Quantum-mechanical investigation of field-emission mechanism of a micrometer-long single-walled carbon nanotube

Nanoscale Three-Dimensional Charge Density and Electric Field Mapping by Electron Holographic Tomography

The operation of nanoscale electronic devices is related intimately to the three-dimensional (3D) charge density distributions within them. Here, we demonstrate the quantitative 3D mapping of the charge density and long-range electric field associated with an electrically biased carbon fiber nanotip with a spatial resolution of approximately 5 nm using electron holographic tomography in the transmission electron microscope combined with model-based iterative reconstruction. The approach presented here can be applied to a wide range of other nanoscale materials and devices.

Field emitter electrostatics: a review with special emphasis on modern high-precision finite-element modelling

This review of the quantitative electrostatics of field emitters, covering analytical, numerical and 'fitted formula' approaches, is thought the first of its kind in the 100 years of the subject. The review relates chiefly to situations where emitters operate in an electronically ideal manner, and zero-current electrostatics is applicable. Terminology is carefully described and is 'polarity independent', so that the review applies to both field electron and field ion emitters. It also applies more generally to charged, pointed electron-conductors-which exhibit the 'electrostatic lightning-rod effect', but are poorly discussed in general electricity and magnetism literature. Modern electron-conductor electrostatics is an application of the chemical thermodynamics and statistical mechanics of electrons. In related theory, the primary role of classical electrostatic potentials (rather than fields) becomes apparent. Space and time limitations have meant that the review cannot be comprehensive in both detail and scope. Rather, it focuses chiefly on the electrostatics of two common basic emitter forms: the needle-shaped emitters used in traditional projection technologies; and the post-shaped emitters often used in modelling large-area multi-emitter electron sources. In the post-on-plane context, we consider in detail both the electrostatics of the single post and the interaction between two identical posts that occurs as a result of electrostatic depolarization (often called 'screening' or 'shielding'). Core to the review are discussions of the 'minimum domain dimensions' method for implementing effective finite-element-method electrostatic simulations, and of the variant of this that leads to very precise estimates of dimensionless field enhancement factors (error typically less than 0.001% in simple situations where analytical comparisons exist). Brief outline discussions, and some core references, are given for each of many 'related considerations' that are relevant to the electrostatic situations, methods and results described. Many areas of field emitter electrostatics are suggested where further research and/or separate mini-reviews would probably be useful.

Modeling the Field Emission Enhancement Factor for Capped Carbon Nanotubes Using the Induced Electron Density

In many field electron emission experiments on single-walled carbon nanotubes (SWCNTs), the SWCNT stands on one of two well-separated parallel plane plates, with a macroscopic field F_M applied between them. For any given location "L" on the SWCNT surface, a field enhancement factor (FEF) is defined as F_L/F_M, where F_L is a local field defined at "L". The best emission measurements from small-radii capped SWCNTs exhibit characteristic FEFs that are constant (i.e., independent of F_M). This paper discusses how to retrieve this result in quantum-mechanical (as opposed to classical electrostatic) calculations. Density functional theory (DFT) is used to analyze the properties of two short, floating SWCNTs, capped at both ends, namely, a (6,6) and a (10,0) structure. Both have effectively the same height (∼5.46 nm) and radius (∼0.42 nm). It is found that apex values of local induced FEF are similar for the two SWCNTs, are independent of F_M, and are similar to FEF values found from classical conductor models. It is suggested that these induced-FEF values are related to the SWCNT longitudinal system polarizabilities, which are presumed similar. The DFT calculations also generate "real", as opposed to "induced", potential-energy (PE) barriers for the two SWCNTs, for F_M values from 3 V/μm to 2 V/nm. PE profiles along the SWCNT axis and along a parallel "observation line" through one of the topmost atoms are similar. At low macroscopic fields, the details of barrier shape differ for the two SWCNT types. Even for F_M = 0, there are distinct PE structures present at the emitter apex (different for the two SWCNTs); this suggests the presence of structure-specific chemically induced charge transfers and related patch-field distributions.

