The quaternary compound semiconductor (InGaO3(ZnO)m); m=1,2,3...)(IGZO) thin films were fabricated by plasma-assisted molecular beam epitaxy. First, the IGZO thin films were grown under the variation of gallium cell temperature to evaluate the fundamental properties of IGZO. A phase transformation between crystalline and amorphous is observed when the gallium content ratio is higher than 28 at%. It revealed redundancy in the metal, which would self-assist the channel or defect state to destroy the crystal structure. The highest mobility of 74.3 cm2/V s was obtained at 28 at% of gallium. By tuning the element content of quaternary compounds, the ternary plots distribution of IGZO thin films exhibits an amorphous structure in most regions. Therefore, the stoichiometric condition of IGZO, which is 1:1:1:4, is demonstrated at the amorphous structure. Additionally, it transitions to crystalline structure after a 1100 °C annealing process.