Closed-loop control of composition and temperature during the growth of InGaAs
lattice matched to InP
S. R. Johnson, E. Grassi, M. Beaudoin, M. D. Boonzaayer, K. S. Tsakalis, and Y. H. Zhang
Citation: Journal of Vacuum Science & Technology B 17, 1237 (1999); doi: 10.1116/1.590729
View online: http://dx.doi.org/10.1116/1.590729
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Published by the AVS: Science & Technology of Materials, Interfaces, and Processing
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Closed-loop control of composition and temperature during the growth
of InGaAs lattice matched to InP
S. R. Johnson,a) E. Grassi, M. Beaudoin, M. D. Boonzaayer, K. S. Tsakalis,
and Y. H. Zhang
Center for Solid State Electronics Research, Department of Electrical Engineering,
Arizona State University, Tempe, Arizona 85287-6206

~Received 5 October 1998; accepted 27 November 1998!
Spectroscopic ellipsometry ~SE! and diffuse reflection spectroscopy ~DRS! are used to control the
Ga mole fraction and substrate temperature, respectively, during the growth of InGaAs lattice
matched to InP. Ga mole fraction is controlled to within 60.002 of its target value and substrate
temperature is controlled to within 62 °C of its target value. The same growth under constant
thermocouple control would result in a 50 °C rise in real substrate temperature and a Ga
composition 1% above its target value. In both cases, feedback control is achieved using a nested
proportional-integral-derivative ~PID! control loop, where, the inner loop consists of the
conventional Eurotherm-thermocouple feedback loop and the outer loop updates the thermocouple
setpoint using a PID control loop implemented in the control software. For composition control, the
Ga cell thermocouple setpoint is increased ~decreased! 0.2 °C for every 0.002 that the Ga mole
fraction, given by the SE sensor, deviates below ~above! the target value. During substrate
temperature control, the thermocouple setpoint is updated based on the temperature difference
between the DRS sensor and the user setpoint. Frequency loop shaping, based on a dynamical model
of the system obtained from an identification experiment, is used to tune the outer PID loop.
© 1999 American Vacuum Society. @S0734-211X~99!01003-3#

I. INTRODUCTION
In situ control of group III mole fraction and substrate
temperature are critical during the molecular-beam epitaxy
~MBE! growth of high-quality lattice-matched InGaAs on
InP. As a first step in controlling substrate temperature, an
accurate reliable temperature measurement method is required. Recently several optical methods that infer substrate
temperature from the band gap of the substrate material have
been developed.1–5 Presently, we use diffuse reflection spectroscopy ~DRS!1,2 to measure the band edge of InP and GaAs
substrates. In this method, the substrate is illuminated by a
broad spectrum W-halogen lamp placed at an effusion cell
port; light that is transmitted through the substrate, diffusely
reflected, and retransmitted back through the substrate, is detected at the pyrometer port. Substrate temperature is inferred from the wavelength of the onset of substrate transparency to the diffusely reflected light.
Spectroscopic ellipsometry ~SE! has proven to be an accurate method for controlling near surface composition during the growth of ternary alloys.6–8 SE is an optical technique that measures ~over a range of wavelengths! the
change in the polarization state of light, that occurs, as it
reflects from the surface layer of the substrate. The change in
the polarization state is related to the near surface optical
functions using a virtual interface model8 and the Fresnel
equations. The near surface composition is determined by
comparing the measured optical functions to a previously
recorded library containing the optical functions for several
different compositions at various growth temperatures. Cura!

