深溝槽隔離(DTI)結構在三維積體電路中是重要角色，而目前最能有效率的蝕刻出非等向性DTI結構的方法，是使用BOSCH蝕刻法。然而設定BOSCH的工作參數相當複雜，若能預先了解工作參數對蝕刻的影響，可以減少試誤法的時間成本並增進製程效率。電漿主要透過離子轟擊來對矽基板進行蝕刻，此離子轟擊是貢獻電漿抵達矽基板的主要能通量。本研究使用理論能通量模型與實驗能通量模型，進行能通量運算。使用ANSYS/LS-DYNA數值分析軟體，加入Johnson-Cook失效準則做為矽破壞條件，模擬DTI蝕刻情形。透過理論能通量模型，能夠分別計算出SF6與C4F8蝕刻氣體在不同線圈功率下之能通量。透過實驗能通量模型，能夠建立SF6/C4F8混和氣體之蝕刻速率與能通量關係，以及氣體流率與能通量關係。結合理論與實驗能通量，可以取得混和氣體中，各氣體貢獻的能通量比例。並能從ANSYS/LS-DYNA 模擬不同能通量下的蝕刻輪廓。此首創模擬蝕刻輪廓的方法，以高斯分布調整電漿探頭形貌，以迭代的方式尋找出施予電漿探頭的壓力大小。比較模擬輪廓與試片蝕刻輪廓，可以控制相對誤差在6.52%以內。

The deep trench isolation (DTI) structure plays an important role in the three-dimensional integrated circuit, and the most efficient way to etch an anisotropic DTI structure is to use the BOSCH etching method. However, setting the operating parameters of the BOSCH is a complicated issue. If the influence of the operating parameters on the etching profile can be known in advance, the process efficiency can be improved. In this study, a theoretical energy flux model and an experimental energy flux model are used to study the correlations between operating parameters and etching profiles. The ANSYS/LS-DYNA numerical analysis software were used to simulate the etching profile, and Johnson-Cook failure criterion was added as the silicon failure condition. Through the theoretical energy flux model, the energy flux of SF6 and C4F8 etching gases at different coil powers can be calculated separately. Through the experimental energy flux model, the relationship between the etch rate and the energy flux of the SF6/C4F8 mixed gas, and the relationship between the gas flow rate and the energy flux can be established. Combining the results of theoretical and experimental energy flux models, the energy flux ratio contributed by each gas in the mixed gas can be obtained. The etching profile obtaining from different energy fluxes can be simulated from ANSYS/LS-DYNA. This study proposes a new way to simulate the etching profile. Using the Gaussian distribution function to adjust the morphology of the plasma indenter and iteratively to find the maximum pressure need to be assumed for the plasma indenter. Comparing the simulated etching profiles with the experimental samples etching profiles obtains the maximum relative error to be controlled within 6.52%.

[1] J. Parasuraman, A. Summanwar, F. Marty, P. Basset, D. E. Angelescu, and T. Bourouina, “Deep reactive ion etching of sub-micrometer trenches with ultra high aspect ratio,” Microelectronic Engineering, vol. 113, pp. 35-39, 2014.
[2] K. J. Owen, B. VanDerElzen, R. L. Peterson, and K. Najaf, “High Aspect Ratio Deep Silicon Etching,” 2012 IEEE 25th International Conference on Micro Electro Mechanical Systems (MEMS), Paris, pp. 251-254, 2012.
[3] T. Xu, Z. Tao, H. Li, X. Tan, and H. Li, “Effects of deep reactive ion etching parameters on etching rate and surface morphology in extremely deep silicon etch process with high aspect ratio,” Advances in Mechanical Engineering, vol. 9, no. 12, pp. 1-19, 2017.
[4] H. Kersten, H. Deutsch, H. Steffen, G. M. W. Kroesen, and R. Hippler, “The energy balance at substrate surfaces during plasma processing,” Vacuum, vol. 63, no. 3, pp. 385-431, 2001.
