Solution of the μτ problem in a-Si: H

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Abstract
The aim of the paper is to explain what we cali the μτ problem in undoped hydrogenated amorphous silicon (a-Si: H), that is the difference of about two orders of magnitude between the mobility-lifetime product (μτ)ss, deduced from steady-state photoconductivity and the mobility-lifetime product μτ cc deduced from time-of-flight (TOF) charge collections. First of all, anisotropy is excluded as a solution. Then primary photocurrent transients are studied by computer modelling, namely carrier thermalization after a laser pulse, the time dependence of drift mobility μ D and the deep-trapping time τD. We assume that multiple trapping is dominant and neglect tunnelling transitions. We demonstrate that, for anomalous dispersive transport, Hecht's formula cannot be used and outline how to deduce μτin this case. We show by computer modelling that μ D τ D deduced from TOF primary photocurrent transients is trap limited, independent of time and equal to μτ (product of free mobility and free lifetime). This allowed us to exclude another recently suggested solution of the μτ problem: the difference between transient and steady-state demarcation levels. We present extensive modelling of the steady-state secondary photocurrent, which is recombination limited. Computed free-carrier concentrations show that there are many more free electrons than holes. Computed lux-ampere characteristics are presented and their basie features confirmed by experimental results. Hole trapping is the bottleneck of recombination and, as a result, the free recombination lifetime of the electron (majority carrier) is much higher than that of the hole (minority carrier). The μτ problem is explained by the fact that photoconductivity is controlled by majority (recombination-limited) τRe, which represents many trapping events before recombination with a hole takes place and contrary to it TOF is controlled in principle by a single-trapping event. From steady-state photoconductivity and grating techniaue measurements the computed values for undoped a-Si:H, (μτ)e≈100(μτ)h, have been experimentally confirmed. Both these techniaues have been used also for slightly doped samples and elear anticorrelated changes in (μτ)e and (μτ)h demonstrated. The ratio (μτ)e/(μτ)h is independent of the number N db of dangling bonds because it is given by the position of Fermi level and effective correlation energy U eff only, neither of which is a function of N db. The method which allows U eff to be deduced is outlined. From this, two possible values are obtained: U eff≈0.2eV or U eff≈0 for undoped a-Si: H. It is shown that the most important parameter responsible for (μτ)e≈100(μτ)h is the dark Fermi Ievel, placed in undoped a-Si: H above the midgap.