Uncovering a widely applicable empirical formula for field emission characteristics of metallic nanotips in nanogaps

Yimeng Li, Linghan Xia, Nan Li, Shilong Tang, Yunsong Ge, Jianyu Wang, Bing Xiao, Yonghong Cheng, Lay Kee Ang () and Guodong Meng ()
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Yimeng Li: Xi’an Jiaotong University
Linghan Xia: Xi’an Jiaotong University
Nan Li: Xi’an Jiaotong University
Shilong Tang: Xi’an Jiaotong University
Yunsong Ge: Xi’an Jiaotong University
Jianyu Wang: Xi’an Jiaotong University
Bing Xiao: Xi’an Jiaotong University
Yonghong Cheng: Xi’an Jiaotong University
Lay Kee Ang: Singapore University of Technology and Design
Guodong Meng: Xi’an Jiaotong University

Nature Communications, 2025, vol. 16, issue 1, 1-8

Abstract: Abstract Field electron emission is a key mechanism in nanoelectronics with nanogaps, offering advantages such as high electron velocity and fast switching speeds. However, nanoscale field emission, affected by geometric asymmetry including quantum tunneling near to the emitter, and quantum space charge effects, remains largely unexplored in experimental studies. Here, we in situ investigated field emission characteristics of pure tungsten nanotips across vacuum nanogaps. We revealed a widely applicable scaling behavior between field emission characteristics and the ratio of apex radius to gap length (R/d), and demonstrated that the effects of quantum tunnelling due to emitter shape are the predominant influence. We further proposed a modified field emission equation, incorporating an empirical formula for the apex shape factor, kMG (kMG = f(R/d) = 1.680 × (R/d + 0.468)−1.066), valid for R/d = 0.04 to 48. These findings provide fundamental insights into the optimization of nanoelectronic device design and the advancement of future technologies.

Date: 2025
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DOI: 10.1038/s41467-025-60607-6

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