Charge carrier extrinsic energy filtering: Theoretical advances, applications, and perspectives in thermoelectricity

Extrinsic energy filtering (EEF) selectively allows high-energy charge carriers to pass through an energy barrier, blocking lower-energy (cold) carriers. This mechanism enhances thermoelectric performance by increasing the Seebeck coefficient S, since only high-energy carriers contribute, while maintaining electrical conductivity sigma due to their higher mobility despite lower carrier density. The combined effect significantly boosts the power factor (PF) sigma S-2. The concept of EEF dates back nearly 50 years, initially demonstrated by embedding metallic nanoparticles in telluride materials. Since then, theoretical models have advanced, and practical implementations have expanded to include elemental semiconductors, chalcogenides, and recently polymers. Nanostructured systems have played a key role by enabling close comparisons between theory, computational simulations, and experiments, deepening the understanding of EEF physics. This review offers a critical overview of both theoretical foundations and experimental progress in EEF over five decades. It highlights criteria for identifying genuine energy filtering effects in real materials and stresses the importance of distinguishing this phenomenon from other mechanisms that also improve the thermoelectric PF.