Quantitative Mechanical Property Mapping at the Nanoscale with
PeakForce QNM
By: Bede Pittenger, Natalia Erina, Chanmin Su
Veeco Instruments Inc.

INTRODUCTION

The scanning probe microscope(SPM)1 has long been recognized as a
useful tool for measuring mechanicalproperties of materials. Until recently
though, it has been impossible toachieve truly quantitative material
property mapping with the resolution
and convenience demanded by SPM
researchers. A number of recent SPM
mode innovations have taken aim atthese limitations, and now, with therelease of PeakForce QNM™ by Veeco, it
is possible to identify material variations
unambiguously and at high resolution
across a topographic image. Thisapplication note discusses the principles
and benefits of the PeakForce QNM
imaging mode.

forward in the functionality of SPM.4 In
TappingMode the probe is vibrated near
the resonant frequency of the cantileverwhile it is scanned across the sample.
The tip only contacts the surface for asmall percentage of the time, keeping
the tapping force low and the lateralforces negligible. Consequently,
TappingMode has the ability to generate
high-quality data for a wide rangeof samples, making it the dominantimaging mode for most SPM applications
over the last ten years.

Researchers often use the SPM toacquire the force on the tip versus
its vertical position. The resulting“force curves” can then be analyzed todetermine a host of characteristics ofthe material beneath the tip. However,these force curves can only provide
data at one point on the sample surface
at a time. The technique of force
volume imaging collects force curves
at each pixel in an image and puts
them together to map the properties
across a larger sample.2 Though more
information is gathered, force volume
imaging is typically very slow, whichmakes detailed mapping impractical.
To solve this problem, Pulsed Force
Mode was developed. This approach
improves speed by using a relatively
fast sinusoidal ramping.3 Unfortunately,
this also makes the material property
measurements less quantitative.

The data types obtained from
TappingMode SPM are primarily
topography and phase. PhaseImagingTM
creates images of the phase of
the tapping response, which is a functionof the forces that the tip is experiencing.
Since the probe is oscillating, it
experiences attractive and repulsive
forces depending on its position in
the cycle in a way that is analogous
to force curves. A drawback to thetechnique is that the resonant behaviorof the probe also acts as a filter,
making it impractical to reconstruct theforce curves with sufficient precision
to extract quantitative mechanicalinformation.5–6 In 2008, Veeco released
HarmoniX® as a solution to thisproblem. HarmoniX adds a second
sensor with a much higher bandwidth
by offsetting the tip and measuring thetorsional signal.7–9 This technique has
been successful in resolving material
components in complex polymericsystems. The downsides of this approach
are that (1) it requires special probes,(2) the operation of the technique canbe complicated (especially in fluid),and (3) interpretation of the results issometimes difficult.

Veeco’s development of TappingMode™
imaging in 19934 was a key stepPeakForce QNM is a new modedeveloped by Veeco that provides

SPM AND MECHANICALPROPERTY MAPPING

the capabilities of HarmoniX without
the complexity of operation andinterpretation. Additionally, no special
probes are required (although carefulchoice of probes is essential for best
performance). PeakForce QNM uses
Veeco’s new Peak Force Tapping™
technology for system feedback todeliver a number of important benefits:• High-resolution mapping of
mechanical properties – Scanningspeeds and number of pixels in animage are similar to TappingMode.
Analysis of force curve data isdone on the fly, providing a mapof multiple mechanical properties
that has the same resolution
as the height image. Sample
deformation depths are limited to a
few nanometers, minimizing
the loss of resolution that can occur
with larger tip-sample contact areas.
• Non-destructive to tips and samples– Peak Force Tapping provides directcontrol of the maximum normal
force (and thus the deformation
depth) of the sample, whileeliminating lateral forces. This
preserves both the tip and sample.
Additionally, Peak Force Tapping
enables Veeco’s new ScanAsyst™
feature, which automatically adjusts
the scanning parameters in realtime to optimize the image andprotect the probe and sample.

• Unambiguous and quantitative dataover a wide range of materials –Analysis of the entire force curve foreach tap allows different properties
to be independently measured.
Since a wide selection of probes
is available, it is possible to covera very broad range of modulus
or adhesion parameters while
maintaining excellent signal-tonoise ratios.
PEAK FORCE TAPPING

