Diffusion and diffusion-like effects of energy in lanthanide-doped nanocrystals
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For quite some time, people have tried to fundamentally understand the processes in lanthanide-doped nanocrystals (NCs). In these materials, the ionic dopants absorb and emit photons, where the emitted photons have a different energy from the absorbed ones. This is possible due to energy transfer (ET) processes, where (a part of) the energy is transferred from one ion to another. And in order to understand the resulting emitted light, it is of importance to understand these microscopic processes. One of these ET processes is the transfer of all its energy to a neighbouring ion, resulting in an effective diffusion of energy. In this thesis we study this diffusion and other diffusion-like effects in a thin film of NaYF4:Er3+Yb3+ NCs, for which we used simulations, differential equations and experiments. First, we performed Monte Carlo simulations in order to connect the ET rate to an effective diffusion coefficient. From these simulations, we found that the diffusion has a transitioning point with respect to the doping concentration, at lower concentrations the diffusion is isotropic and at higher concentrations the diffusion is anisotropic. Secondly we solved the differential equations for two- and three-level energy diagrams in both space and time in order to connect this diffusion coefficient to an experiment. Here we looked at the spatial distribution of the energy, which broadens due to the effective diffusion. Upon solving these equations, however, we found that are also other processes, that are not diffusion, that can lead to broadening and even narrowing of this energy distribution, which is possible due to non-linear behaviour. To test these results, we performed experiments on tuned NCs, such that we can measure these effects independently. For this we used an experimental setup with a pulsed laser that allows us to measure the spatial intensity distribution of the emitted light. This intensity distribution is linearly dependant on the energy distribution and as such we can compare these experiments directly with the results of the differential equations. So first, we measured NCs, solely doped with Yb-ions, and found that there was no diffusion, but there was a broadening effect during the excitation. Next, we measured NCs solely doped with Er-ions and doped with both Er and Yb, where we saw the narrowing effect due to cross-relaxation and the broadening effect due to upconversion. Here, we were able to match all those experiments, without a diffusion term.