Simple theoretical analysis of the Fowler-Nordheim field emission from microstructures and quantum wires of optoelectronic materials

We present a simplified theoretical formulation of the Fowler-Nordheim field emission (FNFE) under magnetic quantization and also in quantum wires of optoelectronic materials on the basis of a newly formulated electron dispersion law in the presence of strong electric field within the framework of k.p formalism taking InAs, InSb, GaAs, Hg(1-x)Cd(x)Te and In(1-x)Ga(x) As(y)P(1-y) lattice matched to InP as examples. The FNFE exhibits oscillations with inverse quantizing magnetic field and electron concentration due to SdH effect and increases with increasing electric field. For quantum wires the FNFE increases with increasing film thickness due to the existence van-Hove singularity and the magnitude of the quantum jumps are not of same height indicating the signature of the band structure of the material concerned. The appearance of the humps of the respective curves is due to the redistribution of the electrons among the quantized energy levels when the quantum numbers corresponding to the highest occupied level changes from one fixed value to the others. Although the field current varies in various manners with all the variables in all the limiting cases as evident from all the curves, the rates of variations are totally band-structure dependent. Under certain limiting conditions, all the results as derived in this paper get transformed in to well known Fowler-Nordheim formula. (C) 2011 Elsevier Ltd. All rights reserved.

Fowler-Nordheim Field Emission from Carbon Nanotubes Under Intense Electric Field

In this paper, we study the Fowler-Nordheim field emission (FNFE) from carbon nanotubes on the basis of a newly formulated electron dispersion law by considering the fact that the intense electric field needed for FNFE changes the band structure in a fundamental way. It has been found that the field emitted current increases with increasing electric field in oscillatory manner due to the appearance of van Hove singularities and exhibits spikes for particular values of the electric field where the singularity occurs. The numerical values of the field emitted current in all the cases vary widely and the determined by the chiral indices and the diameter in the respective cases. The results of this paper find three applications in the fields of nanoscience and technology.

Vibrational analysis of the (B2P{cyrillic}→X2P{cyrillic}) system of NS

A few red degraded bands attributable to NS have been reported earlier by Fowler and Barker, Dressler and Barrow et al, and they occur in the same region (2300 to 2700 Å) as the bands of the known systems (C2∑+-X2P{cyrillic}) and (A2Δ-X2P{cyrillic}). Measurements made on the heads of some of these weak bands led Barrow et al. to believe that these bands may form a system analogous to the β-system of NO and be due to a2P{cyrillic}-2P{cyrillic} transition. The spectrum of NS has now been studied in a little more detail by means of an uncondensed discharge through dry nitrogen and sulphur vapour in the presence of argon and thirty three bands belonging to this system have been recorded in the region 2280 to 2760 Å. It has been found possible to represent the band heads by means of the equation {Mathematical expression}. Taking the lower state doublet interval as 223 cm-1, it is shown that the separation in the upper state is 94 cm-1. The ratio of the force constants in the upper and the ground states is found to be 0·39 and is nearly the same as that in the β-system of NO (0·30). The present vibrational analysis therefore supports the view that these new red degraded bands of NS arise from a (B2P{cyrillic}→X2P{cyrillic}) transition and the observed intensity distribution in the form of a wide parabola is also in qualitative agreement with what is expected from the moderately large Δ re (∼0·12Å) value.

