Distributed Lamé mode resonators for temperature-stable high frequency mems oscillators

This paper presents a high frequency silicon resonator design possessing a quadratic temperature coefficient of frequency (TCF) profile with high-temperature turnover point. The design takes the advantages of a square Lamé mode and extends it to a distributed arrangement, to allow efficient transduction while scaling up the frequency. A Distributed Lamé mode resonator (DLR) with frequency exceeding 160MHz and Q of 77k is measured with a motional impedance of 3.5kΩ, showing one of the highest f-Qs for silicon resonators. A high-temperature turnover point above 100°C is achieved for DLR fabricated on a commercially available highly doped substrate, which will allow ovenized high frequency silicon oscillators that cannot be realized efficiently using a simple square shape Lamé mode resonator due to dimensional constraints. Using this method, it is possible to achieve temperature-stable silicon oscillators at high frequencies comparable to quartz oscillators, which are suitable for very high frequency (VHF) military (navigation, radar, GPS) and consumer applications (mobile phones).