Fowler-Nordheim Plots Research Articles

Fabrication of a sharp Si protrusion with a faceted apex grown from a surface-melted silicon wafer under high electric and magnetic fields: application to field emission electron sources

A silicon (Si) protrusion, grown on a narrow path of a Si(001) wafer by surface melting via resistive heating, was sharpened by applying a local high electric field under a magnetic field during the growth. The electric field caused local stress to the surface-melted Si, which was pulled upward along the field. Consequently, the melted Si formed a sharper protrusion on solidification, with an apex surrounded by {001}, {113}, and {111} facets. The field emission from the protrusions was measured. The onset voltage of the emission from protrusions was lower when they were grown under the electric field. We used Fowler–Nordheim plots to characterize the emission current and voltage conversion factor, β. The results indicated that the application of electric field is beneficial to sharpening Si protrusions grown from Si melt. Such protrusions surrounded by facets are suitable for field emission electron sources with a high local electric field.

Effect of ultraviolet light on field emission performance and lifetime of lateral field emitter devices

Lateral field emission devices have been characterized before and after ultraviolet (UV) light exposure. Two types of planar device structures, diode and bowtie, were studied. These nanoscale devices have 9–15 nm tip-to-tip (bowtie) or tip-to-collector (diode) dimensions with the tips fabricated from Au/Ti. Typical currents of 2–5 nA per tip at 6 V were measured. It was observed that after UV exposure, the collected current was reduced by >28% for the case of a bowtie device; whereas the current was reduced by >39% for the case of a diode device. This reduction can be attributed to water vapor desorption on the dielectric surface between the structures, which in turn reduces surface leakage. The Fowler–Nordheim plot showed a straighter line after UV exposure. After the I-V test, the UV-exposed devices were placed on lifetime tests in a vacuum of <10−8 Torr and were biased at 5 V DC. After 2600 h, an abrupt current decrease was observed: ∼25% for the case of the bowtie and ∼28% for the case of the diode device. Scanning electron microscope images of the bowtie and diode devices showed damage to the tips.

Coupling effects in bipyridines linked to carbon nanowires

In this work, we conducted an investigation into the electronic transport properties of four distinct devices formed by bipyridines (BPY) as the central region, linked to carbon nanowires (polyyne-type carbyne) electrodes. These four devices have two symmetrical (2,2′ and 4,4′ BPY) and two asymmetrical (2,4′ and 2,6′ BPY) configurations. We employed Density Functional Theory combined with Non-Equilibrium Green's Function (DFT-NEGF) to calculate the molecular geometry and the electronic transport properties. Our analysis, using Fowler-Nordheim (F-N) and Millikan-Lauritsen (M-L) plots, reveals that electronic transport primarily occurs through direct tunneling without any inflection points, indicating the absence of nonlinear effects such as resonance or negative differential resistance (NDR). This demonstrates the importance of the study including an analysis of Transition Voltage Spectroscopy (TVS) which shows that the presence of nitrogen atoms in the electrode-molecule contacts, specifically in the cases 2,4′ and 4,4′ BPY, significantly alters the structural and electronic characteristics of the devices. This alteration leads to a strong coupling of the junction, improved structural and electronic properties. These findings are supported by the Device Density of States (DDOS) and Frontier Molecular Orbitals (FMOs). Moreover, we observed that the electronic characteristics of all four devices remain consistent even under bias voltage (Ve).

Field emission from sharp protrusions of graphite fabricated by sandblasting process

The sandblasting process, a novel method for fabricating field emitters, has been adapted to be used on graphite substrates. The sandblasted graphite substrate features numerous sharp protrusions on its surface that serve as effective field emitters. The threshold of the electric field was found to be 0.78 V μm−1, and linear Fowler–Nordheim plots were achieved. These results demonstrate the potential of the sandblasting process for fabricating graphite-based emitters.

