THEORY OF ACOUSTIC PHONONS AT INTERFACES AND BRILLOUIN SCATTERING

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THEORY OF ACOUSTIC PHONONS AT

INTERFACES AND BRILLOUIN SCATTERING

V. Bortolani, F. Nizzoli, G. Santoro, A. Marvin

To cite this version:

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JOURNAL DE PHYSIQUE

CoZZoque C6, suppldment au no 12, Tome 4 2 , ddcembre 1981 page C6-804

THEORY OF ACOUSTIC PHONONS A T INTERFACES AND BRILLOUIN SCATTERING

V. Bortolaci, F. Nizzoli, G. Santoro and A. ~arvin*

I s t i t u t o d i Fisica and G.N.S.M.-C.N.R., Universitd d i Modena, 41100 Modena, I t a l y

' ~ s t i t u t o d i Fisica Teorica, Universitc? d i T r i e s t e , 34014 Miramare-Grignano, [Prieste, ItaZy

Abstract.- We present calculations of the Brillouin cross section for a metal- lic thin film (A1 and Au) on a Si substrate. The results for the A1 coating are explained in terms of scattering from the surface corrugation due to the thermally excited acoustic phonons. In the case of Au we find an appreciable contribution from the elasto-optic coupling in the film.

1. Introduction.- For clean surfaces, it has been found that the light is inelastical ly scattered both from the dynamical corrugation of the surface due to the phonon field (ripple effect) and from the dielectric inhomogeneity of the medium (elasto- optic effect) (2). In both cases the spectral function shows structures related to the surface modes (Rayleigh waves-RW) and to combinations of bulk modes with modes local& zed near the surface (the so called mixed modes) (3r4). In this paper we consider the case of coated surfaces and we show that the interface existing between the coverage and the substrate causes new modes to appear in the Brillouin ~ ~ e c t r a ( ~ ' ~ ) . The calcu lations will refer to a (001) Si substrate and to backscattering geometry, that is the scattered light is assumed to be collected in a certain solid angle around the incidence direction, making an angle 8 to the surface normal. Under these conditions the experiments probes the Fourier components of the phonon field with a fixed paral-

-+

lel wavevector Q,,

,

equal to minus twice the parallel component of the wavevector of the incident light(7). Conversely, due to the lack of translational invariance along the surface normal, all the complex normal wavevectors q

1

of the phonon field are mixed in the experiment and contribute to the spectra. We consider here a parallel

-+

wavevector Q,, directed along

[loo]

and TM light of wavelenght 5145

A.

The angle 8 is equal to 7 0 ' .

2. Calculation of the cross section.- The computed cross section for a coated surface is found to be the square modulus of the sum of four contributions(*), due to: a) scat tering from the surface ripples (proportional to IvZ1 computed at the film suface)

,

b)scattering from the interface ripples (proportional to IvZ12 at the interface), c) and d) elasto-optic coupling in the film and substrate respectively. The latter two terms are complicated combinations of the normal modes of the two media. Let us first shows a cmparison between experiment and theory in the case of an A1 coating. A tan- dem multipass interferometer (5 pass plus 2 pass) has been used(7). The fig.1 refers

Q

to film thickness of 2 0 0 0 A . The experimental points are compared with the cross sec-

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-

QCG Hz)

Fig. 1 : Experimental (dots) and computed (full line) Brillouin cross section for a 2000

A

film of A1 deposited on Si (Stokes spectrum). The broken line shows the spectrum without the contribution of the continuum of phonon mixed modes. tion computed by including the contribution a) only. This is in fact very reasonable for the A1 surface, due to the high value of its dielectric Also in our case of a supported film, an explicit calculation with the elasto-optic coeffi- cients of A1 and Si confirmed that the only important term is a). Although this term depends on the dislacement field at the film surface, it shows important features due to the presence of the interface. In Fig.1 the frequency of the RW, nearly 11.3 GHz, is strongly different from that of Al, that is 10.4 GHz. Indeed the most dramatic effect due to the interface is the appearance of a Sezawa wave (SW1) (') at about 16 GHz and of a Lamb wave (LWl) at 18 GHz. They are followed at higher frequencies by a continuum of phonons, extending from 21 to 30 GHz. These modes eventually give rise to new thin-film modes, on further increasing the thickness.

We pass now to a gold thin-film. The dielectric constant of gold at 5145 A is very small (€=-3.19+i2.47) and we expect an appreciable contribution from the term c).

0

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JOURNAL DE PHYSIQUE

0

Fig. 2 : As in Fig.1. Gold film thickness 1000 A (anti-Stokes spectrum). not depend on the latter coupling.

In conclusion, we have shown that the Brillouin spectra from thermally excited acoustic phonons in coated surfaces differ considerably from those obtained in clean surfaces. In particular, we have found important structures whose number increases as the film becomes thicker. These structures have been explained in terms of thin- film waves polarized in the sagittal plane (Sezawa and Lamb modes).

References

1. R Loudon,phys.Rev.Lett,

40,

581 (1978)

2. V Bortolani, F Nizzoli and G Santoro, Phys.Rev.Lett.41, 39 (1978)

3. A Marvin, V Bortolani and F Nizzoli, J.Phys. C

13,

299 (1980) and references therein

4. &Marvin,V Bortolani, F Nizzoli and G Santoro, J.Phys. C

13,

1607 (1980)

5. V Bortolani, F Nizzoli, G Santoro, A Marvin and J R Sandercock, Phys.Rev.Lett.

43,

224 (1979)

6. N L Rowel1 and G I Stegeman, PHys.Rev.Lett.

41,

970 (1978) 7. J R Sandercock, Solid St. Commun.

26,

547 (1978)

8. V Bortolani, F Nizzoli, G Santoro, J R Sandercock and A Marvin, to be published 9. G W Farnell and E L Adler, Physical Acoustic, vol.IX, pp. 33-127, Academic Press,