Use of spectroscopic ellipsometry for feedback control during the growth of thin AlAs
layers
M. Beaudoin, S. R. Johnson, M. D. Boonzaayer, Y.-H. Zhang, and B. Johs
Citation: Journal of Vacuum Science & Technology B 17, 1233 (1999); doi: 10.1116/1.590728
View online: http://dx.doi.org/10.1116/1.590728
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Published by the AVS: Science & Technology of Materials, Interfaces, and Processing
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Use of spectroscopic ellipsometry for feedback control during the growth
of thin AlAs layers
M. Beaudoin, S. R. Johnson, M. D. Boonzaayer, and Y.-H. Zhanga)
Center for Solid State Electronics Research, Department of Electrical Engineering,
Arizona State University, Tempe, Arizona 85287-6206

B. Johs
J. A. Woollam Co., Inc., 645 M Street, Lincoln, Nebraska 68508

~Received 5 October 1998; accepted 26 February 1999!
Spectroscopic ellipsometry ~SE! is an accurate in situ method for determining the composition and
thickness of III–V semiconductor layers during growth. In order to achieve this control, an optical
constant database is used to compare the modeled and experimental ellipsometric data. This
procedure is very effective for controlling thickness and composition when the film has been
growing for some time but is usually unreliable until several minutes into the growth ~corresponding
to ;50 nm!. To use SE for the control of thinner layers ~1–20 nm!, a different approach has to be
used. A new strategy is proposed which consists in looking at the raw SE signal in a limited
wavelength range where the signal varies almost linearly with the film thickness. For AlAs grown
on GaAs, it is found the phase part of the SE signal for light between 2.5 and 2.8 eV varies nearly
linearly with the AlAs thickness. A series of AlAs/GaAs multiquantum well structures are grown
and analyzed. The thickness determined by this use of the ellipsometric data are in close agreement
with independent thickness measurements obtained from high resolution x-ray diffraction. © 1999
American Vacuum Society. @S0734-211X~99!06003-5#

I. INTRODUCTION
Many high speed electronic and optoelectronic devices
rely on active regions whose thickness is on the order of
monolayers. To integrate devices such as resonant tunneling
diodes ~RTD!1,2 into appropriate circuit architectures, a high
run to run precision is required.3 In fact, for RTDs, even
monolayer discrepancies in the barrier layer thicknesses can
lead to unacceptably high variations in run to run device
performance.3 In molecular beam epitaxy ~MBE!, the usual
method used to control thin layers is with reflection high
energy electron diffraction ~RHEED! oscillations. Until very
recently however,4,5 it was very difficult to obtain RHEED
oscillations during substrate rotation. This prompted Zinck
et al.3,6 to use the photoemission oscillation ~PEO! technique
developed by Eckstein and co-workers7,8 because PEO can
be easily acquired under substrate rotation. One drawback to
both RHEED and PEO is that they can only be observed
under layer by layer growth conditions and both are poorly
suited to the control of thicker layers. A more universal feedback technique is therefore desirable.
Spectroscopic ellipsometry ~SE! is an accurate method for
measuring the thickness and composition of growing semiconductor films.9–12 In MBE, SE has been successfully used
in a feedback loop to grow Fabry–Perot cavities,10 latticematched InGaAs/InP11 and, recently, a complete resonant
cavity enhanced photodetector ~RCEPD!.12 In SE, the signal
is collected during growth and analyzed in real time using
previously acquired optical constant database ~OCDB! in order to extract the film’s thickness and composition. This procedure is very effective when the film has been growing for
a!

