2D Einstein Relation in Quantum Wells Under Strong Electric Field

Abstract

In this paper we study the influence of strong electric field on the two dimensional Einstein Relation (2D ER) in quantum wells of III-V, ternary and quaternary semiconductors within the framework of k.p formalism by formulating a new electron energy spectrum. It appears taking quantum wells of InSb, InAs, Hg 1−x Cd x Te and In 1−x Ga x As 1−y P y lattice matched to InP as examples that the ER decreases with increasing film thickness, electric field and increases with increasing surface electron concentration exhibiting spikey oscillations because of the crossing over of the Fermi level by the quantized level in quantum wells and the quantized oscillation occurs when the Fermi energy touches the sub-band energy. The ER increases with decreasing alloy composition where the variations are totally band structure dependent. Under certain limiting conditions all the results for all the cases get simplified into the well-known parabolic energy bands and thus confirming the compatibility test. We have suggested an experimental method of determining 2D ER for materials having arbitrary dispersion laws.

Heisenberg’s Uncertainty Principle and the Electron Statistics in Quantized Structures

“…Chapter 2 of this book investigates the ES by applying the HUP under intense electric field, chronologically for all the specific cases as given in the content of Chap. 2 [75][76][77][78][79][80][81][82][83][84][85][86][87][88][89][90]. It is interesting to note that the EEM depends on the strong electric field (which is not observed elsewhere) together with the fact that the EEM in the said systems depends on the respective quantum numbers in addition to the Fermi energy the scattering potential and others system constants which are the characteristics features of such hetero-structures.…”