Triaxial AFM Probes for Noncontact Trapping and ManipulationTriaxial AFM Probes for Noncontact Trapping and Manipulation
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CitationCitationBrown, Keith A., and Robert M. Westervelt. 2011. Triaxial AFM
probes for noncontact trapping and manipulation. Nano Letters
Published VersionPublished Versiondoi:10.1021/nl201434t
AccessedAccessedFebruary 19, 2013 7:51:13 PM EST
Citable LinkCitable Linkhttp://nrs.harvard.edu/urn-3:HUL.InstRepos:9453698
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Triaxial AFM probes for non-contact trapping and manipulation
Keith A. Brown and Robert M. Westervelt*
School of Engineering and Applied Sciences, and Department of Physics,
Harvard University, Cambridge, MA 02138
We show that a triaxial AFM probe creates a non-contact trap for a single particle in a fluid via
negative dielectrophoresis (nDEP). A zero in the electric field profile traps the particle above the
probe surface, avoiding adhesion, and the repulsive region surrounding the zero pushes other
particles away, preventing clustering. Triaxial probes are promising for three-dimensional
assembly and for selective imaging of a particular property of a sample using interchangeable
Keywords: Dielectrophoresis, Non-contact trapping, AFM, Assembly, Nanoparticles, Triaxial,
The atomic force microscope (AFM) is an indispensable tool for manipulating and
imaging nanoscale materials.1-3 AFM tips have been used to pattern and assemble small objects
by pushing and dragging,4,5 scanned probe lithography,6,7 and by lifting with two coordinated
AFM probes.8 In addition to applications in assembly, manipulating objects with an AFM tip
allows new types of imaging by using an attached particle to provide a specific tip-sample
interaction. Examples of functionalization-interaction pairs include silica beads to measure
colloidal forces,9 biological cells for measuring cell-cell interactions,10 metallic nanoparticles for
scanning near field optical microscopy,11 and carbon nanotubes12 and nanoneedles13 for high
resolution imaging. Single particle manipulation is limited by clustering of many particles and
the “sticky finger” problem in which nanoscale particles become irreversibly stuck to surfaces or
the AFM probe.14
An atomic force microscope (AFM) probe that can grab and release particles without the
limitations of stiction and clustering would have many applications in manipulation and imaging.
The ability to pick-and-place single nanoscale particles for three-dimensional assembly could
enable the construction of interacting quantum systems.15 A single particle held by the probe
would allow selective imaging with a functionalized material, as in optical tweezing,15,16 and has
great promise for single-molecule force spectroscopy.3
We recently created coaxial AFM probes that can perform pick-and-place manipulation
of microscale objects, and can image with a particle trapped at their tip.17 Coaxial probes use
positive dielectrophoresis (pDEP), the attraction of an induced dipole towards regions of high
electric field, which is widely used in nanotechnology,18 biotechnology,19 and single particle
trapping.20 A coaxial probe consists of a conducting AFM tip surrounded by a grounded shell
that produces a sharp maximum in the electric field E at the tip's end. 17,21,22 Drawbacks of this
approach are clustering of multiple particles, and stiction of attached particles as they must be
held in contact.14,23
In this paper, we present triaxial AFM probes and demonstrate non-contact trapping of
nanoscale objects via negative dielectrophoresis (nDEP).24 The tip of a triaxial probe (Figure 1a)
shows three electrodes: a conducting core surrounded by an inner and an outer conducting shell,
highlighted in Figure 1b. By applying a voltage to the inner shell electrode, the triaxial probe
creates an electric field profile E with a zero at a height zT above the end of the probe, as shown
by the electrostatic simulation in Figure 1c. Objects that are less polarizable than the fluid
medium are trapped in the electric-field zero at zT, which we designate as the nDEP trap. The
trap is physically smaller than the triaxial tip, promising for the manipulation of nanoscale
particles. We can hold a 100 nm radius polystyrene sphere in a region commensurate with its
size using a triaxial probe with tip diameter ~7 µm, much larger than the nanoparticle. By
adjusting the voltage on the core electrode (V1) relative to the voltage on the inner shell electrode
(V2), the trap can be opened and closed, and the height zT of the trapped particle above the tip can
be adjusted, allowing the user to position and assemble particles.
