Volume Dependence in Handel's Model of Quartz Crystal Resonator Noise

Fabrice Sthal (1) , Michel Devel (1) , Santunu Ghosh (1) , Joël Imbaud (1) , Gilles Cibiel (2) , Roger Bourquin (1)

1 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)
2 CNES - Centre National d'Études Spatiales [Toulouse]

Although criticized by many, Handel's quantum model for 1/f noise remains the only model giving a quantitative estimation of the level of intrinsic 1/f noise in quartz crystal resonators that is compatible with the best experimental results. In this paper, we reconsider the volume dependence in this model. We first argue that an acoustic volume, representing the volume in which the vibration energy is trapped, should be used instead of the geometrical volume between the electrodes. Then, we show that because there is an implicit dependence of the quality factor of the resonator with its thickness, the net effect of Handel's formula is not an increase of noise proportionally to the thickness of the resonator, as could be naïvely expected, but a net decrease when thickness increases. Finally, we show that a plot of Q4Sy versus the acoustic volume, instead of the usual Sy plot, could be useful to compare the quality of acoustic resonators having very different resonance frequencies.

Domaines: Micro et nanotechnologies/Microélectronique

Fabrice Sthal, Michel Devel, Santunu Ghosh, Joël Imbaud, Gilles Cibiel, et al.. Volume Dependence in Handel's Model of Quartz Crystal Resonator Noise. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 2013, 60, pp.1971 - 1977. ⟨10.1109/TUFFC.2013.2782⟩. ⟨hal-00877311⟩