Material Property Modes
Any mutual force interaction between surface and AFM probe is subject to AFM measurement.
Properties to which the AFM has been applied include:
Many of these are simply special cases of small-amplitude field gradient sensing, as discussed in
§4.
Mechanical properties
When an AFM probe is scanned across a surface, in close proximity, either by closed loop tracking,
or by open loop placement, the interaction forces between probe and surface alter the parameters
of the mechanical resonance of the probe-cantilever system, as discussed in §2.9. Elasticity
alters the resonant frequency ω0, while losses affect primarily Q. Those changes can be detected
through either amplitude or phase modulation of the cantilever motion relative to its exciting
force.
In either case, the average probe Z-axis elevation is usually maintained at some preset value. That
elevation can be maintained in one of two ways:
Force–distance curves. A force/distance (F/D) curve is a measure of the forces on the probe as a
function of distance of the probe from a SUT. It can be measured directly or indirectly.
Direct force–distance curves. A direct force–distance curve is a record of cantilever deflection,
which is proportional to force, while controlling the distance between the probe and the SUT.
Typically a F/D measurement is initiated with the probe in free space, then lowering it until it
interacts with the hard force in the repulsive regime. The probe is then pulled away from the surface
until it is in free space again. This process is illustrated in Figure 3-1.
While the F/D relationship ideally should not depend on the direction of probe motion, in practice
it often does, due to small dissipative (i.e. viscous) forces.
As the probe begins to interact with the surface, it is pulled into the surface by capillary forces.
This process is called jump to contact ( JTC) and often this step breaks the tip off the probe. The
position of the jump to contact is dependent on the thickness of the contamination layer on the
surface. When retracting as the probe is pulled from the surface, the adhesion causes the probe to
“stick” to the surface, and then disengage from the surface.
Errors can occur in the F/D curve if a position sensor is not used to measure the motion in the Z
axis. The error occurs because the Z ceramic generating the motion is not linear and has hysteresis.
It is also necessary to correct the PZT position for the changes in probe position to determine
 the actual height of the probe above the surface. Failure to properly correct these errors leads to an
artifact displacement in the F/D curve when the probe is in the repulsive region.
Indirect force–distance curves. Indirect force–distance curves are generated not by measuring cantilever
displacement directly, but rather by measuring the Z-derivative of the force, as discussed in
§2.10. That measurement tends to be less noisy, and thus more accurate, than direct force measurements
because it is carried out in vibrating mode. Numeric integration of the measured dF/dZ can then produce the desired F(Z) curve. Some creativity, of course, is needed in determining the
constant of integration for that calculation (see, for example, Martin et al. (1987). The integration
constant is, in effect, the origin of coordinates – the location of the SUT’s “surface”.
Indirect F/D curves are subject to most of the same difficulties as the direct F/D curves, other
than the absolute calibration of the Z-axis motion. Its relative linearity is important, but the origin
is determined from the measurements, not the PZT control voltage. Also, if the force is not a
conservative one, that is, if it is not representable as the gradient of a potential energy, then it may
not be a single-valued function of distance.
 Pulsed force mode. Pulsed force mode (PFM)
is an “all in one” combination of topography,
adhesion, and stiffness measurements, carried
out simultaneously. PFM is implemented by
placing a sinusoidal voltage on the Z PZT
and recording the force profile. These properties
can be deduced from key inflection points
in the profile (Figure 3-2).
Surface loading (“nano-indenting”). The resistance
of a surface to normal force distortions
can be measured through the technique that
might be called “nano-indenting.” A nanoindent
is generated by forcing the probe into a
surface, causing surface material to be dislodged, creating a nano-crater. Surface distortion is measured
as a function of normal force. This relationship is called a “loading curve.”
 Nanoindenting is possible only if the cantilever is stiff enough and
the probe material hard enough. Figure 3-3 shows a nano-crater
created by a silicon probe in a surface of PMMA.
It is difficult to get quantitative data when nano-indenting with
an AFM because:
Lateral (friction) force mode – nanotribology. As shown in Figure 2-5. the cantilever in an AFM can
twist, or rotate as it is scanned across a surface. Use of the twisting response has opened a new
avenue for the study of friction at the nanoscopic level.
The study of interacting surfaces in relative motion from a macroscopic perspective is known as
tribology, and has been pursued for centuries; its pursuit at the nanoscopic scale has come to be
called nanotribology, and is only a few years old.
It was long thought that there were two fundamental laws of tribology:
While these laws of friction were well-established at the macroscopic level, they prove to be quite
subtle and complex at the small scale accessible to lateral force AFM. The friction force is found
to depend not only on the surface asperity (i.e. gross roughness, as a piece of sandpaper) but also
on intermolecular forces even when the asperity is absent or insignificant. Reitsma et al. explain it
well:
“The fundamental difference between the classical laws of friction and
the laws applying to nanometer scale friction is surface roughness. For
contact between two solid bodies, surface roughness at the interface
means that there are two ways to interpret contact. First is the type that
refers to regions of the interface that are in true (or ‘perfect’) contact,
often referred to as interfacial contact. The true contact area (At) of an
interface is the sum of all interfacial contacts. The other is the apparent
or gross contact area. This is the macroscopic surface area of the interface
(Ag). Nanotribology attempts to ‘scale out’ the multiple asperity
contact that describes tribology and the classical laws of friction.
