Recombination-generation noise theory for semiconductors in equilibrium

Abstract

This paper offers a unified discussion of equilibrium recombination-generation noise in semiconductors, and of its relation to the steady-state and transient lifetimes. It extends many existing results and covers situations where certain types of Auger processes, as well as one-electron transitions, contribute to the noise. The cases of degenerate bands, and of centres each able to trap one or more electrons are included. The new general results are, however, on the whole less complicated in form than their already known special cases. This is in part due to the fact that the equations are here expressed in a form which is symmetrical in bands and traps, so that there is no need to distinguish between them in the formal part of the theory. The following procedure is used. The formalism of irreversible thermodynamics is applied to a certain class of systems of which a homogeneous semiconductor is an example. The kinetic equations are written in a form involving generalized resistance and capacitance matrices. An admittance matrix and a lifetime matrix are introduced, and expressions for the steady-state and transient lifetimes in terms of the latter are obtained. Results from semiconductor statistics are used to evaluate these matrices in terms of the equilibrium electron numbers in, and transition rates between, the various groups of states (bands and localized levels) in the semiconductor. It is shown that the transition rates due to a certain class of Auger processes have the same dependence on quasi-Fermi levels as the transition rates due to corresponding single-electron processes. The fluctuation-dissipation theorem is applied, relating the spectral densities and variances of the fluctuating electron numbers to the admittance matrix, and so to the equilibrium numbers and transition rates. Problems involving two or three groups of states are considered in detail, and connexions with previous results are established.