操作於 GHz 頻段之應變耦合多鐵性天線之建模與設計

Abstract

本研究提出一個二維的解析模型，可用以分析在 GHz 頻段運作的薄膜體聲波諧振器 (FBAR) 和固嵌式諧振器 (SMR) 的應變耦合多鐵性天線。將傳統的梅森模型擴展到二維，我們所提出的解析方法能夠全面分析各種聲波諧振器配置下的輻射性能，包括不同的拓撲結構（FBAR 和 SMR）和激發模態（厚度剪切模態和厚度伸展模態）。該模型透過考慮 GHz 輻射固有的頻率相關機械和電氣限制來評估天線性能，並計算 GHz 和 Akhiezer 區域內的效率-頻寬乘積。與朱氏極限的比較分析表明，聲子-聲子散射才是這些元件輻射效率的主要限制因素，而非朱氏極限。

此外，利用高品質因子體聲波諧振器設計的啟發，我們提出了優化多鐵性天線的指導方針，其中包含基於 SMR 的設計，利用布拉格反射器實現厚度伸展波和厚度剪切波的雙波反射，並結合周圍增厚的結構來抑制各種幾何配置中的雜散模態。

最後，本論文透過磁彈性波色散圖，探討了多鐵性天線中可用於提升輻射效率的磁彈性耦合。我們的分析顯示，磁和聲波模態之間的交互作用強度在很大程度上取決於外加偏壓磁場的方向（共平面方向或平面法向量方向）和波數，從而導致強耦合或弱耦合。這些發現為提升多鐵性天線在 GHz 頻段的性能指引出一條途徑。

This study introduces a two-dimensional closed-form model for thin-film bulk acoustic resonator (FBAR) and solidly mounted resonator (SMR) strain-mediated multiferroic antennas operating in the GHz regime, extending the traditional Mason model to two dimensions. The proposed analytical framework enables a comprehensive analysis of radiation performance across various acoustic resonator configurations, including different topologies (FBAR and SMR) and excitation modes (thickness shear (TS) and thickness extensional (TE) modes). The model evaluates antenna performance by addressing the frequency-dependent mechanical and electrical limitations inherent to GHz radiation, computing efficiency-bandwidth products within the GHz and Akhiezer regimes. Comparative analysis with Chu's limit reveals that phonon-phonon scattering, rather than Chu's limit, predominantly constrains radiation efficiency in these devices.

Furthermore, leveraging insights from high-quality factor bulk acoustic wave (BAW) resonator design, we propose guidelines for optimizing multiferroic antennas, incorporating SMR-based designs with Bragg reflectors for dual-wave reflection of thickness extensional and thickness shear waves, alongside raised frames to suppress spurious modes across diverse geometric configurations.

Finally, the magnetoelastic coupling in multiferroic antennas for boosting radiation efficiency is explored through magnetoelastic wave dispersion diagrams. The analysis shows that the interaction strength between magnetic and acoustic modes depends heavily on the external bias magnetic field's direction (in-plane or out-of-plane), and the wavenumber, leading to either robust or weak coupling. These findings offer a pathway to enhance the performance of multiferroic antennas in GHz applications.