The effect of gallium (Ga) concentration on the structural evolution of atomic-layer-deposited indium gallium oxide (IGO) (In1-xGaxO) films as high-mobility n-channel semiconducting layers was investigated. Different Ga concentrations in 10-13 nm thick In1-xGaxO films allowed versatile phase structures to be amorphous, highly ordered, and randomly oriented crystalline by thermal annealing at either 400 or 700 degrees C for 1 h. Heavy Ga concentrations above 34 atom % caused a phase transformation from a polycrystalline bixbyite to an amorphous IGO film at 400 degrees C, while proper Ga concentration produced a highly ordered bixbyite crystal structure at 700 degrees C. The resulting highly ordered In0.66Ga0.34O film show unexpectedly high carrier mobility (mu(FE)) values of 60.7 +/- 1.0 cm(2) V-1 s(-1), a threshold voltage (V-TH) of -0.80 +/- 0.05 V, and an I-ON/OFF ratio of 5.1 x 10(9) in field-effect transistors (FETs). In contrast, the FETs having polycrystalline In1-xGaxO films with higher In fractions (x = 0.18 and 0.25) showed reasonable mu(FE) values of 40.3 +/- 1.6 and 31.5 +/- 2.4 cm(2) V-1 s(-1), V-TH of -0.64 +/- 0.40 and -0.43 +/- 0.06 V, and I-ON/OFF ratios of 2.5 x 10(9) and 1.4 x 10(9), respectively. The resulting superior performance of the In0.66Ga0.34O-film-based FET was attributed to a morphology having fewer grain boundaries, with higher mass densification and lower oxygen vacancy defect density of the bixbyite crystallites. Also, the In0.66Ga0.34O transistor was found to show the most stable behavior against an external gate bias stress.