# Study on the Influence of Sapphire Crystal Orientation on Its Chemical Mechanical Polishing
## 3 Results and Discussion
The material removal rate calculated by Formula (1) of the A-, C-, M- and R-plane were \(3.85\pm 0.47\) nm/min, \(5.93\pm 0.84\) nm/min, \(4.16\pm 0.39\) nm/min, \(2.47\pm 0.22\) nm/min. Therefore, the relationship of material removal rate was approximately as C-plane \(>\) M-plane \(>\) A-plane \(>\) R-plane. \[MRR=\frac{\Delta m}{\rho\pi R^{2}t}\times 10^{7} \tag{1}\]  
Figure 4: The elastic modulus as a function of the indentation depth of the four crystal orientations for the (**a**) A-plane, (**b**) C-plane, (**c**) M-plane and (**d**) R-plane. where MRR is the material removal rate, \(\Delta m\) is the mass change of sapphire substrates, \(\rho\) is the density of sapphire substrates, \(\rho\) = 3.98 g/cm\({}^{3}\), \(R\) is the radius of sapphire substrates, and \(t\) is the polishing time. Figure 6 exhibits the surface roughness Ra as a function of the polishing time of the four crystal orientations. The initial average surface roughness of the A-, C-, M- and R-plane were 687.242, 654.848, 661.969 and 692.124 nm, respectively. It could be found that the surface roughness of sapphire wafers with different crystal planes decreased rapidly at the beginning of processing. As was the case with the MRR, the initial stage was inadequate. Reaching a certain polishing time, the trend of roughness began to slow down. There was almost no obvious change and the value fluctuated within a certain numerical range. It can be clearly observed from the figure that the roughness improvement of the C-plane is significantly better than the other three crystal surfaces, followed by the M surface. In addition, further analysis of the processing data revealed that the roughness of the C-plane sapphire changed very little after the processing time of 7 h. Therefore, it was believed that the C-plane sapphire had reached its processing limit when the processing time was 7 h under this experimental  
Figure 5: Material removal rate (MRR) as a function of the polishing time of the four crystal orientations for the A-plane, C-plane, M-plane and R-plane. Figure 6: Surface roughness \(R_{\mathrm{a}}\) as a function of the polishing time of the four crystal orientations for the A-plane, C-plane, M-plane and R-plane. condition. For the A-, M- and R-plane, the roughness change basically tended to be stable after the processing time was between 10 and 12 h. Finally, the minimum surface roughness Ra of the A-, C-, M- and R-plane were 0.471, 0.307, 0.376 and 0.595 nm by the measured data, respectively. The processing quality of the C-plane after 8 h of polishing was far better than the other three crystal planes from Figure 7, which had achieved a non-destructive surface effect. While the other three crystal surface still had some certain processing defects to achieve the ideal non-damage surface quality. Figure 7: The 500X SEM surface topography with 8 h polishing time of the four crystal orientations for the (**a**) A-plane, (**b**) C-plane, (**c**) M-plane and (**d**) R-plane. For the C-plane sapphire wafer, the surface roughness value almost reached the minimum and tended to be stable after 7 to 8 h of polishing, from which could be inferred that the C-direction sapphire had reached its processing limit. For the A-, M-, and R-planes, the workpiece surface still had defects such as local pits and micro bumps after 8 h of processing time. As the polishing time continued to extend to 12-14 h, the surface roughness was stable near its minimum value. It could be inferred that the sapphire wafers with the crystal orientations of the A-, M-, and R-plane had reached their processing limits. Therefore, the final optimal surface roughness value can be considered as the best surface quality of sapphire wafers with different crystal orientations under the experimental conditions. Crystal models of the four crystal orientations for the A-plane, C-plane, M-plane and R-plane were shown as Figure 1:0 Although the A-plane and C-plane are both parallel to the C axis, they might exhibit different material properties due to their different atomic arrangements.