London forces in highly oriented pyrolytic graphite
The surface of highly oriented pyrolytic graphite with terrace steps was studied using scanning tunneling microscopy with high spatial resolution. Spots with positive and negative charges were found in the vicinity of the steps. Values of the charges depended both on the microscope needle scan veloc...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2017
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| Цитувати: | London forces in highly oriented pyrolytic graphite / L.V. Poperenko, S.G. Rozouvan, I.A. Shaykevich // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2017. — Т. 20, № 2. — С. 185-190. — Бібліогр.: 23 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860279419536408576 |
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| author | Poperenko, L.V. Rozouvan, S.G. Shaykevich, I.A. |
| author_facet | Poperenko, L.V. Rozouvan, S.G. Shaykevich, I.A. |
| citation_txt | London forces in highly oriented pyrolytic graphite / L.V. Poperenko, S.G. Rozouvan, I.A. Shaykevich // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2017. — Т. 20, № 2. — С. 185-190. — Бібліогр.: 23 назв. — англ. |
| collection | DSpace DC |
| container_title | Semiconductor Physics Quantum Electronics & Optoelectronics |
| description | The surface of highly oriented pyrolytic graphite with terrace steps was studied using scanning tunneling microscopy with high spatial resolution. Spots with positive and negative charges were found in the vicinity of the steps. Values of the charges depended both on the microscope needle scan velocity and on its motion direction. The observed effect was theoretically explained with account of London forces that arise between the needle tip and the graphite surface. In this scheme, a terrace step works as a nanoscale diode for surface electric currents.
|
| first_indexed | 2026-03-21T13:45:03Z |
| format | Article |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 2. P. 185-190.
doi: https://doi.org/10.15407/spqeo20.02.185
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
185
PACS 34.20.cf, 81.05.uf
London forces in highly oriented pyrolytic graphite
L.V. Poperenko, S.G. Rozouvan, I.A. Shaykevich
Taras Shevchenko National University of Kyiv,
Department of Physics,
2, Prospect Glushkova,
03187Kyiv, Ukraine
Abstract. Surface of highly oriented pyrolytic graphite with terrace steps was studied
using scanning tunneling microscopy with high spatial resolution. Spots with positive
and negative charges were found in the vicinity of the steps. Values of the charges
depended both on the microscope needle scan velocity and on its motion direction. The
observed effect was theoretically explained with account of London forces that arise
between the needle tip and the graphite surface. In this scheme, a terrace step works as a
nanoscale diode for surface electric currents.
Keywords: London force, pyrolytic graphite, scanning tunneling microscopy.
Manuscript received 14.11.16; revised version received 10.04.17; accepted for
publication 14.06.17; published online 18.07.17.
1. Introduction
Intermolecular forces have been known for centuries, but
it’s only in recent years as a result of progress in
nanoscience that researchers began paying closer
attention to them. As it is well-known, tiny objects on a
conducting surface experience the influence of short
range (van der Waals) forces, which have to be taken
into account as nanodevice constructions. Three similar
phenomena were subsequently shown to contribute to
these “van der Waals” interactions [1]: randomly
orienting dipole-dipole (or orientation) interactions,
described by Keesom [2-5]; randomly orienting dipole-
induced dipole (or induction) interactions, described by
Debye [6, 7]; fluctuating dipole-induced dipole (or
dispersion) interactions, described by London [8]. The
Lifshitz theory of condensed media interaction [9]
describes the short range forces based on continuum
properties. The van der Waals pressure according to
Lifshitz’s theory can be expressed in terms of the
dielectric susceptibilities of interacting phases. Hamaker
developed the theory of van der Waals–London
interactions between macroscopic bodies in 1937 and
showed that the additivity of these interactions renders
them considerably more long-range [10]. If we have
objects of complicated shape and mutual position, an
image method allows computing the dispersion van der
Waals interaction between a neutral but polarizable atom
and a perfectly conducting surface of arbitrary shape.
This method has the advantage of relating the quantum
problem to a well-known classical one in electrostatics
[11]. Casimir force between mirrors in vacuum can now
be measured with good accuracy and according to
theory, when the effect of imperfect reflection of mirrors
is properly taken into account [12]. A simple case of
bulk metallic mirrors can be described by a plasma
model to show that simple scaling laws are obtained at
the limits of long and short distances. The crossover
between the short and long-distance laws is quite similar
to the crossover between van der Waals and Casimir–
Polder forces for two atoms in vacuum. Mechanical
effects in macroscopic physics and the archetype of
these effects is the Casimir force between two mirrors at
rest in vacuum. Casimir force, which operates at short
distances, can be understood as the London interaction
between the elementary excitations of both scatterers.
