**1. Introduction**

Among the various fields of application of Al1-xScxN films, analog signal processing devices for mobile communication play a preeminent role. The working principle of such devices, such as frequency filters and delay lines, is based on bulk or surface acoustic waves (BAW and SAW, respectively). The main reason for the growing interest in AlScN films constitutes their favorable piezoelectric and mechanical properties [1–3]. Piezoelectric properties of this ternary nitride can be enhanced by increasing the scandium concentration x, which has consequences for the electromechanical coupling and also for the elastic properties and hence the velocities of acoustic waves [4–6]. For the design of signal processing devices containing AlScN films, knowledge of the elastic constants is of paramount importance.

For the determination of elastic constants of AlScN films, a fast, non-destructive, and easy-to-handle method is called for. Optimally, such a method could also be employed for quality control of AlScN films. A particular challenge in the case of epitaxial AlScN films is the large number of material constants that have to be determined. The main goal of

**Citation:** Mayer, E.A.; Rogall, O.; Ding, A.; Nair, A.; Žukauskaite, A.; ˙ Pupyrev, P.D.; Lomonosov, A.M.; Mayer, A.P. Laser Ultrasound Investigations of AlScN(0001) and AlScN(11-20) Thin Films Prepared by Magnetron Sputter Epitaxy on Sapphire Substrates. *Micromachines* **2022**, *13*, 1698. https://doi.org/ 10.3390/mi13101698

Academic Editor: Alexandra Joshi-Imre

Received: 12 August 2022 Accepted: 29 September 2022 Published: 9 October 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

this study is to demonstrate that laser ultrasound (LU) is an attractive technique for this purpose.

In the past, elastic constants of AlScN films have been determined with Brillouin scattering [7–9] and via electrical excitation of acoustic vibrations, especially with the help of SAW resonators (called resonator method in the following) [10,11] or delay lines [12] (for a review see for example [10]). However, preparing SAW or other types of resonators requires advanced fabrication capabilities to obtain the full dispersion curves from multiple test structures (phase velocity as a function of frequency).

The piezoelectric constants are yet out of reach for our laser ultrasound set-up. This problem is shared with Brillouin scattering, another non-destructive optical method, which (as with LU) does not require any specific modifications of the sample, unlike the resonator method. However, the LU approach needs much shorter measurement times, especially when being partially automated. A full SAW dispersion curve is obtained in one measurement cycle, taking about 30 min. The propagation direction on the surface can be varied without extra effort. This allows to efficiently exploit the anisotropy of the substrate to determine film properties from SAW dispersion curves, as was done here to investigate the highly anisotropic AlScN-on-sapphire systems. We show here that valuable information can be gained with comparatively robust and inexpensive instrumentation. For additional benchmarking of our experimental approach, a comparison to the results of ab initio calculations, using the density functional theory can be performed [5,13–15]. Here, we compare SAW dispersion curves obtained by LU to those calculated with the most recently published theoretical data on material constants of AlScN [5].

In the past, the determinations of elastic properties of thin films by laser ultrasound were mostly confined to isotropic films. (The only exception known to us are diamond films [16] and a pre-study of AlScN films [17]).

In our previous study, we showed that LU can be used to characterize textured AlScN(0001) films on silicon Si(001) substrates [17]. In these samples, the acoustic pulses were generated by laser pulses at the interface between the transparent AlScN film and the opaque silicon substrate. The fact that sapphire substrates are also transparent to the laser light constitutes an additional challenge and requires a metal layer to absorb the laser pulse. More recently, in-plane oriented AlScN(0001) films were grown on sapphire Al2O3(0001) substrates by magnetron sputter epitaxy [18] and then used for SAW resonator fabrication. The motivation was two-fold: sapphire substrate enables higher phase velocity and higher frequency of SAW and at the same time the higher material quality leads to improved electromechanical coupling and quality factor Q [19]. In order to further increase electromechanical coupling keff 2 , epitaxial a-plane (non-polar) AlScN(11-20) SAW structures were successfully achieved on r-plane Al2O3(1-102) [20,21]. By aligning the SAW propagation direction with the piezoelectric constant d33, an additional 85% improvement in keff <sup>2</sup> was demonstrated. In these earlier studies, a substrate off-cut angle was shown to strongly influence the crystalline quality of AlScN. As the ability to deposit high-quality non-polar AlScN is a rather recent discovery [22], no measurements of elastic constants have been reported so far. In this work we propose using LU to estimate the elastic properties of Al0.77Sc0.23N(11-20)/Al2O3(1-102), especially focusing on high anisotropy in this material system.

