  We study the surface conductivity of a field-effect transistor (FET) made of
periodic array of spherical semiconductor nanocrystals (NCs). We show that
electrons introduced to NCs by the gate voltage occupy one or two layers of the
array. Computer simulations and analytical theory are used to study the array
screening and corresponding evolution of electron concentrations of the first
and second layers with growing gate voltage. When first layer NCs have two
electrons per NC the quantization energy gap between its 1S and 1P levels
induces occupation of 1S levels of second layer NCs. Only at a larger gate
voltage electrons start leaving 1S levels of second layer NCs and filling 1P
levels of first layer NCs. By substantially larger gate voltage, all the
electrons vacate the second layer and move to 1P levels of first layer NCs. As
a result of this nontrivial evolution of the two layers concentrations, the
surface conductivity of FET non-monotonically depends on the gate voltage. The
same evolution of electron concentrations leads to non-monotonous behaviour of
the differential capacitance.