Stabilizing a pulsed field emission from an array of carbon nanotubes

In this paper, we propose a new design configuration for a carbon nanotube (CNT) array based pulsed field emission device to stabilize the field emission current. In the new design, we consider a pointed height distribution of the carbon nanotube array under a diode configuration with two side gates maintained at a negative potential to obtain a highly intense beam of electrons localized at the center of the array. The randomly oriented CNTs are assumed to be grown on a metallic substrate in the form of a thin film. A model of field emission from an array of CNTs under diode configuration was proposed and validated by experiments. Despite high output, the current in such a thin film device often decays drastically. The present paper is focused on understanding this problem. The random orientation of the CNTs and the electromechanical interaction are modeled to explain the self-assembly. The degraded state of the CNTs and the electromechanical force are employed to update the orientation of the CNTs. Pulsed field emission current at the device scale is finally obtained by using the Fowler-Nordheim equation by considering a dynamic electric field across the cathode and the anode and integration of current densities over the computational cell surfaces on the anode side. Furthermore we compare the subsequent performance of the pointed array with the conventionally used random and uniform arrays and show that the proposed design outperforms the conventional designs by several orders of magnitude. Based on the developed model, numerical simulations aimed at understanding the effects of various geometric parameters and their statistical features on the device current history are reported.

Field emission properties of carbon nanotube arrays with defects and impurities

Field emission from carbon nanotubes (CNTs) in the form of arrays or thin films give rise to several strongly correlated process of electromechanical interaction and degradation. Such processes are mainly due to (1) electron-phonon interaction (2) electromechanical force field leading to stretching of CNTs (3) ballistic transport induced thermal spikes, coupled with high dynamic stress, leading to degradation of emission performance at the device scale. Fairly detailed physics based models of CNTs considering the aspects (1) and (2) above have already been developed by these authors, and numerical results indicate good agreement with experimental results. What is missing in such a system level modeling approach is the incorporation of structural defects and vacancies or charge impurities. This is a practical and important problem due to the fact that degradation of field emission performance is indeed observed in experimental I-V curves. What is not clear from these experiments is whether such degradation in the I-V response is due to dynamic reorientation of the CNTs or due to the defects or due to both of these effects combined. Non-equilibrium Green’s function based simulations using a tight-binding Hamiltonian for single CNT segment show up the localization of carrier density at various locations of the CNTs. About 11% decrease in the drive current with steady difference in the drain current in the range of 0.2-0.4V of the gate voltage was reported in literature when negative charge impurity was introduced at various locations of the CNT over a length of ~20nm. In the context of field emission from CNT tips, a simplistic estimate of defects have been introduced by a correction factor in the Fowler-Nordheim formulae. However, a more detailed physics based treatment is required, while at the same time the device-scale simulation is necessary. The novelty of our present approach is the following. We employ a concept of effective stiffness degradation for segments of CNTs, which is due to structural defects, and subsequently, we incorporate the vacancy defects and charge impurity effects in the Green’s function based approach. Field emission induced current-voltage characteristics of a vertically aligned CNT array on a Cu-Cr substrate is then simulated using a detailed nonlinear mechanistic model of CNTs coupled with quantum hydrodynamics. An array of 10 vertically aligned and each 12 m long CNTs is considered for the device scale analysis. Defect regions are introduced randomly over the CNT length. The result shows the decrease in the longitudinal strain due to defects. Contrary to the expected influence of purely mechanical degradation, this result indicates that the charge impurity and hence weaker transport can lead to a different electromechanical force field, which ultimately can reduce the strain. However, there could be significant fluctuation in such strain field due to electron-phonon coupling. The effect of such fluctuations (with defects) is clearly evident in the field emission current history. The average current also decreases significantly due to such defects.

Modeling the Field Emission Current Fluctuation in Carbon Nanotube Thin Films

Owing to their distinct properties, carbon nanotubes (CNTs) have emerged as promising candidate for field emission devices. It has been found experimentally that the results related to the field emission performance show variability. The design of an efficient field emitting device requires the analysis of the variabilities with a systematic and multiphysics based modeling approach. In this paper, we develop a model of randomly oriented CNTs in a thin film by coupling the field emission phenomena, the electron-phonon transport and the mechanics of single isolated CNT. A computational scheme is developed by which the states of CNTs are updated in time incremental manner. The device current is calculated by using Fowler-Nordheim equation for field emission to study the performance at the device scale.