is the Fermi-Dirac distribution for the surface states at energies E SS . C SS depends sensitively on the energy distribution of the surface states and their occupancy; the quantum capacitance directly links density of surface states (D SS ) to the surface state capacitance: D SS (E F ) = C SS . As D SS can be influenced by multiple factors such as doping, applied potential, and surface adsorption processes, C SS is expected to be extremely complex; this has been exemplified