201221926 六、發明說明： 【發明所屬之技術領威】 [0001] 本發明係有關於一種量測方法，特別是指一種薄膜 殘留應力之量測方法。 【先前技彳舒】 隨著光電科技研究與相關產業蓬勃發展，光學薄膜 的應用也隨之重要，然而在光學鍍膜製鍍的過程中，會 有殘餘應力的產生並造成薄膜變形彎曲與缺陷，而直接 影響薄膜的良率、可罪性和穩.定性，要如何製鍵一個高 性志、尚品質、低:鼻力的薄..膜便是個狼重:要的課題。 薄膜殘留應力通常簡單分為張應力和壓應力兩類。 若薄膜在成長的過程中愈長愈疏鬆，，或是薄膜相對於基 板收縮時，會引起表面張力，為維持力學乎衡，當膜受 到約束而拉伸時，基板就相對地收縮，寒薄膜内所產生 的伸張力會被基板的壓縮力所平衡；然而端點力矩未完 全補償，使得膜基板系統並非處在平衡狀態，以彈性彎 曲方式抵消未平衡力矩，於是膜内殘留的張應力，使基 板或膜面向内側彎曲或形成凹面1反之，若薄膜愈長愈 緻密，或膜相對於基板膨脹，膜内會形成壓應力，使得 基板或膜面向外凸。 薄膜殘留應力除了影響薄膜之附著力以及使基板產 生形變，甚至引起薄膜龜裂或翹曲之外，在光學方面， 薄膜殘留應力會使光學窄帶濾光片產生波長飄移；在半 導體製程方面，薄膜殘留應力會影響半導體元件之電導 率。因此薄膜殘留應力之量測技術能作為研究薄膜製程 參數的重要參考依據，以確保優質的薄膜元件得以生產 099139280 表單編號A0101 第3頁/共24頁 0992068482-0 201221926 。光學元件研發上，為要求元件有良好的光學性質表現 ’製程上往往需要鍍膜，光學元件透過薄膜殘留應力的 檢測可作為品質上的控管。 傳統的薄膜殘留應力量測方法包括懸臂樑法、干涉 法、雷射光束掃瞄法及X射線繞射法（XRD)等。 懸臂樑法是將，一基板的一端固定，另一端懸空， 形成機械式懸臂樑。量測原理為將雷射光打在自由端上 的一點，並在鍍膜後再以相同方法量測一次，得到反射 光的偏移量，進而求得薄膜的殘留應力。 牛頓環法是利用基板在鍍膜後，薄膜產生的彎曲面 與一參考平面，產生干涉條紋的牛頓環，利用量測到的 牛頓環間距與條紋數，推算基板的曲率半徑，其中{<與 牛頓環直fe之平方差成正比，並與波長的4倍、牛頓環 條紋數的差成反比，將所求得的只代入牛頓環應力公式， 可求出薄膜殘留應力值。 + X光繞射法是利用布拉格繞射公式藉由X光求出 薄膜叩構中微晶間之距離變化來測定的、通常藉著薄膜 平面晶格常數而獲得薄膜殘留:贏力值。因為在應力作用 下日日格會發生畸變，從而使晶格常數發生變化，因此 測量晶格畸變可以計算出薄膜的應力。 。运些傳統的方法通常用於均向性薄膜殘留應力檢測 操作較為費工費時’也些測量精度也不夠高對於非 均向性薄膜之殘留應力則無法正確量測。因此本發明提 供-種薄膜殘留應力之量測方法，其方式簡單，益需繁 雜的量测步驟，即可測定薄膜平面之主應力方向，以測 定非均向或料㈣膜雙轴應力。 0992068482-0 〇"139280 表單編號侧 第4頁/共24頁 201221926 【發明内容】 [0003] 本發明之目的之一，在於提供一種薄膜殘留應力之 量測方法，其係操取一工件鑛一薄膜前與後之一第一干 涉圖與一第二干涉圖，並由第一干涉圖與第二干涉圖建 立工件之一第一表面輪廓與第二表面輪廓，以擬合複數 個第一曲率半徑與複數個第二曲率半徑，若是均向性薄 膜，則將第一曲率半徑與第二曲率半徑代入Stoney公式 計算出薄膜殘留應力值；若是非均向性薄膜，則由第二 表面輪廓扣除第一表面輪廓可得薄膜第三表面輪廓以擬 〇 合方法計算薄膜之複數個第三曲率半徑，以理論修正後 的Stoney公式計算該薄膜之複數個應力，並計算第三曲 率半徑最大梯度及求出主應力的方向。如此可以簡單的 方式，無需繁雜的量測步驟，即可測定均向及非均向薄 膜殘留應力。 本發明之薄膜殘留應力之量測方法，其包含下列步 驟，首先，擷取一工件之一第一干涉圖，以建立工件之 一第一表面輪廓，並且擬合第一表面輪廓之複數個第一 Ο 曲率半徑，之後再擷取最大梯度之第一曲率半徑；然後 ，擷取工件鍍一薄膜後之一第二干涉圖，以建立工件鍍 薄膜後之一第二表面輪廓，並且擬合第二表面輪廓之複 數個第二曲率半徑，之後再擷取最大梯度之第二曲率半 徑。若是均向性薄膜，則將第一曲率半徑與第二曲率半 徑代入Stoney公式計算出薄膜殘留應力值；接著依據第 二表面輪廓扣除第一表面輪廓可得薄膜第三表面輪廓， 經由擬合方法計算第三表面輪廓之複數個第三曲率半徑 ，然後再依據這些第三曲率半徑以修正後的Stoney公式 099139280 表單編號A0101 第5頁/共24頁 0992068482-0 201221926201221926 VI. Description of the Invention: [Technology Leading to the Invention] [0001] The present invention relates to a measuring method, and more particularly to a method for measuring residual stress of a film. [Previous technology] With the development of optoelectronic technology research and related industries, the application of optical film is also important. However, in the process of optical coating and plating, residual stress will occur and the film will be deformed, bent and defective. It directly affects the yield, sinfulness and stability of the film. How to make a high-sex, high-quality, low-nose: thin film. The film is a wolf: the subject. The residual stress of the film is usually simply divided into two types: tensile stress and compressive stress. If the film grows longer and looser, or when the film shrinks relative to the substrate, it will cause surface tension. To maintain the mechanical balance, when the film is restrained and stretched, the substrate shrinks relatively, and the film is cold. The tensile force generated inside is balanced by the compressive force of the substrate; however, the end point torque is not completely compensated, so that the membrane substrate system is not in equilibrium, the unbalanced moment is cancelled by elastic bending, and the residual tensile stress in the film, The substrate or film is curved inwardly to form a concave surface. Conversely, if the film becomes denser and denser, or the film expands relative to the substrate, compressive stress is formed in the film, so that the substrate or film faces outward. In addition to affecting the adhesion of the film and the deformation of the substrate, and even causing the film to crack or warp, in optical terms, the residual stress of the film causes wavelength shift of the optical narrow band filter; in the semiconductor process, the film Residual stress affects the electrical conductivity of the semiconductor component. Therefore, the measurement technique of residual film stress can be used as an important reference for studying the process parameters of thin films to ensure the production of high quality thin film components. 