Quantum Scale Gas Breakdown

Device miniaturization increases the importance of understanding and predicting gas breakdown and electrical discharge thresholds. At gap sizes on the order of ten microns at atmospheric pressure, field emission drives breakdown rather than Townsend avalanche. While numerical and analytical models can demonstrate this transition, a quantitative understanding of the relative importance of each parameter remains unclear. Starting from a universal model for gas breakdown across the field emission and Townsend avalanche regimes [A. M. Loveless and A. L. Garner, Phys. Plasmas 24, 113522 (2017)], this paper applies the concept of error propagation from ionizing radiation measurements to determine the relative impact of each factor on the predicted breakdown voltage. For limits of both large and small products of the dimensionless ionization coefficient, α¯, and gap distance, d¯, the electrode work function has the largest relative effect on the predicted breakdown voltages with a deviation of 50% in the work function resulting in an uncertainty in the calculated breakdown voltage of ∼84% for both α¯d¯≫1 and α¯d¯≪1. This quantifies the significance of nonuniformities in material surfaces and changes in the surface structure during multiple electric field applications and help predict the breakdown voltage for small gaps, motivating better electrode characterization both initially and during repeated operation.

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

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

Breakdown voltage and prebreakdown current between parallel plane copper electrodes in a vacuum were measured in the gap range from 0.002 to 0.2 mm using an impulse voltage of 550×5000 μs. Breakdown field strength, effective field enhancement factor, and field emission current just prior to breakdown were ascertained as a function of gap spacing. With a decrease in the gap spacing from 0.2 mm, the field emission current just prior to breakdown increased sharply and at about 0.04 mm, it was 10 or 20 times larger than that when the gapspacing is 0.2 mm. However, in the gap range from 0.04 mm to 0.002 mm, the field emission current was maintained at about a constant value. The gap spacing dependence of the field emission current could be explained by the introduction of two ideas, which are a space charge effect by emitted electrons, and a change in the breakdown mechanism.

The miniaturization of electronic devices requires a deeper understanding of electron emission and gas breakdown dynamics at nano- and microscales. Micro- and nanoelectromechanical systems (MEMS and NEMS, respectively) for sensing and scanning, microplasma applications, and directed energy devices require an accurate characterization of electron emission behavior for accurate predictions of device behavior. While breakdown has historically been predicted by Paschen’s law—driven by Townsend avalanche processes—this fails as gap distance decreases to the point where field emission (FE) become relevant. Further decreasing gap distance makes electron emission space-charge-limited as defined by the Child- Langmuir law (CSCL) at vacuum, the Mott-Gurney law (MG) if collisions contribute, or quantum space charge behavior (QSCL) at nanoscales when Schrodinger’s wave equation must be used to consider single particle effects. This study nondimensionalizes the governing equations defining these underlying phenomena to identify transition points between them and understand the underlying physics dominating the emission behavior in these regimes to aid device design and experimental setup. A sample case theorizes a nexus occurring between all emission mechanisms at a pressure of approximately 1780 Torr, a gap distance of 62 nm, and an applied voltage of 6 V. Additionally, we discuss the implications of work function and surface roughness on these behaviors.

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.

Density functional theory for field emission from carbon nano-structures

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

The history of electron emission is reviewed from a standpoint of the work function that determines the electron emission capability and of applications in the fields of scientific instruments and displays. For years, in thermionic emission, a great deal of effort has been devoted to the search for low work function materials with high melting temperature, while reduction of the local change in time of the work function rather than the work function itself has been the main issue of field emission investigations. High brightness and long life are the central targets of emission material investigations for scientific instrument applications, while high current density and low power consumption are the guiding principles for display applications.In most of the present day industries, thermionic emission materials are exclusively used in such fields requiring high current and high reliability as cathode ray tubes, transmission and receiving tubes, x-ray sources and various electron beam machines. Field electron emission sources, however, since applied to high resolution electron microscopes in the 1970s have recently become dominant in research and development in the fields of scientific instruments as well as in the fields of various electron tubes and beam machines.The main issue in this report is to analyse the work function on the atomic scale and thereby to understand the fundamental physics behind the work function, the change in time of the local work function leading to field emission current fluctuation and the relationship between microscopic (on atomic scale) and macroscopic work functions.Our attempt is presented here, where the work function on the atomic scale is measured by utilizing a scanning tunnelling microscopy technique, and it is made clear how far the local work function extends its influence over neighbouring sites. As a result, a simple relationship is established between microscopic and macroscopic work functions.

The current vs. voltage and electrical breakdown behavior for devices with micron and sub-micron gaps between conductors is studied. The limitations of the well-known but often-misinterpreted Paschen curve are discussed. The little-known modified Paschen curve, that includes field emission effects so important in understanding breakdown behavior for devices with sub-micron gaps, is described. Current vs. voltage measurements across metal-air-metal, metal-insulator-metal and metal-insulator-air-insulator-metal gaps with gaps ranging from 4 nm to 4 μm are reported. The breakdown voltage for an air gap of 0.9 μm was found to be 150 V, far below the Paschen curve minimum breakdown limit, and field emission behavior was confirmed via the Fowler-Nordheim plot. Metal-insulator-metal gaps with a diamond-like carbon thin-film with a thickness of 4 nm had a breakdown voltage of only 1V. SEM and AFM analysis show that the breakdown damage is crater-like and through the carbon layer. Other characterization of the damage caused by breakdown is presented. Tribocharging, electrostatic induction, and other ESD-related phenomena, are discussed for several devices with sub-micron gaps. It is concluded that devices with sub-micron gaps can face a serious challenge due to electrical breakdown during manufacturing, handling and operation. These devices include photolithographic reticles, magnetic recording heads, MEMS and field emission displays.

