2.5 DChiplet structure physical field coupling characteristic analysis method

Abstract

The invention discloses a 2.5 D Chiplet structure physical field coupling characteristic analysis method. The method specifically comprises the following steps: step 1, adding a solid heat transfer physical field interface, a solid mechanical physical field interface and a thermal expansion physical field interface to a 2.5 D Chiplet structure; 2, boundary conditions are added to a solid heat transfer physical field interface, and the temperature distribution condition of the 2.5 D Chiplet structure is obtained; step 3, solving the deformation and stress distribution conditions of the 2.5 D Chiplet structure; 4, the solid heat transfer physical field interface and the solid mechanical physical field interface are coupled through the expansion physical field interface; and 5, carrying out grid division on the 2.5 D Chiplet structure to obtain the temperature, stress and deformation distribution conditions of the structure. The method can accurately predict the distribution of the temperature field and the force field on the packaging chip, and facilitates the thermal analysis of the packaging structure.

Description

Technical Field

[0001] The present invention belongs to the field of advanced packaging technology and relates to a method for analyzing physical field coupling characteristics of a 2.5D chiplet structure. Background Art

[0002] In recent years, with the rapid development of semiconductor integration technology, the size of semiconductor processes has gradually approached its physical limit, and semiconductor technology has entered the "post-Moore era". However, with the continuous emergence of applications such as high-performance computing (HPC), artificial intelligence (AI), and 5G, the demand for high bandwidth, high computing power, low latency, and low power consumption has become increasingly strong. In order to solve the above problems, the industry has proposed 2.5D Chiplet advanced packaging technology as an important means to continue Moore's Law.

[0003] 2.5D Chiplet advanced packaging technology can greatly improve the integration density of multiple chips and components, realize the stacking and vertical interconnection between chips, and meet the needs of miniaturization, multi-function and heterogeneous structure device integration of chips. However, due to the higher integration density of the chiplet packaging structure, the heat flux density per unit area of ​​the chip increases during normal operation, and the effective heat dissipation area decreases, which greatly tests the thermomechanical stability and thermoelectric reliability of the entire packaging structure. In addition, the increase in integration density will cause a sharp increase in the current density inside the structure, accompanied by a sharp increase in temperature, which will accelerate the aging of transistors and interconnects, thereby reducing the life of the equipment and interconnects, and in high current density areas, it is also necessary to face problems such as electromigration. In addition, large temperature gradients and mismatched thermal expansion coefficients (CTE, Coefficient of Thermal Expansion) between materials will produce induced gravity, resulting in warping of the entire packaging structure, solder ball shedding and other problems. Therefore, it is very important to perform multi-physics field coupling analysis on 2.5D packaging structures. Summary of the invention

[0004] The purpose of the present invention is to provide a method for analyzing the physical field coupling characteristics of a 2.5D chiplet structure, which can accurately predict the temperature field and force field distribution on a 2.5D chiplet structure chip, and facilitate thermal analysis of the packaging structure.

[0005] The technical solution adopted by the present invention is a method for analyzing the physical field coupling characteristics of a 2.5D chiplet structure, which specifically includes the following steps:

[0006] Step 1: Add a solid heat transfer physics interface, a solid mechanics physics interface, and a thermal expansion physics interface to the 2.5D chiplet structure.

[0007] Step 2: Add boundary conditions to the solid heat transfer physics interface to obtain the temperature distribution of the 2.5D chiplet structure.

[0008] Step 3: Solve the deformation and stress distribution of the 2.5D chiplet structure based on the solid mechanics physics interface;

[0009] Step 4, coupling the Solid Heat Transfer Physics Interface and the Solid Mechanics Physics Interface through the Expansion Physics Interface;

[0010] Step 5: Mesh the 2.5D chiplet structure to obtain the temperature, stress, and deformation distribution of the 2.5D chiplet structure.

[0011] The present invention is also characterized in that:

[0012] In step 1, the 2.5D chiplet structure includes three layers. The top layer includes two memory chips and a logic chip arranged in a horizontal direction, and the logic chip is located between the two memory chips; the middle layer includes an upper silicon dioxide layer, a silicon middle layer and a lower silicon dioxide layer arranged from top to bottom, and a TSV array is arranged in the silicon middle layer; the bottom layer includes a horizontally arranged substrate.