In scanning probe microscopy, there
are two primary causes of tip andsample damage. Any lateral force thatthe tip exerts on the sample can cause
the sample to tear (the tip plows throughthe sample). Likewise, lateral forcesfrom a hard sample can cause the end of
the tip to fracture and break off. Normal
forces can also cause damage to both tip
and sample. Even if there is not enoughnormal force to damage the sample,
there can still be enough to deformthe sample, increasing the contact area
(and the effective probe size) andreducing the resolution of the scan.
In Peak Force Tapping, the probe andsample are intermittently brought
together (similar to TappingMode) tocontact the surface for a short period,
which eliminates lateral forces. Unlike
TappingMode where the feedback loop
keeps the cantilever vibration amplitude
constant, Peak Force Tapping controls

the maximum force (Peak Force) on
the tip. This protects the tip and sample
from damage while allowing the tipsample contact area to be minimized.
Figure 1(i) demonstrates what happens
when the periodically modulated probe
interacts with the surface. The top(dashed) line represents the Z-positionof the modulation as it goes through one
period plotted as a function of time.
The lower line (solid) represents
the measured force on the (TESP type)probe during the approach (blue) of
the tip to the sample, while the redpart represents the force while the tip
moves away from the sample. Since
the modulation frequency is about 2kHzin the current implementation, the timefrom point A to point E is about 0.5ms.
When the tip is far from the surface(point A) there is little or no force on
the tip. As the tip approaches
the surface, the cantilever is pulled down
toward the surface by attractive forces(usually van der Waals, electrostatics,
or capillary forces) as represented by
the negative force (below the horizontalaxis). At point B, the attractive forces
overcome the cantilever stiffness andthe tip is pulled to the surface. The
tip then stays on the surface and theforce increases until the Z position of
the modulation reaches its bottom-mostposition at point C. This is where
the peak force occurs. The peak force

Figure 1. Force curves and information that can be obtained from them:(i) Plot of force and piezo Z position as a function of time, including (B) jump-to-contact, (C) Peak Force, (D) Adhesion(ii) Plot of force vs. time with small Peak Force(iii) A traditional force curve eliminates the time variable, plotting Force vs. Z piezo position(iv) For fitting purposes it is more useful to plot Force vs. Separation where the separation is calculated from the Z piezo position and the		 cantilever deflection
PAGE 2

Quantitative Mechanical Property Mapping at the Nanoscale with PeakForce QNM

(force at point C) during the interaction
period is kept constant by the system
feedback. The probe then starts towithdraw and the force decreases
until it reaches a minimum at point D.
The adhesion is given by the force at thispoint. The point where the tip comes off
the surface is called the pull-off point.
This often coincides with the minimum
force. Once the tip has come off
the surface, only long range forces affectthe tip, so the force is very small or zero
when the tip-sample separation is at its
maximum (point E).
As the system scans the tip acrossthe sample, the feedback loop of
the system maintains the instantaneous
force at point C at a constant value by
adjusting the extension of the Z piezo.
Figure 1(ii) illustrates an interesting
and unique challenge for peak force
control. Here the controlled peak force
at point C is actually attractive. Thiscan occur when the peak force is small
and the attractive forces are relatively
large. Looking at the measured force
in this plot, one might infer that theforce at C is not the maximum force.
In fact, the addition of the long range
attractive forces cause the stressbeneath the center of the probe tip tobe compressive (and greater) at point C
even though the measured force on
the probe is less than that at point A.
The small peak in the attractive
background is caused by the repulsive
force at the very apex point of the tip.
The total interaction force is integrated
over all of the tip atoms. While the tip
apex atoms feel a repulsive force, theneighbor atoms, which consist of far
more volume, can still be feeling an
attractive force. This leads to a net
negative force overall. Even when
the peak force is negative, Peak
Force Tapping can recognize the local
maximum and maintain control of
the imaging process.
Figure 1(iii) shows the same data as
figure1(i) but with the force plotted as afunction of the distance. Since we control
the Z position of the modulation as afunction of time and we measure thedeflection of the cantilever as a functionof time, it is possible to eliminate thetime variable and plot the force against
the Z-position. These plots can thenbe compared directly with the forcedistance curves that have been used
for decades by researchers interested
in measuring mechanical propertiesof their samples with SPM, but at aseveral orders of magnitude fastermeasurement speed. One complicationof the fast data acquisition is theexcitation of cantilever resonance at thepull-off point. This ringing is negligible
for a stiff lever, such as the TESP usedin figure 1. The oscillation is more
pronounced for softer levers. Peak
Force Tapping control has the ability toidentify the repulsive force and respondto this interaction only, regardless ofthe magnitude of the snap-off ringing.
Once a force curve is obtained, it is must
be converted to a force versus separation
plot for fitting and further analysis.
The tip-sample separation is different
from the Z position of the modulation
since the cantilever bends. Figure 1(iv)is a sample of a force-separation plot
illustrating the types of information thatcan be obtained. The most commonlyused quantities are elastic modulus,
tip-sample adhesion, energy dissipation,and maximum deformation.
QUANTITATIVE MATERIAL PROPERTYMAPPING

