Absence of Space-Charge-Limited Current in Unconventional Field Emission

Abstract

For field emission (FE), it is widely expected that its emitting current density J will become space-chargelimited current (SCLC) due the built-up of charge in-transit 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 In this paper, we reveal a peculiar finding in which this expected two-stage transition (from FE to SCLC) is no longer valid for FE not obeying the traditional Fowler-Nordheim (FN) law.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 ln J/V k ∝ −1/V , we show the existence of a critical exponent k c ≡ 3/2 where unusual behaviours occur for k < k c : (a) Only FE at small D (no transition to SCLC even at infinitely large V ), and (b) Three-stage transition from FE first to SCLC then back to FE at large D. For any k > k c , the conventional two-stage transition from FE to SCLC will always occur for all D, which also includes the conventional FN law at k = 2. Using various unconventional FE models with k = 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.