METHOD FOR CALCULATING EMISSION PARAMETERS

Extracting independently the work function and field enhancement factor from thermal-field emission of multi-walled carbon nanotube tips

This work reports the behavior of electron field emission from nanostructured CVD diamond films at elevated temperatures. The study is motivated by the possibility of using these structures in high-temperature electronics or direct energy conversion processes. Four nanostructured CVD diamond films were tested: nanocrystalline diamond, nitrogen-doped nanocrystalline diamond, peaked diamond microtips, and truncated diamond microtips. All samples displayed reasonably efficient field emission characteristics. For each, the onset of field emission decreased as the sample temperature increased. Truncated diamond microtips were found to provide the largest current-carrying capacity and effective emission current density. These values were 90μA and 12 1 1010A/cm2 respectively. At a temperature of 700 K, peaked diamond microtips showed the lowest turn-on field recorded at 38V μm. The highest turn-on field, at this same temperature, was found from the undoped nanocrystalline diamond and recorded at 90V μm. Address all correspondence to this author. NOMENCLATURE A effective emission area D tunneling transmission coefficient, see Eq. 2 E electron energy Ea conduction band energy EF Fermi level Ex axial electron energy F applied electric field h Planck constant h reduced Planck constant J current density kB Boltzmann constant m electron rest mass N electron supply function, see Eq. 5 p electron momentum q electron charge T temperature V voltage x axial coordinate β field enhancement factor φ work function μ chemical potential 1 American Institute of Aeronautics and Astronautics 8th AIAA/ASME Joint Thermophysics and Heat Transfer Conference 24-26 June 2002, St. Louis, Missouri AIAA 2002-3024 Copyright © 2002 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. INTRODUCTION Much attention has been paid to diamond thin films because of their potential applications in optics, high-speed electronics and thermal management devices. Diamond is chemically inert and has superior mechanical stability over typical materials used as electron field emission devices. Diamond’s sp3 tetragonal configuration consists of a central carbon atom with linear covalent bonds to neighboring carbon atoms 10. This particular arrangement facilitates phonon transport through the lattice of the structure, giving diamond a thermal conductivity four times that of pure copper 6. Furthermore, diamond is a wide band gap semiconductor. This material property results in diamond being an excellent electrical insulator. Diamond’s unique characteristic of being an excellent thermal conductor and electrical insulator make it ideal for nanoeletromechanical devices and electronic packaging. Nanocrystalline diamond films show strongly enhanced field emission properties that can be demonstrated reproducibly 9. The success of doping these films coupled with the absence of microscale features (i.e., using as-deposited films) make fabrication and implementation of nanocrystalline diamond relatively straightforward 13. Diamond tip arrays appear to be promising candidates for electron field emission devices (FEDs) because of the field enhancement produced by their geometry 1;8. This geometric enhancement effect occurs due to a deformation of the potential field. The altered potential field enhances the local electric field, enabling emission of electrons into vacuum at lower applied voltages. However, unlike nanocrystalline diamond, manufacturing diamond tips and gated tip arrays often requires many laborious post-fabrication etching processes. The present work reports the thermal effects of field emission for both nanocrystalline diamond and diamond tip arrays. High-temperature field emission experiments were performed on each sample. Current-voltage and FowlerNordheim plots are analyzed and discussed with corresponding theoretical formulations. Results show substantial differences between the electron field emission characteristics of the four samples. THEORETICAL FORMULATION A detailed discussion on the physics of field emission can be found from 5, and 4. The following provides an outline of the major physical concepts. The emission current density is defined as

Experimental Fowler-Nordheim plots taken from orthodoxly behaving carbon nanotube (CNT) field electron emitters are known to be linear. This shows that, for such emitters, there exists a characteristic field enhancement factor (FEF) that is constant for a range of applied voltages and applied macroscopic fields $F_\text{M}$. A constant FEF of this kind can be evaluated for classical CNT emitter models by finite-element and other methods, but (apparently contrary to experiment) several past quantum-mechanical (QM) CNT calculations find FEF-values that vary with $F_\text{M}$. A common feature of most such calculations is that they focus only on deriving the CNT real-charge distributions. Here we report on calculations that use density functional theory (DFT) to derive real-charge distributions, and then use these to generate the related induced-charge distributions and related fields and FEFs. We have analysed three carbon nanostructures involving CNT-like nanoprotrusions of various lengths, and have also simulated geometrically equivalent classical emitter models, using finite-element methods. We find that when the DFT-generated local induced FEFs (LIFEFs) are used, the resulting values are effectively independent of macroscopic field, and behave in the same qualitative manner as the classical FEF-values. Further, there is fair to good quantitative agreement between a characteristic FEF determined classically and the equivalent characteristic LIFEF generated via DFT approaches. Although many issues of detail remain to be explored, this appears to be a significant step forwards in linking classical and QM theories of CNT electrostatics. It also shows clearly that, for ideal CNTs, the known experimental constancy of the FEF value for a range of macroscopic fields can also be found in appropriately developed QM theory.

