The application of the extended pair approximation to hopping conduction in r.f. sputtered amorphous silicon

Abstract

The real and imaginary parts of the frequency-dependent conductivities of amorphous silicon and hydrogenated amorphous silicon samples prepared by r.f. sputtering have been measured over temperatures between 40 and 200 K, where variable-range hopping is the dominant conduction mechanism. The data are interpreted using the extended pair approximation (EPA) of Summerfield and Butcher. This model gives an excellent qualitative fit to the data, describing well the scaling with the reduced frequency ω/σ₁(0) (where σ₁(0) is the d.c. conductivity) and the loss peak observed at the transition from non-dispersive to dispersive conduction (although this feature is rather broader than the EPA theory predicts). Quantitatively the agreement is less good. In particular, the wavefunction decay length (the Bohr radius) derived from the data decreases with increasing temperature in an unphysical manner and becomes very much smaller when hydrogen is introduced into the material. In addition the low-frequency saturation capacitance decreases more rapidly with temperature than predicted by the EPA model. These discrepancies suggest that the conduction mechanism is not adequately described by electron tunnelling in a constant density of localized states. Various recent modifications to this basic model are discussed in the light of the data.