Computational characterization of noise in nonlinear nanomechanical resonators

Recent breakthroughs in nanotechnology have paved the way for huge advances in the field of nano-electro-mechanical systems (NEMS). Nanomechanical resonators are used as accurate mass and force sensors in mass spectrometry and atomic force microscopy. In most current sensing schemes, the resonators operate in the linear regime, where changes in mass and force are detected by tracking the shifts in the resonance frequency. The use of resonators operating in the nonlinear regime has been recently proposed due to shrinking device sizes and some claimed advantages over linear operation. As with linear resonators, the sensor performance is ultimately limited by the inherent frequency fluctuations arising from various sources of noise. However, due to nonlinear behavior, device dynamics is intricate and noise characterization is more challenging. The fundamental sensitivity limits of resonant sensors operating in the nonlinear regime need to be determined quantitatively in order to examine their performance and assess their pros and cons over linear resonators. In this thesis, we present an efficient computational technique for characterizing the frequency fluctuations in nonlinear Duffing resonators due to noise. The method is based on repurposing and adapting a non Monte Carlo stochastic analysis technique that was originally developed for noise analysis of analog electronic circuits. The proposed technique presents the capability for noise characterization under various dynamic sensing schemes, e.g., when drive frequency is time-varying and continually updated in a closed-loop setup. We compare the results obtained with the proposed technique against extensive, carefully run Monte Carlo simulations and demonstrate that the same accuracy can be achieved with drastically reduced computation time and in a more robust manner. We furthermore compare the results of our proposed method with experimental open-loop sweep characterizations reported in the literature. We analyze the open-loop sweep method and highlight its shortcomings as a sensing scheme. Finally, we compare the noise performance in the linear and nonlinear operating regimes, and discuss the advantages of using one over the other.