## 3 Results and Discussions
### Optimal Level of DoE Factors  
From the study of DoE, one can see that the three controlling factors do have a significant impact on the graphene growth and its quality. In order to find an optimal level of different factors for good quality graphene growth, i.e., low \(I_{\rm D}/I_{\rm G}\) peak intensity ratio (Response I) and different numbers of graphene layers, i.e., variable \(I_{\rm 2D}/I_{\rm G}\) peak intensity ratio (Response II), contour plot analysis is performed based on the results from DoE, as shown in Figures 7 and 8, respectively. Figure 7: Contour plots for Response I with respect to the factors “A”, “B” and “C”; insets show the surface plots. High levels of the factor “A” and the factor “C” and a low level of the factor “B” indicate a low value of the \(I_{\rm D}/I_{\rm G}\) peak intensity ratio. Figure 7 depicts the contour and surface plots for Response I, wherein any two factors are displayed on the \(x\)- and \(y\)-scales, and the response (on the \(z\) scale) variable is represented by a contour and smooth surface, respectively. These plots show the required levels of factors in affecting the quality of graphene. They indicate that a high level of the factor \"A\", a low level of the factor \"B\" and a high level of the factor \"C\" are the required levels for producing graphene with a low value of the \(I_{\rm D}/I_{\rm G}\) peak intensity ratio, which is highly desirable for good quality graphene [40, 41]. In other words, a combination of longer annealing time, a thinner a-C layer and a higher annealing temperature will result in a lower \(I_{\rm D}/I_{\rm G}\) peak intensity ratio and, hence, graphene with lesser defects. Figure 8 depicts the contour and surface plots for Response II and shows the required levels of factors affecting the number of synthesized graphene layers. They suggest that a high level of the factor \"A\" and a low level of the factors \"B\" and \"C\" are the required levels for producing graphene with a high value of the \(I_{\rm 2D}/I_{\rm G}\) peak intensity ratio (>1.5), which is highly desirable for single-layer or few-layer graphene [40, 41]. In other words, a treatment combination of higher annealing temperature, thinner a-C layer and smaller annealing time will result in a higher \(I_{\rm 2D}/I_{\rm G}\) peak intensity ratio, and hence, mono-layer/few-layer graphene will be synthesized. On the other hand, if multi-layer graphene is desired, then there is a large region for the choice of levels in each of the contour plots shown in Figure 8. These regions represent the \(I_{\rm 2D}/I_{\rm G}\) peak intensity ratio values below one, which is a signature for multi-layer graphene [40, 41]. The trends suggested by Figures 7 and 8 are instrumental in bringing out a clear relation between the choice of levels for the factors and the quality/number of graphene layers, and they are summarized in Table 5.  
Figure 8: Contour plots for Response II with respect to the factors “A”, “B” and “C”; the insets show the surface plots. The area within dotted boundaries represents multi-layer graphene. For the case of mono-/few-layer graphene, the annealing time is required to be optimized as it affects the two responses in opposite directions, as shown in Table 5. Long annealing time favors low defects, but smaller annealing time favors mono-/few-layer graphene synthesis. Hence, the response surface method [37; 45] must be employed for optimizing growth parameters, which we will present in the future work.