Measurement and modeling of the effective thermal conductivity of sintered silver pastes

Abstract

The effective thermal conductivity of sintered porous pastes of silver is modeled through two theoretical methods and measured by means of three experimental techniques. The first model is based on the differential effective medium theory and provides a simple analytical description considering the air pores like ellipsoidal voids of different sizes, while the second one arises from the analysis of the scanning-electron-microscope images of the paste cross-sections through the finite element method. The predictions of both approaches are consistent with each other and show that the reduction of the thermal conductivity of porous pastes can be minimized with spherical pores and maximized with pancake-shaped ones, which are the most efficient to block the thermal conducting pathways. A thermal conductivity of 151.6 W/m K is numerically determined for a sintered silver sample with 22% of porosity. This thermal conductivity agrees quite well with the one measured by the Lateral Thermal Interface Material Analysis for a suspended sample and matches, within an experimental uncertainty smaller than 16%, with the values obtained by means of Raman thermometry and the 3ω technique, for two samples buried in a silicon chip. The consistence between our theoretical and experimental results demonstrates the good predictive performance of our theoretical models to describe the thermal behavior of porous thermal interface materials and to guide their engineering with a desired thermal conductivity.