Individual Field Emitters Research Articles

Mathematical modeling of field emitter array

In this article a mathematical model of multi-tip field cathode is presented. The field emitters periodic system for rectangular lattice serves as a field cathode on a flat substrate. A flat anode is parallel to the substrate. A unit cell with the individual field emitter is considered to calculate the electrostatic potential distribution. The effect of the field emitter on the distribution of the electrostatic potential is simulated as the effect of a finite charged line that is located at the axis of the system. The variable separation method is used to solve the boundary-value problem. The three-dimensional analytical solution for the Laplace/Poisson equation is obtained in the Cartesian coordinate system. The potential distribution is represented as an Fourier expansion, and the expansion coefficients are found in an explicit form. Values of the emission characteristics are determined by FowlerNordheim equation. The effect of electrostatic shielding on the emission characteristics is presented.

Advances In Vertical Solid-State Current Limiters For Individual Field Emitter Regulation In High-Density Arrays

We report the design, fabrication, and characterization of improved solid-state elements intended for individual regulation of field emitters part of high-density arrays. We demonstrate a high-yield, CMOS compatible fabrication process of single-crystal, vertical, ungated, n-type silicon field-effect transistors (FETs); each device behaves as a current source when is biased at a voltage larger than its drain-source saturation voltage. An ungated FET in saturation connected in series to a field emitter can compensate for the wide variation in current-voltage characteristics of the field emitters due to the tip radii spread present in any field emitter array, which should result in emitter burn-out protection, larger array utilization, and smaller array emission non-uniformity. Using 1-2 Ωcm single-crystal n-Si wafers, we fabricated arrays of 25 μm tall vertical ungated FETs with 0.5 μm diameter that span two orders of magnitude of array size. Experimental characterization of the arrays demonstrates that the current is limited with > 3.5 V bias voltage to the same ∼6 μA (6 A.cm-2) per-FET value. Finite element simulations of the device predict a saturation voltage close to the experimental value and a saturation current within a factor of two of the experimental value.

Modelling field emitter arrays using line charge distributions

Field emitter arrays are high-brightness electron sources with important current and future applications in vacuum electronics, particle accelerators, and directed energy. The current produced by individual emitters in these arrays is controlled by the total electric field on their surfaces, which depends on the background field, the space charge field from previously-emitted electrons, and field enhancements due to geometric features at the macro-, meso-, and micro-scales. To facilitate the study of shielding and space charge effects in these arrays, we have developed a mathematical model using tapered line charges to generate equipotential surfaces which approximate the geometry of high aspect ratio field emitters. This model provides an analytic approach for studying contributions to array performance due to macro-scale and meso-scale features such as array geometry, emitter height, and emitter tip radius. Here we present this model and use it to assess the impact of these parameters on the field enhancement factor of individual field emitters and emitters in 1D and 2D arrays.

Experimental Study of Electric Field Screening of Four Carbon Fiber Cathodes in a Linear Array Configuration

Electric field screening caused by the proximity of individual field emitters in a field emitter array influences the current that can be obtained. This paper describes the image with four carbon fiber field emitters at a 500 μm separation in a linear configuration to isolate and quantify the effect of electric field screening.

Individual field emitters based on rodlike ZnO crystals

A technique for fabricating rodlike ZnO crystals on a platinum substrate is developed. Rodlike ZnO crystals are grown on the tip of a platinum wire by high-temperature pyrolysis and their emission characteristics are measured.

