Finite element method analysis of whispering gallery acoustic sensing

Whispering Gallery Acoustic Sensing (WGAS) has recently been introduced as a sensing feedback mechanism to control the probe-sample separation distance in scanning probe microscopy that uses a quartz tuning fork as a sensor (QTF-SPM) [1]. WGAS exploits the SPM supporting frame as a resonant acoustic cavity to monitor the nanometer-sized amplitude of the QTF oscillations. Optimal WGAS sensitivity depends on attaining an exact match between the cavity's frequency peak response and the TF resonance frequency. However, two aspects play against this objective: i) the unpredictable variability of the TF resonance frequency (upon attaching a SPM-probe to one of its tines), and ii) cavities of arbitrary geometry tend to display complicated (multiple peaks) frequency response, making difficult to identify which cavity dimension control which peak. Practical matching frequency procedures are needed then to operate the Shear-force Acoustic Near-field Microscopy (SANM) more efficiently. As a first step, here we undertake finite-element method (FEM) analysis to find out cavities of simple frequency response and, ideally, easy frequency tuning ability. Based on previous results we focus our studies in analyzing the frequency response of conical cavities within a range around the 32 kHz operating frequency. To first validate our numerical simulation studies, we reproduce the experimental results obtained from a specific conical cavity. Then we proceed to simulate the response of cavities of slightly different geometries, and investigate the dependence on the young modulus, poison ratio, and slight changes in dimensions. This initial success encourages to undertake studies of cavities having more sophisticated geometries.