本研究建立不同研磨液溫度，不同研磨液體積濃度及不同研磨液研磨顆粒直徑之無花紋研磨墊化學機械拋光矽晶圓的研磨移除深度理論模擬模式。並且先將矽晶圓浸泡在不同研磨液溫度下的不同體積濃度研磨液後，接著進行原子力顯微鏡實驗，計算得出浸泡不同研磨液溫度，不同研磨液體積濃度的矽晶圓比下壓能值，再將這些比下壓能值代入創新建立的考慮不同研磨液溫度，不同研磨液體積濃度，不同研磨顆粒直徑，不同下壓力及不同轉速等5種參數之無花紋研磨墊化學機械拋光矽晶圓的每分鐘研磨移除深度理論模擬模式。進而模擬計算出不同研磨液溫度，不同研磨液體積濃度及不同研磨液研磨顆粒直徑、不同下壓力及不同轉速等5種參數所得矽晶圓每分鐘研磨移除深度d_ab之理論模擬值。本研究再利用所得之矽晶圓每分鐘研磨移除深度d_ab之理論模擬值進行迴歸分析，得到不同研磨液溫度，不同研磨液體積濃度，不同研磨顆粒直徑，不同下壓力及不同轉速之每分鐘研磨移除深度的迴歸公式MRR=k_p P^α V^β公式。其中P之α與V之β值在不同研磨液溫度，不同研磨液體積濃度，不同研磨液研磨顆粒直徑，不同下壓力及不同轉速條件下之每分鐘研磨移除深度的P之α與V之β值皆沒改變，只有k_p改變。所以本研究進一步考慮不同研磨液溫度，不同研磨液體積濃度及不同研磨液研磨顆粒直徑的高階多項式之二階迴歸公式二階迴歸公式k_p (x,y,z)，其中x為研磨液溫度，y為研磨液體積濃度，z為研磨顆粒直徑，這樣可以只用一個迴歸公式MRR=k_p (x,y,z) P^α V^β便可計算出不同研磨液溫度，不同研磨液體積濃度及不同研磨顆粒直徑，在不同下壓力及不同轉速的每分鐘研磨移除深度。本研究再利用考慮研磨液溫度之S_tm=(理論模式每分鐘研磨移除深度d_ab 模擬值-k_p P^α V^β )的觀念，得到的S_tm的補償迴歸公式。本研究利用考慮研磨液體積濃度之S_vc=(理論模式每分鐘研磨移除深度d_ab 模擬值-〖(k〗_p P^α V^β+S_tm)) 的觀念，得到的S_vc的補償迴歸公式。本研究再利用考慮研磨顆粒直徑之S_pr=(理論模式每分鐘研磨移除深度d_ab 模擬值-〖(k〗_p P^α V^β+S_tm+S_vc))的觀念，得到的S_pr的補償迴歸公式。最後得到MRR=k_p P^α V^β+S_tm+〖S_vc+S〗_pr的迴歸公式。本研究再進行8組實驗的室溫下，不同研磨液體積濃度，不同研磨顆粒直徑，不同下壓力及不同轉速的化學機械拋光矽晶圓的各別每分鐘研磨移除深度d_ab理論模式模擬值與實驗之平均每分鐘研磨移除深度值的差異百分比值，再計算其平均差異比例值，本文求出平均差異比例值約為4.2%。本研究應用平均差異比例值，建立計算修正後理論模式之接近實驗之平均每分鐘研磨移除深度的公式，進而得到不同研磨液溫度，不同體積濃度及不同研磨液研磨顆粒直徑、不同下壓力及不同轉速等5種參數之修正後理論模式之接近實驗之平均每分鐘研磨移除深度值。進一步用計算所得修正後理論模式接近實驗之平均每分鐘研磨移除深度值，當作輸入值，得到MRR_e=〖k_p〗_e P^(α_e ) V^(β_e )迴歸公式。本研究將其中不同的〖k_p〗_e值當輸入值，用高階多項式的二階迴歸公式，得到〖k_p〗_e (x,y,z)的迴歸公式以及〖〖MRR_e=k〗_p〗_e (x,y,z) P^(α_e ) V^(β_e )迴歸公式。本研究也進行〖〖MRR_e=k〗_p〗_e (x,y,z) P^(α_e ) V^(β_e )+S_tme+〖S_vc〗_e+〖S_pr〗_e的補償迴歸公式。且S_tme，〖S_vc〗_e，〖S_pr〗_e皆為二階迴歸公式。
由於如同上述由每分鐘研磨移除深度d_ab理論模式模擬值所補償迴歸出的S_tm與S_vc與S_pr值影響研磨移除深度值不大，故由修正後理論模式之接近實驗之平均每分鐘研磨移除深度值的〖〖MRR_e=k〗_p〗_e (x,y,z) P^(α_e ) V^(β_e )+S_tme+〖S_vc〗_e+〖S_pr〗_e所得到的S_tme與〖S_vc〗_e與〖S_pr〗_e補償迴歸公式對於修正後理論模式之接近實驗之平均每分鐘研磨移除深度的計算結果影響也不大。所以本研究提出〖〖MRR_e=k〗_p〗_e (x,y,z) P^(α_e ) V^(β_e )為最方便計算修正後理論模式之接近實驗之平均每分鐘研磨移除深度實驗值的較佳迴歸公式。
最後本研究另外進行新的實驗，並將新的實驗結果與迴歸公式〖〖MRR_e=k〗_p〗_e (x,y,z) P^(α_e ) V^(β_e )計算所得之每分鐘研磨移除深度值進行比較後，發現其差異小，由此可驗證修正後理論模式之接近實驗之平均每分鐘研磨移除深度之迴歸公式〖〖MRR_e=k〗_p〗_e (x,y,z) P^(α_e ) V^(β_e )對產業界可為合理實用。

The paper establishes a theoretical simulation model of abrasive removal depth of silicon wafer in chemical mechanical polishing (CMP) by pattern-free polishing pad under different slurry temperatures, different volume concentrations of slurry and different diameters of abrasive particles in slurry. First of all, the paper soaks silicon wafer in slurry at different slurry temperatures and different volume concentrations. After that, atomic force microscopic (AFM) experiment is conducted, achieving the calculated specific downward force energy (SDFE) values of silicon wafer under different slurry temperatures and different volume concentrations of slurry. These SDFE values are substituted in the innovatively established theoretical simulation model of abrasive removal depth per minute of silicon wafer in CMP by pattern-free polishing pad in consideration of 5 parameters, namely different slurry temperatures, different volume concentrations of slurry, different diameters of abrasive particles in slurry, different downward forces and different rotational speeds.
