**4. Discussion**

In layered structures, the effective propagation velocity of a SAW (Equation (5)) depends on the elastic modulus (E) and density (*ρ*) of the particular thin films, which through these the wave propagates [24]. In this regard, both types of diamond substrates have similar stiffness, as the resonance frequency of the SAW modes in both resonators is comparable. Furthermore, when comparing the resonance frequencies with our previous works (Sc0.26Al0.74N/PCD with Pt electrodes), the softening of the piezoelectric thin film with the Sc concentration was apparent, as the resonance frequency of both Rayleigh and Sezawa modes was reduced [25].

$$\mathbf{v\_{eff}} = \sqrt{\frac{\mathbf{E}}{\rho}}\tag{5}$$

However, the single crystal diamond substrate shifted the conductance baseline of the device towards ~0 S (Figure 2D), which showed how the scattering of the SAW wave due to defects such as grain boundaries or voids deteriorated the electrical response of the devices. This is in agreement with previous works, where the grain size of the polycrystalline diamond substrates increased the insertion losses of the devices [26–28].

Focusing on the piezoelectric thin film, particularly in its defects and how they degrade the electrical response of the devices [29], most of the defects in the thin films accumulated within the proximity of layer interfaces, mainly due to lattice mismatches and strain relaxation mechanisms, which usually require heat treatments to be minimized. However, the propagation characteristics of our devices validated the characterization via XRD analysis and the high quality Sc0.43Al0.57N thin films which, as previously mentioned, were synthesized with no intentional heating of the substrate, on both diamond substrates.

The electromechanical coupling coefficients lay between those reported previously in the literature (Table 4). However, there have been several approaches that can be undertaken to increase this value, such as adequate device design or the selection of the substrate or the electrode metal [17,30].

On the other hand, the structure with embedded electrodes (ScAlN/IDT/diamond) has been reported to considerably increase the K 2 eff coefficient [31]. Additionally, in order to boost the SAW propagation, a-plane (instead of c-plane) ScAlN thin films have been recently employed [32].

The filter bandwidth was, without some other circuit elements, constrained by the effective electromechanical coupling coefficient (K 2 eff), as it ultimately constrained the separation between the series and parallel resonance frequencies.

The −3-dB bandwidth of the Sezawa mode in both the layered structures was above 180 MHz at the center frequencies of 4.70 GHz and 4.90 GHz for the PCD and SCD structures, respectively.


**Table 4.** Comparison of resonance frequencies, compound composition, and electromechanical coupling coefficient.

Higher bandwidth for both Rayleigh and Sezawa propagation modes were obtained in our Sc0.43Al0.57N-based heterostructures compared to AlN and ZnO based filters (Table 5). Furthermore, the insertion losses of our devices were similar to these polycrystalline piezoelectric thin films. However, the insertion losses of the devices based on single crystal piezoelectric thin films were lower, showing the importance of the device design and the quality of the polycrystalline thin film in the electrical response of the filters.

**Table 5.** Comparison of center frequencies, −3-dB bandwidth, insertion loss (IL), and the Q factor of the SAW filters with different substrates, piezoelectric thin films, and electrode metals.

