Solid State Luminescence: Theory, materials and devices

Edited by
A.R. Kitai Department of Materials Science and Engineering and Engineering Physics McMaster University, Ontario, Canada
I~nl SPR1NGER-SCIENCE+BUSINESS MEDIA, B.V.
PubIished by Cbapman & HalI, 2-6 Boundary Row, London SEI 8HN
Chapman & Hali, 2-6 Boundary Row, London SEI 8HN, UK
Blackie Academic & Professional, Wester Cleddens Road, Bishopbriggs, Glasgow G64 2NZ, UK
Chapman & Hali Inc., 29 West 35th Street, New York NY1000l, USA
Chapman & Hali Japan, Thomson Publishing Japan, Hirakawacho Nemoto Building,6F, 1-7-11 Hirakawa-cho, Chiyoda-ku, Tokyo 102, Japan
Chapman & Hali Australia, Thomas Nelson Australia, 102 Dodds Street, South Melboume, Victoria 3205, Australia
Chapman & Hali India, R. Seshadri, 32 Second Main Road, CIT East, Madras 600 035, India
First edition 1993
© 1993 Springer Science+Business Media Dordrecht Originally published by Chapman & Hali in 1993 Softcover reprint of the hardcover 1 st edition 1993 Typeset in 10/12 Times by Interprint Limited, Malta
ISBN 978-94-010-4664-0 ISBN 978-94-011-1522-3 (eBook) DOI 10.1007/978-94-011-1522-3
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the UK Copyright Designs and Patents Act, 1988, this publication may not be reproduced, stored, or transmitted, in any form or by any means, without the prior permission in writing of the publishers, or in the case of reprographic reproduction only in accordance with the terms of the Iicences issued by the Copyright Licensing Agency in the UK, or in accordance with the terms of Iicences issued by the appropriate Reproduction Rights Organization outside the UK. Enquiries conceming reproduction outside the terms stated here should be sent to the publishers at the London address printed on this page.
The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or Iiability for any errors or omissions that may be made.
A catalogue record for this book is available from the British Library
Library of Congress Cataloging-in-Publication data available.
@! Printed on permanent acid-free text paper, manufactured in accordance with the proposed ANSIjNISO Z 39,48-199X and AN SI Z 39.48-1984
Contents
2 Luminescent centres in insulators 21 G. Blasse
3 Luminescence spectroscopy 53 U. W. Pohl and H.-E. Gumlich
4 One-photon rare earth optical transitions: recent theoretical developments 97 G. W. Burdick and M.e. Downer
5 Thin film electroluminescence 133 G.O. Muller
6 Powder electro luminescence 159 S.S. Chadha
7 Thin film electroluminescence devices 229 R Mach
8 Light emitting diodes: materials growth and properties 263 S.P. DenBaars
9 Atomic layer epitaxy of phosphor thin films 293 B.W Sanders
10 Lamp phosphors 313 T.E. Peters, RG. Pappalardo and RB. Hunt, Jr
11 Phosphors for other applications 349 G. Blasse
Index 373
v
Contributors
G. Blasse Debye Research Institute University of Utrecht Utrecht The Netherlands
G.W. Burdick The University of Texas at Austin Texas USA
S.S. Chadha School of Biological and Chemical Sciences University of Greenwich London UK
S.P. DenBaars Materials Department University of California, Santa Barbara California USA
M.C. Downer The University of Texas at Austin Texas USA
H.-E. Gumlich Technical University of Berlin Berlin Germany
Vll
R.B. Hunt, Jr GTE Laboratories Inc., Danvers Massach usetts USA
A.K. Kitai Departments of Materials Science and Engineering Physics McMaster University, Hamilton Ontario Canada
R. Mach Central Institute for Electron Physics Berlin Germany
G.O. Muller Central Institute for Electron Physics Berlin Germany
R.G. Pappalardo GTE Laboratories Inc., Danvers Massachusetts USA
T.E. Peters GTE Laboratories Inc., Chelmsford Massachusetts USA
U.W. Pohl Technical University of Berlin Berlin Germany
B.W. Sanders Institute for Environmental Chemistry National Research Council Canada, Ottawa Ontario Canada
Preface
Historically, black body radiation in the tungsten filament lamp was our primary industrial means for producing 'artificial' light, as it replaced gas lamps. Solid state luminescent devices for applications ranging from lamps to displays have proliferated since then, particularly owing to the develop ment of semiconductors and phosphors. Our lighting products are now mostly phosphor based and this 'cold light' is replacing an increasing fraction of tungsten filament lamps. Even light emitting diodes now chal lenge such lamps for automotive brake lights.
In the area of information displays, cathode ray tube phosphors have proved themselves to be outstandingly efficient light emitters with excellent colour capability. The current push for flat panel displays is quite intense, and much confusion exists as to where development and commercialization will occur most rapidly, but with the need for colour, it is now apparent that solid state luminescence will play a primary role, as gas phase plasma displays do not conveniently permit colour at the high resolution needed today. The long term challenge to develop electroluminescent displays continues, and high performance fluorescent lamps currently illuminate liquid crystal monochrome and colour displays. The development of tri component rare earth phosphors is of particular importance.
This book begins with a chapter on the physics of luminescence, covering the classical and quantum mechanical theory of radiation in atoms and solids. Chapter 2 focuses on phosphors, describing the fundamental pro cesses and models that are useful to sort out the rather complex electronic and vibrational interactions. Chapter 3 deals with state of the art experimen tal methods and gives examples of fundamental luminescence processes in solids. Chapter 4 presents a current understanding of rare earth ions in crystalline fields.
The next section of the book focuses on different device and material types: thin film electroluminescence is described from a physics perspective in Chapter 5 and Chapter 6 traces the rather painful but important development of powder phosphors for electroluminescence.
IX
x Preface
Chapter 7 presents the current state of thin film electroluminescence, and Chapter 8 is devoted to both the theory and technology involved in light emitting diodes which are now reaching new levels of efficiency.
Chapter 9 discusses, in some detail, the concept of kinetically limited growth for thin films which allows large area, uniform coverage of both phosphor and semiconductor materials.
Finally Chapters 10 and 11 present a very comprehensive account of phosphors for fluorescent lamps and special applications in for example, medicine.
A.H. Kitai Ontario Canada
A.H. Kitai
1.1 INTRODUCTION
Technologically important forms of luminescence may be broken into several categories, as shown in Table 1.1. Although the means by which the luminescence is excited varies, all luminescence is generated by means of accelerating charges. The portion of the electromagnetic spectrum visible to the human eye has wavelengths from 400 to 700 nm. The evolution of the relatively narrow sensitivity range of the human eye is a complex subject, but is intimately related to the solar spectrum, the absorbing behaviour of the terrestrial atmosphere, and the reflecting properties of organic materials, green being the dominant colour in nature and, not surprisingly, the wavelength at which the human eye is most sensitive. In this chapter, we cover the physical basis for radiation and radiation sources in solids that produce visible light.
Table 1.1 Luminescence types, applications and typical efficiencies (visible output power/electrical input power)
Luminescence type
Typical application
flat panel display
1.2 RADIATION THEORY
0.1-50%
A stationary point charge has an associated electric field E as shown in Fig. 1.1. A charge moving with uniform velocity relative to the observer gives rise to a magnetic field as shown in Fig. 1.2.
1
2 Principles of luminescence
Fig. 1.1 The lines of electric field E due to a point charge q.
B
Fig. 1.2 The lines of magnetic field B due to a point charge q moving into the page with uniform velocity.
Both electric and magnetic fields store energy; the total energy density is given by
It is important to note that the energy density moves with the charge so long as the charge is either stationary or undergoing uniform motion; this is evident since a new reference frame may be constructed in which the observer is stationary with respect to the charge.
For an accelerated charge, however, energy continuously leaves the charge to compensate exactly the work done in causing the charge to accelerate. Consider the charge q in Fig. 1.3. Initially at rest in position A, it accelerates to position B and then stops there. The electric field lines now emanate from position B, but would, further out, have emanated from position A, since the field lines cannot convey information about the location of the charge at speeds greater than the velocity of light c. This results in kinks in the lines of electric field which propagate away from q with velocity c. Each time q accelerates, a new series of propagating kinks is generated. Each kink is made up of a component of E that is transverse to the direction of expansion, which we call E 1-' If the velocity of the charge during its acceleration does not exceed a small fraction of c, then for r large,
qa . () E1- = 2 sm
a -
Fig. 1.3 Lines of electric field emanating from an accelerating charge. (After Eisberg and Resnick [1].)
Here, a is acceleration, and r is the distance between the charge and the position where the electric field is evaluated. The strongest transverse field occurs in directions normal to the direction of acceleration, as suggested by Fig. 1.3.
Likewise, a transverse magnetic field B 1- is generated during the acceler ation of the charge as shown in Fig. 1.4, given by
Iloqa . B1-=--sm8
4ncr
a
Fig. 1.4 Lines of magnetic field B emanating from an accelerating charge. B is perpendicular to the page.
