Optical absorption of s2-configuration ions in alkali halide crystals—IV

1. Phw. Chum. .Wd.s, 1975. Vol

36. pp. 13&1388.

Perganwn Press. Printed inGrnlhitam

OPTICAL ABSORPTION OF s*-CONFIGURATION IONS IN ALKALI HALIDE CRYSTALS-IVt LINE

SHAPE

OF THE C BAND IN Sn*‘-DOPED

CRYSTALS

KEIKOOYAMA CANNONSand P. W. M. JACOBS Department of Chemistry, University of Western Ontario, London, Canada, N6A 5B7

(Receiced 1I November 1974;accepted 9 April 1975) Abstract-The line shape of the C band in the alkali halide phosphors KBr : Sn2’, RbBr : Sn”, and RbCl: Sn*’ has been measured as a function of temperature between about I5 K and room temperature. In contrast to earlier measurements on In’doped phosphors, the C band shows a well-marked triplet structure over the whole temperature range. This triplet structure cannot be accounted for solely in terms of the dynamical Jahn-Teller effect without assuming a very large temperature-dependence for the coupling constant to vibrational modes of trigonal symmetry. The temperaturedependence both of the second moment of the line shape and of the separation between the components of the C band, suggests that there is a contribution to the splitting of the C state from a lowering in the symmetry of the static crystal field and a model which includes such a static splitting in addition lo the dynamical Jahn-Teller effect provides a good representation of the experimental line shapes. 1. INTRODUCTION The C band in alkali halide phosphors containing impurity

ions with the s*-configuration is due to the allowed transition from the ‘A,, ground state to the IC’) excited state which results from vibrational mixing of the IC) = pI’T,.)+ v[‘T,.) state with the IA) and IB) states [see the first two papers of this series[ I, 21 henceforth designated I and II]. A systematic study of the C band in 24 combinations of the impurity ions Ga’, In-, Tl’, Sn2’, and Pb2’ with the alkali halides NaCI, KC], KBr, KI, RbCI, RbBr, CsBr, CsI by Fukuda[3] has confirmed that the C band has a triplet structure although this structure is not clearly marked at low temperatures in several of the systems studied. Both the width of the band and the separation of its components decrease with increasing mass of the halogen ion. It has been suggested[4,5] that the structure of the C band is due to a lowering in the symmetry of the static crystal field but the T”* dependence of the separation of components of the triplet at high temperatures indicates the importance of vibronic effects[3]. The removal of the three-fold degeneracy of the IC’) state by the dynamical Jahn-Teller effect was investigated by Toyozawa and Inoue [6] who predicted a triplet structure for the C band due to the linear electron-lattice interaction of the I’T,,) state with modes of T2, symmetry. Although Toyozawa and Inoue[6], Cho [7] and Honma [8] have made theoretical calculations of the line shape of the C band the only direct comparisons of calculated and experimental line shapes for a specific system are those reported in II. In that paper121 we showed that the line shape of the C band in KBr : In’ could be accounted for by a mode1 that includes spin-orbit coupling, vibrational coupling to the IA) and IB) tPublication No. 130from the Photochemistry Unit, University of Western Ontario. *Present address: Department of Chemistry, McGill University, Montreal,Quebec, Canada.

states, the dynamical Jahn-Teller effect due to trigonal TzI1 modes, and coupling to modes of A,, symmetry. The line shape of the C band in KBr: In’ was reproduced at temperatures of 21,72 and 297 K using a constant value of the coupling constant (c) to modes of TtI symmetry but it was necessary to allow the ratio of the coupling constants to the A,, and T211modes (a/c) to decrease slightly with increasing T (from 0.8 at 21 K to 0.6 at 297 K) to fit the experimental line shape. At low temperatures the C band in KBr : In* appears as a single band and indeed the fine structure is barely noticeable even at high temperatures. In contrast, the C band in KBr:Sn2’, RbBr: Sn*’ and RbCl: Sn*’ has a well-marked fine structure over the whole temperaturerange investigated. It is therefore of interest to see if the model that was successful for KBr : In’ applied also to the Sn”-doped salts. 2. EXPERIMENTAL. PROCEDURE ANDRESULTS

