**4. Discussion**

The described experiments reveal high-temperature effects related to structural degradation and irreversible anomalous non-linear thermal expansion behavior in AlScN thin films depending on Sc content and film microstructure. The non-linear thermal expansion is described by a transition from an initial expansion regime to a fast-expanding hightemperature regime which is divided into intrinsic and extrinsic contributions, dependent on the availability of oxygen. Available oxygen is believed to lead to the oxidation of the material dependent on the film microstructure (oxidation was only observed for fiber textured films with higher density of grain boundaries) but also enhances the expansion effect size at *T* > 800 ◦C and stabilizes the increased lattice parameters. The effect size of high-temperature expansion scales with the Sc content of the films, which could be related to a higher defect density leading to the increased destabilization and easier oxidation. A further indicator for the scaling defect density is the increasing magnitude of the peak broadening, which was discussed as an indicator for defect movement as well. Besides dislocations or grain boundaries, point defects such as nitrogen vacancies V<sup>N</sup> are one major type of defect in AlN and AlScN thin films. Previous studies by Harris et al. have demonstrated that the wurtzite-type structure of AlN can incorporate up to 0.75 at% oxygen under thermal equilibrium conditions by substitution of N (ON) associated with the formation of Al vacancies (VAl) [41]. Further insights into the structure relation of AlN films and oxygen are provided by DFT modeling by Gasparotto et al. [42] showing that oxygen can have significant influence on the lattice parameters.

The discussed examples show potential interrelations of oxygen-induced defect structures and changes to the lattice parameters. As observed in this work on AlScN thin films, such phenomena could provide valid explanation for the discussed intrinsic and extrinsic contributions to the anomalous thermal expansion at high temperatures. In addition, Sc has strong affinity for oxygen [43–45], and the intrinsic oxygen contamination of AlScN thin films is supposed to scale with the Sc content as well. In this respect, Sc- and oxygen-enriched grain boundaries were already evidenced [37] and the photoluminescence emission of low-Sc films (x = 0.05) was already revealed to be dominated by oxygen defects [46]. Further, modeling of the point defects in rocksalt AlScN resulted in preferable defect complexes of substitutional and interstitial oxygen (O<sup>N</sup> + O<sup>i</sup> ) [47]. The observed oxygen content-dependent destabilization of the lattice in Al-O-N is also consistent with the increasing degradation of the crystal quality with Sc concentration and the formation of oxide phases.

To support the above discussion, we designed a third sample of a SiNx-capped AlScN film with high concentration of Sc *x* = 0.4 grown epitaxially on a sapphire substrate, i.e., SiNx/Al0.6Sc0.4N(0001)/epi-Mo(110)/AlN(0001)/Al2O3(0001). For such systems, previous work [29] demonstrated that the special epi-Mo(110) electrode provides a growth template for AlScN with one-dimensional single crystalline properties and low defect density. The following assumptions are made: First, the SiN barrier should protect the thin film from oxidation and interaction of oxygen species with the internal defect structure at high temperatures. Second, by choosing a high amount of Sc, any effect magnitude is expected to be large. Third, this AlScN thin film exhibits high crystalline quality with an FWHM~0.7◦ (from XRC) indicating highly oriented columnar grains originating from epitaxial growth and a low defect density. Hence, the effect of any intrinsic, defect-driven anomalous expansion should be strongly limited. Indeed, the recorded thermal expansion during the first temperature cycle shown in Figure 8 shows almost linear expansion featuring no anomalous behavior. This observation, although not expected so clearly, provides supporting evidence for the above hypothesis.

**Figure 8.** *XRD* in situ (with oxygen atmosphere) experiment. Relative change in lattice parameter *c* with temperature for epitaxial SiNx/Al0.6Sc0.4N(0001) on a template of epi-Mo(110)/AlN(0001)/Al2O3(0001) (sample set #3). **Figure 8.** *XRD* in situ (with oxygen atmosphere) experiment. Relative change in lattice parameter *c* with temperature for epitaxial SiNx/Al0.6Sc0.4N(0001) on a template of epi-Mo(110)/AlN(0001)/Al2O<sup>3</sup> (0001) (sample set #3).

In summary, the irreversible changes in the lattice parameters of Al1-xScxN/Al2O3 when exposed to atmospheric oxygen present in low-vacuum conditions are comparable to fiber textured systems. The estimated transition temperatures between the low-temperature expansion and high-temperature expansion regimes and the magnitude of the superimposed intrinsic and extrinsic contributions show a clear trend with the Sc content of the films. With increasing Sc content, the transition temperature is decreased and the effect sizes of thermal expansion and degradation of crystallinity are increased. The anomalous thermal expansion can only be activated by temperature once. Further, the microstructure and possibly the defect structure seem to impact the stability to oxidation of the films, which seems not to be interrelated with the extrinsic part of high-temperature thermal expansion. However, at very high temperatures >800 °C, hypothetically, oxygen species could diffuse into the material via defects and grain boundaries and interact with thermally activated defect sites to further drive the lattice expansion and act as obstacles to stabilize the expanded lattice. Scandium is known to destabilize the AlN lattice by its larger cation size and structural preference for octahedral coordination. Hence, increasing its concentration in AlN could induce higher defect densities, which are seemingly possible to activate at lower temperatures by the flattened energy landscape. In summary, the irreversible changes in the lattice parameters of Al1−xScxN/Al2O<sup>3</sup> when exposed to atmospheric oxygen present in low-vacuum conditions are comparable to fiber textured systems. The estimated transition temperatures between the low-temperature expansion and high-temperature expansion regimes and the magnitude of the superimposed intrinsic and extrinsic contributions show a clear trend with the Sc content of the films. With increasing Sc content, the transition temperature is decreased and the effect sizes of thermal expansion and degradation of crystallinity are increased. The anomalous thermal expansion can only be activated by temperature once. Further, the microstructure and possibly the defect structure seem to impact the stability to oxidation of the films, which seems not to be interrelated with the extrinsic part of high-temperature thermal expansion. However, at very high temperatures >800 ◦C, hypothetically, oxygen species could diffuse into the material via defects and grain boundaries and interact with thermally activated defect sites to further drive the lattice expansion and act as obstacles to stabilize the expanded lattice. Scandium is known to destabilize the AlN lattice by its larger cation size and structural preference for octahedral coordination. Hence, increasing its concentration in AlN could induce higher defect densities, which are seemingly possible to activate at lower temperatures by the flattened energy landscape.