[0013] The memory chip is connected to the upper silicon dioxide layer via solder ball A; the logic chip is connected to the upper silicon dioxide layer via solder ball B; and the lower silicon dioxide layer is connected to the substrate via solder ball C.

[0014] The materials used for the two memory chips and the logic chip are silicon; the material of the substrate is FR4; the materials of solder balls A, B, and C are all 64Sn-40Pb; and the material of TSV is copper.

[0015] The specific process of step 2 is:

[0016] In step 2.1, add the following boundary conditions to the Heat Transfer in Solids physics interface:

[0017] a) Add a fixed heat source Q to the two memory chips A and the logic chip;

[0018] b) Set the working temperature T of the boundary condition added to the Solid Heat Transfer physics interface e ;

[0019] c) Add heat flux boundary conditions, i.e., heat transfer coefficient h, to the outer surface of the entire 2.5D chiplet structure;

[0020] Step 2.2: Solve the heat transfer equations involved in the following solid heat transfer multiphysics interface according to the boundary conditions a) to c) set in step 2.1 to obtain the distribution of the temperature T of the 2.5D chiplet structure:

[0021] ρC p u▽T+▽·(-K▽T)=Q (1)

[0022] In the formula, ρ represents the material density, C P represents the constant pressure heat capacity of the material, u represents the velocity field, which is usually defined directly or comes from other physics interfaces, ▽T represents the temperature gradient, and K represents the thermal conductivity of the material;

[0023] The equations involved in the heat flux boundary condition are:

[0024] -n·(-K▽T)=h(T e -T) (2)

[0025] Where n is an internal parameter of the physical field.

[0026] The specific process of step 3 is:

[0027] Step 3.1: Since the entire 2.5D chiplet structure is a symmetrical structure, the entire 2.5D chiplet structure is cut along the quarter-cutting lines OE and OF, and symmetric boundary conditions are added to the cut surface.

[0028] Step 3.2, for the quarter 2.5D chiplet structure divided in step 3.1, add a specified displacement at one of the vertices D of the substrate, and the displacement along point D in the x and y directions is a free deformation, and the position along point D in the z direction remains unchanged;

[0029] Step 3.3, based on the conditions set in step 3.2, solve the following equations (3) to (5) to obtain the deformation and stress distribution of the entire 2.5D Chiplet structure:

[0030] Stationary equations for the Solid Mechanics physics interface:

[0031] -▽S=f (3)

[0032] In the formula, ▽ represents gradient, S represents stress, and f represents body force;

[0033] Hooke's law equation:

[0034] S-(S0+S ext +S q )=C:(ε-(ε0+ε th +ε hs +ε pl+ε cr )) (4)

[0035] In the formula, S represents stress, S0 represents prestress, S ext represents the external stress, S q represents viscous stress, C represents elastic matrix, ε represents elastic strain, ε0 represents prestrain, ε th represents thermal strain, ε hs Indicates infiltration and expansion; ε pl represents the plastic strain, ε cr represents creep, where ε pl , ε cr Only for nonlinear structural materials;

[0036] The relationship equation between strain and displacement is:

[0037]

[0038] In the formula, represents displacement and ▽ represents gradient.

[0039] The specific process of step 4 is:

[0040] The temperature T of the 2.5D chiplet structure obtained in step 2 is used as the load. The solid heat transfer physics interface and the solid mechanics physics interface are coupled through the thermal expansion physics interface. The equations involved in the thermal expansion physics interface are as follows:

[0041] ε th =α(T)(TT ref ) (6)

[0042] Where α is the thermal expansion coefficient, T ref Indicates volume reference temperature.

[0043] The beneficial effects of the present invention are as follows:

[0044] (1) The present invention first establishes a 2.5D packaging structure model, and then puts the established model into the solid mechanics multi-physics field interface, solid heat transfer multi-physics field interface, and thermal expansion multi-physics field interface in the COMSOL software for coupled simulation analysis, and finally obtains the temperature distribution, stress distribution, and deformation of the entire structure.