Electronic mail: shane.johnson@asu.edu

1237

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

rently, our optical function library for InGaAs comprises
compositions that are within a 60.03 mole fraction of the
InP lattice-matched condition for growth temperatures ranging from 380 to 520 °C. We expect to publish the InGaAs
database in its final form within the next year.
II. CLOSED-LOOP CONTROL
The nested loop approach shown in Fig. 1 is a convenient
way to add accurate external sensors to the conventional
Eurotherm-thermocouple control loops found in most MBE
systems. In this case, the outer control loop updates the Eurotherm ~thermocouple! setpoint based on the difference between the user setpoint and the value measured by the external sensor, using a proportional-integral-derivative ~PID!
algorithm implemented in control software. This method has
the advantage that the Eurotherm-thermocouple control system is left intact, so that, in the event that the external sensor
or control computer fail, the heater power will continue to be
controlled.
The first ~upper! nested control loop shown in Fig. 1,
controls substrate temperature using DRS as the external
sensor. The second ~lower! loop shown, controls composition using SE as the external sensor. Both control loops are
similar in that the Eurotherm-thermocouple ~or inner! loop
primarily controls the heating element and is limited in its
ability to detect and control either true substrate temperature1
or true group III deposition rates.9 This inability also means
that the Eurotherm-thermocouple control loop only partially
rejects external disturbances, such as the thermal-shutter
transients that occur in effusion cells and at the substrate
when effusion cell shutters are toggled. In this control

0734-211X/99/17„3…/1237/4/$15.00

©1999 American Vacuum Society

1237

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1238

Johnson et al.: Closed-loop control of composition during growth of InGaAs

FIG. 1. Schematic of the nested proportional-integral-derivative ~PID! control loops used to control substrate temperature ~upper sketch! and composition ~lower sketch!. In both cases, the inner loop is the conventional
Eurotherm-thermocouple control loop. The outer loop updates the inner loop
setpoint based on the difference between the outer loop setpoint and, the
substrate temperature measured by diffuse reflectance spectroscopy ~DRS!,
or the Ga mole fraction measured by spectroscopic ellipsometry ~SE!.

scheme, the outer loop periodically updates the thermocouple setpoint, causing the Eurotherm control loop to bring
substrate temperature or effusion cell flux back in line with
its target value.
The parameters relating to substrate temperature and composition during the growth of lattice-matched InGaAs on a
radiatively heated 50 mm semi-insulating InP substrate, are
shown in Figs. 2 and 3. In both figures, growth time and
layer thickness are shown on the lower and upper horizontal
axis, respectively. The growth starts at zero minutes and ends
at 58.3 min, for a total layer thickness of 400 nm. This material was grown in a DCA MBE system, that has the unique
ability to minimize substrate wobble, in situ, using three piezo crystals that individually adjust the length of three ma-

FIG. 2. Closed-loop control of substrate temperature during the growth of
lattice-matched InGaAs on semi-insulating InP, using diffuse reflectance
spectroscopy ~DRS!. Substrate setpoint ~435 °C!, DRS temperature, thermocouple temperature and setpoint, and heater voltage ~at power supply! are
shown.

1238

FIG. 3. Closed-loop control of Ga mole fraction during the growth of
In0.532Ga0.468As on InP, using spectroscopic ellipsometry ~SE!. The Ga mole
fraction given by, SE, secondary ion mass spectrometry ~SIMS!, and x-ray
diffraction ~XRD!, and the Ga cell thermocouple temperature are shown.

nipulator support rods.10 Both substrate temperature and Ga
mole fraction were controlled using the control scheme and
sensors shown in Fig. 1.
Substrate ~DRS! temperature, thermocouple temperature,
and heater voltage recorded during the growth of this layer
are shown in Fig. 2. The supervisory computer samples the
DRS temperature every 30 s, if the DRS temperature has
deviated more than 61 °C from the substrate setpoint of
435 °C, the outer PID loop updates the Eurotherm ~inner!
setpoint. Throughout most of the growth of the InGaAs
layer, the substrate temperature is about 1 °C above its setpoint. Decreasing the update time would bring the substrate
temperature closer to the setpoint during the first part of the
growth. As can be seen in Fig. 2, each time the thermocouple
setpoint is updated, there is a sharp drop in the heater voltage
and the thermocouple temperature quickly moves to its new
setpoint. The thermal response of the thermocouple-heater
system is fast ~4 s time constant! compared to the thermal
response of the substrate ~60 s time constant!; this allows
appropriate control action.
Radiatively heated substrates are known to heat up dramatically during the growth of absorbing overlayers, such as
near-lattice-matched InGaAs on InP, when constant thermocouple control is used.11,12 In this case, the thermocouple is
insensitive to the substrate temperature increase caused by
the strong absorption of heater radiation in the overlayer.
The small-band gap epilayer absorbs a larger part of the
heater radiation spectrum than the InP substrate, which is
transparent to much of the blackbody spectrum at these temperatures. Therefore, as the InGaAs layer thickens, the transmission losses of heater radiation are reduced. In order to
maintain constant substrate temperature, the control system
continually reduces the heater power by decreasing the Eurotherm ~thermocouple! setpoint over the course of the
growth.
The small oscillations in the substrate temperature at the
start and stop points are caused by the abrupt changes in the
thermal load on the substrate when the In and Ga cells are

