Thiago Albuquerque de Assis

Field emission properties of an array of pyramidal structures

The properties and efficiency of the emission current density produced by a metallic array of pyramidal structures are investigated. The theoretical results obtained by numerical integration of the corresponding Laplace equation using a finite differences scheme offer useful information for the optimization of field emission devices based on cathodes with this geometry. Our study shows that the inter-pyramidal distance strongly affects the current density, and even more important for this issue is the protrusion characteristics of these structures. Another relevant, although less important, parameter determining this density is the anode–cathode distance. The effect of the array characteristics on the maximum local electric field intensity is also discussed.

Field and electric potential of conductors with fractal geometry

In this study, the behavior of the electric field and its potential are investigated in a region bounded by a rough fractal surface and a distant plane. Both boundaries, maintained at distinct potential values, are assumed to be conductors and, as such, the electric potential is obtained by numerically solving Laplaces equation subject to the appropriate Dirichlets condition. The rough boundaries, generated by the ballistic deposition and fractal Brownian motion methods, are characterized by the values of the surface roughness W and the local fractal dimension df = 3−α, where α is the usual roughness exponent. The equipotential surfaces, obtained from Laplaces equation, are characterized by these same parameters. Results presented show how df depends on the potential value, on the method used to generate the boundary and on W. The behavior of the electric field with respect to the equipotential surface is also considered. Its average intensity was found to increase as a function of the average distance from the equipotential to the fractal boundary; however, its intensity reaches a maximum before decreasing towards an asymptotic constant value, an effect that increases as the value of W increases.

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 surfaces 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.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 surfaces 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 n...

Unexpected validity of Schottky's conjecture for two-stage field emitters: A response via Schwarz–Christoffel transformation

The electric field in the vicinity of the top of an emitter with a profile consisting of a triangular protrusion on an infinite line is analytically obtained when this system is under an external uniform electric field. The same problem is also studied when the profile features a two-stage system, consisting of a triangular protrusion centered on the top of a rectangular one on a line. These problems are approached by using a Schwarz–Christoffel conformal mapping, and the validity of Schottkys conjecture (SC) is discussed. The authors provide an analytical proof of SC when the dimensions of the upper-stage structure are much smaller than those of the lower-stage structure, for large enough aspect ratios and considering that the field enhancement factor (FEF) of the rectangular structure is evaluated on the center of the top of the structure, while the FEF of the triangular stage is evaluated near the upper corner of the protrusion. The numerical solution of our exact equations shows that SC may remain va...

Effect of irregularities in the work function and field emission properties of metals

The effect of geometrical irregularities in the work function and emitting properties of metallic surfaces at low potentials is studied. For this purpose, we propose a simplified model consisting of rectangular fractures and a classical formalism for the work function determination. The dependence of the work function with the fractures size is determined by using the electrostatic image potential method. The emission current density properties when an external electric field is applied are also analyzed.