酸蝕刻清洗槽內的流體流動以及質傳現象十分重要，晶圓表面蝕刻均勻性會受到此兩者因素的影響，而晶圓表面經過蝕刻清洗後的平坦度會接著影響到半導體的後續製程和最後的生產良率，故為了解酸蝕刻清洗槽內的現象，為此建立數值模型，藉此深入探討，釐清系統。
本研究依據酸蝕刻的機制及清洗槽兩相流的特性建立數學模型，在與實驗相同條件之操作條件下進行數值模擬，與實驗數據比較，驗證模擬的有效性，接著探討清洗槽內的流動狀態與蝕刻液傳遞到晶圓表面進行反應的形式，再透過改變模型輸入的流量、晶圓轉速、輪桿數量等參數，了解晶圓平坦度在不同邊界條件下會有何變化。發現到流量與轉速會以不同的趨勢影響晶圓平坦度，較大的入口流量會使晶圓邊緣的蝕刻速率大幅上升，較高的晶圓轉速會提高整體的蝕刻速率，而支撐並帶動晶圓旋轉的輪桿會造成速度邊界層縮減，產生晶圓邊緣蝕刻的反曲現象，這是影響蝕刻晶圓造成晶圓邊緣平坦度不佳的主要因素。

The fluid flow and mass transfer phenomenon in the acid etching cleaning tank are very important, and the etching uniformity of the wafer surface will be affected by these two factors. The flatness of the wafer surface after etching and cleaning will then affect the subsequent semiconductor process and the final production yield. Therefore, in order to understand the phenomenon in the acid etching cleaning tank, a numerical model is established for this purpose, so as to conduct in-depth discussions and clarify the system.
In this study, a mathematical model was established based on the mechanism of acid etching and the characteristics of the two-phase flow in the cleaning tank. Numerical simulation is carried out under the same operating conditions as the experiment, and the validity of the simulation is verified by comparing with the experimental data. Then, the flow state in the cleaning tank and the form of reaction of the etchant delivered to the wafer surface are discussed. Then, by changing the parameters such as flow rate, wafer rotation speed, and number of roller input by the model, we can understand how the wafer flatness changes under different boundary conditions. We found that the flow rate and the rotational speed will affect the wafer flatness in different trends. A larger inlet flow rate will greatly increase the etching rate of the wafer edge. A higher wafer rotational speed will increase the overall etching rate. The roller that supports and drives the wafer to rotate is the main factor affecting the poor flatness of the wafer edge caused by the etching wafer.

參考文獻
[1] M. S. Kulkarni, H. F. Erk “Acid‐Based Etching of Silicon Wafers: Mass‐Transfer and Kinetic Effects” Journal of The Electrochemical Society, Vol. 147, pp.176-188 (2000)
[2] M. Steinert, J. Acker, S. Oswald, K. Wetzig “Study on the Mechanism of Silicon Etching in HNO3-Rich HF/HNO3 Mixtures” The Journal of Physical Chemistry, Vol. 111, pp.2133-2140 (2007)
[3] H. Robbins, B. Schwartz “Chemical Etching of Silicon: I . The System HF, HNO3 and H2O” Journal of The Electrochemical Society, Vol. 106, pp. 505-510 (1959)
[4] S. Hosokawa, A. Tomiyama “Bubble-Induced Pseudo Turbulence in Laminar Pipe Flows” International Journal of Heat and Fluid Flow, Vol. 40, pp. 97-105 (2013)
[5] R. Rzehak, E. Krepper “CFD Modeling of Bubble-Induced Turbulence” International Journal of Multiphase Flow, Vol. 55, pp.138-155 (2013)
[6] H. Kolbel, H. Ackermann “Large Scale Tests on the Fischer-Tropsch Liquid Phase Synthesis” Chemistry Engineer Technology, vol. 28, pp. 381 (1956)
[7] J. Schweitzer, J. C. Vigui “Reactor Modeling of a Slurry Bubble Column for Fischer-Tropsch Synthesis” Oil & Gas Science and Technology-revue De L Institut Francais Du Petrole, Vol.64, pp.63-77 (2009)
[8] G. Riboux, F. Risso, D. Legendre “Experimental Characterization of the Agitation Generated by Bubbles Rising at High Reynolds Number” Journal of Fluid Mechanics, Vol. 643, pp. 509-539 (2010‬)
[9] C. Garnier, M. Lance, J.L. Marie “Measurement of Local Flow Characteristics in Buoyancy-Driven Bubbly Flow at High Void Fraction” Experimental Thermal and Fluid Science, Vol. 26, pp.811-815 (2002)
[10] S. H. Park, C. Park, J. Y. Lee, B. Lee “A Simple Parameterization for the Rising Velocity of Bubbles in a Liquid Pool” Nuclear Engineering and Technology, Vol. 49, pp.692-699 (2017)
‬[11] Y. Liao, D. Lucas “A Literature Review of Theoretical Models for Drop and Bubble Breakup in Turbulent Dispersions” Chemical Engineering Science, Vol. 64, pp. 3389-3406 (2009)
[12] M. E. Shawkat, C. Y. Ching, M. Shoukri “Bubble and Liquid Turbulence Characteristics of Bubbly Flow in a Large Diameter Vertical Pipe” International Journal of Multiphase Flow, Vol. 34, pp. 767-785 (2008)
[13] Y. Sato, M. Sadatomi, K. Sekoguchi “Momentum and Heat Transfer in Two-Phase Bubble Flow—I. Theory” International Journal of Multiphase Flow, Vol. 7, pp. 167-177 (1981)
[14] A. Serizawa, I. Kataoka “Turbulence Suppression in Bubbly Two-Phase Flow” Nuclear Engineering and Design, Vol. 122, pp. 1-16 (1990)
[15] E. Alméras, F. Risso, V. Roig, S. Cazin, C. Plais, F. Augier “Mixing by Bubble-Induced Turbulence” Journal of Fluid Mechanics, Vol. 776, pp. 458-474 (2015)
[16] A. Das “Analytical Solution to the Flow between Two Coaxial Rotating Disks Using HAM” Procedia Engineering, Vol. 127, pp. 377-382 (2015)
[17] D. J. Monk, D. S. Soane, R. T. Howe “Determination of the Etching Kinetics for the Hydrofluoric Acid/Silicon Dioxide System” Journal of The Electrochemical Society, Vol. 140, pp. 2339-2346 (1993)