An experimentally founded rate equation model for NIR-photon upconversion

The efficiency of modern photovoltaic units are getting close to the SQ-limit [http://dx.doi.org/10.1063/1.1736034], that is, the maximum obtainable efficiency of a standard photovoltaic unit. Thus, new methods, are in demand,... [ view full abstract ]

The efficiency of modern photovoltaic units are getting close to the SQ-limit [http://dx.doi.org/10.1063/1.1736034], that is, the maximum obtainable efficiency of a standard photovoltaic unit. Thus, new methods, are in demand, to increase this limit in the process towards a renewable energy-system. Upconversion of sub-band-gap photons has proven to be a fruitful way of achieving this goal [http://dx.doi.org/10.1002/adom.201500024]. Upconversion is the process of creating a higher energy photon out of two or more low energy photons. A standard silicon solar cell cannot absorb photons with energy below 1.11 eV. This amounts to 20% of the light from the sun witch reaches the surface of the earth. Moreover -- as silicon is transparent to the sub-band-gab photons -- the upconverting unit can beneficially be attached to the rear side of a photovoltaic unit and hereby improving existing as well as future developed units.

Trivalent rare earth ions, and especially erbium ions, have proven to be a promising candidate for upconversion [http://dx.doi.org/10.1063/1.1844592]. The erbium ions are doped into a host matrix -- in our case TiO_2. The aim of this work is to construct a model for the upconversion dynamics based on rate equations. The parameters of the model will be measured and cross-related through different experiments. The main parameters of the model are the absorption cross-section of the erbium ions, and the different transition rates governing population decay and increase. The absorption cross-section will be determined through absorption spectra using a spectrophotometer cross-related to measurements of the complex index-of-refraction obtained with an ellipsometer. From the ground-state-absorption cross-section combined with the theories of McCumber [http://dx.doi.org/10.1103/PhysRev.136.A954], and Judd & Ofelt [http://dx.doi.org/10.1103/PhysRev.127.750] it is possible to compute the exited-state cross-sections as well. The transition rates will be determined through the exited-state life-time of the erbium ions, measured from time-resolved-luminescence experiments. The accuracy of the model will be demonstrated via comparison of the model output with quantum-efficiency measurements of the upconversion yield.

Besides enabling investigation of the upconversion dynamics the model paves the way for a direct investigation of transition rates such as multi-phonon relaxation and Förster-resonance energy-transfer.