Very high frequency probes for atomic force microscopy with silicon optomechanics

Atomic force microscopy (AFM) has been constantly supporting nanosciences and nanotechnologies for over 30 years, being present in many fields from condensed matter physics to biology. It enables measuring very weak forces at the nanoscale, thus elucidating interactions at play in fundamental processes. Here we leverage the combined benefits of micro/nanoelectromechanical systems and cavity optomechanics to fabricate a sensor for dynamic mode AFM at a frequency above 100 MHz. This is two decades above the fastest commercial AFM probes, suggesting opportunity for measuring forces at timescales unexplored so far. The fabrication is achieved using very-large scale integration technologies inherited from photonic silicon circuits. The probe's ring optomechanical cavity is coupled to a 1.55 um laser light and features a 130 MHz mechanical resonance mode with a quality factor of 900 in air. A limit of detection in displacement of 3.10-16 m/sqrt(Hz) is obtained, enabling the detection of the Brownian motion of the probe and paving the way for force sensing experiments in the dynamic mode with a working vibration amplitude in the picometer range. Inserted in a custom AFM instrument embodiment, this optomechanical sensor demonstrates the capacity to perform force-distance measurements and to maintain a constant interaction strength between tip and sample, an essential requirement for AFM applications. Experiments show indeed a stable closed-loop operation with a setpoint of 4 nN/nm for an unprecedented sub-picometer vibration amplitude, where the tip-sample interaction is mediated by a stretched water meniscus.


Introduction
Atomic Force Microscopy (AFM) has many applications in nanosciences, from micro and nanotechnologies to nanobiology. AFM has rapidly become a standard technique for surface observation and force spectroscopy at the nanoscale, the instruments having constantly gained in performance 1,2,3,4,5 . This is particularly true for the dynamic mode, where the probe tip is driven in oscillation close to a mechanical resonance of the probe 6,7 . This mode was progressively preferred to the contact mode as it increases the measurement sensitivity while reducing the degradation of fragile and soft samples like those found in biological experiments 8 .
In this oscillating mode, the parameters of the probe, namely mechanical resonance frequency, quality factor and stiffness, have a direct impact on measurement bandwidth, vibration amplitude and force sensitivity. They bound in turn the achievable imaging rate and time and spatial resolution in force tracking. Over the last 15 years, impressive results have been obtained on the way to improve the temporal and spatial resolution in AFM, with great impact in basic science and technology. On one hand, up to tens of frames per second imaging is now achieved, allowing the direct observation of biological processes under native-like conditions 4,5,9 . On the other hand, operation at sub-nanometer amplitude, typically 100 pm, gives access to atomic resolution in vacuum, in air and in liquids 10,11,12 .
Molecular bonds imaging has even been achieved in this regime of low vibration 13 .
However, such a speed and such extreme resolution cannot be obtained simultaneously. Here, we propose an AFM probe technology based on silicon optomechanics able to overcome the limitation.
The AFM probe is basically a force sensor built from a mechanical resonator. The existing AFM probe technologies are presented in Figure 1. Depending on the vibration mode, dimension and mechanical properties of the resonator, different ranges of frequency and vibration amplitude may be reached. Fig. 1: Existing AFM probe technologies for the dynamic mode. The colored ellipses represent the typical range of vibration amplitude and mechanical resonance frequency for each probe technology. The red plain surface corresponds to the achievement of this work, while the red dashed ellipse indicates more broadly the potential of the very-highfrequency / ultra-high-frequency optomechanical technology. The lower bound of the vibration amplitude corresponds to the Brownian motion at room temperature, the upper bound to the maximum value typically met in AFM experiments.
The prevailing AFM probe, used since the beginning of the AFM age 1 , has been the microfabricated cantilever, whose displacement has usually been transduced by optical beam deflection 14 or laser interferometry 15 . Its fundamental flexural mode of vibration features a low stiffness, 0.1-100 N/m, typically, which is an advantage as far as the mechanical responsivity to the measured force is concerned. The cantilever technology has benefited from numerous developments, in particular aiming at

