EINSTEINS RELATIONSHIP FOR HOPPING ELECTRONS

Photoconductivity in amorphous semiconductors at very low temperatures is temperature-independent. being determined by the energy-loss hoppi ng of carriers through localized band-tail states. In such a hopping r elaxation, neither diffusion coefficient, D, nor mobility of carriers, mu, depend on temperature and the conventional form of the Einstein's relationship mu = eD/kT is not valid. The relationship between mu and D for the hopping relaxation of electrons in the exponential band tai l is calculated and it is shown that it has the form mu proportional t o eD/epsilon(0), where epsilon(0) is the energy scale of the exponenti al band tail.