Authors: Choudhury, S.; De, D.; Mukherjee, S.; Neogi, A.; Sinha, A.; Pal, M.; Biswas, S.K.; Pahari, S.; Bhattacharya, S.; Ghatak, K.P.

Source: Journal of Computational and Theoretical Nanoscience, Volume 5, Number 3, March 2008 , pp. 375-400(26)

Publisher: American Scientific Publishers

Abstract:

In this paper, an attempt is made to study the Einstein relation for the diffusivity-to-mobility ratio (DMR) in carbon nanotubes (CNTs) and quantum wires (QWs) of non-linear 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 DMR has also been investigated in QWs of II-VI, IV-VI, stressed materials, n-Ge, n-GaP, p-PtSb₂, n-GaSb, zero gap compounds and bismuth on the basis of the dispersion relations of the carriers in the respective cases by incorporating the appropriate spectrum constants. It has been found, taking QWs of n-CdGeAs₂, n-Cd₃As₂, n-InAs, n-InSb, n-GaAs, n-Hg_1-xCd_xTe, n-In_{1- x}Ga_xAs_yP_{1- y} lattice matched to InP, p-CdS, n-PbTe, n-PbSnTe, n-Pb_{1- x}Sn_xSe, stressed n-InSb, n-Ge, n-GaP, p-PtSb₂, n-GaSb, p-HgTe and bismuth as examples, that the respective DMR in the QWs of aforementioned materials exhibits increasing quantum steps with the increasing electron statistics with different numerical values and the nature of the variations are totally band structure dependent. In CNTs, the DMR exhibits periodic oscillations with increasing electron statistics and the nature is radically different as compared with the corresponding DMR of QWs since they depend exclusively on the respective band structures and the energy band constants emphasizing the different signatures of the two entirely different one dimensional nanostructured systems in various cases. 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. In addition, we have suggested an experimental method of determining the DMR for CNTs and QWs having arbitrary dispersion laws.

Keywords: EINSTEIN RELATION; CARBON NANOTUBES; QUANTUM WIRES; NONLINEAR OPTICAL AND OPTOELECTRONIC MATERIALS; EXPERIMENTAL SUGGESTION

Document Type: Research article

DOI: http://dx.doi.org/10.1166/jctn.2008.018

Publication date: 2008-03-01

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• Journal of Computational and Theoretical Nanoscience is an international peer-reviewed journal with a wide-ranging coverage, consolidates research activities in all aspects of computational and theoretical nanoscience into a single reference source. This journal offers scientists and engineers peer-reviewed research papers in all aspects of computational and theoretical nanoscience and nanotechnology in chemistry, physics, materials science, engineering and biology to publish original full papers and timely state-of-the-art reviews and short communications encompassing the fundamental and applied research.
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