The two transverse fields propagate outward with velocity c each time q undergoes an acceleration, giving rise to the electromagnetic radiation whose frequency matches the frequency with which q acclerates. Note that E.l and B.l are perpendicular to each other. The energy density of the radiation is
.1. 2 1 2 Iff = 21::0E.l + -2 B.l
f.lo
The Poynting vector or energy flow per unit area (radiation intensity) is
1 S=-E.l xB.l
f.lo 2 2
-q-=---a-=--=-sin20 f 16nl::oc3 r 2
Maximum energy is emitted in a ring perpendicular to the direction of acceleration, and none is emitted along the line of motion. To obtain the total radiated energy per unit time or power P leaving q due to its acceleration, we integrate S over a sphere surrounding q to obtain
P= f S(O) dA= f: S(0)2nr2 sin 0 dO
since dA is a ring of area 2nr2 sin 0 dO. Substituting for S(O), we obtain
1.3 SIMPLE HARMONIC RADIATOR
If a charge q moves about the origin of the x-axis with position x = A sin wt then we can easily calculate the average power radiated away from the oscillating charge. Note that
and
4nl::03c3
Now, average power P is the root-mean-square power which gives
_ q2 A2w4 P=-=-----;;-
Quantum description 5
If we now consider that an equal and opposite stationary charge - q is located at x=o then we have a dipole radiator with electric dipole moment of amplitude p = qA. Now we may write
_ p2W 4
P=---:o 12n80c3
Non-oscillatory radiation does exist also; the synchroton radiation source is an example of a radiator that relies on the constant centripetal acceleration of an orbiting charge. Quadrupole and higher-order poles may exist even in the absence of a dipole moment; however, they have lower rates of energy release.
1.4 QUANTUM DESCRIPTION
A charge q (quite possibly an electron) does not exhibit energy loss or radiation when in a stationary state or eigenstate of a potential energy field. This requires that no net acceleration of the charge occurs, in spite of its uncertainty in position and momentum dictated by the Heisenberg uncertainty principle. Experience tells us, however, that radiation may be produced when a charge moves from one stationary state to another; it will be the purpose of this section to show that radiation may only be produced if an oscillating dipole results from a charge moving from one stationary state to another.
Consider a charge q initially in stationary state I/In and eventually in state I/In'. During the transition, a superposition state is created which we shall call 1/1.:
where a and b are time-dependent coefficients. Initially, a = 1, b = ° and finally, a=O, b= 1.
Quantum mechanics allows us to calculate the expected value of the position (r) of a particle in a quantum state. For example, for stationary state I/In,
provided I/In is normalized, and V represents all space. Since, by definition II/Inl 2 is not a function of time because I/In is a stationary state, the answer to this integral is always time independent and may be written as ro, Note that the time dependence of a stationary state is given by le(iE/h)tI2= e(iE/h)te(-iE/h)t = 1. If we now calculate the expectation value of the position of q for the superposition state 1/1., we obtain
(r). = (al/ln + bl/ln, I rl al/ln + bl/ln,) = I a 12 (1/1 n I r 11/1 n) + b2 < 1/1 n' I r 11/1 n' ) + a* b< 1/1 n I r 11/1 n' )
+ b*a( 1/1 n' I r II/In)
where ¢n is the spatially dependent part of "'n' Hence
since the position must be a real number. This may be written as
<r(t)s = 21 a*b< ¢n Irl¢n') 1 cos(wnn' t + b)
=2Irnn'l cos(wnn't+b) (1.2)
Note that we have introduced the relationship E = hw that defines the energy of one photon generated by the charge q as it moves from "'n to "'n" Note also that <r(t) is oscillating with frequency W nn' = (En - En,)/h such that the required number of oscillations at the required frequency releases one photon having energy E = hwnn, from the oscillating charge. The term r nn' also varies with time, but does so slowly compared with the cosine term. Consider that an electron oscillates about x = 0 with amplitude A = 1 A to produce a photon with A = 550 nm. From equation (1.1 ),
_ (16 X 10- 19 )2 x (10- 10 )2 X (2n)4 x (3 x 108 ) p= . =4xlO- 12 w
12n(8.85 x 10- 12 )(5.5 x 10- 7 )4
since
2nc w=T
One photon of this wavelength has energy E = hel A = 3 x 10 - 19 1. Hence, the approximate length of time taken to release the photon is (3 x 10- 19 J)j (4 x 10 - 12 J s - 1) = 7.7 x 10 - 8 s. Since the period of electromagnetic oscilla tion is T= Alc = 1.8 x 10- 15 s, approximately 107 oscillations take place. We have assumed 1 r nn' 1 to be a constant which will be shown not to be the case in a later section.
We may define a photon emission rate Rnn , of a continuously oscillating charge. We use equations (1.1) and (1.2) and E=hw to obtain
P q2w 3
W neoe
Selection rules 7
1.5 SELECTION RULES
A particle cannot change quantum states without conserving energy. When energy is released as electromagnetic radiation, we can determine whether or not a particular transition is allowed by calculating the term I r nn' I, and seeing whether it is zero or non-zero. The results over a variety of possible transitions give selection rules that name allowed and forbidden transitions.
The transitions involved in the hydrogen atom are of particular import ance. We will now derive the well-known selection rules for the electron in hydrogen states, or more generally in one-electron atomic states. We use polar coordinates and begin by calculating r nn'.
rnn,=(nlrln')= r I/I:rl/ln,dV J all space
Note that since we are working in three dimensions, we must consider r in vector form, and let I/I(r, (), ¢)=Rn(r)8Im(())tPm(¢). Now,
rnn,= tXl Rn,(r)r3Rn(r)dr[t 2
1[ f: 8I'm,(())8Im(()) sin ()rtP!(¢)tPm,(¢)d()d¢ ]
The term in brackets may be broken up into orthogonal components of unit vector r = sin () cos ¢ x + sin () sin ¢ y + cos () z to obtain three terms:
(1.3)
since tPm(¢)=eim</>, the three integrals in ¢ may be written
f 21[
f 21[
f21[
11 may be written:
which is zero unless m' = m ± 1. 12 gives the same result. Now consider the integrals in () which multiply 11 ,12, and 13 , We shall
name them J 1, J 2, and J 3' If 13 is non-zero, then m' = m. Hence we obtain
The integral
is zero unless l' = 1, a property of the associated Legendre polynomials which, being eigenfunctions, are orthogonal to each other [2]. Since cos () is an odd function over the range 0 ~ () ~ n, the parity is reversed in J 3 and hence J 3 =0 unless l' = 1 ± 1.
If 11 is non-zero, then m' = m ± 1. Hence, we obtain
Using the properties of associated Legendre polynomials once again, we note that it is always possible to write B'm(())=aBI-1.m+1(())+bB,+1.m+1(()), where a and b are constants. Choosing m' = m + 1, we obtain
For a non-zero result, l' = 1 ± 1 using the orthogonality property. The same conclusion obtains from the case m' = m - 1 and from the J 2 integral. We have therefore shown that the selection rules for a one-electron atom are
L1m=O, ± 1 and Al= ± 1
Note that we have neglected spin-orbit coupling here. Its inclusion would give
L11= ± 1 and L1j=O, ± 1
Selection rules do not absolutely prohibit transitions that violate them, but they are far less likely to occur. Transitions may take place from oscillating magnetic dipole moments, or higher-order electric pole moments.
Einstein coefficients 9
These alternatives are easily distinguished from allowed transitions since they occur much more slowly, resulting in photon release times of mil liseconds to seconds rather than nanoseconds as calculated earlier. It is important to realize that practical phosphors having atomic luminescent centres often release photons via 'forbidden' transitions. The surrounding atoms in a crystal may lift the restrictions of ideal selections rules because they lower the symmetry of atomic states.
1.6 EINSTEIN COEFFICIENTS
Consider that an ensemble of atoms has electrons in quantum states k of energy Ek which may make transitions to states 1 of energy E, with the release of photons (see Fig. 1.5).
many atoms
many atoms
Fig. 1.5 The decay of an electron from state k to state I results in the release of a photon.
In order to begin making such transitions, something is needed to perturb the electrons in states k, otherwise they would not initiate the transitions, and would not populate superposition states I/Is. The study of quantum electrodynamics shows that there is always some electromagnetic field present in the vicinity of an atom at whatever frequency is required to induce the charge oscillations, and to initiate the radiation process. This is because electromagnetic fields are quantized and hence a zero-point energy exists in the field. We call this process spontaneous emission.
Alternatively, the transition may be initiated by applied photons (an applied electromagnetic field) which gives rise to stimulated emission. It is also possible to excite electrons in state 1 to state k using photons of suitable energy.
These ideas may be summarized as follows. The rate at which atoms in the Ek state decay is Wkl . This is proportional to the number of photons of frequency (J) supplied by the radiation field, which is proportional to photon energy density u(v) and to the number of atoms in the Ek state. The spontaneous process occurs without supplying radiation, and hence its rate is determined simply by the number of atoms in the Ek state, N k • We may write
(1.4 a)
The proportionality constants A and B are called the Einstein A and B coefficients, and OJkl is the rate on a per atom basis.
Atoms in the El state may not spontaneously become excited to the Ek
state; however, photons of energy Ek-E1 may be absorbed. Hence,
(1.4 b)
At this point, the idea of stimulated emission needs to be developed in order to explain why transition rates are proportional to u(v). It is, however, clear that Akl is simply another name for Rnn" the photon emission rate, in the case of dipole radiation.