[0045] (2) Since the 2.5D Chiplet structure has a higher integration level than the traditional packaging structure, the high integration density leads to a sharp increase in the current density inside the structure, resulting in a sharp increase in temperature, which will accelerate the aging of transistors and interconnects, thereby reducing the life of the equipment and interconnects. High temperature will also cause reliability problems such as warping of the structure. This method can accurately predict the temperature distribution, stress distribution and deformation of the entire packaging structure. Based on the obtained temperature, stress and deformation results, it can guide us to perform thermal analysis and stress analysis on the entire structure, and can be used to assist in the physical optimization design of the 2.5D Chiplet structure, thereby improving the reliability of the entire packaging structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 This is a flow chart of the physical field coupling characteristics analysis method of the 2.5D chiplet structure of the present invention;

[0047] Figure 2 It is a front view of the 2.5D Chiplet structure used in the 2.5D Chiplet structure physical field coupling characteristic analysis method of the present invention;

[0048] Figure 3 It is a quarter of the model position selected during the simulation process of the 2.5D chiplet structure physical field coupling characteristic analysis method of the present invention;

[0049] Figure 4 It is a front view of a quarter 2.5D chiplet structure used in the 2.5D chiplet structure physical field coupling characteristic analysis method of the present invention;

[0050] Figure 5 It is a partial enlarged view of the middle layer of the 2.5D Chiplet structure used in the 2.5D Chiplet structure physical field coupling characteristic analysis method of the present invention;

[0051] Figure 6 A top view of the temperature distribution of the entire 2.5D Chiplet structure in the 2.5D Chiplet structure physical field coupling characteristic analysis method of the present invention;

[0052] Figure 7 It is a front view of the temperature distribution of the entire 2.5D Chiplet structure in the 2.5D chiplet structure physical field coupling characteristic analysis method of the present invention;

[0053] Figure 8 The deformation distribution of the entire 2.5D Chiplet structure in the physical field coupling characteristic analysis method of the present invention;

[0054] Fig. 9 It is a 2.5D Chiplet structure diagram after deformation in the 2.5D Chiplet structure physical field coupling characteristic analysis method of the present invention;

[0055] Fig.10 It is the stress distribution diagram of the entire 2.5D Chiplet structure in the 2.5D Chiplet structure physical field coupling characteristic analysis method of the present invention.

[0056] In the figure, 1. substrate, 2. memory chip, 3. logic chip, 5. selected quarter model position, 6. solder ball A, 7. solder ball B, 8. solder ball C, 9. silicon middle layer, 10. upper silicon dioxide layer, 11. lower silicon dioxide layer. DETAILED DESCRIPTION

[0057] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0058] Example 1

[0059] The physical field coupling characteristic analysis method of the 2.5D chiplet structure of the present invention mainly considers the electrical performance, thermal performance, and stress performance of the entire packaging structure under normal working conditions. Figure 1 As shown, the specific steps include:

[0060] Step 1: Use COMSOL's own geometric modeling tools or professional modeling software such as Solidwork and CAD to effectively model the 2.5D chiplet structure for subsequent analysis steps. The design parameters of the entire 2.5D chiplet structure model in step 1 are as follows:

[0061]

[0062]

[0063] In Table 1, R1 represents the radius of solder ball B7, and H1 represents the height of solder ball B7; R2 represents the radius of solder ball A6, and H2 represents the height of solder ball A6; R3 represents the radius of solder ball C8, and H3 represents the height of solder ball C8; R TSV represents the radius of TSV, H TSV Indicates the height of TSV.

[0064] The 2.5D chiplet structure model established based on the design parameters given above is as follows: Figure 2 , Figure 3 The entire model mainly includes three layers. The top layer includes a memory chip 2, a logic chip 3 and a memory chip 2 arranged horizontally in sequence. The materials used for the two memory chips 2 and the logic chip 3 are silicon. Figure 4As shown, the middle layer includes an upper silicon dioxide layer 10, a silicon middle layer 9 and a lower silicon dioxide layer 11; the bottom layer includes a (packaging) substrate 1, and the material of the substrate 1 is FR4.

[0065] The memory chip 2 is connected to the upper silicon dioxide layer 10 via solder ball A6, the logic chip 3 is connected to the upper silicon dioxide layer 10 via solder ball B7, and the lower silicon dioxide layer 11 is connected to the substrate 1 via solder ball C8. The materials of solder ball A6, solder ball B7, and solder ball C8 are all 64Sn-40Pb.

[0066] The TSV array is placed inside the silicon intermediate layer 9 , and the upper and lower ends of each TSV are connected to the upper silicon dioxide layer 10 and the lower silicon dioxide layer 11 respectively. The material of the TSV is copper.

