Model-based design of MEMS resonant pressure sensors (2011)

The massive integration of micromechanical structures on ICs to allow microsystems to sense and control the environment is expected to be one of the most important technological breakthroughs of the future. At present, cheap and small MEMS sensors are emerging in countless applications. Automotive and telecommunication industry have fueled the biggest R&D effort so far in this area. Prominent results, among others, are the accelerometer guarding the safety systems in vehicles, the miniature microphone in cellphones and inkjet printing heads. Although miniaturization is the main driver of MEMS development in industry – reducing cost by decreasing material consumption and allowing batch fabrication, MEMS offer an important collateral benefit with respect to traditional systems: an increase of applicability and reliability. This development very much concerns existing microelectronic building blocks that by efficient integration with each other can grow to more functional, intelligent systems on the same chip. One such block is the crystal oscillator for frequency reference used in clocks, radios, computers and cellphones etc. to provide a stable clock signal for digital integrated circuits, and to stabilize frequencies for radio transmitters and receivers. Regarding the vast demand of timing devices for time-keeping and frequency reference applications, the research of MEMS based oscillators has a lot of attention. It is expected that these oscillators – built with a MEMS resonator – will offer smaller form factor, improved reliability, and lower solution cost than the common crystal oscillator with its IC incompatible quartz resonator. Efforts over recent years have shown that MEMS resonators are capable of high quality factor Q, exhibit low temperature drift and pair excellent phase noise performance to low power consumption. As MEMS based oscillators need vacuum conditions for proper and reliable operation of the mechanical resonator, the packaging process of these devices must provide direct caps to the resonators that make a hermetic sealing. The life-time testing of these sealings pose a big challenge to in-situ pressure detection methods in resonator samples during fabrication. We have realized a sensitive pressure sensing operation of the resonator itself by reading out the damping forces exerted by the residual gas in an out-of-plane, low frequency resonance mode. No additional structures or signals other than the common resonance parameters, Q and !0, required! The behavior of the damping forces in the resonator agrees well to a new model that we particularly developed for designing resonators as pressure sensors in the mbar range. Thanks to free molecular flow in the cavity of typical resonators these forces can be formulated analytically with just one parameter dependent on numerical evaluation. Because of the direct physical significance of this and other parameters in the derived formulas, the model provides valuable clues for the optimization of sensor design. It saves time-consuming trial-and-error loops of design and fabrication that would be needed alternatively. The methods and results of this thesis demonstrate that out-of-plane, low frequency resonance mode operation of resonator samples establishes sensitive detection of cavity pressure offering cheap and easy life-time testing in industry. Our designoriented model for the governing forces between residual gas and resonator structure holds for a multitude of different geometries within a margin of error of 12%, making model-based design of MEMS resonant pressure sensors to a reality.