4 .5. Photoionization and Electron-Transfer Quenching
`
`87
`
`e
`
`g
`
`A
`
`CB
`
`E g
`
`VB
`
`Fig. 4.12. The excited state e of the centre A lies in the conduction band of the host lattice.
`Photo-excitation of A (arrow) may be followed by photoionization
`
`is strongly changed or even completely quenched by photoionization. The principle
`is illustrated in Figure 4.12. The luminescent center A has its ground state in the
`forbidden zone between valence and conduction bands. Its excited state lies in the
`conduction band. This implies that in the excited state an electron can easily be ionized
`from the center to the conduction band. It may recombine nonradiatively with a hole
`somewhere else, so that the luminescence is quenched. On the other hand the electron
`in the conduction band and the hole on the ionized centre will attract each other and
`may form an exciton. Since this exciton is bound to the luminescent center, radiative
`recombination of this exciton is known as impurity-bound exciton recombination [ 14].
`However, the recombination may also be nonradiative.
`A nice example is the isostructural series CaF2 : Yb2 +, SrF2 : Yb 2+ and BaF2 : Yb 2+
`[ 14]. The calcium compound shows normal Yb2+ emission (Sect. 3.3.3), the stron(cid:173)
`tium compound shows a strikingly different emission, viz. impurity-bound exciton
`emission, and the barium compound does not show any emission at all. Obviously
`the Yb2+ energy level scheme moves upwards in the energy band picture of the host
`lattice going from CaF2 to BaF2 .
`Also BaF2 : Eu 2+ does not show Eu2+ emission, but impurity-bound exciton emis(cid:173)
`sion. The same holds for NaF: Cu+ where the excited state consists of a Jahn(cid:173)
`-Teller distorted Cu 2+ ion which binds an electron. The absence of luminescence in
`La2 0 3 : Ce3+ has also been ascribed to quenching by photoionization [ 15].
`Closely related to photoionization and its consequences is quenching of lumines(cid:173)
`cence by electron transfer. This process is well known in coordination chemistry, but
`has been overlooked in solid state studies. The principle is outlined in Figure 4.13 for
`a system of two species, A and B. The first excited state is one in which only A is
`excited (A* +B). At higher energies we find a charge-transfer state A++ B- with a
`large offset. Although A++ B- lies at higher energy than A* +B, judging from the
`absorption spectrum, the luminescence A* ---* A is quenched via the charge-transfer
`state.
`This implies that a combination of a center which has a tendency to become
`oxidized with a center which has a tendency to become reduced will probably not
`show efficient luminescence. This is illustrated by some examples:
`
`Vizio EX1018 Page 0098
`
`

`

`88
`
`4. Nonradiative Transitions
`
`E
`
`b
`
`a
`
`R
`
`Fig. 4.13. Luminescence quenching by electron transfer. The ground state a consists of two
`species, A + B. In the excited states b and c the A ion is excited: A * +B. State d is the
`electron-transfer state A+ +B-. Luminescence from the level c is quenched by electron transfer
`as indicated by the arrow
`
`- whereas many rare earth ions show efficient luminescence in YV04, the ions Ce3+,
`Pr3+ and Tb3+ do not. This is due to quenching via a charge-transfer state (RE4+ + V4+)
`which is at low energy for these three ions and at much higher energy for the others.
`- whereas many rare earth ions show efficient luminescence in cerium compounds,
`Eu 3+ does not. Quenching occurs via a charge-transfer state (Ce4+ + Eu 2+) which is
`at low energy. Further examples are given in Ref. [ 16).
`Note that quenching by electron transfer is a special case of quenching via a
`charge-transfer state as discussed above (Sect. 4.2.2) for Eu3+. There is also no prin(cid:173)
`cipal difference between quenching by electron transfer and quenching via photoion(cid:173)
`ization. However, the former has a localized character, the latter is used in energy
`band models where delocalization is more important.
`
`4.6 Nonradiative Transitions in Semiconductors
`
`Finally nonradiative transitions which are specific for semiconductors are mentioned.
`In order to do so, we consider a specific radiative transition, viz. the donor-acceptor(cid:173)
`pair emission (Sect. 3.3.9). In the excited state the donor and acceptor are occupied
`(Fig. 4.14). This excited luminescent center may show radiative and nonradiative
`transitions within the center itself (similar to the discussion in Sect. 4.2). In addition,
`however, there are other processes which are related to the valence and/or conduction
`band.
`If the donor is thermally ionized (Fig. 4.14), the luminescence will be quenched
`unless it is trapped again at a donor site. A different nonradiative mechanism is
`
`Vizio EX1018 Page 0099
`
`

