# Strain Relaxation Effect on the Peak Wavelength of Blue InGaN/GaN Multi-Quantum Well Micro-LEDs
## 3 Results and Discussion
### Single InGaN/GaN Micro-Pillar Raman Measurements and Analysis  
In order to verify the above micro-pillar arrays' strain-related PL results, confocal Raman microscopy measurements were employed to characterize micro-pillar strain relaxation. Figure 4 shows the InGaN/GaN wafer Raman spectra collected in the geometric configuration of Z(X,X)Z. There are distinct peaks at approximately 567 cm\({}^{-1}\) and 734 cm\({}^{-1}\), which are assigned to the \(\mathrm{E_{2}}^{\mathrm{H}}\) and \(\mathrm{A_{1}}^{\mathrm{LO}}\) modes of wurtzite GaN, respectively. The Raman \(\mathrm{E_{2}}^{\mathrm{H}}\) mode shift can provide strain relief information due to the biaxial stress caused by lattice mismatch between GaN and InGaN [15; 16]. Figure 3: Features of PL spectral data: **(a)** PL spectrum of the GaN blue LED epitaxial wafer before etching, denoted as ORI; **(b)** PL spectrum of the epitaxial wafer after micro-pillar etching, denoted as AFT; **(c)** micro-pillar arrays’ wavelength shift, ORI-AFT wavelength shift; **(d)** average wavelength shift for different pillar sizes. Through our measurements, the strain relaxation at the edge of the micro-pillar has the same characteristics, so we choose a large InGaN/GaN pillar (diameter of 19 \(\upmu\)m) to analyze more Raman information on the pillar surface. The center position of the cylindrical sample was taken as the Raman test starting point, the step size along the radius was approximately 1 \(\upmu\)m, and the endpoint was the cylinder boundary. Figure 5a shows the E\({}_{2}\)H mode from the center to the edge and it can be seen that the Raman E\({}_{2}\)H mode tends to shift to the right as the distance increases. The peak of the E\({}_{2}\)H mode at a different distance from the center was collected in Figure 5b and the movement of the E\({}_{2}\)H peak position could be observed in more detail. As the distance from the center of the micro-pillar increases, the frequency of the Raman peak remains relatively stable near 566.82 cm\({}^{-1}\) until a distance \(\geq\) 8 \(\upmu\)m, when the Raman frequency shift starts to move significantly towards the high-frequency direction. At the boundary position, the frequency shift reaches 567.93 cm\({}^{-1}\), which is close to the bulk GaN E\({}_{2}\)H mode. The change of E\({}_{2}\)H indicates that there is strain inside the pillar, while there is full strain relaxation at the edge. The stress and strain relief at the pillar edge along the \(x\)-axis (\(\Delta\sigma_{xx}\), \(\Delta\varepsilon_{xx}\)) can be calculated through Equations (1) and (2). Figure 4: The Raman spectra of InGaN/GaN blue LED wafer. Figure 5: (**a**) E\({}_{2}\)H modes of Raman spectra after Gaussian fitting and normalization at different distances from center; (**b**) E\({}_{2}\)H peaks at different distances from the center. \[\Delta\sigma_{xx}=\frac{\Delta\omega}{k}=\frac{Edge\ Raman\ shift\left(E_{2}^{H} \right)-Center\ Raman\ shift\left(E_{2}^{H}\right)}{2.56} \tag{1}\]  
\[\Delta\varepsilon_{xx}=\frac{\Delta\sigma_{xx}}{C_{11}+C_{12}} \tag{2}\]  
Here, \(k\) is the stress coefficient, and \(C_{11}\) and \(C_{12}\) are the elastic moduli of In\({}_{0.25}\)Ga\({}_{0.75}\)N (listed in Table 1). From our fitted results in Figure 5b, the Raman frequency shift near the center area is 566.82 cm\({}^{-1}\) and the Raman frequency shift at the edge position is 567.93 cm\({}^{-1}\). According to Equations (1) and (2), it can be calculated that there is a stress release of \(\Delta\sigma_{xx}=0.43\) GPa and a strain release of \(\Delta\varepsilon_{xx}=0.10\%\) at the pillar edge. Furthermore, the micro-pillar strain-related bandgap and peak wavelength shift were derived from Equations (3)-(8).