Quantitative analysis of scanning microwave microscopy on dielectric thin film by finite element calculation

Using numerical calculations based on a finite element method, we present a quantitative analysis of the dielectric constant of thin films on thick substrates in order to fit the experimental data measured by a scanning microwave microscope. The shift of the resonance frequency of the probe was calculated for the case of dielectric thin films on LaAlO3 (ε=24) and MgO (ε=10) substrates and, at the same time, the fitting functions were derived as a function of the tip–sample distance. The experimental data were found to agree well with our fitting functions, rendering our quantitative analysis reasonable. We have also discussed the effect of the anisotropy of dielectric constants.