The paper is organized in the following way. In Section 2, the geometries of the systems investigated in this work are defined and their fabrication process and characterization are described. Moreover, details of the LU technique, as applied to the investigation of AlScN films, are given.

In the first part of Section 3, the results of our investigations of the elastic properties of the sapphire substrates are presented. This knowledge is a prerequisite for the determination of film properties by SAW-based LU. Values for the elastic moduli of sapphire were compiled from the literature. They were used as input for simulations of the SAW slowness curves of c-plane and r-plane sapphire. Simulated SAW velocities are compared with corresponding LU measurement results.

Next, experimental data are presented for dispersion curves of SAW propagating in Al0.77Sc0.23N films. Both AlScN(0001)/Al2O3(0001) and AlScN(11-20)/Al2O3(1-102) were investigated. These first LU measurement results for AlScN films on sapphire are compared with simulated dispersion curves using the ab initio elastic and piezoelectric constants of [5]. Very good agreement is found between theory and experiment. Al0.77Sc0.23N films. Both AlScN(0001)/Al2O3(0001) and AlScN(11-20)/Al2O3(1-102) were investigated. These first LU measurement results for AlScN films on sapphire are compared with simulated dispersion curves using the ab initio elastic and piezoelectric constants of [5]. Very good agreement is found between theory and experiment. In order to assess the significance of this agreement for the individual material con-

Next, experimental data are presented for dispersion curves of SAW propagating in

*Micromachines* **2022**, *13*, x FOR PEER REVIEW 3 of 18

In order to assess the significance of this agreement for the individual material constants of Al0.77Sc0.23N, a sensitivity analysis is presented for the SAW dispersion curves in the frequency range accessible for our LU setup for both geometries studied. stants of Al0.77Sc0.23N, a sensitivity analysis is presented for the SAW dispersion curves in the frequency range accessible for our LU setup for both geometries studied. **2. Materials and Methods** 

#### **2. Materials and Methods** *2.1. Substrate and film geometries*

#### *2.1. Substrate and Film Geometries* As already mentioned, for the LU investigations of elastic properties of AlScN films

As already mentioned, for the LU investigations of elastic properties of AlScN films reported here, two different layered structures were considered, i.e., AlScN(0001)/Al2O3(0001) and AlScN(11-20)/Al2O3(1-102). In Figure 1, the epitaxial relationship between the film and substrate material is shown schematically for the two systems. The Cartesian coordinate systems introduced after rotation with the x3-axis normal to the surface correspond to the Euler angles (*λ*, *µ*, *θ*) = (0◦ , 0◦ , *θ*) for c-plane sapphire and (*λ*, *µ*, *θ*) = (60◦ , 57.6◦ , *θ*) for r-plane sapphire, respectively. The Euler angle *µ* = 57.6◦ for perfect r-plane orientation results from a ratio of lattice constants c/a = 2.73 for sapphire. For optimal growth conditions of the non-polar AlScN film, substrate off-cut angle *χ* is needed, which is related to the second Euler angle via *χ = µ* − 57.6◦ . reported here, two different layered structures were considered, i.e., AlScN(0001)/Al2O3(0001) and AlScN(11-20)/Al2O3(1-102). In Figure 1, the epitaxial relationship between the film and substrate material is shown schematically for the two systems. The Cartesian coordinate systems introduced after rotation with the x3-axis normal to the surface correspond to the Euler angles (λ, μ, θ ) = (0°, 0°, θ ) for c-plane sapphire and (λ, μ, θ ) = (60°, 57.6°, θ ) for r-plane sapphire, respectively. The Euler angle μ = 57.6° for perfect r-plane orientation results from a ratio of lattice constants c/a = 2.73 for sapphire. For optimal growth conditions of the non-polar AlScN film, substrate off-cut angle χ is needed, which is related to the second Euler angle via χ *=* μ - 57.6°. We note that the angle θ defines the wavevector direction of SAW propagating on the corresponding surface.

