基於彎曲梁結構之CMOS-MEMS共振器頻率溫度補償技術

Abstract

本論文研究在0.35-μm CMOS-MEMS製程平台上開發一作為溫度補償之共振器，由於MEMS計時裝置技術開始漸漸取代石英振盪器，應用在對於那些品質與可靠度要求較高或嚴苛環境下運轉的系統，因此本研究目的為在CMOS平台上建立具有溫度補償性能的元件，以減低環境溫度變化下造成的頻率變化導致計時器產生誤差，而此溫度補償元件利用彎曲電極被動式電剛性頻率補償技術，其優點是不需要過於複雜的後製程處理，特別的是，占晶片面積比小的優點使此彎曲電極可適用於CMOS-MEMS技術中幾乎所有類型的共振器，其是基於間隙變窄的彎曲梁和共振器之間產生與溫度相依的傳感間隙，進而抵銷溫度變化下，隨溫度變化的機械剛性。 本研究成功使其共振器之頻率溫度係數(Temperature Coefficient of Frequency, TCF)由原本未經補償約-88.56 ppm/°C下降為+10.75 ppm/°C、在0-90°C範圍整體頻率飄移由8236.07 ppm下降為1984.87 ppm，對於整體頻率飄移有近4.14倍的改善。 為了本研究亦提出預測頻率偏差的理論模型，考慮熱應力造成結構退縮程度，預測傳感間隙隨溫度變化的影響，並且與實驗結果互相驗證，並提出不同CMOS-MEMS共振器形式補償結果例如：兩端自由梁、兩端固定梁。最後，在修正過後的理論模型中提出最佳化補償結構與補償電壓設計，達到最小頻率偏移結果。

This thesis studies the development of a resonator as a temperature compensation on the 0.35-μm CMOS-MEMS manufacturing platform. The objective is to incorporate temperature compensation characteristics in the component to mitigate frequency variations caused by changes in ambient temperature. The temperature compensation component employs arc-beam electrodes, leveraging the advantages of passive electrical stiffness frequency compensation technique, which simplifies post-processing requirements. Notably, the small chip area ratio of the arc-beam electrode makes it compatible with nearly all types or resonators in CMOS-MEMS technology. The proposed approach is based on the temperature-dependent gap spacing between the narrowed arc-beam and the main resonator. By counteracting temperature changes and adapting to mechanical stiffness variations with temperature, the temperature coefficient of frequency (TCF) of the resonator is effectively reduced from approximately -88.56 ppm/°C (without compensation) to +10.75 ppm/°C. Consequently, the overall frequency drift within the temperature range of 0°C - 90°C experiences a significant improvement, decreasing from 8236.07 ppm to 1984.87 ppm, representing an enhancement of nearly 4.14 times. Furthermore, this thesis introduces a theoretical model for predicting frequency deviations resulting from changes in the gap spacing due to temperature variations. The predictions are validated through experimental results, and a variety of compensation techniques for different CMOS-MEMS resonators are proposed, including free-free beam, double-clamped beam resonators.