Real-time composition control of InAlAs grown on InP using spectroscopic
ellipsometry
M. Beaudoin, E. Grassi, S. R. Johnson, K. Ramaswamy, K. Tsakalis, T. L. Alford, and Y.-H. Zhang
Citation: Journal of Vacuum Science & Technology B 18, 1435 (2000); doi: 10.1116/1.591398
View online: http://dx.doi.org/10.1116/1.591398
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Real-time composition control of InAlAs grown on InP using
spectroscopic ellipsometry
M. Beaudoin,a) E. Grassi, S. R. Johnson, K. Ramaswamy, K. Tsakalis, T. L. Alford,
and Y.-H. Zhangb)
Center for Solid State Electronics Research and Department of Electrical Engineering, Arizona State
University, Tempe, Arizona 85287-6206

共Received 10 October 1999; accepted 11 February 2000兲
Spectroscopic ellipsometry 共SE兲 was shown to be an accurate in situ method for determining the
composition and thickness of III–V semiconductor layers during growth. In order to fully exploit
the potential of SE for real-time in situ control, one needs to acquire a database of optical constants.
In this article, we present the acquisition and parameterization 共both composition and temperature兲
of a fully dynamic database and its use in the real-time composition control of InAlAs grown on InP.
This is accomplished by acquiring SE data from growing films of different compositions, while the
temperature is controlled using feedback from band-gap thermometry. The layer compositions are
assessed by fitting high-resolution x-ray diffraction patterns with a simulation based on dynamical
diffraction theory. In order to improve the stability during real-time control, the database was
parameterized using a transfer function model. The parameterized database was then used, in real
time, during growth to control the Inx Al1⫺x As film composition 共x兲 to within ⫾0.003. © 2000
American Vacuum Society. 关S0734-211X共00兲05803-0兴

I. INTRODUCTION
Molecular-beam epitaxy 共MBE兲 has been widely used to
grow commercial wafers for electronic devices such as high
electron mobility transistors 共HEMT兲. It has also been used
to grow much more complicated optoelectronic devices such
as vertical cavity surface emitting lasers 共VCSEL兲1–3 and
other microcavity devices.4–6 In traditional MBE, growths of
such complicated structures with high reproducibility on a
day to day basis is very difficult. In order to improve the
growth reproducibility, substantial research effort has been
devoted to the development of in situ sensors capable of
providing real-time information about the growing film: temperature, composition, and layer thickness.6–15
Following the work of Aspnes,16,17 great effort has been
devoted to the use of spectroscopic ellipsometry 共SE兲 for
in situ monitoring and real-time control of growth. It has
been used with success to control, in a feedback loop, the
thickness18 and alloy composition19–21 of the growing films.
Moreover, in conjunction with other sensors, it has been
proven to yield improved reproducibility in the growths of
devices.6,7 SE based feedback control is implemented by
comparing the measured SE signal of a growing film to a
previously acquired database of optical constants 共OC兲,
which yields the composition and, provided that interference
fringes are present, the thickness of the film. If it is
parametrized,22,23 the precision of this database is improved
over that obtained by straight interpolation between experimental data points. For the composition control of ternary
compounds, such as AlGaAs, InGaAs or InAlAs, one of the
group III effusion cells is kept at constant temperature during
a兲

Current address: Bandwidth9, Inc., 46410 Fremont Blvd., Fremont, CA
94538-6409; electronic mail: mbeaudoin@bw9.com
b兲
Author to whom correspondence should be addressed; electronic mail:
yhzhang@asu.edu
1435

J. Vac. Sci. Technol. B 18„3…, MayÕJun 2000

the entire growth, while the difference between the target and
measured compositions is used to change the temperature of
the other cell.7,20 Hence, the accuracy of the control depends
on the accuracy of the database of optical constants against
which the growing film is compared. Since SE is surface
sensitive, it has been found that the optical constants of a
growing layer, which we call the ‘‘dynamic’’ OC, actually
differ from those of an ‘‘identical’’ layer just sitting at the
growth temperature 共under group-V overpressure兲 and which
we refer to as ‘‘static’’ OC.21 Also, because SE uses polarized light, the signal is sensitive to the crystal orientation of
the substrate; this dependence can be averaged out by taking
measurements under substrate rotation. In this article, we
present the acquisition, parameterization and validation of a
dynamic OC database for InAlAs alloys with compositions
near the lattice-matched condition to InP.

