  We present a study of transport in graphene devices on polar insulating
substrates using a tight-binding model. The mobility is computed using a
multiband Boltzmann treatment. We provide the scaling of the surface polar
phonon contribution to the low-field mobility with carrier density,
temperature, and distance from the substrate. At high bias, we find that
graphene self-heating effect is essential to account for the observed saturated
current behavior. We predict that by optimizing the device cooling, the high
bias currents can be significantly enhanced.
