Measuring low loss dielectric substrates with scanning probe microscopes

This letter presents an algorithm for measuring the relative permittivity of thick dielectric substrates with scanning probe microscopy. Our technique does not rely on a specific type of microscopy setup and does not require expensive numerical field simulations. To demonstrate the versatility of our method, we perform measurements at high frequencies (18 GHz) with a scanning microwave microscope and at low frequencies (2 kHz) with electrostatic force microscopy. In our experiments, we study dielectric materials with epsilon values ranging from 4 (SiO₂) to 300 (SrTiO₃). For low epsilon values, the accuracy of the algorithm is better than 2% for tips with less than 80 nm tip radius.