Gap distance dependence on field emission at the nanogap between silicon cleavage surfaces

In this study, we developed a model of field emission at a vacuum nanogap composed of semiconductor electrodes and conducted numerical calculations to evaluate its field emission characteristics. The current at the silicon nanogap was also measured, and the results were compared with the calculated results. Large-area vacuum nanogaps are expected to be used for highly efficient room-temperature thermionic power generation owing to their good thermal insulation, and their electrical conduction of tunneling current is sufficient for practical use. Because vacuum nanogaps should be parallel and smooth with a large area, we proposed and examined the use of cleavage to fabricate nanogaps in single-crystal materials. A nanogap with a nominal area of 26.5 μm2 was fabricated in a microelectromechanical device to evaluate its properties, and the model was used for the analysis. The calculated current–voltage characteristics of the semiconductor nanogap of both n-type and p-type silicon were affected by the bandgap and the presence of carriers, i.e., electrons and holes. Moreover, the Fowler–Nordheim plot was confirmed to be valid for semiconductor nanogaps based on the calculated results. We proposed an effective work function that compensates for the discrepancy between semiconductor nanogaps and the Fowler–Nordheim theory and enables a more accurate analysis. Field-emission currents flowing through a 1.1 nm nanogap were measured and matched with the calculated results by adjusting the field enhancement factor and emission area. The model developed and confirmed experimentally in this work will be helpful in examining field emissions at semiconductor nanogaps.

Proposal that interpretation of field emission current–voltage characteristics should be treated as a specialized form of electrical engineering

This article proposes that we should think differently about predicting and interpreting measured field electron emission (FE) current–voltage [Im(Vm)] characteristics. It is commonly assumed that Im(Vm) data interpretation is a problem in emission physics and related electrostatics. Many experimentalists then apply the Fowler–Nordheim plot methodology, developed in 1929. However, with modern emitting materials, this 90-year-old interpretation methodology often fails (maybe in nearly 50% of cases) and yields spurious values for characterization parameters, particularly field enhancement factors. This has generated an unreliable literature. Hence, validity checks on experimental Im(Vm) data are nearly always needed before use. A new check, supplementing existing checks, is described. Twelve different “system complications” that, acting singly or in combinations, can cause validity-check failure are identified. A top-level path forward from this unsatisfactory situation is proposed. The term “field electron emission system (FE system)” is defined to include all aspects of an experimental system that affect the measured Im(Vm) characteristics. The analysis of FE systems should now be regarded as a specialized form of electronic/electrical engineering, provisionally called “FE Systems Engineering.” In this approach, the Im(Vm) relationship is split as follows: (a) the current is expressed as a function Im(FC) of the local surface-field magnitude FC at some defined emitter surface location “C,” and (b) the relationship between FC and measured voltage Vm is expressed and determined separately. Determining Im(FC) is mostly a problem in emission physics. Determining the relationship FC(Vm) depends on system electrostatics and (for systems failing a validity check) on the other aspects of FE Systems Engineering, in particular, electrical-circuit modeling. The scope of FE Systems Engineering and some related research implications and problems are outlined.

All field emission experiments are noisy, … are any meaningful?

Representing field emission data on a Fowler–Nordheim plot is both very common and strongly not recommended. It leads to a spurious estimation of the emitter parameters despite a very good data fit. There is a lack of a reliable method of analysis and a proper estimation of the uncertainty in the extracted parameters. In this article, we show that the uncertainty in the estimation of the field enhancement factor or the emission area can be as high as ±50% even for a tungsten single emitter in good ultrahigh vacuum conditions analyzed by the Murphy–Good model. Moreover, the choice of the exact Murphy–Good method can have a noticeable impact. We found that advanced analysis methods, based on the measurement of the differential conductance of the emitter, are so demanding in terms of emitter stability that up to now its requirements are probably out of reach in any field emission laboratory.

