Heavily Doped Semiconductors and the Diffusion Coefficient to Mobility Relationship

In this paper we study the diffusion coefficient to mobility relationship (DMR) in quantum wells (QWs) of heavily doped (HD) nonlinear optical semiconductors on the basis of a newly formulated electron statistics considering all types of anisotropies of the energy band spectrum within the frame-work of k.p formalism in the presence of Gaussian band tails. The results for III-V, ternary and quaternary materials form a special case of our more generalized analysis of non-linear optical compounds. We have also investigated the DMR for QWs of HD II-VI, IV-VI, stressed Kane type semiconductors, Te, GaP, PtSb2, Bi2Te3, Ge and GaSb on the basis of newly derived respective E-k relation under the condition of heavy doping. We observe that the DMR increases with increasing electron concentration and decreasing film thickness in step like manner which is the characteristic feature of such two dimensional (2D) structures and the numerical values are totally band structure dependent. The analyses for bulk HD materials have also been performed for the purpose of relative comparison. The most striking features are that the presence of poles in the dispersion relation of the materials in the absence of band tails create the complex energy spectrum in the corresponding HD samples and effective electron mass exists within the band gap which is impossible without the concept of the band tails. In the absence of band tails and under certain limiting conditions all the results for all the cases get simplified into the well-known parabolic energy bands as derived for the first time by Landsberg and thus confirming the compatibility test. We have suggested an experimental method of determining 2D and 3D DMRs for materials having arbitrary dispersion laws and the content of this paper finds eight applications in the realm of low dimensional electronics.