1.7 HARMONIC PERTURBATION
Consider an atom possessing electron levels k and I that experiences a weak electromagnetic field. By 'weak' we require that the potential energy experi enced by the electrons due to this field is small compared with the Coulomb potential from the nucleus and other electrons. The total Hamiltonian is given by the sum of the atomic term Ho(r) and the perturbation term H'(r, t):
H(r, t)=Ho(r)+H'(r, t) with H'(r, t)=H'(r)f(t)
If the field is turned on at t = 0 with frequency OJ then
'( ) {O t<O H r,t = 2H'(r) cOSOJt t~O
Time-dependent perturbation theory [2J may be used to determine the wavefunction that results from the perturbation which is harmonic in this case. Assume the electron is initially in eigenstate t/llr, t). In general, if t/lk(r, t) are all eigenstates of Ho(r) then the wavefunctions after the perturba tion term H'(r, t) is added will be of the form
t/I(r, t)= L Ck(t)t/lk(r, t) k
where
and
t/I(r, t) = cPk(r )eiwkt
The probability of a transition from the initial eigenstate t/ll(r, t) to a new eigenstate t/lk(r, t) is given simply by ICk(tW. We write
Pl_k(t)=ICk(t)12=(~~ly 1 t eiwkI''j(t')dt' 12
Harmonic perturbation 11
Because of the weak electromagnetic field, f(t)=2 cos wt, and therefore
= 2iHkl {ei (o)kl- W)t/ 2 sin[(wkl-w)t/2] + ei (Wkl+ W )t/ 2 Sin[(Wk1 +W)t/2]}
h Wkl-W Wkl+W
Resonance occurs when Wkl = ± w. The two signs signify either a sti mulated absorption process (Wkl = w) or a stimulated emission process (Wkl= -w) since energy is then released (Ekl negative). If Wkl~W,
(1.5)
The probability of the transition (stimulated emission or absorption) is always proportional to 1 Hkzl 2. P1k is shown in Fig. 1.6, which should be thought of as a graph that grows rapidly in height with time t. Note, however, that being taller to begin with, the central peak grows faster than the others with time, and the function resembles a delta function for long time evolution. This is consistent with the uncertainty relationship I1E M ~ h/2 since, as time increases, the uncertainty in energy approaches zero.
The term IHkzl2 may be expressed in terms of the electric field E of the electromagnetic perturbation. If p is the dipole moment of the electron as it undergoes the lk transition, then H' = 1-P • E 1 ex 1 E I.
-61t -t-
-41t t
-21t -t-
21t -t-
41t t
61t -t-
Fig. 1.6 Dependence of transition probability on Wk1-W as a result of harmonic perturbation.
Since energy density u( v) is proportional to 1 E 12, it is clear that IHkI12OCU(v) and hence we have shown that the Einstein B coefficients must be multiplied by u(v), as in equations (1.4 a,b).
When we wish to describe the time evolution of the rate of emission for an ensemble of N atoms undergoing stimulated emission, we may use
( . . -1 N1P1k (transitions) Wzk tranSItIons s ) = t (s)
Thus it is evident that when P1k OCt 2, then the transition rate increases linearly with time. This situation obtains for small t, since from equation (1.5) we see that
P 1· sin2 [!-(Wkl-W)tJ IHkti 2 1. 2 Ik OC 1m = 2 4t
n-+oo (Wkl-W)
Of course, for long times, W1k becomes constant as equilibrium is reached. Note that Blk = Bkl since P1k=Pkl .
1.8 BLACKBODY RADIA nON
In an ensemble of electron states, in equilibrium, W1k = Wk!. However, the spontaneous emission process may only take place in one direction, and we can write
Therefore
and
Since the populations of atoms having excited states of certain energies will obey Boltzmann statistics,
it follows that
(1.6)
Blackbody radiation 13
Consider a cavity with metallic walls uniformly heated to temperature T. If we could observe the cavity through a small hole through a cavity wall, we would detect electromagnetic radiation due to the thermally agitated elec trons in the cavity walls.
For analysis, suppose the cavity is cubic with edge length a, and principal axes x, y and z, as shown in Fig. 1.7. Since the cavity walls are electrically conductive, the electric field in the radiation field must be zero at the cavity walls, and, because of electromagnetic reflections at metallic surfaces, standing waves only will exist in equilibrium. Hence, the E field for waves travelling in the x-direction will be given by
E(x, t)=Eo Sine~x) sin(2;rrvt) where v=l
To satisfy boundary conditions, E(a, t)=O and therefore
Note that the frequencies are quantized and may be counted using integers nx • Similar expressions may be written for Ey and Ez • Consider an artificial
z
>-~~--------~~y
x
Fig. 1.7 Cavity of cubic shape with edge length a. (After Solymar and Walsh, [3].)
space having axes (nx , ny, nz ). Such a space consists of a lattice of points, each of which uniquely describes a particular three-dimensional radiation pattern or mode. It is easy to show that all points (nx , ny, nz ) at a given distance r = 2av/c from the origin represent standing waves of the same frequency v, but along different directions within the cavity [1]. We can then count the number of cavity modes between spheres of radii 2av/c and 2a(v + dv)/c as shown in Fig. 1.8. Since each point occupies a unit 'volume', the number of points in the spherical shell is shell volume 4;rrrw 2 dr=4;rr(2a/c)3v2 dv. Since we wish only to consider positive values of
nx
Fig. 1.8 Spherical shell enclosing points in (nx, ny, nz ) space lattice that represent standing waves that range in frequency from v to v+dv. (After Solymar and Walsh [3].)
n, we divide by 8 to count only one octant of the shell, and multiply by 2 because each standing wave has two possible polarizations. Hence, the number of modes over frequency range dv is
N(v)= 8na 3 v2 dv= 8nV v2 dv c 3 c 3
Because each mode has a degree of freedom, namely the choice of electric field amplitude, on average, each mode will have the same energy E which, from classical kinetic theory, is E = kT. Should one mode gain in E, it would lose it owing to collisions of electrons in the cavity walls which would transfer it to other modes. Therefore the energy per unit cavity volume over the frequency interval dv may be expressed in terms of the energy density u(v) as
8nv2
(1.7)
This expression clearly differs from equation (1.6). This is because our classical wave theory assumes that the energy of each cavity mode is continuously variable as just stated, even though the allowed cavity modes have discrete frequencies v. In our treatment leading to equation (1.6), however, we treated the energy levels giving rise to modes at frequency v as discrete, such that hv = 11E. Starting with lowest frequency mode, for example along the x-direction, nx = 1 and V1 = c/2a. If nx = 2, V2 = cia. This implies a pair of discrete energy levels, E1 =hV1 and E2=hv2 with difference I1E = hc/2a. So long as I1E ~ kT, there is no real problem with the classical treatment; however, for higher-order modes, or for lower temperatures, the energy spacing between modes may by far exceed kT and it becomes essential to
Blackbody radiation 15
take the energy of each mode as discrete. Since equation (1.7) gives the correct result for
I· () I' 8nv 2 kT lmuv=lm 3 V-a) v-co C
we can now evaluate AlB in equation (1.6) by requiring that
Therefore
hvlkT c 3
(1.8)
and the final result, valid over all v and T, is Planck's famous blackbody radiation energy density function
8nv 3
This is shown in Fig. 1.9 for three different temperatures.
12,0000 K
--..... / " / ........ 3,OoooK
'I , " ........
° ~ ~ ~ ~ 1~ 1~ 1~ 1~ 1~ ~ Wavelength Injlm
Fig. 1.9 Blackbody radiation spectrum showing spectral power density for sources at temperatures of 3000 K, 6000 K and 12000 K. Note that the 6000 K curve matches the visible range best, and is similar to the solar spectrum. The three curves are artificially normalized to appear identical in height.
For visible light sources, tungsten filament lamps which are blackbody radiators are limited in filament temperature to somewhat below the melting point of tungsten, or '" 3000 K. As is clear from Fig. 1.9, only a small fraction of the area under the curve corresponding to this temperature is in the visible range: the physical basis for the low efficiency of such lamps. A considerable attenuation of short-wavelength (blue-violet) compared with long-wavelength (red) visible is also evident. A lamp operating at 6000 K would approximately match the sun's surface temperature (5700 K) and be far more efficient. The tungsten halogen lamp allows for a modest gain in performance over a regular tungsten lamp by chemically stabilizing the tungsten filament, allowing for higher filament temperature.
1.9 DIPOLE-DIPOLE ENERGY TRANSFER
We can now explain how energy may be transferred from one atom to another without the actual release of a photon.
Consider an excited atom, S, and a nearby unexcited, but otherwise identical atom, A (see Fig. 1.10). As S radiates, it generates an oscillating
RSA ------I Fig. 1.10 Excited atom S a distance RSA from atom A.
electric field E due to its oscillating dipole. This field falls off as l/r3 [4] and, provided that its energy does not have time to escape as a photon, it will directly stimulate a transition in A by means of the same process described by equation (1.4). Since E falls off as l/r 3, then the energy density in the electric field
U(V)=160 E 2
falls off as l/r6. From equation (1.4), therefore, the rate (or the probability) of energy transfer from S to A depends on R;1. Energy transfer is discussed further in Chapter 2.
