Universal scaling laws of electron emission phenomena in two-dimensional material electrical contacts*

Electrically contacting two-dimensional (2D) material with another material often leads to the formation of an interfacial Schottky barrier. Charge injection across such barrier is commonly analysed using the classic Richardson-Dushman (thermionic emission) and Fowler-Nordheim (field emission) models despite the fact that the assumptions underlying such models are often inconsistent with the physical properties of most 2D materials. Here we formulate generalized models of electron injection across 2D material interfaces^1-3. We show that the thermionic transport across a 2D material Schottky contact is governed by universal scaling laws broadly applicable for large classes of 2D systems. We further uncover a new universal scaling behavior in the vertical electron tunneling across 2D material van der waals heterostructures⁴. Our models signal the breakdown of century-old classic electron emission models in 2D materials, and paves the way towards the better understanding and design of 2D material electronic devices.

1. Y.S. Ang et al, Phys Rev Lett 121, 056802 (2018)
2. Y.S. Ang et al, MRS Bull 42, 505 (2017)
3. Y.S. Ang et al, Phys Rev Appl 6, 034013 (2016)
4. S. Wang et al, Nano Lett 17, 5156 (2017)