RESONANT BRILLOUIN SCATTERING IN OPAQUE REGION OF CdS

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RESONANT BRILLOUIN SCATTERING IN OPAQUE

REGION OF CdS

Y. Itoh, C. Hamaguchi, Y. Inuishi

To cite this version:

JOURNAL DE PHYSIQUE

CoZloque C6, suppZlment au n o 12, Tome 42, de'cernbre 1981 page c6-810

RESONANT B R I L L O U I N S C A T T E R I N G I N OPAQUE REGION OF C d S

Y. Itoh, C. Hamaguchi and Y. Inuishi

Faculty of Engineering, Osaka University, Suita C i t y , Osaka 565, Japan

Abstract.

-

Resonant Brillouin scattering has been investigated in CdS above and below the fundamental absorption edge at room temperature w i n g acousto- electrically amplified phonon domains. Experimentally observed resonant behaviour has been analyzed on the basis of light-scattering theory and piezobirefringence theory. A good agreement is found when we take into account both the real and imaginary parts of the Brillouin tensor and piezo- birefringence coefficients, especially near the absorption edges.

1. Experiment.

-

Resonant Brillouin scattering studies making use of the acousto- electrically amplified phonon domains have been reported by many workers. 1-51 In these experiments, the incident photon energies were restricted to the region in which the samples were transparent because of the experimental conditions that the transmitted light signals were measured. Therefore, it is difficult to obtain the dispersion of the Brillouin scattering cross section in the opaque region due to the strong absorption. To overcome this restriction, Chang et al. proposed to utilize the scattering of reflected light and a high intensity Ar ion laser line between 457.9 nm and 514.5 nma6) In the present work we adopted similar method except Fabry-Perot interferometer. The samples used in the present work are single crystals with ?. 20 ohm-cm resistivity and with the scattering surface of optical

flat mechanically polished and etched. The T2-mode phonons amplified through acoustoelectric effect propagate in the direction perpendicular to the c-axis with shear polarization parallel to the c-axis. The laser light beam is incident on a polished surface parallel to the c-axis and the scattering plane was perpendicular to the c-axis. Here, the Brillouin scattering process produces a scattered light out of the propagation direction of the reflected light beam. The light scattered by the ripple mechanism shows no rotation of the polarization, but the scattering by the elasto-optic mechanism is rotated by 900.~) Our main interest in the present work is the latter mechanism in the opaque region. Therefore, we choose the

polarization direction of the scattered light perpendicular to the incident light. The interaction length between phonon and photon is comparable to the penetrating

-1

depth (a ) and restricted to the surface region. Thus the scattering is induced by the surface acoustic waves. The identification of the surface acoustic waves was

5

made by the sound velocity v(T2) = = (1.80+0.05)x10 cm/sec and selection rules of the light polarization. Experiments in the transparent region were made by

using the method reported elsewhere. 1-5)

2. Discussions.

-

Figure 1 shows wavelength dependence of the Brillouin scattering cross section u _B (in arbitrary units) for 0.5 GHz T2-mode phonons at room temperature, where the open circles with error bars are obtained by the reflected light scattering geometry and the solid circles are the experimental data obtained by the transmission light scattering geometry. These two independent data were plotted by comparing with the theoretical curves. According to the theory for surface elasto-optic scattering in isotropic opaque materials, the cross section varies with absorption coefficient a, as [l+(a~/21m)~]-~. 6, For CdS at room temperature, the refractive index n=2.8 and

a

is nearly constant 10' cm-l, for 450 nm < 1 < 500 nm. In the region, the measured Brillouin scattering cross section is reduced by less than

5 % . 6 ) Therefore, absorption correction can be neglected. In the wavelength region below the fundamental absorption edge, the Brillouin scattering cross section has a deep minimum (resonant cancellation) at around 560 nme2) At shorter wave- lengths, a resonant enhancement is observed in the neighbourhood of the absorption singularities. We find in Fig. 1 a clear resonant enhancement in the opaque region, where the three absorption edges 506 nm, 503 nm, and 491 nm exist. Similar enhance- ment in this region is observed in CdS by Chang et alS6) The resonant features

(resonant cancellation and resonant enhancement) in the transparent region have been well explained by the following light scattering theory. It is interesting to check whether the resonant enhancement in opaque region is explained by the same theory

WAVELENGTH (n m ) _{WAVELENGTH (nrn)}

C6-8 12 JOURNAL DE PHYSIQUE

with the same parameters. In order to clarify this problem, we extend the existing

theory in the opaque region. The scattering cross section aB, derived by Loudon has the form: 1-5,7)

where Ris is the frequency dependent Brillouin tensor, h w and hs are the energy i

of the incident and scattered photons, fiu is the phonon energy, is the matrix

4

element of the deformation potential scattering, PoB and Pao are the appropriate momentum matrix elements, and Ro is the non-resonant term arising from far off

critical points. Equation (1) indicates that the scattering cross section increases as the incident photon energy fiui approaches the electron-hole pair energy tiu or

a

nu6. The resonant cancellation (oB=O) occurs when Ris+R =O.

r

is a phenemeno- logical damping factor which is important in the resonant regions. A solid curve in Fig. 1 is calculated by eq. (1) including both the real and imaginary parts of R

is' where the exciton effect is taken into account in the manner derived by Zeyher et a1.478) On the other hand, a dashed curve is calculated by taking into account the real part of eq. (1) only. The experimental data show a good agreement with the former results but a poor agreement with the latter calculation. From these results, we conclude that the imaginary part of R plays an important role, in particular, in

is the region of the absorption edges.

It has been shown that the Brillouin sca~tering cross section is analyzed from

phenomenological aspect by incorporating the piezobirefringence theory. 3-5) In Fig. 2 we show the dispersion curves of the photoelastic constant P44 determined by the relation oB(T2)

I

PL

+

ipi4

1:

where the superscript r and i indicate the real and imaginary part of Pq4, respectively. Since the present method does not give signs and absolute values of the photoelastic constant but relative values, they are adjusted to the values of Yu and Cardona, pr =-0.054 at 630 t~m.~) The theoretical

44

curve of the absolute value of P44 ( Ipi4

+

iP44

1

) obtained from piezobirefringence analysis shows a good agreement with the experimental data in the region investi- gated. This indicates again that the imaginary part of the photoelastic constant plays an important role to determine the dispersion and thus the dispersion of the Brillouin scattering cross section in the resonant enhancement region.

References.

D.K.Garrod and R.Bray, Phys. Rev. B6 (1972) 1314. K.Ando and C.Hamaguchi, Phys. Rev. B11 (1975) 938. S.Adachi and C.Hamaguchi, Phys. Rev. B19 (1979) 938.

Y.Itoh, M.Fujii, C. Hamaguchi, and Y.Inuishi, J. Phys. Soc. Jpn. 48 (1980) 1972. R.Berkowicz and T.Skettrup, Phys. Rev. Bll (1975) 2316.

W.C.Chang, S.Mishra and R.Bray, Proc. 15th I n t . Conf. Physics of Semiconductors,

Kyoto, J. Phys. Soc. Jpn. 59 (1980) Suppl. A, p711.