Figure 2 illustrates how polystyrene beads are drawn toward and trapped by the triaxial
probe. Triaxial electrodes are nanofabricated onto commercial AFM probes (see Supporting
Information). A probe is held in a suspension of fluorescent polystyrene beads with radius
a = 100 nm, suspended in a 1:1 v/v mixture of deionized water : glycerol and observed with a
fluorescence microscope (see Supporting Information). The way the polystyrene beads interact
with a radio frequency (RF) electric field E depends on the frequency f of E (see Supporting
Information).25-27 In particular, these beads exhibit a crossover frequency fC ≈ 800 kHz such that
if f < fC, their surface conductance increases their polarizability sufficiently so that they
experience pDEP and are pulled to regions of high electric field. Conversely, if f > fC, they will
be repelled from regions of high field with nDEP. An attractive field profile (Figure 2a) is
created by applying 10 V peak-to-peak to the inner shell at a low frequency (f = 100 kHz) while
grounding the core and outer shell electrodes. The sequence of images shown in Figures 2b-f,
taken at 200 ms intervals, show how beads are attracted toward the high field region near the
triaxial tip - the bead marked by an arrow moves towards the probe, and becomes trapped on its
surface in Figure 2f.
By increasing the RF frequency to f = 5 MHz, we turn on the nDEP trap above the
triaxial probe. The polystyrene beads are now repelled from high field regions - some are drawn
into the nDEP trap and the rest are pushed out into the medium, as shown in Figure 2g. Before f
is increased (Figure 2h), many beads are attached to the probe surface. Just after the increase
(Figure 2i), the beads on the probe are jettisoned. In the subsequent frames (Figures 2j-l), the
majority of the beads are pushed away from the probe, while those marked with the red arrow are
pushed to the electric field zero at the center of the nDEP trap.
Figure 3 shows the triaxial probe holding a polystyrene bead in the nDEP trap within a
region comparable to the size of the bead. Figure 3a is a sequence of images that show the
motion of a bead (red) trapped above the triaxial probe, and a bead (blue) adhered to the probe
surface. The distribution of trapped and adhered bead positions (Figure 3b) is found by fitting
two-dimensional Gaussians to the beads in each image. The position of the trapped bead relative
to the probe (Figure 3c), is found by comparing the positions of the trapped and adhered bead in
each image. Principle component analysis is used to find the tight (x') and loose (y') axes of the
spatial distribution over time. The strength of the nDEP trap is represented by histograms of the
displacements along the x' and y' axes, shown in Figures 3d and 3e. The spatial distributions are
fit very well by Gaussians, appropriate for thermal fluctuations against a linear restoring force.28
The Gaussian fits provide standard deviations σx' = 133 nm and σy' = 204 nm that are comparable
to the 100 nm radius of the bead.
The measured shape and strength of the nDEP trap are in agreement with those predicted
by theoretical simulations. The magnitude of the thermal fluctuations in the bead’s position can
be estimated from the triaxial probe geometry, the dielectric properties of the system, and our
theoretical model for triaxial probes.24 For an ideal triaxial tip, this analysis (see Supporting
Information) predicts standard deviations σz = 66 nm and σr = 102 nm in the axial and radial
directions respectively, comparable to our observations. The experimental standard deviations
and the observed DEP velocities (see Supporting Information) are both consistent with the values
of V1 and V2 being attenuated to ~50% of the applied values. The ratio σx'/σy' = 0.65 of the
experimental standard deviations, which is a measure of the trap shape, is in excellent agreement
with the theoretically determined ratio σz/σr = 0.64, indicating that the shape of the trap matches
our theoretical predictions.