“With reverence to the second classical law of friction (i.e. the proportionality
between friction and load recently both SFA and in particular,
AFM experiments, measuring interfacial friction have demonstrated a
clear non-linear relation between friction and load ….”
The frictional coefficient of a probe moving over a surface is defined as the loading force divided
by the horizontal force:
 With both vertical and lateral deflections (and thus estimates of the forces) available (see §2.5), it
is possible to determine a friction coefficient. Recalling that the sense of the lateral force is always
in opposition to the scan direction, measurements usually record a curve with hysteresis, as shown
in Figure 3-4. With modest simplifying assumptions, and some dimensional information about
the probe, an effective coefficient of friction may be calculated. Accuracy of the result is often
questionable due to uncertainties in those assumptions.
Figure 3-5 shows lateral force images from a very flat gold test sample. The topography image is
featureless, but the LFM image shows the drawn pattern. It is noteworthy that the appearance of
the pattern is different, depending upon the scan direction.
Thermal modes
Special thermal sensing probes incorporating thermocouples or resistors (Figure 3-6) permit
nano-scale measurement of:
Electrical Modes
Electrical modes involve measurements of localized surface responses to various electric or magnetic
stimuli. Some require direct probe-surface metallic contact and others only near proximity.
Parametric (contact) measurements. By “contact measurements” we mean those that treat the
probe-plus-surface as a two-terminal circuit device. Some sort of V-I characteristic is measured
point-by-point as the probe scans the surface.
 Although direct contact is simple in principle, it is difficult
in practice. The interface between probe and surface is
complicated by:
A conductive diamond coat can mitigate issues (b) and (c),
though it increases the diameter of the probe significantly.
The contamination problem is largely independent of
probe material. Scanning versus static measurements. Although direct contact seems suitable for measuring electrical
properties of nanostructures such as nanotubes or quantum dots, it proves problematic. Positioning
error is a problem. Such structures as nanotubes and quantum dots are extremely small
and difficult to locate. Although smooth scanning at the nanometer scale is easily achievable, it
requires only relative positioning. Absolute, repeatable positioning at that scale, however, is very
difficult.
Ohmic conductivity. Local conductivity of a surface or structures located thereon can be measured
by an AFM. The probe should have high conductivity compared to the SUT, through either its
bulk or through a suitable coating.
Dielectric constant. A conductive probe above a surface, with a constant voltage applied between
them can be considered a simple capacitor. Any capacitor having an adjustable mechanical coordinate, say Z, held at constant voltage, can be shown from energy principles, to exert a force against
that coordinate
 where the negative sign signifies the direction that will reduce the capacitance. Our prior analysis
of force gradient sensing (§2.10) remains valid, and equation (2-15) is once again applicable, so
that
 SHARK (simultaneous conductivity-topography). In the animal world, the elasmobranchs (the subclass
of cartilaginous fishes that includes skates, rays and sharks), have a unique ability to sense
electric fields (see, for example, Adair et al (1998)). That sense is thought to have played an
important role in their evolution. They use it both for locating prey and for orientation, via
motion-induced sensitivity to the earth's magnetic field. Threshold sensitivity is said to be of the
order of microvolts per meter or less.
SHARK technology®, whimsically named for these remarkable animals, brings similar electric
field sensing to atomic force microscopy. As an acronym it is said to stand for “surface height and
resistivity camera” (if one accepts the German spelling “kamera” …). It is an AFM imaging technique
that produces simultaneous topographic and conductivity maps.
The spatial map of electrical conductivity, as measured with SHARK, once again uses the stimulus–
response apparatus shown in Figure 3-7. The stimulus in this case is constant voltage applied
between the sample and the probe, while the response is current. Measurement of current yields a
conductivity map, while topography is sensed in the conventional contact fashion. The advantage
of SHARK is that the topogram and conductivity map are captured simultaneously during one
scan, reducing test time. Figure 3-9 is a SHARK image of a carbon nanotube held perpendicular
to a conductive substrate.
Contact potential difference (Kelvin probe). Contact potential difference (CPD) is unfortunately
named, as it is something that is invariably measured without contact. It is defined as the potential
difference between dissimilar conductive materials whose mobile electrons are in thermal equilibrium.
It is the difference in work functions of the two materials. That equilibrium leads to small
charge imbalance, and thus a potential difference between the surfaces if they are electrically connected.
Two surfaces, considered as a capacitor, behave as though there were an internal potential
source polarizing the capacitor. That internal potential is equal to the tiny charge difference
divided by the capacitance.
