- 學位論文
次世代微影術及其非破壞式光學量測系統之研究
Studies on Next Generation Lithography and Its Non-destructive Optical Measurement Systems
摘要
本論文可概分為三部分:1.改善用於極紫外光(extreme ultraviolet, EUV)微影系統之多層膜反射鏡之反射率以及其等效計算方法、2.開發用於多尺度(multi-scale)電子束直寫(electron-beam directwrite, EBDW)微影系統之數值計算方法、以及3.開發非破壞式光學檢測系統用於量測光阻線(photo-resist lines)之幾何外型與多層膜彩色濾光片(color filter)之光學性質。 對於極紫外光反射鏡之研究，我們設計了以40層鉬/矽多層膜為基底之光子晶體(photonic crystal)反射鏡。 從數值結果得知我們的設計具有高於以往之反射率，並且能承受更高之製程處理溫度與入射光能量。再者，由於不易精準的計算此類多層膜反射鏡，我們修改了傳輸線理論(transmission line theory)使其於多角度下能將多層膜結構視為單層以加速計算。從二維以及三維有限時域差分(finite-difference time-domain, FDTD)計算結果可知，完整多層膜計算與等效單層結構計算之均方根誤差為可容忍值，並且等效單層計算所耗時間為完整多層計算之一半。因此，所修改之傳輸線理論可節省多層膜結構之計算時間並達到合理之精確度。 對於電子束直寫微影系統之研究，我們提出求解細緻化方法(solution-refined method)來計算其三維靜電場。考慮到製程誤差，其靜電場無法利用圓柱對稱來簡化。因此，我們使用求解細緻化方法結合基於訊息傳輸介面(message passing interface)之平行計算架構來計算此多尺度問題。從計算結果可知雖然求解細緻化方法之使用需權衡計算時間，但所需之計算資源較少。此方法亦可使用於求解其它由拉普拉斯方程(Laplace’s equation)所控制之大尺度問題，亦包含求解更高解析度以及所需儲存記憶超載之問題。 對於光學檢測之研究，我們建立了兩種非破壞檢測系統分別用來量測不同性質。此兩系統分別為1.基於ASML YieldStar (YS) S-100之光學散射量測(scatterometry)系統與2.包含等效層模型(effective layer-included model)之多角度分光橢圓儀。此兩系統分別用於量測包含邊緣粗糙(line edge roughness, LER)之光阻線外觀輪廓以及多層膜彩色濾光片之光學性質。光學散射量測系統部分，我們利用直接聚集多角度散射之光譜，用以量測投射瞳像(projection pupil)可避免額外的機械動作。我們亦將瞳像具有之曲面性質加入計算權重以提高凝合(fitting)精確度。從數值計算之結果可知，光學散射量測系統於系統數值孔徑(numerical aperture, NA) = 0.71，0.77，0.82，0.87，0.91，以及0.95其雜訊標準差(standard deviation, σ)分別 ≤ 0.7%，2%，4%，6%，8%，以及9%時可辨識出邊緣粗糙。另外，此模型亦使用於推算由ASML YS S-100實體機台所量測之瞳像。由結果可得知，當系統數值孔徑值 0.87時此模型推算之結果與掃描式電子顯微鏡(scanning electron microscope, SEM)之結果相符。對於偵測細微之光阻線寬變化，我們於凝合函數中考慮正規化(normalized) Zernike多項式函數，由結果可知高次項(high-order)Zernike係數對瞳像之微小變化敏感，適合用於偵測光阻線之細微變化。接著，於包含等效層模型之多角度分光儀之部分，我們於標準多層膜模型中加入包含位於多層膜之頂層與夾層的等效層，用以消除因頂層與夾層之粗糙面所造成之散射效應並量測(n, k, d)。為測試此模型，我們利用數個包含不同型式散射體的虛擬系統來檢驗此模型。由測試結果可得知，相較於傳統之標準模型，由包含等效層之模型所推算出之(n, k, d)更接近於期望值。我們亦探討於精確結果下可容忍的初始(n, k, d)給定範圍。接著，兩模型均用於量測由奇美電子所提供之彩色濾光片樣本。結果為由包含等效層之模型所量測之(n, k, d)較為符合表面輪廓儀(profilemetry)之結果與所量測之穿透率。因此，我們所提出之非破壞式量測方法有助於使用於量測奈米尺度輪廓以及多層膜之光學性質。
並列摘要
This dissertation is classified into three parts, which are, the efficient calculation method of the multilayer (ML) mirror and the reflectivity improvement for extreme ultraviolet (EUV) lithography system, the development of a numerical algorithm to solve large-scale calculations for electron-beam direct-write (EBDW) lithography system, and the non-destructive optical inspection techniques to detect the shapes of the photo-resist lines and the optical properties of the ML based color filters. In the EUV-mirror part, the photonic crystal mirror is designed. From the numerical results, the mirror can not only achieve the high reflectivity but also tolerate much higher processing temperatures as well as higher incident powers. Also, considering it is hard to achieve accurate calculation for such ML mirror. The modified transmission line theory which treats ML structure as a bulk material is derived to quicken the calculations. Based on two- and three-dimensional (3-D) finite-difference time-domain (FDTD) calculations, the results show that the root mean square errors between ML calculations and the bulk material calculations are tolerated, and the computational time of bulk material is approximately half as compared with original ML computation. Therefore, the derived theory can not only