  In order to make a densely packed assembly of undoped semiconductor
nanocrystals conductive, it is usually gated by a room temperature ionic
liquid. The ionic liquid enters the pores of the super-crystal assembly under
the influence of an applied voltage. We study the capacitance of such a device
as a function of the gate voltage. We show that, counter-intuitively, the
capacitance of the system is the sum of delta-functions located at a sequence
of critical gate voltages. At each critical voltage every nanocrystal acquires
one additional electron.