II. GROWTH AND ACQUISITION OF OC DATABASE
The experimental setup has been described
previously.18,19 We use a DCA™ MBE chamber equipped
with ellipsometer ports. Each port makes an angle of 75°
with the normal to the substrate and is equipped with a
BOMCO™ low birefringence window. On an MBE manipulator, samples are normally mounted with a surface normal at
a small angle with the rotation axis. During substrate rotation, this angle processes and is commonly referred to as
substrate wobble in MBE jargon. In the DCA™ machine,
this wobble is minimized through the use of three piezoelectric crystals in the substrate manipulator. The measured SE
signal, ␳, is given by

␳⫽

R P 兩 R P兩 i共 ␦ ⫺␦ 兲
⫽
e P S ⫽tan共 ⌿ 兲 e i⌬ ,
R S 兩 R S兩

0734-211XÕ2000Õ18„3…Õ1435Õ4Õ$17.00

©2000 American Vacuum Society

共1兲
1435

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1436

Beaudoin et al.: Real-time composition control of InAlAs

1436

FIG. 2. Symmetric 共004兲 high-resolution x-ray diffraction pattern of a structure consisting of five InAlAs films grown on InP. The bottom pattern is
from a simulation using dynamical diffraction theory and is shifted down for
clarity. These patterns are used to determine the compositions of the epitaxial layers grown during the acquisition of the optical constant database.

FIG. 1. Typical optical functions of InAlAs showing both the real 共Eps1兲 and
imaginary 共Eps2兲 parts. The solid lines are measured by spectroscopic ellipsometry while the dashed lines are from a parameterization using a transfer
function model.

where R P and R S are the reflection coefficients for light polarized perpendicular and parallel to the plane of incidence.
This is expressed mathematically by the amplitude, tan共⌿兲,
and phase, ⌬, difference between the p and s components of
the electric field. The ⌿ and ⌬ parameters are directly related
to the Fresnel coefficients of the material. A J. A. Woollam
M88™ ellipsometer and its GrowthManager™ 共GMan兲 software were used to measured ⌿ and ⌬ parameters as a function of wavelength 共88 wavelengths ranging from 277 to 765
nm兲. The measurement is then analyzed with GMan in order
to extract the film’s OC. Despite the use of BOMCO™ windows, a residual birefringence remains which needs to be
corrected for the OC. Fortunately, the latest versions of J. A.
Woollam’s GMan software is able to accurately measure
both the in-plane and out-of-plane window birefringence.24
The InAlAs OC database presented here has been corrected
for residual window birefringence. The solid lines of Fig. 1
show typical dynamic OC, both real 共Eps1兲 and imaginary
共Eps2兲 parts, for InAlAs along with the parameterization
scheme 共see below兲.
Since the SE signal is used to extract the film’s OC, it is
imperative that the proper angle of incidence be given to
GMan; if a wrong angle is used, GMan will return an incorrect value for the OC. Determination of the angle was accomplished by measuring the room temperature SE signal of
a bare InP substrate; this SE signal was then compared to an
accurate InP OC database acquired ex situ. The substrate
temperature was controlled at room temperature using bandgap thermometry.25 To improve the reproducibility in angle
between runs and to measure the substrate wobble under rotation, a screen was installed in the exit optical path perpendicular to the reflected polarized light. Both the absolute
angle and wobble could then easily be measured by looking
at the spot mean position and displacement on the screen

