Analysis of AC and DC hopping conductivity in impurity bands and amorphous semiconductors

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The extended pair approximation is used to compare the predictions of the Miller-Abrahams rate equation theory (1960) for AC and DC hopping conductivity with experiment. For an analysis of impurity conduction the authors consider data for n-type silicon and gallium arsenide. In both cases the theory accurately predicts the DC conductivity when reasonable assumptions concerning the density of states are made. In the AC regime the theory provides a good description of the data on silicon but in the case of the gallium arsenide data the theory predicts an onset of AC behaviour at a frequency about six orders of magnitude higher than that observed. Data for amorphous germanium are also analysed. The theory fits the DC conductivity which follows a T-1/4 law, with a characteristic frequency R0, of 1021 Hz. The AC conductivity is qualitatively in agreement but the onset of AC behaviour is two orders of magnitude higher in frequency than is observed.