Theory of Lateral Electron Tunneling Injection in 2D-metal/2D-Semicnductor Contact

Simmons tunneling diode model represent a key theoretical framework in the understanding and the modelling of quantum mechanical electron injection from bulk metal into bulk semiconductor, covering both low-voltage direct tunneling and the high-voltage field emission regime [1] . For two-dimensional (2D) semiconductor devices, Simmons model is expected to be invalid due to the reduced dimensionality and the nonparabolic energy dispersion of 2D materials [2] . Particularly, in the device setup of a 2D semiconductor field-effect transistor [3] , the physics of electron laterally injected from the highly-doped metallic 2D source region into the 2D semiconducting channel region remain an open question thus far. In this work, we generalise Simmons 3D tunneling diode model into the case of 2D elecrical contacts. Both parabolic and nonparabolic energy dispersions are considered in our 2D tunneling diode model. The 2D tunneling diode retains the Ohmic linear current-voltage scaling law. However, in the moderate to high voltage regime where field emission process dominates, the current-voltage scaling law exhibits a radical departure from the conventioonal Simmons tunneling diode model. The 2D tunneling diode model represent a quantum extension of the previously developed 2D thermionic injection model [4] and shall provide a theoretical basis for describing the carrier injection phenomena in 2D semiconductor nanochannel tunneling devices.