Suitability of Raman Spectroscopy for Assessing Anisotropic Strain in Thin Films of Doped Ceria

Abstract

A protocol for characterizing relaxation of anisotropic strain in thin films of 10 mol% Eu-or Sm-doped ceria is described. The method is based on comparison of Raman spectra and X-ray diffraction patterns from substratesupported films, displaying in-plane compressive strain (initial state), with analogous data from 2 mm diameter self-supported films (i.e., membranes), prepared by partial substrate removal (final state). These membranes are found to be relaxed, i.e., approximately unstrained, but with increased unit cell volume. The effective (i.e., 2-state) Grüneisen parameter of the F 2g Raman active mode for these films is calculated to be 0.4 ± 0.1, which is ≈30% of the literature value for the corresponding ceramics under isostatic pressure. On this basis, it is found that the observed red-shift of the F 2g mode frequency following isothermal strain relaxation of the doped ceria thin films cannot be determined solely by the increase in average unit cell volume. The study presented here may shed light on the suitability of Raman spectroscopy as a technique for characterizing strain in lanthanide-doped ceria thin films.

A review of defect structure and chemistry in ceria and its solid solutions

“…Kraynis et al studied the Grüneisen parameter of Eu 3+ and Sm 3+ -doped ceria thin films under biaxial strain relaxation. 209 Similar to the trivalent doping effect discussed above, a value of 0.4-0.6 was found for the equivalent Grüneisen parameter. Gopal et al showed that biaxial strain, whether compressive and tensile, increases the reducibility of CeO 2 thin films.…”

“…Even though an effect of anisotropic strain on Raman shifts of ceria films was reported by various authors, 26,201,209,212 the effect of strain on vibrational lattice dynamics -and thereby Grüneisen parameters remains only partly understood. Iguchi et al 207 suggested that since films of ceria and doped ceria experience anisotropic stress conditions, the Grüneisen relation as derived from high pressure experiments has to be modified for the biaxial modulus.…”

“…208 Most importantly, thin films are usually strained, due to mechanical interaction with the substrate, even when they are polycrystalline. 26,59,209 In epitaxial films, strain is proportional to the mismatch in substrate and film lattice parameters, but also appears in polycrystalline films, due to the deposition process. This strain, can increase or impede the ionic conductivity, e.g.…”

“…Iguchi et al 207 suggested that since films of ceria and doped ceria experience anisotropic stress conditions, the Grüneisen relation as derived from high pressure experiments has to be modified for the biaxial modulus. This approach has also been adapted by Li et al 201 However, deviations from the relation in eqn (35) are also useful to learn about the properties of ceria materials: Kraynis et al 209 directly measured the equivalent Grüneisen parameter for doped ceria thin films, by comparing lattice volume and F 2g peak position between strained thin films and relaxed fee-standing membranes. They found that the F 2g Raman shift correlates qualitatively with the unit cell volume in agreement with eqn (35), but the equivalent Grüneisen parameter under biaxial strain is much lower than under isostatic pressure.…”

All‐Solid‐State Electro‐Chemo‐Mechanical Actuator Operating at Room Temperature

“…Etching a well in the Si substrate produces 2 mm diameter, tethered, circular membranes. Since even after annealing, the sputtered film stack retains residual in‐plane, compressive strain (0.3–0.8%), [ 17 ] the tethered membrane buckles upon substrate removal with buckling depth ≈70 µm (Figure 1d). The membrane thus assumes the shape of a “soup‐bowl” with an almost flat, circular base, ≈1 mm in diameter, surrounded by a petal‐like, wrinkled periphery (see Section S2, Supporting Information).…”