We study thermoelectric power under strong magnetic field (TPM) in carbon nanotubes (CNTs) and quantum wires (QWs) of nonlinear optical, optoelectronic, and related materials. The corresponding results for QWs of III-V, ternary, and quaternary compounds form a special case of our generalized analysis. The TPM has also been investigated in QWs of II-VI, IV-VI, stressed materials, n-GaP, p -PtSb2, n-GaSb, and bismuth on the basis of the appropriate carrier dispersion laws in the respective cases. It has been found, taking QWs of n -CdGeAs2, n -Cd3 As2, n-InAs, n-InSb, n-GaAs, n -Hg1-x Cdx Te, n -In1-x Gax Asy P1-y lattice-matched to InP, p-CdS, n-PbTe, n-PbSnTe, n -Pb1-x Snx Se, stressed n-InSb, n-GaP, p -PtSb2, n-GaSb, and bismuth as examples, that the respective TPM in the QWs of the aforementioned materials exhibits increasing quantum steps with the decreasing electron statistics with different numerical values, and the nature of the variations are totally band-structure-dependent. In CNTs, the TPM exhibits periodic oscillations with decreasing amplitudes for increasing electron statistics, and its nature is radically different as compared with the corresponding TPM of QWs since they depend exclusively on the respective band structures emphasizing the different signatures of the two entirely different one-dimensional nanostructured systems in various cases. The well-known expression of the TPM 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. In addition, we have suggested the experimental methods of determining the Einstein relation for the diffusivity-mobility ratio and the carrier contribution to the elastic constants for materials having arbitrary dispersion laws. © 2008 American Institute of Physics.

K P GHATAK

S BHATTACHARYA

S CHOUDHURY

Fulltext

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.

&nbsp;

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.

&nbsp;

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

Journal of Applied Physics

In this paper we study the influence of strong electric field on the two dimensional magneto thermoelectric power (2D MTP) in ultrathin films (UFs) of III-V, ternary and quaternary semiconductors within the framework of k 'p formalism by formulating a new electron energy spectrum. It appears, taking UFs of InSb, InAs, Hg1-xCdxTe and In1-xGaxAs1-yPy lattice matched to InP as examples, that the 2D MTP increases with increasing film thickness, decreasing surface electron concentration and increasing electric field exhibiting quantum jumps because of the crossing over of the Fermi level by the quantized level in UFs and the quantized oscillation occurs when the Fermi energy touches the sub-band energy. The MTP increases with increasing 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 classical result and thus confirming the compatibility test. The content of this paper finds three applications in the domain of nano-science and nano technology. Copyright © 2017 American Scientific Publishers All rights reserved.

Journal of Nanoscience and Nanotechnology

The two dimensional magneto thermo power in ultra thin films under intense electric field

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

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. © 2009 Elsevier B.V. All rights reserved.

Physica B: Condensed Matter

Thermoelectric power in ultrathin films, quantum wires and carbon nanotubes under classically large magnetic field: Simplified theory and relative comparison

We present a simplified theoretical formulation of the thermoelectric power (TP) under magnetic quantization in quantum wells (QWs) of nonlinear optical materials on the basis of a newly formulated magneto-dispersion law. We consider the anisotropies in the effective electron masses and the spinorbit constants within the framework of k.p formalism by incorporating the influence of the crystal field splitting. The corresponding results for IIIV materials form a special case of our generalized analysis under certain limiting conditions. The TP in QWs of Bismuth, IIVI, IVVI and stressed materials has been studied by formulating appropriate electron magneto-dispersion laws. We also address the fact that the TP exhibits composite oscillations with a varying quantizing magnetic field in QWs of n- Cd3As2, n- CdGeAs2, n-InSb, p-CdS, stressed InSb, PbTe and Bismuth. This reflects the combined signatures of magnetic and spatial quantizations of the carriers in such structures. The TP also decreases with increasing electron statistics and under the condition of non-degeneracy, all the results as derived in this paper get transformed into the well-known classical equation of TP and thus confirming the compatibility test. We have also suggested an experimental method of determining the elastic constants in such systems with arbitrary carrier energy spectra from the known value of the TP. © 2010 Elsevier Ltd. All rights reserved.

Superlattices and Microstructures

On the two-dimensional thermoelectric power in quantum wells of non-parabolic materials under magnetic quantization

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 thermoelectric power in the presence of a large magnetic field (TPM) in heavily doped III-V, II-VI, PbTe/PbSnTe, strained layer and HgTe/CdTe quantum dot superlattices (QDSLs) with graded structures on the basis of newly formulated electron energy spectra and compare the same with that of the constituent materials. It has been found, taking heavily doped GaAs/Ga1-xAlxAs, CdS/CdTe, PbTe/PbSnTe, InAs/GaSb and HgTe/CdTe QDSLs as examples, that the TPM increases with increasing inverse electron concentration and film thickness, respectively, in different oscillatory manners and the nature of oscillations is totally band structure dependent. We have also suggested the experimental methods of determining the Einstein relation for the diffusivity-mobility ratio, the Debye screening length and the electronic contribution to the elastic constants for materials having arbitrary dispersion laws. © 2006 Elsevier B.V. All rights reserved.

