Tải bản đầy đủ - 0 (trang)
2 Atomic Force Microscopy (AFM)

2 Atomic Force Microscopy (AFM)

Tải bản đầy đủ - 0trang


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

spring constant.

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

conducting samples.

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

nanometer resolution.

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

two components:

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

Tài liệu bạn tìm kiếm đã sẵn sàng tải về

2 Atomic Force Microscopy (AFM)

Tải bản đầy đủ ngay(0 tr)