A review on temperature coefficient of frequency (TCf) in resonant microelectromechanical systems (MEMS)

Microelectromechanical systems (MEMS) have emerged as highly attractive alternatives to conventional commercial off-the-shelf electronic sensors and systems due to their ability to offer miniature size, reduced weight, and low power consumption (i.e., SWaP advantages). These features make MEMS particularly appealing for a wide range of critical applications, including communication, biomedical, automotive, aerospace, and defense sectors. Resonant MEMS play crucial roles in these applications by providing precise timing references and channel selections for electronic devices, facilitating accurate filtering, mixing, synchronization, and tracking via their high stability and low phase noise. Additionally, they serve as key components in sensing applications, enabling detection and precise measurement of physical quantities for monitoring and control purposes across various fields. Temperature stability stands as a paramount performance specification for MEMS resonators and oscillators. It relates to the responsivity of a resonator's frequency to temperature variations and is typically quantified by the temperature coefficient of frequency (TCf). A constant and substantially large absolute TCf is preferred in MEMS temperature sensing applications, while a near-zero TCf is required for timing and other MEMS transducers that necessitate the decoupling of temperature effects on the resonance frequency. This comprehensive review aims to provide an in-depth overview of recent advancements in studying TCf in MEMS resonators. The review explores the compensation and engineering techniques employed across a range of resonator types, utilizing diverse materials. Various aspects are covered, including the design of MEMS resonators, theoretical analysis of TCf, temperature regulation techniques, and the metallization effect at high temperatures. The discussion encompasses TCf analysis of MEMS resonators operating in flexural, torsional, surface, and bulk modes, employing materials such as silicon (Si), lithium niobate (LiNbO3), silicon carbide (SiC), aluminum nitride (AlN), and gallium nitride (GaN). Furthermore, the review identifies areas that require continued development to fully exploit the TCf of MEMS resonators.