Nonlinear Fowler-Nordheim Plots Research Articles

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.

Field emission from a nanometric paraboloidal emitter

When the radius of curvature R of an electron emitter is below 5 nm existing theories of field emission from curved surfaces fail because they assume a constant supply of electrons which is a characteristic only of planar surface emitters. In a previous work of ours we proved that the eigenfuctions of a rotationally symmetric parabolic emitter-the common shape of present nanoscopic emitters- are Whittaker functions and exhibit strong localization. In this paper we calculate the transmitted current density of such an emitter as a function of angle of emission θ and R. The angular dependence of the emitted current density is not very different from that of the classical model of a hemisphere on a post. However, when use is made of the parabolic image potential it is observed that the emission falls significantly. Finally, strongly non-linear Fowler-Nordheim plots are obtained. The significance of this is discussed.

Improving the extraction of characteristic field enhancement factors from nonlinear Fowler–Nordheim plots: Call for experimental tests

The author shows that the dependence between the effective emission area and the macroscopic electric field allow for the introduction of a new correction, ω, in the elementary slope characterization parameter (SCP) for extracting the characteristic field enhancement factor, γC, from (precise) orthodox cold-field electron emission measurements. The authors assume that the local macroscopic enhancement factors, γ, are Gaussian-distributed, as has been experimentally determined for the potential candidates of cold-field electron emission applications. Using the recent developments in cold-field electron emission theory, the authors found that for the typical experimental range of 1 V/μm ≤ FM ≤ 10 V/μm, the nonlinearities that are often observed in cold-field electron emission experiments may appear in JM-FM-type Fowler–Nordheim plots. Finally, our results show that depending on the dispersion in the distribution of γ, Δγ/γ0, where γ0 is the average value, the error in estimating the γC using the elementary SCP (a common practice for experimentalists) may be relevant.

Amazing ageing property and in situ comparative study of field emission from tungstenoxide nanowires

In this work, needle-shaping of tungsten oxide nanowires occurredduring field emission characterization. Compared with nanowires witha flat apex, needle-shaped emitters showed a lower threshold field of11.9 V µm − 1 for1 mA cm − 2 and a higheremission current of 1120 µA at 16.2 V µm − 1. Most notably, the measured ageing current dramatically increased by more than fourtimes until it slightly decreased, tending towards stability. In addition, the samples showedstriking difference in their nonlinear Fowler–Nordheim plot before and after ageing tests.Selected area diffraction and transmission electron microscope characterizations were usedto further study these amazing results.

Strong deviations from Fowler-Nordheim behavior for field emission from individual SiC nanowires due to restricted bulk carrier generation

We report here field-emission (FE) studies of individual single-crystal SiC nanowires that showed several distinct $I/V$ regimes including strong saturation resulting in highly nonlinear Fowler-Nordheim plots. The saturation is due to the formation of a depletion layer near the nanowire ends as predicted for FE from semiconductors and appears after in situ control of the surface cleanliness. This work opens the door to improving the uniformity, stability, and photon control of mass-produced planar nanowire FE cathodes and shows how FE can be used for transport measurements on individual semiconducting nanowires.

Fitting nonlinear Fowler-Nordheim plots of field emission strips with a self-consistent parallel plane model

The saturation behavior of field emission strips is investigated by using a finite-difference time-domain (FDTD) particle-in-cell (PIC) simulation. The field-emission process is described quantum mechanically by the Fowler-Nordheim (FN) equation. Space charge effects are automatically included in the FDTD PIC simulations. The simulation results have confirmed that the saturation is caused by the space charge effects. A self-consistent parallel plane (SCPP) model has been developed for fitting the nonlinear FN plots of field emission strips. Within the framework of an effective work function approximation and energy conservation, the FN and Poisson’s equations are solved self-consistently in the SCPP model. It is demonstrated that the nonlinear FN plots of the field emission strips can be fitted by the SCPP model very well. The electric properties of the field emission strips can be characterized by the effective work function and the effective emission area. In addition, the field emission of Spindt-type ...

A single In-doped SnO2 submicrometre sized wire as a field emitter

Indium doped tin oxide submicrometre sized wires have been synthesized by thermal evaporation and characterized by field emission (FE) microscopy. The non-linear Fowler–Nordheim plot corresponds to the typical semiconducting behaviour of the emitter. The field enhancement factor has been estimated to be 29 900 cm−1 indicating that electron emission is due to the nanometric features of the emitter. A current density of the order of 6.36 × 103 A cm−2 with an applied electric field of 1 × 104 V µm−1 has been obtained. The long term FE current stability tested at the preset current level of 1 µA exhibits no severe fluctuations.

