Luminescence of inorganic solids: from isolated centres to concentrated systems

Prog. SolidSt. Chem. Vol. 18, pp. 79--171, 1988 0079--6786/88 $0.00 + .50

Printed in Great Britain. All rights reserved. Copyright © 1988 Pergamon Journals Ltd.

LUMINESCENCE OF INORGANIC SOLIDS:

FROM ISOLATED CENTRES TO

CONCENTRATED SYSTEMS

George Blasse

Physical Laboratory, University Utrecht, PO Box 80.000, 3508 TA,

The Netherlands

CONTENTS

1. Introduction

2. The isolated luminescent centre

2.1. The configurational coordinate diagram

2.2. Spectroscopy of isolated centres

2.3. Examples

2.4. Nonradiative processes

3. Energy transfer between unlike centres

4. Energy transfer between identical centres:

energy migration and concentration quenching

4.1. Weak-coupling scheme ions

4.2. Intermediate- and strong-coupllng scheme ions

80

81

81

86

87

114

124

129

130

146

5. Delocalisation vs relaxation in the excited state 152

5.1. Examples of strong relaxation 153

5.2. Examples of delocalisation; the transition to semiconductors 154

6. Applications

References

JPSSC 18:2-A

157

159

79

80 G. Blasse

I. INTRODUCTION

Luminescence of solids is an extensively studied field of research with

many important applications. Our general understanding of the processes

taking place is nowadays at a reasonable level. Nevertheless many

problems are still left. One of these, especially intriguing for

chemists, is the way in which luminescence properties depend on crystal

structure and chemical composition. In contrast to properties llke

magnetism and electrical conductivity, luminescence is a property

related to the difference between two electronic states, viz. the

emitting state and the ground state. This makes a general approach

rather difficult. Especially if we consider changes in the surroundings

of a luminescent centre, it must be realized that the ground state as

well as the excited state are influenced by such a change, and that we

are interested in their difference.

It is the purpose of this review to deal with the physical models which

are used to describe the luminescence processes in an isolated centre

and the interaction between luminescent centres mutually. In doing so,

we will also try to describe the way in which the luminescence

properties depend on the chemistry of the system, i.e. the crystal

structure and/or the surroundings of the centre in the crystal lattice.

It will become clear that this dependence can be very strong indeed.

This is not only an interesting type of fundamental study, but it can

also result in important new phosphors (luminescent materials).

Our approach will be as follows. First we will consider the isolated

luminescent centre, i.e. a centre without interaction with other

(luminescent) centres. The physical model here is the conflguratlonal

coordinate diagram. This will be applied to the spectroscopy of such a

centre. Later we consider interaction between luminescent centres,

resulting in (one-step) energy transfer, (multi-step) energy migration,

and delocalisatlon of the excited state. Finally some applications are

considered.

Readers who are interested to consult more detailed reviews are referred

to the reports of the Erlce Summer Schools on spectroscopy (I-5). The

scientiEic progress in this field can be judged by consulting the

trlannual issues of the Journal of Luminescence presenting the

proceedings of the international conferences on luminescence (l~J) (see

e.g. refs. 6-8). Readers interested in the recent new luminescent

materials are referred to a special issue of the journal Materials

~nemistry and Physics (9).

The present presentation will consider mainly insulating substances, but

here and there the field of semiconductors is reached more or less

Luminescence of inorganic solids 81

automatically. The approach will not aim at a high level of theoretical

sophistication. The theory and the models used will be illustrated by

many representative examples of a very different nature.

2. THE ISOLATED LUMINESCENT CENTRE

Let us consider a dopant ion in a crystal lattice and assume that the

excited electronic energy levels of the host are at much higher energy

than those of the dopant ion. A classic example is Cr 3+ in Ai203 (ruby).

The dopant ion colours the colourless host lattice red. If the

concentration of the dopant ion is low, the interaction between the

dopant ions can be neglected. This is what we consider here as an

isolated luminescent centre. In this review the electronic energy level

diagrams of the dopant ions will not be derived. They can be found in

the literature, for example those of the transition-metal ions in a book

on crystal-field theory, and so on. References will be given when

appropriate.

