Correction to: Co-sputtering of Al1−xScxN thin films on Pt(111): a characterization by Raman and IR spectroscopies

Nature 2020 ABSTRACT In this work, aluminium scandium nitride (Al1 xScxN) thin films are deposited by reactive DC magnetron co-sputtering on Pt(111) layers. The sputtering power of the Sc target is varied in a broad range up to 900 W to effectively vary the Sc content later assessed using energy-dispersive X-ray spectroscopy (EDX). We show that commonly used X-ray diffraction techniques may yield ambiguous results, and thus, additional verification is crucial to substantiate the actual composition of the sputtered thin films. Therefore, we employ optical spectroscopy techniques, such as Raman and Fourier transformed infra-red (FTIR) spectroscopies in order to study the vibrational properties of the alloys. Our Raman spectra show that low Sc content leads to a phase separation with the formation of cubic ScN and AlScN phases during the sputtering process. Nevertheless, small amounts of the wurtzite phase are detected in the rock-salt dominated samples owing to the enhancement of the A1(LO) phonon mode by the Berreman effect in the FTIR spectra. The Sc-induced shifts of the AlN phonon modes are determined in a broad range of Sc content.


Introduction
The alloys of aluminium nitride (AlN) with group III atoms, such as Scandium and Yttrium, are known to exhibit improved piezoelectric performance in comparison with pure AlN. The formation of purely wurtzite alloys remains a challenging task due to the complex phase diagram with pure wurtzite and rocksalt (ScN) phases at the extremities. Aluminium nitride, a III-V wide-band gap semiconductor, is successfully utilized as a piezoactive layer in various modern micro-electro-mechanical systems [1,2]. Such prevalence of AlN-based devices stems from the possibility of the low-temperature wafer-scale synthesis of AlN, its compatibility with CMOS technology, and environmental considerations [3,4]. Nevertheless, the quality of the piezoelectric performance of AlN is rather low [5][6][7] in comparison with prominent piezoelectric materials, such as lead zirconate titanate [8], and slightly lower than another tetrahedrally bonded semiconductor, ZnO [9]. This inherently limits its broader application. One common solution for the improvement of piezoelectric coefficients of AlN is alloying with Sc atoms [10,11], which was shown to increase the d 33 piezoelectric constant up to 400% in the case of 43% Sc content in the ternary AlScN compound [12]. This effect was shown to be linked to the modification of the wurtzite matrix by Sc atoms, which results in the softening of the structure manifested by the decrease in the stiffness constants and the increase in the internal strain [13,14]. The precise Sc incorporation, however, remains challenging due to a complex phase diagram, where a simultaneous formation of wurtzite, hexagonal, and cubic phases of Al xÀ1 Sc x N as well as its parental phases cannot be fully avoided [12,15]. Provided that the growth method of choice for industrial applications is reactive magnetron sputtering (RMS), an accurate control over the phase formation is impeded by the stochastic nature of this method. Nevertheless, it was successfully demonstrated that RMS is capable to produce AlScN thin films of a considerable crystalline quality [10,16]. The influence of growth conditions and underlying substrates on the formation of AlScN utilizing tilted targets of Al and Sc, which are co-sputtered with pure N 2 gas under vacuum conditions of about 1 Pa, was investigated. [17,18]. The quality of AlScN films can be further improved by normal-incidence sputtering of a single target with an Al-Sc alloy [11,19,20], which, however, limits the variation of the compositional ratio between the metal atoms.
Due to the intricate phase diagram of the AlScN alloy, where AlN is predominantly wurtzite on one end, whereas ScN is predominantly cubic on the other one, careful determination of the intermediate stages must be performed. At present, such samples are routinely studied by X-ray diffraction (XRD) [10,16,21], which mainly provides information on the phase composition, the orientation, and the size of AlScN grains. Yet, the success of this method is prone to large volumes of the crystallites probed, and thus, it is not suitable for very thin films or layers within the films. Moreover, it is difficult to distinguish between the alloy broadening, which is typical for such crystals, and the structural disorder in the samples by analysing XRD data. An alternative way to investigate the structural quality of AlScN films is to employ optical methods, such as Raman and infrared (IR) spectroscopies. Both techniques provide the phonon properties of crystals, which allow the geometric and compositional changes upon alloying to be tracked with high sensitivity and measurement speed, being essential for the industrial manufacturing of AlScN. Moreover, the optical methods have negligible limitations towards the crystallite size or film thicknesses, making them extremely suitable for studies of binary and ternary III-V compounds [22].
