of thermo-mechanical coupling can be written as

[0134]

[0135] where the superscript T represents the thermal field, and the mass matrix M T , the stiffness matrix K T , the load matrix Q T The expressions are as follows:

[0136]

[0137] The system matrix of thermo-mechanical coupling in elasticity can be written as

[0138]

[0139] where the superscript S represents the field of elasticity mechanics, the mass matrix M S , the stiffness matrix K S , the damping matrix N S , the thermal stress matrix K TS The expressions are as follows:

[0140]

[0141] Combining equation (22) and equation (24) together, equation (26) obtained is the thermo-mechanical coupling system equation to be solved, which can be written as

[0142]

[0143] where x = [u T], and are the first and second derivatives of time respectively, the superscript n represents the nth time step, is

[0144]

[0145] Step S7: Use the Newmark-beta implicit iteration method to iteratively solve the thermo-mechanical coupling system equation to be solved based on the solved thermodynamics weakening equation and solid mechanics weakening equation, and obtain the transient temperature field and stress field.

[0146]

[0147] Among them, Δt represents the increment of the time step, that is, the time interval. In this way, by solving formula (31) at each time step, the values of the unknown quantity x = [u T] at each time step can be obtained, and then the values of the displacement field and the temperature field can be obtained. Among them, x represents the overall unknown quantity, u represents the unknown displacement value, T represents the unknown temperature value, and the superscript represents the transpose.

[0148] The present invention uses the Newmark-beta implicit iteration method to achieve unconditional stability during time integration, and at the same time supports the independent inversion of the system matrices of the temperature field and the stress field, avoiding the increase in computational resource consumption caused by the coupling of multi-physics equations. In addition, the nodal numerical integration calculation is directly realized through the Vandermonde matrix, avoiding the problems of numerical dissipation and numerical dispersion caused by Gaussian integration in the traditional finite element method.

[0149] The present invention uses TSEM to simulate the thermo-mechanical coupling of complex electronic devices. Through quantitative comparison with COMSOL software, the advantages of TSEM in numerical accuracy, efficiency, and stability can be demonstrated.

[0150] The present invention provides a thermo-mechanical coupling transient simulation method for complex electronic devices, which can realize the thermo-mechanical coupling transient simulation of micro-resistance beam models, chip models, and chip array models.

[0151] The present invention also provides a thermo-mechanical coupling transient simulation system for complex electronic devices, and the system includes:

[0152] A mechanical equation construction module for constructing thermodynamic equations and solid mechanics equations.

[0153] An orthogonal basis function construction module for applying the GLL polynomials in the hexahedron to the tetrahedral elements through mathematical transformation to construct orthogonal basis functions of any order.

[0154] An interpolation node construction module for generating non-uniform GLL spectral interpolation nodes of the tetrahedron by using triangular construction transformation.

[0155] An interpolation function construction module for discretizing the interpolation approximation equation based on the orthogonal basis functions at the non-uniform GLL spectral interpolation nodes to obtain interpolation functions.

[0156] A weakening equation construction module for using the Galerkin method to weaken the thermodynamic equation and the solid mechanics equation respectively by using the interpolation functions to obtain a thermodynamic weakening equation and a solid mechanics weakening equation respectively.

[0157] A thermo-mechanical coupling system equation construction module is used to construct a thermo-mechanical coupling system equation to be solved based on mass matrices, stiffness matrices, damping matrices, and thermal stress matrices in different fields.

[0158] An iterative solution module is used to iteratively solve the thermo-mechanical coupling system equation to be solved using the Newmark-beta implicit iterative method based on the solved thermodynamic weakening equation and the solid mechanics weakening equation, and obtain a transient temperature field and stress field.

[0159] As an optional implementation manner, the interpolation node construction module of the present invention specifically includes:

[0160] A vector distortion function generation unit is used to mix the triangle construction transformation into the interior of the tetrahedron to obtain vector distortion functions for these four faces.

