Design method of insulating thermal interface materials with non-uniform orientation structure of binary fillers

By designing a composite thermal interface material with a non-consistent orientation structure of binary filler, and regulating the orientation of the filler is solved by using permeability theory, the contradiction between thermal conductivity and electrical insulation of thermal interface material is achieved, and the performance and life of the device is improved.

CN120248521BActive Publication Date: 2025-08-19SHANGHAI SECOND POLYTECHNIC UNIVERSITY
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Patent Information

Application Number
CN202510755439.3
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2025-06-06
Publication Date
2025-08-19
Estimated Expiration
2045-06-06

AI Technical Summary

Technical Problem

There is a trade-off between thermal conductivity and electrical insulation in existing thermal interface materials, making it difficult to achieve high thermal conductivity and electrical insulation at the same time, which can easily lead to problems such as electrical breakdown.

Method used

A composite thermal interface material with a non-consistent orientation structure of binary fillers is designed, and the specific spatial orientation of metal fillers and electrically insulating fillers is set through numerical simulation to form thermal permeability without electropermeability. The distribution of fillers in organic polymer matrix is used to regulate the distribution of fillers in organic polymer matrix.

Benefits of technology

A highly thermally conductive and electrically insulated composite thermal interface material can effectively conduct heat without causing electrical damage to the device, improving device performance and life.

✦ Generated by Eureka AI based on patent content.

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Abstract

The present invention discloses a method for designing an insulating thermal interface material with a binary filler non-uniformly oriented structure. The composite thermal interface material is composed of binary fillers (metal fillers and electrically insulating fillers) with specific spatial orientations and an organic polymer matrix. The metal fillers and electrically insulating fillers are modified to exhibit specific spatial orientations (or within a specific spatial orientation angle range) within the matrix, thereby enabling thermal percolation of the fillers without electrical percolation, thereby obtaining a composite thermal interface material with high thermal conductivity and electrical insulation properties. The resulting thermal interface material exhibits excellent ductility and is suitable for a variety of thermal interface applications. Its superior thermal conductivity and electrical insulation properties allow it to efficiently transfer excess heat without causing electrical performance issues such as short circuits or breakdown, significantly improving device performance and lifespan.
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Description

Technical Field

[0001] The present invention relates to the field of new materials and application technology, and in particular to a design method for an insulating thermal interface material with a binary filler non-uniform orientation structure. Background Art

[0002] With the rapid development of electronic technology, electronic components are evolving towards high integration and miniaturization. However, the reduction in component size and the increase in operating frequency have led to a continuous increase in heat flux density per unit area, posing a significant challenge to system thermal management. Efficient heat dissipation design has become a key step in ensuring device performance and lifespan, and thermal interface materials (TIMs) play a vital role in the thermal path. They are typically placed between electronic components and heat dissipation structures, effectively improving heat transfer efficiency by eliminating air gaps between the contact surfaces.

[0003] Currently, the most widely used thermal interface materials are composed of a polymer matrix and thermally conductive fillers. While these composite materials offer a certain degree of formability and flexibility, there is often a trade-off between thermal conductivity and electrical insulation. On the one hand, the high interfacial thermal resistance between the thermally conductive fillers makes it difficult to form a continuous heat conduction network, thus limiting the improvement of overall thermal conductivity. On the other hand, the introduction of high filling ratios of conductive fillers to achieve higher thermal conductivity can easily lead to electrical breakdown and other issues, reducing the material's electrical insulation performance and even damaging electronic devices.

[0004] At the microscopic scale, heat conduction relies on the coordinated transport of electrons and phonons. Conductive materials provide both electron heat transfer pathways and phonon participation, resulting in relatively low interfacial thermal resistance. In contrast, electrically insulating materials rely primarily on phonon heat transfer, resulting in inefficient interfacial energy coupling and limited overall thermal conductivity of the composite material. This conflicting relationship between thermal conductivity and electrical insulation is a core challenge currently underway in the design of thermal interface materials. Percolation theory offers a new approach to resolving this contradiction. This theory describes the sudden emergence of global connectivity in complex systems once the composition reaches a critical value. This insight allows precise control of the filler composition and layout in material design, achieving "thermal percolation" while avoiding "electrical percolation," thereby balancing high thermal conductivity with excellent electrical insulation. Leveraging this physical mechanism, we hope to develop next-generation thermal interface materials that combine efficient heat dissipation with electrical safety. Summary of the Invention

