  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 nanometer size. The disordered structure of porous
Silicon is modeled 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 neighbor 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 the experiments.
The present model is a prototype for a larger class of models describing
diffusion of particles in a complex disordered system.
