Hopping-Randomwalk in Random Fractal Fluctuation and the Application to Photoluminescence Decay in Amorphous Si : H and Nanometer Film

A simulation of hopping-randomwalk of an electron in localized band tail states in random fractal fluctuations has been performed. The exponent ξ in the power law t—ξ (ξ < 1.5), which is obeyed by the electrons at the starting site of the randomwalk increases with increasing temperature and at high temperatures approaches 1.5, the exponent in the case of three-dimensional uniform space. The simulation has been applied to the geminate recombination of a trapped hole with an electron hopping in localized band tail states in the random fluctuation with the fractal dimension of 3.9. The simulated curve of the photoluminescence decay changes from the stretched exponential to the decay described with two power law decay functions with increasing temperature, which agrees with the behavior observed in a-Si : H.