## 3 Results and Discussions
### DoE Analysis Results  
The data recorded in Table 2 are fed to Minitab software (trial package, version 17, Minitab Inc., Philadelphia, PA, USA, 2016) for DoE analysis. The analysis results of factors \"A\", \"B\" and \"C\" for two responses I and II, namely \"\(I_{\text{D}}/I_{\text{G}}\) peak intensity ratio\" and \"\(I_{\text{2D}}/I_{\text{G}}\) peak intensity ratio\", respectively, are discussed as follows. Figure 2 shows the main effect plots of factors \"A\", \"B\" and \"C\" for the two responses. Main effect plots represent the average change in output that follows from a change in the level [43]. If a main effect plot is not horizontal, then different levels of the factor affect the response differently, and the steeper the slope of the plotted line, the greater the magnitude of the main effect that exists; whereas, if the plotted line is horizontal (parallel to the \(x\)-axis), there is no main effect present. In such a case, each level of the factor affects the response in the same way, and the response mean is the same across all factor levels [44]. Figure 2 indicates that for both the responses of \(I_{\text{D}}/I_{\text{G}}\) and \(I_{\text{2D}}/I_{\text{G}}\) peak intensity ratios, the plotted line of all three factors \"A\", \"B\" and \"C\" are not parallel to the \(x\)-axis, and thus, they seem to affect the respective responses. The interaction plots of the factors \"A\", \"B\" and \"C\" for the two responses in Table 2 are shown in Figure 3. An interaction plot indicates the dissimilarity in the response variation between the levels of one factor at different levels of other factors [45]. In other words, the interaction between two factors shows that the effect of one factor on the response depends on the level chosen for its counterpart. Parallel plots are an indication of non-significant interaction, whereas non-parallel plots show interaction between the factors [46]. Figure 3 shows that all of the factors \"A\", \"B\" and \"C\" interact, producing interaction terms \"AB\" and \"AC\" for Response I and interaction terms \"AC\" and \"C\" for Response II, as their plots are non-parallel. In other words, the responses at different levels of annealing temperature, a-C layer thickness and annealing time chosen for our PVD-based graphene synthesis are dependent on the levels of each other. The observed change in the two responses due to the factors individually and interactively could be due to the noise occurring in the experiments, and only statistically-significant changes can be considered as the main or interaction effects. Furthermore, the presence of a significant interaction term can mask the significance of the main effects. Hence, both the test for statistical significance and DoE plots need to be analyzed concurrently [32]. Figure 2: Main effect plots of the factors “A”, “B” and “C” for Response I (**a**) and Response II (**b**). All of the factors seem to show the main effect on both responses. In order to test for statistical significance, Analysis of Variance (ANOVA) statistics is employed, and the analysis results are presented in Tables 3 and 4 for the two responses, respectively.