This Application Note describes a method by which Xidex’s NanoBot® nanomanipulator can be used to calibrate the spring constant of an atomic force microscope (AFM) cantilever by deflecting the AFM tip with a calibrated force sensor module mounted as an end effector. The method as described here uses a NanoBot system installed in a scanning electron microscope (SEM). However the method can also be applied in air using a high resolution optical microscope. Spring constants determined by the method apply directly to situations where static deflection is of primary importance. These involve contact mode and colloidal probe AFM measurements, and other measurements involving interfacial forces or bonding forces between atoms or molecules. Xidex manufactures and sells the NanoBot® system, an easy-to-use, highly versatile, user programmable nanomanipulator featuring specialized end-effectors for nanodevice fabrication and testing inside scanning electron microscopes (SEMs) and focused ion beam (FIB) tools. Our mission is to enhance the R&D productivity of nanoscientists and nanotechnologists in both industry and academia. We offer best-in-class turnkey solutions to customers with well-defined requirements that are stable over time, and highly adaptable solutions to customers who need a system that can easily be augmented with additional plug-and-play nanopositioners and end-effectors as their needs evolve.

1. Xidex
AFM Cantilever Spring Constant
Calibration Using the NanoBot®
Nanomanipulator with a Force
Sensor Attachment
Application Note
Vladimir Mancevski, Paul McClure, Xidex Corporation
Method for Measurement of an AFM Cantilever The NanoBot nanopositioner, which has low drift of < 1
Spring Constant nm/min, is able to hold the AFM cantilever stationary in
This Application Note describes a method by which its fully deflected position while the corresponding static
Xidex’s NanoBot ® nanomanipulator can be used to force is displayed and recorded by a LabVIEW TM
calibrate the spring constant of an atomic force software application provided with the product. The
microscope (AFM) cantilever by deflecting the AFM tip measured force is divided by cantilever deflection,
with a calibrated force sensor module mounted as an recorded from the SEM image, to determine the spring
end effector. The method as described here uses a constant. The accuracy of the measurement is limited
NanoBot system installed in a scanning electron by small nonlinearity of the force sensor calibration
microscope (SEM). However the method can also be curve, which typically ranges from 3-4% for the force
applied in air using a high resolution optical sensor modules provided for use with the NanoBot
microscope. Spring constants determined by the system. Higher measurement accuracy could be
method apply directly to situations where static obtained, if needed, by taking advantage of the user-
deflection is of primary importance. These involve programmability of the fully LabVIEW-based NanoBot
contact mode and colloidal probe AFM measurements, system to replace the linear calibration constant of the
and other measurements involving interfacial forces or force sensor with a quadratic or higher power fit to raw
bonding forces between atoms or molecules. sensor calibration data.
Descriptions of the NanoBot sytem and the available
force sensor attachments can be downloaded from the
NanoBot System with Force Sensor Attachment
Products section of Xidex’s web site (www.xidex.com).
Figure 1 shows a NanoBot Model NX-1000 outfitted with
This Application Note is also the subject of a YouTube
a force sensor attachment. The force sensor can also
video, which can be accessed from the Applications
be mounted on one of the two nanopositioners provided
section of the web site.
with the NanoBot Model NX-2000.
Force Sensor
Probe
Force Sensor
NanoBot XYZ Module
Nanopositioner
Figure 1 – NanoBot model NX-1000 outfitted with a
Model FS-2000 force sensor attachment
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2. The force sensor operates as a load cell for measuring
End of Force
forces with nanoNewton resolution. The Model FS-2000
Sensor Probe
force sensor accommodates loads up to 2000 µN. The
Model FS-180 accommodates loads up to 180 µN. Both
compression and tension forces can be measured. The
sensor element, which is based on single crystalline
silicon, measures small forces with high precision.
Unlike other load cells based on strain gages, the force
sensors available for use with the NanoBot system
measure the load by a change of capacitance. The
readout electronics integrated in the sensor package
convert the load into an output voltage proportional to AFM Tip
the force. A LabVIEW™ based application for force
feedback display is installed on a laptop computer
running Windows OS which is provided with the system.
Figure 3 – Force sensor probe and AFM tip with no
Users can also create custom LabVIEW applications cantilever deflection
and add these to the applications library provided with
the NanoBot system.
Cantilever Deflection
Setup for Spring Constant Measurement The LabVIEW application for displaying and recording
Figure 2 shows the setup for measuring the spring the force measured by the sensor is started with an on
constant. The chip to which the AFM cantilever is screen command, or by using the joystick trigger. This
attached is mounted on a fixture attached to an SEM starts a real time recording of force vs. time. With the
stage. The Cantilever is a Budget Sensors model Tap LabVIEW Action running, the NanoBot nanopositioner is
300 G (www.budgetsensors.com) for which the spring commanded to move the stage carrying the force
constant has a nominal specified value of 40 N/m and is sensor module so as to deflect the AFM cantilever from
specified to lie in the range 20-75 N/m. The fine motion its initial position (Figures 2 & 3) to a new position, as
mode of the NanoBot system is used to bring the 50 x shown in Figure 4, at which point the motion stops and
50 micron square end of the Si force sensor probe near, the static force remains constant. Figure 5 is an
but not quite touching the AFM tip. Figure 3 is an expanded view showing the force sensor probe and
expanded view showing the end of the force sensor AFM tip with the cantilever at maximum deflection.
probe and the AFM tip in their initial positions, for which
there is no cantilever deflection.
