Force spectroscopy using a quartz length-extension resonator

Abstract

Frequency modulation atomic force microscopy detects the interaction force between the tip and the sample by measuring the change in the resonance frequency of an oscillating force sensor. Short-range interaction force can be selectively detected by a small oscillation amplitude. A quartz length-extension resonator (LER) offers the advantage of small-amplitude operation by virtue of its ultrahigh stiffness. Here, we demonstrate that an LER can accurately measure the short-range interaction force at cryogenic temperature even under a high magnetic field. We derive a formula for calculating the effective stiffness of an oscillating LER by using the theory of elasticity. The obtained dynamic stiffness is 1.23 times greater than the static stiffness, and this difference significantly affects the estimation of the interaction force. Using a properly calibrated LER, force curves are measured on Si(111)-(7 × 7) surfaces. The maximum attractive short-range forces above Si adatoms using several tip apex states are in the ranges of the values previously obtained by Si cantilevers.