`

`References
`
`89
`
`...
`
`•
`
`CB
`
`Eg
`
`VB
`
`D - - -
`
`-o- A
`
`a
`
`D ---
`I
`
`-o- A
`
`b
`
`Fig. 4.14. Nonradiative transitions in a semiconductor. The donor-acceptor pair emission (DA)
`can be quenched by thermal ionization of one of the centers (a) or by an Auger process (b). In
`the latter case a conduction electron is promoted high into the conduction band
`
`an Auger transition [17]. This is also illustrated in Figure 4.14. The energy of the
`excited donor-acceptor pair is used to excite a conduction band electron to a higher
`state in the conduction band. The hot conduction-band electron which has been created
`relaxes subsequently by intraband transitions. As a consequence the donor-acceptor
`pair emission is quenched.
`More generally, an Auger transition can be defined as a transition in which energy
`is transferred from one electronic particle to another in such a way that in the final
`state the energy of one of the particles lies in a continuum. Auger processes can
`be classified as intrinsic or extrinsic. The former occur in the pure semiconductor,
`the latter involve electronic states of impurities like in the example in Figure 4 . 14.
`All types of luminescence transitions described in Section 3.3 .9 can be quenched by
`Auger processes.
`
`References
`
`I. DiBartolo B (ed) ( 1980) Radiation less processes. Plenum, New York
`2. DiBartolo B (ed) ( 1991) Advances in nonradiative processes in solids. Plenum, New York
`3. Struck CW, Fonger WH (1991) Understanding luminescence spectra and efficiency using
`Wp and related functions, Springer, Berlin Heidelberg New York
`4. Yen WM, Selzer PM (eds) ( 1981) Laser spectroscopy of solids. Springer, Berlin Heidelberg
`New York
`5. Riseberg LA, Weber MJ ((1976) Progress in optics. In: WolfE (ed) vol XIV. North-Holland,
`Amsterdam
`6. van Dijk JMF, Schuurmans MFH (1983) , J Chem Phys 78:5317
`7. Berdowski PAM, Blasse G (1984) Chem Phys Letters I 07:351
`8. de Hair JThW, Blasse G (1976) J Luminescence 14:307; J Solid State Chem 19:263
`9. Blasse G, van Vliet JPM, Verweij JWM, Hoogendam R, Wiegel M ( 1989) J Phys Chem
`Solids 50:583
`I 0. Sabbatini N, Blasse G (1988) J Luminescence 40/41:288
`
`Vizio EX1018 Page 0100
`
`

`

`90
`
`4. Nonradiative Transitions
`
`11. Bleijenberg KC, Blasse G ( 1979) J Solid State Chern 28:303
`12. Bril A ( 1962) in Kallman and Spruch (eds), Luminescence of organic and inorganic mate-
`rials. Wiley, New York p 479; de Poorter JA, Bril A (1975) J Electrochem Soc 122:1086
`13. Robbins OJ ( 1980) J Electrochem Soc 127:2694
`14. Moine B, Courtois B, Pedrini C ( 1989) J Phys France 50:2105
`15. Blasse G, Schipper W, Hamelink JJ (1991) Inorg Chim Acta 189:77
`16. Blasse G, p 314 in ref. I
`17. Williams F, Berry DE, Bernard JE, p 409 in ref. I
`
`Vizio EX1018 Page 0101
`
`