AFM probe technology
This work 10 fm reducing its dimensions. Indeed, smaller dimensions imply higher resonance frequencies enabling high-speed applications while maintaining the desired stiffness.
State-of-the-art commercially-available fast microscopes typically employ 30 µmlong cantilevers 16 . Most advanced experiments, allowing the direct observation of biomolecules in liquid at the video rate, have used even smaller cantilevers 5,9 . The vibration frequency f reaches here a few MHz, while the optical detection spot faces the diffraction limit, setting a limit to the performance improvement by mere downsizing. It is interesting to note that in the last decades, many works were devoted to the integration of transducers for driving and sensing the vibration of mechanical probes, based on capacitive, piezoelectric, thermal or piezoresistive principles 17,18,19,20 . Even though these options could enable smaller cantilever dimensions and higher vibration frequencies (up to 100 MHz in ref. 20), they have not been massively adopted yet. In particular, the batch fabrication of tiny AFM cantilevers is hampered by the difficulty to produce the tips at their extremity.  23,24,25,26 . The in-plane geometry of the device also facilitates the fabrication of high-aspect ratio tips with nanometer apex 24,26,27 .
The characteristics of these MEMS probes are represented in Figure 1. They combine a resonance frequency of up to 15 MHz and a vibration amplitude below 100 pm, extending the experimental window offered by cantilevers and quartz probes for AFM 24,26 . The limit of detection (LOD) of the vibration is at best 10 -15 m/ÖHz (ref. 24,27) and the efficiency of the electromechanical transduction quickly degrades with decreasing dimensions, setting a strict limit to the maximum operation frequency reachable by such MEMS technology 28 . The LOD, being inversely proportional to the transduction efficiency, must indeed be kept below the probe's Brownian motion amplitude to benefit from optimal force resolution set at the thermomechanical limit. This constraint is all the more stringent that a higher resonance frequency generally comes along with a higher stiffness, further lowering Brownian motion amplitude.
For a bit more than a decade, the growing understanding of optomechanical interactions in semiconductor materials combined with advances in micro-and nano-fabrication have enabled the realization of miniature devices combining high quality factor (Qopt) optical cavities and mechanical resonators on a chip 29 . In such systems, the large optomechanical coupling at play between the optical and mechanical modes allows the on-chip detection of sub-femtometer displacements 30 . It was identified that such a level of performance could impact mechanical sensing applications and in particular AFM probe technology 31,32,33 .

Results and discussion
Principle of operation Figure 2 gives an overview of the concept of the optomechanical AFM probe. As shown in Figure 2a, an AFM probe is basically a harmonic mechanical resonator driven by an actuation signal. Any interaction force between the probe's tip and the sample surface impacts the eigenfrequency and/or the dissipation of the resonator, which impacts in turn the amplitude and/or the phase of the vibration signal. In a reduced-order mechanical model, the probe is described by its free resonance frequency f0, quality factor Q and effective stiffness Keff (See "Methods"). Our specific optomechanical AFM probe design is illustrated in Figure 2b. It consists of a silicon ring acting both as the mechanical resonator and an optical cavity. In such a structure, the extensional mechanical modes and the optical ring modes are strongly coupled 29,40 , which leads to an efficient optical transduction of mechanical motion.
The laser light traveling in the waveguide evanescently couples in and out of the ring. The detection of motion, carried through the output optical signal, is also favored by the high quality factor of the optical resonance. The device is designed to operate at a wavelength close to 1.55 µm. Actuation of the vibration of the ring can be obtained through electrostatic forces by applying a sine voltage to the electrodes in close proximity of the ring or through optical forces by modulating the intensity of the optical field injected and stored in the cavity. Figure 2c shows the shape of the extensional mechanical mode used in the present study to reach the VHF range. Its azimuthal order is 9, allowing to locate the 3 spokes at nodes and the tip at a maximum of vibration amplitude. In this configuration the probe's tip is set into a quasi-1D vertical oscillation by the vibration of the ring, which is actuated with a significant amplitude.  Ne manque-t-il pas un schéma pour expliquer la transduction optomécanique ? (mode de cavité et variation de la transmission optique) at the edges of the chip give access to the capacitive transducers of the probe. The optical waveguide coupled to the ring extends up to the center of the chip where grating couplers allow a convenient interconnection with optical fibers. A schematic overview of the fabrication procedure is depicted in Figure 3b. A first lithographic step and reactive ion etching (RIE) are used to pattern the grating couplers in the 220-nm silicon device layer of the SOI wafer. In a second step, variable shape electron beam lithography followed by a RIE step defines the main elements of the probe in the whole device layer thickness, including the ring, its anchors and its tip, the waveguide, the capacitive transducers and their associated electrical interconnects. Back-side deep RIE, or alternatively a combination of saw dicing and RIE, is realized through the whole thickness of the underlying silicon substrate in order to make the probe chips detachable from the wafer. The ring of the probe is finally released by etching the 1 µm-thick sacrificial oxide layer using vapor HF, the under-etching being controlled so that the ring becomes free to vibrate but remains anchored to the substrate through the spokes and the wider central post. Results of the fabrication process are shown in Figure 3c-e. In particular, Figure 3d shows a device with fiber transposers aligned and glued to the probe chip to ensure interconnects between the grating couplers and the optical fibers. Figure 3e gives a closer view of the optomechanical resonator of an AFM probe. The tip length is 5 µm and we estimate that the curvature radius at its apex is smaller than 30 nm (See Fig. S1 in "Supplementary Information"). The waveguide-ring optical coupling is obtained by spatial overlap of the evanescent tails of the propagative mode of the waveguide and of the mode of interest of the ring cavity. It scales exponentially with the gap distance g between both objects. Total transfer is achievable at the optical resonance for the so-called critical coupling. In our devices, the critical coupling condition is typically met for a gap distance g = 100 nm, a distance that maximizes here the efficiency of the optomechanical transduction. This value was determined first by Finite Element Modeling (FEM) and then finely tuned by experimental characterizations. The VLSI process is well-controlled and reproducible in terms of fabrication precision, typically less than 10 nm with respect to the design, which ensures that the devices can routinely operate close to the optimal condition. The intrinsic quality factor of the optical cavity mode depends on many parameters such as the roughness of the sidewalls after fabrication or the exact design of the structure (tip and spoke positions). In our experiments we observe optical ring modes featuring intrinsic quality factors in the range of 10 4 to 10 5 (refer to ref. 41 for a detailed study of the optical losses).     . We estimate that the optical modulation is linear with Vdrive in the range 0 to 800 mV and that the modulation is about 30% for Vdrive = 800 mV. A slope is clearly visible on the phase signal: -8 degrees over 400 kHz. It corresponds to a delay of 55 ns between the input signal and the internal reference of the LIA that we attribute to a propagation delay in the measurement chain.

