An attempt is made to investigate the Einstein relation for the diffusivity–mobility ratio of the carriers in n‐channel inversion layers on ternary semiconductors in the presence of a quantizing magnetic field, on the basis of the fourth order in effective mass theory and taking into account the interactions of the conduction, heavy‐hole, light‐hole and split‐off bands, without any approximations of weak or strong electric field limits and incorporating the influences of electron spin and Dingle temperature, respectively. It is found, taking n‐channel inversion layers on Hg1−xCdxTe as an example, that the Einstein relation exhibits an oscillatory magnetic field dependence and the oscillatory spikes are much sharper with large numerical magnitudes even in the presence of broadening in inversion layers. The nature of oscillation is quite different to those obtained for bulk specimen of the same material under magnetic quantization. In addition, the corresponding well‐known results for isotropic parabolic energy bands form the special cases of the generalized expressions. Copyright © 1988 WILEY‐VCH Verlag GmbH &amp; Co. KGaA

K P GHATAK

M MONDAL

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

physica status solidi (b)

In this paper we study the effective electron mass (EEM) in Nano wires (NWs) of nonlinear optical materials on the basis of newly formulated electron dispersion relation by considering all types of anisotropies of the energy band constants within the framework of k . p formalism. The results for NWs of III-V, ternary and quaternary semiconductors form special cases of our generalized analysis. We have also investigated the EEM in NWs of Bi, IV-VI, stressed Kane type materials, Ge, GaSb and Bi2Te3 by formulating the appropriate 1D dispersion law in each case by considering the influence of energy band constants in the respective cases. It has been found that the 1D EEM in nonlinear optical materials depend on the size quantum numbers and Fermi energy due to the anisotropic spin orbit splitting constant and the crystal field splitting respectively. The 1D EEM is Bi, IV-VI, stressed Kane type semiconductors and Ge also depends on both the Fermi energy and the size quantum numbers which are the characteristic features of such NWs. The EEM increases with increase in concentration and decreasing film thickness and for ternary and quaternary compounds the EEM increases with increase in alloy composition. Under certain special conditions all the results for all the materials get simplified into the well known parabolic energy bands and thus confirming the compatibility test.

Journal of Computational and Theoretical Nanoscience

Simple theoretical analysis of the effective electron mass in semiconductor nanowires

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 kp formalism. It has been found, taking QWs of InAs, InSb, GaAs, Hg1-xCdxTe and In1-xGaxAs1-yPy 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. Copyright © 2012 American Scientific Publishers All rights reserved.

Journal of Nanoscience and Nanotechnology

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

In this paper, we study the Einstein relation for the diffusivity to mobility ratio (DMR) in n-channel inversion layers of non-linear optical materials on the basis of a newly formulated electron disper- sion relation by considering their special properties within the frame work of k · p formalism. The results for the n-channel inversion layers of III-V, ternary and quaternary materials form a spe- cial case of our generalized analysis. The DMR for n-channel inversion layers of II-VI, IV-VI and stressed materials has been investigated by formulating the respective 2D electron dispersion laws. It has been found, taking n-channel inversion layers of CdGeAs2, Cd 3As2, InAs, InSb, Hg1-x^CdxTe, In1-xGaxAsyP1-y lattice matched to InP, CdS, PbTe, PbSnTe, Pb1-xSnxSe and stressed InSb as examples, that the DMR increases with the increasing surface electric field with different numeri- cal values and the nature of the variations are totally band structure dependent. The well-known expression of the DMR for wide gap materials has been obtained as a special case under certain limiting conditions and this compatibility is an indirect test for our generalized formalism. Besides, an experimental method of determining the 2D DMR for n-channel inversion layers having arbitrary dispersion laws has been suggested. Copyright © 2009 American Scientific Publishers.

Einstein relation In n-channel inversion layers of nonlinear optical, optoelectronic and related materials: Simplified theory, relative comparison and suggestion for an experimental determination

We study theoretically the energy spectrum of the conduction electrons and the Einstein relation for the diffusivity-mobility ratio (DMR) for III-V, ternary and quaternary materials, whose unperturbed energy band structures are defined by the three-band model of Kane, in the presence of light waves. The solution of the Boltzmann transport equation on the basis of this newly formulated electron dispersion law will introduce new physical ideas and experimental findings under different external conditions. It has been observed that the unperturbed isotropic energy spectrum in the presence of light changes into an anisotropic dispersion relation with the energy-dependent mass anisotropy. It has been found taking n-InAs, n-InSb, n-Hg1-xCdxTe and n-In1-xGaxAsyP1- y lattice matched to InP, as examples that the DMR increases with increasing electron concentration, decreasing with increasing intensity and wavelength in various manners. The rate of change is totally band structure dependent and is influenced by the presence of the different energy band constants. The well-known result for the DMR for degenerate wide gap materials in the absence of light waves has been obtained as a special case of the present analysis under certain limiting conditions and this compatibility is the indirect test of our generalized formalism. Besides, we have suggested an experimental method of determining the DMR in degenerate materials having arbitrary dispersion laws. © 2007 Elsevier B.V. All rights reserved.

Physica B: Condensed Matter

Influence of light on the Einstein relation in III-V, ternary and quaternary materials: Simplified theory and a suggestion for experimental determination

An attempt is made to present a simplified analysis of the thermoelectric power in II-VI semiconductors in the presence of quantization of band states under different physical conditions. The thermopower decreases with increasing electron concentration in different manners, which is a direct consequence of band state quantization. We have plotted the thermopower with various other physical variables and the same power exhibits different types of oscillations in low-dimensions, respectively. The well-known results for parabolic energy bands have also been obtained as special cases of our generalized formulations under certain limiting conditions. In addition, the theoretical results are in quantitative agreement with the experimental data. © 1996 Società Italiana di Fisica.

Il Nuovo Cimento D

Influence of quantization of band states on the thermoelectric power in II-VI semiconductors

On the Modification of the Einstein Relation in Quasiâ€Oneâ€Dimensional Systems of Bismuth

An attempt is made to study the effect of crystal-field splitting on the Einstein relation for the diffusivity-mobility ratio of the carriers in ternary chalcopyrite semiconductors, taking degenerate n-CdGeAs2 as an example. It is found on the basis of Kildal model, that the above ratio increases with increasing carrier concentration is expected for degenerate semiconductors, it is also shown that the crystal-field splitting parameter effectively reduces the ratio with increasing amount of reduction with increasing carrier concentration. Besides, the corresponding results for parabolic semiconductors are also obtained from the expressions derived. © 1984 IOP publishing Ltd.