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Title:
Theories of scanning probe microscopes at the atomic scale
Year: 2003
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Please cite the original version:
Hofer, Werner A. & Foster, Adam S. & Shluger, Alexander L. 2003. Theories of scanning
probe microscopes at the atomic scale. Reviews of Modern Physics. Volume 75, Issue 4.
1287-1331. ISSN 0034-6861 (printed). DOI: 10.1103/revmodphys.75.1287.
Rights: © 2003 American Physical Society (APS). This is the accepted version of the following article: Hofer, Werner
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scale. Reviews of Modern Physics. Volume 75, Issue 4. 1287-1331. ISSN 0034-6861 (printed). DOI:
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Theories of scanning probe microscopes at the atomic scale
Werner A. Hofer
Surface Science Research Centre, The University of Liverpool, Liverpool, L69 3BX,
United Kingdom
Adam S. Foster
Laboratory of Physics, Helsinki University of Technology, P.O. Box 1100, Helsinki 02015,
Finland
Alexander L. Shluger
Department of Physics and Astronomy, University College London, Gower Street,
London WC1E 6BT, United Kingdom
(Published 20 October 2003)
Significant progress has been made both in experimentation and in theoretical modeling of scanning
probe microscopy. The theoretical models used to analyze and interpret experimental scanning probe
microscope (SPM) images and spectroscopic data now provide information not only about the surface,
but also the probe tip and physical changes occurring during the scanning process. The aim of this
review is to discuss and compare the present status of computational modeling of two of the most
popular SPM methods—scanning tunneling microscopy and scanning force microscopy—in
conjunction with their applications to studies of surface structure and properties with atomic
resolution. In the context of these atomic-scale applications, for the scanning force microscope (SFM),
this review focuses primarily on recent noncontact SFM (NC-SFM) results. After a brief introduction
to the experimental techniques and the main factors determining image formation, the authors
consider the theoretical models developed for the scanning tunneling microscope (STM) and the SFM.
Both techniques are treated from the same general perspective of a sharp tip interacting with the
surface—the only difference being that the control parameter in the STM is the tunneling current and
in the SFM it is the force. The existing methods for calculating STM and SFM images are described
and illustrated using numerous examples, primarily from the authors’ own simulations, but also from
the literature. Theoretical and practical aspects of the techniques applied in STM and SFM modeling
are compared. Finally, the authors discuss modeling as it relates to SPM applications in studying
surface properties, such as adsorption, point defects, spin manipulation, and phonon excitation.
CONTENTS
I. Introduction 1288
II. Experimental Setups 1288
III. Main Factors Determining Image Formation 1291
A. Controling interactions 1291
B. Tunneling current 1291
C. Bias voltage 1292
D. Electrostatic forces 1292
1. Effect of electrostatic forces in scanning
tunneling microscopy 1292
2. Macroscopic electrostatic forces in scanning
force microscopy 1293
E. Chemical forces 1294
F. Magnetic forces 1294
G. Summary 1295
IV. Model Development 1295
A. The surface 1296
B. The tip 1296
1. Idealized tips 1297
2. Modeling of real tips 1297
3. Combining microscopic and macroscopic tip
models 1299
C. Tip-surface interaction 1299
1. van der Waals forces 1299
2. Calculating microscopic forces 1300
D. Modeling currents 1301
1. Tersoff-Hamann approach 1301
2. Perturbation approach 1301
3. Easy modeling: applying the Tersoff-
Hamann model 1302
4. Magnetic tunneling junctions 1303
5. Landauer-Bu
¨
tticker approach 1304
6. Keldysh-Green’s-function approach 1304
E. Modeling oscillations 1304
F. Generating a theoretical surface image 1305
G. Summary 1305
V. Studying the Surface 1305
A. Metal surfaces 1306
B. Semiconductor surfaces 1308
1. Silicon surfaces 1308
2. Binary semiconductor surfaces 1309
C. Insulating surfaces 1309
1. The calcium fluoride (111) surface 1310
a. Tip characterization with force curves 1311
b. Simulating scanning 1311
c. Standard images 1312
d. Distance dependence of images 1314
e. Ideal silicon tip 1317
2.
