基於非線性耦合共振器之微機械頻率梳

Abstract

本論文基於互補式金屬氧化物半導體微機電系統 (CMOS-MEMS) 靜電共振器與鈧摻雜氮化鋁 (ScAlN) 壓電共振器之非線性動力學行為，探討其在分散式感測網路新興應用的潛力。相比於傳統微機電共振器多以線性方式操作並作為參考時脈訊號，本研究運用微機電共振器中的非線性效應，成功實現線性共振器無法達成的前瞻應用。這些技術突破涵蓋了感測器性能提升、簡化訊號處理架構與密碼學領域，用於提供不可預測之亂度源。具體的應用包括超高靈敏度感測器、真隨機數產生器、物理不可複製功能以及射頻訊號解調器等。 相較於傳統的頻率偏移或振幅偏移感測機制，本論文提出頻率梳計量方法，運用頻譜中相鄰譜線間的間距作為一種新的計量標準。此一機制能有效反映溫度變化與射頻訊號強度等物理量的改變。此外，本論文亦成功 (1) 將內共振現象轉換為混沌動力學以及 (2) 利用脈衝撞振機制產生孤子頻率梳。其中，混沌動力學因其不可預測的振盪波型，用於高熵真隨機數生成；孤子頻率梳則首次在微機械領域產生可與光學領域相比的高密度寬頻頻率梳。 針對上述非線性現象與應用，本論文進行了理論建模與實驗驗證。本論文基於Adomian decomposition method，針對幾何非線性共振器的形貌進行最佳化設計；本研究亦利用降階多尺度模型，推導了內共振的運動方程式及相應的混沌現象。 綜合以上技術，可實現高靈敏高可靠度及輕量化分散式感測器網路系統。

This dissertation explores emerging applications for distributed sensor networks by harnessing nonlinear dynamics in complementary metal-oxide-semiconductor micro-electro-mechanical systems (CMOS-MEMS) capacitive resonators and scandium-doped aluminum nitride (ScAlN) piezoelectric resonators. While traditional MEMS devices predominantly operate in the linear regime, this work demonstrates that triggering nonlinearities unlocks remarkable improvements in device performance and enables advanced functionalities inaccessible to linear counterparts. These advancements span critical fields including ultrahigh-sensitivity sensing, signal processing, and hardware security primitives such as true random number generation (TRNG), physical unclonable functions (PUF), and radio frequency (RF) signal demodulation. Specifically, this research establishes a new metrology paradigm based on mechanical frequency combs. Unlike traditional frequency- or amplitude-shift schemes, the spacing between neighboring comb teeth serves as a robust metric for detecting physical variations, such as temperature fluctuations and RF signal strength. Furthermore, the dissertation introduces novel mechanisms to enrich nonlinear dynamics, including the transition of regular internal resonance (IR) into chaotic regimes and the generation of solitary frequency combs via pulsed vibro-impacts. The unpredictable time histories inherent to the chaotic states are exploited as high-entropy seeds for random number generation, while the solitary frequency combs show significant potential for mechanical photothermal spectroscopy and frequency-division multiplexing. Collectively, these functional innovations pave the way toward more secure, lightweight, and reliable sensor networks. Theoretical and experimental characterizations are rigorously conducted to validate these nonlinear phenomena. First, an analytical shape optimization framework for geometrically nonlinear resonators is proposed utilizing the Adomian decomposition method (ADM). Additionally, the equations of motion governing both regular and chaotic IR are derived based on a reduced-order multiple-scale model. This comprehensive modeling approach not only elucidates the underlying physics but also provides a design guideline for optimizing the aforementioned applications.