Uncertainties in the permittivity of thin films extracted from measurements with near field microwave microscopy calibrated by an image charge model

The microwave microscope is a device which utilises near fields to characterise material properties of samples on length scales smaller than the operating wavelength. The errors associated with extracting the permittivity of a high permittivity thin film on a low permittivity substrate from measurements using such a device are found to be of the order of 25 % when using a widely used image charge model of the tip-sample interaction. The uncertainties arise from the model-based extraction of the permittivity from the raw frequency shift data, and in the current case are shown to come from the assumption in the model that the tip of the microwave probe can be modelled as a sphere.
The raw data from the microscope contain random uncertainties of the order of 1 % and reveal variations in the properties of the thin film with sub-wavelength resolution demonstrating the microwave microscope as a sub-wavelength characterisation technique for thin films.