Measurement of conservative and dissipative tip-sample interaction forces with a dynamic force microscope using the frequency modulation technique

The measurement principle of dynamic-force microscopy using the frequency-modulation (FM) detection scheme is investigated by analytical as well as numerical approaches. As the detection method is based on the properties of a self-driven oscillator, we discuss the main differences from an externally driven oscillator. We then derive an analytical expression, which clarifies how the measured quantities of the FM technique, the frequency shift, and the gain factor (or “excitation amplitude”) are influenced by the time (“phase”) shift. Introducing a very general tip-sample force law, we show that the frequency shift is determined by the mean tip-sample force whereas the gain factor is directly related to dissipative processes like hysteresis or viscous damping.