[0005] In order to solve the above-mentioned problems encountered in the application of thermal interface materials, the purpose of the present invention is to provide a design method for a composite thermal interface material that achieves high thermal conductivity and electrical insulation through the non-uniform orientation structure of a binary filler. The composite interface material is composed of a binary filler with a non-uniform orientation structure and an organic polymer material matrix. The non-uniform spatial orientation structure of the binary filler enables the filler to undergo thermal percolation in the matrix without undergoing electrical percolation. Utilizing this principle, a composite thermal interface material with high thermal conductivity and electrical insulation properties can be obtained, wherein: the binary filler with a non-uniform orientation structure is randomly distributed in the organic polymer material matrix; the binary filler undergoes thermal percolation in the matrix while the metal filler does not undergo electrical percolation (that is, the binary filler forms a heat flow path in the matrix, while the metal filler does not form a current path).

[0006] The technical solution of the present invention is specifically described as follows.

[0007] The present invention provides a design method for an insulating thermal interface material having a binary filler non-uniform orientation structure. The insulating thermal interface material is composed of a binary filler having a specific spatial orientation and an organic polymer material matrix. The binary filler includes a metal filler and an electrically insulating filler. The specific steps are as follows:

[0008] Step 1: The organic polymer substrate is dimensionless transformed into a 1×1×1 cube, a certain volume fraction of binary fillers is randomly dispersed in the organic polymer matrix, and a composite thermal interface material system is simulated using numerical simulation methods;

[0009] Step 2: Set the heat conduction direction to the x-direction, set the angles between the metal filler's spatial orientation angle and the y-direction, and the electrical insulation filler's spatial orientation angle and the heat conduction direction, and apply boundary conditions to cut off fillers that extend beyond the heat conduction direction, and cut off fillers that extend beyond the direction perpendicular to the heat conduction direction and periodically translate them into the cube.

[0010] Step 3: Design the electrical and thermal transport channels of the composite thermal interface material in the direction of heat conduction, and adjust one or more of the design parameters of the internal metal filler and the electrical insulation filler, the aspect ratio, the spatial orientation angle, and the volume fraction of the filler filled into the organic polymer matrix. Through numerical simulation, when the thermal conductivity of the composite thermal interface material is in the range of 5~8Wm -1 K -1 , the conductivity range is 1×10 -5 ~1×10 -3 Sm -1 The design of an insulating thermal interface material with high thermal conductivity and electrical insulation is completed through the non-uniform orientation structure of binary fillers.

[0011] In the present invention, in step 1, the material of the electrically insulating filler is one or more materials with good thermal conductivity and electrical insulation properties such as aluminum nitride (AlN), silicon dioxide (SiO2), aluminum oxide (Al2O3), silicon carbide (SiC), and boron nitride (BN).

[0012] In the present invention, in step 1, the Monte Carlo method is used to perform numerical simulation.

[0013] In the present invention, in step 1, the shape of the electrically insulating filler is designed to be rod-shaped, preferably a rod-shaped filler with a relatively large aspect ratio.

[0014] In the present invention, in step 1, the length of the electrically insulating filler is designed to be in the range of 0.05 to 1000 microns, and the diameter thereof is designed to be in the range of 0.001 to 200 microns.

[0015] In the present invention, in step 1, the volume percentage of the electrically insulating filler in the composite thermal interface material is 10% to 70%, preferably 15% to 30%.

[0016] In the present invention, in step 1, the material of the metal filler is one or more metal materials with good electrical conductivity, such as silver (Ag), gold (Au), copper (Cu), and aluminum (Al).

[0017] In the present invention, in step 1, the shape of the metal filler is designed to be rod-shaped, preferably a rod-shaped filler with a relatively large aspect ratio.

[0018] In the present invention, in step 1, the length of the metal filler is designed to range from 0.01 to 200 microns, preferably one-quarter to one-sixth of the characteristic size of the electrically insulating filler, and the diameter is designed to range from 0.0002 to 40 microns.

[0019] In the present invention, in step 1, the volume percentage of the metal filler in the composite thermal interface material is 5% to 50%, preferably 5% to 10%.

