2002-08-012024-05-17https://scholars.lib.ntu.edu.tw/handle/123456789/677548摘要：近年來眾人對於光子晶體之興趣逐年增長。所謂光子晶體，即為週期性之介電質結構，因週期性結構之緣故，導致電磁波通過晶體時，發生所謂頻溝現象，阻擋某些頻率振盪之電磁波通過。由於光子與聲子之類比性，可推斷由彈性振動材料組成之週期性結構，在適當調整其材料常數後通過之聲波亦有頻溝現象存在，則將此類結構稱為聲子晶體。本計劃將探討表面波於二維非等向聲子晶體之波傳行為與頻溝現象。理論部分將延伸Tanaka與Tamura提出的立方晶系材料表面波理論，提出一套適用於三斜晶系材料的聲子晶體表面波傳理論。內容為利用有限個倒晶格向量以及布拉克定理展開波動方程式，並配合表面波條件與邊界條件，推導出高度異向性材料組成的聲子晶體之波傳理論，可計算二維聲子晶體表面波之頻散曲線，預測頻溝出現之頻段與寬度，進而可針對指定入射角度及結構尺寸設計濾波頻率。實驗部分將以微機電製程製作二維聲子晶體，並佈上指叉電極產生高頻表面聲波，分析測試聲子晶體之頻溝現象。 <br> Abstract: There has been a growing interest in recent years in the study of man-made two-dimensional periodic structures of dielectric materials known as “photonic crystals.” A major reason for this is the fact that these systems exhibit forbidden frequency bands (photonic band gaps) extending throughout the Brillouin zone. In these regions, electromagnetic waves are absent along all directions since they are strongly reflected by the structure. The existence of band gaps can lead to numerous practical interests such as DWDM in the optical communication application. The analogy between photons and phonons suggests that band gaps would also be found in the systems comprised of two materials with different elastic properties called “phononic crystals.” Acoustic waves propagating in such structures also exhibit band gaps and may find applications in the high frequency acoustic wave devices. The purpose of this proposal is to elucidate theoretically and experimentally the characteristics of surface acoustic waves in 2D phononic crystals with fully accounts of the elastic anisotropy of both the cylindrical filler and background material. In the theoretical part, band gaps will be studied using the plane-wave expansion method, which is composed of the Bloch’s theorem and the reciprocal lattice vectors. The cases of surface acoustic waves of anisotropic materials in square and hexagonal lattices will be examined in particular. In the experimental part, high frequency SAW device will be designed and fabricated to generate broadband surface waves propagating in a 2D phononic structure with silicon as the background material. Standard MEMS process such as Reactive Ionic Etching (RIE) technique will be employed to fabricate a two dimensional phononic structure with square lattice arrangement.聲子晶體週期性構表面聲波頻溝Phononic crystalsperiodic structuressurface acoustic wavesband gaps