Thickness-Lamé Thin-Film Piezoelectric-on-Silicon Resonators

Abstract

In this paper, Thickness-Lame (TL) mode piezoelectrically-transduced silicon resonators are studied and demonstrated. It will be shown that unlike Planar-Lame resonance modes, Thickness-Lame modes could be efficiently excited using sputtered polycrystalline piezoelectric films such as Scandium Aluminum Nitride (ScAlN) due to the constructive contribution of both $d_{31}$ and $d_{33}$ piezoelectric coefficients in the coupling coefficient. Moreover, it is shown through finite element analysis and experimental results that the coupling coefficient improves with the order of the TL harmonic mode excited in a silicon slab. It is also confirmed that the quality-factor of TL resonators substantially enhances through utilization of properly-designed acoustic reflectors (i.e. acoustic isolation frames) around the tethered resonator block. The temperature coefficient of frequency is also modeled using finite-element eigen-frequency analysis. It is shown that the turnover temperature of TL resonators aligned to the [100] plane of a degenerately-doped n-type silicon substrate varies considerably as the mode shape transitions from a Thickness-Lame to a Lateral-Extensional mode with the gradual increase of wavelength to thickness ratio. A record $Q$ of 23.2k is measured for a $\sim 185$ MHz fundamental TL resonator in vacuum ( $fxQ=4.3\times 10^{12}$ ) while quality factors of 12.6k ( $fxQ=4.6\times 10^{12}$ ) and 6k are also measured in vacuum for second- and third-harmonic TL resonators at 326 MHz and 555 MHz respectively. The combination of high turnover temperatures (>80 °C), high quality factor, and low motional resistance, promises the suitability of such resonators for extremely-stable oven-controlled oscillator applications.