高Q声子晶体声波传感机理及实验研究
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摘要
本论文结合新型人工声学材料声子晶体对声波传播独特的调制作用以及声子晶体的点缺陷态特性，对声子晶体用于声波传感来实现高品质因数（Q值）进行了理论和实验研究。其中利用平面波展开法研究了平板声子晶体的复能带结构和声子晶体对材料各向异性的调节作用；用有限元方法对平板声子晶体禁带和点缺陷模式、Lamb波A0模式的慢声效应进行了分析；同时利用激光测振技术对点缺陷模式的振型进行了验证以及对点缺陷模式的用于声波传感的性能进行了研究。主要研究内容包括：
1.利用平面波展开法计算了平板声子晶体的复能带结构，理论上给出了平板声子晶体不同点缺陷模式的消逝场深度不同的原因，是由于各个缺陷模式对应的波数的虚数部分是不同造成的，该计算结果为进一步研究点缺陷模式的支撑损失对点缺陷Q值的影响提供了理论依据；
2.制作出了含有点缺陷的硅基平板声子晶体样品，分析了单晶硅的各向异性对声子禁带的影响；对点缺陷模式进行了验证；获得了点缺陷模式Q值在空气中高于16000，而在低压下（o500Pa）可以达到49800；对点缺陷的Q的影响因素进行了理论和实验分析，结果表明：对该样品，在常压下，空气粘性损耗占主导作用，在低压（o500Pa）下，模式有效表面积与体积比对Q值的影响起主导作用；初步对硅基平板声子晶体点缺陷模式的质量灵敏度进行了测试，质量灵敏度约为9.1Hz/ng,质量分辨率约为0.71ng；结果为点缺陷模式应用于声波传感来提高Q值的进一步设计和研究提供了理论和实验上指导；
3.利用平面波展开法研究了声子晶体结构对声波在单晶硅等各向异性材料中传播的调节作用，结果表明：将声子晶体引入到各向异性材料中，可以有效的将该复合材料调节为各向同性或者是更强的各向异性。将材料调节为各向同性，理论上对声波传感器的阵列化设计，避免单元间的耦合，减小材料晶向位置对声子晶体禁带的影响，避免在器件制作过程中过多考虑材料晶向问题提供了一种手段；另外，通过增强材料的各向异性，可以明显提高声波定向发射的效率，这在声波定向发射技术的应用上具有重要意义。
4.研究了一维平板声子晶体中Lamb波A0模式的慢声效应，结果表明，通过引入声子晶体结构，可以实现(a)降低Lamb波A0模式的群速度，(b)A0模式群速度为0，(c) A0模式群速度方向与相速度方向相反；(d)理论上证明了0群速度可以获得窄带响应特性，理论上为提高Lamb器件Q值提供了一种方法。
本论文的研究结果对声子晶体这种新型人工声学材料用于声波传感具有重要的理论意义和工程价值。
In this thesis，due to the low resolution of the acoustic wave sensors, the phononiccrystals have been investigated theoretically and experimentally to improve thequality factor of acoustic wave sensors based on the unique modification of the elasticwaves and the properties of the point defect states. The plane wave expansion methodand the finite element method were used to calculate the complex band structures ofthe phononic crystal plates, the band gaps and the point defect modes of the siliconphononic crystal plates and the slow wave mode of the Lamb wave in the phononiccrystal plates. Then the vibration pattern, the Q factor and the mass sensitivity of thepoint defect modes were investigated by using the heterodyne laser interferometer.
1. The complex band structures of the perfect phononic crystal plates wereobtained by applying supercell plane wave expansion method. The calculationresults can provide decay factors of the elastic waves with frequencies in theband gap as propagating in the phononic crystal plates.
2. The characters of the point defect modes in silicon PC plate were investigated.Firstly, the micro fabrication processes of the point defect PC plate wereproposed. Secondly, the vibration patterns of point defect modes weretheoretically and experimentally identified. Finally, the Q factor and the masssensitivity of the point defect modes were investigated.
3. The anisotropy of mixed modes in phononic crystals with square lattice epoxycylinders embedded in single crystalline silicon were theoretically investigatedby using the PWE method in the long wavelength limit. It is found that: by changing the filling fraction and the crystalline orientation of the material, a) theanisotropy of effective velocities can be tuned in a large range; it can evenapproach to isotropy for the given filling fraction and the crystalline orientation;b) the polarization vector and the energy flow vector (or the deviation angle andthe power flow angle) can be changed; c) the pure vibration mode direction andthe pure propagation mode direction can be tuned to deviate simultaneouslyfrom the symmetric direction of the PC lattice and the material.
