Determination of the density of states of the conduction-band tail in amorphous materials: Application to a-Si_1−xGe_x:H alloys

Abstract

Electronic transport in hydrogenated amorphous silicon (a-Si:H) and in hydrogenated amorphous silicon-germanium alloys (a-Si_1-xGe_x:H) has been studied by means of time-of-flight experiments, mainly in the temperature range where the transport is dispersive. It is shown that the use of the pre-transit slope of the current in a plot of In I against In t, in addition to the determination of the transit times, can lead to an estimate of the shape of the density of states. First, we apply this technique to the results of a numerical simulation based on a matrix method; the deduced densities of states agree well with those introduced. Then we apply the method to a sample of a-Si: H, whose density of states had already been deduced using a completely different method based on the Fourier transform of the derivative of the current obtained when the transport is non-dispersive. The agreement between the results of the two methods is excellent. In this a-Si: H sample it is found that the density of tail states could be approximated by a double-exponential distribution, the characteristic temperatures of which are T _c1 ≈ 400 K (0eV<E _c—E<0·20eV) and T _c2≈200K (0·20eV<E _c—E). Time-of-flight measurements on a sample of a-Si_1-xGe_x: H (x = 0·18) have shown that transport is dispersive in the whole range of measurement temperatures (210K<T<320K). For this alloy sample, it is found that the density of states can be approximated by three exponential distributions, the characteristic temperatures of which are T _c1≈600K (0eV<E _c-E<0·28eV), T _c2≈400K (0·28eV<E _c -E< 0·35eV) and T _c3≈800K (0·35eV<E _c-E). We have also found that under the hypothesis of a constant attempt-to-escape frequency the extended-state mobility varies as T ⁻¹ in amorphous silicon alloys.