Figure 4 demonstrates that we can precisely control the height zT of the trap above the
probe surface by changing the voltages on the core and shell electrodes. By setting V1 = VB
sin(2πft) and V2 = [VB + ΔV] sin(2πft), we make zT a monotonic function of the control voltage
VB (see Supporting Information). Figures 4a and 4b show images of a single trapped fluorescent
polystyrene bead for VB = 0 V and VB = –ΔV/2 respectively, with bead radius a = 460 nm,
ΔV = 7.5 V, and f = 5 MHz. The positions of a bead trapped in the nDEP trap (red X) and a bead
adhered to the back of the probe (blue X) are found with two-dimensional Gaussian fitting. The
movement of the trapped bead relative to the probe is found for each pair of beads. As VB is
swept from 0 V in Figure 4a to –ΔV/2 in Figure 4b, the bead moves away from the tip. By
driving VB sinusoidally at 2 Hz, the periodic motion of the bead may be tracked (Figure 4c). The
height zT of the trap center relative to the tip (Figure 4d), is a smooth and monotonic function of
VB, allowing the user to precisely control the height of a trapped bead above the triaxial probe
surface. By changing VB from 0 V to -ΔV/2, the bead is moved ~ 1
µm. A straight line (red) fits
the trap motion well with a slope -270 nm/V, in agreement with the theoretical estimate
~ -200 nm/V (see Supporting Information). The residual (Figure 4e), fit by a Gaussian, gives a
standard deviation in trap height of only 54 nm about the average value, much smaller than the
460 nm radius of the bead.
Triaxial probes are well suited to pick-and-place nanoassembly, because the dimensions
of the trap are much smaller than the tip24, as shown in Figure 1c. A relatively large tip and bead
size were chosen for this experiment to allow optical imaging, but much smaller dimensions are
possible. The trap's electric field pattern, shown in Figure 1c, is universal; if the scale bar and
the tip voltage are scaled down by the same factor, the pattern of the electric field and its
amplitude will remain precisely the same. The limit on how tightly an object can be held is
determined by dielectric breakdown of the medium. Simulations show that a Si sphere with
radius a = 5 nm can be trapped at room temperature by a triaxial tip with radius 300 nm (see
Supporting Information). Smaller objects can be trapped by increasing the tip voltage or by
reducing the tip radius R. The standard deviation σ in particle position at room temperature
scales as σ? a3/2Vrms-1R2 where a is the particle radius, Vrms is the root mean square voltage, and
R is the electrode spacing. In this experiment, we measure σ ≤ 200 nm for a = 100 nm,
R = 1.6 µm, and Vrms = 5.3 V. By increasing Vrms by a factor of 25, the scaling relation predicts
that we can achieve a smaller standard deviation σ ≤ 8 nm without risking dielectric breakdown.
A sharper probe with R = 64 nm can trap a smaller nanoparticle with a = 10 nm in a space
smaller than its radius, σ < a, for the same tip voltage Vrms = 5.3 V.
In this paper, we have shown that a triaxial AFM probe provides a non-contact approach
for trapping a single nanoparticle at room temperature. Triaxial probes are strong candidates for
pick-and-place assembly of nanoscale objects. Particles much smaller than the end of the triaxial
probe can be grabbed out of a suspension using negative dielectrophoresis (Figure 2) and held in
a potential well comparable to their size (Figure 3 and Video S1). The trapped particle can then
be moved to the desired location (Video S3). The trapped particle can then be placed by pushing
it away from the probe end by adjusting the tip voltages (Figure 4 and Video S2), or released into
suspension by turning off the trapping field (Video S4). This pick-and-place technique works for
particles as small as 5 nm at room temperature, and is promising for the construction of quantum
devices.5 The triaxial probe presented here is compatible with commercial AFMs, and the full
capabilities of a triaxial probe will be realized by leveraging nanometer scale positioning and
force-measurement afforded by the AFM apparatus. Dielectrophoresis has been used for imaging
using conventional AFM probes29 and with coaxial AFM probes30 for enhanced spatial
resolution. Triaxial probes offer more control of the electric field distribution and new
opportunities for imaging. For a system with a nonlinear response, the electric field zero above a
triaxial probe can provide high spatial resolution images in analogy with nonlinear optical
stimulated emission depletion (STED) microscopy.31
We acknowledge Evangelos Gatzogiannis for assistance with the optical microscope and Jim
MacArthur help with electronics. We acknowledge support by the Department of Defense
through a National Defense Science & Engineering Graduate (NDSEG) Fellowship, the National
Cancer Institute MIT-Harvard Center of Cancer Nanotechnology Excellence, and the
Department of Energy under grant DE-FG02-07ER46422.
