CALCULATION OF NATURAL RADIATIVE LIFETIMES FROM THE ABSORPTION AND FLUORESCENCE PROPERTIES OF SEMICONDUCTORS AND MOLECULES

Using a detailed balance approach to treat the upper and lower thermalized electronic states of a broadband absorber, equations have been derived from which radiative lifetimes tau(r) can be calculated from the known absorption and fluorescence properties of semiconductors and molecular chromophores. Three methods for calculating these lifetimes are outlined. Method 1 utilizes the absorption coefficients and fluorescence distribution in the frequency range where they overlap. These lifetimes tau(r)(ovl) are very sensitive to small errors in the choice of the bandgap energy U(g). Method 2 utilizes the absorption coefficients through the entire fluorescence range and is applicable only to systems in which the fluorescence lies within the absorption spectrum. For semiconductors, method 2 results in the previously derived van Roosbroeck-Shockley equation. These tau(r)(abs) lifetimes are also very sensitive to the choice of U(g), but for semiconductors this is usually known to sufficient accuracy. Method 3 assumes a mirror image relation between the absorption and fluorescence spectra and is particularly useful for molecular chromophores, for which method 2 and (usually) method 1 are not applicable. Tau(r)(mir) values obtained by method 3 will give a good account of tau(r)(exp) values only when the mirror image assumptions hold. Quantum mechanical arguments, based on the relation between upward and downward transition moments, have also been used to calculate radiative lifetimes for molecules. We comment on the Strickler-Berg (SB) equation for molecules, derived from this approach, and show that it reduces to the Forster equation when the mirror image assumptions are imposed. Finally we treat GaAs and rhodamine 6G as examples and compare tau(r) values calculated using the methods we describe.