  We study the disorder potential induced by random Coulomb impurities at the
surface of a topological insulator (TI). We use a simple model in which
positive and negative impurities are distributed uniformly throughout the bulk
of the TI, and we derive the magnitude of the disorder potential at the TI
surface using a self-consistent theory based on the Thomas-Fermi approximation
for screening by the Dirac mode. Simple formulas are presented for the mean
squared potential both at the Dirac point and far from it, as well as for the
characteristic size of electron/hole puddles at the Dirac point and the total
concentration of electrons/holes that they contain. We also derive an
expression for the autocorrelation function for the potential at the surface
and show that it has an unusually slow decay, which can be used to verify the
bulk origin of disorder. The implications of our model for the electron
conductivity of the surface are also presented.
