Dielectric constant measurement using atomic force microscopy of dielectric films: a system theory approach

A technique was developed to measure dielectric constant at microscale based on the system theory approach using an atomic force microscopy (AFM), this makes possible the electrical characterization of dielectric materials using an optimized instrumentation. This technique is capable of measuring capacitance on either metallic contact–insulator–metallic contact or metallic contact–insulator with the AFM tip as the upper contact, the dielectric constant can be calculated from these results. The technique compares the frequency response between the input voltage and the output voltage of an equivalent RC-circuit (resistance–capacitance) in the frequency range 1 Hz–60 kHz. This comparison is analyzed using a transfer function model and a least-squares process to get the time constant involved in this kind of circuit, facilitating the implementation of this technique with any atomic force microscopy equipment. Additionally, the measurements can be carried out in a single point or in a mapping. The measurements were carried out on two hybrid films, PMMA–TiO 2 –SiO 2 and PMMA–TiO 2 –BT, which were prepared by sol–gel technique and deposited on indium tin oxide (ITO)-coated glass substrates. The results obtained with this technique agreed with conventional measurements that use commercial capacitance–voltage analyzer, and indicated that dielectric constant is 11.31 for PMMA–TiO 2 –SiO 2 , and 15.41 for PMMA–TiO 2 –BT.