Experimental and Theoretical Investigations in Semiconductors Concerning the Boltzmann Equation

Abstract

Transport phenomena in solids including semiconductors are described by the Boltzmann equation. For obtaining solutions it is essential whether the scattering processes cause a weak or a strong anisotropy of the distribution function. The former case is known as the “diffusion approximation” and has been investigated very carefully while the second case (spiked distribution, streaming effect) occurs mainly at strong interaction of hot carriers with the optical modes of lattice vibration at low lattice temperatures. Essentially four methods have been applied for an investigation of transport phenomena:

• (1) The assumption of a drifted Maxwell-Boltzmann distribution in non-degenerate semiconductors and the transformation of the transport equation into balance equations for momentum and energy,

• (2) Variational methods,

• (3) Monte Carlo methods, and

• (4) Methods of iteration.

All four methods have been applied in interpreting experimental data on energy relaxation both in non-polar and polar semiconductors. The Monte Carlo method has been for static and dynamical calculations which demonstrate the influence of various physical constants on the mechanisms of heating and intervalley transfer of carriers. Finally the relaxation of the high-frequency conductivity of hot electrons in InSb has been calculated by the iterative method.