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\begin{document}
\title{ATOMIC FORCE MICROSCOPY}
\author{ Tak Gurung\\
     \\
         Department of Physics\\
         University of Cincinnati \\
         Cincinnati, Ohio 45221\\[1em]}

\date{}
\maketitle
\begin{abstract}
In this paper some of experimental techniques of Atomic Force
Microscope are studied. Some of techniques for the use of AFM in
the manipulation of nanoparticles and nanotubes are also discussed
in this paper.
\end{abstract}

\pagebreak

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\bf INTRODUCTION:\rm

\vspace{0.1in}

Atomic Force Microscope(AFM) is a kind of scanning probe
microscopes, which scans the surface of sample with a sharp tip
much the same way as a monograph needle scans a record. AFM
provides pictures of atoms on or in the surface of the sample. In
general, AFM enables one to detect surface morphology, nanoscale
structures and molecular and atomic-scale lattices. In addition it
is employed  to probe the mechanical properties of surfaces such
as indentation, adhesion and friction. Now a days it has been used
as a tool for the nanomanipulation, lithography, etching etc. AFM
can be used to study insulators and semiconductors as well as
electrical conductors. It can also be used to study biological
materials.

\vspace{0.1in}

\bf GENERAL PRINCIPLE:\rm

\vspace{0.1in}

Basically, AFM works in the principle of deflection of  a
cantilever due to the interatomic forces. This deflection of the
cantilever generates the map of  surface topography of the sample.
The schematic figure of the optical block of AFM is given below.

\vspace{0.1in}
\begin{figure}[htb]
\centerline{\psfig{figure=force1.eps,height=2.5in}}

\caption{\em{Schematic diagram of the optical block incorporating
the optical deflection system \cite{ref1}.}}
\end{figure}
\vspace{0.1in}

The sharp tip, which probes the surface of  a sample, is attached
to the cantilever of spring constant typically 0.001-100 N/m. The
tip is made of Si or $Si_{3}N_{4}$\cite{ref2}. When the tip scans
the surface, it deflects because of the different forces between
atoms of tip and the sample surface.  The most commonly associated
interatomic force with AFM is van der Waals (VDW) force. The
dependence of the interatomic force upon the distance between the
tip and the sample is shown in Fig.1.

Three distance regimes are labeled on this figure:

1)Contact regime

2)Non-contact regime

3)Intermittent-contact regime.

In the contact regime, the cantilever is held less than a few
angstroms from the sample surface, and the interatomic force
between the cantilever and the sample is repulsive. In the
non-contact regime, the cantilever is held on the order of tens to
hundreds of angstroms from the sample surface, and the interatomic
force between the cantilever and the sample surface is attractive
(largely a result of the long-range van der Waals interactions).



\vspace{0.1in}
\begin{figure}[htb]
\centerline{\psfig{figure=force2.eps,height=3.5in}}

\caption{\em{Interatomic force vs. distance curve \cite{ref2}.}}
\end{figure}
\vspace{0.1in}

The sample to be scanned is mounted on to  the piezoscanner, which
provides the driving motion for the sample. Piezoscanner  is made
up of piezoceramic, which changes its dimensions under applied
voltage. The most frequently used piezodrive is a hollow-tube
scanner, which can move the tip or sample in all three mutually
perpendicular directions. For the detection of the atomic-scale
images the scanner tube with a piezomechanical coefficient in the
range of $15-20\AA/V$ is used, which allows the movement of the
tip with $0.01\AA$ accuracy. A feedback mechanism is used to
protect from the crash of scanning tip into the sample surface
because of surface roughness and imperfect tip-sample alignment.
In order to record the deflection of the cantilever, optical
signal is sent to the cantilever from the laser source and the
reflected signal from the cantilever, which is the strength of the
probing interaction as a function of the tip position, is detected
by the position-sensitive photodectector. The electronic unit in
turn converts the collected information into the image on the
screen.

