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

Abstract

This work presents a theoretical explanation for a crossover in the linear behavior in Fowler-Nordheim (FN) plots based on 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 $F_M$. 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 $\left\{{\gamma }_j\right\}$, which are randomly assigned to each distinct emitter of a conducting CFE surface, from a discrete probability distribution $\rho ({\gamma }_j)$, with $j=1,2$. It is assumed that $\rho ({\gamma }_1)<\rho ({\gamma }_2)$, and that ${\gamma }_1>{\gamma }_2$. 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 $F_M\in$ $[2,20]$ V/$\mu$m and are analyzed by taking into account the apparent formal area efficiency, the distribution $\rho$, 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.

References in corpus (3)

• Development of simple quantitative test for lack of field emission orthodoxy
• Improved approach to Fowler-Nordheim plot analysis
• The role of Hurst exponent on cold field electron emission from conducting materials: from electric field distribution to Fowler-Nordheim plots

Cited by in corpus (1)

• Interpreting the empirical field emission equation for large area field emitters