However, the measured spectra cannot be approached in a straightforward manner as in the case of X-ray diffractograms, directly extracting the orientation and inter-planar distances of a crystal without a prior calibration. Deng et al. [23] showed the relation between the positions of the spectral bands and the Sc content, demonstrating that the Sc alloying of AlN leads to the softening of its vibrational modes as a result of an increased ionicity, leading to the decrease in bond angles and their extension. In the range of the Sc content investigated (up to 16%), the alloy is supposed to retain the wurtzite structure since the formation of the other phases, mainly, the cubic one, is expected at higher Sc content (around 40%). However, the vanishing of the spectral band of wurtzite AlN (E 2 (high)) can be seen in the Raman spectra already at 10% of Sc. This suggests that either no wurtzite phase is formed at such low Sc content or the sensitivity of the experimental set-up was not sufficient for its detection. The latter can be improved using an excitation wavelength closer to the optical absorption edge, which, in the case of AlScN, lies in the UV range (ca. 6 eV) [24].
In this work, we study the dependence of the Sc content related to the sputtering power of the corresponding target on the vibrational properties of Al 1Àx Sc x N thin films. We show that the optical spectroscopy results can be used to detect various crystalline phases formed during the co-sputtering procedure surpassing the sensitivity of the XRD results. In particular, we observe the formation of the wurtzite phase in the case of the highest Sc content via the presence of the A 1 (LO) mode in the IR spectrum because of the Berreman enhancement mechanism. Combining the evidence from the methods used, we conclude that the Al 1Àx Sc x N films grown with high Sc content relative to Al exhibit the presence of wurtzite-like and cubic-like alloys. The compositional disorder seems to remain a common outcome of the magnetron sputtering of Al 1Àx Sc x N films.

Experimental details
The Al 1Àx Sc x N thin films were prepared utilizing reactive magnetron sputtering from pure Al and Sc targets with a size of 236 mm using a MS150x4 AE-B set-up (FHR Anlagenbau GmbH, Germany). (100)oriented Si wafers of 150 mm in diameter with 500 nm SiO 2 and 100 nm Si 3 N 4 layers were used as substrates onto which an underlying thin Pt film of 100 nm on a buffer of 20 nm Ti was deposited for all samples completing the multi-layer stack used in the MEMS devices. During the deposition process, the substrates were heated to 350 C . The chamber was evacuated to a base pressure of 7 Â 10 À3 Pa. A pure N 2 flow of 200 sccm was introduced into the chamber as sputtering gas. During the thin film deposition, the power of the Al target was constant at 1000 W corresponding to a power density of 0:9 W Á cm À2 , while the power of the Sc target, P Sc , was varied from 0 to 900 W corresponding to a variation in power density up to 0:8 W Á cm À2 in order to grow Al 1Àx Sc x N thin films with different Sc concentration. As the pulsed direct current sputtering method was used, no arcing between the charged elements was observed. The X-ray diffraction (XRD) measurements, 2h=h scans, were performed using a Rigaku Smartlab diffractometer equipped with a Ge(220) 2-bounce monochromator providing CuKa radiation at a wavelength of 1.5406 Å . The scans were fitted with pseudo-Voigt functions. The energy-dispersive spectrometry of X-rays (EDX) was performed using a Scanning Electron Microscope Nova NanoSEM (FEI) with Schottky field emission gun. The measurements to determine the scandium content of the films by the aluminium and scandium Ka-lines were performed using an Al X-ray source at the acceleration voltage of 15 kV. It is well known that a precise assessment of the N content by EDX is difficult since the nitrogen Ka-and scandium La-lines are largely superimposed [17,18]. Therefore, the estimation of the scandium concentrations was performed without consideration of nitrogen relating it to aluminium and scandium contents in atomic percent. The Raman scattering experiments were performed with a Lab-Ram HR800 micro-Raman system at room temperature. The excitation source was a k ¼ 514.7 nm line from a Cobolt DPSS laser with a power of 0.83 mW. The laser beam was focused on the sample surface with a 100Â objective lens (NA=0.9) and then the scattering light was dispersed by a 600 ln Á mm À1 diffraction grating with a spectral resolution of 3:1 cm À1 . The Raman spectra were recorded with a charge-coupled device (CCD) detector in the zðxxÞ z backscattering configuration. The k ¼ 325:0 nm line of a HeCd laser with a power of 4.74 mW was also used in this study. For the latter, the light was focused using a 40Â objective and a 2400 ln Á mm À1 grating was used with a spectral resolution of 2:3 cm À1 . Infrared reflectance spectra in the mid-IR range (400 À À6500 cm À1 ) were obtained using a Bruker Vertex 80v FTIR spectrometer with a spectral resolution of 4 cm À1 . An angle of incidence of 75 was chosen to excite phonon modes polarized perpendicular to the film surface. The analysis of FTIR reflectance spectra was performed with the SCOUT software [25]. The thicknesses of the grown Al 1Àx Sc x N thin films were determined as a result of the spectral fitting showing a variation in the range of 100-300 nm. The surface morphology of the samples was obtained and analysed by an atomic force microscopy (AFM) Keysight 5500 operating in tapping mode with a tip apex radius of 10 nm. Roughness and grain size were determined using the Gwyddion software [26].