Supporting Information Available
Additional information is available on the theory of DEP, measuring velocity of nanoparticles
near a triaxial probe (Figure S1), the electrostatic model of a triaxial probe (Figure S2 and S3),
details of triaxial probe fabrication, and a description of the apparatus (Figure S4). Four videos
are available that demonstrate the trapping of nanoparticles with triaxial probes, Video S1
depicts the Brownian motion of a 100 nm radius bead in the nDEP trap and Video S2 depicts
moving a 460 nm radius bead relative to the tip. Video S3 shows holding a 100 nm radius bead
while moving the triaxial probe with the three axis controller. Video S4 depicts beads being
released back into suspension by turning off the trapping field. This material is available free of
charge via the Internet at http://pubs.acs.org
1. Giessibl, F. J. Rev. Mod. Phys. 2003, 75, 949–983.
2. Benstetter, G.; Biberger, R.; Liu, D. Thin Solid Films 2009, 517, 5100–5105.
3. Müller, D. J.; DuFrêne, Y. F. Nature Nanotechnology 2008, 3, 261-269.
4. Requicha, A. A. G. Proc. IEEE 2003, 91, 1922–1933.
5. Barth, M.; Nüsse, N.; Löchel, B.; Benson, O. Optics Letters 2009, 34, 1108–1110.
6. Tseng, A. A.; Notargiacomo, A.; Chen, T. P. J. Vac. Sci. Technol. B 2005, 23, 877–894.
7. Salaita, K.; Wang, Y.; Mirkin, C. A. Nat. Nanotechnol. 2007, 2, 145–155.
8. Xie, H.; Haliyo, D. S.; Régnier, S. A. Nanotechnology 2009, 20, 215301.
9. Ducker, W. A.; Senden, T. J.; Pashley, R. M. Nature 1991, 353, 239–241.
10. Lower, S. K.; Tadanier, C. J.; Hochella, M. F. Jr. Geochim. Cosmochim. Acta 2000, 64,
11. Gan, Y. Rev. Sci. Instrum. 2007, 78, 081101.
12. Hafner, J. H.; Cheung, C.-L.; Woolley, A. T.; Lieber, C. M. Prog. Biophys. Mol. Biol.
2001, 77, 73–110.
13. Yazdanpanah, M. M.; Harfenist, S. A.; Safir, A.; Cohn, R. W. J. Appl. Phys. 2005, 98,
14. Komvopoulos, K. J. Adhesion Sci. Technol. 2003, 17, 477–517.
15. Moffitt, J. R.; Chemla, Y. R.; Smith, S. B.; Bustamante, C. Annu. Rev. Biochem. 2008,
16. Akerlof, G. J. Am. Chem. Soc. 1932, 54, 4125–4139.
17. Brown, K. A.; Aguilar, J. A.; Westervelt, R. M. Appl. Phys. Lett. 2010, 96, 123109.
18. Hughes, M. P. Nanotechnology 2000, 11, 124–132.
19. Voldman, J. Annu. Rev. Biomed. Eng. 2006, 8, 425–454.
20. Zheng, L.; Brody, J. P.; Burke, P. J. Biosens. Bioelectron. 2004, 20, 606–619.
21. Rosner, B. T.; Bork, T.; Agrawal, V.; Weide, D. W. v. d. Sens. Actuators, A 2002, 102,
22. Noh, J. H.; Nikiforov, M.; Kalinin, S. V.; Vertegel, A. A.; Rack, P. D. Nanotechnology
2010, 21, 365302.
23. Jones, T. B.; Bliss, G. W. J. Appl. Phys. 1977, 48, 1412–1417.
24. Brown, K. A.; Westervelt, R. M. Nanotechnology 2009, 20, 385302.
25. Akerlof, G. J. Am. Chem. Soc. 1932, 54, 4125–4139.
26. Weast, R. C. Handbook of Chemistry and Physics. 67th Ed.; CRC Press Inc.: Boca Raton,
27. Cui, L.; Holmes, D.; Morgan, H. Electrophoresis 2001, 22, 3893–3901.
28. Reif, F. Fundamentals of statistical and thermal physics; McGraw-Hill Inc.: Boston,
29. Hilton, A. M.; Lynch, B. P.; Simpson, G. J. Anal. Chem. 2005, 77, 8008-8012.
30. Brown, K. A.; Berezovsky, J.; Westervelt, R. M. Appl. Phys. Lett. 2011, 98, 183103.
31. Willig, K. I.; Harke, B.; Medda, R.; Hell, S. W. Nat. Meth. 2007, 4, 915-918.
FIGURE 1. A triaxial AFM probe and its electric field showing the nDEP trap. (a) Scanning
electron micrograph of a triaxial AFM probe. The triaxial electrodes are visible at the bottom of
the image and the cantilever extends off the top of the image. The scale bar is 20 µm.