1.10 ENERGY LEVELS IN ATOMS
It is always possible to formulate Schrodinger's equation to give the energy levels of electron states for an atom. Consider an optically active
Crystal field splitting 17
atom in a crystal surrounded by a space lattice of atoms. The total Hamiltonian is:
H tot = H isolated + H electrostatic lattice + H dynamic lattice
Hisolated involves a Coulomb potential due to the atom nucleus and appro priate screening effects of inner shell electrons (Ho). The optically active electrons are now affected by spin-orbit coupling (Hso), and LS coupling or exchange energy (H c):
Hisolated = H 0 + Hso + H c
Ho is spherically symmetric and yields the one-electron atom states having quantum numbers n, I, m, s. Spectroscopists use notation to describe the shell according to n levels s, p, d, f, g that correspond to 1=0, 1, 2, 3, 4 respectively, which represent subshells. For example, a subs hell containing five electrons with n = 3 and 1=2 would be written 3d 5. Such a subshell exists in manganese.
Spin-orbit coupling requires the introduction of a new quantum number j, and is caused by the magnetic moments due to electron orbit and electron spin. In fact, j = I ± 1/2, which gives rise to a splitting of each energy level into two levels unless 1=0 (no orbital magnetic moment).
In LS coupling, the effects of more than one electron within unfilled subshells are considered. A Coulombic electron--electron interaction energy term exists. The spin angular momenta of individual electrons add together, as do orbital angular momenta, giving rise to a total spin s' and a total orbital angular momentum I'. For example, consider an atom with configur ation 3d14pl. There are, because of both Hso and H c , 12 levels in this case [1] which are labelled 3D3, 1 F 3,1 P b etc. The superscript is 2s' + 1; the letter designates I' (the same scheme as for I, but now using capital letters to acknowledge addition of orbital angular momenta) and the subscript is j' which is formed by adding s' and I' as vectors. Energy splittings occur since the average separation and therefore Coulombic energy between electrons depends upon the way in which angular momenta are added.
Additional complication arises if Hso and Hc are similar in strength. The level splittings become more complex, and the LS coupling exclusion principle forbids the existence of certain states.
1.11 CRYSTAL FIELD SPLITTING
When an atom S is placed in a crystal, it experiences the crystal field, or the electric field due to surrounding atoms. We will assume that the electrons involved in the energy levels of interest for luminescence are not involved in bonding. This is generally true in practice. Because of crystal symmetry, atoms surrounding S will give rise to an electric field with some symmetry. For example, a tetrahedral crystal site will have tetrahedral symmetry; an
octahedral site will have octahedral symmetry. The electric potential of an electron in atom S due to the crystalline environment may always be expressed in the form
y'(8, ¢)= L aim yr(8, ¢) I.m
where yr are the spherical harmonics. This is analogous to a Fourier series expansion, but is specifically applicable to an atom or sphere surrounded by a field that has angular dependence. The crystal field may now be taken into account, using time-independent perturbation theory if Vs is small. If we know the eigenstates of H o and add perturbation H', then, to first order,
and
En=E~O) + <¢~O)IH'I¢~O»
Note that the new eigenstates ¢n and eigenenergies En are based on the eigenstates ¢~O) and eigenenergies E~O) of the unperturbed system. To account for the crystal field, we simply substitute H'(8, ¢) = Vs(8, ¢) and determine the new states due to the crystal field.
If the symmetry of the crystal field is different from eigenstates involved, which is usually the case, then degenerate states will probably split because of the crystal field. This is known as crystal field splitting. In this case, E ~O) - E lO) = 0 for some n, i, n 01= i. In order to determine the ¢n and En, we must first make the matrix element < ¢lO) I H' I ¢~O» zero whenever ElO) = E~O) such that these singular terms vanish. This may be accomplished by diagonalizing the submatrix of H;n which contains the degenerate states. The energy splittings are then obtained directly.
For transition metal ions placed in a crystal field, the three-dimensional states may be more influenced by the crystal field than by He. This is known as the strong field scheme [5]. For such an ion in an octahedral crystal field, for example, the five-fold degenerate three-dimensional orbitals split into a two-fold degenerate eg state and a three-fold degenerate t2g state. The energy separation between the two states is called lODq where Dq is a parameter that is determined by the crystal field strength. Now, He may be accounted for in a manner analogous to free-ion LS coupling.
In Cr3+, for example, there is a 3d3 configuration. If placed in an octa hedral crystal field, the splitting depends on the term Dq/B which is a measure of the crystal field influence. A theoretical treatment [6] gives the splittings. Results for Cr3 + are shown in Fig. 2.16.
Transitions that were forbidden in the free ion may become dipole transitions with a crystal field. The lower symmetry allows a dipole moment
References 19
to exist, and these new transitions can take place, although with small rates. Radiative lifetimes of 10- 3 s are not unusual for transition metal ions such as Mn2+ in a tetrahedral crystal field.
REFERENCES
1. Eisberg, R and Resnick, R (1985) Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles, 2nd edn, Wiley, New York.
2. Liboff, RL. (1980) Introductory Quantum Mechanics, Holden-Day. 3. Solymar, L. and Walsh, D. (1985) Lectures on the Electrical Properties of
Materials, 3rd edn, Oxford University Press. 4. Kip, A.F. (1969) Fundamentals of Electricity and Magnetism, 2nd edn, McGraw
Hill, New York. 5. Yen, W.M. and Selzer, P.M. (1986) Laser Spectroscopy of Solids, Vol. 49, 2nd edn,
Springer, Berlin. 6. Tanabe, Y. and Sugano, S. (1954) J. Phys. Soc. Japan, 9, 766.
2
G. Blasse
2.1 INTRODUCTION
The existence of optically active centres in solids, liquids and molecules is now well known. Their properties have been studied intensively, not only for fundamental reasons, but also in view of their potential applications. Energy-saving fluorescent lamps, X-ray photography, and television display tubes are well-known examples [1].
This can be hardly better illustrated than by the case of ruby (AI2 0 3 :Cr3+). The optical properties of ruby have been studied for over a century starting with the work of Becquerel in 1867 [2] who excited ruby with sunlight. He claimed that the properties of ruby were intrinsic, but it soon became clear that they are due to the Cr3 + ion that is an optically active centre in the nonabsorbing Al2 0 3 host. Later crystal field theory was able to explain the spectroscopy of Cr3 + in Al2 0 3 in detail. The application followed rather soon: the first solid state laser was based on a ruby crystal. In the development of tunable infrared lasers the Cr3 + ion plays an important role [3,4].
The purpose of this chapter is to present the theories which are at present in use to describe the luminescent properties of optically active centres in solids. This will be done in such a way that even the unexperienced reader can apply the theoretical results to practical cases. In order to do so, section 2.2 treats the interaction between an optical centre and its immediate surroundings by presenting the configurational coordinate diagram. Radi ative as well as nonradiative transitions will be dealt with. In Section 2.3 we will consider the mutual interactions between optical centres, and especially those leading to energy transfer and energy migration. In section 2.4 we will illustrate how theory applies to specific cases by discussing some carefully selected case studies relating to important optically active centres.
For those who are not familiar with these types of phenomena, this introduction gives now a schematic, first picture of the physical properties of optically active centres. Figure 2.1 shows an optical centre (an ion or a
21
x M
q H
Fig. 2.1 Luminescence processes in a centre A in a solid: X, excitation; M, emission; H, heat (nonradiative return to the ground state).
complex ion) in a solid or a liquid. The centre is irradiated. For simplicity we assume that the surroundings do not absorb the irradiating light. The centre shows optical absorption, so that it makes a transition from the ground state to the excited state. If the irradiation is with visible light, the sample is coloured. The excited state will ultimately return to the ground state. This may occur by a nonradiative or a radiative process.
In the former case the energy of the excited state is used to excite the vibrations of the surroundings (generation of heat). The latter case is known as luminescence (see Fig. 2.1). In this field of research the irradiation is called excitation. Usually the emission is situated at longer wavelengths than the excitation. The energy difference between these two is called the Stokes shift.
The quantum efficiency (q) of the luminescence is the ratio of the number of photons emitted and the number of photons absorbed. If there are no competing nonradiative transitions, q = 1; if the non-radiative transitions are dominating, q~O, and there is practically no emission.
A more complicated situation occurs if two (equal or unequal) centres are close together (Fig. 2.2). The excited centre may transfer its excitation energy to the neighbouring centre that is still in the ground state:
centre S * + centre A --+centre S + centre A * (2.1)
where the excited state is marked by an asterisk. This process may be followed by emission from A or by a nonradiative decay on A. In the former case we speak of sensitized emission (A is sensitized by S); in the latter case A is called a quenching centre.
