Absence of Space-Charge-Limited Current in Unconventional Field Emission
Cherq Chua, Chun Yun Kee, Yee Sin Ang, L. K. Ang
Abstract
For field emission (FE), it is widely expected that its emitting current density $J$ will become space-charge-limited current (SCLC) within a gap spacing $D$ biased at sufficiently large voltage $V$. In this paper, we reveal a peculiar finding in which this expected two-stage transition (from FE to SCLC) is no longer valid for FE not obeying the traditional Fowler-Nordheim (FN) law. By employing a generalized FN scaling of $\mathrm{ln}(J/{E}_{s}^{k})\ensuremath{\propto}\ensuremath{-}1/{E}_{s}$, where ${E}_{s}$ is the surface electric field at the cathode, we show the existence of a critical exponent ${k}_{c}\ensuremath{\equiv}3/2$ where unusual behaviors occur for $k<{k}_{c}$: (a) only FE at small $D$ (no transition to SCLC possible) and (b) three-stage transition from FE first to SCLC then back to FE at large $D$. For $k>{k}_{c}$, the conventional two-stage transition from FE to SCLC will always occur for all $D$, including the classical case of $k$ = 2. Using various unconventional FE models with $k\ensuremath{\ne}\phantom{\rule{0.2em}{0ex}}2$, we specifically demonstrate these peculiar transitions. Under a normalized model, our findings uncover the rich interplay between the source-limited FE and bulk-limited SCLC over a wide range of operating conditions.