[0161] A scalar surface mixing function construction unit is used to construct four scalar surface mixing functions.

[0162] A Warp&Blend transformation generation unit is used to combine and deform the vector distortion functions of the four faces and the four scalar surface mixing functions to obtain a Warp&Blend transformation.

[0163] An interpolation node generation unit is used to generate non-uniform GLL spectral interpolation nodes of the tetrahedron through the Warp&Blend transformation.

[0164] The present invention also discloses an electronic device, including a storage medium, a processor, and a computer program stored on the storage medium and executable on the processor. When the processor executes the computer program, the above method is implemented.

[0165] Case comparison:

[0166] (1). Model discretization and parameter setting. The computational domain is divided into tetrahedral meshes, and the element size is determined according to the minimum wavelength. Material parameters (density, specific heat capacity, thermal conductivity, thermal expansion coefficient, etc.) are set layer by layer.

[0167] (2). Generate non-uniform GLL nodes, construct a Vandermonde matrix to calculate integrals. Assemble the global mass matrix and stiffness matrix, and apply convective and absorption boundary conditions. Use the implicit Newmark-beta method to iteratively solve the transient temperature field and stress field.

[0168] (3). Numerical verification and comparison. Compare the calculation results obtained using the TSEM solver based on the implicit Newmark-beta method with the commercial software COMSOL.

[0169] Case 1: Micro resistorBeam model is asFigure 2 As shown, this is a radiator model, which is a symmetric model with aluminum on the top and a silicon chip at the bottom. The material parameters of the Micro resistor Beam model are shown in Table 1:

[0170] Table 1 Material parameters of the model in Case 1

[0171]

[0172]

[0173] From Figure 3 and Figure 4 it can be seen that the error between the results obtained by TSEM calculation and COMOSL is very small, which proves the high-precision characteristics of the TSEM algorithm.

[0174] The consumption between the two calculation methods is shown in Table 2.

[0175] Table 2 Comparison of calculation consumption in Case 1

[0176] Solvers DoF Memory(GB) TimeStep Time(s) COMSOL 96424 5.4 1200 608 TSEM 96424 3.1 1200 87

[0177] It can be seen from Table 2 that the efficiency of the TSEM solver is significantly higher than that of the COMSOL solver. Specifically, under the same degrees of freedom in calculation, the efficiency of TSEM is 7 times that of the COMSOL solver, indicating the efficiency of the TSEM algorithm.

[0178] Case 2: Chip model, as Figure 5 shown, the uppermost cuboid is a silicon chip, which is connected to the copper panel through the aluminum solder balls below, and the resin is at the bottom. The material parameters of the chip model are shown in Table 3 below:

[0179] Table 3 Material parameters of the model in Case 2

[0180]

[0181]

[0182] Figure 6 is the stress distribution at the 30th second after the chip generates heat. From Figure 6 it can be seen that the positions with relatively large stress are mainly at the contact position between the chip and the solder ball, and there is a possibility of fracture at this position.

[0183] Case 3: Chip array model, as Figure 7 shown, the chip array is composed of 9 identical chips combined together, and the length of each chip is 0.036 m and the width is 0.038 m. The material parameters of the chip array model are shown in Table 4 below:

[0184] Table 4 Material Parameters of the Model in Case 3

[0185]

[0186]

[0187] From Figure 8 it can be seen that the stress is mainly distributed at the edge of the chip array. From this invention, it can be known that in such a chip array, the places at the four corners are most likely to break. From Figure 8 it can be seen that the stress is larger at the places where the chips generate heat and smaller in other places, and the stress on each chip is symmetrically distributed.

[0188] (4) Result output. Generate contour maps of temperature, displacement, and stress distribution, locate high-heat-generation, large-deformation, and stress-concentration regions, and guide heat dissipation design and reliability optimization.

[0189] Compared with the existing numerical discretization schemes, the innovation and advantages of TSEM are as follows:

[0190] (1) Improved geometric adaptability: Compatible with the geometric structures of complex electronic devices through tetrahedral meshes and collapse transformations.