Before starting the presentation of the physical models in use to explain the properties of optically active centres, it seems appropriate to mention a few excellent literature reviews on our topic of discussion. A recent, clear and rather elaborate discussion of the configurational coordinate diagram is given in the book by Henderson and Imbusch [5]. This book deals also with energy transfer. However, the report on the relevant Erice meeting [6]
The configurational coordinate diagram 23
x M
Fig. 2.2 Energy transfer between two centres in a solid. The excitation X excites centre S which transfers its excitation energy to A (T). Finally A shows emission (M).
can also be used. A more chemical approach to these topics was presented by ourselves [7,8].
2.2 THE CONFIGURATIONAL COORDINATE DIAGRAM
Let us consider a dopant ion in a host lattice and assume that it shows luminescence on illumination. What we will have to discuss is the interac tion 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.
In this model we consider only one vibrational mode, i.e. 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 configurational coordinate (Q) describes the vibration. In our approximation it represents the distance between the dopant ion and the surrounding ions. In ruby this Q would be the Cr3 + _02 - distance.
If we plot energy versus Q we obtain for the electronic states parabolae (harmonic approximation). This is presented in Fig. 2.3 for the electronic ground state u and one electronic excited state v. Further, Qo represents the equilibrium distance in the ground state, and Qb that in the excited state. Note that in general these will be different. The u parabola is given by
(2.2)
where k is the force constant. Within the parabolae the (equidistant) vibra tional energy levels have been drawn. They are numbered by n=O, 1,2, ... for the ground state parabola u, and m = 0, 1,2, .. , for the excited state
24 Luminescent centres in insulators
E
v
Q
Q' o
Fig. 2.3 A configurational coordinate diagram. The potential energy E is plotted versus the configurational coordinate Q for the ground state u and an excited state v. The equilibrium positions are Qo and Q~ respectively. Absorption (lines pointing upwards) is at higher energy than emission (lines pointing downwards). The absorption and emission band maxima correspond to the full lines. The thin horizontal lines indicate the vibrational levels in the states u and v.
parabola v. 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 more weakly bound than the ground state, this is a representative situation.
Optical absorption corresponds to a transition from the u to the v 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 wavefunction of the lowest vibrational state (i.e. n=O or m=O) is Gaussian; that is, the most likely value of Q is Qo (or Qo in the excited state). For the higher vibrational states, however, the most likely value is at the edges of the parabola (i.e. at the turning points, as in the classical pendulum).
The most probable transition in absorption at low temperatures is from the n = 0 level in u, starting at the value Q o. Optical absorption corresponds to a vertical transition, because the transition u--+v 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 v, since it is there that the vibrational states have their highest amplitude. This transition, drawn as a solid line in Fig. 2.3, 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. 2.3 by broken lines. It can be shown that the probability of the optical transition between the n=O vibrational level of the ground state and the mth vibrational level of the excited state is proportional to
(2.3)
where r represents the electric dipole operator and Vm and Uo the vibrational wavefunctions. The first term, the electronic matrix element, is independent of the vibrational levels; the second term gives the vibrational overlap. The transition from n = 0 to m = 0 does not involve the vibrations. It is called the zero-vibrational transition (or no-phonon transition). Equation (2.3) 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 electronic matrix element).
What happens after the absorption transition? First we return to the lowest vibrational level of the excited state; that is, the excited state v 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. 2.3 in the same way as for the absorption transition. Finally the system relaxes within the u 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 = 1, and possibly from even higher levels. This leads to a further broaden ing of the absorption and emission bands, but does not change our arguments essentially.
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 that occur after the optical transitions. It is obvious that the larger Qo - 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:
tk(Qo - QO)2 = Shw (2.4)
where hw is the energy difference between the vibrational levels. The Stokes shift is then given by
!lE. = k(Qo - Q)2 - hw = 2Shw (2.5)
340 310nm
The parameter S measures the interaction between the dopant ion and the vibrating lattice. Equation (2.5) shows that, if S is large, the Stokes shift is also large. Equation (2.4) shows that S is immediately related to the offset of the parabolae in the configurational coordinate diagram (Fig. 2.3). This offset, LlQ = Qo - Qo, 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 (n=O~m=O) is exp( -S) [5]. We can now divide our lumines cent centres into three classes:
1. those with weak coupling (i.e. S < 1), so that the zero-vibrational transi tion dominates the spectrum;
2. those with intermediate coupling (i.e. 1 < S < 5), so that the zero-vibra tional transition is observable, but not the strongest line in the absorp tion or emission band;
3. 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 Stokes shifts.)
Figure 2.4 shows three emission spectra that are representative of the three cases. Characteristic examples of case 1 are the trivalent rare earth ions. The value of S is so small for these ions that the spectra consist in good approximation of the zero-vibrational transitions only. Figure 2.4(a) gives as an example the emission spectrum of the Gd3+ ion in LaB3 0 6 • It consists of one strong electronic line at about 310 nm, whereas the weak repetition at 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 LaB 3 0 6 .
A characteristic example of case 2 is the uranyl ion (UO~ +). The m = 0--+ n = 2 line dominates in the spectrum (Fig. 2.4(b)). The tungstate ion (WOi -) is a good example of case 3. The very broad emission spectrum (see Fig. 2.4(c)) does not show any vibrational structure at all, the Stokes shift is very large (,...., 16 000 cm -1) and the zero-vibrational transition is not observable, not even at the lowest possible temperatures, or for the highest possible resolving powers.
Fig. 2.4 (a) An example of an emission spectrum in the weak-coupling case. The spectrum consists of a line which corresponds to the zero-phonon transition. The weak line at about 325 nm is a vibronic transition. This spectrum is the Gd 3 +
emission spectrum of LaB30 6 :Gd3 +. (b) An example of an emission spectrum in the medium-coupling case. There is a progression of vibronic lines. The line on the left-hand side is the zero-phonon line. This spectrum is the uranyl (UO~ +) emission spectrum. (c) An example of an emission spectrum (M) in the strong-coupling case. The spectrum consists of a broad, structureless band which shows a large Stokes shift (SS) relative to the absorption (excitation) band (X). The spectra relate to the tungstate luminescence of Ca W04 .
Finally we draw attention to the fact that the single configurational 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.
If we measure an absorption or emission spectrum, the following proper ties of the bands or lines are of importance:
1. their spectral position, that is, the energy at which the transition occurs;
2. their shape, that is, sharp line, structured narrow band, or structureless broad band;
3. 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 discussed above (see Figs 2.3 and 2.4). The intensity is contained in the electronic matrix element
<v(Q)lrlu(Q) (2.6)
in equation (2.3). The intensity can be very low if selection rules apply. Here we mention a few, well-known examples.
For electric dipole transitions the parities 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 opposite-parity states due to the crystal field, or by vibrations of suitable symmetry.
Optical transitions are forbidden between states of different spin multi plicity (spin selection rule). This selection rule may be relaxed by 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 specialized nature are known.
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 that the crystal field at the dopant ion varies slightly from ion to ion owing to the presence of defects, such as impurities, vacancies, dislocations, or the surface [9]. As a matter of fact the in homogeneous broadening will be more pronounced for line spectra than for broadband spectra. Its magnitude is also much larger in disordered solids (glasses) than in ordered solids [10].
An exceptional application of the configurational coordinate diagram has been given by Giidel [11] in order to explain the nature of light-induced metastable states in nitroprussides. Irradiation with visible radiation can
convert up to about 50% of sodium nitroprusside (Na2[Fe(CN)sNO]' 2H20) into a metastable excited state with a very long lifetime at low temperatures (> 107 s at 0 K). This is of interest for optical information storage. An explanation of this phenomenon has been proposed in terms of a configurational coordinate diagram where the excited (metastable) state lies far outside the ground state parabola (Fig. 2.5). Return from the lowest vibrational level of the excited parabola to the ground state is now very difficult, since the vibrational overlap (unlvo> is very small. This return can be achieved by thermal activation (> 165 K) or by irradiation with red light. The explanation requires a large offset between the two parabolae. However, since the proposed electronic transition is a two-electron transition, this may well be possible.
E
v
Q
Fig. 2.5 A configurational coordinate diagram in which the excited state v has its equilibrium position outside the u ground state parabola. Return from the v minimum to the ground state u is difficult and therefore slow. See also text.
After this extreme example we now tum to a very difficult problem in luminescence, i.e. the nonradiative transitions [12, 13].
Up to this point it was assumed that the return from the excited state to the ground state is radiative. In other words, the quantum efficiency (q), which gives the ratio of the numbers of emitted and absorbed quanta, was assumed to be 100%. This is usually not the case. Actually there are many centres which do not luminesce at all. We will try to describe here the present situation of our knowledge of nonradiative transitions that is satisfactory only for the weak-coupling case.
Let us consider the configurational coordinate diagrams of Fig. 2.6 in order to understand in a qualitative and rough way the relevant physical processes. Figure 2.6(a) presents essentially the same information as Fig. 2.3. Absorption and emission transitions are quite possible and are Stokes shifted relative to each other. The relaxed-excited state may, however, reach the crossing of the two parabolae if the temperature is high enough. Via the
E E
Fig. 2.6 Nonradiative transitions in the configurational coordinate diagram: (a) strong coupling; (b) weak coupling; (c) combination of both.
crossing, it is possible to return to the ground state in a nonradiative manner. The excitation energy is then completely given up as heat to the lattice. This model accounts for the thermal quenching of luminescence.
