Thickness-Lamé Thin-Film Piezoelectric-on-Silicon Resonators
Sarah Shahraini, Hakhamanesh Mansoorzare, Amirreza Mahigir, Reza Abdolvand
Abstract
In this paper, Thickness-Lamé (TL) mode piezoelectrically-transduced silicon resonators are studied and demonstrated. It will be shown that unlike Planar-Lamé resonance modes, Thickness-Lamé modes could be efficiently excited using sputtered polycrystalline piezoelectric films such as Scandium Aluminum Nitride (ScAlN) due to the constructive contribution of both d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">31</sub> and d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">33</sub> 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 eigenfrequency 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-Lamé to a Lateral-Extensional mode with the gradual increase of wavelength to thickness ratio. A record Q of 23.2k is measured for a ~185 MHz fundamental TL resonator in vacuum (f x Q = 4.3 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sup> ) while quality factors of 12.6k (f x Q = 4.6 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sup> ) 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.