c-Axis-tilted ScAlN films grown on silicon substrates for surface acoustic wave devices

The propagation characteristics of SAWs were theoretically analyzed to investigate the effect of the c-axis tilt angle on the electromechanical coupling coefficient K² of SAW propagating in the ScAlN film/silicon substrate structure. Figure 1 shows two types of theoretical analysis models for SAW propagation in a ScAlN film/silicon substrate layered structure. The IDT electrodes were placed on the surface of the ScAlN films in both models. The boundary between the ScAlN films and silicon substrates is electrically open in the A structure and electrically short-circuited in the B structure. The piezoelectric coefficients, e_ij , and elastic constants, c_ij , calculated using density function theory for a single-crystal ScAlN were used in the ScAlN layer of these models. ⁴¹⁾ The relative permittivity, ε_ij , of the ScAlN layer was set to 1.9 times the relative permittivity of the single-crystal AlN ⁴²⁾ to consider the experimental value. The density of the ScAN layer is an experimental value (3638 kg m⁻³) measured using Archimedes' method. The material constants of silicon substrates are used the values reported as a single-crystal silicon. ⁴³⁾ We analyzed SAW K² values using the Campbell and Jones' method ⁴⁴⁾ when normalized ScAlN film thickness H/λ and the c-axis tilt angle χ of the ScAlN film were varied for these structures. The effect of the piezoelectric constant e₃₃, which is largest value among the piezoelectric constants of ScAlN, on the Rayleigh-mode SAW excitation is maximized when the SAW propagates in the c-axis tilt direction. The particle displacement for the shear horizontal (SH) component increases with the increase in angle between the SAW propagation direction and the c-axis tilt direction, which reduces the effect of the piezoelectric constant e₃₃ on Rayleigh-mode SAW excitation. Therefore, The Euler angle of the ScAlN films and silicon substrates in these structures is set to (0°, χ, 90°) and (0°, 0°, 0°), respectively. The K² value is calculated using the equation K² = 2(v_f − v_m)/v_f, where v_f and v_m are the phase velocities in an electrically open surface and electrically short-circuited surface, respectively.

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Figures 2(a) and 2(b) show phase velocities of the Rayleigh-mode SAW in an electrically open surface for A and B structure, respectively. The horizontal and vertical axes present H/λ and the c-axis tilt angle χ, respectively. The phase velocity depends largely on H/λ because SAW velocities in silicon are larger than those in ScAlN. In addition, phase velocities depend on the c-axis tilt angle χ. This is because the phase velocity of the quasi-shear wave in ScAlN depends on the c-axis tilt angle χ and affects the SAW phase velocity. The phase velocity of the quasi-shear wave in ScAlN decreases until the c-axis tilt angle χ reaches approximately 45° and then increases until it reaches 90°. Figures 3(a) and 3(b) show the K² value of the Rayleigh-mode SAW for A and B structure, respectively. The horizontal and vertical axes present H/λ and the c-axis tilt angle χ, respectively. The maximum K² values at χ = 0° are 0.31% (H/λ = 0.10) and 1.52% (H/λ = 0.04) for the A and B structures, respectively. χ = 0° represents the c-axis-oriented ScAlN film/silicon substrate structure. Conversely, the maximum K² value of SAW propagating in the c-axis-tilted ScAlN film/silicon substrate structure is 3.88% (H/λ = 0.53 and χ = 56°) and 3.90% (H/λ = 0.51 and χ = 46°) for the A and B structures, respectively. The K² value increased significantly with the c-axis tilt angle χ. The phase velocities under the analysis conditions where the maximum K² values were obtained for the A and B structures were 4256 m s⁻¹ and 4175 m s⁻¹, respectively. Figures 4(a) and 4(b) show phase velocities of the Sezawa-mode SAW in an electrically open surface for A and B structure, respectively. The phase velocities of the Sezawa-mode SAW is higher than those of the Rayleigh-mode SAW and depend on H/λ and the c-axis tilt angle χ similar to those of Rayleigh-mode SAW. Figures 5(a) and 5(b) show the K² value of the Sezawa-mode SAW. The maximum K² values of the Sezawa-mode SAW are 2.48% (H/λ = 0.61 and χ = 0°) and 2.61% (H/λ = 0.58 and χ = 0°) for the A and B structures, respectively. The phase velocities under the analysis conditions where the maximum K² values were obtained were 5584 m s⁻¹ and 5601 m s⁻¹ for the A and B structures, respectively. There was no effect of ScAlN film c-axis tilt on the increase in the K² value, because the maximum K² value was obtained at χ = 0° in both structures. These results indicate that the c-axis-tilted ScAlN film/silicon substrate layered structure is suitable for Rayleigh-mode SAW devices.

