石英聲子晶體之單埠板波共振器

Abstract

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，使聲波無法於該頻段內傳遞，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，探討以石英聲子晶體為反射體之共振器的共振現象。 文中以布拉格(Bloch)理論為基礎，結合有限元素法（finite element method, FEM）建立週期性邊界條件，來分析石英聲子晶體平板之頻散關係。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，本研究成功研製出具正方晶格聲子晶體反射體之石英單埠板波共振器，其實驗結果與導納數值模擬相當吻合。量測結果顯示，此共振器在共振頻率17.00 MHz和18.52 MHz處，具有相當高的品質因數（quality factor）。

This thesis reports numerical analysis and experimental results of a one-port quartz plate wave resonator using two-dimensional phononic crystal (PC) gratings. Based on the band gap effect, 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 focused on the 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 the supercell technique. On the experimental side, one-port quartz 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 admittance simulation. In addition, the measurement result showed that a high Q factor of 3541 and 3407 can be achieved at 17.00 MHz and 18.52 MHz resonant frequency respectively.