Tải bản đầy đủ - 0trang
2 Atomic Force Microscopy (AFM)
Atomic Force Microscopy (AFM)
Fig. 2.8 Schematic set-up of an atomic force microscope (AFM) with a four-segment photodiode
for detection of the laser beam deflection due to bending and twisting of the cantilever. (Reprinted
with permission from [2.34]. © 1999 Karlsruher Institut für Technologie)
Mainly optical techniques (see Fig. 2.8) are employed in order to detect the
cantilever deflection. In this set-up a laser beam is reflected from the cantilever
and the cantilever displacement is measured by the detection of the reflected
laser beam using a position-sensitive detector consisting of, e.g., four photoactive segments with eventually sub-Ångström sensitivity. By the four photoactive
cells, vertical and lateral deflections (for, e.g., friction measurements) can be
2.2.1 Topographic Imaging by AFM in Contact Mode
In this mode, where the tip and the sample are in contact, the interaction force causes
the cantilever to deflect. In the constant force imaging (CFI) mode of AFM which
is analogous to the constant current mode in STM, the cantilever deflection is kept
constant by means of a feedback circuit. The output signal of the feedback loop
Uz is recorded as a function of the (x, y) coordinates and can be translated into
the “topography” z (x, y). As equiforce surfaces are measured by AFM we have to
consider the tip-surface interaction forces in the contact regime.
The invention of the AFM has considerably contributed to an increased interest
in the force picture of quantum mechanical systems. The fundamental relationship
Microscopy – Nanoscopy
between energy and force pictures in quantum theory is expressed by the Hellmann–
Feynman theorem [2.35–2.37] which states that if ψ is an exact eigenfunction of a
Hamiltonian H with the eigenvalue E, then
ψ |ψ = ψ
for any parameter λ occurring in the Hamiltonian H. This means that for a normalized wave function, the derivative of the energy with respect to a parameter λ is
equal to the expectation value of the corresponding derivative of the Hamiltonian.
If λ is taken as a coordinate of a nucleus, then one can derive the electrostatic
Hellmann–Feynman theorem [2.37] resulting in the statement that the force acting
on a nucleus in a system of nuclei and electrons can exclusively be interpreted in
terms of classical electrostatics, once the electronic charge density has been obtained
by an accurate self-consistent quantum-mechanical electronic structure calculation.
The theorem is of central importance for the interpretation of AFM data similar to
Bardeen’s transfer Hamiltonian formalism for STM.
From these considerations one can deduce that in the contact regime, AFM
measurements are expected to probe primarily the ion–ion repulsion forces which
decrease rapidly with increasing tip-surface separation. This is in contrast to STM
where the observation is dominated by the local surface electronic structure near the
Fermi level which can substantially differ from the location of the ion cores. The
strong distance dependence of the ion repulsion forces provides the key for the high
spatial resolution achieved by contact force microscopy.
The atomic forces in real space can be derived by differentiating those terms in
the Hamiltonian which explicitly depend on the positions of the ions [2.38].
The expression obtained exhibits two components. The first – denoted as Fion –
originates from the Coulomb repulsion between the ion cores, and the second, which
is denoted by Fel , is due to the interaction of the valence electrons with the ion cores.
From this it is expected that in an AFM operated in the repulsive contact mode,
|Fion | > |Fel | varies more rapidly with the position of the outermost tip atom than
does Fel .
