## 2 Materials and Methods
### Experimental Design  
The experiments were designed by central composite design (CCD), which is part of the RSM to analyze the influences of the factors and the interactions among them. A quadratic model with several variables (the number of variables was more than 2 and less than 6) were built with CCD. Each variable had five levels: low (-1), high (+1), median (0), and extreme (\(\pm\alpha\), denoted as \(\pm 1.68\) in this work) values. The extreme values were used to obtain a good prediction of the responses in this domain. The experimental values of factors (defined as \(X_{i}\)) were coded by Equation (2) to compare different factors with different units. \[A_{i}=\frac{X_{i}-X_{0}}{\Delta X} \tag{2}\]  
where \(A_{i}\) is the coded value of the factor, \(X_{0}\) defines the median value of the factor, and \(\Delta X\) refers to the difference between the high and the median values of the factor. In this study, curing time (t), treatment temperature (T), and curing agent dosage (m) were analyzed as the variables (independent factors) and adhesion strength (Y) as the response (dependentfactor). The mass fraction of the three main parts of the HJT silver paste in this study were 80, 13, and 7 wt%, respectively, without specific reference. Table 1 shows the coded and experimental values of t, T, and m. The experimental design in terms of coded values and the results are shown in Table 2. As can be seen in Table 2, the experiments were designed in terms of coded values. There are 19 runs designed in Table 2, which shows 9 experiments based on factorial design (Run no. 1-9), 4 experiments corresponding to the center to evaluate the errors (Run no. 10-13), and 6 experiments corresponding to the expansions (Run no. 14-19). A quadratic model was used to reveal the relationships between the response and these variables (Equation (3)). \[\mathrm{Y}=\mathrm{b}_{0}+\sum_{i=1}^{n}\mathrm{b}_{i}\mathrm{x}_{i}+\sum_{i=1 }^{n}\mathrm{b}_{i}\mathrm{x}_{i}^{2}+\sum_{j>1}^{n}\sum_{i=1}^{n}\mathrm{b}_{ \bar{\mathrm{\mathrm{\eta}}}}\mathrm{x}_{i}\mathrm{x}_{j} \tag{3}\]  
where Y is the response (adhesion strength); \(\mathrm{b}_{0}\) is a constant; \(\mathrm{b}_{i}\), \(\mathrm{b}_{i\bar{\mathrm{\mathrm{\eta}}}}\), and \(\mathrm{b}_{\bar{\mathrm{\eta}}}\) are the coefficients which reflect the linear, quadratic, and interaction relationship, respectively; \(\mathrm{x}_{i}\) and \(\mathrm{x}_{j}\) are the coded values of different factors (i and j vary between 1 and 3 in this study for t, T, and m, respectively); and n is the number of independent factors. The CCD experimental design (Table 2) and data analysis were carried out using the software Design-Expert. The significance test of the quadratic model was carried out through the analysis of the variance (ANOVA) and [PERSON]'s F-test. A three-dimensional coordinate was used to show the relationships among different factors and the response in this work. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Variable**} & \multicolumn{6}{c}{**Level (Coded Value)**} \\ \cline{2-6}  & \(-\)**1.68** & \(-\)**1** & **0** & **1** & **1.68** \\ \hline t (min) & 30 & 34 & 40 & 46 & 50 \\ T (\({}^{\circ}\)C) & 170 & 180 & 195 & 210 & 220 \\ m (wt\%) & 23 & 30 & 40 & 50 & 57 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Levels of investigated factors in this study.