Carbon nanosheets have recently evolved into useful edge emitters with high emission current densities, low threshold electric fields, and long lifetimes. In addition to further improvement in these characteristics, good stability and repeatability are also essential for these materials to be suitable for high vacuum applications such as microwave tubes and flat panel displays. Since the work function of graphite, carbon nanotubes, and amorphous carbon is relatively high, 4.6–4.8eV, selective thin film coatings may offer significant advantages. Carbides are a good film choice for their corrosive resistance, chemical stability, and substantially lower work function. Approximately 3 ML (monolayer) (∼1nm) of molybdenum were deposited on carbon nanosheets by physical vapor deposition and the carbide (Mo2C) formed by heating to >200°C at 1×10−8Torr. The carbide stoichiometry was confirmed in situ by the characteristic Auger triple peak at 272eV. A stoichiometric Mo2C calibration sample was used to acquire the Auger electron spectroscopy asymmetric ratio of 0.7 and this was used to determine the carbide growth as a function of temperature (from room temperature to 1000°C). Field emission currents of up to 400μA were compared with uncoated CNS at a given electric field. The Mo2C∕CNS cathodes were shown to have greater than a factor of 100 increase in current and greater than 2V∕μm decrease in threshold. The Fowler-Nordheim plots were exceptionally linear and quite repeatable (correlation coefficient R2=0.999+). Using the slope and vertical intercept, an emission area for the 0.07cm2 Mo2C∕CNS dot sample was determined to be ∼3×10−9cm2 and the field enhancement factor was found to be β∼530.

SUMMARYDark current based on field emission current is considered to be a factor causing the vacuum electrical breakdown between multiaperture acceleration grids in the JT‐60 negative ion source. In this paper, we focus on field enhancement factor, which is a key parameter of field emission from the electrode. Vacuum breakdown testing for small‐sized electrodes simulating the multiaperture acceleration grids of the negative ion source was performed. We found the field enhancement factor and breakdown field for multiaperture electrodes, and we investigated the dependence of each parameter on the number of apertures. The results revealed that an increase in the average field enhancement factor after the end of conditioning resulting from an increase in the number of apertures led to a decrease in the dielectric strength of the multiaperture electrodes.

While commonly used to predict gas breakdown voltage, measured breakdown voltage deviates from the classical Paschen law for microscale gaps at atmospheric pressure due to the contribution of field emission <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> . Recent studies have derived analytic expressions to predict breakdown voltage for gap distances down to the mean free path of an electron that agree well with numerical solutions, particle-in-cell simulations, and experiment <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . However, device sizes continue to shrink and some applications, such as electron emission in a graphene nanogap with sharp edges <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> , consider gap sizes on the order of the electron mean free path. Furthermore, variations in critical field emission parameters, such as field enhancement factor and work function, due to surface roughness become more important for these smaller gaps. As a first step to elucidating this behavior, we couple the one-dimensional Schrödinger equation with Poisson's equation, as done previously for the quantum extension of the Child-Langmuir law <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> , and integrate this with previous analytic work for coupling field emission to Townsend avalanche to predict the deviation from the classical Paschen's law <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> . Applying a matched asymptotic analysis as we did at microscale <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> enables us to assess the transition from quantum breakdown back to the combined field emission and Townsend regime. Implications for developing a linked breakdown model from Townsend avalanche to field emission to quantum scale with decreasing gap distance and from field emission and quantum behavior to space-charge limited flow as a function of voltage and pressure will be discussed.

The simulation results of the electric field intensity and the enhancement factor, γ, for an individual CNT imaged as a conducting rod is presented. The field enhancement factor, γ, for the CNT paste array is evaluated experimentally by varying the cathode-anode (CA) spacing, d. The simulations indicate that the distribution of electric field intensity and the enhancement factor as a function of cathode-anode spacing, d, could be divided into the two parts: strong (d 100 μm) dependences of the enhancement factor γ(d). Furthermore, the field enhancement factor, γ, estimated experimentally for the CNT paste FEA indicates that the two-region field emission model (TRFE) is adequate for estimation of the field enhancement factor, γ. Moreover, the effective enhancement factor, γ, for the CNT paste FEA was found to be ≈50γ and is attributed to the additions of the emission currents from the individual CNTs in an array. In addition, the empiric functions of the geometrical enhancement factor, β(d), and γ(d) were estimated from the Fowler–Nordheim plot for the CNT paste FEA. One can use the empiric functions β(d) and γ(d) for the design and fabrication of the devices based on the CNT paste FEA with a variable CA spacing.

This work examines the electron field emission characteristics of polycrystalline diamond films at elevated temperatures. In recent years, considerable interest has developed in energy conversion applications of polycrystalline diamond films. However, little work has been considered for the field emission characteristics of diamond at elevated temperatures. The motivation behind this study involves direct energy conversion applications in power generation systems, where high temperatures exist. N-doped polycrystalline diamond films were grown by plasma-enhanced chemical-vapor deposition (PECVD). To investigate the effect of increased temperatures on field emission, current-voltage measurements were taken from the same diamond film at varying temperatures. Results from these measurements indicate a decrease in the turn-on voltage with increasing temperature. Further analysis of the temperature dependency of diamond was achieved through the parameter estimation of the effective emitting area, field enhancement factor, and work function. These results suggest that high-energy electrons are responsible for improved emission at high temperature.

