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Time-of-flight (TOF) experiments of a-Si: H, in which carrier transport proceeds via multiple trapping in, and re-emission from, a continuous distribution of localized states below the mobility edge, have been analysed using a computer simulation technique based on a numerical inversion of the Laplace transform. A detailed discussion of experimental (TOF) transit time, the moment when the centre of charge leaves the sample at the back contact, and the physical interpretation of activation energies calculated from log(μeff) against 1/T plots is presented. The activation energy is used to determine the trapping region of the tail-state distribution which dominates carrier transport and it is shown that the experimental transit time is approximately the free-carrier transit time plus the total resting time of carriers in traps visited at least once. TOF experiments have been carried out over a wide range of temperature and electric field. Experimental drift mobility data are evaluated to calculate the tail-state distribution at the conduction band for the case of strong and weak electron - multiphonon coupling (SEMPC and WEMPC). Calculations reveal a hybrid distribution of tail states g(E) (for example a linear decay close to the mobility edge followed by a steep exponential) for both SEMPC and WEMPC. It is shown that interpretations of drift mobility data with respect to parameters such as g(E), attempt-to-escape-frequency, and demarcation-energy movement depend strongly on the assumed electron - phonon interaction.