Reflection high-energy electron diffraction oscillations on rotating substrates
W. Braun, H. Möller, S. R. Johnson, and Y.-H. Zhang
Citation: Journal of Vacuum Science & Technology B 17, 474 (1999); doi: 10.1116/1.590579
View online: http://dx.doi.org/10.1116/1.590579
View Table of Contents: http://scitation.aip.org/content/avs/journal/jvstb/17/2?ver=pdfcov
Published by the AVS: Science & Technology of Materials, Interfaces, and Processing
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Reflection high-energy electron diffraction oscillations
on rotating substrates
W. Brauna)
Center for Solid State Electronics Research and Department of Electrical Engineering,
Arizona State University, Tempe, Arizona 85287-6206

H. Möller
Fraunhofer-Insitut für Integrierte Schaltungen-A, D-91058 Erlangen, Germany

S. R. Johnson and Y.-H. Zhang
Center for Solid State Electronics Research and Department of Electrical Engineering,
Arizona State University, Tempe, Arizona 85287-6206

~Received 22 October 1998; accepted 18 December 1998!
We compare different methods to measure reflection high-energy electron diffraction oscillations on
rotating substrates. The best signal-to-noise ratio as well as the highest accuracy is obtained by
measuring the full width at half maximum of the specular spot perpendicular to the surface. The
accuracy of the method is well within 1% and offers a practical way to accurately determine growth
rates for device fabrication. © 1999 American Vacuum Society. @S0734-211X~99!04502-3#

I. INTRODUCTION
Although reflection high-energy electron diffraction
~RHEED! has always been a popular characterization
method in molecular beam epitaxy ~MBE!,1 the number of
studies investigating RHEED with substrate rotation is limited. This is mainly due to the high noise levels introduced
by mechanical vibrations and the periodic modulation of the
signal with the rotation frequency and its harmonics.2
Whereas azimuthal scanning techniques3 allow access to almost the entire upper half of reciprocal space, the data in
these measurement modes are updated only once per revolution. Azimuthal scans are therefore not suitable for the measurement of growth oscillations due to the layer-by-layer
growth of the crystal. The only part of the diffraction pattern
that is visible continuously during rotation is the ~00! rod.
The specularly reflected spot moves up and down along this
rod during rotation depending on substrate wobble and miscut. Its intensity typically varies about three orders of magnitude during one rotation for a nongrowing surface.4 In addition, both the phase and the amplitude of RHEED intensity
oscillations are strong functions of the azimuthal5 and
polar6–8 angles of the electron beam. This leads to ill-defined
growth frequencies and beating in intensity oscillation measurements.
In one approach, the substrate is therefore rotated at high
speeds, resulting in an averaging of these variations on a
timescale much smaller than the growth oscillation period.9
This method works well from a diffraction point of view, but
leads to excessive wear of the rotation drive and has not been
widely adopted. A different method uses a spot tracking algorithm combined with numerical filtering techniques to determine the specular spot size and measure its variations during growth.10 The signal in this case is quite noisy and a
narrow filter window needs to be applied to determine the
a!

Current address: Paul-Drude-Institut für Festkörperelektronik, Hausvogteiplatz 5-7, D-10117 Berlin, Germany; electronic mail: braun@pdi-berlin.de

474

J. Vac. Sci. Technol. B 17„2…, Mar/Apr 1999

growth frequency, which means that the growth frequency
has to be known quite accurately before the measurement.
The use of the specular spot size or full width at half maximum ~FWHM!, though, is advantageous, since this signal
typically varies by not more than one order of magnitude,
allowing simple and fast processing of the digitized data.
Also, the spot size does not vary as much as its intensity with
changing diffraction conditions for a given static surface.
In this article, we extend this approach by making use of
the strongly anisotropic sensitivity of RHEED parallel and
perpendicular to the beam along the surface. Instead of measuring the total spot size, we study its FWHM perpendicular
to the surface along the ~00! beam. Due to the small angle
the Ewald sphere makes with the ~00! rod, the resulting signal is already amplified by approximately a factor of cot u,
where u is the angle the electron beam makes with the
sample surface. This greatly reduces the noise levels. In addition, the FWHM algorithm already compensates for substrate miscut and wobble without having to resort to twodimensional spot tracking algorithms. Finally, phase-locked
substrate rotation results in improved accuracy through the
inclusion of satellite peaks in the measurement.
II. EXPERIMENTS AND DISCUSSION
The experiments were performed in a VG V80 MBE system using the standard right angle substrate manipulator and
2 in. GaAs ~001! substrates. The substrate rotation motor was
replaced by a phase-locked dc motor synchronized to the
timebase the RHEED charge coupled device ~CCD! camera
was using. The CCD camera and the PC-based data acquisition system11 allowed an acquisition rate of 50 Hz, twice that
of a standard video frame rate. The RHEED gun was the
standard VG type. For the measurements during rotation, the
RHEED intensities were measured along a line perpendicular
to the substrate surface through the specular spot.
Figure 1 shows a comparison of the data from three different measurement methods. The top line represents the tra-

0734-211X/99/17„2…/474/3/$15.00

©1999 American Vacuum Society

474

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475

Braun et al.: RHEED oscillations on rotating substrates

FIG. 1. GaAs-on-GaAs RHEED oscillation signals obtained by three different measurement methods for identical growth conditions. Top curve: Integrated specular spot intensity, nonrotating; center curve: integrated intensity
from measurement line along the ~00! streak, rotating; bottom curve:
FWHM of the specular spot along ~00!, rotating.