CaCO
3
(101
¯
4) surface 1318
D. Thin insulating films 1320
1. NaCl trilayer on Al(111) surface 1320
2. MgO thin films on Ag(001) surface 1320
3. NaCl thin films on Cu(111) surface 1321
VI. Studying Surface Properties 1321
A. Adsorbates on surfaces 1322
REVIEWS OF MODERN PHYSICS, VOLUME 75, OCTOBER 2003
0034-6861/2003/75(4)/1287(45)/$35.00 ©2003 The American Physical Society1287
1. C
4
O
3
H
2
on Si(100) (2⫻ 1) surface 1322
2. O on Fe(100) surface 1323
B. Point defects 1324
C. Surface magnetism 1324
1. Mn surface 1324
2. NiO surface 1325
D. Spin manipulation 1326
E. Phonon excitations 1326
F. Electron dynamics 1327
VII. Conclusion and Outlook 1327
Acknowledgments 1327
References 1327
I. INTRODUCTION
Scanning probe methods have developed into ubiqui-
tous tools in surface science, and the range of phenom-
ena studied by these techniques is continuing to grow.
These include surface topography, electronic and vibra-
tional properties, film growth, measurements of adhe-
sion and strength of individual chemical bonds, friction,
studies of lubrication, dielectric and magnetic proper-
ties, contact charging, molecular manipulation, and
many other phenomena from the micrometer down to
the subnanometer scale. The family of scanning probe
microscope (SPM) techniques is very diverse, with dif-
ferent methods specializing in different surface proper-
ties. In this review, we shall focus on the two most com-
monly used techniques—scanning tunneling microscopy
and scanning force microscopy. In both techniques a
sharp tip is interacting with the surface and a topo-
graphic surface image is produced by scanning. How-
ever, the parameters controlling the image formation are
different. In a scanning tunneling microscope (STM) the
control parameters of operation are the tunneling cur-
rent and/or the voltage, whereas in a scanning force mi-
croscope (SFM) the control parameter is the force be-
tween tip and sample. In both cases information about
the system under research is encoded in a change of
these parameters as the tip scans along the surface. The
highly nontrivial relationship between these variables
and the physical environment they reveal is the main
topic of this review.
While early research in these fields often took experi-
mental results at face value, many seemingly paradoxical
results have now taught experimentalists to be cautious
and even skeptical when they are confronted with an
image. This is where theoretical modeling has proven to
be essential and a driving force in any progress made. In
addition, SPM methods increasingly employ other meth-
ods of analysis like external magnetic fields or electron/
phonon excitations, so that ever more subtle changes of
the current in an STM, or the force in an SFM need to
be measured and accounted for. In itself this poses tre-
mendous challenges to experimental methods and thus
drives the development of new tools to keep track of
subtle changes. As the complexity of the experimental
techniques continues to increase, experimental and the-
oretical groups have started to work together, realizing
that both sides of a problem need to be studied in order
to arrive at sustainable models. The aim of theory is to
provide an understanding of the basic principles of op-
eration and the origins of image contrast, and to inter-
pret particular experimental images. In this paper we
review the potentials and pitfalls of different approaches
and hope to give newcomers and nonspecialists some
sense of how experimental results can be backed by so-
phisticated theoretical models. We also discuss the real
computational cost of these models and where the cur-
rent frontier lies in our abilities and our understanding
of the physical processes. We compare theoretical mod-
eling of two of the most popular SPM methods—
scanning tunneling microscopy and scanning force
microscopy—from a common perspective, and demon-
strate many similarities of these two methods. However,
when discussing applications of the methods, we focus
on those demonstrating true atomic resolution, and in
particular for the SFM, this has only been achieved us-
ing a noncontact SFM (NC-SFM) in ultrahigh-vacuum
(UHV) conditions.