Nanowires of a variety of materials have gained importance in the past decade owing to their potential for reliable integration into electronic devices.In particular, this importance is due to their application in flat panel display technology as well as in the cold cathode technology for electron tube devices such as microwave tubes.This is because the conventional thermionic emission devices are accompanied with high power dissipation due to high cathode temperature.With the emergence of nanomaterials, there has been an upsurge in the research publications reporting on their field emission behaviour.This is because of the advantage of nanometric dimensions, making them suitable for field emission.Several metallic and semiconducting nanomaterials are found to operate delivering high current density at a lower applied potential as compared to the conventional field emitter counterparts.The nanowire form of various materials is suitable for the observed field emission properties.Additionally, the materials to be investigated must possess vacuum compatibility (low vapour pressure), high mechanical strength (should be able to withstand mechanical stress due to high electric field), and resistance to ion bombardment (due to residual gases in the vacuum chamber) and low work function.The emission current density is usually in the range of 10-100 mA/cm 2 for the applied field of 1-20 V/µm.It should be possible to deposit the nanomaterials on the flat substrate such as Si, with uniform density and with relative ease, to be used as a field emitter cathode.The materials of interest from field emission point of view can be classified into the following broad classes: Carbon nanotubes, graphene, carbon fibre; Nanoforms of wide band gap materials such as SiC, GaN, AlN, BN, ZnO; other semiconductors such as Si, CdTe, CdS; and nanostructures and nanowires of established electron emitters such as LaB 6 .In this chapter, emphasis will be given on the field emission phenomenon, an account of development in theory of field emission, basic methodology; and a brief review of the field emission work carried out on nanowires. The field emission phenomenonField electron emission from metals and semiconductors has attracted the attention of researchers for the past more than sixty years.In the phenomenon called field emission, www.intechopen.com

In this paper, we report a simple analytical model for carbon nanotube (CNT) based electron emitters and triode field emission devices on silicon substrates. Carbon nano-tubes have been grown in a direct current plasma enhanced chemical vapour deposition (dc PECVD) reactor from Ni catalyst islands. CNTs are electrically isolated by a TiO2 film and a chromium layer acts as the metal gate. The effects of the surrounding gate as well as the current–voltage behavior are investigated. To verify the experimental results of this structure a theoretical model is developed, using the Fowler–Nordheim tunneling effect combined with the electrodynamics theory. With certain simplifying assumptions, we replace the complex structure of triode devices with a simple structure which arrives at a closed formulation to predict field emission properties. Field enhancement factor is an important factor that depends on the CNT shape, gate opening and the applied voltage. In our fabrication process, the gate opening diameter can be of the order of the CNT diameter. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Polyaniline (PAni)/Se nanocomposites have been synthesized in different compositions employing chemical route and shown excellent field emission behaviour. Detailed studies on the field emission for all composites with different concentrations of dopant are performed in an indigenously fabricated set up in a vacuum chamber with a base pressure of 10(-6) Torr at room temperature and analysed with current density versus Electric field (J-E) and Fowler-Nordheim (FN) plots. Comparative field emission results showed that 10% (w/w) doped PAni/Se nanocomposite depicts highest emission characteristics, current density and field enhancement factor with turn-on field as low as 1.2 V/µm in comparison with other composites, while pure PAni shows no field emission characteristics. These composites have also been characterized by Scanning Electron Microscope (SEM) and Fourier Transform Infrared Spectrometry (FTIR). FTIR results supply the evidence for the occurrence of the polymer in its conducting state. The ease of synthesis route and interesting field emission properties recommend these composites as a promising material for field emission based applications in vacuum micro-nanoelectronic devices and also for plastic display industry.

This paper describes the influence of ballast resistor and field screening on the electron field emission behavior of nano-diamond emitter arrays fabricated on micropatterned silicon pillars. Arrays of 50×50 silicon pillars with different ballast resistances, pillar separations, capped with nano-diamond, have been fabricated on different silicon substrates as cathode for field emission testing. The goal of this study is to evaluate the fabrication method and electron emission characteristics in this configuration for field emission applications. The electron field emission results have been compared to observe the effect of the ballast resistive behavior and array spacing of micropatterned silicon pillars on the nano-diamond field emission behaviors.

The history of electron emission is reviewed from a standpoint of the work function and the applications. For years, in the field of thermionic emission, a great deal of efforts have been devoted to search for low work function materials with high melting temperature, while the reduction of the local change in time of the work function rather than the work function itself has been the main issue of field emission researches. High brightness and long life are the central targets of the emission material researches for scientific instrument application, while high current density and low power consumption are the guiding principles for display application. In both cases, field emission has been dominating the applications recently. In all above cases the main issue in the future researches will be to analyze the work function in atomic level and thereby to understand the mechanism of the work function reduction by atom adsorption, the change in time of the local work function leading to the current fluctuation, and the relationship between microscopic and macroscopic work functions. Our attempt is discussed, where the work function in atomic level is measured by utilizing the STM-technique and it is made clear how far the work function in atomic level extends its influence over the neighboring sites. As a result, a simple relationship is established between microscopic and macroscopic work functions.