  In this work, a compact transport model has been developed for monolayer
transition metal dichalcogenide (TMDC) channel MOSFET. The analytical model
solves the Poisson's equation for the inversion charge density to get the
electrostatic potential in the channel. Current is then calculated by solving
the drift-diffusion equation. The model makes gradual channel approximation to
simplify the solution procedure. The appropriate density of states obtained
from the first principle density functional theory simulation has been
considered to keep the model physically accurate for monolayer TMDC channel
FET. The outcome of the model has been benchmarked against both experimental
and numerical quantum simulation results with the help of a few fitting
parameters. Using the compact model, detailed output and transfer
characteristics of monolayer $WSe_2$ FET have been studied, and various
performance parameters have been determined. The study confirms excellent ON
and OFF state performances of monolayer $WSe_2$ FET which could be viable for
the next generation high-speed, low power applications. Also, the proposed
model has been extended to study the operation of a biosensor. A monolayer
$MoS_2$ channel based dielectric modulated FET is investigated using the
compact model for detection of a biomolecule in a dry environment.