Results and discussion
The Sc content in Al 1Àx Sc x N can be varied with the sputtering power of the Sc target [17,18]. Provided that the power is directly proportional to the sputtering rate, it is surmised that the amount of Sc incorporated in the films is proportional to it as well. The proportionality is demonstrated, when the fraction of Sc atoms, determined using EDX data, is plotted as a function of the sputtering power (Fig.1a). The type of relation between the Sc content and the sputtering power is revealed by fitting the experimental data with a Boltzmann sigmoid. This function commonly describes processes of continuous transitions between two states triggered by an external factor. Such transitions are especially common for physical vapour deposition techniques such as reactive co-sputtering [27,28].
Even though the Sc content in AlScN can be tuned by the power of the Sc target suggesting that Sc fully incorporates into the AlN matrix during the deposition, it may not be the only outcome of such deposition. In order to substantiate the premise of the AlScN alloying, X-ray diffraction profiles of the samples were recorded (Fig.1b). The diffractogram of the pristine AlN film (P Sc ¼ 0 W) exhibits two narrow peaks around 35:97 and 40:06 , which are attributed to the (002) plane of wurtzite AlN and the (111) plane of the Pt underlayer, respectively. The broad background between the peaks originates from their overlap with another, weaker, peak around 37:36 , which may be assigned to the diffraction from the (101) plane of wurtzite AlN as no other possible candidates were identified. The narrow peak at 40 also shows a shoulder at lower angles with a maximum around 39:81 , which is attributed to the (110) plane of Ti, deposited as a buffer layer between Si 3 N 4 and Pt layers. No contributions from other underlayers (SiO 2 , Si 3 N 4 ) are observed, which corroborates their amorphous nature. Even though highly c-axis textured AlN films are expected to form on Pt(111) [29], a misorientation of the grains occurs as a result of the geometry of the sputtering chamber, including the tilted Al target [30], which is an unavoidable condition for the co-sputtering technique, and the short distance between the target and the substrate. The latter plays a crucial role on the distribution of the sputtered ions in RMS [31]. Nevertheless, the amount of AlN grains, oriented with the c axis normal to the substrate, dominates over the tilted ones as inferred from the intensity ratio of the (002) and (101) peaks.
