A CMOS-Integrated MEMS Platform for Frequency Stable Resonators-Part II: Design and Analysis

The Part II of this paper presents the numerical model and experimental validations of the CMOS-MEMS resonant transducers fabricated by a reliable TiN-composite (TiN-C) platform. To characterize the frequency behavior of the proposed resonator, an analytical model based on average displacement is used to determine the equivalent lumped parameters of the proposed devices. Considering the free-free beam (FFB) design elaborated in Part I, the oxide fin provides a very strong boundary restriction, which forces the vibration like a short clamped-clamped beam (CCB) combined with two additional tip cantilevers. This segmented analytical model shows a good agreement with our measurement results. In addition, the implementation of TiN-to-TiN transduction gap and oxide-rich composite structure has enabled a deep sub-micron (<400 nm) gap capacitive resonators and controllable temperature-dependent response while attaining a low frequency drift over time due to mitigation of dielectric charging. Although the constituent materials of the CMOS-MEMS resonator are still limited by commercial foundry service, a low-temperature coefficient of frequency (TC (f)) is achievable by taking temperature coefficient of Young's modulus (TCE), the coefficient of thermal expansion (CTE), and residual stress of standard BEOL into consideration. As a result, the proposed TiN-C pseudo free-free beam (PFFB) resonator shows the lowest passively compensated TC (f) of 0.6 ppm/K in CMOS-MEMS technology to date, revealing the excellent frequency stability over temperature and time for practical applications in the future.