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The K² value of the Rayleigh-mode SAW increased with the c-axis tilt angle χ because of the increased excitation of bulk shear waves. Figure 6 illustrates the calculated electromechanical coupling coefficient of the ScAlN quasi-longitudinal wave k'_L ² and the quasi-shear wave k'_S ², as functions of the c-axis tilt angle χ; the propagation direction is x₁. The angle χ is the angle from the x₃ direction. The k'_L ² and k'_S ² values increase with χ and are maximized at 90° and 58°, respectively. These results show the same tendency as the angle χ dependence on the K² value of the Rayleigh-mode SAW, as shown in Fig. 3. In particular, the angle χ at the maximum K² value of the Rayleigh-mode SAW in the A structure is in good agreement with the angle χ at the maximum value of k'_S ² value. In addition, IDT electrodes mainly form an electric field in the x₁ direction in the A structure, as shown in Fig. 1. Therefore, the angle χ at the maximum K² value in the A structure is influenced by the excitation of the quasi-shear wave propagating in the x₁ direction. However, the angle χ at the maximum K² value in the B structure is 46°, which is lower than that in the A structure. This is because an electric field in the x₃ direction is generated from the IDT electrodes owing to the short-circuited boundary between the ScAlN films and silicon substrates. The k'_S ² value of the quasi-shear wave propagating in the x₃ direction is maximized when χ is approximately 32°. Therefore, the excitation and propagation of SAWs in the B structure are influenced by these conditions. Accordingly, the excitation of quasi-shear waves affects the Rayleigh-mode SAW.

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Particle displacements of the Rayleigh-mode SAW in periodic IDT/ScAlN film/silicon substrate structures were simulated using two-dimensional finite element analysis (2D-FEM) to consider the increase in the K² value in terms of SAW propagation characteristics. The simulation was performed using Femtet^® software (Murata Software Co., Ltd.). In the analysis, the wavelength λ was 8 μm, the thickness of the substrate was 10λ, and a perfectly matching layer of 3λ was constructed on the bottom of the substrate. The mechanical and dielectric losses of each layer were not considered. Particle displacement analysis was performed on the structures in which the maximum K² was obtained in the A and B structures, as shown in Fig. 3. Specifically, the ScAlN film (H/λ = 0.53 and χ = 56°)/silicon substrate layered structure with K² = 3.88% in the A structure and the ScAlN film (H/λ = 0.51 and χ = 46°)/silicon substrate layered structure with K² = 3.90% in the B structure were analyzed. To compare these results, we analyzed the structure with the maximum K² value at χ = 0°, which is the ScAlN film (H/λ = 0.04)/silicon substrate layered structure with K² = 1.52% in the B structure. Figure 7 demonstrates the particle displacement contours for the longitudinal (L) and shear vertical (SV) components. The displacements were normalized using the maximum value of the SV component in each structure. In all the structures, the SV component had a larger particle displacement than the L component. The area where the SV component shows a large particle displacement in Figs. 7(b) and 7(c) is larger than that in Fig. 7(a). The SV component is mostly concentrated in the ScAlN films, which is approximately half a wavelength thick. The c-axis-tilted ScAlN films/silicon substrate structure provides relatively less energy leakage to the substrate layer, and thus offers efficient SAW propagation and a larger K² value.

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In addition, particle displacements of the Sezawa-mode SAW in periodic IDT/ScAlN film/silicon substrate structures were simulated. Figure 8 demonstrates the particle displacement contours for the L and SV components of the Sezawa-mode SAW. The L and SV components are concentrated in the film layer for the ScAlN film (H/λ = 0.61 and χ = 0°)/silicon substrate layered structure with K² = 2.48% in the A structure, as shown in Fig. 8(a). The same is true for the ScAlN film (H/λ = 0.58 and χ = 0°)/silicon substrate layered structure with K² = 2.61% in the B structure. However, the particle displacements for the L and SV components leak into the silicon substrate due to the increase in the c-axis tilt angle χ, as shown in Fig. 8(b). The K² value of the Sezawa-mode SAW propagating in the ScAlN film (H/λ = 0.91 and χ = 56°)/silicon substrate layered structure is 0.09%. Whereas the K² value of the Rayleigh-mode SAW propagating in the A structure is maximized at the χ = 56°, the K² value of the Sezawa-mode SAW is significantly decreased due to the relatively large energy leakage to the substrate. In short, there was no effect of ScAlN film c-axis tilt on the increase in the K² value of Swzawa-mode SAW.

