Application Note

#156

Characterizing Ferroelectric Materials with
SS-PFM and DCUBE PFM
Piezoresponse force microscopy (PFM) is a powerful technique for studying ferroelectricmaterials due to the high sensitivity and nanometer-level resolution that it inherits fromatomic force microscopy (AFM). PFM-based spectroscopic methods, such as switching
spectroscopy PFM (SS-PFM) and DataCube™ PFM (DCUBE PFM), allow characterization of
key parameters of ferroelectrics, such as coercive voltages, nucleation voltages, saturation
responses, and more. Unfortunately, quantification and interpretation of PFM results can becomplicated by artifacts. In this application note, we discuss the best modes and practices
for optimizing PFM measurements to achieve reliable results.
PFM has many variants optimized to solve different problems and study different aspects ofelectromechanical response (Table 1). This application note focuses on the DCUBE PFM and
SS-PFM modes and how they can help with many of these issues. Additionally, the benefitsof both resonance and sub-resonance PFM are discussed along with how laser position canbe optimized to improve measurement accuracy.
PFM Mode/Method

Benefits

Sub-resonance PFM with laser at
electrostatic blind spot

Eliminates electrostatics, simple calibration

Sub-resonance PFM with laser at tip No need to position laser at ESBS, simple calibration
Contact Resonance PFM

Significant PFM signal amplification, but must consider
CR shape factor for quantitative measurements

Contact Mode PFM

Fast and simple especially for sub-resonance PFM

DCUBE PFM mapping

Minimizes tip wear and sample damage, simultaneous
mapping of PFM response and mechanical properties
such as modulus & adhesion, works with either contact
resonance or sub-resonance PFM

SS-PFM spectroscopy and mappingSame as DCUBE, but additionally allows separationof read and write segments, and use of multiple
read segments at different voltages for cKPFM andPFM spectroscopy

Vector PFM (vertical and lateral)

Characterize different components of piezoelectric
response tensor

High Voltage PFM

Switch samples with high coercive voltages and/or
measure low-response samples

PFM Lithography

Control ferroelectric domain structure and/or investigate
domain wall propagation

Table 1
AFM modes and methods
for PFM.

BackgroundTo investigate the electromechanical response of materials with PFM, a sinusoidal (AC)drive voltage is applied between a conductive AFM probe and the sample substrate. The
inverse piezoelectric effect then causes the sample to expand and contract sinusoidally,
which is detected by an AFM probe tip in contact with the sample.
For materials with a positive electrostrictive coefficient, such as lead zirconate
titanate (PZT), the sample expands when the polarization of a piezoelectric domain
beneath the tip is parallel to an increasing electric field (and vice versa). When the sample
expands, the AFM tip is displaced and the cantilever bends, producing a sinusoidal signal
in deflection at the same frequency as the AC drive voltage (Figure 1a). It is worth notingthat some piezoelectric materials, such as polyvinylidene difluoride (PVDF), have negativeelectrostrictive coefficients, inverting the previous discussion.
abc
FIGURE 1

Since the AFM can measure deflection normal to the sample surface or parallel tothe surface (perpendicular to the cantilever), it is possible to simultaneously measure
two orthogonal components of the piezoelectric displacement vector. Rotating thesample by 90° can provide the third component, allowing full characterization of thedisplacement vector.1
If the material is ferroelectric, a large enough applied voltage (called the coercive bias)
can cause the domain polarization to flip. The new polarization is then maintained after
the voltage is removed. Figure 1b depicts a typical ferroelectric hysteresis loop for amaterial like PZT with a positive electrostrictive coefficient. Key parameters in the loop
include coercive voltages ( V0±), nucleation voltages ( Vc±), remnant responses (R0±), andsaturation responses (RS±). The local measurement of these hysteresis loops and associatedparameters is the goal of PFM spectroscopy.2
Switching spectroscopy PFM (SS-PFM) improves on the accuracy of PFM spectroscopy
by separating measurements of the PFM response during read voltages from those during
write voltages (see Figure 1c).3 In its simplest form, the AC voltage is turned off during eachwrite segment, and then turned back on during each read segment to study the stability of
domains after poling.
Quantitative PFM makes possible the validation of results using different probes and byother labs. However, there are challenges related to conducting quality PFM measurements:
 Signal levels are often quite small (<10 pm/V), making detection difficult.
 PFM is sensitive to several different types of electromechanical response of the sample,
which can be difficult to separate.4

Piezoresponse ForceMicroscopy (PFM)basics: (a) an increasing
electric field in parallelwith the polarization ofa piezoelectric sample
will cause the sample toexpand if the material has
a positive electrostrictive
coefficient, (b) a typicalhysteresis loop describing
the response and domain
switching characteristics
of a ferroelectricmaterial, and (c) aseries of read and write
pulses applied duringswitching spectroscopy
PFM (SS-PFM). The
write segments use
successively larger (orsmaller) DC voltages
to switch the polarityof the domain beneaththe tip, while an AC
voltage is applied
during read segmentsallow observation of
the polarization andresponse of the domain
after switching.

