Computer aided design of Langasite resonant cantilevers: analytical models and simulations

¹ Frequency and Time Dept., FEMTO-ST Institute, 26 chemin de l'Épitaphe, 25030 Besançon Cedex, France
² MN2S Dept., FEMTO-ST Institute, 32 avenue de l'Observatoire, 25044 Besançon Cedex, France
³ LAUM, Rue Aristote, 72085 Le Mans Cedex 9, France

Corresponding author: ctellier@ens2m.fr

Received: 1 December 2009
Revised: 5 February 2010
Accepted: 16 February 2010
Published online: 31 March 2010

Abstract

Analytical models for the piezoelectric excitation and for the wet micromachining of resonant cantilevers are proposed. Firstly, computations of metrological performances of micro-resonators allow us to select special cuts and special alignment of the cantilevers. Secondly the self-elaborated simulator TENSOSIM based on the kinematic and tensorial model furnishes etching shapes of cantilevers. As the result the number of selected cuts is reduced. Finally the simulator COMSOL^® is used to evaluate the influence of final etching shape on metrological performances and especially on the resonance frequency. Changes in frequency are evaluated and deviating behaviours of structures with less favourable built-ins are tested showing that the X cut is the best cut for LGS resonant cantilevers vibrating in flexural modes (type 1 and type 2) or in torsion mode.