The foundation of material property
mapping with PeakForce QNM is
the ability of the system to acquire andanalyze the individual force curves fromeach tap that occurs during the imaging
process. To separate the contributions
from different material properties suchas adhesion, modulus, dissipation,and deformation, it is necessary tomeasure the instantaneous force on
the tip rather than a time-average ofthe force or dissipation over time, as isdone in TappingMode PhaseImaging™.
This requires a force sensor that has asignificantly higher bandwidth than thefrequency of the periodic interactions. In
Peak Force Tapping, the modulation
frequency is intentionally chosen to besignificantly lower than the cantileverresonant frequency. The force
measurement bandwidth of a cantileveris approximately equal to the resonant
frequency of the fundamental bending
mode used for force detection. As aresult, a properly chosen cantileveris able to respond to changes ininstantaneous interaction force with animmediate deflection change during
Peak Force Tapping.
As mentioned above, the force curve isconverted to a force versus separation
plot (see figure 1(iv)) for fitting andfurther analysis. The separation, whichis the negative of the deformation(sometimes called indentation
depth), is obtained by adding the Z
position of the piezo modulation to
the cantilever deflection. A constantcan be added to the separation to
make it zero at the point of contact
if it can be determined, but this is
not required for many analyses. This
process is equivalent to removing
frame compliance in indentation
measurements. These force-separation
curves are analogous to the loadindentation curves commonly usedin nanoindentation.
The curves are then analyzed to obtain
the properties of the sample (adhesion,
modulus, deformation, and dissipation)and the information is sent to one of
the image data channels while imaging
continues at usual imaging speeds.
The result is images that contain mapsof material properties (false coloredwith a user selectable color table).
Since the system can acquire up to eightchannels at once, it is possible to map
all of the currently calculated properties
in a single pass. Offline analysis
functions can calculate statistics ofthe mechanical properties of different
regions and sections through the data toshow the spatial distribution of
the properties.
Figure 1(iv) illustrates how common
mechanical properties are extracted
from calibrated force-separation
curves. Analysis of the force curves withother models is possible by capturing
raw data with the “High-Speed Data
Capture” function. High-speed data
capture provides about 64,000 raw force
curves (typically several scan lines)that can be captured at any time during
scanning and can later be correlatedwith the analyzed data in the image. This
allows users to apply their own models
to the raw data to study more unusualmaterials and properties.

Quantitative Mechanical Property Mapping at the Nanoscale with PeakForce QNM

PAGE 3

Elastic Modulus
To obtain the Young’s Modulus,
the retract curve is fit (see the boldgreen line in figure 1(iv)) using
the Derjaguin–Muller–Toporov (DMT)model10F – Fadh = 43 E*

R(d – d0) 3 .

F – Fadh is the force on the cantileverrelative to the adhesion force, R is the tip
end radius, and d – d0 is the deformationof the sample. The result of the fit is
the reduced modulus E*. If the Poisson’s
ratio is known, the software can usethat information to calculate the Young’s
Modulus of the sample (Es). This isrelated to the sample modulus by
the equation1 – νs2 1 – ν2tip
E* =
+
Es
Etip

–1

.

We assume that the tip modulus Etip
is infinite, and calculate the sample
modulus using the sample Poisson’s
Ratio (which must be entered by the user
into the NanoScope® “Cantilever
Parameters”). The Poisson’s ratio
generally ranges between about 0.2 and
0.5 (perfectly incompressible) giving a
difference between the reduced
modulus and the sample modulus
between 4% and 25%. Since
the Poisson’s ratio is not generally
accurately known, many publications
report only the reduced modulus.
Entering zero for the parameter willcause the system to returnthe reduced modulus.
PeakForce QNM provides quantitative
modulus results over the rangeof 700kPa to 70GPa provided
the appropriate probe is selected andcalibrated, and provided that the DMTmodel is applicable. Calibration is done
either by comparing to a reference
sample (relative method), or bymeasurement of tip end radius andspring constant (absolute method).
In either method, the deflection
sensitivity must also be measured. Whilecalibration is still a several step process,it has been made significantly easierthan HarmoniX calibration by eliminating
several steps and by automating
PAGE 4

Figure 2. Plot of Measured Modulus vs. expected Young’s Modulus (from the literature or from SPM
Nanoindentation). Multiple probes were used with different spring constants to cover the entire range.
Each probe was individually calibrated using the absolute method.

Figure 3. Modulus ranges covered by various probes. The modulus and Veeco part number of the reference
sample for each range is also indicated.

the calculation of several parameters.
An experienced user can complete acalibration in less than ten minutes.
Figure 2 demonstrates that this works
for a wide range of materials frompolydimethylsiloxanes to silica. The
data in figure 2 was collected with aset of probes that were selected tohave the most accuracy over a range ofmodulus. Figure 3 lists the probe types
used and gives the approximate modulus
range for each probe type. The data was
acquired on homogeneous samples andthe system was calibrated using
the absolute method.