 The observed signal is influenced by the measurement system (AFM and probe) inaddition to the sample. For example, electrostatic forces between cantilever and surface
or background signals from within the AFM can result in a response similar to that of apiezoelectric material.5
 PFM results can be inconsistent if the tip or sample is damaged by the uncontrolled
lateral forces that occur during contact mode scanning (the traditional mode for
PFM scanning).

Maximizing Sensitivity
The signal levels in PFM are generally very small, with typical amplitudes <10 pm/V. This is
close to the limit of what an AFM can detect. To address this, one of four approaches are
generally taken:
1. Increase the AC stimulation voltage
Since the PFM amplitude is proportional to the AC stimulation voltage (to a first orderapproximation), doubling the AC voltage will approximately double the PFM response.
However, arbitrarily increasing the AC stimulation voltage is not a generally practical
approach. Many samples have weak points where leakage current occurs, leading todielectric breakdown and sample damage at high voltages. Additionally, ferroelectric sample
domains will flip (pole) if the coercive voltage is exceeded by the AC voltage. At this point,
the measured amplitude will no longer reflect a purely piezoelectric response and thehysteresis loop will begin to collapse. For thin films, the nucleation voltage is often <5 V,
significantly limiting the practical AC amplitude.
2. Increase the amplification of the deflection signal
A second approach to improving PFM signal levels is to increase the amplification.
Amplification eliminates bit-noise, but the signal-to-noise ratio (SNR) is only slightly
improved. Signal amplification (by a factor of 16) is available to all Dimension Icon® users bychoosing the “Optimized Vertical” or “Vx16” workspace.
3. Increase the time constant of the lock-in amplifier
Increasing the lock-in amplifier’s time constant increases averaging, thereby decreasing
noise. This noise reduction comes at the cost in update time, resulting in slower dataacquisition, but is worth considering for low-response samples.
4. Amplify the PFM motion mechanically
PFM vibration can be mechanically amplified by using the cantilever contact resonance.
This method, known as contact resonance PFM (CR-PFM), can provide a significant(as much as 100x) boost to PFM sensitivity, allowing detection of amplitudes down to<1 pm, but adding an element of complexity.
Quantification of the CR-PFM amplitude requires calculation of the CR shape factor from thecontact resonance frequency, amplitude, and quality factor (Q).6 CR-PFM measurements canbe collected at fixed frequency or by using a resonance tracking method, such as frequency
sweeps, dual-frequency resonance tracking (DFRT), or band excitation (BE). Since the CR
frequency usually shifts during scanning, fixed-frequency measurements near resonance are
not recommended for quantitative PFM. Instead, it is preferred to use Ramp, RampScript,
or force volume (FV)-based methods that can precisely control the forces while collecting
detailed frequency spectra.

Improving Repeatability with DataCube Methods
DataCube (DCUBE) CR-PFM is a FV-based hyperspectral imaging technique that provides
maps of CR-PFM amplitude with associated frequency, Q factor, and phase on resonance.
Figure 2 provides example DCUBE CR-PFM results collected on a PMN-PT sample todemonstrate how the method works:
1. At each pixel in the image, a force curve is collected with a surface hold segment (Figure 2a).
2. During the hold segment the frequency of the AC stimulation voltage is swept
over a user specified range while collecting deflection amplitude and phase spectra(Figures 2b and 2c respectively).
3. Spectra are analyzed and used to create maps of sample properties over the scan area
(Figures 2d-f).
ad
FIGURE 2

b

e

c

f

It is important to note that the usual force curve approach and retract data is available alongwith the hold segment, so it is possible to do the usual fitting and obtain maps of mechanicalproperties such as modulus and adhesion (Figure 2d) from the same dataset.
Since duration, sweep width, and sampling rate of the hold segment are user-controlled, the
CR-PFM maps can be optimized for accuracy and SNR. Figure 2b shows how two typical
CR-PFM spectra are fit to generate maps of CR Amplitude (Figure 2e). Once the precise
CR frequency is known, the CR Phase can be obtained (Figure 2c) and the associated map
generated (Figure 2f). The contact resonance frequency, amplitude, and Q are defined byfitting hundreds of points, allowing for improved accuracy over dual-frequency resonancetracking (DFRT)-based methods – especially for Q. Additionally, long integration times(increased lock-in time constants) are possible when longer hold times are acceptable. If
multiple CR eigenmodes are of interest, they can be collected in a single pass by simply
increasing the frequency sweep width (though some care is required to avoid distorting theresonance peaks by sweeping too quickly).

