Abstract
Q-control technique enables to actively change the quality factor of the probe oscillation in dynamic atomic force microscopy. The Q-control is realized by adding a self-feedback loop into the original actuation-detection system, in which a damping force with controllable damping coefficient in magnitude and sign is applied to the oscillating probe. While the applied force alters the total damping interaction and thus the overall ‘signal’ of the probe motion, the added feedback system changes the ‘noise’ of the motion as well. Here, we systematically investigate the signal, the noise, and the signal-to-noise ratio of the qPlus sensor under the active Q-control. We quantify the noise of the qPlus motion by measuring the noise spectral density, which is reproduced by a harmonic oscillator model including the thermal and the measurement noises. We show that the noise signal increases with the quality factor controlled, scaling as the square root of the quality factor. Because the overall signal is linearly proportional to the quality factor, the signal-to-noise ratio scales as the square root of the quality factor. The Q-controlled qPlus with a highly enhanced Q, up to 10,000 in air, leads to the minimum detectable force gradient of 0.001 N/m, which would enhance the capability of the qPlus sensor for atomic force microscopy and spectroscopy.
Highlights
The quality factor is one of the critical parameters for probes in dynamic atomic force microscopy (AFM)
In the previous theoretical study,[8] we showed the signal-to-noise ratio (SNR) enhancement by Q increment, but direct experimental measurement and analysis based on the noise spectral density under Q-control were not made
We systematically investigate the motion signal, the noise, and the SNR for a qPlus sensor, the quartz tuning fork based electromechanical resonator used for dynamic AFM.[9]
Summary
The quality factor is one of the critical parameters for probes in dynamic atomic force microscopy (AFM). Since the quality factor is inversely proportional to the damping constant of the system, it varies depending on the damping force exerted on the probe oscillator. The instantaneous velocity of the probe is measured and the velocity-dependent damping force with variable damping constant is applied back to the probe.[2] While the applied damping force alters the total damping interaction and the quality factor of the probe oscillation, the applied force changes the noise of the measured motion, as pointed out by Ashby.[3] the signal-to-noise ratio (SNR) associated with the probe sensitivity varies under Q-control. The Q-control changes the noise in the measured motion of qPlus, because the measurement noise is fed into the Q-control feedback loop and acts as an additional noise source to the probe oscillation
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