On the derivation and integration of stochastic reaction equations for electronic processes in semiconductors

Abstract

Stochastic reaction equations for electrons in semiconductors contain differential transition probabilities for radiative and nonradiative processes. The radiative transition probabilities are well known, the nonradiative ones have to be calculated. Nonradiative processes occur only if they are accompanied by resonance phonon states (dressed phonons). The dressed phonon states are calculated in the lowest order and the nonradiative transition probabilities are given. Then the reaction equations contain electronic and phonon quantum numbers. For the integration the stochastic phonon subsystem is solved exactly. This allows a solution of the total system, and the long time behaviour of electronic reactions is calculated.