Decay Dynamics in Disordered Systems: Application to Heavily Doped Semiconductors

We have calculated, quantitatively, the time decay of donor-acceptor pair luminescence in compensated semiconductors, incorporating the effect of the potential fluctuations which exist in such materials. We show that the often-reported stretched-exponential decay law can here be derived rigorously, but only to a very close approximation, and, moreover, only provided that there is an alternate, activated, decay path. We also show that in the absence of such an alternate path, the decay is slower. We thus conclude that the stretched-exponential ``law'' provides good empirical fitting, but has no fundamental significance.