Manu Agarwal – Doctoral Research Summary
Title: Advanced Considerations in Electrostatic Transduction & Nonlinearities in Resonant Microstructures
Electrostatic sensing and actuation (transduction) have been well explored and modeled for different kinds of displacement sensing, viz., detecting changes in capactive-gap width. These include devices like electrostatic accelerometers where the acceleration information is contained in the change of the capacitive gap size, induced from the acceleration induced displacement of a proof mass mounted on a mechanical spring.
With the advent of microresonator technology for replacing quartz in timing/frequency references and filters and also resonant sensors such as resonant- mass, strain or acceleration sensors, there has been an increased interest in using electrostatic transduction for interfacing with these resonant microstructures. These microstructures are different from those used for displacement sensing in several ways. These have higher quality factors and are generally operated on or very near their resonance frequency, typically using a self-oscillating circuit. The information of interest is contained in the resonant frequency, rather than change in gap, and hence the limits to resolution are caused by the phase (frequency) noise in the oscillator.
In this new paradigm, we need to revisit the physics of electrostatic transduction. E.g., electrostatic spring softening, or the frequency dependence on the DC polarization voltage (or DC bias voltage, needed for electrostatic transduction) would cause a small and generally negligible change in the sensitivity of a capacitive displacement sensor. However, in resonant microstructures this phenomenon causes undesirable resonant frequency shifts which could throw off a calibration, or it could also couple in frequency (phase) noise in the presence of voltage noise in the DC voltage supply.
Higher order nonlinearities in the stiffness due to mechanical (geometrical or material) properties or the electrostatics lead to modification of the 2nd order linear differential equation of motion into a Duffing equation. For high Quality factor (Q) systems, such as the resonators in question, a closed form solution can be obtained for it by treating it as a perturbed simple harmonic oscillator. This leads to what is popularly known as the amplitude-frequency dependence (A-f) effect, where the eigen-frequency of the system becomes dependent on the amplitude of oscillation. This effect limits the linearity range of the resonator and hence dictates the sustainable power or current handling. This nonlinear A-f effect in MEMS resonators is one of the focal points of this research. Models for this A-f effect have been developed and scaling and optimization of current handling by optimization of both DC bias voltage as well as the structural design and scaling are being studied.