GaAs layers free of antiphase domains (APD's) have been grown by molecular beam epitaxy (MBE) on nominally (001)-oriented Si substrates. This is achieved by preheating the substrates at 950 °C over 60 min or at 1000 °C over 5 min in an ultrahigh vacuum. The maximum Hall mobility at 293 K is 5300 cm2 /Vs for the APD-free GaAs layer doped with Si at a concentration of 2×1016 cm−3 . Selective epitaxial growth of GaAs has been carried out on a Si substrate pattrened with SiO2, which was formed by wet O2 oxidation. By choosing an appropriate thickness of the SiO2 layer, the warpage of wafers can be reduced to zero. While single-crystalline GaAs is grown on Si-exposed areas, highly-resistive (ρ ≧ 105 Ωcm) poly-crystalline GaAs is deposited on SiO2 . This technique has been successfully applied for the device isolation of modulation-doped FET's (MODFET's, HEMT's, etc.) on Si without mesa-etching. The transconductance of the MODFET with a 3 µm-long gate reaches 88 mS/mm at 293 K.