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.
Date of this Version
K. Banoo, F. Assad, and M. S. Lundstrom, “Formulation of the Boltzmann Equation as a Multi-Mode Drift-Diffusion Equation,” VLSI Design, vol. 8, no. 1-4, pp. 539-544, 1998. doi:10.1155/1998/59373