A Study of Love Waves in a Phononic Structure

聲子晶體泛指材料性質或幾何形狀週期排列之彈性結構。近二十年，由於聲子晶體具有特殊波傳效應，如完全頻隙、負折射、聲波聚焦等，已引起相當多學者的興趣與投入。由於壓電晶圓較難進行精密蝕刻，目前文獻大都以矽基聲子晶體元件為主，但矽不具壓電特性，須將氧化鋅或氮化鋁等壓電薄膜鍍於叉指電極部分以激發表面波或板波，元件插入損失較高 另一方面，在層狀介質的表面波研究中，除了偏振方向與波傳矢狀平面(sagittal plane)平行的雷利表面波外，亦存在有偏振方向與矢狀平面垂直的拉福波(Love wave)。拉福波存在於表面鍍上橫波波速小於基底材料橫波波速材料之層狀半無限域結構，大部分波的能量局限於表面的薄層中，形成一理想的橫波波導。在壓電晶體表面亦存在各類偏振方向與矢狀平面垂直的水平剪切式表面聲波，其發生原理與拉福波相似，可歸類為廣義拉福波。此類聲波常具有較雷利波為高的機電耦合係數及波速，因此廣泛用於高頻、寬頻濾波器用途。 基於拉福波之特性，如能於不易蝕刻的壓電基板鍍上一具聲子晶體結構之薄層，除具有高激發效率之波源外，亦可經由聲子晶體之頻隙特性製做高效能之濾波器或感測器。有鑒於此，本文提出具聲子晶體薄鍍層於壓電基材上之結構，使用有限元素法搭配布洛赫理論(Bloch theorem)，分析此類結構之頻散特性，證實此類結構具有拉福波的可傳頻帶及頻隙，並藉由複數波數頻散關係進一步分析頻隙內聲波之衰減現象。此外，本文也探討頻隙內聲波由均勻介質進入聲子晶體介面之反射、透射及散射現象，並設計一聲子晶體共振器結構。 實驗部分則是以奈米機電系統製程，利用電子束微影系統產生次微米級之叉指電極及聲子晶體圖案，並以反應離子蝕刻法製作出聲子晶體結構。使用斜叉指電極激發及接收寬頻聲波驗證聲子晶體之頻溝，發現在頻溝處有超過40分貝之插入損失，且其頻率範圍與理論之預測相當吻合。而設計於1.25 GHz之共振器也實現，並具有約400之Q值。A phononic crystal (PC) is a structure whose mechanical properties are periodical-ly arranged. 2-D PCs started to attract great attentions two decades ago. A lot of concern has been focused on their acoustic reflecting phenomenon due to the band gap. However the PC can also be an acoustic conductor, which its conductance is determined by the band structure. Novel properties such as negative refraction or acoustic lensing effect can be achieved with PCs. Among the many applications, in the area of ultra-high frequency (UHF) acoustic wave devices, complete or partial band gap of air/silicon PC was utilized as the reflec-tive gratings to reduce the devices’ size. In those devices, a piezoelectric thin film has to be deposited on the silicon substrate to generate acoustic waves for silicon is non-piezoelectric. Although the fabrication process of the silicon based phononic device has the CMOS compatible advantage, the insertion loss of such a device is high rela-tively. The other more straightforward way of making a phononic acoustic wave device is to construct periodically micro-holes directly on a piezoelectric substrate. Although the electro-acoustic conversion is higher, it suffered from the anisotropic nature of lith-ium niobate that lead to a complicated fabrication process. On the other hand, SH-type SAWs have several advantages compared to conven-tional Rayleigh-type SAWs. For example SH-type SAWs possess larger piezoelectricity than Rayleigh-type SAWs on the same substrate material. Also they are faster than Rayleigh-type SAWs therefore desirable for high frequency applications. And in liquids, SH-type SAWs lose less energy than Rayleigh-type SAWs do due to their polarization, also they are sensitive to surface loadings, so they are desirable for (bio-) sensing appli-cations. Love wave, being one of the SH-type SAWs, shares similar physical character-istics with other SH-type SAWs. Investigating the propagating of Love waves in PCs will expand the PC applications to SH-type SAWs that have bright outlook. In this study, we investigate Love waves propagating in a piezoelectric substrate coated with a phononic guiding layer. The phononic layer is consisted of a thin layer with periodic machined holes. It is worth noting that the thin phononic layer can be non-piezoelectric which makes the fabrication process relatively simple. And since most energy is trapped in the guiding layer it may serve as efficient reflective gratings in Love wave devices. The method proposed in this study is suitable for other SH-type SAWs also.口試委員會審定書 # 誌謝 i 中文摘要 ii ABSTRACT iii CONTENTS v LIST OF FIGURES viii LIST OF TABLES xiv Chapter 1 Introduction 15 1.1 Motivation 15 1.2 Literature Review 17 1.3 Contents of the Chapters 18 Chapter 2 Love Wave Dispersions of a Phononic SiO2/Quartz Layered Structure 19 2.1 The Mathematical Model of Acoustic Waves in Piezoelectric solids 20 2.1.1 Piezoelectric acoustic wave equations 20 2.1.2 Coordinate transformation for material constants 22 2.1.3 Materials 23 2.2 Waves in periodic structures 25 2.2.1 Direct and reciprocal lattices 25 2.2.2 Bloch’s theorem 28 2.3 Love wave dispersion of a layered half-space 29 2.3.1 Numerical methods 30 2.3.2 Determination of the SiO2 film thickness 34 2.4 Love wave dispersion in a SiO2/IDT/quartz structure. 36 2.4.1 Background 36 2.4.2 Dispersion relation 37 2.4.3 Frequency-pitch relation 38 2.5 Love wave dispersion in phononic layered structures 38 2.5.1 Geometries 38 2.5.2 M-Y-Γ-X-M-Γ band structures 39 2.5.3 More on the Γ-X band structures 43 Chapter 3 Design of a One-port Resonator 65 3.1 Design parameters of a one-port resonator 65 3.2 Reflection on the PC border 66 3.3 Optimization for the delay distance 68 3.4 Resonator evaluation 69 3.5 Experiment setup 70 Chapter 4 Fabrications 83 4.1 Brief of EB lithography 83 4.1.1 Why EB lithography 84 4.1.2 Anti-charging 84 4.1.3 Dose determination and the proximity effect 84 4.2 Making the alignment marks for EB lithography 86 4.2.1 Background 86 4.2.2 Process and parameters 87 4.3 Fabrication of the aluminum IDT 90 4.4 Fabrication of the aluminum wire 90 4.4.1 Background 90 4.4.2 Process and parameters 92 4.5 Deposition of SiO2 film 93 4.6 Revealing of the contact pad 94 4.7 Fabrication of the PC structure 96 Chapter 5 Experiment Results 131 5.1 Transmission of PCs 131 5.1.1 SFIT without PC —verification of SFIT designs 131 5.1.2 SFIT with PC 133 5.2 One-port resonator 133 Chapter 6 Conclusions and Future Works 150 6.1 Conclusions 150 6.2 Future works 151 Appendix Determination of the Elastic Stiffness of the PECVD SiO2 152 REFERENCE 16