We report an in situ fabrication method of self-organized quantum wire structures on patterned GaAs substrates by molecular beam epitaxy. The present method is based upon a selective doping mechanism of amphoteric silicon dopant both on patterned (311)A and on (100) GaAs substrates. The surface electrostatic potential distribution on these patterns was investigated by electrostatic force microscope (EFM) and quantum wire structures were verified. A minimum wire width of approximate to 80 nm was obtained for samples based on both substrate orientations. Good agreement of the wire width estimation by the EFM estimation and the magnetoresistance measurement on modulation-doped heterojunction single quantum wire transistor confirms the validity of the present approach to fabricate self-assembled quantum wires.