Field Electron Emission Characteristics of Tungsten–Polyethylene Composite Material As a Source of Electron Emission

Abstract: This work provides an experimental study on the effects of polyethylene coating on the field electron emission characteristics of clean (uncoated) tungsten tips. Several tungsten tips, with different apex radii, have been prepared, coated with different thicknesses of polyethylene layers and then examined using a standard field electron emission microscope. Various field electron emission characteristics have been measured under high-vacuum conditions. These include current-voltage characteristics, Fowler-Nordheim plots, scanning electron micrographs and spatial current distributions (electron-emission images). Based on this work, it is proved that coating tungsten tips with polyethylene layers has caused dramatic improvements on the tip emission properties. In particular, coating the tips improves the current-voltage characteristics, which is reflected in lowering the extraction voltage, getting more stable emission currents, expressing the current-voltage characteristics using Fowler-Nordheim plots and finally, the spatial distributions of the emitted electrons for the coated tips are more stable and uniform. Keywords: Field electron emitter, Polyethylene dielectric layer, Composite emitter, Field electron microscope, Scanning electron microscope.

Processing of experimental current-voltage characteristics of single tip emitters taking into account the functional dependence of the emission area on the applied voltage

The work addresses the question of the field-dependence of the notional emission area for a field-emitter tip using computer simulation and experimental data. Based on finite-element method calculations, it was determined that for single field emitters having a given shape, there is a stable and characteristic shift of the degree of voltage in the pre-exponential voltage exponent of the field emission equation relative to the “planar” case. A power-law fit to the 3D-data was applied so as to use it in the analysis of the current-voltage data using a k-power plot (KP-plot) of semilogarithmic type. A comparison of effective emission parameters obtained from the model current-voltage characteristic with the classical Fowler–Nordheim plot, modern Murphy–Good plot, and new KP-plot is carried out. The KP-plot is subsequently used to analyze the experimental data of Tungsten emitters having a scanning emission microscope determined apex radius. The new semilogarithmic analysis reveals that the apex radius of curvature is within the observed range.

Quantitative Analysis on the Field Strength in the Addressable Gated ZnO Nanowire Field Emitter Arrays: Model and Experiment

Addressable gated field emitter arrays (FEAs) have important applications in vacuum microelectronic devices. To fabricate high-performance device, a comprehensive understanding on the field emission characteristics of gated FEAs is necessary, which requires a quantitative analysis method. In this work, a general model based on Fowler-Nordheim (FN) theory has been established to fulfill this blank. It is found that nonlinear FN plot with positive and negative slopes could occur in gated FEAs, which its turning point is related to the proportion of anode and gate field. This provides a way for obtaining the field strengths applied by the anode and gate structures. Besides, the transconductance of the gated FEAs increases exponentially with the total surface field, which indicates that both the anode and gate field need to be increased for achieving a high transconductance device. As a demonstration, the addressable gated ZnO nanowire FEAs using multimicrosize pattern with radius as small as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2.5 ~\mu \text{m}$ </tex-math></inline-formula> have been designed and fabricated. The relationship between the transconductance and anode voltage can be well fitted by using the model, which deduces the proportion of anode and gate field in the device to be about 3:1.

Investigation and correlation between surface modifications and field emission properties of laser-induced silicon plasma ion irradiated stainless steel

