The AFM was used with frequency modulation (FM) mode . The sensor was mechanically vibrated at its resonance frequency by a lead zirconate titanate (PZT) piezoelectric plate attached to the sensor clamp, and the deflection of the sensor was detected as a signal from the QTF amplified by a low noise differential amplifier invented by Giessibl et al. . The sensor was selfexcited at its resonant frequency by a PLL-excitation loop using a digital lock-in amplifier (MFLI, Zurich Instruments), which is also used for the detection of the resonance frequency shift (∆ƒ) and the vibrating amplitude (Ap-p). The vibrating amplitude of the sensor Ap-p was kept constant during the AFM experiments by automatic gain control using a PID controller in the lock-in amplifier.