[5] A. Giri, and P. E. Hopkins, “Analytical model for thermal boundary conductance and equilibrium thermal accommodation coefficient at solid/gas interfaces,” J Chem Phys, vol. 144, no. 084705, 2016.
[6] D. Remi, T. Anne-Lise, and S. Nadjib, “A Heat Flux Microsensor for Direct Measurements in Plasma Surface Interactions, ” IntechOpen, Microsensor, pp. 87-108, 2011.
[7] M. Mao, Y. N. Wang, and A. Bogaerts, “Numerical study of the plasma chemistry in inductively coupled SF6 and SF6/Ar plasmas used for deep silicon etching applications,” Journal of Physics D: Applied Physics, vol. 44, no. 435202, 2011.
[8] “ANSYS Mechanical Basic Structural Nonlinearities Training Material,” ANSYS, Inc., 2016.
[9] K. J. Bathe, “Finite Element Procedures, 2nd Edition, ” Prentice-Hall, Pearson Education, Inc. 2014.
[10] R. Courant, K. Friedrichs, and H. Lewy, “On the Partial Difference Equations of Mathematical Physics,” IBM Journal of Research and Development, vol. 11, pp. 215-234, 1967.
[11] J. O. Hallquist, “ LS-DYNA Theory Manual, ” LSTC, 2006.
[12] G. R. Johnson, and W. H. Cook, “Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures,” Engineering Fracture Mechanics, vol. 21, no. 1, pp. 31-48, 1985.
[13] C.-F. Han, and J.-F. Lin, “Thermally-induced failures of copper through-silicon via structures evaluated by the strain energy density model,” Thin Solid Films, vol. 615, pp. 281-291, 2016.
[14] C.-F. Han, Y.-Z. Guo, C.-J. Chung, C.-H. Shen, and J.-F. Lin, “Effects of SiO2 film thickness and operating temperature on thermally-induced failures in through-silicon-via structures,” Microelectronics Reliability, vol. 83, pp. 1-13, 2018.
[15] G. Rajesh Chandra, and K. Ramchand H. Rao, “Tumor Detection In Brain Using Genetic Algorithm, ” Procedia Computer Science, vol. 79, pp. 449-457, 2016.
[16] C. Xavier, E. Amorim, V. da Fonseca Vieira, and R. Weber dos Santos, “Genetic Algorithm for the History Matching Problem, ” Procedia Computer Science, vol. 18, pp. 946-955, 2013.
[17] D. Yang, K. Rao, B. Xu, and W. Sheng, “PIR Sensors Deployment with the Accessible Priority in Smart Home Using Genetic Algorithm, ” International Journal of Distributed Sensor Networks, pp. 1-10, 2015.
[18] M. I. Ribeiro, “Gaussian Probability Density Functions: Properties and Error Characterization,” Institute for Systems and Robotics, Instituto Superior Tecnico, 2004.
[19] H. Xiao, “Introduction to semiconductor manufacturing technology,” 2015.
[20] A. Michelmore, J. D. Whittle, J. W. Bradley, and R. D. Short, “Where physics meets chemistry: Thin film deposition from reactive plasmas,” Frontiers of Chemical Science and Engineering, vol. 10, no. 4, pp. 441-458, 2016.
[21] S. McColman, “Bosch processing on the ICPRIE,” NanoFab University of Alberta.
[22] R.-H. Tsai, “Effect of heat Treatment on the Polymer Adhesive Bonding and the Thermal Failure of Through Silicon Via Structure,” National Cheng Kung University, 2017.
[23] A. Doshita, K. Ohtani, and A. Namiki, “Dynamical aspect of Cl2 reaction on Si surfaces,” J Vac Sci Technol A, vol. 16, pp. 265-269, 1998.
[24] K. J. Laidler, “The development of the Arrhenius equation,” Journal of Chemical Education, vol. 61, no. 6, pp. 494-498, 1984.
[25] T. Takayoshi, “Study on atomic-scale plasma process based on substrate-temperature control by frequency-domain low-coherence interferometry,” Department of Electrical Engineering and Computer Science Graduate School of Engineering, Nagoya University, 2015.