The experimental procedure and data analysis have been described in I. The temperature-dependence of the absorption spectrum of RbBr : Sn2* in the region of the C band is illustrated in Fig. I. The small band at 278 nm is the B band which is associated with the vibronically assisted transitions ‘A,, +‘E,, ‘Tzu. The triplet structure of the C band is well marked over the whole temperature range U-295 K. KBr:Sn*’ and RbCl:Sn*’ behave similarly. An example of the resolution of the absorption spectrum (for KBr: Sn2’ at 79 K) into four components (B, C,, C2, C, in order of increasing energy) is shown in Fig. 2. The zeroth moment of the line shape of the B and C bands of RbBr : Sn2’ is shown in Fig. 3 as a function of temperature. The intensity of the B band increases with temperature while that of the C band decreases correspondingly indicating vibrational mixing of the (B) and IC) states. The temperature-dependence of the positions of the maxima of the C,, CZ,and C3 bands for RbBr: Sn” is shown in Fig. 4. The C, and CI components exhibit a

1383

K. 0.

GANNON

and P. W. M. JACOBS

I

,- 3

5

2

54

z e h

43

77 II9

5 t% 6 204

WAVELENGTH

Fig.

2950

I. Temperaturedependence

2&o

2750

2550

/nm

of the C band in RbBr

25%

: Sn“. d

2450

2350

ISO-

1.20-

OOO4.20

450

4.80

I540

5.10

PHOTON EHRGY/eV

Fig. 2. Computer resolution of the B and C bands in KBr: Sn” at 79 K.

00

5.021 4g8 ~0000 .

c

C-band 0

0;

0

T

0

4.90 0

5

o) 4.86--‘oooo . band

O O

A

0

uE

000

c 0 ‘0 0

4.82 i

0

00 0

Oo

50

100

150

200

250

300

00

T/K

c, 00

Fig. 3. Temperaturedependence of the zeroth moment of the B and C bands in RbBr : Sn*‘. and the C, component a small blue-shift. The second moment about the mean of the C band for RbBr:Sn” is shown in Fig. 5 as a function of temperature. The continuous line represents a non-linear least squares fit of the data to the equation

0

4.641

0

’

’ 100

’

200

0

300

T/K

red-shift

Fig. 4. Temperature-dependence of the peak positions of the C,. C,, and C, componentsin RbBr : Sn’*.

frequency for all the modes involved. The numerical values of the parameters that give the best fit to ((E -(E))*) = m%O) + m(O) ~0th d hn/W (1) the experimental data are: m;(O) = 1.18x lo-* (eV)‘, m*(O)= 3.57 x lo-’ (eV)‘, oII = 1.23x IO” rad s -‘. For where E denotes photon energy and w,n is a weighted KBr: In’ m;(O) is zero[2]. Since the second moment is m2

=

average

Opticalabsorptionof s’-contigurationions-IV

1385

The splitting between the components of the C band of RbCl : Sn*’ and RbBr : Sn2+is shown in Fig. 6 as a function

of T’“. The continuous lines are non-linear least squares fits to the experimental data of the equation n 25 > al 7 0 20 .

AE = AE, + AE2 (coth (iho,fi/ZkT)]“’

(2)

Numerical values of the parameters appear in Table 1.

EN 15

Table 1. Numericalvalues of the parametersin eqn (2) which describesthe temperature-dependence of the splittingbetweenthe componentsof the C band

RDO

od ’ 100’

ASc

300

200

=

a.

AEl/eV

0.1016

0.0811

0.0773

Ah/W

0.0376

0.0375

0.0395

1.76

1.75

1.33

AWN

0.0787

0.0647

0.0643

A&/W

0.0442

0.0488

0.0532

1.26

1.31

1.34

T/K u&10"

Fig. 5. Temperature-dependence of the second momentaboutthe mean for the C band in RbBr:Sn”. The conti~~uousline was caIuIatedfromeqn (1).

related to the square of the full width of an absorption band at half height[9] a finite value for m;(O) implies a contribution to the width of the band additional to that which comes from the electron-phonon coupling and which is the source of the second term in eqn (1).

