  We compute both electron- and phonon transmissions in thin disordered silicon
nanowires. Our atomistic approach is based on tight-binding and empirical
potential descriptions of the electronic and phononic systems, respectively.
Surface disorder is modeled by including surface silicon vacancies. It is shown
that the average phonon- and electron transmissions through long SiNWs
containing many vacancies can be accurately estimated from the scattering
properties of the isolated vacancies using a recently proposed averaging method
[Phys. Rev. Lett. 99, 076803 (2007)]. We apply this averaging method to surface
disordered SiNWs in the diameter range 1-3 nm to compute the thermoelectric
figure of merit, ZT. It is found that the phonon transmission is affected more
by the vacancies than the electronic transmission leading to an increased
thermoelectric performance of disordered wires, in qualitative agreement with
recent experiments. The largest ZT>3 is found in strongly disordered <111>
oriented wires with a diameter of 2 nm.
