Elastic characterization of thin films by Brillouin light scattering


           The problem of the determination of the whole set of elastic constants of thin film materials has attracted much attention in recent years, because of the growing importance of layered structures in both theoretical studies and applications.  Measurement of the whole set of constants is usually out of the reach of conventional static techniques, which can only give information about specific elastic moduli.[i] On the other hand, use of acoustic techniques based on surface acoustic waves (SAW) presents technical difficulties connected  with the fabrication of the acoustical delay line. In addition, one has to consider that in the frequency range commonly used, the large values of the acoustic wavelength, compared to the film thickness, require a careful consideration of the effect of the substrate on the propagation of the SAW.[ii] 

These limitations can be overcome using the Surface Brillouin Scattering (SBS) technique which relies upon the inelastic scattering of photons by thermally activated elastic waves (phonons). During the last twenty yeas, SBS has proved to be very effective for achieving a complete elastic characterization of thin films and multilayered structures.[iii]  It has many advantages over conventional ultrasonics techniques since it does not require external generation of acoustic waves and it probes acoustic phonons with wavelength in the submicron range. In a SBS experiment, a beam of monochromatic light is used as a probe to reveal acoustic phonons which are naturally present in the medium under investigation. The power spectrum of these phonons is mapped out from frequency analysis of the light scattered within a solid angle. Because of the wavevector conservation in the magnon-photon interaction, the wavelength of the revealed elastic waves is of the same order of magnitude of that of light. This means that the wavelength is much larger than the interatomic distances, so the material can be described as a continuum within an effective-medium approach. From SBS measurements of the phonon frequencies as a function of the the in-plane wavevector, a determination of the elastic constants can be attained. Another important characteristic of SBS is that it is a non-destructive local technique (the probed area of the sample is of the order of 10x10 mm) and this permits to operate a scan of the magnetic properties of inhomogeneous specimens. Both transparent and opaque materials can be investigated. Note that in spite of the small penetration depth of light in metallic media (about ten nanometers), the information gained by SBS concerns the whole coherence depth of the acoustic waves, which is of the order of a few hundreds of nanometers. From a technical point of view, due to the very weak signal to noise ratio and to the small frequency of the excitations, it was still impossible to detect acoustic waves in thin films and in opaque solids until the advent of a new class of spectrometers designed and fabricated for the first time by Sandercock in the seventies. He demonstrated that the sensitivity of a Fabry-Perot interferometer could be dramatically increased by passing the scattered light several times through the same interferometer.[iv] Such an improvement led to the observation of light scattering from acoustic phonons in thin film structures, both transparent and opaque.



It is well known that collective excitations in a solid can inelastically scatter incident light, through the induced modulation of the optical constants of the medium. This modulation is usually induced in transparent media via the elasto-optic effect. However, in the case of opaque media, either metals or semiconductors, also the rippling of the free surface induced by the presence of thermal phonons can scatter light.  As an alternative approach to that based on the modulation of the optical constant of the medium, Brillouin scattering can be understood in very simple terms either as a Doppler shift of the frequency of light scattered from a propagating spin wave or as a photon-magnon collision in which the frequency and the momentum are conserved. 

In a typical Brillouin scattering experiment one measures spin waves with frequencies in the range between about 1 and 150 GHz. In order to extract the weak inelastic component of light from the elastically scattered contribution, a high-resolution spectrometer is required. To this aim, the best combination of high resolution and good throughput is achieved using a tandem Fabry-Perot interferometer (FPI) as a scanning spectrometer


Most of the SBS investigations performed in the past for determining the elastic constants of thin films were concerned with layers of thicknesses lower than the acoustic wavelength (0.3 - 0.4 micron), supported by substrates with acoustic phase velocities higher than that of the films (slow film / fast substrate). Under these conditions,  a number of discrete acoustic modes, namely the Rayleigh and the Sezawa modes,[v] are revealed in Brillouin spectra and the corresponding phase velocity can be measured.