And that is described as surface plasmons of the two
bulk mirrors. At short distances, this is the van der
Waals force, at large distances, the finite velocity of
light becomes important (retardation effects) and the
result is the Casimir force. Attractive Casimir forces
were found between gold surfaces [13]. The forces were
repulsive between gold and silica surfaces. The vacuum
stress between closely spaced conducting surfaces, due
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 2. P. 185-190.
doi: https://doi.org/10.15407/spqeo20.02.185
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
186
to the modification of the zeropoint fluctuations of the
electromagnetic field in the 0.6 to 6 mm range, has been
conclusively demonstrated [14]. The non-retarded
Casimir–Polder interaction between a neutral but polari-
zable particle and a plane with a complicated topology –
perfectly reacting sheet containing a circular hole was
found [15]. The calculation reveals a strong dependence
of the interaction on the orientation of the particle’s
electric dipole moment with respect to the surface.
Scanning probe microscopies (scanning tunneling
microscopy (STM) and especially atomic force
microscopy (AFM)) proved to be a basic tool to study
nanoobjects while taking into account van der Waals
forces. Significant progress has been made both in
experiments and in theoretical modeling of scanning
probe microscopies. See, for example, review [16] with
discussions and comparison of the present status of
computational modeling of scanning tunneling
microscopy and scanning force microscopy in relation
with their studies of surface structure and properties with
atomic spatial resolution. The first stage of performing
nanoscale measurements is ascertaining a good quality
of the surface being studied. Metal and semiconductor
crystals with lattice planes on its surface can play an
important role taking into account both fabrication of
nanostructures and quality of STM/AFM experiments.
From the point of view, highly oriented pyrolytic
graphite (HOPG) was chosen for experiments because of
its close to perfect crystal lattice, which allows
controlling the nanometer scale distance between
interacting bodies – HOPG surface and scanning needle
tip. Lattice planes on HOPG surface with sharp edges
were detected applying STM in [17]. The terrace steps
were characterized as crystal lattice defect though the
organic impurities were mostly studied. Coiled
structures with a helix pattern were studied by STM in
[18]. The terraces morphology was changed by applying
electrochemical reductive etching [19]. The lattice plane
edges were proposed to be carbon based electrodes. The
two terrace planes – edge and basal planes taken as
electrodes – would exhibit different kinetics because of
edge plane sites/defects [20].
The goal of this article is to study short range
intermolecular forces applying atomic spatial resolution
STM for lattice planes on the HOPG surface.
2. Experimental
To study the HOPG structure, we applied STM tech-
nique, which allowed us to reach an atomic spatial scale
resolution. A microscope INTEGRA NT-MDT was used
to conduct measurements in tunneling microscopy
regime. Scanning tunneling microscopy spatial
resolution reached up to 0.2 nm. A sharp needle for STM
measurements was fabricated from 0.5 mm Pt0.8Ir0.2 wire
by mechanically cutting its end. We performed our
measurements in a regime when STM setup supported a
constant tunneling current through the needle, which was
completed by tuning the sample position along the
vertical direction. Sample of HOPG had rectangular
shape with 1 cm sides. STM measurements were
performed in different places of the sample surface with
a particular interest toward lattice planes edges in order
to study surface effects in these spots. HOPG samples
were cleaved by applying scotch tape, and the
measurements were performed during the following days
in order to avoid the sample surface degradation.
Examples of the HOPG surface profile studied by
STM with different spatial resolution are presented in
Figs 1 to 3. In Fig. 1, we can see lattice planes that form
perfectly shaped terrace steps having the maximal length
up to ten micrometers. The steps visible as direct straight
lines separate two neighboring lattice planes that have
distinct difference in brightness. The terrace steps have
narrow black and white “shadows”, beside which they
are visible as straight and narrow bands. Fig. 2 demon-
strates a high spatial resolution STM scan of a terrace
step that is formed by two neighboring lattice planes.
HOPG crystal lattice structure is visible on the planes.
The white and black neighboring bands from Fig. 1 are
marked in 3D Fig. 2 by W and B arrows that indicate
sharp maximum and minimum on the edge of the step.
