Calculation of electromechanical coupling coefficient of quartz crystal in decoupling plane

Abstract

Quartz crystal is a good piezoelectric crystal and it can be used as substrate of surface acoustic wave (SAW) devices. How to cut the substrate crystal is important in design of the SAW devices, and the optimum cut direction is determined by the direction of the largest electromechanical coupling coefficient. In this paper, SAW basic equation group strengthened by piezoelectric effect and boundary condition equation group including mechanical boundary conditions and electric boundary conditions are deduced. The electric boundary conditions have two kinds: free boundary condition and short-circuit boundary condition. Two kinds of SAW velocities using the two kinds of electric boundary conditions are systematically calculated for the quartz crystal respectively in decoupling of <i>yz</i> plane. The SAW velocities are calculated using a circle iterative method, which calculation velocity is quick and calculation precision is high. Electromechanical coupling coefficient is calculated using these two SAW velocities in <i>yz</i> plane of the quartz crystal. Calculation results indicate that the maximum electro-mechanical coupling coefficient is 0.2885 at direction, which makes an angle of 73&#176; with <i>y</i> axis, in <i>yz</i> plane of the quartz crystal. The calculation results lay a solid foundation for design and manufacture of the SAW devices.