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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
Abstract
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.
Keywords:
Scientific Reports on Micro and Nanosystems
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