Furthermore, the paper performs simulation and calculates the theoretical simulation value of abrasive removal depth per minute of silicon wafer d_ab obtained under 5 parameters, namely different slurry temperatures, different volume concentrations of slurry, different diameters of abrasive particles in slurry, different downward forces and different rotational speeds. The paper also uses the obtained theoretical simulation value of abrasive removal depth per minute of silicon wafer dab to perform regression analysis, obtaining a regression equation of abrasive removal depth per minute, MRR=k_p P^α V^β under different slurry temperatures, different volume concentrations of slurry, different diameters of abrasive particles in slurry, different downward forces and different rotational speeds. Regarding the α value of P and the β value of V in the equation, the α value of P and the β value of V of abrasive removal depth per minute under the conditions of different slurry temperatures, different volume concentrations of slurry, different diameters of abrasive particles in slurry, different downward forces and different rotational speeds are all unchanged, only that kp is changed. Therefore, the paper further considers the second-order polynomial regression equation of high order k_p (x,y,z) in consideration of different slurry temperatures, different volume concentrations of slurry and different diameters of abrasive particles in slurry. For k_p (x,y,z), x denotes the slurry temperature, y denotes the volume concentration of slurry, and z denotes the diameter of abrasive particles in slurry. Then with only one regression equation MRR=k_p (x,y,z) P^α V^β, the abrasive removal depth per minute under different slurry temperatures, different volume concentrations of slurry, different diameters of abrasive particles in slurry, different downward forces and different rotational speeds can be calculated.The paper further uses the concept in consideration of slurry temperature that S_tm= (Theoretical model’s simulation value d_ab of abrasive remove depth per minute,-k_p P^α V^β), to obtain the compensatory regression equation of S_tm. The paper further uses the concept in consideration of the volume concentration of slurry that S_vc= (Theoretical model’s simulation value d_ab of abrasive removal depth per minute,-〖(k〗_p P^α V^β+S_tm)), to obtain the compensatory regression equation of S_vc. The paper also uses the concept in consideration of the diameter of abrasive particles that S_pr= (Theoretical model’s simulation value d_ab of abrasive removal depth per minute, -〖(k〗_p P^α V^β+S_tm+S_vc)), to obtain the compensatory regression equation of S_pr. Finally, obtains the regression equation of MRR=k_p P^α V^β+S_tm+〖S_vc+S〗_pr. After that, the paper conducts 8 experiments of silicon wafer in CMP by pattern-free polishing pad at room temperature, under different volume concentrations of slurry, different diameters of abrasive particles in slurry, different downward forces and different rotational speeds. The paper calculates the percentage of difference between the results of each theoretical model’s simulation value d_ab of abrasive removal depth per minute of silicon wafer by CMP at room temperature, under different volume concentrations of slurry, different