DataCube (DCUBE)
CR-PFM of a PMN-PT
ferroelectric sample:(a) Typical force vs. timeplots showing 30 ms
hold segments where
frequency is swept
and highlighted pulloff points for adhesion
map, (b) PFM Amplitude
spectra from holdsegment and Lorentzianfits used to calculate
CR Amplitude (peaks
highlighted), Frequency,
and Q, (c) PFM Phase
spectra used todetermine CR Phase(region of CR highlighted),(d) Adhesion map withapproximate locationsof curves in (a), (e) CR
Amplitude map withlocations of curves in (b),and (f) CR Phase mapwith locations of curvesin (c).

Because DCUBE methods are based on FV, the tip is not dragging on the surface between
measurements, which eliminates the lateral force that occurs in contact mode andoften damages samples and probes. Thus, the tip apex is preserved, resulting in moreconsistent measurements than comparable contact mode techniques. DCUBE also enables
measurements on samples that are susceptible to damage or displacement by the AFM
tip dragging across the surface, like nanoribbons and fibers. Softer cantilevers can partiallymitigate this issue but are more prone to electrostatic artifacts than stiffer cantilevers – moreon this later.

Phase Considerations
For reliable PFM results, it is necessary to compensate for any instrument-induced phaseshift. Digital lock-ins have a fixed time delay for processing data. As the frequency increases,
this fixed time delay leads to an approximately linear increasing phase shift. Since theshift varies relatively slowly with frequency (Figure 3a: ~0.4°/kHz), a simple subtractionof an offset phase is generally sufficient to compensate for the issue.7 When working
with the same type of probe, the needed offset phase will be very similar because thecantilever resonance frequencies are similar. However, any change to signal path, including
microscope cable length, may change the phase shift. If the instrumental phase shift is notcompensated, this can lead to an inversion of the PFM hysteresis loops (Figure 3c).
ab
FIGURE 3cdCompensating for
instrumental phase shifts:(a) the measured phasefrom the lock-in depends
approximately linearly onfrequency, with a phaseshift of about -4 deg/kHz,(b) domain polarizationand expected phase after
applying negative andpositive DC tip voltages
to pole concentricdomains in a ferroelectric
sample with known
positive electrostrictive
coefficient, (c) if thisphase shift is notcompensated, thedirection of ferroelectric
hysteresis loops may be
inverted when probes ofdifferent frequencies areused, and (d) histogramof phase data from a
DCUBE CR-PFM map(inset) after poling withpattern in (b) has peaks
at -109° (outer domain)
and +71°.

To determine the phase shift at a given frequency, we follow the method of
Neumayer et al.7 in using a reference ferroelectric sample to first create and then measuredomains of known orientation. Materials like PZT and PMN-PT are known to havepositive electrostrictive coefficients, so an increasing electric field applied in parallel tothe polarization of a domain in the material will result in an expansion of the material. By
applying a sufficiently large negative voltage to the tip (electric field up), it is possible toflip the domain polarization up. One can then pole and measure two concentric squares(Figure 3b):
1. negative DC voltage (<V0-) to the tip for the outer square
2. positive DC voltage (>V0+) to the tip for the inner square
3. set DC voltage to zero and scan the area to measure the PFM phase
When the AC voltage is applied to the sample, the outer square should have phase of 0°(inner at 180°). However, the lock-in phase range is ±180°, so the inner domain will tend to
wrap (noise causing the phase to jump between +180° and -180°). To avoid this wrapping,
it is generally preferable to adjust a lock-in parameter called the drive phase to make theouter domain +90° (inner at -90°): if this is done the -90° should be added back to the data
during analysis. In Figure 3d, a Bruker SCM-PIT-V2 probe was used with free resonancefrequency 62.7 kHz (CR frequency 282 kHz). The outer domain had a mean value of-109° (with lock-in drive phase of 0°), so subsequent data was collected with a lock-in
drive phase of +90° + 109° -0° = -161°. The resulting hysteresis loops have the expected
clockwise direction.