We shall limit our discussion to working methods,
which is to say we do not consider in full detail the large
number of published papers which contain theoretical
suggestions and propose new methods that have not yet
been implemented. In principle, it is the goal of theory
to develop a reliable model that can be used to interpret
experimental images without resorting to direct simula-
tion. However, this goal has not yet been achieved with
either SPM technique. For the STM, the various meth-
ods that neglect the effect of a tip on the tunneling cur-
rent and the obtained images have provided some in-
sight into the imaging mechanism and can be trusted in
standard situations. Yet even so, groundbreaking experi-
ments require complex simulation for their interpreta-
tion. For the SFM, no simple model yet exists, and all
unambiguous assignment of chemical identities to image
features is based on direct simulation.
Theoretical methods used in scanning probe micros-
copy are in many ways similar to those used in other
branches of surface science. The main difference be-
tween SPM modeling and, for example, studies of ad-
sorption, adhesion, or cluster growth at surfaces, is that
the SPM tip is a macroscopic object and is very rarely in
force or thermal equilibrium with the surface. Image
contrast represents the difference in the tip-surface in-
teraction (with the SFM), or the tip-surface current
(with the STM) at different surface sites, and all non-
equivalent surface sites should be probed. Many events
observed experimentally are unique and are not subject
to statistical averaging. Until recently, theory has been
mainly concerned with qualitative predictions. However,
continuous refinement of experimental and theoretical
methods makes quantitative comparison increasingly
possible. This requires determination of parameters for
comparison, formulation of criteria of agreement, and
common calibration for theory and experiment.
II. EXPERIMENTAL SETUPS
The experimental setup of scanning probes for an
STM or an SFM (Binnig and Rohrer, 1982; Binnig et al.,
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W. A. Hofer, A. Foster, and A. Shluger: Theories of scanning probe microscopes at the atomic scale
Rev. Mod. Phys., Vol. 75, No. 4, October 2003
1982a, 1982b, 1986; Gu
¨
ntherodt et al., 1995; Bonnell,
2000; Garcı
´
a and Pe
´
rez, 2002; Morita et al., 2002;
Giessibl, 2003) is determined mainly by the desired ther-
mal and chemical environment. For traditional applica-
tions in surface science like the research of surface re-
constructions, surface growth, surface dynamics, and
surface chemistry, the instrument is mounted in a UHV
chamber of less than 10
⫺ 9
Torr. The UHV chamber and
the analytical instruments themselves are mounted on
rigid frames. This frame is externally damped by active
(this is the latest trend) or passive damping elements, or
mounted on rubber legs. Internally, vibrations of the
UHV chamber and the analytical instruments are mini-
mized by a combination of springs and eddy-current
damping. The purpose of this elaborate scheme is to
eliminate all vibrations from the environment, which
would make the periodic motion of an SPM tip of less
than 1 Å invisible due to background noise. The best
instruments today, which are mostly homebuilt, are ca-
pable of a vertical resolution better than 1 pm, or one
two-hundredth of an atomic diameter.
For biological applications, e.g., research on DNA and
single cells, as well as for electrochemical purposes, the
SPM is operating under liquid conditions (see, for ex-
ample, Driscoll et al., 1990; Ohnesorge and Binnig, 1993;
Gu
¨
ntherodt et al., 1995; Engel and Mu
¨
ller, 2000; Aoki
et al., 2001; James et al., 2001; Jandt, 2001; Philippsen
et al., 2002). From an experimental point of view these
conditions substantially limit the obtainable information
and spatial resolution at a given surface structure. It is,
however, an important step towards a realistic environ-
ment. In biological applications a liquid is the environ-
ment of all living organisms, and is therefore in a sense
indispensable. True atomic resolution, however, has yet
to be achieved under these conditions, hence we do not
treat that aspect of scanning probe microscopy in this
review.
