階梯式結構用於CMOS-MEMS共振器頻率溫度補償

Abstract

此研究主要在CMOS-MEMS平台上，針對金屬基垂直出平面電容式共振器輸出頻率進行被動式溫度補償。無須搭配額外的補償電路或晶片便可以實現垂直式出平面共振器對溫度的穩定輸出，對於垂直式振盪器、感測器、制動器皆能應用本研究的被動補償機制。 利用CMOS製程平台後道工序（BEOL）上設計一階梯狀結構微機電共振器。當溫度變化時，由於CMOS後道工序中，材料的熱膨脹係數有所差異，階梯狀結構各層將因熱應變產生開口向上的彎曲形變，進而被動式改變共振器與驅動電極間的距離。隨著溫度上升，傳感間隙持續加大、電剛性降低，進一步抵抗高溫造成結構機械剛性下降的問題，使得共振器頻率輸出能維持穩定而不隨溫度飄移。通過理論分析與有限元素輔助，設計出一最適合階梯狀結構，通過調整驅動時的直流偏壓，可以找到一最適合之驅動條件，降低整體共振器受溫度的影響，提高穩定性。在溫度範圍-20至80攝氏度之間，共振器之TCF1從每度368.4 ppm降至每度0.164 ppm，整體頻率飄移從36745 ppm降至2420 ppm，有近15倍改善。雖然相比於其他主動式補償或商用振盪器的表現，被動式補償依舊有很大的進步空間。

This study focuses on passive temperature compensation for the output frequency of metal-based out-of-plane capacitive resonators on the CMOS-MEMS platform. The proposed mechanism enables stable temperature-independent output for vertical out-of-plane resonators without the need for additional compensation circuits or chips. This passive compensation approach can be applied to vertical oscillators, sensors, and actuators. A stepped-structure MEMS resonator is designed using the back-end-of-line (BEOL) process of the CMOS platform. Due to differences in the thermal expansion coefficients of materials in the CMOS BEOL process, the layers of the stepped structure undergo upward bending deformation caused by thermal strain as the temperature changes. This deformation passively alters the gap between the resonator and the driving electrode. As the temperature increases, the sensing gap widens, reducing electrostatic stiffness, which counteracts the reduction in mechanical stiffness of the structure caused by high temperatures. Consequently, the resonator’s frequency output remains stable without temperature drift. Through theoretical analysis and finite element simulations, an optimal stepped structure design is developed. By adjusting the DC bias during operation, the best driving conditions can be identified to minimize the resonator’s temperature influence and improve stability. Within the temperature range of -20°C to 80°C, the resonator’s TCF1 is reduced from 368.4 ppm/°C to 0.164 ppm/°C, and the overall frequency drift is improved from 36,745 ppm to 2,420 ppm, achieving nearly 15-fold enhancement.