diameters of abrasive particles in slurry, different downward forces and different rotational speeds in the values of average abrasive removal depth per minute in the aforesaid 8 experiments and the results of 8 experiments. The paper also calculates the ratio of mean difference, which is found to be around 4.2%. The paper applies the ratio of mean difference to establish an equation of the average abrasive removal depth per minute being close to the experimental value of the modified theoretical model. The paper further obtains the average abrasive removal depth per minute being close to the experimental value of the modified theoretical model under 5 parameters, namely different slurry temperatures, different volume concentrations of slurry, different diameters of abrasive particles in slurry, different downward forces and different rotational speeds. Furthermore, the paper takes the calculated average abrasive removal depth per minute being close to the experimental value of the modified theoretical model as the input value, obtaining the regression equation MRR_e=〖k_p〗_e P^(α_e ) V^(β_e ). The paper takes its various 〖k_p〗_e values as the input values, and uses a second-order polynomial regression equation of higher order to obtain the regression equation of 〖k_p〗_e (x,y,z) as well as the regression equation 〖〖MRR_e=k〗_p〗_e (x,y,z) P^(α_e ) V^(β_e ). The paper also obtains the compensatory regression equation of 〖〖MRR_e=k〗_p〗_e (x,y,z) P^(α_e ) V^(β_e )+S_tme+〖S_vc〗_e+〖S_pr〗_e, with S_tme，〖S_vc〗_e，〖S_pr〗_e all being two-order regression equations.
As shown from the above, since the values of S_tm 〖,S〗_vc and S_pr obtained after compensatory regression of the theoretical model’s simulation value d_ab of abrasive removal depth per minute does not have great effect on the abrasive removal depth, the compensatory regression equations of S_tme, 〖S_vc〗_e and 〖S_pr〗_e obtained from 〖〖MRR_e=k〗_p〗_e (x,y,z) P^(α_e ) V^(β_e )+S_tme+〖S_vc〗_e+〖S_pr〗_e of the average abrasive removal depth per minute being close to the experimental value of the modified theoretical model also does not have great effect on the calculation result of the average abrasive removal depth per minute being close to the experimental value of the modified theoretical model. Therefore, the paper proposes that 〖〖MRR_e=k〗_p〗_e (x,y,z) P^(α_e ) V^(β_e ) is a better regression equation that can most easily calculate the experimental value of average abrasive removal depth per minute being close to the experimental value of the modified theoretical model.
Finally, the paper conducts new experiments. After the paper compares the abrasive removal depths per minute obtained in the new experiments with the abrasive removal depths per minute calculated from the regression equation 〖〖MRR_e=k〗_p〗_e (x,y,z) P^(α_e ) V^(β_e ), it is found that the difference in between is small. From here, it is proved that the regression equation 〖〖MRR_e=k〗_p〗_e (x,y,z) P^(α_e ) V^(β_e ) of the average abrasive removal depth per minute being close to the experimental value of the modified theoretical model is reasonable and practical for industries.

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