Sensing of tip mechanical interaction in the AFM configuration
The optomechanical probes were integrated in a dedicated scanning-probe instrument, depicted in Figure 5a.     Labview software. Several input/output modules allow to acquire/generate the signals. A 20-bit DAC and a high-voltage amplifier were specifically designed for the application, offering the resolution and speed required to drive the Z piezo actuator. Extra input/output signals are available for the purpose of the control of the instrument and for a future evolution of the system.
The instrument was first used to characterize an optomechanical probe in air. The vector signal was fitted to cancel the measurement background signal. Figure 6a shows the obtained result, demonstrating that the Lorentzian shape of the mechanical information was recovered, as well as a 180-degree phase rotation at resonance. The resonance frequency of this probe was f0 = 130.61 MHz and the quality factor Q = 870. The vibration amplitude at resonance was 0.32 pm for the drive parameters chosen in the experiment. This value is typically one order of magnitude lower than what was obtained under vacuum (Figure 4), resulting from a lower mechanical quality factor in air. In spite of a lower Q, the Brownian displacement noise was significantly higher than the noise floor (LOD < 3.10 -16 m/ÖHz) and remained the main noise contribution to the probe signal. We then performed approach-retract cycles where the sample, here a massive golden tip, was moved towards the optomechanical probe tip using the Z piezo actuator. During the experiment we recorded the piezo displacement command and the variation of the probe resonance frequency versus time, as illustrated in Figure 6b. Figure Figure 7 from approach-retract experiments.   Figure 7a. Before closing the regulation loop, the probe was oscillating freely at its resonance frequency with an amplitude of 0.32 pm. The resonance frequency was used as the PID input signal and the setpoint is set to a relative shift of +55 ppm, corresponding to a force gradient of +4 nN/nm. At t = 0, the probe tip is far from the sample and the PID commands the Z piezo actuator to reduce the distance (blue line). At t = 90 µs, the mechanical tip-sample interaction occurs, inducing a positive frequency shift. As described in the previous section, it corresponds to the sudden formation of a water meniscus bridging the probe tip to the sample, adding a stiffness to the probe's mechanical resonator. As the control signal exceeds the setpoint, the PID commands in turn an increase in the tip-sample distance. A stabilization stage takes place during the following 120 µs (red line) leading to a steady state (green line) where the PID input signal equals the setpoint value, and the Z piezo position remains constant. A certain time is required to reach an equilibrium where the generated meniscus yields a spring constant that sums to the probe spring to reach the targeted setpoint. Figure 7b gives a supplementary insight into the phenomenon: once the mechanical interaction is detected, the tip-sample separation is increased by 95 nm so as to reach the equilibrium state corresponding to the setpoint. If we refer to Figure 6c, this displacement is lower than the 110 nm separation needed to break the meniscus, indicating that for the equilibrium reached in closed-loop, the tipsample interaction is mediated by the liquid meniscus. As a consequence, the Z feedback is operated with the probe tip in contact with a stretched meniscus, corresponding to the retract curve in Figure 6c (purple line). This is made possible thanks to the very low amplitude of vibration of our probe technology. In particular, such dynamic operation mode is drastically different from what occurs with cantilevers at large vibration amplitude (> 10 nm) that allow the tip to go in and out of the water meniscus when approaching the surface in ambient conditions.   the sample, the Z piezo actuator decreases the tip-to-sample distance. Red line: the mechanical interaction occurs at t = 90 µs and the PID adjusts the piezo displacement to keep the signal equal to the setpoint. Green line: a steady state is reached. The Z piezo position and the probe signal (relative frequency shift) are kept stable. The measurement raw data are plotted in thin lines (acquisition rate: 1 MSa/s). Bold lines result from a moving average. (b) Variation of the probe signal (relative frequency shift) versus the piezo command when the feedback loop is closed. The chart is a representation of the signals of the time response in (a) using the same color code. The right axis represents the force gradient derived from the relative frequency shift (See "Methods").

