We present experimental evidence for cooperative energy transfer from ${\mathrm{Tb}}^{3+}$ to two ${\mathrm{Yb}}^{3+}$ ions and a determination of the energy-transfer rate. Energy transfer from ${\mathrm{Tb}}^{3+}$ to ${\mathrm{Yb}}^{3+}$ was investigated by luminescence measurements on $\left({\mathrm{Yb}}_x{\mathrm{Y}}_{1-x}\right)\mathrm{P}{\mathrm{O}}_4$ doped with 1% ${\mathrm{Tb}}^{3+}$. Time-resolved luminescence experiments were analyzed using Monte Carlo simulations based on theories for phonon-assisted, cooperative, and accretive energy transfer. The luminescence decay curves of the ${}^{5}D_4$ emission from ${\mathrm{Tb}}^{3+}$ show an excellent agreement with simulations based on cooperative energy transfer via dipole-dipole interaction, while a phonon-assisted or an accretive energy-transfer mechanism cannot explain the experimental results. The energy-transfer rate to two nearest-neighbor ${\mathrm{Yb}}^{3+}$ ions is $0.26{\mathrm{ms}}^{-1}$. This corresponds to an upper limit of the energy-transfer efficiency of 88% in $\mathrm{Yb}\mathrm{P}{\mathrm{O}}_4$. Application of cooperative energy transfer has prospects for increasing the energy efficiency of crystalline Si solar cells by photon doubling of the high energy part of the solar spectrum.

• Received 10 May 2004

DOI:https://doi.org/10.1103/PhysRevB.71.014119