Electrostatic Signal
One of the biggest challenges for researchers looking to quantify their PFM measurements
is the influence of electrostatic forces from the sample acting on the entire length ofthe cantilever (Figure 4a). This electrostatic signal is proportional the contact potential
difference (CPD) between tip and sample and adds linearly to the piezoelectric responseof the material. When charge injection from the tip changes the CPD, this phenomenon
can result in non-ferroelectric materials exhibiting a PFM response that is very similar to aferroelectric, even exhibiting the classic hysteresis loops and butterfly amplitude loops.5
To understand and begin to decouple this electrostatic signal from the piezoelectric
signal, one or more of a few approaches is generally used, each with advantages
and disadvantages:
Increase the cantilever stiffness
Under the same electrostatic force, stiffer cantilevers bend less, leading to a smaller
contribution from the electrostatic signal (in contrast, the piezoelectric response is notsensitive to the cantilever stiffness except for very soft samples). This has recently beenverified for sub-resonance PFM, where the electrostatic contribution was less than that ofthe piezoelectric contribution for spring constant (kc) over about 25 N/m on periodically poledlithium niobate (PPLN).8
Unfortunately, tip wear and sample damage can occur with very stiff probes in contact
mode. Cantilevers softer than kc=10 N/m are usually preferred for all but low-resolution PFM
measurements on stiff samples. However, with DCUBE PFM and SS-PFM, the uncontrolled
lateral forces that occur in contact mode are avoided, enabling the use of relatively stiffprobes with minimal damage to tip or sample.

ab

FIGURE 4
Understanding theinfluence of electrostatics
on the PFM response:(a) the electrostaticforce on the cantileveris proportional tothe contact potential
difference or thedifference between theapplied voltage (VDC) andthe surface potential (VSP),(b) comparing PFM
hysteresis loops
collected during readsegments (black) andwrite segments (red) canbe used to discriminate
between ferroelectricand non-ferroelectricmaterials, and (c) bymeasuring SS-PFM
hysteresis loops (bottom)
at different read voltages(top) it is possible
to directly study the
influence of varying
contact potential
difference on PFM
measurements.

c

Use SS-PFM to investigate bias dependence
Another approach is to use an applied DC bias during SS-PFM spectroscopy to investigatechanges in electrostatic forces that occur after charge injection. Bruker’s SS-PFM
implementation allows this to be done in two different ways: 5
1. Comparing the hysteresis loops with measurements acquired during the read segments(at zero bias) with those acquired during the write segments (at a range of voltages)
2. Sequentially performing the SS-PFM measurements at multiple different read voltages
Figure 4b is an example of the first method, showing PFM response for the off-field (0 V
read segments) and on-field (write segments). Note that the on-field case looks very similar
to the off-field case, except that it is tilted due to the electrostatic force on the cantileverfrom the DC voltage that is applied during the write segments. For a non-ferroelectricmaterial, the tilt remains, but there is little or no hysteresis in the on-field loop, and loop
direction may change. Figure 4c (top) shows a schematic of the DC voltage applied during
the second method with five different read voltages. It is clear (Figure 4c bottom) thatdoing the SS-PFM at different read voltages changes the shape and shifts the position of
the hysteresis loop as if the surface potential had changed. The effect of the combined(constant) ferroelectric and (linear) electrostatic response, i.e.,
is shown schematically in Figure 5a.6

