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High resolution resonant brillouin scattering of exciton-polaritons in cadmium sulphide
~
Solid State Communications, Voi.38, pp.777-781. Pergamon Press Led. 1981. Printed in Great Britain.
HIGH RESOLUTION
RESONANT
J. Wicksted, Physics Department,
0038- 1098/81/210777-05502.00/0
BRILLOUIN SCATTERING IN C A D M I U M S U L P H I D E
M. Matsushita*
OF E X C I T O N - P O L A R I T O N S
and H. Z. Cummmins
City College of the City University New York, New York 10031, USA
(Received
23 January
of New York
1981 by G. Burns)
Resonant Brillouin scattering in CdS in the vicinity of the A exciton was investigated with a high resolution spectroscopic system that combines a triple-pass Fabry-Perot interferometer and a tandem grating spectrometer. Scattering from both inner and outer exciton-polariton branches was observed, as well as broadening of both TA and LA components near resonance. Additional resonant enhancement was observed at the I2B bound exciton.
Resonant Brillouin scattering (RBS) of exciton-polaritons in semiconducting crystals, predicted by Brenig, Zeyher and Birman (BZB),(1)has been observed in the cubic zincblendes GaAs, CdTe and ZnSe, the wurtzites CdS and CdSe, and the layered semiconductor HgI2. (2) The experiments, which have been described extensively in several recent review articles,(3-5) verified many of the features predicted by BZB. However, the limited resolution of the grating spectrometers used in these experiments masked the predicted increase of Brillouin linewidth near resonance, except in the case of CdSe where the linewidth is unusually large.(6) Similarly, the simultaneous observation of intrabranch Brillouin components involving both inner and outer branch exciton-polaritons as intermediate states has only been reported for GaAs(7) and ZnSe.(8) In order to further elucidate the properties of exciton-polaritons as well as the additional boundary conditions which govern the electrodynamics in these spatially dispersive materials, higher resolution experimental investigations are clearly desirable. In this communication we report preliminary results of a high resolution resonant Brillouin scattering study of CdS in the vicinity of the A exciton. In distinction to previous CdS experiments, we have observed broadening of both the longitudinal (LA) and transverse (TA) Brillouin components near resonance as well as both intrabranch (2-2'), (1-1') and interbranch (2-1') polariton transitions. Experiments were performed on single crystal CdS platelets,~9) generously provided by D. M. Roessler of the Genera] *
Permanent address: Research Institute of Electrical Communication, Tohoku University, Sendal 980, Japan.
Motors Research Laboratory. The crystals, with the c-axis in the plane of the sample, were maintained at 4.2°K in a helium dewar. A Coherent Radiation model 590 tunable dye laser using coumarin 102 dye, equipped with an intra-cavity double etalon assembly and pumped by a Spectra Physics model 171 krypton ion laser provided discretely tunable single mode excitation of about 20 mW. Experiments were performed in backscattering geometry with incident way,vector normal to the sample surface (~I~). Light scattered from the crystal was analyzed by a Tropel model 350 triple-pass piezoelectric Fabry-Perot interferometer placed in series with a Spex model 1401 tandem grating spectrometer. The operating finesse of the (unstabilized) interferometer was -35; the free spectral ranges employed were 6.1 and 4.72 cm -I. The data acquisition procedure is described as follows, with r e f e r e n c e t o the spectra of Figure 1 for which the incident frequency ~i = 20584 cm-lis -3 cm -I below wT. First, spectra were recorded using the grating spectrometer alone, with slitwidths narrowed to give a resolution of -0.5 cm -I. This spectrum (a) exhibits RBS involving outer-branch polaritons (2-2') with strong Stokes and anti-Stokes LA components. The Stokes TA component, although strong, is not completely resolved, while the anti-Stokes TA is obscured by the wing of the Rayleigh line. With the interferometer in place, the spectrometer slits were opened to provide a passband slightly larger than the free spectral range of the FabryPerot, while the gratings were adjusted so that either the Stokes (b) or antiStokes (c) spectrum would be passed by the spectrometer. The interferometer was then scanned through its free spectral range in ~I00 seconds, and the
778
EXCITON-POLARITONS
IN CADMIUM SULPHIDE
LA
(a)
Elc
i,-
Vol. 38, No. 9
/
wi =20584 cm-' /
/: xl
/I
m ¢Y v
, j
)I-
I
I I i
I I
z w kz
,
(c)
, ,,
+6 +5 ÷4 +3 ÷2 *1
(b)
0 -I - 2 - 3 - 4
w
(b)
I,.-
, -5 -6
TA
LA
TA
L.)
x I0
I0
).v
.
