隨著半導體產業的快速發展，對於小尺寸電晶體的要求是越來越嚴苛了，平面式電晶體MOSFET已經無法再做到更小尺寸，取而代之的是立體結構的FinFET電晶體，因此本論文利用名為RETICOLO的光學模擬軟體來建構出FinFET中fin結構的部分，利用高度(H)、週期(Pitch)、側壁角(side-wall angle, SWA)這三個結構參數來組合出不同形貌的fin結構。接著分別將可見光波長段與極紫外光波長段之光波入射於結構，再透過嚴格耦合波分析(RCWA)原理來獲得反射電場資訊，經過瓊斯矩陣與穆勒矩陣之運算，將電場資訊轉換成由橢偏角Ψ(psi，振幅比)和Δ(delta，相位差)組成的連續光譜，透過以上的方法模擬出在實際情況下，待測結構如何經過橢偏散射儀(Ellipsometric scatterometry)的量測後得到光譜資訊。
有了結構參數與其相對應的光譜資訊來做為神經網路的輸入及輸出資料後，可以建立出以卷積神經網路(Convolution Neural Network)作為基本架構的前向神經網路(Forward Neural Network)與反向神經網路(Inverse Neural Network)，目標為成功利用訓練好的模型來預測輸出結果，並將比較不同神經網路模型的訓練過程與其最終的預測準確度及泛化能力(Generalization ability)。當FNN模型訓練成熟後，輸入結構參數即可由模型預測出其產生之橢偏角資訊；反之，當INN的模型訓練成熟後，僅需輸入橢偏角訊號，即可由模型預測出其相對應之結構參數，並且其預測結果也有一定的準確度，這樣的模型實現了「反向重建結構」的能力。
本研究利用兩個不同的深度神經網路，分別完成了FNN與INN模型的訓練及預測結果比較，並且透過兩個不同的波長段之特性與各別的實驗結果，分別找到了各自適合使用的模型，至於這些模型可以如何運用，將使往後的實驗更有發展及討論空間。

This paper utilizes an optical simulation software called RETICOLO to simulate the fin structures in FinFETs. We use three structural parameters—height(H), pitch, and side-wall angle(SWA)—to create various fin structure morphologies. Subsequently, light waves in the visible spectrum and extreme ultraviolet spectrum are incident on the structures, and the reflected electric field information is obtained through the principle of rigorous coupled-wave analysis (RCWA). By performing calculations using Jones and Mueller matrices, the electric field information is converted into continuous spectra composed of ellipsometric angles Ψ(psi) and Δ(delta). This method simulates how the measured structures yield spectral information after being measured by an ellipsometric scatterometer in real-world scenarios.
With the structural parameters and their corresponding spectral information serving as the input and output data for a neural network, forward neural networks (FNN) and inverse neural networks (INN) based on the convolutional neural network (CNN) architecture can be established. The goal is to successfully use the trained models to predict output results and compare the prediction accuracy and generalization ability of each model.
From the experimental results, it is known that if one wishes to use the FNN model to accurately obtain ellipsometric angle information through structural parameters, choosing incident light in the visible wavelength range will yield better results. However, if one wishes to use the INN model to inversely reconstruct structural parameters through ellipsometric angle information, selecting incident light in the extreme ultraviolet wavelength range will yield better results.

[1] M. G. Moharam, T. K. Gaylord, "Rigorous coupled-wave analysis of planar-grating diffraction" Journal of the Optical Society of America, vol.71, no.7, pp.811-818, 1981
[2] R.R. Schaller, "Moore's law: past, present and future", IEEE Spectrum, vol.34, no.6, pp.52-59, 1997
[3] D. Bhattacharya, N. Jha, "Digitally-Assisted Analog and Analog-Assisted Digital IC Design", Cambridge University Press, chp.2, pp.21-55, 2015
[4] J.P. Hugonin, P. Lalanne, "RETICOLO software for grating analysis", arXiv, arXiv:2101.00901 ,2021
[5] U. Peralagu et al., "(Invited) Towards a Vertical and Damage Free Post-Etch InGaAs Fin Profile: Dry Etch Processing, Sidewall Damage Assessment and Mitigation Options", ECS Transactions, vol.69, no.5, pp.15-36, 2015
[6] L. Gao, "A Bidirectional Deep Neural Network for Accurate Silicon Color Design", Advanced Materials, vol.31, no.51, 2019
[7] S. Liu et al., "Machine learning aided solution to the inverse problem in optical scatterometry", Measurement, vol.191, 2022
[8] 林大貴, "圖解TensorFlow 2初學篇：實作tf.keras + Colab雲端、深度學習、人工智慧、影像辨識", 博碩文化, 2022
[9] X. Zhang, L. Yao, F. Yuan, "KDD'19: The 25th ACM SIGKDD Conference on Knowledge Discovery and Data Mining", Association for Computing Machinery, PP.139-147, 2019
[10] M. I. Jordan, T. M. Mitchell, "Machine learning: Trends, perspectives, and prospects", Science, vol.349, no.6245, pp.255-260, 2015
[11] C. Song et al., "Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications.", Springer, Berlin, Heidelberg, pp.117-124, 2013
[12] L. P. Kaelbling, M. L. Littman, A. W. Moore, "Reinforcement Learning: A Survey", Journal of Artificial Intelligence Research, vol.4, pp.237-285, 1996
[13] Y. LeCun, Y. Bengio, G. Hinton, "Deep learning", Nature, vol.539, pp.436-444, 2015
[14] E. Stevens, L. Antiga, T. Viehmann, "Deep Learning with PyTorch", Manning, USA, 2020
