SOLUTION OF THE MU-TAU PROBLEM IN A-SI-H

The aim of the paper is to explain what we call the mu-tau problem in undoped hydrogenated amorphous silicon (a-Si:H), that is the difference of about two orders of magnitude between the mobility-lifetime product (mu-tau)ss, deduced from steady-state photoconductivity and the mobility-lifetime product (mu-tau)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 mu-D and the deep-trapping time tau-D. 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 mu-tau in this case. We show by computer modelling that mu-D-tau-D deduced from TOF primary photocurrent transients is trap limited, independent of time and equal to mu-tau (product of free mobility and free lifetime). This allowed us to exclude another recently suggested solution of the mu-tau 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 basic 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 mu-tau problem is explained by the fact that photoconductivity is controlled by majority (recombination-limited)tau-Re, 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 technique measurements the computed values for undoped a-Si:H, (mu-tau)e almost-equal-to 100(mu-tau)h, have been experimentally confirmed. Both these techniques have been used also for slightly doped samples and clear anticorrelated changes in (mu-tau)e and (mu-tau)h demonstrated. The ratio (mu-tau)e/(mu-tau)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) almost-equal-to 0.2 eV or U(eff) almost-equal-to 0 for undoped a-Si:H. It is shown that the most important parameter responsible for (mu-tau)e almost-equal-to 100(mu-tau)h is the dark Fermi level, placed in undoped a-Si:H above the midgap.