**Figure 1.** Crystal cuts of Al2O3 substrate and AlScN film, defined in the hexagonal crystal system (a1,a2,a3,c) and with the help of the two first Euler angles λ and μ (rotation with respect to Cartesian coordinate system XYZ). The third Euler angle θ defines the direction of SAW propagation (red arrows) on the surface planes (x1x2). (**a**) The c-plane (0001) cuts of both film and substrate; (**b**) aplane AlScN(11-20) film on the r-plane Al2O3(1-102) substrate. **Figure 1.** Crystal cuts of Al2O<sup>3</sup> substrate and AlScN film, defined in the hexagonal crystal system (a1,a2,a3,c) and with the help of the two first Euler angles *λ* and *µ* (rotation with respect to Cartesian coordinate system XYZ). The third Euler angle *θ* defines the direction of SAW propagation (red arrows) on the surface planes (x1x2). (**a**) The c-plane (0001) cuts of both film and substrate; (**b**) a-plane AlScN(11-20) film on the r-plane Al2O<sup>3</sup> (1-102) substrate.

AlScN(0001)/Al2O3(0001) and AlScN(11-20)/Al2O3(1-102) thin films were grown by the magnetron sputter epitaxy method [18,20,22]. In the case of non-polar AlScN, 3° sub-We note that the angle *θ* defines the wavevector direction of SAW propagating on the corresponding surface.

#### strate off-cut was found to be the best for high crystalline quality [20], a detailed growth optimization study including a proposed growth model for non-polar III-nitrides and dif-*2.2. Fabrication of AlScN Films*

*2.2. Fabrication of AlScN films* 

ferent off-cut angles is published elsewhere [22]. All films were grown on ⌀ = 100 mm substrates in an Evatec sputter cluster tool (base pressure ~5 × 10-6 Pa), using reactive AlScN(0001)/Al2O3(0001) and AlScN(11-20)/Al2O3(1-102) thin films were grown by the magnetron sputter epitaxy method [18,20,22]. In the case of non-polar AlScN, 3◦ substrate off-cut was found to be the best for high crystalline quality [20], a detailed growth optimization study including a proposed growth model for non-polar III-nitrides and different off-cut angles is published elsewhere [22]. All films were grown on ∅ = 100 mm substrates in an Evatec sputter cluster tool (base pressure ~5 <sup>×</sup> <sup>10</sup>−<sup>6</sup> Pa), using reactive pulsed-DC magnetron co-sputtering. Substrate rotation ensured the composition and thickness uniformity of the films. The scandium concentration x = 0.23 was achieved by setting the P(Al, 99.9995% pure) = 684 W and P(Sc, 99.99% pure) = 316 W. This specific Sc concentration was chosen as it allowed us to deposit AlScN thin films with very high crystalline quality and low density of abnormally oriented grains, leading to reliable evaluation of material properties by LU. Prior to deposition, the sapphire substrates were cleaned in-situ using Ar inductively coupled plasma (ICP) etching and the targets were pre-sputtered in Ar behind a closed shutter. More details about the growth conditions can be found in [18,20,22], all parameters except for the N<sup>2</sup> gas flow were kept the same, as summarized in Table 1.


