Contact Resonance
Viscoelastic Mapping ModeAFM

Asylum ResearchIntroduction

Asylum Research’s Contact Resonance Viscoelastic Mapping Mode option for
the MFP-3D™ and Cypher™ S Atomic Force Microscopes (AFMs) enableshigh resolution, quantitative imaging of both elastic storage modulus andviscoelastic loss modulus. It is just one of the many nanomechanical tools in
Asylum’s NanomechPro™ Toolkit. The contact resonance technique isparticularly well suited for characterizing moderate to high modulus materials
in the range of about 1 GPa to 200 GPa.

How it works
The contact resonance principle
The contact resonance technique, first developed in the1990s by the Yamanaka and Arnold groups,1,2 is based on theprinciple that the resonance of an AFM cantilever changes
when it is in contact with a sample. As shown in Figure 1, thecantilever and sample in contact can be thought of as one
spring coupled in series to a second spring and dashpot inparallel. Here, the first spring represents the elastic responseof the cantilever and the second spring and dashpot represent
the viscoelastic response of the sample. Therefore, as thestiffness of the sample contact changes, the frequency ofthe contact resonance changes (higher stiffness = higherfrequency). Changes in the viscous response of the sample
are reflected in the Quality factor (Q) of the contact resonance(more viscous = lower Q). Standard contact mechanics models
can be used to then convert these stiffness and dissipation
measurements to elastic modulus and loss modulus.

Contact resonance imaging
The contact resonance technique is based on contact modeimaging. This means that the AFM cantilever scans along thesample surface at a constant force (the setpoint), measured
by the cantilever deflection. As the tip encounters higher(or lower) features, the tip-sample force begins to increase(or decrease). A feedback loop continuously adjusts the heightup (or down) to keep the force at a constant value (thesetpoint). This motion is recorded as the sample topography.
While the tip scans the sample in contact mode, the contact
resonance is continuously changing with the sample
mechanical properties. In order to measure the contact
resonance, a very low amplitude vertical modulation is
introduced by driving either the cantilever or the sample.
The drive is at a relatively high frequency, so this modulation
does not affect the contact mode feedback loop, but themodulation nevertheless couples to the cantilever deflection
and can be measured using a lock-in amplifier.

Figure 1: The cantilever-sample contact is modeled as a Kelvin–Voigt
mechanical equivalent, where a spring represents sample stiffness anda dashpot represents sample dissipation. The frequency of the contact
resonance is proportional to sample stiffness and the quality factor of
the contact resonance is proportional to the sample dissipation.

Contact resonance implementations
Various implementations of the general contact resonancetechnique have been developed as summarized in the tableon the next page. Dual AC Resonance Tracking (DART) will
be discussed in greater detail in following sections. Note that
it is also possible to make contact resonance measurements
at single points rather than during continuous imaging or
point-wise mapping, though this is less popular since theintroduction of faster imaging techniques.

Faster and more quantitativeMethods

What it does

Benefits

Disadvantages

Fixedfrequency 1

The cantilever response is measured ata fixed frequency which varies as thecontact resonance frequency shifts.

Simple to implement and produceselastic contrast images.

Produces only qualitative results since
the frequency shift itself is not measured.
Contrast is lost if the peak shifts too far
from the selected frequency.

PLL
frequency
tracking 2

A phase-locked loop (PL L) uses thephase of the cantilever response to track
the contact resonance frequency.

The actual contact resonance frequency
is tracked.

Difficult to tune the PLL to achieve stablefrequency tracking due to spurious
phase shifts in the response. Does notmeasure the Q of the resonance.

Frequencysweep(chirp) 3,4,5

A frequency sweep (chirp) is done ateach point. The cantilever response
is Fourier analyzed to recover the full
frequency response.

Measures the entire frequency response,
so both the frequency and Q are
obtained. Additional analysis is possible
based on more complex models.

Mapping is quite slow when collecting
large numbers of pixels. Each sweep
must be done slow enough for thecantilever to respond (rate limited by Q).

DART 6,7,8

The amplitude and phase response at
two frequencies (bracketing the contactresonance) is measured, which enables
the contact resonance to be tracked.

Provides both the contact resonancefrequency and Q. The tracking is
extremely fast, so DART imaging can bedone at normal imaging rates.

The full response is not measured, soanalysis is more limited than frequency
sweep methods.

