Trade-off between the electrostatic efficiency and mechanical stability of two-stage field emitter structures

作者：de Assis Thiago A^*; Dall'Agnol Fernando F

来源：Journal of Applied Physics, 2017, 121(1): 014503.

DOI：10.1063/1.4973584

The electrostatic effects and mechanical stability of systems formed of nanostructures mounted on cylindrical/conical base structures were studied numerically using the finite element method. We modeled a base structure (lower-stage structure) with a height of h(1), a base radius of r(1), and a characteristic field enhancement factor (FEF) of gamma(1). The nanostructure on top (upper-stage structure) had a height of h(2), a radius of r(2)<r(1), an FEF of gamma(2), and a hemisphere-on-post shape. The resulting two-stage system had a characteristic FEF of gamma(C). We define the electrostatic efficiency as eta(R) = (gamma(C) - gamma(1))/(gamma(3) - gamma(1)), where gamma(3) is the reference FEF for a hemisphere-on-post structure of radius r(3) = r(2) and height h(3) = h(1) + h(2). The results suggest a scaling of eta(R) = f(u equivalent to lambda theta(-n)), where lambda equivalent to h(2)/h(1); theta equivalent to r(1)/r(2), the exponent n depends on the geometry of the lower-stage structure, and u is a scale parameter of the two-stage system that arises from the scale-invariant nature of the electrostatic effects. Regarding the mechanical stability of the twostage system, our results show that there are characteristic lambda* and theta* values that result in the maximum mechanical stability. For a given relative difference delta between gamma(C) and gamma(3), our results suggest lambda(*)theta(*)similar to delta(alpha) da, where alpha approximate to 0.2 for both cylindrical and conical lower-stage structures. This result provides a relation between the electrostatic efficiency and the mechanical stability, allowing one to predict the necessary conditions for two-stage structures with the maximum sturdiness for a given FEF. This study, therefore, provides theoretical guidance for field electron emission applications, for the construction of needles for high-resolution probe microscopy, and for applications that require very high brightness but low emittance. Published by AIP Publishing.

• 出版日期2017-1-7