Connection between the Meyer-Neldel rule and stretched-exponential relaxation

We demonstrate that the key element for a thermally activated process to follow the stretched-exponential relaxation and the Meyer-Neldel rule is the exponential energy distribution of defect traps. We point out that the characteristic temperature associated with the exponential energy distribution obtained from the stretched-exponential relaxation and the Meyer-Neldel rule should have the same value. This criterion provides a very good test for the underlying mechanism as proposed. The model is applied to the data in semi-insulating GaAs. We show that the decay of the persistent photoconductivity of the studied material after different illumination time follows the stretched-exponential relaxation. The obtained characteristic temperature ${\mathit{T}}_0$=453 K is in excellent agreement with that from the Meyer-Neldel rule for the dc conductivity measurement. The model is also successfully confirmed by the data in hydrogenated amorphous silicon.