The Electronic Contribution to The Elastic Constants of Strained III–V Materials Under High Magnetic Fields

Abstract: An attempt is made to study the two dimensional (2D) effective electron mass (EEM) in quantum wells (Qws), inversion layers (ILs) and NIPI superlattices of Kane type semiconductors in the presence of strong external photoexcitation on the basis of a newly formulated electron dispersion laws within the framework of k.p. formalism. It has been found, taking InAs and InSb as examples, that the EEM in Qws, ILs and superlattices increases with increasing concentration, light intensity and wavelength of the incident light waves, respectively and the numerical magnitudes in each case is band structure dependent. The EEM in ILs is quantum number dependent exhibiting quantum jumps for specified values of the surface electric field and in NIPI superlattices; the same is the function of Fermi energy and the subband index characterizing such 2D structures. The appearance of the humps of the respective curves is due to the redistribution of the electrons among the quantized energy levels when the quantum numbers corresponding to the highest occupied level changes from one fixed value to the others. Although the EEM varies in various manners with all the variables as evident from all the curves, the rates of variations totally depend on the specific dispersion relation of the particular 2D structure. Under certain limiting conditions, all the results as derived in this paper get transformed into well known formulas of the EEM and the electron statistics in the absence of external photo-excitation and thus confirming the compatibility test. The results of this paper find three applications in the field of microstructures.

Abstract: We study the thermoelectric power under classically large magnetic field (TPM) in ultrathin films (UFs), quantum wires (QWs) of non-linear optical materials on the basis of a newly formulated electron dispersion law considering the anisotropies of the effective electron masses, the spin-orbit splitting constants and the presence of the crystal field splitting within the framework of k.p formalism. The results of quantum confined III-V compounds form the special cases of our generalized analysis. The TPM has also been studied for quantum confined II-VI, stressed materials, bismuth and carbon nanotubes (CNs) on the basis of respective dispersion relations. It is found taking quantum confined CdGeAs2, InAs, InSb, CdS, stressed n-InSb and Bi that the TPM increases with increasing film thickness and decreasing electron statistics exhibiting quantized nature for all types of quantum confinement. The TPM in CNs exhibits oscillatory dependence with increasing carrier concentration and the signature of the entirely different types of quantum systems are evident from the plots. Besides, under certain special conditions, all the results for all the materials gets simplified to the well-known expression of the TPM for non-degenerate materials having parabolic energy bands, leading to the compatibility test. (C) 2009 Elsevier B.V. All rights reserved.

Abstract: This chapter explores the quantum capacitance (\( C_{\text{g}} \)) in quantum wire field-effect transistors (QWFETs) manufactured from completely different technologically vital nonstandard materials by using all types of anisotropies of band structures in addition to splitting of bands due to large fields of the crystals inside the framework of Kane’s matrix methodology that successively generates new 1D dimensional electron energy versus wave vector relation. We derive the \( C_{\text{g}} \) under very low temperature so that the Fermi function tends to unity for QWFETs of \( {\text{Cd}}_{3} {\text{As}}_{2} ,{\text{CdGeAs}}_{2} ,{\text{InSb}},{\text{Hg}}_{1 - x} {\text{Cd}}_{x} {\text{Te}},{\text{InAs}},{\text{GaAs}},{\text{In}}_{1 - x} {\text{Ga}}_{x} {\text{As}}_{y} {\text{P}}_{1 - y} \) IV–VI, stressed materials,\( {\text{Te}},{\text{GaP,PtSb}}_{2} ,{\text{Bi}}_{2} {\text{Te}}_{3} ,{\text{Ge}},{\text{GaSb}} \) and II–V compounds using the appropriate band models. The \( C_{\text{g}} \) becomes the functions of the thickness of the quantum-confined transistors. The \( C_{\text{g}} \) varies with varying film thickness in various quantized steps and saw-tooth manners with different numerical values.

Abstract: In this book, we have discussed many aspects of TPSM based on the dispersion relations of the nanostructures of different technologically important materials having different band structures in the presence of 1D, 2D, and 3D confinements of the wave-vector space of the charge carriers, respectively. In this chapter, we discuss few applications in this context in Sect. 14.2 and we shall also present a very brief review of the experimental investigations in Sect. 14.3 which is a sea in itself. Section 14.4 contains the single experimental open research problem.

Abstract: This chapter suggests the experimental determinations of 2D and 3D ERs for HD materials having arbitrary dispersion laws. The theoretical results for bulk specimens of n-Cd3As2 in the absences of band tailing are in good agreement with the suggested relationship. The concept of band gap measurement in the presence of intense external light waves is also discussed and we present additional five related applications in this context. This chapter contains a single multi-dimensional deep open research problem.

Abstract: An attempt is made to investigate theoretically the effects of varying the orientation of a quantizing magnetic field on the Einstein relation for the diffusivity-mobility ratio of the electrons in stressed Kane-type semiconductors, taking stressed n-InSb as an example. It is found, that the above ratio oscillates in a periodic manner with changes in the orientation of the magnetic field and increases with increasing electron concentration as expected in degenerate semiconductors. The ratio also exhibits oscillatory magnetic field dependence since the origin of the oscillations in the Einstein relation is the same as that of the Shubnikov de Hass oscillations. The corresponding well-known results for unstressed parabolic energy bands are also obtained from the generalized expressions as special cases.

Abstract: An attempt is made to study the Einstein relation for the diffusivity‐mobility ratio of the electrons in degenerate n‐type small‐gap semiconductors under strong magnetic field on the basis of three‐band Kane model without any approximations of band parameters and incorporating the electron spin and broadening of Landau levels, respectively. It is found, taking n‐Hg1−xCdxTe as an example, that the Einstein relation exhibits an oscillatory magnetic field dependence due to Shubnikov–de Haas effect and decreases with increasing alloy composition. Besides the same ratio increases with increasing electron concentration and is in close agreement with the suggested experimental method of determining the Einstein relation in degenerate semiconductors having arbitrary dispersion laws. In addition, the corresponding well‐known results of parabolic semiconductors both in the presence and absence of magnetic field have been obtained from the generalized expressions under certain limiting conditions.

Abstract: We present here the first demonstration that oxide‐free anodic sulfide layers can be grown on HgCdTe from aqueous electrolytic solutions. Previous work has shown that anodic sulfide films grown from nonaqueous solutions have great potential as passivating layers for HgCdTe. In this work Auger electron spectroscopy depth profiles are used to show that little or no oxide is left at the HgCdTe/CdS interface even when an aqueous growth electrolyte is utilized. Capacitance‐voltage data on metal‐insulator‐semiconductor structures show that the temperature stability of the aqueous sulfide films may be superior to those grown from nonaqueous electrolytes.

Abstract: Data are presented showing that the native oxide that can be formed on high Al composition AlxGa1−xAs (x≳0.7) confining layers commonly employed on AlxGa1−xAs‐AlyGa1−yAs‐AlzGa1−zAs (y≳z) superlattices or quantum‐well heterostructures serves as an effective mask against Si diffusion, and thus impurity‐induced layer disordering. The high‐quality native oxide is produced by the conversion of high‐composition AlxGa1−xAs (x≳0.7) confining layers via H2O vapor oxidation (≳400 °C) in N2 carrier gas.