Atomic Force Nanoscope

TL;DR

This paper introduces an Atomic Force Nanoscope that uses nanotube resonators and electron beam detection to achieve ultra-sensitive, high-resolution surface imaging and mechanical property measurement at the nanoscale.

Contribution

It presents a novel AFM technique combining nanotube resonators with electron beam detection for real-time nanoscale surface imaging and mechanical analysis.

Findings

Nanotube resonators enable ultra-sensitive force detection.

Electron beam detection allows real-time mechanical property measurement.

The method achieves high-resolution surface topography imaging.

Abstract

Atomic Force Microscopy (AFM) allows to probe matter at atomic scale by measuring the perturbation of a nanomechanical oscillator induced by near-field interaction forces. The quest to improve sensitivity and resolution of AFM has forced the introduction of a new class of resonators with dimensions well below the micrometer scale. In this context, nanotube resonators are the ultimate mechanical oscillators because of their one dimensional nature, small mass and almost perfect crystallinity, coupled to the possibility of functionalisation, these properties make them the perfect candidates as ultra sensitive, on-demand force sensors. However their tiny dimensions make the measurement of the mechanical properties a very challenging task in particular when working in cavity free geometry at ambient temperature. By using a highly focused electron beam, we show that the mechanical response of nanotubes can be quantitatively measured while approaching to a surface sample. By coupling electron beam detection of individual nanotubes with a custom AFM we can image the surface topography of a sample by measuring in real time the mechanical properties of the nanoresonators. The combination of very small size and mass together with the high resolution of the electron beam detection method offers unprecedented opportunities for the development of a new class of Atomic Force Nanoscope (AFN).

Equations

$$A(\omega )=\frac{F_{ext}}{\sqrt{m_{eff}^2({\omega }_0^2-{\omega }^2{)}^2+{\gamma }^2{\omega }^2}}$$

$$\varphi (\omega )=\arctan \left(\frac{\gamma \omega }{m_{eff}({\omega }_0^2-{\omega }^2)}\right)$$

$$\frac{\partial F_i}{\partial r_i}=2k_i\frac{\delta f_i}{f_{0,i}}\text{ and }{F}_{D,i}=\frac{k_i}{\sqrt{3}}\left(\frac{1}{Q_0}-\frac{1}{Q_1}\right)$$

Full text

In this context, nanotube resonators are the ultimate mechanical oscillators because of their one dimensional nature, small mass and almost perfect crystallinity, coupled to the possibility of functionalisation , these properties make them the perfect candidates as ultra sensitive, on-demand force sensors. However their tiny dimensions make the measurement of the mechanical properties a very challenging task in particular when working in cavity free geometry at ambient temperature. By using a highly focused electron beam, we show that the mechanical response of nanotubes can be quantitatively measured while approaching to a surface sample. By coupling electron beam detection of individual nanotubes with a custom AFM we can image the surface topography of a sample by measuring in real time the mechanical properties of the nanoresonators. The combination of very small size and mass together with the high resolution of the electron beam detection method offers unprecedented opportunities for the development of a new class of Atomic Force Nanoscope (AFN).

Nanoscience and nanotechnology rely on the ability to manipulate and probe objects with a resolution in the deep nanometer range [1,2,3,4]. In the last three decades, advances in the field have been possible mainly thanks to the development of Atomic Force Microscopy (AFM) [5,6,7]. The idea behind the technique is at the same time very simple to understand and impressive in the attainable results: a tiny mechanical oscillator with a sharp tip at the extremity is approached to a surface and the evolution of the mechanical properties of the probe is monitored in real time to get information about the sample topography and properties. Generally the mechanical oscillator used in AFM is a micrometer sized silicon cantilever presenting a very sharp tip at the extremity [8]. The need to increase the force sensitivity and spatial resolution, pushed the researchers to develop alternative mechanical oscillators based on self-assembled structures with submicrometer dimensions. Prominent examples are silicon based nanowires [9,10] and carbon or boron nitride nanotubes [11,12,13,14] and even bidimensional suspended membranes [15,16]. These new probes, because of their minute size and mass and almost perfect cristallinity, couple high spatial resolution and force sensitivity reaching the zepto-newton ($10^{-24}$ N) range [17] for carbon nanotubes working in cryogenic environment. Despite their potentiality for Scanning Probe Micriscopy, so far nanotubes have never been used in microscopy paractical applications. The major drawback for the further development of this new kind of probes is the extreme difficulty to detect their position and motion. It is worth mentioning that the mechanical properties of suspended nanowires have been elegantly measured via optical interferometry [18] leading to a first proof of concept of nanowire based scanning force microscope [19]. Despite the effort and recent progress, optical detection schemes can be hardly applied to nanotubes which are the ultimate mechanical oscillators and force sensors: their diameter, in fact, ranging from 1 nm to few tens of nanometers, is too small to be possibly detected with optical techniques. Very recently, electron microscopy has been shown to detect the thermally induced resonant properties of nanomechanical resonators with picogram effective masses [9] and even attogram scale carbon nanotubes [20]. However, to the best of our knowledge, this technique has not been applied for nanotube based force microscopy.