Quantitative Mechanical Property Mapping at the Nanoscale with PeakForce QNM

If the DMT model is not appropriate,
the modulus map will still return the fit
result, but it will be only qualitative.
Some cases where the DMT model
are not appropriate include cases
where the tip-sample geometry is not
approximated by a hard sphere (thetip) contacting an elastic plane, cases
where mechanisms of deformation
other than elastic deformation are
active during the retracting part ofthe curve (at these time scales), andcases where the sample is confinedvertically or laterally by surrounding
material (close enough to effect thestrain in the deformed region). If thisis suspected, High Speed Data Capturecan acquire the individual force curves
across a section of interest to examine
the force curves directly and potentiallyapply more advanced fitting models.
PeakForce QNM can be quite repeatable
if care is taken in the calibration process.
Recent experiments on homogeneous
samples where the absolute method
was used to measure samples in a range
between 1MPa and 400MPa ten times
each (with different probes) resulted
in a relative standard deviation of lessthan 25% for all samples. If the goal is
to discriminate between components
in a multi-component system where
the modulus of one component is
known, the modulus noise level is moreinteresting. For the measurements inthe study, the relative standard deviation
was never more than 6%.
Adhesion
The second mechanical property
acquired in the mapping is the adhesion
force, illustrated by the minimum
force in figure 1(iv). The source of
the adhesion force can be any attractive
force between the tip and sample. In
air, van der Waals, electrostatics, andforces due to the formation of a capillarymeniscus can all contribute with therelative strengths of the contributions
depending on such parameters as
Hamaker constants, surface charges,
and hydrophilicity. For example, ifeither sample or the probe surface
is hydrophilic, a capillary meniscus
will typically form, leading to higher
adhesion that extends nanometers
beyond the surface. For polymers inwhich the long molecules serve as ameniscus, the adhesion can extend
tens of nanometers beyond the surface.
The adhesion typically increases withincreasing probe end radius. Simple
models based on surface energy
arguments predict the adhesion to be
proportional to the tip end radius.11
The area below the zero force reference(the horizontal line in the force curve)
and above the withdrawing curve isreferred to as “the work of adhesion.”
The energy dissipation is dominated bywork of adhesion if the peak force set
point is chosen such that the non-elastic
deformation area (the hysteresis above
the zero force reference) in the loading-unloading curve is negligible comparedto the work of adhesion.
Adhesion force becomes a much moremeaningful and important quantity if
the tip is functionalized. In this case,the adhesion reflects the chemicalinteraction between specific moleculeson the tip and sample. The adhesion map
in this case carries thechemical information.
Dissipation
Energy dissipation is given by the force
times the velocity integrated over one
period of the vibration (represented by
the gold area in the figure 1(iv)):

W = F • dZ =T0F • νdt ,where W represents energy dissipatedin a cycle of interaction. F is
the interaction force vector and dZ isthe displacement vector. Because thevelocity reverses its direction in eachhalf cycle, the integration is zero if theloading and unloading curves coincide.
For pure elastic deformation there isno hysteresis betweenthe repulsive
parts of the loading-unloading curve,
corresponding to very low dissipation.
In this case the work of adhesion
becomes the dominant contributor toenergy dissipation. Energy dissipatedis presented in electron volts as
the mechanical energy lost per
tapping cycle.
Deformation
The fourth property is the maximum
deformation, defined as the penetrationof the tip into the surface at the peakforce, after subtracting cantilevercompliance. As the load on the sample
under the tip increases, the deformation
also increases, reaching a maximum
at the peak force. The measured
deformation may include both elastic
and plastic contributions. With known tip
shape and contact area, this parametercan also be converted to the hardness(although this is usually only applied incases where the dominant deformation
mechanism is plastic deformation).
Maximum sample deformation is
calculated from the difference inseparation from the point where

the force is zero to the peak force point
along the approach curve (see figure1(iv)). There may be some error in thismeasurement due to the fact that the tip
first contacts the surface at the jump-tocontact point (figure 1(i), point B) rather
than at the zero crossing.
COMPARISON WITH FORCE VOLUME AND
PULSED FORCE MODE

The earliest mechanical property
mapping was performed by force
volume, which is still often used toacquire quantitative nanomechanicaldata. Force volume collects force
curves triggered by the same maximum
repulsive force while scanning back andforth over the surface. Collecting a force
volume image usually takes several
hours because individual force curves
generally take about a second to collect,and a map needs thousands of force
curves to be useful. This speed limitation
was greatly improved by Pulsed Force
Mode, which modulates the Z piezo at
about 1 kHz, allowing property mappingin much shorter time. Pulsed Force
Mode is primarily used as a property
mapping method with the trigger force
of a few nanonewtons or more. Below
one nanonewton, parasitic motion of
the cantilever can dominate and cause
feedback instability.
Peak Force Tapping modulates the Z
piezo in a similar fashion to force volume
and Pulsed Force Mode. However, it canoperate with interaction forces orders ofmagnitude lower, i.e., piconewtons. Suchhigh-precision force control is enabledby data pattern analysis within eachinteraction period. When the relative Z
position between the probe and sample
is modulated, various parasitic cantilever
motions can occur (defined as variationin the cantilever deflection that occurs
when the tip is not interacting withthe sample). These motions include
cantilever oscillation excited by the pulloff, as well as deflections triggered byharmonics of the piezo motion or viscous
forces in air or fluid. The parasitic
deflection limits the ability of Pulsed
Force Mode to operate with very low
forces. Low force control happens to be
the most important factor in achieving
high-resolution imaging and property
measurements. For example, if the tip