Improved field emission properties of carbon nanotubes decorated with Ta layer

Highly enhanced field emission from copper oxide nanoparticle decorated vertically aligned carbon nanotubes: Role of interfacial electronic structure

Theoretical analysis of field electron emission must consider many parameters, one of the most critical being the field enhancement factor (FEF). In a single tip form, the FEF can vary several orders of magnitude and depends only on the system geometry, when the gap length between the emitter and counter-electrode is much greater than the height of the emitter. In this work, we determine very accurate analytical expressions for the FEF of five emitters with various shapes, which are often considered in the literature: Ellipsoidal, Hemisphere-on-Cylindrical post, Hemisphere-on-Orthogonal cone, Paraboloidal, and Hyperboloidal. We map the FEF as a function of the aspect ratio with an error smaller than 2% to serve as a quick reference database. Additionally, we calculate the electric field distribution over the emitters, which can give an insight into the effective notional emission area and the influence of the emitter’s base.

We report the formation of self-organized microconical arrays on copper surface when exposed to high flux (5.4 × 1015 cm−2 s−1) of 2 keV argon ion beams at normal incidence. The created microconical arrays are explored for field emission properties. The surface morphologies are investigated by scanning electron microscopy and atomic force microscopy. The local work function variation is analyzed by Kelvin probe force microscopy, and the argon content in the irradiated layer is measured with X-ray Photoelectron Spectroscopy. The average aspect ratio (base width/height) of microstructures for individual irradiated samples is found to increase from 0.7 to 1.5 with a decrease in ion fluence. The ion concentration is highest (3.89 %) for a fluence of 4.7 × 1018 cm−2, which asserts the formation of atomically heterogeneous surface due to subsurface ion implantation. An enhancement in the field emission properties of the argon ion–treated copper substrates at a fluence of 4.7 × 1018 cm−2 with a low turn-on voltage of 2.33 kV and with electron emission current 0.5 nA has been observed. From the Fowler–Nordheim equations, the field enhancement factor is calculated to be 5,561 for pristine copper, which gets enhanced by a factor of 2–8 times for irradiated substrates. A parametric model is considered, by taking into account the modified local work function caused due to structural undulations of the microstructures and presence of implanted argon ions, for explaining the experimental results on the field enhancement factor and emission current.

An important parameter used to characterize large-area field electron emitters (LAFEs) is the characteristic apex field enhancement factor γC. This parameter is normally extracted from the slope of a Fowler-Nordheim (FN) plot. Several years ago, the development of an “orthodoxy test” allowed a sample of 19 published FN plots relating to LAFEs to be tested, and it was found that about 40% of the related papers were reporting spuriously high values for γC. In technological papers relating to LAFE characterization, the common practice is to preconvert the measured voltage into an (apparent) value of the macroscopic field before making and analyzing an FN plot. This paper suggests that the cause of the “spurious field enhancement factor value” problem is the widespread use of a preconversion equation that is defective (for example, not compatible with ordinary electrical circuit theory) when it is applied to so-called “nonideal” field emission devices/systems. Many real devices/systems are nonideal. The author argues that FN plots should be made using raw experimental current-voltage data, that an orthodoxy test should be applied to the resulting FN plot before any more-detailed analysis, and that (in view of growing concerns over the reliability of published “scientific” results) reviewers should scrutinize field emission materials characterization papers with enhanced care.

To obtain large electric field enhancement while mitigating material losses, an all-dielectric nanoantenna composed of a heptamer and nanocubes is designed and analyzed. A numerical simulation by the finite element method reveals that the nanoantenna achieves the optical electric anapole modes, thereby significantly enhancing the coupling between different dielectrics to further improve the near-field enhancement and spontaneous radiation. Field enhancement factors |E/E 0|2 of 3,563 and 5,395 (AM1 and AM2) and a Purcell factor of 3,872 are observed in the wavelength range between 350 and 800nm. This nanoantenna has promising potential in applications involving surface-enhanced Raman scattering and nonlinearities due to its low cost and excellent compatibility.

We report results of the measurement of local work function, or apparent barrier height, on the Au/Cu(111) surface using scanning tunneling microscopy (STM). By measuring a response of tunneling current to a change of the tunneling gap distance during scanning, we can obtain a work function image simultaneously with a topographic STM image. In this way, we could successfully observe the difference in local work function due to different elements and atomic structures. Our results show that the mean work function value of the Au overlayer is 7±3% larger than that of the Cu(111) substrate and the value of the work function of the second Au layer is the same as that of the first Au layers within the measurement uncertainty. At the step edges, the work function values are lower than that on the terrace. The width and depth of the low work function trough at Au–Au, and Cu–Au single height steps were also obtained. The measured values are consistent with those measured on vicinal surfaces. This work also suggests that the local work function measurement can be used to identify the element on a surface and that the STM is quite useful to get information on how the work function is related with surface structures and how the work function spatially changes on nanometer scales.