Uncovering a Universal Scaling for the Field Emission Characteristics from Metallic Nanotips in Nanogap

Electron field emission is a key mechanism in nanoelectronics with nanogaps, offering advantages such as high electron velocity, fast switching speeds, operation at extreme temperatures, and exceptional radiation resilience. However, traditional field emission theory inadequately describes the electron emission and charge transport behaviors at the nanoscale, as it lacks consideration of geometric asymmetry effects, quantum effects and nanosize effects. Here, we carried out an in situ investigation on the intrinsic field emission characteristics of pure tungsten nanotips across vacuum nanogaps. For the first time, we revealed a universal scaling behaviour between field emission characteristics and the ratio R/d , and demonstrated that the nonlinear geometrical effect, rather than quantum effects, is predominant. We further proposed a modified Fowler-Nordheim (FN) equation considering geometric effects, where the electric field ( F ) in the FN equation is substituted by F=V _exp /(k×R) with k=f(R⁄d)=1.680× (R/d+0.468) ^(-1.066) , which is valid for R/d  = 0.04 to 48. The proposed FN equation for nanoscale field emission regime is validated by well matching with the reported experimental results. These findings, grounded in theoretical insights, are essential for refining the design and performance of nanoelectronics, driving advancements in next-generation technologies.