A unified statistical approach to recombination-generation noise in semiconductors

Abstract

This paper outlines a unified discussion of equilibrium recombination—generation noise in semiconductors. It extends existing results in order to cover situations where certain types of Auger (electron collision) processes, as well as one-electron transitions, contribute to the noise. In order to achieve this, irreversible thermodynamics is used. The kinetic equations are written in a form involving generalized resistance and capacitance matrices. An admittance matrix and a lifetime matrix are also introduced. Results from semiconductor statistics are applied to evaluate these matrices in terms of the equilibrium electron numbers in, and equilibrium transition rates between, the various groups of states (bands and localized levels). The spectral densities and variances of the fluctuating electron numbers are related to the admittance matrix, and so finally to the equilibrium numbers and the transition rates, by means of the fluctuation-dissipation theorem. The spectral densities are in all cases superpositions of familiar terms of the form A k (1 +ω 2τ 2 k) , and the paper outlines a general method of obtaining the coefficients A k and the transient lifetimes τ k .