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1239

Johnson et al.: Closed-loop control of composition during growth of InGaAs

toggled. At the start of growth the thermocouple setpoint is
reduced by 6 °C in an effort to correct for the thermal disturbance caused by additional radiant heat load of the In and
Ga effusion cells. This is the simplest way of rejecting thermal disturbances. At the end of the growth, no shutter disturbance rejection is used and the substrate momentarily
drops 4 °C below the setpoint. A more sophisticated approach to disturbance rejection is discussed in the following
section.
The Ga mole fraction, as measured by SE, secondary ion
mass spectroscopy ~SIMS!, and x-ray diffraction ~XRD!, and
the Ga cell thermocouple temperature, for the InGaAs
growth, are shown in Fig. 3. The supervisory computer
samples the Ga mole fraction given by the SE computer8
every 30 s, if the mole fraction has deviated more than
60.002 from the 0.468 target value, the outer PID loop updates the Eurotherm ~inner! setpoint. When the outer loop
gain is one, the setpoint change is 70.2 °C for every 60.002
deviation in Ga mole fraction. The thermal response of the
thermocouple-cell heater system is fast ~6 s time constant!
compared to the thermal response of the Ga melt ~45 s time
constant!; again, this allows appropriate control action.
We have found that SE cannot accurately determine the
composition of thin InGaAs layers, most likely, because the
thin layer optical functions differ from those of the bulk
material. Consequently, the extraction of composition from
SE data is not initiated until 6.0 min ~or 41 nm! into the
growth and composition control is not initiated until 7.7 min
~or 53 nm! into the growth. At the start of control, the Ga cell
temperature is 920.0 °C and GA mole fraction is 0.480, at
which time the outer control loop decreases the Ga cell temperature. The initial Ga and In effusion cell settings, for the
lattice matched condition, were estimated from previous
growths of near-lattice-matched InGaAs. In this particular
run the outer loop PID parameters were not well tuned and
the Ga cell temperature and mole fraction oscillated for 25
min before stabilizing.
Though not well tuned, this experiment is a good illustration of the type of dynamics that occur within the effusion
cell and the sensors in the closed-loop control system. The
oscillations in the Ga cell flux lag those of the Ga cell temperature by 1.7 min ~90° phase lag!. This occurs because the
Ga melt responds much more slowly to the heater than the
thermocouple. This is an important consideration for anyone
growing graded layers using dead reckoning thermocouple
control. The GA cell temperature stabilized at 918.5 °C,
which corresponds to the lattice matched condition. If grown
using dead reckoning, the resulting Ga mole fraction would
be about 1% too high for this run. The nice clear oscillations
in the Ga mole fraction measured by SE, indicate that SE is
a reliable sensor of the near surface composition of InGaAs.
The InGaAs composition was measured using XRD and
found to be lattice matched to InP, within the resolution of
the XRD measurement, which in mole fraction, is 60.001.
The lattice matched mole fractions are given as
In0.532Ga0.468As, 13 as suggested by Vegard’s law. The XRD
measurement gives an average composition for the InGaAs

1239

FIG. 4. Identification experiment used to determine the state space model
that relates heater voltage to substrate temperature. The identification signal
~Eurotherm thermocouple setpoint!, substrate temperature measured by diffuse reflectance spectroscopy ~DRS!, and substrate temperature predicted by
the model, are shown.

