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S

Scientific Reports on Micro and Nanosystems

edited by Christofer Hierold

Vol. 42

Morten Vollmann

Combination of Axial Strain Tuning

and Gate Bias Tuning for

Carbon Nano Tube Resonators

1^stEdition 2025. (8), XX, 188 pages. € 64,00.
ISBN 978-3-86628-855-3

Contents

Abstract

Carbon nanotube (CNT) resonators exhibit exceptional potential for high-frequency and large-range eigenfrequency tuning, yet practical demonstrations have long been limited by the difficulty of precisely applying axial strain. This thesis overcomes that challenge by introducing a custom micro-electro-mechanical system (MEMS) with chevron-style thermal actuators capable of displacing the CNT’s clamping ends and generating pure tensile strain levels up to 1.4%. By combining this axial strain with gate-bias-induced strain, frequency tuning of 67MHz was achieved, equivalent to over 150% relative tuning, reaching eigenfrequencies over 120MHz across multiple devices.

To perform such axially straining experiments, new MEMS structures were designed and fabricated according to design restrictions such as the compatibility with dry-CNT transfer methods. Suspended CNT lengths were between 2 and 4.2 μm with gate distances between 490 nm and 2 μm. Different designs of the actuators, thermally heated by electrical current, showed different ability to displace the ends of the electrodes with an efficiency of between 1 and 2.6 nmA−2. Including semi-conducting behaviour in FEM simulations explained the displacement response to current not just for low temperatures, but across the full operation range.

Straining experiments on the new MEMS platform included the analysis of the static strain response with gauge factors up to 108 for low gate biases, isolating the axial straining effect from gate bias straining and the combination of both.

A central contribution of this work is the detailed modelling of CNT resonators subject to uniaxial and/or gate bias induced straining. The modelling framework employs solutions to the nonlinear Duffing equation via harmonic balancing, a technique that captures both amplitude and phase behaviour of the resonator’s motional current. By including the transfercharacteristic directly into to modelling of the current, even more complex and asymmetric phases and different shapes of resonance peak were explained. This approach proves indispensable for accurately describing the interplay between electrostatic (gate) and mechanical (axial) strain, enabling detailed predictions of device performance. This has been possible only due to the knowledge of applied strain from the characterized actuators. The framework also allowed for the quantification of maximum axial strain of 1.4% before the CNT slipped from the electrodes.