Study On Stress Sensitivity Mechanism Of TE Mode Bulk Acoustic Wave Resonator

With the development of thin film bulk acoustic resonator(FBAR),FBAR sensors are applied widely,such as mass sensors,micro-accelerometers,pressure sensors,temperature sensors,biosensors and so on.Micro-accelerometers and pressure sensors belong to mechanical sensors.The basic principle of the mechanical sensor is the FBAR stress sensitive mechanism.That is,the force load acts on the mechanical sensor,which causes the deformation of FBAR and results in the FBAR resonance frequency offset.This thesis aims to solve two key problems of FBAR stress sensitive mechanism: theoretical basis and prediction method.The FBAR stress sensitivity mechanism can be divided into stress loading effect and electric poling effect.Stress loading effect is a phenomenon of FBAR resonance frequency offset caused by internal stress.Electric poling effect is a phenomenon of FBAR resonance frequency offset caused by internal electric field.The stress loading effect and electric poling effect are studied respectively,and the mathematical models of the two effects are established.The stress loading effect is the main one.Aiming at the non-linear stress loading effect,a method for accurately predicting the sensitivity of FBAR mechanical sensors is proposed.The mathematical model of stress loading effect is established.Based on nonlinear theory of electroelasticity,the stress loading effect is described by the theory for infinitesimal incremental fields superposed on finite biasing fields.The piezoelectric body is divided into three configurations: reference configuration,initial configuration and present configuration.The external force load is a biasing field,which makes the piezoelectric body transform from the reference configuration to the initial configuration.The alternating electric field is a small incremental field,which makes the piezoelectric body transform from the initial configuration to the current configuration.The piezoelectric constitutive equation of small incremental field is constructed.The coefficients of the equations are related to the biasing field and are expressed by the effective material parameters.Combining the boundary conditions and variational formulas,a complete mathematical model of stress loading effect is obtained.A combined method of perturbation and finite element is proposed.The average bias stress of the piezoelectric layer AlN of FBAR mechanical sensor under external load is calculated by COMSOL.The resonant frequency and corresponding mode of FBAR are calculated in COMSOL.The relationship between internal stress and elastic constant is obtained by first-principle,and the sensitivity of FBAR mechanical sensor is obtained by perturbation method.The feasibility of this method is verified by two cases.The accuracy of this method is verified by comparing with the multiscale method based on Mason model and the multiscale method based on finite element method.An analytical model of the electric poling effect is established.Based on linear piezoelectric theory,the relationship between FBAR resonant frequency and DC bias voltage is deduced.The relationship between external force load and FBAR resonance frequency is obtained by using the expression of external force and DC voltage in the positive piezoelectric effect.A case shows that the electric poling effect can be neglected,and the stress loading effect is the main FBAR stress sensitive mechanism.