  Ionic liquid gating has a number of advantages over solid-state gating,
especially for flexible or transparent devices and for applications requiring
high carrier densities. However, the large number of charged ions near the
channel inevitably results in Coulomb scattering, which limits the carrier
mobility in otherwise clean systems. We develop a model for this Coulomb
scattering. We validate our model experimentally using ionic liquid gating of
graphene across varying thicknesses of hexagonal boron nitride, demonstrating
that disorder in the bulk ionic liquid often dominates the scattering.