The only experimental limitation for an STM is the
requirement of conducting surfaces. Insulator interfaces
for STM analysis are therefore grown to a few monolay-
ers on a metal base [e.g., NaCl (Hebenstreit et al., 2000),
or MgO (Schintke et al., 2001)]. Provided the tunneling
current is still detectable, the insulator can be scanned in
the same way as a conducting crystal interface. An SFM
is generally free from these limitations and could be
used to study any surface. However, for achieving
atomic resolution it seems crucial that surfaces be
smooth enough and that there be no strong, long-range,
tip-surface forces, e.g., those due to charging. In recent
years, the emphasis in both STM and SFM studies has
gradually shifted from surface topography and surface
reconstructions (Behm et al., 1990; Chen, 1993) to sur-
face chemistry (Fukui et al., 1997b; Hla et al., 2000;
Hahn and Ho, 2001a; Sasahara et al., 2001) and surface
dynamics (Molinas-Mata et al., 1998; Nishiguchi et al.,
1998; Bennewitz et al., 2000; Lauhon and Ho, 2000;
Schulz et al., 2000; Hoffmann et al., 2001).
Most STM experiments on semiconductors are done
at room temperature, while high-resolution scans on
metals rely, with but few exceptions (Biedermann, 1991),
on a low-temperature environment of 4–16 K. Low-
temperature scanning force microscopy is still a less than
common practice. However, several home-built instru-
ments have already demonstrated great improvement in
resolution with respect to room-temperature instru-
ments (Allers et al., 1998; Lantz et al., 2000; Uozumi
et al., 2002) and there are commercial low-temperature
SFM’s on the market. In this case the sample and/or the
whole SPM system are cooled by liquid helium. Thermal
motion in this temperature range is greatly reduced, and
high-resolution images of close-packed atomic structures
can then be obtained much more routinely.
Figure 1 shows the setup of an STM. In most cases the
STM is built into a UHV chamber. Its main components
are a sample holder, on which the surface under study is
mounted; a piezotube, which holds the STM tip; an elec-
tronic feedback loop; and a computer to monitor and
record the operation.
An SFM has quite similar components, as shown sche-
matically in Fig. 2. They can be effectively categorized
into three areas: (i) tip—macroscopic size and shape,
conductivity, microscopic chemical structure, charge; (ii)
surface—macroscopic thickness, conductivity, micro-
scopic chemical structure, charge; and (iii) experimental
setup—type of control of cantilever motion, electric cir-
cuit and bias between tip and sample or sample holder.
Thus, to really simulate the experimental process, one
needs not only to know the tip-surface interaction and
model the cantilever oscillations, but also to take into
account capacitance force, possible sample charging, and
other macroscopic effects.
Measuring very small forces and force variations over
the surface places more emphasis on the cantilever and
the tip. Most observations are made by monitoring nor-
mal and torsional cantilever deflections induced by the
FIG. 1. (Color in online edition) Setup of a scanning tunneling
microscope (STM). The tip is mounted on a piezotube, which
is deformed by applied electric fields. This deformation trans-
lates into lateral and vertical manipulation of the tip. Via an
electronic feedback loop, the position of the tip is adjusted
according to the tunneling current (constant-current mode),
and a two-dimensional current contour is recorded. This con-
tour encodes all the information about the measurement.
Courtesy of M. Schmid (Schmid, 1998).
1289
W. A. Hofer, A. Foster, and A. Shluger: Theories of scanning probe microscopes at the atomic scale
Rev. Mod. Phys., Vol. 75, No. 4, October 2003
tip-surface interaction using various optical methods
(Gu
¨
ntherodt et al., 1995; Morita et al., 2002). In early
SFM designs the tip was pressed to a surface either by
the van der Waals force or by the external elastic force
of the cantilever, and imaging was performed in the so-
called ‘‘contact mode.’’ However, relatively recently it
has been demonstrated that one can obtain much better
sensitivity in measuring force variations on the atomic
scale by employing dynamic force microscopy (Garcı
´
a
and Pe
´
rez, 2002; Morita et al., 2002). In this case the
cantilever is vibrated above the surface at a certain fre-
quency, and the surface image is constructed by moni-
toring minute frequency changes due to the tip-surface
interaction. Since in this case the tip is thought not to be
in direct hard contact with the surface, this technique is
often called noncontact scanning force microscopy (NC-
SFM). It is currently the only reliable way of achieving
true atomic resolution in an SFM, and in this review we
shall focus primarily on the theoretical modeling under-
pinning this method. In later discussion, if a section of
the review applies to SFM’s in general then it will be
specifically stated, otherwise it is written in the context
of NC-SFM. Several reviews of contact-mode SFM’s can
be found (Giessibl, 1994; Gu
¨
ntherodt et al., 1995;
Shluger et al., 1999; Bonnell, 2000).
