表面聲波量測層狀介質材料常數之研究

Abstract

本文主要探討雷射超音波技術量測層狀介質表面聲波相速度與薄膜鍍層材料常數的反算。以Stroh理論推導為基礎，數值計算層狀介質表面聲波的相速度頻散曲線。實驗試片採用微機電製程技術製作含壓電材料之層狀試片，以交指叉電極產生窄頻之表面聲波，並建立一套共焦式法布里派洛光干涉儀，量測介質表面粒子因表面聲波傳遞引致的都卜勒頻移訊號，應用相位頻譜法計算表面聲波的相速度。不論層狀介質為等向性或非等向性材料，表面聲波的波速與材料性質、波傳方向及頻率相關。本文採用準牛頓法則與簡單體法兩種最佳化搜尋法則，以延伸拉格蘭吉乘子取代材料常數反算的等式或不等式限制條件。並利用多起始點方式求得滿足最小平方誤差之層狀介質材料常數，可供反算程序的可靠度評估。

This thesis studies determination of material constants in a thin film deposited on a half space through the measurement of phase velocities of surface acoustic waves propagating in layered media using laser-based ultrasonic technique. Based on the Stroh formulation, the phase velocity dispersion equation of surface acoustic waves is derived and numerically calculated. The experimental specimens made of a thin film sputtered on a substrate or a layer of piezoelectric material are fabricated by micro-electro- mechanical system (MEMS) process. The inter-digital transducer (IDT) deposited on the surface of specimen is used to launch narrow-band surface acoustic waves. A system of confocal Fabry-P□rot interferometer was developed during this research and used to measure the Doppler frequency shifts due to surface particle oscillations during surface acoustic wave propagation. The phase spectrum method is used to calculate phase velocities of the surface acoustic waves, which depend on the material properties of the thin film and substrate, frequencies and directions of wave propagation. The quasi-Newton method with and/or without constraints and simplex method are employed to search the minimum values of sum of the squared roots of errors. The augmented Lagrange multipliers are introduced to replace the equality and inequality constraints on material properties in inversion scheme. A process of multiple initial guess selected by random number is adopted for reliability assessment.