Laser-induced silicon (Si) plasma has been used as a source of ion irradiation for modifications in surface, structural and field emission properties of Stainless Steel (SS). Nd:YAG (532 nm, 10 ns) laser at irradiance of 15 GW/cm2 was used to generate Si-plasma ions which were detected by solid-state nuclear track detector (CR-39) and Faraday Cup (FC). Both the energy and fluence of Si ions were measured by FCs. In response to a stepwise increase in the number of laser pulses from 3000 to 12000, the ion fluence varies from 4.6 × 1014 to 18.3 × 1014 ions/cm2 with constant energy of 30 keV. Fourier Transformation Infrared (FTIR) spectroscopy analysis revealed that irradiated silicon makes the stretch band with oxygen Si–O–Si. X-Ray Diffraction (XRD) analysis confirmed the identification of new phase of Si (111) with an anomalous trend in crystallite size, dislocation line density and induced stresses in response to the irradiation with various Si ion fluences. Optical microscopy analysis showed the formation of pits, voids and tracks. Scanning electron microscope (SEM) analysis revealed the formation of nanoscale surface features including pores, craters, embedded particulates and protruded disk-like structures with multiple ablative layers at the fluence of 4.6 × 1014 to 13.7 × 1014 ions/cm2. At the highest ion fluence of 18.3 × 1014 ions/cm2, the flake/flower-like morphology is observed. Field emission (FE) properties were studied under ultra-high vacuum condition in a parallel plate configuration using planar virgin SS as an anode and structured SS as a cathode. The Fowler–Nordheim plots were obtained from I–V characteristics to evaluate the turn-on field, field enhancement factor β and a maximum current density ranging 1.5–4.5 V/µm, 5008–12807 and 96–454 nA/cm2, respectively. The variation in the FE properties is attributed to the different morphological features at varying silicon ion fluences.

Interpretation of field emission current–voltage data: Background theory and detailed simulation testing of a user-friendly webtool

In field electron emission (FE) studies, interpretation of measured current–voltage characteristics and extraction of emitter characterization parameters are usually carried out within the framework of “smooth planar metal-like emitter (SPME) methodology”, using a data-analysis plot. This methodology was originally introduced in the 1920s. Three main data-plot types now exist: Millikan–Lauritsen (ML) plots, Fowler–Nordheim (FN) plots, and Murphy–Good (MG) plots. ML plots were commonly used in early FE studies, but most modern analysis uses FN plots. MG plots are a recent introduction.Theoretically, it is now known that ML and FN plots are predicted to be slightly curved in SPME methodology, but a Murphy–Good plot will be very nearly straight. Hence (because 1956 Murphy–Good emission theory is “better physics” than 1928 Fowler–Nordheim emission theory as corrected in 1929), expectation is that parameter extraction using a MG plot will be more precise than extraction using either ML plots or FN plots.In technological FE studies, current–voltage characteristics are often converted into other forms. Thus, measured voltage may be converted to (apparent) macroscopic field, and/or current values may be converted to macroscopic current densities. Thus, four data-input forms can be found in the context of analysing FE current–voltage results.It is also the case that over-simplified models of measurement-system behaviour are very widely assumed, and the question of whether simple use of a data-analysis plot is a valid data-interpretation procedure for the particular system under investigation has often been neglected. Past published studies on field emitter materials development appear to contain a high incidence of spurious values for the emitter characterization parameter “characteristic field enhancement factor”. A procedure (the so-called “Orthodoxy Test”) was described in 2013 that allows a validity check on measurement-system behaviour, and found that around 40% of a small sample of results tested were spuriously high, but has had limited uptake so far.To assist with FE current–voltage data interpretation and validity checks, a simple user-friendly webtool has been under design by the lead author. The webtool needs as user input some system specification data and some “range-limits” data from any of the three forms of data-analysis plot, using any of the four data-input variations. The webtool then applies the Orthodoxy Test, and—if the Test is passed—calculates values of relevant emitter characterization parameters.The present study reports the following: (1) systematic tests of the webtool functionality, using simulated input data prepared using Extended Murphy–Good field electron emission theory; and (2) systematic comparisons of the three different data-plot types, again using simulated input data, in respect of the accuracy with which extracted characterization parameter values match the simulation input values. The paper is introduced by a thorough summary review of the theory on which modern SPME-based current–voltage data-analysis procedures are based. The need in principle to move on (in due course) to data-analysis procedures based on curved-emitter emission theory is noted.An important result is to confirm (by simulations) that, particularly in respect of the extraction of formal emission areas, the performance of the Murphy–Good plot is noticeably better than the performances of Fowler–Nordheim and Millikan–Lauritsen plots. This result is important for field electron emission science because it is now known that differences as between different theories of field electron emission often affect the formal emission area.

