Abstract
The theories of thermionic emission and field emission (also known as the Richardson-Dushman [RD] and Fowler-Nordheim [FN] Laws, respectively) were formulated more than 80 years ago for bulk materials. In single-layer graphene, electrons mimic massless Dirac fermions and follow relativistic carrier dynamics. Thus, their behavior deviates significantly from the nonrelativistic electrons that reside in traditional bulk materials with a parabolic energy-momentum dispersion relation. In this article, we assert that due to linear energy dispersion, the traditional thermionic emission and field emission models are no longer valid for graphene and two-dimensional Dirac-like materials. We have proposed models that show better agreement with experimental data and also show a smooth transition to the traditional RD and FN Laws.