# Thermomechanical Stresses in Silicon Chips for
## 4 Discussion
Figure 12: Stress distribution at \(-\)50 \({}^{\circ}\)C, on a Si\({}_{-}\)Unmounted chip (panel **a**), A\({}_{-}\)AuSn\({}_{-}\)p sample (**b**), and A\({}_{-}\)AuSn sample (**c**). Figure 13: Stress distribution at 180 \({}^{\circ}\)C, on Si\({}_{-}\)Unmounted chip (**a**), A\({}_{-}\)AuSn\({}_{-}\)p sample (**b**), and A\({}_{-}\)AuSn sample (**c**). Figures 11c, 12c and 13c show an unstable stress distribution. This can be correlated with mechanical defects after the soldering process. Cross sections of the samples confirmed the experimental results that the samples had cracks within the solder joint. An alternative method to test the integrity of the solder joint is transient thermal testing, which is a nondestructive tool [27]. It is worth also recalling that samples with cracks detected by Raman spectroscopy and confirmed by transient thermal analysis and cross section can still have functioning electric contacts, as demonstrated with high power LEDs, which passed the light-on test [28]. The Raman results of the current study suggest the high potentiality, accuracy, and precision of this optical spectroscopy to estimate the quality of samples. These results are compared in Tables 4-6, reporting the overview of the maximum, minimum, and average values of the Raman shift and stress for each sample, at different temperatures: \(-\)50, 20, and 180 \({}^{\circ}\)C.  
All data are reported with their respective uncertainties obtained from the Lorentzian fit of the peaks. In all tables, the highest variation in Raman shift and stress calculated on the chip surface at the three temperatures is also reported. The errors in the stress values are obtained with the quadrature propagation method. Considering the unmounted sample (Table 4), as expected, the position of the peak does not change significantly on the surface when the temperature is constant: this reflects that the unmounted sample presents only weak stress values, randomly distributed on the area of the chip, which fall in a range slightly higher than 100 MPa. From the calculation of the uncertainties of the stress values, it emerges that the measurements show stress values \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Temperature** & **Maximum** & **Minimum** & **Average** & **Maximum** & **Unit for Shift** \\
[\({}^{\circ}\)C] & **Value** & **Value** & **Value** & **Variation** & **and Stress** \\ \hline \multirow{3}{*}{\(-\)50} & 523.2 \(\pm\) 0.05 & 520.61 \(\pm\) 0.05 & 522.31 \(\pm\) 0.05 & 2.59 \(\pm\) 0.01 & [cm\({}^{-1}\)] \\  & 200 \(\pm\) 20 & \(-\)928 \(\pm\) 20 & \(-\)535 \(\pm\) 30 & 1128 \(\pm\) 40 & [MPa] \\  & 520.51 \(\pm\) 0.05 & 518.63 \(\pm\) 0.04 & 519.85 \(\pm\) 0.05 & 1.88 \(\pm\) 0.09 & [cm\({}^{-1}\)] \\  & 28 \(\pm\) 20 & \(-\)747 \(\pm\) 20 & \(-\)471 \(\pm\) 20 & 775 \(\pm\) 40 & [MPa] \\  & 515.86 \(\pm\) 0.03 & 515.31 \(\pm\) 0.03 & 515.62 \(\pm\) 0.02 & 0.55 \(\pm\) 0.06 & [cm\({}^{-1}\)] \\  & 57 \(\pm\) 20 & \(-\)219 \(\pm\) 20 & \(-\)111 \(\pm\) 6 & 276 \(\pm\) 40 & [MPa] \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Raman shift [cm\({}^{-1}\)] and stress values [MPa] obtained for the A\({}_{\text{-}}\)AuSn sample.