On the description of hopping-energy relaxation and transport in disordered systems

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Some recent theoretical approaches to the hopping of electrons through localized band-tail states are discussed. Particular attention is given to the approximation in which energy relaxation of non-equilibrium electrons is treated as diffusion in energy space and to the approximation based on the averaging of hopping rates. It is shown that both approaches lead to results different from those based on Mott's semiquantitative technique with averaging hopping distances, not the rates. Detailed analysis shows that both diffusion approximation and averaging of hopping rates are inapplicable to hopping relaxation and transport of carriers in band tails.