We analyze the nonlinear voltage dependence of elelctrochemical capacitance for nano-scale conductors. This voltage dependence is due to finite density of states of the conductors. We derive an exact expression for the electrochemical capacitance-voltage curve for a parallel plate system. The result suggests a quantum scanning capacitance microscopy at the nano-scale: by inverting the capacitance-voltage expression one is able to deduce the local spectral function of the nano-scale conductor.
@article{arxiv.cond-mat/9902309,
title = {Nonlinear Quantum Capacitance},
author = {Baigeng Wang and Xuean Zhao and Jian Wang and Hong Guo},
journal= {arXiv preprint arXiv:cond-mat/9902309},
year = {2009}
}