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To obtain a high electromechanical coupling coefficient K² in SAW propagating in the ScAlN film/silicon substrate structure, it is crucial to prepare c-axis-tilted ScAlN films on silicon substrates. GLAD is a deposition technique, based on self-shadowing effects, used to fabricate highly tilted polycrystalline films. ^33–36) The self-shadowing effect occurs in crystal growth on the vacuum/substrate interface, as shown in Fig. 9. In the initial stage of film deposition, islands of different sizes are randomly formed on the substrates. As the deposition progresses, the small islands enter the shadows of tall islands due to the oblique particle flux and cannot receive any more particles. Conversely, tall islands on the substrates receive the particles and grow longer and larger in the direction of the oblique particle flux. Therefore, unique nanostructure designs, such as tilts, zigzags, and helices, can be fabricated using the GLAD technique. ^33–36) Sputtering deposition is widely used to prepare ScAlN films, and is applicable of GLAD technique. It has recently been shown to be effective in preparing c-axis-tilted wurtzite films, such as ZnO and AlN films. ³⁷⁾ Therefore, it is highly possible that c-axis-tilted ScAlN films can be prepared on silicon substrates using this deposition technique.

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The c-axis-tilted ScAlN film with an Sc concentration of 30% was deposited on a (100) silicon substrate (SEIREN KST Corp.) using an RF magnetron sputtering system, as shown in Fig. 10. Table I lists the deposition conditions. The substrate tilt angle γ was set to 0°, 30°, 60°, and 90° to take advantage of the self-shadowing effects. As a sputtering target, an 80 mm diameter Al disc (Furuuchi Chemical Co.) was used, on which 3.2 g Sc ingots (JX Nippon Mining & Metals Co.) were placed. The target-substrate distance was 25 mm. A sputtering chamber was evacuated to a pressure below 3.0 × 10⁻⁴ Pa, and argon gas (99.999%) and nitrogen gas (99.999%) were introduced into the chamber. The deposition conditions were set to an Ar:N₂-flow ratio of 2:1, sputtering pressure of 0.6 Pa, and RF power of 200 W with 13.56 MHz. The temperature of the cathode cooling water was set to 2 °C to cool the target. The thickness of the ScAlN films was controlled to 4.0–4.5 μm.

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The c-axis tilt angle and crystalline orientations of the samples were investigated using X-ray diffraction (XRD) with Cu Kα₁ radiation. Figure 11 presents the χ-scan profile curves of the ScAlN (0002) pole of the samples. The χ angle at the ScAlN (0002) pole increased with the substrate tilt angle γ. The angle χ at the ScAlN (0002) pole corresponds to the c-axis tilt angle. Therefore, ScAlN films, which were deposited on silicon substrates using oblique particle flux, exhibit a c-axis-tilted orientation, and the tilt angle χ increases with the substrate tilt angle γ. The maximum c-axis tilt angle χ is 50.0°, which is obtained when the substrate tilt angle γ is 90°. The degrees of out-of-plane and in-plane crystalline orientations were evaluated by the full width at half maximum (FWHM) values for the χ-scan and ϕ-scan profile curves, respectively. Table II lists the FWHM values, along with the c-axis tilt angle χ, film thickness, and Sc concentration of the samples. In addition, Table II shows the theoretical K² values of the Rayleigh-mode SAW for each sample when the wavelength λ is 8 μm and Sc concentration is 30%. The FWHM values of the χ-scan XRD were the smallest for the sample deposited at γ = 0°. No significant increase in the FWHM values was confirmed due to the c-axis tilt angle χ. In addition, the FWHM of the ϕ-scan XRD decreased with the c-axis tilt angle χ, and the minimum FWHM was 4.4^o, which was obtained when the substrate tilt angle γ was 90^o. This indicates that the highly c-axis-tilted ScAlN films on silicon substrates have a relatively high in-plane and out-of-plane crystalline orientation. However, the theoretical K² value of SAW propagating in the Sc_0.3Al_0.7N film/silicon substrate structure is smaller than that of the Sc_0.4Al_0.6N film/silicon structure due to the relatively low piezoelectricity of the ScAlN films with an Sc concentration of 30%. The piezoelectric constant e₃₃ of ScAlN films, which has a large effect on SAW excitation, increase monotonically until the Sc concentration reaches approximately 40%. ⁴¹⁾ In addition, the ScAlN BAW velocity decreases as the Sc concentration increases. ⁸⁾ The gap between the SAW velocities in ScAlN films and silicon substrates increases K² value. Therefore, it is important to fabricate ScAlN films with an Sc concentration of 40% on silicon substrates to obtain a high K² value.

