Modelling an Electrostatic Screening Effect in Field Assisted Electron Emitter Arrays

Nirupama M. P.; Ashok Bhattachary; Satyanarayana B. S.

doi:10.36648/2472-9893.9.8.173

Modelling an Electrostatic Screening Effect in Field Assisted Electron Emitter Arrays

Nirupama M. P.^*, Ashok Bhattachary and Satyanarayana B. S.

Department of Electronics Engineering, BML Munjal University, Gurgaon, Haryana, India

*Corresponding Author:: Nirupama M. P.
Department of Electronics Engineering,
BML Munjal University,
Gurgaon,
Haryana,
India;
Email: nirupama@bmu.edu.in

Received: January 21, 2020, Manuscript No. ipnto-23-3238; Editor assigned: January 27, 2020, PreQC No. ipnto-23-3238 (PQ); Reviewed: February 10, 2020, QC No. ipnto-23-3238; Revised: October 18, 2023, Manuscript No. ipnto-23-3238 (R); Published: November 15, 2023, DOI: 10.36648/2472-9893.9.8.173

Citation: Nirupama MP, Bhattachary A, Satyanarayan BS (2023) Modelling an Electrostatic Screening Effect in Field Assisted Electron Emitter Arrays. Nano Res Appl Vol.09 No.8:173.

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Abstract

Field assisted electron emitters are becoming increasingly attractive for a wide range of sensors and instrumentation like X-ray sources, GHz and THz devices and potential electrical propulsion for Pico/Nano satellites. Both deposited patterned electrodes and self-aligned as grown emitters have been used for field assisted electron emission study. One of the biggest challenges in emitter design is the effective utilization of the applied field for actual electron emission. In the case of closely packed emitters of high aspect ratio, the electric field of individual emitters start interacting with the neighboring emitters, leading to a lowering of the electric field-referred to as ‘screening’. It is important to take this into account while growing and fabricating high density emitters, especially patterned arrays, based on CNT and other technologies. Presented in this paper is a simulation based study of the dependence of screening on emitter spacing using a simple model simulated on COMSOL multi physics. It is found that the screening effects predominant when the emitter spacing is less than the height of the emitters. It is virtually absent when the spacing is twice the emitter height.

Keywords

Field emission; Filed emission array; Electrostatic screening; Field enhancement factor; Simulation

Introduction

Micro dimensioned emitters in vacuum were first proposed by shoulders. Spindt implemented the idea using Si semiconductor processes [1]. They demonstrated sub-100 V vacuum device operation using micron sized conical arrays of metal deposited on Si wafer. Numerous researchers have since demonstrated field emission from nano structures of metals, alloys, oxides and various carbon forms-including CNTs, nano fibers and spines, graphites, nano diamond and tetrahedral carbon films etc. While the nano structures have been shown as efficient emitters, the current from individual emitters range from nano to a few micro amperes [2]. Hence a very large numbers of such emitters must be used to generate milliamp to ampere level currents needed for devices such as x-ray sources or propulsion systems.

Nanostructures created by in-situ deposition processes such as CVD are naturally formed as closely packed arrays, with the inter element spacing being generally much less than the element height. Such arrangement of emitters experience strong 'screening' of electrostatic fields throughout the surface-except at the periphery and in those areas where growth has not taken place for any reason [3]. Hence, despite having a large number of emitters in a small area, the overall current from the assembly remains low and predominantly contributed by a very small number of emitters at the periphery and those substantially taller than the neighbouring elements owing to process and geometry variations. The dominant emitters also experience joule heating and frequently burn out, resulting in current instability and device failure. An important consideration for any deposition or fabrication process is therefore a predictable control over the packing density and aspect ratio-which seems to be a challenge with the available technologies of the day, especially if cost is important [4].