The Fowler–Nordheim plot behaviour from virtual field emitters arrays of zinc oxide nanorods mixed with carbon nanotubes

ABSTRACT The Fowler–Nordheim plot behaviour is investigated for large area field emitters arrays composed of mixtures of ZnO nanorods and single-wall carbon nanotubes (CNTs). The field emission current–voltage characteristics are calculated using the Murphy-Good equation based on the Fowler–Nordheim model. The influencing factors taken into consideration are the radii of the ZnO rods, the heights of the CNTs, the variation of the onset voltage of the saturation of the ZnO conduction band (CB) emission current and the degradation of the CNTs at high applied voltages. The results show that the FN plots of the mixed arrays exhibit nonlinear behaviour near the high-field region which could be related to the FN plot behaviour of the constituting emitters arrays. The distribution of the emitters geometrical parameters and the onset of saturation of the ZnO CB current are found to affect the FN plot behaviour of the pure ZnO, CNTs arrays as well as mixed arrays. The comparisons between the FN plots from the present work and those measured experimentally are found useful to shed light on the field emission mechanism. This may in turn aid the development of complex field emission arrays for future technological applications. The work also shows the possibility to apply the standard FN model to complex large area field emitters arrays.

All field emission models are wrong, … but are any of them useful?

Field emission data are often represented on a Fowler–Nordheim plot but a new empirical equation has been recently proposed to better analyze experiments. Such an equation is based on approximations of the Murphy and Good model and predicts that a constant parameter κ, depending only on the work function of the emitter, can be extracted from the data. We compared this empirical equation with simulations of the Murphy and Good model in order to determine the range of validity of the approximations and the robustness of the relationship between κ and the work function. We found that κ is constant only over a limited range of electric fields and so depends significantly on the field enhancement factor. This result calls into question the usefulness of the new empirical equation.

Application of Murphy – Good Plot Parameters Extraction Method on Electron Emission from Carbon Fibers

The significance of the Fowler-Nordheim-type plots lies in the possibility of extracting useful and reliable physical parameters of the field electron emitters. This is achieved by the parameter's extraction methods. We report on the application of two parameters extraction methods on field emission data from bundles of carbon fibers (CFs) grouped in nickel tubes and operated inside a typical field emission microscope setup. These methods are the Murphy-Good plot and the conventional Fowler-Nordheim plot iterative method. The physical parameters include the area extraction parameter, the notional (actual) emission area, the formal area efficiency factor and the voltage conversion length. The results obtained from the two methods are discussed and compared to shed light on the controversial nature of these methods. The mechanism of field electron emission is analyzed based on the parameters extracted.

Using static linear response theory to describe field emission field enhancement and a field-induced insulator-conductor transition

Experiments on field electron emission (FE) of single carbon nanotubes (CNTs) indicate that they exhibit a nearly linear Fowler–Nordheim plot, and the field enhancement factor (FEF) near the CNT apex is independent of the applied (macroscopic) field (FM) for small radii field emitters. Recent results, based on density functional theory calculations considering CNTs with small radii, retrieved the constancy of the FEF defined in terms of the corresponding induced electron density. As a consequence, it has been reported that the constancy of the FEF with FM could be connected with the linear response of the CNT. In this paper, we reinforce this connection, considering the problem of a floating (6,6) hybrid single-walled nanotube, whose cylindrical body is an insulating one and composed of alternating boron and nitrogen atoms end-capped with carbon atoms. Our results show that the constancy of the FEF is achieved when a linear dependence between the longitudinal component of the induced system dipole moment (μi,z) and FM is observed. Two regimes of constant polarizabilities have been found at sufficiently low and high FM-values. In the intermediate range 0.3V/nm≲FM≲5 V/nm, a crossover from insulating-to-conducting behavior, exhibiting a nonlinear dependence of μi,z on FM, is found accompanied by an increase of the FEF with FM. This result reveals circumstances that could lead to dependence of the FEF on FM, being timely for interpretation of FE characteristics in the context of vacuum nanoelectronic devices.