Antenna-coupled vacuum channel nano-diode with high quantum efficiency

Vacuum channel diodes have the potential to serve as a platform for converting free-space electromagnetic radiation into electronic signals within ultrafast timescales. However, the conversion efficiency is typically very low because conventional vacuum channel diode structures suffer from high surface barriers, especially when using lower energy photon excitation (near-infrared photons or lower). Here, we report on an optical antenna-coupled vacuum channel nano-diode, which demonstrates a greatly improved quantum efficiency up to ∼4% at 800 nm excitation; an efficiency several orders of magnitude higher than any previously reported value. The nano diodes are formed at the cleaved edge of a metal-insulator-semiconductor (MIS) structure, where a gold thin film with nanohole array serves as both the metal electrode and light-harvesting antenna. At the nanoholes-insulator interface, the tunneling barrier is greatly reduced due to the coulombic repulsion induced high local electron density, such that the resonant plasmon induced hot electron population can readily inject into the vacuum channel. The presented vertical tertiary MIS junction enables a new class of high-efficiency, polarization-specific and wavelength- sensitive optical modulated photodetector that has the potential for developing a new generation of opto-electronic systems.

Analysis of a capped carbon nanotube by linear-scaling density-functional theory

The apex region of a capped (5,5) carbon nanotube (CNT) has been modelled with the DFT package ONETEP, using boundary conditions provided by a classical calculation with a conducting surface in place of the CNT. Results from the DFT solution include the Fermi level and the physical distribution and energies of individual orbitals for the CNT tip. Application of an external electric field changes the orbital number of the highest occupied molecular orbital (HOMO) and consequently changes its distribution on the CNT.

Density functional theory for field emission from carbon nano-structures

Electron field emission is understood as a quantum mechanical many-body problem in which an electronic quasi-particle of the emitter is converted into an electron in vacuum. Fundamental concepts of field emission, such as the field enhancement factor, work-function, edge barrier and emission current density, will be investigated, using carbon nanotubes and graphene as examples. A multi-scale algorithm basing on density functional theory is introduced. We will argue that such a first principle approach is necessary and appropriate for field emission of nano-structures, not only for a more accurate quantitative description, but, more importantly, for deeper insight into field emission.

Enhanced cold field emission of large-area arrays of vertically aligned ZnO-nanotapers via sharpening: experiment and theory

Large-area arrays of vertically aligned ZnO-nanotapers with tailored taper angle and height are electrodeposited on planar Zn-plate via continuously tuning the Zn(NH3)4(NO3)2 concentration in the electrolyte. Experimental measurements reveal that the field-emission performance of the ZnO-nanotaper arrays is enhanced with the sharpness and height of the ZnO-nanotapers. Theoretically, the ZnO-nanotaper is simplified to a "charge disc" model, based on which the characteristic macroscopic field enhancement factor (γC) is quantified. The theoretically calculated γC values are in good agreement with the experimental ones measured from arrays of ZnO-nanotapers with a series of geometrical parameters. The ZnO-nanotaper arrays have promising potentials in field-emission. The electrochemical synthetic strategy we developed may be extended to nanotaper arrays of other materials that are amenable to electrodeposition, and the "charge disc" model can be used for quasi-one-dimensional field emitters of other materials with nano-sized diameters.

Theory of Carbon Nanotube (CNT)-Based Electron Field Emitters

Theoretical problems arising in connection with development and operation of electron field emitters on the basis of carbon nanotubes are reviewed. The physical aspects of electron field emission that underlie the unique emission properties of carbon nanotubes (CNTs) are considered. Physical effects and phenomena affecting the emission characteristics of CNT cathodes are analyzed. Effects given particular attention include: the electric field amplification near a CNT tip with taking into account the shape of the tip, the deviation from the vertical orientation of nanotubes and electrical field-induced alignment of those; electric field screening by neighboring nanotubes; statistical spread of the parameters of the individual CNTs comprising the cathode; the thermal effects resulting in degradation of nanotubes during emission. Simultaneous consideration of the above-listed effects permitted the development of the optimization procedure for CNT array in terms of the maximum reachable emission current density. In accordance with this procedure, the optimum inter-tube distance in the array depends on the region of the external voltage applied. The phenomenon of self-misalignment of nanotubes in an array has been predicted and analyzed in terms of the recent experiments performed. A mechanism of degradation of CNT-based electron field emitters has been analyzed consisting of the bombardment of the emitters by ions formed as a result of electron impact ionization of the residual gas molecules.