`

`CHAPTER 5
`
`Energy Transfer
`
`5.1 Introduction
`
`In Chapter 2, the luminescent center was brought into the excited state, whereas
`in Chapters 3 and 4 the return to the ground state was considered, radiatively and
`nonradiatively, respectively. In this chapter another possibility to return to the ground
`state is considered, viz. by transfer of the excitation energy from the excited centre
`(S*) to another centre (A):
`S* +A--* S +A* (Figs 1.3 and 1.4).
`The energy transfer may be followed by emission from A. Species Sis then said to
`sensitize species A. However, A* may also decay nonradiatively; in this case species
`A is said to be a quencher of the S emission.
`Energy transfer between two centres requires a certain interaction between these
`centres. Nowadays the process of energy transfer is a well-understood phenomenon
`of which the more important aspects will be discussed here. For more profound
`treatments the reader is referred to the literature cited [ 1-3].
`The organization of this chapter is as follows. In Sect. 5 .2, we consider energy
`transfer between a pair of unlike luminescent centers. The theories of Forster and
`Dexter will be introduced. In Sect. 5 .3, the topic is extended to energy transfer be(cid:173)
`tween identical centers. As a consequence of this, the phenomenon of concentration
`quenching of luminescence takes place. The section is split into two parts, one deal(cid:173)
`ing with centers to which the weak-coupling scheme applies, the other dealing with
`centers to which the strong-coupling scheme applies. In Sect. 5.4, energy transfer in
`semiconductors is very briefly mentioned.
`
`5.2 Energy Transfer Between Unlike Luminescent Centers
`
`Consider two centers, S and A, separated in a solid by distance R (Fig. 5.1). We use
`the (classic) notation S and A (for sensitiser and activator); other authors useD and
`A (for donor and acceptor). The energy level schemes are also given in Fig. 5.1. An
`asterisk indicates the excited state. Let us assume that the distance R is so short that
`the centres S and A have a non-vanishing interaction with each other. If S is in the
`excited state and A in the ground state, the relaxed excited state of S may transfer
`
`Vizio EX1018 Page 0102
`
`

`

`92
`
`5. Energy Tra nsfer
`
`-------- ---------------------
`R
`
`0
`
`s
`
`-----0
`
`A
`
`-
`
`----.---
`
`lA* >
`
`H
`
`SA
`
`__ __J_ _
`
`_
`
`IS >
`
`--~--lA >
`
`E
`
`Fig. 5.1. Energy transfer between the centers S and A and an illustration o f Eq. (5.1 ). The two
`centers are at a distance R (top) . The energy level schemes and the interaction HsA are given
`in the middle . The spectral overlap is illustrated at the bottom (hatched part)
`
`its energy to A. The rate of such energy transfer processes has been calculated by
`Forster. Later Dexter extended this treatment to other interaction types.
`Energy transfer can only occur if the energy differences between the ground- and
`excited states of S and A are equal (resonance condition) and if a suitable interaction
`between both systems exists. The interaction may be either an exchange interaction
`(if we have wave function overlap) or an electric or magnetic multipolar interaction.
`In practice the resonance condition can be tested by considering the spectral overlap
`of the S emission and the A absorption spectra. The Dexter result looks as follows:
`
`2 J
`
`*
`*
`27T
`PsA =hi < S, A IHsAIS , A> I .
`
`gs(E).gA(E)dE
`
`(5.1)
`
`In Eq. (5.1) the integral presents the spectral overlap, gx (E) being the normalized
`optical line shape function of centre X (see Fig. 5.1 , where the spectral overlap has
`been hatched) . Equation [5.1] shows that the transfer rate PsA vanishes for vanishing
`spectral overlap. The matrix element in Eq. (5.1) represents the interaction (HsA
`being the interaction Hamiltonian) between the initial state IS*, A > and the final
`state IS, A* >.
`The distance dependence of the transfer rate depends on the type of interaction. For
`electric multipolar interaction the distance dependence is given by R-n (n = 6, 8, .. .
`
`Vizio EX1018 Page 0103
`
`