2.1. The confi~urational coordinate diagram

Let us consider a dopant ion in a host lattice and assume that it shows

luminescence upon illumination. ~lat we will have to discuss is the

interaction of the dopant ion with the vibrations of the lattice. The

environment of the dopant ion is not static: the surrounding ions

vibrate about some average positions, so that the crystalline field

varies. The simplest model to account for the interaction between the

dopant ion and the vibrating lattice is the single-configurational

coordinate model (10,11).

In this model we consider only one vibrational mode, viz. the so-called

breathing mode in which the surrounding lattice pulsates in and out

around the dopant ion (symmetrical stretching mode). This mode is

assumed to be described by the harmonic oscillator model. The

configuratlonal coordinate (Q) describes the vibration. In our

approximation it presents the distance between the dopant ion and the

surrounding ions. In ruby this Q would be the Cr 3+ - 0 2- distance.

If we plot energy vs Q we obtain for the electronic states parabolae

(harmonic approximation). This is presented in fig. l for the electronic

ground state g and one electronic excited state e. Further Qo presents

the equilibrium distance in the ground state, Q~ that in the excited

82 G. Blasse

state. Note that in general these will be different! The g parabola is

given by

V = ~ k (Q - qo )2,

where k is the force constant. Within the parabolae the (equidistant)

vibrational energy levels have been drawn. They are numbered by n = 0,

I, 2 ... The excited state parabola is drawn in such a way that the

force constant is weaker than in the ground state. Since the excited

state is usually weaker bound than the ground state, this is a

representative situation.

I I

t I

I/

t'

s S I

/ : /

AQ % <

)

0

Fig. 1 The configuratlonal coordinate diagram. The energy E is plotted

vs the coordinate Q. Parabolae g and e refer to the ground

state and excited state, respectively. Horizontal lines

indicate the vibrational levels. The vertical transitions are

discussed in the text. AQ gives the parabolae offset. The

absorption transition is indicated by AB~ the emission

transition by EM.

Optical absorption corresponds to a transition from the g to the e state

under absorption of electromagnetic radiation. Emission is the reverse

transition. Let us now consider how these transitions have to be

described in the configurational coordinate model. It is essential to

remember that the wave function of the lowest vibrational state (i.e. n

= 0) is Gausslan, i.e. the most likely value of Q is Qo (or Q~ in the

excited state). For the higher vibrational states, however~ the most

Luminescence of inorganic solids 83

likely value is at the edges of the parabola, i.e. at the turning points

(llke in the classic pendulum).

The most likely transition in absorption at low temperatures is from the

n = 0 level in g, starting at the value Qo" Optical absorption

corresponds to a vertical transition, because the transition g ÷ e on

the dopant ion occurs so rapidly that the surrounding lattice does not

change during the transition (Born-Oppenheimer approximation). Our

transition will end on the edge of parabola e, since it is there that

the vibrational states have their highest amplitude. This transition,

drawn as a solid line in fig.l, corresponds to the maximum in the

absorption band. However, we may also start at Q values different from

Qo' although the probability is lower. This leads to the width of the

absorption band, indicated in fig. 1 by broken lines. It can be shown

that the probability of the optical transition between the n = 0

vibrational level of the ground state and the n = n' vibrational level

of the excited state is proportional to

<e(Q) Irlg(Q)><Xn,/Xo> (~),

where r presents the electric-dipole operator and X the vibrational wave

functions. The first term, the electronic matrix element, is independent

of the vibrational levels; the second term gives the vibrational

overlap. The transition fron n = 0 to n' = 0 does not involve the

vibrations. It is called the zero-vibrational transition (or no-phonon

transition). Equation 1 shows that the effect of the vibrations is

mainly to change the shape of the absorption line (or band), but not the

strength of the transition (which is given by the electron matrix

element).