Corresponding author; electronic mail: yhzhang@asu.edu

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J. Vac. Sci. Technol. B 17„3…, May/Jun 1999

some time but is usually unreliable until several minutes into
the growth ~corresponding to approximately 50 nm! and cannot, therefore, be used to control very thin layers such as
quantum wells or the barrier layers of RTDs. It has, however,
two main advantages over RHEED and PEO: ~1! it is independent of the growth mode and ~2! it can be used for control of thick devices. To extend the use of SE to the control
of much thinner layers, an approach different from the one
based on comparison with an OCDB needs to be developed.
In this article we propose to consider the raw SE data in a
limited wavelength range where the SE parameters vary
close to linearly with the film thickness. A series of GaAs/
AlAs multiquantum well structures ~MQW! were grown in
order to independently assess the layer thicknesses by x-ray
diffraction ~XRD! rocking curves. A sample consisting of
11.7 nm AlAs barriers was used to calibrate the technique.
An algorithm is then developed and used to measure the
thickness of two other samples with different AlAs barrier
thicknesses. These thicknesses are in excellent agreement
with those directly determined from independent XRD measurements.
II. EXPERIMENT
The experiments were carried out on a DCA™ molecular
beam epitaxy ~MBE! chamber equipped with ellipsometer
ports as has been described previously.10–12 The SE signal is
given by the ratio of the complex reflectivities r p and r s
where the subscripts p and s refer to light polarized parallel
and perpendicular to the plane of incidence, respectively,

r5

r p u r pu i~ d 2d !
5
e p s 5tan~ C ! e iD .
r s u r su

0734-211X/99/17„3…/1233/4/$15.00

©1999 American Vacuum Society

~1!
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Beaudoin et al.: Use of spectroscopic ellipsometry for feedback control

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TABLE I. AlAs thickness measurement using the variation of D parameter in
the range between 2.5 and 2.8 eV. The last column gives the average thickness and standard deviations for the 13 wavelengths in the range of 2.5–2.8
eV. This column clearly shows that the algorithm is able to determine thickness precisely.
HRXRD
thickness ~nm!

Growth time
~s!

Time base
thickness ~nm!

Thickness from
SE D ~nm!

11.760.2
5.560.3
3.060.4

200
100
50

¯
5.9
2.9

¯
5.4960.08
2.5660.05

The SE signal is most conveniently expressed mathematically by an amplitude, tan~C!, and phase, D, difference between the p and s components of the electric field. The C
and D SE parameters are sensitive to the structure ~thickness,
composition, etc.! and the optical constants of the growing
film.13 The signal is acquired with a J. A. Woollam M88™
ellipsometer in the rotating analyzer configuration ~88 wavelengths ranging from 277 to 765 nm! using their WVASE™
control and acquisition software.
A series of three GaAs/AlAs samples were grown by
solid source MBE using an As4 overpressure. The samples
were grown on semi-insulating GaAs and consisted of a
GaAs buffer layer, a 100 nm AlAs layer, and an 100 nm
GaAs layer followed by a 10 period GaAs/AlAs multiple
quantum well ~MQW! structure. Each well in the MQW was
nominally kept at 33.0 nm while the AlAs barriers were
grown with different growth times as reported in Table I.
The growths were carried out at a substrate temperature of
600 °C, as controlled by optical band edge thermometry.14,15
The 100 nm AlAs and GaAs layers were grown under conventional OCDB based SE feedback control.10–12 The MQW
structures were grown under time-based control and SE was
used to monitor the growth. The sample structures were assessed by double-crystal x-ray diffraction rocking curves and
analyzed by simulations using dynamical diffraction
theory.16

FIG. 1. Variation of the amplitude parameter, Y, of the SE signal with time
during the growth of a GaAs/AlAs MQW structure. The SE data is first
acquired during the growth of a 100 nm AlAs layer and a 100 nm GaAs
layer before the MQW growth.

shows an additional modulation. The additional modulation
comes from the fact that longer wavelength light penetrates
deeper in the film and ‘‘sees’’ more periods whereas the
shorter wavelengths are more sensitive to the film thickness
near the surface. In fact, for the shortest wavelength light
shown in Fig. 1 ~3.5 eV!, the optical path is such that an
interference fringe is visible in the AlAs layer. Since the
signal at 2.6 eV appears nearly linear during the growth of
the AlAs layer, a simple thickness determination algorithm
may be developed.
Figure 2 shows the XRD rocking curve for the sample
structure shown in the inset. Also shown, shifted down for
clarity, is the result of a fit based on dynamical diffraction
theory.16 The agreement between the experimental and simulated patterns are excellent. The MQW structure satellite
peaks and the shorter period thickness interference fringes