The value of the height of the terrace step equals to 6…7
lattice parameters (~2 nm). The crystal lattice orientation
of this HOPG sample was close to [101]. The terrace
steps were formed during mechanical HOPG cleaving
and a few terrace steps may form a group – parallel rows
containing a few parallel terrace steps separated by a
space interval of ten nanometers (Fig. 3). For Fig. 3
experiments, we chose terrace steps with small terrace
step heights that reached 1 to 2 lattice parameters. It
allowed us to register artifacts in the vicinity of the steps
more noticeably. Figs 3a and 3b show the same spot of
HOPG surface with parallel terrace steps, which was
measured with different velocities and with different
directions of needle movement along the HOPG surface.
Fig. 1. STM scan of HOPG surface. Spatial resolution 60 nm.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 2. P. 185-190.
doi: https://doi.org/10.15407/spqeo20.02.185
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
187
Fig. 2. STM scan of a terrace step on HOPG surface. Spatial
resolution 0.2 nm. SD indicates direction of scans, W and B
arrows indicate dark and white bands near the terrace step
edges.
White and black areas near the terrace steps on
HOPG surface are visible in Fig. 3a and have distinctly
higher contrast in Fig. 3b as a result of higher scanning
velocity in the latter case. The widths of the white/black
bands in Fig. 3b reach 10 nm. The white/black bands are
absent in Fig. 3c due to the opposite directions of the
needle movement, despite the needle had the same scan-
ning velocity as in Fig. 3b. The white spots on the two
neighboring atomic planes beside of its edges indicate
higher concentration of the surface charges in these areas.
The electric charges contributed to the tunneling current
and resulted in the large distances between the needle tip
and sample surface (experimental set-up worked in the
constant tunneling current regime). The dark spot
similarly indicates lower surface charges in this point.
Cross sections of Fig. 3 STM scans are presented in
Fig. 4. The cross sections are marked in Fig. 3 as white
straight lines. The cross sections are taken in the same
spot of the scanned terrace step. As we can see from
plots of Fig. 4, the differences in Z coordinate near the
terrace steps reach 7 nm for (a) curve and is almost
unnoticeable for (c) curve (STM scan with opposite
direction). For lower scan velocity ((b) curve) ΔZ is
approximately 2 nm. ΔZ numbers for Fig. 4 (a) and (b)
curves exceed HOPG crystal lattice parameter by almost
one order of magnitude.
3. Discussion
Randomly appearing dipole on the STM needle tip
induces electrical charge on the surface of HOPG. If we
introduce the Green function which satisfies the
expression
( ) ( )rrrrG
rrrr ′′−′δ−=′′′∇ ,2 (1)
for the non-retarded interacting energy in this case
between an atom with a dipole moment oriented along Z
axis, and the conducting surface can be written as a
simplified ratio obtained in [21]
( )( )
0
41,
2
1 2
0
rrrzzz rrrrGdU rrr
rrrr
=′′=′
′′−′π−′′′∇ ′′∇′
ε
= . (2)
a b c
Fig. 3. STM scan of the HOPG terrace step. (a) Direction of scan from the upper part of the figure to the lower part. Velocity of
scan 0.6 µm/s. Spatial resolution 0.8 nm. W and B arrows indicate dark and white bands near the terrace step edges. (b) Direction
of scan from the upper part of the figure to the lower part. The velocity of scan 6 μm/s. Spatial resolution is 0.8 nm. W and B
arrows indicate dark and white bands near the terrace step edges. (c) Direction of scan from the lower part of the figure to the
upper part. The velocity of scan 6 μm/s. Spatial resolution is 0.8 nm.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 2. P. 185-190.
doi: https://doi.org/10.15407/spqeo20.02.185
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
188
Fig. 4. Cross sections of STM scans for: a) Fig. 3b, b) Fig. 3a,
c) Fig. 3c.
Here, d is a quantum operator of dipole moment
that in classical approximation is equal to ql (Fig. 5), and
the energy depends on its projection on Z axis.
Orthogonal to the sample surface electric field E can be
found with account of the image method [11], which
enables to reduce the quantum mechanical problem to
the related classical electrostatic one by putting
additional point charges into specific places in bulk
media. The electric potential in this configuration can be
calculated as being induced by the original dipole and
the image dipole (Fig. 4). Two dipole vectors of the both
original and image dipoles are co-linear and orthogonal
to the perfectly conducted sample surface in order to
minimize the dipole interaction electric energy. The
electric field vector in the vicinity of the sample surface
is orthogonal to the surface. If applying the Coulomb
law, one can calculate the electric field in an arbitrary
point of the surface:
( )
( )
( )( ) ( )
.
