Gold thin film viscoelastic losses of a length extension mode resonator

In [1] we presented a new length extension mode (LEM) piezoelectric micro-resonator. Thanks to a specific design, anchor losses were lowered to maximize the Q.f product and the resonator. Viscous fluid damping is neglected since the resonator is under vacuum and so is the thermoelastic damping for a length extension mode. With a Q predicted over one million the resonator is well suited for MEMS oscillator devices. Nevertheless it appears that one remaining loss source was not evaluated through our previous work: the viscoelastic damping arising from the presence of gold electrodes on the resonator surface. To investigate the influence of the gold thin film on this new resonator, we studied several papers on the quality factor of gold coated resonators and deduced a frequency dependence of the viscoelastic behavior of the gold thin film. This dependence shows that the damping for the LEM resonator won't be as important as firstly predicted and is compliant for time and frequency applications. Furthermore, the damping can be reduced to improve the quality factor with new electrode designs. These designs shall also provide low motional resistances in order not to deteriorate the phase noise far from the carrier. Two different approaches are compared to reduce electrode damping for the LEM resonator: contactless electrodes and partial electrode coating on the resonator surface. It appears that both approaches are interesting regarding the available processing technologies and give promising phase noise predictions.