  We analyze the effect of low dimensionality on the electrical conductivity
({\sigma}) and Seebeck coefficient (S) in ultra-narrow Si nanowires (NWs) by
employing atomistic considerations for the electronic structures and linearized
Boltzmann transport theory. We show that changes in the geometrical features of
the NWs such as diameter and orientation, mostly affect {\sigma} and S in two
ways: i) the distance of the band edges from the Fermi level ({\eta}F) changes,
and ii) quantum confinement in some cases strongly affect the effective mass of
the subbands, which influences the conductivity of the NWs and {\eta}F. Changes
in eta_F cause exponential changes in {\sigma}, but linear changes in S. S
seems to be only weakly dependent on the curvature of the bands, the strength
of the scattering mechanisms, and the shape of the DOS(E) function, contrary to
current view. Our results indicate that low dimensionality has a stronger
influence on {\sigma} than on S due to the stronger sensitivity of {\sigma} on
{\eta}F. We identify cases where bandstructure engineering through confinement
can improve {\sigma} without significantly affecting S, which can result in
power factor improvements.
