CORRECTIONS TO THE CAPACITANCE BETWEEN 2 ELECTRODES DUE TO THE PRESENCE OF QUANTUM-CONFINED SYSTEM

We have studied the capacitance between two parallel plates enclosing a quantum confined system and its dependence on the applied voltage. T he concepts of capacitance and differential capacitance are discussed together with their applicability to systems characterized by single-e lectron tunneling. We determine the tunneling thresholds by means of a formalism based on the minimization of the system free energy and we retrieve, as a special case, Luryi's quantum capacitance formula. We a pply our method to the study of an idealized system made up of a numbe r of quantum dots with random size distributed according to a gaussian , Results are shown for different choices of the position of the dots between the plates and of the voltage span applied to perform the meas urement of the differential capacitance.