`

`5 .2. Energy Transfer Between Unlike Luminescent Centers
`
`93
`
`for electric-dipole electric-dipole interaction, electric-dipole electric-quadrupole inter(cid:173)
`action, ... respectively). For exchange interaction the distance dependence is exponen(cid:173)
`tial, since exchange interaction requires wave function overlap.
`A high transfer rate, i.e. a high value of PsA, requires a considerable amount of:
`(1) resonance, i.e. the S emission band should overlap spectrally the A absorption
`band(s),
`(2) interaction, which may be of the multipole-multipole type or of the exchange
`type. Only for some specific cases, is the interaction type known. The intensity of the
`optical transitions determines the strength of the electric multipolar interaction. High
`transfer rates can only be expected if the optical transitions involved are allowed
`electric-dipole transitions. If the absorption strength vanishes, the transfer rate for
`electric multipolar interaction vanishes too. However, the overall transfer rate does not
`necessarily vanish, because there may be contributions by exchange interaction. The
`transfer rate due to exchange interaction depends on wave function overlap (and, of
`course, spectral overlap), but not on the spectral properties of the transitions involved.
`Over what distances can energy be transferred in this way? To answer this question
`it is important to realize that S* has several ways to decay to the ground state: energy
`transfer with a rate PsA, and radiative decay with a rate Ps (the radiative rate). We
`neglect nonradiative decay (but it can be included in Ps). The critical distance for
`energy transfer (R:) is defined as the distance for which PsA equals Ps, i.e. if S and A
`are separated by a distance R:, the transfer rate equals the radiative rate. For R > R:
`radiative emission from S prevails, for R < R: energy transfer from S to A dominates.
`If the optical transitions of S and A are allowed electric-dipole transitions with a
`considerable spectral overlap, Rc may be some 30 A. If these transitions are forbidden,
`we need exchange interaction for the transfer to occur. This restricts the value of R:
`to some 5-8 A.
`If the spectral overlap consists of a considerable amount of overlap of an emission
`band and an allowed absorption band, there can be a considerable amount of radiative
`energy transfer: S* decays radiatively and the emitted radiation is reabsorbed. This
`can be observed from the fact that the emission band vanishes at the wavelengths
`where A absorbs strongly.
`Energy transfer as described by Eq. (5.1) is nonradiative energy transfer. The
`occurrence of nonradiative energy transfer can be detected in several ways. If the
`excitation spectrum of the A emission is measured, the absorption bands of S will be
`found as well, since excitation of S yields emission from A via energy transfer. If S
`is excited selectively, the presence of A emission in the emission spectrum points to
`S --+ A energy transfer. Finally, the decay time of the S emission should be shortened
`by the presence of nonradiative energy transfer, since the transfer process shortens
`the life time of the excited state S* .
`To obtain some feeling for transfer rates and critical distances, we will perform
`some simple calculations. We assume that the interaction is of the electric-dipolar
`type. In that case Eq. (5.1) together with PsA (Rc) = Ps yields for Rc the following
`expression [4]:
`
`(5.2)
`
`Vizio EX1018 Page 0104
`
`

`

`94
`
`5 . Energy Transfer
`
`Table 5.1. Schematic energy transfer calculations between a broad-band and a narrow-line centre
`(see text)
`
`A
`
`A
`
`s
`
`s
`
`spectra*
`
`spectral overlap
`f gsg~E
`energy of maximum
`spectral overlap, E
`
`oscillator strength
`accepting ion, fA
`
`Rc
`
`s
`
`A
`
`2 ev-l
`
`0.2 ev- 1
`
`2 ev-l
`
`0.2 ev- 1
`
`3 eV
`
`3 eY
`
`10-6
`
`6.5 A
`
`10-6
`
`4.5 A
`
`3 eY
`
`10-2
`
`30 A
`
`3 eY
`
`10-2
`
`20 A
`
`* S: sensitizer (energy-transferring ion).
`A: activator (energy-accepting ion) . Height at band maximum 2 ev- 1
`
`• Band width 0.5 eY .
`
`Here fA presents the oscillator strength [ 1 ,5] of the optical absorption transitiOn on
`A, E the energy of maximum spectral overlap, and SO the spectral overlap integral
`as given in Eq. (5.1). Equation (5.2) makes it possible to calculate Rc from spectral
`data.
`In Table 5.1 the results of the calculation are presented. An S and an A center are
`considered, and R is always 4 A. Transfer from a broad-band emitter to a narrow(cid:173)
`line absorber is considered (the first two cases) as well as the reverse. The spectral
`overlap is optimal (Pt and 3rct case) or marginal. For the narrow-line absorber, fA is
`taken to be 1 o- 6 ' for the broad-band absorber 1 o- 2 (forbidden and allowed transitions,
`respectively). E is taken to be 3 eV. These values are rather realistic, although lower
`f values may occur.
`From Table 5.1 we can learn the following:
`energy transfer from a broad-band emitter to a line absorber is only possible for
`nearest neighbours in the crystal lattice
`transfer from a line emitter to a band absorber proceeds over fairly long distances.
`Let us finally illustrate Eq. (5.1) by some examples:
`(a) The Gd3+ ion shows energy transfer from the 6 P 7 12 level to most rare earth ions,
`but not to pi3+ and Tm3+. Figure 2.14 shows that these two ions do not have energy
`
`Vizio EX1018 Page 0105
`
`

