Quantitative electrostatic force microscopy-phase measurements

The phase mode of electrostatic force microscopy (EFM-phase) is a scanning probe microscopy (SPM) technique used to measure electrostatic force gradient. EFM-phase has a higher resolution than scanning Kelvin probe microscopy (SKPM or SKM), but unlike SKPM it does not yield a direct measurement of local potential. Analytical calculations of tip-surface capacitances and their gradients are presented, and the origin of the measurement resolution in EFM-phase and SKPM is explained based on the calculation results. We show that EFM-phase data fit the analytical calculation well, and can be interpreted using a simple analytic model, which allows phase shift to be related to the local surface potential. The analytic formula is easy to calibrate and can be used to convert the EFM-phase data to potential data. This procedure is demonstrated on a poly-(3-hexylthiophene-2,5-diyl) (P3HT) thin film, contacted with Au electrodes, and the potential distributions of the Au/P3HT/Au structure under various biases are presented.