隨著電子產品性能與需求提升與墨爾定律(moore’s law)的成長，傳統的平面MOSFET結構面臨到尺寸縮小的極限，取而代之的是一種三維的MOSFET結構FinFET電晶體，它的通道區域是垂直於基板方向向上延伸，使得等效的通道面積相對增大，所以更能有效地控制通道中的電子流動，進而提升元件的性能與開關速度。以往的結構測量方式為穿透是顯微鏡TEM和電子顯微鏡SEM，而我們採用橢偏散射儀(Ellipsometric scatterometer)，藉由光學散射及繞射的方式量測結構，量測對光的偏振性(旋光性)和光強度計算出偏振器間的相位角度變與待測物之關係，再利用穆勒矩陣(Mueller matrix)轉換得到橢偏訊號psi和delta，具有非破壞性、時效性和相對便宜的特點。
本篇論文探討類FinFET半導體之奈米結構，在不同的結構參數下被橢偏射散儀量測出的光譜訊號變化，利用嚴格耦合波分析(RCWA)模擬方法，在MATLAB程式中計算該結構參數下相對應之光譜訊號(psi和delta)。將上述摸擬出來的資料導入深層學習之神經網路中訓練，由反向和正向兩種神經網路模型來相互轉換結構參數與光譜訊號，反向神經網路模型以光譜訊號當作輸入，輸出為對應之結構參數，藉由卷積運算萃取出特徵信號，再送到全連接層作標籤分類；反之，正向神經網路模型以結構參數當作輸入，輸出為對應之光譜訊號，以轉置卷積運算放大結構參數，再送到全連接層還原出對應光譜。有別於傳統的量測方法和數值模擬，成熟的模型就能準確地預測出該結構的特徵或是光譜訊號， 在往後的實驗中創造更多可能性。

This paper mainly focuses on using deep neural networks to reconstruct structural parameters from spectral information. Firstly, the rigorous coupled wave analysis (RCWA) is employed in the MATLAB program to simulate the spectral signals (Psi and Delta) corresponding to different FinFET-Fin semiconductor structural parameters. Instead of conducting actual experiments, ellipsometer measurements are simulated for the structures, and the simulated data is used as the training data for the neural network model.The neural network model used is an inverse neural network (INN) implemented under the PYTORCH framework in the PYTHON programming language. The model uses convolutional calculations to extract essential features for classification. Its goal is to predict accurate structural parameters by comparing the model's output with the actual structural parameters, using spectral information for parameter prediction. Additionally, by reversing the INN model and using structural parameters as input and spectral signals as output, this model is called a forward neural network (FNN). The FNN model predicts spectral signals from input parameters and evaluates the accuracy and performance of the reconstructed spectrum through transposed convolutional layer computations, amplifying the information-poor structural parameters to spectral information.If both of the above neural networks can make accurate predictions, it will be highly beneficial for future semiconductor processing or simulation research.

[1] T. Cui, J. Li, Y. Wang, S. Nazarian, and 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, pp. 172-183, 2018, doi: 10.1109/tetc.2016.2640185.
[2] N. G. Orji et al., "Metrology for the next generation of semiconductor devices," Nat Electron, vol. 1, 2018, doi: 10.1038/s41928-018-0150-9.
[3] Y. Atalla, Y. Hashim, A. N. A. Ghafar, and W. A. Jabbar, "A temperature characterization of (Si-FinFET) based on channel oxide thickness," TELKOMNIKA (Telecommunication Computing Electronics and Control), vol. 17, no. 5, 2019, doi: 10.12928/telkomnika.v17i5.11798.
[4] C. C. Hu, Modern Semiconductor Devices for Integrated Circuits. Pearson College Div, 2009.
[5] A. C. Diebold, A. Antonelli, and N. Keller, "Perspective: Optical measurement of feature dimensions and shapes by scatterometry," APL Materials, vol. 6, no. 5, 2018, doi: 10.1063/1.5018310.
[6] 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, doi: 10.1149/06905.0015.
[7] H. Kawahira et al., "Control of the sidewall angle of an absorber stack using the Faraday cage system for the change of pattern printability in EUVL," presented at the Photomask Technology 2008, 2008.
[8] O. Ros Bengoetxea, "Development and characterization of plasma etching processes for the dimensional control and LWR issues during High-k Metal gate stack patterning for 14FDSOI technologies," Université Grenoble Alpes (ComUE), 2016.
[9] S. Liu et al., "Machine learning aided solution to the inverse problem in optical scatterometry," Measurement, vol. 191, 2022, doi: 10.1016/j.measurement.2022.110811.
[10] X. Chen and S. Liu, "Optical Scatterometry for Nanostructure Metrology," in Metrology, (Precision Manufacturing, 2019, ch. Chapter 17, pp. 477-513.
[11] G. E. Hinton, S. Osindero, and Y.-W. Teh, "A fast learning algorithm for deep belief nets," Neural computation, vol. 18, no. 7, pp. 1527-1554, 2006.
[12] A. Krizhevsky, I. Sutskever, and G. E. Hinton, "ImageNet classification with deep convolutional neural networks," Communications of the ACM, vol. 60, no. 6, pp. 84-90, 2017, doi: 10.1145/3065386.
