Temperature Coefficient of Frequency in Silicon-Based Cross-Sectional Quasi Lam e; Mode Resonators

Abstract

Temperature coefficient of frequency (TCF) is studied in silicon-based cross-sectional quasi Lamé modes (CQLMs). Such modes are demonstrated in thin-film piezoelectric-on-silicon (TPoS) resonators and the TCF curves are modeled using eigenfrequency analysis in COMSOL for highly n-type doped silicon. It is shown that the ratio between the finger-pitch and the resonator thickness affects the turnover temperature of these resonators which could be predicted using this model. The CQLM-TPoS resonators fabricated on a $40\mu\mathbf{m}$ thick SOI substrate, are characterized and the measured TCF values are confirmed to be in close agreement with the prediction. A relatively high turnover temperature of >100°C is reported for a third-order CQLM-TPoS resonator aligned to <100> silicon plane while a turnover temperature of <20°C is recorded for the <110> counterpart.