From

rad

AEC

m-l

-c a

aI

/lo"

ra*

3.

m-1

CALCULAllON OF THE L.lNE SEAPE

The

equation for the line shape of the C band which was derived in II from the semiclassical model and the Condon approximation allowing for spin-orbit coupling, vibrational coupling to the ]A) and ]B) states (see Fig. 3), and a dynamical electron lattice interaction to modes of Tzl and A,, symmetry is

0.16 > ,” 0.12 u” $

0.06

X

I ‘0

4

8

12

16

exp [ ;hy;c),yd*]

(3)

where

$1 Kt (4

I(Y,~)=~~dA~d~q’exp(-q’lp)6[(a+~t~)q’ +Yrrq-Yl

(4)

y=hv-EC

0.16

(5)

> hv is the photon energy, EC is the photon energy for the transition ‘A,, -+C at Q = 0,

T o 0.12 > :

0.08

p = cW*

ol-___ 0

4

8.

I2

I6

T’/K+ (b) Fig. 6. Temperaturedependenceof the splitting behveen the components of the C band in RbCI:Sn” and RbBr:Sn’*. (a) sptittingbetween the C, and C1components.(b) splittingbetween the CI and C, components.

(6)

c is the coupling constant to modes of Tt, symmetry kT* = f &J=,,coth (k&ZkT)

(7)

D is the coupling constant to modes of A,, symmetry q=cQ=c[Q:+Q:tQ:]‘R

(8)

Q,, 05, Q6 are the interaction mode coordinates for

1386

K. 0.

GANNON

and P. W. M.

vibrations of Ta symmetry, introduced by Toyozawa and Inoue[6], fi are the eigenvalues of the matrix

JACOBS

is increased. A qualitative comparison with the experimental line shape shows that the value of a/c is about 0.3.

The calculated line shape for c2=O*93 eV, a/c =0*3 is shown by the dotted line in Fig. 8. The overall width of the (9) band agrees poorly with experiment. Therefore keeping T constant the line shape was recalculated using large values of c’. A value of c2 = 3.36 eV gives a rather better 1, m, n are the direction cosines of Q, do = (dfI/dh)dh agreement with experiment. However, when the line denotes the differential solid angle in which A = 21mn lies shape at 79 K is calculated, with this value of c* the between A and A +dA and (I, p, y are coefficients in the agreement is again poor and an empirical adjustment to electron-lattice perturbation c2 = 2.70 eV is needed to fit the data (Fig. 9). The need for a temperature-dependent coupling conHdC; Tzs) = r$Q + (ai + /3~%*Q* (10) stant for KBr : Sn*+is in sharp contrast to the calculations for KBr: In+ which reproduced the line shape at (Rtl) (11) temperatures from 15 to 295 K with a constant value of c*. Figure 10 shows the calculated line shape at 18K with a = l/(R + l)Ec~ (12) c* = 0.93 eV, as determined from AEz, but with an additional static splitting. y3 has been shifted up by 3119R 1 -0.07 eV and y1 has been decreased by 0.06eV. It is (13) B=-jRtlEcs+~(Rtl)s% obvious that the three components of the triplet appear in R = /.L’/v’ (14) the correct positions but the band is too narrow and the components too sharply separated. These defects can be and rectified (Fig. 11) by an empirical adjustment of c* to ]C) = pI’T,u)+ vl’T,u) (15) 0 T= n m i

1

nm 0 I 1 0

In eqn (13) EC* = EC - EB, ECA= EC - E, and EB, EA are the photon energies for the transitions ‘A,, +B and ‘A,, +A respectively. All the parameters needed for the calculation of the line shape from (3) and (4) are available from the experimental data (see Table 2 of III, Ref.[lO]) with the exception of the coupling constants. A preliminary value of c2 was estimated from the temperature-dependence of the G-C, separation using the approximate formula given by Toyozawa and Inoue [6] AEc = 0.91[(R -f)/(R t 1)] ICI(kT*)“*

P;;TO;.8ENERGY 4.6

I

!

