Spatially resolved measurements of the capacitance by scanning tunneling microscope combined with a capacitance bridge

Abstract
We have measured spatially resolved capacitance between a metal surface and the tip of a scanning tunneling microscope (STM) by using a capacitance bridge combined with STM. The spatial variation of the capacitance can be correlated with the topographic image for the carbon grating and the gold film with a capacitance resolution of about 10 aF (1aF=10−18 F). The observed spatial resolution is about 50 nm along the surface as well as normal to the surface. The spatial resolution of this method is discussed in relation to the STM-tip radius and the corrugation of the sample. The resolution estimated by theoretical calculations is consistent with the experimental results.