Physica E: Low-Dimensional Systems and Nanostructures

Simple theoretical analysis of the thermoelectric power in quantum dot superlattices of non-parabolic heavily doped semiconductors with graded interfaces under strong magnetic field

We study the electron energy spectrum and the Debye screening length (DSL) for III-V, ternary, and quaternary materials in the presence of light waves, whose unperturbed energy band structures are defined by the three-band model of Kane. 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 in the presence of external photoexcitation. It has been found taking n -InAs, n -InSb, n -Hg1-x Cdx Te, and n -In1-x Gax Asy P1-y lattice matched to InP, as examples that the DSL decreases with the increase in electron concentration, intensity, and wavelength, respectively in various manners. The strong dependence of the DSL on both light intensity and wavelength reflects the direct signature of light waves which is in contrast as compared with the corresponding bulk specimens of the said materials in the absence of external photoexcitation. The rate of change is totally band structure dependent and is significantly influenced by the presence of the different energy band constants. The classical DSL equation 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. We have also suggested an experimental method of determining the DSL in degenerate materials having arbitrary dispersion laws. © 2007 American Institute of Physics.

Influence of light on the Debye screening length in III-V, ternary, and quaternary materials

In this paper, an attempt is made to study the Einstein relation for the diffusivity-to-mobility ratio (DMR) in quantum wells (QWs) and nipi structures 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 influence of crystal field splitting within the framework of k · p formalism. The corresponding results for III-V, ternary and quaternary compounds form a special case of our generalized analysis. The DMR has also been investigated for QWs and nipi structures of II-VI, IV-VI, stressed materials, n-Ge, n-GaP, p-PtSb2, n-GaSb, and zero gap compounds on the basis of the appropriate carrier energy spectra by incorporating the respective energy band constants. It has been found, taking QWs and nipi structures of n-CdGeAs2, n-InAs, n-InSb, n-Hg1-x CdxTe, n-In1-x GaxAsy P1-y lattice matched to InP, p-CdS, n-PbS, n-PbSe, n-PbTe, stressed n-InSb, n-Ge, n-GaP, p-PtSb2, n-GaSb, and p-HgTe, as examples, that the DMR in QWs of aforementioned materials exhibits oscillatory dependences with the increasing electron statistics with different numerical values and the nature of oscillations are totally different as compared with the corresponding nipi structures although they depend exclusively on the respective band structures and the energy band constants emphasizing the different signatures of the two entirely different two dimensional nanostructured systems in various cases. The well-known expression of the 2D DMR for wide gap materials has been obtained as special cases from all the results under certain limiting conditions and this compatibility is the indirect test of our generalized formalism. In addition, we have suggested an experimental method of determining the Einstein relation for the diffusivity-mobility-ratio for nanomaterials having arbitrary dispersion laws. Copyright © 2007 American Scientific Publishers All rights reserved.

Einstein relation in quantum wells and nipi structures of nonlinear optical, optoelectronic and related materials: Simplified theory, relative comparison and suggestion for an experimental determination

We present a simple theoretical analysis of the effective electron mass (EEM) at the Fermi level for III-V, ternary and quaternary materials, on the basis of a newly formulated electron energy spectra in the presence of light waves whose unperturbed energy band structures are defined by the three-band model of Kane. 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. In the presence of light, the conduction band moves vertically upward and the band gap increases with the intensity and colours of light. 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 EEM increases with increasing electron concentration, intensity and wavelength in various manners. The strong dependence of the effective momentum mass (EMM) at the Fermi level on both the light intensity and wavelength reflects the direct signature of the light waves which is in contrast with the corresponding bulk specimens of the said materials in the absence of photo-excitation. 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 EEM at the Fermi level 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. © 2007 The Royal Swedish Academy of Sciences.

Physica Scripta

A simple theoretical analysis of the effective electron mass in III-V, ternary and quaternary materials in the presence of light waves

Hired Daughters

REFERENCES CITED

Thermoelectric power in carbon nanotubes and quantum wires of nonlinear optical, optoelectronic, and related materials under strong magnetic field: Simplified theory and relative comparison

Journal	Journal of Applied Physics
Publisher	AMER INST PHYSICS
ISSN	0021-8979
Open Access	Yes