Transverse semiclassical corrections to field emission in curved nanoscale emitters

Abstract

Nanoscale field emitters develop strong curvature-induced transverse confinement under applied electrostatic fields, a physical effect absent in conventional Fowler–Nordheim-type models. In this work, we show that this confinement introduces geometric zero-point energy that effectively raises the potential barrier encountered by tunneling electrons. As a result, the tunneling probability is suppressed through a semiclassical correction to the Gamow exponent. By modeling the quantum state of the tunneling electron with a Gaussian ansatz that captures its transverse confinement, we derive a correction term, ε, that scales as ε∼(λR)−1/2(I/νF), where λ is the tunneling length, R is the apex radius of the emitter, I a barrier integral influenced by geometry and image forces, and νF the Burgess–Kroemer–Houston function. This curvature-induced transverse quantization alters the predicted local emission current due to the exponential sensitivity of tunneling probabilities. In large emitter arrays, it leads to measurable deviations in total current that can affect device performance and spatial resolution. These findings highlight the need for improved field emission models that incorporate the quantum confinement effects associated with the classical transverse curvature of the electrostatic potential around the emitter apex, particularly in applications, such as vacuum nanoelectronics, high-precision lithography, and compact electron sources.