  The quantum capacitance model is applied to obtain an exact solution for the
space-resolved carrier density in a multigated doped graphene sheet at zero
temperature, with quantum correction arising from the finite electron capacity
of the graphene itself taken into account. The exact solution is demonstrated
to be equivalent to the self-consistent Poisson-Dirac iteration method by
showing an illustrative example, where multiple gates with irregular shapes and
a nonuniform dopant concentration are considered. The solution therefore
provides a fast and accurate way to compute spatially varying carrier density,
on-site electric potential energy, as well as quantum capacitance for bulk
graphene, allowing for any kind of gating geometry with any number of gates and
any types of intrinsic doping.
