結合聲子晶體反射體之單埠板波共振器研製

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）。

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.