Modeling of the electron field emission from carbon nanotubes

Filip, V.; Nicolaescu, D.; Okuyama, F.

doi:10.1116/1.1349202

Cited by 53 publications

(46 citation statements)

References 37 publications

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“…For a single, isolated CNT, the value of enhancement factor is believed to be dependant on the length, radius, and type of structure, i.e., multiwalled ͑MWNT͒, singlewalled ͑SWNT͒, open or closed cap: This has been subject to several computational and experimental investigations. [3][4][5][6][7][8] Geometric enhancement is not just applicable to CNT but also exists in a number of other tip-based structures including: SiC nanowires, 9 MoO 3 nanobelts, 10 tungsten nanowires, 11 spindt tips, 12 and copper sulphide nanowire arrays. 13 Much of the analysis performed on experimental data has relied upon analysis of the emission current I to field E ͑or voltage V͒ characteristics using the wellknown field emission mechanism of Fowler and Nordheim.…”

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confidence: 99%

Effect of aspect ratio and anode location on the field emission properties of a single tip based emitter

Smith¹,

Carey²,

Forrest³

et al. 2005

Journal of Vacuum Science &Amp; Technology B: Microelectronics and Nanometer Structures Processing, Measurement, and Phenomena

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The effect on the field emission characteristics of the aspect ratio of an isolated emitter, together with the position of the anode electrode are reported. We show by computational simulation that the field enhancement factor ␤ is only dependant on the emitter height h, radius r, when the anode to cathode separation D is greater than three times the height of the emitter away from the tip. In this regime the enhancement factor is independent of the anode location and approaches a value depicted by h and r alone and is described by the expression ␤ 0 = ͑1+ ͱ h / ␣r͒ m where ␣ = 2 and m = 1. As the anode is brought close to the tip of the emitter, the emitter tip and anode approximate a parallel plate configuration and the enhancement factor tends to unity. Extracted enhancement factor and threshold fields are described by a modified applied electric field taking D − h as the separation. 1 have shown to possess a fascinating structure, and their use as electron sources in vacuum microelectronics and nanoelectronics has been widely reported.2 The mechanism of field-induced electron emission from a nanotube is understood to be due to the applied electric field undergoing an increase at the tip of the CNT, often referred to as the field enhancement factor ␤. For a single, isolated CNT, the value of enhancement factor is believed to be dependant on the length, radius, and type of structure, i.e., multiwalled ͑MWNT͒, singlewalled ͑SWNT͒, open or closed cap: This has been subject to several computational and experimental investigations.3-8 Geometric enhancement is not just applicable to CNT but also exists in a number of other tip-based structures including: SiC nanowires, 9 MoO 3 nanobelts, 10 tungsten nanowires, 11 spindt tips, 12 and copper sulphide nanowire arrays. 13 Much of the analysis performed on experimental data has relied upon analysis of the emission current I to field E ͑or voltage V͒ characteristics using the wellknown field emission mechanism of Fowler and Nordheim.14 The standard analysis often involves a plot of the log͑I / E 2 ͒ versus 1 / E ͑or equally log I / V 2 against 1 / V͒ and from the slope of the graph an approximate value for the field enhancement factor ␤ can be extracted. The role of ␤ is the enhancement of the applied macroscopic electric field such that under the action of the local electric field, tunneling of electrons from the Fermi level, into the vacuum, through the potential barrier becomes possible. The interpretation of ␤, which is a dimensionless quantity if electric field rather than voltage is used in the analysis, is therefore of great importance.There have been a number of attempts to model the behaviour of ␤ for a range of nanotube height and radius. Early work by Dyke and Dolan 15 showed that for a planar anode and a sphere-on-cone emitter the local field enhancement ͑neglecting V / d͒ close to the tip of the emitter was given bywhere ␤ L is the local field enhancement due to the emitter shape, d is the emitter-anode gap, and n is related to the cone opening angle ͑for ...

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mentioning

confidence: 99%

Effect of aspect ratio and anode location on the field emission properties of a single tip based emitter

Smith¹,

Carey²,

Forrest³

et al. 2005

Journal of Vacuum Science &Amp; Technology B: Microelectronics and Nanometer Structures Processing, Measurement, and Phenomena

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“…For instance, it has been attributed to the curvature of the apex [82]; to small size and strong local fields that lead to localized states at the apex [20,59,83]; to the space charge vs thermionic emission [15,60]; to the adsorbate effects [21]; to the back contact resistance [84]; and so on. The emission current from CNTs have been estimated by taking into account the band structures of CNTs [47,48,49]. It is found that current depends on the chirality only at very high temperatures [49].…”

Section: The Fowler-nordheim Theorymentioning

confidence: 99%

“…The SWCNT can either be metallic or semiconducting. The field emission properties have been calculated by the tight-binding theory and scattering theory [47,48,49]. In recent years, quantum mechanical simulations of the field emission of CNTs have been performed [50,51,52,53,54,55].…”