[0020] In the present invention, in step 1, the organic polymer material substrate is one or more organic polymer elastic materials with good elasticity and flexibility and electrical insulation, such as polylactide, polycarbonate, silicone resin, vinyl silicone oil, polyimide, polybenzoxazine, methyl vinyl silicone rubber, epoxy resin, polyurethane, polydimethylsiloxane and polyacrylate.

[0021] In the present invention, in step 1, the angle (or angle range) between the specific spatial orientation angle of the electrical insulating filler and the heat conduction direction is 0 to 60 degrees, preferably 0 to 5 degrees.

[0022] In the present invention, in step 2, the angle (or angle range) between the specific spatial orientation angle of the metal filler and the vertical heat conduction direction is 0 to 60 degrees, preferably 0 to 5 degrees.

[0023] In the present invention, in step three, the electrical transport channel and the heat transport channel refer to the percolation conductive channel formed by the metal filler and the electrical insulating filler in the system by changing the angle and volume.

[0024] In the present invention, in step three, based on the properties of the metal filler and the electrically insulating filler, namely, electrical conductivity, thermal conductivity, electrical resistance and thermal resistance, as well as the interface resistance and thermal resistance between the metal filler and the electrically insulating filler, the interface resistance and thermal resistance between the metal filler and the metal filler, the interface resistance and thermal resistance between the electrically insulating filler and the electrically insulating filler, and the electrical conductivity and thermal conductivity of the matrix itself, the resistance network algorithm and Kirchhoff's current law are used to obtain the current and heat flow, and the conjugate gradient algorithm is used for self-consistent solution, that is, the electrical conductivity and thermal conductivity of the system are solved.

[0025] Compared with the prior art, the present invention has the following beneficial effects:

[0026] Compared with existing thermal interface materials, the present invention uses the basic principle of percolation phenomenon to reconcile the high thermal conductivity and electrical insulation properties of thermal interface materials. The designed composite interface material is composed of a binary filler with a non-uniform orientation structure and an organic polymer material matrix. The non-uniform spatial orientation structure of the binary filler allows the filler to undergo thermal percolation in the matrix without electrical percolation. By utilizing this principle, a composite thermal interface material with high thermal conductivity and electrical insulation properties can be obtained. This innovative thermal interface material has excellent ductility and can be flexibly applied between various thermal interfaces. At the same time, its excellent thermal conductivity and electrical insulation properties enable it to efficiently and quickly conduct away excess heat from the device without causing electrical damage to the device, such as short circuit or breakdown, thereby improving the performance release and service life of the device. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 It is a cross-sectional schematic diagram of the composite thermal interface material with a binary filler non-uniform orientation structure of the present invention.

[0028] Figure 2 It is a schematic diagram of adjusting the spatial orientation angle of the electrical insulating filler and the metal filler according to the present invention.

[0029] Figure 3 This is a schematic diagram of the calculation results of the filler spatial orientation angle-percolation threshold when the filler aspect ratio is changed.

[0030] Figure 4 It is a temperature field cloud diagram of a system with a specific spatial orientation angle of a metal filler and an electrical insulating filler that has been distributed and changed. DETAILED DESCRIPTION

[0031] The present invention will be further described below.

[0032] Existing filler-type thermal interface materials usually face two major problems: first, due to the large interfacial thermal resistance between fillers, thermal percolation does not occur within the composite material, resulting in low thermal conductivity of the material; second, due to the high electrical conductivity of the filler itself, electrical percolation also occurs within the composite material at the same time as thermal percolation, which can lead to electrical problems such as electron transport-induced breakdown, thereby damaging the electrical performance of the device and thus affecting the performance and life of the device.

[0033] In order to solve the above technical problems, the present invention provides a novel composite thermal interface material and a design method thereof that realizes high thermal conductivity and electrical insulation through a binary filler non-uniform orientation structure, such as Figure 1 As shown, the following steps are included:

[0034] Step 1: Add metal fillers and electrically insulating fillers to an organic polymer material substrate, and use numerical simulation methods to randomly disperse the fillers in the substrate, ultimately obtaining a mixed system of metal fillers, electrically insulating fillers, and organic polymer materials;

[0035] Step 2: Further using numerical simulation methods, the internal metal filler and the electrical insulation filler of the mixed material designed in Step 1 are set to have a specific spatial orientation (or a specific spatial orientation angle range);

