APPLIED PHYSICS LETTERS 94, 103507 共2009兲

Preamplifying cantilevers for dynamic atomic force microscopy
Benedikt Zeyen,1,a兲 Kumar Virwani,2,b兲 Bede Pittenger,2 and Kimberly L. Turner1
1Department of Mechanical Engineering, University of California, Santa Barbara, California 93106, USA
Veeco Metrology, Santa Barbara, California 93117, USA

2共Received 3 October 2008; accepted 11 February 2009; published online 11 March 2009兲
A cantilever type has been developed for dynamic force microscopy by the addition of a harmonicoscillator in the form of a paddle to atomic force microscopy cantilevers. These cantilevers provide
resonant amplification of periodic interactions between the probe and the substrate when the laser isaligned on the paddle. The cantilevers were explored for their use in piezoresponse force
microscopy. Application of the cantilevers for measurements on periodically poled lithium niobate
ferroelectric material is presented. A comparison with commonly used cantilevers showed an as
good as or better performance of the presented cantilevers. © 2009 American Institute of Physics.
关DOI: 10.1063/1.3093814兴
Piezoresponse force microscopy1 共PFM兲 is a contact
mode scanning probe microscopy2 共SPM兲 technique, whichin its most basic form is used to measure out-of-plane andin-plane displacement response of ferro- and piezoelectricmaterials. A micromachined metal-coated probe scans thesurface, controlled via a feedback loop based on laser deflection signal from the back of the probe. An ac bias applied tothe sample causes the displacement of the sample surface
and hence of the probe scanning on it. This displacement isusually expressed in picometer per volt of applied ac bias.
These very small displacements necessitate the use of a lockin-amplifier to detect the motion and the amplitude as well as
the phase. Thus the piezoresponse 共PR兲 vector of the sample
is quantified. One of the means to amplify these displacements is to use resonance enhancement. The ability of a system to amplify an input signal is determined by its quality
factor3 “Q.” During PFM operation, the system consisting ofa SPM probe and an oscillating surface 共due to the applied acbias兲 can be considered as a driven oscillator. Without any
resonance enhancement, the quality factor of this driven oscillator far below its first resonance 共the usual mode of operation兲 is equal to unity.3 More recently, techniques basedon contact resonance4,5 PFM were being developed and used.
Contact resonance6 frequency is the frequency at which asystem consisting of the SPM probe in contact with an oscillating surface reaches resonance. Contact resonance-PFM
has been used to amplify the out-of-plane response and also
to measure higher order electromechanical coefficients7 offerroelectric thin film materials. The trade-offs8 as a result ofcontact resonance enhancement are the coupling of the cantilever inertia and elastic response of the sample into themeasured signal, complex cantilever mode shape, and thedependence of contact resonance-PFM quality factor on thecontact area between the probe and the sample. All theseeffects are very difficult to physically quantify and hence
present challenges when interpreting contact resonance-PFM
data.
In order to overcome the challenges presented by contact
resonance-PFM, the authors have developed a cantilever de-sign, as illustrated in Fig. 1共a兲, called “preamplifying cantilever” or PAC. The PACs are optimized for a maximum
transfer function between the probe and the optical detector
during contact mode operation. This is achieved by adding asecond cantilever or a “paddle” to the cantilever as illustrateda兲FIG. 1. 共a兲 Scanning electron microscope image of a PAC showing positionof the paddle used for resonant enhancement. 共b兲 Operation of a PAC in a
SPM setup for PFM illustrating the alignment of the laser on the paddle.

