Optimization of CMP processing parameters for Si based on response surface method
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摘要: 为提高单晶硅化学机械抛光(chemical mechanical polishing,CMP)的表面质量和抛光速度,通过响应面法优化CMP抛光压力、抛光盘转速和抛光液流量3个工艺参数,结果表明抛光压力、抛光盘转速、抛光液流量对材料去除率和抛光后表面粗糙度的影响依次减小。通过数学模型和试验验证获得最优的工艺参数为:抛光压力,48.3 kPa;抛光盘转速,70 r/min;抛光液流量,65 mL/min。在此工艺下,单晶硅CMP的材料去除率为1 058.2 nm/min,表面粗糙度为0.771 nm,其抛光速度和表面质量得到显著提高。Abstract: To improve the polishing efficiency and precision, the optimum processing parameters of Si in the chemical mechanical polishing (CMP) process were analysed by CMP experiments and response surface methodology. The results show that polishing pressure has the largest influence on the material removal rate and surface roughness of Si polishing. The second largest influential factor is polishing rotational speed and the third is polishing fluid flow rate. The prediction models of material removal rate and surface roughness are established. The optimum processing parameters are obtained when the polishing pressure is 48.3 kPa, polishing rotational speed is 70 r/min and polishing fluid flow rate is 65 mL/min with the prediction models and by experiments. With these processing parameters, the material removal rate and surface roughness are 1 058.2 nm/min and 0.771 nm, respectively.
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表 1 响应面因素及水平值
Table 1. Experimental parameters and levels
水平 抛光压力
p/ kPa
A
抛光盘转速
n/ (r·min−1)
B
抛光液流量
q/ (mL·min−1)
C
−1 29.0 60 40 0 38.6 80 60 1 48.3 100 80 表 2 试验设计方案及试验结果
Table 2. Experimental plan and result
编号 A
kPaB
r/mimC
mL/minX
nm/minY
nm1 38.6 80 60 1 008.2 0.808 2 48.3 80 40 1 064.1 0.834 3 48.3 80 80 1 138.7 0.792 4 38.6 100 80 1 051.6 0.846 5 38.6 80 60 982.1 0.807 6 29.0 100 60 867.0 0.861 7 29.0 60 60 734.6 0.984 8 48.3 100 60 1 180.9 0.832 9 29.0 80 80 854.8 0.919 10 38.6 80 60 978.9 0.797 11 48.3 60 60 1 034.2 0.837 12 38.6 80 60 989.9 0.818 13 38.6 60 80 861.1 0.866 14 38.6 60 40 835.4 0.910 15 38.6 100 40 1 017.6 0.874 16 38.6 80 60 994.4 0.822 17 29.0 80 40 798.4 0.952 表 3 材料去除率的回归模型方差分析结果
Table 3. Variance analysis results of material removal rate model
来源 平方和 自由度 均方差 F值 P值 模型 25 876.75 9 25 876.75 65.28 <0.000 1 A 1.691 × 105 1 1.691 × 105 426.60 <0.000 1 B 53 105.40 1 53 105.40 133.97 <0.000 1 C 4 545.81 1 4 545.81 11.47 0.011 7 AB 51.12 1 51.12 0.13 0.730 1 AC 82.81 1 82.81 0.21 0.661 5 BC 17.22 1 17.22 0.04 0.840 8 A2 204.84 1 204.84 0.52 0.495 5 B2 3 676.64 1 3 676.64 9.28 0.018 7 C2 1 638.21 1 1 638.21 4.13 0.081 6 残差 2 774.76 7 396.39 失拟项 2 240.98 3 746.99 5.60 0.064 8 纯误差 533.78 4 133.45 总离差 2.357 × 105 16 表 4 表面粗糙度的回归模型方差分析结果
Table 4. Variance analysis results of surface roughness model
来源 平方和 自由度 均方差 F值 P值 模型 4.800 × 10−2 9 5.300 × 10−3 22.71 0.000 2 A 2.200 × 10−2 1 2.200 × 10−2 94.94 <0.000 1 B 4.232 × 10−3 1 4.232 × 10−3 18.14 0.003 8 C 2.701 × 10−3 1 2.701 × 10−3 11.58 0.011 4 AB 3.481 × 10−3 1 3.481 × 10−3 14.92 0.006 2 AC 2.025 × 10−5 1 2.025 × 10−5 0.09 0.776 9 BC 6.400 × 10−5 1 6.400 × 10−5 0.27 0.616 7 A2 4.918 × 10−3 1 4.918 × 10−3 21.07 0.002 5 B2 4.846 × 10−3 1 4.846 × 10−3 20.77 0.002 6 C2 3.708 × 10−3 1 3.708 × 10−3 15.89 0.005 3 残差 1.633 × 10−3 7 2.333 × 10−4 失拟项 1.244 × 10−3 3 4.147 × 10−4 4.26 0.097 6 纯误差 3.892 × 10−4 4 9.730 × 10−5 总离差 4.900 × 10−2 16 表 5 模型可信度分析
Table 5. Model reliability analysis
响应值 相关系数
R1
校正相关系数
R2模型精密系数
R3变异系数
R4/ %X 0.988 2 0.973 1 29.713 2.06 Y 0.966 9 0.924 3 15.588 1.78 表 6 模型预测值与试验结果对比
Table 6. Model predictions vs test results
目标参数 预测值 试验值 相对误差 材料去除率 dMRR / (nm·min−1) 1 194.2 1 238.4 3.7% 表面粗糙度 Ra / nm 0.789 0.771 −2.3% -
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