Toward 4D modelization of thermal-field emission from semiconductors

The theoretical understanding 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 involved in TFE from semiconductors, which makes the calculations cumbersome. Such limitations result in a partial understanding of the underlying physics of the surface of a semiconductor under a high electrical field—which requires the addition of the temporal dimension (4D) to yield a realistic model of the electro-thermal dynamics. Here, we develop a 3D model of TFE from semiconductors that covers arbitrary geometries and doping levels. Our model successfully reproduces the characteristic saturation plateau of some semiconductors, as well as their temperature dependence. The model gives good qualitative agreement with experimental data from n-type germanium. We propose this model as a platform for future extensions into the full 4D framework, incorporating temporal dynamics for a more coherent explanation of thermal-field emission from semiconductors.