[0036] Step 3: According to specific requirements, the mixed material with binary non-uniform orientation structure designed in step 2 is used to design the electrical and thermal transport channels of the composite thermal interface material, and one or more design parameters such as the material, aspect ratio, spatial orientation angle and volume fraction of the internal metal filler and the electrical insulation filler are adjusted. The electrical and thermal conductivity of the composite thermal interface material are solved by numerical simulation methods. When the thermal conductivity of the composite thermal interface material is in the range of 5~8Wm -1 K -1 , the conductivity range is 1×10 -5 ~1×10 -3 Sm -1 The design of a composite thermal interface material with high thermal conductivity and electrical insulation is completed through the non-uniform orientation structure of binary fillers.

[0037] Furthermore, in step 1, the material of the electrically insulating filler is one or more materials with good thermal conductivity and electrical insulation properties, such as aluminum nitride (AlN), silicon dioxide (SiO2), aluminum oxide (Al2O3), silicon carbide (SiC), and boron nitride (BN).

[0038] Furthermore, in step 1, the shape of the electrically insulating filler is designed to be rod-shaped, preferably a rod-shaped filler with a relatively large aspect ratio.

[0039] Furthermore, in step 1, the length of the electrically insulating filler is designed to be in the range of 0.05 to 1000 microns, and the diameter thereof is designed to be in the range of 0.001 to 200 microns.

[0040] Furthermore, in step 1, the volume percentage of the electrically insulating filler in the composite material is 10% to 70% (preferably 15% to 30%).

[0041] Furthermore, in step 1, the material of the metal filler is one or more metal materials with good electrical conductivity, such as silver (Ag), gold (Au), copper (Cu), and aluminum (Al).

[0042] Furthermore, in step 1, the shape of the metal filler is designed to be rod-shaped, preferably a rod-shaped filler with a relatively large aspect ratio.

[0043] Furthermore, in step 1, the length of the metal filler is designed to be in the range of 0.01 to 200 microns, preferably about one-fifth of the characteristic size of the electrically insulating filler, and the diameter is designed to be in the range of 0.0002 to 40 microns.

[0044] Furthermore, in step 1, the volume percentage of the metal filler in the composite material is 5% to 50% (preferably 5% to 10%).

[0045] Furthermore, in step one, the organic polymer material substrate is one or more organic polymer elastic materials with good elasticity and flexibility and electrical insulation, such as polylactide, polycarbonate, silicone resin, vinyl silicone oil, polyimide, polybenzoxazine, methyl vinyl silicone rubber, epoxy resin, polyurethane, polydimethylsiloxane and polyacrylate.

[0046] Furthermore, in step 2, the metal filler and the electrical insulation filler in the mixed material are designed to have a specific spatial orientation angle through numerical simulation.

[0047] Furthermore, in step 2, the angle (or angle range) between the specific spatial orientation angle of the electrically insulating filler and the heat conduction direction is 0 to 60 degrees (or 0 to 60 degrees), preferably 0 degree (or 0 to 5 degrees).

[0048] Furthermore, in step 2, the angle (or angle range) between the specific spatial orientation angle of the metal filler and the vertical heat conduction direction is 0 to 60 degrees (or 0 to 60 degrees), preferably 0 degree (or 0 to 5 degrees).

[0049] Example 1

[0050] like Figure 3As shown in the figure, the metal filler is silver (Ag) nanowire, the electrical insulating filler is silicon carbide (SiC) and the organic polymer material is polyvinylidene fluoride (PVDF). The composite thermal interface material with non-uniform orientation structure of binary fillers is designed. The metal filler and the electrical insulating filler are added to the organic polymer material substrate. The aspect ratio l is selected first. Ag / d=20 Ag nanowire filler, the relationship between its specific spatial orientation angle and the percolation threshold when the filler undergoes electrical percolation is studied, where the black dotted line represents the percolation threshold when the randomly oriented nanowire undergoes percolation, and the conduction direction of the electrical transport path is selected in the X direction. By changing the angle between the specific spatial orientation angle of the Ag nanowire filler and the vertical conduction direction, that is, the angle γ with the Y axis, it is found that when the angle γ is within 0°~180°, the percolation threshold of the Ag nanowire filler with the specific angle γ is higher than that of the randomly oriented nanowire. Further research found that when 0°≤γ≤60°, the threshold when the filler inside the system undergoes percolation is higher, so the angle γ between the specific spatial orientation angle of the Ag nanowire filler and the vertical conduction direction is selected to be 0°~5°. The percolation threshold φ under this specific spatial orientation angle Ag Percolation threshold φ for random orientation c At this time, it is difficult for the metal fillers inside the system to undergo electrical percolation, which can effectively achieve the electrical insulation design in the composite thermal interface material, and more metal fillers can be filled to increase the contribution to heat transport, thereby further studying the relationship between the specific spatial orientation angle of the electrical insulation filler and the effective thermal conductivity.

