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# Estimation of Effective Thermal and Mechanical Properties of Particulate Thermal Interface Materials by a Random Network Model

[+] Author and Article Information
Pavan Kumar Vaitheeswaran

Department of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47907
e-mail: pvaithee@purdue.edu

Ganesh Subbarayan

Department of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47907
e-mail: gss@purdue.edu

1Corresponding author.

Contributed by the Electronic and Photonic Packaging Division of ASME for publication in the JOURNAL OF ELECTRONIC PACKAGING. Manuscript received September 20, 2017; final manuscript received January 12, 2018; published online May 9, 2018. Assoc. Editor: Reza Khiabani.

J. Electron. Packag 140(2), 020901 (May 09, 2018) (7 pages) Paper No: EP-17-1092; doi: 10.1115/1.4039136 History: Received September 20, 2017; Revised January 12, 2018

## Abstract

Particulate thermal interface materials (TIMs) are commonly used to transport heat from chip to heat sink. While high thermal conductance is achieved by large volume loadings of highly conducting particles in a compliant matrix, small volume loadings of stiff particles will ensure reduced thermal stresses in the brittle silicon device. Developing numerical models to estimate effective thermal and mechanical properties of TIM systems would help optimize TIM performance with respect to these conflicting requirements. Classical models, often based on single particle solutions or regular arrangement of particles, are insufficient as real-life TIM systems contain a distribution of particles at high volume fractions, where classical models are invalid. In our earlier work, a computationally efficient random network model (RNM) was developed to estimate the effective thermal conductivity of TIM systems (Kanuparthi et al., 2008, “An Efficient Network Model for Determining the Effective Thermal Conductivity of Particulate Thermal Interface Materials,” IEEE Trans. Compon. Packag. Technol., 31(3), pp. 611–621; Dan et al., 2009, “An Improved Network Model for Determining the Effective Thermal Conductivity of Particulate Thermal Interface Materials,” ASME Paper No. InterPACK2009-89116.) . This model is extended in this paper to estimate the effective elastic modulus of TIMs. Realistic microstructures are simulated and analyzed using the proposed method. Factors affecting the modulus (volume fraction and particle size distribution (PSD)) are also studied.

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## Figures

Fig. 1

RVE of microstructure (left) with 58% volume fraction of alumina particles in silicone matrix with (right) heat flux field observed at the midsection (y = 0.5) using HPFC

Fig. 2

Equivalent network of conductors for a given microstructure

Fig. 3

Interparticle conductance as a series combination of gap conductance and particle conductances

Fig. 4

Effective conductance for the interaction between a particle and a wall

Fig. 5

Comparing the results of the random network model with those obtained using full-field simulations

Fig. 6

Heat flux transport within particle extended to entire hemisphere instead of just a cylindrical region

Fig. 7

Force transfer across the matrix as an effective gap stiffness

Fig. 8

Particle divided into infinitesimal stiffnesses in series

Fig. 9

Illustration of the drop-fall-shake procedure used to generate realistic random microstructures from a given particle size distribution

Fig. 10

Random network model predictions against experimental measurements. Accuracy improves with increase in particle volume fractions.

Fig. 11

The effective elastic modulus of the system increases exponentially with filler fraction

Fig. 12

Different log-normal particle size distributions generated and analyzed

Fig. 13

The effective elastic modulus shows a slight increase with polydispersity at high volume fractions

## Errata

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