Scaling of High-Aspect-Ratio Current Limiters for the Individual Ballasting of Large Arrays of Field Emitters

We report the fabrication and characterization of high-aspect-ratio silicon pillar current limiters [vertical ungated field-effect transistors (FETs)] for ballasting individual field emitters within field-emitter arrays (FEAs). Dense (1- <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\mu\hbox{m}$</tex></formula> pitch) FEAs that are individually ballasted by 100-nm-diameter and 10- <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\mu\hbox{m}$</tex></formula> -tall current limiters were fabricated, resulting in an emitter tip radius under 10 nm. When characterized without field emitters, the vertical current limiters (ungated FETs) show current-source-like behavior, with saturation currents up to 15 pA/FET. When the current limiters are incorporated into large arrays of field emitters, the current–voltage characteristics of the FEA show evidence of current limitation at high extraction gate voltages. Emission current densities of over 200 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\mu\hbox{A/cm}^{2}$</tex></formula> were obtained from 1.36 million emitter arrays with 5- <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\mu\hbox{m}$</tex></formula> pitch.

Growth of needle-like RuO 2 nanocrystals on carbon nanotubes and their field emission characteristics

To enhance the field emission characteristics, needle-like ruthenium dioxide (RuO 2) nanocrystals (NCs) were grown on vertically aligned carbon nanotubes (VACNTs) using metal organic chemical vapor deposition (MOCVD). The VACNTs were the principal part and template with the needle-like RuO 2 NCs grown outwardly from the VACNTs. Each needle-like RuO 2 NC can be regarded as an individual field emitter, resulting in field emission site enhancement. The results demonstrated that the RuO 2/VACNTs composite is an emitter material with great potential.

Operation of individual integrally gated carbon nanotube field emitter cells

In this work, we examine the operation of individual field emitter cells contained in a field emitter array composed of integrally gated multiwalled carbon nanotube (MWNT)-based field emission cathodes. These devices were found to behave in a manner consistent with a multiple emission site model of Fowler–Nordheim field emission. These results show considerable variation in the operational characteristics of cells contained within the same array and indicate that data obtained from arrays of cells are not necessarily indicative of individual cell performance.

Direct measurement of emission current distribution of Spindt-type field emitters

A specially designed Spindt-type emitter array is used to study field emission characteristics of the Spindt-type field emitter. Each pixel in the array contains only one tip, is independently addressable, and is spaced 110 μm from the adjacent pixels. The pixels are electrically and optically distinguishable from each other. The emission current distribution of 2560 field emitters in an array is directly measured as a function of gate voltage. The ratio of maximum current to minimum current is as high as 100:1. There are two peaks observed in the current distribution. The position of the high current peak is strongly dependent on the gate voltage, while the position of the low current peak is less sensitive to the gate voltage. The variations in beam size and beam position of individual field emitters are also measured. These variations within individual emitters are partly responsible for large beam size observed in field emission displays with pixels containing hundreds of emitters. Change in the current distribution of individual emitters was recorded as the emitters were aging. Statistically, the emitters operating at high current age faster than those at low current.

Field emission observations from CVD diamond-coated silicon emitters

The self-aligned fabrication of diamond-coated silicon field emitters was performed by a selective chemical vapor deposition of diamond on p-type (100)-oriented silicon followed by argon ion milling of the patterned structures. Field emission measurements of as-prepared and thermally as well as hydrogen plasma treated diamond-coated silicon emitter arrays with base diamters ranged from 1.2 to 10 μm were carried out by field emission scanning microscopy with μm resolution. The applied electrical surface field has been varied between 20 and 250 MV m −1. It was found that the combination of thermal and hydrogen plasma treatments can substantially improve the electron emission of diamond-coated silicon emitters. Depending on their base diameter the field emitters demonstrated stable electron emission for E>80–120 MV m −1. Fowler-Nordheim analysis for arrays and individual field emitters was performed.

Measurement of gated field emitter failures

The emerging field of vacuum microelectronics has many promising applications including flat-panel displays, microwave devices, and ionization sources. The technology is based on arrays of microfabricated micrometer-scaled gated field emitters. Applications are currently limited by unacceptable reliability due primarily to failures of individual field emitters. The failure of an individual emitter produces a characteristic electrical pulse. A circuit is used to monitor and count these pulses. The technique provides a powerful tool for exploration of stable operating regimes for vacuum microelectronic devices and may be useful in other areas in which vacuum discharges must be monitored.