Temperature and energy gap dependence of energy transfer between rare-earth ions in solids

Abstract

In this paper we develop a model to explain the temperature dependence of energy transfer between rare-earth ions for situations in which the energy gap is small. When the gap is large, and many phonons are required the transfer rate follows the well-known exponential law. When just a few phonons are required, however, the temperature dependence may be quite different, and may even be more efficient at low temperatures; this is shown to be the case of Er to Ho transfer in YAG. We show that for small energy gaps, the redistribution of the ions with temperature may be a driving factor in the transfer. As the number of phonons increases, this redistribution becomes less important and the exponential law emerges.