An extended thermodynamic model for size-dependent thermoelectric properties at nanometric scales: Application to nanofilms, nanocomposites and thin nanocomposite films

A new mathematical model is developed, describing size-dependent subcontinuum thermoelectric properties from an extended thermodynamic point of view. This model takes into account the non-local effects of heat transfer through phonons and electrons that are important at nanometric scales. These phenomena are extended to apply also for electric transfer as well as the Seebeck coefficient. This model includes at nanoscale size-dependent electron and phonon thermal conductivities, electric conductivity, Seebeck coefficient and carrier concentrations. We compared nanofilms to nanocomposites and assessed their thermoelectric performances in the form of a figure of merit using as an example Bismuth and BismuthTelluride materials. It appeared that the figure of merit increases considerably for nanofilms and nanocomposites with respect to bulk materials. This is caused by the scattering of phonons and electrons. Our model shows that this scattering effect is not only present at the boundary or particle-matrix interface of the nanosized material, but also within it. The effect of particle size and surface specularity has been investigated, showing that a decreasing value of the particle size and specularity increases the scattering effect and improves the thermoelectric properties. An extension towards thin films of nanocomposite has been presented.