5.2

5.1

L

(16)

Using this value of c2 =0*93 eV the line shape was calculated at the value of p appropriate to 18 K with various values of a/c. The results of this calculation are given in Fig. 7. For small values of a/c the band is an asymmetric triplet and the fine structure becomes increasingly smeared out as the coupling to the A,, modes

/ eV 5.0

4.9

(hQ-

EC) /eV

Fig. 8. Line shape of the C band in KBr : St? at 18K calculated from ecm (3) and (4) with a/c =0.3. Line (1) c2= 0.93 eV, p = O&I1 e+; line‘ (2) c2 = 3.36eV, p = Ok eV*; line (3) c* = 6.23 eV, p = 0.028eV2.Circles show experimental data.

1 4

4.6

PHOTON ENERGY 4.7 4.0 4.9

1

/ eV 5.0

I

5.1

5.2

I

A;

’ \

Y =(hJ-EC)

/eV

Fig. 7. Theoretical line shape of the C band for KBr : St?’ at 18K calculated from eqn (3) and (4) with c* = 0.93 eV (p = 0@041eV’) and (1) a/c = 0.1, (2) a/c = 0.3, (3) a/c = 0.5.

Fig. 9. Line shape of the C band in KBr : St?’ at 79 K calculated from eqn (3) and (4) with c* =2.70eV (p =0.021 eV’) and (1) a/c = 0.2, (2) a/c = 0.3. Circles show experimental data.

Opticalabsorption of sz-configurationions-IV 4.6

I

PHOTON ENERGY 4.7 4.8 4.9

/ eV 5.0

1

5. I

5.2

I

IL 4-

2-

0

In -0.3

-a2

-Ql

0 (hS - EC) / eV

Fig. 10. Line shape of the C band in KBr : Sri’+at 18K allowing for a static splitting in addition to the dynamical Jahn-Teller effect. Circles show experimental data. Ay, = -0*06 eV, Ayz= 0, Ay3= +0@7eV; c* = 0.93 eV, p = 0~0041eV*. Line (1) a/c = 0.3, line (2) a/c = 0.4, line (3) a/c = 0.5. Circles show experimental data.

PHOTON ENERGY 4.7 4.8 4.9

4.6 5

/

eV 5.0

5. I

5.2

I

4 3 IL 2 I 0

-0.3

-0.2

-0.1 (h3-

0

0.

I

0.2

0.3

EC) / eV

Fig. 11. Line shape of the C band in KBr : St? at 18K allowing for a static splitting in addition to the dynamical Jahn-Teller effect. Ay, = -0.028 eV, Ay, = 0, Ay, = +OGtOeV; c2 = 2.04eV; p =OW91 eV*. Line (1) a/c =0.3, line (2) a/c = 0.4, line (3) a/c = O-5.Circles show experimental data.

4.6

PHOTON ENERGY 4.7 4.8 4.9

/ eV 50

5.1

52

.h 3-

-Q3

-Q2

-Ql

0 (ht’-

El/

Ql eV

Q2

Q3

Fig. 12. Line shape of the C band in KBr: %I’+at 79 K allowing for a static splitting in addition to the dynamical Jahn-Teller effect. Ay, = -0.28 eV, Ay, = 0, Ay, = +O+MO eV, c* = 2.04eV: p =O.O16eV*. Line (1) a/c = 0.3, line (2) o/c =0.4, tine (3) a/c = 0.5. Circles show experimental data.

