Surface Science 446 (2000) 294–300
www.elsevier.nl/locate/susc
Oscillating low-energy electron diffraction for
studying nanostructured surfaces
S. Dorel, F. Pesty *, P. Garoche
Laboratoire de Physique des Solides Université de Paris-Sud, CNRS UMR8502, Bât.510 91405 Orsay cedex, France
Received 20 August 1999; accepted for publication 9 November 1999
Abstract
Low-energy electron diffraction is widely used as an efficient tool for the direct characterisation of the atomic
structure of perfect surfaces. However, because of the low signal-to-noise ratio, it cannot be used with confidence to
characterise nanostructured surfaces. Here, we show that a significant improvement of the diffraction data is obtained
by using a modulated beam current, associated with a time correlation undertaken on a continuous sequence of
digitised images. This is illustrated by the diffraction pattern of a mica surface that displays rings around the Bragg
spots, which reveal the existence of nanostructures on the surface. © 2000 Elsevier Science B.V. All rights reserved.
Keywords: Insulating surfaces; Low-energy electron diffraction (LEED); Mica; Surface defects; Surface structure, morphology,
roughness, and topography
1. Introduction
Low-energy electron diffraction is a very useful
method, used almost universally to qualitatively
monitor the condition of atomic surfaces and
establish that they can be prepared in a reproducible way. It can also be used to give a quantitative
crystallographic description of the atomic positions. Such a description implies a full multiplescattering theory of the electronic diffraction at
low energy, in order to extract from the diffraction
pattern a precise description of the atomic arrangement at the surface [1]. Here, we are concerned
with the structure of the surfaces on the nanometre
scale or greater, i.e. we are interested in the correlation of inter-atomic distances on a large scale that
does not require a full multiple-scattering theory
* Corresponding author. Fax: +33-1-69156086.
E-mail address: [email protected] ( F. Pesty)
[2]. Recent active studies of surface nanostructures, for example self-organised steps or islands,
require a characterisation tool with a higher level
of sensitivity, because these objects contribute
poorly to the intensity of the electron diffraction
pattern, and cannot be identified on a regular
LEED result. Various methods have been proposed
to increase the signal-to-noise ratio of diffraction
patterns [3]. They are mostly based on a onedimensional scanning associated with highly sensitive detectors [4], such as a scintillator–photomultiplicator assembly [5]. These devices produce
extremely well defined one-dimensional line scans
across a given diffraction peak. Either the detector
[6 ] or the beam [7] can be scanned, and several
lines are joined to build up a grid of the diffracted
intensity.
Here we propose a fast two-dimensional data
collection that yields a large contrast enhancement
for the full diffraction image. The video image
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PII: S0 0 39 - 6 0 28 ( 99 ) 0 11 5 8 -9
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S. Dorel et al. / Surface Science 446 (2000) 294–300
information of the diffraction pattern is collected
and simultaneously analysed. Such a two-dimensional treatment implies a fast computer analysis
for a large volume of information, which can be
easily achieved with today’s microprocessors. It
allows a very good noise reduction for the diffraction image, with an acquisition time of less than
1 min. It is based on both a sine wave modulation
of the electron beam current and a time analysis
of the resulting intensity oscillation of the diffraction pattern.
As an example of its application, we present
new results on a mica crystal of muscovite structure. Our new method allows us to obtain LEED
diffraction patterns exhibiting a series of ring-like
structures, revealing a surface nanostructuration
with characteristic distances between 1 and 5 nm.
2. Experimental set-up
The experimental set-up is based on a standard
reverse view LEED (RVL900 from VG
Microtech). The gun (LEG24 from VG Microtech)
is placed in the centre of the three-grid detector.
The grids are used in a standard manner: the two
outside grids are grounded and used as shields,
whereas the potential of the central grid is adjusted
in order to reject most of the inelastic backwardscattered electrons [8]. The filtered electrons are
then accelerated and visualised on a phosphorus
screen. A monochrome video camera ( WW-BP500
from Panasonic), placed in front of the screen,
collects the information, as shown in Fig. 1. The
base pressure of the UHV chamber is below
10−10 Torr.
We have modified the electronic circuit driving
the electron gun to provide a remote modulation,
for instance a sine wave, to the Wehnelt voltage,
yielding an oscillating low-energy beam current.
