Field Emission Model with Diminishing Thickness from Bulk to 2D materials

Two-dimensional (2D) materials-based field emitters, such as graphene and 2D topological materials, have attracted enormous attention due to their excellent field emission properties and performance. However, the modelling of the out-of-plane electron emission still poses a serious physics challenge. The lack of crystal periodicity and the confinement of electrons within the 2D material atomic plane have challenged the conventional physical picture of field emission from 3D metals developed in the past century. To resolve this problem for field emission, a quasi-2D model two-barrier model has been developed to study the behaviour of field emission when the material geometry is continuously shrunken from 3D bulk emitters to 2D emitters using a phenomenological quantum well method. The predicted findings agree well with the respective limits of large and thin materials, corresponding to the field emission by 3D (or bulk) and 2D materials, respectively. The model provides a comprehensive understanding of the field emission for finite layers of 2D materials in addition to the well-studied 2D thermionic electron emission. These recent works have suggested that the classical scaling laws developed decades ago for field and thermal-field emission may not be valid in the 2D flatland.