`

`5.3. Energy Transfer Between Identical Luminescent Centers
`
`95
`
`levels at the same energy as the 6 P 7 12 level, so that the resonance condition is not
`satisfied, the spectral overlap vanishes, and the transfer rate becomes zero.
`(b) In Ca5 (P04 )3F: Sb3+ ,Mn2+ the Sb3+ ion can transfer energy to the Mn2+ ion.
`The Sb3+ emission covers several Mn 2+ absorption transitions. These have very low
`f values (spin- and parity forbidden), and the transfer occurs by exchange interaction
`with R: "' 7 A.
`(c) In Rb2 ZnBr4 : Eu 2+ two types of Eu2+ ions are found with different spectra due
`to the presence of two types of crystallographic sites for Rb+ in Rb2 ZnBr4 • Energy
`transfer occurs from the higher-emitting Eu2+ (415 nm) to the lower-emitting Eu 2+
`( 435 nm). Since all optical transitions involved are allowed, it is not surprising that
`R: has a high value (35 A) [6] .
`
`5.3 Energy Transfer Between Identical Luminescent
`Centers
`
`If we consider now transfer between two identical ions, for example between S and
`S, the same considerations can be used. If transfer between two S ions occurs with
`a high rate, what will happen in a lattice of S ions, for example in a compound
`of S? There is no reason why the transfer should be restricted to one step, so that
`we expect that the first transfer step is followed by many others. This can bring the
`excitation energy far from the site where the absorption took place: energy migration.
`If in this way, the excitation energy reaches a site where it is lost nonradiatively (a
`killer or quenching site), the luminescence efficiency of that composition will be low.
`This phenomenon is called concentration quenching. This type of quenching will not
`occur at low concentrations, because then the average distance between the S ions is
`so large that the migration is hampered and the killers are not reached.
`Energy migration in concentrated systems has been an issue of research over
`the last two decades. Especially since lasers became readily available, the progress
`has been impressive. Here we will first consider the case that S is an ion to which
`the weak-coupling scheme applies. In practice this case consists of the trivalent rare
`earth ions. Subsequently we will deal with the case where S is an ion to which the
`intermediate- or strong-coupling scheme applies.
`
`5.3.1 Weak-Coupling Scheme Ions
`
`At first sight, energy transfer between identical rare earth ions seems to be a process
`with a low rate, because their interaction will be weak in view of the well-shielded
`character of the 4felectrons. However, although the radiative rates are small, the
`spectral overlap can be large. This originates from the fact that LlR ::::::: 0, so that
`the absorption and emission lines will coincide. Further the transfer rate will easily
`surpass the radiative rate, since the latter is low. In fact energy migration has been
`
`Vizio EX1018 Page 0106
`
`

`

`96
`
`5. Energy Transfer
`
`observed in many rare earth compounds, and concentration quenching usually be(cid:173)
`comes effective for concentrations of a few atomic percent of dopant ions. Energy
`transfer over distances of up to some 10 A is possible. As an example, we mention
`the transfer rate between Eu 3+ ions or between Gd3+ ions which may be of the order
`of 107 s- 1 if the distance is 4 A or shorter. This has to be compared with a radiative
`rate of 102-103 s- 1
`• Consequently the excitation energy may be transferred more than
`104 times during the life time of the excited state.
`This type of research uses pulsed and tunable lasers as an excitation source. The
`rare earth ion is excited selectively with a laser pulse,and its decay is analyzed. The
`shape of the decay curve is characteristic of the physical processes in the compound
`under study . For a detailed review the reader is referred to the literature [1-3]. Here
`we give some results for specific situations. We assume that the object of our study
`consists of a compound of a rare earth ion S which contains also some ions A which
`are able to trap the migrating excitation energy of S by SA transfer.
`( 1) If excitation into S is followed by emission from the same S ion (i.e. the isolated
`ion case), or if excitation into S is followed after some migration by emission from
`S only, the decay is described by
`
`I= I 0 exp(-yt),
`
`(5.3)
`
`where Io is the emission intensity at timet= 0, i.e. immediately after the pulse, andy
`is the radiative rate. The decay is exponential. Equation (5.3) is identical to Eq. (3.3) .
`(2) If some SA transfer occurs, but no SS transfer at all, the S decay is given by
`
`I = I 0 exp( -yt- Ct31"),
`
`(5.4)
`
`where C is a parameter containing the A concentration (CA) and the SA interaction
`strength, and n :::: 6 depending on the nature of the multipolar interaction. This decay
`is not exponential. Immediately after the pulse the decay is faster than in the absence
`of A. This is due to the presence of SA transfer. After a long time the decay becomes
`exponential with the radiative rate as a slope. This represents the decay of S ions
`which do not have A ions in the surroundings.
`(3) If we allow for SS transfer, the situation becomes difficult. We consider first the
`extreme case that the rate of SS transfer (Pss) is much higher than PsA (fast diffusion).
`The decay rate is exponential and fast:
`
`I = I 0 exp( -yt) exp( -CA.PSA·t)·
`(4) If Pss << PsA, we are dealing with diffusion-limited energy migration. Fort--+ oo
`the decay curve can be described by
`
`(5.5)
`
`I= Io exp( -yt) exp( -11.404CA.C 114 .D314 .t)
`
`(5.6)
`
`if the sublattice of S ions is three dimensional. C is a parameter describing the SA
`interaction and D the diffusion constant of the migrating excitation energy. For lower
`dimensions non-exponential decays are to be expected.
`In Fig. 5.2, we have given some of these decay curves. The temperature depen(cid:173)
`dence of Pss is very complicated. Due to inhomogeneous broadening, the S ions
`
`Vizio EX1018 Page 0107
`
`

