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Einstein Relation in Quantum Wells and Nipi Structures of Nonlinear Optical, Optoelectronic and Related Materials: Simplified Theory, Relative Comparison and Suggestion for an Experimental Determination

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Abstract:

In this paper, an attempt is made to study the Einstein relation for the diffusivity-to-mobility ratio (DMR) in quantum wells (QWs) and nipi structures of non-linear optical materials on the basis of a newly formulated electron dispersion law considering the anisotropies of the effective electron masses, the spin orbit splitting constants and the influence of crystal field splitting within the framework of k ยท p formalism. The corresponding results for III–V, ternary and quaternary compounds form a special case of our generalized analysis. The DMR has also been investigated for QWs and nipi structures of II–VI, IV–VI, stressed materials, n-Ge, n-GaP, p-PtSb2, n-GaSb, and zero gap compounds on the basis of the appropriate carrier energy spectra by incorporating the respective energy band constants. It has been found, taking QWs and nipi structures of n-CdGeAs2, n-InAs, n-InSb, n-Hg1−xCdxTe, n-In1−xGaxAsyP1−y lattice matched to InP, p-CdS, n-PbS, n-PbSe, n-PbTe, stressed n-InSb, n-Ge, n-GaP, p-PtSb2, n-GaSb, and p-HgTe, as examples, that the DMR in QWs of aforementioned materials exhibits oscillatory dependences with the increasing electron statistics with different numerical values and the nature of oscillations are totally different as compared with the corresponding nipi structures although they depend exclusively on the respective band structures and the energy band constants emphasizing the different signatures of the two entirely different two dimensional nanostructured systems in various cases. The well-known expression of the 2D DMR for wide gap materials has been obtained as special cases from all the results under certain limiting conditions and this compatibility is the indirect test of our generalized formalism. In addition, we have suggested an experimental method of determining the Einstein relation for the diffusivity-mobility-ratio for nanomaterials having arbitrary dispersion laws.
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  • Journal of Computational and Theoretical Nanoscience is an international peer-reviewed journal with a wide-ranging coverage, consolidates research activities in all aspects of computational and theoretical nanoscience into a single reference source. This journal offers scientists and engineers peer-reviewed research papers in all aspects of computational and theoretical nanoscience and nanotechnology in chemistry, physics, materials science, engineering and biology to publish original full papers and timely state-of-the-art reviews and short communications encompassing the fundamental and applied research.
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