具殘留應力薄膜結構的熱彈聲波波傳

Abstract

光聲效應主要應用於量測材料的光學、熱物理性質與微結構的次表面性質。本文根據徹體波的聲彈理論，推導層狀介質殘留應力的熱彈聲波理論，模擬薄膜材料的光聲效應。薄膜材料廣泛應用於半導體與光電元件，當薄膜材料的晶格大小與基材不一致，甚或兩者熱膨脹係數相異時，在薄膜上會產生殘留應力。本文推導高斯分佈之強度調制雷射光束照射薄膜結構表面，模擬單晶立方材料承受單軸與雙軸面內殘留應力的光聲效應變化。以數值分析塊材的徹體波與熱波之相速度與振幅衰減，兩者的變化均與殘留應力大小呈線性關係。薄膜結構的熱彈性波頻散分析遭遇數值不穩定問題，故以定性方式探討熱彈性藍姆波頻散方程之波數複數根的變化。

Photoacoustic effect is used to measure optical, thermal physical properties of materials and to characterize the subsurface properties of microstructures. This thesis presents a formulation for thermal acoustic wave propagation in stressed layered media based on the acoustoelasticity for bulk acoustic waves in order to simulate photoacoustic effect of thin-film materials. Thin-film materials are broadly used in many applications of semiconductor and electro-optic devices. Due to misfit between different lattices or distinction of coefficients of thermal expansion of the heterostructures, residual stresses are frequently induced in thin film structures during fabrication. The stressed thin-film structure is insonified by an intensity modulated laser which is modeled as a Gaussian beam. The photoacoustic effects for single crystalline cubic thin-films under in-plane, uniaxial and biaxial stresses are investigated numerically. The azimuthal dependent phase velocities and attenuation factors for bulk acoustic waves and thermal waves are calculated. Variations of both are proportional to the residual stress values. Unfortunately, numerical instability occurred in solving the dispersion of thermal acoustic waves in thin-film structures. Instead, the complex-value roots of the dispersion equation for thermal acoustic Lamb waves were qualitatively discussed.