Carrier Lifetimes in Semiconductors with Two Interacting or Two Independent Recombination Levels

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Abstract
Carrier recombination under (a) arbitrary steady-state and (b) small-signal near-equilibrium transient conditions has been studied theoretically for a two-interacting-level (ITL) model and a two-independent-level (IDL) model. Analytic solutions for carrier lifetimes have been obtained and manipulated into a form which facilitates comparison between the two models, as well as comparison between the steady-state and transient lifetimes as predicted by each model. It is shown that under small-signal steady-state and transient conditions the two interacting levels may be treated, with little loss of accuracy, as two independent levels, provided we describe the effective flaw density at each level by interacting-level equilibrium statistics. However, under appropriate conditions, the use of either ITL or IDL equilibrium statistics leads to essentially the same lifetimes; the ITL model is then indistinguishable from the IDL model. A comparison of the steady-state and transient lifetimes, whether of two interacting or two independent levels, shows that in certain circumstances the transient lifetime can exceed the sum of the steady-state electron and hole lifetimes, a possibility which does not exist if only one level is present. As a numerical example, the lifetimes in gold-doped silicon have been calculated and compared. Some possible applications of this work are proposed.