`

`5.3. Energy Transfer Between Identical Luminescent Centers
`
`97
`
`1
`
`c:
`
`t----
`Fig. 5.2. Several possibilities for the decay curve of the excited S ion. The S emission intensity
`is plotted logarithmically versus time. Curve I: no SS transfer (Eq. (5.3)); curve 2 : rapid SS
`migration (Eq. (5.5)); curve 3: intermediate case (for example, Eq. (5.6))
`
`are not exactly resonant, but their energy levels show very small mismatches. We
`need phonons to overcome these. At room temperature, the lines are broadened and
`phonons are available, so that these mismatches do not hamper the energy migra(cid:173)
`tion. However, at very low temperatures they hamper the energy migration, or make
`it even impossible. The theory of phonon-assisted energy transfer has been treated
`elsewhere [2]. For identical ions, one-phonon assisted processes are not of much
`importance. Two-phonon assisted processes have a much higher probability. One of
`these (a two-site nonresonant process) yields a T 3 dependence. Another (a one-site
`resonant process), which uses a higher energy level gives an exp( -k~E) dependence,
`where D.E is the energy difference between the level concemed and the higher level.
`Figure 5.3 gives a schematical presentation of these two processes.
`Let us now consider some examples. First we consider Eu 3+ compounds. In
`EuA1 3B 4 0 12 , there is a three-dimensional Eu3+ sublattice with shortest Eu-Eu dis(cid:173)
`tance equal to 5.9 A. At 4.2 K there is no energy migration at all, but at 300 K
`diffusion-limited energy migration occurs. The temperature dependence of Pss is ex(cid:173)
`ponential with .6.E "'"' 240 cm- 1
`. This is due to the fact that the 5 D 0 -
`7 F 0 transition is
`forbidden under the relevant site symmetry (D3 ), so that the multipolar interactions
`vanish. The distance of 5.9 A is prohibitive for transfer by exchange interaction. At
`higher temperatures the 7 F 1 level is thermally populated and multipolar interaction
`becomes effective. The experimental value of .6.E corresponds to the energy difference
`7 F 0 - 7F 1 (compare Fig. 2.14). Analysis shows that the excited state makes 1400 jumps
`during its life time at room temperature with a diffusion length of 230 A. Table 5 .2
`gives values of the transfer rate and the diffusion constant, together with those for
`other Eu3+ compounds.
`
`Vizio EX1018 Page 0108
`
`

