The Magneto Electron Statistics in Heavily Doped N Type-Intrinsic-P Type-Intrinsic Structures.

In this paper we study the Electron Statistics in Heavily Doped N Type-Intrinsic-P Type-Intrinsic structures of non-linear optical, tetragonal and opto-electronic materials in the presence of magnetic quantization. It is found taking such heavily doped structures of Cd3As2, CdGeAs2, InAs, InSb, Hg1-xCdxTe, In1-xGaxAsyP1-y as examples that the Fermi energy (EF) oscillates with inverse quantizing magnetic field (1/B) and increases with increasing electron concentration with different numerical magnitudes which is the signature of respective band structure. The numerical value of the Fermi energy is different in different cases due to the different values of the energy band constants.

2D Effective Electron Mass at the Fermi Level in Accumulation and Inversion Layers of MOSFET Nano Devices.

In this paper an attempt is made to study the 2D Fermi Level Mass (FLM) in accumulation and inversion layers of nano MOSFET devices made of nonlinear optical, III-V, ternary, Quaternary, II-VI, IV-VI, Ge and stressed materials by formulating 2D carrier dispersion laws on the basis of k → ⋅ p → ⋅ formalism and considering the energy band constants of a particular material. It is observed taking accumulation and inversion layers of Cd3As2, CdGeAs2, InSb, Hg1-xCdxTe and In1-xGaxAsyP1-y lattice matched to InP, CdS, GaSb and Ge as examples that the FLM depends on sub band index for nano MOSFET devices made of Cd3As2 and CdGeAs2 materials which is the characteristic features such 2D systems. Besides, the FLM depends on the scattering potential in all the cases and the same mass changes with increasing surface electric field. The FLM exists in the band gap which is impossible without heavy doping.

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 III­V, 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.

Entropy, Electric Field and Heavily Doped Nanowires.

In this paper an attempt is made to study, the entropy in the presence of intense electric field in nanowires (NWs) of heavily doped (HD) III­V and optoelectronic materials on the basis of newly formulated electron dispersion relations within the frame work of k → ⋅ p → formalism. It is found taking HD NWs of InSb, InAs, Hg(1­ x) Cd (x)Te and In(1­ x) Ga( x) As( y) P(1­ y) lattice matched to InP as examples III­V, ternary and quaternary compounds that the entropy increases with increasing electron concentration per unit length and decreasing film thickness in different spiky manners, since the coincidence of Fermi energy with the sub-band energy leads to the step functional dependence of the density state function and this fact is being reflected in the quantized variations of the entropy with the said variables. The entropy increases with increasing electric field and decreasing alloy composition respectively. The numerical values of entropy 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 creates the complex energy spectra in the corresponding opto-electronic HD NWs and the effective electron mass exists within the band gap which is impossible without the concept of band tailing. The well-known classical result of entropy for non-degenerate bulk semiconductors having parabolic energy bands has been obtained as a special case of our generalized formulation and thus confirming the compatibility test. The content of this paper finds four important applications in the field of quantum effect devices of nanoscience and nanotechnology.

Einstein's Photoemission from Quantum Confined Superlattices.

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.

Einstein's 1D Photo Emission and the Von Klitzing Constant.

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.

Two Dimensional Effective Electron Mass at the Fermi Level in Quantum Wells of III-V, Ternary and Quaternary Semiconductors.

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.

Effective electron mass in quantum wires of III-V, ternary and quaternary materials.

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.

Simple theoretical analysis of the photoemission from quantum confined effective mass superlattices of optoelectronic materials.

The photoemission from quantum wires and dots of effective mass superlattices of optoelectronic materials was investigated on the basis of newly formulated electron energy spectra, in the presence of external light waves, which controls the transport properties of ultra-small electronic devices under intense radiation. The effect of magnetic quantization on the photoemission from the aforementioned superlattices, together with quantum well superlattices under magnetic quantization, has also been investigated in this regard. It appears, taking HgTe/Hg(1-) (x)Cd(x)Te and In(x)Ga(1-) (x)As/InP effective mass superlattices, that the photoemission from these quantized structures is enhanced with increasing photon energy in quantized steps and shows oscillatory dependences with the increasing carrier concentration. In addition, the photoemission decreases with increasing light intensity and wavelength as well as with increasing thickness exhibiting oscillatory spikes. The strong dependence of the photoemission on the light intensity reflects the direct signature of light waves on the carrier energy spectra. The content of this paper finds six different applications in the fields of low dimensional systems in general.