AN EFFICIENT SOLUTION OF THE MULTI‐BAND BOLTZMANN TRANSPORT EQUATION IN SILICON

A computationally very efficient solution of the multi‐band homogeneous Boltzmann transport equation (MB‐HBTE) for Silicon is presented. We used a Legendre polynomial (LP) expansion approach to solve coupled Boltzmann transport equations. To account for the multi‐band model, a Boltzmann transport equation is formulated for each of four conduction energy bands. The respective Boltzmann equations are coupled through the interband phonon scatterings. Analytical methods using Legendre polynomials are combined with numerical techniques using matrices to solve the coupled system of MB‐HBTE's. The multi‐band calculation requires approximately 8 GPU seconds on a SUN SPARC workstation. The efficiency of this method proves to be appropriate for use in computer‐aided design (CAD) tools for semiconductor devices, and results for the distribution function agree with Monte Carlo (MC) calculations.