  We present an analytical model for the Seebeck coefficient S of superlattice
materials that explicitly takes into account the energy relaxation due to
electron-optical phonon (e-ph) scattering. In such materials, the Seebeck
coefficient is not only determined by the bulk Seebeck values of the materials
but, in addition, is dependent on the energy relaxation process of charge
carriers as they propagate from the less-conductive barrier region into the
more-conductive well region. We calculate S as a function of the well size d,
where carrier energy becomes increasingly relaxed within the well for d greater
than l, where l is the energy relaxation length. We validate the model against
more advanced quantum transport simulations based on the nonequilibrium Green
function (NEGF) method and also with an experiment, and we find very good
agreement. In the case in which no energy relaxation is taken into account, the
results deviate substantially from the NEGF results. The model also yields
accurate results with only a small deviation (up to ~3%) when varying the
optical phonon energy hw or the e-ph coupling strength D0, physical parameters
that would determine l. As a first order approximation, the model is valid for
nanocomposite materials, and it could prove useful in the identification of
material combinations and in the estimation of ideal sizes in the design of
nanoengineered thermoelectric materials with enhanced power factor performance.