[0067] Step 2: Import the package model created in step 1 into COMSOL software and add the required materials for each part. The materials are generally from the material library that comes with COMSOL software, or you can create new materials yourself. If you directly use the geometric modeling tool that comes with COMSOL for modeling, there is no need to import.

[0068] Step 3: Add a solid heat transfer physics interface, a solid mechanics physics interface, and a thermal expansion physics interface to the 2.5D chiplet structure after adding materials in step 2, so that the electrical-thermal-mechanical multi-physics coupling characteristics of the entire packaging structure can be analyzed later.

[0069] Step 4, in order to obtain the temperature distribution of the entire packaging structure, it is necessary to add the corresponding boundary conditions to the solid heat transfer physics interface in step 3. First, it is necessary to add a fixed heat source Q to the two memory chips 2 and the logic chip 3. Its function is to simulate the heat generated by the chip during normal operation. The value of Q needs to be set according to the actual situation and there is no fixed range. Next, since the outer surface of the entire packaging structure is exposed to the air, the two memory chips 2 and the logic chip 3 will generate heat under normal working conditions, causing the temperature of the entire packaging structure to rise, making its temperature higher than the room temperature T e (Generally T e =293.15K), so in the simulation process, the convective heat transfer between the outer surface of the entire packaging structure and the surrounding environment should also be considered. Therefore, it is necessary to add a heat flux boundary condition on the outer surface of the entire structure. Its heat transfer coefficient is h. In the process of air convection heat transfer, the heat transfer coefficient h is generally (5-20) W / m 3 .

[0070] The heat transfer equation involved in the Heat Transfer in Solids multiphysics interface is:

[0071] ρC pu▽T+▽·(-K▽T)=Q (1)

[0072] Where ρ represents the material density (the material selected for each component in the 2.5D chiplet structure), C P represents the constant-pressure heat capacity of the material, u represents the velocity field, which is usually defined directly or comes from other physics interfaces, ▽T represents the temperature gradient, K represents the thermal conductivity of the material, and Q is the heat source.

[0073] The equations involved in the heat flux boundary condition are:

[0074] -n·(-K▽T)=h(T e -T) (2)

[0075] Where n is an internal parameter of the physical field. By adding the boundary conditions (Q, h, Te) set above and solving equations (1) and (2) simultaneously, the distribution of temperature T on the entire packaging structure can be obtained.

[0076] Step 5: The solid mechanics physics interface in step 3 is used to solve the deformation and stress distribution of the entire packaging structure. Certain boundary conditions need to be added to constrain it during the solution process.

[0077] Since the whole model is highly symmetrical, in order to reduce the simulation cost and shorten the simulation time, a quarter model is used instead of the whole model for simulation analysis during the simulation process. Figure 3 As shown in the figure, the entire structure is cut along the dotted lines OE and OF, and symmetric boundary conditions are added to the cut surface. In order to better obtain the deformation of the entire packaging structure, it is necessary to Figure 4 Add a specified displacement at the position of point D (the vertex of substrate 1 of the quarter model) to constrain point D, and set the displacement of point D in the x and y directions to free deformation, that is, the 2.5D chiplet structure expands freely along the x and y directions at point D, and specifies its displacement in the z direction as 0m, that is, the z direction at point D does not move.

[0078] The equations involved in the Solid Mechanics physics interface (steady state) are as follows:

[0079] -▽S=f (3)

[0080] In the formula, ▽ represents the gradient, S represents the stress, which is caused by the mismatch of thermal expansion coefficients between various materials in the packaging structure at high temperature, and f represents the volume force.

[0081] Hooke's law is also involved in the solution process, and its basic equation is as follows:

[0082] S-(S0+S ext +S q)=C:(ε-(ε0+ε th +ε hs +ε pl +ε cr )) (4)

[0083] In the formula, S represents stress, S0 represents prestress, S ext represents the external stress, S q represents viscous stress, C represents elastic matrix, ε represents elastic strain, ε0 represents prestrain, ε th represents thermal strain, ε hs Indicates infiltration and expansion; ε pl represents the plastic strain, ε cr represents creep, where ε pl , ε cr For nonlinear structural materials only.

[0084] The relationship between strain and displacement is as follows:

[0085]

[0086] In the formula represents displacement and ▽ represents gradient.

