Design, fabrication and characterization of a MEMS gravity gradiometer

Abstract

Gravity gradiometers have been developed to determine the gravity gradient for a number of terrestrial observations including oil and mineral exploration, measurement of the crustal anomaly, and archaeology since their first demonstration in the 1890s by the Hungarian physicist Lorand Eotvos. However, conventional gravity gradiometers weigh hundreds of kilograms to several tens. In order to integrate a gravity gradiometer into a weight- and volume-limited spacecraft or cube satellite, miniaturization becomes a priority. Microelectromechanical systems (MEMS) technologies offer a possible route. Only two MEMS gravity gradiometers have been developed so far but neither of them can be operated under Earth’s gravity to allow pre-flight validation. There are two possible approaches for implementation of a gravity gradiometer: differential-accelerometer and torsion-balance that depend on how the force difference is measured. For the former, the gravity gradient is determined by the difference between two accelerometers’ outputs divided by the separation. The latter transduces the force difference applied on two coupled masses as a torque, which is then balanced by a rotary suspension. The latter is approved to be a better option for implementing a MEMS gravity gradiometer. The aim of this thesis is to develop a torsion-balance-based MEMS gravity gradiometer for operation both on a satellite for planetary explorations and on Earth for airborne or shipborne gravity gradient surveys. The design rationales and noise analysis are introduced. With a feasibility study to achieve 1 Eo/rtHz, exploration for Mars gravitational field is possible. A seesaw-lever force-balancing suspension is designed to bear the gravity offset and to be compliant with respect to in-plane rotation but stiff with respect to other spurious vibrations. Closed-form solutions of gradiometer dynamics are derived and agree with finite element analysis (FEA) simulations and experimental results. Several prototypes of the MEMS gravity gradiometer based on this suspension are fabricated by through-wafer deep reactive-ion etching (DRIE) with their measured resonant frequencies varying from 6.6 Hz to 27 Hz. A normalized lateral capacitive array transducer (LCAT) is analysed. Its angular counterpart rotational capacitive array transducer (RCAT) is designed to be applied on the MEMS gravity gradiometer to determine the angular displacement induced by the gravity gradient. A frontend circuit is designed for the gravity gradiometer chip and implemented on a printed circuit board (PCB) that is also used to accommodate the MEMS chip. With the shortest paths from the MEMS chip to the front-end, the pre-amp noise is minimized. A conditioning circuit is designed to amplify, demodulate, and low-pass filter the pre-amplification signal. The MEMS gravity gradiometer chips were fabricated by four-mask processes on single-crystal silicon substrates using two metal layers insulated by a deposited silicon dioxide layer to form the RCAT, and using DRIE to etch through silicon wafers to define the mechanical structures. Both the stator and rotor dies were fabricated on the same wafer, singulated by pressing dicing-free features, and integrated by flip-chip technology. Then, the fully functional MEMS gravity gradiometer was characterized by a customized platform that provides angular accelerations. The transfer function of the gradiometer prototype was investigated and proved to be operational on Earth. Silicon suspensions suffer from changes in stiffness due to the temperature-dependent Young’s modulus of silicon. The sag displacement drift of a differential-accelerometer-based silicon gravity gradiometer due to temperature is problematic. A silicon/solder bilayer thermal actuator is developed to compensate the sag thermal-drift using the mismatching of the coefficient of thermal expansion of different materials. This design has been applied on a MEMS seismometer as a contribution to NASA’s InSight Mars mission.