We have performed atomistic simulations of the phonon-limited high field carrier transport in < 110 > Si nanowires with small diameter. The carrier drift velocities are obtained from a direct solution of the non-linear Boltzmann transport equation. The relationship between the drift velocity and the electric field considerably depends on the carrier, temperature, and diameter of the nanowires. In particular, the threshold between the linear and non-linear regimes exhibits important variations. The drift velocity reaches a maximum value and then drops. These trends can be related to the effects of quantum confinement on the band structure of the nanowires. We also discuss the impact of the different phonon modes and show that high-energy phonons can, unexpectedly, increase the drift velocity at a high electric field. (C) 2015 AIP Publishing LLC.