Thermal noise limit for ultra-high vacuum noncontact atomic force microscopy

The noise of the frequency-shift signal Δf in noncontact atomic force microscopy (NC-AFM) consists of cantilever thermal noise, tip-surface-interaction noise and instrumental noise from the detection and signal processing systems. We investigate how the displacement-noise spectral density d(z) at the input of the frequency demodulator propagates to the frequency-shift-noise spectral density d(Δ) (f) at the demodulator output in dependence of cantilever properties and settings of the signal processing electronics in the limit of a negligible tip-surface interaction and a measurement under ultrahigh-vacuum conditions. For a quantification of the noise figures, we calibrate the cantilever displacement signal and determine the transfer function of the signal-processing electronics. From the transfer function and the measured d(z), we predict d(Δ) (f) for specific filter settings, a given level of detection-system noise spectral density d(z) (ds) and the cantilever-thermal-noise spectral density d(z) (th). We find an excellent agreement between the calculated and measured values for d(Δ) (f). Furthermore, we demonstrate that thermal noise in d(Δ) (f), defining the ultimate limit in NC-AFM signal detection, can be kept low by a proper choice of the cantilever whereby its Q-factor should be given most attention. A system with a low-noise signal detection and a suitable cantilever, operated with appropriate filter and feedback-loop settings allows room temperature NC-AFM measurements at a low thermal-noise limit with a significant bandwidth.