Influence of light on the Einstein relation in III–V, ternary and quaternary materials: Simplified theory and a suggestion for experimental determination

We study theoretically the energy spectrum of the conduction electrons and the Einstein relation for the diffusivity–mobility ratio (DMR) for III–V, ternary and quaternary materials, whose unperturbed energy band structures are defined by the three-band model of Kane, in the presence of light waves. The solution of the Boltzmann transport equation on the basis of this newly formulated electron dispersion law will introduce new physical ideas and experimental findings under different external conditions. It has been observed that the unperturbed isotropic energy spectrum in the presence of light changes into an anisotropic dispersion relation with the energy-dependent mass anisotropy. It has been found taking n-InAs, n-InSb, n-Hg1−xCdxTe and n-In1−xGaxAsyP1−y lattice matched to InP, as examples that the DMR increases with increasing electron concentration, decreasing with increasing intensity and wavelength in various manners. The rate of change is totally band structure dependent and is influenced by the presence of the different energy band constants. The well-known result for the DMR for degenerate wide gap materials in the absence of light waves has been obtained as a special case of the present analysis under certain limiting conditions and this compatibility is the indirect test of our generalized formalism. Besides, we have suggested an experimental method of determining the DMR in degenerate materials having arbitrary dispersion laws.