Influence of Size Quantization on the Screening Length in Non-Parabolic Semiconductors

摘要

In this paper an attempt is made to investigate the Screening Length (hereafter referred to as SL) of the electrons in size quantized non-linear optical materials on the basis of a newly formulated electron energy spectrum by considering the anisotropies of the effective electron masses,spin orbit splitting constant of the valence band and the crystal field splitting within the frame work of Kane's ~(→)k · ~(→)p formalism. The results for three and two band models of Kane are the consequence of our generalized study. We alsoinvestigated the influence of size quantization on the SL in III–V, ternary, Quaternary, II–VI, IV–VI, GaP, Te, Ge, Ptsb_(2), GaSb, Bi_(2)Te_(3) and Bi by using the respective energy band models of the said materials. It appears taking size quantized n -type CdGeAs_(2), InAs, InSb, GaAs, Hg_(1–x )Cd_(x) Te, In_(1–x )Ga_(x) As_(y) P_(1–y ) lattice matched to InP, p -CdS, Pb_(1–x )Cdx Te, PbSnTe,PbTe, stressed InSb, GaSb and Bismuth as examples of different technologically important non parabolic semiconductors that the SL decreases with increasing surface electron concentration per unit area and nano thickness in step like fashion where the numerical magnitudes depend on the valuesof the energy band constants. For size quantized Hg_(1–x )Cd_(x) Te and In_(1–x )Ga_(x) As_(y) P_(1–y ) lattice matched to InP, the SL increases with decreasing alloy composition where therates of variations are totally band structure dependent. Under certain limiting conditions all the results convert into the well-known form of the SL for size quantized parabolic energy bands leading to the confirmatory test of our generalized analyses.