It is suggested that low dimensionality can improve the thermoelectric (TE) power factor of a device, offering an enhancement of the ZT figure of merit. In this work the atomistic sp3d5s*-spin-orbit-coupled tight-binding model and the linearized Boltzmann transport theory is applied to calculate the room temperature electrical conductivity, Seebeck coefficient, and power factor of narrow 1D silicon nanowires (NWs). We present a comprehensive analysis of the thermoelectric coefficients of n-type and p-type NWs of diameters from 12nm down to 3nm, in [100], [110], and [111] transport orientations at different carrier concentrations. We find that the length scale at which the influence of confinement on the power factor can be observed is at diameters below 7nm. We show that contrary to the current view, the effect of confinement and geometry on the power factor originates mostly from changes in the conductivity which is strongly affected, rather than the Seebeck coefficient. In general, enhanced scattering at these diameter scales strongly degrades the conductivity and power factor of the device. We identify cases, however, for which confinement largely improves the channel's conductivity, resulting in ~2-3X power factor improvements. Our results may provide guidance in the design of efficient low dimensional thermoelectric devices.

49 pages, 11 figures