B R NAG

A N CHAKRAVARTI

P K BASU

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 (a)

In this paper we study the influence of strong electric field on the two dimensional Einstein Relation (2D ER) in quantum wells of III-V, ternary and quaternary semiconductors within the framework of k.p formalism by formulating a new electron energy spectrum. It appears taking quantum wells of InSb, InAs, Hg1-xCdxTe and In1-xGaxAs1-yPy lattice matched to InP as examples that the ER decreases with increasing film thickness, 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 ER 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. We have suggested an experimental method of determining 2D ER for materials having arbitrary dispersion laws. Copyright © 2015 American Scientific Publishers All rights reserved.

Journal of Computational and Theoretical Nanoscience

2D Einstein Relation in quantum wells under strong electric field

In this paper we investigate the influence of strong light waves on the two dimensional diffusivity mobility ratio in heavily doped quantum wells of III-V, ternary and quaternary semiconductors within the framework of k.p formalism by formulating a new electron energy spectrum. It appears taking heavily doped quantum wells of InSb, InAs, Hg1-xCdxTe and In1-xGaxAs1-yPylattice matched to InP as examples that the said ratio decreases with increasing film thickness, intensity, wave length 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 ratio 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. We have suggested an experimental method of determining heavily doped two dimensional diffusivity mobility ratios for materials having arbitrary dispersion laws. Copyright © 2014 American Scientific Publishers. All rights reserved.

Diffusivity-mobility ratio in heavily doped quantum wells under intense light waves

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 investigate the Einstein relation for the diffusivity-mobility ratio (DMR) for n-i-p-i and the microstructures of nonlinear optical compounds on the basis of a newly formulated electron dispersion law. The corresponding results for III-V, ternary and quaternary materials form a special case of our generalized analysis. The respective DMRs for II-VI, IV-VI and stressed materials have been studied. It has been found that taking CdGeAs2, Cd3As2, InAs, InSb, Hg1-xCdxTe, In1-xGaxAsyP1-y lattices matched to InP, CdS, PbTe, PbSnTe and Pb1-xSnxSe and stressed InSb as examples that the DMR increases with increasing electron concentration in various manners with different numerical magnitudes which reflect the different signatures of the n-i-p-i systems and the corresponding microstructures. We have suggested an experimental method of determining the DMR in this case and the present simplified analysis is in agreement with the suggested relationship. In addition, our results find three applications in the field of quantum effect devices. © 2009 Elsevier Ltd. All rights reserved.

Superlattices and Microstructures

Einstein relation in n-i-p-i and microstructures of nonlinear optical, optoelectronic and related materials: Simplified theory, relative comparison and suggestions for an experimental determination

In this paper, we study the Debye screening length (DSL) in ultrathin films of optoelectronic materials in the presence of light waves. The solution of the Boltzmann transport equation on the basis of the newly formulated electron dispersion laws will introduce new physical ideas and experimental findings under different external conditions. It has been found, taking ultrathin films of n-Hg1-xCdxTe, as an example, that the respective two-dimensional (2D) DSL in the aforementioned materials exhibits decreasing quantum step dependence with the increasing film thickness, surface electron concentration, light intensity and wavelength, respectively, with different numerical values. The nature of the variations is totally band structure dependent which is influenced by the presence of the different energy band constants. The strong dependence of the 2D DSL on both the light intensity and the wavelength reflects the direct signature of the light waves. The well-known result for the 2D DSL for nondegenerate wide gap materials in the absence of any field 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 2D DSL in ultrathin materials in the presence of light waves having arbitrary dispersion laws. © 2008 Elsevier B.V. All rights reserved.

Physica B: Condensed Matter

Influence of light on the Debye screening length in ultrathin films of optoelectronic materials

An attempt is made to derive an expression for the electronic heat capacity in heavily‐doped semiconductors having Gaussian band‐tails. With the help of this expression, the electronic heat capacity is studied as a function of the electron concentration corresponding to different temperatures, taking heavily‐doped n‐GaAs having Gaussian band‐tails as an example. It is concluded that the nature of the dependence is determined exclusively by the movement of the Fermi level with changing electron concentration through the allowed energy states. Copyright © 1982 WILEY‐VCH Verlag GmbH & Co. KGaA

physica status solidi (b)

Effect of Heavy Doping on the Electronic Heat Capacity in Semiconductors

An analytical expression of the modified form of the Einstein relation in heavily doped semiconductors in which Gaussian band tails are formed near the lower limit of heavy doping is derived for studying the temperature dependence of the diffusivity-mobility ratio of the carriers in such semiconductors. It is found that, with increasing temperature from relatively low values, the ratio first increases in a nonlinear manner and then decreases till, at high temperatures, it approaches its value corresponding to the non-degenerate condition resulting in a peak over a narrow range of temperatures. © 1980 Springer-Verlag.

Applied Physics

Effect of temperature on the validity of the einstein relation in heavily doped semiconductors

On the oscillatory nature of the magnetic field dependence of the diffusivityâ€mobility ratio in degenerate semiconductors under the influence of magnetic quantization