Fowler-Nordheim Plots Research Articles

Field electron emission area revisited: an integrated method for the area extraction model

For electron field emitters, the emitter's physical and geometrical parameters, namely the emitter work function and its geometrical factor, are extracted from the slope of the Fowler-Nordheim (FN) plot. The literature contains few investigations and reviews of extended parameter extraction models based on the slope and intercept of the FN plot. However, due to the complexity of these reviews, there is a great need for an integrated approach to the area extraction model whereby a simplified account of the derivation and implementation of the model is presented and made convenient, especially for scholars other than physicists and engineers. This is precisely the aim of the present article, where the standard FN equation and Schottky-Nordheim barrier functions are preserved and only measurable parameters are involved in the extraction model and the derivation of the area extraction equation. In addition, the model is applied to experimental field emission data from a single LaB$_{6}$ nanoemitter to support the discussion and to elaborate on the model's applicability, significance, and advantages.

Adsorption of Gold on Iridium

The work described in this paper is a study of gold adsorption on the whole tip surface of iridium field emitter. The study has been carried out using field emission microscope. Changes in electron work function of the iridium substrate which are produced by vapor of deposition of submonolayers of gold in ultra high vacuum have been measured by noting the changes in the slope of Fowler-Nordheim plots. The same procedure for studying the adsorption of copper on iridium [1] was followed to study the adsorption of gold on iridium. Adsorption of gold was examined on the iridium surface containing the (100) ring which could not be removed thermally.

The effect of the enhanced field emission on the characteristics of the superconducting radio frequency cavities

Electron field emission limiting the accelerating gradient in superconducting cavities remains the dominant setback in cavity production. The need to understand and control the field emission has become increasingly important because of the prospect of using high-gradient structures in linear colliders. Since building an accelerator structure is a complicated and costly process, elimination of unnecessary steps has priority. In this paper an analysis of the influence of the enhanced field emission in superconducting radio frequency cavity together with modal field calculations by using COMSOL finite elements package has been presented. The obtained results reveal that the electric field required for the field emission is generated in the cavity irises. The imperfection of the cavity surface leading to very high fields is modelled by a simple cone. The estimated value of the enhancement factor for the cone tip of around 4 is in a good agreement with the data found in the literature. In addition, from the slopes and the intercepts of the Fowler-Nordheim plots, a dependence of the enhancement factor and the effective area on the work function has been estimated.

Application of radio frequency inductively coupled plasma in chemical vapor deposition process of diamond-like carbon films for modification of properties of deposited films

Abstract The authors have deposited the diamond-like carbon (DLC) films by radio frequency inductively coupled plasma enhanced chemical vapor deposition (RF ICP PECVD) method. The investigated DLC films with different sp3 fraction content were deposited on polished and textured silicon substrates. The sp3 fraction content of the deposited DLC films was ranging from 35 % to 70 % and was estimated from acquired Raman scattering spectra (excitation wavelength: 325 nm and 514.5 nm). The measurements of field emission characteristics were carried out in diode configuration. Emission properties of the DLC films were calculated from Fowler-Nordheim plots. The calculated electric field enhancement factor β was ranging from 56 to 198 for the DLC films deposited on polished substrates and from 115 to 445 for films deposited on textured substrates. The surface of the DLC films was observed by scanning electron microscope (SEM) after field emission measurements. The acquired SEM images reveled that the activation of field emission from the DLC films is connected with generation of structural damage to the DLC films.

Field emission properties of a DWCNT bundle and a single MWCNT

The field emission properties of a bundle of double-walled carbon nanotubes (DWCNTs) and a single multiwalled carbon nanotube (MWCNT) were investigated. A DWCNT bundle or a single MWCNT was attached to the head of sharpened tip of tungsten by electrophoresis; the tungsten tip was dipped into a drop of a carbon nanotube/1,2-dichloroethane suspension on a stainless plate, and a high-frequency AC voltage (20 V peak to peak with a frequency of 15 MHz) was applied between the tungsten tip and the stainless steel plate. The turn-on fields of the DWCNT and MWCNT tips for 1 nA/cm2 were 0.05 and 0.48 V/μm, respectively. From the Fowler-Nordheim plots, the field enhancement factor (β) of the tips was estimated to be 109,600 (DWCNT) and 6780 (MWCNT). The present DWCNT emitter is characterized by a very small turn-on field and large β. The field emission performance is discussed in terms of the sizes of the bundle of DWCNTs and a single MWCNT.