Mechanism of field electron emission from carbon nanotubes

Field electron emission (FE) is a quantum tunneling process in which electrons are injected from materials (usually metals) into a vacuum under the influence of an applied electric field. In order to obtain usable electron current, the conventional way is to increase the local field at the surface of an emitter. For a plane metal emitter with a typical work function of 5 eV, an applied field of over 1 000 V/μm is needed to obtain a significant current. The high working field (and/or the voltage between the electrodes) has been the bottleneck for many applications of the FE technique. Since the 1960s, enormous effort has been devoted to reduce the working macroscopic field (voltage). A widely adopted idea is to sharpen the emitters to get a large surface field enhancement. The materials of emitters should have good electronic conductivity, high melting points, good chemical inertness, and high mechanical stiffness. Carbon nanotubes (CNTs) are built with such needed properties. As a quasi-one-dimensional material, the CNT is expected to have a large surface field enhancement factor. The experiments have proved the excellent FE performance of CNTs. The turn-on field (the macroscopic field for obtaining a density of 10 μA/cm2) of CNT based emitters can be as low as 1 V/μm. However, this turn-on field is too good to be explained by conventional theory. There are other observations, such as the non-linear Fowler-Nordheim plot and multi-peaks field emission energy distribution spectra, indicating that the field enhancement is not the only story in the FE of CNTs. Since the discovery of CNTs, people have employed more serious quantum mechanical methods, including the electronic band theory, tight-binding theory, scattering theory and density function theory, to investigate FE of CNTs. A few theoretical models have been developed at the same time. The multi-walled carbon nanotubes (MWCNTs) should be assembled with a sharp metal needle of nano-scale radius, for which the FE mechanism is more or less clear. Although MWCNTs are more common in present FE applications, the single-walled carbon nanotubes (SWCNTs) are more interesting in the theoretical point of view since the SWCNTs have unique atomic structures and electronic properties. It would be very interesting if people can predict the behavior of the well-defined SWCNTs quantitatively (for MWCNTs, this is currently impossible). The FE as a tunneling process is sensitive to the apex-vacuum potential barrier of CNTs. On the other hand, the barrier could be significantly altered by the redistribution of excessive charges in the micrometer long SWCNTs, which have only one layer of carbon atoms. Therefore, the conventional theories based upon the hypothesis of fixed potential (work function) would not be valid in this quasi-one-dimensional system. In this review, we shall focus on the mechanism that would be responsible for the superior field emission characteristics of CNTs. We shall introduce a multi-scale simulation algorithm that deals with the entire carbon nanotube as well as the substrate as a whole. The simulation for (5, 5) capped SWCNTs with lengths in the order of micrometers is given as an example. The results show that the field dependence of the apex-vacuum electron potential barrier of a long carbon nanotube is a more pronounced effect, besides the local field enhancement phenomenon.

Nonlinear Fowler–Nordheim plots of the field electron emission from graphitic nanocones: influence of non-uniform field enhancement factors

Well-aligned graphitic nanocones were synthesized on polished pristine p-type (100) silicon wafers through plasma enhanced hot filament chemical vapour deposition. The field electron emission properties were investigated using anode probes of different diameters. Non-linearity was observed in the field electron emission (FEE) Fowler–Nordheim (FN) plots at high electric field. The numerical calculations based on the superposition of two types of characteristic emission sites are consistent with the experimental data. The non-linearity in the FN plot may be attributed to the non-uniform field enhancement factor (FEF) of the graphitic nanocones. At low electric field, electrons are emitted mainly from nanocones with large FEF, corresponding to a small slope magnitude in the FN plots. With the increasing electric field, the nanocones with small FEFs also contribute to the emission current, which results in a reduced average FEF and so a larger slope magnitude. If the difference in FEFs of the two types of emission sites is large, the emission sites with smaller FEF may not be able to participate in emission even at the highest electric field tested in the experiments and the FN plot remains a straight line determined presumably by the emission sites with larger FEF.

Quantifying temperature-enhanced electron field emission from individual carbon nanotubes

The electron field emission properties of individual multiwalled carbon nanotubes have been examined using a combined STM-TEM microscope. The measured electron emission, for low emission currents, can be fitted with a standard Fowler-Nordheim model. For higher electron emission, above $10\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{A}$ for an individual carbon nanotube, we observe a significantly increased emission current leading to a nonlinear Fowler-Nordheim plot. The nonlinearity is caused by thermally enhanced electron emission due to Ohmic heating of the carbon nanotube. This is verified by modeling the electron field emission current. In addition to the influence of radiative cooling and the temperature dependence of the nanotube resistivity, we clearly show that a consideration of the temperature change due to the electron emission process itself, known as the Nottingham effect, is crucial to obtain good agreement with the experimental data.

Field emission from crystalline copper sulphide nanowire arrays

Straight crystalline copper sulphide (Cu2S) nanowire arrays have been grown by using a simple gas–solid reaction at room temperature. These were demonstrated to exhibit semiconductor properties. Field emission was observed at a field of ∼6 MV/m, and its current-field characteristics deviate from Fowler–Nordheim theory, i.e., showing a nonlinear Fowler–Nordheim plot. The uniform emission from the whole arrays was observed using transparent anode technique, and their variation with applied field was recorded. The emission from individual nanowires was also studied using a field emission microscope, and was found to consist of a number of spatially resolved diffuse spots. Finally, stable emission current at different levels and over time was recorded. These findings indicate that semiconductor nanowires as cold cathode have a potential future, worthy of further comprehensive investigation. The technical importance of using semiconductor nanowires as cold cathode emitter is given.