[0087] By solving the above equations (3), (4) and (5), the deformation and stress distribution of the entire structure can be obtained.

[0088] Step 6: During the solution of the three equations in step 5, the temperature result obtained in step 4 needs to be used as the load. Therefore, a thermal expansion physical field interface needs to be set up to couple the solid heat transfer physical field interface and the solid mechanics physical field interface in step 4 to ensure that the temperature result obtained in step 4 is used as the load for the initial condition of solving the equations in step 5. The internal settings of the thermal expansion physical field interface generally use the initial default settings (no need to change the internal conditions), and only the thermal expansion physical field interface needs to be added. The equations involved in the thermal expansion physical field interface are as follows:

[0089] ε th =α(T)(TT ref ) (6)

[0090] Where α is the thermal expansion coefficient, T ref Indicates volume reference temperature.

[0091] Step 7: After setting all the above conditions, you need to set the boundary conditions (Q, h, T e , two symmetric boundary conditions after cutting along the dotted lines OE and OF, Figure 4Finally, add a steady-state study solver and solve the above equations (1) to (6), and you can get the temperature, stress, and deformation distribution of the entire package structure at the same time.

[0092] Since the entire structure is highly symmetrical, in order to reduce simulation costs and shorten simulation time, a quarter model is used instead of the entire model for simulation analysis. Figure 3 , 4 As shown, the partial enlarged view is shown in Figure 5 .

[0093] Example 2

[0094] The boundary conditions added to the solid heat transfer module in step 4 are as follows: The heat source Q added on the chip is 3×10 6 W / m 3 , heat flux h = 15W / m 3 , ambient temperature T e =293.15K.

[0095] For the solid mechanics multiphysics interface in step 5, it is necessary to add corresponding symmetry boundary conditions on the symmetry plane and add a specified displacement at point D to constrain it. Set the displacement of point D in the x and y directions to free deformation and specify its displacement in the z direction to 0m. After setting the above conditions, finally perform meshing and solve.

[0096] Figure 6 and Figure 7 The temperature distribution of the entire 2.5D chiplet structure is shown. Figure 6 It can be seen that the temperature near the chip is the highest, and the farther away from the chip, the lower the temperature, with the highest temperature being 94.4°C. Figure 7 It can be seen that the temperature of the entire structure decreases gradually from top to bottom, which indicates that solder balls C8, B7, and A6 are more susceptible to thermal effects and therefore have worse reliability.

[0097] Example 3

[0098] Figure 8 and Fig. 9 The deformation trend of the entire 2.5D chiplet structure is shown. In order to make the deformed structure easier to observe, Fig. 9 The deformation factor in is 10. Figure 8 The deformation trend of the entire package structure can be seen in the figure, and the closer to the edge, the more serious the warping. Fig. 9It can be clearly seen that the entire packaging structure will produce a large warp under high temperature. The maximum deformation of the entire structure is 63.8μm, which may seriously lead to risks such as fracture of the middle layer and fall off of the solder balls, posing a great threat to the reliability of the entire packaging structure.

[0099] Fig.10 The stress distribution on the entire 2.5D chiplet structure is shown. It can be seen from the figure that greater stress will be generated around the TSV through hole, which is caused by the mismatch of thermal expansion coefficients of different materials around the TSV.

[0100] This result helps to perform thermal analysis on the entire packaging structure and can be used to assist in the physical optimization design of the 2.5D chiplet structure.

Claims

1. 2.5D Chiplet structure physical field coupling characteristics analysis method, characterized by: The specific steps include: Step 1: Add a solid heat transfer physics interface, a solid mechanics physics interface, and a thermal expansion physics interface to the 2.5D chiplet structure. Step 2: Add boundary conditions to the solid heat transfer physics interface to obtain the temperature distribution of the 2.5D chiplet structure. Step 3: Solve the deformation and stress distribution of the 2.5D chiplet structure based on the solid mechanics physics interface; Step 4, coupling the Solid Heat Transfer Physics Interface and the Solid Mechanics Physics Interface through the Expansion Physics Interface; Step 5: Mesh the 2.5D chiplet structure to obtain the temperature, stress, and deformation distribution of the 2.5D chiplet structure.