Emitters have also been fabricated from bulk material such as metals (SS, Cu, Pt, Au, W etc.) as well as graphite in wire, needle, wedge and cone forms. Microstructures are created on such materials, especially on the tips, by chemical etching, plasma etching, electron beam etching and flame treatment or laser ablation. Tips have also been decorated by nanostructures of various materials which are either deposited in situ or bonded using some organic glue followed by sintering. Emitters made of such designs have shown much higher current capacities and better temporal stability, after initial activation and stabilization. Such emitters can be used singly or as arrays-for producing larger area devices or for spatial scanning purposes. When used as arrays, the spatial separation needs to be such that field screening is avoided [5].

There is an increased interest in developing low-voltage electronic field emitters for possible applications in space propulsion, display devices, microwave power amplification, ebeam lithography and many more. Several nanostructures including tungsten nanorods, silicon based emitters, carbon nanotubes etc. Have shown highly promising field emission properties for large-area flexible microelectronics and space applications. Unfortunately, these materials involve expensive equipment for deposition and often need high temperature processing. The room temperature grown nanocluster carbon exhibit unique properties, which attract interests for possible application in nano scale electronic devices and space propulsion [6]. Therefore, the study is focused on growth and characterization of nanocluster carbon based field emitters for its field emission properties and possible application in Field Emission Electrical Propulsion (FEEP) system for nanosatellite.

Materials and Methods

Experimental study

Nanocarbon based films are popular cathode in tip free field emission devices. Nanocarbon with mixed sp³ and sp² bonding, like nanocluster carbon films exhibit high emission site density at lower fields. The nanocluster carbon films are grown using cathodic arc system under various optimized deposition parameters and characterized for its various properties. The nanocluster carbon grown using cathodic arc deposition system at room temperature, offers unique field emission properties. It is possible to grow nanocluster carbon with different deposition parameters which can vary the surface morphology and emission characteristics. The low field electron emission from nanocluster carbon, finds application in many vacuum nanoelectonic based devices [7].

Nanocarbons such as as-grown nanocarbon films, nitrogen incorporated and Helium incorporated nanocluster carbon films were considered for field emission measurement. The growth of the nanocarbon thin films from cathodic arc system are influenced by parameters such as: Arc voltage, arc current, arctype, substrate material, substrate temperature, substrate distance, magnetic field, deposition rate, deposition time and gaseous environment of the chamber. The characterization of samples were carried out using NSOM (Near Field Scanning Optical Microscope-ALPHA 300RAS), which is capable of three imaging techniques in a single instrument consists of a high resolution Confocal Raman Microscopy (CRM), Atomic Force Microscopy (AFM) and Scanning Near Field Optical Microscopy (SNOM) [8]. For characterizing the samples an excitation wavelength of 532 nm used for Raman analysis and for AFM measurements cantilever with 42 N/m and 285 KHz, AC mode tapping/non tapping both the modes (non-contact/contact mode) method was implemented. The SEM imaging of the films were carried out using SEM (SU-1500 HITACHI) and conductivity measurements using semiconductor device analyser were conducted to study different properties. The field emission experiments were carried out at a vacuum of about 10 Torr-7 Torr using the custom designed FE measurement system.

It is generally difficult to experimentally measure the electric field at the emission sites, owing to very small dimensions involved. Hence simulation is desirable to evaluate the design of an emitter array and predict the expected performance. There are likely to be variations of the results in actual fabrication, owing to process variations and lack of control. However a first order verification of the capabilities of the design is always useful. The intention of the current study is to aid in this respect [9].

It is well known that micro sized features and high aspect ratio (height to diameter) of emitters are conducive to field emission as high electric fields are established in such geometries. Field emission requires high enough electric fields (>10⁷ V/m) to be present normal to the emitting surfaces to enable overcoming of material work function and facilitate electron tunnelling from conduction band to vacuum, as proposed by Fowler and Nordheim. The emission current from metal surfaces is given by the Fowler Nordheim (FN) equation:

equation

Where J, E, φ and β are the emission current density, macro electric field, work function, and field enhancement factor, respectively and a, b are constants.

