**3. Results and Discussion**

The SAW phase velocity (*VP*), electromechanical coupling coefficient *K* 2 and temperature coefficient of delay (*TCD*) of bilayer BeO/128◦ YX LiNbO<sup>3</sup> SAW structure were first calculated as a function of normalized thickness (*hBeO*/*λ*) of BeO over layer, where *hBeO* is the BeO over layer thickness, and *λ* is the acoustic wavelength.

The change in SAW phase velocity (*VP*) and electromechanical coupling coefficient *K* 2 with the normalized thickness of BeO over layer is shown in Figure 2. It is found that the SAW phase velocity increases from 3800 ms−<sup>1</sup> (SAW velocity of bare 128◦ YX LiNbO<sup>3</sup> single crystal) to 4476 ms−<sup>1</sup> with increase in the BeO over layer thickness from 0 to 0.08 λ. The enhanced SAW velocity is principally due to the higher velocity (7800 ms−<sup>1</sup> ) of BeO film in comparison to LiNbO3, and with the increasing over layer thickness of BeO, SAW energy is assembled more into BeO [9].

**Figure 2.** Variation of SAW phase velocity (*VP*) and electromechanical coupling coefficient *K* 2 with normalized thickness of BeO over layer in BeO/128◦ YX LiNBO<sup>3</sup> SAW layered structure.

Figure 2 shows the rise in the value of electromechanical coupling coefficient *K* 2 for BeO/128◦ YX LiNbO<sup>3</sup> bilayer structure. The value of *K* 2 increases nearly twofold, i.e., from ∼5% (*K* <sup>2</sup> of bare 128◦ YX LiNbO<sup>3</sup> single crystal) to <sup>∼</sup>9.66% with the change in BeO over layer thickness from 0 to 0.08 λ. And with further increase in the BeO over layer thickness (beyond 0.08 λ), its value decreases. The significant rise in the value of coupling coefficient with the integration of a BeO over layer (in the range 0 to 0.08 λ) on the top of LiNbO<sup>3</sup> single crystal is accounted to the stiffening effect produced by the over layer [28]. The stiffened layer escalates the stress and raises the potential at the interface [29]. Thus, in addition to the piezoelectric coefficients, stress also makes a noteworthy contribution in raising the electric potential and thereby augments the coupling coefficient. With the increase in the over layer thickness from 0.08 λ to 0.15 λ, the value of *K* 2 reduces to ∼8% from 9.7% because, at greater thickness, the impact of mass loading influences the propagation [28].

The temperature coefficient of delay for the BeO/128◦ YX LiNbO<sup>3</sup> bilayer structure is calculated using Equation (4), and its dispersion with normalized BeO over layer thickness is shown in the Figure 3. It is found to reduce a little from 76 to ∼66 ppm ◦C <sup>−</sup><sup>1</sup> with an increase in the BeO over thickness from 0 λ to 0.08 λ. The small reduction in the value of TCD is credited to the fact that BeO film has comparatively lower but positive TCD value than for LiNbO<sup>3</sup> crystal [24]. And with the addition of greater BeO over layer thickness, the SAW energy is more accumulated in BeO; hence, it exhibits the reduced value of TCD for BeO/128◦ YX LiNbO<sup>3</sup> bilayer structure. It can be inferred from Figure 3 that the BeO/128◦ YX LiNbO<sup>3</sup> bilayer structure is thermally unstable as both LiNbO<sup>3</sup> and BeO are positive TCD materials. The positive TCD BeO/128◦ YX LiNbO<sup>3</sup> bilayer structure can be made temperature stable by integrating it with an over layer (i.e., SiO<sup>2</sup> and TeO3) possessing negative TCD [21,29–31]. Previously reported results show that in comparison to SiO2, TeO<sup>3</sup> thin films possess high value of negative TCD [18,20,21,30,31]. So, with the integration of relatively less thick TeO<sup>3</sup> over layer, a positive TCD device can be made temperature stable [18,19].

**Figure 3.** Variation of temperature coefficient of delay (TCD) with normalized thickness of BeO over layer in BeO/128◦ YX LiNBO<sup>3</sup> SAW layered structure.

