  In this work we theoretically explore the effect of dimensionality on the
thermoelectric power factor of InAs nanowires by coupling atomistic
tight-binding calculations to the Linearized Boltzmann transport formalism. We
consider nanowires with diameters from 40nm (bulk-like) down to 3nm (1D), which
allows for the proper exploration of the power factor within a unified
large-scale atomistic description across a large diameter range. We find that
as the diameter of the nanowires is reduced below d < 10 nm, the Seebeck
coefficient increases substantially, a consequence of strong subband
quantization. Under phonon-limited scattering conditions, a considerable
improvement of ~6x in the power factor is observed around d = 10 nm. The
introduction of surface roughness scattering in the calculation reduces this
power factor improvement to ~2x. As the diameter is decreased down to d = 3 nm,
the power factor is diminished. Our results show that, although low effective
mass materials such as InAs can reach low-dimensional behavior at larger
diameters and demonstrate significant thermoelectric power factor improvements,
surface roughness is also stronger at larger diameters, which takes most of the
anticipated power factor advantages away. However, the power factor improvement
that can be observed around d = 10 nm, could prove to be beneficial as both the
Lorenz number and the phonon thermal conductivity are reduced at that diameter.
Thus, this work, by using large-scale full-band simulations that span the
corresponding length scales, clarifies properly the reasons behind power factor
improvements (or degradations) in low-dimensional materials. The elaborate
computational method presented can serve as a platform to develop similar
schemes for 2D and 3D material electronic structures.
