  In this work, we describe the charge transport in two-dimensional (2D)
Schottky barrier field-effect transistors (SB-FETs) based on the carrier
injection at the Schottky contacts. We first develop a numerical model for
thermionic and field-emission processes of carrier injection that occur at a
Schottky contact. The numerical model is then simplified to yield an analytic
equation for current versus voltage ($I$-$V$) in the SB-FET. The lateral
electric field at the junction, controlling the carrier injection, is obtained
by accurately modeling the electrostatics and the tunneling barrier width.
Unlike previous SB-FET models that are valid for near-equilibrium conditions,
this model is applicable for a broad bias range as it incorporates the
pertinent physics of thermionic, thermionic field-emission, and field-emission
processes from a 3D metal into a 2D semiconductor. The $I$-$V$ model is
validated against the measurement data of 2-, 3-, and 4-layer ambipolar
MoTe$_2$ SB-FETs fabricated in our lab, as well as the published data of
unipolar 2D SB-FETs using MoS$_2$. Finally, the model's physics is tested
rigorously by comparing model-generated data against TCAD simulation data.
