臺灣博碩士論文加值系統

聲子晶體是由數種彈性材料週期性排列而成，當聲波在聲子晶體結構中傳遞時，由於波傳之頻散曲線不連續，造成該不連續的頻段內，聲波無法傳遞，此現象稱之為聲波頻溝(acoustic band gap)。若在此頻段內聲波不論沿任何方向均無法傳遞，則稱之為全頻溝(complete band gap)。在頻溝範圍內，若將無窮週期的聲子晶體結構移除一或數排，形成之線缺陷可做為聲子晶體波導(phononic-crystal waveguide)，則原本在頻溝內無法形成模態的頻率，將會在此缺陷結構中形成可傳遞的缺陷模態(defect mode)，藉此可引導聲波在該波導中傳遞。
本文將以平面波展開法(Plane Wave Expansion Method)為基礎，探討二維矽基聲子晶體平板之頻溝現象。因矽基材為半導體常用的材料，可與現行的半導體製程整合，提升其實際應用範圍；但由於矽基材並非壓電材料，板波無法以電性方式直接在矽基材上激發。本文提供了一種新的耦合方法，利用橋接方式，將矽基材與壓電材料鋰酸鈮(128°YX-LiNbO3)結合，藉由交指叉電極(Interdigital Transducer)於鋰酸鈮表面以壓電效應激發出板波。一般而言，交指叉電極主要為在壓電基材上激發高頻表面波(Surface Acoustic Wave)，其波長相當於交指叉狀電極之週期，若考慮其波長與壓電基材厚度相當，則此交指叉電極將可激發出板波。
利用橋接的結構，本文針對聲子晶體平板的頻溝效應與波導效率進行實驗驗證與探討，其實驗結果與理論計算結果相符，驗證聲子晶體平板之頻溝效應。此效應可更進一步的將其應用於波導結構中，將聲波控制在所設計的路徑中傳遞。

During the past decades, there has been a great interest in phononic crystals that are composite elastic materials distributed periodically. The most interesting character of phononic crystals is the band-gap phenomenon, prohibiting acoustic waves traveling through in a specific frequency range. To predict the band-gap width of phononic-crystal plate, the plane wave expansion (PWE) is applied to predict the dispersion relation of two-dimensional air/silicon phononic crystal plate.
By increasing the wavelength of the interdigital transducer (IDT) to the order that is comparable with the plate thickness, the surface acoustic wave (SAW) could be viewed as a Lamb wave. Since silicon is not the piezoelectric material, another piezoelectric material LiNbO3 is used. The calculated Lamb wave mode frequency of LiNbO3 shows good agreement with experimental results.
Air/silicon as phononic crystal plate and LiNbO3 as a Lamb wave generator are coupled together. The band gap of phononic crystal plate and the waveguide phenomenon along Γ-X direction is measured by this measuring setup.

致謝………………………………………………………………………………………I
摘要…………………………………………………………………..………………….II
Abstract………………………………………………………………...……………III
Contents……….…………………………………………….…………………………IV
List of Notations……………………………………………..………………………VI
List of Figures……………………………………………….………………………IX
List of Tables………………………………………………..………………………XII

Chapter 1 Introduction………………………………………………………………1
1-1 Research Motivation………………………………………………...…………1
1-2 Literature Review………………………………………………………………4
1-3 Contents of the Chapters…………………………………………………….…5
Chapter 2 Dispersion of Lamb Waves in Two-dimensioanl Air/Silicon Phononic-Crystal Plate………………………………………………….9
2-1 Plane Wave Expansion Method………………………………………..……….9
2-1.1 Equation of Motion……………………………………………………….10
2-1.2 Mass Density and Elastic Constants……………………………………..11
2-1.3 Displacement Vector……………………………………………………...12
2-1.4 Lamb waves in Two-Dimensional Phononic Crystals. …………………..13
2-2 Band Gaps and Dispersion Relations of Lamb Waves in the Air/Silicon Phononic-Crystal Plate………………………………………………………16
2-3 Experimental Design ………………………………………...……………….19
2-3.1 Design of the Phononic-Crystal Plate for Band-Gap Verification………19
2-3.2 Design of the IDTs on the LiNbO3 Substrate for Generation and Detection of Lamb Waves………………………………………………………..….21
2-3.3 Design of Phononic-Crystal Waveguide………………………………….22
Chapter 3 Fabrications of the Phononic Plate Wave Measuring System……..…33
3-1 Fabrication of Interdigital Transducer……………………………………...…33
3-2 Fabrication of Phononic-Crystal Structure…………………………...……….37
3-2.1 Manufacturing Process of the Phononic-Crystal Plate………………….37
3-3.2 Manufacturing Process of the Phononic-Crystal Waveguide…………….40
3-3 Coupled Measurement Frame………………………………………………...40
Chapter 4 Experimental Results of Lamb-Wave Band Gap and Phononic-Crystal Waveguide………………………………………………………..…….50
4-1 Time Gating Approach……………………………………………………….50
4-2 Band Gap Measurement……………………………………………………...53
4-3 Waveguide Measurement…………………………………………………….57
Chapter 5 Conclusions and Future Work……………………………………..…71
5-1 Conclusions…………………………………………………………………...71
5-2 Future Work………………………………………………………………….72

Appendix……………………………………………………………………………….74
References……………………………………………………………………………...77

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