Theory of a field-effect transistor based on a semiconductor nanocrystal array

We study the surface conductivity of a field-effect transistor (FET) made of a 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. At substantially larger gate voltage, all 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 the FET nonmonotonically depends on the gate voltage. The same evolution of electron concentrations leads to nonmonotonic behavior of the differential capacitance.