Theoretical Simulation and Regression Analysis for Abrasive Removal Depth of Chemical Mechanical Polishing with Pattern-free Polishing Pad at Different Volume Concentrations of Slurry and Experiment

不同體積濃度研磨液之無花紋研磨墊化學機械拋光之研磨移除深度理論模擬及迴歸分析與實驗

林榮慶(Zone-Ching Lin) ； 吳宗儒(Tzung-Ru Wu)

《中國機械工程學刊》 41卷6期 (2020/12) Pp. 713-723

摘要

Considering that the contact area between the asperity peak surface of pattern-free polishing pad and wafer is of Gaussian distribution, the paper dippd silicon wafer in slurry at different volume concentrations at room temperature, and then performs atomic force microscopic (AFM) experiment. The paper calculates the specific down force energy (SDFE) values of silicon wafer dipped in slurry at different volume concentrations at room temperature. Then the paper substitutes these values in an innovatively established theoretical model of abrasive removal depth in chemical mechanical polishing (CMP) by pattern-free polishing pad with slurry at different volume concentrations. Then the paper makes a comparison between the simulation calculated abrasive removal depth value per minute obtained from calculation and the result of average abrasive removal depth per minute obtained from CMP experiment by pattern-free polishing pad. Finally, the calculated result obtained from theoretical simulation is proved to be reasonable. Furthermore, the paper proposes a correction concept for the average difference ratio of the simulation result to the experimental result, making the abrasive removal depth value per minute obtained from simulation after compensatory correction become closer to the experimental result. The paper, giving consideration for slurry at different volume concentrations at room temperature, also establishes a new regression model and a new equation of average abrasive removal depth per minute in CMP by pattern-free polishing pad at different down forces and rotational velocities, and with slurry at different volume concentrations so as to make it close to the experimental result. The paper also completes the compensatory regression equation after adding the effects of slurry at different volume concentrations, and makes analysis.

關鍵字

abrasive removal depth ； regression model ； volume concentration ； pattern-free polishing pad ； chemical mechanical polishing (CMP)

並列摘要

本研究考慮無花紋研磨墊之粗度峰表面與晶圓接觸面積為高斯分佈，且將矽晶圓浸泡在室溫下不同體積濃度研磨液後，再進行原子力顯微鏡實驗，計算得出浸泡室溫不同體積濃度研磨液的矽晶圓比下壓能值，再將這些值代入創新建立的不同體積濃度之無花紋研磨墊化學機械拋光的研磨移除深度理論模式。將模擬計算所得之每分鐘研磨移除深度值與用無花紋研磨墊的化學機械拋光（CMP）實驗所得平均每分鐘研磨移除深度的結果相比較最後驗證理論模擬計算所得之結果為合理的。本研究進一步提出模擬與實驗所得結果的平均差異比例的修正觀念，使得補償修正後模擬所得之每分鐘研磨移除深度值將能更接近實驗的結果。本研究也建立室溫下考慮不同體積濃度研磨液，不同下壓力及轉速的不同體積濃度之無花紋研磨墊化學機械拋光的接近實驗的平均每分鐘研磨移除深度新的迴歸模式及公式，並完成加上不同體積濃度研磨液影響的補償迴歸公式與分析。