Fig. 1. Schematic of thin film system. (a) Sapphire-GaN heterogeneous film system; (b) force free body in specified interface

Fig. 2. Finite element model of sapphire-GaN heterogeneous film system

Fig. 3. Temperature distribution of sapphire-GaN heterogeneous film system after cooling for 1 min

Fig. 4. Warpage deformation of sapphire-GaN heterogeneous film system after cooling for 1 min

Fig. 5. von Mises stress distribution of sapphire-GaN heterogeneous film system after cooling for 1 min

Fig. 6. Interfacial stress distribution of different thicknesses of GaN films for cooling to 1073 K. (a) 2 inch substrate; (b) 4 inch substrate

Fig. 7. Variation of interfacial stress with the thickness of GaN film (ignore edges). (a) 2 inch substrate; (b) 4 inch substrate

Fig. 8. Interfacial stress distribution of different sapphire substrate thickness for cooling to 1073 K. (a) 2 inch substrate; (b) 4 inch substrate

Fig. 9. Variation of interfacial stress with d_s/d_f. (a) 2 inch substrate; (b) 4 inch substrate

Fig. 10. Variation of the maximum warpage of film system with the thickness of GaN film. (a) 2 inch substrate; (b) 4 inch substrate

Fig. 11. Change of stress caused by lattice mismatch and thermal mismatch with cooling time