Electron-transport parameters and tail-state distribution in hydrogenated amorphous silicon obtained from position and tail-state matrix simulation of drift experiments

A new matrix simulation method has been developed in order to predict transient charge transport in amorphous semiconductors. This matrix method takes into account the simultaneous evolution of spatial positions and trap energy levels of carriers by means of a discretization of time, space, and energy of the trapping levels. Diffusion and space-charge effects, either static or due to the moving carriers, are taken into account. It is shown that these effects are noticeable for small drift fields (smaller than 5×${10}^3$ V/cm for a-Si:H). Our calculational method agrees with the thermalization approximation or the Schmidlin approximation in the regions where these approximations are valid; these validity regions are analyzed. The published experimental time-of-flight data on a-Si:H can be fully understood in the framework of multiple-trapping model with the following characteristics: the trap density of states consists of two exponential functions of energy crossing 140 meV below the conduction-band edge, with slopes defined by equivalent temperature $T_1$=370 K and $T_2$=200 K. Neither the dominant state, linear distribution, nor the single exponential tail proposed in the literature is able to describe the whole set of data. The capture cross section σ is independent of trap level energy and is equal to ${10}^{\mathrm{-}15}$ ${\mathrm{cm}}^2$; the weak electron-photon coupling, which implies an exponential behavior of the capture cross section, is then ruled out. Extended-state mobility (${\mu }_{\mathrm{ext}}$) temperature dependence as $T^{\mathrm{-}1}$ is favored. Room-temperature ${\mu }_{\mathrm{ext}}$ is 30 ${\mathrm{cm}}^2$ ${\mathrm{V}}^{\mathrm{-}1}$ ${\mathrm{s}}^{\mathrm{-}1}$ if the first exponential extends from conduction band to 140 meV; this mobility increases up to 130 ${\mathrm{cm}}^2$ ${\mathrm{V}}^{\mathrm{-}1}$ ${\mathrm{s}}^{\mathrm{-}1}$ if the density of states is flat between the conduction band and 90 meV.