Light Emission by Nonequilibrium Bodies: Local Kirchhoff Law

Abstract

The goal of this paper is to introduce a local form of Kirchhoff law to model light emission by nonequilibrium bodies. While absorption by a finite-size body is usually described using the absorption cross section, we introduce a local absorption rate per unit volume and also a local thermal emission rate per unit volume. Their equality is a local form of Kirchhoff law. We revisit the derivation of this equality and extend it to situations with subsystems in local thermodynamic equilibrium but not in equilibrium between them, such as hot electrons in a metal or electrons with different Fermi levels in the conduction band and in the valence band of a semiconductor. This form of Kirchhoff law can be used to model (i) thermal emission by nonisothermal finite-size bodies, (ii) thermal emission by bodies with carriers at different temperatures, and (iii) spontaneous emission by semiconductors under optical (photoluminescence) or electrical pumping (electroluminescence). Finally, we show that the reciprocity relation connecting light-emitting diodes and photovoltaic cells derived by Rau is a particular case of the local Kirchhoff law.Received 21 December 2017DOI:https://doi.org/10.1103/PhysRevX.8.021008Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasElectroluminescenceNanoantennasPhotovoltaic absorbersSpontaneous emissionPhysical SystemsOptical microcavitiesTechniquesPhotoluminescenceCondensed Matter, Materials & Applied Physics