Stretched-exponential relaxation modeled without invoking statistical distributions

Relaxation phenomena in disordered systems are often described by stretched exponentials; such behavior has traditionally been explained by invoking statistical distributions. In hydrogenated amorphous silicon, the relaxation has been associated with dispersive diffusion of hydrogen, related to a distribution of energies for trap states and barrier heights. Here we show that invoking such energy distributions is unnecessary; a treatment of hydrogen motion which includes retrapping leads to a functional form of the decay curve which closely resembles a stretched exponential, and provides an excellent fit to experimental data. The implications of the new microscopic model are discussed. {} 1996 The American Physical Society.