As the tip surface separation is increased, |Fel | decays more slowly than |Fion |
and Ftotal = Fion + Fel changes sign yielding a net attractive force. Yet, many AFM
studies are performed in the strongly repulsive regime. With the high AFM spatial resolution, atomic-scale periodicities can be resolved by AFM in the case of,
e.g., graphite, BN, Na, Cl, Au etc. Under the assumption of a monatomic tip it
has been shown theoretically that repulsive forces of around 10−8 N can lead to a
large elastic compression of, e.g., a graphite surface (see [2.20]). For a conclusive
demonstration of the AFM atomic resolution capability of contact force microscopy,
the observation of surface defects has particularly been important (see [2.20]). This
means that the force interaction must, indeed, be highly spatially localized offering the possibility of probing single atomic sites with AFM, similar to the STM
Atomic Force Microscopy (AFM)
2.2.2 Frictional Force Microscopy
In friction of two contacting bodies the frictional force
Ff = μ × F1
is proportional to the loading force F1 and independent of the apparent area of
contact. The AFM geometry is well suited for nanoscale friction studies [2.39]. In
addition to the cantilever bending normal to the surface, torsion mode deflections of
the cantilever while scanning may occur in lateral motion with friction (see Fig. 2.9).
The tip sliding process was found to be non-uniform with a stick-slip behavior. The
slips actually exhibit the same spatial periodicity as, e.g., the graphite surface leading to the conclusion that the atomic surface structure determines the tip-surface
interface (see Fig. 2.9).
Fig. 2.9 (a) Comparison of the measured lateral forces F1 on a graphite surface and (b) the correspondingly simulated forces. The image dimensions are 2 nm × 2 nm. (Reprinted with permission
from [2.40]. © 1998 Wiley-VCH)
2.2.3 Non-contact Force Microscopy
The short-range interatomic forces are probed by measuring the quasistatic deflections of a cantilever beam with a well-known effective spring constant when the
sample is scanned against the cantilever tip.
By increasing the tip-surface separation to 10–100 nm, only the long-range interaction forces as, e.g., van der Waals, electrostatic, or magnetic dipole forces remain.
These forces can be probed by non-contact force microscopy. Instead of measuring quasistatic cantilever deflections, the cantilever is driven to vibrate near its
resonance frequency by means of a piezoelectric element [2.33]. Changes in the
resonance frequency as a result of tip-surface interaction are measured. This a. c.
Microscopy – Nanoscopy
technique is sensitive to force gradients rather than to the interaction forces themselves. The presence of the force gradient results in a modification of the effective
If tip and sample are clean, electrically neutral and non-magnetic van der Waals
forces are the sole sources of tip-sample interactions in the non-contact regime. In
this case the spatial resolution achievable depends critically on the tip geometry and
the tip-surface separation. For a good lateral resolution a, both the tip radius R and
the tip surface separation s have to be small.
Van der Waals forces measured in vacuum are always attractive. An important
field of electrostatic force microscopy (EFM) is direct imaging of domains and
domain walls in ferroelectrics [2.41]. The charge signal changes its sign as the tip
passes over the ferroelectric domain wall.
2.2.4 Chemical Identification of Individual Surface Atoms by AFM
By the force patterns emerging in AFM, the chemical nature of individual atoms on
a surface that contains a mixture of elements can be identified [2.5, 2.42]. This is of
interest because – in contrast to STM – AFM can be used for both insulating and
In the non-contact mode of the AFM, the resonance frequency of the AFM
changes according to the specific interaction of the tip with the surface of the sample. By this the characteristic dependence of the force on the distance between the
AFM tip and an individual atom can be measured [2.5]. The interaction between
the tip and Si atoms in a Si–Sn–Pb surface alloy (see Fig. 2.10a, b) is strongest.
The interaction forces observed between the tip and Si, Sn, or Pb atoms well match
Fig. 2.10 (Fig. 698 P.C.): Single atom chemical identification of a Si–Sn–Pb surface alloy by
AFM. (a) Local chemical composition of the surface. Blue, green, and red atoms correspond to
Sn, Pb, and Si atoms, respectively. (b) Distribution of maximum attractive total forces measured
over the atoms in (a). By using the relative interaction ratio determined for Sn/Si and Pb/Si, each
of the three groups of forces can be attributed to interactions measured over Sn, Pb, and Si atoms.
(Reprinted with permission from [2.5]. © 2007 Nature Publishing Group)
Scanning Near-Field Optical Microscopy (SNOM)
with atomistic modeling [2.5]. This technique provides the local composition and
structure of a semiconductor surface on the atomic level.