099139280 Form No. A0101 Page 3 of 24 0992068482-0 201221926 . In the development of optical components, it is required to have good optical properties of the components. In the process, coating is often required, and the detection of residual stress of the optical components through the film can be used as a quality control. Conventional methods for measuring residual film stress include cantilever beam method, interference method, laser beam scanning method and X-ray diffraction method (XRD). The cantilever beam method is to fix one end of a substrate and the other end to form a mechanical cantilever beam. The measuring principle is that the laser light is hit on the free end, and after the coating, the same method is used to measure the offset of the reflected light, and the residual stress of the film is obtained. Newton's ring method is to use the curved surface generated by the film after coating, and a reference plane to generate interference fringe Newton's ring. Using the measured Newton's ring spacing and the number of stripes, the radius of curvature of the substrate is estimated, where {< The squared difference of Newton's ring is proportional to the difference between the four times the wavelength and the number of Newton's ring fringes. The calculated residual stress value can be obtained by substituting only the Newton's ring stress formula. + X-ray diffraction method is determined by using the Bragg diffraction formula to determine the change in the distance between the crystallites in the film structure by X-ray, and the film residual is usually obtained by the plane lattice constant of the film: the win value. Since the lattice distortion occurs under stress and the lattice constant changes, the stress of the film can be calculated by measuring the lattice distortion. . These conventional methods are generally used for the inspection of the residual film residual stress, which is time-consuming and labor-intensive, and the measurement accuracy is not high enough. The residual stress of the non-uniform film cannot be measured correctly. Therefore, the present invention provides a method for measuring the residual stress of a film in a simple manner, which requires a complicated measurement step to determine the principal stress direction of the film plane to determine the biaxial stress of the non-uniform or material (four) film. 0992068482-0 〇"139280 Form No. Side Page 4 of 24 201221926 [Invention] [0003] One of the objects of the present invention is to provide a method for measuring the residual stress of a film, which is to operate a workpiece ore. a first interferogram and a second interferogram of the front and back of the film, and the first surface profile and the second surface profile of the workpiece are established by the first interferogram and the second interferogram to fit the plurality of first a radius of curvature and a plurality of second radii of curvature. If the film is an isotropic film, the first radius of curvature and the second radius of curvature are substituted into the Stoney formula to calculate the residual stress value of the film; if the film is non-uniform, the second surface profile is obtained. After deducting the first surface profile, the third surface profile of the film is calculated by a pseudo-combination method to calculate a plurality of third radii of curvature of the film, and the theoretically corrected Stoney formula is used to calculate the plurality of stresses of the film, and the maximum gradient of the third radius of curvature is calculated. And find the direction of the principal stress. In this way, the residual stress of the uniform and non-uniform film can be measured in a simple manner without complicated measurement steps. The