Designing MEMS Disk Resonator Based Biological Mass Sensors Under Fabrication Uncertainty

A radial-contour mode disk resonator has its own advantages, less energy loss and less airflow damping, over existing counterparts such as surface acoustic wave (SAW) resonators and quartz crystal microbalance (QCM) sensors. Taking these advantages of the disk resonators, we design a biological mass sensor in this paper. One of the important challenges in the design of biological mass sensors is inherent uncertainties of MEMS fabrication processes that may strongly affect to the disk resonator performances. Parameters of main effect on the sensor performance (i.e., mass sensitivity, S_m) are identified among many inputs based on response surface method screening process. The shape of the circular disk deviates from a desired perfect circle due to the fabrication uncertainty. Degree of deviation from perfect circularity significantly affects to the disk frequency. In addition, because of the presence of electrodes in sides, the disk rotation angle must be considered as a parameter that can affect the frequency. In this work, the disk resonator is designed to perform robust to the geometric parameter variations. A series of simulation models is developed to obtain natural frequency and mass sensitivity because analytical solutions cannot predict the resonant frequency variation originated such geometric variances. A non-deterministic metamodeling technique is introduced to replace the time consuming simulation models and used for the efficient local sensitivity analysis which is the main challenge of simulation based robust design. The design problem is to find the mean disk diameter in-between 800 μm and 1400μm to achieve robust maximum S_m. A mathematical construct, Error Margin Index (EMI) combining performance mean and deviation, is employed in the solution search algorithm to find a robust optimum design. Our design solution is the mean disk diameter of 1280 μm. The difference of mean mass sensitivity between traditional optimum design and our robust design is about 0.7μm²/ng. The standard deviation of mass sensitivity at optimal design is high (0.68 μm²/ng) and that of our design is low (0.39 μm²/ng).