Differential relaxation times and diffusivities of hot carriers in isotropic semiconductors

Abstract

The differential relaxation time τ (k,F) defined in a previous paper for isotropic semiconductors in the hot‐carrier range is shown to depend on the orientation with respect to the field force F. τ (k,F) is expressed using the collision operator and the distribution function. In the Ohmic range τ (k,F=0) is found to be equal to the usual relaxation time τ (k) related to transition probabilities per unit time. Longitudinal τ_N(k,E) and transverse τ_n(k,E) differential relaxation times are numerically computed for p‐type germanium and are found to be actually different although of the same order of magnitude, namely 10⁻¹²–10⁻¹³ sec. It is proved that the distribution function for hot carriers may be a displaced Maxwellian only if τ (k) is k independent, which does not hold for most of the situations of physical interest. It is shown that the differential relaxation times involved in longitudinal D_∥(E) and transverse D_⊥(E) diffusion coefficients are τ_∥(k,E) and τ_⊥(k,E). D_∥(E) and D_⊥(E) are numerically computed for p‐type germanium and are found to be in excellent agreement with experimental results. Longitudinal and transverse noise temperatures are identical to the electronic temperature for displaced Maxwellian distribution functions.