The equation can also be written as:

equation

Where V is the applied voltage.

The field enhancement factor β is critical to efficient field emission-as a high value of β translates into a reduced electrode voltage, which leads to ease of implementation and energy efficiency. A good estimation of β is highly desirable for optimal design of any field emitter.

Simulation study

The objective of our study are to:

• Simulate a realistic scenario of a single nano-dimensioned emitter placed in diode configuration. Verify the resulting electric potential and field distribution.
• Simulate a small 2-D array of nano-dimensioned emitters in diode configuration. Verify the resulting electric potential and field distribution and study the effect of varying the element spacing [10].

The simulation tool used was COMSOL multiphysics V5.0. The AC/DC interface is adequate for modelling the electric potential and the fields (Table 1).

Study was carried on the cone as well as the tube geometry for single and array elements. The basic setup is shown in Figure 1.

Figure 1: a) Single cone; b) 5-element wire array.

Geometry data	Values
Single cone
Base r	10 µm
Tip r	50 nm
Height	50 µm
Plate r	50 µm
Thickness	10 µm
Cone to plate gap	10 µm
Sphere radius	100 µm
5-Element wire array
Radius of air sphere	5000 nm
Array gap in x dir	1000 nm
Array gap in y dir	1000 nm
Wire height	1000 nm
Wire tip to anode gap	500 nm
Wire radius	2 nm
Cathode radius	3000 nm
Anode radius	1500 nm
Electrode thickness	1000 nm

Table 1: Geometry data for single cone and 5-element wire array.

Mesh chosen is extra fine around the cone and wire elements and normal elsewhere. The cone, wires and the cathode are at zero potential while a potential (1 V or 10 V) is applied to anode. Material is Cu for emitters and electrodes. The surrounding sphere is held at zero potential [11].

Results and Discussion

For the defined geometry, the electric potential and field intensity are plotted (Figure 2). The shape of the potential distribution is as expected-showing concentration of field lines around the sharp tips (Figures 3 and 4) [12].

Figure 2: Potential distribution for a single cone.

Figure 3: RMS field at the cone tip.

Figure 4: Potential distribution and E_rms for the wire array.

Electric field enhancement is clearly visible at the tips in Figures 5 and 6 notice the white contours at the tip which denote the high field locations having field values much above the macro electric field value. Owing to finite resolution of mesh grids, complex contours are seen.

Numerical data from the simulation can be used for the computation of β as shown in Figure 5. It is possible to get an average value of β for the tip face by surface integration over the active surface in question, i.e.

equation

Where En=Component of electric field vector normal to the surface.

equation

ds=Incremental area S=Surface area

Figure 5: The computation of β.

β_av can then be plugged into the FN equation (1) and correlated with the experimentally observed current.

Electrostatic screening

The potential distribution was compared for three different spacing of the array elements (1000 nm, 500 nm and 250 nm) as shown in Figure 6. The wire height (1000 nm), radius (2 nm) and other parameters were held constant.

Figure 6: Field crowding for different spacing.

A quantitative comparison of the field crowding can be made by looking at the ratio of the field penetration at the periphery and the middle of the array. For a spacing of two times the wire height (i.e. 2000 nm), the crowding ratio was unity, which means no crowding. The ratio is 0.2 for a spacing of 250 nm (i.e. 25% of height) which signifies extreme crowding [13].

Conclusion

It is found that the screening effect is predominant when the spacing between emitters is less than the height of the emitters. It is virtually absent when the spacing is twice the emitter height. This can be used as a guiding principle in field emission array design, where emitter current is to be maximized while avoiding adverse impact on the turn on field value. While it may be difficult to enforce this within an in-situ grown nano cluster, it is feasible to use this guidance for inter-cluster gap in patterned arrays made by conventional as well as nanosphere lithography. This method also allows numerical estimation of β (to first order accuracy at least) for an arbitrary geometry of emitter-collector, through the use of simulated spatial electric field data, with appropriate integration over the active surfaces.