Electrical and Computer Engineering Commons^™

Formulation Of The Boltzmann Equation As A Multi-Mode Drift-Diffusion Equation, Kausar Banoo, Farzin Assad, Mark S. Lundstrom

Department of Electrical and Computer Engineering Faculty Publications

We present a multi-mode drift-diffusion equation as reformulation of the Boltzmann equation in the discrete momentum space. This is shown to be similar to the conventional drift-diffusion equation except that it is a more rigorous solution to the Boltzmann equation because the current and carrier densities are resolved into M x 1 vectors, where M is the number of modes in the discrete momentum space. The mobility and diffusion coefficient become M M matrices which connect the M momentum space modes. This approach is demonstrated by simulating electron transport in bulk silicon.