General theory of carrier lifetime in semiconductors with multiple localized states

The Shockley-Read-Hall rate equations determine the average carrier transitions via a single-level defect in the band gap of a nondegenerate semiconductor. In the present work the differential rate equations for multiple levels, or localized states systems, are derived from first principles. These multiple level systems comprise the multiple discrete defects system and the coupled or excited states system. The solution for the single-level rate equations, developed recently for transient decay, is represented by an infinite series of monoexponential terms, the frequencies or inverse time constants of which are a linear combination of the fundamental frequencies v=1/t. For the multiple localized state solution expressions for the fundamental time constants t1+k are derived for m states with k=1,2 , . . . ,m without an approximation at a given temperature for an excess carrier concentration below nondegenerate doping, arbitrary uniform doping concentration NA,D, defect level concentration Nk, cross section snk,pk, and energy level Ek. Verification of the set of rate equations for each system is performed by comparing the analysis of the numerical solution for component time constants with the prediction of the theory. The variation of the fundamental time constant t1 with excess carrier concentration indicates the behavior of minority carrier trapping. © 2004 American Institute of Physics. [DOI: 10.1063/1.1805192]