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Rare Earth-Doped Phosphors for White LEDs Chapter 278 13 (i) Multipolar interaction. The energy transfer occurs in the case where both transitions in D and A are of electric multipole character. There are three types of interactions, that is, dipole–dipole (dd), dipole– quadrupole (dq), and quadrupole–quadrupole (qq). The probability of the energy transfer through multipolar interaction is expressed as: PsðRÞ1⁄4add +adq +aqq +... R6 R8 R10 where R is the distance between D and A and as s are the magnitudes of the interactions (Yamamoto, 2006). Among the three interactions, the dd interaction yields the highest transfer probability. However, if the dipole transition is not completely allowed for D and/or A, as in the case of 4f–4f transitions, it is probable that the higher order interactions, dq or qq, may have a larger probability for small dis- tance (R) ion pairs (Nakazawa and Shionoya, 1967). (ii) Exchange interaction. This energy transfer occurs when the donor and the acceptor are located closely enough for their electronic wave functions to overlap and the transfer is due to a quantum mechanical interaction. (iii) Phonon-assisted energy transfer. This energy transfer occurs when there is a difference DE between the transition energies of D and A, that is compensated by either a phonon emission or an absorption. The transfer probability is given by the equation (Miyakawa and Dexter, 1970): Pas ðDEÞ 1⁄4 Pas ð0ÞebDE where Pas(0) is equal to the resonant transfer probability and b is a parameter that depends on the energy and occupation number of par- ticipating phonons. The energy difference DE is equal to the largest phonon energy. The energy transfer rates for various systems of rare earth ions in Y2O3 host showed excellent agreement with the above equation (Yamada et al., 1972). (2) Sensitization of luminescence This energy transfer process is often used in practical phosphors in order to enhance the emission efficiency. A donor (sensitizer) that absorbs strongly transfers its excitation energy very efficiently to an acceptor (activator). The resulting emission is greatly enhanced. For instance, the emission of Tb3+ is sensitized by Ce3+ ions in many green-emitting phos- phors, as will be discussed later. Sensitization is the most important process for developing various color-emitting phosphors excited by LEDs and based on trivalent rare earth ions such as Sm3+, Eu3+, Tb3+, etc. (3) Concentration quenching of luminescence An unwanted, and very common, feature of energy transfer is reduction in emission intensities when the emitting ions lie too close to each other.PDF Image | HANDBOOK ON THE PHYSICS AND CHEMISTRY OF RARE EARTHS
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