[15] S. Mittal, S. Vaishay, "A survey of techniques for optimizing deep learning on GPUs", Journal of Systems Architecture, vol.99, 2019
[16] A. Krizhevsky, I. Sutskever, G. E. Hinton, "ImageNet Classification with Deep Convolutional Neural Networks", Advances in Neural Information Processing Systems, vol.25, 2012
[17] A. C. Diebold, A. Antonelli; N. Keller, "Perspective: Optical measurement of feature dimensions and shapes by scatterometry", APL Materials, vol.6, no.5, 2018
[18] M. Seo, J. Lee, M. Lee, "Grating-coupled surface plasmon resonance on bulk stainless steel", Optics Express, vol. 25, no. 22, pp.26939-26949 ,2017
[19] T. Cui, J Li, Y. Wang, S. Nazarian, M. Pedram, "An Exploration of Applying Gate-Length-Biasing Techniques to Deeply-Scaled FinFETs Operating in Multiple Voltage Regimes", IEEE Transactions on Emerging Topics in Computing, vol.6, no.2, 172-183, 2016
[20] N. Okada et al., "Formation of distinctive structures of GaN by inductively-coupled-plasma and reactive ion etching under optimized chemical etching conditions", AIP Advances, vol.7, no.6, 2017
[21] M. G. Moharam, T. K. Gaylord, E. B. Grann, D. A. Pommet, "Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings" Journal of the Optical Society of America, vol.12, no.5, pp.1068-1076, 1995
[22] H. T. Huang, F. L. Terry Jr, "Spectroscopic ellipsometry and reflectometry from gratings (Scatterometry) for critical dimension measurement and in situ, real-time process monitoring", Thin Solid Films, vol.455-456, pp.828-836, 2004
[23] M. Huber, J. Schoeberl, A. Pechstein, S. Zaglmayr, "Simulation of Diffraction in Periodic Media with a Coupled Finite Element and Plane Wave Approach", SIAM Journal on Scientific Computing, vol.31, no.2, 2009
[24] N. Yao, Z. L. Wang, "Handbook of Microscopy for Nanotechnology", Kluwer Academic Publishers, 2005
[25] X. Chen, S. Liu, "Optical Scatterometry for Nanostructure Metrology", Metrology, pp.477-513, 2019
[26] H. Tompkins, E. A. Irene, "Handbook of Ellipsometry", William Andrew, 2005
[27] C. Raymond, "Overview Of Scatterometry Applications In High Volume Silicon Manufacturing", AIP Conference Proceedings, vol.788, no.1, pp394-402, 2005
[28] S. A. Coulombe et al.,"Scatterometry measurement of sub-0.1 μm linewidth gratings", Journal of Vacuum Science & Technology B, vol.16, no.1,pp.80-87, 1998
[29] B. K. Minhas et al.,"Ellipsometric scatterometry for the metrology of sub-0.1-mm-linewidth structures", Applied Optics, vol.37, no.22, pp.5112-5115, 1998
[30] M. P. Newell, R. A. M. Keski-Kuha, "Extreme ultraviolet scatterometer: design and capability", Applied Optics, vol.36, no.13, pp.2897-2904, 1997
[31] Y. S. Ku et al., "EUV scatterometer with a high-harmonic-generation EUV source", Optics Express, vol.24, no.24, pp.28014-28025, 2016
[32] J. W. Hovenier, "Structure of a general pure Mueller matrix", Applied Optics, vol.33, no.36, pp.8318-8324, 1994
[33] P.S. Hauge, R.H. Muller, C.G. Smith, "Conventions and formulas for using the Mueller-Stokes calculus in ellipsometry", Surface Science, vol.96, no.1-3, pp.81-107, 1980
[34] K. Suzuki, "Artificial Neural Networks - Methodological Advances and Biomedical Applications", IntechOpen, pp.3-68, 2011
[35] D. Liu et al., "Training Deep Neural Networks for the Inverse Design of Nanophotonic Structures", ACS Photonics, vol.5, no.4, 2018
[36] R. Yamashita, M. Nishio et al., "Convolutional neural networks: an overview and application in radiology. ", Insights Imaging, vol.9, pp.611–629, 2018
[37] Y. Lecun et al., "Gradient-based learning applied to document recognition", Proceedings of the IEEE, vol.86, no.11,pp.2278-2324, 1998
[38] J. Gu, Z. Wang, J. Kuen et al., "Recent advances in convolutional neural networks", Pattern Recognition, vol.77, pp.354-377, 2018
[39] https://idiotdeveloper.com/what-is-deep-convolutional-generative-adversarial-networks
[40] S. Ioffe, C. Szegedy, "Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift", Proceedings of Machine Learning Research, vol.37, pp.448-456, 2015
[41] J. Xu et al., "Reluplex made more practical: Leaky ReLU", 2020 IEEE Symposium on Computers and Communications (ISCC), pp.1-7, 2020
[42] T. Ma et al., "Benchmarking deep learning-based models on nanophotonic inverse design problems", Opto-Electron Sci, vol.1, no.1, 2022
[43] D. P. Kingma, J. Ba, "Adam: A Method for Stochastic Optimization", arXiv, arXiv: 1412.6980 ,2014
[44] https://ogre51.medium.com/computer-vision-cnns-for-images-why-caa14bcd70c0