method for measuring residual stress of a film of the present invention comprises the steps of: firstly, drawing a first interferogram of a workpiece to establish a first surface profile of the workpiece, and fitting a plurality of first surface contours a radius of curvature, and then a first radius of curvature of the maximum gradient; and then drawing a second interferogram of the workpiece after plating a film to establish a second surface profile of the workpiece after coating, and fitting A plurality of second radii of curvature of the two surface contours, followed by a second radius of curvature of the largest gradient. If it is an isotropic film, the first radius of curvature and the second radius of curvature are substituted into the Stoney formula to calculate a residual film stress value; then the first surface profile is subtracted according to the second surface profile to obtain a third surface profile of the film, by fitting method Calculating a plurality of third radii of curvature of the third surface profile, and then correcting the Stoney formula according to the third radii of curvature 099139280 Form No. A0101 Page 5 / Total 24 Page 0992068482-0 201221926
計算薄膜之複數個雙軸向應力，並計算第三曲率半^最 大梯度及求出主應力的方向。如此可用簡單的方弋無 需繁雜的量測步驟，即可測定薄臈平面之主應力χ 以測定非均向薄膜雙軸應力。 D 【實施方式】 [0004] 099139280 茲為使貴審查委員對本發明之結構特徵及所達成 之功效有更進一步之瞭解與認識，謹佐以較佳之實施例 及配合詳細之說明，說明如後： 請參閱第一圖與至第二圖，其係為本發明較佳實施 例之薄膜殘留應力之量測裝置之結構示意圖與薄膜殘留 應力之量測方法之流程圖；如圖所示，本發明之量:則聲 置包含一光源11 ’光源11為氣氛雷射或是其他雷射等， 氦氖雷射之中心波長為632. 8 nm，入射後首先經過一個 由顯微物鏡12和針孔13所組成的空間遽波器，並成為一 個點光源，再通過一個凸透鏡14，使該雷射光成為一個 平行光。接著該平行光又再經^過分光鏡15而被分成兩道 光，反射及穿透的兩道光束會分別投射在一參考平面鏡 16及一工件17上，工件17為單面反射的玻璃基板，玻璃 基板一面拋光’一面打毛。 工件17是放置在一傾量載台18上，而經由參考平面 鏡16及工件17所反射的兩道光束，會在分光鏡丨5處又重 新結合，並經一成像透鏡1 9投射到屏幕2 〇上’利用一數 位攝影機30拍攝干涉條紋圖’最後以電腦40儲存干涉條 紋圖，並以應力程式分析。使用一MaUab軟體以數值方 法及快速傅立葉轉換（F F T)法’將干涉圖之相位訊號抽離 以得到相位圖’再經由相位展開（Phase unwrapping) 表單編號A0101 帛6頁/共24胃 0992068482-0 201221926 技術還原薄膜三維表面輪廓圖，由曲率半徑擬合之方法 求得曲率半徑，最後判斷薄膜為均向性或非均向性，並 依據其特性以適當的公式來測定薄膜殘留應力。 而本發明之量測方法如圖二A至圖二B所示，該方法 首先，進行步驟S1，擷取一工件17之一第一干涉圖；之 後，進行步驟S2，建立該工件17之一第一表面輪廓；接 著，進行步驟S3，擬合該第一表面輪廓之複數個第一曲 率半徑；之後，進行步驟S4，擷取最大梯度之該第一曲 率半徑；然後，進行步驟S5，擷取該工件17鍍一薄膜後 之一第二干涉圖；接續，進行步驟S6，建立該工件17鍍 該薄膜後之一第二表面輪廓；之後，進行步驟S7，擬合 該第二表面輪廓之複數個第二曲率半徑；然後，進行步 驟S8，擷取最大梯度之該第二曲率半徑，接著，進行步 驟S9，判斷薄膜為均向性或非均向性；最後進行步驟10 ，根據薄膜為均向性或非均向性，在依據第一表面輪廓 與第二表面輪廓以計算薄膜之複數個應力。 請一併參閱第三圖，其係為本發明較佳實施例之檢 測工件17之表面平整之流程圓；如圖所示，本發明於於 步驟S1前更包含一步驟SO，檢測工件17之表面是否平整 。本發明之工件17於鍍膜前須將工件17進行平整度的檢 視，將工件17置入干涉儀中進行工件17凹凸面及平整度 之判別；干涉儀標準平面鏡的平整度為；1/20 (又為雷射 光的波長），以數位攝影機擷取工件17影像干涉條紋，藉 由雙光束干涉產生的干涉條紋圖可以檢測工件Π表面平 整度，將干涉圖儲存於電腦作為薄膜殘留應力分析使用 。若因工件17不平坦而造成所量測到的干涉條紋圈數過 099139280 表單編號A0101 第7頁/共24頁 0992068482-0 201221926 多或面形並非正圓者，則將工件17排除，並且將工件17 重新研磨拋光。若干涉條紋圈數較少且形狀約為正圓形（ 似牛頓環），則進行鍍膜製程。針對工件17檢測之步驟。 因此，在步驟SO之步驟中包含下列步驟，於步驟 S01，研磨並拋光工件17，步驟S02，檢測工件17為凸面 或凹面，進行步驟S03，量測工件17之一干涉影像之複數 個條紋，步驟S04，判斷干涉影像之複數個條紋是否少且 呈對稱，步驟S05，鍍膜於工件17。而於步驟S04中，若 是則進行步驟S05，鍍膜於工件17，若否則進行步驟S01 ，研磨並抛光工件17。 請一併參閱第四A圖與第四B圖，其係為本發明較佳 實施例之第一表面輪廓與第二表面輪廓之建立的流程圖 :如圖所示，本發明利用三軸平台調整光路和控制工件 17的傾斜量以及干涉條紋載波的頻率，以數位攝影機擷 取有載波的干涉圖，以建立第一表面輪廓。而於步驟S2 中，包含下列步驟：於步驟S21，量測第一干涉圖之干涉 條紋之一第一載波頻率，於步驟S22，擷取第一載波頻率 之一第一載波頻譜訊號。此步驟擷取已施加傾斜量的測 第一干涉圖，並以程式選取分析的範圍，將所選定的範 圍作使用二維快速傅立葉轉換，以將第一載波頻率轉換 為第一載波頻譜訊號，以得到干涉訊號之頻譜強度。 於步驟S 2 3，過滤第一載波頻譜訊號，以過遽第一載 波頻譜訊號之一高頻雜訊訊號，透過頻域數位滤波器對 第一載波頻譜訊號之頻譜做擷取，並消除不必要的訊號 ，諸如低頻雜訊或是高頻雜訊等。之後將第一載波頻譜 訊號平移至頻率域最低頻處以消除空間載波頻率。而於 099139280 表單編號A0101 第8頁/共24頁 0992068482-0 201221926 步驟S24，計算第一載波頻譜訊號之一第一相位資訊，使 用二維反快速傅立葉轉換（IFFT)第一載波頻譜訊號為第 一相位資訊，將處理過的傅立葉轉換平面進行傅立葉反 轉換，可得到相位資訊。 