This work investigates the methods for lowering the motional impedance of CMOS-MEMS resonators and attaining high Q. The main ideas of motional impedance reduction used in this thesis are active gap reduction through electrostatic pull-in and mechanically-coupled arraying. The power handling enhancement and the passive temperature compensation is also discussed.
The CMOS-MEMS clamped-clamped beam array resonators designed in this work have been demonstrated that takes advantage of pull-in effect to surmount limitations of CMOS foundry process and attains electrode-to-resonator gap spacing at a deep-submicron range, leading to much smaller motional impedance compared to conventional CMOS-MEMS technologies, while possessing unique frequency tuning capability by modulating their mechanical boundary conditions. With the increase of applied dc-bias voltage which simultaneously serves for functions of pull-in and resonator operation, the upward frequency shift of resonance caused by boundary condition change offers opposite tuning mechanism to well-known effect of electrical stiffness. Therefore, frequency variation induced by BC-modulation and electrical-stiffness would yield a frequency-insensitive region under a certain dc-bias.
On the other hand, the integrated CMOS-MEMS free-free beam resonator arrays operated in a standard two-port electrical configuration simultaneously with low motional impedance and high power handling capability centered at 10.5 MHz have also been demonstrated by the combination of pull-in gap reduction mechanism and mechanically-coupled array design. The mechanical links (i.e., coupling elements) using short stubs connect each constituent resonator of an array to its adjacent ones at the high-velocity vibrating locations to accentuate the desired mode and reject all other spurious modes. A single second-mode free-free beam resonator with quality factor Q > 2,200 and motional impedance Rm < 150 k□ has been utilized to achieve mechanically-coupled resonator array. In array design, a 9-resonator array has been experimentally characterized to have around 10X performance improvement on motional impedance and power handling with respect to a single resonator. In addition, two-port electrical configuration is much preferred due to its low feedthrough nature and high design flexibilities for the future oscillator and filter implementations rather than its one-port counterpart.

在本文中我們探討了一些特殊的設計方法試圖提升CMOS-MEMS微機械共振器的性能，使共振器具備低運動阻抗的特性並同時保有高品質因數。為了達成此目標，我們結合了靜電吸附效應與機械耦合陣列設計以減少靜電換能間隙並大幅提升共振器的換能面積以及等效剛性。本論文對於共振器的極限功率負載以及被動溫度補償也有所著墨。
在論文中首先以CMOS-MEMS製程為平台開發出深次微米間隙雙鉗樑共振器陣列並探討其性能。藉由靜電吸附效應，我們能在傳統CMOS製程平台中實現深次微米換能間隙並大幅減少共振器的運動電阻。同時，在本設計中發生的邊界條件調變效應對於頻率的影響也已被定性的探討。我們也觀察到邊界條件調變效應與電致軟化效應兩種物理機制在不同的直流偏壓下會互相消長，最終會在特定的偏壓下產生一穩定頻率。
此外，我們也利用相同的設計概念來設計雙端自由樑共振器，目標頻率約在10.5百萬赫茲。由於雙端自由樑共振器只藉由細小的支撐樑來連結共振器與外部支撐框架，因此能夠消除邊界條件調變效應所帶來的負面影響。在此研究中，我們適當的設計機械耦合樑的耦合位置，成功的解決共振器陣列中容易產生的多餘模態問題。本篇論文不僅設計出高性能CMOS-MEMS共振器，並探討了單一共振器、五個共振器耦合陣列與九個共振器耦合陣列在不同直流偏壓下的特性以及不同陣列中極限功率負載的變化。
本文中所設計的高頻高Q值CMOS-MEMS微機械共振器非常適合作為振盪器或濾波器中的共振元件，其最終可與電路結合並應用於射頻電路或高性能數位電路當中，取代體積龐大的石英震盪器，以達成系統整合與體積縮小的目標。

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