A full band deterministic model for semiclassical carrier transport in semiconductors

• Published in: Journal of applied physics Vol. 99; no. 6
• Main Authors: Smirnov, S., Jungemann, C.
• Format: Journal Article
• Language: English
• Published: 15.03.2006
• ISSN: 0021-8979; 1089-7550
• DOI: 10.1063/1.2181429

We present a deterministic semiclassical transport model taking into account the full band structure of a solid. The method is based on the spherical harmonics expansion of the distribution function and band structure. As an example the approach is applied to the specific case of stationary hole transport in bulk relaxed silicon and strained silicon exposed to external uniform electric and magnetic fields with arbitrary directions. To keep the structure of the method clear we only consider simple acoustic and optical phonon scatterings. First, the Boltzmann equation is rewritten in terms of energy. The limitations implied by the band structure on this form of the kinetic equation are then discussed. After expansion and projection onto the complete set of spherical harmonics the kinetic equation is reformulated as a system of ordinary differential equations which is solved numerically. Finally, the simulation results obtained for the chosen physical model are shown and discussed. It should be stressed that in contrast to early works not only the group velocity and the density of states are taken from the full band structure but the whole Boltzmann equation is completely treated within the full band picture and, therefore, when it is applicable, the method represents a deterministic equivalent of the full band Monte Carlo method.