An Approximated Model of Boltzmann Transport Equation for Nano-Scale Thermal Analysis

Under the current trend of process evolution, nano-scale (transistor-level) thermal analysis will become more and more important. The thermal model framework of traditional thermal analysis is no longer adequate, so the mathematical model of nano-scale thermal analysis becomes the framework that must be included. To explore the physical behaviors of nano-scale thermal analysis, the mainstream of research depends on the Boltzmann transport equation (BTE). In these days, the existing solutions that are able to accurately solve the BTE are very time-consuming. In this work, we propose a method in the same way as solving the traditional heat transfer equation to obtain high accuracy results compared with the BTE for nano-scale thermal analysis. Compared with the state-of-the-art BTE solver, the proposed method can speed up by at least 2, 000×.