  Angle resolved photoemission spectroscopy is used to observe changes in the
electronic structure of bulk-doped topological insulator Cu$_x$Bi$_2$Se$_3$ as
additional copper atoms are deposited onto the cleaved crystal surface. Carrier
density and surface-normal electrical field strength near the crystal surface
are estimated to consider the effect of chemical surface gating on atypical
superconducting properties associated with topological insulator order, such as
the dynamics of theoretically predicted Majorana Fermion vortices.