4
2
4
2,
2
0
222
0
22
0
2
0
222
0
22
0
lzyx
lz
lzyx
q
zyx
z
zyx
qyxE
+++
+
⋅
+++πε
−
−
++
⋅
++πε
=
(3)
The electrical vector in (x, y) point near the surface
in Eq. (3) is orthogonal to the surface and is produced by
the both local surface charges and the electric dipole in
the needle tip. The local electric charge density on the
surface σ(x, y) and the electric field vector E(x, y) satisfy
the relationship:
( ) ( ) 02,2, εσ= yxyxE . (4)
Here, only half value of the electric field E(x, y) is
generated by the surface charge and another half – by the
dipole in the needle tip. In the image method formalism,
the former part of the electric field is formed by the
image dipole beneath the surface. In assumption of small
l (comparing to the distance between the needle tie and
the surface), we can obtain a ratio for the surface electric
charge density:
( ) ( ) ( ) ⎥⎦
⎤
⎢⎣
⎡ ++−+
π
=σ
−− 232
0
2225222
03
2
, zyxyxzdyx . (5)
If we put an electrical dipole near a terrace step that
is formed by two conducting planes, the electric field
distribution cannot be found by applying the image
method. First, let us take a closer look at a simple case of
an electric charge near the corner of two infinite
conducting semi-planes (Fig. 6a), which can be solved
using the image method. In this configuration, the
distribution of electric potential is generated by the real
charge +q(x0, y0) and additionally by the three mirror
image charges (–q(x0, –y0), –q(–x0, y0), +q(–x0, –y0)).
The electric potential is equal to zero on the two
conducting semi-planes – x = 0 (y ≥ 0) and y = 0 (x ≥ 0)).
One real charge and three image charges form the
quadruple configuration. As a result, the electric field as
well as the electric charge surface density in the corner
point (x = 0, y = 0 – the geometrical center of the four
charges in the quadrupole) are equal to zero. If the
needle tip slides along the sample surface during STM
experiments, the induced surface charges on the surface
also move following the moving tip. As a result, a
surface current is formed.
The corner point with zero surface charge density
represents a barrier or a trap, which prevents surface
charge displacement from the right to the left side and
from left to right. The induced surface current is equal to
zero in the corner point, because as we can see from
Fig. 5 calculations, surface charge density in the point is
equal to zero.
Fig. 5. A conducting needle tip with induced dipole near
the conducting plane.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 2. P. 185-190.
doi: https://doi.org/10.15407/spqeo20.02.185
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
189
A terrace step on a surface plane is a more
complicated topological configuration as compared
with that of the corner that is formed by two semi-
infinite steps. We cannot apply the image method to
obtain the electric potential distribution in this case.
We tried to model the electric potential distribution in
this configuration by solving numerically the Maxwell
equations. The result of numerical simulation of a
dipole on the STM needle tip near the terrace step on a
conducting surface is presented in Fig. 6b. The
calculations were performed using MEEP software in
Debian Linux environment. The field distribution is
shown both as equilines and gray scale surface plot.
The obtained field distribution is to some extent similar
to the scheme in Fig. 6a. The equilines allow us
evaluating qualitatively the electric vector numbers by
counting the space gap between the lines. The electric
field is zero in the corner of the terrace step (similar to
the scheme in Fig. 6a) and has high values near the
terrace step rim. The arrow in Fig. 6b indicates possible
surface charge movements through the substrate bulk
material, when STM scan is performed from right to
the left side. The opposite direction (from the left to the
right) of surface charges movement is impossible,
because the charges cannot move through the air. This
scheme of surface charges movement could be a
possible explanation of Fig. 3 effect, when charge is
collected near the terrace step on a conducting surface,
when the needle moves in one direction, and freely
passes the terrace step, when the needle moves in the
opposite direction. The terrace step is operating in a
regime that creates a barrier (or trap) for the electric
charge moving in one direction. Basically, it works as a
surface nanoscale diode.
The electric current in STM experiments is formed
by electrons from conduction graphite band. These
electrons form ideal Fermi gas with the temperature that
is below the Fermi temperature. Because of the degene-
racy of the gas, we cannot register edge or defect states
in the valence band of our sample similarly to [22, 23]
results. If the localized surface states are registered
either by spreading resistance atomic force microscopy
or by Kelvin probe force microscopy, the results have to
be invariant to the both scan velocity and direction.
