Deterministic Boltzmann Transport Equation Solver: Validation and Heat Generation Modeling

Abstract

The heat generation rate is commonly calculated via phonon energy transfer rate. To ensure consistency with the energy balance equation, we reformulate the heat generation rate based on the carrier energy loss and demonstrate the equivalence of both approaches. The deterministic Boltzmann Transport Equation (BTE) solver is validated under low-field conditions using the distribution function and the mobility derived from the relaxation time approximation. Additionally, we introduce an approximation to address a non-removable singularity in the mobility calculation. These results demonstrate the potential of the deterministic BTE solver for predictive simulations of self-heating effects and hot-carrier degradation in advanced semiconductor devices.