Cooperative charging in a nanocrystal assembly gated by ionic liquid

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 supercrystal 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, counterintuitively, the capacitance of the system is the sum of δ-functions located at a sequence of critical gate voltages. At each critical voltage, every nanocrystal acquires one additional electron.