[0051] The present invention designs a composite thermal interface material that realizes high thermal conductivity and electrical insulation through a binary filler non-uniform orientation structure, and selects l Ag =0.8 micron, aspect ratio l Ag / d=10, thermal conductivity is 429Wm -1 K -1 Rod-shaped Ag nanowires are used as metal fillers, and l SiC =4 microns, aspect ratio l SiC / d=20, thermal conductivity is 490Wm -1 K -1 Rod-shaped SiC nanowires are used as electrical insulating fillers with a thermal conductivity of 0.19 Wm -1 K -1 PVDF is used as the organic polymer substrate, and the interface thermal resistance R between Ag and Ag, Ag and SiC, and SiC and SiC is calculated by weighted average. Ag-Ag 、R Ag-SiC 、R SiC-SiC 2×10 -10 , 2×10 -9 , 2×10 -8 m2 KW -1 , using numerical simulation means and Monte Carlo method, the organic polymer substrate is dimensionless into a 1×1×1 cube, and two fillers are randomly filled into the organic polymer substrate. The specific spatial orientation angle and volume fraction between the metal filler and the electrical insulation filler are set by numerical simulation means, and boundary conditions are imposed, that is, the filler exceeding the area along the heat conduction direction is cut off, and the filler exceeding the area along the perpendicular heat conduction direction is cut off and periodically translated into the cube, giving the metal filler and the electrical insulation filler their own basic properties (thermal conductivity, electrical conductivity, thermal resistance, electrical resistance), the interface thermal resistance and interface resistance between the fillers, and the thermal conductivity and electrical conductivity of the organic polymer substrate itself. The resistance network algorithm and Kirchhoff's current law are used to obtain the current and heat flow, and the conjugate gradient algorithm is used for self-consistent solution to solve the thermal conductivity and electrical conductivity of the system. Figure 4 As shown, the heat conduction direction is defined as transmission along the X direction. When the specific spatial orientation angle of the metal filler Ag nanowires and the vertical heat conduction direction are about 0°~5°, the volume fraction of the metal filler φ Ag <0.1, the specific spatial orientation angle of the electrical insulating filler SiC and the heat conduction direction are about 0°~5°, that is, the angle with the X-axis is 0°≤θ≤5°, and the volume fraction φ SiC When the thermal conductivity is >0.25, a composite thermal interface material with high thermal conductivity and electrical insulation can be successfully designed through the non-uniform orientation structure of the binary filler. At this time, the thermal conductivity of the composite thermal interface material is 6Wm -1 K -1 .

[0052] As described above, the method of the present invention achieves the purpose of controlling thermal percolation within the system without electrical percolation by regulating parameters such as the material, aspect ratio, spatial orientation angle, and volume fraction of the internal metal filler and the electrically insulating filler, thereby realizing the design of a composite thermal interface material with high thermal conductivity and electrical insulation. Compared with existing thermal interface materials, the present invention utilizes the basic principle of percolation phenomenon to reconcile the high thermal conductivity and electrical insulation properties of the thermal interface material. The invented composite thermal interface material is composed of a binary filler with a non-uniform orientation structure and an organic polymer material matrix, ensuring that the designed thermal interface material can undergo thermal percolation without electrical percolation. This innovative thermal interface material has excellent ductility and can be flexibly applied between various thermal interfaces. At the same time, its excellent thermal conductivity and electrical insulation properties enable it to efficiently and quickly conduct away excess heat from the device without causing electrical damage to the device, thereby improving the performance release and service life of the device.

