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We present a successful synthesis of single crystalline homogeneous Si1-xGex nanowires (diameter: 7~52 nm) via vapor-liquid-solid mechanism. Results show that quality, density, and growth rate of Si1-xGex nanowires are greatly affected by the growth temperature and the single crystalline Si1-xGex nanowires without amorphous sheath layer can be obtained at optimized growth temperature. Control of the amount of Ge in nanowire was obtained with different GeH4 gas flow rates. Using back-gated field effect transistor integrated with HfO2 gate dielectric, TaN/Ta metal gate and Pd source/drain electrode, Si1-xGex nanowire transistor exhibits p-MOS operation with Ion/Ioff~104, sub-threshold swing of 97 mV/dec.