+6 +5 +4
Figure i:
~-~
x l
xlO t
.
.
.
.
+3 *2
0 -I -2 -3 - 4 *1 0 FREQUENCY SHIFT ( c m " )
-5
-6
Brillouin spectrum of CdS with ui = 20584 cm-I, analyzed with: (a) double-grating spectrometer alone; (b) and (c) Fabry-Perot interferometer and grating spectrometer in series.
For the
Stokes (h) and anti-Stokes (c) high resolution spectra, the free spectral range of the Fabry-Perot was 6.1 cm-I and the grating slits were adjusted to give the passband indicated in (a). The Brillouin components result from LA (2-2') and TA (2-2') scattering.
output of the combined system was again recorded on a strip chart recorder. The resulting Stokes and anti-Stokes spectra, both e x h i b i t i n g well resolved TA and LA components, are shown in Fig. ib and lc, respectively, (I0) with effective ressolution ~0.15 cm -I. Figure 2 shows results o b t a i n e d by the same procedure, but with the incident frequency e i ~80 om-i above ~T. The small peaks are the LA c o m p o n e n t s involving i n n e r - b r a n c h e x c i t o n - p o l a r i t o n s (i-i'). The larger peaks, which were seen only when the laser was tuned to within z15 cm -I of the I2B bound exciton at 20671 cm -1 (B exciton bound tO a neutral donor),(ll) o c c u r r e d both in ~I~ and E I ~. We attribute these peaks to resonant scattering of TA p h o n o n s from the I2B bound excitons, similar to the RBS from 12 bound e x c i t o n s o b s e r v e d in CdSe by H e r m a n n and Yu.(6) These B r i l l o u i n shifts are independent of the laser frequency since the dominant q of p a r t i c i p a t i n g phonons is d e t e r m i n e d by the exciton radius rather than by the p o l a r i t o n wavevector. In Figure 3 we have plotted the Brillouin shifts of the observed o n e - p h o n o n peaks including intrabranch [ LA (1-1'),
TA (2-2') and LA (2-2') ] and interbranch [ TA (2-I') or TA (i-2')] as well as the TA bound exciton features which are c o n n e c t e d by a dashed vertical line. The solid lines through the data points represent the t h e o r e t i c a l p r e d i c t i o n s derived from the polariton dispersion curves( 12 )
cZk z E~Z
-
1
+
eL z -eT z eTZ+~Tk2/m._ez_ieF
(1)
combined with b a c k s c a t t e r i n g k i n ~ a t i c s , with the longitudinal and transverse sound velocities taken as 4.25 x 105 and 1.76 x 105 cm/sec, respectively.(13) The values used in Eq. (i) were: eT = 20587.5 cm -I, e L- ~T = 15.4 cm -I, e o = 9.3, m* = 0.89 m e and F = 1.0 cm -I (the p r e d i c t i o n s are e s s e n t i a l l [ ind e p e n d e n t of F for 0 S F ~ 5 cm- ). These p a r a m e t e r s agree with the values found by W i n t e r l i n g and Koteles(14), with the e x c e p t i o n of ~m for which our value is lower by 2 cm-I. (15) We note that the LA (i-i') data points diverge from the p r e d i c t i o n s of Eq. (i) at the highest
Vol. 38, No. 9
EXCITON-POLARITONS IN CADMIIJM SULPHIDE
(o) I--
.4 <~
II
CdS EIC ~i = 2 0 6 6 8 cm-' T=4.2 K
v
>. I-
=,
1
I
f !
z
;
,
I !
(c).~ . ~ ,
(c)
-'{l'-
xlO'
A
LA
I
xlO'
(b)
(b)
x I%=
%A
x I0=
I
+4
Figure 2:
I iOt ix I
! ! I I i
w Iz Q IJJ IIu
779
*3
+2
0 -I -2 +1 0 FREQUENCY SHIFT ( c m " )
-3
-4
Brillouln spectrum of CdS with m. = 20668 cm-I, analyzed as in i -i In this figure, the free spectral range was 4.72 cm
Figure i.
