ELECTRONIC-ENERGY SPECTRUM AND THE CONCEPT OF CAPACITANCE IN QUANTUM DOTS

The chemical potential and the capacitance of a model quantum dot have been computed, including contributions of exchange and correlation in the limit of 0 K temperature. The Schrodinger equation has been solve d self-consistently, taking into account the electron-electron Coulomb interaction and many-body effects within the framework of density-fun ctional theory. We have also studied the effect of conducting backgate s and of nearby electrodes using the method of images. Depending on th e size of the dot, we derive a prevalence of either the quantization e nergy or the electrostatic energy: there is a smooth transition from p redominant quantum effects for small dots to classical capacitance beh avior for large dots. Our simulation reproduces characteristic effects that have been experimentally observed, such as the capacitance incre ase for increasing electron numbers and irregularities in the chemical potential values when randomly distributed charged impurities are pre sent.