(Digital Presentation) Characterization of Anisotropic Strain in Anelastic Material By Raman Spectroscopy
Authors: Freidzon Daniel , Kraynis Olga , Wachtel Ellen , Lubomirsky Igor , Livneh Tsachi 
Published: July 2022

Raman spectroscopy has recently been applied for non-destructive characterization of strain in crystalline thin films. It makes use of the numerical value of the mode Grüneisen parameter γ , which equals (minus) the ratio of the relative change in the frequency of a Raman-active vibrational mode and the strain-induced relative change in the unit cell volume. In the presence of in-plane, compressive biaxial strain, aliovalent doped CeO2-films exhibit values of γ which are ~30% smaller than the literature values for the bulk ceramics under isostatic stress. This discrepancy is due in large part to the negative contribution from the anelastic (time-dependent) mechanical properties of oxygen-deficient ceria, thereby raising questions concerning the relationship between Raman mode frequency and anelastic strain. Here we propose a way to "separate" anelastic and elastic contributions to the Grüneisen parameter.

500-650nm thick films , x=0.1-0.2, were deposited by RF magnetron sputtering on (100) p-Si wafers (1Ω-cm, tSi=280mm). The films (S-films) were in the fluorite phase with pronounced (111) texture and exhibited biaxial , compressive strain. The in- and out-of-plane lattice parameters (aS
||
, aS
⊥

) of the S-films were determined by XRD at different sample tilt angles. The in-plane stress (σbi) in the S-films was determined by profilometry from the change in Si-wafer curvature following film deposition. From σbi and the film biaxial modulus, the elastic component of the in-plane compressive strain (ue
) was calculated (~ -0.2%).

Strain-free (relaxed) R-films were obtained by partial substrate removal, forming 2 mm diameter self-supported membranes. Pronounced membrane buckling indicated that residual strain was negligible (aR
||
≈ aR

^

). From the increase in area upon substrate removal, measured with optical profilometry, the total S-film in-plane strain (ut
) was calculated from aS
||/aR-1 ≈ -0.5%. The anelastic strain component may be calculated as ua= ut-ue
. The small, anisotropic strain-induced blue shift of the frequency of the F2g
-phonon mode for S-films suggests that the F2g
mode responds primarily to the elastic component of the strain.

As a control, 430nm thick films of mechanically elastic Y2O3 were deposited by sputtering on a Si wafer covered with a 1.5 µm thick PECVD deposited SiO2 layer. This layer supported the Y2O3-films upon membrane formation, but prevented complete strain relaxation. The Y2O3-films were in the double fluorite phase with strong (222) texture and, as with the S-films, were under in-plane compressive strain. The Y2O3 S-film lattice parameters were determined by acquiring XRD-patterns at different sample tilt angles, while membrane in- and out-of-plane lattice parameters were determined with XRD in the transmission and reflection modes, respectively. The values of γ calculated from the Raman frequency of the [Fg
+Ag
] peak position were close to the literature values for bulk yttria under isostatic stress.

This work should serve as a sample protocol for strain characterization of doped ceria thin films. It supports the concept that the discrepancy between the behavior of Raman modes of isostatically and anisotropically strained doped ceria is related to anelasticity. Our results shed light upon strain characterization by Raman spectroscopy and may lay the foundation for future studies to elucidate selective sensitivity to various strain components.