# High-Frequency and Spectrum-Clean Shear-Horizontal Acoustic Wave Resonators with AlN Overlay
## 4 Propagation Characteristics of SH Wave in AlN/LiNbO\({}_{3}\)/Si
### Trade-Offs between \(v_{\text{p,o}}\) and \(k_{\text{eff}}\)2
Footnote 2: The trade-offs between the \(v_{\text{p,o}}\) and \(k_{\text{eff}}\)2 by varying AlN thickness are compared for the nonleaky SH wave propagating in AlN/LiNbO\({}_{3}\)/Si with two different rotation angles of the piezoelectric LiNbO\({}_{3}\), as presented in Figure 7a,b. It can be noted that both the \(v_{\text{p,o}}\) and \(k_{\text{eff}}\)2 saturate when \(h_{\text{AIN}}>0.4\lambda\). For both 15\({}^{\circ}\)\(Y\)X-LiNbO\({}_{3}\) and 30\({}^{\circ}\)\(Y\)X-LiNbO\({}_{3}\), the \(v_{\text{p,o}}\) is much higher for the case of \(h_{\text{LiNbO}3}=0.25\lambda\) than \(h_{\text{LiNbO}3}=0.5\lambda\), and the \(k_{\text{eff}}\)2 is also slightly higher for the thinner case. At \(\theta=15^{\circ}\), the saturated \(v_{\text{p,o}}\) is as high as 5280 m/s when \(h_{\text{LiNbO}3}=0.25\lambda\); at \(\theta=30^{\circ}\), the saturated \(v_{\text{p,o}}\) is 5240 m/s when \(h_{\text{LiNbO}3}=0.25\lambda\). The preferred AlN thickness design range would be between \(0.2\lambda\) and \(0.4\lambda\) right before the convergence in order to avoid additional mass loading on the device coupling. Footnote 2: The \(v_{\text{p,o}}\) and \(k_{\text{eff}}\)2 are the same as the \(v_{\text{p,o}}\) and \(k_{\text{eff}}\)2 are the same as the \(v_{\text{p,o}}\) and \(k_{\text{eff}}\)2. Figure 8 depicts the displacement field as well as the first principal stress field of the nonleaky SH mode on the AlN/LiNbO\({}_{3}\)/Si with increasing AlN normalized thicknesses. It is most obvious that the mechanical fields become more penetrated and uniform when AlN becomes thicker. It is also intriguing to note that when the AlN layer is thicker than \(0.4\lambda\), the vibration becomes off the surface and concentrated in the highly piezo LiNbO\({}_{3}\) layer; the AlN film then starts to be free of the mechanical vibration and transduction, indicating a stable mechanical-loading effect only instead of wave perturbation. Both the saturated values of \(v_{\text{p,o}}\) and \(k_{\text{eff}}\)2 are larger in the case of \(h_{\text{LiNbO}3}=0.25\lambda\) compared to \(h_{\text{LiNbO}3}=0.5\lambda\) for either 15\({}^{\circ}\)\(Y\)X-LiNbO\({}_{3}\) or 30\({}^{\circ}\)\(Y\)X-LiNbO\({}_{3}\). Note at for  
Figure 8: FEM-simulated mode shapes and the first principal stress field of the nonleaky SH mode on the AlN/LiNbO\({}_{3}\)/Si substrate stack with (**a**) \(h_{\text{AIN}}\)/\(\lambda=0\), (**b**) \(h_{\text{AIN}}\)/\(\lambda=0.1\), (**c**) \(h_{\text{AIN}}\)/\(\lambda=0.2\), and (**d**) \(h_{\text{AIN}}\)/\(\lambda=0.4\). Figure 7: Trade-offs between the open-surface phase velocities \(v_{\text{p,o}}\) and coupling coefficient \(k_{\text{eff}}\)2 by varying AlN thickness for the SH wave propagating in AlN/ LiNbO\({}_{3}\)/Si based on (**a**) 15\({}^{\circ}\)\(Y\)X-LiNbO\({}_{3}\) and (**b**) 30\({}^{\circ}\)\(Y\)X-LiNbO\({}_{3}\) with \(h_{\text{LiNbO}3}\)/\(\lambda=0.25\) and \(h_{\text{LiNbO}3}\)/\(\lambda=0.5\). the 15\({}^{\circ}\)\(Y\)X-LiNbO\({}_{3}\) case, 0.5\(\lambda\)-thick LiNbO\({}_{3}\) yields larger \(k_{\rm eff}\)\({}^{2}\) than 0.25\(\lambda\)-thick LiNbO\({}_{3}\) when AlN overlay is not applied and \(h_{\rm AlN}\) = 0, which can also be observed from Figure 4b. However, even with slight AlN overlay, the \(k_{\rm eff}\)\({}^{2}\) of 0.25\(\lambda\)-thick LiNbO\({}_{3}\) becomes similar or larger. As a result, for both rotation-angle cases, the 0.25\(\lambda\)-thick LiNbO\({}_{3}\) enables much higher \(v_{\rm p,o}\) and similar \(k_{\rm eff}\)\({}^{2}\). When \(h_{\rm LiNbO3}\) = 0.25\(\lambda\), the \(v_{\rm p,o}\) can be effectively boosted from 4420 m/s to 5280 m/s, showing a near 20% increase when \(h_{\rm AlN}\) is up to \(>\)0.4\(\lambda\).