Dispersion Relations of Heavily Doped Quantum Wells

In this paper an attempt is made to study the Dispersion Relations (DRs) of Quantum Wells (QWs) of Heavily Doped (HD) nonlinear optical semiconductors on the basis of a newly formulated DR considering all types of anisotropies of the energy band spectrum within the framework of k·p formalism in the presence of Gaussian band tails. We have also investigated the DRs of QWs of HD III–V, II–VI, IV–VI, stressed Kane type semiconductors, Te, GaP, PtSb2, Bi2Te3, Ge, GaSb, II–V, Lead Germanium Telluride, Zinc and Cadmium Diphosphides respectively. The constant energy wave-vector space is a three dimensional close volume and for 2D electrons E – k2 s plots are the quantized circles, quantized ellipses and closed 2D quantized surfaces in both real and complex planes respectively. As a direct consequential study we have also investigated the 2D sub-band energies, the density-of-states (DOS) functions and the effective electron mass (EEM) for the aforementioned cases. The most striking features are that the presence of poles in the DRs of the materials in the absence of band tails creates the complex energy spectrum in the corresponding HD samples and the complex DOS function. Besides, the EEM exists within the band gap which is impossible without the concept of band tailing effects. The EEM at any energy and the sub-band energies are concentration dependent, a fact only possible as the consequence of heavy doping for all types of HD QWs. In the absence of band-tails, the imaginary part vanishes and all the HD DRs get simplified to the well-known results of the electron energy spectra of all the materials and thus confirming the compatibility test. The content of this paper finds twenty-seven applications in the fields of Quantum Science and Technology in general.