  We calculate the thermoelectric figure of merit,
zT=S^2GT/(\kappa_l+\kappa_e), for p-type Si nanowires with axial Ge
heterostructures using a combination of first-principles density-functional
theory, interatomic potentials, and Landauer-Buttiker transport theory. We
consider nanowires with up to 8400 atoms and twelve Ge axial heterostructures
along their length. We find that introducing heterostructures always reduces
S^2G, and that our calculated increases in zT are predominantly driven by
associated decreases in \kappa_l. Of the systems considered, <111> nanowires
with a regular distribution of Ge heterostructures have the highest
figure-of-merit: zT=3, an order of magnitude larger than the equivalent
pristine nanowire. Even in the presence of realistic structural disorder, in
the form of small variations in length of the heterostructures, zT remains
several times larger than that of the pristine case, suggesting that axial
heterostructuring is a promising route to high-zT thermoelectric nanowires.
