It is suggested that low dimensionality can improve the thermoelectric (TE) power factor of a device, offering an enhancement of the $\mathit{ZT}$ figure of merit. In this paper, the atomistic ${\mathit{sp}}^3$$d^5{s}^{*}$-spin-orbit-coupled tight-binding model and the linearized Boltzmann transport theory is applied to calculate the room-temperature electrical conductivity, the Seebeck coefficient, and the power factor of narrow one-dimensional silicon nanowires (NWs). We present a comprehensive analysis of the TE coefficients of $n$-type and $p$-type NWs of diameters from 12 nm down to 3 nm, 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 7 nm. We show that, contrary to the current view, the effect of confinement and geometry on the power factor mostly originates 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. However, we identify cases for which confinement largely improves the channel's conductivity, resulting in ∼2× to 3× power factor improvements. Our results may provide guidance in the design of efficient low-dimensional TE devices.

• Received 1 March 2011

DOI:https://doi.org/10.1103/PhysRevB.83.245305