 \vspace{0.1in}

\bf CONTACT AFM MODE:\rm

\vspace{0.1in}

In contact-AFM mode, also known as repulsive mode, an AFM tip
makes soft physical contact with the sample.  The tip is attached
to the end of a cantilever with a low spring constant, lower than
the effective spring constant holding the atoms of the sample
together. As the scanner gently traces the sample under the tip (
or the tip across the sample), the contact force causes the
cantilever to bend to accommodate changes in topography. This mode
has been shown in the Fig. 2. Clearly, as the atoms are gradually
brought together, they first weakly attract each other. This
attraction increase until the atoms are so close together that
their electron clouds begin to repel each other electrostatically.
This electrostatic repulsion progressively weakens the attractive
force as the interatomic separation continues to decrease. The
force goes to zero when the distance between the atoms reaches a
couple of angstroms, about the length of a chemical bond. When the
total van der Waals force becomes positive ( repulsive), the atoms
are in contact. Thus, this mode is also known as the repulsive
mode. In addition to the repulsive VWF, two other forces are
generally present during contact-AFM operation: a capillary force
exerted by the thin water layer often present in an ambient
environment, and the force exerted by the cantilever itself. The
capillary force arises when water wicks its way around the tip,
applying a strong attractive force that holds the tip in contact
with the surface. The magnitude of the capillary force depends
upon the tip-sample separation. The force exerted by the
cantilever is like the force of a compressed spring. The magnitude
and the sign of the cantilever force depends upon the deflection
of the cantilever and upon its spring constant. The
position-sensitive photodetector detects the position of the
cantilever with optical techniques. This microscope can be
operated in two different modes:

a) constant-height and

b) constant force mode.

In the constant-height mode, the spatial variation of the
cantilever deflection can be used directly to generate the
topographic data set because the height of the scanner is fixed as
it scans. This mode is often used for taking atomic-scale images
of atomically flat surfaces, where the cantilever deflection and
thus variation in applied force are small. This mode is also
essential for recording real-time images of changing surfaces,
where high scan speed is essential.

In constant-force mode, the deflection of the cantilever can be
used as input to a feedback circuit that moves the scanner up and
down in Z-direction, responding to the topography by keeping the
cantilever deflection constant. In this case, the images is
generated from the scanner's motion. With the cantilever
deflection held constant, the total force applied to the sample is
constant. In this mode, the speed of scanning is limited by the
response time of the feedback circuit, but the total force exerted
on the sample by the tip is well controlled. This is mode is
generally preferred for the most applications.

\vspace{0.1in}

\bf NON-CONTACT AFM MODE:\rm

\vspace{0.1in}

 Non-contact AFM (NC-AFM) mode is one in which the
cantilever is vibrated near the surface of a sample. The spacing
between the tip and the sample for this mode is on the order of
tens to hundreds of angstroms. This spacing is indicated on the
van der Waals curve in Fig.2 as the non-contact regime.Like
contact AFM, non-contact AFM can be used to measure the topography
of insulator and semiconductors as well as electrical conductors.
The total force between the tip and the sample in the non-contact
regime is very low, generally about $10^{-12}N$. This force is
advantageous for studying soft or elastic samples.It is more
difficult to measure than the force in the contact regime because
of the small force between the tip and the sample. In addition,
cantilevers used for this mode must be stiffer than those used for
contact mode because the soft cantilevers can be pulled into
contact with the sample surface. In the NC mode, the system
vibrates a stiff cantilever near its resonant frequency (typically
from 100 to 400 KHZ) with an amplitude of a few tens to hundreds
of angstroms. Then, it detects changes in the resonant frequency
or vibration amplitude as the tip comes near the sample surface.
The sensitivity of this detection scheme provides sub-angstrom
vertical resolution in the image, as in contact AFM mode. The
relation between the resonant frequency of the cantilever and
variations in sample topography can be explained as follows. The
resonant frequency of a cantilever varies as the square root of
its spring constant. In addition, the spring constant of the
cantilever varies with the force gradient experienced by the
cantilever. Finally, the force gradient, which is the derivative
of the force versus distance curve shown in the Fig.2, changes
with tip to sample separation. Thus, changes in the resonant
frequency of the cantilever can be used as a measure of changes in
the force gradient, which reflect changes in the tip to sample
spacing, or sample topography.

In NC mode, the system monitors the resonant frequency or
vibrational amplitude of the cantilever and keeps it constant with
the aid of a feedback system that moves the scanner up and down.
By keeping the resonant frequency or amplitude constant, the
system also keeps the average tip to sample distance constant. As
in contact AFM (in constant-force mode), the motion of the scanner
is used to generate the data set.