As a result, the diffraction image displays a periodic oscillation for each pixel intensity. At a fixed
energy, no modification of the diffraction process
is expected. The modulation is generated by a state
machine (signal generator in Fig. 1), implemented
in a logic array.
The video signal captured by the camera is sent
to a frame grabber, then the diffraction images are
Fig. 1. Schematics of the oscillating LEED acquisition set-up.
The gun generates a modulated electron beam intensity, controlled by the signal generator. The video camera continuously
acquires diffraction images that are synchronised with the beam
oscillation. Digitised data are processed in real-time in the PC.
digitised and analysed using a Pentium microcomputer. The signal generator provides an external
signal to synchronise the video camera with the
beam current oscillation (Fig. 1). A code is written
on each video image, by using the grey level of the
image first line, which stamps the value of the
exact acquisition time.
Our video camera is interlaced with an aperture
time of approximately 20 ms and a period of 40 ms
. The latter defines the imaging frequency:
f
=25 Hz. The synchronisation between the
video
electron beam oscillation — at frequency f
—
beam
and the video image rate — at frequency f
—
video
is done in such a way that each oscillation period
contains exactly an integer number, N, of images,
and the total acquisition time, T , is chosen as
acq
an exact multiple, L, of the oscillation period [Eq.
(1)]:
=N1 f
,T =
beam acq f
L
.
(1)
beam
Each image of an acquisition sequence can be
labelled using two indexes: j (from 1 to L), the
rank of the oscillation period, and k (from 1 to
N ), the rank of the image in the period (Fig. 2).
The latter rank indicates the phase relationship of
the image with respect to the beam modulation.
Each image corresponds to P=768×576=442 368
pixels, so about 10.5 Mb must be processed every
f
video
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S. Dorel et al. / Surface Science 446 (2000) 294–300
Fig. 2. Acquired images consist of a sequence of L series of N images. The images with the same rank, k, are summed pixel by pixel.
This leaves a set of N averaged images, which covers exactly one period of the beam modulation.
second. We average the images with the same k in
real time, pixel by pixel, over the L oscillation
periods. This divides the required memory size by
an L factor.
For a given pixel of position i (from 1 to P),
we obtain a sequence of N values that are equally
time-spaced, covering exactly one period of the
beam modulation (Fig. 2). The time evolution of
the intensity, p , of each pixel, is fitted to a sine
i
wave function, according to Eq. (2):
p (t)=m +a sin(2pf
t+w ),
(2)
i
i
i
beam
i
using a least-squares method (where t is the time).
The fitting parameters m , a and w are, respeci i
i
tively, the mean value, the amplitude of the modulation and the phase shift of the intensity. This
gives three sets of P values, from which we build
three images: an ‘m-image’, an ‘a-image’ and a
‘w-image’.
Our data processing acts as a sequence of two
filters. The upper part of Fig. 3 displays the frequency spectrum of the first filter. This results
from the correlation between the video frequency
and the beam modulation frequency and consists
of thin peaks, at f
and at its harmonic frequenbeam
cies. These peaks are weighted by a (sin x)/x
envelope, related to f
. The width of the thin
video
peaks is proportional to the inverse of the total
acquisition time (typically 30 s; bottom insert).
The second filter (middle part of Fig. 3), resulting
from the least-squares fit, is built from f
with
beam
an aliasing at f
. This filter is particularly effivideo
cient in suppressing the harmonics of f
. As a
beam
result, the total filter acts as a very narrow bandpass filter at the beam frequency, with a small
aliasing at f
(bottom of Fig. 3).
video
It should be noted out that each image received
by the computer is perfectly time-indexed by an
encoder (Fig. 1), irrespective of the reliability of
the data acquisition system. This is a key point
because the noise-rejection principle due to the
above digital filter, based on time correlation
between images, implies a perfect control of the
time base. This is achieved by using the same
oscillator to generate the Wehnelt modulation as
well as the synchronising signal. When averaging
N =N1L images, we improve the signal-to-noise
tot
ratio by a factor of 앀N . The time correlation
tot
allows us to improve the statistics by another
factor, 앀N (insert of Fig. 3). This results in an
tot
efficient noise reduction that scales as the inverse
of the acquisition time.
