Influence of Light on the Einstein Relation in Ultra-Thin Films of III–V, Ternary and Quaternary Materials: Simplified Theory, Relative Comparison and Suggestion for Experimental Determination

In this paper, we study the Einstein relation for the diffusivity-mobility ratio (DMR) in ultra-thin films of III–V, ternary and quaternary materials in the presence of light waves, whose unperturbed energy band structures are defined by the three-band and two band models of Kane together with parabolic energy bands. The solution of the Boltzmann transport equation on the basis of the newly formulated electron dispersion laws will introduce new physical ideas and experimental findings under different external conditions. It has been found, taking ultrathin films of n-InAs, n-InSb, n-Hg_1−x Cd _x Te, n-In_1−x Ga _x As _y P_1−y lattice matched to InP, as examples, that the respective DMR in the aforementioned materials exhibits decreasing quantum step dependence with the increasing film thickness, decreasing electron statistics, increasing light intensity and wavelength, with different numerical values. The DMR decreases with increasing alloy composition and the nature of the variations are totally band structure dependent which is influenced by the presence of the different energy band constants. The strong dependence of the DMR on both the light intensity and the wavelength reflects the direct signature of the light waves which is in contrast as compared with the corresponding ultra-thin films of the said materials in the absence of photo-excitation. The well-known result for the DMR for degenerate wide gap materials in the absence of any field 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 ultrathin materials in the presence of light waves having arbitrary dispersion laws.