The arrows in (a) and (b) indicate Stokes LA (i-I') Brillouin components.
The larger Stokes and anti-Stokes peaks result from
TA phonon scattering via the I2B bound exciton.
frequencies, indicating the onset of d i s p e r s i o n at the B exciton.(16) The e x c i t o n damping constant F in Eq. (i) leads to broadening of the B r i l l o u i n c o m p o n e n t s which is most significant near resonance.(I) We observed b r o a d e n i n g of both the LA and TA components. In Figure 4 we show the a p p r o x i m a t e full width at half m a x i m u m of the Stokes TA (2-2') components, determined by s u b t r a c t i o n of the instrum e n t a l l i n e w i d t h (the half width of the R a y l e i g h line) from the B r i l l o u i n linewidth. The solid curves are theoretical predictions( 1 ) [ ~ = 2 Cs(ki"+ks"); c s is the sound velocity, ki" and ks" are the imaginary parts of the incident and scattered p o l a r i t o n w a v e v e c t o r s resp e c t i v e l y ] with several d i f f e r e n t values of F. Q u a l i t a t i v e agreement between the d a t a and the t h e o r e t i c a l p r e d i c t i o n occurs with F -0.5 um-l. W h e n the crystal was immersed in s u p e r f l u i d helium, the Brillouin linewidth d e c r e a s e d but still ex-
ceeded the instrumental linewidth near resonance. Our results clearly demonstrate the advantages of the combined interferometerspectrometer instrumentation. Interbranch and intrabranch p o l a r i t o n scattering events and B r i l l o u i n line broadening have been observed, opening the way for a more extensive attack on the additional houndary condition problem which Yu and Evangelisti have investigated in CdS through the dependence of the ~ (2-2' ) intensity on laser frequency.(17) E x p e r i m e n t s to provide m o r e accurate B r i l l o u i n linewidths by d e c o n v o l u t i o n of d i g i t a l l y recorded spectra at higher resolution are in progress and will be reported in a future publication. We wish to acknowledge m a n y helpful d i s c u s s i o n s with J. L. Birman, and the p a r t i c i p a t i o n of E. S. Koteles and W. Yao in the early phases of this experiment. Support for this work was provided by the National Science F o u n d a t i o n under grants DMR 77-23788 and DMR 79-05534.
780
EXCITON-POLARITONS
'
I
'
IN CADMIUM SULPHIDE
,T r I i
?
20680 I
CdS
?
Ti I i
i
l
l
i
T I I
?
I I
f
,
I i
I I I
20660
L i
Vol.
I
t
I I
I
?
f
I
I
20640 i
E
Z hi
20620
0 n." b_ n"
20600
._1
20580
20560
+8
Figure 3 :
+6
+4 +2 0 -2 -4 BRILLOUIN SHIFT (cm")
-6
-8
Brillouin shifts of observed one phonon Stokes and anti-Stokes peaks as a function of incident laser frequency.
The solid
curves are theoretical predictions based on the exciton-polariton model as described in the text. connect points attributed
The dashed vertical lines
to scattering via the 12B bound exciton.
38, No. 9
Vol. 38, No. 9
EXCITON-POLARITONS
IN CADMIUM SS~LPHIDE
781
0.16
0.12 '= 1.0 cm-'
i
E (.)
v
-1-
a 0.08 I.LI Z _.1
+
+
0.04
~
F=o.5
+ +
F:O.2
4..
F=O.I
0.00
20560
20580
20600
20620
20640
LASER FREQUENCY ( c m - ' )
Figure 4:
Approximate experimental linewidths at T~4.2~Kof the Stokes TA (2-2') Brillouin components (FWHM with laser linewidth subtracted) as a function of incident laser frequency.
The solid curves are
theoretical predictions with four different values of the exciton damping constant F.
REFERENCES
I. 2.
3.
4.
5. 6. 7. 8. 9.