於步驟S25，依據第一相位資訊建立第一表面輪廓， 經由相位展開技術以展開第一相位資訊，將不連續之第 一相位資訊展開為連續之第一相位資訊，並依據連續之 第一相位資訊建立第一表面輪廓，因此可得到完整的相 位分布圖，然後重建物體三維表面輪廓，以進行曲率半Calculate the multiple biaxial stresses of the film, calculate the third curvature and the maximum gradient and find the direction of the principal stress. Thus, a simple method can be used to determine the principal stress 臈 of the thin meander plane without the need for complicated measurement steps to determine the biaxial stress of the non-uniform film. D [Embodiment] [0004] 099139280 For a better understanding and understanding of the structural features and efficacies of the present invention, the preferred embodiment and the detailed description are as follows: Please refer to the first figure and the second figure, which are a schematic diagram of a structure diagram of a film residual stress measuring device and a method for measuring a residual stress of a film according to a preferred embodiment of the present invention; The amount: the sound contains a light source 11 'the light source 11 is an atmospheric laser or other laser, etc., the center wavelength of the laser is 632. 8 nm, after the incident, first passes through a microscope objective 12 and a pinhole A space chopper composed of 13 is used as a point source, and then passed through a convex lens 14 to make the laser light a parallel light. Then, the parallel light is further divided into two lights by the beam splitter 15, and the two beams reflected and penetrated are respectively projected on a reference plane mirror 16 and a workpiece 17, and the workpiece 17 is a single-sided reflective glass substrate. The glass substrate is polished on one side. The workpiece 17 is placed on a tilting stage 18, and the two beams reflected by the reference plane mirror 16 and the workpiece 17 are recombined at the beam splitter 丨5 and projected onto the screen 2 via an imaging lens 19. The image of the interference fringe is captured by a digital camera 30. Finally, the interference fringe pattern is stored by the computer 40 and analyzed by the stress program. Use a MaUab software to extract the phase signal of the interferogram by numerical method and fast Fourier transform (FFT) method to obtain the phase map 'Phase unwrapping'. Form No. A0101 帛6 pages / Total 24 stomach 0992068482-0 201221926 The three-dimensional surface contour map of the technically reduced film is obtained by the method of fitting the radius of curvature to obtain the radius of curvature. Finally, the film is judged to be uniform or non-uniform, and the residual stress of the film is determined by an appropriate formula according to its characteristics. As shown in FIG. 2A to FIG. 2B, the method of the present invention firstly performs step S1 to capture a first interferogram of a workpiece 17; thereafter, step S2 is performed to establish one of the workpieces 17. a first surface contour; then, step S3 is performed to fit a plurality of first curvature radii of the first surface contour; then, step S4 is performed to extract the first radius of curvature of the maximum gradient; and then, proceeding to step S5, Taking a second interferogram of the workpiece 17 after plating a film; continuing, performing step S6 to establish a second surface profile of the workpiece 17 after plating the film; and then performing step S7 to fit the second surface profile a plurality of second radii of curvature; then, performing step S8, extracting the second radius of curvature of the maximum gradient, and then performing step S9 to determine whether the film is uniform or non-uniform; and finally performing step 10, according to the film Orotropic or non-uniform, based on the first surface profile and the second surface profile to calculate a plurality of stresses of the film. Please refer to the third figure, which is a flow circle for detecting the surface smoothing of the workpiece 17 according to the preferred embodiment of the present invention; as shown in the figure, the present invention further includes a step SO before the step S1 to detect the workpiece 17 Whether the surface is flat. The workpiece 17 of the present invention is required to perform flatness inspection of the workpiece 17 before coating, and the workpiece 17 is placed in the interferometer to determine the uneven surface and flatness of the workpiece 17; the flatness of the standard flat mirror of the interferometer is 1/20 (again For the wavelength of the laser light, the image interference