Fundamental limits to force detection using quartz tuning forks

This paper explores the fundamental limits of the use of quartz tuning forks as force detectors in scanned probe microscopy. It is demonstrated that at room temperature, pressure, and atmosphere these force sensors have a noise floor of $\text{0.62\hspace{0.5em}}\mathrm{pN}/\sqrt{\mathrm{Hz}}$ and exhibit a root mean square Brownian motion of only 0.32 pm. When operated as a shear force sensor both dissipative and reactive forces are detected on approach to the sample. These forces are sufficient to reduce the amplitude of motion of the probe nearly to zero without physically contacting the surface. It is also demonstrated that conventional proportional-integral feedback control yields closed loop responses at least 40 times faster than their open loop response.