**Table 1.** Growth parameters of Al0.77Sc0.23N.

1 for AlScN(0001)/Al2O3(0001). <sup>2</sup> for AlScN(11-20)/Al2O3(1-102)

The scandium concentration (+/−2% error) was estimated using energy dispersive x-ray (scanning electron microscope Zeiss Auriga Crossbeam FIB-SEM with EDX spectroscopy from Bruker Quantax) on AlScN(0001)/Si(001) films deposited under the same conditions. This was done in order to avoid the overlap of Al emission peaks from the sapphire substrate and AlScN film [18]. No variation of composition was observed between the edge and the center of the wafers. The average film thickness (+/−3% error) was determined by spectroscopic ellipsometry (J.A. Woollam M-2000X), using a model optimized for AlScN from [23]. Thickness uniformity analysis indicated <3% variation in thickness across the wafer. The surface roughness of the films and the thickness of the metal layers were evaluated by atomic force microscopy (AFM, Bruker Dimension Icon) in tapping mode (not shown). The crystalline quality and in-plane orientation of AlScN films were confirmed by X-ray diffraction (XRD) [18,20] (not shown). Based on XRD pole figures analysis, the epitaxial relationship for c-plane AlScN could be defined as [10-10]AlScN//[11-20]sapphire and (0001)AlScN//(0001)sapphire and for a-plane AlScN [0001]AlScN//[1-101]sapphire and [1-100]AlScN//[11-20]sapphire, respectively.

Details on the samples investigated by LU in this work are given in Table 2.


**Table 2.** Samples investigated in this work.

### *2.3. Application of the Laser Ultrasound Approach*

A schematic drawing of the LU set-up is shown in Figure 2. Acoustic pulses, traveling along the sample surface, are excited by laser pulses via the thermoelastic effect. This excitation mechanism is explained in detail in [24,25]. The optical pulses are generated by a passively Q-switched Nd:YAG laser (pulse duration: 1 ns; wavelength: 1064 nm, frequency-doubled to 532 nm). They are focused on a straight line on the surface with a

cylindrical lens to minimize diffraction of the excited SAW and to achieve a well-defined wavevector direction. lindrical lens to minimize diffraction of the excited SAW and to achieve a well-defined wavevector direction.

quency-doubled to 532 nm). They are focused on a straight line on the surface with a cy-

**Figure 2.** Experimental setup. **Figure 2.** Experimental setup.

With the help of a continuous-wave laser, the acoustic surface pulses are detected with the probe-beam deflection method at a fixed observation point at the surface for various positions of the movable line source. Their shapes are recorded along with the distances of the observation points from the source. The presence of a film on the substrate surface causes the pulse shape to change with distance from the source. The quantity measured by probe-beam deflection at each observation point is the local surface slope as a function of time [25]. If the film and substrate are both transparent at the frequency of laser light used for the excitation of ultrasound pulses, the surface has to be coated with a thin metal film to ensure absorption of the laser pulses and enable thermoelastic excitation of SAW pulses. The effect of this additional layer has to be accounted for in the data interpretation and analysis. By Fourier decomposition of the pulse shapes at the different distances between the With the help of a continuous-wave laser, the acoustic surface pulses are detected with the probe-beam deflection method at a fixed observation point at the surface for various positions of the movable line source. Their shapes are recorded along with the distances of the observation points from the source. The presence of a film on the substrate surface causes the pulse shape to change with distance from the source. The quantity measured by probe-beam deflection at each observation point is the local surface slope as a function of time [25]. If the film and substrate are both transparent at the frequency of laser light used for the excitation of ultrasound pulses, the surface has to be coated with a thin metal film to ensure absorption of the laser pulses and enable thermoelastic excitation of SAW pulses. The effect of this additional layer has to be accounted for in the data interpretation and analysis.