Quantitative Mechanical Property Mapping at the Nanoscale with PeakForce QNM

PAGE 5

end has 1 nm2 area, 1nN force will lead
to 1GPa stress at the tip end. Suchstress is sufficient to break a silicon tip.
To lower the stress below the fracture
stress of silicon, the control force needs
to be no more than a few hundred
piconewtons. For samples softer thansilicon, the required controlling force to
avoid significant deformation or damage
is even lower.
During Peak Force Tapping operation,
the parasitic deflection signal and its
data pattern are analyzed by comparing
the known sources of force artifacts,
such as cantilever resonance at pull-off,harmonics of the modulations, and othersystem actuation sources. The signatureof the interaction is extracted fromthe parasitic deflections. The feedback

loop can choose any point in the force
curve to control tip-sample interactions
instantaneously. For Peak ForceTapping, the peak point in the repulsive
interaction is chosen as the control
parameter, similar to the triggered levelin force volume mapping.
A major advantage of Peak ForceTapping is its broad operating force
range, from piconewtons tomicronewtons. At the high-force end, it
coincides with traditional mechanicalmapping techniques, namely force
volume and Pulsed Force Mode, yet cangenerate quantitative data with the newadvanced quantitative nanomechanicalprocedure. In the low-force regime, itmatches the interaction force achievable
by light tapping in TappingMode but withmuch improved stability and ease of use
in all environments.
COMPARISON WITH TAPPINGMODE
AND HARMONIX

The phase of the TappingMode
cantilever vibration relative to the drive
is a useful indication of different
mechanical properties. Unfortunately,
the phase signal reflects a mixture ofmaterial properties, depending both on
dissipative and conservative forces.12–13
Since elasticity, hardness, adhesion
and energy dissipation all contributeto phase shift, phase alone does notprovide enough information to quantify
or discriminate between all of theseproperties. Additionally, the phase signal
depends on imaging parameters suchas drive amplitude, drive frequency,

Figure 4. Multilayer polymer optical film comparing results obtained with Tapping Mode Phase Imaging (a-c) and PeakForce QNM (d-f) (10µm scan size).
The phase image in (b) was collected with an amplitude setpoint of 80% of the free amplitude, while the amplitude setpoint in (c) was 40%. The trace profile from(f) is the modulus along the line in (f) from left to right. Note that the tapping phase result (b) is nearly identical to the PeakForce QNM adhesion image (e) andthe contrast is inverted relative to the modulus image.
PAGE 6

Quantitative Mechanical Property Mapping at the Nanoscale with PeakForce QNM

and setpoint. This makes it difficult andsometimes impossible to interpretthe source of the contrast, leaving
the user to conclude that there aredifferences in the sample without
further knowledge of contributing
physical factors. Figure 4 demonstrates
this difficulty with phase imaging andcompares it to PeakForce QNM for a
multilayer polymer sample. It is often
assumed that the phase contrast is
primarily caused by variations in sample
modulus. Comparing figure 4(f) and(b), it is clear that this is not true in thiscase. By tapping harder (reducing
the amplitude setpoint), one would
expect to deform the sample more,increasing the contribution of
the modulus to the phase. Surprisingly,in (c) the contrast does not change
significantly. The PeakForce QNM
data (e) shows that the phase signal isdominated by the adhesion independentof tapping setpoint for this tip-sample
interaction. It is easy to see that one
must be very careful in interpreting
phase results, even for qualitative use.
The PeakForce QNM modulus channel,
on the other hand, has unambiguous
contrast that can be quantified, as shownin the trace of (f). The narrow strips
have a modulus of about 300MPa, while
the wide ones have a modulus of
about 100MPa.

