表面聲波元件之條紋陣列的反射與透射

Abstract

本研究分析層狀結構表面聲波受到表面金屬條紋陣列之反射與透射波傳，討論不同條紋陣列及各項設計參數對於表面聲波傳遞特性的影響。本文以Stroh的推導方式建立八階壓電波動方程式，計算Al/ZnO/Glass層狀介質表面聲波相速度頻散曲線。條紋陣列的反射與透射波傳分析係利用位移應力狀態向量與水平方向波傳傳遞矩陣，搭配條紋金屬柵極的邊界連續條件進行推導。模擬分析結果顯示，當表面聲波斜向入射條紋陣列時，若條紋寬度與間距等距，反射波傳的建設性干涉發生在條紋寬與波長比值為0.25的奇數倍處。條紋寬度與間距不等時，反射波傳的建設性干涉趨向條紋寬與波長比值為0.5的奇數倍處。條紋數量增加將使得反射率的極值頻率集中，條紋高度提昇卻使得極值頻率的頻寬增加，兩者都會加強反射波傳的建設性干涉。本文將可作為表面聲波濾波器設計的參考，提昇設計的精準度。

This thesis presents a study of the propagation of surface acoustic waves in a single and periodic array of metal strip overlays on the surface of layered substrates. Responses of reflected and transmitted surface acoustic waves due to various geometric design parameters of the grating arrays are investigated. An eight-dimensional matrix formulation based on Stroh formalism is adopted to analyze wave propagation in piezoelectric layered media. The dispersion curves for aluminum-zinc oxide films on glass substrates are determined using surface impedance tensor method. A transfer matrix in terms of the state vectors in cooperation with continuity conditions on edges of the grating array is used to determine the reflectivity and transmittance of the horizontally propagating surface acoustic waves. Simulation results indicate that constructive interferences occur in reflectivity at one quarter of an odd number times the ratio of strip width to wavelength perpendicular to the gratings in case that surface acoustic waves obliquely impinge on an array of gratings for the strip width equal to the gap between strips. The constructive interferences move to one half of an odd number times the ratio of strip width to the wavelength in case of the strip width unequal to the gap. The bandwidth of extreme reflectivity becomes broader if the number of gratings decreases or the height of the strip increases. Both cases enhanced the constructive interference in reflectivity spectra. The present method provides an accurate model for design of surface acoustic wave filters.