during substrate rotation. Through the use of the three piezoelectric crystals on the substrate manipulator, the sample
wobble during the OC database acquisition was kept below
⫾0.019°.
The process of acquiring an OC database consists in
growing films of different compositions and temperatures,
extracting the OC and measuring the film composition accurately by an ex situ method. We used optical band edge
thermometry25 共Thermionics DRS 1000™ system兲 to control
the growth temperature to precision of ⫾1 °C. The accuracy
of this measurement depends on independent calibrations but
is typically around ⫾5 °C at typical growth temperatures.26
The oxide was desorbed from InP wafers under an As4 overpressure up to temperatures of 535 °C. At this point, the reflection high-energy electron diffraction 共RHEED兲 showed a
4⫻2 surface reconstruction. The temperature was then lowered to the desired growth temperature and InAlAs was
grown directly on InP. Three samples were grown to acquire
the dynamic OC database. Each sample consists of five layers with different compositions around the lattice matching
condition (x⫽0.520) ranging from x⫽0.490 to x⫽0.536
共InAs mole fraction兲. The composition values quoted here
assume Vegard’s rule and room temperature lattice constants
of 0.58684, 0.60590, and 0.56618 nm for InP, InAs, and
AlAs, respectively. Within each sample the growth is carried
out at only one temperature, while each sample is grown at a
different temperature: 439, 475, and 513 °C. Hence, with
three samples, a dynamic OC database consisting of three
temperatures and five compositions could be acquired. By
stopping the growth between each layer, a complete static
OC database consisting of five temperatures and five compositions was also acquired using the first sample.
The film compositions were determined ex situ using
high-resolution x-ray diffraction 共HRXRD兲 and reciprocal
space mapping on a Philips™ five-crystal diffractometer.
Figure 2 shows a typical 共004兲 HRXRD patterns where the
five InAlAs film peaks are observed on either side of the InP
Bragg peak. The composition of each of the five layers is

J. Vac. Sci. Technol. B, Vol. 18, No. 3, MayÕJun 2000

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1437

Beaudoin et al.: Real-time composition control of InAlAs

FIG. 3. Asymmetric 共115兲 glancing exit reciprocal lattice map of the sample
shown in Fig. 2. The layer peaks are sharp, indicating good crystallinity with
low mosaicity, and line up at the same k 储 value indicating highly coherent
unrelaxed InAlAs layers.

extracted by comparing the experimental pattern with a theoretical simulation based on dynamical diffraction theory27
and assuming that the film is fully coherently strained 共unrelaxed兲. To ensure this, a 共115兲 reciprocal lattice map 共RLM兲
was also acquired in the glancing exit geometry as shown in
Fig. 3 for the sample of Fig. 2. The 共115兲 contours are all
perfectly aligned in the k 储 direction of reciprocal space indicating that the film is coherently strained. The film peaks on
the RLM are narrow and sharp; this indicates that the films
are of high quality with very little mosaicity.
III. PARAMETERIZATION AND TESTING OF OC
DATABASE
Several methods for parameterizing the optical functions
exist.28–30 Some methods are based on physical principles.
These attempt to model the optical functions from other
known material parameters of which the band gap is the
dominant feature in semiconductors. Other methods neglect
the underlying physical principles and simply model the optical functions using a purely mathematical approach. Either
method has its own advantages and drawbacks. The transfer
function 共TF兲 model used here belongs to the second group
of models. It emphasizes the robustness and convergence of
the fitting algorithm.23,24 This TF model is used to determine
the temperature 共T兲 and composition 共x兲 from the real-time
OC measurements. This is referred to as model inversion. A
good fit to the original OC database is essential for accurate
T and x prediction since the performance of the inverse
model will deteriorate rapidly with the fitting error.
The TF model used here has been presented in detail
previously.22,23 To summarize, the complex dielectric constant of the material 共OC database兲 is fit using an eight-order
transfer function with temperature and composition dependent coefficients. These coefficients are adjusted to minimize
the mean square error between the model and the experimental values. The dashed lines in Fig. 1 show typical parameterization fits to both the real and imaginary parts of the

1437

FIG. 4. Comparison of SE and XRD determined In mole fractions 共x兲 in
several Inx Al1⫺x As samples. The full squares show the results from the
real-time composition control during the growth of InAlAs. The full circles
are results from post-growth analyses of the data used to create the OC
database while the full diamonds are post-growth analyses on samples not
used in the creation of the database. The accuracy of the SE based real-time
control is within ⫾0.003 of the In mole fractions using the present parameterized database.

