Final Report Summary - MACNEMS (Mechanical Amplification in Carbon-based NanoElectroMechanical Systems)
In the framework of the Seventh Framework Programme (FP7) project MACNEMS, we have set out to explore ways to amplify the mechanical vibrations of nanoresonators made from single carbon nanotubes and graphene sheets. These resonators are the subject of intense research due to their exceptional features, which make them promising candidates for a number of applications. For instance, the low masses, low spring constants, and/or high resonant frequencies make these resonators ideally suited as sensors for extremely small masses or forces. One of the main problems for the realisations of such applications is the fact that the mechanical vibration amplitudes of nanotube and graphene resonators are very small and therefore hard to detect. Typically, these small amplitudes are transduced into an electrical signal and then amplified with high gain. In this way, however, one cannot improve the 'intrinsic' signal-to-noise ratio of the resonator itself. If the mechanical signal of the resonator does not surpass the mechanical noise, the electrical amplification is basically useless, because it amplifies mechanical signal and noise by the same amount. In contrast to electrical amplification, our project had as a goal to explore methods to directly amplify the mechanical signal before it is converted into an electrical signal. We proposed two methods, namely parametric amplification and self-sustained oscillations, to reach this goal.
Early on, we managed to grow ultra-clean carbon nanotubes following the fabrication method pioneered at TU Delft. These nanotubes are grown in the last step of the fabrication process and are not contaminated with solvents or resists. They display a very high degree of purity, both concerning their (quantum-) electrical and mechanical properties. In addition, they have shown mechanical quality factors up to Q = 100 000. A high quality factor is a sign of low damping and is important for many experiments, because it increases the mechanical amplitude and determines the width (in frequency) of the mechanical resonance. These ultra-clean carbon nanotube devices were used in a majority of the experiments described in the following.
We demonstrated for the first time parametric amplification with nanotube resonators (A. Eichler et al., Nano Lett. 11, 2699, 2011). As suspected, we found that nanotube resonators are ideal candidates for parametric driving due to the ease and efficiency with which the mechanical spring constant is modulated with an external signal. We achieved an amplification of the mechanical amplitude of a factor 10 and found that the amplification is limited by nonlinear damping.
Nonlinear damping is usually not found in nanoresonators made from semiconductors or metals, but we found that nanotube and graphene mechanical resonators feature strong nonlinear damping (A. Eichler et al., Nature Nanotech. 6, 339, 2011). This surprising result has far-reaching implications for the use of nanotube and graphene resonators for many experiments like mass sensing or the detection of quantum motion, because it means that large driving forces decrease the mechanical quality factor. By using very small driving forces, we achieved a record quality factor of 100 000 with a graphene resonator.
Years ago, it was predicted that mass sensors made from carbon nanotubes might reach a sensitivity corresponding to the mass of a single hydrogen atom (or a single proton). We achieved this sensitivity for the first time in an experiment (J. Chaste et al., Nature Nanotech. 7, 301, 2012). This corresponds to an improvement of the resolution by two orders of magnitude and might lead to many new applications for nanomechanical mass sensors. For instance, we used a nanotube mass sensor to monitor the temperature dependence of desorption of Xenon atoms from the nanotube surface and determined the corresponding binding energy. The implementation of parametric amplification in a mass sensing experiment might allow even better mass sensitivity. Efforts to realise this implementation experimentally are part of ongoing work in the group.
Carbon nanotubes offer the prospect of mechanical self-oscillation that is induced by electrical transport through the nanotube. The nanotube acts as a so-called 'quantum dot' with a well-defined number of electrons. We studied the electrical characteristics of nanoresonators made from ultra-clean nanotubes and found very exotic electrical signatures that, in earlier work from TU Delft, were assigned to mechanical self-oscillation. In order to prove this relation, we tried measuring the motion of the resonator induced by the electrical current in the absence of a direct driving force, but found that our detection technique is not suitable for this experiment. We therefore started developing a novel detection technique based on cross-correlation noise measurements (of the electrical signal generated by the mechanical motion). In a first series of measurements, we recently demonstrated unprecedented force sensitivity with a nanotube resonator (J. Moser et al., submitted). In future work, we hope to conclusively measure self-oscillation by combining measurements of electrical current with this new technique for detecting mechanical signals.