A Comparative Study of Field Emission From Semiconducting and Metallic Single‐Walled Carbon Nanotube Planar Emitters

Field electron emission from thin films composed of solely metallic or semiconducting single‐walled carbon nanotubes is investigated using a scanning tip anode technique. Metallic and semiconducting nanotubes are separated by aqueous two‐phase extraction. Local field emission centers observed on nanotube films of both types showed non‐linear Fowler–Nordheim (FN) plots bent downwards. The curving of FN plots is much stronger for semiconducting nanotubes which is explained by their higher electrical resistance and stronger field penetration effect compared to metallic nanotubes. Particular nanotubes of both types revealed oscillations in current–voltage characteristics. The periodic oscillations indicated that the field emission current is modulated either by resonant tunnelling from confinement states in nano‐objects formed by adsorbates or by the Coulomb blockade effect that can occur for emission from short carbon nanotubes.

Field emission of graphene oxide decorated ZnO nanorods grown on Fe alloy substrates

Graphene oxides (GO) are decorated on the top surface of ZnO nanorods (NRs) grown on Fe alloy substrates for efficient field emission. The GO decorated ZnO NRs acting as cold electron emitters exhibit excellent field emission performance with the turn-on field Eto as low as 1.63 V/μm and the threshold field Ethr down to 3.12 V/μm. ZnO NRs grown on the alloy substrates have a low interfacial resistance and intend to enhance electrical conduction. A schottky contact of Fe-ZnO and matched Fermi levels of ZnO-GO interface contribute to the enhanced current emission efficiency. Besides, some nanometer-scaled sharp protrusions have been formed in the GO sheets, and GO itself owns abundant C-O-C oxygen functional groups that also help to improve the field emission current. A straight line Fowler-Nordheim plot of the field emission current from the emitter is obtained and the effective work function for the decorated GO sheets is calculated from the slope with a value below 1.5 eV. Finally, field emission mechanism of the GO decorated ZnO NRs has been proposed. This work may help the development of the practical electron sources and advanced optronic devices based on GO field emitters.

Characterization of GaN nanostructures by electron field and photo-field emission

The electron field and photo-field emission from GaN nanostructures has been analyzed in this review. In order to explain the obtained experimental results, a model was proposed taking into account the change in carrier concentration distribution in the main and the satellite valley during the emission process. The lowering of work function (due to the increased number of carriers in the satellite valley) can explain the decrease in the Fowler-Nordheim plot slope. It was shown that the energy difference between the main and satellite valley in GaN was decreased in the case of quantum confinement, thus increasing the probability of electron transition from Γ to X valley at same electric fields.

Extracting scaled barrier field from experiments with conducting large-area field emitters: Considerations by inclusion of the dependence between area of emission and the applied field

With a large-area field electron emitter (LAFE), the area of emission is expected to be dependent of the applied field. One possible explanation for this behavior is the statistical distribution of the local field enhancement factors (FEFs), as a consequence of an irregular surface's morphology of the LAFE. In this paper, the authors present a simple and more general theory for extracting the scaled barrier field, f, by considering the dependence of the formal area of emission of conducting LAFEs with an applied field. In our model, the local FEFs of LAFE sites are exponentially distributed, which is consistent with thin film electron emitters. As a byproduct of technological relevance, our results show that general effective f values extracted from linear Fowler–Nordheim plots are outside of the “experimentally reasonable” range of values for physically orthodox emission, when the area of emission varies significantly with the applied field. Thus, a more general criterion for detecting and interpreting nonorthodox field emission is proposed and can be applied to any distribution of local FEFs in conducting LAFEs.