What happens after the absorption transition? First we return to the

lowest vibrational level of the excited state, i.e. the excited state

relaxes to its equilibrium position, giving up the excess energy as heat

to the lattice. The system of dopant ion and surroundings is then in the

relaxed excited state. The emission transition can be described in

exactly the same way as the absorption transition. This is indicated in

fig.l in the same way as for the absorption transition. Finally the

system relaxes within the g parabola to the lowest vibrational level.

If the temperature is not low, higher vibrational levels may be occupied

thermally, so that we start the process not only from n = 0, but also

from n = I, and possibly from even higher levels. This leads to a

further broadening of the absorption and emission bands, but does not

change our arguments essentially.

84 G. Blasse

750 650 600

h(nm)

xr

i

0

700 550

CI

t

340

CI

320

X (nm)

300

(

l

SS

I

300

Fig. 2

)

500 nm /.-,

I

5OO 600 n m

Emission spectra for several coupling strengths.

a. Weak coupling strength (S < I). Emission spectrum of the

Eu 3+ ion in LAB30 6 (red spectral region; the notation J-J'

stands for the transition 5Dj ÷ 7FJ) and of the Gd 3+ ion in

LAB30 6 (ultraviolet spectral region). In these, and all

other figures of emission spectra below, ~k denotes the

spectral radiant power per constant wavelength interval in

arbitrary units.

b. Intermediate coupling strength (I<S<5). Emission spectrum of

the UO22+ ion in SrZnP20 7 at 300 K. Note the progression in

the uranyl stretching vibration.

c. Strong coupling strength (S>5). Emission (EM) and excitation

(EX) spectrum of the tungstate group in CaWO 4. SS indicates

the Stokes shift.

Luminescence of inorganic solids 85

The emission transition will usually be situated at lower energy than

the absorption transition. This phenomenon is known as the Stokes shift.

Only the zero-vibrational transition is expected to occur at the same

energy in the absorption and emission spectra. The Stokes shift is a

direct consequence of the relaxation processes which occur after the

optical transitions. It is obvious that the larger Q~ - Qo is, the

larger the Stokes shift will be. If the two parabolae have the same

shape and vibrational frequency, it is possible to define a parameter S

(the so-called Huang-Rhys parameter) as follows

~k(Q~ - Qo )2 = S~ (2),

where h~ is the energy difference between the vibrational levels. The

Stokes shift is then given by

AE S = k(Q~ - Q) 2_ h~ = 2Sh~ (3).

The parameter S measures the interaction between the dopant ion and the

vibrating lattice. Equation 3 shows that if S is large, the Stokes shift

is also large. Equation 2 shows that S is immediately related to the

offset of the parabolae in the configurational coordinate diagram

(fig. l). This offset, AQ(= Q~ - Q), may vary considerably as a function

of the dopant ion and as a function of the vibrating lattice, as we will

see below.

It can be shown that the relative intensity of the zero-vibrational

transition (ng = 0 - n~ = 0) is exp(-S) (10,11). We can now divide our

luminescent centres in three classes, vlz.

(i) those with weak coupling, i.e. S < I, so that the zero-vlbrational

transition dominates the spectrum,

(ii) those with intermediate coupling, i.e. 1 < S < 5, so that the zero￾vibrational transition is observable, but not the strongest line in the

absorption or emission band,

(lii) those with strong coupling, i.e. S > 5, so that the zero￾vibrational transition is so weak that it is not observable in the

spectra. This case is also characterized by large ~okes shifts.

Figure 2 shows three emission spectra which are representative of each

case. ~aracteristlc examples of case (1) are the trlvalent rare earth

ions. The value of S is so small for these ions, that the spectra

consist in good approximation of the zero-vlbratlonal transitions only.

Figure 2a gives as an example the emission spectra of the Eu 3+ ion in

LaB306 and of the C~ 3+ ion in LAB306. The former consists of many

transitions which are all purely electronic; the latter consists of one

strong electronic line at about 310 nm, whereas the weak repetition at

86 G. Blasse

about 325 nm is a vibronic transition. Actually the energy difference

between these two lines corresponds to the vibrational stretching

frequency of the borate group in LaB306.