3. Application of the method to an air-cleaved
surface of mica
An example of diffraction pattern obtained
using this new experimental method is presented
in Fig. 4, for an air-cleaved crystal of muscovite
mica. The conventional LEED pattern, a
‘m-image’, is shown in Fig. 4a and the corresponding ‘a-image’, in Fig. 4b. The ‘w-image’ is not
S. Dorel et al. / Surface Science 446 (2000) 294–300
Fig. 3. Digital filter applied on the acquired diffraction images,
for a 5 Hz beam oscillation, and a 30 s total acquisition time.
The 20 ms CCD aperture time is responsible for the general
sin x/x shape of the upper filter. By aliasing, frequency peaks
occur at all harmonics of the beam frequency. The peaks of the
middle filter result from the least-squares fit to a sine-wave
response. The total filter (bottom) only exhibits peaks at f
beam
with a small aliasing at f
. It acts as a very narrow bandpass
video
filter, centred at f
. The insert shows that the peak width at
beam
f
(and its aliases) varies as the inverse of the total acquisibeam
tion time.
presented because it displays a flat structure, as
expected for a synchronous acquisition. The
experiment has been carried out at an electron
energy of 132 eV, by applying a Wehnelt bias of
−8.4 V, superimposed with a sine wave oscillation
of ±1.4 V, at a modulation frequency of
f
=0.5 Hz. The latter corresponds to a number
beam
297
N=50 images per oscillation period, with an
average number of L=25 periods.
The usual diffraction pattern is observed, with
a hexagonal periodicity. The diffraction process
involves several atomic layers below the surface,
due to the finite penetration depth of low energy
electrons (a few nanometres at 132 eV ).
Consequently, the intensity of each spot depends
on a three-dimensional Bragg condition. A given
spot may vanish if a destructive interference condition is met, for a particular incident wave vector
(out-of-phase condition). At this energy, the
diffraction pattern of the ‘m-image’ exhibits the
usual intensity symmetry (across the diagonal line
in the [12: ] direction, in Fig. 4a) [9].
A series of rings appears around most of the
diffraction spots of the ‘a-image’, exemplified by
white arrows in Fig. 4b. The rings present various
magnitudes as well as different characteristic
periods in the reciprocal space, corresponding to
real-space distances ranging from 2 to 10 lattice
parameters, i.e. between about 1 and 5 nm.
On the left-hand side of Fig. 5, the diffraction
patterns (‘m-image’ on the top, ‘a-image’ on the
bottom) both show four particular diffraction
spots (zooms in Fig. 4). Two line profiles are
plotted on the right-hand side of Fig. 5. They are
drawn across the (11) diffraction spot, along the
[11: ] direction (arrow). The vertical scale corresponds to the grey levels of the video camera. Note
the different orders of magnitude of the ring peaks
of the ‘a-image’ with respect to the Bragg spot of
the ‘m-image’: only 0.2 grey levels, as compared
with 14, indicating the greater sensitivity of the
oscillating LEED.
The power of our oscillating method is demonstrated with the lower profile of Fig. 5. It corresponds to a perfect out-of-phase situation for the
Bragg spot: the intensity of the latter is reduced
to zero, within the experimental uncertainty.
Usually, such a condition cannot be achieved using
the conventional LEED method, because of a finite
instrumental response. For instance, the Bragg
peak of the ‘m-image’, presented in the upper part
of Fig. 5, still represents 15% of the maximum
Bragg intensity at an in-phase energy. The equivalent ratio in the oscillating case is better than 2%.
The oscillating profile of Fig. 5 also shows a
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S. Dorel et al. / Surface Science 446 (2000) 294–300
clear enhancement of the instrumental resolution
power: the ring peak FWHM only represents onefifth of that of the peak of the ‘m-image’, fixing a
maximum value to the width of instrumental
origin. Thus, the oscillating technique allows us to
improve both the resolution power and the signalto-noise ratio. The latter can easily be explained
by just considering the improvement of the measurement statistics, thanks to our digital filter. The
former is not yet fully understood. We propose
that the applied Wehnelt oscillation can produce
a beam consisting of several electron populations:
most of them do not contribute to the intensity
oscillation, forming a zero-frequency background
and leading to the diffraction pattern of the
‘m-image’. These electrons would exhibit a wide
distribution of incident wave vectors, causing the
rather wide Bragg peak of upper Fig. 5. By contrast, the ‘oscillating’ electrons accelerated in the
gun would present a much thinner wave vector
distribution, as indicated by the lower part of
Fig. 5. The difference in magnitudes is an indication that the number of the latter population
would only represent 4% of the former population.
