Heisenberg's Uncertainty Principle, Intense Electric Field, Heavily Doped Optoelectronic Quantized Structures and the Electron Statistics

In this paper we show that the direct application of Heisenberg’s uncertainty principle (HUP) leads to the expression of the electron statistics (ES) under extreme degeneracy and intense electric field in bulk, quantum wells, nano wires and in the presence of quantizing magnetic field in III–V, ternary and quaternary materials on the basis of a newly formulated electron dispersion laws without using the usual density-of-states (DOS) function approach for finding out the ES under different physical lattice matched to InP conditions. It appears taking HD InSb, InAs, Hg1−xCdxTe, In1−xGaxAsyP1−y as examples that the Fermi energy increases with increasing electron concentration and the surface electric field in all the cases. Besides the Fermi energy decreases with increasing alloy composition and film thickness in different manners which depend totally on the values of the energy band constants. The Fermi energy oscillates with inverse quantizing magnetic field due to SdH effect. We have also shown that under certain limiting conditions all our generalized results lead to the well known formulas as given in the literature.