Determination of the density of states of the conduction-band tail in hydrogenated amorphous silicon

The electronic transport in hydrogenated amorphous silicon (a-Si:H) is studied by means of a time-of-flight experiment performed on samples presenting a classical sandwich configuration. Both macroscopic and microscopic behaviors are analyzed. From the experimental results we determine, when the transport is nondispersive or slightly dispersive and with a minimum of assumptions, the density of carriers reaching the rear collection electrode. By means of a Fourier transform we can compare this quantity to the solution of the general transport equations of the ``conventional'' multiple-trapping problem in the Fourier space. The determination of the time constants controlling the interaction of the conduction-band tail with the extended states during the transit of the carriers results from the comparison of these two expressions. Therefore we can derive the shape of the density of states of the conduction-band tail in the energy range 0.1Ec-E0.3 eV. We have applied this method to the results of various numerical simulations. The range of validity of the method is given: The diffusion has simultaneously a negligible effect on the transport mechanism in the conduction band and a negligible enlargement of the packet width.From the computed transits the introduced densities of states were found again. As these tests were positive, we have carried out experiments on different samples. These time-of-flight experiments were performed at various applied fields (10³{≤}{}scrE{}{≤}3×{}10⁴ V/cm) and various temperatures (200{≤}T{≤}350 K) with a very low injected charge ({}10^-12 C) and reasonably thick samples ({}4.5 {μ}m). Our method applied to our experimental results shows that the density of states of the conduction-band tail can be roughly approximated by an exponential distribution, the characteristic temperature of which is 200 K for the states located in the (0.2--0.3)-eV energy range. Near the conduction-band edge, the density of states can be approximated by another exponential distribution, the characteristic temperature of which is mainly related to the assumed mobility and the attempt-to-escape--frequency values. This temperature is typically 400 K.