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Research Papers

# An Improved Efficient Network Model for Determining the Effective Thermal Conductivity of Particulate Thermal Interface Materials

[+] Author and Article Information
B. Dan

e-mail: bdan1@binghamton.edu

B. G. Sammakia

State University of New York,
Binghamton, NY 13902

G. Subbarayan

Purdue University,
West Lafayette, IN 47906

S. Kanuparthi

Amkor Technology,
Chandler, AZ 85286

Contributed by the Electronic and Photonic Packaging Division of ASME for publication in the JOURNAL OF ELECTRONIC PACKAGING. Manuscript received October 15, 2012; final manuscript received March 19, 2013; published online June 4, 2013. Assoc. Editor: Amy Fleischer.

J. Electron. Packag 135(3), 031003 (Jun 04, 2013) (8 pages) Paper No: EP-12-1098; doi: 10.1115/1.4024392 History: Received October 15, 2012; Revised March 19, 2013

## Abstract

Thermal interface materials (TIMs) are particulate composite materials widely used in the microelectronics industry to reduce the thermal resistance between the device and heat sink. Predictive modeling using fundamental physical principles is critical to developing new TIMs since it can be used to quantify the effect of particle volume fraction and arrangements on the effective thermal conductivity. The existing analytical descriptions of thermal transport in particulate systems do not accurately account for the effect of interparticle interactions, especially in the intermediate volume fractions of 30–80%. An efficient random network model (RNM) that captures the near-percolation transport in these particle-filled systems, taking into account the interparticle interactions and random size distributions, was previously developed by Kanuparthi et al. The RNM approach uses a cylindrical region to approximate the thermal transport within the filler particles and to capture the interparticle interactions. However, this approximation is less accurate when the polydispersivity of the particulate system increases. In addition, the accuracy of the RNM is dependent on the parameters inherent in an analytical description of thermal transport between two spherical particles and their numerical approximation into the network model. In the current paper, a novel semispherical approximation to the conductance of the fillers is presented as an alternative to the cylindrical region approximation used earlier. Compared with the cylindrical model, the thermal conductivities of the semispherical model are more closely to the finite element (FE) results. Based on the FE analysis, the network model is improved by developing an approximation of the critical cylindrical region between two spherical particles over which energy is transported. Comparing the RNM results with FE results and experimental data, a linear relationship of the critical parameter with the thermal conductivity ratio and the volume fraction was found that provides a more accurate prediction of the effective thermal conductivity of the particulate TIMs.

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## Figures

Fig. 5

Comparison of cylindrical model and spherical model

Fig. 4

Illustration of the modeled cylindrical zone between two spherical particles embedded in the polymer matrix, through which the heat is transported

Fig. 3

The cylindrical region between two spherical particles

Fig. 2

Comparison of analytical models against experimental measurements

Fig. 1

Thermal interface material and contact resistance. (a) A typical flip chip assembly [1]. (b) Voids between two contact surfaces [5]. (c) Temperature jump due to contact resistance [5].

Fig. 6

Sketch of particle conductance calculation

Fig. 7

Thermal conductance integration volume

Fig. 8

The impact of each parameter on spherical model

Fig. 9

Thermal conductance comparison of FE, semispherical model and cylindrical model

Fig. 10

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