Modeling multi-band effects of hot electron transport in silicon by self-consistent solution of the Boltzmann transport and Poisson equations

This paper presents a self-consistent numerical technique for the solution of the multi-band Boltzmann transport equation (BTE) and the Poisson equation in silicon. The effects of high energy bands ( 3 eV) are modeled in the formulation. The numerical technique utilizes a new curvilinear boundary-fitted coordinate grid which is tailored for self-consistent calculations. A new Scharfetter-Gummel like discretization of the BTE is presented. The numerical algorithm is tested on a n⁺ − n − n⁺ device structure.