Improvements of crystal quality in GaAs/Si heterostructure by solid phase epitaxy (SPE) are described. RBS and TEM measurements indicate that high density defects are located near the GaAs/Si interface after “2-step MBE”. Utilization of post SPE process (amorphization plus regrowth) significantly improve crystal qujali ty at the GaAs/Si interface, although a small stress field is introduced. In addition a new relation between photoluminecence intensity ratio and stress field is established. This provides a useful too] for measuring small stresses remaining in the GaAs/Si hetero-structure.