Abstract
An attempt is made to study the Einstein relation for the diffusivity-mobility ratio of the carriers in quantum confined non-parabolic semiconductors in the presence of a parallel magnetic field at low temperatures on the basis of new electron dispersion laws of quantum wells (QWs) and quantum wells wires (QWWs) of such materials. It is found, taking QW and QWWs of Hg1−xCdxTe and In1−xGaxAsyP1−y lattice-matched to InP as examples, that the diffusivity-mobility ratio increases with increasing electron concentration, decreasing alloy composition and decreasing film thickness in various oscillatory manners in both the cases. The magnetic field and the quantum wire structure enhance the numerical values of the same ratio. We have suggested an experimental method of determining the Einstein relation in degenerate materials having arbitrary dispersion laws. In addition, the corresponding well-known results of relatively wide-gap quantum confined materials in the absence of the magnetic field have been obtained as special cases of our generalized formulations, under certain limiting conditions.
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