The reported remarkably high electron mobility of two-dimensional (2D) ${\mathrm{Ga}}_2{\mathrm{O}}_3$ brings this ultrawide band-gap semiconductor to the forefront of high-speed power electronics applications. Using the generalized gradient approximation+U approach, we systematically investigate the electric-field-dependent structural evolution, electronic structures and transport characteristics of 2D ${\mathrm{Ga}}_2{\mathrm{O}}_3$ and its alloys, 2D ${\mathrm{TM}}_{0.5}{\mathrm{Ga}}_{1.5}{\mathrm{O}}_3$ ($\mathrm{TM}=\mathrm{Al}$, In). Our analysis reveals marked anisotropic responses in metal-oxygen bond lengths: field-parallel bonds demonstrate progressive contraction while transverse bonds systematically elongate with the increase in field strength. The nearly free electron gas states emerge in the conduction band of these materials under applied electric fields, progressively shifting toward the conduction-band minimum—a direct consequence of the Stark effect that drives continuous band-gap reduction until complete closure. The band-gap reduction of 2D ${\mathrm{Ga}}_2{\mathrm{O}}_3$ transitions from parabolic dependence in low fields $\left(|E_{fd}|\le 1.02\mathrm{V}/\AA \right)$ to linear regimes at moderate field and high field $\left(|E_{fd}|\ge 1.46\mathrm{V}/\AA \right)$. Notably, 2D ${\mathrm{Ga}}_2{\mathrm{O}}_3$ undergoes a semiconductor-to-metal transition at the critical fields of ±1.48 V/Å, while Al- and In-doped 2D ${\mathrm{Ga}}_2{\mathrm{O}}_3$ alloys exhibit asymmetric closure thresholds due to structural asymmetry. Electron mobility displays a distinctive nonmonotonic field dependence, reaching minima in moderate fields before sharply increasing to maxima at band-gap collapse. The 2D ${\mathrm{In}}_{0.5}{\mathrm{Ga}}_{1.5}{\mathrm{O}}_3$ alloy achieves exceptional field-tunable performance, attaining a peak mobility of $28254.92\mathrm{c}{\mathrm{m}}^2/\mathrm{V}\mathrm{s}$ at −1.87 V/Å, an improvement of more than 200 times over bulk β-${\mathrm{Ga}}_2{\mathrm{O}}_3$. These results not only demonstrate the potential of 2D InGaO alloy as an electron transport material and gate-tunable platform for ultrafast electronics but also establish field-engineering strategies through alloy content for tailoring ultrawide band-gap semiconductor performance.

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• Charge density waves
• Density of states
• Electronic structure of atoms & molecules
• 2-dimensional systems
• Density functional theory