Electron-hole recombination, disordered spins and the nearest-available-neighbour distribution

The unsolved problem of the recombination of randomly distributed electrons and holes is discussed through the nearest-available-neighbour distribution, for which an asymptotic form is found, An interpolation provides an expression for the pair survival time, in excellent agreement with numerical simulations. It also provides a quantitative basis for understanding the slow decay of luminescence, light-induced ESR and photoabsorption in semiconductors like a-Si: H. The nearest-available-neighbour distribution does not provide a satisfactory description of disordered spin systems in which pairing provides only a crude approximation to the temperature dependence of the susceptibility.