聲子晶體通道與薄膜共振互制行為之探討

Interaction between Phononic Crystal Channel and Resonance of Membrane

阮薰儀(Hsun-Yi Juan)

指導教授 ： 吳政忠

國立臺灣大學/工學院/應用力學研究所/碩士(2017年)

https://doi.org/10.6342/NTU201700523

摘要

聲子晶體(phononic crystal)為多種彈性材料於空間中以週期性排列而成的結構，彈性波在此結構中傳遞時，會改變原有的波傳現象。適當的選擇與調整彈性材料的比例，波傳模態在某些特殊頻帶會出現不連續的現象，因此彈性波無法在該頻帶內傳遞，稱此現象為頻溝(band gaps)。基於布拉格散射的聲子晶體中，結構存在缺陷時，彈性波會被侷限於缺陷處，聲子晶體通道即是從完整結構中移除一排單胞形成線缺陷，彈性波僅能於通道中傳遞，形成波導結構。
薄膜的應用涵蓋非常廣泛，從大尺寸的鼓膜、喇叭共振膜及壓電薄膜感測器等至微米級的微型幫浦或是主動式混合器，皆是利用薄膜結構在受到張力後，提供垂直於波傳方向振動的特點，加上適當的設計能有效地將薄膜位移放大。
本論文將聲子晶體波導與共振薄膜結合，提出不同以往的微液珠控制架構，搭配有限元素法(finite element method, FEM)與布拉格(Bloch theorem)理論作為分析基礎。分析幾何尺寸對於薄膜共振模態及頻率的影響，進行薄膜結構的設計。透過設計聲子晶體之尺寸，使聲子晶體頻溝涵蓋薄膜之共振頻率389kHz，並利用超晶格設計最佳聲子晶體通道寬度。本文採用高機電耦合係數的壓電基底材料128oYX-LiNbO3，並在壓電基底上放置電極以激發出板波作為波源。將元件整合後，進行聲子晶體通道與薄膜互制現象之分析。
激發源、薄膜結構與聲子晶體通道之間存在互制行為，由於元件間聲阻抗的差異，激發源與薄膜結構如同反射面，彈性波經激發後在激發源與薄膜結構間形成駐波，駐波波長為通道傳遞模態波長之1/2。適當地設計激發源與聲子晶體通道間的距離，使得能量更完整地進入聲子晶體通道中，並調整激發源與薄膜間的距離，因建設性干涉下，使得彈性波於激發源和薄膜之間能有效地來回反射，薄膜中心振幅累加放大，即可得到薄膜之最佳效應。根據本論文之設計，相較於無薄膜結構的情況，薄膜中心振幅放大倍率可達300倍。
經由這樣的模擬結果預期在未來結合微液珠控制應用，微液珠可以為生物檢測之樣品，利用通道引導樣品，並於通道內進行樣品檢測，最後藉由是否激發薄膜共振頻率進行樣品之篩選。

關鍵字

共振薄膜、聲子晶體頻散 ； 聲子晶體通道 ； 蘭姆波 ； 板波元件

並列摘要

In phononic crystals (PCs), the density or elastic constants of the structure change periodically. The propagation of elastic waves changes in the periodic structures. The dispersion curves tailored with appropriate choices of materials, crystal lattices, and topology of inclusions exhibit band gaps, in which the propagation of waves is forbidden. By introducing line defects within PC structures, new guiding modes emerge inside the band gaps. The elastic waves are trapped and guided along the line defects.
Membranes are widely applied in daily life such as drum head, speaker diaphragm, the film of piezoelectric sensors, and etc. A two dimensional elastic membrane under tension supports transverse vibration. With the phenome of resonance, the membrane can store vibrational energy and has a specific increase in the amplitude of the membrane at certain frequencies.
In this thesis, a new kind of micro-droplet control planer manipulation device, constructed by phononic crystal channel and membrane, is proposed and analyzed by the finite element method. The relation between geometry and resonant frequency is obtained by simulation. Then the membrane is designed according to the rules from simulation results. After deciding the frequency of the membrane, the architecture design of phononic crystal channel is presented. Lamb waves, generated by the interdigitated electrodes on 128oYX-LiNbO3 substrate, act as an energy source in the designed system. Combining the above designed elements, micro-droplet device can be constructed.
Due to acoustic impedance difference, elastic waves reflect and transmit partially at the interface between source and membrane, and a standing wave occurs in phononic crystal channel. The wave length of standing wave is 0.5 times of guiding wave. The energy is completely guided into the phononic crystal channel through appropriate choice of delay distance between the first row of phononic crystal channel and the edge of source. When the constructive interference occurs, the resonant membrane has the optimal performance. The amplitude of membrane is 300 times larger than the membrane-free system.
In the future, the proposed micro-droplet manipulation device can be utilized for processing bio samples detection. When elastic waves are generated by interdigitated electrodes, the micro-droplet moves along a phononic crystal channel and is implemented specific processing at the same time. Once arriving the center of a resonant membrane, the micro-droplets which meet requirements will jump and be collected.

並列關鍵字

Resonant membrane ； Dispersion relation of phononic crystal ； Phononic crystal channel ； Lamb wave ； Lamb wave resonator

參考文獻

[1] E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Physical Review Letters, vol. 58, p. 2059, 1987.

[2] S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Physical Review Letters, vol. 58, p. 2486, 1987.

[3] S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Photonic band gaps in periodic dielectric structures: The scalar-wave approximation,” Physical Review B, vol. 46, p. 10650, 1992.

[4] S. Fan, and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Physical Review B, vol. 65, 235112, 2002.

[5] M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,” Physical Review B, vol. 62, p. 10696, 2000.