4. Discussion: what origin for the observed ring
structures?
Fig. 4. LEED diffraction patterns of an air-cleaved mica,
obtained at an energy of 132 eV. The ‘m-image’ (pixels m ) is
i
shown in (a), the ‘a-image’ (pixels a ) in (b). In the latter case,
i
the filtering method explained in Fig. 3 is used to compute each
image pixel, the grey level of which represents its oscillating
amplitude intensity at the given beam frequency (0.5 Hz). Bragg
spots are observed in both images, with the usual hexagonal
symmetry (e.g. black arrows). A series of rings is observed
around the spots of the ‘a-image’, exemplified by white arrows.
Note that because the electron beam impinges the surface at
normal incidence, the gun masks the specular spot.
Similar rings have been observed in several
physical contexts, using a very high sensitivity
LEED [10–12]. They are called ‘Henzler rings’.
The rings exhibited in Figs. 4 and 5 can be interpreted as resulting from the presence of periodic
defects at the crystal surface. These defects could
result from the intrinsic structure of the potassiumterminated sheet of the mica sample, since the
cleavage operation is in fact a rather rough process,
involving separating a potassium layer between
two half atomic layers: one on each side of the
crystal [9]. It could also arise from the presence
of impurities that would be adsorbed onto the
potassium layer during the in-air cleavage process.
In the absence of a chemical characterisation of
the surface, we cannot rule out this possibility.
The conventional LEED technique is usually
not suitable for investigating the defects located at
the topmost layers, because their contributions are
S. Dorel et al. / Surface Science 446 (2000) 294–300
299
Fig. 5. Comparison between conventional LEED (upper part) and oscillating LEED ( lower part). Both images on the left side are
formed from the same data, acquired in the same run. On the right side, the intensity profiles of the (11) spot are drawn along the
[11: ] direction. The profiles are averaged along a three-pixel-wide line. For the sake of clarity, the intensities have been arbitrarily
shifted by −47 (resp. −0.45) grey levels for the upper ( lower) profile. Notice the large difference in peak heights between the
‘m-image’ and the ‘a-image’.
smeared out by the larger ‘bulk’ contribution, due
to the finite penetration depth of low-energy
electrons. To circumvent this difficulty, we must
carefully tune the electron beam wave vector at an
out-of-phase condition. As a result, only the
diffracted intensity related to the defects of the
topmost layers will remain. As shown in Fig. 5,
we have shown that our oscillating LEED is able
to achieve such a fine tuning, which is impossible
using the conventional LEED.
Little is known about the defects of the mica
surface. The mica surface is often chosen as a
substrate because it is well accepted that it exhibits
a flat, crystalline surface after cleavage. The conventional LEED pattern ( Fig. 4a) seems indeed to
be the signature of a perfect long-range atomic
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S. Dorel et al. / Surface Science 446 (2000) 294–300
order. Previous LEED studies showed no evidence
of a fine structure, or ordering of the surface layers
[9,13], and high-resolution LEED investigations
have not been carried out on this system so far.
However, two recent studies have shed a new light
on this issue. Helium atom diffraction indicates
the presence of superstructures and steps [14].
Atomic force microscopy also shows the existence
of potassium domains, indicated by very smallheight steps (0.1 nm), on freshly air-cleaved crystals [15].
The rings that we observe in this work also
indicate the presence of defects. They allow us to
provide information about their characteristic distances: 2–10 lattice parameters. More work is
needed to elucidate which atomic species is responsible for the observed diffraction patterns, and
how many sites are involved in the process.
5. Conclusions
To summarise, we have presented a novel experimental approach based upon a simple LEED
device — a three-grid commercial optics —, associated with a modulation of the electron beam
current. A real-time image processing allows the
production of full-size diffraction images with a
high resolution, in less than 1 min. Thanks to this
method, we have been able to observe fine diffraction structures, such as Henzler rings, in an aircleaved surface of mica. They indicate the presence
of defects at the surface on the scale of 1–5 nm.
Acknowledgements
This work has benefited from fruitful discussions with M. Bernheim, C. Henry, C. Noguera,
S. Ravy, and D. Spanjaard. We thank ISMANS
for supporting this work.
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