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In this paper, we have extensively investigated the silicon thickness dependence of the low field electron mobility in ultrathin silicon-on-insulator (UT-SOI) MOSFETs operated both in single- and in double-gate mode. A physically based model including all the scattering mechanisms that are known to be most relevant in bulk MOSFETs has been extended and applied to SOI structures. A systematic comparison with the measurements shows that the experimental mobility dependence on the silicon thickness (TSI) cannot be quantitatively explained within the transport picture that seems adequate for bulk transistors. In an attempt to improve the agreement with the experiments, we have critically rediscussed our model for the phonon scattering and developed a model for the scattering induced by the TSI fluctuations. Our results suggest that the importance of the surface optical (SO) phonons could be significantly enhanced in UT-SOI MOSFETs with respect to bulk transistors. Furthermore, both the SO phonon and the TSI fluctuation scattering are remarkably enhanced with reducing TSI, so that they could help explain the experimental mobility behavior.