HarmoniX microscopy is a TappingMode
technique that uses many harmonics ofthe tapping drive signal to reconstruct
the force curves that occur during
tapping. From these force curves
the material properties can be measured
independently. The harmonic signals are
excited at each tap in the TappingModeoscillation period. They are detectedby measuring the torsional motion of
the special HarmoniX cantilever during
TappingMode imaging. The torsional
bending of the cantilever acts as
the high-bandwidth force sensor andallows force separation plots to be
extracted during tapping and analyzed
in real-time. HarmoniX is a very
powerful mode, and it has the benefit
of working with TappingMode feedback
and phase imaging for easy comparison
with previous results. On the other
hand, HarmoniX mode shares all
the difficulties of TappingMode in
imaging control. It can be challenging
to use, especially in fluids where
the cantilever Q is much lower.
Additionally, interpretation can becomplex if the torsional sensor doesn’t
have enough bandwidth, if perturbations
to the flexural motion become
significant, or if cantilever overtones
coincide with integer multiples ofthe drive frequency.

PeakForce QNM

HarmoniX

Young’s modulus andadhesion mapping

Yes

Yes

Deformation depth mapping

Yes

No

There are two other TappingModederived modes that have recently
gained popularity: TappingMode
while observing a separate harmonicof the tapping drive,5 and Dual AC
mode.14–15 Single harmonic imaging
depends on either special cantilevers ora lucky coincidence of an overtone with aharmonic, while Dual AC adds a second
frequency (usually at an overtone) tothe vibration driving the cantilever. Bothof these techniques provide contrast
that is analogous to phase contrast
in that they do not fully separate
the mechanical properties and therefore
cannot be quantified.
A common characteristic of all thesetapping-based nanomechanicalmapping technologies is that they are
all dependent on higher frequency
components. Theoretically, in order toaccurately reconstruct the real-time
tip-surface interaction, an infinite
number of frequency components areneeded. HarmoniX can detect 15 to 20
harmonic components, rendering a good
approximation, and thus is effective
for many materials in reconstructing
tip surface interaction and deriving
quantitative data. Fewer frequency
components will further limit the abilityof a technique to derive quantitative data.

TappingMode
Single Harmonic
Dual AC
Phase Imaging
Mixed & Parameter Mixed & Parameter Mixed & Parameter
dependent
dependent
dependent

Pulsed Force
Mode

Force Volume

Qualitative

Possible offline

No

No

No

No

Possible offline

Quantitative modulus range 0.7 MPa – 70 GPa 10 MPa – 10 GPa

—

—

—

—

<1 MPa – 100 GPa

Adhesion noise level<10 pN

200 pN

—

—

—

<1 nN

<10 pN

Feedback on peak force?

Yes

No

No

No

No

Yes

Yes

Minimum peak force<100 pN

<5 nN

<3 nN

<10 nN<5 nN<20 nN<50 nN

Lateral resolution

<5 nm

<5 nm

<5 nm

<10 nm<10 nm<50 nm<100 nm

Simultaneous highresolution imaging

Yes

Yes

Yes

Yes

Yes

Moderate

No

Mapping time

4 minutes

4 minutes

4 minutes

4 minutes

4 minutes

4 minutes

18 hours

Easy to use?

Yes

No

Yes

No

No

No

No

Figure 5. Comparison of different SPM modes for mapping mechanical properties at the nanoscale.
Quantitative Mechanical Property Mapping at the Nanoscale with PeakForce QNM

PAGE 7

In all TappingMode techniques,
the feedback uses the near-resonanceamplitude as a control parameter. Ina normal tapping control, the peakinteraction force varies from a fraction of
a nanonewton to tens of nanonewtons,
depending on the operating amplitude,
cantilever spring constant, and set point.
Such interaction force is well controlled
when cantilever oscillation is in a steadystate. However, when the tip is scanningon a sample surface, especially a roughsurface, the amplitude error occurringat the sharp edges can correspond tointeraction force one order of magnitude
higher than that of a steady-state.
Amplitude error incurred force is aleading cause of tip damage. Suchdamage occurs because the feedback is
not directly controlling interaction force.
In contrast, Peak Force Tapping directly
controls the peak force on the sample.
This protects the tip and sample while
maintaining excellent surface tracking.

modulus ranges from hydrogels tometals and semiconductors.
PRACTICAL APPLICATIONSPolymer Blend
It is often interesting or necessary
to image samples under fluid or attemperatures above or below room
temperature. PeakForce QNM works
well in these environments and has
several benefits over TappingMode.
For one, it is not necessary to re-tune
the cantilever when the temperature
is changed or when changing from air
to fluid operation. In TappingMode, atemperature change causes changes
in resonant frequency and Q of
the cantilever, making it imperative thatthe drive amplitude and frequency are
adjusted whenever the temperature ischanged significantly. With Peak ForceTapping, the system is not being driven

at the cantilever resonance, so it is notsensitive to changes in probe resonant
frequency and Q.
A temperature-controlled experiment
done with PeakForce QNM is shown infigure 6. In this example, a mechanicalblend of syndiotactic polypropylene(sPP) and polyethylene oxide (PEO)
was exposed to a sequential heatingcooling procedure with different rates
of temperature change. The sample
temperature was increased enough that
the PEO-matrix melted, but the sPPdomains stayed in the solid state toserve as reference marks in the areaof interest. In the first cycle the sample
was rapidly heated up until the PEO
completely melted (b). The temperature
was then allowed to rapidly drop,
causing quick crystallization of the PEO(c). One can see that when compared