III. RESULTS AND DISCUSSION
Figure 1 shows the time variation of the C parameter for
three wavelengths of light ~expressed in eV! during the
growth of a sample with 11.7 nm AlAs barrier layers. The
sample cross-section is shown in the inset of Fig. 2. The last
GaAs cap layer, which should show a maximum in the C
signal, is not seen as the WVASE buffer filled up and data
collection stopped. The 2.6 eV C curve shows a nearly linear
down sloping segment during the growth of each AlAs barrier. The first AlAs barrier, grown on top of the 100 nm
GaAs layer begins at a lower value than the remaining nine
barriers grown on top of a thinner GaAs quantum well. Its
slope does appear to be very close to that of the last nine
barriers however. Figure 1 also shows the different periods
of the interference fringes caused by the different optical
paths for light of different wavelengths. During the growth
of the MQW structure, the C signal is very periodic at the
shorter wavelengths while the longer wavelength signal

FIG. 2. X-ray rocking curve of a GaAs/AlAs MQW structure. The inset
shows the sample structure. The bottom curve is the simulated pattern from
dynamical diffraction theory and is shifted down for clarity.

J. Vac. Sci. Technol. B, Vol. 17, No. 3, May/Jun 1999

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Beaudoin et al.: Use of spectroscopic ellipsometry for feedback control

due to the 100 nm AlAs and GaAs layers are clearly visible
in the experimental pattern and exactly reproduced by the
simulation. Extracting the thickness of the AlAs and GaAs
layers of the MQW structure is simplified by the fact that
only binaries are used in each layer. The splitting between
the zeroth order satellite peak and the main GaAs Bragg
peak, which gives the average MQW lattice constant, can
thus be used directly to compute the AlAs/GaAs thickness
ratios. This was done using 0.56535 and 0.56618 nm for the
lattice constants of GaAs and AlAs, respectively; these are
widely used values. This analysis has been done on the three
samples presented here. In order to use the thickness algorithm meaningfully, the GaAs quantum well thicknesses had
to be kept constant for the entire series. The uncertainty in
the total AlAs1GaAs thickness for each period is 0.1 nm as
determined visually from the fit using dynamical diffraction
theory. For very thin AlAs layers, the superlattice zeroth order sattelite peak nearly coincides with the substrate peak;
dynamical theory fits with different thickness ratios were
qualitatively compared with the experimental patterns to determine the uncertainties in AlAs thickness. The XRD results
with their associated uncertainties are reported in Table I.
Figures 3~a! and 3~b! show blowups of the time variations
of the D and C SE parameters for the same three wavelengths shown in Fig. 1. The blowups cover the growth of
three AlAs barriers as shown on the figures by the doubleended arrows. In order to develop an algorithm for thickness
determination, we chose to concentrate on wavelength
ranges where the SE signal showed a nearly linear variation.
Figure 3 show even more clearly that long wavelength light
displays interference fringes which span several alternating
layers ~i.e., long wavelength light sees deeper below the surface!. On the other hand, the short wavelength light, although periodic with the layer thicknesses, shows elaborate
interference oscillation shapes. The 2.6 eV light shows a
nearly linear dependence on time ~thickness! with a more
pronounced variation in its D parameter than in its C parameter; hence, the D variation is more sensitive to thickness
variation than the corresponding C variation. With further
analysis, we determined that light between 2.5 and 2.8 eV
showed a nearly linear response with film thickness and was
easy to analyze. One should note ‘‘glitches’’ on either side of
the AlAs layers where both the D and C parameters are
constant in time. These glitches were intentionally introduced with growth interrupts in order to highlight the AlAs
layers and simplify the analysis.
Figure 4 shows the variation of D with AlAs thickness for
the 11.7 nm AlAs barriers sample for light between 2.5 and
2.8 eV. This range represents 13 of the 88 wavelengths available with the M88 ellipsometer. The total AlAs thickness is
determined from XRD and a constant growth rate is assumed
throughout the AlAs layer growth; the thickness axis is
therefore a simple translation of time to thickness and its
magnitude is only meant to be valid over the AlAs interval.
Assuming a constant growth rate neglects the effect of shutter transients which we expect to be small in this case anyway. Figure 4 clearly shows the effect of the growth inter-