Properties of SiO<sub>2</sub>/4H-SiC Interfaces with an Oxide Deposited by a High-Temperature Process

This work reports on the physical and electrical characterization of the oxide/semiconductor interface in MOS capacitors with the SiO2 layer deposited by a high temperature process from dichlorosilane and nitrogen-based vapor precursors and subjected to a post deposition annealing process in N2O. Low interface state density (Dit ≈ 9.0×1011cm-2eV-1) was found at 0.2 eV from EC, which is comparable to the values typically obtained in other lower temperature deposited oxides (e.g., TEOS). A barrier height of 2.8 eV was derived from the Fowler-Nordheim plot, very close to the ideal value expected for SiO2/4H-SiC interface. Basing on these preliminary results, the integration in MOSFETs devices can be envisaged.

Fabrication of Gas Ionization Sensor to Recognize Gases and Measure Pressure and Humidity

Single Ionic gas sensor (IGS) was fabricated to measure pressure, humidity and recognizes the gases. Anodic method was used to create TiO2 nanotubes (TNTs) (with internal diameter from 45 to 90 nm) on the surfaces of pure Ti and Ti-6Al-7Nb alloy. Covered surface with TNTs was operated as negative electrode to build high localized electric field and minimize breakdown voltage (Vbd). The distance between the electrodes was fixed at 60 μm. Local electric field enhancement β factor was calculated by Fowler–Nordheim plot. Its value was 857 for anodized Ti (ATi). After annealing at 800 °C; TNTs on pure Ti surface transformed to parallel rods with diameters (from 95 to 550 nm). But on alloy surface, TNTs were transformed to protrusions. Sensitivity of measuring pressure for anodized samples decreased with increasing mean free path of testing gases. For all gases; there was increment in Vbd with pressure increasing. For each gas there was specific Vbd at definite pressure and humidity; this value represented a “fingerprint” for each gas recognized it from other gases. Sensitivity of humidity for both anodized and annealed IGSs increased with increasing of relative humidity (%RH). (Vbd, Humidity) curve was approximately linear for annealed Ti and its alloy.

Control of tunnel barriers in multi-wall carbon nanotubes using focused ion beam irradiation

We have formed tunnel barriers in individual multi-wall carbon nanotubes using the Ga focused ion beam irradiation. The barrier height was estimated by the temperature dependence of the current (Arrhenius plot) and the current–voltage curves (Fowler–Nordheim plot). It is shown that the barrier height has a strong correlation with the barrier resistance that is controlled by the dose. Possible origins for the variation in observed barrier characteristics are discussed. Finally, the single electron transistor with two barriers is demonstrated.

The theoretical link between voltage loss, reduction in field enhancement factor, and Fowler-Nordheim-plot saturation

With a large-area field electron emitter, when an individual post-like emitter is sufficiently resistive, and current through it is sufficiently large, then voltage loss occurs along it. This letter provides a simple analytical and conceptual demonstration that this voltage loss is directly and inextricably linked to a reduction in the field enhancement factor (FEF) at the post apex. A formula relating apex-FEF reduction to this voltage loss was obtained in the paper by Minoux et al. [Nano Lett. 5, 2135 (2005)] by fitting to numerical results from a Laplace solver. This letter derives the same formula analytically, by using a “floating sphere” model. The analytical proof brings out the underlying physics more clearly and shows that the effect is a general phenomenon, related to reduction in the magnitude of the surface charge in the most protruding parts of an emitter. Voltage-dependent FEF-reduction is one cause of “saturation” in Fowler-Nordheim (FN) plots. Another is a voltage-divider effect, due to measurement-circuit resistance. An integrated theory of both effects is presented. Both together, or either by itself, can cause saturation. Experimentally, if saturation occurs but voltage loss is small (<20 V, say), then saturation is more probably due to FEF-reduction than voltage division. In this case, existing treatments of electrostatic interaction ("shielding") between closely spaced emitters may need modification. Other putative causes of saturation exist, so the present theory is a partial story. Its extension seems possible and could lead to a more general physical understanding of the causes of FN-plot saturation.

