Force Spectroscopy with AFM
The distance is changed between the AFM probe and the sample,
while the cantilever’s position (deflection in z) is detected andrecorded. The deflection is a measure of the force between thesample surface and the probe’s sharp tip. From the deflection data,
we can extract the force data. This force may be a result of directcontact between sample surface and tip, or it may be mediatedthrough mechanical contact of a molecule or other object that isattached at one end to the sample surface and at the other end
to the probe tip. It may also be mediated through a force field,e.g., electric, magnetic. The operational details of the AFM force
measurement are largely the same across these applications, andthis is one reason that makes the AFM a uniquely useful tool forforce measurements. The force data provides information about thesample, and sometimes about the probe itself.

Figure 2. AFM force spectroscopy on amacromolecule. Pico-Newton range
measurements are relevant to intermolecular andintra-molecular forces. These measurements aremade more accurate with a better estimate of
the value of cantilever spring constant.

With advances in nanofabrication, it is
now possible to make AFM cantilevers
with extremely small spring constants.
Cantilevers with spring constants
smaller than 10 -4 N/m have been
made and used for AFM-based force
measurements in the attonewton regime(10 -18 N) in research laboratories.1,2Cantilevers with spring constants
as low as 10 -2 N/m are readily
available from numerous commercial
manufacturers. This, together with theAFM’s capability to measure subnanometer cantilever deflection,
enables force sensitivities on the orderof 100pN (10 -10 N) routine on many
commercially available AFMs.
Piconewton sensitivity (10 -12 N) is
available on more advanced AFMs
such as the MultiMode PicoForceand the NanoMan II system from
Veeco Instruments.

(Right) The AFM changes the separation
between the probe and sample surface,either by “Extending” the sample towards
the probe, or by “Extending” the probe
towards the samples at the position of thebase of the cantilever. At the same time,
the AFM detects and plots the motion(usually at or near the free end) of thecantilever. In the graph shown here(below), the cantilever’s vertical (or updown) deflection is plotted (“Deflection”).
As the tip nears the sample surface but is
too far to sense any force from the sample
surface, the cantilever remains undeflectedfrom its equilibrium position. This
corresponds to “A” in the plot and thedrawings. The tip jumps into contact withthe sample surface when it is near enoughto feel attractive forces, bending thecantilever slightly down in the process (B).
The cantilever bends up as the AFM
continues to move the sample (or thecantilever) and pushes the tip further
against the sample surface (C), and bends
down again as the AFM pulls the cantilever
and the sample apart (“Retracting”) but thetip is adhering to the sample (D). Finallythe tip snaps free of the surface (E) andthe cantilever returns to its equilibrium
position (A). The cycle may repeat.

The Force Measurement
Accuracy Problem
The accuracy of force measurements
depends in part on the sensitivity of theAFM, but also in part on the accuracyof the knowledge we have of thespring constant. The value of thespring constant is most sensitive to thevariation of the cantilever thickness,
which is also the most difficult tocontrol in fabrication. The spring
constant of an AFM cantilever is usuallyestimated by the manufacturer, andnoted on the documentation that
accompanies the probe. This estimate
is usually quite gross (though goodenough for many applications).
Increasingly, however, the AFM isbeing used in force spectroscopy
applications that demand moreaccurate measurements. These aremeasurements of the strength andpolarity (attractive or repulsive) ofthe force that the cantilever bears
interacting with the sample surface, ina gas, or in a liquid. The force may berelated, for example, to the binding
strength between different parts of amacromolecule on the sample surface(Figure 2), or between a moleculeand the sample surface, or between
a cell receptor molecule and a target
molecule. The force may also berelated to the mechanical properties(e.g., compliance) of a hard or soft
sample, or of a thin film deposited
on a substrate (for example in nanoindentation experiments). Moreaccurate force spectroscopy requires
better estimates of the spring constant.

The Thermal Tune Solution
One method to arrive at a moreaccurate estimate of the spring constantinvolves measuring the cantilever’s
mechanical response to thermal noise.
This is the cantilever’s motion inresponse to thermal agitations,
including from the Brownian motion of
the molecules of the encompassing
fluid. That fluid is usually ambient airor water. This method offers a
combination of speed and ease-of-use,
and is now widely accepted andadopted by AFM users worldwide.

Figure 3. Thermal tune data (power spectral density) extracted from time-series measurements andplotted (blue) for an AFM cantilever in air, and a Lorentzian line shape fit (red). Veeco’s
NanoScope software includes numerous options and user-adjustable parameters, for example fortemperature, for model-based corrections (e.g., deflection sensitivity correction), and for excluding
spurious data from the fit.

In the thermal tune method, as it iscommonly called, the AFM hardware
measures the cantilever’s fluctuations as
a function of time, and from the timedomain measurement, it extracts thefrequency spectrum of the cantilever’s
mechanical response (proportional tothe power spectral density, PSD). By
fitting the frequency spectrum to a
Lorentzian line shape (Figure 3), theAFM software arrives at an estimateof the cantilever’s spring constant.
The method assumes the cantilever
has a single degree of freedom, andmakes use of the energy equipartition
theorem. This theorem relates thetemperature to the cantilever’s average
fluctuation energy, which is foundthrough integrating the Lorentzian fit.3,4With the cantilever’s spring constantestimated more accurately using thethermal tune method, plots of cantileverdeflection (see sidebar page 2) areconverted to equally more accurate
force spectroscopy plots, which in turnimprove the reliability of the force
estimates. Not only that, but thisconversion is done in real-time; that is,the data is now displayed, and fromthe outset recorded, as a plot offorce-versus-distance (as opposed tocantilever deflection-versus-distance.)
The thermal tune solution is available
to work with several Veeco Instruments
NanoScope controllers, including
NanoScope IIIa, IV, and IVa, andseveral SPMs, including the MultiMode
PicoForce, the NanoMan II nanomanipulation and nanolithographysystem, and the BioScope II. The
thermal tune package includes
numerous software options, including
provisions for distinguishing between
air and liquid, for changing thetemperature value used in thecomputations, and for improving theaccuracy of the computations evenfurther by accounting for correction
factors related to assumptions that go