FridayAFM - Let's do the twist


Héctor here, your AFM expert at Nanosurf calling out for people to share their Friday afternoon experiments. Today I explore torsional resonance imaging as a way to increase lateral resolution.

In order to properly dance the Twist one has to twist the legs in one direction and the torso, arms, and head on the oposite direction, then reverse, then repeat. Something like this:


or like this, demonstrated with music:



In AFM, that sort of twisting movement receives the name of torsional, and refers to one of the modes in which an AFM cantilever can bend (the other two being flexural and lateral, see Ref 1 for an in-detail analysis for rectangular cantilevers). Why it is interesting? Because in theory torsional has better lateral resolution than flexural, and allows detection with a laser system, which is something that is more difficult with lateral oscillations (although in principle they are also good for lateral imaging resolution). So in principle... by oscillating the AFM probe in torsional mode we should be able to overcome the tip geometrical limitations and see atoms.


torsional 01
1 AFM cantilevers can oscillate in several ways, how they bend as they oscillate determines which signal should be used for detection. DFL for flexural, Lat for torsional, and something not shown here for lateral (e.g. self sensing with a built-in piezo)


Want a proof that torsional gives better lateral resolution? Use your finger! Find a surface with some roughness and poke it. Are you able to distinguish the individual elements? Try now sliding your finger sideways. 


torsional 02
1 By sliding your finger on a rough surface you can feel the small features better than if you just poke in several different locations.


Ok, you convinced me. How do I find the torsional modes and use them? Well, the most basic thing you can do is a frequency sweep using the DFL channel as input of your lock-in. There you will easily find the 1st harmonic of the flexural mode and its higher harmonics. Anything else that shows a peak (and a change in phase), is likely to be a torsional mode. How to confirm? Repeat the sweep but now using the Lat channel as input for your lock-in doing the sweep. The flexural peaks will decrease in amplitude and the torsional will increase. Then it is down to modelling to decide which is the peak you are after and which one gives you better signal. For instance, for Multi-75 probes these are the peaks in DFL and in Lat.


torsional 03
1 A frequency sweep can reveal the different oscillation modes, and by switching between DFL and Lat as input of your lock-in you will be able to tell which is which.


Important note: In order to excite the torsional modes the excitation needs to be asymmetrical. It doesn't matter if the frequency is the right one, if you shake the cantilever up and down only, you will never make it twist. This is where using photothermal excitation becomes handy, because by moving the photothermal excitation laser to one side you can easily provide energy for the torsional modes. 

By the way, on the figure above I provide you with some guidance of where to place the lasers, but don't take it as the perfect location, use it as starting point for optimization, you will need to move and adjust the laser positions looking at the peak amplitude and the overall noise in the generated signal.

So, once we know the frequency of the torsional modes, how can we use them? There are several ways they can be used. For instance, you can set a desired amplitude for the amplitude of the oscillation and use it as feedback, the closer you come to the surface, the smaller the amplitude, so the feedback responds rising the probe, the further you are, the larger the amplitude, so the feedback lowers the probe. Another way is to oscillate the probe at the torsional resonance and monitor it, but use static DFL as feedback, the closer you are, the more the probe bends up, the further you are, the more the probe bends down (or relaxes). In my case, I use this last one because it is easier to implement, and if the probe gets contaminated and its resonant frequencies shift, it doesn't matter for the static DFL.

How to mount the sample? Well, as I always say, start with something known, and since this mode is unknown to me, I'll go for something easy, HOPG, which is something conductive (conductive is always good), it can be atomically clean by peeling off the top layer with cell tape, and I know how it supposed to look like (see Ref 4).

The result? Judge by yourselves:

torsional 04
1 HOPG atomic lattice imaged with a Multi-75E probe using static DFL as feedback while oscillating the probe at its first torsional mode.

Important: Drift and noise are your enemies, you will need a noise-free environment and a solid floor and table, otherwise it doesn't matter how hard you try. Drift can occur for many reasons, the most common, thermal, so leave the sample and system on for as much as you can before trying imaging. Also, have in mind that sometimes you need to scan for a while until the surface or probe cleans up and the image starts to be clear. 

Important 2: Sometimes noise can be periodic and look a lot like the atomic lattice. A trick to discern it is keeping all scan parameters the same and zoom in or zoom out, noise will remain the same, atomic lattice will scale.


torsional 05
1 HOPG atomic lattice imaged with a Multi-75E probe using static DFL as feedback while oscillating the probe at its first torsional mode.

Note that I'm not including lateral scale bars, this is because in order to ease capturing these images, I switched the x-y feedback off, and hence I cannot provide lateral dimensions with confidence. However, we know the lattice dimensions of HOPG from other means, and this matches my estimation of distances in the images (you see, I do have numbers, I just prefer not giving them to you as I'm uncertain of the uncertainty).


torsional 06-1
1 HOPG atomic lattice imaged with a Multi-75E probe using static DFL as feedback while oscillating the probe at its first torsional mode.


Let's recap. Torsional resonance can seem like a strange new mode, however, exploring it carefully, using known samples and modes as stepping stones, it has a lot to offer. It can improve lateral resolution enabling you to see atoms. However, sample preparation and probe quality are always important, so don't despair if it doesn't work at the beginning. Here you got some guidance of how to look for oscillation modes, where to place lasers, and what to expect (at least for HOPG).

I hope you find this useful, entertaining, and try it yourselves. Please let me know if you use some of this, and as usual, if you have suggestions or requests, don't hesitate to contact me. 


Further reading:

[1] Bircher, Benjamin A.. Fluid characterization by resonant nanomechanical sensing. 2014, Doctoral Thesis, University of Basel, Faculty of Science.  10.5451/unibas-006331515

[2] Look for other atomic (or atomic lattice) resolution images in our gallery: 

[3] STM on HOPG: 

[4] Eichhorn, A.L., Dietz, C. Torsional and lateral eigenmode oscillations for atomic resolution imaging of HOPG in air under ambient conditions. Sci Rep 12, 8981 (2022). 





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