Claims

1. A design method for an insulating thermal interface material with a binary filler non-uniform orientation structure, characterized in that: The insulating thermal interface material is composed of a binary filler with a specific spatial orientation and an organic polymer material matrix, wherein the binary filler includes a metal filler and an electrical insulating filler. The specific steps are as follows: Step 1: The organic polymer substrate is dimensionless transformed into a 1*1*1 cube, a certain volume fraction of binary fillers is randomly dispersed in the organic polymer matrix, and numerical simulation is used to simulate the composite thermal interface material system; Step 2: Set the heat conduction direction to the x-direction, set the angles between the metal filler's spatial orientation angle and the y-direction, and the electrical insulation filler's spatial orientation angle and the heat conduction direction, and apply boundary conditions to cut off fillers that extend beyond the heat conduction direction, and cut off fillers that extend beyond the direction perpendicular to the heat conduction direction and periodically translate them into the cube. Step 3: Design the electrical and thermal transport channels of the composite thermal interface material in the direction of heat conduction, and adjust one or more of the design parameters of the material, aspect ratio, spatial orientation angle and volume fraction of the internal metal filler and the electrical insulation filler into the organic polymer matrix. Through numerical simulation, when the thermal conductivity of the composite thermal interface material is in the range of 5~8Wm -1 K -1 , the conductivity range is 1×10 -5 ~1×10 -3 Sm -1 The design of an insulating thermal interface material with high thermal conductivity and electrical insulation is completed by using a binary filler non-uniform orientation structure; wherein: In step 1, the shape of the electrically insulating filler is rod-shaped, the length of the electrically insulating filler is designed to be in the range of 0.05 to 1000 microns, and the diameter thereof is designed to be in the range of 0.001 to 200 microns; In step 2, the angle between the spatial orientation angle of the electrical insulating filler and the heat conduction direction is 0 to 60 degrees; the angle between the spatial orientation angle of the metal filler and the vertical heat conduction direction is 0 to 60 degrees.

2. The design method of the insulating thermal interface material with a binary filler non-uniform orientation structure according to claim 1, characterized in that: In step 1, the material of the electrically insulating filler is one or more of aluminum nitride AlN, silicon dioxide SiO2, aluminum oxide Al2O3, silicon carbide SiC or boron nitride BN; the material of the metal filler is one or more of silver Ag, gold Au, copper Cu, and aluminum Al; the organic polymer material substrate is selected from one or more of polylactide, polycarbonate, silicone resin, vinyl silicone oil, polyimide, polybenzoxazine, methyl vinyl silicone rubber, epoxy resin, polyurethane, polydimethylsiloxane or polyacrylate.

3. The design method of the insulating thermal interface material with a binary filler non-uniform orientation structure according to claim 1, characterized in that: In step 1, the volume percentage of the electrically insulating filler in the composite thermal interface material is 10% to 70%.

4. The design method of the insulating thermal interface material with a binary filler non-uniform orientation structure according to claim 1, characterized in that: In step 1, the shape of the metal filler is designed to be rod-shaped, with a length design range of 0.01 to 200 microns, which is one-fourth to one-sixth of the characteristic size of the electrical insulating filler, and a diameter design range of 0.0002 to 40 microns.

5. The design method of the insulating thermal interface material with a binary filler non-uniform orientation structure according to claim 1, characterized in that: In step 1, the volume percentage of the metal filler in the composite thermal interface material is 5% to 50%.

6. The design method of the insulating thermal interface material with a binary filler non-uniform orientation structure according to claim 1, characterized in that: The angle between the spatial orientation angle of the electrical insulating filler and the heat conduction direction is 0 degrees to 5 degrees; the angle between the spatial orientation angle of the metal filler and the vertical heat conduction direction is 0 degrees to 5 degrees.

7. The design method of the insulating thermal interface material with a binary filler non-uniform orientation structure according to claim 1, characterized in that: In step three, based on the properties of the metal filler and the electrically insulating filler, namely electrical conductivity, thermal conductivity, electrical resistance and thermal resistance, as well as the interface resistance and thermal resistance between the metal filler and the electrically insulating filler, the interface resistance and thermal resistance between the metal filler and the metal filler, the interface resistance and thermal resistance between the electrically insulating filler and the electrically insulating filler, and the electrical conductivity and thermal conductivity of the matrix itself, the resistance network algorithm and Kirchhoff's current law are used to obtain the current and heat flow, and the conjugate gradient algorithm is used for self-consistent solution, that is, the electrical conductivity and thermal conductivity of the system are solved.

Citation Information

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