Ultrasonic force microscopy (ufm): nanomechanics and subsurface detection
Atomic Force Microscopy (AFM) was introduced around 30 years ago to investigate solid surfaces with nanoscale resolution . It started with simply measuring the topography and then it was extended to a wealth of properties ranging from magnetic and electric ones to elasticity and viscosity . However, standard AFM is limited in sensitivity when it comes to measure mechanical properties; in fact it is mainly restricted to materials in a medium range of elastic modulus values, e.g. polymers.
Ultrasonic Force Microscopy (UFM) has been then introduced as a possible approach to overcome these limitations, while maintaining a high sensitivity to morphology . In particular it allows one to map locally heterogeneous materials with high elastic moduli or ultrathin molecular layers [4-9].
In Figure 1, the UFM setup is shown in a schematic way. It is basically an AFM working in standard Contact Mode (CM), but the samples are rigidly mounted on a piezo-disc, which excites a periodical vertical displacement. With the help of the drawing, we can address the main characteristics of the technique:
• The vertical vibration is performed at a frequency f<sub>U</sub> >> f<sub>C</sub>, the cantilever first resonance, and off higher resonant modes of the cantilever itself. f<sub>U</sub> is between 2 and 8 MHz and the wavelength is around a few mm, larger than the sample thickness.
• A cantilever with a low stiffness constant (k) can be considered “infinitely” rigid at f<sub>U</sub>. The sample indentation (d<sub>cont</sub>) can be thus modulated even for relatively high elastic moduli, otherwise not possible at f<sub> </sub>C</sub>, due to the low k value.
• An amplitude modulation is also introduced at f<sub>D</sub> co</sub>, the feedback cut-off frequency, with a maximum amplitude below 1 nm (Agilent 33220A). Thus the detection of the cantilever deflection is performed at a frequency f<sub>D</sub> around a few kHz,<sub> </sub>where it is very soft thus maintaining high sensitivity to force and morphology.
• d<sub>cont</sub> depends on the reduced Young’s Modulus (E<sup>*</sup>) of the materials. The higher E<sup>*</sup> the lower d<sub>cont</sub> and the higher the UFM signal.
• To collect the UFM data, a digital lock-in amplifier (Zurich, HF2LI) is employed.
As described by contact mechanics, UFM can sense a certain volume of the sample in the area of contact. If any, defects present at some depth below the surface can be located. UFM thus allows for subsurface imaging [10-11] and in particular the exploration of buried interfaces. In Figure 2 we show an example of how UFM can perform subsurface detection. The sample is represented by a thick Multiple Layer Graphene (MLG) placed on a polymeric film (COC, with a T<sub>g</sub> around 150°C) and structured by means of hot embossing.
• The suspended areas are not visible with standard Tapping Mode (TM), but show up with a dark contrast in UFM: they are even more compliant than COC.
• These areas behave like plates bending and the total indentation (d<sub>tot</sub>) is the sum of d<sub>cont</sub> plus the plate bending (d<sub>flex</sub>).
• In the suspended areas, d<sub>tot</sub> can be thus larger than d<sub>cont</sub> on COC though d<sub>cont</sub> on Graphite is lower than that.
Graphene is nowadays one of the most investigated new materials  and it is representative of a wider group, the so called 2D materials such as MoS<sub>2</sub>. We have recently demonstrated that UFM can study single or multiple Graphene interfaces in real devices. One can also characterize the properties of suspended flakes, including in particular their eigen‑modes [13-14].
Our efforts are presently, and will be in the near future, directed towards the development and the improvement of these kinds of investigations, highly relevant for nanoscale science and for nanotechnology applications.
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