Revised Fowler–Dubridge model for multiphoton over-barrier electron emission from two-dimensional materials

Abstract

We revise the Fowler–Dubridge model for multiphoton over-barrier photoemission from two-dimensional (2D) materials to include the effects of reduced dimensionality, non-parabolic, and anisotropic energy dispersion of 2D materials. Two different directions of electron emission are studied, namely, vertical emission from the surface and lateral emission from the edge. Our analytical model reveals a universal temperature scaling of Tβ with β = 1 for the surface emission over a wide class of 2D materials and β = 3/2 for the edge emission from the 2D material with anisotropic parabolic energy dispersion, which are distinct from the traditional scaling of β = 2 originally derived for the traditional bulk materials. Our comparison shows good agreement with two experiments of photoelectron emitted from graphene for both surface and edge emission. Our calculations also show that the photoelectron emission is more pronounced than the coexisting thermionic emission for materials with low temperature and Fermi energy. This model provides helpful guidance in choosing proper combinations of light intensity, temperature range, and type of 2D materials for the design of photoemitters, photodetectors and other optoelectronics.