  Experimental studies on two-dimensional (2D) materials are still in the early
stages, and most of the theoretical studies performed to screen these materials
are limited to the room-temperature carrier-mobility in the free standing 2D
layers. With the dimensions of devices moving towards nanometer-scale lengths,
the room-temperature carrier-mobility -- an equilibrium concept -- may not be
the main quantity that controls the performance of devices based on these 2D
materials, since electronic transport occurs under strong off--equilibrium
conditions. Here we account for these non-equilibrium conditions and, for the
case of monolayer phosphorene (monolayer black phosphorus), show the results of
device simulations for a short channel n-MOSFET, using the Monte Carlo method
coupled with the Poisson equation, including full bands and full
electron-phonon matrix elements obtained from density functional theory. Our
simulations reveal significant intrinsic limitations to the performance of
phosphorene as a channel material in nanotransistors.