These modes are dispersive, so that measurements are usually performed on films of different thicknesses and with different angles of incidence. In most practical cases one deals with polycrystalline films with a preferential orientation of the crystallites along the normal to the plane of the free surface. These films have a hexagonal (cylindrical) elastic symmetry which is characterized by five independent effective elastic constants.  In these cases, four of the five effective elastic constants, namely c11, c113, c33 and c44, influence the Rayleigh and Sezawa modes, so that they can be evaluated by a best fit procedure of the experimental velocities to the calculated dispersion curves. People therefore tried to analyse films of different thickness, deposited under identical conditions[vi]. Two main problems can limit the reliability of the above procedure. First, the different elastic constants can influence the acoustic modes in a similar way, so that a strong correlation among the fitting parameters can occur.  Second, the best fit procedure relies upon measurements from films of  different thicknesses (typically, from 10 to 400 nm), neglecting possible structural and elastic differences among them. It may happen, for instance, that a transition layer at the interface between substrate and film material can occur[vii]. This can particularly occur for the films which are produced by processes which involve high energies and particle momentum and are thus far from thermodynamical equilibrium. As for the fifth elastic constant c66 it can be determined  from measurement of the phase velocity of  shear horizontal modes  (Love modes). We notice, however, that since these modes are polarized parallel to the surface,  their scattering efficiency is very low. Use of an opaque substrate (typically crystalline silicon) is recommended in order to take advantage from the presence of a reflecting interface which enhances the Brillouin cross section.[viii] In the case of film thickness approaching 1 micron or more, the number of discrete modes (Sezawa and Love modes) can be very large, so it it can become very difficult to resolve the individual modes. In this case, however, one can see some resonances in the spectrum, resulting from a group of Sezava or Love modes which merge together. These resonances in micrometric thick films happen at  frequencies which correspond to either a longitudinal or a shear horizontal wave propagating parallel to the film surface, named longitudinal guided mode (LGM) and shear horizontal mode (SHM), respectively.  During the last fifteen years the group at the GHOST laboratory, University of Perugia, extensively exploited SBS to characterize semiconductor and/or dielectric films of different materials, such as C60, AlN, GaSe,  InSe, InGaAs, SiO2 , SnO2, a-Ge:H, a-C and even multilayered metallic structures (Ag/Ni, Nb/Fe, Ta/Al, FeNi/Cu, FeNi/Nb).     

 PUBLICATIONS of our group concerning elastic properties of thin films


[i] Review articles can be found in: MRS Bulletin, Vol. XVII, Number 7,  (Material Research Society, Pittsburgh, 1992) pp.25-45

[ii] See for instance H. Coufal, K. Meyer, R.K. Grygier, M. de Vries, D. Jenrich and P. Hess, Appl. Phys. A 59, 83 (1994)

[iii] G.I. Stegemann, F. Nizzoli, in Surface Excitations, edited by V.M. Agranovich and R. Loudon (Elsevier, North Holland, 1984), Chapter 2, pp.195-378.

F. Nizzoli, J.R. Sandercock, in Dynamical Properties of Solids, edited by G.K. Horton and A.A. Maradudin (Elsevier, North Holland 1990), pp. 281-335.

P. Mutti, C.E. Bottani, G. Ghislotti, M. Beghi, G.A.D. Briggs, J.R. Sandercock, in Advances in Acoustic Microscopy, Vol. 1, edited by A. Briggs (Plenum, New York, 1995), Chapter 7, pp. 249-300.

J.D. Comins, in Handbook of Elastic Properties of Solids, Liquids, and Gases, Vol. 1,

edited by Levy, Bass, and Stern (Academic, New York, 2001), Chapter 15, pp. 349-378.

F. Nizzoli and J.R. Sandercock, in  Dynamical Properties of Solids, edited by G.K. Horton and A.A. Maradudin (North-Holland, Amsterdam, 1990), Vol. 6, p 307

[iv] J.R. Sandercock Optics Commun. 2, 73 (1970).

[v] G.W. Farnell, E.L. Adler, in Physical Acoustics, Vol. 9, edited by W.P. Mason and R.N. Thurston (Academic, New York, 1972), pp. 35-127.

[vi] B. Hillebrands, P. Baumgart, R. Mock, G. Güntherodt, P.S. Bechthold, J. Appl. Phys. 58, 3166 (1985).

F. Nizzoli, R. Bhadra, O.F. de Lima, M.B. Brodsky, M. Grimsditch, Phys. Rev. B 37, 1007 (1988).

S. Lee, B. Hillebrands, G.I. Stegeman, H. Cheng, J.E. Potts, F. Nizzoli, J. Appl. Phys. 63, 1914 (1988).

T. Wittkowski, J. Jorzick, K. Jung, B. Hillebrands, Thin Solid Films 353, 137 (1999).

G.Carlotti, D.Fioretto, L.Palmieri, G.Socino, L.Verdini and E.Verona,  IEEE Trans. Ultrason., Ferroelect. Freq. Contr., 38, 56-61 (1991)

G. Carlotti, D. Fioretto, L. Giovannini, G. Socino, V. Pelosin and B. Rodmacq, , Solid State Comm. 81, 487-489 (1992);

G. Carlotti, D. Fioretto, G. Socino, B. Rodmacq and V. Pelosin,  J. Appl. Phys. 71, 4897-4902 (1992);

G. Carlotti, G. Socino and L. Doucet, Appl. Phys. Lett. 66, 2682-2684 (1995);

G. Carlotti, L. Doucet, , J. Vac. Sci. Technol. 14, 3460-3464 (1996).

M.G. Beghi, C.E. Bottani, P.M. Ossi, T.A. Lafford, B.K. Tanner, J. Appl. Phys. 81, 672 (1997).

V. Panella, G. Carlotti, G. Socino, L. Giovannini, M. Eddrief, C. Sébenne, J. Phys.: Condens. Matter 11, 6661 (1999).

 W. Pang, A.G. Every, J.D. Comins, P.R. Stoddart, X. Zhang, J. Appl. Phys. 86, 311 (1999).

[vii]  A.G. Every, W. Pang, J.D. Comins, P.R. Stoddart, Ultrasonics 36, 223 (1998).

 T. Wittkowski, P. Cortina, J. Jorzick, K. Jung, B. Hillebrands, Diam. Rel. Mat. 9, 1957 (2000).

T. Wittkowski, V. Wiehn, J. Jorzick, K. Jung, B. Hillebrands, Thin Solid Films 368, 216 (2000).

P. Zinin, M.H. Manghnani, X. Zhang, H. Feldermann, C. Ronning, H. Hofsäss, J. Appl. Phys. 91, 4196 (2002).

 X. Zhang, R. Sooryakumar, Appl. Phys. Lett. 80, 4501 (2002).

[viii] G. Carlotti, D. Fioretto, L. Palmieri, G. Socino, V.I. Anisimkin and I.M. Kotelyanskii, 1993 IEEE Ultrasonics Symposium Proceedings,  (IEEE, New York, 1993)  p. 811

D. Fioretto, G. Carlotti, L. Palmieri, G. Socino and L. Verdini and A. Livi, Phys. Rev. B., 47,  15286 (1993)




We have worked in the following project:

STREAM: Stress minimisation on deep sub-micron CMOS processes, measured by a high spatial resolution technique, and its application to 0.15 mm non volatile memories

Funded by European Commission within the

The objective of this project is to measure strain in CMOS devices with a linewidth down to 0.15 mm for non volatile memories. Involved are eight different partners of five european countries.



La spettroscopia Brillouin di superficie (SBS) è una tecnica di indagine non distruttiva capace di indagare le proprietà elastiche di film sottili e strutture a multistrato. Queste brevi note costituiscono una introduzione alle potenzialità di tale tecnica, con particolare riferimento alla attività svolta nell'utimo quinquennio dal gruppo operante presso il Dipartimento di Fisica dell'Università di Perugia.

- Cos'è la spettroscopia Brillouin di superficie ?

