Universal Scaling Law for Electron Field Emission from 2d Semimetals

Due to their atomic-thin body and novel physical properties, two-dimensional (2D) material offers a new route towards the design of ultimately compact and high-performance solid-state and vacuum devices. The extreme confinement of electrons within sub-nanometer scale thickness leads to the emergence of exotic electronic band structures not commonly found in three-dimensional (3D) bulk solids. Their unusual electronic properties have led to highly unusual electron emission physics 1 , 2 , 3 and new scaling laws that differ dramatically with the conventional Richardson-Dushman (thermionic), Fowler-Nordheim (field-induced) and Murphy-Good (thermal-field) models. In this work 4 , we discover a universal scaling law for the field-induced electron emission from the planar surface of a large variety of 2D metals and semimetals. Based on the Murphy-Good (MG) formalism, we construct the thermal-field emission equation for 2D thin film. The MG law is generalized to a universal scaling law, \begin{equation*}\mathcal{J}(V,T) \propto \pi \frac{{d_F^{3 - D}}}{{c\sin (\pi /c)}}{D_F}\end{equation*} where d F ~ F and c ~ F/T are field ( F ) and temperature( T )-dependent parameters, D F is a tunneling exponent, and D = 2, 3 denotes the dimensionality of the electron emitter. Our findings shall provide a theoretical foundation for the analysis and the computational design of 2D material electron source and vacuum nanoelectronics.