In this paper, an attempt is made to study the effective electron mass (EEM) in Quantum wires (QWs) of III-V, ternary and quaternary materials on the basis of three and two band models of Kane within the framework of k x p formalism. It has been found, taking QWs of InAs, InSb, GaAs, Hg(1-x)Cd(x)Te and In(1-x)Ga(x)As(1-y)P(t) that the 1D EEM increases with electron concentration per unit length and decreases with increasing film thickness respectively. For ternary and quaternary materials the EEM increases with increase in alloy composition. Under certain special conditions all the results for all the 1-D materials get simplified into the well known parabolic energy bands and thus confirming the compatibility test. The results of this paper find two applications in the fields of nanoscience and technology.

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An attempt is made to present a very easy integration which generates Von Klitzing constant in one hand and Einstein's 1D photo current from quantum wires having arbitrary band structures under the practical conditions of extreme degeneracy and quantum limits on the other hand, the two radically different concepts, depending on the selection of the values of the upper and lower limits of the integral.

In this paper we study the influence of strong electric field on the two dimensional (2D)effective electron mass (EEM) at the Fermi level in quantum wells of III-V, ternary and quaternary semiconductors within the framework of k x p formalism by formulating a new 2D 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 EEM increases with decreasing film thickness, increasing 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 electric field makes the mass quantum number dependent and the oscillatory mass introduces quantum number dependent mass anisotropy in addition to energy. The EEM 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. The content of this paper finds three applications in the fields of nano-science and technology.

This paper is dedicated to the 83th Birthday of Late Professor B. R. Nag, D.Sc., formerly Head of the Departments of Radio Physics and Electronics and Electronic Science of the University of Calcutta, a firm believer of the concept of theoretical minimum of Landau and an internationally well known semiconductor physicist, to whom the second author remains ever grateful as a student and research worker from 1974-2004. In this paper, an attempt is made to study, the Einstein's photoemission (EP) from III-V, II-VI, IV-VI, HgTe/CdTe and strained layer quantum well heavily doped superlattices (QWHDSLs) with graded interfaces in the presence of quantizing magnetic field on the basis of newly formulated electron dispersion relations within the frame work of k · p formalism. The EP from III-V, II-VI, IV-VI, HgTe/CdTe and strained layer quantum wells of heavily doped effective mass superlattices respectively has been presented under magnetic quantization. Besides the said emissions, from the quantum dots of the aforementioned heavily doped SLs have further investigated for the purpose of comparison and complete investigation in the context of EP from quantum confined superlattices. Using appropriate SLs, it appears that the EP increases with increasing surface electron concentration and decreasing film thickness in spiky manners, which are the characteristic features of such quantized hetero structures. Under magnetic quantization, the EP oscillates with inverse quantizing magnetic field due to Shuvnikov-de Haas effect. The EP increases with increasing photo energy in a step-like manner and the numerical values of EP with all the physical variables are totally band structure dependent for all the cases. The most striking features are that the presence of poles in the dispersion relation of the materials in the absence of band tails create the complex energy spectra in the corresponding HD constituent materials of such quantum confined superlattices and effective electron mass exists within the band gap which is impossible without the concept of band tails. The well-known result of EP for bulk semiconductors having parabolic energy bands can be obtained as a special case of our generalized formulation and thus confirming the compatibility test. The content of this paper finds four important applications and we have suggested the methods of experimental determinations of important transport quantities in the field of quantum effect devices of nanoscience and nanotechnology.