Analytical solutions of temperature distributions based on fourier series for wafer level heterogeneous integrations

This paper established a general heat model of a multi-layer packaging. By using analytical solutions based on Fourier series, we were able to capture the temperature distributions of a realistic packages. We then fabricated photosensitive BCB based power MMICs packages and tested the temperature distributions. The fabrication process are given in detail. we were able to accurately calculate the temperature distributions of the power MMICs packages. Calculated, simulated and measured results show close correlations. This research will be useful in thermal management for further 3 dimensional packaging.