The thermoelectric conversion efficiency problem: Insights from the electron gas thermodynamics close to a phase transition

The bottleneck in modern thermoelectric power generation and cooling is the low energy conversion efficiency of thermoelectric materials. The detrimental effects of lattice phonons on performance can be mitigated, but achieving a high thermoelectric power factor remains a major problem because the Seebeck coefficient and electrical conductivity cannot be jointly increased. The conducting electron gas in thermoelectric materials is the actual working fluid that performs the energy conversion, so its properties determine the maximum efficiency that can theoretically be achieved. By relating the thermoelastic properties of the electronic working fluid to its transport properties (considering noninteracting electron systems), we show why the performance of conventional semiconductor materials is doomed to remain low. Analyzing the temperature dependence of the power factor theoretically in 2D systems and experimentally in a thin film, we find that in the fluctuation regimes of an electronic phase transition, the thermoelectric power factor can significantly increase owing to the increased compressibility of the electron gas. We also calculate the ideal thermoelectric conversion efficiency in noninteracting electron systems across a wide temperature range neglecting phonon effects and dissipative coupling to the heat source and sink. Our results show that driving the electronic system to the vicinity of a phase transition can indeed be an innovative route to strong efficiency enhancement, but at the cost of an extremely narrow temperature range for the use of such materials, which in turn precludes potential development for the desired wide range of thermoelectric energy conversion applications.