## 3 Results and Discussion  
Figure 2a,b present the XRD 2 theta-omega scan of the (002)-plane for the InGaN/GaN heterostructures grown at the temperature of 760 \({}^{\circ}\)C both on AlGaN/GaN-on-Si HEMT and GaN/sapphire template, respectively. Although the growth conditions are the same, the intensity of the InGaN peak for the (002) reflection on AlGaN/GaN-on-Si HEMT is much lower than that on GaN/sapphire template. This suggests a poor crystalline quality of the InGaN epilayer although the thickness is the same. The peak of the (002)-plane diffraction for the InGaN epilayer on the GaN/sapphire template is located at 33.93\({}^{\circ}\), while this peak shifts to 33.98\({}^{\circ}\) when the InGaN is grown on the HEMT template. It should be noted that the peak of the GaN (002)-plane diffraction grown on sapphire is 34.56\({}^{\circ}\), while it is 34.61\({}^{\circ}\) for that on the HEMT template. The different peak positions in the XRD diffraction are resulted from the different strain states in the GaN epilayers grown on different templates. Figure S1 in the supplementary material shows the XRD 2 theta-omega scan of the GaN (002)-plane in the initial HEMT and sapphire substrate. It is found that, before InGaN deposition, the peak of the GaN (002)-plane is located at 34.56\({}^{\circ}\) on sapphire and changes to 34.61\({}^{\circ}\) on the HEMT template. Comparing to the standard peak of GaN (002)-plane diffraction which is located at 34.5692\({}^{\circ}\), the strain in the GaN channel on the HEMT template is much higher than that in the GaN grown on sapphire substrate. The out-of-plane lattice constant \(c\) of the GaN channel in the HEMT structure is smaller (5.179 A) than that on the sapphire substrate (5.186 A), which indicates a tensile strain inside the in-plane direction. On the other hand, the (002)-plane diffraction peak of the GaN layer grown on the sapphire substrate is nearly the same as the standard one with little residual strain. The large strain in the GaN channel results in the different strain behaviors in the following InGaN layer. The crystalline quality of the GaN and InGaN layers on the two templates is further evaluated by the XRD rocking curves. The full-width-at-half-maximum (FWHM) values of the GaN on sapphire around (002)-plane is -280 arcsec, while this value for GaN on the HEMT template is quite wide (1033 arcsec). The poor quality of the GaN channel on the HEMT template greatly influences the quality of the following InGaN epilayer. The (002)-planes of the InGaN on the AlGaN/GaN-on-Si HEMT and GaN/sapphire template are shown in Figure 2c,d, respectively. The FWHM values of the InGaN on the HEMT template and GaN/sapphire are 1590 and 1100 arcsec, respectively. The deteriorated crystalline quality of the InGaN on AlGaN/GaN-on-Si HEMT has originated from the poor-quality GaN channel with a high dislocation density. Figure 1: (**a**) Schematic diagram for the deposition process of the InGaN/GaN heterostructures, and (**b**) structure of the InGaN/GaN heterostructure on the AlGaN/GaN-on-Si high electron mobility transistor (HEMT) template. As a result of the existence of the strain, the In composition cannot be simply calculated by the positions of XRD (002)-planes. The accurate estimation of the In composition, lattice constant, and relaxation degree is performed by analyzing the XRD reciprocal space mappings around the asymmetric diffraction planes. The relaxation degree is defined as: \(R\) (InGaN) = \((a_{InGaN}-a_{GaN})\)/\((a_{InGaN}-a_{GaN})\), where \(a_{InGaN}\) and \(a_{GaN}\) is the measured lattice parameters from RSMs, the \(a_{InGaN}\) is the relaxed parameters predicted by [PERSON]'s law, and the \(a_{GaN}\) is the relaxed GaN lattice constant [15]. Figure 3a,b are the RSMs of the two samples scanned around the (104)-plane for the InGaN/GaN on the AlGaN/GaN-on-Si HEMT and GaN/sapphire template, respectively.