# Thermomechanical Stresses in Silicon Chips for
## 2 Materials and Methods
### Methods  
The optical characterization of the samples was performed by recording Raman spectra at different positions on the surface of the chip, in the temperature range from \(-50\) to \(180\)\({}^{\circ}\)C.  
The Raman setup consists of a micro-Raman instrument working in a backscattering configuration. An argon-ion laser operating at a wavelength of 514.5 nm (Spectra Physics(r) Stabilite 2017-output power 1 W) is used as an excitation source. The focalization of the laser was realized through an optical microscope (Olympus(r) BX 40), equipped with interchangeable lenses 4\(\times\), 10\(\times\), 20\(\times\), 50\(\times\), 100\(\times\), and with a sample holder table movable in three directions (x, y, z) to regulate the sample position. A camera was coupled to the microscope to observe and correctly choose the area of the sample that was scanned by the laser beam. The typical spot diameter in the focus, working with a 20\(\times\) objective, was 3 \(\upmu\)m. The backscattered radiation was analyzed using a 2400 grid spectrograph and converted into an electronic signal by a nitrogen-cooled charge coupled device (CCD). A temperature controller (Linkam(r) THMS600) was used to conduct micro-Raman measurements at specific temperatures, where a modified atmosphere with 100% nitrogen was created to avoid problems due to water in the chamber.  
The Raman signal of the samples was measured by mapping the surface of the chip in 10 \(\times\) 10 positions (reported in Figure 4a) or by detecting the signal along the diagonal in 11 positions (Figure 4b) or in two defined positions, corresponding to the corner \([1,1]\) and the central \([6,6]\) positions of the chip (Figure 4c). In all cases, the instrument was set to ensure that the Raman signal was recorded in the central position of each squared area of the desired location.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Sample Name** & **N\({}^{\circ}\) Samples** & **Substrate Material** & **Soldering Pressure [N]** \\ \hline Si\_unmounted & 1 & / & / \\ A\_AuSn\_p & 3 & Copper & 5 \\ A\_AuSn & 3 & Copper & 0 \\ B\_AuSn\_p & 3 & Ceramics & 5 \\ B\_AuSn & 3 & Ceramics & 0 \\ \hline \end{tabular}
\end{table}
Table 1: Investigated samples: unmounted Si chips or mounted with a soldering process using an interconnection of AuSn.  
Figure 3: Temperature profile used for the soldering process with AuSn alloy as the interconnection material, without **(a)** and with **(b)** pressure. The grey regions indicate an N\({}_{2}\) atmosphere, while the light-yellow region indicates the additional presence of formic acid gas in the oven.  
Each point was recorded using the 20\(\times\) lens and setting the software with an acquisition time of 5 s. The final spectrum was obtained by averaging five repeated measurements. The slit of the spectrograph was set at 40 \(\upmu\)m and kept constant during the analysis of all samples. The input power of the laser was set at 40 mW.  
The Raman spectra were acquired at different temperatures, ranging from \(-50\) to 180 \({}^{\circ}\)C, using the temperature controller: starting from \(-50\)\({}^{\circ}\)C and raising the temperature to 180 \({}^{\circ}\)C, waiting 5 min at a constant temperature before signal acquisition, and vice versa, starting from 180 \({}^{\circ}\)C and cooling to \(-50\)\({}^{\circ}\)C.  
To ensure a correct calibration of the spectrograph, we used the Raman signal from a standard commercial silicon wafer. Moreover, all the spectra of samples were normalized with respect to a plasma line signal, to ensure that the position of the band of interest is not affected by instrumental errors. All of the collected Raman spectra were interpolated with a Lorentzian function to determine their parameters, such as area, intensity, amplitude, and peak position.