# Study on the Influence of Sapphire Crystal Orientation on Its Chemical Mechanical Polishing
## 3 Results and Discussion  
The relationship between the hardness (H) and the indentation depth (h) of the four crystal orientations of sapphire is shown in Figure 3. It was suggested that the experimental data were true and reliable because of the high curve overlap of the six experiments. The hardness value of sapphire with different crystal orientations increased rapidly in range of 0-100 nm of the indentation depth, and then the hardness rapidly decreased to the normal value. Subsequently, the value slowly decreased with increasing displacement. Figure 1: Three-dimension surface morphologies on the area of \(490\times 490\) μm\({}^{2}\) by optical profiler for the (**a**) A-plane, (**b**) C-plane, (**c**) R-plane and (**d**) M-plane. Figure 2: The distribution of the sapphire wafers on the carrier plate. As it was shown in Figure 4, the nanoindentation results of the elastic modulus (E) exhibited a good repeatability for the four crystal orientations of the A-plane, C-plane, M-plane and R-plane. The change of the elastic modulus with the indentation depth (h) was similar to the change of the hardness. After a rapid decrease in some range, the numerical change tended to be gentle. Figure 4: _Cont._  
Figure 3: The hardness 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. In this experiment, the trend of the elastic modulus and hardness value changing with the change of indentation depth h was in good accordance with previous reports in other materials, as well known as the indentation size effect [22; 23]. In order to compare the hardness and elastic modulus of different crystal orientations under the same conditions, a certain depth of the indentation depth range between 400 and 600 nm was selected for statistics. The value of hardness and elastic modulus changes both tended to level off within this interval. Finally, the hardness and elastic modulus were counted at the indentation depth of 500 nm. The hardness at the indentation depth of 500 nm was \(28.7\pm 0.45\) GPa, \(24.9\pm 0.55\) GPa, \(25.9\pm 0.34\) GPa, and \(29.6\pm 0.56\) GPa for the A-plane, C-plane, M-plane and R-plane, respectively. The elastic modulus recorded at the depth of 500 nm was \(417.2\pm 4.63\) GPa, \(402.6\pm 8.24\) GPa, \(407.8\pm 4.29\) GPa, \(418.6\pm 4.16\) GPa for the A-plane, C-plane, M-plane and R-plane, respectively. It could be concluded that the hardness value and elastic modulus increased in sequence according to the C-plane, M-plane, A-plane, R-plane from the statistical data. Figure 5 exhibited the material removal rate (MRR) as a function of the polishing time of the four crystal orientations. The material removal rate of all sapphire wafers with different crystal orientations was very fast in the initial processing stage. This is because the surface quality of the sapphire workpiece in the initial stage was not sufficiently good, and there were a lot of rough peaks with different heights. The material removal rate began to decrease with a period of processing, then stabilized within a certain range as the polishing time continued to extend. As the processing time increased, the surface quality of the sapphire workpiece would become better, and the number of rough peaks and the height of the protrusions would gradually decrease, which was equivalent to the gradual decrease in the load acting on the unit area. Therefore, the material removal rate (MRR) slowed down as the processing time increased. Moreover, it could be clearly observed from the figure that the material removal rate of the C-plane was almost faster than the other three crystal planes in the processing time period, and the material removal rate of the R surface was the lowest. There was little difference between the A-plane and the M-plane, but the M-plane was slightly faster than the A-plane. The mean value of the material removal rate was counted when the MRR became stable in this period.