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.


The following article appeared in VLSI Design 1998, Vol. 8, Nos. (1-4), pp. 539-544 and may be found at http://dx.doi.org/10.1155/1998/59373 and has been submitted to/accepted by VLSI Design. Copyright (1998) K. Banoo, F. Assad, and M. S. Lundstrom. This article is distributed under a Creative Commons Attribution 3.0 Unported License.

Date of this Version


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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



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