SUMMARIZING MECHANICAL PROPERTYMAPPING MODES

Figure 5 summarizes the nanoscale
mechanical mapping techniques
available with SPM. Of the mechanicalproperty mapping techniques, PeakForceQNM has by far the most precise controlof peak force, while retaining the speed
and resolution of TappingMode.
The TappingMode-based techniques
are relatively fast and high resolution,but only HarmoniX has the ability
to independently measure different
mechanical properties, and none ofthem directly control the peak force.
The key factor that allows PeakForceQNM to cover such a broad rangeof quantitative nanomechanicalmeasurements is its ability to use awide range of cantilever probes in allenvironments. Using cantilevers witha spring constant between 0.3N/m and300N/m, allows Peak Force QNM toachieve force control from piconewtons
to micronewtons. Piconewton force
control, normally only possible influid, can also be applied in ambientconditions, yielding improved image
quality and tip protection over evenbest practice TappingMode. This
force range can facilitate quantitative
characterization of materials, with

PAGE 8Figure 6. Cycle of heating and cooling of polymer blend of syndiotactic polypropylene and polyethyleneoxide. Images a–f show height of the surface during the process, while g–i show the modulus of frames d–f
respectively. Scan size 5um.

Quantitative Mechanical Property Mapping at the Nanoscale with PeakForce QNM

to the initial morphology (a), the PEO
topography underwent minor changes.
This demonstrates the so-called“memory” effect of fast cooling, where
the original crystallization nuclei are still
active even though polymer appears to
be totally melted.
During the second heating-coolingcycle, the temperature was lowered
more gradually. Figure 6(e) shows
abrupt transition from melt to solidstate 1/3 of the way from the framebottom (the system was scanning up
the frame at the time). It’s worth noting
that, in this case, the PEO morphology
becomes completely different fromthe original morphology in (a), indicating
reorientation of the lamellae from anedge-on (a) state to a flat-on state(f). The images in (g–i) are modulus
maps corresponding to the second
crystallization cycle. Based on
the topography in the upper portion of(e) you might conclude that the PEO
is completely crystallized, but looking
at the corresponding modulus mapin (h), you can see that there is a soft
(dark) circular area just to the right ofthe center of the image that disappears
when the sample has fully
crystallized (i).
If this experiment were done in
TappingMode, it would be necessary toadjust drive amplitude and frequency
several times during each heatingcooling cycle (generally this is done
just before collecting an image if
the temperature has changed by morethan about 10°C). Since Peak ForceTapping operates far from the cantileverresonance frequency, heating induced
resonance frequency drift has no effecton the feedback, so it was not necessary
to adjust the drive amplitude or
frequency during the entire experiment.
In fact, as long as the laser reflection
stays on the photodetector, the imaging
can proceed continuously and without
adjustment during any experiment
involving sample heating and cooling.
Operation of Peak Force Tapping is
intrinsically identical in fluid, ambientand vacuum. This is in contrast to
TappingMode where dramatic changes
in the resonant dynamics of the probe
in the three environments result inmuch more complexity in operationand variation in performance. By
operating at a frequency far below
the resonance, Peak Force Tapping
removes the complex resonant dynamics
and replaces it with simple and stable
feedback on the peak force. Cantilevertuning is not required and it is notnecessary to adjust drive amplitude
and setpoint when imaging conditions
change. Furthermore, Peak ForceTapping can achieve equal or better
force control than TappingMode imaging
in all the environments by using a broad
range of cantilevers, making high-quality
imaging much easier to achieve with thiscontrol mode. Finally, the lack of a needfor special probes means that PeakForceQNM can be used with other techniquesthat do require special probes, such as
Nanoscale Thermal Analysis with VITA.18
Brush Molecules
Polymer macromolecules havebeen an interesting, but challenging
sample for SPM since the 1990s.16 One
example of this class of molecule isthe poly(butyl acrylate) (PBA) brushmolecule.17 This molecule has a long
backbone with many short, flexible side
chains. The conformation and physicalproperties of these molecules arecontrolled by a competition between
steric repulsion of densely grafted side
chains (brushes) and attractive forces
between the brushes and the substrate.
They can be either flexible or stiff,
depending on the grafting density andthe length of side chains. Molecules can
switch their conformation in response
to alterations in the surrounding
environment, such as surface pressure,temperature, humidity, pH, ionicstrength, and other external stimuli.
Molecular brushes are a very informativemodel system for experimental studies
of polymer properties.17
Figure 7 shows a set of images collectedof PBA using PeakForce QNM. In
the height image (a) the backbone isclearly visible both as a long isolated
molecule and as a folded set ofmolecules (a molecular ensemble). In
the modulus map (b) it is clear thatthe soft (dark) backbones are
surrounded by areas that are slightly
stiffer, presumably where the shortside chains are present. Figure 7(d)is a histogram showing the relative
frequency of various modulus values
in the image. The peak at 62MPa isfrom the background (mica coveredby low molecular weight amorphous
polymer), while the broad peak at 31.9
MPa is from the brush molecules andmolecular ensembles. By examining
the region given by the red square in (b)it is possible to see that there are two
peaks in the modulus of the molecularensemble, as shown in figure 7(e).
The one at about 25MPa corresponds
to the backbone of the chains, andthe one at about 32MPa corresponds
to the surrounding region filled withshort brushes. These numbers are
not expected to be quantitative since
the molecules are small in comparison
to the tip and the deformation of thesample. Even though the DMT model
is not appropriate in this case, thequalitative interpretation that darker
regions are softer than the brighter
regions leads us to speculate that thepolymer backbones are being partially
supported by the short side chains.
In the adhesion image (c),the background appears dark withvery little adhesion as indicated in
the adhesion histogram (f) by the peak
at 0.47nN. The histogram also has threeother peaks: the backbones at about
0.63nN, the brushes of single molecules
at about 0.71nN, and the brushes ofmolecular ensembles at about 0.8nN.
The greater adhesion for the molecularensembles is likely due to the greaternumber of brushes available to bind withthe tip in those regions.
SPM has provided unique opportunities
to observe single polymer molecules as
they move, order, and react on surfaces.
PeakForce QNM now makes it possible
to map their mechanical properties
as well, providing new insight into
the behavior of these macromolecules.
Nanoparticles
The adhesion data type is sensitive
to attractive interactions between
the tip and sample in a way that issimilar to chemical force microscopy(which uses lateral force microscopy
in contact mode). Unlike with lateralforce microscopy, PeakForce QNM
can measure the attractive forces with