For the films prepared at low power supplied to the Sc target, which corresponds to Sc contents of 23-42%, the reduction of an intensity, a broadening, and a shift towards lower angles for the (002) peak are observed. However, as the power of Sc target sputtering increases further, a peak around 36 distinctly emerges gaining in intensity and shifting towards lower angles proportionally to the Sc content in the range of 48-67%. For the highest Sc content, the diffractogram shows two clear peaks at 35 (labelled as ''I.'' and ''II.''), as well as another one at 37:76 (labelled as ''III.'') (Fig.1b). The peak ''III.'' is more intense in comparison with the one observed in the diffractogram of pure AlN and is possibly related to the formation of the abnormally oriented grains [18,32]. The origin of the peaks at around 35 should be scrutinized. It is characterized by a large linewidth and a clear asymmetry, originating from two contributions (''I.'' and ''II.'') revealed by the fitting. Hence, we can discuss them separately. The maximum of the contribution ''II.'' lies at a 2h angle, which is well below the one corresponding to the (002) plane of wurtzite AlN. It is known that the substitution of Al atom by Sc atoms in AlN can result in the shift of the (002) diffraction peak towards lower angles at small Sc concentrations (\ 25 %) [10,16,20] as well as higher ones for the concentrations above 25 % [18,33] due to increasing and decreasing of the c-lattice constant, respectively. Thus, this peak cannot be assigned to the hexagonal Al 1Àx Sc x N alloy, since the (002)-peak should shift towards higher angles at such high () 50%) Sc content. At the same time, the peak may belong to highly strained AlN, which is often observed in sputtered films. Despite the fact that it seems unlikely to observe pure AlN, when a large number of Sc atoms is simultaneously co-sputtered, we shall not exclude the possibility of a phase separation. The contribution ''I.'' could be related to the (111) plane of cubic ScN (ca. 34:5 [34,35]) if it is under large tensile strain. Such an interpretation seems more likely since the Al 1Àx Sc x N alloy with a Sc content ! 50% predominantly forms in the rock-salt crystal structure [15], therefore, rs-ScN, if separated, may be well primed by the already-formed rock-salt alloy. The formation of cubic AlN might be also considered being primed by the ScN domains, however, since it requires relatively high formation temperatures ( ! 1000 C), the probability of its formation is rather low. Thus, the sample with the highest Sc content may contain two cubic phases: rs-ScN and rs-Al 1Àx Sc x N alloy. Such growth process, which leads to multi-phase formation, is also supported by the analysis of the surface morphology obtained from the AFM measurements showing an average grain size in the order of 30 nm (cf. Supplemental Information). Despite the likelihood of the interpretation, while being based solely on the XRD results, it is ambiguous owing to small sizes of grains and the poor texturing [36]. Figure 2 shows a set of Raman spectra recorded from the Al 1Àx Sc x N films grown with varied Sc content. The spectrum of pure AlN shows a strong narrow peak at 654:9 cm À1 and a weak broad peak centred around 880 cm À1 (Fig. 2a). These Raman bands can be assigned to E 2 (high) and A 1 (LO) phonon modes, respectively [22,37,38]. In general, the AlN crystal may exhibit up to six Raman bands, related to six zone-centre optical phonon modes (A 1 (TO), A 1 (LO), E 1 (TO), E 1 (LO) and 2 E 2 modes) depending on the scattering configuration [22]. Such large number of optical phonons reflects the anisotropy of the wurtzite (point group: C 6v ) polar crystal, for which splitting of the phonon modes along the ordinary and extraordinary optical axis as well as splitting between transverse and longitudinal modes are expected [39,40]. In the present configuration, only E 2 -and A 1 -symmetry modes are observable accounting for the highly oriented c-axis growth of AlN films. The absence of the E 2 (low) mode in the Raman spectrum is explained by the low thickness of the film, while the weak A 1 (LO) mode corroborates the dominant orientation of the crystal grains along the c-axis.
