Thermoelectric effects and size dependency of the figure-of-merit in cylindrical nanowires

Nonlocal transport equations for phonon and electron contributions to the heat flux, and for the electron contribution to the electric current, including thermoelectric effects, are proposed. The consequences of the nonlocal contributions on the figure-of-merit in nanowires are examined in two different situations regarding the relative values of the particles’ mean-free path and the radius of nanowires. In both cases a dependence of the figure of merit on the transversal radius of the nanowire, as well as on some material coefficients related to the roughness of the walls, is pointed out. It is also shown how the figure-of-merit could be improved by controlling these coefficients.