*3.1. Resonators*

The reflection coefficient of the polycrystalline diamond resonators showed that several resonance frequency modes are generated together with second and third order reflections (Figure 2A). Among these, the reflection coefficient of the Rayleigh mode (1.20 GHz) outstands (~−40 dB). The Sezawa mode (2.06 GHz) and the second order Rayleigh mode (2.30 GHz) propagated with reflection coefficients below −15 dB.

**Figure 2.** Measured reflection coefficient (inset: Smith chart) and admittance characteristics of the one-port resonators fabricated with the Sc0.43Al0.57N/polycrystalline (**A**,**C**) and single crystal diamond (**B**,**D**) heterostructures.

The devices using the SCD substrate reported lower insertion losses (Figure 2B). Furthermore, in these devices, the reflection coefficient of the Sezawa mode (2.03 GHz) below −45 dB indicated the efficient excitation of this mode. The Rayleigh mode (1.21 GHz) propagated with a reflection coefficient below −5 dB, whereas its second order reflection mode (2.25 GHz) propagated with a reflection coefficient below −15 dB. In both heterostructures, higher reflection modes propagated above 2.50 GHz.

From the admittance characteristics (Figure 2C,D), the series (fs) and parallel (fp) frequencies can be extracted and then the effective propagation velocity (veff) (Equation (1)) can be calculated, as can the effective electromechanical coupling coefficient (K 2 eff) (Equation (2)), where λ is the designed IDT wavelength (Table 1) [19,20].

$$\mathbf{v\_{eff}} = \frac{\mathbf{f\_p} - \mathbf{f\_s}}{2}\lambda \tag{1}$$

$$\mathbf{K}\_{\rm eff}^2 = \frac{\pi^2}{8} \frac{\mathbf{f}\_\mathbf{p}^2 - \mathbf{f}\_\mathbf{s}^2}{\mathbf{f}\_\mathbf{s}^2} \tag{2}$$

A figure of merit (Table 2), usually employed to compare the performance of SAW devices, multiplied the Bode Q-factor (Equation (3)) by the electromechanical coupling coefficient. The Q-factor (Equation (4)) is defined as the ratio between the series or parallel resonance frequency and the −3-dB width of the frequency [21–23].

$$\text{FOM}\_{\text{s},\text{P}} = \text{K}\_{\text{eff}}^2 \ast \text{Q}\_{\text{s},\text{P}} \tag{3}$$

$$\mathbf{Q}\_{\rm s,p} = \frac{\mathbf{f}\_{\rm s,p}}{\Delta \mathbf{f}\_{-3\rm dB(s,p)}} \tag{4}$$

**Table 1.** Effective velocity (veff) and effective electromechanical coupling coefficient (K 2 eff) from the series and parallel resonance frequencies.


**Table 2.** Quality factors and figure of merit (FOM) values from the series and parallel resonance frequencies.