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ab
FIGURE 5

Plotting the response data for each write bias is as a function of read bias results in acKPFM plot.5 Figure 5b shows a cKPFM plot of data collected on a ferroelectric (PZT).
The electrostatic response is indicated by the tilt in the linear parts of the curve at theextremes of write bias (where the ferroelectric response is saturated: black dashed lines).
In contrast, the non-linearity in the cKPFM plots indicate ferroelectric response. For an
ideal dielectric material, all plots would be linear, with the x-intercepts (red box in Figure 5b)
indicating the surface potential for the sample after charge injection by the associated write
segment. Similarly, the y-intercepts (blue box) indicate the PFM response for the off-field
hysteresis loop.
For ferroelectric materials, it is difficult to separate the electrostatic and ferroelectric
response because the surface potential (and therefore the electrostatic contribution
to displacement) changes from one write segment to the next. Therefore, even if oneof the read voltages precisely cancels out the surface potential at the beginning of themeasurement, it cannot do so for the whole hysteresis loop. To address this, Balke et al.
used a combination of on-field SS-PFM (for PFM response and electrostatic slope) and noncontact KPFM (for surface potential) with the same write waveform.6 This worked well for
PPLN with DC voltages below the coercive voltage (avoiding domain switching), but does
not allow correction of the entire hysteresis loop.
Position the beam-bounce laser at the electrostatic blind spot
A third approach involves using sub-resonance PFM and carefully positioning the beambounce laser used to detect the cantilever deflection angle at the electrostatic blindspot (ESBS) for the lever.9 The ESBS is the location at which the distributed electrostaticforce on the cantilever does not influence its slope and as a result does not affect the
deflection measured by the AFM.
This ESBS method works well with both stiff and soft cantilevers but does not work for
CR-PFM, where the cantilever shape is dominated by contact resonance behavior. For
frequencies well below contact resonance, the relative contribution of the electrostatic force
to the slope of the cantilever depends on where along the cantilever it is measured. For
most cantilevers, the ESBS is located at about 2/3 of the way from the base of the cantileverto the tip, though the precise position depends on the contact stiffness.

PFM responsewith applied bias
on ferroelectric
samples: (a) schematicof ferroelectric
hysteresis without
electrostatics (green),
with electrostatics
on a non-ferroelectric
sample (red), and withboth electrostatics andferroelectric behavior(blue). (b) cKPFM plots
from a ferroelectricmaterial at different write
voltages. The dashedblack lines indicate theelectrostatic response in
the part of the hysteresis
curve where theferroelectric response of
the sample is saturated. If
the sample were an ideal
dielectric, the red dashedbox would indicate
the surface potential
for the sample whichchanges from one write
voltage to the next due
to charge injection fromthe tip. The blue dashed
box indicates the PFM
response for the off-field
hysteresis loop. Data isfrom a PZT sample withDC voltage applied to tip,
AC to sample.

ab
FIGURE 6

Figure 6a illustrates the effects of pure tip displacement (piezoelectric) and distributed force
on the cantilever (electrostatic) bending of the cantilever. PFM is sensitive to the sum of theslope from both sources, so positioning the laser at the ESBS will result in significantly lesselectrostatic artifact than the usual laser at tip (LAT) position. For best performance, thelaser position is iteratively adjusted until one of the following occurs: Amp|↑domain = Amp|↓domain for a sample where this is expected (like PPLN);
 Amp is minimized on a non-piezoelectric sample; ∂Amp/∂VDC is minimized.

Figure 6b compares PFM images collected on PPLN at different tip voltages using a
Bruker SCM-PIT-V2 probe with spring constant kc = 2.7 N/m. The leftmost two columns
compare PFM amplitudes with LAT and at the ESBS, while the rightmost columns compare
PFM phase. As expected, the ESBS amplitude of the center domain matches the outerdomains across tip voltages from -10 V to +10 V, but there is a wide range of amplitude
for LAT. Likewise, the ESBS phase is very consistent over the voltage range, but not sofor LAT. Quantifying this for the ESBS case, we find d33 =9.3±0.3 pm/V for the centerdomain and 10.7±0.9 pm/V for the left domain. Placing the laser at the end (LAT) resultsin d33 =5.9±2.8 pm/V for the center domain and 12.4±6.6 pm/V for the left domain –more than a factor of two difference. The difference is even more extreme in the phasechannel – for ESBS the phase difference between domains ranges from +178.1° to +179.9°(where the expected value is +180°). In contrast, the LAT phase difference ranges from
-15.3° to +201.4°. These results demonstrate that, by simply positioning the laser at theESBS, the electrostatic component of the PFM signal is nearly completely eliminated.
Combining SS-PFM with sub-resonance PFM at either LAT or ESBS, the influence of
imposed electrostatics can be examined (via the read bias) on PFM spectra. Figure 7 shows
PFM amplitude ‘butterfly loops’ on a PZT thin film with write voltages from -11 V to +11 V.
To see the influence of the electrostatic force on the measurements, the read voltages werealso varied from -2.7 to +2.7 V. In Figure 7a (LAT), only the loop for read (0 V) has the usual
symmetric loop. All the others are skewed one way or the other. In contrast, Figure 7b (laser
at ESBS) produced loops that are reasonably consistent up to ±1.8 V.