Quantitative Mechanical Property Mapping at the Nanoscale with PeakForce QNM

PAGE 9Figure 7. Poly(butyl acrylate) brush-like macromolecules and molecular ensembles on a mica substrate. (a) Height, (b) modulus, (c) adhesion, (d) histogram of area
within red box in modulus map, (e) histogram of modulus map (f) histogram of adhesion map. Sample was imaged with a MultiMode® 8 using PeakForce QNM witha scan size of 500nm. Sample courtesy of Sergei Sheiko (University of North Carolina, Chapel Hill, NC) and Krzysztof Matyjaszewski (Carnegie Mellon University,
Pittsburgh, PA).

Figure 8. Anti-bacterial film consisting of poly(methyl methacrylate) (PMMA) and silver nanoparticles.
Sample was imaged on a Dimension® Icon® using PeakForce QNM at a scan size of 13.5μm. Sample
courtesy of Mishae Khan and Daniel Bubb (Rutgers University, New Brunswick, NJ).

PAGE 10

Quantitative Mechanical Property Mapping at the Nanoscale with PeakForce QNM

negligible lateral force and very low
normal force, allowing it to be used withvery delicate or weakly bound samples.
For example, figure 8 shows an antibacterial film consisting of poly(methyl
methacrylate) (PMMA) and silver
nanoparticles. From topography alone(a), it is difficult to tell the locations of
the silver nanoparticles. The adhesionmap (b), however, reveals distinct
nanoparticles (indicated by smaller
circles) as well as an area enriched inmany particles (large circle). Contact
mode imaging would likely push theparticles out of the way, making it
impossible to see them. TappingMode
PhaseImaging might be able to see
the difference in the particles if
the probe and imaging parameters
were chosen correctly, but PeakForceQNM can see differences in adhesion,
modulus and dissipation independently,
making it more likely that there will be adifference in one of the data channels.
CONCLUSION

The unambiguous and quantitative
modulus and adhesion data provided by
PeakForce QNM can help researchers
answer the critical question of whatmaterials they are seeing in their
topographic images. Additionally, it
is now possible to study the variationand position of mechanical properties
across a surface with ease, and at
previously unattainable resolution.
This imaging mode is non-destructive
to both tip and sample since it directly
controls the peak normal force andminimizes the lateral force on the probe.
Maps of mechanical properties suchas Young’s Modulus, adhesion anddissipation are automatically calculated
at the rates and resolutions expectedby advanced SPM users. Since force
distance data is analyzed directly, there
is no ambiguity regarding the source ofimage contrast, as often occurs in othertechniques. Mechanical property maps
are quantitative, low noise, and can spana very wide range of property values.
These capabilities of PeakForce QNM
will provide researchers with criticalmaterial property information to enable
better understanding of their samples at
the nanoscale.

Quantitative Mechanical Property Mapping at the Nanoscale with PeakForce QNM

PAGE 11

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