Dielectric-constant measurement of thin insulating films at low frequency by nanoscale capacitance microscopy

We demonstrate a method for quantitatively probing the local low-frequency dielectric constant of thin insulating films by nanoscale capacitance microscopy. The calibrated capacitance-distance curves are measured on the dielectric film and analyzed by using a tip-sample capacitance model here proposed. Applied to $SiO2$ films as small as $1×1μm2$ area and $20–30nm$ thickness, the method gives a dielectric constant on the submicron scale in agreement with the value determined on the large scale. The observed precision is set by the capacitance noise level of the instrument and the tip radius.