Exciton mobility and trapping in europium doped vanadate phosphors described by Markov processes
A.V.E. Enthoven (TU Delft - Electrical Engineering, Mathematics and Computer Science)
F. REDIG – Mentor (TU Delft - Applied Probability)
Erik Van Der Kolk – Mentor (TU Delft - RST/Luminescence Materials)
J. Zom – Mentor (TU Delft - RST/Luminescence Materials)
A.B.T. Barbaro – Graduation committee member (TU Delft - Mathematical Physics)
Danny Lathouwers – Graduation committee member (TU Delft - RST/Reactor Physics and Nuclear Materials)
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Abstract
Diffusion-like
behavior of excitons within europium doped vanadate phosphors is studied, with
emphasis on the trapping potential induced by Eu3+ and VO43− luminescence. We
describe the hopping, energy transfer, and decay of excitons by means of a
continuous-time Markov chain distinguished by a local and delocalized trapping
potential. Our model compares luminescence from decay of excitons with the
trapping problem, where VO43− traps are present everywhere, while Eu3+ ions are
placed randomly. We distinguish two types of trapping potentials induced by
europium traps. In the localized model, simplify the lattice to Zd where the
trapping potential of europium traps is only present at randomized sites in the
lattice. By applying the large deviation principle for the occupation times
measure, as done by Donsker and Varadhan previously, we find probability mass
asymptotics of the form exp td/(d+2). For a simulation-like approach, we
describe the delocalized model, where exciton movement and trapping in crystal
lattices of Rb3LuV2O8:Eu3+ and YVO4:Eu3+ and is modeled using parameters such
as temperature, migration rates, emission lifetimes, and europium concentration
to estimate luminescent properties of the materials. Experimental data from
vanadate lifetimes of Rb3LuV2O8:Eu3+ and VO43− /Eu3+ emission ratio’s of
YVO4:Eu3+ are compared to the model, which agree relatively well within the
confidence of the model. For YVO4:Eu3+, we have found an activation energy of
Ea = (101 ± 4) meV. We discuss how our simplified model can be extended to
incorporate thermal and concentration quenching, and how to account for defects
in the lattice. While we discuss our findings for europium doped vanadate
phosphors, the results we have found are applicable for a range of other
luminescent materials.