Theory of High-Energy Electron Thermionic Emission from Graphene

Graphene thermionic electron emission across high barrier involves energetic electrons residing far away from the Dirac point. In this work, we construct a full-band model beyond the simple Dirac cone approximation for the thermionic injection of high-energy electrons in graphene [1]. We show that the thermionic emission model based on the Dirac cone approximation is valid only in the graphene/semiconductor Schottky interface operating near room temperature but breaks down in the cases involving high-energy electrons. We further reveal a critical potential barrier height beyond which the Dirac cone approximation crosses over from underestimation to overestimation. In the high-temperature thermionic emission regime, the Dirac cone approximation severely overestimates the electrical and heat current densities by more than 50% compared to the more accurate full-band model. Our findings reveal the fallacy of Dirac cone approximation in the thermionic injection of high-energy electrons in graphene. The full-band model developed here can be readily generalized to other 2D materials and shall provide an improved theoretical avenue for the accurate analysis, modeling and design of graphene-based thermionic energy devices.
[1] Y. S. Ang et al, Phys. Rev. Appl. 12, 014057 (2019)