Towards 4D modelisation of thermal-field emission from semiconductors

TL;DR

This paper develops a 3D model of thermal-field emission from semiconductors that accounts for complex geometries and doping, providing insights into temperature dependence and matching experimental data, paving the way for a full 4D dynamic model.

Contribution

It introduces a novel 3D modeling framework for TFE in semiconductors that can incorporate arbitrary geometries and doping levels, advancing beyond previous 1D and 2D models.

Findings

Successfully reproduces saturation plateau in TFE from semiconductors

Shows good qualitative agreement with experimental data on n-type Germanium

Provides a foundation for future 4D dynamic modeling of TFE

Abstract

The theoretical picture of thermal field-emission (TFE) from semiconductors has been limited to 1D and 2D models. This can be attributed to the complex and interdependent phenomena that is involved in TFE from semiconductors which makes the calculations cumbersome. Such limitations result in a partial understanding of the underlying physics of semiconducting surfaces under high electrical fields, which requires the addition of the temporal dimension (4D) to yield a realistic model. Here we develop a 3D model of TFE from semiconductors that can take arbitrary geometries and doping levels. Our model successfully reproduces the characteristic saturation plateau of some semiconductors, as well as its dependence in temperature. The model is found to be in good agreement with experimental data from ntype Germanium at a qualitative level. We propose this model as a platform for future extensions into the full 4D framework, incorporating temporal dynamics for a more complete and predictive description of thermal-field emission from semiconductors.