Field electron emission from a nanostructured tungsten surface

In this paper, the electron emission from a nanostructured tungsten surface was investigated. A method for measuring an extremely low current (10−12 – 10−14 A) has been tested. It made possible to reduce the effect of the electric field on the sample surface and to minimize the probability of spontaneous breakdowns. For a detailed study of tungsten fuzz, a point tungsten anode (diameter 90 μm) was used. Field enhancement factor (β = 2000 – 3000) and effective emission area were calculated using the Fowler–Nordheim plots. The pre-breakdown current rise was studied. The emission current waveforms suggest the formation of several emission structures before the breakdown.

Scaling in large area field emitters and the emission dimension

Electrostatic shielding is an important consideration for large area field emitters (LAFEs) and results in a distribution of field enhancement factors even when the constituent emitters are identical. Ideally, the mean and variance together with the nature of the distribution should characterize a LAFE. In practice, however, it is generally characterized by an effective field enhancement factor obtained from a linear fit to a Fowler–Nordheim plot of the I−V data. An alternate characterization is proposed here based on the observation that for a dense packing of emitters, shielding is large and LAFE emission occurs largely from the periphery, while well separated emitter tips show a more uniform or two-dimensional emission. This observation naturally leads to the question of the existence of an emission dimension, De, for characterizing LAFEs. We show here that the number of patches of size LP in the ON-state (above average emission) scales as N(LP)∼LP−De in a given LAFE. The exponent De is found to depend on the applied field (or voltage) and approaches De=2 asymptotically.

The effect of size distribution and degradation of carbon nanotubes on the Fowler–Nordheim plot behavior

The behavior of the Folwer-Nordheim (FN) plot is investigated for large-area emitters arrays composed of perfectly aligned single-walled carbon nanotubes (CNTs). The field emission currents are calculated based on the standard FN model using the Murphy-Good equation. The aspect ratio of the CNTs is varied such that the height of the CNT has predefined uniform or Gaussian distributions. Continuous degradation of the high-aspect-ratio CNTs is assumed to take place at predefined values of the scaled barrier field. The effects, on the FN plot behavior, of the size distribution and the scenario of the degradation of the emitter are determined and discussed. These factors are found to produce the two behaviors of the experimental FN plots, i.e. the upward and the downward bending behaviors. This work shows the possibility to expand the application of the standard FN model for the investigation of the field emission characteristics from nanoscaled emitters such as CNTs.

Influence of Polystyrene Layer on the Field Electron Emission Performance of Nano-Apex Carbon Fibre Emitters

ABSTRACT A comprehensive investigation has been carried out to determine the source of an inherent temporal instability in the spatial distribution and the emission current obtained from field electron-emitting carbon fiber tips of type Polyacrylonitrile VPR – 19, thermally treated at 2800 °C. These instability effects have been successfully overcome by coating the carbon fiber tip with a sub-micron layer of polystyrene . The current-voltage characteristics, Fowler-Nordheim plots, Murphy-Good plots and the scanning electron micrographs in addition to the field electron emission patterns were used in this investigation to study the emission characteristics of carbon fiber tips before and after samples are being coated with polystyrene layer. Comparison between the emission process from the clean and composite tips are reported and the current-voltage characteristics were obtained at a threshold field that is a few times lower than that of the clean tip. At low emission current levels linear Fowler-Nordheim and Murphy-Good plots were obtained with a slope value lower than that of the clean tip. The spatial distribution consisted of a very bright spot without any internal structure. These results suggest that a polystyrene coated fiber tip offers better performance than the clean carbon fiber tip as a new field electron emission source.