Close proximity electrostatic effect from small clusters of emitters

Using a numerical simulation based on the finite-element technique, this work investigates the field emission properties from clusters of a few emitters at close proximity, by analyzing the properties of the maximum local field enhancement factor (gamma(m)) and the corresponding emission current. At short distances between the emitters, we show the existence of a nonintuitive behavior, which consists of the increasing of gamma(m) as the distance c between the emitters decreases. Here we investigate this phenomenon for clusters with 2, 3, 4 and 7 identical emitters and study the influence of the proximity effect in the emission current, considering the role of the aspect ratio of the individual emitters. Importantly, our results show that peripheral emitters with high aspect-ratios in large clusters can, in principle, significantly increase the emitted current as a consequence only of the close proximity electrostatic effect (CPEE). This phenomenon can be seen as a physical mechanism to produce self-oscillations of individual emitters. We discuss new insights for understanding the nature of self-oscillations in emitters based on the CPEE, including applications to nanometric oscillators.