As the power of Sc sputtering is increased yielding a Sc content of 23%, a redshift and broadening of the E 2 (high) phonon mode are observed. The further increase in the Sc amount results in the vanishing of the wurtzite-related Raman bands. This is interpreted as the deterioration of wz-structure in the Al 1Àx Sc x N solid solution, which agrees with the XRD results. The Raman spectra of the samples with a high Sc content ([40%) exhibit one major broad band centred around 715 cm À1 . This band persistently appears in the spectra of the samples deposited with a high Sc power. Also a weaker band around 1010 cm À1 gains in intensity proportionally to the Sc content. The frequency of the E 2 (high) band in the pristine AlN thin film is lower by 2:5 cm À1 than the value of bulk material, 657:4 cm À1 , reported by Davydov et al. [41]. The frequency difference is attributed to the internal tensile strain naturally appearing in thin films prepared by reactive magnetron sputtering [38,42]. The inverse relation between the phonon lifetime and the fullwidth at half maximum (FWHM) of a corresponding Raman peak allows the crystal quality of thin films to be assessed [43]. The FWHM of the E 2 (high) band is 22:4 cm À1 , which is larger than the one of a high quality AlN bulk crystal, which was reported by Kuball et al. [44] to be around 3 cm À1 or even the one of AlN films produced by magnetron sputtering [45]. This corroborates the high level of defect density in the deposited thin films. With increase in Sc content, the E 2 (high) mode shifts from 654.9 to 647:6 cm À1 and the FWHM increases from 22.4 to 44:0 cm À1 , indicating the bond softening and increasing disorder in the wurtzite Al 1Àx Sc x N lattice due to the incorporation of Sc atoms as reported by Deng et al. [23]. The broad spectral feature around 715 cm À1 , observed in the spectra of the samples with a Sc content [ 25%, could be associated with the contribution of the rock-salt structure in the alloys [46][47][48][49][50]. One-phonon bands are Raman-inactive in a crystal with the rock-salt structure because of symmetry considerations [51]. Thus, this broad band can be attributed to multiple-phonon Raman scattering such as (i) second-order phonon scattering or (ii) defect-induced phonon density of states (pDOS) [46]. According to the density of states of rock-salt AlN reported by Manjó n et al. [46], the broad band at 715 cm À1 can combine the contribution of TA?TO(L) phonon modes near 700 cm À1 , and the one from TA?TO(C-K-X-L) modes at approximately 760 cm À1 . On the other hand, the high density of defects can relax the Raman selection rules and thus the pDOS of rs-AlN or rs-ScN can also be observed. According to the pDOS of rs-AlN, a high density of states is located around 700 cm À1 , which is associated with the LO(X) phonon mode [46,47], being close to the frequency observed. From the theoretical studies of rs-ScN by Paudel et al. [48], the pDOS shows a high density of states at about 657 cm À1 , which corresponds to the LO(L) phonon mode. Such mode of rs-ScN was experimentally reported at 677 cm À1 [48][49][50]. One can see that the phonon modes of the rock-salt compounds are found in the spectral range of 657-760 cm À1 . Therefore, we cannot unambiguously distinguish between rs-AlN and rs-ScN phases as well as the alloy of rs-Al 1Àx Sc x N; however, it is clear that the very broad band centred around 715 cm À1 belongs to one of these cubic phases or their combination.
In order to exclude the possibility to assign the observed modes to species, which are unrelated to AlN or Al 1Àx Sc x N, we recorded Raman spectra using an UV excitation source, which improves the Raman intensity of the AlN bands approaching the conditions for the resonance Raman scattering. Additionally, the short-wavelength excitation also has a lower penetration depth as the absorption coefficient commences to increase with higher energies. Such situation is beneficial for the investigation of thin films since a larger amount of scattered light originates from the film itself and thus the spectrum is less influenced by the light scattered of the substrate. The penetration depth dðkÞ for a semiconductor is approximated by dðkÞ ¼ 1=aðkÞ, where a is the absorption coefficient. Due to the back-scattering geometry, the light propagates inside a thin film twice: along the incident and scattered channels. Hence, the equation, which describes the information depth is d % 1=ð2aÞ [52,53]. Using this equation and the values of a for AlN, reported by Zarwasch et al. [54], we estimate the penetration depths for the laserlines used for our measurements: dð514:7Þ %190 nm and dð325:0Þ %7 nm. Figure 2b shows the Raman spectra of the samples recorded using the k=325 nm laserline. The E 2 (high) and A 1 (LO) modes for pristine wz-AlN are detected at about 654:5 cm À1 and 880:3 cm À1 . The mode positions are found in a very good agreement with the ones recorded using k exc ¼ 514:7 nm (within an error bar of 0:4 cm À1 ), which indicates the out-ofplane homogeneity of the thin film. The FWHM of the E 2 (high) band is 20:3 cm À1 . The Raman peak of the A 1 (LO) mode has a more pronounced appearance. Both the A 1 (LO) band and the narrow peak of the E 2 (high) mode suggest a smaller defect density close to the surface of the thin film in comparison with the average one obtained with longer excitation wavelength. The trends in Raman spectra with increase in Sc content are also reproduced. The E 2 (high) mode can be followed only at very low Sc concentrations. Starting from the sample with a Sc content of 42%, which corresponds to P Sc ¼ 400 W, only broad spectral features located in the range of 600-900 cm À1 are seen. We treat these bands as a whole since their fine structure is obscure due to low signals and thus a visible impact of the detector sensitivity. The latter is indicated by the jagged spectral profile. The linewidths of these broad bands in Fig. 2b are in the range of 140-180 cm À1 , which is broader than the ones observed with k exc ¼ 514:7 nm. This can indicate that there is an additional mechanism that decreases the phonon lifetime, in particular, free charge carriers excited with the k exc =325 nm laserline and trapped at oxygen vacancies [55].