During our project, we frequently came across rather exotic features that stem from the large mechanical nonlinearities of nanotube and graphene resonators. Nanotubes are narrow wires with a diameter of about 1 nm, and graphene sheets are only one atom thick. As a result, mechanical nonlinearities are particularly pronounced in comparison to other nanomechanical resonators. The discovery of large nonlinear damping mentioned above is an example of this. Another effect related to nonlinear forces is strong coupling between different mechanical eigenmodes of a resonator. Strong coupling, also called 'internal resonance', describes the exchange of energy between eigenmodes of a system when their resonance frequencies have an integer ratio. We demonstrated such coupling with a carbon nanotube resonator for the first time (A. Eichler et al., Phys. Rev. Lett. 109, 025503, 2012). Interestingly, the coupling can be switched on and off by changing the resonance frequencies of the eigenmodes with a gate voltage. This opens up new possibilities for fast manipulation of radio-frequency signals with nanotube resonators. A further example of nonlinear behaviour is related to symmetry breaking in the oscillation potential of a nanotube. Potential symmetry breaking, which has not been studied in nanoresonators so far, produces a shift of the equilibrium position of the resonator upon driving it to high amplitude (in loose analogy to the effect of thermal dilatation that stems from the asymmetry in the potential of neighbouring atoms in solid state materials). We recently succeeded in measuring this shift with an ultra-clean carbon nanotube resonator (A. Eichler et al., in preparation). The symmetry breaking is brought about by a static deformation of the nanotube shape. Such static deformations are quite common in our devices. We believe therefore that the shift of the equilibrium position, although it has been overlooked so far, is also a commonly occurring effect that needs to be understood.
In conclusion, we believe that we have made significant progress towards using mechanical amplification techniques in real applications. In particular, we have demonstrated that parametric amplification is possible with carbon nanotube resonators, and we have established that the technique is in principle compatible with state-of-the-art experiments like mass sensing. Maybe more importantly, we have gained surprising new insights into the complex nonlinear behaviour of nanotube and graphene resonators. Since nonlinearities are typically large in these devices, it is of great importance to understand these phenomena. In some cases, these nonlinear effects might allow new functionality, such as the strong and tunable coupling between different mechanical eigenmodes of a nanotube resonator.
Early on, we managed to grow ultra-clean carbon nanotubes following the fabrication method pioneered at TU Delft. These nanotubes are grown in the last step of the fabrication process and are not contaminated with solvents or resists. They display a very high degree of purity, both concerning their (quantum-) electrical and mechanical properties. In addition, they have shown mechanical quality factors up to Q = 100 000. A high quality factor is a sign of low damping and is important for many experiments, because it increases the mechanical amplitude and determines the width (in frequency) of the mechanical resonance. These ultra-clean carbon nanotube devices were used in a majority of the experiments described in the following.
We demonstrated for the first time parametric amplification with nanotube resonators (A. Eichler et al., Nano Lett. 11, 2699, 2011). As suspected, we found that nanotube resonators are ideal candidates for parametric driving due to the ease and efficiency with which the mechanical spring constant is modulated with an external signal. We achieved an amplification of the mechanical amplitude of a factor 10 and found that the amplification is limited by nonlinear damping.
Nonlinear damping is usually not found in nanoresonators made from semiconductors or metals, but we found that nanotube and graphene mechanical resonators feature strong nonlinear damping (A. Eichler et al., Nature Nanotech. 6, 339, 2011). This surprising result has far-reaching implications for the use of nanotube and graphene resonators for many experiments like mass sensing or the detection of quantum motion, because it means that large driving forces decrease the mechanical quality factor. By using very small driving forces, we achieved a record quality factor of 100 000 with a graphene resonator.