In Fig. 2.6(b) the parabolae are parallel (S=O) and will never cross. It is impossible to reach the ground state in the way described for Fig. 2.6(a). However, nonradiative return to the ground state is possible if certain conditions are fulfilled; that is, the energy difference ~E should be equal to or less than 4-5 times the highest vibrational frequency of the surroundings. In that case this amount of energy can excite simultaneously a few high energy vibrations and is then lost for the radiative process. Usually this nonradiative process is called multi phonon emission.
In Fig. 2.6(c) both processes are possible in a three-parabola diagram. The parallel parabolae will belong to the same configuration, so that they are connected by forbidden optical transitions only. The third one originates from a different configuration and is probably connected to the ground state by an allowed transition. This situation occurs often. Excitation (absorption) occurs now from the ground state to the highest parabola in the allowed transition. From here the system relaxes to the relaxed-excited state of the second parabola. Figure 2.6(c) shows that the nonradiative transition between the two upper parabolae is easy. Emission occurs now from the second parabola (line emission). This situation is found for AI20 3 :Cr3+ (4Ar-+4T2 excitation, 4Tr-+2E relaxation, 2E--+4A2 emission), Eu3+ CF --+charge transfer state excitation, charge transfer state to 5D relaxation, 5D--+ 7F emission), and Tb3+ CF --+4f?Sd excitation, 4f?Sd--+ 5D relaxation, 5D--+ 7F emission).
In general the temperature dependence of the nonradiative processes is reasonably well understood. However, the magnitude of the non radiative rate is not, and cannot be calculated with any accuracy except in the weak-coupling case. The reason for this is that the temperature dependence stems from the phonon statistics which are known. How ever, the physical processes are not accurately known. In particular, the deviation from parabolic behaviour in the configurational coordinate dia gram (anharmonicity) may influence the nonradiative rate by many orders of magnitude.
Certain aspects of our qualitative considerations can be put on a more quantitative basis as shown by Struck and Fonger [14, 15]. These authors have given a unified model of the temperature quenching of narrow-line and broadband emission using a quantum mechanical single configurational coordinate model (see also Fig. 2.7). Calculations were made possible by evaluating the vibrational overlap integrals exactly using the Manneback recursion formulae. In addition to the parameters used above we introduce auv , the parabolae offset, defined by a;v = 2(Su + Sv)' The relaxation energies after emission and absorption are Suhwu and Svhwv respectively. Further, we assume thermal equilibrium for the initial vibrational levels. Then the radiative rate between Vm and Un is given by
Rnm=Ruv(1-rv)r::,<unlvm)2
(2.7)
(2.8)
Here Ruv and N uv are the electronic parts of the transition integral and rv=exp( -hwv/kT) is the Boltzmann factor. The expression (l-rv)r::' gives the thermal weight.
The electronic factors are considered to be constants. However, this has been criticized, for example by Englman and Barnett [16]. Coupling
12
6
Q oL---~~~~------~---
Fig. 2.7 Configurational coordinate diagram showing nonradiative transitions in the Struck and Fonger approach. The excited state v shows an offset relative to the excited state u and the ground state g. Full horizontal lines indicate the lowest vibrational state in the parabolae, broken horizontal lines those which are at the same energy in a lower parabola. The latter have their wavefunction maxima on the parabolic curves. Therefore a nonradiative transition from u to g has a low probability and that from v to u has a high probability, whereas that from v to g has an intermediate probability.
between the electronic states U and v cannot be neglected. For Cr3 + this has been shown theoretically as well as experimentally [16, 17].
However, let us take the approximation that the electronic parts of equations (2.7) and (2.8) can be considered to be constants. The total radiative rate is obtained by summing over all initial and final states Un and Vm' For nonradiative transitions the rate is obtained by summing over all nearly resonant Vm, Un states.
Figure 2.8 shows the results of a model calculation for a red-emitting phosphor [18]. Ruv and N uv are taken to be 104 s- 1 and 1014 s- 1 respect ively. Further, hw=500cm- 1 in the U and v states, and auv =7.746 (large offset). The distance between the parabolae minima is 25000 cm -1. Such a phosphor has a thermal quenching temperature T1/2 of 450 K (at T1/2
the emission intensity at 0 K has dropped to 50%). The results show how a variation of one of the parameters influences the thermal quenching, i.e. the nonradiative rate. Shifting the excited parabola to lower energy
q
1
Fig. 2.8 Calculations with the Struck-Fonger approach on a model phosphor. The quantum efficiency q is calculated as function of temperature. In each of the three pictures only one parameter is varied: in the picture on top the energy of the zero phonon transition (Ezp), in the centre the vibrational frequency (hw.) and in the lower one the parabolae offset a.v• The latter two parameters in particular show a drastic influence on the temperature dependence of q. (After Bleijenberg and Blasse [18].)
decreases Tl/2 • Increasing hw increases the nonradiative rate drastically; even at 0 K there is a considerable influence of the nonradiative processes. A larger offset implies also a faster nonradiative rate.
These considerations can be used to predict the occurrence of lumines cence with high thermal quenching temperature. A full account has been given elsewhere [7,8,12]. As examples we mention here the use of very stiff host lattices [7,8], the application of surroundings around the luminescent centre which can hardly expand, and the use of well-fitting organic cages around a luminescent ion [8,19].
Nonradiative transitions between parallel parabolae (Fig. 2.6(b», of special importance for rare earth ions, are theoretically more easy to handle. The ex perimental and theoretical situation at the moment is quite satisfactory [12,20].
For transitions between 4f n levels, the temperature dependence of the nonradiative rate is given by
N(T)=N(O)(l +nY (2.9)
where N(T) is the rate at temperature T, p=I1E/hw, I1E is the energy difference between the levels involved, and
n= [exp(hw/kT)-lr 1 (2.10)
N(T) is large for low p, that is for smalll1E or high vibrational frequencies. Further,
N=/3 exp[ -(I1E-2hwmax )a] (2.11)
with a and /3 constants and Wmax the highest available vibrational frequency of the surroundings of the rare earth ion. This is the energy gap law in the revised form of van Dijk and Schuurmans [20] that makes it possible to calculate N with an accuracy of one order of magnitude.
In solids recently a new mechanism for loss of excitation energy gained interest, although in principle this was already known for molecular species in solution. Let us start with the latter where this mechanism is known as quenching by electron transfer [21]. Figure 2.9 shows schematically the essentials of this process. Parabolae a, band c represent energy levels of a species A, parabola d that of a state A + B -. This state is obtained by electron transfer from species A to a nearby species B. The offset of parabola d relative to the other parabolae is large, and its position is at not too high an energy. It is clear that from parabola c we can reach the ground state
E
Q
Fig. 2.9 Schematic representation of luminescence quenching by electron transfer. The state d is a strongly shifted electron transfer state via which nonradiative return to the ground state is possible.
parabola a via parabola d in a nonradiative way. This process is expected to be of importance if the energy difference between the electron transfer state A +B - is not too high above the ground state A + B. The requirement of a large offset is usually satisfied for electron transfer states.
This quenching mechanism has been observed for ion pairs in solution [22]. As an example we mention here [Eu3+ c 2.2.1], where c stands for encapsulation, and M(CN)~ - (M2 + = Fe2+, Os2+ or Ru2 +) [23]. The electron transfer state involved can be written schematically as Eu2 + _M3 +.
Molecular complexes where this process is of importance are the lanthanide decatungstates [RE3+ • W 10036]9 - [8]. For RE = Eu efficient emission is observed, while for RE = Tb only quenching occurs because of a low-lying Tb4 + -W5+ electron transfer state.
In nonmolecular solids the examples are abundant, but often not recog nized. We mention the absence of luminescence in YV04 :Tb due to a Tb4 + _V4 + electron transfer state and the quenching of Ce3+ and Eu3+ luminescence in Ce3+ -Eu3+ pairs owing to an electron transfer state Ce4 + -Eu2+ [7, 8].
These examples all relate to ion pairs. However, it has recently been shown that photoionization can also quench luminescence [24, 25]. This process is very similar to quenching by electron transfer in an ion pair [26]. As a well-studied example we take Y3AI5 0 12:Ce3+ [24,27]. Figure 2.10 shows the energy levels of the Ce3+ ion relative to the valence and conduction band of the host lattice. The ground state of Ce3 + is 4f 1, and the excited state consists of the crystal-field levels of the 5d 1 configur ation. As long as we excite in the lowest crystal-field level, band emission from Ce3 +, Stokes-shifted but with high quantum efficiency, is observed. However, on excitation into higher levels the quantum efficiency of the Ce3+ emission drops considerably, and simultaneously photoconductivity is
----5d CB
----5d
----4f
VB Fig. 2.10 Schematic representation of the Ce3+ energy levels in Y 3Als012' VB and CB indicate the top of the valence band and the bottom of the conduction band of Y 3Als012 respectively. 4f gives the ground state of the Ce3 + ion. The lowest excited 5d s-tate of Ce3+ is situated in the forbidden zone, but the lowest-but-one state is in the conduction band making photoionization of Ce3 + possible when the ion is promoted into that state.
observed. Because these higher levels are situated in the conduction band, photoionization of the Ce3 + ion can take place. In analogy to the electron transfer in ion pairs described above, the electron-transfer state involved can be indicated as Ce4 + --(HL)-, where HL denotes the host lattice.
