  Low dimensional materials provide the possibility of improved thermoelectric
performance due to the additional length scale degree of freedom for
engineering their electronic and thermal properties. As a result of suppressed
phonon conduction, large improvements on the thermoelectric figure of merit,
ZT, have been recently reported in nanostructures, compared to the raw
materials' ZT values. In addition, low dimensionality can improve a device's
power factor, offering an additional enhancement in ZT. In this work the
atomistic sp3d5s*-spin-orbit-coupled tight-binding model is used to calculate
the electronic structure of silicon nanowires (NWs). The Landauer formalism is
applied to calculate an upper limit for the electrical conductivity, the
Seebeck coefficient, and the power factor. We examine n-type and p-type
nanowires of diameters from 3nm to 12nm, in [100], [110], and [111] transport
orientations at different doping concentrations. Using experimental values for
the lattice thermal conductivity in nanowires, an upper limit for ZT is
computed. We find that at room temperature, scaling the diameter below 7nm can
at most double the power factor and enhance ZT. In some cases, however, scaling
does not enhance the performance at all. Orientations, geometries, and subband
engineering techniques for optimized designs are discussed.
