  Upconversion of infrared photons is a promising possibility to enhance solar
cell efficiency by producing electricity from otherwise unused sub-band-gap
photons. We present a rate equation model, and the relevant processes, in order
to describe upconversion of near-infrared photons. The model considers
stimulated and spontaneous processes, multi-phonon relaxation and energy
transfer between neighboring ions. The input parameters for the model are
experimentally determined for the material system \beta-NaEr0.2Y0.8F4. The
determination of the transition probabilities, also known as the Einstein
coefficients, is in the focus of the parameterization. The influence of
multi-phonon relaxation and energy transfer on the upconversion are evaluated
and discussed in detail. Since upconversion is a non-linear process, the
irradiance dependence of the simulations is investigated and compared to
experimental data of quantum efficiency measurements. The results are very
promising and indicate that upconversion is physically reasonably described by
the rate equations. Therefore, the presented model will be the basis for
further simulations concerning various applications of upconversion, such as in
combination with plasmon resonances in metal nanoparticles.
