Accurate growth rate determination on rotating substrates using electron diffraction
dynamics
W. Braun, H. Möller, and Y.-H. Zhang
Citation: Applied Physics Letters 74, 138 (1999); doi: 10.1063/1.122975
View online: http://dx.doi.org/10.1063/1.122975
View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/74/1?ver=pdfcov
Published by the AIP Publishing
Articles you may be interested in
Substrate preparation and low-temperature boron doped silicon growth on wafer-scale charge-coupled devices
by molecular beam epitaxy
J. Vac. Sci. Technol. B 20, 1170 (2002); 10.1116/1.1477200
Enabling electron diffraction as a tool for determining substrate temperature and surface morphology
Appl. Phys. Lett. 79, 3065 (2001); 10.1063/1.1416477
Growth of ZnSe and ZnS films on Si(111) substrates with a nitrogen surface treatment
J. Vac. Sci. Technol. B 17, 1259 (1999); 10.1116/1.590735
Reflection high-energy electron diffraction oscillations on rotating substrates
J. Vac. Sci. Technol. B 17, 474 (1999); 10.1116/1.590579
Reflection high-energy electron diffraction during substrate rotation: A new dimension for in situ characterization
J. Vac. Sci. Technol. B 16, 1507 (1998); 10.1116/1.589976

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
209.147.144.10 On: Wed, 11 Feb 2015 19:41:01

APPLIED PHYSICS LETTERS

VOLUME 74, NUMBER 1

4 JANUARY 1999

Accurate growth rate determination on rotating substrates
using electron diffraction dynamics
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

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

~Received 24 August 1998; accepted for publication 27 October 1998!
Reflection high-energy electron diffraction oscillation frequencies are determined by measuring the
width of the specular spot perpendicular to the surface during substrate rotation. Substrate rotation
and data acquisition are phase locked to obtain exact rotation frequencies, allowing the inclusion of
satellite peaks in the measurement. The method has a typical accuracy of well below 1% and
provides a practical means to measure growth rates on rotating substrates. © 1999 American
Institute of Physics. @S0003-6951~99!02301-3#

Reflection high-energy electron diffraction ~RHEED! intensity oscillations are routinely used for growth rate determination in molecular beam epitaxy ~MBE!. Usually, these
oscillations are measured with the substrate held at a fixed
position. The accuracy of this approach is limited by the
usually strong damping of the oscillations.1 Since much of
this damping is due to flux nonuniformities along the surface
area probed by the RHEED beam,2 measurements during rotation have the potential for greater accuracy. Attempts to
measure RHEED oscillations during substrate rotation,3–5
however, have been hampered by the significant noise levels
introduced by mechanical vibrations of the substrate
manipulator.3 Also, the intensity of the specularly reflected
spot is a very strong function of the azimuthal angle,6 requiring detectors with a very high dynamic range. In addition,
substrate misorientation and wobble complicate the measurement, since the phase of the intensity oscillations is a strong
function of both the azimuthal7 and the polar angle8–10 of the
incident beam. Previous approaches have therefore relied on
very high rotation speeds4 or spot tracking algorithms combined with numerical filtering.5
In this letter, we demonstrate a method that significantly
increases the accuracy of the growth rate determination by
measuring the full width at half maximum ~FWHM! of the
specular spot perpendicular to the substrate during sample
rotation. Our experiments indicate reliable results for substrate miscut below 0.5°, wobble below 2° and visibility of
the specular spot for most of the rotation. The imaging sensor and the substrate rotation are phase locked to the same
timebase, allowing us to exactly fix the rotation frequency in
the measured data. We can therefore include the positions of
satellite peaks in the frequency spectrum to improve the accuracy.
a!

