Boundary scattering of charge carriers and phonons

It is now well established that the lattice thermal conductivity can be significantly reduced at ordinary temperatures by boundary scattering. However, it is equally clear that the beneficial effect on the thermoelectric figure of merit can sometimes be more than offset by boundary scattering of the charge carriers. Here we show that the relative magnitude of the effects of boundary scattering on the phonons and charge carriers can be predicted. We extend the simple theory of boundary scattering of phonons at high temperatures into the region of very small grain size. We illustrate our predictions by applying them to the cases of Si-Ge alloys, Bi-Sb alloys, and Bi/sub 2/Te/sub 3/ alloys. It is shown that boundary scattering improves the figure of merit in the Si-Ge system but is unlikely to do so for the other systems.