Energy-specific equilibrium in nanowires for efficient thermoelectric power generation
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Energy-specific equilibrium in nanowires for efficient thermoelectric power generation Heiner Linke a and Tammy E. Humphrey b and Mark O’Dwyer c a Materials Science Institute and Physics Department, University of Oregon, Eugene, OR 974031274, U.S.A. b Département de Physique Théorique, University of Geneva, CH – 1211, Geneva, Switzerland c School of Engineering Physics and Institute for Superconducting and Electronic Materials, University of Wollongong, Wollongong NSW 2522, Australia
ABSTRACT There is great scientific, economic and environmental interest in the development of thermoelectric materials capable of direct thermal-to-electric energy conversion with high efficiency. Recent theory predicts that in materials with a fine-tuned electronic density of states, electrons can be placed in energy-specific equilibrium, and the efficiency of thermoelectric power generation can approach the fundamental Carnot limit. Here we review the relevant theory of energy-specific equilibrium. We describe a concept for a proof-of principle demonstration of near-Carnot efficient power conversion involving a single, ballistic nanowire at low temperatures, and we discuss the potential for room-temperature applications in diffusive materials.
INTRODUCTION Thermoelectric materials work by selectively transmitting “hot” (high-energy) electrons from a warm reservoir to a cold reservoir, such that a thermal gradient can drive current flow against a bias voltage V, leading to power generation. In recent years several authors recognized that the exact form of the electronic density of states (DOS) in a thermoelectric material has a strong impact on the efficiency of power generation [3-6]. This is because, whereas each electron contributes the same energy eV to the power output, regardless of the electron’s initial energy, the efficiency is highest when the electrons that contribute to the current possess only the minimum thermal energy required to surmount the bias voltage. Electrons that leave the hot reservoir with an excess of thermal energy cool the hot reservoir more than necessary, reducing efficiency. Semiconductor heterostructures grown by modern epitaxial methods are an important candidate for high-efficiency thermoelectrics because it is possible to carefully engineer the electronic DOS [3, 4, 7, 8], employing both band offsets and quantum confinement phenomena. Mahan and Sofo pointed out the advantage of delta-like singularities in the electronic DOS and suggested the use of narrow states in rare earth metals [9], and Hicks and Dresselhaus proposed that the reduced dimensionality of superlattices could be used to enhance the electronic density of states in energy ranges near the conduction band edge to improve the efficiency of power generation [3]. An additional advantage of the use of superlattices is the expected reduced thermal conductivity due to increased phonon scattering rates and phonon-localization, such that parasitic heat leaks can be reduced. Indeed, several authors have shown that thermal conducti
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