\vspace{0.1in}

\bf INTERMITTENT-CONTACT AFM MODE (TAPPING MODE):\rm

\vspace{0.1in}

Intermittent-contact AFM mode(Tapping mode) is similar to NC-AFM
mode, except that for this mode the vibrating cantilever tip is
brought to closer to the sample so that at the bottom of its
travel it just barely hits, or taps the sample. The IC-AFM
operating region is indicated on the van der Waals curve in the
Fig.2. As for NC mode, for this mode the cantilever's oscillation
amplitude changes in response to tip to sample spacing. An image
representing surface topography is obtained by monitoring these
changes. In this mode, the tip-sample lateral forces (friction or
drag) is greatly reduced and the short tip-sample contact time
prevents inelastic surface modification, i.e. this mode is less
likely to damage the sample. This mode has become an important
technique since it overcomes some of the limitations of both
contact and non-contact modes.

\vspace{0.1in}

\bf AFM AS NANOMANIPULATOR:\rm

\vspace{0.1in}

AFM can be used as a nanomanipulator. The tip of AFM is used to
manipulate nanoparticles. For the manipulation of nanoparticles,
generally, the AFM is used in NC mode or IC mode. The Fig. 3 shows
the process of the manipulation of gold nanoparticles and the
construction of 3-D structure from single nanoparticles.

These images are taken by AFM in NC mode. Manipulation of the
nanoparticles has been performed by utilizing the Probe Control
Software. The software allows one to take single line scan by
setting an arrow in a previously recorded NC mode image.The arrow
determines the direction and length of the subsequent scan line
and can be moved in the x- and y-direction until the displayed
topography indicates that its path is centered over the particle.
The feedback mechanism is turned off before starting the
manipulation and switched back on after reaching the desired
lateral position. Here the nanoparticle (1) has been pushed
between particles (2) and (3) forming a pyramid-like structure.
After then particle (1) has again been pushed away form particles
(2) and (3). This demonstrates that construction of a 3-D
structure by controlled manipulation of a single nanoparticles
with the help of AFM.

\vspace{0.1in}
\begin{figure}[htb]
\centerline{\psfig{figure=force3.eps,height=3.5in}}

\caption{\em{Pushing of a gold nanoparticle(1) with a diameter of
30 nm up and between two others (2 and 3) and back\cite{ref3}.}}
\end{figure}

\vspace{0.1in}

AFM can also be employed as a tool for the manipulation of carbon
nanotubes. The tip of an AFM is used to change the position and
shape of the nanotubes. For manipulation, the feedback is turned
off and the cantilever is pressed down onto the substrate, and
dragged along the predefined path over the surface, one can shift
the nanotubes laterally. This is the basis of manipulation
technique for the nanotubes. Using this kind of manipulation
technique, one can bend, buckle,cross and break nanotubes, and
unravel a nanotube crop circle into a single tube. The following
Fig.4 shows the images of carbon nanotube manipulation in tapping
mode.

\vspace{0.1in}
\begin{figure}[htb]
\centerline{\psfig{figure=force5.eps,height=2.5in}}

\caption{\em{Tapping mode AFM height images of intermediate stages
of a typical manipulation experiment \cite{ref4}.}}
\end{figure}

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Originally developed to provide images at resolutions ranging from
microns to angstroms, the AFM can also deposit or remove single
atoms at desired locations on surfaces. It can also be used as a
cutting device at the nanometer scale.


\vspace{0.1in}

\begin{thebibliography}{99}
\bibitem{ref1} S.N.Magonov, M.H.Whangbo\it Surface Analysis
with STM and AFM\em, VCH Publishers, USA, 1996.
\bibitem{ref2} \it Atomic Force Microscope\em, Thermo Microscopes
Manufacturer, 2001.
\bibitem{ref3} R.Resch, et al \it Journal of Surfaces and
Colloids\em, 14, 23, 6613, 1998.
\bibitem{ref4} W.C.Postma, A.Sellmeijer and C. Dekker,\it
Advanced Materials\em, 12, 17, 1299, 2000.

\end{thebibliography}
\end{document}
