In this paper, we study the Fowler-Nordheim field emission (FNFE) from carbon nanotubes on the basis of a newly formulated electron dispersion law by considering the fact that the intense electric field needed for FNFE changes the band structure in a fundamental way. It has been found that the field emitted current increases with increasing electric field in oscillatory manner due to the appearance of van Hove singularities and exhibits spikes for particular values of the electric field where the singularity occurs. The numerical values of the field emitted current in all the cases vary widely and the determined by the chiral indices and the diameter in the respective cases. The results of this paper find three applications in the fields of nanoscience and technology. Copyright © 2013 American Scientific Publishers. All rights reserved.

S BHATTACHARYA

S GHOSH

K P GHATAK

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

Journal of Computational and Theoretical Nanoscience

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, an attempt is made to investigate the influence of quantizing magnetic field on the Fowler-Nordheim field emission (FNFE) from non-linear optical materials by formulating the respective electron dispersion laws under magnetic quantization by considering the influence of the energy band constants in each case on the basis of the k.p formalism. It has been observed, taking n-CdGeAs2 as example that the field emitted current density oscillates with the inverse quantizing magnetic field due to SdH effect. The FNFE is a product of two functions inside the summation sign and both of them are functions of Fermi energy, effective mass and various system constants in a complex way. If the rate of increase of first function overcomes the rate of change of the second one, the FNFE will increase, whereas, for the opposite case, the FNFE will decrease where the rates of variations totally depend on the specific dispersion relation of the particular quantized structure. Under certain limiting conditions, all the results as derived in this paper get transformed into well known formulas of the FNFE and the electron statistics in the absence of quantizing magnetic field and thus confirming the compatibility test. The results of this paper find three applications in the field of quantized materials. © 2014 American Scientific Publishers.

Analysis of magneto fowler-nordheim field emission from semiconductor nanostructures of non-linear optoelectronic materials

An attempt is made to present a simplified theoretical formulation of the Fowler-Nordheim field emission (FNFE) in quantum wires (Qws) of non-linear optical materials on the basis of a newly formulated electron dispersion law by considering various types of anisotropies of the energy band constants within the framework of k.p formalism. We also study FNFE from Qws of III-V, II-VI and Bismuth by using the appropriate band models. Taking Qws of CdGeAs 2, InAs, InSb, GaAs, Hg 1-xCd xTe and In 1-xGa xAsP 1-y lattice matched to InP, CdS and Bi as examples, we observe that, the FNFE increases with increasing film thickness due to the existence van- Hove singularity and the magnitude of the quantum jumps are not of same height indicating the signature of the band structure of the material concerned. The appearance of the humps of the respective curves is due to the redistribution of the electrons among the quantized energy levels when the quantum numbers corresponding to the highest occupied level changes from one fixed value to the others. Although the field current varies in various manners with all the variables in all the cases as evident from all the curves, the rates of variations are totally band-structure dependent. All the results as derived in this paper get transformed in to the well known Fowler-Nordheim formula under certain limiting conditions, and thus confirming the compatibility test. © 2012 American Scientific Publishers. All rights reserved.

Advanced Science Letters

On the field emission from quantum wires of non-parabolic semiconductors: Simplified theory and relative assessment

We present a simplified theoretical formulation of the Fowler-Nordheim field emission (FNFE) under magnetic quantization and also in quantum wires of optoelectronic materials on the basis of a newly formulated electron dispersion law in the presence of strong electric field within the framework of k.p formalism taking InAs, InSb, GaAs, Hg1-xCdxTe and In 1-xGax AsyP1-y lattice matched to InP as examples. The FNFE exhibits oscillations with inverse quantizing magnetic field and electron concentration due to SdH effect and increases with increasing electric field. For quantum wires the FNFE increases with increasing film thickness due to the existence van-Hove singularity and the magnitude of the quantum jumps are not of same height indicating the signature of the band structure of the material concerned. The appearance of the humps of the respective curves is due to the redistribution of the electrons among the quantized energy levels when the quantum numbers corresponding to the highest occupied level changes from one fixed value to the others. Although the field current varies in various manners with all the variables in all the limiting cases as evident from all the curves, the rates of variations are totally band-structure dependent. Under certain limiting conditions, all the results as derived in this paper get transformed in to well known Fowler-Nordheim formula. © 2011 Elsevier Ltd. All rights reserved.

Superlattices and Microstructures

Simple theoretical analysis of the Fowler-Nordheim field emission from microstructures and quantum wires of optoelectronic materials

We study theoretically the energy spectrum of conduction electrons and the corresponding density-of- states function (DOS) of III-V, ternary and quaternary semiconductors, whose unperturbed energy band structures are defined by the three band model of Kane, in the presence of an external electric field. It has been observed that the unperturbed isotropic energy spectrum becomes modified under external electric field and changes into an anisotropic dispersion relation with the energy-dependent mass anisotropy. Besides, the band gap of semiconductors increases with the electric field; a phenomenon never explained earlier either theoretically (Franz-Keldysh effect) or experimentally. In addition, from the study of the DOS, it indicates that the carriers disappear from the edge of the conduction band after certain values of the applied electric field. It has been found taking n-InSb, n-InAs, Hg1-xCdxTe and In 1-xGaxAsyP1-y lattice matched to InP as examples of Kane-type semiconductors for numerical computation that the increase of band gap and disappearance of carriers from the edges of the conduction band do happen for all types of materials in the presence of external electric field. The well-known energy spectrum and the corresponding DOS for wide-gap semiconductors in the absence of electric field have been obtained under certain limiting conditions from the theoretical expressions. This compatibility is an indirect mathematical test of our generalized analysis. © 2006 Elsevier B.V. All rights reserved.

Physica B: Condensed Matter

Simple theoretical analysis of the density-of-states function of Kane type semiconductors in the presence of an external electric field

An attempt is made to study theoretically the influence of an arbitrarily oriented quantizing magnetic field on the field emission from AII3BV2 compounds on the basis of a newly derived magneto-energy spectrum, based on k.p formalism, considering the anisotropies of the various band parameters. It is found, taking n-Cd3As2, as an example that the current density due to field emission under arbitrary magnetic quantization increases with increasing electron concentration in an oscillatory manner. Besides, the same current density increases with increasing electric field and decreasing magnetic field, respectively, in the magnetic quantum limit. In addition, the corresponding well-known results of parabolic energy bands are also obtained from the generalized expressions under limiting conditions. © 1988.

Journal	Journal of Computational and Theoretical Nanoscience
Publisher	AMER SCIENTIFIC PUBLISHERS
ISSN	1546-1955