W. Brenig, R. Zeyher and J. L. Birman, Phys. Rev. B__6, 4617(1972) T. Goto and Y. Nishina, Solid State Commun. 31, 751 (1979). (This publication--{s not referenced in any of the p u b l i s h e d RBS review articles). R. G. Ulbrich and C. Weisbuch, Festk o r p e r p r o b l e m e XVIII - A d v a n c e s in Solid State Physics edited by J. Treusch, Braunschweig: Vieweg, (1978) p. 217. P. Y. Yu, in: Light S c a t t e r i n g in Solids edited by J. L. Birman, H. Z. Cummins and K. K. Rebane (Plenum Press, New York, 1979) p. 143. E. S. Koteles, in: Excitons edited by E. Rashba and M. Sturge (North Holland Press, to be p u b l i s h e d - 1981). C. Hermann and P. Y. Yu, Solid State Ccmmun. 28, 313 (1978). R. G. Ulbrich and C. Weisbuch, Phys. Rev. Lett. 38, 865 (1977). B. Sermage and G. F i s ~ a n , Phys. Rev. Lett. 4_/3, 1043 (1979). P r e l i m i n a r y B r i l l o u i n and reflectivity m e a s u r e m e n t s of these crystals
10.
ii. 12. 13. 14.
15. 16. 17.
were reported by R. H. Bruce and H. Z Cummins, Phys. Rev. B16, 4462 (1977). Spectra obtained with the grating spectrometer set to pass the entire spectrum exhibited both Stokes and anti-Stokes components in each order and were m u c h more difficult to interpret. D. G. Thomas and J. J. Hopfield, Phys. Rev. 128, 2135 (1962). J. J. H o p f ~ 6 1 d and D. G. Thomas, Phys. Rev. 132, 563 (1963). D. Gerlich, J. Phys. Chem. Solids 28, 2575 (1967). G. W i n t e r l i n g and E. S. Koteles, in: Lattice Dynamics edited by M. Balkanski (Flammarion Sciences, Paris, 1978) p. 170. This is the air value. The corresponding vacuum value is ~T (vac) = 20581.7 ca -I. E. S. Koteles and G. W i n t e r l i n g , Phys. Rev. Lett. 44, 948 (1980), P. Y. Yu and F. Evangelisti, Phys. Rev. Lett. 4__22, 1642 (1979); P. Y. Yu, Solid State Ccmmun. 3__22,29(1979).
Solid State Communications, Voi.38, pp.777-781. Pergamon Press Led. 1981. Printed in Great Britain.
HIGH RESOLUTION
RESONANT
J. Wicksted, Physics Department,
0038- 1098/81/210777-05502.00/0
BRILLOUIN SCATTERING IN C A D M I U M S U L P H I D E
M. Matsushita*
OF E X C I T O N - P O L A R I T O N S
and H. Z. Cummmins
City College of the City University New York, New York 10031, USA
(Received
23 January
of New York
1981 by G. Burns)
Resonant Brillouin scattering in CdS in the vicinity of the A exciton was investigated with a high resolution spectroscopic system that combines a triple-pass Fabry-Perot interferometer and a tandem grating spectrometer. Scattering from both inner and outer exciton-polariton branches was observed, as well as broadening of both TA and LA components near resonance. Additional resonant enhancement was observed at the I2B bound exciton.
Resonant Brillouin scattering (RBS) of exciton-polaritons in semiconducting crystals, predicted by Brenig, Zeyher and Birman (BZB),(1)has been observed in the cubic zincblendes GaAs, CdTe and ZnSe, the wurtzites CdS and CdSe, and the layered semiconductor HgI2. (2) The experiments, which have been described extensively in several recent review articles,(3-5) verified many of the features predicted by BZB. However, the limited resolution of the grating spectrometers used in these experiments masked the predicted increase of Brillouin linewidth near resonance, except in the case of CdSe where the linewidth is unusually large.(6) Similarly, the simultaneous observation of intrabranch Brillouin components involving both inner and outer branch exciton-polaritons as intermediate states has only been reported for GaAs(7) and ZnSe.(8) In order to further elucidate the properties of exciton-polaritons as well as the additional boundary conditions which govern the electrodynamics in these spatially dispersive materials, higher resolution experimental investigations are clearly desirable. In this communication we report preliminary results of a high resolution resonant Brillouin scattering study of CdS in the vicinity of the A exciton. In distinction to previous CdS experiments, we have observed broadening of both the longitudinal (LA) and transverse (TA) Brillouin components near resonance as well as both intrabranch (2-2'), (1-1') and interbranch (2-1') polariton transitions. Experiments were performed on single crystal CdS platelets,~9) generously provided by D. M. Roessler of the Genera] *
Permanent address: Research Institute of Electrical Communication, Tohoku University, Sendal 980, Japan.
