Rate equation analysis of nanocrystal-enhanced upconversion in neodymium-doped glass ceramics

Abstract

Rare-earth ions embedded in glassy matrices are promising materials for photon upconversion processes, e.g. to convert near infrared light to frequencies above the band gap of a solar cell to make it available for electrical power generation. One strategy to optimize the efficiency of such upconversion processes is to embed the active ions in a host matrix with minimal losses to non-radiative relaxation. For the model system of trivalent neodymium in fluorochlorozirconate (FCZ) glass it has been shown recently that a uniform growth of BaCl₂ nanocrystals inside such glasses can decrease the probability of multi-phonon relaxation (MPR) drastically, leading to a huge increase in upconversion intensity for monochromatic illumination. To identify the key processes which may enhance or diminish the total upconversion efficiency, a comprehensive description for the optical dynamics of neodymium in FCZ glass ceramics has been developed on the basis of a rate equation system, including ion-photon, ion-phonon, and ion-ion interactions. An effective medium approach is utilized to account for the neodymium located in BaCl₂ nanocrystals or the FCZ glass bulk, respectively. The numerous parameters required to enable for a reliable numerical simulation of the processes are obtained from theoretical approaches like Judd-Ofelt theory, as well as from experimental studies of luminescence decay after femtosecond excitation at various wavelengths and luminescence spectra under cw illumination at 800 nm wavelength. This rate equation model enables for a convenient, self-consistent description of all time-resolved and cw experiments on samples with different neodymium concentration. On this basis, the power dependence of upconversion spectra can be simulated in good agreement with the experimental result for 800 nm cw illumination. The model therefore forms an excellent tool for optimizing the upconversion efficiency of rare-earth doped luminescent material also under realistic (broadband illumination) conditions.