結合聲子晶體反射體之單埠板波共振器研製

Design and Fabrication of a One-Port Phononic Plate Wave Resonator

郭鎮宇(Chen-Yu Kuo)

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(2010年)

https://doi.org/10.6342/NTU.2010.02236

摘要

聲子晶體是由數種彈性材料在空間中週期性排列而成，當聲波在此結構中傳遞時，由於波傳模態在某頻率範圍出現不連續的現象，使該頻段內聲波無法傳遞，此現象稱之為聲波頻溝(acoustic band gap)。本研究即利用此頻溝現象，配合數值分析及微機電製程，探討以聲子晶體為反射體之共振器的共振現象。
本文以布拉格(Bloch)理論為基礎，並結合有限元素法（finite element method, FEM）建立週期性邊界條件，分析聲子晶體之頻散關係。此外，藉由計算延遲距離（delay distance）探討等效反射面在共振腔內之位置，進而最佳化共振器之共振效果。本文也同時探討共振腔內相鄰反對稱共振模態之頻率間隙，並利用超晶格技術（supercell technique）分析其頻率間隙與共振腔長度之關係。
在實驗方面，本研究亦成功研製出具正方晶格聲子晶體反射體之矽─氧化鋅複合薄膜單埠板波共振器，其實驗結果與數值模擬相當吻合；如數值分析所預期，對於兩相異共振腔長度的共振器，亦量測到不同數目之頻率響應，驗證了共振腔長度與共振模態之頻率間隙的關係。此外，量測結果顯示，此共振器在共振頻率159.08 MHz處，具有相當高的品質因數（quality factor）。

關鍵字

板波共振器 ； 聲子晶體 ； 頻溝 ； 有限元素法 ； 共振模態 ； 品質因數

並列摘要

This thesis reports numerical analysis and experimental results of a one-port plate wave resonator using two-dimensional phononic crystal (PC) gratings. Based on the band gap effect of the PC, i.e. acoustic waves in a specific frequency are blocked by the PC, PC was utilized as the reflectors of a resonator. The dispersion relations of phononic crystals were calculated by using the finite element method (FEM). To optimize the resonance inside the cavity, the effective reflective plane was obtained through a series of numerical simulations. Attention has been also focused on frequency differences between the lowest anti-symmetric (A0) modes within a resonant cavity. The relation between the cavity length and the frequency difference was analyzed by supercell technique.
On the experimental side, one-port ZnO/Si plate wave resonators with square-lattice PC reflective gratings were fabricated. The measured resonant frequencies of the cavity are in a good agreement with the numerical predictions. In addition, the measurement result showed that a high Q factor of 3885 can be achieved at 159.08 MHz resonant frequency.

並列關鍵字

Plate wave resonator ； Phononic crystal ； Band gap ； Finite element method ； Resonant mode ； Q factor

參考文獻

[1] M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani, “Acoustic band structure of Periodic elastic composites,” Phys. Rev. Lett. 71, 2022-2025, 1993.

[2] R. Sainidou, B. Djafari-Rouhani, and J. O. Vasseur, “Surface acoustic waves in finite slabs of three-dimensional phononic crystals,” Phys. Rev. B 77, 094304, 2008.

[3] Y. Tanaka and S. I. Tamura, “Surface acoustic waves in two-dimensional periodic elastic structures,” Phys. Rev. B 58, 7958, 1998.

[4] F. Meseguer, M. Holgado, D. Caballero, N. Benaches, J. Sánchez-Dehesa, C. López, and J. Llinares, “Rayleigh-wave attenuation by a semi-infinite two-dimensional elastic-band-gap crystal,” Phys. Rev. B 59, 12169, 1999.

[5] T. T. Wu, Z. G. Huang, and S. Lin, “Surface and bulk acoustic waves in two-dimensional phononic crystal consisting of materials with general anisotropy,” Phys. Rev. B 69, 094301, 2004.