Motors Research Laboratory. The crystals, with the c-axis in the plane of the sample, were maintained at 4.2°K in a helium dewar. A Coherent Radiation model 590 tunable dye laser using coumarin 102 dye, equipped with an intra-cavity double etalon assembly and pumped by a Spectra Physics model 171 krypton ion laser provided discretely tunable single mode excitation of about 20 mW. Experiments were performed in backscattering geometry with incident way,vector normal to the sample surface (~I~). Light scattered from the crystal was analyzed by a Tropel model 350 triple-pass piezoelectric Fabry-Perot interferometer placed in series with a Spex model 1401 tandem grating spectrometer. The operating finesse of the (unstabilized) interferometer was -35; the free spectral ranges employed were 6.1 and 4.72 cm -I. The data acquisition procedure is described as follows, with r e f e r e n c e t o the spectra of Figure 1 for which the incident frequency ~i = 20584 cm-lis -3 cm -I below wT. First, spectra were recorded using the grating spectrometer alone, with slitwidths narrowed to give a resolution of -0.5 cm -I. This spectrum (a) exhibits RBS involving outer-branch polaritons (2-2') with strong Stokes and anti-Stokes LA components. The Stokes TA component, although strong, is not completely resolved, while the anti-Stokes TA is obscured by the wing of the Rayleigh line. With the interferometer in place, the spectrometer slits were opened to provide a passband slightly larger than the free spectral range of the FabryPerot, while the gratings were adjusted so that either the Stokes (b) or antiStokes (c) spectrum would be passed by the spectrometer. The interferometer was then scanned through its free spectral range in ~I00 seconds, and the
778
EXCITON-POLARITONS
IN CADMIUM SULPHIDE
LA
(a)
Elc
i,-
Vol. 38, No. 9
/
wi =20584 cm-' /
/: xl
/I
m ¢Y v
, j
)I-
I
I I i
I I
z w kz
,
(c)
, ,,
+6 +5 ÷4 +3 ÷2 *1
(b)
0 -I - 2 - 3 - 4
w
(b)
I,.-
, -5 -6
TA
LA
TA
L.)
x I0
I0
).v
.
+6 +5 +4
Figure i:
~-~
x l
xlO t
.
.
.
.
+3 *2
0 -I -2 -3 - 4 *1 0 FREQUENCY SHIFT ( c m " )
-5
-6
Brillouin spectrum of CdS with ui = 20584 cm-I, analyzed with: (a) double-grating spectrometer alone; (b) and (c) Fabry-Perot interferometer and grating spectrometer in series.
For the
Stokes (h) and anti-Stokes (c) high resolution spectra, the free spectral range of the Fabry-Perot was 6.1 cm-I and the grating slits were adjusted to give the passband indicated in (a). The Brillouin components result from LA (2-2') and TA (2-2') scattering.
