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

## TL;DR

This paper develops a new theory for thermionic emission from two-dimensional conductors like graphene, accounting for out-of-plane charge motion due to finite quasiparticle lifetime, and applies it to graphene-semiconductor Schottky junctions.

## Contribution

It introduces a fundamental theory for thermionic emission in 2D materials, differing from traditional 3D models, and derives a new thermionic constant for graphene-semiconductor interfaces.

## Key findings

- The out-of-plane charge motion in 2D conductors arises from finite quasiparticle lifetime.
- The thermionic constant depends on Schottky barrier height and Fermi level, not the Richardson constant.
- The theory accurately describes thermionic emission in graphene-based Schottky junctions.

## Abstract

The standard theory of thermionic emission developed for three-dimensional semiconductors does not apply to two-dimensional materials even for making qualitative predictions because of the vanishing out-of-plane quasiparticle velocity. This study reveals the fundamental origin of the out-of-plane charge carrier motion in a two-dimensional 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, is determined by the Schottky barrier height and Fermi level in graphene.