Acoustoelastic anomaly in stressed heterostructures E. Chilla,* A. V. Osetrov, † and R. Koch Paul-Drude-Institute for Solid State Electronics, Nanoacoustics group, Hausvogteiplatz 5-7, 10117 Berlin, Germany Received 18 September 2000; published 1 March 2001 We investigated the influence of stress on the acoustic wave propagation in single crystalline heterostruc- tures using a transfer matrix method. Both Rayleigh-type and Sezawa modes exhibit an acoustoelastic anomaly, where the stress-induced change of the phase velocity is maximum for finite film thicknesses, considerably smaller than the acoustic wavelength. For Ge/Si001 compressed by 1 GPa the velocity shift of Sezawa modes reaches exceptionally high values of about 2%. These results demonstrate the importance of stress effects on the determination of elastic constants of thin film heterostructures. DOI: 10.1103/PhysRevB.63.113308 PACS numbers: 62.20.Dc, 81.40.Jj, 62.65.+k Ultrasonic waves are a unique tool for the nondestructive investigation of bulk materials, particularly for the precise determination of the elastic constants. 1 More recently ultra- sonic waves have also been employed to measure the elastic properties of polycrystalline and epitaxial thin films. 2–5 Though still rare, such measurements are particularly impor- tant for heterostructures as the elastic constants play a key role for the understanding of the interdependence of stress and strain—with particular impact for electronic and opto- electronic devices. So far it is not clear whether the elastic constants of thin films deviate from the respective bulk val- ues, which usually are used to calculate stress from strain and vice versa. Moreover, an increasing number of techno- logically interesting materials—such as cubic GaN or AlAs—are stable only in the thin film configuration and therefore require thin film measurements. For thin film inves- tigations the higher surface sensitivity of surface acoustic waves SAW’s is utilized, which have the vibration energy localized close to the surface, typically within a region of few wavelengths only. In the presence of a thin film SAW’s become dispersive, i.e., the phase velocity depends on the frequency. Moreover, at certain material parameters and film thicknesses new surface guided modes, e.g., Love or Sezawa modes, arise. 6 Hence, a variety of different acoustic reso- nances are available to derive also the elastic constants of thin films with the necessary high accuracy. It is well known from solid state acoustics that the phase velocity of acoustic waves is influenced by stress, a phenom- enon called the acoustoelastic AE effect. Usually the rela- tive change of the wave velocity is very small, e.g., 10 -5 /MPa for aluminum. 7 Hence, stresses as high as 100 MPa typically applied in bulk experiments alter the phase velocity of the acoustic waves only by about 0.1%. In het- eroepitaxial thin films, however, due to the misfit between film and substrate the residual stress can easily exceed the 1 GPa limit, 8 thus giving rise to phase velocity changes, which no longer are negligible. For the stress dependence it is widely accepted that maxi- mum change of phase velocity appears when the wave is completely localized within the stressed material. Conse- quently the wavelength of SAW’s in layered structures has to be much smaller than the layer i.e., film thickness. In con- trast to this presumption we recently found that the AE effect in stressed layered system assumes significant values for sur- face modes with penetration depths considerably larger than the film thickness. 9 For thin Ge films deposited on Si001 the velocity change of Love modes increases rapidly with frequency and film thickness and reaches almost its maxi- mum value when the wave is still penetrating deeply into the unstressed substrate. In 50 nm thick Ge films biaxially com- pressed by 1 GPa the velocity of the Love modes propagat- ing parallel to the  110 direction changes by about 1% at 10 GHz operation frequency. Recent developments in high fre- quency SAW detection, in particular of surface Brillouin spectroscopy 10,11 and scanning acoustic probe microscopy 12 indeed promise an experimental accuracy of about 1%. Hence, the AE effect has to be carefully considered when recovering exactly the elastic properties of stressed systems by acoustic measurements. In this study we calculated the influence of stress on the wave propagation in single crystalline heterostructures. Our calculations reveal an acoustoelastic anomaly, where the AE effect reaches its maximum value already at film thicknesses considerably smaller than the ultrasonic wavelength. For Rayleigh-type waves we find that the maximum velocity change occurs when the wave is not yet completely localized within the film. An analogous behavior is calculated for higher order Rayleigh modes, so called Sezawa modes, with the maximum velocity changes being even significantly higher. The physical model has been explained in detail elsewhere. 9 The calculations are based on the prototype ge- ometry shown in Fig. 1. A stressed layer is deposited onto a FIG. 1. Sketch of the SAW propagation geometry in a layered system. The x 3 =0 plane is the interface between the layer and the substrate. PHYSICAL REVIEW B, VOLUME 63, 113308 0163-1829/2001/6311/1133084/$15.00 ©2001 The American Physical Society 63 113308-1