reduces the computational time but also has accuracy with tolerable numerical errors. In the EBDW lithography part, the solution-refined method is proposed to calculate the full 3-D electrostatic field. Considering the fabrication errors, the electrostatic fields cannot be solved by using the cylindrical symmetry. Therefore, the solution-refined algorithm combined with Message Passing Interface (MPI) based parallel computational scheme is used to solve this multi-scale problem. Our findings show that the proposed solution-refined technique has the tradeoff with longer computational time but the fewer number of CPUs are needed. Anyhow, the proposed technique can be used to solve the Laplace’s equation dominated system with high resolution and the problems exceed its equipped storage memory. In the optical inspection part, two non-destructive measurement systems are built to detect different properties, which are, the scatterometry system based on the measured pupils and the effective-layer included model based in-house variable angle spectroscopic ellipsometry (VASE) system. These two systems are used to measure the profile shapes of the photo-resist lines with line edge roughness (LER) and the optical properties of the ML based color filters respectively. For the scatterometry system, it is efficient to collect the angle-resolved diffraction spectrum without additional mechanical scanning by measuring the projection pupil. The concavity of the pupil is considered as the weight function to raise the fitting accuracy. Our numerical results show that the scatterometry model can identify the LER target when the standard deviation of the white noise (σ) ≤ 0.7%, 2%, 4%, 6%, 8%, and 9% for numerical aperture (NA) = 0.71, 0.77, 0.82, 0.87, 0.91,and 0.95 respectively. Moreover, our model is used to fit the pupil images which measured from the ASML YS S-100. The findings indicate that the fittings match with the results from scanning electron microscope (SEM) measurements when NA 0.87 is applied. To detect tiny shape variations, the normalized Zernike polynomials are used for the fitting. We found that the high-order Zernike coefficients are sensitive to the tiny variations. For the in-house VASE system, the effective layer-included model is considered in determining the (n, k, d) by including effective layers to reside between and above the ML. The model is examined by fitting the (n, k, d) for different virtual systems which contain different kinds of scatters reside between and above it. From the findings, the fitted (n, k, d) can be closer to the assumed (n, k, d) by using the effective layer-included model rather than the standard model. Also, the tolerance of initial assigned (n, k, d) regions to obtain the accurate results are investigated. Furthermore, both models are used to determine the (n, k, d) of the fabricated red, green, and blue (RGB) color filter samples (provided by Chi Mei Corp.). Consequently, the (n, k, d) determined from the effective layer-included model are closer to the results from profilemetry (Alpha-step 100) and the measured transmissions. Therefore, the proposed non-destructive measurement methods can be useful to measure the nano-scale profile shapes and the optical properties of the imperfect ML.