End of Force Sensor Probe Mounted End of Force Sensor Probe Mounted
on NanoBot Nanopositioner on NanoBot Nanopositioner
AFM
Cantilever
AFM Cantilever
(Fully Deflected)
Chip Mounted
on SEM Stage
Chip Mounted
on SEM Stage
Figure 2 – Setup for Measurement of AFM Cantilever Figure 4 – Force sensor probe and AFM tip at maximum
Spring Constant 2 cantilever deflection

3. End of Force
Sensor Probe
AFM Tip
Figure 7 – Force sensor calibration data provided for
individual sensor module
Figure 5 – Force sensor probe and the AFM tip with
cantilever at maximum deflection
Spring Constant Determination
Figure 6 shows the force vs. time history displayed by The maximum cantilever deflection, D MAX , is determined
the LabVIEW application provided for use with the force by importing the captured video frames used to create
sensor module. The measured force increases from Figures 3 and 5 into Adobe Photoshop, finding the
zero to a maximum value F MAX = 197.38 µN. deflection in units of pixels, and then converting to µm
Calibration data for the individual force sensor, like that using the pixel count associated with the scale bar
shown in Figure 7, determines a linear calibrat ion provided with the SEM image. The result of this
constant CFS, in Volts/ µN,for the individual module. A exercise is D MAX = 10.9 µm. The spring constant, k, is
calibration constant determined this way has been then determined as
entered into the LabVIEW Action prior to conducting the
experiment.
k = F MAX / D MAX = 18.1 N/m
This measured spring constant is just below the 20-75
N/m range specified by the AFM tip manufacturer.
Large deviations from the nominal spring constants
provided by AFM tip manufacturers are not unusual.
For example, a study [1] involving multiple laboratories
Force
Zero Force and different methods for spring constant determination
Measured at
Recorded Prior to showed similar large deviations of measured spring
Maximum
Deflection constants from manufacturers’ specifications. Inspection
Deflection
the reference cantilevers used in the study revealed
chipping damage on the edge of the handle chip and
debris particles on surfaces of the test cantilevers. The
inference is that these two are related and chipping
damage produced during handling of the test chips
generated the debris particles.
Figure 6 – Force vs. time history displayed by LabVIEW Users of a NanoBot system equipped with a force
application sensor can measure the spring constant of an AFM
cantilever intended for use in an application that
requires accurate knowledge of its spring constant in a
few minutes using the method described here. If no
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4. SEM is available, the same technique can be used in air Xidex Corporation
with a high resolution optical microscope equipped with
digital image capture. Unlike alternative methods for Xidex manufactures and sells the NanoBot ® system, an
determining the spring constants of AFM cantilevers easy-to-use, highly versatile, user-programmable
[refs 2 to 5], there is no need to measure the resonant nanomanipulator built for use inside scanning elec tron
frequency of the cantilever, add test masses, perform microscopes (SEMs) and focused ion beam (FIB) tools.
finite element analysis, or make detailed measurements The NanoBot transforms a SEM or FIB into a workshop
of cantilever geometry. for nanodevice fabrication and testing.
Xidex Corporation was founded in 1997 as an Austin-
References based Texas Corporation by Vladimir Mancevski,
President and Chief Technology Officer and Dr. Paul F.
[1] Richard S. Gates, David Mendels and Daisuke McClure, CEO.
Fujita, “Mini Round Robin on AFM Cantilever
Spring Constant Calibration,” VAMAS Technical
Report No 49, March 2009 NanoBot Sales
(http://www.vamas.org/twa29/documents/2009_vam
as_twa29_report_49_mrr_afm_cantilever_calibratio
n.pdf) For product inquiries please contact:
[2] J. E. Sader, I. Larson, P. Mulvaney and L. R. Dr. Ray Eby
White, "Method for the calibration of atomic force Nanobiosystems, Inc.
microscope cantilevers,” Review of Scientific phone: 312-545-6527
Instruments, 66, 3789-3798 (1995) e-mail: nanoray@sbcglobal.net
[3] J. E. Sader "Calibration of atomic force microscope
cantilevers" (REVIEW) Encyclopedia of Surface
and Colloid Science, Ed: A. Hubbard, 846-856 For direct contact:
(2002)
Xidex Corporation
[4] Christopher T. Gibson, Daniel J. Johnson,
8906 Wall Street, Suite 703
Christopher Anderson, Chris Abell, and Trevor Ray,
Austin, Texas 78754
“Method to determine the spring constant of atomic
phone: 512-339-0608
force microscope cantilevers,” Rev. Sci. Instrum.
fax: 512-339-9497
75, 565 (2004).
e-mail: info@xidex.com
[5] Bo-Yi Chen, Meng-Kao Yeh, and Nyan-Hwa Tai, web: www.xidex.com
“Accuracy of the Spring Constant of Atomic Force
Microscopy Cantilevers by Finite Element Method,”
Anal. Chem., 2007, 79 (4), pp 1333–1338.
© 2011, Xidex Corporation. All right reserved. NanoBot, Xidex,
and the Xidex logo are trademarks of Xidex Corporation. Other
trademarks are property of their respective owners. Product
specifications and descriptions in this document are subject to
change without notice.
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