Simple scaling rules governing work functions of two-dimensional materials

Abstract

This paper demonstrates that values of work functions W for a variety of planar and buckled two-dimensional (2D) materials scale linearly as a function of the quantity 1/r_{WS}, where r_{WS} is the Wigner-Seitz radius for a 2D material. Simple procedures are prescribed for estimating r_{WS}. Using them, this linear scaling relation, which is founded in electrostatics, provides a quick and easy method for calculating values of W from basic, readily available structural information about the materials. These easily determined values of W are seen to be very accurate when compared to values from the literature. Those derive from experiment or from challenging, computationally intensive density-functional-theory calculations. Values from those sources also conform to the linear scaling rules. Since values of W predicted by the rules so closely match known values of W, the simple scaling methods described here also are applied to predict W for 2D materials (TiN, BSb, SiGe, and GaP) for which no values have appeared previously in the literature.