Intermodulation electrostatic force microscopy for imaging surface photo-voltage

We demonstrate an alternative to Kelvin Probe Force Microscopy for imaging surface potential. The open-loop, single-pass technique applies a low-frequency AC voltage to the atomic force microscopy tip while driving the cantilever near its resonance frequency. Frequency mixing due to the nonlinear capacitance gives intermodulation products of the two drive frequencies near the cantilever resonance, where they are measured with high signal to noise ratio. Analysis of this intermodulation response allows for quantitative reconstruction of the contact potential difference. We derive the theory of the method, validate it with numerical simulation and a control experiment, and we demonstrate its utility for fast imaging of the surface photo-voltage on an organic photo-voltaic material.