| Summary: | 博士 === 國立臺灣大學 === 機械工程學研究所 === 92 === This work presents a novel method based on the plate wave sensor for in-situ monitoring of the thickness of a wafer during wet etching. Some acoustic wave devices require that the thickness of a wafer be known precisely. Precisely controlling the thickness of a wafer during wet etching is important, because it strongly influences post-processing, frequency control and device performance. In the theoretical simulation, a formulation based on the eight-dimensional matrix method was used for calculating the dispersion relations for a general piezoelectric layered medium. Additionally this study described the principles of the method, including the detailed process flows, measurement set-up and the simulation and experimental results. The experimental and theoretical values correlate well with each other.
In the plate wave sensor based on a quartz substrate, the eight-dimensional matrix formalism was employed for propagating surface waves in piezoelectric plate loaded with viscous liquid. This formulation derives the dispersion equation of surface waves in such a structure from continuity conditions at the solid-liquid interface. The size of the matrix in the computation is independent of the number of layers. The formulation based on the surface impedance tensor method was used to calculate the dispersion curve of the viscous liquid loaded an AT-cut quartz substrate. The simulation results, which are phase velocity with respect to the thickness of a quartz substrate. The theoretical and measured values differ by an error of less than 2�慆.
Similarly, in the plate wave sensor based on a silicon substrate, the eight-dimensional matrix formalism was also employed for propagating surface waves in piezoelectric film based on a multi-layered structure, and this formulation derives the dispersion equation of surface waves in such a structure based on continuity conditions at the solid-liquid interface. The size of the matrix in the computation is independent of the number of layers. This characteristic is helpful in analyzing wave behavior in a multi-layered structure. The proposed plate wave sensor allows the thickness of a silicon membrane, from a few μm to hundreds of μm, to be monitored, depending on the periodicity of the interdigital transducer (IDT). In case one, the attenuation of surface acoustic wave has little effect on the determination of silicon membrane thickness if the membrane thickness is greater than 75�慆. The attenuation increases with decreasing thickness of silicon. In this design, the wavelength of the IDT is 80�慆, and the attenuation become large over 50db when the thickness of a silicon is below 50�慆, preventing any experimental data of this area from being obtained. The theoretical and measured values differ by an error of less than 3�慆. Similarly, in case two, the wavelength of the IDT is 40�慆, the attenuation becomes significant over 50db when the thickness of a silicon is less than 20�慆, and consequently the proposed plate wave sensor allows the thickness of a silicon membrane, from 20μm to 40μm can be monitored. The theoretical and measured values differ by an error of less than 1.5�慆.
Additional, the proposed method can be applied to an acoustic wave device fabricated using the same process. If the acoustic wave device is fabricated by a different process, the plate wave sensor as the testing chip by soaking the etchant solution in the same time. The measured values differ by an error of less than few �慆 because of the two devices not being integrated on the same wafer. By repeating numerous experiments, the error can be compensated to achieve in-situ monitoring of the thickness of a wafer during wet etching.
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