Parallel Cross-sectional Lamé Mode Rod Resonator with high effective electromechanical coupling coefficient and temperature stability

Abstract Lamb wave resonators (LWR) have the advantages of high frequency, small size and lithographically defined resonant frequency. To solve the problems of low effective electromechanical coupling coefficient ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>k</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>e</mml:mi> <mml:mi>f</mml:mi> <mml:mi>f</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> ) and high temperature coefficient of frequency (TCF) in the application of LWR, a method of etching off the AlN film not covered by the top interdigital transducers (IDTs) is proposed to form a Parallel Cross-sectional Lamé Mode Rods Resonator (PCLMRR). The formed rods confine more longitudinal electric field and weaken the lateral capacitance between lateral rods. PCLMRR takes advantage of the high <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>k</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>e</mml:mi> <mml:mi>f</mml:mi> <mml:mi>f</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> of one order Cross-sectional Lamé Mode Resonator (CLMR) and the low impedance of array structure. The complexity of manufacturing PCLMRR has been reduced by etching grooves using the same mask of IDTs. For the same thickness of AlN film, the critical dimension for PCLMRR in photolithography is twice of CLMR, reducing the demand for photolithography resolution. Compared to plate LWR with a trade-off between TCF and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>k</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>e</mml:mi> <mml:mi>f</mml:mi> <mml:mi>f</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> , the PCLMRR adjusts the electric field, capacitance and stress-free boundaries, resulting in a higher <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>k</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>e</mml:mi> <mml:mi>f</mml:mi> <mml:mi>f</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> and lower TCF simultaneously. The variation of quality factor (Q) with temperature in PCLMRR is also smaller than that of the plate LWR due to the groove cutting the heat flow off and raising the thermal relaxation time.