## 3 Results and Discussion
The results are listed in Table 1. From the calculation, the In composition considering strain in the InGaN on GaN/sapphire is 11% with an in-plane relaxation degree of 3.9% with regard to the GaN layer. On the other hand, for the InGaN/GaN heterostructure grown on the HEMT template, the In incorporation is increased to 16% and a higher relaxation degree approaching 30% is obtained. The higher In composition in the InGaN layer on the HEMT template is considered to have resulted from the compositional pulling effect by the higher relaxation degree. From the thermodynamic analysis, the compressive strain suppresses the In incorporation, whereas tensile strain promotes it [16]. The GaN channel in HEMT suffers from the tensile strain, leading to a relatively larger in-plane lattice constant \(a_{GaN}\). Therefore, the compressive strain between InGaN and GaN is reduced, resulting in a relatively higher In incorporation. On the other hand, the relaxation of epitaxial film by high-density dislocations also tends to induce a higher In incorporation. Figure 2: XRD 2 theta-omega scan of the (002)-plane for the InGaN/GaN heterostructures at the growth temperature of 760 \({}^{\circ}\)C both on the (**a**) AlGaN/GaN-on-Si HEMT and (**b**) GaN/sapphire template. Corresponding XRD rocking curves of InGaN epitaxial layers on the (**c**) AlGaN/GaN-on-Si HEMT and (**d**) GaN/sapphire template, respectively. The crystalline quality and the interface quality of the InGaN on HEMT templates can be improved by optimizing the growth conditions. The growth temperature of the InGaN is increased to 780 \({}^{\circ}\)C and the growth interruption during transition is controlled. The (002)-plane 2 theta-omega scan by XRD of the heterostructure grown at 780 \({}^{\circ}\)C is displayed in Figure 4a. As can be seen, the diffraction intensity of the InGaN in the XRD has increased compared to that grown at 760 \({}^{\circ}\)C. The reflection fringes start to appear, indicating an abrupt interface morphology. The crystalline quality of the InGaN layer has greatly improved, as shown in Figure 4b of the rocking curve around the (002)-plane. The FWHM value is reduced to be 1260 arcsec. It should be pointed out that even grown on the poor-quality GaN channel (1033 arcsec), the quality of the InGaN is comparable to that grown on GaN/sapphire (280 arcsec for GaN/sapphire). Figure 5 is the XRD RSM of the InGaN/GaN around (104)-plane grown on the HEMT template at 780 \({}^{\circ}\)C. Table 1 summarizes the estimated lattice constant \(c\) of both GaN and InGaN, and relaxation degree from XRD reciprocal space mapping of the three samples. As can be seen, the In composition in the InGaN grown at 780 \({}^{\circ}\)C on the HEMT template is \(\sim\)14%, slightly lower than that grown at 760 \({}^{\circ}\)C, but still higher than the In composition in the InGaN/GaN/sapphire grown at 760 \({}^{\circ}\)C. The relaxation degree of the InGaN layer is increased (73%). The reason for the higher relaxation degree is unclear. One possible reason may be the indium precipitation or the formation of three-dimensional islands when the temperature is higher. The PL spectra of the InGaN/GaN heterostructures grown on the HEMT template at different temperatures are shown in Figure S2. Compared to the luminescence of the InGaN/GaN on HEMT at 760 \({}^{\circ}\)C, the intensity of the InGaN/GaN at 780 \({}^{\circ}\)C is increased. The peak at \(\sim\)365 nm is from the GaN near-band-edge (NBE) emission, and that at \(\sim\)385 nm is corresponding to the NBE emission from the InGaN. The yellow band luminescence at \(\sim\)550 nm is usually considered to be originated from the nitrogen vacancy-related defects in the structure. The ratio between the near-band-edge (NBE) and yellow band luminescence (YL) (\(I_{\text{NBE}}\)/\(I_{\text{YL}}\)) can be a reflection for the quality of the epitaxial film.