Conclusions
The purpose of this work was threefold: (1) to produce VHF optomechanical probes for the purpose of future AFM applications using a batch fabrication process, (2) to implement the probe sensors in an instrument in the AFM configuration, and (3) to demonstrate the capability to meet the basic requirements of AFM operation.
Optomechanical probes were fabricated on 200-mm wafers using very-large scale integration (VLSI) technologies derived from the fabrication process of photonics circuits on silicon. A major feature of these probes is their very-high resonance frequency, about 130 MHz, which is greater than that of any other AFM probe technology, like short cantilevers, quartz or MEMS probes. As fabricated, the radius of curvature at the tip apex is currently of less than 30 nm. We characterized the probes under vacuum and in air, using capacitive and optical actuation, combined with optical detection. Results evidenced that the optomechanical detection enabled the observation of the Brownian motion, well above the setup noise floor lower than 3.10 -16 m/ÖHz. This paves the way for exquisite measurements resolutions, limited only by the thermomechanical noise at room temperature. In particular, we showed that the probes vibrate down to sub-picometer amplitudes, which is an operation regime out of reach of any other AFM technology. The probes were equipped with optical fiber interconnects and implemented in air in a dedicated instrument in the AFM configuration. Approach-retract experiments evidenced the sensitivity to the mechanical interaction with a sample, as well as the formation of a water meniscus responsible for the hysteretic behavior of the liquid-mediated contact between the probe and the sample. Moreover, we demonstrated a stable closed-loop operation of the instrument, where the probe-sample distance was adjusted to stabilize the force gradient between the tip and the sample surface. These two latter results: sensitivity to the mechanical interaction and closed-loop operation, were obtained with an ultralow vibration amplitude of 0.32 pm. They are the central ingredients demonstrating that AFM experiments with these VHF optomechanical probes are achievable in a close future. They will be a key element for next-generation of AFM experiments, where ultra-high-speed imaging and nanosecond force tracking will be combined with a spatial resolution at the scale of the chemical bonds offered by very-low vibration amplitudes.

Governing mechanics
The probe mechanical resonator is considered here as one-dimensional as shown in Figure 4d. The second-order differential equation for the lumped resonator model can be expressed as "((̈+̇+ "(( = )*$+" ( ) + ,% ( ) where )*$+" is the actuation force of the probe vibration, ,% is the interaction force between the tip and the sample, "(( is the effective mass, "(( is the effective spring constant, is the damping coefficient, is the tip displacement. The lumped model assumes that the total energy is conserved as well as the displacement amplitude of the probe tip, leading to the calculation of "(( from the shape of the vibration mode ( ) obtained by Finite Element Modeling (FEM) and shown in The damping coefficient can be deduced from the experimental value Q of the mechanical quality factor:

Calibration of the vibration amplitude
The displacements indicated in the charts in Figures 4 and 6 are calibrated from the Brownian motion spectrum, assuming the linearity of the measurement chain. The displacement noise )$%AB_#=$%" coming from the thermal fluctuations is given at the resonance frequency @ by 48 : )$%AB_#=$%" = L 9D -E; where G is the Boltzmann constant and is the temperature ( = 300 K).

Measurement of the relative frequency shift
The relative frequency shift ∆ ⁄ is obtained from the variation ∆ of the phase between the probe signal and the driving signal given by the lock-in amplifier. The phase variation is converted to the relative shift of the resonator eigenfrequency knowing the characteristics of the phase rotation versus frequency. Experiments in Figure 6b-c and Figure 7 were carried out driving the probe at its free resonance frequency, i.e. !=) = @ = 130.61 MHz, where the slope s of the phase rotation versus the frequency is maximal (s = 836´10 -6 °/Hz in Figure 6a). Assuming small frequency shift around @ , the relative frequency shift is then given by:

Measurement of the force gradient
The force gradient ∆ experienced by the probe tip is deduced from the relative frequency shift (Eq. 8) as a change of the effective spring constant of the probe: