## 1 Introduction
### Transparent Films with Deeply Submicrometric Thickness: Dispersion Curves and Interference Effects  
A relatively different situation occurs when the film thickness is submicrometric, i.e., comparable to, (or lower than) the acoustic wavelength. In the usual case of a film supported by a substrate, whose acoustic phase velocities are higher than those of the film (slow film/fast substrate), a number of discrete acoustic modes, namely the Rayleigh-Sezawa and Love modes are present [25] and can be revealed in Brillouin spectra. The former modes are polarized in the sagittal plane (i.e., in the plane of incidence of light, while the latter modes are polarized perpendicularly to the above plane). This transformation from a spectrum typical of thick films to the discretized spectrum typical of thin films is seen in the left panel of Figure 6, relative to GaSe films of different thickness [32]. Here, it is seen that the Rayleigh and a few Sezawa discrete modes are seen for film thickness of 77 and 251 nm. Taking measurements at different angles of incidence, one can obtain the dispersion curves shown in Figure 6, right panel. A detailed theory about the theoretical cross section of these modes has been presented in [33], and it has been shown that strong interference effects can arise when one considers all the possible scattering mechanisms (ripple scattering from both the free surface and the interface, elastooptic scattering from the interior of the film) [34]. However, these modes are dispersive, so that measurements are usually performed on films of different thicknesses and with different angles of  
Figure 5: Experimental surf-BLS spectra relative to the SiOC:H/Si film, taken for an angle of incidence of light \(\theta=65^{\circ}\) (**left panel**) and \(25^{\circ}\) (**right panel**). The upper spectra were taken using p-polarized incident light, while s-polarized light was used for the lower ones. The peaks corresponding to the Rayleigh surface wave (RW), to the longitudinal guided mode (LGM) and to longitudinal bulk wave (LB) are indicated on the anti-Stokes side of each spectrum. It can be seen that the RW peak has a large cross section for p-polarized incoming light and large angle of incidence. Instead, the LGM has a larger cross section for s-polarized light and small angle of incidence. Reprinted with permission from [27], Elsevier, 2005.  
incidence, in order to span a large interval of the ratio between the film thickness and the phonon wavelength. In the case of a hexagonal elastic symmetry, four of the five effective elastic constants, namely \(C_{11}\), \(C_{13}\), \(C_{33}\) and \(C_{44}\), influence the Rayleigh-Sezawa modes, so that they can be evaluated by a best fit procedure of the experimental velocities to the calculated dispersion curves. This procedure has been used in the past for a number of different thin film materials, such as cubic Zinc Selenide [35], hexagonal and cubic Boron Nitride [36; 37; 38], hexagonal Zinc Oxyde [39], Tin Dioxide [40], Gallium- [32] or Indium- [41] Selenide, and isotropic dielectrics [42; 43; 44]. In all the above studies it has been put in evidence that the different elastic constants can influence the acoustic modes in a similar way, so that one has to face the problem of the correlation among the fitting parameters. It follows that is useful to exploit films of different thickness (in the range between a few tens to a few hundreds of nanometers), but in his case a further complication may arise, if the structural and elastic differences among films of different thickness are not negligible, due for instance to the occurrence of a modified transition layer at the interface between substrate and film material. This is illustrated in Figure 7, where it is shown that the experimental data for the ZnO/Si films fit the expected theoretical dispersion curves fairly well for film thicknesses greater than 150 nm, while they appreciably depart from the same curves for smaller thicknesses [39].