[13] Y. B. Ian Goodfellow, Aaron Courville, Deep Learning MIT, 2016.
[14] A. G. B. Richard S. Sutton, Reinforcement Learning: An Introduction, 2 ed. USA: Bradford Book, 2018.
[15] D. E. Rumelhart, G. E. Hinton, and R. J. Williams, "Learning representations by back-propagating errors," nature, vol. 323, no. 6088, pp. 533-536, 1986.
[16] Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner, "Gradient-based learning applied to document recognition," Proceedings of the IEEE, vol. 86, no. 11, pp. 2278-2324, 1998.
[17] 郭至恩, 深度學習-從入門到實戰(使用MATLAB). 臺灣: 全華圖書, 2020.
[18] V. B. Jakub Langr, GAN對抗式生成網路. 臺北: 旗標, 2020.
[19] W. Lee and F. L. Degertekin, "Rigorous Coupled-Wave Analysis of Multilayered Grating Structures," Journal of Lightwave Technology, vol. 22, no. 10, pp. 2359-2363, 2004, doi: 10.1109/jlt.2004.833278.
[20] N. Y. Chang and C. J. Kuo, "Algorithm based on rigorous coupled-wave analysis for diffractive optical element design," JOSA A, vol. 18, no. 10, pp. 2491-2501, 2001.
[21] H. Kim, I.-M. Lee, and B. Lee, "Extended scattering-matrix method for efficient full parallel implementation of rigorous coupled-wave analysis," JOSA A, vol. 24, no. 8, pp. 2313-2327, 2007.
[22] C. J. Raymond, "Multiparameter grating metrology using optical scatterometry," Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures, vol. 15, no. 2, 1997, doi: 10.1116/1.589320.
[23] G. L. Whitworth, A. Francone, C. M. Sotomayor-Torres, and N. Kehagias, "Real-time Optical Dimensional Metrology via Diffractometry for Nanofabrication," Sci Rep, vol. 10, no. 1, p. 5371, Mar 25 2020, doi: 10.1038/s41598-020-61975-3.
[24] Y. S. Ku, S. C. Wang, D. M. Shyu, and N. Smith, "Scatterometry-based metrology with feature region signatures matching," Opt Express, vol. 14, no. 19, pp. 8482-91, Sep 18 2006, doi: 10.1364/oe.14.008482.
[25] J. P. Hugonin and P. Lalanne, "Reticolo software for grating analysis," arXiv preprint arXiv:2101.00901, 2021.
[26] 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, doi: 10.1063/1.4986766.
[27] L. Cisotto and H. Paul Urbach, "Amplitude and phase beam shaping for highest sensitivity in sidewall angle detection," J Opt Soc Am A Opt Image Sci Vis, vol. 34, no. 1, pp. 52-60, Jan 1 2017, doi: 10.1364/JOSAA.34.000052.
[28] S. N. Savenkov, "Jones and Mueller matrices: structure, symmetry relations and information content," Light Scattering Reviews 4: Single Light Scattering and Radiative Transfer, pp. 71-119, 2009.
[29] S. Liu, X. Chen, and C. Zhang, "Development of a broadband Mueller matrix ellipsometer as a powerful tool for nanostructure metrology," Thin Solid Films, vol. 584, pp. 176-185, 2015, doi: 10.1016/j.tsf.2015.02.006.
[30] X. Li, H. Hu, L. Wu, and T. Liu, "Optimization of instrument matrix for Mueller matrix ellipsometry based on partial elements analysis of the Mueller matrix," Opt Express, vol. 25, no. 16, pp. 18872-18884, Aug 7 2017, doi: 10.1364/OE.25.018872.
[31] M. Korde et al., "Nondestructive characterization of nanoscale subsurface features fabricated by selective etching of multilayered nanowire test structures using Mueller matrix spectroscopic ellipsometry based scatterometry," Journal of Vacuum Science & Technology B, vol. 38, no. 2, 2020, doi: 10.1116/1.5136291.
[32] M. T. Taigao Ma1, Haozhu Wang, L. Jay Guo, "Benchmarking_deep_learning-based_models_on_nanophotonic_inverse_ design_problems," Opto-Electronic Science, pp. 2-5, 2000.
[33] S. Ruder, "An overview of gradient descent optimization algorithms," arXiv preprint arXiv:1609.04747, 2016.
[34] M. Lin, Q. Chen, and S. Yan, "Network in network," arXiv preprint arXiv:1312.4400, 2013.
[33] https://www.javatpoint.com/single-layer-perceptron-in-tensorflow
[34] https://pytorch.org/docs/stable/generated/torch.nn.functional.conv1d.html
[35] https://www.intel.com.tw/content/www/tw/zh/products/sku/197098/intel-xeon-silver-4210r-processor-13-75m-cache-2-40-ghz/specifications.html
[36] https://www.leadtek.com/cht/products/workstaion_graphics(2)
[37] https://dyfeiyang.net/2020/12/05/2020-nov/
[38] https://www.linkedin.com/pulse/must-read-path-breaking-papers-image-classification-muktabh-mayank/