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VLSI Design
Volume 8 (1998), Issue 1-4, Pages 539-544

Formulation of the Boltzmann Equation as a Multi-Mode Drift-Diffusion Equation

1285 School of Electrical Engineering, Purdue University, West Lafayette, IN 47907, USA

Received 2 June 1997; Accepted 10 June 1997

Copyright © 1998 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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×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.