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 (TCf ) 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 TCf of 0.6 ppm/K in CMOSMEMS technology to date, revealing the excellent frequency stability over temperature and time for practical applications in the future.