  Electrical contact resistance to two-dimensional (2D) semiconductors such as
monolayer MoS_{2} is a key bottleneck in scaling the 2D field effect
transistors (FETs). The 2D semiconductor in contact with three-dimensional
metal creates unique current crowding that leads to increased contact
resistance. We developed a model to separate the contribution of the current
crowding from the intrinsic contact resistivity. We show that current crowding
can be alleviated by doping and contact patterning. Using Landauer-B\"uttiker
formalism, we show that van der Waals (vdW) gap at the interface will
ultimately limit the electrical contact resistance. We compare our models with
experimental data for doped and undoped MoS_{2} FETs. Even with heavy
charge-transfer doping of > 2x10^{13} cm^{-2}, we show that the
state-of-the-art contact resistance is 100 times larger than the ballistic
limit. Our study highlights the need to develop efficient interface to achieve
contact resistance of < 10 {\Omega}.{\mu}m, which will be ideal for extremely
scaled devices.
