INTRODUCTION
Piezoelectric devices that can be electrically excited into a shear mode of vibration can be used to probe interfacial processes at surfaces and thin films. These devices typically consist of a thin AT-cut quartz wafer with electrodes patterned on opposite sides. When excited at resonance, the crystal vibrates in a thickness-shear mode (TSM) with faces undergoing in-plane displacement. The resonant frequency of a free resonator is established when a standing transverse acoustic wave condition is fulfilled. It increases with decreasing crystal thickness according to$$f_{0}={\sqrt{\mu_{q}/\rho_{q}}\over 2t_{q}} \eqno{\hbox{(1)}}$$ where and are the shear modulus and the density, respectively, and is the thickness of the quartz resonator [4]).