  Capacitance-voltage ($\textit{C-V}$) traces in
n-type-(Bi$_{1-x}$Sb$_x$)$_2$Te$_3$/oxide/metal capacitor structures using an
AC capacitance bridge are investigated. By tuning the top gate voltage from
positive to negative values, the system at the interface is tuned from
accumulation, via depletion into inversion. Our results show the typical
low-frequency and high frequency $\textit{C-V}$ traces, depending on measuring
frequency, temperature and illumination intensity and reflecting their
sensitive dependence on recombination/generation rates. Superimposed a strong
hysteresis under inversion is also observed which is ascribed to the presence
of conventional localized surface states which coexist with topological surface
states.
