Sensors and Actuators A 190 (2013) 127–135 Contents lists available at SciVerse ScienceDirect Sensors and Actuators A: Physical jo u rn al hom epage: www.elsevier.com/locate/sna Analysis of anchor and interface losses in piezoelectric MEMS resonators A. Frangi a,∗ , M. Cremonesi a , A. Jaakkola b , T. Pensala b a Politecnico of Milano, P.za L. da Vinci 32, 20133 Milano, Italy b VTT, Technical Research Centre of Finland, 02015 Espoo, Finland a r t i c l e i n f o Article history: Received 11 June 2012 Received in revised form 18 October 2012 Accepted 18 October 2012 Available online xxx a b s t r a c t This paper presents a numerical study on anchor and interfacial dissipation in piezoelectric MEMS res- onators with in-plane longitudinal-mode vibrations. According to recent proposals, interfacial dissipation is formulated in terms of the stress jump across the interface. A refined dedicated numerical tool is employed both to evaluate anchor losses and to implement the model of interface dissipation. Extensive comparisons with experimental data are performed showing excellent quantitative agreement. © 2012 Elsevier B.V. All rights reserved. 1. Introduction Single crystal silicon MEMS resonators are a potential alterna- tive to quartz for timing and frequency control applications. Even if capacitive resonators with very high Q have been demonstrated e.g. by [24,25,29] and produced commercially, in order to achieve a good electromechanical coupling and admissible impedance levels, large bias voltages and submicron gaps are required. To over- come these challenges, piezotransduced bulk MEMS resonators have rapidly emerged as a valid alternative. Among the various piezoelectric block resonators developed so far, some utilize silicon as a structural layer and a piezoelectric material as a transduction layer [16,17,21,28,30]. However it has been observed experimen- tally that the presence of the piezoelectric layer may degrade the quality factor considerably, a phenomenon which is some- how puzzling due to the very limited thickness of the added layer. When MEMS are packed in near-vacuum, which is typical of high frequency resonators, fluid dissipation is negligible [8,9] and the mechanical dissipation is essentially connected to loss mechanisms in the solid material, and for this reason it is often called “intrinsic damping” or “solid damping” [1,26]. Solid damping is induced by numerous physical and chemical processes and many of them are still needing further investigation. Sources of dissipation generally include attachment losses and thermal processes like thermoelas- tic and, to a minor extent, Akhieser losses [30,31,36,37]. Since a piezoelectric block resonator operates in one of its bulk-modes, thermoelastic damping is generally negligible and can anyway be computed with reasonable accuracy. The issue of anchor dissipation deserves specific attention. In order to predict anchor losses it is generally accepted that ∗ Corresponding author. E-mail address: attilio.frangi@polimi.it (A. Frangi). all the elastic waves radiating from the anchor of the resonator into the elastic subspace are finally dissipated. From the numer- ical standpoint this can be simulated using suitable absorbing conditions. Among the different options, the Perfectly Matched Layer (PML) technique is gaining increasing attention [3] and can be adapted to a fully general 3D context. Extensive validation for MEMS applications has been presented recently in [10] and, whenever meaningful, anchor losses can be estimated with good confidence. Nevertheless, neither thermal effects [4,5], nor anchor losses can account alone for the measured dissipation of piezotransduced resonators and there is experimental evidence that other effects should be considered. Indeed the capacitive counterparts with sim- ilar design have demonstrated a much higher Q. Since capacitive devices contain all these loss sources, the low Q measured in piezo- resonator should result from dissipation of different nature. Possible dissipation sources include bulk losses in the piezo material. This issue, however, has been recently addressed in [15] where capacitive-piezoelectric sputtered thin film AlN resonators have been analysed. By separating electrodes from the piezo layer a large increase in quality factor was measured over similar devices using conventional contacting electrodes. This seems to suggest that indeed sputtered AlN is a high-Q material and that energy loss associated with contacting electrodes should be primarily respon- sible for the low Qs of previous AlN resonators. This conclusion is also supported by the experimental data presented in [12,27]. The latter contribution concerns a doubly clamped beam piezo- transduced by means of a thin layer of ZnO. By etching the ZnO layer in a portion of the central span of the beam they were able to double the measured quality factor. It is moreover a rather com- mon practice to eliminate the bottom metal electrode to minimise the number of stacked layers and increase the quality factor (see e.g. [14]). In particular, electrodes in contact with the piezoelectric mate- rial may dissipate energy in numerous ways, from direct strain 0924-4247/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.sna.2012.10.022