Q optimization via quarter wave acoustic transformers in the body of aln contour-mode resonators

Abstract

This paper investigates the dependence of the quality factor in aluminum nitride contour mode resonators (CMRs) on the size of the inactive region between the resonator body and the lateral edges orthogonal to the main direction of vibration. Our work shows that an optimized length of this region exists and it is such that little energy leaks into the substrate through the supporting anchors. It turns out that the use of the optimum length makes the resonator inactive region behave as an equivalent λ/4 transformer. The reduction of the energy that is lost through the device anchors improves the device Q without substantial degradation of the electromechanical coupling, kt2. To validate this concept we built four different configurations of 207 MHz AlN CMRs, differing just in the length of the resonator inactive region, d (Fig. 1). An almost 40% improvement in the Figure of Merit, FoM, defined as the product between Q and kt2, was attained when d was varied from the minimum value we tested (~8 µm) to the equivalent acoustic quarter wavelength of the resonator inactive region (~11 µm).