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Rare Earth-Doped Phosphors for White LEDs Chapter 278 11 temperature quenching. One can assume that this nonradiative relaxation pro- cess with activation energy, DU, and transition probability, N, is given by N ∝ exp ðDU=kTÞ. The spatial distribution of an electronic orbital is differ- ent between the ground and excited states, giving rise to differences in the electron wave function overlaps with neighboring ions. This difference further includes a change in the equilibrium position and the force constant of the ground and excited states, and is the origin of the Stokes shift. Since the phosphor may be heated up to about 100°C by a LED chip, this phenomenon is crucially important for selecting the host material. How can the thermal quenching at the operating temperature be reduced? One of the answers may be to increase DU. As U is a parabolic function of Q, the increase in DU can be achieved by increasing the curvature of the excited state Ue, this corresponding to an increase in Ke, ie, a decrease in lattice vibrations. In addi- tion, the magnitude of the Stokes shift has a large influence on the efficiency of the emission because its value is related to the waste of the absorption energy. As shown in Fig. 5, the reduction of Stokes shift corresponds to the decrease in Q0, requiring the suppression of electron cloud expansion in the excite state. 3.1.2 Electronic Transitions in Rare Earth Ions The characteristic properties of the rare earth ions are attributable to the pres- ence of a deep-lying 4f shell. The electrons of this shell are screened by those in the outer shells, and, as a result, they give rise to number of discrete energy levels. Since environment around a rare earth ion in a crystal lattice scarcely affects the position of these levels, there is a resemblance with the energy level diagrams of the free ions. In spite of this, there is an important difference in the emission properties. Rare earth ions are usually trivalent. For under- standing the luminescent properties of rare earth ions, it is necessary to know their key energy levels. The energy level may be divided into three categories: those corresponding to 4fn configuration, 4fn15d configuration, and those corresponding to CT involving the neighboring ions. 3.1.2.1 4f–4f Transitions This is concerned with the 4fn configurations. Except for Ce3+ and Yb3+, the number of discrete 4f energy levels is large. These levels further increase in number due to crystal-field splitting. Electric dipole transitions within the 4f shell are strictly forbidden because the parity does not change. However, the forbidden transitions are actually observed due to the fact that the interaction of rare earth ion with crystal field or with the lattice vibrations can mix states of different parities into 4f states. Coupling of 4f electrons with transient dipoles induced in the ligands by the radiation field leads to an amplifica- tion of the even-parity multipolar transition amplitudes for transitions within the 4f shell. These transitions are called “induced (or forced) electric dipole transitions.” The transitions that are not allowed as electric dipole may takePDF Image | HANDBOOK ON THE PHYSICS AND CHEMISTRY OF RARE EARTHS
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