Precision Manufacturing and Inspection of Optical Components Chap. 13.7~13.9 Speaker: Ching-Yao Huang(黃靖堯) Advisor: Prof. Yi-Pai Huang(黃乙白教授) Prof. Chung-Hao Tien(田仲豪教授) Institute of Electro-Optical Engineering, National Chiao Tung University, Hsinchu, Taiwan Jul. 7 2008

Outline Residual Stress - Cantilever Method Thin Film Stress and CET - X-ray diffraction method - Cantilever Method - Newton’s Ring Method Thin Film Stress and CET - Introduction - Measurement Method Analysis of Ingredients Conclusions

Introduction of Thin Film Stress Thin film stress is composed by External stress Thermal stress Intrinsic stress Tensile Compressive

Principle Balance condition: E:Young’s modulus Stoney’s equation dθ/2

X-ray Diffraction Method This method can get the stress or strain by the change of the interplanar spacing. 2d sin θ = λ λ: the wave length of x-ray θ: the Bragg’s angle If do is the original interplanar spacing. Ef: the Young’s modulus of thin film vf: the Poisson’s ratio of thin film It can not use for amorphous thin film.

Cantilever Method L Fixed point θ θ: deflection Cantilever v: Poisson’s ratio of substrate Es: Young’s modulus of substrate ts: Thickness of substrate tf: Thickness of thin film

Newton’s Ring Method Dn Dm R: the radius of curvature of substrate

Outline Residual Stress - Cantilever Method Thin Film Stress and CET. - X-ray diffraction method - Cantilever Method - Newton’s Ring Method Thin Film Stress and CET. - Introduction - Measurement Method Analysis of Ingredients Conclusions

Coefficient of Thermal Expansion Definition: Δl:The change of length from T1 to T2 : the strain of thin film(or substrate) w: the width of substrate : the thickness of thin film(or substrate) : the force of thin film(or substrate) receiving Boundary condition =

Methods Residual stress measurement method Laser lever method Measure the arcuation change of substrate Measure the change of interplanar spacing Measure under different temperature Bending-beam method Disk method X-ray diffraction

Methods Interference phase shifting Five interference pictures (each π/2 difference) Substitute to Hariharan PSI Zernike polynomial fitting

Outline Residual Stress - Cantilever Method Thin Film Stress and CET. - X-ray diffraction method - Cantilever Method - Newton’s Ring Method Thin Film Stress and CET. - Introduction - Measurement Method Analysis of Ingredients Conclusions

Energy Dispersive spectrometer(EDS) Principle: Measurement modes: Area-scan: the concentration of the elements diagram of the analyzed area. Line-scan: the change of concentration along the line. Point calculation: the element and the number of it. n: the pairs of electron-hole E:the energy of incident x-ray

X-ray photoelectron spectroscope(XPS) Sample :the kinetic energy of photoelectron :the binding energy :the working function The element can be determined by the kinetic energy of the photoelectron.

Outline Residual Stress - Cantilever Method Thin Film Stress and CET. - X-ray diffraction method - Cantilever Method - Newton’s Ring Method Thin Film Stress and CET. - Introduction - Measurement Method Analysis of Ingredients Conclusions

Conclusions The residual stress is the important issue that should be concerned. Which method you use to measure the stress depends on the material of thin film and substrate.

Thanks for your kind attention

Newton’s ring The phenomenon of Newton's rings, named after Isaac Newton, is an interference pattern caused by the reflection of light between two surfaces - a spherical surface and an adjacent flat surface. Newton's bright ring is given by

撓度：橫截面形心在垂直於梁軸線方向的位移稱為撓度。 應變：在力學中定義為一微小材料元素承受應力時所產生的單位長 度變形量。 材 料 若 只 有 x 方 向 受 拉 力， 則 除 了 x 方 向 會 伸 長 外， 其 餘 二 方 向 亦 會 隨 之 變 形 (縮短)。 而 y、 z 方 向 應 變 與 x 方向 應 變 的 比 值 即 為 Poisson's ratio

PSI(phase shift interferometry) 用五步相位還原法，假設相位移動量的大小為α，五張干涉圖中每一像素 點的數位化強度分別為：

Zernike 多項式是為了表示單位圓上的波面像差而發展出的集合，而且這 種多項式符合下列兩個性質： （1）Zernike 多項式是一完全集合：其意義為任何函數（或波前）k 階 之w(r,q )可以用Zernike 多項式的線性組合來表示，如下式： 其中w(r,q )必須是實數，且R 為r 的函數，也必須是實數，而Cnl 可能為實數或虛數，其亦滿足：

（2）此多項式在單位圓內（即波前邊界內）有正交的特性： 其中，各項Zernike 多項式，其數學形式和像差有相關連，我們使用 Zernike 多項式來做波前擬合，所獲得的係數，正好就代表此待測波波前 所包含的像差的大小。

Five interference pictures(each π/2 difference) Substitute to Hariharan PSI(Check if 90°) No Yes Zernike polynomial fitting