# Thermomechanical Stresses in Silicon Chips for
## 3 Results
### Effect of Temperature on Si Samples  
Raman spectra were collected at different temperatures, from \(-50\) to \(180\)\({}^{\circ}\)C. Sample A_AuSn was measured on the diagonal, at \(-50\), \(-40\), \(-20\), \(0\), \(20\), \(50\), \(80\), \(110\), \(140\), and \(180\)\({}^{\circ}\)C, at increasing and decreasing temperatures. By acting in this way, no strong differences were observed between the data collected at the same temperature during the heating and cooling process (see Table S1 in SI for details). This is clear evidence that, independently of the thermal history of the sample, the assembly has high stability between \(-50\) and \(180\)\({}^{\circ}\)C.  
The slight differences in signal position may be due to the micrometric shift of the sample inside the sample holder as the temperature changes. This fact leads to inevitable random errors due to the sampling of a chip position that is not exactly identical to the previous one.  
For the Si_Unmounted, A_AuSn_p, and A_AuSn samples, the Raman-shift values of the \(520\) cm\({}^{-1}\) peak were collected from \(-50\) to \(180\)\({}^{\circ}\)C, at increasing temperature, in the center of the chip (position [6; 6]) and in a corner (position [1; 1]), which are the positions that typically correspond, respectively, to a more and a less stressed area of the sample [6; 7; 13]. These Raman shifts are reported in Figure 8 and show a linear trend with different intercept and slope values, whose values are reported in Table 3. It is evident how temperature affects the Raman shift value of all samples: as temperature increases, the Raman shift values decrease. Moreover, in the central position, there is a marked difference between Si_Unmounted and mounted samples, reaching the higher values with the A_AuSn assembly, whereas in the corners there are no marked differences in intercepts and slopes. This means that the center, the most stressed area, is more affected by thermal processes than the corner.  
Additionally, the intercept values and the slopes of the fitting outline the differences between the mounted and unmounted samples.  
Figure 8: Central [6; 6] (squares) and corner (triangles) [1; 1] Raman shift recorded at temperatures from \(-50\) to \(180\)\({}^{\circ}\)C with the Si_Unmounted chip (**a**), the A_AuSn_p sample (**b**) and the A_AuSn sample (**c**).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(\mathbf{R^{2}}\) & **Intercept** & **Slope** \\ \hline \multicolumn{4}{c}{**Central position [6; 6]**} \\ \hline
**Si\_Unmounted** & 0.980 & 519.53 \(\pm\) 0.07 & \(-\)0.0248 \(\pm\) 0.0007 \\
**A\_AuSn\_p** & 0.997 & 519.78 \(\pm\) 0.05 & \(-\)0.0265 \(\pm\) 0.0005 \\
**A\_AuSn** & 0.999 & 521.43 \(\pm\) 0.01 & \(-\)0.0324 \(\pm\) 0.0002 \\ \multicolumn{4}{c}{**Corner position [1; 1]**} \\
**Si\_Unmounted** & 0.986 & 519.44 \(\pm\) 0.09 & \(-\)0.0248 \(\pm\) 0.0007 \\
**A\_AuSn\_p** & 0.996 & 519.69 \(\pm\) 0.05 & \(-\)0.0268 \(\pm\) 0.0005 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Linear fit parameters of the Raman peak position signal of the chips at different temperatures.  
The Raman shift values, collected on the diagonal of the chips on copper substrates, at \(-50\)\({}^{\circ}\)C, \(20\)\({}^{\circ}\)C, and \(180\)\({}^{\circ}\)C are reported in Figure 9: the Raman shift values decrease at increasing temperature.  
The position of the peak does not change significantly along the diagonals of unmounted and mounted pressure samples when the temperature is constant: this reflects that the samples present only weak stress values. The Raman shift values along the diagonal of the sample without pressure show a variation in the shift that has a similar trend at constant temperatures: lower values at the corner positions [1; 1] and [11; 11], which increase symmetrically as the temperature moves closer to the center; moreover, it increases in absolute value with decreasing temperature, in particular in the central area.