Substrate Viscoelastic Properties and Thermal Expansion Mismatch in MEMS Packaging
Substrate viscoelastic relaxation and thermal expansion mismatch induce time-dependent, hysteretic offset drift in MEMS requiring mechanical anchor isolation.
Coriolis Resonance Split
Frequency Relationship
Phenomenon in vibratory gyroscopes where the frequency difference between the primary and secondary oscillation modes deviates from the ideal zero-offset state. Achieving high sensitivity in a micro-electromechanical system requires the drive and sense frequencies to overlap perfectly. When coriolis resonance split occurs, the energy transfer between the modes becomes inefficient.
The separation reduces the mechanical gain of the sensor.
Manufacturing Asymmetry
Imperfections in the etching process or material inhomogeneities create structural imbalances in the resonator. Tiny variations in mass or stiffness along the vibrating arms lead to coriolis resonance split by shifting the natural frequencies of the degenerate modes. Even a sub-micron deviation in beam width can cause a noticeable gap.
Quality control at the wafer level involves measuring these offsets to determine the yield of high performance units.
Operational Impact
Sensitivity to angular rate decreases as the frequency gap widens. A large coriolis resonance split also increases the phase sensitivity of the device, making it more prone to quadrature errors and bias drift. Temperature changes often worsen the split because the thermal expansion of the substrate is rarely perfectly uniform.
The drift necessitates sophisticated electronics to maintain stable performance over a broad operating range.
Compensation Method
Electrostatic tuning provides a means to narrow the frequency gap after the sensor is sealed. By applying a dc bias voltage to specific electrodes, technicians can adjust the effective stiffness of the resonator and eliminate the coriolis resonance split. The process, known as frequency pulling, allows a lower grade part to meet tighter specifications.
Laser trimming of the resonator mass is an alternative approach used during the initial stages of calibration. Tuning must be performed at several temperatures to ensure stability across the operating range. Modern control electronics can automate this alignment process in real time.