Theory of thermionic emission from two-dimensional conductors.*

The standard theory of thermionic emission developed for three-dimensional (3D) conductors does not apply to two-dimensional (2D) materials even for making qualitative predictions because of the vanishing out-of-plane quasiparticle velocity [1]. Here, we focus on two mechanisms possibly responsible for out-of-plane electron transport in 2D-3D and 2D-2D heterojunctions. First, we consider the fundamental origin of the out-of-plane charge carrier motion in a perfect 2D conductor due to the finite quasiparticle lifetime and huge uncertainty of the out-of-plane momentum. The theory is applied to a Schottky junction between graphene and a bulk semiconductor to derive a thermionic constant, which, in contrast to the conventional Richardson constant, depends on the barrier height and Fermi level [2]. Second, we focus on electron transport from a 2D conductor to a 2D semiconductor assuming some short-range interface disorder that results in momentum randomization and interlayer hopping. The model is applied to electron transport in graphene-MoS₂ heterostructures [3].

[1] C. Crowell, Solid-State Electron. 8, 395 (1965).
[2] M. Trushin, Appl. Phys. Lett. 112, 171109 (2018).
[3] M. Trushin, Phys. Rev. B 97, 195447 (2018).