On spherical harmonics expansion type modelsfor electron–phonon collisions

✍ Scribed by J.-P. Bourgade

• Publisher: John Wiley and Sons
• Year: 2003
• Tongue: English
• Weight: 219 KB
• Volume: 26
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.353

✦ Synopsis

Abstract

In this paper, we give the rigorous derivation of a diffusion model for semiconductor devices, the starting point being a microscopic description of electron transport by means of a kinetic equation of Boltzmann type. The limit of a small mean free path at a large time leads to a diffusion equation of ‘SHE’ type (spherical harmonics expansion). We deal with a collision operator that models interactions between electron and phonons. This induces a peculiar form for the diffusion tensor: electron–phonon collisions happen to be discontinuous in energy and inelastic, and, as a consequence, the diffusion tensor appears as an infinite dimensional matrix. Copyright © 2003 John Wiley & Sons, Ltd.