## 3 Results and Discussions
### Theoretical Analyzation of SEE Processes in a Double-Layer Structure  
Considering that the MgO coating samples prepared on Si surface by the technique of ALD is very smooth, we can employ an ideal model, as shown in Figure 7, to imitate the MgO/Si double-layer structures. Here, the ideal model refers to the structure with homogeneous density and uniform thickness of coating layer and substrate, as well as the surface being smooth. Figure 7 shows the SEE process in the ideal double-layer structure, including the incident of the primary electrons and the excitation of the inner secondary electrons in the motion path, as well as the escaping process of the inner secondary electrons. For the ideal double-layer structure, the SEE process can be divided into the following two situations. Situation #1, if the energy of the primary electron is too low to penetrate the top  
Figure 6: Secondary electron energy spectrum of MgO/Si double-layer structures. coating, only the top layer affects the SEY of the sample, and the bottom substrate has no influence on SEY. Situation #2, if the primary electrons possess enough energy to penetrate through the top layer and enter the bottom substrate, the SEY is determined by the top layer and bottom substrate conjointly. For situation #1, inner secondary electrons are only generated inside the top layer, therefore, they just need to jump over the interface between top layer and vacuum for becoming escaped electrons, namely the interface #1 shown in Figure 7. Therefore, SEY is only dominated by the top layer at this time. For the situation #2, the inner secondary electrons generated inside the substrate need to jump over two interfaces, including interface #1 and #2 shown in Figure 7, as well as travel a long path for becoming escaped electrons. Out of the consideration that a SEY curve contains the electron yield information in different energy ranges, therefore, the situation #1 and #2 ought to be analyzed comprehensively for the primary electrons in various energy ranges. In actuality, the real SEE situation for double-layer structures is much more complicated than that of single-layer pure material. The following paragraphs will discuss the SEE processes of the double-layer structures in detail. According to the report in literature [30], SEY of an ideal double-layer structure can be expressed by the following piecewise function:  
\[\delta_{\text{t}}=\left\{ \begin{array}{cc}C_{1}[1-\exp(-d_{\text{m1}}/ \lambda_{1})],&d_{\text{m1}}\leq d_{1}\\ C_{1}[1-\exp(-d_{1}/\lambda_{1})]+C_{2}B_{1}[1-\exp(-d_{2}/\lambda_{2})]\exp(- d_{1}/\lambda_{1}),&d_{\text{m1}}>d_{1}\end{array} \right. \tag{2}\]  
The calculation formula of \(C_{1}\) and \(C_{2}\) is as follows:  
\[C_{1}=(B_{1}/E_{a1})(A_{1}n)^{1/n}\lambda_{1}d_{\text{m1}}^{1/n-1} \tag{3}\]  
\[C_{2}=(B_{2-1}/E_{a2})(A_{2}n)^{1/n}\lambda_{2}d_{2}^{1/n-1} \tag{4}\]  
The parameters in the above Equations (2)-(4) have the following physical meanings: \(\lambda_{1}\) and \(\lambda_{2}\) represent the mean free path of the excited inner secondary electrons in the top layer and the bottom layer respectively, and this parameter is negatively correlated with the concentration and mobility of the carrier in the material, which can also be considered to be negatively correlated with the material conductivity. \(E_{a1}\) and \(E_{a2}\) refer to the average energy required to excite an inner secondary electron in the top film and the bottom substrate respectively, which is numerically equal to the energy gap of the material. \(B_{1}\) and \(B_{2\text{-}1}\) represent the escape probability constant of the excited inner secondary electrons passing through interface #1 and interface #2 in Figure 7 respectively, which is related to the states of the material surface and interface.