output of the combined system was again recorded on a strip chart recorder. The resulting Stokes and anti-Stokes spectra, both e x h i b i t i n g well resolved TA and LA components, are shown in Fig. ib and lc, respectively, (I0) with effective ressolution ~0.15 cm -I. Figure 2 shows results o b t a i n e d by the same procedure, but with the incident frequency e i ~80 om-i above ~T. The small peaks are the LA c o m p o n e n t s involving i n n e r - b r a n c h e x c i t o n - p o l a r i t o n s (i-i'). The larger peaks, which were seen only when the laser was tuned to within z15 cm -I of the I2B bound exciton at 20671 cm -1 (B exciton bound tO a neutral donor),(ll) o c c u r r e d both in ~I~ and E I ~. We attribute these peaks to resonant scattering of TA p h o n o n s from the I2B bound excitons, similar to the RBS from 12 bound e x c i t o n s o b s e r v e d in CdSe by H e r m a n n and Yu.(6) These B r i l l o u i n shifts are independent of the laser frequency since the dominant q of p a r t i c i p a t i n g phonons is d e t e r m i n e d by the exciton radius rather than by the p o l a r i t o n wavevector. In Figure 3 we have plotted the Brillouin shifts of the observed o n e - p h o n o n peaks including intrabranch [ LA (1-1'),
TA (2-2') and LA (2-2') ] and interbranch [ TA (2-I') or TA (i-2')] as well as the TA bound exciton features which are c o n n e c t e d by a dashed vertical line. The solid lines through the data points represent the t h e o r e t i c a l p r e d i c t i o n s derived from the polariton dispersion curves( 12 )
cZk z E~Z
-
1
+
eL z -eT z eTZ+~Tk2/m._ez_ieF
(1)
combined with b a c k s c a t t e r i n g k i n ~ a t i c s , with the longitudinal and transverse sound velocities taken as 4.25 x 105 and 1.76 x 105 cm/sec, respectively.(13) The values used in Eq. (i) were: eT = 20587.5 cm -I, e L- ~T = 15.4 cm -I, e o = 9.3, m* = 0.89 m e and F = 1.0 cm -I (the p r e d i c t i o n s are e s s e n t i a l l [ ind e p e n d e n t of F for 0 S F ~ 5 cm- ). These p a r a m e t e r s agree with the values found by W i n t e r l i n g and Koteles(14), with the e x c e p t i o n of ~m for which our value is lower by 2 cm-I. (15) We note that the LA (i-i') data points diverge from the p r e d i c t i o n s of Eq. (i) at the highest
Vol. 38, No. 9
EXCITON-POLARITONS IN CADMIIJM SULPHIDE
(o) I--
.4 <~
II
CdS EIC ~i = 2 0 6 6 8 cm-' T=4.2 K
v
>. I-
=,
1
I
f !
z
;
,
I !
(c).~ . ~ ,
(c)
-'{l'-
xlO'
A
LA
I
xlO'
(b)
(b)
x I%=
%A
x I0=
I
+4
Figure 2:
I iOt ix I
! ! I I i
w Iz Q IJJ IIu
779
*3
+2
0 -I -2 +1 0 FREQUENCY SHIFT ( c m " )
-3
-4
Brillouln spectrum of CdS with m. = 20668 cm-I, analyzed as in i -i In this figure, the free spectral range was 4.72 cm
Figure i.
The arrows in (a) and (b) indicate Stokes LA (i-I') Brillouin components.
The larger Stokes and anti-Stokes peaks result from
TA phonon scattering via the I2B bound exciton.
frequencies, indicating the onset of d i s p e r s i o n at the B exciton.(16) The e x c i t o n damping constant F in Eq. (i) leads to broadening of the B r i l l o u i n c o m p o n e n t s which is most significant near resonance.(I) We observed b r o a d e n i n g of both the LA and TA components. In Figure 4 we show the a p p r o x i m a t e full width at half m a x i m u m of the Stokes TA (2-2') components, determined by s u b t r a c t i o n of the instrum e n t a l l i n e w i d t h (the half width of the R a y l e i g h line) from the B r i l l o u i n linewidth. The solid curves are theoretical predictions( 1 ) [ ~ = 2 Cs(ki"+ks"); c s is the sound velocity, ki" and ks" are the imaginary parts of the incident and scattered p o l a r i t o n w a v e v e c t o r s resp e c t i v e l y ] with several d i f f e r e n t values of F. Q u a l i t a t i v e agreement between the d a t a and the t h e o r e t i c a l p r e d i c t i o n occurs with F -0.5 um-l. W h e n the crystal was immersed in s u p e r f l u i d helium, the Brillouin linewidth d e c r e a s e d but still ex-
ceeded the instrumental linewidth near resonance. Our results clearly demonstrate the advantages of the combined interferometerspectrometer instrumentation. Interbranch and intrabranch p o l a r i t o n scattering events and B r i l l o u i n line broadening have been observed, opening the way for a more extensive attack on the additional houndary condition problem which Yu and Evangelisti have investigated in CdS through the dependence of the ~ (2-2' ) intensity on laser frequency.(17) E x p e r i m e n t s to provide m o r e accurate B r i l l o u i n linewidths by d e c o n v o l u t i o n of d i g i t a l l y recorded spectra at higher resolution are in progress and will be reported in a future publication. We wish to acknowledge m a n y helpful d i s c u s s i o n s with J. L. Birman, and the p a r t i c i p a t i o n of E. S. Koteles and W. Yao in the early phases of this experiment. Support for this work was provided by the National Science F o u n d a t i o n under grants DMR 77-23788 and DMR 79-05534.
