Easy and direct method for calibrating atomic force microscopy lateral
force measurements
Wenhua Liu, Keith Bonin, and Martin Guthold
a͒
Department of Physics, Wake Forest University, Winston-Salem, North Carolina 27109
͑Received 24 February 2007; accepted 7 May 2007; published online 15 June 2007͒
We have designed and tested a new, inexpensive, easy-to-make and easy-to-use calibration standard
for atomic force microscopy ͑AFM͒ lateral force measurements. This new standard simply consists
of a small glass fiber of known dimensions and Young’s modulus, which is fixed at one end to a
substrate and which can be bent laterally with the AFM tip at the other end. This standard has equal
or less error than the commonly used method of using beam mechanics to determine a cantilever’s
lateral force constant. It is transferable, thus providing a universal tool for comparing the
calibrations of different instruments. It does not require knowledge of the cantilever dimensions and
composition or its tip height. This standard also allows direct conversion of the photodiode signal
to force and, thus, circumvents the requirement for a sensor response ͑sensitivity͒ measurement.
© 2007 American Institute of Physics. ͓DOI: 10.1063/1.2745733͔
INTRODUCTION
The atomic force microscope ͑AFM͒ is not only a good
tool in imaging sample topography at high resolution, but it
is also frequently used in probing the mechanical properties
of materials on the nanometer scale. For example, AFMs
have been used to study the compliance, stiffness, adhesion,
and frictional properties of biological and nonbiological
samples.
1–3
AFM force measurements may be divided into
normal force and lateral force measurements. In normal force
measurements, the cantilever is moved normally to the sur-
face. This method has been used in compliance measure-
ments of cells,
4
in single-protein unfolding,
3
and single-
molecule stretching experiments.
5
In lateral force
measurements, the cantilever is moved parallel to the sur-
face. This method has been used in friction measurements or
to stretch fibers. For example, the nanoscopic, frictional
forces between functionalized tips and surfaces have been
determined
2,6
and the mechanical properties of viruses,
DNA, carbon nanotubes, and fibrin fibers have been
measured.
7–9
In all AFM force measurements, the AFM cantilever is
used to apply forces to the sample under investigation. To
extract reliable, quantitative values for material properties
from these measurements, the applied forces need to be ac-
curately known, which, in turn, critically depends on reliable
and universally applicable force calibration methods for
AFM instruments. As outlined below, several calibration
methods, each with its own advantages and disadvantages,
have been described to date. To better understand some lat-
eral force calibration methods, normal force calibration
methods will also need to be discussed peripherally.
Typically, in an AFM, a laser beam is focused on the
back of the cantilever, which has a mirrored surface that
reflects the beam into a four-quadrant photodiode ͑Fig. 1͒.
An up-down deflection of the cantilever x
n
caused by a nor-
mal force F
n
results in a change in the top −bottom photo-
current I
n
. A lateral ͑torsional͒ deflection of the cantilever x
l
,
caused by a lateral force F
l
, results in a change in the
left−right photocurrent I
l
. The challenge in all AFM force
measurements is to convert the measured signal, photocur-
rent, to the desired quantity: force.
The lateral force calibration methods that are used for
this conversion may generally be divided into the following
categories:
• Theoretical methods, in which the cantilever force con-
stant is calculated from beam mechanics using elasticity
theory. It requires accurate knowledge of the dimen-
sions and moduli of the cantilever.
• Dynamic methods, in which the cantilever force con-
stant is obtained by analyzing the resonance frequency
of cantilevers. These methods may be combined with
the theoretical method to yield better results.
10
• The wedge method, in which both normal and lateral
force responses of the cantilever are examined during
friction measurements on sloped surfaces.
• Methods in which a known force is applied to the can-
tilever via artifacts or external means. Our method is of
this type.
Theoretical and dynamic methods. Perhaps the quickest
and most commonly used calibration method is using beam
mechanics ͑elasticity theory͒ to calculate the normal and lat-
eral force constants of a cantilever.
10–12
When performing
normal force measurements, the tip is deflected by an
amount x
n
normal to the surface, either by pushing down on
the surface or by pulling on a molecule that is anchored
between the tip and the surface. The applied force may be
a͒
Author to whom correspondence should be addressed; Tel.: 336-758-4977;
Fax: 336-758-6142; electronic mail: gutholdm@wfu.edu
REVIEW OF SCIENTIFIC INSTRUMENTS 78, 063707 ͑2007͒
0034-6748/2007/78͑6͒/063707/7/$23.00 © 2007 American Institute of Physics78, 063707-1