[0191] (2) Optimized computational efficiency: Vandermonde integration replaces Gaussian integration, improving the matrix assembly efficiency.

[0192] (3) Unconditional stability: The implicit Newmark-beta method supports any time step, improving the transient simulation efficiency.

[0193] (4) Reduced resource consumption: The segregated solver reduces memory occupancy, and the memory requirement is reduced under the same degrees of freedom.

[0194] In this specification, each embodiment is described in a progressive manner. The key point of each embodiment is to illustrate the differences from other embodiments. For the same or similar parts among the embodiments, reference can be made to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and reference can be made to the description in the method part for the relevant parts.

[0195] In this article, specific examples are used to elaborate on the principle and implementation manner of the present invention. The descriptions of the above embodiments are only used to help understand the method of the present invention and its core idea; at the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation manner and application scope. In summary, the content of this specification should not be construed as a limitation to the present invention.

Claims

1. A thermal-mechanical coupling transient simulation method for complex electronic devices, characterized in that, The method includes: Constructing a thermodynamic equation and a solid mechanics equation; Applying the GLL polynomials in a hexahedron to a tetrahedron element through mathematical transformation to construct orthogonal basis functions of any order; Generating non-equidistant GLL spectral interpolation nodes of a tetrahedron by using a triangular construction transformation; Discretizing an interpolation approximation equation based on the orthogonal basis functions at the non-equidistant GLL spectral interpolation nodes to obtain an interpolation function; Using the Galerkin method, weakening the thermodynamic equation and the solid mechanics equation respectively by using the interpolation function to obtain a thermodynamic weakened equation and a solid mechanics weakened equation; Constructing a thermo-mechanical coupling system equation to be solved based on mass matrices, stiffness matrices, damping matrices and thermal stress matrices in different fields; Using the Newmark-beta implicit iteration method, iteratively solving the thermo-mechanical coupling system equation to be solved based on the solved thermodynamic weakened equation and solid mechanics weakened equation to obtain a transient temperature field and a stress field.

2. The method for thermo-mechanical coupling transient simulation for complex electronic devices according to claim 1, wherein The generating non-equidistant GLL spectral interpolation nodes of a tetrahedron by using a triangular construction transformation specifically includes: Mixing a triangular construction transformation into the interior of a tetrahedron to obtain vector distortion functions of the four faces; Constructing four scalar surface mixing functions; Combining and deforming the vector distortion functions of the four faces and the four scalar surface mixing functions to obtain a Warp&Blend transformation; Generating non-equidistant GLL spectral interpolation nodes of a tetrahedron through the Warp&Blend transformation.

3. A transient simulation method for thermo-mechanical coupling of complex electronic devices according to claim 1, characterized in that Applying the GLL polynomials in a hexahedron to a tetrahedron element through mathematical transformation to construct orthogonal basis functions of any order, and the specific formula is: where r represents the reference coordinate system corresponding to the x-axis, s represents the reference coordinate system corresponding to the y-axis, t represents the reference coordinate system corresponding to the z-axis, i, j, and k are integers respectively, and P i (a) represents the i-th Jacobi polynomial, and ψ m (r, s, t) represents the basis function expression on the reference coordinate system, and N represents the order of the basis function.

4. A transient simulation method for thermo-mechanical coupling of complex electronic devices according to claim 1, characterized in that The constructing a thermo-mechanical coupling system equation to be solved based on mass matrices, stiffness matrices, damping matrices and thermal stress matrices in different fields, and the specific formula is: Among them, M T represents the mass matrix in the field of thermotics, K T represents the stiffness matrix in the field of thermotics, Q T represents the load matrix in the field of thermotics, K TS represents the thermal stress matrix in the field of elasticity, K S represents the stiffness matrix in the field of elasticity, N S represents the damping matrix in the field of elasticity, M S represents the mass matrix in the field of elasticity, ns represents the ns-th moment, x = [u T], x represents the unknown quantity to be solved, u represents the stress field, T represents the transient temperature field, the superscript S represents the field of elasticity, and the superscript T represents the field of thermotics.