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

The experiments were performed using a VG V80 MBE
chamber equipped with the standard RHEED gun and the
standard right angle sample manipulator. The substrate rotation was driven by a specially designed phase-locked motor
synchronized to the same timebase as the charge coupled
device ~CCD! camera that recorded the RHEED signal. The
RHEED image processing system11 was capable of measuring at a rate of 50 Hz, leading to twice the frequency resolution compared to standard CCD-based systems. GaAs
growth was monitored at a sample temperature of 560 °C
measured by a Pyritte pyrometer. The measurement geometry together with a plot of the raw signal are shown in Fig.
1. The RHEED intensity is measured along a line perpendicular to the substrate surface through the center of the
specular spot. During rotation, the specular spot follows a
very narrow elliptical trace determined by the added contributions of substrate wobble and sample miscut. Usually, the
approximation of this movement by a straight line is good
enough for an accurate determination of the spot dimension
along the surface normal.
The line profiles plotted as a function of time are shown
in the right panel of the figure. The oscillation signal is then
obtained by measuring the FWHM of the peak in each trace
with a subpixel-accuracy interpolation algorithm. The resulting trace of specular spot FWHM as a function of time is
shown in Fig. 2. For low substrate wobble and misorienta-

FIG. 1. Measurement geometry and raw signal measured from a rotating
substrate. Growth oscillations are measured by determining the FWHM of
the specular spot perpendicular to the substrate surface.

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
0003-6951/99/74(1)/138/3/$15.00
138
© 1999 American Institute of Physics
209.147.144.10 On: Wed, 11 Feb 2015 19:41:01

Appl. Phys. Lett., Vol. 74, No. 1, 4 January 1999

Braun, Möller, and Zhang

139

FIG. 2. FWHM of the specular spot perpendicular to the substrate as a
function of time in units of CCD pixels. Growth starts at 20 s and terminates
at 80 s.
FIG. 3. Frequency spectra of FWHM measurements at three different
growth rates, but identical rotation frequency. The measurement time was
tion, the signal is usually good enough to directly count the
180 s.
oscillations. Additional experiments ~not shown! indicate
that the signal-to-noise ratio of the FWHM signal perpenerror as An with the number n of satellite positions meadicular to the sample surface is much better than both the
sured. At least four satellites are usually discernible, resultintensity signal integrated along the line or the FWHM signal
ing in an improvement by more than a factor of 2 and a final
parallel to the sample surface. This is mainly due to the
accuracy of below 0.5%. For the data in Fig. 3, this resolumuch higher transfer width12 of RHEED along the beam dition corresponds to about 0.2° in the Ga cell temperature,
rection compared to perpendicular to the beam. It is therefore
which is getting close to the absolute temperature resolution
advantageous to measure only perpendicular to the surface
of MBE systems and which is certainly good enough to caliinstead of tracking the spot size in two dimensions.5 Theobrate even sensitive structures such as vertical cavity surface
retical treatments of the ~01! spot size as a function of step
emitting lasers.
density13 indicate a strong increase in the FWHM perpenUsually, the rotation frequency is an adjustable paramdicular to the substrate with increasing step density. Qualitaeter in MBE, the case of the growth frequency being an exact
tively similar results may be expected for the specular spot.
multiple of the rotation frequency can therefore be avoided.
It is therefore possible that the FWHM of the specular spot
If the frequency spectrum is ambiguous, a change in the
perpendicular to the substrate is related to the surface step
rotation frequency by 32 clearly separates the peaks. The
density in a much more direct way than the intensity of the
method works best with the rotation frequency and the
specular spot.9
growth frequency being within the same order of magnitude.
In contrast to the intensity signal, the FWHM does not
If the rotation frequency is too low, the effects of growth rate
change by orders of magnitude in one revolution.6 The signal
nonuniformity across the wafer broaden the peak. The specshows very little damping. Instead of the signal level droptra of three different measurements are shown in Fig. 4. The
ping at constant noise level as in standard intensity oscillasolid line represents the Fourier spectrum of the specular
tion measurements, the noise level increases at constant sigspot intensity signal without rotation, the dashed line is the
nal level. Both properties together with the flat baseline of
result from the integrated intensity signal along the measurethe signal in Fig. 2 make these measurements ideal candidates for Fourier transform. The transformed signals for
three measurements are superimposed in Fig. 3. At a fixed
rotation frequency, the growth rate was set at three different
values in the measurements. The comparison of the power
spectra clearly reveals the structure of the data in frequency
space. The rotation frequency peaks at 0.16̄ Hz and its harmonics remain unaffected by the change in growth rate. The
growth frequency exhibits a set of distinct satellites on both
sides at distances of multiples of the rotation frequency.
Measuring at 50 Hz sampling frequency, the FWHM of the
growth frequency peak is usually very close to the limit set
by the frequency–time uncertainty relationship, being approximately equal to the data point spacing in frequency
space. For measurement times above 150 s, this results in a
FWHM of around 1% of the absolute value for growth freFIG. 4. Comparison of the growth frequency peaks ~normalized! for three
different measurement methods: ~solid line! specular spot intensity, no roquencies around 1 Hz.
tation, ~dashed line! integrated intensity along the line perpendicular to the
Due to the phase-locked rotation, the rotation frequency
substrate through the specular spot during rotation, ~dotted line! FWHM
values in the power spectrum are exact. One can therefore
along
perpendicular
to the substrate through the specularDownloaded
spot during to IP:
This article is copyrighted as indicated in the article. Reuse of AIP content is subject
to the
theline
terms
at: http://scitation.aip.org/termsconditions.
measure the positions of the satellites as well, reducing the
rotation.