Pedrini et al. have shown that this is an important mechanism for other ions too, for example Eu2 +, Sm2 + and Yb2 + [24,25]. Not always does this mechanism prevent the occurrence of emission. In several cases they observe what is called impurity-bound exciton emission. A nice example is Yb2 + in the fluorides CaF 2, SrF 2 and BaF 2. The former two yield impurity-bound exciton emission, but in BaF 2 there is no emission at all [25]. The emission is ascribed to exciton recombination: the hole resides on the (photoionized) Yb2 + ion, the electron on the surroundings. In Fig. 2.9 this emission transition would be described by a transition from parabola d to the ground state.
The processes described in the final part of this section may be of importance for every optically active centre which can easily change its valency, as will be clear from the examples presented.
Let us now turn to phenomena which are due to interaction between centres.
2.3 ENERGY TRANSFER
If luminescent centres come closer together, they may show interaction with each other that results in new phenomena. Consider two centres, S and A, with a certain interaction. The relaxed excited state of S may transfer its energy to A. This energy transfer has been treated by Forster and Dexter and is now well understood [5-7].
Dexter, following the classic work by Forster, considered energy transfer between a donor (or a sensitizer) S and an acceptor (or activator) A in a solid. This process occurs 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 there is wavefunction 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.
Figure 2.11 shows the energy level scheme and parameters involved. The emission transition S*--+S and the absorption transition A--+A* have normalized line shape functions gs(E) and gA(E). The initial state is IS*, A), and the final state (after energy transfer) 1 S, A *). The transfer is brought about by an interaction HSA ' The resulting transfer probability is
(2.12)
------+ E
Fig. 2.11 Energy transfer from S to A. R is the SA separation, H is the SA interaction. The hatched area in the lower picture presents the spectral overlap. See also text.
Here the integral represents the spectral overlap. The distance dependence of PSA depends on the interaction mechanism.
If the interaction is of the exchange type, PSA decreases exponentially with the S-A distance (RSA)' because the wavefunctions do so too. If the interaction is of the multipolar type, PSA decreases as Rs; where n depends on the type of interaction. For electric dipole-dipole interaction, for example, n = 6 (see Chapter 1).
It should be realized that a high value of PSA does not imply automati cally that transfer will occur. The excited state of S, i.e. S*, has other ways to decay, i.e. radiatively (Pr ) and/or nonradiatively (Por)' Transfer occurs if PSA>Pr+Por' The distance for which the transfer rate equals the internal decay rate is called the critical distance Re. For exchange-mediated transfer Re is not much larger than 7-8 A, determined by wavefunction overlap. For transfer by multipolar interactions Re can be much larger, i.e. 50--100 A if favourable spectral overlap of allowed S*-+S and A-+A* transitions occurs.
An example of energy transfer can be found in the classic lamp phosphor Ca5(p04h(F, CI):Sb3+, Mn2+ [28]. Short wavelength ultraviolet excitation excites only the Sb3 + ion which yields blue emission. Some of these ions, however, transfer their excitation energy to Mn2 + which yields yellow emission. In this way white emission occurs. The emission colour can be varied by varying the Sb3+:Mn2 + ratio. The Sb3+ -Mn2+ transfer occurs by exchange; its critical radius is 12 A.
Not always is all of the excitation energy transferred. If only part of it is transferred, this is called cross-relaxation. Let us consider an example. The higher energy level emissions of Tb3+ and Eu3+ (Fig. 2.12) can be quenched if the concentration is high. The following cross-relaxations may occur:
Tb3+eD3)+ Tb3+CF6 )--+Tb3 +eD4 )+ Tb3+CFo)
Eu3+eD 1)+ Eu3+CF o)--+Eu3 +eDoH Eu3+CF 3)
(2.13)
(2.14)
The higher energy level emission is quenched in favour of the lower energy level emission.
If we consider now transfer between two identical ions, for example between 8 and 8, the same considerations can be used. If transfer between two 8 ions occurs with a high rate, what will happen in a lattice of 8 ions, for example in a compound of 8? 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
20
10
o
o
Fig. 2.12 Cross-relaxation for two Eu3 + ions (left-hand side) and for two Tb3 +
ions (right-hand side). The arrow indicates the amount of energy which is trans ferred from one ion to the other. As a consequence the higher-level emission is quenched.
Energy transfer 39
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 transfer is often studied by measuring the time dependence of the S emission intensity after a short excitation pulse. We will discuss now a couple of expressions often used in the literature. Simultaneously they illustrate the several regimes of energy migration which have been observed. Here energy migration is defined as a large number of subsequent energy transfer steps between identical centres.
Consider first a crystal with donors and acceptors and assume that only one-step energy transfer from S to A is possible. The S and A ions will be distributed at random. An excited donor can interact with all unexcited acceptors and it is necessary to account for the distribution in SA separa tions. This problem has been treated by Inokuti and Hirayama [29]. They obtained the following expression for the decay of S in the presence of A:
(2.15)
Here 1:0 is the decay constant of S in the absence of A, CA is the concentration of A, Co is the critical activator concentration and n = 6, 8 or 10 depending on the electric multipole interaction. For exchange interaction their result reads
(2.16)
where y = 2RjL with Rc the critical distance and L an effective Bohr radius. Note that I(t) is not an exponential in the presence of A. In this treatment only SA transfer is considered and SS transfer is assumed not to occur. In the absence of A, the S species decays exponentially according to
I(t)=I(O) exp ( - :J (2.17)
Until now we have considered only the microscopic, single-step donor acceptor energy transfer. It is possible, however, that donor-donor transfer also plays a role. Excitation energy may migrate among the donor species before being transferred to an acceptor. A good survey of earlier and recent work on this problem has been given by Huber [30]. From this survey we derive the following for our purpose.
Consider the time evolution of Pit), the probability that species n is excited and all other atoms are in their ground state:
dPn(t)/dt= -(YR+Xn+ n~n Wnn)Pn(t) + n~n Wn'nPn,(t) (2.18)
The first term on the right-hand side corresponds to processes which bring the species n back to the ground state: YR is the radiative probability, Xn is the transfer rate to acceptors and Ln' Wnn, gives the transfer rate from species n to other donor species n'. The second term describes the reverse process. For simplicity back-transfer from the acceptors is neglected.
The energy difference between ground and excited state, En" will vary from donor to donor owing to perturbations from impurities, strains, etc. This yields the inhomogeneous line broadening observed under broad band excitation. There are two techniques to follow the excitation energy migration in the donor system, i.e. fluorescence line narrowing (FLN) and the time evolution of the donor luminescence in the presence of acceptors.
In FLN a pulsed, narrow band light source (a laser) excites those donors whose resonance frequencies span a small part of the inhomogeneous line. After the pulse, the luminescence evolves as shown schematically in Fig. 2.13. Broadband luminescence arises due to energy transfer to donors which were not excited directly. The decay of the narrow component yields information on the microscopic transfer process.
A well-known example is the case of Lao.sPro.2F 3 [31]. In Fig. 2.14 we give the time evolution of the emission of the 3Po--+ep6)1 transition on the Pr3 + ion. Excitation is at 12 cm -1 higher energy than the line centre. Note
Fig. 2.13 Schematic representation of the time development of the luminescence in FLN: (a) t=O; (b) t>O. The broad area in (b) corresponds to ions which were not initially excited. Excitation occurred only for the ions emitting in the narrow line.
Energy transfer 41
that the line decreases in time, whereas the background luminescence increases. This shows that energy transfer occurs within the Pr3 + subsystem and that the temperature is high enough (14 K) to make the transfer process independent of the energy mismatch. From these experiments we can find the ratio R(t):
R(t)= narrow b~nd in~ensity.at time t total mtensIty at hme t
Theoretical expressions for R(t) have been derived in the literature. In this way it becomes possible to derive transfer characteristics from a comparison between experiment and theory. For the case of Fig. 2.14, for example, it has been found that electric dipole-dipole transfer is dominant in the system Lao.sPro.2F 3 and that the nearest-neighbour transfer rate is 0.4 x 106 S-l
(14 K).
6v(cm-')
Fig. 2.14 Time-resolved emission spectra for the 3PO-.eH6h luminescence in Lao.SPrO.2F 3. Excitation is 12 cm -1 above the line centre. T= 14 K. (a) Immediately after the excitation pulse, (b) 0.811S after the pulse, and (c) 311S after the pulse. (Constructed after data by Huber et al. [31].)
The time evolution of the donor fluorescence on broadband excitation is an old problem in luminescence. By measuring the time dependence of the donor fluorescence it is possible to obtain information about the donor-donor and donor-acceptor transfers by analysing the decay curve.
Since the integrated intensity at a time t is proportional to the number of excited donors at that time, No(t), the decay can be described by
(2.19)
Here N 0(0) is the number of excited donors at the time the pulse is turned off and f(t) is the fraction of excited donors if the radiative lifetime (YR" 1) were infinite. The function f(t) depends on time as described above for Pn(t), if YR =0.