1235

FIG. 3. Time variation of the SE parameters ~a! D and ~b! C over a few
AlAs layers for three wavelengths of light. The variation of both D and C
are nearly linear for light of 2.6 eV.

rupts and the nearly linear variation of D with thickness
during the AlAs growth. The D variation was modeled with a
quadratic, as a function of thickness x, for each of the 13
wavelengths included in the interval:
D5cx 2 1bx1D 0 .

~2!

One has to be careful when extending the results of the quadratic fits to determine the thickness of other samples. In
fact, this numerical algorithm is only expected to be valid for
AlAs layers grown on GaAs layers of the same thickness as
those grown here! In general, the quadratic relationships are
expected to depend on the initial D 0 value. As the first AlAs
layer in Fig. 1 shows, this variation appears almost independent of its starting value but more work will be required to
clarify this point and determine if a universal algorithm is
possible or if a different algorithm will need to be developed
for each different structure that one wishes to grow. Even in
the case of our nominally identical structures, we found a 1%
variation in the initial D 0 values for MQW samples grown
under time base control.

JVST B - Microelectronics and Nanometer Structures

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Beaudoin et al.: Use of spectroscopic ellipsometry for feedback control

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idea. Samples with varying GaAs quantum well thicknesses
will also be used in order to verify the sensitivity of Eq. ~3!
to variations in D 0 .
IV. CONCLUSION
An algorithm has been proposed which promises to extend the applicability of spectroscopic ellipsometry to thickness measurements in layers as thin as 3 nm, such as those
found in quantum wells or barriers. The algorithm uses the
initial variation of the raw ellipsometric signal in a range of
wavelengths where the signal is nearly linear. For AlAs barriers grown on GaAs, the proposed algorithm gave thickness
results in excellent agreement with independent assessments
by x-ray diffraction. More investigation is required in order
to determine if the proposed algorithm is universal or if it is
material and structure specific.
FIG. 4. Variation of D at several wavelengths with AlAs layer thickness for
one period of a MQW sample with 11.7 nm AlAs barriers sandwiched
between GaAs layers. Vertical arrows show the growth interruptions at both
interfaces. At all wavelengths, D varies nearly linearly with thickness although a quadratic correction improves the fit ~not shown!.

ACKNOWLEDGMENTS
This work was supported by DARPA under Contract No.
MDA 972-95-1-0016 managed by Lt. Col. Gernot S. Pomrenke.
1

Equation ~2! shows that D will vary in a prescribed way
with the AlAs film thickness. To subtract out the 1% variations in D 0 , we invert Eq. ~2! using d D5D2D 0 :
x5

SA

D

b2 dD
b
2 ,
22
4c
c
2c

~3!

where x is the AlAs thickness while b and c are fixed from
the fit to the calibration sample ~11.7 nm AlAs barriers!.
Equation ~3! can now be applied to the other two samples.
The results are reported in Table I where they are also compared to the XRD results. As Table I shows, the agreement is
excellent. The last column of Table I shows that the standard
deviation in the 13 wavelengths average is smaller than the
uncertainty of the independent XRD thickness measurements. In this case, the advantage of using SE instead of time
base control is not clear. What is clear however is that the
idea of using the variation of D does work. In the next series
of planned experiments, the Al cell temperature will be varied between samples so that time base control becomes more
difficult and the sample structures will be designed to minimize the uncertainty in XRD measurements. These experiments will constitute a more stringent test of the proposed

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J. Vac. Sci. Technol. B, Vol. 17, No. 3, May/Jun 1999

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