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The standard theory of thermionic emission developed for three-dimensionalsemiconductors does not apply to two-dimensional materials even for makingqualitative predictions because of the vanishing out-of-plane quasiparticlevelocity. This study reveals the fundamental origin of the out-of-plane chargecarrier motion in a two-dimensional conductor due to the finite quasiparticlelifetime and huge uncertainty of the out-of-plane momentum. The theory isapplied to a Schottky junction between graphene and a bulk semiconductor toderive a thermionic constant, which, in contrast to the conventional Richardsonconstant, is determined by the Schottky barrier height and Fermi level ingraphene.

Theory of thermionic emission from a two-dimensional conductor and its application to a graphene-semiconductor Schottky junction