By AFM techniques also the charge state of individual Au and Ag atoms on a
NaCl film can be determined by quantifying the force response of a few piconewtons
caused by a surplus charge [2.43].
2.2.5 AFM in Bionanotechnology
Atomic force microscopy is the only technique that provides sub-nanometer resolution under physiological conditions, needed for imaging biological species like
proteins and living cells. Measurements of molecular recognition forces provide
insight into the function and structure of biomolecular assemblies [2.44]. AFM is
a companion technique to x-ray crystallography and electron microscopy (EM) for
the determination of protein structures (see [2.44]).
For the investigation of soft biological membranes and supramolecular complexes, unfavorable probe-surface interactions in contact mode AFM, especially
lateral forces, have been largely overcome by the development of dynamic force
microscopy (DFM). The cantilever is oscillated close to its resonance frequency at
an amplitude of a few nanometers as it scans the surface and touches the sample
only at the end of its downward movement.
AFM images of plasmid DNA (pDNA) immobilized on mica (Fig. 2.11a)
show the DNA molecules in a supercoiled state with two or more chains tightly
overwound. DFM has been also used for studying the human rhinovirus (HRV),
which causes the common cold, under physiological conditions (Fig. 2.11b).
Topographical imaging of the virus capsid reveals a regular arrangement of 3 nm
sized protrusions similar to that seen in cryoelectron microscopy studies (see
[2.44]). Moreover, the binding of an antibody to surface antigens embedded in
cell membranes has been studied by DFM. This is the primary event in the specific immune defense of vertebrates. Figure 2.11c, d shows a high-resolution image
of a single antibody bound to its antigenic recognition sites (epitopes) on the
2D crystalline arrangement of bacteriorhodopsin (BR) molecules of mutant purple membranes from Halobacterium salinarum. Fab fragments, i.e., the fragment
antigen binding regions (∼50 kDa) on membrane-bound antibodies, are allocated
to antigenic sites at 1.5 nm lateral resolution on the purple membrane, allowing the
identification and localization of individual epitopes [2.44].
2.3 Scanning Near-Field Optical Microscopy (SNOM)
By making use of scanning near-field optical microscopy, the spatial resolution can
be substantially enhanced compared to classical optical microscopy and can reach
In classical optical microscopy the spatial resolution is limited by diffraction to
about half the wavelength λ/2 (Abbé limit [2.48]). This limit originates from the
Microscopy – Nanoscopy
Fig. 2.11 High-resolution topographical imaging of biomolecular assemblies by atomic force
microscopy (AFM). (a) 3 kbp (base pairs) plasmid DNA (pDNA) on mica; scale bar 150 nm
[2.45]. (b) Dense packing of human rhinovirus (HRV) particles with regular patterns of small
protrusions ∼ 0.5 nm high and ∼ 3 nm in diameter; width of the figure, ca. 70 nm [2.46]. (c)
Topographical image of the purple membrane to which a single antibody is bound and (d) a 3D
representation of two Fabs (fragment antigen binding regions of an antibody) bound to the bacteriorhodopsin (BR) molecules of mutant purple membranes from Halobacterium salinarum [2.44,
2.47]. (Reprinted with permission from [2.45] (a), [2.46] (b) and [2.47] (c) (d). © 2007 Elsevier
(a), © 2005 Elsevier (b), © 2004 Nature Publishing Group (c) (d))
fact that electromagnetic waves interacting with an object are always diffracted into
1. Propagating waves with low spatial frequencies (< s/λ), and
2. evanescent waves with high spatial frequencies (> s/λ)
where s is the tip-to-specimen spacing in near-field microscopy.
Whereas classical optics are concerned with the far-field regime where only the
propagating fields survive, the evanescent waves are confined to sub-wavelength
distances from the object corresponding to the near-field regime. Information about
the high spatial frequency components of the diffracted waves is lost in the far-field