Tuning TCF and Spurious-Free Response in SH-SAW Resonators via Energy Distribution

Thermal stability and spurious modes are the common challenges in high-performance shear horizontal surface acoustic wave (SH-SAW) resonators based on LiNbO3 platform. This study explores the design and optimization of SH-SAW multilayer resonators on 0.75 μm 36Y-cut LiNbO3/2 μm SiO2/Si substrates, acquiring zero temperature coefficient of frequency (TCF) and spurious-free performance via energy dispersion. First, we develop a novel theoretical model that correlates the energy distribution (W<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">\(_\textit{i}\)</tex-math></inline-formula> for layer <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</i> within the multilayer stack to the effective temperature coefficient of elastic modulus (TCE) and, consequently, affecting the TCF. By analyzing the dispersion characteristics of SH mode in the LiNbO<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">\(_3\)</tex-math></inline-formula> film thickness to interdigital transducer (IDT) wavelength (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">\(\lambda\)</tex-math></inline-formula>) ratios (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</i>LN/<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">\(\lambda\)</tex-math></inline-formula>), zero-TCF resonator is achieved at <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</i>LN/<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">\(\lambda\)</tex-math></inline-formula> = 0.27. Further research shows that energy distribution governs spurious mode excitation: energy in the SiO<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">\(_2\)</tex-math></inline-formula> layer excites the first-order shear horizontal (SH1) mode, while that in the metal IDT triggers the Rayleigh mode. For <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</i>LN/<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">\(\lambda\)</tex-math></inline-formula> between 0.42 and 0.48, these modes are completely suppressed. Moreover, reducing the LiNbO<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">\(_3\)</tex-math></inline-formula> thickness to 0.25 μm aligns the zero-TCF frequency with the spurious-free region, enabling operation above 2 GHz. Fabricated resonators exhibit a TCF range from –150 to 27 ppm/K, with zero-TCF and spurious-free responses at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">\(\lambda\)</tex-math></inline-formula> = 2.8 and 1.6 μm, respectively, in excellent agreement with simulations. In addition, transverse spurious modes on this platform are analyzed and effectively suppressed by employing an apodized IDT design. This study offers a more comprehensive understanding of the TCF and spurious-free mechanism in LiNbO3/SiO2/Si surface acoustic wave (SAW) resonators, providing essential guidance for designing LiNbO3/SiO2/Si acoustic devices with different TCF requirements.