橢偏儀在位表征電化學(xué)沉積的系統(tǒng)搭建（九）- 光學(xué)模型的建立與數(shù)據(jù)的提取

正文

橢偏儀在位表征電化學(xué)沉積的系統(tǒng)搭建（九）- 光學(xué)模型的建立與數(shù)據(jù)的提取

4.3在位測試裝置

目前的在位橢偏儀監(jiān)測電化學(xué)沉積的關(guān)鍵在于系統(tǒng)的集成。實(shí)驗(yàn)室的橢偏儀光源為氙燈晰房，可以進(jìn)行全譜的測試求摇，但是這也導(dǎo)致單波長的光強(qiáng)度較弱，因此裝置設(shè)計(jì)中的光路設(shè)計(jì)尤為重要殊者，另外是光斑的大小問題与境，光斑大小會(huì)隨著測試角度的變化而變化。另外其設(shè)計(jì)需要滿足電化學(xué)薄膜沉積的需求猖吴，又要同時(shí)滿足橢偏儀測試的需求摔刁。如作為電解池它需要滿足容電解液充足，且可以放置好工作電極海蔽、對(duì)電極和參比電極共屈。橢偏儀的在位裝置首先要滿足透光，其次是保證工作電極易于調(diào)節(jié)入射光和出射光在同一光平面党窜，需考慮溶液的光程拗引，原則上越小越好，這樣可以減小光的衰減幌衣，更易得到沉積薄膜的信息寺擂。因此需要根據(jù)系統(tǒng)進(jìn)行設(shè)計(jì)。

4.4光學(xué)模型的建立與數(shù)據(jù)的提取

在位橢偏儀測試的另外一個(gè)挑戰(zhàn)在于數(shù)據(jù)的分析泼掠。通過橢偏光譜的在位監(jiān)測可以獲得(ψ怔软，Δ)值，利用這些光譜择镇，需要進(jìn)行建模從而獲取其光學(xué)參數(shù)挡逼。表1-1總結(jié)了在位橢偏儀數(shù)據(jù)分析常用的分析方法。

表1-1在位橢偏儀數(shù)據(jù)分析方法

表1-1所示的線性回歸分析(LRA)必須知道樣品所有的介電函數(shù)腻豌，通過擬合得到誤差的zui小值來確定光學(xué)常數(shù)和薄膜結(jié)構(gòu)家坎。當(dāng)樣品中有未知的介電函數(shù)時(shí)，需要進(jìn)行介電函數(shù)建模吝梅，使用數(shù)值反演法可以提取樣品的介電函數(shù)虱疏。圖1-17是用LRA橢偏儀數(shù)據(jù)分析的流程圖，可以看出橢偏儀數(shù)據(jù)提取與分析的步驟為：(1)建立適合的光學(xué)模型苏携；(2)確定每一層的介電常數(shù)做瞪；(3)對(duì)橢偏譜譜(ψ，Δ)進(jìn)行擬合；(4)誤差計(jì)算装蓬。通過不斷重復(fù)以上四個(gè)步驟得到zui小誤差著拭，然后進(jìn)行(5)光學(xué)常數(shù)和厚度的測定及(6)結(jié)果可靠性判斷。

圖1-17橢偏光譜法數(shù)據(jù)分析程序流程圖

表1-1中的全局誤差zui小化法(GEM)是Collins團(tuán)隊(duì)開發(fā)的數(shù)據(jù)分析方法牍帚，該方法使我們能夠同時(shí)確定樣品的介電函數(shù)和結(jié)構(gòu)儡遮。因此，當(dāng)樣品的介電函數(shù)未知時(shí)暗赶，GEM是一種相當(dāng)強(qiáng)大的分析方法鄙币。

圖1-18展示了GEM的數(shù)據(jù)分析過程。圖1-18(a)為橢偏譜的光學(xué)模型蹂随。在這個(gè)模型中十嘿，和分別表示表面粗糙度層、本體層和基底的介電函數(shù)糙及。在分析過程中详幽，先要確定本體層筛欢、基底層的介電常數(shù)浸锨。通常基底層介電函數(shù)可以從薄膜沉積前的(ψ,Δ)光譜使用數(shù)值反演法得到版姑。表面粗糙度層的由EMA計(jì)算柱搜。如圖1-18(b)所示，該光學(xué)模型中的未知參數(shù)為體積層的介電函數(shù)表面粗糙度層厚度d_s剥险，和本體層厚度d_b聪蘸。如果隨時(shí)間的變化可知，則d_s和d_b可以直接從測量的光譜(ψ,Δ)使用數(shù)值反演得到表制。然后用線性回歸分析健爬，可以確定測量層的光學(xué)常數(shù)和厚度，如圖1-18(b)和(c)所示么介。不斷重復(fù)以上步驟使得誤差小zui娜遵，從而得到材料的光學(xué)常數(shù)和厚度，zui后進(jìn)行結(jié)果的可靠性判斷完成整個(gè)分析過程壤短。

圖1-18全局誤差zui小化(GEM)法數(shù)據(jù)分析步驟

表1-1中的虛擬襯底近似法(VSA)设拟，是1993年Aspnes開發(fā)的，其要求薄膜和襯底表現(xiàn)出相對(duì)較大的光吸收久脯。VSA常用于半導(dǎo)體襯底上形成的半導(dǎo)體層纳胧。VSA可以描述介電函數(shù)在厚度方向上連續(xù)變化的梯度層。將VSA應(yīng)用于成分梯度層的分析帘撰，則可以確定每一層的成分跑慕。從VSA中也可以看出晶體體積分?jǐn)?shù)在生長方向上的變化。然而摧找，與LRA和GEM相比相赁，VSA不能應(yīng)用于光吸收較低的樣品相寇。

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