Analytic and Quasi-analytic Results in High-Field Transport in a Semiconductor
Dr. Richard Liboff
Friday, February 10, 2006
1:30PM-3:00PM in HPA-112
Abstract
A general introduction to elements of semiconductor physics is presented, including discussions of E-k diagrams as well as the four fundamental electron-phonon interactions. The quantum-generalized Boltzmann equation is reviewed and applied to high-field transport in a semiconductor. From this analysis a new kinetic equation for the electron distribution function is derived which includes terms corresponding to the four electron-phonon interactions. In the quasi-classical limit, it is found that the acoustic strain interaction dominates, which gives rise to a reduced kinetic equation. In the steady-state limit this equation yields a second-order nonlinear differential equation for the perturbation distribution. The exact solution of the related nonlinear equation represents a significant new result. The distribution function is a generalized Fermi-Dirac distribution which contains the electric field explicitly and is found to reduce to correct forms in various limits. The analysis is then extended to Silicon, where `equivalent' intervalley scattering comes into play. Drift velocity obtained from the approximate solution of resulting equations is found to agree with observed values for electric fields up to $10^{5}$ V/cm. A criterion is described discerning between linear and nonlinear electric field effects.
Short Bio
Dr. Liboff has nearly 150 publications in many areas of pure and applied physics, pure and applied mathematics, planetary physics, galaxy correlations, cosmology, and quantum chaos. He is the author of four texts of which the most well known is his work, Introductory Quantum Mechanics, 4th edition.
At present he is Distinguished Professor of Physics at the University of Central Florida.
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