Resonant frequency tunableness of solidly mounted resonators

The performance of solidly mounted resonator (SMR) depends on the thickness control of each layer. Since thickness variation is inevitable in film deposition, the resonant frequency will shift from the desired value. In order to calculate the required electrode thickness for a given resonant frequency, an SMR is treated as a combination of two substructures, the top electrode and the remaining layers. The substructure synthesis method is employed to calculate the required thickness of electrode. Monte Carlo simulation is adopted to investigate tunableness of resonant frequency with random thickness deviation in every layer. An SMR with a 6-period-reflector and 2.4GHz series resonant frequency is chosen for the investigation. The material of piezoelectric layer is aluminum nitride and the reflector is composed of tungsten and aluminum films. The top electrode is a half-wavelength Al film and the SMR is mounted on a silicon substrate of 525μm in thickness. Monte Carlo simulation shows that the 3σ of electrode trimming value is 0.03μm when the layer thickness deviation with 3σ value equals to 1% of the mean thickness.