Corrections to the Capacitance between Two 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. The concepts of capacitance and differential capacitance are discussed together with their applicability to systems characterized by single-electron 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 apply our method to the study of an idealized system made up of a number 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 measurement of the differential capacitance