5. A transient simulation method for thermo-mechanical coupling of complex electronic devices according to claim 4, characterized in that The using the Newmark-beta implicit iteration method, iteratively solving the thermo-mechanical coupling system equation to be solved based on the solved thermodynamic weakened equation and solid mechanics weakened equation to obtain a transient temperature field and a stress field, and the specific formula is: Where, Δt represents a time interval, β represents a constant in the implicit iteration method, taking 0.25 here, and K represents a stiffness matrix.

6. A transient simulation method for thermo-mechanical coupling of complex electronic devices according to claim 1, characterized in that The thermodynamic weakened equation is expressed as: where ρ represents the density of the medium, represents the partial derivative of temperature with respect to time, T represents the transient temperature field, κ represents the thermal conductivity of the medium, ▽ represents the differential operator, ▽T represents the differential with respect to time, Q represents the externally applied heat source, h represents the heat transfer coefficient, Γ represents the surface integral, T a represents the external reference temperature, Γ q represents the surface integral of the heat dissipation surface, n represents the unit normal vector, L k represents the k-th basis function, V represents the volume integral, and c represents the specific heat capacity.

7. According to a thermo-mechanical coupling transient simulation method for complex electronic devices as claimed in claim 6, It is characterized in that The solid mechanics weakened equation is expressed as: where, u represents the displacement vector, C ij represents the elastic tensor, ε ij represents the strain tensor, τ represents the stress tensor, n represents the unit normal vector, ɑ ij represents the coefficient of thermal expansion, where the subscripts i, j take the values 1, 2, 3 corresponding to the x, y, z directions respectively.

8. A thermal-mechanical coupling transient simulation system for complex electronic devices, characterized in that, The system includes: A mechanical equation construction module for constructing a thermodynamic equation and a solid mechanics equation; An orthogonal basis function construction module for applying the GLL polynomials in a hexahedron to a tetrahedron element through mathematical transformation to construct orthogonal basis functions of any order; An interpolation node construction module for generating non-equidistant GLL spectral interpolation nodes of a tetrahedron by using a triangular construction transformation; An interpolation function construction module for discretizing an interpolation approximation equation based on the orthogonal basis functions at the non-equidistant GLL spectral interpolation nodes to obtain an interpolation function; A weakening equation construction module, which is used to weaken the thermodynamic equation and the solid mechanics equation respectively by using the Galerkin method with the interpolation function, and obtain a thermodynamic weakening equation and a solid mechanics weakening equation respectively; A thermal-mechanical coupling system equation construction module, which is used to construct a thermal-mechanical coupling system equation to be solved based on the mass matrix, stiffness matrix, damping matrix and thermal stress matrix in different fields; An iterative solution module, which is used to iteratively solve the thermal-mechanical coupling system equation to be solved based on the solved thermodynamic weakening equation and solid mechanics weakening equation by using the Newmark-beta implicit iteration method, and obtain a transient temperature field and a stress field.

9. A thermo-mechanical coupling transient simulation system for complex electronic devices according to claim 8, characterized in that, The interpolation node construction module specifically includes: A vector distortion function generation unit, which is used to mix the triangle construction transformation into the interior of the tetrahedron to obtain the vector distortion functions of these four faces; A scalar surface mixing function construction unit, which is used to construct four scalar surface mixing functions; A Warp&Blend transformation generation unit, which is used to combine and deform the vector distortion functions of the four faces and the four scalar surface mixing functions to obtain a Warp&Blend transformation; An interpolation node generation unit, which is used to generate non-uniform GLL spectral interpolation nodes of the tetrahedron through the Warp&Blend transformation.

10. An electronic device, comprising a storage medium, a processor, and a computer program stored on the storage medium and executable on the processor, characterized in that, When the processor executes the computer program, the method according to any one of claims 1 to 7 is implemented.

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