Modeling recombination processe in RE doped Up-Conversion nanocrystals
  Up-conversion nanocrystals (UCNCs) are a new class of nonlinear optical materials converting low energy excitation to high energy emission. Recent advances in synthesis techniques enable a control over size, shape, emission color purity as well as optical tuning [1]. Those UCNCs are characterized by high surface to volume ratio allowing interesting attributes such as water solubility and biological functionality. UCNCs usually consist of an inorganic host that is doped with Ln^{3+} ions. The most efficient host matrix known is the one used to test our model, namely, NaGdF_4 nanocrystals co-doped with Er^{3+} as an acceptor/activator and Yb^{3+} as a donor/sensitizer. In this work, we introduce the theoretical background needed to understand the nature of ion-ion interactions occurring in these systems as well as the details of the 4f transitions characteristic of RE-ions. In the second chapter, we present our model through a system of rate equations corresponding to a custom energy diagram. Then, we show our simulations producing fits of Time Resolved Photo Luminescence (TRPL) data. Finally, we construct an improved model aiming to encompass all the processes that seem to be involved in the luminescence of the samples studied and we present the achievements of such approach. 
Ziyad Chaker, Artur Podhorodecki
cond-mat.mtrl-sci