Calibrated nanoscale capacitance measurements using a scanning microwave microscope

A scanning microwave microscope (SMM) for spatially resolved capacitance measurements in the attofarad-to-femtofarad regime is presented. The system is based on the combination of an atomic force microscope (AFM) and a performance network analyzer (PNA). For the determination of absolute capacitance values from PNA reflection amplitudes, a calibration sample of conductive gold pads of various sizes on a $SiO2$ staircase structure was used. The thickness of the dielectric $SiO2$ staircase ranged from 10 to 200 nm. The quantitative capacitance values determined from the PNA reflection amplitude were compared to control measurements using an external capacitance bridge. Depending on the area of the gold top electrode and the $SiO2$ step height, the corresponding capacitance values, as measured with the SMM, ranged from 0.1 to 22 fF at a noise level of $∼2aF$ and a relative accuracy of 20%. The sample capacitance could be modeled to a good degree as idealized parallel plates with the $SiO2$ dielectric sandwiched in between. The cantilever/sample stray capacitance was measured by lifting the tip away from the surface. By bringing the AFM tip into direct contact with the $SiO2$ staircase structure, the electrical footprint of the tip was determined, resulting in an effective tip radius of $∼60nm$ and a tip-sample capacitance of $∼20aF$ at the smallest dielectric thickness.