`

`98
`
`5. Energy Transfer
`
`7 )(
`
`2
`
`H
`
`2
`
`-
`
`-
`
`-
`
`-
`
`- - . , r - -
`
`3
`H
`
`a
`
`b
`
`Fig. 5.3. A. Two-site nonresonant process in phonon-assisted energy transfer. (/) and (3) present
`the ion-phonon interaction, (2) the site-site coupling H. B. One-site resonant process in phonon(cid:173)
`assisted energy tran sfer. (I) and (2) present the ion-phonon interaction, (3) the site-site coupling
`
`Table 5.2. Energy migration characteri stics in some Eu3+ compounds at 300 K (data from Ref.
`[7])
`
`Compound
`
`EuAl3B4012
`NaEuTi04
`EuMgBsOw
`Eu2Ti207
`
`Li6Eu(B03)3
`EuOCl
`
`Shortest Eu- Eu
`distance
`5.9 A
`3.7 A
`4.0 A
`3.7 A
`
`3.9 A
`3 .7 A
`
`Diffusion
`constant (cm2s- 1 )
`8 x w- 10
`2 X 10-S a
`~ to-s
`9 x 10-12b
`3 x to- 9 c
`2 x w- 9
`5.8 x w- 10
`
`Hopping time 0
`(s)
`8 x w-7
`2 x w- 8
`~ w-7
`3 x w- 5 b
`8 X JO-S c
`~ w-7
`4 x w- 7
`
`aD= 8 x 10- 11 c m 2 s- 1 at 1.2 K.
`b values at 15 K .
`c values at 43 K .
`d average time for one Eu3+ -Eu3+ transfer step.
`
`Vizio EX1018 Page 0109
`
`

`

`5 .3 . Energy Transfer Between Identical Luminescent Centers
`
`99
`
`4
`10
`
`t 10 3
`
`~ 2
`10
`'7
`.!:!!.-
`o...gj
`
`10 1
`
`10°
`
`0
`
`80
`
`160
`
`T(K) ---
`
`240
`
`Fig. 5.4. Temperature dependence of the Eu3+ - Eu3+ transfer rate in EuMgB 50 10 . Line I is a
`fit using thermally activated migration via the 7 F 1 level of the Eu 3+ ion; line 2 is a fit to the T 3
`temperature dependence predicted by a two-site nonresonant process
`
`Samples of EuA1 3 B 4 0 12 which are so pure that the excited state does not reach
`a killer site during its life time, show efficient luminescence. Samples which contain
`a low concentration of killer sites do not show luminescence at 300 K . However, at
`4.2 K they do, the migration being slowed down considerably or even completely.
`An example is a crystal of EuAhB4 0 12 , grown from a K 2 S04/Mo03 flux [8]. These
`crystals contain '"'"'25 ppm Mo3+ (on Al3+ sites). This ion is an efficient killer of the
`Eu 3+ emission.
`Two-dimensional energy migration was observed for NaEuTi04 and EuMgA1 11 0 19 ,
`and one-dimensional energy migration for EuMgB 5 0 10 and Li 6 Eu(B03 )3. In the rel(cid:173)
`evant crystal structures the Eu 3+ ions form a two- and a one-dimensional sublattice,
`respectively.
`The temperature dependence of Pss is given for EuMgB 5 0 10 in Fig. 5.4. At lower
`temperatures, we find the T 3 dependence expected for two-phonon assisted energy
`migration involving the 7 F 0 and 5 D 0 levels. At higher temperatures the temperature
`dependence becomes exponential, indicating transfer involving the 7 F 1 and 5D 0 levels.
`The situation in Eu3+ compounds can be characterized as follows:
`if the Eu-Eu distance is larger than 5 A, exchange interaction becomes ineffective.
`Only multipolar interactions are of importance, and they will be weak anyhow. Ac(cid:173)
`tually, if sufficiently pure, EuA1 3B 40 12 (Eu-Eu 5.9 A) , Eu(l03 )3 (Eu-Eu 5.9 A) ,
`and CsEuW20 8 (Eu-Eu 5.2 A) luminesce efficiently at 300 K.
`if the Eu-Eu distance is shorter than 5 A, exchange interaction becomes effective.
`Examples are the intrachain migration in EuMgB 5 0 10 and Li6 Eu(B03 )3 and the
`
`Vizio EX1018 Page 0110
`
`

