The transient current of the time-of-flight (TOF) in amorphous hydrogenated silicon calculated from the hopping at localized band tail states with the Monte Carlo simulation is shown to agree with that of the experiment in the line shape and the transit time. The attempt-to-escape frequencies obtained by fitting the electric field dependence of the transit time in the simulation with the Pfister-Ohno equation for the transit time derived from the hopping model, have been far beyond the phonon frequencies as in the case of the experiment. The attempt-toescape frequency has been empirically described with the Meyer-Neldel (MN) rule as well as in the experiment. The MN rule for the attempt-to-escape frequency in the TOF has been concluded to originate in the hopping controlled by the deep localized band tail states from the simulation.

Monte Carlo simulation of hopping‐randomwalk at localized band tail states with the exponential density has been executed. The mean square hopping distance of electrons and the average density of electrons at the starting site after s steps are shown to be given by ∼ sα and ∼ s–γ, respectively. The exponents α andγ increase with temperature and reach 1 and 3/2 at high temperatures, respectively. α is shown to be equal to the dispersion parameter, αi, at short time in the time‐of‐flight experiment. The temperature behaviour of α are shown to agree with that of αi in amorphous hydrogenated silicon (a‐Si:H) observed in the electric field lower than 1×104 V/cm. The average depth of electrons and holes in the exponential tail increases with steps and thermally balance at an energy, which is named the hopping‐edge. The temperature dependence of the hopping‐gap, which means the energy difference between electron and hole hopping‐edges, agrees with that obtained from the excitation energy dependence of the luminescence peak energy in a‐Si:H. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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