We calculate the phonon-limited carrier mobility in (001) Si films with a fully atomistic framework based on a tight-binding (TB) model for the electronic structure, a valence-force-field model for the phonons, and the Boltzmann transport equation. This framework reproduces the electron and phonon bands over the whole first Brillouin zone and accounts for all possible carrier-phonon scattering processes. It can also handle one-dimensional (wires) and three-dimensional (bulk) structures and therefore provides a consistent description of the effects of dimensionality on the phonon-limited mobilities. We first discuss the dependence of the electron and hole mobilities on the film thickness and carrier density. The mobility tends to decrease with decreasing film thickness and increasing carrier density, as the structural and electric confinement enhances the electron-phonon interactions. We then compare hydrogen-passivated and oxidized films in order to understand the impact of surface passivation on the mobility and discuss the transition from nanowires to films and bulk. Finally, we compare the semi-classical TB mobilities with quantum Non-Equilibrium Green's Function calculations based on k . p band structures and on deformation potentials for the electron-phonon interactions (KP-NEGF). The TB mobilities show a stronger dependence on carrier density than the KP-NEGF mobilities, yet weaker than the experimental data on Fully Depleted-Silicon-on-Insulator devices. We discuss the implications of these results on the nature of the apparent increase of the electron-phonon deformation potentials in silicon thin films