Defect relaxation in amorphous silicon: Stretched exponentials, the Meyer-Neldel rule, and the Staebler-Wronski effect.

Annealing and production of metastable defects in disordered solids is explained quantitatively with a model in which defect relaxation is a local phenomenon. The stretched-exponential time dependence of defect relaxation and the Meyer-Neldel rule for the relaxation-time constant are natural consequences of this model. The results are obtained by using an exponential distribution of activation barriers for transitions between the two states of the local defect. The model, applied to data in hydrogenated amorphous silicon, a-Si:H, gives an exponential distribution of barriers with a characteristic temperature of 220 \ifmmode^\circ\else\textdegree\fi{}C, roughly equal to the accepted freeze-in temperature for defect distributions in a-Si:H. The model explains that long degradation times convert defects with higher barriers and this results in longer annealing times. The microscopic models of the metastable defects in a-Si:H, weak-bond breaking and carrier trapping by charged dangling bonds, are discussed in the framework of this defect-relaxation model.