# Assessing the Stress Induced by Novel Packaging in GaN HEMT Devices via Raman Spectroscopy
## 3 Results and Discussion
The inset of Figure 7 shows the trend of the frequency of mode E2(high) in the HEMT-B sample (red line) and HEMT-PD sample (blue line) when moving along the vertical path represented by the red line in Figure 5, i.e., crossing the AlGaN/GaN heterostructure starting from the package side and moving towards the silicon substrate. The E2(high) \(\omega\) values allow calculation of the residual stress point by point within the AlGaN/GaN HEMT devices. Indeed, the frequency shift (\(\Delta\omega\)) linearly depends on the residual stress (\(\sigma\)) according to the relationship:  
\[\langle\Delta\omega\rangle =\mathrm{K}\langle\sigma\rangle\]  
Figure 6: Micro-Raman spectra collected at the GaN epitaxy layer (**a**) and at the GaN/Si interface (**b**) of HEMT-B. where K represents the stress coefficient, equal to 4.3 cm\({}^{-1}\)/GPa for GaN grown on c-direction silicon [30]. The frequency shift, \(\Delta\omega\), is defined as \(\Delta\omega=\omega-\omega_{0}\), where \(\omega\) is the peak frequency center, and \(\omega_{0}\) accounts for the corresponding stress-free E2(high) peak frequency center, fixed at 568 cm\({}^{-1}\)[31]. It should be noted that, even if there was a slight influence on the stress due to the ion milling treatment, this influence would be the same in both samples since the milling conditions were the same. Therefore, \(\Delta\omega\) was not affected by the preparation of the samples. Figure 7 shows the residual stress \(\sigma\) in GPa, inferred from the frequency shift E2(high) \(\Delta\omega\), as a function of position along the studied path for both HEMT-B (red line) and HEMT-PD (blue line) devices. Due to the linear correlation between stress and frequency shift, the E2(high) mode frequency center follows a pattern mirroring that of the stress, as can be deduced by observing the inset of Figure 7. Analyzing the residual stress trend along the AlGaN/GaN HEMT structure (Figure 7), it is worth noting that the influence of the package was mainly visible in the range from 5 \(\upmu\)m to 6 \(\upmu\)m (zone of interest). In the range between 6.55 \(\upmu\)m and 7 \(\upmu\)m, the lattice mismatch at the GaN/Si interface induced a more pronounced tensile stress compared to that generated by the presence of packaging, as highlighted by the redshift (a shift towards lower frequencies) of the E2(high) mode. Furthermore, the non-monotonic behavior observed can be attributed to both the characteristics of the multilayer structure and/or the doping of the layers composing the device. The behavior of E2(high) in HEMT-B (red curve in the graph shown in Figure 7) showed a slight initial shift towards lower frequency values as it moved through the layers from 5 \(\upmu\)m to -5.5 \(\upmu\)m, indicating the presence of tensile stress. This was followed by a clear shift towards the blue in E2(high), attributed to compression stress likely induced by additional forces or applied loads. Subsequently, near the silicon substrate, a noticeable tensile stress was observed, characterized by a frequency shift towards lower frequencies, probably stemming from  
Figure 7: Stress distribution along the uniaxial direction, covering a range from 5 \(\upmu\)m to 7 \(\upmu\)m within the GaN layer, for both AlGaN/GaN HEMT-B and AlGaN/GaN HEMT-PD devices. The inset graph represents the E2(high) peak frequency center plotted against the position along the uniaxial direction in \(\upmu\)m.  
the lattice mismatch between the GaN and silicon. The behavior of the E2 mode in the HEMT-PD device was entirely similar. However, the observed stress values were generally lower across the entire device (blue curve in the graph shown in Figure 7). The influence of packaging was evident only within the specified area of interest (from 5 \(\upmu\)m to 6.55 \(\upmu\)m) located near the surface of the device. Within this region, the packaged device (HEMT-PD) showed a decrease in stress levels of about 0.1 GPa compared to the bare one (HEMT-B).