Charges are localized near HOPG terrace steps, be-
cause the surface charges cannot move across this linear
surface defect. A possible qualitative explanation can be
based on a high surface curvature near terrace steps on
HOPG surface and, as a result, higher values of electric
field in the spots near the rims of the terrace step. The
field prevents the induced surface charges from moving.
In more general terms, we usually have dipole configura-
tions of induced charge distributions in macroscopic
volumes of an electric circuit, because the charges are in-
duced there by bipolar voltage source. In nanoscale
volumes, induced charges may form higher order multi-
pole moments because of non-planar (e.g., a terrace) sur-
face topology in some spots of the surface. The induced
charges in the corner of two semi-infinite conducting
planes may form quadrupole configuration (quadrupole
polarizability) having the zero dipole moment. This in-
duced quadrupole forms a barrier for surface currents. The
extra charges on HOPG surface are accumulated during
STM needle movement and the changing local electric
potential in the vicinities of terraces, which results in
white/black artifact bands on STM scans. Actually, the
pairs of black/white bands localized near the terrace steps
indicate presence of surface nanodipoles with the vector
oriented perpendicular to the terrace step direction.
a b
Fig. 6. A charge near the corner of two conducting planes (a), electric potential distribution induced by a dipole near
a terrace step (b).
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 2. P. 185-190.
doi: https://doi.org/10.15407/spqeo20.02.185
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
190
4. Conclusions
London forces which arise between the needle tip and a
conducting crystal surface during STM experiments
result in induced charge in the spot beneath the needle
tip. The charged spot below the needle tip on the sample
surface follows the needle movement along the sample
lattice plane creating a surface current. If the lattice
plane has linear defects (e.g., terrace steps on the
surface), it can result in the electric charges
accumulation along the surface defect lines, when the
needle moves in a specific direction. A step on a surface
that forms an electric junction allows flowing surface
electric current only in one direction. Practically, this
effect can be used as a basic element for nanoscale diode
construction. The diode dimensions could be as small as
crystal lattice primitive vectors lengths. Applying
another voltage polarity, one can induce a nanodipole
along a sharp edge of the terrace. From pure practical
point of view, it can be used as a nanoscale voltage
source. This effect takes place in nanoscale volumes
near the surface, because it is originated from second-
order term of multipole expansion. At large distances
comparing to dimensions of charge distribution the
electric potential and field are dominated by the main
dipole term of the expansion, and high order terms are
negligible.
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| id | nasplib_isofts_kiev_ua-123456789-214935 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2026-03-21T13:45:03Z |
| publishDate | 2017 |
| publisher | Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| record_format | dspace |
| spelling | Poperenko, L.V. Rozouvan, S.G. Shaykevich, I.A. 2026-03-04T12:53:41Z 2017 London forces in highly oriented pyrolytic graphite / L.V. Poperenko, S.G. Rozouvan, I.A. Shaykevich // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2017. — Т. 20, № 2. — С. 185-190. — Бібліогр.: 23 назв. — англ. 1560-8034 PACS: 34.20.cf, 81.05.uf https://nasplib.isofts.kiev.ua/handle/123456789/214935 https://doi.org/10.15407/spqeo20.02.185 The surface of highly oriented pyrolytic graphite with terrace steps was studied using scanning tunneling microscopy with high spatial resolution. Spots with positive and negative charges were found in the vicinity of the steps. Values of the charges depended both on the microscope needle scan velocity and on its motion direction. The observed effect was theoretically explained with account of London forces that arise between the needle tip and the graphite surface. In this scheme, a terrace step works as a nanoscale diode for surface electric currents. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics London forces in highly oriented pyrolytic graphite Article published earlier |
| spellingShingle | London forces in highly oriented pyrolytic graphite Poperenko, L.V. Rozouvan, S.G. Shaykevich, I.A. |
| title | London forces in highly oriented pyrolytic graphite |
| title_full | London forces in highly oriented pyrolytic graphite |
| title_fullStr | London forces in highly oriented pyrolytic graphite |
| title_full_unstemmed | London forces in highly oriented pyrolytic graphite |
| title_short | London forces in highly oriented pyrolytic graphite |
| title_sort | london forces in highly oriented pyrolytic graphite |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214935 |
| work_keys_str_mv | AT poperenkolv londonforcesinhighlyorientedpyrolyticgraphite AT rozouvansg londonforcesinhighlyorientedpyrolyticgraphite AT shaykevichia londonforcesinhighlyorientedpyrolyticgraphite |