2. The method for analyzing physical field coupling characteristics of a 2.5D chiplet structure according to claim 1, characterized in that: In step 1, the 2.5D chiplet structure includes three layers, the top layer includes two memory chips (2) and a logic chip (3) arranged in a horizontal direction, and the logic chip (3) is located between the two memory chips (2); the middle layer includes an upper silicon dioxide layer (10), a silicon middle layer (9) and a lower silicon dioxide layer (11) arranged in sequence from top to bottom, and a TSV array is arranged in the silicon middle layer (9); and the bottom layer includes a substrate (1) arranged horizontally.

3. The method for analyzing physical field coupling characteristics of a 2.5D chiplet structure according to claim 2, characterized in that: The memory chip (2) is connected to the upper silicon dioxide layer (10) via a solder ball A (6); the logic chip (3) is connected to the upper silicon dioxide layer (10) via a solder ball B (7); and the lower silicon dioxide layer (11) is connected to the substrate (1) via a solder ball C (8).

4. The method for analyzing physical field coupling characteristics of a 2.5D chiplet structure according to claim 3, characterized in that: The materials used for the two memory chips (2) and the logic chip (3) are silicon; the material of the substrate (1) is FR4; the materials of the solder balls A (6), B (7) and C (8) are all 64Sn-40Pb; and the material of the TSV is copper.

5. The method for analyzing physical field coupling characteristics of a 2.5D chiplet structure according to claim 3, characterized in that: The specific process of step 2 is: In step 2.1, add the following boundary conditions to the Heat Transfer in Solids physics interface: a) Add a fixed heat source Q to the two memory chips A (2) and the logic chip (3); b) Set the working temperature T of the boundary condition added to the Solid Heat Transfer physics interface e ; c) Add heat flux boundary conditions, i.e., heat transfer coefficient h, to the outer surface of the entire 2.5D chiplet structure; Step 2.2: Solve the heat transfer equations involved in the following solid heat transfer multiphysics interface according to the boundary conditions a) to c) set in step 2.1 to obtain the distribution of the temperature T of the 2.5D chiplet structure: In the formula, ρ represents the material density, C P represents the constant pressure heat capacity of the material, u represents the velocity field, which is usually defined directly or comes from other physics interfaces, ▽T represents the temperature gradient, and K represents the thermal conductivity of the material; The equations involved in the heat flux boundary condition are: Where n is an internal parameter of the physical field.

6. The method for analyzing physical field coupling characteristics of a 2.5D chiplet structure according to claim 5, characterized in that: The specific process of step 3 is as follows: Step 3.1: Since the entire 2.5D chiplet structure is a symmetrical structure, the entire 2.5D chiplet structure is cut along the quarter-cutting lines OE and OF, and symmetric boundary conditions are added to the cut surface. Step 3.2, for the quarter 2.5D chiplet structure divided in step 3.1, add a specified displacement at one of the vertices D of the substrate (1), the displacement along point D in the x and y directions is a free deformation, and the position along point D in the z direction remains unchanged; Step 3.3: Based on the conditions set in step 3.2, solve the following equations (3) to (5) to obtain the deformation and stress distribution of the entire 2.5D chiplet structure: Stationary equations for the Solid Mechanics physics interface: In the formula, represents gradient, S represents stress, and f represents body force; Hooke's law equation: S-(S0+S ext +S q )=C:(ε-(ε0+ε th +e hs +e pl +e cr )) (4) In the formula, S represents stress, S0 represents prestress, S ext represents the external stress, S q represents viscous stress, C represents elastic matrix, ε represents elastic strain, ε0 represents prestrain, ε th represents thermal strain, ε hs Indicates infiltration and expansion; ε pl represents the plastic strain, ε cr represents creep, where ε pl , ε cr Only for nonlinear structural materials; The relationship equation between strain and displacement is: In the formula, represents displacement, Represents the gradient.

7. The method for analyzing physical field coupling characteristics of a 2.5D chiplet structure according to claim 6, characterized in that: The specific process of step 4 is as follows: The temperature T of the 2.5D chiplet structure obtained in step 2 is used as the load. The solid heat transfer physics interface and the solid mechanics physics interface are coupled through the thermal expansion physics interface. The equations involved in the thermal expansion physics interface are as follows: e th =α(T)(TT ref ) (6) Where α is the thermal expansion coefficient, T ref Indicates volume reference temperature.

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