A self-consistent approach to linear and nonlinear transport in an electric field

✍ Scribed by H. Moraal

• Publisher: Elsevier Science
• Year: 1982
• Tongue: English
• Weight: 899 KB
• Volume: 113
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/0378-4371(82)90148-0

✦ Synopsis

The Boltzmann equation for charge carriers (obeying any statistics) is solved analytically in terms of electric-field-dependent relaxation times for a model collision operator. This operator is a linear, rotationally invariant one, which reduces to a multiplicative operator in each irreducible tensor subspace. The relaxation times are given by a self-consistency requirement. This gives (i) an exact solution of the Boltzmann equation for energy-independent multiplicative factors and (ii) exact asymptotic solutions for low-and high-field situations. Ohm's law is shown to hold exactly in case (i). Furthermore, a number of simple models is shown to be exactly soluble. For more complicated cases, perturbative and iterative methods of solution are discussed.