Kennard's detailed balance relation for photoluminescence: General proof and experimental results for InP/ZnS core-shell nanocrystals

According to the principle of detailed balance, the luminescence intensity at a wavelength λ1 as a result of excitation at a wavelength λ2 must be related in some way to the luminescence intensity at λ2 as a result of excitation at λ1. In 1926, E. H. Kennard derived such a relation by applying the concept of the Einstein coefficients to some model system. Our study provides a general thermodynamic proof that Kennard's relation is valid for arbitrary macroscopic photoluminescent bodies. An experimental test of this relation is also given for InP/ZnS core-shell colloidal quantum dots synthesized by the conventional high-temperature organometallic procedure. For these particles, the emission spectra at various excitation wavelengths and the photoluminescence excitation spectra at various emission wavelengths have been obtained. It was found that Kennard's relation does hold for the obtained spectra.