Years ago, it was predicted that mass sensors made from carbon nanotubes might reach a sensitivity corresponding to the mass of a single hydrogen atom (or a single proton). We achieved this sensitivity for the first time in an experiment (J. Chaste et al., Nature Nanotech. 7, 301, 2012). This corresponds to an improvement of the resolution by two orders of magnitude and might lead to many new applications for nanomechanical mass sensors. For instance, we used a nanotube mass sensor to monitor the temperature dependence of desorption of Xenon atoms from the nanotube surface and determined the corresponding binding energy. The implementation of parametric amplification in a mass sensing experiment might allow even better mass sensitivity. Efforts to realise this implementation experimentally are part of ongoing work in the group.
Carbon nanotubes offer the prospect of mechanical self-oscillation that is induced by electrical transport through the nanotube. The nanotube acts as a so-called 'quantum dot' with a well-defined number of electrons. We studied the electrical characteristics of nanoresonators made from ultra-clean nanotubes and found very exotic electrical signatures that, in earlier work from TU Delft, were assigned to mechanical self-oscillation. In order to prove this relation, we tried measuring the motion of the resonator induced by the electrical current in the absence of a direct driving force, but found that our detection technique is not suitable for this experiment. We therefore started developing a novel detection technique based on cross-correlation noise measurements (of the electrical signal generated by the mechanical motion). In a first series of measurements, we recently demonstrated unprecedented force sensitivity with a nanotube resonator (J. Moser et al., submitted). In future work, we hope to conclusively measure self-oscillation by combining measurements of electrical current with this new technique for detecting mechanical signals.
During our project, we frequently came across rather exotic features that stem from the large mechanical nonlinearities of nanotube and graphene resonators. Nanotubes are narrow wires with a diameter of about 1 nm, and graphene sheets are only one atom thick. As a result, mechanical nonlinearities are particularly pronounced in comparison to other nanomechanical resonators. The discovery of large nonlinear damping mentioned above is an example of this. Another effect related to nonlinear forces is strong coupling between different mechanical eigenmodes of a resonator. Strong coupling, also called 'internal resonance', describes the exchange of energy between eigenmodes of a system when their resonance frequencies have an integer ratio. We demonstrated such coupling with a carbon nanotube resonator for the first time (A. Eichler et al., Phys. Rev. Lett. 109, 025503, 2012). Interestingly, the coupling can be switched on and off by changing the resonance frequencies of the eigenmodes with a gate voltage. This opens up new possibilities for fast manipulation of radio-frequency signals with nanotube resonators. A further example of nonlinear behaviour is related to symmetry breaking in the oscillation potential of a nanotube. Potential symmetry breaking, which has not been studied in nanoresonators so far, produces a shift of the equilibrium position of the resonator upon driving it to high amplitude (in loose analogy to the effect of thermal dilatation that stems from the asymmetry in the potential of neighbouring atoms in solid state materials). We recently succeeded in measuring this shift with an ultra-clean carbon nanotube resonator (A. Eichler et al., in preparation). The symmetry breaking is brought about by a static deformation of the nanotube shape. Such static deformations are quite common in our devices. We believe therefore that the shift of the equilibrium position, although it has been overlooked so far, is also a commonly occurring effect that needs to be understood.
In conclusion, we believe that we have made significant progress towards using mechanical amplification techniques in real applications. In particular, we have demonstrated that parametric amplification is possible with carbon nanotube resonators, and we have established that the technique is in principle compatible with state-of-the-art experiments like mass sensing. Maybe more importantly, we have gained surprising new insights into the complex nonlinear behaviour of nanotube and graphene resonators. Since nonlinearities are typically large in these devices, it is of great importance to understand these phenomena. In some cases, these nonlinear effects might allow new functionality, such as the strong and tunable coupling between different mechanical eigenmodes of a nanotube resonator.