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We have investigated the electron mobility in ultrathin-body InGaAs-on-insulator devices using physics-based modeling that self-consistently accounts for quantum confinement and covers band-structure effects in ultrathin III-V layers. Scattering by nonpolar and polar acoustic and optical phonons, surface roughness, and thickness fluctuations, Coulomb and alloy disorder have been included in the calculations. The modeling, calibrated and verified on experimental data from the literature, has revealed a strong influence of thickness fluctuations caused by the light effective mass of Γ valley electrons. Our results indicate that InGaAs-on-insulator MOSFETs are more influenced by interface properties compared with silicon-on-insulator devices and outperform them only above certain body thickness that depends on interface quality.