By comparing the spectra recorded using two different excitation energies, the peak marked with asterisk at 819:6 cm À1 and the peak at 1015 cm À1 (Figure 2a) can be assigned. The Al 1Àx Sc x thin films were grown with a thickness in the range of 100-200 nm. Taking into account the penetration depth of the k ¼ 514:7 nm laserline (d a ð514:7Þ % 190 nm), these bands could originate from the underlying Pt layer, and thus, one possible assignment for these peaks is PtN 2 [56].
The observed redshift and the broadening of the E 2 (high) band due to the incorporation of Sc atoms, clearly indicate the deterioration of the wurtzite Al 1Àx Sc x N phase. However, its dependence on Sc content cannot be followed at high Sc content values. This might be interpreted as the absence of the wurtzite phase for x ! 0.25. In fact, the rock-salt phase should dominate in a solid solution only for x ! 0.5, in accordance with the calculated mixing enthalpy in this ternary alloy reported by Hö glund et al. [15]. Yet, the amount of rock-salt structures seems to dominate at low Sc concentration, when judged from Raman data only. Nevertheless, the Raman results confirm previous reports, allowing only qualitative analysis in the case of Sc-rich Al 1Àx Sc x N alloys. Figure 3a shows the FTIR reflectance spectra of the Al 1Àx Sc x N samples deposited with varied Sc content recorded at room temperature. The IR spectrum of pure AlN exhibits 3 bands at 611:1 cm À1 , 665:0 cm À1 , and 889:3 cm À1 , which correspond to A 1 (TO), E 1 (TO), and A 1 (LO) phonon modes of wz-AlN, respectively. The frequencies are shifted in comparison with the bulk values of 611:0 cm À1 , 670:8 cm À1 , and 890:0 cm À1 [41]. This mismatch is attributed to biaxial strain in the AlN thin film [57], verifying the XRD and Raman results.
The bands related to the transverse modes exhibit an intensity much lower than the one of the longitudinal phonon (Fig. 3a, inset). The strong intensity of the A 1 (LO) band is caused by the Berreman effect (BE) [58]. The BE can be observed in an ultra-thin film deposited on a metallic substrate having a thickness much less than the wavelength of the incident light. The surface charges in metal excited by the normal component of electric field generate a resonance at longitudinal optical mode frequencies [59].
It corresponds to the frequency at which the real part of the dielectric function of a crystal approaches zero [60,61], which corresponds to the LO modes in a polar crystal. In the case of AlN films with high c-axis orientation, the coupling with the metallic substrate via the Berreman effect concerns the A 1 (LO) mode only [62]. At the oblique incidence of unpolarized light, both TO and LO modes are detected simultaneously since the electric field of unpolarized light has components, which are parallel and perpendicular to the surface of the film. On the other hand, the proximity of the AlN film to the Pt layer has the side effect of suppressing the TO modes because the electric field within a film is strongly weakened [59].
With an increase in the Sc content, the A 1 (LO) mode clearly exhibits a redshift and an intensity loss. For the Sc content of 67%, the position of the mode reaches ca. 790 cm À1 , being softened by over 100 cm À1 with respect to the case of pure AlN. Similar trends can be observed for the transverse phonon modes as well, but, due of their low intensity, their tracking is complicated. We explain this behaviour by the Al-N bond softening and a reduction in the crystalline quality of the films as a result of the incorporation of Sc atoms. The latter is corroborated by the broadening of this mode, which becomes broader as more Sc atoms are alloyed into the AlN lattice.