La spettroscopia Brillouin di superficie è una tecnica di indagine basata sul processo di diffusione anelastica(inelastic scattering) della luce da parte dei fononi di superficie presenti nel mezzo in esame per attivazione termica. Misurando la variazione di frequenza della luce che ha interagito col mezzo in esame e conoscendo la geometria di interazione, è possibile dedurre la velocità e l’attenuazione dei modi acustici presenti nel mezzo e, da questi, ricavare informazioni circa le sue proprietà elastiche. Questa tecnica è particolarmente adatta alla caratterizzazione elastica di film sottili e strutture a multistrato con spessori variabili da qualche nanometro fino a decine di micrometri. Concettualmente dunque è una tecnica simile alla spettroscopia Raman, ma rispetto a quest'ultima la SBS analizza intervalli di frequenza di gran lunga inferiori (1-200 GHz, cioè 0.03-7 cm-1) per poter rivelare fononi acustici e necessita quindi di uno strumento (interferometro Fabry-Perot) che consenta di ottenere risoluzioni più elevate di quelle normalmente ottenibili mediante spettrometri convenzionali a reticolo di diffrazione.

- Per quale tipo di indagine può essere utile ?

La spettroscopia Brillouin di superficie è utile per caratterizzare le proprietà elastiche di strati sottili e di materiali con ridotta dimensionalità, sia opachi che trasparenti alla luce. Il suo impiego richiede una superficie piana di qualità ottica ed è perciò particolarmente adatta all'analisi di wafers di materiali impiegati in elettronica ed in optoelettronica. La porzione di campione analizzata coincide con la piccola areola su cui viene focalizzato il raggio laser, tipicamente dell'ordine di 10x10 microns. Molte applicazioni riguardano materiali mono-cristallini ma essa si applica con eguale successo al caso di materiali amorfi o nanocristallini. Una analisi dettagliata della forma di riga degli spettri Brillouin consente poi di studiare l’attenuazine dei modi acustici e di ricavare quindi informazioni sui fenomeni di rilassamento in sistemi complessi, come ad esempio film polimerici. 

Esempi notevoli di materiali sui quali sono state condotte indagini mediante SBS dal gruppo di Perugia sono i seguenti:

- film piezoelettrici di ZnO ed AlN

- multistrati metallici policristallini

- film e multistrati a base di Si amorfo 

- film e superreticoli monocristallini a semiconduttore

- film amorfi di vetri silicati 

- film di fullerene

- film polimerici.

Le informazioni ottenibili mediante la SBS permettono di determinare le costanti elastiche e viscoelastiche dei mezzi esaminatie di indagare dettagliatamente alcune caratteristiche fisiche quali ad esempio:

- la qualità e la omogeneità dei materiali costituenti i film;

- l'influenza sulle proprietà elastiche degli effetti di interfaccia, quali il disordine atomico, l'interdiffusione, la presenza di sforzi, ecc.

- la dipendenza delle proprietà elastiche dalletecniche o dalle condizioni di crescita;

- processi di rilassamento in mezzi disordinati (film vetrosi e/o poimerici). 

- Su quale meccanismo di interazione si basa ?

La diffusione anelastica della luce da parte dei fononi termici presenti nel mezzo in esame avviene essenzialmente attraverso due meccanismi di interazione. Il primo, dominante nel caso di mezzi opachi alla luce (metalli e semiconduttori), è basato sulla corrugazione della superficie del mezzo in esame da parte dei fononi termici. Questa corrugazione fa si’ che la superficie si comporta come un reticolo di diffrazione mobile e quindi introduce una variazione della frequenza luce diffusa per effetto Doppler. Il secondo meccanismo, dominante nei materiali trasparenti alla luce, è basato sull'accoppiamento tra la luce e le fluttuazioni di densità nel mezzo, mediante l'effetto elasto-ottico. In entrambi i casi, la conservazione del vettore d'onda nell'interazione fotone-fonone fa sì che i fononi rivelati abbiano lunghezza d'onda comparabile con quelle della luce, cioè molto maggiore della distanza interatomica. Questo permette di poter interpretare i dati Brillouin all'interno della teoria della elasticità, assumendo il mezzo in esame come un continuo elastico.