Now with A.M. Fitzgerald and Associates, LLC, San Carlos, CA 94070,
USA. Electronic mail: bzeyen@web.de.
b兲
Now with IBM Almaden Research Center, San Jose, CA, USA.
0003-6951/2009/94共10兲/103507/3/$25.00

94, 103507-1© 2009 American Institute of Physics

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Zeyen et al.

in Fig. 1. With this paddle a certain frequency bandwidth of
the sample’s displacement response to the applied ac bias
gets amplified. The laser for feedback and PFM signal measurements is now aligned on the paddle instead of the cantilever apex. The PACs were designed such that the paddle
frequency was higher than the frequency of the topographical features and lower than the cantilever contact resonancefrequency. These cantilevers preamplify the oscillation signal
before it reaches the photodiode detectors, hence the name
PACs.
The method of operation for the PACs, the characterization of their amplification, and comparisons to contact
resonance-PFM were developed using samples of periodically poled lithium niobate 共PPLN兲. The choice of this material was based on its two characteristics, viz., smoothsurface 共roughness of ⬍1 nm兲 and well distinguished ferroelectric domains9 with vertically up and downward oriented
PR vectors of equal amplitude. Thus one PPLN domain oscillates in phase with the electric field, the other out of phasewith it. In comparison to contact resonance-PFM operation,commercially available metal-coated rectangular cantilevers关nominal length of 225 ␮m, spring constant of 2–5 N/m,
trade name: Veeco Probes metal coated etched silicon probe
共MESP兲兴 were chosen because of their accepted general usefor PFM studies. The PR vector amplitudes were comparedwhen the applied ac bias frequency was equal to the paddle
resonance frequency for the PAC with contact resonancePFM operation of a MESP cantilever, providing a one-to-one
comparison. The PR vector amplitudes can be expressed inpicometer per volt of applied ac bias by converting the measured signal in mV to picometer using the static displacement sensitivity, also known as the inverse optical lever sensitivity.
The method of operation for a PAC was developed
analogous to contact resonance-PFM of a MESP. The laser
was aligned on the paddle of a PAC and positioned on thecenter of the photodiode detector. The probe then approachedthe PPLN sample, and the surface was scanned by maintaining tip-sample force enough to track the surface. An ac biasof 1 V amplitude 共2 V peak-to-peak兲 was applied to thesample. A frequency sweep of the ac bias was performed tomeasure the first resonance of the paddle. Similarly for aMESP probe, the laser was aligned at the apex of the cantilever and once on the PPLN sample, the contact resonancefrequency determined by sweeping the ac bias frequency.
The static displacement sensitivities were then determinedfor both a PAC and a MESP cantilever to convert the response in mV to picometer. Finally, in order to normalize thedata the PR vector was converted into picometer 共or nanometer兲 per volt of applied ac bias.
Figure 2共a兲 shows the measured PR vector amplitude asa function of frequency for a MESP cantilever operating at
its contact resonance, and Fig. 2共b兲 shows the PR vector
amplitude with the laser aligned on the paddle for a PAC.
The maximum response of MESP cantilever operating incontact resonance-PFM was measured to be about 700 pm/V,
whereas the maximum response of PAC at resonance wasmeasured to be 3000 pm/V. The maximum amplitude10
reached will depend on the time for which the oscillator wasallowed to “ring up.” In order to ensure an equivalent comparison, both MESP and PAC cantilevers were allowed toring up for the same amount of time. As can be inferred fromthe measured PR vector amplitudes, the amplitude response

Appl. Phys. Lett. 94, 103507 共2009兲

FIG. 2. PR amplitude in picometer per volt of applied ac sample bias as afunction of function of ac bias frequency for contact resonance-PFM withMESP cantilever and paddle resonance of a PAC.

