  We study charged impurity scattering and static screening in a top-gated
substrate-supported graphene nanostructure. Our model describes how boundary
conditions can be incorporated into scattering, sheds light on the dielectric
response of these nanostructures, provides insights into the effect of the top
gate on impurity scattering, and predicts that the carrier mobility in such
graphene heterostructures decreases with increasing top dielectric thickness
and higher carrier density. An increase of up to almost 60 percent in carrier
mobility in ultrathin top-gated graphene is predicted.
