Pseudoultrarelativistic behavior and specification of spinlike effects in the two-dimensional electron gas in Kane semiconductors with direct and inverted band structure.

Abstract

found to be independent of surface densities ns , subband index i, and uEgu at high enough ns when the band bending sufficiently exceeds the gapEg and the conditions corresponding to pseudoultrarelativistic behavior of surface electrons are fulfilled. However, they are different for Eg.0 and Eg,0 cases. To analyze spinlike effects in narrow-gap and gapless semiconductors, we employed for Kane Hamiltonian the conception, offered by Zel’dovich and Migdal for the description of vacuum condensate of Dirac’s electrons near supercritical nuclei. In this way, we obtain ‘‘usual’’ Schrodinger-like subband equations with some effective potential. The terms responsible for nonparabolicity, spin-orbit splitting, and ‘‘resonant’’ shift, due to interband mixing by surface electric fields, are easily singled out. Such equations admit the simple physical interpretation, and difference in values of ‘‘spin’’ effects for Eg.0 and Eg,0 cases is easily seen. The dependencies of total subband occupations ni5n i 1n i and average cyclotron masses on ns nevertheless are close for both cases in agreement with previous experimental observations. In a pseudoultrarelativistic limit Eg50 the simple analytical expressions for subband parameters of experimental interest are obtained with an allowance for spin effects. The calculations agree with experiment for HgxCd12xTe with both direct and inverted bands, excluding the region of low ns in heavily doped samples. Possible reasons for disagreement are discussed. @S01631829~96!00420-1# The interest in both theoretical 1‐11 and experimental 12‐21 investigations of two-dimensional electron gas in the surface layers on the narrow-gap semiconductors, essentially extensive since the mid 1980s, is caused by a various number of the specific peculiarities inherent to these systems. Part of them directly follows from the smallness of effective mass: ~a! the large depth and width of surface quantum well and as a result the multisubband character of spectrum; ~b! the high values of Fermi energy and, consequently, the weak impact of many-body effects and fluctuations of potential; ~c! the degeneration of electron gas in substrate for accumulation layers leading to the effects caused by the involvement of continuum electrons in the screening of surface field. 22‐24 The most important peculiarities of these systems follow from the multiband nature of the Hamiltonian describing the bulk spectrum in narrow-gap semiconductors. Neglecting spinlike effects ~but keeping the Fermi statistic!, the effective-mass equation for electrons in surface potential is reduced to Klein-Gordon ~KG!-like equation, i.e., such systems are the relativistic analog, with respect to twodimensional ~2D! systems based on wide-gap semiconductors. 17,25 This leads to such relativisticlike effects as strong nonparabolicity and kinetic confinement ~motional binding!. 24,26,27