Not every surface can be imaged with high resolution
in an STM or SFM. To achieve atomic resolution, the
surface in most cases needs extensive preparation. Sput-
tering (bombardment with ions, mostly Ar
⫹
), and an-
nealing (heating to the point where the surface defects
are smoothed out) over weeks and even months in con-
trolled cycles is not uncommon for studies of metal sur-
faces (Bischoff et al., 2001). Surface preparation in itself
is a sophisticated art and one of the keys to successful
imaging (Chen, 1993; Himpsel et al., 1998; Briggs and
Fisher, 1999). In contrast to k-space methods like ion
scattering or electron diffraction, a surface need not be
ordered to be imaged by SPM. In fact, single impurities
and step edges on a surface are often used by experi-
mentalists to check the quality of their images. Such an
impurity is only imaged as a single structure, assuming
no distorting effects like double tips are present.
The tip is the crucial part in imaging for all SPM
methods. STM tips are often made from a pure metal
[tungsten, iridium (Chen, 1993)], a metal alloy [PtIr
(Braun and Rieder, 2002)], or a metal base coated with
10–20 layers of a different material [e.g., Gd or Fe on
polycrystalline tungsten (Wiesendanger and Bode,
2001)], and are often produced in the lab from metal
wire. In some cases heavily doped Si tips are also used
for STM imaging. Although similar tips could also be
used for SFM measurements, this is very rare. This is
due to the fact that the cantilever holding the tip plays a
very important role in monitoring force changes in an
SFM: (i) in many SFM realizations, cantilever deflec-
tions are measured by detecting light reflected from the
back of the cantilever; and (ii) the cantilever spring con-
stant, tip shape, and tip sharpness all play crucial roles in
image formation. Standard cantilevers are therefore re-
quired. In most cases these are produced from silicon by
microfabrication in very much the same way as semicon-
ductor chips.
In some cases the tip is modified by controlled adsorp-
tion of molecules (Wertz et al., 1997; Capella and
Dietler, 1999; Hahn and Ho, 2001b; Nishino et al., 2001).
In STM’s it has been shown that this affects the apparent
height of molecules on a surface (Hahn and Ho, 2001b;
Nishino et al., 2001). The exact geometry of the tip is
commonly unknown except for some outstanding STM
measurements, where the tip structure was determined
before and after a scan by field-ion microscopy (Cross
et al., 1998). To complicate matters further, the tip geom-
etry is decisive for reproducible scanning tunneling spec-
troscopy measurements (Crommie et al., 1993). Unfortu-
nately, the tip most suitable for scanning tunneling
spectroscopy is also shown to be unsuited for topo-
graphic measurements because it does not yield a high
enough resolution (Feenstra et al., 1987). Currently the
most widely held opinion is that SPM tips consist of a
base with rather low curvature and an atomic tip cluster
with a single atom at the foremost position.
In an STM, all the current in the tunneling junction is
transported via this ‘‘apex’’ atom. The area of conduc-
tance is consequently rather small and in the range of a
few Å
2
(Chen, 1993; see Fig. 3). This is the origin of
STM precision: the current is very sensitive to the elec-
tronic environment of a very small area of the surface.
FIG. 2. (Color in online edition) Idealized schematic of the
setup needed to model a noncontact scanning force micro-
scope (NC-SFM) experiment on an insulating surface. The tip
approaches the surface with frequency f
0
and U is a bias volt-
age between the conducting tip and the conductive sample
support.
FIG. 3. (Color in online edition) Tunneling current in a scan-
ning tunneling microscope. The surface of the tip is generally
not smooth. A microtip of a few atoms will bear the bulk of the
tunneling current; due to this spatial limitation of current flow,
the electronic properties of a scanned surface can be extremely
well resolved (resolution laterally better than 1 Å).
1290
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Rev. Mod. Phys., Vol. 75, No. 4, October 2003
