Kelvin force microscopy at the second cantilever resonance: an out-of-vacuum crosstalk compensation setup

We investigate the gap-voltage control loop in a Kelvin force microscopy setup with simultaneous non-contact topography imaging. The Kelvin controller electrostatically excites the second resonance of the cantilever at about 6.3 times the first resonance frequency and adjusts the DC component of the gap voltage to cancel the oscillation amplitude at this frequency, while the non-contact topography imaging is based on a frequency control loop that maintains a constant frequency of the mechanically excited first resonance of the cantilever by adjusting the tip-sample separation. Due to the self-excitation of the first resonance in our setup, it has to be considered that the electrostatic excitation at the second resonance frequency is applied to a closed feedback loop and cannot be considered as a simple superposition to the oscillation at the first resonance frequency. In particular, special care has to be taken about internal capacitive crosstalk between the tip bias and the cantilever deflection output signal. It is shown that such a coupling cannot be corrected by subtraction of a constant offset at the demodulator output since the crosstalk is sent into the self-excitation loop and is multiplied by the closed loop transfer function. We present a circuit that actively compensates, outside the vacuum environment, the internal crosstalk by adding to the deflection output a dephased fraction of the electrostatic excitation signal.