Thin-film thermoelectric cooler: thermodynamic modelling and its temperature-entropy flux formulation

Thermodynamic performances of a thin-film thermoelectric cooler are analysed from the point of view of irreversible thermodynamics using the Boltzmann transport equation, which includes the collision effects as well as those accounted for by the Gibbs law. Using this methodology, the article presents unique conservation equations for electrons, holes, and phonons as well as their necessary expressions for entropy generation within the thin films. A temperature-entropy (T-s) diagram is plotted for describing the processes of a thin-film thermoelectric cooler. This diagram demarcates how the energy input to the thin films could be apportioned and utilize in overcoming the dissipative and finite heat transfer losses. The dissipative effects of electron-hole collisions at high current densities have been found to be significant, up to 25 per cent of the total power input in a current field exceeding 2 A within the thin films.