# Strain Relaxation Effect on the Peak Wavelength of Blue InGaN/GaN Multi-Quantum Well Micro-LEDs
## 3 Results and Discussion
### InGaN/GaN Quantum Well Finite Element Method (FEM) Simulation
The emission wavelength in the strained relaxation region is blueshifted by up to 43 nm. According to the cylindrical symmetry, the distance from the edge (in Figure 7a) is assumed to be the micro-LED pillar radius. With the simulation results in Figure 7a, we statistically analyzed the intensity of the peak wavelengths in the 12 quantum wells in the radius of 100 nm, 200 nm, 400 nm, and 800 nm. The results are shown in Figure 7b. According to our simulations, the 800 nm radius pillar emission peak wavelength is about 457 nm. When the radius is reduced to 400 nm, 200 nm, and 100 nm, the corresponding peak wavelengths are 456 nm, 455 nm, and 451 nm. The peak wavelength offset changes from 1-4 nm. We can draw a conclusion that the piezoelectric polarization generated by the strain in the quantum well directly affects the radiation wavelength. The range of strain relaxation and wavelength shift is mainly related to the thickness of the quantum well and the size of the pillar. The smaller the pillar size, the greater the size modulation effect on the peak wavelength of the device. With this method, the simulations were expanded to a series of columns with diameters from 3 \(\upmu\)m to 20 \(\upmu\)m and the peak wavelength shift versus pillar size was explored. As shown in Figure 7c, the red datapoints represent the calculated peak wavelength of GaN/InGaN pillars of different diameter. When the column diameter increases from 3 to 20 um, the peak wavelength shift calculated by the simulation decreases from 1.92 nm to 0.32 nm. With an increase in the diameter of the column, the proportion of the strain relief area decreases continuously and the influence on the peak wavelength of the whole micro-column is weakened. The black datapoints in Figure 7c represent the results of the corresponding PL experiment (also in Figure 3), which are in good agreement with the trends of the FEM simulation results. However, there is a 0.5-1.1 nm difference between the simulation and the PL test data. We attribute these offset deviations to the following reasons: the P GaN on the original wafer is etched to 100 nm, which will create a strain relaxation from the top of the InGaN/GaN quantum well, and subsequently create a peak wavelength offset increase between the original wafer PL (ORI) and the PL wafer after ICP etching (AFT). On the other hand, the GaN micro-pillar over-etching in the direction of the diameter will create extra edge strain relaxation, which is another reason for the enhancement of the PL peak  
Figure 6: The simulated strain (\(\epsilon_{\text{xx}}\)) of In\({}_{0.25}\)Ga\({}_{0.75}\)N well layer with a diameter of 19 \(\upmu\)m GaN/InGaN pillar: (**a**) the strain distribution at the boundaries of the 12 quantum wells; (**b**) the division of strained regions after synthesizing 12 pairs of wells. wavelength offset. These results confirm that the micro size has a modulation effect on the devices' emission wavelength. Figure 7: (**a**) The simulated peak wavelength distribution (0–1000 nm) of In\({}_{0.25}\)Ga\({}_{0.75}\)N well layer with a diameter of 20 \(\upmu\)m; (**b**) the intensity of peak wavelengths in 12 pairs of wells in the radius of 100 nm, 200 nm, 400 nm, 800 nm, starting from the boundary; (**c**) experimental and simulated peak wavelength shift as a function of pillar diameter.