The so-called Kelvin probe method is an age-old technique for measuring CPD. If the two electrically
connected conductors are brought into near proximity, there is a small electric field
between them due to the tiny charge imbalance.
  Conventional Kelvin probe measurement places a
fixed voltage across a capacitance formed of the materials to be tested (right). One of the surfaces is
then mechanically vibrated. From elementary circuit
theory one has
The external applied voltage is adjusted until the AC current induced by the vibration is reduced
to zero. The applied is then known to be equal and opposite to the CPD. Readout of that value of
V0 thus provides the desired measurement, after a sign change.
 A slight variation on this technique is
eminently well-suited for the AFM,
which adds imaging capability. This
technique is best called Kelvin probe
microscopy (KPM), avoiding the oxymoronic-
seeming “contact potential
difference” that involves no contact.
The AFM version (Figure 3-11)
turns the macroscopic Kelvin probe
method on its head: It applies an AC
voltage to the capacitance formed of
the materials under test, and detects
the resultant vibration. It is easily shown from elementary principles that, for a capacitor whose
capacitance depends on a mechanical coordinate, say, in this case, Z, then there is a force exerted
by the capacitor on its supports: 
Using for V the sum of a DC nulling voltage and an AC sense voltage 
leads to a component of force at frequency ω that is proportional to V 0, viz: 
A major advantage of this technique is that there is no need to calibrate the capacitance or its Z
derivative. It is a nulling method. All that is necessary is to adjust V 0 until the force component at
frequency ω goes to zero. As in a macroscopic Kelvin probe measurement, it is then known that V0 at null is thus equal to the negative of the CPD. If the nulling process can be carried out sufficiently
rapidly, then recording V0 while raster scanning provides a desired two-dimensional KPM
image.
Several instrumental configurations for KPM are possible. There are two applied stimuli involved:
the cantilever Z-axis mechanical driving force, and the applied voltage. They may be distinguished
by frequency. This permits two-loop configurations in which topography is measured in
conventional fashion, simultaneously with the contact potential map. One such apparatus is
shown in Figure 3-12.
 Unlike other imaging methods, scanning
Kelvin probe microscopy is a
quantitative. It measures absolute
potential difference (cf EFM, §3.4,
which measures electric field
strength). Because KPM uses noncontact
VCM to track topography,
there is less tendency to damage the
probe. KPM, however, is more costly
to implement because it requires a
lock-in amplifier and PID controller. Electric force microscopyElectric force microscopy (EFM) is the examination of surfaces via non-contact electric field
interactions. Primarily this pertains to ferroelectric and piezoelectric materials. Ferroelectric
(“electret”) materials have a permanent electric polarization. Piezoelectric materials have a dimensional
change in response to applied electric fields, and vice versa. The two properties are often
both present, as the crystal symmetry group requirements are identical. An electret, in effect, is a
piezoelectric material with memory.
The advantage of the AFM probe for ferroelectric measurements is that the probe has high spatial
resolution and localized measurements are possible. There are two primary types of measurements
made on ferro/piezo films: purely electrical properties, and electro-spatial properties.
Electrical responses to electrical stimuli are measured with an apparatus similar to that described
§3.3. The probe is placed in contact with the ferro/piezo film and the electrical measurement is
made.
Dimensional responses to electrical stimuli are measured through cantilever deflection in response
to an applied voltage.
In both cases the response has memory (a.k.a. hysteresis), that is, the result depends on whether
the applied stimulus is increasing or decreasing. Stimulus-response curves have a “butterfly” character,
as illustrated in Figure 3-14, if they are recorded through a full cycle of the stimulus.
 The spatial resolution of either type
of measurement is governed primarily
by the probe diameter,though
grain size of Polycrystalline materials
also plays a role.
Magnetic field microscopy
Magnet field microscopy (MFM) is
the examination of surfaces via noncontact
magnetic field interactions.
A probe coated with a ferromagnetic
film is vibrated slightly above a
surface while scanning. Modelling
the magnetization as sparsely distributed
surface dipoles, it can be
shown that the force gradient is
where
s = tip-surface distance
δ= nonmagnetic thickness
R = tip radius
mp = magnetic moment of surface dipole
mt = magnetic moment of probe tip
dm = mean magnetic diameter
and
Though the detailed relationship, derived from (3-11) and (4-5), is somewhat complex, the general
conclusion is that the frequency change is roughly proportional to a moderately high (third to
fifth) power of the separation. It is thus very sensitive to the three-dimensional structure of the
magnetic domains.
 AFM in magnetostatic mode is especially useful for examination
of the nanoscale structure of magnetic recording media.
See, for example, Figure 3-15.
As with EFM, the resolution achievable with MFM depends on
the thickness and quality of the probe coating. This is difficult
to control, so that the results from MFM are often inconsistent.
Also, when trying to measure the magnetic domains on a soft
magnetic material, magnetic domains on the probe can alter the
magnetization of the SUT, masking or obliterating the original
properties that were to be measured.
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