Therefore, in the present study, the result of adding TeO<sup>3</sup> over layer over BeO/128◦ YX LiNbO<sup>3</sup> bilayer structure on its SAW propagation characteristics have been investigated further. In TeO3/BeO/128◦ YX LiNbO<sup>3</sup> multi- layered SAW structure, the thickness of BeO layer is fixed at 0.08 λ because it is observed in Figure 2 that, at this BeO over layer thickness, the BeO/128◦ YX LiNbO<sup>3</sup> bilayer structure has maximum value of *K* 2 (∼9.66%) and appreciable phase velocity (∼4467 ms−<sup>1</sup> ).

Figure 4 presents the TCD variation of TeO3/BeO (0.08 λ)/128◦ YX LiNbO<sup>3</sup> multilayered SAW structure as a function of normalized thickness *h*TeO<sup>3</sup> /*λ* of TeO<sup>3</sup> over layer, where *h*TeO<sup>3</sup> is the TeO<sup>3</sup> over layer thickness. The TCD of TeO3/BeO(0.08 λ)/128◦ YX LiNbO<sup>3</sup> layered structure reduces to 0 from 66 ppm ◦C <sup>−</sup><sup>1</sup> with an increase in the (negative TCD) TeO<sup>3</sup> over layer thickness from 0 to 0.026 λ. Thus, a temperature stable TeO3/BeO(0.08 λ)/128◦ YX LiNbO<sup>3</sup> multi-layered SAW device can be achieved with the integration of 0.026 λ thick TeO<sup>3</sup> over layer.

**Figure 4.** (**a**): Variation of TCD of TeO3/BeO(0.08 λ)/128◦ YX LiNbO<sup>3</sup> SAW structure with normalized thickness of TeO<sup>3</sup> over layer. (**b**) Variation of phase velocity and *K* 2 for TeO3/BeO(0.08 λ)/128◦ YX LiNbO<sup>3</sup> SAW structure with normalized thickness of TeO<sup>3</sup> over layer.

The effect of integrating TeO<sup>3</sup> over layer is examined on SAW phase velocity and *K* 2 , as well. The inset in Figure 4b shows the change of *K* <sup>2</sup> and SAW phase velocity for TeO3/BeO (0.08 λ)/128◦ YX LiNbO<sup>3</sup> with the normalized thickness of TeO<sup>3</sup> over layer. It may be seen that the value of SAW phase velocity declines faintly from 4467 to 4266 ms−<sup>1</sup> with an increase in the TeO<sup>3</sup> over layer thickness from 0 to 0.026 λ owing to the point that TeO<sup>3</sup> has lower SAW phase velocity in comparison to BeO(0.08 λ)/128◦ YX LiNbO<sup>3</sup> bilayer structure. Moreover, with the rise in the TeO<sup>3</sup> over layer thickness from 0 to 0.026 λ, the value of *K* 2 increases further from 9.66% to ∼9.85%. This is because the thickness of TeO<sup>3</sup> over layer is much less than the acoustic wavelength leading to the stiffening and further increase in the potential and hence electromechanical coupling coefficient [21,28]. It may be noted that the introduction of 0.026 λ thick TeO<sup>3</sup> over layer in BeO (0.08 λ)/128◦YX LiNbO<sup>3</sup> bilayer structure not only marginally increases the value of *K* 2 (from 9.70% to 9.85%) but also makes the device temperature stable. With the further increase in the TeO<sup>3</sup> over layer thickness, the TCD of TeO3/BeO (0.08 λ)/128◦ YX LiNbO<sup>3</sup> multi-layered SAW structure becomes negative, making the device temperature unstable again. Hence the optimum thickness of TeO<sup>3</sup> over layer is taken to be 0.026 λ. Therefore, a temperature stable TeO<sup>3</sup> (0.026 λ)/BeO(0.08 λ)/128◦ YX LiNbO<sup>3</sup> multi-layered SAW structure with high value of *K* 2 (∼9.85%) and the phase velocity (∼4266 ms−<sup>1</sup> ) is proposed, which is suitable for its applications in narrow band filters in GHz range.