The effect of electrostaticforce on the cantileverdepends on beambounce laser position:(a) the electrostatic force
on the cantilever has
minimal influence on the
cantilever deflection when
the laser is positioned
at the electrostatic
blind spot (ESBS, see
red-dashed line), (b) PFM
maps of amplitude (left)
and phase (right) collected
at different tip voltages
on PPLN demonstrate
the significant variationin response with surface
potential when thelaser is positioned at
the tip (LAT) and theimprovement possible
with the ESBS.

a
FIGURE 7
Investigating the influenceof beam-bounce laser
position on PFM responseusing sub-resonance SSPFM; (a) PFM amplitude
vs. write voltage spectra(‘butterfly loops’) at
different read voltages
with laser positioned near
the end of the cantilever(LAT). (b) PFM spectra atdifferent read voltages
with laser positioned at
the electrostatic blindspot (ESBS).

b

Mapping ferroelectric parameters
If spectroscopy is conducted at multiple positions across a surface, a map of any parameterfrom the hysteresis loop can be generated.10 In Figure 8a, a single piezoelectric loop (top)is analyzed to obtain ferroelectric parameter at one point. This is repeated for every point
in a 20x20 array, and maps of coercive voltages V0+ and V0 - are generated (bottom). The
mapping is done using MIROView™, allowing the array to be co-located with other AFM
measurements (topography, adhesion, dissipation, elastic modulus, etc.), previously poled
regions, or optical images. Figure 8b correlates a CR-PFM phase image collected after the
spectroscopic map showing poled regions with the positive coercive bias by overlaying a
map of contour lines with constant V0+. This type of correlation can be used to understandthe influence of nanostructures like grain boundaries and defects on the ferroelectric
behavior of the material.

Sample: PZTProbe: SCM-PIT-V2

a

FIGURE 8b

Maps of ferroelectric
properties can beextracted from arraysof spectra: (a) top is aferroelectric hysteresis
loop from resonant
SS-PFM on PZT, in (a)bottom key parameterssuch as coercive voltages
V0+ and V0- are extracted
from the loops andmapped; (b) V0+ map
is overlaid upon asubsequent PFM phase
map to look for influenceof domain structure on
coercive voltages.

If desired, PeakForce Tapping® can be used to find the region of interest instead ofcontact mode, protecting the tip even further and avoiding damage to even the mostdelicate samples. If high levels of detail are required, MIROView supports arrays of up
to 50x50 = 2500 spectra of 10 to 20 MB each, resulting in a full data set of 25 to 50 GB.
Collecting such large data sets takes time, but Bruker’s DSP-based RampScripting minimizes
the total acquisition time by eliminating system latencies between different segments in thescript (switching times are on the order of 10 µs).

Conclusions
While there are several challenges regarding collecting and analyzing quality PFM data,
the resolution and sensitivity of the AFM make it a compelling choice for investigating
ferroelectric materials. If care is taken to compensate for electrostatics and instrumental
artifacts, results can be compared across different labs and types of instruments anddevelopment of structure-property relationships are facilitated.
Bruker’s DCUBE PFM and SS-PFM both work with either contact resonance or subresonance PFM and can be used with PeakForce Tapping for survey scanning, eliminating
contact mode and its attendant lateral forces. They thereby provide more repeatable results,
enable interrogation of delicate samples, and allow for use of stiffer levers, lessening
electrostatic artifacts.
Key practical solutions
 If sample response is weak or coercive voltages are low, contact resonance isrecommended to maximize signal to noise, but careful analysis is needed forquantification of response amplitude. When sample response is stronger, sub-resonance
PFM is the most direct way to obtain quantitative amplitude data (and d33).
 By poling a sample with known electrostrictive coefficient sign, it is possible to calibrate
the system phase offset at a given frequency, allowing correct interpretation ofspectroscopic data.
 The electrostatic force on the cantilever can induce a PFM artifact that is very similar to
the ferroelectric response. For sub-resonance PFM this can be mitigated by positioning
the beam bounce laser at the electrostatic blind spot on the cantilever.
 SS-PFM can be used to investigate the influence of electrostatics on the PFM spectra
for both resonance and sub-resonance PFM using varying read voltages.
 Arrays of SS-PFM spectra can be analyzed and used to generate maps of key
ferroelectric parameters, enabling correlation with nanostructures at the sample surface.

Acknowledgements
We thank Jason Killgore (NIST) and Liam Collins (ORNL) for many useful discussions andclarifications, which significantly improved this document.

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of Bruker Corporation. All other trademarks are the property of their respective companies. AN156, Rev. A0.

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https://doi.org/10.1021/acsnano.5b02227©2023 Bruker Corporation. All rights reserved. DataCube, Dimension Icon, MIROView, and PeakForce Tapping are trademarks

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