780
EXCITON-POLARITONS
'
I
'
IN CADMIUM SULPHIDE
,T r I i
?
20680 I
CdS
?
Ti I i
i
l
l
i
T I I
?
I I
f
,
I i
I I I
20660
L i
Vol.
I
t
I I
I
?
f
I
I
20640 i
E
Z hi
20620
0 n." b_ n"
20600
._1
20580
20560
+8
Figure 3 :
+6
+4 +2 0 -2 -4 BRILLOUIN SHIFT (cm")
-6
-8
Brillouin shifts of observed one phonon Stokes and anti-Stokes peaks as a function of incident laser frequency.
The solid
curves are theoretical predictions based on the exciton-polariton model as described in the text. connect points attributed
The dashed vertical lines
to scattering via the 12B bound exciton.
38, No. 9
Vol. 38, No. 9
EXCITON-POLARITONS
IN CADMIUM SS~LPHIDE
781
0.16
0.12 '= 1.0 cm-'
i
E (.)
v
-1-
a 0.08 I.LI Z _.1
+
+
0.04
~
F=o.5
+ +
F:O.2
4..
F=O.I
0.00
20560
20580
20600
20620
20640
LASER FREQUENCY ( c m - ' )
Figure 4:
Approximate experimental linewidths at T~4.2~Kof the Stokes TA (2-2') Brillouin components (FWHM with laser linewidth subtracted) as a function of incident laser frequency.
The solid curves are
theoretical predictions with four different values of the exciton damping constant F.
REFERENCES
I. 2.
3.
4.
5. 6. 7. 8. 9.
W. Brenig, R. Zeyher and J. L. Birman, Phys. Rev. B__6, 4617(1972) T. Goto and Y. Nishina, Solid State Commun. 31, 751 (1979). (This publication--{s not referenced in any of the p u b l i s h e d RBS review articles). R. G. Ulbrich and C. Weisbuch, Festk o r p e r p r o b l e m e XVIII - A d v a n c e s in Solid State Physics edited by J. Treusch, Braunschweig: Vieweg, (1978) p. 217. P. Y. Yu, in: Light S c a t t e r i n g in Solids edited by J. L. Birman, H. Z. Cummins and K. K. Rebane (Plenum Press, New York, 1979) p. 143. E. S. Koteles, in: Excitons edited by E. Rashba and M. Sturge (North Holland Press, to be p u b l i s h e d - 1981). C. Hermann and P. Y. Yu, Solid State Ccmmun. 28, 313 (1978). R. G. Ulbrich and C. Weisbuch, Phys. Rev. Lett. 38, 865 (1977). B. Sermage and G. F i s ~ a n , Phys. Rev. Lett. 4_/3, 1043 (1979). P r e l i m i n a r y B r i l l o u i n and reflectivity m e a s u r e m e n t s of these crystals
10.
ii. 12. 13. 14.
15. 16. 17.
were reported by R. H. Bruce and H. Z Cummins, Phys. Rev. B16, 4462 (1977). Spectra obtained with the grating spectrometer set to pass the entire spectrum exhibited both Stokes and anti-Stokes components in each order and were m u c h more difficult to interpret. D. G. Thomas and J. J. Hopfield, Phys. Rev. 128, 2135 (1962). J. J. H o p f ~ 6 1 d and D. G. Thomas, Phys. Rev. 132, 563 (1963). D. Gerlich, J. Phys. Chem. Solids 28, 2575 (1967). G. W i n t e r l i n g and E. S. Koteles, in: Lattice Dynamics edited by M. Balkanski (Flammarion Sciences, Paris, 1978) p. 170. This is the air value. The corresponding vacuum value is ~T (vac) = 20581.7 ca -I. E. S. Koteles and G. W i n t e r l i n g , Phys. Rev. Lett. 44, 948 (1980), P. Y. Yu and F. Evangelisti, Phys. Rev. Lett. 4__22, 1642 (1979); P. Y. Yu, Solid State Ccmmun. 3__22,29(1979).