An analytical model of a thermally excited microcantilever vibrating laterally in a viscous fluid

To achieve higher quality factors (Q) for microcantilevers used in liquid-phase sensing applications, recent studies have explored the use of the lateral (in-plane) flexural mode. In particular, we have recently shown that this mode may be excited electrothermally using integrated heating resistors near the micro cantilever support, and that the resulting increase in Q helps to make low-ppb limits of detection a possibility in liquids. However, because the use of electrothermally excited, liquid-phase, microcantilever-based sensors in lateral flexure is relatively new, theoretical models are lacking. Therefore, we present here a new analytical model for predicting the vibratory response of these devices. The model is also used to successfully confirm the validity of our previously derived Q formula, which was based on a single-degree-of-freedom (SDOF) model and a harmonic tip force. Comparisons with experimental data show that the present model and, thus, the analytical formula provide excellent Q estimates for sufficiently thin beams vibrating laterally in water and reasonable upper-bound estimates for thicker beams.