Using a tunneling approach for the field emission from a single carbon nanotube, expressions for the emission current as a function of the anode voltage and of the emitted electron energy spectrum are obtained. The low dimensionality of the electronic system of a carbon nanotube is taken into account. The extraction field on the nanotube’s tip is evaluated using numerical computations. For nanotubes of practical interest, having large enough diameters, it is demonstrated that the influence of the detailed form of the electron energy dispersion relations is not of major importance. This influence could be generally embedded in a numerical factor entering the expression of the emission current. The influence of the various tube parameters on the characteristics is also identified and analyzed. An approximate formula for use in practical analysis in field emission is deduced and its validity for different nanotube sizes is verified.
The purpose of this work is to show that the Fowler–Nordheim (FN) current–voltage (I–V) plot [log(I/V2) as a function of 1/V] must be treated, on principle, as nonlinear. The cause of this behavior is outlined to be the fact that the electric field and current density are not constant over the emitter’s surface. Traditional approach of the FN I–V plot as being linear may lead to physical contradictions. These contradictions are brought into light. A field emitter model is then developed, which allows to express in closed analytical equations the above statements. Expressions for field enhancement factor, area factor and also for the I–V relationship are obtained. The FN I–V plot nonlinearities are shown to be greater for smaller voltages. Within this model, the FN I–V plot can be taken as quasilinear, under some assumptions. Suggestions for technological parameter extraction from I–V data through nonlinear or linear least-squares optimization techniques are done.
High current density field emission from arrays of carbon nanotubes and diamond-clad Si tipsA nonlinear least-squares fitting procedure for array model parameter extraction using field emission ͑FE͒ data has been developed and extensively applied for Si and Si/HfC-coated arrays with 1024, 4000, and 16 000 tips measured in ultrahigh vacuum conditions. The array FE model is built up using equations that describe the electron emission current from individual emitters of given radius R and work function together with nonuniform distribution functions giving the dispersion of these parameters within the array. A combined numerical/analytical approach is used to accurately express the electric field for the actual gated emitter configuration. The FE current is computed through integration of the current density over the emitter tip surface and as a sum of all tip currents in the array. The program, developed as a MATHCAD application using the intrinsic ''minerr'' routine, extracts array parameters of physical interest and does not make use of ''area'' and ''field enhancement'' factors. HfC-coated FE arrays perform better than ͑noncoated͒ Si arrays when comparing the total emission current, the spatial uniformity and number of active tips, and the stability in long-term operation.
A two-dimensional model of quasi-free-electrons is used to compute the electron axial distribution on a carbon nanotube and the energy distribution of the field emitted electrons. The nature of the substrate-nanotube contact is taken into account by varying the boundary condition for the electronic wave function. In qualitative agreement with the experimental results to date, regular patterns of the axial electron density and electron accumulation on the nanotube cap are obtained. The energy distribution of the field emitted electrons shows a multiple peak structure superimposed over a very fine distribution of maxima. Such a multiple peak structure is also qualitatively confirmed in experiments. The behavior of the distribution of the emitted electrons with the extraction voltage and with the operation temperature is investigated.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.