本研究主要為將徑向基函數網路(radial basis function networks, RBFN)應用於同調傅立葉散射儀(coherent Fourier scatterometry, CFS)中，重建奈米結構的幾何參數。由於週期性奈米結構的尺寸越趨緊密且其圖形越趨複雜，需要更多精確且敏感度高的量測工具。CFS為非傳統的量測工具，主要用於重建光柵的幾何結構，能利用廣泛不同的入射角增加量測敏感度，達到快速量測的效果，可重複量測並能夠應用於先進微影製程系統。
利用CFS重建光柵主要有以下兩個步驟：第一步為利用繞射理論精確模擬奈米結構的繞射圖形，在此研究中，使用時域有限差分法(finite difference time domain, FDTD)分析其理論繞射圖形，並用多種不同的光柵參數建立模擬所需的理論繞射圖形資料庫，光柵參數包含底部線寬(bottom critical dimension, BCD)、光柵高度、側壁角度(sidewall angle, SWA)，將資料庫圖形繪成50x50 pixel的影像轉換成輸出輸入的資料使電腦學習。第二步為利用理論繞射圖形和CFS量測的實驗繞射圖形，重建奈米結構的幾何參數，在此研究中，使用RBFN解決重建結構的問題，RBFN利用FDTD所分析的繞射圖形資料庫進行學習，為了最佳化此網路(RBFN)，需要使用兩項驗證方式re-substitusion 和k-fold交叉驗證。
此方法應用於量測五個不同週期的矽光柵，其實驗結果顯示樣品D有最大BCD誤差13nm、樣品A有最小BCD誤差2nm。而比較使用CFS和AFM量測BCD的結果顯示兩者相關性高，相關係數為R^2=0.9549。

This study applies radial basis function networks (RBFN) in coherent Fourier scatterometry (CFS) to reconstruct the geometrical parameters of nanostructures. As the dimension of periodic nanostructures is denser and more complex, the demand of precise and sensitive metrology tools is increasing. CFS is emerging as an alternative metrology tools to reconstruct the geometrical parameters of the structures known as the gratings. CFS allows fast measurement with broadband incident angle to increase the sensitivity of measurement. It is repeatable and able to integrate in advanced lithography system.
There are two successive steps which are used to reconstruct the grating parameters in CFS: the forward problem and the inverse problem. The forward problem is a process to obtain the theoretical diffraction maps by the nanostructures using the rigorous simulation. This thesis utilizes finite difference time domain (FDTD) analysis to obtain the theoretical signatures. The simulation is conducted by varying the grating parameters including the bottom critical dimension (BCD), height, and sidewall angle (SWA) to create the library of signature. The library of signature then is mapped to 50 × 50 pixel image and converted to input-output data training. The following step is to inversely reconstruct the geometrical parameters of nanostructures using theoretical signatures and experiment signature obtained by CFS measurement. In this thesis, we employ RBFN to solve the inverse problem in CFS. RBFN is then trained using the library of signature obtained by FDTD analysis. To optimize the networks, two cross validations are employed: re-substitution and k-fold cross validation.
The proposed method is applied to measure 5 fabricated surface relief silicon gratings with different CD and period. The experiment results show that the maximum BCD difference is 13 nm deviation for the sample D and the minimum BCD difference is 2 nm for sample A. The correlation coefficient of the BCD measurement is strong between the CFS and AFM metrology with R2 of 0.9549.

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