DART
Fastest contact resonance frequency and quality factor imaging
Dual AC Resonance Tracking (DART) is an exclusive technology invented by Asylum Research in collaboration with Oak Ridge
National Laboratory10 that tracks the contact resonance as it shifts in response to changing material properties (see Figure 2). It
provides both the frequency and the Q of the contact resonance, to characterize both stiffness and dissipation. It accomplishes
this while operating at normal imaging rates or even at fast scanning rates with small cantilevers on the Cypher AFM. Figure 3
shows a DART contact resonance image of a 80 / 20 polypropylene (PP) / polystyrene (PS) blend. Since both the resonancefrequency and the quality factor are measured with DART, we can detect differences in both the elasticity and dissipationof the two materials.

Figure 2: DART drives the actuator at two frequencies that bracket
the contact resonance. By measuring the amplitude and phase of
the cantilever response at both frequencies, the equivalent simple
harmonic oscillator can be calculated, yielding both the contact
resonance frequency and Q. The two frequencies are continuously
adjusted to track the contact resonance peak.

2

Figure 3: DART images of the PP/PS blend show high dissipation (Q)contrast, but much less stiffness (frequency) contrast. This is consistent
with bulk measurements on PP and PS which indicate that their elastic
modulus is very close (2.8 GPa vs. 2.4 GPa) but their loss modulus isquite different (134 MPa vs. 49 MPa). Adapted from reference 7.

Where does contact resonance fit inwith other techniques?
Contact resonance is just one tool in the NanomechPro
Toolkit. One should understand and explore the full rangeof options, including AM-FM Viscoelastic Mapping Mode,instrumented nanoindentation, and force curves. Asylum
believes that the ability to compare results from multiple
techniques is valuable and adds confidence to the results.

Figure 7: Elastic modulus image of a patterned titanium film onsilicon, overlaid on topography. blueDrive photothermal excitation on
the Cypher AFM was used for DART contact resonance imaging. Notethe strong contrast between these two very high modulus materials.

ModeMaster™ software interface
Simpler quantitative results
ModeMaster is an exclusive Asylum software feature that
automatically configures the software for the desired
measurement type and guides the user through theexperiment. For DART contact resonance, the ModeMaster
panel assists in setting up both the stiffness measurement
and calibrating contact mechanics models using a reference
sample with known modulus. This makes it possible torapidly and simply start making measurements, all based onwell-established methods,7 but without the full complexity.
Experts are, of course, free to delve into as many advanced
operational and analysis options as they like.

AM-FM Viscoelastic Mapping Mode is another exclusive
Asylum technique for quantitative nanomechanics. Like
contact resonance methods, AM-FM can measure both theelastic and loss modulus over a very wide range. This makes ita useful direct comparison to contact resonance results.
Asylum’s MFP NanoIndenter option allows users to readilyswitch between true, ISO-compliant nanoindentation modulus
measurements and AFM techniques. However, it makes
much larger indentations than AFM techniques, which limits
its applicability on thin films and limits it to relatively coarse
lateral resolution for modulus mapping applications.
Force curves, measured individually or with force mapping, arealso widely used for indentation measurements. However, on
moderate to high modulus materials, the curves rapidly begin
to approach the constant compliance case that one wouldmeasure on an infinitely stiff sample. That is, the difference incontact slope in the two cases becomes vanishingly small andthe uncertainty grows large. In contrast, the frequency shiftassociated with contact resonance can be measured with far
greater accuracy and precision.

References
1. U. Rabe and W. Arnold, Appl. Phys. Lett. 64, 1493 (1994).

6. B.J. Rodriguez et al., Nanotechnology 18, 475504 (2007).

2. K. Yamanaka et. al., Appl. Phys. Lett. 64, 178 (1994).

7. A. Gannepalli et al., Nanotechnology 22, 355705 (2011).

3. K. Yamanaka et al., Appl. Phys. Lett. 78, 1939 (2001).

8. D. Yablon et al., Macromolecules 45, 4363 (2012).

4. U. Rabe et al., J. Phys. D: Appl. Phys. 35, 2621 (2002).

9. S. Jesse et al., Nanotechnology 18, 435503 (2007).

5. A.B. Kos and D.C. Hurley, Meas. Sci. Technol. 19, 015504 (2008).

10. Protected by certain U.S. patents assigned to or licensed by
Oxford Instruments Asylum Research, Inc., including: 8,448,501;
8,024,963; 7,603,891; 8,448,502; 7,775,086.

Visit AFM.oxinst.com for more informationThe foregoing datasheet is copyrighted by Oxford Instruments Asylum Research, Inc. Oxford Instruments Asylum Research, Inc. does
not intend the datasheet or any part thereof to form part of any order or contract or regarded as a representation relating to theproducts or service concerned, but it may, with acknowledgement to Oxford Instruments Asylum Research, Inc., be used, applied orreproduced for any purpose. Oxford Instruments Asylum Research, Inc. reserves the right to alter, without notice the specification,
design or conditions of supply of any product or service. Application Note 29 – 6/2014.

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