Electron extraction electrode for a high-performance electron beam from carbon nanotube cold cathodes

The effect of an electron extraction electrode on electron emission for a high-performance electron beam was studied using vertically aligned carbon nanotube emitters as a cold cathode. For the lower electron emission regime (anode current less than 1 mA), the gate electrode structure and materials used had little effect on the electron emission current. However, at the higher electron emission regime (anode current higher than 1 mA), the gate electrode materials and structure do begin to deviate from an ideal Fowler–Nordheim plot by the thermal and electrostatic load on the gate electrode, especially for the small cathode area. The gate mesh bends upward under a higher current load, which then increases the gate leakage current. The upward bending in the gate mesh electrode could reduce the effective electric field by increasing the gate to cathode distance, resulting in saturation of the electron emission current. For higher electron emission currents on the anode, a gate electrode comprising a lower thermal expansion coefficient material is suitable for small cathode area electron beams.

尖鋭構造を持たない炭素膜からの電界放出

Field emission features from Si and W tips are drastically improved upon coating even with simple carbon films. In this paper, in order to obtain clues to clarify the mechanism, we examine atomistic STM observations including local barrier height (LBH) and field emission imagings of the carbon films. And we also examine the field emission features from the shape-controlled W tips before and after the carbon coatings, enabling us to estimate the local electric field at the tip apex. From the STM observations, we find that the carbon film consists of nm-scale grains with various electronic properties and that the FE current varies grain by grain and is higher near the edge of each grain. The effective work functions evaluated from the slopes of the Fowler-Nordheim (FN) plot are constant regardless of the thickness of the carbon coating, although they are largely scattered for the films thinner than 1 nm. On the basis of the observed results, we discuss the mechanism of low macroscopic field emission from carbon films.

Fowler Nordheim theory of carbon nanotube based field emitters

Field emission (FE) phenomena are generally explained in the frame-work of Fowler Nordheim (FN) theory which was given for flat metal surfaces. In this work, an effort has been made to present the field emission mechanism in carbon nanotubes (CNTs) which have tip type geometry at nanoscale. High aspect ratio of CNTs leads to large field enhancement factor and lower operating voltages because the electric field strength in the vicinity of the nanotubes tip can be enhanced by thousand times. The work function of nanostructure by using FN plot has been calculated with reverse engineering. With the help of modified FN equation, an important formula for effective emitting area (active area for emission of electrons) has been derived and employed to calculate the active emitting area for CNT field emitters. Therefore, it is of great interest to present a state of art study on the complete solution of FN equation for CNTs based field emitter displays. This manuscript will also provide a better understanding of calculation of different FE parameters of CNTs field emitters using FN equation.

Annealing effects on electrical behavior of gold nanoparticle film: Conversion of ohmic to non-ohmic conductivity

This paper reports on the electrical behavior of self-assembled gold nanoparticle films before and after high-temperature annealing in ambient environment. These films are made by depositing gold nanoparticles from a colloidal solution on glass substrates using centrifuge deposition technique. The current-voltage (I–V) characteristics of these films exhibits ohmic and non-ohmic properties for un-annealed and annealed films respectively. As the annealing time duration increases, the onset of non-ohmic behavior occurs at higher voltages. To understand the underlying mechanisms for the observed electrical conduction behavior in these films and how electrical conduction is effected by film morphology and structural properties before and after annealing, systematic comparative studies based on scanning electron microscopy (SEM), UV–vis absorption spectroscopy and X-ray photoelectron spectroscopy (XPS) have been performed. The morphology of the films shows that the assembled gold nanoparticles are distributed on the substrate in a random way before annealing. After 2h annealing gold nanoparticles exhibit a higher filling fraction when examined by SEM, which means that they coalesce, upon annealing, with respect to un-annealed films. The UV–vis absorption spectra of the films show that there is a red-shift and broadening in the absorption band for the annealed films. The observed phenomenon is related to the plasmon near-field coupling effect and suggests that the nanoparticle ensembles interspacing has decreased. The structural and crystallinity of the films exhibit amorphous structure before annealing and pure crystalline phases with a preferential growth direction along the (111) plane after annealing. The XPS analysis further suggests the existence of the stable thin oxide layer in the phase of Au2O3 in the annealed films. The I–V characteristics have been described by Simmons’ model for tunnel transport through metal-insulator-metal (MIM) junctions. The Fowler-Nordheim (F-N) plots show the transition of the in-plane charge transport mechanism from direct tunneling to field emission in annealed films. Our results suggest that, the formation of a thin layer of Au2O3, the proximity of the nanoparticles as well as their higher filling fraction are important parameters related with the tunneling process enhancement. The observed non-ohmic conductivity property can make these self-assembled gold nanoparticle films very useful structures in different applications such as sensing, resistors and other nanoelectronic applications.