In this study we demonstrate that electron beam detection of mechanical oscillators can be harnessed to develop the first example of scanning force microscope based on individual suspended nanotubes. The individual nanotube is mounted on top of a custom AFM working in situ in a Scanning Electron Microscope (SEM) at a pressure of $\approx 10^{-5}$ mbar. The highly focused electron beam of the SEM is positioned, in the so-called ”spot mode”, on the externally driven nano-oscillator and the inelastically scattered electrons (SE) are monitored to measure the resonator motion with a spatial resolution of 0.4 nm. As in standard non-contact AFM, the mechanical response of the nanotube is monitored in real time via amplitude and phase locking, while approaching a sample, allowing to reconstruct the surface topography. This new technique allows to take advantage of the exceptional properties of nanotubes as force sensors for scanning microscopy. For standard electron microscopy, the spatial resolution, given by the electron beam size, is below 1 nm and it represents a three orders of magnitude improvement with respect to optical techniques. The high focusing of the electron beam further increases the motion detection resolution for unidimensional systems[9,20]. We therefore demonstrate for the first time, that one dimensional oscillators can be really harnessed and used for scanning force microscopy.

In this work we used boron nitride multiwalled nanotubes (BNNTs) realized via Chemical Vapour Deposition (CVD) [21]. CVD BNNTs present a very high structural purity with no evident defects in a spatial region reaching the micrometric range. The nanotubes are glued at the extremity of an electrochemically etched tungsten tip, fixed on a three axis piezo inertial motor mounted inside a SEM (FEI-Nova nanoSEM). In figure 1 we present a scheme of the experimental set-up and a SEM picture of one nanotube used in this study in front of an electrochemically etched tungsten tip. The electron beam is set fixed at a chosen working point along the section of the NT. This working point is chosen so that the variation of the SE intensity around this working point stays linear, see figure 1e. To counteract the drift of the nanotube with respect to the electron beam, a feedback loop acts directly on the SEM deflection coils to control the position of the electron beam and keep constant the low frequency component of emitted secondary electron (SE) intensity detected via a Everhart-Thornley Detector (ETD).This method is a significant breaktrough in the field of position control and act like a 1D nano-GPS. This allows to maintain, for the whole duration of the experiment, the electron beam at a constant working position. The intensity of the emitted SE are recorded in real time via a Specs Nanonis SPM electronics and analyzed to extract the DC and AC fluctuating components.

BN nanotubes are mechanically excited with an external piezo dither and the variations of SE, related to the relative displacement of the NT around the working point, are recorded as a function of the excitation frequency. When excited by an external sinusoidal force $F_{ext}(\omega)=F_{ext}e^{i\omega t}$, the nanotube behaves in first approximation as a spring-mass system with oscillation amplitude and phase with respect to the excitation given by:

[TABLE]

with $m_{eff}$ the oscillator effective mass, $\omega_{0}=\sqrt{\frac{k}{m_{eff}}}$ the resonant frequency and $\gamma$ the damping factor. In figure 2a we present the response of a nanotube with diameter $D\approx$50 nm and length $L=18\ \mu$m, when varying the frequency of excitation. The mechanical response is characterised by a resonance at $f_{0}=\omega_{0}/2\pi\approx 270$ kHz and a quality factor, defining the inverse of the damping rate, $Q\approx 250$. In contrast to previous studies on nanowires and single walled carbon nanotubes [19,9,20], we do not observe a double resonant peak due to non degeneracy of polarisations. This further confirms the high structural quality and geometrical symmetry of BN nanotubes used during this work.

To confirm that the detected resonance is due to the mechanical motion of the nanotube, we switch the SEM operation mode from ”spot mode” to the conventional full frame imaging: when excited at the resonance the nanotube position exhibits the standard resonant profile for the fundamental mode of a single clamped oscillator, as described by the Euler-Bernoulli equation. In figure 2c we plot the SEM images for different excitation amplitudes confirming that for the range of excitations used during the experiment, the oscillator stays in its linear regime.