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Figures 12(a) and 12(b) present cross-sectional SEM images of ScAlN films deposited at γ = 0° and 90°, respectively, on silicon substrates. Figure 12(a) shows that the ScAlN films have a columnar structure and grow perpendicular to the silicon substrates. Conversely, Fig. 12(b) shows that the columnar structure of the ScAlN films is significantly tilted. In addition, the thickness of the crystal grains is several hundred nanometers, which is larger than that shown in Fig. 12(a). These results are in good agreement with the χ-scan profile curves shown in Fig. 11 and the columnar structure of the polycrystalline films fabricated by the GLAD technique based on the self-shadowing effects. These results demonstrate that the c-axis-tilted ScAlN films grew on the silicon substrates due to the self-shadowing effects. The sputtering method using the self-shadowing effect is suitable for preparing c-axis-tilted ScAlN films on silicon substrates.

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The atomic arrangement of the substrates also affect the film growth. In general, films with an atomic arrangement close to that of the substrates are prone to grow on substrates. It has been reported that ScAlN films on diamond-like carbon do not crystallize when the Sc concentration exceeds 35%. ³⁹⁾ One reason is that the main phase is separated into AlN and ScN because of the atomic arrangement of the substrate. In this study, we attempted to prepare ScAlN films with an Sc concentration of 40% on (100) silicon substrates; however, the ScAlN films did not crystallize. This is because silicon has the same cubic structure as diamond-like carbon. This is a problem in SAW device applications, because the piezoelectricity of ScAlN films is maximized at an Sc concentration of 40%. In the semiconductor field, oxide-covered silicon substrates are used to electrically insulate semiconductor films and silicon substrates. Additionally, the SiO₂ buffer layer is an effective method for eliminating the effect of the atomic arrangement of the substrates. ^45,46) Therefore, we predicted that oxide-covered silicon substrates play the role of the SiO₂ buffer layer.

The c-axis-tilted ScAlN film with an Sc concentration of 40% was deposited on an oxide-covered (100) silicon substrate (SEIREN KST Corp.) with an oxide film thickness of 300 nm. As a result of the theoretical analysis of K² values, the 300 nm oxide film on the silicon substrate has almost no effect on the K² value of SAW devices in the case of a wavelength λ of 8 μm. Table I lists the deposition conditions. The Sc ingots placed on the Al disc target weigh 3.4 g.

Figure 13 presents χ-scan profile curves of the ScAlN (0002) pole of the samples. ScAlN (0002) poles were observed in all ScAlN films prepared at various substrate tilt angles in the range of 0°–90°. This result shows that the thin buffer layer is effective in removing the influence of the atomic arrangement of the silicon substrate. In addition, although the peak intensity of the c-axis-tilted ScAlN films is smaller than that of the c-axis-oriented films, the c-axis tilt angle of the sample increased with the substrate tilt angle γ. The maximum c-axis tilt angle χ is 57.4°, which is obtained when γ is 90°. Table III lists the FWHM values, as well as the c-axis tilt angle χ, film thickness, and Sc concentration of the samples. In addition, Table III shows the theoretical K² values of the Rayleigh-mode SAW for each sample when the wavelength λ is 8 μm and Sc concentration is 40%. Although the χ-scan FWHM values increase with angle γ, the ϕ-scan FWHM values decrease with the angle γ. The FWHM of the film deposited at angle γ = 90° was 5.2°. An appropriate in-plane crystal orientation of the highly c-axis-tilted ScAlN films was observed.

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Figure 14 presents the cross-sectional SEM images of the ScAlN films deposited on silicon substrates at γ = 90°. The crystal grains are rounded due to the higher Sc concentration compared to those in Fig. 12. The crystal grains are thin near the silicon substrate, which then become thicker as the crystals grow. Moreover, the warpage of the crystal grains was confirmed. Consequently, the crystal orientation in the out-of-plane direction deteriorated in the sample with an Sc concentration of 40%. However, the technique for preparing highly c-axis-tilted ScAlN films with an Sc concentration of 40% is crucial. These results suggest a high potential for the fabrication of c-axis-tilted ScAlN films with an Sc concentration of 40% on silicon substrates and for SAW device applications using this structure.

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