of PACs at resonance is as good as or better than the MESP
cantilevers in contact resonance-PFM. When comparing amplitudes away from and at resonance, at least an order ofmagnitude improvement 共⬃3000 pm compared to 100 pm兲
in the signal was measured.
The next step was to evaluate the PR imaging performance of PACs and compare that to MESP cantilevers incontact resonance-PFM. Figures 3共a兲–3共c兲 show height, PR
amplitude, and PR phase scans, respectively, of the PPLNsurface obtained with a MESP cantilever operating at its contact resonance at 338.1 kHz when 1 V amplitude ac bias wasapplied to the sample. Figures 3共d兲–3共f兲 show height, PR
amplitude, and PR phase scans, respectively, obtained with aPAC operating at a paddle resonance of 104.5 kHz for thesame applied sample bias. The scan velocity was maintained
at 70 ␮m / s, and the static displacement sensitivity for bothMESP as well as PAC was about 78 nm/V. The surface scan关Fig. 3共d兲兴 with the laser aligned on the paddle clearly showsthat good topographical imaging is possible using PACs. Because the frequency of the topographical features is expected
to be much smaller than the paddle resonance 共⬃104 kHz兲,the height signal had a unity gain for the dc deflection signal
with the laser aligned on the paddle. The domains on thePPLN surface were also clearly distinguishable in the PR
amplitude data. A phase difference of 180° was measured
between adjacent oppositely polarized ferroelectric domains.
For PR imaging, the bandwidth is determined only by thegeometry of the paddle. Since the paddle oscillates independent of the rest of the cantilever, this helps decouple thecantilever inertia from affecting the PR vector measurements. 共The cantilever contact resonance frequency wasmeasured at 328 kHz, which was far away from paddle resonance.兲 At resonance, the paddle was oscillating in its first

FIG. 3. 共Color online兲 Contact resonance-PFM with MESP cantilever at338.1 kHz. 共a兲 Height, 共b兲 PR amplitude, and 共c兲 PR phase. PFM with PAC
at 104.5 kHz. 共d兲 Height, 共e兲 PR amplitude, and 共f兲 PR phase. Applied acbias amplitude was 1 V. The dashed lines denote the position of the section
analysis data in Fig. 4.

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Appl. Phys. Lett. 94, 103507 共2009兲

Zeyen et al.

were as good as or better than traditional rectangular 共MESP兲
cantilevers operating in contact resonance mode. Hence
PACs provide an alternative to contact resonance-PFM while
overcoming some of its limitations, such as coupling of cantilever inertia into the measured signal and complex vibration modes of the cantilever. Ongoing work will provide anunderstanding of the signal to noise ratio of the cantilevers
and effect of contact area on PR measurements. We predictthat these cantilevers have more applications than just PR
force imaging. We expect a similar resonance enhancement
for electrostatic force microscopy,11 magnetic force
microscopy,12 and higher harmonic tapping.13
FIG. 4. Section line through amplitude as measured in Fig. 3共b兲 for contact
resonance-PFM of a MESP cantilever 共bottom兲 and Fig. 3共e兲 for paddleresonance operation of a PAC 共top兲.

mode of vibration, which was in-plane and out-of-plane. Thiscan be easily modeled with a simple harmonic oscillator approximation. In contrast a rectangular cantilever in contact
resonance has a vibration mode of higher complexity,7 which
is difficult to model. Any changes in the frequency of thepaddle can be easily achieved by changing just its geometry
while keeping the overall shape of the cantilever the same.
This provides immense design extensibility while retaining
the inherent imaging performance of PACs. In order to compare the response amplitudes and to understand the signal tonoise ratio during scanning, section analysis was performedon Figs. 3共b兲 and 3共e兲, respectively, as shown in Fig. 4. The
dotted line denotes the PAC PR amplitude, whereas the complete line denotes the MESP PR amplitude. The PAC showsat least three times as much signal as MESP cantilever, validating the frequency response data from Fig. 2. However, thesignal as well as noise in the measurements gets amplified.
This effect and the influence of probe area on the measurements are currently under investigation. Thus the out-ofplane PR vector was completely measured and quantified
using PACs with signals as good as or better than commonlyused MESP cantilevers in contact resonance mode.
In conclusion, PACs were presented for PR imaging ofPPLN. With the laser aligned on the paddle of a PAC, good
topographical scans were obtained. The out-of-plane PR amplitude and phase data measured and quantified with PACs

This research was partially supported by Grant No.
SB060001 from the Center for Nanoscale Mechatronics andManufacturing, one of the 21st century frontier research programs, which are supported by the Ministry of Science andTechnology, Korea. Authors would like to thank Dr. BobShelby from the IBM Almaden Research Center for his helpful feedback and comments on the paper.
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