1387

2+MeV and a reduction in the static splitting to Ay, = +O+MeV, Ay2= 0, Ay, = -0,028 eV. These values are somewhat smaller than A& for C2- C, and C, - C2 respectively (Table 1). This shows that the effective frequency approximation eqn. (2) offers a qualitative but not a quantitative description of the splitting of the C band components. When the static splitting is included the line shape of the C band can be described by temperatureindependent parameters, for Fig. 12 shows the calculated line shape at 79K with the same values of the coupling constants and static splittings as were used to calculate the shape at 18 K, Fig. 11. The fit is not quite as good as at low temperatures but much closer than that achieved with a temperature-independent c and no static splitting. 4. CONCLUSION final line shape of the C band in KBr : Sn’+ using the empirically adjusted parameters c2 = 2.04 eV, a/c = 0.4 (line 2 in Fig. 11) is in good agreement with the experimental line shape except that the separation between the peaks is a little too sharp and the asymmetry of the C, and C, peaks a little too pronounced. At 79 K (line 2 in Fig. 12) the calculated band is a little too broad. The good overall agreement with peak positions and line width supports the applicability to Sn”-doped crystals of the theory developed for In’ phosphors. The observed triplet structure is due in part to a static splitting, caused presumably by a lowering in the symmetry of the crystal field, and partly to the dynamical Mm-Teller effect on the C’ state. The asymmetry of the C band is due to the quadratic terms in the electron-lattice Hamiltonian eqn (10). The coupling constant c for coupling to modes of Tzg symmetry differs somewhat for the singlet and triplet T,. states but this is not too surprising in view of the fact that the King and Van Vleck parameter[lO], [ll] which accounts for the differences in the singlet and triplet wave functions has the relatively low value of 0.75 for KBr *. Sri*’. Alternative approaches to the semiclassical theory have been presented by Englman, Caner and Toatf [ 121and by Nasu and Kojima[l3]. The former authors have diagonalized the Hamiltonian for the vibronic interaction of a triply degenerate electronic state with modes of Tz, symmetry and have used these results to calculate absorption band line shapes for transitions from a ground state electronic singlet. The discrete lines that result from the 6 function in the transition probability were combined with a broadening function of Gaussian form. The resulting line shapes show the expected triplet structure but are very asymmetric, this asymmetry becoming less pronounced as the temperature or the coupling constant is increased. Apart from confirming that the triplet structure of the C band is due to the dynamical Jahn-Teller effect these calculations bear little relevance to the experimentally investigated C band in heavy metal phosphors because of the much higher coupling constants that prevail in these systems. Also the theory neglects spin-orbit coupling and is limited to the linear vibronic interaction. While the linear interaction with modes of Tzg symmetry is undoubtedly the most important single factor in determining the line shape of the C band our The

1388

K. 0.

GANNONand

calculations[2] have shown the important influence of the quadratic terms in the Hamiltonian on the asymmetry of the line shape. Also the importance of the static crystal field in St?+ doped crystals has been demonstrated in this paper. Nasu and Kojima[l3] have recently utilized the independent ordering approximation]141 in performing a quantum mechanical calculation of the line shape for an A,, + ‘I;:. transition. For large coupling constants it is possible to neglect the time dependence of the phonon correlation function and in this approximation they recover the semiclassical adiabatic approximation employed in this series of papers. Thus the usefulness of the semiclassical approximation in strong coupling constant situations is substantiated. Acknowledgement-We are grateful for the support of this research programme by the National Research Council of Canada and the Province of Ontario (through a graduate fellowship to K. 0. G.).

P. W. M.

JACOBS REFERENCE3

1. Jacobs P. W. M. and Oyama K., J. Phys. C 8,851 (1975). 2. Jacobs P. W. M. and Oyama K., .I. Phys. C 8, 865 (1975). 3. Fukuda A., .I. Phys. Sot. Japan 27,% (1969). 4. Lushchik N. E. and Lushchik Ch. B., Optika i Spekfrosk. 8, 839 (1960). 5. Zazubovich S. G., Lushchik N. E. and Lushchik Ch. B., Opfika i Spektrosk 15, 381 (1%3). 6. Toyozawa Y. and Inoue M., .I. Phys. Sot. Japan 21, 1663 (1966). I. Cho K., .I. Phys. Sot. Japan 25, 1372(1968). 8. Honma A., Sci. Lighf, Tokyo 29, 33 (1%9). 9. Jacobs P. W. M. and Thorsley S. A., Crystal Lattice Dejects 5, 51 (1974). 10. Oyama Gamton K. and Jacobs P. W. M., .I. Phys. Chem. Solids 36,1375(1975).

11. KingG. W. and Van Vleck J. H., Phys. Rev. 56,464 (1939). 12. Englman R., Caner M. and ToatI S., J, Phys. Sot. Japan 29, 3% (1970). 13. Nasu K. and Kojima T., Prog. Theoret. Phys. 51, 26 (1974). 14. Vekhter B. G., Perlin Yh. E., Polinger V. Z., Rosenfeld Y. B. and Tsukerblat B. S., Crystal Lattice Defects 3,61,69 (1972).