# High-Frequency and Spectrum-Clean Shear-Horizontal Acoustic Wave Resonators with AlN Overlay
## 1 Introduction  
The propagation-loss mechanisms of shear-horizontal (SH)-type waves on LiNbO\({}_{3}\) and LiTaO\({}_{3}\) have been intensively studied recently [1; 2; 3; 4; 5; 6]. By bonding the sub-wavelength-thick LiNbO\({}_{3}\) or LiTaO\({}_{3}\) layer to a high-velocity substrate, the SH mode no longer couples with the bulk mode in substrate and the leaky component is effectively eliminated [1; 2; 3; 4; 5; 6]; thus, the SH wave can abandon its traditional name--\"leaky-surface acoustic wave (SAW)\" but a favorable \"nonleaky\" feature instead. There are many choices of high-velocity substrates, such as AlN, Si, quartz, diamond, etc. [1; 2; 3; 4; 5], and Si is used as an example in this study for its wide availability and cheap price. In addition, given that the acoustic propagation loss no longer dictates the choice of piezoelectric-substrate cut angle and ultra-large effective coupling coefficient (\(k_{\rm eff}\)\({}^{2}\)), cuts can be taken advantage of, such as low rotation from _YX_-LiNbO\({}_{3}\)[3; 4; 5; 6; 7].  
Long-Term Evolution (LTE)--Advancement Pro, 5G sub-6 GHz new radio (NR), and emerging 6G standards require low-loss and wide-bandwidth (fractional bandwidth \(>\) 5%) filters that push the frequency limits SAW technology using optical lithography up to more than 2.5 GHz range [8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58  
high \(Q\) is achieved [4]. The multilayered LiNbO\({}_{3}\) SAW devices with ultralarge \({k_{\text{eff}}}^{2}\) and high \(Q\) meet requirements in low frequency (<2.5 GHz). However, the \(v_{\text{p}}\) is still relatively low (~4000 m/s), limiting its application in LTE high-band (2.5-3.5 GHz, such as band 7, band41, etc.) filters and 5G NR applications. A high-velocity layer beneath the piezoelectric LiNbO\({}_{3}\) or LiTaO\({}_{3}\) does not effectively increase the phase velocity of the SH mode; rather, by adding a high-velocity layer, such as AlN, overlaid on top of the transducer and LiNbO\({}_{3}\), the phase velocity of the SH mode is visibly increased with only minimal trade-off on the \({k_{\text{eff}}}^{2}\), which can be much larger than needed for majority of the bands. In this way, a desirable nonleaky SH wave resonator with low propagation loss, high frequency (\(f\)), and large-\({k_{\text{eff}}}^{2}\) can be achieved.  
In addition, without a careful design of the substrate, the layered SH potentially has spurious responses in the out-of-band frequencies (Lamb modes) and near-band frequencies. This paper focuses on the design of layered substrate not only to optimize its narrow-band characteristics--\(f\), \(Q\), \({k_{\text{eff}}}^{2}\), temperature coefficient of frequency (TCF)--but also for eliminating the out-of-band spurious responses.  
By using the numerical calculation and finite-element-method (FEM) approaches, propagation characteristics of the SH modes in LiNbO\({}_{3}\)/Si and AlN/LiNbO\({}_{3}\)/Si are derived with varied substrate designs and the device performance is optimized as well as the presence of spurious modes avoided. Based on the analyses, new stacks with optimized substrate design are obtained, demonstrating the high frequency of 3 GHz at 1 \(\upmu\)m inter-digital transducer (IDT) pitch, high \({k_{\text{eff}}}^{2}\) (14.4%) and a spurious free response at 0-6 GHz. After optimizations, these novel AlN/LiNbO\({}_{3}\)/Si nonleaky SH devices, featuring superb performance with high frequency ability and being spurious-free, show great potential for filters in next-generation RF front ends.  
Symbols used in this paper are listed in Table 1.