Metal-oxide-semiconductor field-effect transistor with a vacuum channel

High-speed electronic devices rely on short carrier transport times, which are usually achieved by decreasing the channel length and/or increasing the carrier velocity. Ideally, the carriers enter into a ballistic transport regime in which they are not scattered. However, it is difficult to achieve ballistic transport in a solid-state medium because the high electric fields used to increase the carrier velocity also increase scattering. Vacuum is an ideal medium for ballistic transport, but vacuum electronic devices commonly suffer from low emission currents and high operating voltages. Here, we report the fabrication of a low-voltage field-effect transistor with a vertical vacuum channel (channel length of ~20 nm) etched into a metal-oxide-semiconductor substrate. We measure a transconductance of 20 nS µm(-1), an on/off ratio of 500 and a turn-on gate voltage of 0.5 V under ambient conditions. Coulombic repulsion in the two-dimensional electron system at the interface between the oxide and the metal or the semiconductor reduces the energy barrier to electron emission, leading to a high emission current density (~1 × 10(5) A cm(-2)) under a bias of only 1 V. The emission of two-dimensional electron systems into vacuum channels could enable a new class of low-power, high-speed transistors.

Field emission from in situ-grown vertically aligned SnO2 nanowire arrays

Vertically aligned SnO2 nanowire arrays have been in situ fabricated on a silicon substrate via thermal evaporation method in the presence of a Pt catalyst. The field emission properties of the SnO2 nanowire arrays have been investigated. Low turn-on fields of 1.6 to 2.8 V/μm were obtained at anode-cathode separations of 100 to 200 μm. The current density fluctuation was lower than 5% during a 120-min stability test measured at a fixed applied electric field of 5 V/μm. The favorable field-emission performance indicates that the fabricated SnO2 nanowire arrays are promising candidates as field emitters.

Electrical failure behaviors of semiconductor oxide nanowires

Electrical failure studies on semiconductor oxide nanowires (NWs) were performed in situ inside a transmission electron microscope (TEM). A high driven current leads to a sudden fracture of the SnO(2) NW and creates ultra-sharp and high aspect ratio tips at the broken ends, which provides a simple and reliable way for in situ nanoprobe fabrication. As a comparison, the TiO(2) NW fails due to Joule-heating-induced melting and retracts back into a nanosphere. The distinct behaviors are rooted in the different bonding nature. The strong ionic bonding between titanium and oxygen ions preserves the stoichiometry, while the covalently bonded SnO(2) NW decomposes before melting. The decomposition process is observed by resistively heating an SnO(2)/TiO(2) core-shell structure. It has been demonstrated that the needle-like geometry greatly enhanced field emission properties of SnO(2) NWs.

Density-fragment interaction approach for quantum-mechanical/molecular-mechanical calculations with application to the excited states of a Mg(2+)-sensitive dye

A density-fragment interaction (DFI) approach for large-scale calculations is proposed. The DFI scheme describes electron density interaction between many quantum-mechanical (QM) fragments, which overcomes errors in electrostatic interactions with the fixed point-charge description in the conventional quantum-mechanical/molecular-mechanical (QM/MM) method. A self-consistent method, which is a mean-field treatment of the QM fragment interactions, was adopted to include equally the electron density interactions between the QM fragments. As a result, this method enables the evaluation of the polarization effects of the solvent and the protein surroundings. This method was combined with not only density functional theory (DFT) but also time-dependent DFT. In order to evaluate the solvent polarization effects in the DFI-QM/MM method, we have applied it to the excited states of the magnesium-sensitive dye, KMG-20. The DFI-QM/MM method succeeds in including solvent polarization effects and predicting accurately the spectral shift caused by Mg(2+) binding.