Exact solution is possible for two extreme cases, i.e. no donor-donor transfer at all (see above) and very rapid donor-donor transfer. The behaviour of f(t) between these two cases is extremely complicated.
In the limit of no donor-donor transfer at all we obtain
(2.20)
This is a generalization of the results obtained by Inokuti and Hirayama [29]. C A gives the acceptor concentration and X 01 the transfer rate from a donor at site 0 to an acceptor at site l. The value of 1-C A gives the probability to find no acceptor on site l. If site 1 is occupied by an ac ceptor, it contributes a factor exp( -XOlt) to exp( -Xnt). Here Xn is the total donor-acceptor transfer rate for the nth donor. Our equation represents therefore an average of exp( - X nt) over all configurations of acceptors.
In the case of rapid transfer (or fast diffusion) the donor-donor transfer takes place so rapidly that for t>O all donors have equal probability to be excited. f(t) has now a very simple form, i.e.
f(t)=ex p( -CA~ XOlt) (2.21)
In Fig. 2.15 we present some schematic plots of f(t) versus t. In general f(t) is initially nonexponential, but becomes exponential after a certain time. In the rapid transfer case (curve b in Fig. 2.15) No(t) is exponential in the whole time region. In the absence of donor-donor transfer N o(t) becomes exponential after long times only, with a slope equal to the radiative decay time. Also in the intermediate case N o(t) is initially nonexponential, but becomes exponential in the limit t-HX!. The slope, however, is steeper than in the absence of donor-donor transfer (curve c in Fig. 2.15). In order to describe this case several theories have been presented in the literature, for example a hopping model [32] and a diffusion model [33]. The latter solution in particular has become popular if the diffusion is not fast enough
Energy transfer 43
o 4 8 t
Fig. 2.15 Schematic plot of f(t) versus t: curve a, donor-donor transfer absent (equations (2.15) and (2.16»; curve b, rapid transfer (equation (2.21»; curve c, intermediate between curves a and b (e.g. equation (2.22».
to maintain the initial distribution of excitation (diffusion-limited transfer). The following expression was found:
ND(t) = ND(O) exp( -yRt)
[ ~ 3/2 (C )1/2 (1 + 10.87x+ 15.50X2)3/4] exp -3n CA t 1 +8.743x (2.22)
Here C is the interaction parameter for donor-acceptor transfer, and x = DC - 1/3 t 2/3 where D is the diffusion constant. For t -+ 00 an exponential time dependence is predicted with decay rate L01 = 11.404CAC1/4D3/4. Here the diffusion is assumed to be isotropic. For one- and two-dimensional diffusion, however, f(t) has the asymptotic limits [4n(CA/a)2Dtr 1/2 and (4nCAa- 2Dt)-1 respectively, where a is the lattice constant [30]. A more fundamental theory of energy transfer has been given by Huber [30].
Note finally that back-transfer from acceptor to donor has been neglected until now. It is possible, however, to incorporate back-transfer in the existing theories [30].
Let us close this section with an important example of energy migration and its application. The luminescent material GdMgB 50 1o :Ce,Tb [1] is the green-emitting phosphor in energy-saving luminescent lamps. Excitation is into the Ce3 + ion at 254 nm. The excited Ce3 + ion transfers its energy to one of the neighbouring Gd 3 + ions. The transfer rate is much higher than the Ce3+ radiative rate, so that Ce3 + emission is practically absent. Subsequently the energy migrates over the Gd3+ sublattice (fast diffusion). Every transfer step has a rate of 106-107 S-1, whereas the radiative rate is only some 102 s -1. Consequently the excitation energy would, in an un doped compound, make some 104-105 steps before ending its life radiatively. In the phosphor the migrating excitation energy is trapped by the Tb3 +
ions, from where emission occurs. The quantum efficiency of the overall process is close to 1. This makes gadolinium compounds one of the most promising hosts for photoluminescent materials.
2.4 SOME CASE STUDIES
2.4.1 The Cr3 + (3,P) ion
As mentioned above the luminescence of Cr3 + has been studied extensively because of its intriguing luminescence properties. Figure 2.16 gives its energy level diagram as far as necessary to understand the luminescence. Depending on the strength of the crystal field ..1, the emission can be the spin-forbidden 2E-+ 4 A2 transition (strong field), or the spin-allowed 4T 2 -+ 4 A2 transition (weak field). The former occurs within the octahedral t~ subconfiguration,
Fig. 2.16 Schematic representation of the lower energy levels of Cr3+ (d3) as a function of the crystal field ..1. To the left of the broken line the emission is from 4T 2
to 4Az (broad band, infrared, spin allowed); to the right of the broken line the emission is from 2E to 4A2 (narrow line, red, spin forbidden).
Some case studies 45
i.e. between parabolae without offset, and consists mainly of a sharp line. The latter consists of a broad band because it occurs between the two subconfigurations t~e and t~. This illustrates nicely how the parabolae offset determines the band shape of the optical transition. For the isoelectronic ion Mn4+ (in Cs2GeF 6) the relevant parameters have been carefully deter mined: for 4A2-+2E the expansion is only 0.003 A, for 4A2-+4T 2 it is 0.053 A (8=3) [34].
Ruby (Ah03:Cr3+) is the most famous case of 2E line emission. The quenching temperature of this emission is very high (800 K); quenching occurs via thermal population of the higher 4T 2 level.
Broadband 4T 2 emission has been reported for SC203: Cr3+, ScB03 :Cr3+ and Cr3 + -doped glasses. In these lattices the crystal field is much smaller. In the crystalline host the quantum efficiency of this emission may be high at room temperature; however, in the glass modifications it is always low with values of about 20% as a maximum. This phenomenon has prompted much research. The explanation is in principle simple and derives directly from a consideration given above, i.e. the value of AQ, the parabolae offset, needs to be small for high quantum efficiency. Glasses with their loose structure do not favour small AQ values [7,8]. This can be seen directly from the Stokes shift of the 4T 2 emission of Cr3 +: in oxide crystals it varies from 2400 to 3500 cm -1, in oxide glasses from 4500 to 5300 em - 1 [35, 36].
In conclusion, the luminescence of Cr3 + illustrates our theoretical con siderations of the influence of parabolae offset on emission band shape and the nonradiative rate.
2.4.2 The rare earth ions Eu3+ (4f6), Gd3+ (4f7) and Tb3+ (4f8)
Absorption spectra of the rare earth ions consist of sharp and weak lines and, at higher energy, of broad band(s). Figure 2.17 gives an example. The sharp lines are parity-forbidden transitions within the 4fn configuration, and the broad bands are allowed transitions from the 4fn to excited configur ations. These are either 4fn -15d or 4fn + 1 L -1 (charge transfer, L = ligand). This situation bears an analogy with the Cr3 + ion, and shows again the influence of parabolae offset on spectral band shape, since AQ ~O for intraconfigurational and AQ =/: 0 for interconfigurational transitions.
The emission of the three ions under discussion consists usually of sharp lines due to transitions from the excited level to the ground levels: 5Do- 7F J for Eu3+ in the red, 6P7/2-+8S for Gd3+ in the ultraviolet, and 5D4 -+ 7F J for Tb3 + in the green. However, under special conditions other emissions appear, for example 5D2- 7 F J for Eu3+ in the blue, 5D3-7FJ for Tb3+ in the blue, and for Gd3+ even vacuum ultraviolet (187 nm). Higher level emission is only possible if (i) the vibrational frequencies in the lattice are not too high, and (ii) cross-relaxation is absent owing to a low concentration.
20 30 40 10 3 cm-1
Fig. 2.17 Schematic absorption spectrum of the Eu3 + (4f 6 ) ion in an oxide. The broad band on the high-energy side is due to the charge-transfer transition. The lines are due to transitions within the 4f6 configuration.
The latter point is immediately clear from our discussion above. The former will become clear from equation (2.11). The higher COmax is, the larger is N. Indeed, the higher level emissions mentioned here do not occur at all in hosts such as borates and phosphates.
If the vibrational frequencies become exceptionally high, as in aqueous solutions (comax ~ 3500 cm -1), the quantum efficiency of even the lowest level emission decreases. Only in Gd3+ (AE ~ 32 000 cm -1) does the radiative rate still exceed the nonradiative rate by many orders of magnitude, but in Tb3+ (AE ~ 15 000 cm - 1) and Eu 3+ (AE ~ 12 000 cm - 1) a drastic decrease of the quantum efficiency occurs, whereas the other rare earth ions practi cally do not emit in aqueous solution. If, however, heavy water is used (D20, Vmax ~ 2200 cm -1) the efficiencies go up again. For solids these effects can be studied in NaLa(S04h· H20 where the rare earth site is coordinated to one H20 molecule only. The q values are 100% for Gd3+, 70% for Tb3+, 10% for Eu3+ and 1 % for Sm3+ and Dy3+ [7,8].
In many compounds of Eu3+, Gd3+ and Tb3+ energy migration has been observed [6-8]. An example was given above for Gd3+. The Gd3+ ion transfers efficientl

Solid State Luminescence: Theory, materials and devices

Documents

Transcript of Solid State Luminescence: Theory, materials and devices