The consequences of dependence between the formal area efficiency and the macroscopic electric field on linearity behavior in Fowler–Nordheim plots

This work presents a theoretical explanation for a crossover in the linear behavior in Fowler–Nordheim (FN) plots based on orthodox cold field electron emission (CFE) experimental data. It is characterized by a clear change in the decay rate of usually single-slope FN plots, and has been reported when non-uniform nano-emitters are subject to high macroscopic electric field FM. We assume that the number of emitting spots, which defines an apparent formal area efficiency of CFE surfaces, depends on the macroscopic electric field. Non-uniformity is described by local enhancement factors , which are randomly assigned to each distinct emitter of a conducting CFE surface, from a discrete probability distribution , with j = 1, 2. It is assumed that , and that . The local current density is evaluated by considering a usual Schottky–Nordheim barrier. The results reproduce the two distinct slope regimes in FN plots when [2, 20] V μm−1 and are analyzed by taking into account the apparent formal area efficiency, the distribution ρ, and the slopes in the corresponding FN plot. Finally, we remark that our results from numerical solution of Laplace’s equation, for an array of conducting nano-emitters with uniform apex radii 50 nm but different local height, supports our theoretical assumptions and could used in orthodox CFE experiments to test our predictions.

Aqueous Phase Synthesis and Enhanced Field Emission Properties of ZnO-Sulfide Heterojunction Nanowires

ZnO-CdS, ZnO-ZnS, and ZnO-Ag2S core-shell heterojunction structures were fabricated using low-temperature, facile and simple aqueous solution approaches. The polycrystalline sulfide shells effectively enhance the field emission (FE) properties of ZnO nanowires arrays (NWAs). This results from the formation of the staggered gap heterointerface (ZnO-sulfide) which could lead to an energy well at the interfaces. Hence, electrons can be collected when an electric field is applied. It is observed that ZnO-ZnS NWAs have the lowest turn-on field (3.0 Vμm−1), compared with ZnO-CdS NWAs (6.3 Vμm−1) and ZnO-Ag2S NWAs (5.0 Vμm−1). This may be associated with the pyramid-like ZnS shell which increases the number of emission nanotips. Moreover, the Fowler-Nordheim (F-N) plot displays a nonlinear relationship in the low and high electric field regions caused by the double well potential effect of the heterojunction structures.

Field emission analysis of band bending in donor/acceptor heterojunction

The donor/acceptor heterojunction plays an important role in organic solar cells. An investigation of band bending in the donor/acceptor heterojunction is helpful in analysis of the charge transport behavior and for the improvement of the device performance. In this work, we report an approach for detection of band bending in a donor/acceptor heterojunction that has been prepared on a small and sharp tungsten tip. In situ field emission measurements are performed after the deposition process, and a linear Fowler-Nordheim plot is obtained from the fresh organic film surface. The thickness-dependent work function is then measured in the layer-by-layer deposited heterojunction. Several different types of heterojunction (zinc phthalocyanine (ZnPc)/C60, copper phthalocyanine (CuPc)/3,4,9,10-perylenetetracarboxylic bisbenzimidazole, and CuPc/C60) are fabricated and analyzed. The different charge transfer directions in the heterojunctions are distinguished by field emission measurements. The calculation method used to determine the band bending is then discussed in detail. A triple layer heterojunction (C60/ZnPc/CuPc) is also analyzed using this method. A small amount of band bending is measured in the outer CuPc layer. This method provides an independent reference method for determination of the band bending in an organic heterojunction that will complement photoemission spectroscopy and current-voltage measurement methods.