Section: Introductionmentioning

confidence: 99%

Mechanism of field electron emission from carbon nanotubes

Deng

2006

Front. Phys. China

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Field electron emission (FE) is a quantum tunneling process in which electrons are injected from materials (usually metals) into a vacuum under the influence of an applied electric field. In order to obtain usable electron current, the conventional way is to increase the local field at the surface of an emitter. For a plane metal emitter with a typical work function of 5 eV, an applied field of over 1 000 V/µm is needed to obtain a significant current. The high working field (and/or the voltage between the electrodes) has been the bottleneck for many applications of the FE technique. Since the 1960s, enormous effort has been devoted to reduce the working macroscopic field (voltage). A widely adopted idea is to sharpen the emitters to get a large surface field enhancement. The materials of emitters should have good electronic conductivity, high melting points, good chemical inertness, and high mechanical stiffness. Carbon nanotubes (CNTs) are built with such needed properties. As a quasi-one-dimensional material, the CNT is expected to have a large surface field enhancement factor. The experiments have proved the excellent FE performance of CNTs. The turn-on field (the macroscopic field for obtaining a density of 10 µA/cm 2 ) of CNT based emitters can be as low as 1 V/µm. However, this turn-on field is too good to be explained by conventional theory. There are other observations, such as the non-linear Fowler-Nordheim plot and multi -peaks field emission energy distribution spectra, indicating that the field enhancement is not the only story in the FE of CNTs. Since the discovery of CNTs, people have employed more serious quantum mechanical methods, including the electronic band theory, tight-binding theory, scattering theory and density function theory, to investigate FE of CNTs.time. The multi-walled carbon nanotubes (MWCNTs) should be assembled with a sharp metal needle of nano-scale radius, for which the FE mechanism is more or less clear. Although MWCNTs are more common in present FE applications, the single-walled carbon nanotubes (SWCNTs) are more interesting in the theoretical point of view since the SWCNTs have unique atomic structures and electronic properties. It would be very interesting if people can predict the behavior of the well-defined SWCNTs quantitatively (for MWCNTs, this is currently impossible). The FE as a tunneling process is sensitive to the apex-vacuum potential barrier of CNTs. On the other hand, the barrier could be significantly altered by the redistribution of excessive charges in the micrometer long SWCNTs, which have only one layer of carbon atoms. Therefore, the conventional theories based upon the hypothesis of fixed potential (work function) would not be valid in this quasi-one-dimensional system. In this review, we shall focus on the mechanism that would be responsible for the superior field emission characteristics of CNTs. We shall introduce a multi-scale simulation algorithm that deals with the entire carbon nanotube as well as the substrate as a whole. The simulation for (5...

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“…4 However, in this study the potential all around the emitting CNT tip has been assigned a constant value equal to an average local field, an approximation, the effects of which are still not clear to us. In another approach Filip et al 5,6 have modelled emission from CNTs with large radii but have still used a one-dimensional transmission coefficient of the Fowler-Nordheim type. In this paper we calculate the transmission coefficient as a function of the angle to the axis of the tube and of the energy.…”

Section: Introductionmentioning

confidence: 99%

Theoretical calculation of spatial variation of the transmission coefficient of closed carbon nanotubes

Xanthakis

Kokkorakis

2004

Surface & Interface Analysis

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We have calculated the spatial (angular) variation of the transmission coefficient of closed carbon nanotubes (CNT). For the evaluation of the local field outside the tip of the CNT we have used the method described in J. Appl. Phys. 2002; 91: 4580. In the present work we require the local field only inside the classically forbidden area, so we have managed to simplify our previous results and obtain an analytical form for the local potential. This potential was then inserted into the method of Das and Mahanty (Phys. Rev. B 1987; 36: 898) to obtain the transmission coefficient T.q/ at an angle q to the axis of the tube. We have found a substantial angular variation of T.q/, the determining factor being the local field at the surface of the CNT and, to a lesser extent, the radius of the tube. Decreasing the local field increases the directionality of T.q/ but also decreases the current by several orders of magnitude so that a compromise between directionality and value of the current has to be sought. The directionality also increases with decreasing radius of the tube. The ratio of the height to the radius (h/R) of the CNTs per se plays a minor role, i.e. if one compares CNTs with different h/R but the same local field then minor changes are found.

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Modeling of the electron field emission from carbon nanotubes

Cited by 53 publications

References 37 publications

Effect of aspect ratio and anode location on the field emission properties of a single tip based emitter

Effect of aspect ratio and anode location on the field emission properties of a single tip based emitter

Mechanism of field electron emission from carbon nanotubes

Theoretical calculation of spatial variation of the transmission coefficient of closed carbon nanotubes

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