[26] F. Adler, H. Kersten, and H. Steffen, “Investigation of the Plasma of a Magnetron Discharge during Titanium Deposition,” Contributions to Plasma Physics, vol. 35, no. 3, pp. 213-223, 1995.
[27] H. Kersten, and G. M. W. Kroesen, “The Thermal Balance of Substrates During Plasma Processing,” Contributions to Plasma Physics, vol. 30, no. 6, pp. 725-731, 1990.
[28] J. A. G. Baggerman, R. J. Visser, and E. J. H. Collart, “Ion‐induced etching of organic polymers in argon and oxygen radio‐frequency plasmas,” Journal of Applied Physics, vol. 75, no. 2, pp. 758-769, 1994.
[29] J. Ding, J. S. Jenq, G. H. Kim, H. L. Maynard, J. S. Hamers, N. Hershkowitz, and J. W. Taylor, “Etching rate characterization of SiO2 and Si using ion energy flux and atomic fluorine density in a CF4/O2/Ar electron cyclotron resonance plasma,” Journal of Vacuum Science & Technology A, vol. 11, no. 4, pp. 1283-1288, 1993.
[30] F. M. Devienne, “Low Density Heat Transfer, ” Advances in Heat Transfer, J. P. Hartnett and T. F. Irvine, eds., pp. 271-356, 1965.
[31] N. P. Tandian, and E. Pfender, “Heat transfer in RF plasma sintering: Modeling and experiments,” Plasma Chemistry and Plasma Processing, vol. 17, no. 3, pp. 353-370, 1997.
[32] K. Martin, “Die Molekularströmung der Gase durch Offnungen und die Effusion,” Annalen der Physik, vol. 333, no. 5, pp. 999-1016, 1909.
[33] G. Fan, and J. R. Manson, “Calculations of the energy accommodation coefficient for gas–surface interactions,” Chemical Physics, vol. 370, pp. 175-179, 2010.
[34] R. Piejak, V. Godyak, B. Alexandrovich, and N. Tishchenko, “Surface temperature and thermal balance of probes immersed in high density plasma,” Plasma Sources Science and Technology, vol. 7, no. 4, pp. 590-598, 1998.
[35] M. A. Lieberman, and A. J. Lichtenberg, “Principles of Plasma Discharges and Materials Processing,” Wiley, 2005.
[36] D. Bohm, “The Characteristics of Electrical Discharge in Magnetic Fields,” McGraw-Hill, New York, 1949.
[37] D. R. Lide, “CRC Handbook of Chemistry and Physics, Internet Version,” 2005.
[38] G. Kokkoris, A. Goodyear, M. Cooke, and E. Gogolides, “A global model for C4F8 plasmas coupling gas phase and wall surface reaction kinetics,” Journal of Physics D: Applied Physics, vol. 41, no. 195211, 2008.
[39] C.-F. Han, and J.-F. Lin, “The model developed for stress-induced structural phase transformations of micro-crystalline silicon films,” Nano-Micro Letters, vol. 2, no. 2, pp. 68-73, 2010.
[40] R. A. Cooke, “Electrostatic chuck, ” Google Patents, 2017.
[41] .Robert L. Bates, P. L. Stephan Thamban, Matthew J. Goeckner, Lawrence. J. Overzet, “Silicon etch using SF6/C4F8/Ar gas mixtures, ” Journal of Vacuum Science & Technology A, vol. 32, no. 041302, 2014.
[42] T. Stefan, T. Thomas, D. Rémi, C. N. Erik, and B. Annemie, “Elucidating the effects of gas flow rate on an SF6 inductively coupled plasma and on the silicon etch rate, by a combined experimental and theoretical investigation,” Journal of Physics D: Applied Physics, vol. 49, no. 385201, 2016.
[43] T. R. Chandrupatla, and A. D. Belegundu, “Introduction to Finite Elements in Engineering, 4th Edition,” 2012.