Numerical homogenization of thermal conductivity of particle-filled thermal interface material by fast Fourier transform method

Abstract

Thermal interface material (TIM) is pivotal for the heat dissipation between layers of high-density electronic packaging. The most widely used TIMs are particle-filled composite materials, in which highly conductive particulate fillers are added into the polymer matrix to promote heat conduction. The numerical simulation of heat transfer in the composites is essential for the design of TIMs; however, the widely used finite element method (FEM) requires large memory and presents limited computational time for the composites with dense particles. In this work, a numerical homogenization algorithm based on fast Fourier transform was adopted to estimate the thermal conductivity of composites with randomly dispersed particles in 3D space. The unit cell problem is solved by means of a polarization-based iterative scheme, which can accelerate the convergence procedure regardless of the contrast between various components. The algorithm shows good precision and requires dramatically reduced computation time and cost compared with FEM. Moreover, the effect of the particle volume fraction, interface thermal resistance between particles (R-PP), interface thermal resistance between particle and matrix (R-PM), and particle size have been estimated. It turns out that the effective conductivity of the particulate composites increases sharply at a critical filler volume fraction, after which it is sensitive to the variation of filler loading. We can observe that the effective thermal conductivity of the composites with low filler volume fraction is sensitive to R-PM, whereas the it is governed by R-PP for the composites with high filler content. The algorithm presents excellent efficiency and accuracy, showing potential for the future design of highly thermally conductive TIMs.

Data-Driven Framework toward Accurate Prediction of Interfacial Thermal Resistance in Particulate-Filled Composites

“…To this end, we have employed the FFT algorithm-based numerical method to solve the heat transfer problems in the particulate composites in our previous work. We discussed the effect of ITRs on the effective TCs, and pointed out that the experimental measured TC of the composite can be reproduced by selecting the proper ITRs, confirming the relationships between ITRs and TCs . Those facts ensure to get the exact solution of the TC of a composite material when its basic attributes are given as input parameters with arbitrary values (such as the intrisic TCs of polymer and fillers, the ITRs between ingredients inside the composite).…”

“…To solve the equation and determine the temperature distribution in the composite system, the periodic boundary conditions are employed on the domain boundary ∂Ω. In our previous report, the ITR is taken into account as a thin additional phase which is different from either the filler or the matrix, and a FFT-based iterative scheme in terms of polarization has been utilized to solve the mathematical equations of the heat transfer . In this work, if two neighboring voxels correspond to different materials, the interface between them is represented by an imperfect interface through which the temperature is continuous, while the heat flux suffers a jump in the normal direction, as shown in Figure . [ T l ] false| bold-italicx = bold-italicx * = 0 [ k ∂ T l ∂ x i ] false| bold-italicx = bold-italicx * = prefix− δ i l false[ k false] bold-italicx = bold-italicx * goodbreak0em2em⁣ normalf normalo normalr .25em i = 1,2.3 where δ il is the Kronecker symbol δ i l = { lefttrue 1 , ⁣ f o r i = l , 0 , …”

Accurate determination of interfacial thermal resistance inside particle-laden composites based on high-throughput computation and machine learning

“…GeoDict calculates the TC tensors based on the so-called explicit jump immersed interface approach, which solves the equations in parallel by combing the fast Fourier transform (FFT) and GiGGStab methods. We have recently shown that the approach dramatically reduces the computational time and requirement of memory without losing precision compared with the finite element modeling, which enables the efficient and accurate high-throughput calculations [28]. The input parameters for the numerical simulations are the TCs of the fillers, the ITR between the fillers and silicone matrix (ITR f −p ), and the ITR between the fillers (ITR f −f ).…”

Optimization of Effective Thermal Conductivity of Thermal Interface Materials Based on the Genetic Algorithm-Driven Random Thermal Network Model

“…Although the experimental approach to improve the thermal conductivity of TIM is important, numerical studies are necessary to better understand the heat-transfer mechanism between filler particles and matrix materials and optimize filler-matching methods. , The finite element method (FEM) is a full-field numerical simulation method that has been used in the prediction and optimization of the effective thermal conductivity of TIMs. − However, the FEM generally has a higher computational cost when simulating the TIM with a real microstructure, and the larger particle size distribution gradient of multiscale particles will result in a large number of meshes, especially at a high volume particle-packing fraction. Therefore, it is difficult for the FEM to realize the multivariable problem of multiscale particle size matching optimization.…”