A characteristic example of case (ii) is the uranyl ion (U02~+). The n e =

0 ÷ng = 2 line dominates in the spectrum (fig. To). The tungstate ion

(WO~-) is a good example of case (iii). The very broad emission spectrum

(see fig. 2c) does not show any vibrational structure at all, the Stokes

shift is very large (~ 16.000 cm -I) and the zero-vibrational transition

is not observable, not even at the lowest possible temperatures nor for

the highest possible resolving powers.

Finally we draw attention to the fact that the single conflgurational

coordinate diagram is only an approximation. In practice there is more

than one vibrational mode involved and the system is not harmonic.

Therefore the value of S is not so easy to determine as suggested above.

However, for a general understanding the simple model is extremely

useful as we will see below.

2.2 Spectroscopy of isolated centres

If we measure an absorption or emission spectrum, the following

properties of the bands or lines are of importance

- their spectral position, i.e. the energy at which the transition

occurs,

- their shape, i.e. sharp llne, structured narrow band, or

structureless broad band.

- their intensity.

For the spectral position the reader will be referred to the literature,

except for details of importance. The shape of the bands was essentially

discussed in section 2.1 (see figs. I and 2). The intensity is contained

in the electronic matrix element

<e(Q) Irlg(Q)>

in eq.l. The intensity can be very low if selection rules apply. Here we

mention a few, well-known examples.

For electric-dipole transitions the parity of the initial and final

states should be different (parity selection rule). This implies that

transitions within one and the same shell, for example 3d or 4f, are

forbidden. This selection rule may be relaxed by the admixture of

opposlte-parity states due to the crystal field, or by vibrations of

suitable symmetry.

Luminescence of inorganic solids 87

Optical transitions are forbidden between states of different spin

multiplicity (spin selection rule). This selection rule may be relaxed

by the spin-orbit coupling. Since the latter increases strongly with the

atomic number, the value of this selection rule decreases if we proceed

from top to bottom through the periodic table.

Many other selection rules of a more specialised nature will be

mentioned where applicable and as far as necessary.

If we consider dopant ions in a solid, their spectral features will show

inhomogeneous broadening, even if their mutual interaction is neglected.

The reason for this is the fact that the crystal field at the dopant ion

varies slightly from ion to ion due to the presence of defects, as, for

example, impurities, vacancies, dislocations, or the surface (I~. As a

matter of fact the inhomogeneous broadening will be more pronounced for

line spectra than for broad-band spectra. Its magnitude is also much

larger in disordered solids (glasses!) than in ordered solids (13).

2.3. Examples

2.3.1. The weak-couplin$ case (S < I)

In inorganic solids there are only a few examples of the weak-coupling

case. The most important one is that of the trivalent rare-earth ions.

They have an incompletely-filled 4f shell. The energy levels originating

from this configuration are well known. They can be found everywhere in

the literature (11, 14). Figure 3 gives some examples, viz. Ce3+(4fl),

Sm3+(4f5), Eu3+(4f6), Gd3+(4f 7) and Tb3+(4fS).

Transitions between energy levels of a given 4f n configuration are

parity forbidden as electric-dipole transitions. It is not easy to relax

this selection rule in view of the fact that the 4f electrons are well

shielded from the surroundings by the ~ and 5p electrons. However, the

theories to explain the intensities of the sharp-line absorption and

emission spectra are nowadays well developed (15). In general it can be

said that the theoretical and experimental situations are satisfactory,

and that the agreement between both is good. Nevertheless there are new

developments and results of which we mention a few here.

For Eu3+(4f~, an ion with malnly red emission, but sometimes also green

and blue emission, there has recently been reported an ultraviolet

emission, viz. 5H 3 ÷ 7Fj (16). This emission can only be expected to

occur if the next-hlgher configuration, in this case a charge-transfer

transition, is at much higher energy, as e.g. in fluorides.