## 3 Results and Discussions
### Theoretical Explanation on the SEE Properties of MgO/Si Double-Layer Structures  
To make a theoretical analysis of the relationship between SEY and the thickness of the double-layer structures, it is necessary to fit the SEY curves of the top layer and bottom layer respectively. Here, the classic SEE semi-empirical model [33] summarized by [PERSON] in 1973 is utilized to fit the SEY curves of pure MgO and bare Si. The fitting formula is expressed as:  
\[\delta=(B/E_{a})(An)^{1/n}\lambda d_{\rm m}^{1/n-1}[1-\exp(-x/\lambda)] \tag{9}\]  
The physical meanings of each parameter in Equation (9) are the same as those in Equations (2)-(4). The fitted SEY curves of pure MgO and bare Si by using Equation (9) are shown in Figure 8, and the fitting parameters are shown in Table 2. On the basis of the fitting data in Table 2, SEY of the double-layer structures can be calculated by using Equation (2). Figure 8 shows the fitted SEY curves of MgO/Si double-layer structures by using Equation (2). It can be seen from Figure 8 that the SEY variation regularities of the MgO/Si double-layer structures can be well explained by the SEE semi-empirical theory developed in literature [30]. In order to further quantitatively reveal the influence of film thickness on SEE characteristics of double-layer structures, we use Equations (7) and (8) to calculate the SEY contribution of the top layer and the bottom layer respectively, when the thickness of the MgO coating equals to 1 nm and 20 nm, as shown in Figure 9. As can be seen from Figure 9, there is a critical energy point on the \(E_{\rm p}\)-\(\delta_{\rm t}\) curve, denoted as \(E_{\rm pc}\); here, \(E_{\rm pc}\) point represents the minimum energy required for the primary electron to just penetrate through the top layer. For the primary electrons whose \(E_{\rm p}\) is less than \(E_{\rm pc}\), their energy will be exhausted in the top layer and they can only excite the inner secondary electrons in the top layer. In this case, \(\delta_{\rm t}\) is only determined by the SEY generated by the top layer, its value equals to \(\delta_{1}\). Once \(E_{\rm p}\) rises beyond \(E_{\rm pc}\), \(\delta_{1}\) decreases gradually and \(\delta_{2}\) begins to increase from 0, indicating that the bottom substrate begins to have an effect on \(\delta_{\rm t}\) at this time. The SEY decomposition results in Figure 9a show that when the thickness of the film is relatively thin, the influence of substrate on SEY is more obvious, and the proportion of the secondary electrons contributed by the substrate increases gradually with the rise of the primary electron energy \(E_{\rm p}\). The SEY decomposition results in Figure 9b show that when the top coating is relatively thicker, \(\delta_{\rm t}\) becomes less affected by the substrate due to the little contribution of SEY by the substrate. For example, in Figure 9b, \(\delta_{\rm t}\) equals to 5.90 when \(E_{\rm p}\) is 700 eV, and the SEY contributed by Si substrate is only 0.09 at this time, which accounts for 1.53% of \(\delta_{\rm t}\), whereas the SEY contributed by the MgO coating is 5.81 under the circumstances, and accounts for 98.47% of \(\delta_{\rm t}\). The calculation results quantitatively show that when the thickness of the top coating reaches a certain value (usually greater than 10 nm), the contribution of the substrate to the SEY of double-layer structure is very small. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Material** & \(A\) & \(B\) & \(\lambda\)/nm & \(E_{\rm a}\)/eV \\ \hline Si & 2400 & 0.023 & 0.2 & 1.12 \\ MgO & 3500 & 0.225 & 1.3 & 9.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Fitting parameters of SEY curves for MgO/Si double-layer samples. Figure 8: Fitted (lines) and measured (symbols) SEY curves of MgO/Si double-layer samples. Figure 9: Calculated SEY of MgO/Si double-layer samples for (**a**) \(d_{1}=1\) nm and (**b**) \(d_{1}=20\) nm.