Monte Carlo simulations of the recombination dynamics in porous silicon

A simple lattice model describing the recombination dynamics in visible-light-emitting porous silicon is presented. In the model, each occupied lattice site represents a Si crystal of nanometre size. The disordered structure of porous silicon is modelled by modified random percolation networks in two and three dimensions. Both correlated (excitons) and uncorrelated electron - hole pairs have been studied. Radiative and non-radiative processes as well as hopping between nearest-neighbour occupied sites are taken into account. By means of extensive Monte Carlo simulations, we show that the recombination dynamics in porous silicon is due to a dispersive diffusion of excitons in a disordered arrangement of interconnected Si quantum dots. The simulated luminescence decay for the excitons shows a stretched exponential lineshape while for uncorrelated electron - hole pairs a power-law decay is suggested. Our results successfully account for the recombination dynamics recently observed in experiments. The present model is a prototype for a larger class of models describing diffusion of particles in a complex disordered system.