Abstract Compared with the other micro acoustic wave devices, the flexural plate-wave (FPW) device is more suitable for being used in liquid-sensing applications due to its higher mass sensitivity, lower phase velocity and lower operation frequency. However, conventional FPW devices usually present a high insertion loss and low fabrication yield. To reduce the insertion loss and enhance the fabrication yield of FPW device, a 1.5 £gm-thick silicon-trench reflective grating structure (RGS), a high electromechanical coupling coefficient ZnO thin-film and a 5 £gm-thick silicon oxide membrane substrate are adopted in this research. The influences of the amount of silicon trench and the distance between inter-digital transducer (IDT) and RGS on the insertion loss and quality factor of FPW device are investigated. The main fabrication technology adopted in the study is bulk micromachining technology and the main fabrication steps include six thin-film deposition and five photolithography processes. Under the optimized conditions of the sputtering deposition processes (200¢J substrate temperature, 200 W radio-frequency power and 75% gas flow ratio), a high C-axis (002) orientation ZnO piezoelectric thin-film with 31.33% electromechanical coupling coefficient can be demonstrated. The peak of XRD intensity of the standard ZnO film occurs at diffraction angle 2£c = 34.422¢X, which matches well with our results (2£c = 34.282¢X). By controlling the thickness of ZnO/Au/Cr/SiO2/Si3N4 sensing membrane less than 6.5 £gm-thick, the fabrication yield of FPW device can be improved and a low operation frequency (6.286 MHz) and high mass sensitivity (-113.63 cm2 / g) can be achieved. In addition, as the implemented FPW device with four silicon trenches RGS and 37.5 £gm distance between IDT and RGS, a low insertion loss (-40.854 dB) and very high quality factor (Q=206) can be obtained. Keywords¡Gflexural plate-wave; silicon-trench reflective grating structure; electromechanical coupling coefficient; ZnO; bulk micromachining technology

This dissertation includes the study of effective medium theories (EMTs) and their applications in describing wave propagation in anisotropic metamaterials, which can guide the design of metamaterials. An EMT based on field averaging is proposed to describe a peculiar anisotropic dispersion relation that is linear along the symmetry line but quadratic in the perpendicular direction. This dispersion relation is associated with the topological transition of the iso-frequency contours (IFCs), suggesting interesting wave propagation behaviors from beam shaping to beam splitting. In the framework of coherent potential approximation, an analytical EMT is further developed, with the ability to build a direct connection between the microscopic structure and the macroscopic material properties, which overcomes the requirement of prior knowledge of the field distributions. The derived EMT is valid beyond the long-wavelength limit. Using the EMT, an anisotropic zero-index metamaterial is designed. Moreover, the derived EMT imposes a condition that no scattered wave is generated in the ambient medium, which suggests the input signal cannot detect any object that might exist, making it invisible. Such correspondence between the EMT and the invisibilityinspires us to explore the wave cloaking in the same framework of coherent potential approximation. To further broaden the application realm of EMT, an EMT using the parameter retrieval method is studied in the regimes where the previously-developed EMTs are no longer accurate. Based on this study, in conjunction with the EMT mentioned above, a general scheme to realize coherent perfect absorption (CPA) in anisotropic metamaterials is proposed. As an exciting area in metamaterials, the field of metasurfaces has drawn great attention recently. As an easily attainable device, a grating may be the simplest version of metasurfaces. Here, an analytical EMT for gratings made of cylinders is developed by using the multiple scattering theory (MST) method and the lattice sum. Validation of the theory is verified by the agreement between the EMT predictions and the numerical calculations. It is found the EMT is capable of accurately predicting the wave transport behaviors, even for frequencies where the Mie resonances happen.