layer and is shown by the solid horizontal line at 0.468 Ga
mole fraction. The Ga mole fraction given by the SIMS measurement is about 0.025 too low, however, it does verify the
oscillations seen by SE. The drop in the SIMS data at the
surface of the sample is due to surface effects.
III. OUTER LOOP TUNING
In order to improve the closed-loop control of substrate
temperature and composition, the outer PID is tuned using
frequency loop shaping ~FLS!,14 which attempts to approximate in a minimax sense the loop transfer function of the
system to a desired one in the frequency domain. The ideal
loop transfer function is selected, based on stability and performance considerations, and on the characteristics of the
system. FLS requires a model of the system ~in the frequency
domain!; this model can be obtained using standard systems
identification techniques.
As a first step, an input signal is designed that covers the
frequency range of interest. Next, the temperature of the substrate is brought to, and allowed to stabilize at, the desired
operating point. With the external ~outer! control loop open,
the identification signal is applied at the Eurotherm ~inner!
setpoint ~see Fig. 1!, while the external sensor measurements
are collected. Using the method described in Ref. 15, a state
space model is found,16 that describes the dynamic behavior
of the system from the power supply input to the external
sensor measurement. ~A state space model is a set of forced
linear ordinary differential equations.! The DRS temperature,
the temperature predicted by the model, and the identification signal are shown in Fig. 4. A second order state space
model was used to identify the system. The model was verified using a separate data set.
The desired time constant of the controlled system is
about 15 s. Therefore, we need to obtain a model of the
system around the frequency, 1/15 rad/s. The input signal for
the identification experiment is a random-switching binary
signal with levels of 610 °C around the desired operating
point. The switching time is uniformly distributed over
1–160 s, with a mean of 80 s. Since the sampling interval is

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1240

Johnson et al.: Closed-loop control of composition during growth of InGaAs

1 s, the maximum frequency spanned is 1 Hz. This is adequate for our goals. The frequency resolution is 1/N Hz,
where N is the number of data points collected. Usually a
resolution of 1/30 of the closed loop bandwidth is enough for
this type of system where no sharp resonant peaks are
present.
The PID parameters obtained with FLS are very different
from those obtained with the traditional step response PID
tuning method ~Ziegler–Nichols method 1!.16 The Ziegler–
Nichols rule gives @ K p ,T i ,T d # 5 @ 8.4, 12 s, 3.0 s#, while FLS
gives @ K p ,T i ,T d # 5 @ 2.1, 34 s, 0.7 s#, for the outer substrate
temperature control loop. The Ziegler–Nichols method approximates the system by a first order model with delay, and
is only applicable for ‘‘s’’ shaped step responses ~see Ref.
16!. As can be seen in Fig. 4, the lag in the step response ~6
s! is very short compared with the rise time ~42 s!, which
makes the Ziegler–Nichols rules inappropriate for the
present system. Using the Ziegler–Nichols rule to tune the
outer substrate temperature control loop results in a closed
loop system that is unstable. Since the Ga effusion cell identification experiments and modeling of the dynamics are currently in progress, we are unable to report the PID parameters given by FLS for the Ga cell.
During the growth of thick absorbing overlayers, the
absorption-emission properties of the substrate-epilayer system change considerably. This means that in general, the
optimal PID parameters would change accordingly and several PIDs would have to be scheduled. Gain scheduling was
not used in the growth shown in Fig. 2; in this case a single
set of PID parameters was sufficient to control temperature.
Finally, the DRS signal is reduced when an absorbing layer
is present, as can be seen by an increase in the noise of the
DRS data in Fig. 2. Since the data acquisition frequency of
the DRS data is much larger than that of the control system,
much of the noise in the DRS data is removed at the DRS
sensor input, using a low pass filter.
Another important control objective is good temperature
regulation during external disturbances, such as thermal
shutter transients. Since it is precisely known when each effusion cell shutter is toggled, control algorithms that take
preventive action can be used to correct for the thermal transients that may occur at the substrate or in the effusion cell
melt. Identification experiments similar to the one described
above can be used to model the disturbance signal associated
with shutter operations. Based on the inverse model, corrective action in the form of a time dependent signal added at
the Eurotherm ~inner! setpoint can be used to reject the disturbance. This time dependent signal takes into account the
dynamics of the system, which are not included in the simple
step adjustment used in Fig. 2. Inclusion of the system dynamics will be most visible in cases where the substrate or
melt response lags the shutter disturbance.

