Simulation and Single Regression Models of Average Abrasive Removal Depth Being Close to Experimental Value of CMP with Different Volume Concentrations and Diameters of Abrasive Particles of Slurry and Experiments

The paper establishes a theoretical simulation model of abrasive removal depths of silicon wafer under chemical mechanical polishing (CMP) by a pattern-free polishing pad with different volume concentrations of slurry and different diameters of abrasive particles. The paper firstly obtains specific downward force energy (SDFEreaction) values of silicon wafer under different volume concentrations of slurry. Furthermore, the paper uses the SDFEreaction value to obtain the theoretical simulation value of the abrasive removal depths per minute of silicon wafer obtained under different volume concentrations of slurry, different diameters of abrasive particles, different downward forces and different rotational velocities. The paper compares the theoretical simulation values of the respective abrasive removal depth per minute of silicon wafer under CMP with the results of 8 experiments under different volume concentrations of slurry at room temperature and different diameters of abrasive particles, and then calculates the ratio of mean difference, which is found to be around 4.2%. Then the value of the ratio of mean difference is used to obtain the average abrasive removal depths per minute being close to the experimental values, under different volume concentrations of slurry, different diameters of abrasive particles, different downward forces and different rotational velocities, and uses these values as the input values, to establish a regression equation MRRe = k(pe)P(alpha e)V(beta e) where alpha(e) and beta(e) are different constants. This paper uses the different k(pe) values as the input values for regression, obtaining the regression equation of k(pe)(x, y), where x denotes the volume concentration of slurry, and y denotes the diameter of abrasive particles. Therefore, the paper establishes a regression equation of the average abrasive removal depth per minute MRRe = k(pe)(x,y)(PV beta e)-V-alpha e being close to the experimental value. Finally, the paper carries out a new experiment to prove that the regression equation MRRe = k(pe)(x,y)(PV beta e)-V-alpha e is reasonable and practical.