Workshop on Nanomechanics – Montpellier, France

This workshop organized with CNRS customers in Montpellier among the RéMiSoL network (Réseau des Microscopies à Sondes Locales) focused on all aspects of contact mechanics at the nanoscale and in particular using resonant contact AFM mode (CR-AFM). Contact Resonance tracking measures the shift in resonance frequencies of the cantilever while the tip is scanning the surface in contact mode (Z-feedback on the vertical deflection signal). This contact resonance frequency depends on the contact stiffness and it is therefore possible to translate it into the sample elastic modulus via a standard calibration procedure.

In practice, the resonance frequency shift is controlled using the so-called DRFT technique (Dual Resonance Frequency Tracking) performed using a Zurich Instruments HF2LI lock-in Amplifier. The drive excitation is fed via a mechanical transducer from Olympus (V103-RM for example) placed on the sample holder (the sample is then glued with an epoxy).

DFRT schematics

Figure 1: HF2LI Connection diagram for DFRT measurements

Figure 1 shows the functional diagram of contact resonance tracking by applying an Amplitude Modulated drive with direct sideband detection at fc+fm and fc-fm around the resonance. The frequency fc stands for the carrier (or cantilever) frequency while fm is the modulation frequency. It is sometime also referred to as Double-sideband Suppressed-carrier (DSB-SC) modulation. The difference of the sideband measured amplitude is then fed into a PID loop to control the carrier reference oscillator. Please note that for simplicity only the first 3 demodulators, used to track the first eigenmode, are displayed but the next 3 demodulators are used in a similar fashion for the second eigenmode. Such a configuration is also used for DFRT-PFM, for measurement of both the in-plane and out-of-plane piezoresponse force contribution.

An introduction to the theory of contact mechanics, from Richard Arinero [1], was followed by application examples of domain walls in a wood cell as well as in material composites. Below are example images obtained with a Bruker microscope connected to the HF2LI via a SAM box (Signal Access Module):

Stiffness map at 2 different eigenmodes

Please note the better contrast at the higher eigenmode. The reason is that the cantilever stiffness better matches the sample stiffness. Such behavior provides the motivation to track several eigenmodes with difference spring constants and Q-factors. The measurements’ sensitivity as a function of expected sample stiffness exhibits a S-shape behavior as shown in this slide (see complete presentation by following the link in the reference):

 

Modeling of cantilever dynamics

Figure 2: contact stiffness and free cantilever stiffness relationship for the first 3 eigenmodes

From this figure it is clear that for a soft sample, with low intrinsic rigidity, a softer cantilever should be chosen while for a hard sample stiff cantilevers are better. The important relation is the ratio of contact stiffness to free cantilever stiffness. The advantage of multiple eigenmode tracking is that one can be sensitive to both soft and hard sample properties simultaneously (of course within the cantilever mechanical properties), which is particularly useful in the case of samples with various compositions.

To conclude, this workshop allowed the participants to confront both theory and experiment, hands-on practicals being organized in 2 groups to look at different samples in a studious yet friendly atmosphere.

Travaux pratiques

Figure 3: Two ‘hands-on’ parallel sessions with Nanoscope V Controller and LabOne running on the same PC with different screens.

 

Acknowledgment

I am very grateful to Michel Ramonda for hosting and organizing this workshop at the Centrale de Technologie en Micro et nanoélectronique (CTM) in Montpellier as well as David Albertini for coordinating this event within the RéMiSoL network.

Reference

[1] https://indico.mathrice.fr/event/35/