fringe of the workpiece 17 is captured by the digital camera, and the interference fringe pattern generated by the interference of the two beams can detect the flatness of the surface of the workpiece, and the interferogram is stored in the computer as the residual stress analysis of the film. If the measured interference fringe circle number is 099139280 due to the unevenness of the workpiece 17, Form No. A0101 Page 7 / Total 24 Page 0992068482-0 201221926 If the polygon or the surface shape is not a perfect circle, the workpiece 17 is excluded and will be The workpiece 17 is reground and polished. If the number of interference fringes is small and the shape is approximately a perfect circle (like Newton's ring), the coating process is performed. The step of detecting for the workpiece 17. Therefore, in the step of step S, the following steps are included. In step S01, the workpiece 17 is ground and polished, and in step S02, the workpiece 17 is detected as a convex or concave surface, and in step S03, a plurality of stripes of the interference image of one of the workpieces 17 are measured. In step S04, it is determined whether the plurality of stripes of the interference image are small and symmetrical, and in step S05, the film is coated on the workpiece 17. In step S04, if yes, step S05 is performed to coat the workpiece 17, and if otherwise, step S01 is performed to grind and polish the workpiece 17. Please refer to FIG. 4A and FIG. 4B together, which are flowcharts for establishing the first surface contour and the second surface contour according to the preferred embodiment of the present invention. As shown, the present invention utilizes a three-axis platform. The optical path is adjusted and the amount of tilt of the workpiece 17 and the frequency of the interference fringe carrier are adjusted, and the interferogram of the carrier is captured by the digital camera to establish a first surface profile. In step S2, the following steps are included: in step S21, one of the first carrier frequencies of the interference fringes of the first interferogram is measured, and in step S22, one of the first carrier frequency signals of the first carrier frequency is captured. In this step, the first interferogram is applied, and the range of the analysis is selected by the program, and the selected range is used to perform the two-dimensional fast Fourier transform to convert the first carrier frequency into the first carrier spectrum signal. To obtain the spectral intensity of the interference signal. In step S23, filtering the first carrier spectrum signal to pass through the high frequency noise signal of the first carrier spectrum signal, and extracting the spectrum of the first carrier spectrum signal through the frequency domain digital filter, and eliminating the Necessary signals, such as low frequency noise or high frequency noise. The first carrier spectrum signal is then translated to the lowest frequency domain to eliminate the spatial carrier frequency. In 099139280, the form number A0101, page 8 / 24 pages 0992068482-0 201221926, step S24, calculating the first phase information of one of the first carrier spectrum signals, using the two-dimensional inverse fast Fourier transform (IFFT) first carrier spectrum signal as the first The phase information is obtained by performing Fourier inverse transformation on the processed Fourier transform plane to obtain phase information. In step S25, a first surface contour is established according to the first phase information, and the first phase information is expanded by the phase unwrapping technique to expand the discontinuous first phase information into continuous first phase information, and according to the continuous first phase. The information establishes the first surface contour, so that a complete phase distribution map can be obtained, and then the three-dimensional surface contour of the object is reconstructed to perform the curvature half
...： 徑擬合。而於步驟S25後，更包含一於步驟S26，消除第 一表面輪廓之一第一傾斜量。 本發明之空間載波頻率之雙光束干涉方程式，其表 達式如下： ......(1) 其中/(X，另為第一干涉圖之蒐摩分布圖，為DC 訊號強度，忍爲AC訊號之對比度#，...: Path fit. After step S25, the method further includes the step of removing the first tilt amount of the first surface contour. The double-beam interference equation of the spatial carrier frequency of the present invention has the following expression: (1) where /(X, the search pattern of the first interferogram is the DC signal strength, forbearance AC signal contrast #,
分別為第一載波頻率之X轴與y軸之分量，其目 的為讓第一載波頻率產生頻譜平移，以擷取第一載波頻 譜訊號。之後使用二維快速傅立葉轉換後阢和“訊號分 離，為相位資訊，將/(Λ：，>；)經二維傅立葉轉換後 可得： ipri^y)=a(^y)+c(x,y)+c(x,y)............(2) 099139280 為之傅立葉轉換 表單編號A0101 第9頁/共24頁 a{x,y) ' c{x^y) 0992068482-0 201221926 和少)刀別為低頻訊號和載波頻率加相位的共輛函 數將c(x,少)以濾波态提出並且平移至頻譜低頻處以消 除空間載波頻率，經過傅立葉反轉換可以得到： J ..... £ΐρτ{χ^)^-Β(χ,γ)ζ^φ[φ(χ^γ)\ (3) 將分別取其實部與虛部，並將其比值取反正 切函數可得到相位函數〆x，W : φ{χ,γ) = tan_1[i^£ll]......... ............................(4) 而（4)式中的#〇，>0即為相位（Phase)函數，藉由相位 展開（phase unwrapping)技術將不連續的相位展開成 連續的相位。相位展開方法是將（4)式中的相位函數 卢(工，少）由；Γ模式轉換成2刀·模式，因arc tan的數學 特性其週期為—三也就焉所謂丨的苁模式，但為了 2~ ~2 要符合原先諧波（Harmonic Wave)在—j冗的週期 性也就是所謂的之兀模式，所以要將原本的苁模式展 開成2刀》模式形成連續的相位。再將連續的相位函數 多(Α7)乘上；I得到工件17表面高差變化量，其表達式 4π 如下：They are respectively the components of the X-axis and the y-axis of the first carrier frequency, the purpose of which is to cause the first carrier frequency to produce a spectral shift to capture the first carrier spectral signal. After using two-dimensional fast Fourier transform and then "signal separation, for phase information, /(Λ:,>;) can be obtained by two-dimensional Fourier transform: ipri^y)=a(^y)+c( x,y)+c(x,y)............(2) 099139280 For Fourier transform form number A0101 Page 9 of 24 a{x,y) ' c{ x^y) 0992068482-0 201221926 and less) The common vehicle function for the low frequency signal and carrier frequency plus phase sends c(x, less) in the filtered state and translates to the low frequency of the spectrum to eliminate the spatial carrier frequency, after Fourier inverse The conversion can be obtained: J ..... £ΐρτ{χ^)^-Β(χ,γ)ζ^φ[φ(χ^γ)\ (3) The actual and imaginary parts will be taken separately, and The ratio takes the inverse tangent function to obtain the phase function 〆x, W : φ{χ, γ) = tan_1[i^£ll]........................... ...............(4) And #〇, >0 in (4) is the phase function, which will not be phase unwrapping. The continuous phase is developed into a continuous phase. The phase unwrapping method is to convert the phase function Lu (work, less) in (4); the Γ mode into a 2-knife mode, due to the mathematical properties of arc tan. The period is - three is also the so-called 苁 苁 mode, but in order to 2 ~ ~ 2 to comply with the original harmonic (Harmonic Wave) - j redundant period is also called the so-called mode, so the original 苁 mode Expand into a 2 knife mode to form a continuous phase. Then multiply the continuous phase function by more (Α7); I get the surface height difference variation of the workpiece 17, the expression 4π is as follows:
•(5) 0992C ............... 099139280 Η^γ) = ~Φ(χ,γ) 表單編號A〇ftf 第10頁/共24頁 201221926 其中h(X，y)為待測物的表面形貌變化量，經 開技術以得狀整的滅分布圖，接著重建物體表面輪 廓並進行曲率半徑擬合。 復請參閱第二圖，若於步驟财，薄膜為均向性， 薄膜的殘留應力依據下列公式計算，分別將鑛膜前後所 求得的曲率半徑代入Stoney公式： cr = —___L、- Es.t^ ...........................•(5) 0992C ............... 099139280 Η^γ) = ~Φ(χ,γ) Form number A〇ftf Page 10 of 24 201221926 where h(X , y) is the amount of surface topography change of the object to be tested, and the extinction distribution pattern is obtained by the open technique, and then the surface contour of the object is reconstructed and the radius of curvature is fitted. Please refer to the second figure. If the film is uniform in the process, the residual stress of the film is calculated according to the following formula. The radius of curvature obtained before and after the film is substituted into the Stoney formula: cr = —___L, - Es. t^ ...........................
其令σ為均向性之薄膜之應力，R1為第一曲率半徑，R2 為第二曲率半徑，R為曲率半徑變化量，^為工件^之 楊氏係數，[為王件17之帕松比，（經由查表得知道， 工件17(此實施例工件17之材質以玻璃為範例作說明）的 揚氏係數Es = 71·5 (GPa)，帕松比Vs = 〇 2〇8)， 匕為工件17厚度’[為薄膜厚度，⑻式即為-般測定 均向性薄膜殘留應力所採甩的理論公式。 右於步驟S9中，薄膜為非均向性，則依據第二表面 輪廓扣除第一表面輪廓可得薄膜第三表面輪廓，經由擬 合方法以計算該薄膜之-第三表面輪廓之複數個第三曲 率半#。為了測定非均向薄膜殘留應力，則須由雙抽曲 率的變化做推算得到修正後的雙轴向Stoney公式，而此 非均向性之薄膜的㈣應力敎據下縣式計算：Let σ be the stress of the film of the uniformity, R1 is the first radius of curvature, R2 is the second radius of curvature, R is the radius of curvature change, ^ is the Young's coefficient of the workpiece ^, [for the piece of 17 Ratio, (by looking up the table, the workpiece 17 (the material of the workpiece 17 in this embodiment is illustrated by the example of glass) has a Young's modulus Es = 71·5 (GPa), Passon's ratio Vs = 〇2〇8),匕 is the thickness of the workpiece 17 '[is the film thickness, (8) is the theoretical formula for measuring the residual stress of the uniform film. Right in step S9, the film is non-uniform, and the third surface profile of the film is obtained by subtracting the first surface profile according to the second surface profile, and calculating a plurality of the third surface profile of the film via a fitting method. Three curvatures half #. In order to determine the residual stress of the non-uniform film, the modified biaxial Stoney formula must be calculated from the change of the double extraction rate, and the (four) stress of the non-uniform film is calculated according to the county formula:
(7) 099139280 表單編號A0101 第11頁/共24頁 0992068482-0 201221926 σ.(7) 099139280 Form No. A0101 Page 11 of 24 0992068482-0 201221926 σ.
(8) σ. 及 σ 其中 力 分別為薄膜在χ軸及y軸方向上的雙轴主應 A及分別為薄膜在X軸及y軸方向之第三曲率半徑 晃及匕分別為工件丨7的楊氏係數及帕松比，及 J為工件17厚度及薄膜之厚度。通常σ的符號，張應 力取正號’壓應力為負號。若假設滿足均向性條件 及= <=、，則得出σ = σ =之結果，故可從（7)式(8) σ. and σ where the force is the biaxial principal A of the film in the x-axis and y-axis directions, and the third radius of curvature of the film in the X-axis and y-axis directions, respectively, and the workpiece 丨7 The Young's modulus and the Passon's ratio, and J are the thickness of the workpiece 17 and the thickness of the film. Usually the sign of σ, Zhang Yingli takes the positive sign 'the compressive stress is the negative sign. If it is assumed that the homogeneity condition is satisfied and = <=, then the result of σ = σ = is obtained, so it can be obtained from (7)
X V 矛（8)式得到均向薄膜之應力公式，即（6 )式。 另外，於建立第二表面輪廓之步驟$6中，包含下列 '驟於步驟S61 ’量測第二干涉圖之干涉條紋之一第二 載：頻率’於步驟S62，擷取第二載波頻率之—第二載波 頻。曰Λ號’使用：維快速傅減轉㈣二載波頻率為第 二載波頻譜訊號’於㈣S63，過解二載波歷訊號， I濾第一載波頻譜訊號之一高頻訊號，於步驟％4，計算 第二載波頻譜訊號之-第二相位資訊，使用二維反快速 傅立葉轉換第二載波頻譜訊號為第二相位資訊於步驟 別5，依據第二相位資訊建立第二表面輪廓，將不連續之 第-相位貝訊展開為連續之第二相位資訊，並依據連續 之第一相位貧訊建立第二表面輪廓，而於步驟s65後更 包含-於步驟S66，消除第二表面輪麻之_第二傾斜量。 由於步驟S6卜S62之表面輪廓建立之方法皆分別與步驟 S2卜S22之表面輪廓建立之方法相同，故在此不多加贅述 099139280 表單編號A0101 第12頁/共24頁 0992068482-0 201221926 綜上所述，本發明係有關於一種薄膜殘留應力之量 測方法，首先，擷取一工件鍵一薄膜之前與後之一第一 干涉圖與一第二干涉圖，以分別建立一第一表面輪廓與 一第二表面輪廓，並分別擷取第一表面輪廓與第二表面 輪廓之最大梯度之第一曲率半徑與第二曲率半徑，之後 依據薄膜為均向性或非均向之特性以計算薄膜之複數個 應力。如此可用簡單的方式，無需繁雜的量測步驟，即 可測定非均向薄膜雙軸應力，亦可測定均向薄膜殘留應 、力。 故本發明係實為一具有新穎性、進步性及可供產業 利用者，應符合我國專利法所規定之專利申請要件無疑 ，爰依法提出發明專利申請，祈鈞局早日賜准專利， 至感為禱。 惟以上所述者，僅為本發明之一較佳實施例而已， 並非用來限定本發明實施之範圍，舉凡依本發明申請專 利範圍所述之形狀、構造、特徵及精神所為之均等變化 # 與修飾，均應包括於本發明之申請專利範圍内。 【圖式簡單說明】 [0005] 第一圖為本發明較佳實施例之非均向薄膜殘留應力之量 測裝置之結構示意圖 第二圖為本發明較佳實施例之非均向薄膜殘留應力之量 測方法之流程圖； 第三圖為本發明較佳實施例之檢測工件之表面平整之流 程圖； 第四A圖為本發明較佳實施例之第一表面輪廓之建立的流 099139280 表單編號 A0101 第 13 頁/共 24 頁 0992068482-0 201221926 程圖；以及 第四B圖為本發明較佳實施例之第二表面輪廓之建立的流 程圖。 【主要元件符號說明】 [0006] 11 光源 12顯微物鏡 13針孔 14凸透鏡 15分光鏡 16參考平面鏡 17工件 18傾量載台 19成像透鏡 20屏幕 30數位攝影機 40電腦 0992068482-0 099139280 表單編號A0101 第14頁/共24頁The X V spear (8) formula gives the stress formula of the uniform film, that is, the formula (6). In addition, in the step of constructing the second surface contour, the following one of the interference fringes of the second interferogram is measured in the following step S61: the second carrier: the frequency 'in step S62, the second carrier frequency is taken— Second carrier frequency.