Cooperative and Stepwise Excitation of Luminescence: Trivalent Rare-Earth Ions inYb3+-Sensitized Crystals

The probability of cooperative energy transfer from two excited ions to a nearby ion is computed and compared with the probability of excitation by stepwise energy transfer. For ${\mathrm{Yb}}^{3+}$ sensitization of ${\mathrm{Er}}^{3+}$, ${\mathrm{Ho}}^{3+}$, and ${\mathrm{Tm}}^{3+}$ activated hosts, the cooperative transition rate from two excited ${\mathrm{Yb}}^{3+}$ ions is estimated to be in the range ${10}^7$-${10}^9$ ${\sec }^{-1\mathrm{}}$, depending on the degree of overlaps of absorption and emission bands. In the case of the ${\mathrm{Er}}^{3+}$+${\mathrm{Yb}}^{3+}$ and ${\mathrm{Ho}}^{3+}$+${\mathrm{Yb}}^{3+}$ systems, the dependence of output intensity on the exciting light intensity $I_E$ and the concentration of Yb cannot discriminate between cooperative and serial transfer, but estimates of the transfer probabilities show that the stepwise process dominates. It is suggested that the ${\mathrm{Tb}}^{3+}$+${\mathrm{Yb}}^{3+}$ system would be an excellent system in which to observe the cooperative effect unambiguously. In the ${\mathrm{Tm}}^{3+}$+${\mathrm{Yb}}^{3+}$ system also, we expect stepwise transfer to dominate except for unfeasibly low $I_E$.