Quartz tuning fork (QTF) sensors offer an attractive alternative to traditional silicon microcantilevers for sensing applications in dynamic atomic force microscopy (DAFM). The QTF sensor consists of two identical, weakly-coupled tines with a sharp tip affixed to the distal end of one tine. The fundamental anti-phase mode of the QTF achieves a stable resonant frequency with a high Quality factor making it ideal for DAFM applications in which a small shift in the resonant frequency is linked to a tip-sample force. The addition of the tip-sample force also breaks the symmetry of the QTF leading to a classic eigenvalue veering scenario. The eigenvalue veering and accompanying mode localization phenomena violate the standard DAFM modeling assumptions which treat the addition of the tip-sample force as a small perturbation to a single-degree-of-freedom oscillator. We find that the eigenvalue veering can contribute a systematic error in force measurements on the order of 20%. Methodology for correcting the systematic error caused by eigenvalue veering is proposed.
Force-gradient-induced mechanical dissipation of quartz tuning fork force sensors used in atomic force microscopy