As the interaction of the oscillator with its environment is modified, one observes a change in both the frequency and the amplitude at resonance. The shift in resonance frequency $\delta f$ is related to the conservative force response, whereas the broadening of the resonance (change of quality factor $Q_{0}\rightarrow Q_{1}$) is related to dissipation [22]:

[TABLE]

where the index $i$, indicates the component of the position vector. In practice, during a typical experiment, two feedback loops allow us to work at the resonance and maintain constant the oscillation amplitude $a_{0}$. Monitoring the frequency shift $\delta f$ and the resonance quality factor $Q_{i}$, obtained from the excitation voltage or the oscillation amplitude, thus provides a direct measurement of real and imaginary parts of the mechanical impedance.

To demonstrate the possibility to use a nanotube as the force sensor of a scanning probe microscope, we firstly approached a very sharp tungsten tip to the oscillating nanotube. While approaching the tungsten tip down to the contact we record the evolution of the phase between the nanotube oscillation and the exciting dither and of the oscillation amplitude. This first experiment is performed in an open-loop configuration: any variation of the interacting environment is directly measured by a change of both the oscillation amplitude and the phase with respect to the excitation. Once the mechanical response of the NT is modified by the tip-NT interaction, we kept the distance constant and we performed a scanning picture of the tungsten tip, as in standard AFM. As shown in figure 3a, the amplitude and phase shift as a function of the position of the tip correctly detect the spatial force field induced by the tungsten, and consequently reconstruct the tip shape.

As a further demonstration of the potentialities of the NT-SFM, a BNNT (diameter $D=80$ nm and length $L=20\ \mu$m) with resonant frequency $f_{0}\approx 350$ kHz and oscillation amplitude of $\approx$ 10 nm scans at a distance of $\approx$ 10 nm a (100) silicon surface while a double feedback loop acts on both the phase and the amplitude. In figure 3b we plot a cartography of a 1 micron silicon terrace, recording at the same time the excitation voltage applied to keep constant the amplitude and the frequency shift. Variations of both quantities allow to reconstruct the surface topography with a resolution of $\approx$ 100 nm, given by the size of the nanotube apex.

Eventually we take benefit from the versatility of the NT-SFM and in addition to what is presented above, we show in figure 3c, a static AFM and a SEM picture of gold nanoparticles deposited on a HOPG sample. In this case, by static we mean that the nanotube is neither excited nor oscillating: this operation mode is the analog of the static mode employed in standard Atomic Force Microscopy. The static AFM picture is obtained by recording the deflection of the nanotube during the scan; experimentally this quantity is given by the voltage command to the deflection coils to keep constant the SE emission intensity. When the nanotube deflects because of the interaction with the surface, its relative position with respect to the electron beam changes, therefore modifying the SE emission intensity. The feedback loop acting on the beam position allows to reconstruct precisely the displacement of the nanotube and consequently the surface topography.

In addition, it is worth mentioning the complementarity of this operation mode with the AC mode presented before: by recording the deflection of the nanotube it is in fact possible to quantitatively measure the total force which the nanotube is submitted to. Together with the measurement of the conservative force gradient via the frequency shift and the dissipative forces via the change in the quality factor, this method allows to completely characterise the force environment with an unprecedented resolution.

Altogether our pioneering work demonstrates that one dimensional oscillators such as boron nitride nanotubes can be harnessed as probe sensors for Scanning Force Microscopy. By using a highly focused electron beam we can detect and record the mechanical response of an individual nanotube. Coupling atomic force microscopy technology together with high resolution electron beam detection, allows to measure, in real-time, conservative and dissipative interactions as well as the complete static interactions of a nanotube with its environment. We elegantly exploited this new detection method to measure the surface topography of samples approached by the extremity of an individual nanotube. More in general, the highly focused electron beam allows to detect oscillators with diameters in the nanometer range, drastically increasing the force sensitivity and spatial resolution compared to standard atomic force microscope cantilevers and even more recent nanowires. Despite the current low quality of the images obtained in this first work, the technique here presented represents a clear breakthorugh for the field and pave the way for the development of a new class of ultrasensitive nanotube-based scanning force microscopes.

Acknowledgements

Authors acknowledge funding from the European Union’s H2020 Framework Programme / ERC Starting Grant agreement number 637748 - NanoSOFT.