SPM Blog: Why you shouldn’t just pick a cantilever that is “lying around”

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In this week’s blog I am concluding my little two-part series about the cantilever. Why so much space and effort dedicated to the SPM cantilever?  Because too often I encounter users who just grab whatever cantilever is available (i.e. lying around that someone else purchased or just lying around) and then they wonder why their image quality is poor or they cannot reproduce data.  The problem with the approach of “whatever is lying around” is that this little cantilever – before you mount your sample or optimize any operating parameters – will dictate the kind of interaction the cantilever has with the sample.   Most of the time I ask users in my various classes what kind of cantilevers/spring constants they use and they have no idea, which is really not good.

So…don’t just pick any cantilever – know its spring constant! Read below to be convinced…

The AFM cantilever is typically made of silicon or silicon nitride.  It does not have to be made of the same material as the tip.  Most cantilevers are made of silicon, but the very soft cantilevers require a different fabrication process and so they are manufactured from silicon nitride.  There are many manufacturers of AFM probes today such as AppNano, Asylum Research, Budget Sensors, Bruker, NanoWorld, Nanosensors, Mikromasch, and Olympus.   Probes can typically be purchased directly from the manufacturer or from distributors such as nanoscience and nanoandmore.

Most cantilevers users encounter probes that are in a rectangular or “diving board” geometry as the one shown here. 

Rectangular lever

Softer cantilevers made of silicon nitride are made in a triangular geometry, as in the one shown below, in order to achieve the softer spring constants.

Vscan air probe from AppNano

The cantilever’s dimensions – its thickness, length, and width – are critical as they govern the “stiffness” or “spring constant” of the ultimate probe.  Why do we care about the stiffness or spring constant?  Because that will control the interaction with your sample. 

Pick a cantilever that is too stiff (spring constant that is too high) and the cantilever will not bend or deflect (i.e. sense) your surface when it interacts with it.  Pick a cantilever that is too soft (spring constant that is too low) and the cantilever will be too compliant so that all the bending and deflection will be due to the softness of the lever, but not because of the interaction of the lever with the surface. 

So what is the spring constant of a cantilever?  Every box of cantilevers you buy will have a nominal spring constant value on it from the manufacturer. How accurate is it? Unfortunately, the manufacturer value can be off by quite a bit.  Why?

 For a perfectly rectangular beam (which is an excellent approximation for most AFM cantilevers in a diving board or rectangular geometry), the equation is

K=Ewt3/4L3

Where k= spring constant, E=Youngs modulus of cantilever material (typically silicon), w=cantilever width, t=cantilever thickness, L=cantilever length.  Manufacturers have a pretty good idea of the dimensions of the width and length, but the accuracy of the thickness remains a challenge since these cantilevers are typically only a few microns thick.  So a small error on a parameter that is cubed….can result in a large uncertainty in the value of the spring constant! 

Another important relationship to understand is derived from single harmonic oscillator theory:

w2=K/m

Where w=cantilever resonance frequency and m=mass. Now we don’t typically measure the mass of the cantilever, but we very often do measure its resonance frequency when conducting a tune for tapping mode.  You can see from this equation that cantilevers with higher resonance frequencies correspond to stiffer spring constants.

If you really want to know the spring constant with certainty, there are many methods the user can employ to calibrate the spring constant. Maybe we will leave that for a topic for another blog.   But the most important thing:  don’t just grab any spring constant lever for your image – consider its spring constant and the material properties (i.e. stiffness and adhesion) or your sample and select accordingly!

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