Generalized Fowler-Nordheim theory of field emission of carbon nanotubes

Based on the low-energy band structure of carbon nanotubes (CNs), we develop a generalized Fowler-Nordheim theory of the CN field emission, in which the behavior of the current-voltage (I-V) characteristics depends on the electric field and the diameter of the CNs. This formalism reveals the key differences of field emission between conventional bulk metallic emitters and low-dimensional emitters and gives a clear physical understanding of the non-Fowler-Nordheim feature of the I-V characteristics of the CN field emission.

Geometry dependence of the electrostatic and thermal response of a carbon nanotube during field emission

In this paper we present an analysis to simulate heating within an isolated carbon nanotube (CNT) attached to an etched tungsten tip during field emission of an electron beam. The length, radius, wall thickness and shape of the tip (closed with a hemispherical shape or open and flat) of the CNT and its separation distance from the flat surface are considered as variables. Using a finite element method, we predict the field enhancement, emission current and temperature of the CNT as a function of these parameters. The electrostatic and transient thermal analyses are integrated with the field-emission models based on the Fowler-Nordheim approximation and heating/cooling due to emitting energetic electrons (the Nottingham effect). These simulations suggest that the main mechanism responsible for heating of the CNT is Joule heating, which is significantly larger than the Nottingham effect. Results also indicate that the electrostatic characteristics of CNTs are very sensitive to the considered parameters whereas the transient thermal response is only a function of the CNT radius and wall thickness. Further, the thermal response of the CNT is independent of its geometry, meaning that, as long as a given set of geometrical conditions are present that result in a given emission current, the maximum temperature a CNT attains will be the same.

Ab initio modeling of the interaction of electron beams and single-walled carbon nanotubes

Single-walled carbon nanotubes are readily observable in a scanning electron microscope, which traditional models fail to explain. We present an ab initio model to explain how the electron beam can interact with these structures despite the very small, nanoscale, interaction volume. In particular, we show how the electron beam can generate very strong secondary electron emission from the tip of a nanotube under external electric field. The approach may also be used in modeling the interaction of charged particles with nanostructures in other applications such as electron detection.

Field emission patterns from first-principles electronic structures: application to pristine and cesium-doped carbon nanotubes

A general approach is introduced to calculate field emission properties of any kind of nanostructure based on the first-principles local density of states (LDOS) and effective potentials. The experimental field emission spectroscopy images are explained as LDOS at the structure-vacuum barrier, weighted by the probability of electron tunneling. The method excellently reproduces the experimental field emission patterns of pristine capped carbon nanotubes. We show that cesium adsorbates even with a low doping ratio of one dopant per nanotube increase the emission current around 2.5 times, due to a generated dipole field.

Modeling and calculation of field emission enhancement factor for carbon nanotubes array

To estimate the apex field enhancement factor associated with carbon nanotubes (CNTs) array on a planar cathode surface, the image model of floated sphere between parallel anode and cathode plates was proposed. Firstly, the field enhancement factor of individual CNT was given as the following expression, beta0=h/rho+3.5, where h is the height and rho is the radius of CNTs. Then the field enhancement factor of CNTs array was discussed and the above expression was modified to be beta=h/rho+3.5-W, in which W is the function of the intertube distance R and represents the coulomb field interaction between the CNTs. All results show that the intertube distance of CNTs array critically affects the field emission. When the intertube distance is less than the height of tube, the field enhancement factor will decrease rapidly with decreasing the intertube distance. According to the calculated results and considering the field emission current density, the filed emission is optimal theoretically when the intertube distance is comparable with the height of CNTs.

Periodic field emission from an isolated nanoscale electron island

We observe field emission from an isolated nanomachined gold island. The island is able to mechanically oscillate between two facing electrodes, which provide recharging and detection of the emission current. We are able to trace and reproduce the transition from current flow through a rectangular tunneling barrier to the regime of field emission. A theoretical model via a master equation reproduces the experimental data and shows deviation from the Fowler-Nordheim description due to the island's electric isolation.