optical functions. The fit is almost indistinguishable from the
real data. If the model is used to predict x only while fixing
the temperature to the experimentally measured growth temperature an accuracy of ⫾0.0022 共InAs mole fraction兲 is
achieved. When it is used to predict both T and x, the accuracy on x improves to ⫾0.00044 with a T accuracy of
⫾4.9 °C. Presumably, this accuracy would improve if the OC
database had been acquired using a finer temperature grid.
In order to verify the accuracy of our OC database and TF
model in real time use, the TF model was used to create a
parameterized OC database that can be used in the GMan
software. GMan was then used to compare the predictions of
this database on itself, on previously acquired data and, finally, used in real-time to control the composition of growing InAlAs films. Everytime an experiment is performed, SE
data as a function of time are acquired and stored in a file.
GMan can be used to analyze the data in real time, as it is
acquired, or postgrowth by loading a file of previously stored
data. This feature is especially useful to set up the best analysis conditions for real-time feedback control. In all cases,
GMan returns composition and thickness values against
growth time. Figure 4 shows the average InAlAs composition returned from the SE data analysis of GMan and our
parameterized OC database against the composition measured by HRXRD for several samples, film compositions,
and growth temperatures. The full circles show the postgrowth analysis of the same data which was used to generate
the OC database while the full diamonds show the same type
of analysis performed on the SE data of samples acquired
prior to the acquisition and parameterization of the database.
This exercise is a necessary step if one wishes to use the OC
database for real-time feedback control. It allows the operator to set up the fit parameters of the GMan software to
obtain rapid convergence and credible results.
The final test of our database consists in using it to control

JVST B - Microelectronics and Nanometer Structures

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1438

Beaudoin et al.: Real-time composition control of InAlAs

the composition of growing InAlAs films. This was accomplished by deliberately choosing an Al cell temperature
which would give an offset from the target composition 共every 2 °C corresponds to ⬃0.01 In mole fraction兲. After approximately 5 min of growth, at ⬃1 ␮m/h, the composition
values returned by GMan begin to converge to a stable value.
We chose to begin feedback control of the Al cell temperature after 8 min of growth using a PID approach.20 The full
squares of Fig. 4 again show the composition value controlled under feedback control by GMan against the subsequent ex situ composition measured by HRXRD.
In Fig. 4, the full line with a slope of 1 is a best fit to all
the data. The dashed lines above and below this line are the
⫾0.002 composition difference with the full line. Of the 24
data points plotted, 16 fall within these lines or 67%. Hence,
⫾0.002 is the standard deviation of the control that can be
achieved with our parameterized dynamic OC database on
the subset of growth conditions shown here: 0.490⭐x
⭐0.540 共InAs mole fraction兲 and 439 °C⭐T growth
⭐513 °C. The real-time feedback control experiments were
all performed at 475 °C. If we want to include all the data
points analyzed or controlled in real time, then the parameterized dynamic OC database allows composition control to
within ⫾0.003 of InAs mole fraction in InAlAs closely lattice matched to InP.
IV. CONCLUSION
A fully dynamic optical constant database has been acquired, parameterized and tested for Inx Al1⫺x As close to
lattice-matched composition to InP. The OC database is valid
for 0.490⭐x⭐0.540 and 439 °C⭐T growth ⭐513 °C and is
corrected for window birefringence. The database has been
successfully used in a feedback loop to control the composition of InAlAs films to ⫾0.002 in standard deviation or
⫾0.003 maximum deviation from the target composition.
This database is publicly available on Arizona State’s MBE
optoelectronics group website.31
ACKNOWLEDGMENT
This work was supported by DARPA under Contract No.
MDA972-95-1-0016 managed by G. S. Pomrenke.
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31
The ASU OC database can be found on the MBE group’s FTP site at
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addition to AlAs, GaAs, and AlGaAs OC database.

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