`

`100
`
`5. Energy Transfer
`
`migration in Eu 2 0 3 which is more rapid than in other compounds, even at very
`low temperatures.
`For Tb3+ compounds, the situation is not essentially different, but the temperature
`dependence of the transfer rate shows another behavior, because the 7 F 6 and 5 0 4
`levels are connected by an optical transition with a higher absorption strength than
`the 7 F 0 and 5 0 0 levels in the case of Eu3+.
`Recently, there has been a lot of interest in energy migration in Gd3+ compounds,
`because this opens interesting possibilities for obtaining new, efficient luminescent
`materials (see Chapter 6). The Gd3+ sublattice is sensitized and activated. The sensi(cid:173)
`tizer absorbs efficiently ultraviolet radiation and transfers this to the Gd3+ sublattice.
`By energy migration in this sublattice the activator is fed, and emission results. Ab(cid:173)
`sorption and quantum efficiencies of over 90% have been attained. The physical
`processes can be schematically presented as follows:
`
`exc
`nx
`---+ S ---+ Gd3+ ---+ Gd3 + ---+ A
`
`e1nission
`---+
`
`Here nx indicates the occurrence of many Gd3+ -Gd3+ jumps. A suitable choice of S
`is Ce3+, Bi 3+, Pr3+ or Pb2 +. For A there are many possibilities: Sm3+, Eu3+, Tb3+,
`Dy3+, Mn2+, uog- and probably many more.
`Not always is all of the excitation energy transferred. If only part of it is trans(cid:173)
`ferred, this is called cross-relaxation. Let us consider some examples. The higher(cid:173)
`energy level emissions of Tb3+ and Eu 3+ (Fig. 5.5) can also be quenched if the
`concentration is high. The following cross-relaxations may occur (compare Fig. 5.5) :
`
`The higher-energy level emission is quenched in favour of the lower energy level
`emiSSIOn.
`It is important to realize that we have met now two processes which will sup(cid:173)
`press higher-level emission, viz. multi phonon emission (Sect. 4.2.1) which is only of
`importance if the energy difference between the levels involved is less than about 5
`times the highest vibrational frequency of the host lattice and which is independent
`of the concentration of the luminescent centres, and cross relaxation which will occur
`only above a certain concentration of luminescent centers since this process depends
`on the interaction between two centers.
`Consider as an example the Eu 3+ ion in YB03 and Y 2 0 3 . For low Eu 3+ con(cid:173)
`centrations (say 0.1 mole %) we find in YB03 only 5 D 0 emission, since the higher(cid:173)
`level emissions are quenched by multiphonon emission (highest borate frequency
`"'"' 1050 cm- 1). In Y 2 0 3 , however, such a low concentration of Eu3+ ions gives 5 D 3 ,
`5 D 2 ,
`5D 1 and 5 D 0 emission (highest lattice frequency '"""' 600 cm- 1
`). For 3% Eu 3+
`in Y 2 0 3 the emission spectrum is dominated by the 5D 0 emission. The higher-level
`emission is quenched by cross relaxation in favour of the 5D 0 emission.
`
`Vizio EX1018 Page 0111
`
`

`

`5.3. Energy Transfer Between Identical Luminescent Centers
`
`I 01
`
`- -·- --
`- - -- -
`-
`
`5
`
`- 03
`5 - 02
`<r:=:o,
`
`Do
`
`_ ___
`
`_ 7 F6
`
`4
`
`- 2I 3
`
`2
`1
`0
`
`3+
`Eu
`
`--
`
`-
`
`-
`
`-
`
`5
`
`L10
`
`:t=_:D,
`
`04
`
`~~
`
`3+
`
`Tb
`
`Fig. 5.5. Quenching of higher-level emission by cross relaxation. Left-hand side Eu 3+: the 5 D 1
`emission on ion I is quenched by transferring the energy difference 5 D 1- 5 D 0 to ion 2 which
`is promoted to the 7 F3 level. Right-hand side Tb3+: the 5 D 3 emission on ion I is quenched by
`transferring the energy difference 5 D 3 - 5 D 4 to ion 2 which is promoted to the 7 F 0 level
`
`Up to now it has been demonstrated that concentration quenching of the lumines(cid:173)
`cence of rare earth compounds consists of energy migration to killers in the case of
`Eu 3+ , Gd3+, Tb3+. In the case of Sm3+ and Dy3+ , the above-mentioned cross relax(cid:173)
`ation is responsible for concentration quenching: the quenching of the luminescence
`occurs in ion pairs and not by migration. For other rare earth ions the situation is
`in between. We can use pi3+ to illustrate the situation, and consider, in addition to
`energy migration, cross relaxation between Pi3+ ions, i.e. every Pr3+ ion can be a
`killer of its neighbours luminescence. Figure 5.6 gives pos