曰Λ 'Use: dimension fast Fu-reduction (four) two carrier frequency is the second carrier spectrum signal 'in (four) S63, over-resolved two-carrier history signal, I filter one of the first carrier spectrum signal high-frequency signal, in step %4, Calculating the second phase information of the second carrier spectrum signal, using the two-dimensional inverse fast Fourier transform second carrier spectrum signal as the second phase information in step 5, establishing the second surface contour according to the second phase information, and discontinuous The first phase of the phase information is expanded into a continuous second phase information, and the second surface contour is established according to the continuous first phase difference, and after step s65 is further included - in step S66, the second surface is removed. Two tilt amounts. Since the methods for establishing the surface contour of step S6 and S62 are respectively the same as the method for establishing the surface contour of step S2 and S22, no further description is made here. 099139280 Form No. A0101 Page 12 / Total 24 Page 0992068482-0 201221926 The invention relates to a method for measuring residual stress of a film. First, a first key pattern and a second interferogram are formed before and after a workpiece key-film to establish a first surface contour and a second surface profile, and respectively capturing a first radius of curvature and a second radius of curvature of the maximum gradient of the first surface contour and the second surface contour, respectively, and then calculating the film according to the uniformity or non-uniformity of the film Multiple stresses. In this way, the biaxial stress of the non-uniform film can be measured in a simple manner without complicated measurement steps, and the residual film force and force can be measured. Therefore, the present invention is a novelty, progressive and available for industrial use. It should be in accordance with the patent application requirements stipulated in the Patent Law of China, and the invention patent application is filed according to law, and the prayer bureau will grant the patent as soon as possible. For prayer. However, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention, and the shapes, structures, features, and spirits described in the claims of the present invention are equally varied. And modifications are intended to be included in the scope of the invention. BRIEF DESCRIPTION OF THE DRAWINGS [0005] The first figure is a schematic structural view of a non-uniform film residual stress measuring device according to a preferred embodiment of the present invention. The second figure is a non-uniform film residual stress according to a preferred embodiment of the present invention. Flowchart of the measuring method; the third drawing is a flow chart for detecting the surface smoothing of the workpiece according to a preferred embodiment of the present invention; and FIG. 4A is a flow of the first surface contour of the preferred embodiment of the present invention 099139280 No. A0101, page 13 of 24, 0992068482-0 201221926; and FIG. 4B is a flow chart showing the establishment of a second surface profile in accordance with a preferred embodiment of the present invention. [Main component symbol description] [0006] 11 light source 12 microscope objective 13 pinhole 14 convex lens 15 beam splitter 16 reference plane mirror 17 workpiece 18 tilting stage 19 imaging lens 20 screen 30 digital camera 40 computer 0992068482-0 099139280 form number A0101 Page 14 of 24