209.147.144.10 On: Wed, 11 Feb 2015 19:41:01

140

Appl. Phys. Lett., Vol. 74, No. 1, 4 January 1999

ment line perpendicular to the substrate and the dotted line is
the FWHM signal. The latter two were obtained from the
same measurement using 0.25 Hz rotation. In all three cases,
the growth interval was 160 s long.
The FWHM of the frequency peak for the static intensity
measurement is 0.027 Hz. With rotation, the width decreases
to 0.021 Hz for the intensity and 0.013 Hz for the FWHM
signal. The measurement based on the FWHM perpendicular
to the sample surface is clearly superior, both in accuracy
and also in the ratio of the growth rate peak intensity to the
rotation peak intensity. The larger width for the nonrotating
measurement can be explained by the strong damping of
intensity oscillations.1 Much of this damping is due to
growth rate nonuniformities that are strongly reduced with
rotation. While it is well known that the phase of the intensity oscillations of the specular spot strongly varies with
azimuthal7 as well as polar angle,8–10 which would lead to a
broadening of the peak, the behavior of the specular spot
FWHM oscillation phase as a function of diffraction conditions is not well known. The strong difference of the peak
widths in Fig. 4 seems to imply that the FWHM of the specular spot perpendicular to the substrate is much less sensitive
to these variations. Further studies are needed to clarify this
point.

Braun, Möller, and Zhang

Part of this work was supported by a DARPA program
~Contract No. MDA972-95-1-0016! managed by G. Pomrenke.

1

J. E. Cunningham, R. N. Pathak, and W. Y. Jan, Appl. Phys. Lett. 68, 394
~1996!.
2
J. P. A. van der Wagt, K. L. Bacher, G. S. Solomon, and J. S. Harris, Jr.,
J. Vac. Sci. Technol. B 10, 825 ~1992!.
3
G. W. Turner and A. J. Isles, J. Vac. Sci. Technol. B 10, 1784 ~1992!.
4
J. P. A. van der Wagt and J. S. Harris, Jr., J. Vac. Sci. Technol. B 12, 1236
~1992!.
5
D. A. Collins, G. O. Papa, and T. C. McGill, J. Vac. Sci. Technol. B 13,
1953 ~1995!.
6
Z. Mitura and P. Maksym, Phys. Rev. Lett. 70, 2904 ~1993! and references therein.
7
J. Resh, K. D. Jamison, J. Strozier, A. Bensaoula, and A. Ignatiev, Phys.
Rev. B 40, 11799 ~1989!.
8
J. Zhang, J. H. Neave, P. J. Dobson, and B. A. Joyce, Appl. Phys. A:
Solids Surf. 42, 317 ~1987!.
9
W. Braun, L. Däweritz, and K. H. Ploog, Phys. Rev. Lett. 80, 4935
~1998!.
10
W. Braun, L. Däweritz, and K. H. Ploog, J. Vac. Sci. Technol. B 16, 2404
~1998!.
11
SAFIRE by VTS Schwarz/FhG Erlangen; vts.js@t-online.de
12
M. Henzler, Appl. Surf. Sci. 11/12, 450 ~1982!.
13
Y. Ma, S. Lordi, and J. A. Eades, Mater. Res. Soc. Symp. Proc. 399, 3
~1996!.

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
209.147.144.10 On: Wed, 11 Feb 2015 19:41:01