矽晶圓的板波波傳與雷射超音波非破壞評估

Abstract

立方晶體材料屬異向性結構，板波特性與波傳的方向有關。本研究將探討矽晶圓之點、線聚焦雷射超音波的生成機制，以一階剪變形板理論推導撓性波與延性波之格林函數及其導函數，以力矩張量模擬矽晶圓受脈衝雷射加熱產生的熱膨脹應變體波源及替代理論模擬雷射超音波之波傳。應用相位頻譜法與小波轉換分析，分析板波訊號的相速度與群速度，檢驗雷射生成超音波的暫態響應解的正確性，並探討點聚焦時近距、遠距板波訊號與線聚焦時近場、遠場板波訊號對速度分析的影響。 根據板波群速度量測值以簡單體法反算矽晶圓的材料性質，並探討相速度與群速度偏角的關係。反算問題的目標函數特性甚為重要，本文引用延伸性拉格蘭吉乘子改進簡單體法，加入剪變形修正係數之限制條件以縮小尋優範圍，減少找到局部最小值造成誤差的機會，並觀察此方法對反算結果的影響及受限制條件約束之參數的收斂情形。

This thesis studies the mechanism of point-focused and line-focused laser-generated ultrasound in a silicon wafer to establish theoretical background for laser-based ultrasonic nondestructive evaluation technology. The Lamb wave propagation in a cubic crystal plate has properties of anisotropy and dispersion. The thermal strain suddenly heated by the pulsed laser is a volume source to generate ultrasound and was modeled as a moment tensor. Transient response of the plate waves is a convolution of the moment tensor and its corresponding spatial derivatives of the Green’s functions, which was derived by the first order shear deformation plate theory. Using the phase-spectrum and wavelet-transform method to analyze phase velocity and group velocity of plate waves to verify the accuracy of transient response of the plate waves and discuss with the influence of the near field and the far field on plate wave velocity analysis.