The value of monophasic capacitance of few-electron systems

Due to the discreteness of electronic charges in a nanoscale system, capacitance is defined in terms of the total interaction energy of N-electrons confined in a dielectric sphere. Specifically, the distribution of N-electrons is obtained from minimization of the total Coulomb and polarization interaction energy and the formation energy, the work done on the system. Our discrete charge dielectric (DCD) model gives rise to an electrostatic capacitance agreeing with the N=1 and ∞ cases. For nanometer-size devices, the Schrödinger equation should be used; however, for size greater than 10 nm, the Poisson equation accounts for spatial symmetry properties resulting from the discrete nature of interacting electrons. Without metallic components, the equal potential landscape does not coincide with our spherical boundary except for the N=1 case. There is a special configuration associated with each N. Hence, the capacitance defined is monophasic, representing a single electrostatic phase. The most important application of this work may lie in optoelectronics and biological systems.