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Scientific Reports on Micro and Nanosystems

edited by Christofer Hierold

Vol. 31




Lalit Kumar


Energy Dissipation, Clamping and Motional

Currents in Suspended Room Temperature

Carbon Nanotube Resonators


1st Edition 2019. XXIV, 182 pages. € 64,00.
ISBN 978-3-86628-650-4












With continuous downscaling in NEMS based devices such as nanomechanical resonators, clamping is argued to be of significant importance as it controls two important aspects - mechanical stability and energy dissipation mechanisms. While theoretical work including analytical and atomistic simulations has been reported, the lack of sufficient experimental investigations currently limits our understanding of clamping mechanisms, especially at the nanoscale. This thesis reports on the experimental investigation of clamping effects performed with an individual suspended carbon nanotube based nanomechanical resonator at room temperature. Non-linear dynamics of resonators were exploited for insights into clamping strength and energy dissipation at room temperature. The research was carried out in collaboration with Laura V. Jenni and Miroslav Haluska.

The resonator devices were based on a bottom gate field effect transistor based architecture with a designed channel length of 2 μm and a channel gate distance of 270 nm. A selectively pre-characterized individual carbon nanotube was dry-transfered onto the source-drain palladium electrodes resulting in a bottom clamped configuration. Subsequent optional top-metallization of contact electrodes with 20 nm platinum using atomic layer deposition was performed to obtain a top-bottom clamped configuration. The clamping between the nanotube and the metal was presumably governed by surface interactions such as van der Waals and frictional forces.

The mechanical resonances of suspended carbon nanotubes were characterized by measuring both conduction modulation current and piezoresistive current. The former was attributed to the gate induced field effect while the latter was the result of strain modulation, both being proportional to nanotube motional amplitude. As a result of static displacement, induced by the DC gate bias, mixing of both motional currents at resonance was observed. For instance, at a DC gate bias of 1.4 V, 75% of the output current was conduction modulation current. The remaining 25% was piezoresistive current generated from the DC pre-strain of 0.0056% in the nanotube. For a 2.1 μm long and 1.8 nm diameter small bandgap semiconducting nanotube, the intermixing of motional currents was used to extract the low strain Gauge factor of 1.8.

The mechanical resonances were used to investigate clamping stability of both bottom clamped and top-bottom clamped devices. Under high DC gate bias > 1.5 V, non-linear Duffing response, attributed to large nanotube motional amplitude, was observed for all devices. Continuous operation under large DC gate bias resulted in an irreversible downshift in the resonance frequency. The Large motional amplitude of the nanotube initiated slipping which led to the decrease in the nanotube tension, or mechanical stress relaxation, which was observed as a decrease in the resonance frequency. For a bottom clamped nanotube device with a 2.1 μm suspended length and 2.4 nm diameter clamped on either side onto palladium electrodes, the onset of slipping was observed at a motional amplitude of 7.4 nm at a DC gate bias of 1.1 V. An additional nanotube tension of 70 pN was estimated to overcome the clamping forces to initiate slipping, quantifying the weak nature of clamping strength. The resonance frequencies decreased until saturation was attained. The saturated resonance frequencies were two to three times higher than the fundamental beam mode and were attributed to clamping induced residual strains. Residual strains for both clamping configurations were estimated in the range of 94-130 pN.

Weak clamping behavior was also assumed to influence energy dissipation through clamping losses. An already saturated bottom clamped device was subjected to top metallization resulting in two di erent clamping configurations for the same device. Top-bottom clamped device showed an improvement in quality factors up to two times and was attributed to the reduction in the non-linear damping. The amplitude dependent non-linear damping was significantly observed in bottom clamped devices. The same bottom clamped device, which observed an onset of slipping behavior at 7.4 nm, exhibited amplitude dependent non-linear damping at a motional amplitude of 11 nm (and higher). The non-linearity in energy losses and improved quality factors were attributed to possible external dissipation channels associated with clamping, which previously has only been discussed from a phenomenological and mathematical point of view.

The dynamic measurements based on resonance frequency downshift and saturation provides an alternative way for investigation of clamping effects on both mechanical stability and energy dissipation. The dependency on motional amplitude suggested a significant role of surface interactions on the clamped edges with forces in the order of pN. The experimental findings reported here argues against the assumption of perfect clamping conditions, which are often taken into consideration in various reported experimental and theoretical studies. Such assumptions might explain the discrepancies between the experimental findings and analytical or simulation based models for nanomechanical resonators.



Scientific Reports on Micro and Nanosystems

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