High Electromechanical Coupling Radial Extension Mode Resonators Realized in Al _0.7 Sc _0.3 N

This work reports aluminum scandium nitride (Al<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{\mathrm {1-x}}$ </tex-math></inline-formula>ScxN/AlScN) (x =0.3/Al0.7Sc0.3N) Lamb wave resonators (LWR) operating in length extensional (LE), width extensional (WE), and radial extensional (RE) modes. COMSOL Multiphysics and experimental measurements show that the RE mode achieves a much higher electromechanical coupling, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k_{t}^{2}$ </tex-math></inline-formula>, when compared to the more traditionally utilized LE and WE modes. The higher <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${k} _{t}^{2}$ </tex-math></inline-formula> is due to the constructive addition of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d_{31}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d_{32}$ </tex-math></inline-formula> piezoelectric coefficients due to the RE mode shape. Experimentally, the RE mode resonator achieved a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k_{t}^{2}$ </tex-math></inline-formula> of 14.1%, which was much larger than the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k_{t}^{2}$ </tex-math></inline-formula> of 9.1% and 4.8% measured for the WE and LE mode devices fabricated on the same wafer. The RE mode achieves a high <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q_{p}$ </tex-math></inline-formula> of 1302 measured in air yielding a figure-of-merit (FOM <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$= k_{t}^{2}Q_{p}$ </tex-math></inline-formula>) of 157. Based on the high <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k_{t}^{2}$ </tex-math></inline-formula> and FOM, Al0.7Sc0.3N-based RE resonators show potential for applications in piezoelectric microelectromechanical filters and oscillators. [2024-0231]