line source and observation point, the phase velocities of each individual Fourier component are determined. In this way, a full dispersion curve of SAW with wavevectors vertical to the line source is obtained in one measurement cycle. Using a translation stage with a controlled stepper motor, the measurements are partly automated. The broad-band character of the LU method and its semi-automated operation renders it a fast tool for the characterization of near-surface elastic properties of materials. The achievable frequency range is partly material-dependent with an upper limit of 400 to 600 MHz for the materials investigated here with our set-up. With the help of a rotary positioning table for the sample, SAW dispersion curves can be measured for any wavevector direction on the surface. Since even the third harmonic of the carrier frequency of the Nd:YAG pulse laser is below the absorption edges of sapphire and AlN, a thin absorbing layer is needed to ena-By Fourier decomposition of the pulse shapes at the different distances between the line source and observation point, the phase velocities of each individual Fourier component are determined. In this way, a full dispersion curve of SAW with wavevectors vertical to the line source is obtained in one measurement cycle. Using a translation stage with a controlled stepper motor, the measurements are partly automated. The broad-band character of the LU method and its semi-automated operation renders it a fast tool for the characterization of near-surface elastic properties of materials. The achievable frequency range is partly material-dependent with an upper limit of 400 to 600 MHz for the materials investigated here with our set-up. With the help of a rotary positioning table for the sample, SAW dispersion curves can be measured for any wavevector direction on the surface.

ble thermoelastic excitation of acoustic waves. Test measurements have been carried out to find a suitable surface metallization Main criteria were signal quality, availability, and especially the influence of the metal coating on the SAW dispersion, which should be kept as small as possible. After careful consideration, molybdenum and titanium were identified as suitable metal coatings, but only data with Mo are shown here (Table 2). The thickness of the AlScN film, together with the frequency range of the average SAW phase velocity, and to some extent, the mode character, determine the minimal pen-Since even the third harmonic of the carrier frequency of the Nd:YAG pulse laser is below the absorption edges of sapphire and AlN, a thin absorbing layer is needed to enable thermoelastic excitation of acoustic waves. Test measurements have been carried out to find a suitable surface metallization Main criteria were signal quality, availability, and especially the influence of the metal coating on the SAW dispersion, which should be kept as small as possible. After careful consideration, molybdenum and titanium were identified as suitable metal coatings, but only data with Mo are shown here (Table 2).

etration depth of the SAW in the substrate. For a rough estimate, we assume that the displacement field associated with a SAW has an appreciable magnitude up to distances of a wavelength from the surface. Our investigations refer to samples with AlScN films with a thickness of ≤ 1000 nm and reached frequencies up to 600 MHz. This suggests that even The thickness of the AlScN film, together with the frequency range of the average SAW phase velocity, and to some extent, the mode character, determine the minimal penetration depth of the SAW in the substrate. For a rough estimate, we assume that the displacement field associated with a SAW has an appreciable magnitude up to distances of a wavelength from the surface. Our investigations refer to samples with AlScN films with a thickness of ≤1000 nm and reached frequencies up to 600 MHz. This suggests that even at the upper edge of the frequency range accessible for our LU experiments, the SAWs penetrate deeply into the substrate and consequently, their dispersion is strongly influenced by the density and elastic constants of the substrate. Therefore, these quantities have to be known to a high precision in order to be able to extract the elastic properties of the film from the SAW dispersion curves. The determination of elastic constants of the sapphire using LU is described in Section 3.1.1 and the off-cut angle assessment in Section 3.1.2, respectively.

For data processing and evaluation and the interpretation of the measurement results, simulations of dispersion curves and displacement fields have been carried out with a computer program based on a semi-analytic Greens function approach (see e.g., [26]). In these simulations, a time (*t*) and position (*x*) dependent traction vector

$$T = \hat{\mathbf{k}} \ T\_0 \exp[i(\omega t - \mathbf{k} \cdot \mathbf{x})] \tag{1}$$

is applied to the surface, where *k* is a wavevector in the surface plane, *k*ˆ the unit vector pointing into the wavevector direction, *ω*/(2*π*) a frequency, and *T*<sup>0</sup> an arbitrary traction amplitude, respectively.