ditional measurement of the integrated spot intensity during
growth without substrate rotation. The center and bottom
traces were processed from the same linescan along the ~00!
streak. In the center curve, the intensity along the line was
integrated, whereas the bottom curve shows the FWHM
along the line. Compared to the signals obtained during rotation, the top trace shows stronger damping. The difference
in the damping rates can be explained by variations of the
growth rate along the probed surface area in nonrotating
growth.12 This type of damping should be reduced during
rotation since the growth rate is averaged across the wafer.
For the integrated intensity during rotation, however, the
noise level also increases strongly, resulting in about the
same number of usable oscillations until the signal vanishes
in the noise. The FWHM signal, on the other hand, shows a
good signal-to-noise ratio, and the crossover between signal
and noise is reached after typically twice the number of oscillations compared to the nonrotating intensity signal.
Another important factor for the measurements on rotating substrates is the suppression of the rotation frequency in
the signal. The dashed lines in Fig. 1 indicate the period of
the growth oscillations. The fourfold rotational symmetry of
the cubic crystal structure underlying the GaAs ~001! surface
results in a modulation of the rotating intensity signal ~center
curve!, coinciding with the growth frequency roughly every
11 growth oscillations. This component with a slightly
higher frequency is also present in the FWHM signal, but in
contrast to the intensity data there is also a strong peak at
each marker line. In the intensity measurement, minima at
the dashed line positions are weak if they do not coincide
with the rotation minima. This means that the suppression of
the rotation frequency and its harmonics is stronger in the
FWHM measurement.
The difference can be more clearly visualized in frequency space. The Fourier transform of the measurements in
Fig. 1 are shown in Fig. 2. The solid line represents the

475

FIG. 2. Comparison of the Fourier spectra ~power spectral density, PSD!
obtained by transforming the three signals in Fig. 1. The results are normalized to the growth frequency peak. The solid line corresponds to the nonrotating integrated specular spot intensity, the dashed line to the integrated line
intensity during rotation, and the dotted line to the FWHM of the specular
spot along ~00!.

nonrotating intensity signal, the dashed line is from the rotating intensity signal, and the dotted line is the transform of
the rotating FWHM signal. All traces are normalized to the
magnitude of the growth oscillation peak maximum. The
fourfold rotation frequency peak is 10 times stronger for the
intensity measurement during rotation compared to that of
the FWHM measurement. In addition to the strong rotation
frequency suppression, the FWHM measurement also has the
best frequency resolution, measured by the FWHM of the
growth oscillation peak. The values are 0.027 Hz for nonrotating intensity, 0.021 Hz for rotating intensity, and 0.013 Hz
for rotating FWHM. The width of this peak is affected by
damping and noise of the time space signal and by the duration of the measurement. The measurement time for all three
curves was identical. The broadening of the nonrotating intensity peak is mainly due to the strong damping of the
signal.13 Based on the present data, we cannot unambigu-

FIG. 3. FWHM signals taken perpendicular and parallel to the substrate
surface at different positions along the streak. The substrate is not rotating.
The positions of the measurement lines are shown in the inset of Fig. 4.

JVST B - Microelectronics and Nanometer Structures

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476

Braun et al.: RHEED oscillations on rotating substrates

FIG. 4. Comparison of the rotation frequency peak magnitudes for the different FWHM signals measured along the lines given in the inset. The
measurement perpendicular to the surface ~trace 7! results in the largest
peak.

476

parallel to the surface are more strongly damped, combined
with an initial increase for curves 1 and 2. These amplitude
variations should broaden the frequency peaks. The short
measurement time of 40 s, however, results in uncertaintyrelation limited peak widths in Fig. 4 and, with the exception
of line 6, these differences cannot be resolved. It is clear,
however, that the absolute noise levels for the different measurement directions are comparable and therefore the signalto-noise ratio of curve 7 is better due to its larger absolute
signal, even despite the fact that the spot is split in this direction.
In conclusion, we have demonstrated that the measurement of the specular spot width perpendicular to the surface
allows growth oscillation frequency determination on rotating substrates with dramatically increased accuracy. This is
due to a strong suppression of rotation-related frequency
contributions, an intrinsic signal amplification due to the
scattering geometry, and a resulting increase of the signal-tonoise ratio.
ACKNOWLEDGMENT

ously decide whether the difference between the two rotating
signal peaks is due to the different noise levels or due to
differences in damping.
The accuracy of the rotating measurement modes can be
further increased by using phase-locked substrate rotation.
This means that each substrate rotation corresponds exactly
to a certain number of measurement points. The satellite
peaks to the growth frequency are then spaced at an exactly
known distance and can be included in the position determination as well, thereby increasing the accuracy of the
measurement.14 For long measurements, accuracies within
0.5% can be achieved.
To study the dependence of the FWHM measurement on
the measurement direction across the specular spot, FWHM
measurements of GaAs homoepitaxy were performed parallel and perpendicular to the surface on a nonrotating substrate. The time–space results are shown in Fig. 3. The geometry of the measurement lines as well as the frequency–
space results are shown in Fig. 4. Since the Ga shutter was
magnetically coupled, the specular spot moved left during
growth, as seen in the inset of Fig. 4, resulting in large noise
levels before and after growth in trace 7.
The results in Fig. 3, plotted on the same scale, clearly
show the intrinsic amplification of the signal measured perpendicular to the substrate surface. In addition, the signals

Part of this work was supported by a DARPA program
~Contract No. MDA972-95-1-0016! managed by G. Pomrenke.
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J. Vac. Sci. Technol. B, Vol. 17, No. 2, Mar/Apr 1999

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