Generally, the simulation of the optical properties of layer stacks is mandatory for the analysis of FTIR spectra since the interplay between mode parameters, layer thicknesses, and refractive indices of the layers affects positions and shapes of IR bands. The samples are considered as a stack of 4 layers, which consists of (i) a thin film layer of deposited Al 1Àx Sc x N alloy with thickness d; (ii) a 100 nm Pt layer; (iii) a 500 nm silicon dioxide film; (iv) and a semi-infinite layer of the Si substrate. In order to describe the scattering losses at the surface, we also applied a roughness layer on top of the Al 1Àx Sc x N layer. The complete layer structure is shown in Figure 3b. The A 1 and E 1 transverse optical phonon modes of Al 1Àx Sc x N were modelled using the Kim oscillator function, which is an extension of the harmonic oscillator model with a flexible broadening parameter [63]. The choice of this model is motivated by the consistency in the fitting of the results of the vibrational spectroscopy measurements. The complex dielectric function is given by: The parameter r k ! 0 is the so-called Gauss-Lorentzswitch and used to introduce the Gaussian broadening in addition to the Lorentzian one coupled to the damping factor c k ðxÞ [64]. The position of LO modes depends on the resonance frequency of oscillators and can be described with the energy loss function, The simulated spectra nearly perfectly overlap with the experimental data (Fig. 3a). This allows not only an accurate determination of the position of the LO mode but also the determination of the transverse phonon frequencies. The latter directly comprises the dielectric function model. Thus, the phonon frequencies are plotted as a function of the Sc content (Fig.3c). Linear negative slopes are found and fitted for each mode: x A 1 ðLOÞ ¼ð895:4 À 135:8 Á xÞcm À1 ð3Þ x E 1 ðTOÞ ¼ð675:1 À 114 Á xÞcm À1 ð4Þ x A 1 ðTOÞ ¼ð618:2 À 95:3 Á xÞcm À1 ð5Þ Up to a Sc content of 58%, the modes linearly shift towards lower energies. When the Sc concentration is above 58%, the intensity of the transverse modes dramatically drops. This introduces a considerable uncertainty in the determination of their positions and hence they should not be trusted. However, the trend of the longitudinal mode remains linear even at high concentrations of Sc. This indicates the presence of the wurtzite phase in seemingly rock-salt dominating part of the Al 1Àx Sc x N phase diagram [15]. However, the size of the crystallites with wurtzite structure is small and thus their presence cannot be deduced from the XRD results. At the same time, the crystallites with the rock-salt structure must also be considerably small and show no preferable orientation, as judged from the XRD results and confirmed by the absence of the phonon mode of ScN around 363 cm À1 in the far-IR region [50] (not shown). Nevertheless, the presence of the rock-salt structure cannot be debated taking into account the Raman results. Using our FTIR data, the alloying also affects the effective value of the high-frequency dielectric constant, obtained from fitting results: 1 ¼ 3:45 þ 2:27 Á x. Its direct proportionality to the Sc content indicates the semi-metallic nature of ScN [50]. Despite that the linear dependence of the highfrequency dielectric constant agrees with the previously published reports [23], a difference in the values is observed. The lower values of the optical dielectric constant stem from a low density of the films produced, being decreased by the crystalline grains of non-AlN origin as well as voids.

Conclusion
The dependence of the structural properties of Al 1Àx Sc x N thin films deposited on Pt(111) by reactive magnetron co-sputtering with varied power applied to the Sc target is studied. The sputtering power is proportional to the amount of deposited Sc atoms within the Boltzmann sigmoidal framework. The alloying of AlN with Sc atoms is observed via the combination of diffraction and optical spectroscopy techniques, which enabled the multiple phase coformation to be unravelled. Both Raman spectroscopy and XRD results clearly indicate the presence of cubic Al 1Àx Sc x N and ScN phases for Sc contents of[ 25% but cease to detect a wurtzite phase entirely. The latter problem is circumvented by the infrared reflectance measurements, which demonstrate high sensitivity of the detection possible due to the Berreman effect, enhancing the signal in the proximity of the metallic underlayer. In particular, the red-shift of the A 1 (LO) mode, stemming from the Sc-induced softening of the hexagonal lattice of AlN, is shown to be directly proportional to the Sc amount, and thus, it can be used for its determination in the solid Al 1Àx Sc x N solutions. This allows us to surmise the effective piezoelectric performance of such thin films, being strongly dependent on the amount of the crystallites with the rock-salt structure, prior to a laborious quantification of the piezoelectric tensor.