Two modes are better than one - Advanced AFM methods

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For the first 20 years or so, resonant AFM modes such as tapping modes - that take advantage of oscillating the cantilever at its resonance frequency - occurred at the frequency of the cantilever’s first or primary eigenmode.   An eigenmode is the cantilever’s natural vibration.  Note the difference between an eigenmode (a specific vibrating motion) and a harmonic, which is simply an integer multiple of a frequency (but the same vibrating motion).  The first eigenmode of a purely rectangular cantilever looks something like this:

Eigenmode 1

Oscillating at this fundamental resonance frequency (which is typically in the 10’s or 100’s of kilohertz), useful information is collected in terms of the amplitude of oscillation (which is actually the feedback parameter in tapping mode) and phase response.  These channels are mapped simultaneously with the topography to provide additional information on the surface such as material properties or highlighting edges.

But over the past decade, measurements at higher order eigenmodes have begun to bear some fruit.  By oscillating at a higher frequency, different vibrations or eigenmodes can be accessed. For example, for a purely rectangular beam, the second and third eigenmode occur at a frequency ~6.2 and 17.5 times the fundamental (i.e. so clearly different than harmonics), and look something like this:

Mode 2 and 3 (Eigenmode schematics courtesy of Asylum Research, an Oxford Instruments company.)

Why is this useful?  Because higher order eigenmodes are significantly stiffer than the fundamental mode; the stiffness increases fairly quickly with eigenmode. This means that different modes of a cantilever provides different interactions between the lever and sample because the interaction is largely governed by the cantilever stiffness. So one cantilever can provide a spectrum of interactions with the surface by taking advantage of higher order modes.

Multifrequency measurements, which actually combine oscillation at two or more eigenmodes, have been among the most useful modes to take advantage of higher order eigenmodes.  One of my favorite multifrequency measurements is Bimodal AC imaging.  This method is currently commercially available on Asylum Research Oxford Instrument AFMs.  In this technique, a small amplitude oscillation of the higher order mode is superimposed or piggybacked onto the fundamental mode resulting in a cantilever vibration such as this for combining modes 1 and mode 3:

Piggyback mode 1+3

My favorite implementation is when there is no feedback on this higher order mode. So now, in addition to the regular information you obtain from tapping mode, you can also obtain higher order mode amplitude (no feedback this time) and phase data, which provide new opportunities for contrast.  An example of this is shown below.

Bimodal image example

This blend has 3 polymers. On the right is the conventional phase image where you really only get one image contrast. On the left is the phase in the higher order mode, where now you can clearly see three sources of contrast – light orange, light purple, and dark purple. The 3 components now are easily visualized.  Bimodal imaging mode has provided new methods of contrast to better identify individual components in our heterogeneous material. Additional variations of bimodal AC imaging include putting feedback on that higher order mode (you can either feedback off the frequency, amplitude, or phase) to try and get some additional information on the surface.

Finally, why stop at 2 modes?  My colleague Santiago Solares out of George Washington University is an expert at pushing the envelope with trimodal imaging and even beyond!

Dalia Yablon, Ph.D.

SurfaceChar LLC

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