4. The group velocity of the zero order Lamb modes (A0) of the phononic crystalplate with single layer cylindrical holes parallel to the surface of the plate wereinvestigated theoretically. It is shown that, by increasing the radius or the fillingfractions,(a) the A0mode can be efficiently slowed,(b) the group velocity ofthe A0mode can be changed from the positive to the negative and (c) the zerogroup velocity of the A0mode can be obtained. This zero group velocity of theA0mode can benefit to obtain the high Q factor frequency response.The results can provide valuable methods for the phononic crystals applied in theacoustic sensing for improving the performance of the acoustic wave sensing.
1.利用平面波展开法计算了平板声子晶体的复能带结构，理论上给出了平板声子晶体不同点缺陷模式的消逝场深度不同的原因，是由于各个缺陷模式对应的波数的虚数部分是不同造成的，该计算结果为进一步研究点缺陷模式的支撑损失对点缺陷Q值的影响提供了理论依据；
2.制作出了含有点缺陷的硅基平板声子晶体样品，分析了单晶硅的各向异性对声子禁带的影响；对点缺陷模式进行了验证；获得了点缺陷模式Q值在空气中高于16000，而在低压下（o500Pa）可以达到49800；对点缺陷的Q的影响因素进行了理论和实验分析，结果表明：对该样品，在常压下，空气粘性损耗占主导作用，在低压（o500Pa）下，模式有效表面积与体积比对Q值的影响起主导作用；初步对硅基平板声子晶体点缺陷模式的质量灵敏度进行了测试，质量灵敏度约为9.1Hz/ng,质量分辨率约为0.71ng；结果为点缺陷模式应用于声波传感来提高Q值的进一步设计和研究提供了理论和实验上指导；
3.利用平面波展开法研究了声子晶体结构对声波在单晶硅等各向异性材料中传播的调节作用，结果表明：将声子晶体引入到各向异性材料中，可以有效的将该复合材料调节为各向同性或者是更强的各向异性。将材料调节为各向同性，理论上对声波传感器的阵列化设计，避免单元间的耦合，减小材料晶向位置对声子晶体禁带的影响，避免在器件制作过程中过多考虑材料晶向问题提供了一种手段；另外，通过增强材料的各向异性，可以明显提高声波定向发射的效率，这在声波定向发射技术的应用上具有重要意义。
4.研究了一维平板声子晶体中Lamb波A0模式的慢声效应，结果表明，通过引入声子晶体结构，可以实现(a)降低Lamb波A0模式的群速度，(b)A0模式群速度为0，(c) A0模式群速度方向与相速度方向相反；(d)理论上证明了0群速度可以获得窄带响应特性，理论上为提高Lamb器件Q值提供了一种方法。
本论文的研究结果对声子晶体这种新型人工声学材料用于声波传感具有重要的理论意义和工程价值。
In this thesis，due to the low resolution of the acoustic wave sensors, the phononiccrystals have been investigated theoretically and experimentally to improve thequality factor of acoustic wave sensors based on the unique modification of the elasticwaves and the properties of the point defect states. The plane wave expansion methodand the finite element method were used to calculate the complex band structures ofthe phononic crystal plates, the band gaps and the point defect modes of the siliconphononic crystal plates and the slow wave mode of the Lamb wave in the phononiccrystal plates. Then the vibration pattern, the Q factor and the mass sensitivity of thepoint defect modes were investigated by using the heterodyne laser interferometer.
1. The complex band structures of the perfect phononic crystal plates wereobtained by applying supercell plane wave expansion method. The calculationresults can provide decay factors of the elastic waves with frequencies in theband gap as propagating in the phononic crystal plates.
2. The characters of the point defect modes in silicon PC plate were investigated.Firstly, the micro fabrication processes of the point defect PC plate wereproposed. Secondly, the vibration patterns of point defect modes weretheoretically and experimentally identified. Finally, the Q factor and the masssensitivity of the point defect modes were investigated.
3. The anisotropy of mixed modes in phononic crystals with square lattice epoxycylinders embedded in single crystalline silicon were theoretically investigatedby using the PWE method in the long wavelength limit. It is found that: by changing the filling fraction and the crystalline orientation of the material, a) theanisotropy of effective velocities can be tuned in a large range; it can evenapproach to isotropy for the given filling fraction and the crystalline orientation;b) the polarization vector and the energy flow vector (or the deviation angle andthe power flow angle) can be changed; c) the pure vibration mode direction andthe pure propagation mode direction can be tuned to deviate simultaneouslyfrom the symmetric direction of the PC lattice and the material.
4. The group velocity of the zero order Lamb modes (A0) of the phononic crystalplate with single layer cylindrical holes parallel to the surface of the plate wereinvestigated theoretically. It is shown that, by increasing the radius or the fillingfractions,(a) the A0mode can be efficiently slowed,(b) the group velocity ofthe A0mode can be changed from the positive to the negative and (c) the zerogroup velocity of the A0mode can be obtained. This zero group velocity of theA0mode can benefit to obtain the high Q factor frequency response.The results can provide valuable methods for the phononic crystals applied in theacoustic sensing for improving the performance of the acoustic wave sensing.
引文
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