Resonant Nanomechanical Motion At Gigahertz Frequencies PDF Download

Abstract: The focus of this thesis is the study of gigahertz-range resonance modes in a hybrid nanomechanical resonator. The applications are numerous in the fields of high speed communications, frequency filtering, and micromechanical sensor technologies. Equally important is the potential impact at the fundamental physics level, where this ultra-high frequency mechanical resonator cooled to millikelvin temperatures could be used to probe quantum effects. The design of the resonator is a modification of the doubly-clamped nanobeam to include arrays of high-frequency sub-micron cantilevers. In a certain set of collective resonance modes of the structure, the arrays act as frequency determining elements by resonating phase-coherently at gigahertz frequencies, while the large central beam effectively amplifies the cantilever motion. The resulting advantages of the high frequency response of the resonator over the conventional doubly-clamped nanobeam include two orders of magnitude net signal increase as well as enhancement of the quality factor through suppression of acoustic clamping losses. The resonator model is solved both analytically and numerically to extract the relevant modal dynamics. The analytical solution captures the main features of the linear modal structure. In the nonlinear driving regime, a solution using perturbation theory yields the frequency-response interaction. The resulting relations describe both the standard nonlinear response of the modes as well the mechanism of anharmonic modal coupling between widely spaced modes of the resonator. Resonators from both silicon and nano-crystalline diamond have been fabricated and their vibration response measured over a 3-GHz wide spectral range at temperatures down to 30 millikelvin. The structure exhibits resonances up to 1.5 GHz - the highest frequency mechanical motion reported to date. The data set also includes measurements of the temperature dependence of the material sound velocity and dissipation in the millikelvin range. Finally, the mechanism of nonlinear modal coupling is used as a new technique of monitoring the energy of a gigahertz-range mechanical mode through the frequency shift induced on a low order mode. This technique has potential applications to the current experimental efforts to demonstrate quantum mechanical effects in macroscopic resonators.