1240

IV. CONCLUSIONS
A nested proportional-integral-derivative control loop is
used to achieve closed-loop control of substrate temperature
and Ga mole fraction during the growth of lattice-matched
InGaAs on InP, to within 62 °C and 60.002 of the user
specified setpoints, respectively. Diffuse reflection spectroscopy is used as an external sensor for substrate temperature
and spectroscopic ellipsometry is used as an external sensor
for near surface InGaAs composition. The outer loop controls the inner loop ~thermocouple! setpoint, using information supplied by the external sensor. The inner loop is the
standard Eurotherm-thermocouple control loop found on
most MBE systems. A system identification experiment and
frequency loop shaping are used to optimally tune the PID
parameters of the outer control loop for substrate temperature.
ACKNOWLEDGMENTS
This work is part of a DARPA-funded program entitled
‘‘Integrated MultiSensor Control of Molecular Beam Epitaxy,’’ under Grant No. MDA972-95-1-0016, monitored by
Lt. Col. Gernot S. Pomrenke, which is a collaborative effort
between scientists from HRL Laboratories, the J. A. Woollam Company, Arizona State University, and the University
of Colorado.
1

S. R. Johnson, C. Lavoie, T. Tiedje, and J. A. Mackenzie, J. Vac. Sci.
Technol. B 11, 1007 ~1993!.
2
S. R. Johnson, C. Lavoie, M. K. Nissen, and T. Tiedje, U.S. Patent No.
5,388,909 ~1995!.
3
J. A. Roth, T. J. DeLyon, and M. E. Adel, Mater. Res. Soc. Symp. Proc.
324, 353 ~1994!.
4
E. S. Hellman and J. S. Harris, J. Cryst. Growth 81, 38 ~1987!.
5
D. M. Kirillov and R. A. Powell, U.S. Patent No. 5,118,200 ~1992!.
6
D. E. Aspnes, W. E. Quinn, M. C. Tamargo, M. A. A. Pudensi, S. A.
Schwarz, M. J. S. P. Brasil, R. E. Nahory, and S. Gregory, Appl. Phys.
Lett. 60, 1244 ~1992!.
7
C.-H. Kuo, M. D. Boonzaayer, M. DeHerrera, T. Kyong, and Y.-H.
Zhang, J. Vac. Sci. Technol. B 16, 1007 ~1998!.
8
The SE hardware and data analysis software are described in: B. Johs, J.
Hale, C. Herzinger, D. Doctor, K. Elliott, G. Olson, D. Chow, J. Roth, I.
Ferguson, M. Pelczynski, C.-H. Kuo, and S. R. Johnson, Mater. Res. Soc.
Symp. Proc. 502, 3 ~1998!.
9
K. G. Eyink, J. K. Patterson, S. J. Adams, T. W. Haas, and W. V.
Lampert, J. Cryst. Growth 175/176, 262 ~1997!.
10
C.-H. Kuo, M. D. Boonzaayer, M. F. DeHerrera, D. K. Schroder, G. N.
Maracas, and B. Johs, J. Cryst. Growth 175/176, 281 ~1997!.
11
B. V. Shanabrook, J. R. Waterman, J. L. Davis, and R. J. Wagner, Appl.
Phys. Lett. 61, 2338 ~1992!.
12
J. A. Roth, Mater. Res. Soc. Symp. Proc. 502, 97 ~1998!.
13
S. Adachi, Physical Properties of III-V Semiconductor Compounds, InP,
InAs, GaAs, GaP, InGaAs, and InGaAsP ~Wiley, New York, 1992!.
14
E. Grassi and K. S. Tsakalis, Proceedings of the 35th CDC, Kobe, Japan,
Dec. 1996 ~unpublished!, pp. 4776–4781.
15
K. Tsakalis and K. Stoddard, Proceedings of the 6th IEEE International
ETFA Conference, Los Angeles, CA, Sept. 1997 ~unpublished!, pp. 514–
519.
16
K. Ogata, Modern Control Engineering, third ed. ~Prentice–Hall, Englewood Cliffs, NJ, 1997!, p. 670.

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