(b) Magnified view of the triaxial electrodes. The light triangle at the center is the original AFM
probe that makes up the core conductor. The inner shell electrode is visible as a thin line around
the core. The outer shell is visible at the edge of the electrodes. The scale bar is 2 µm. In the
schematic diagram of the triaxial probe tip below, the electrodes are black and the insulating
layers are blue. The dashed line shows the location of the side-view cross section shown in
Figure 1c. (c) Axisymmetric simulation (Maxwell 2D – Ansys) of the electric field magnitude E
field near the tip of the triaxial probe with V1 = 0 and V2 = 10 V. The field decays quickly away
from the tip and there is an electric field zero visible displaced from the surface of the probe. The
scale bar is 2 µm. The inset shows a magnification of the trapping region. The electric field zero
is visible a distance zT from the surface of the probe. The scale bar of the inset is 400 nm.
FIGURE 2. Attracting particles with pDEP and repelling and holding them with nDEP.
All scale bars 5 µm. (a) Schematic of a particle being drawn into the field maxima with pDEP.
(b)-(f) A time sequence of fluorescence images depicting the bead marked with the red arrow
being drawn into the tip with pDEP. A 10 V peak-to-peak voltage at 100 kHz is applied to V2
while V1 = 0. Frames are separated by 200 ms. The schematic cross section is overlayed in the
approximate position of the triaxial probe as a guide to the eye. (g) Schematic of one particle
being repelled from the probe by nDEP and another being held in the nDEP trap. (h)-(l) A time
sequence of fluorescence images depicting the triaxial probe repelling beads with nDEP. Just
after the first frame, a 15 V peak-to-peak excitation is applied to V2 at 5 MHz while V1 = 0. The
majority of the beads are pushed back into suspension while the beads marked with the red arrow
are held in the nDEP trap. Frames are separated by 200 ms.
FIGURE 3. Determining the strength of the nDEP trap. (a) Schematic and three
representative fluorescence images of a 100 nm radius bead trapped in the nDEP trap. The bead
identified with the red dot is held in the nDEP trap while the bead identified with a blue dot is
adhered to the tip. A schematic of the tip is superimposed in the approximate location of the tip
as a guide to the eye. A 15 V peak-to-peak excitation at 1 MHz is applied to V2 while V1 = 0. The
scale bar 4 µm. These images are taken from a dataset of 5000 images used for the analysis. The
full movie of this dataset is available as Video S1. (b) Scatter plots of the position of the bead in
the trap (red dot) and the tip inferred from the position of an attached bead (blue dot). (c) Scatter
plot of the separation between the trapped bead and the triaxial tip given by the separation of
trapped bead/adhered bead pairs. The axes of tightest and loosest trapping are determined with
principle component analysis and are shown on the plot as the x’-axis and y’-axis respectively.
(d) Histogram of the spread of the trapped bead about the x’-axis. A Gaussian fits the data very
well with a standard deviation σx’ = 133 nm. (e) Histogram of the spread of the trapped bead
about the y’-axis. A Gaussian fits the data very well with a standard deviation σy’ = 204 nm.
FIGURE 4. Controlling the position of a single trapped bead relative to the triaxial probe.
(a) Fluorescence image of a 460 nm radius sphere held in the nDEP trap (red X). A bead adhered
to the back of the probe (blue X) is used as a reference to localize the tip. A 15 V peak-to-peak
excitation at 5 MHz is applied to V2 while V1 = 0. The scale bar is 4 µm. The full movie of this
dataset is available as Video S2. (b) Now, the bead is held further from the tip as 7.5 V peak-to-
peak excitation at 5 MHz is applied to V2 while the same excitation is applied 180⁰ out of phase
to V1. (c) A control voltage VB is used to move the nDEP trap location smoothly (see Supporting
Information). The position zT of the trap relative to the probe is determined by the distance
between the trapped bead and the reference bead. (d) The position of the trap is a monotonic
function of VB and we are able to move the bead ~1 µm relative to the probe. The data is well fit
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by a line, shown in red. (e) Histogram of the residual zT about the linear fit. A Gaussian fits the
data very well and produces a standard deviation of 54 nm.