In situ temperature control of molecular beam epitaxy growth using band-edge
thermometry
Shane Johnson, Chau-Hong Kuo, Martin Boonzaayer, Wolfgang Braun, Ulrich Koelle, Yong-Hang Zhang, and
John Roth
Citation: Journal of Vacuum Science & Technology B 16, 1502 (1998); doi: 10.1116/1.589975
View online: http://dx.doi.org/10.1116/1.589975
View Table of Contents: http://scitation.aip.org/content/avs/journal/jvstb/16/3?ver=pdfcov
Published by the AVS: Science & Technology of Materials, Interfaces, and Processing
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In situ temperature control of molecular beam epitaxy growth
using band-edge thermometry
Shane Johnson,a) Chau-Hong Kuo, Martin Boonzaayer, Wolfgang Braun, Ulrich Koelle,
and Yong-Hang Zhang
Center for Solid State Electronics Research, Arizona State University, Tempe, Arizona 85287-6206

John Roth
HRL Laboratories, LLC, Malibu, California 90265-4799

~Received 22 December 1997; accepted 27 January 1998!
Band-edge thermometry is becoming an established noncontact method for determining substrate
temperature during molecular beam epitaxy. However, with this technique thin-film interference
and/or absorption in the growing epilayer can cause shape distortions of the spectrum that may be
interpreted erroneously as real temperature shifts of the substrate. An algorithm is presented that
uses the width of the spectrum to correct for apparent temperature errors caused by interference and
absorption in the epilayer. This correction procedure is tested on substrate temperature data taken
during the growth of a l5930 nm resonant cavity, where the apparent substrate temperature
oscillates 65 °C during the growth of the mirror stacks. These oscillations are reduced to 63 °C
using the correction algorithm. A recently developed model for the substrate temperature dynamics
in molecular beam epitaxy shows that roughly 61 °C of the remaining 63 °C temperature
oscillations are real. Band-edge thermometry is also used to control the substrate temperature to
within 62 °C during the growth of near-lattice-matched InGaAs on InP, whereas the same growth
under constant thermocouple temperature would result in a 50 °C rise in the actual substrate
temperature. © 1998 American Vacuum Society. @S0734-211X~98!09103-3#

I. INTRODUCTION
As the physical dimensions of semiconductor devices
have become progressively smaller and device designs progressively more sophisticated, the requirements for control
over the fabrication processes have become more stringent.
Substrate temperature is a critical parameter in determining
the quality and composition of deposited layers in molecular
beam epitaxy ~MBE!. Recently, several noncontact optical
methods that infer substrate temperature from the band gap
~or band edge! of the substrate material have been developed.
The common implementations of band-edge thermometry
are diffuse reflectance spectroscopy ~DRS!,1,2 specular
reflectance,3 and transmission spectroscopy.4–6 In these
methods the temperature of the substrate is inferred from the
band edge ~i.e., the onset of transparency! of the substrate.
To determine the temperature accurately, a spectral signature
is needed that can be related to the position of the band edge,
and hence, the temperature.
In the work described in this article we determine the
temperature of the substrate from the knee region ~solid
circles! of the band-edge spectrum shown in Fig. 1, as depicted by the solid circles on the plot of reflectance versus
wavelength. The knee region of the spectrum is characterized
by a fit to the following expression, which has an asymptotic
linear behavior away from the knee:

F

y5y 0 1m 2 l a ln 11exp

S

~ l2l k !
la

DG

.

a!

Corresponding author; electronic mail: shane.johnson@asu.edu

1502

J. Vac. Sci. Technol. B 16„3…, May/Jun 1998

~1!

The two fitting parameters l k and l a are independent of the
absolute intensity of the spectrum and can be used to determine temperature. The asymptotes of Eq. ~1! are shown in
Fig. 1, as line 1 (y 0 ) and line 2 ~which has slope m 2 !. The
intersection of these two lines, l k , which defines the location of the band edge, will henceforth be referred to as the
‘‘position of the knee.’’ The curvature or sharpness of the
bend in the spectrum at the knee determines l a , which is a
measure of the width of the spectrum. Henceforth, l a will be
referred to as the ‘‘width of the knee.’’ l k is related to the
band-gap energy ~or absorption-edge position! and l a is related to the Urbach parameter ~or absorption-edge width!.7,8

II. EXTRACTING TEMPERATURE FROM THE
BAND-EDGE SPECTRUM
In band-edge thermometry, substrate temperature is typically inferred from the position of the spectrum using a previously determined calibration curve. Since the position of
the band-edge spectrum depends on the physical properties
of the substrate,7,8 one has to make a separate calibration
curve for each set of wafers with a different thickness or a
different back-surface texture, even though the substrate material is identical. Therefore, a more general way to get temperature from the spectra is needed.
For direct-band-gap semiconductor materials such as
GaAs and InP, that have an exponential absorption edge ~or
Urbach edge!,9 the relationship between the position and the
width of the knee of a calibration wafer and the position and
the width of the knee of the measured substrate is given by7,8

0734-211X/98/16„3…/1502/5/$15.00

©1998 American Vacuum Society

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Johnson et al.: In situ temperature control of MBE growth

1503

the right-hand side of Eq. ~3! can be rewritten as a linear
function of the position of the knee of the measured substrate:
l cal
k 5l k 2A 1 ~ l k 2l 1 ! ln

S

a 0d
cal cal
a0 d

D

2C s @ 3.6l a 2A 2 ~ l k 2l 2 !#

FIG. 1. Illustration of a fit of an asymptotic function to the knee region of the
diffuse reflection spectrum, showing the position of the knee in the spectrum.

F

S DG

l cal
1
l aa 0d
1
E0
k
ln cal cal cal
5 cal2
lk lk
hc
l
la a0 d
k

2

.

~2!

In Eq. ~2!, E 0 is the Urbach parameter ~or width of the absorption edge!, d is substrate thickness, and a 0 is 1 for transmission measurements and 2 for diffuse reflection measurements. ~Diffuse reflection is equivalent to double-pass
transmission.8! The term a 0 d accounts for any differences in
optical path length inside the substrate. The superscript cal
designates parameters that describe the calibration wafer.
Linearizing Eq. ~2! ~neglecting the higher-order terms in
l a ! and using the relationship 3.6l a 5l 2k E 0 /hc, 7,8 we get
l cal
k 5l k 2

l 2k E 0
hc

ln

S

a 0d
cal
a cal
0 d

D

23.6@ l a 2l cal
a #.

~3!

The second term in Eq. ~3! corrects for differences in the
position of the knee caused by differences in the optical path
of the reference and measured substrates. Since the absorption edge is exponential, this correction is given by the natural logarithm of the ratio of the optical path lengths. The
third term in Eq. ~3! corrects for spurious shifts in the position of the knee that may be caused by any of the following
factors: ~1! thin-film interference; ~2! absorbing overlayers;
~3! variations in light scattering at the back of the substrate;
~4! higher-order effects of the optical configuration used to
determine the band edge; ~5! time-dependent variations in
the signal from the band edge caused by anisotropic scattering during substrate rotation; and ~6! nonuniformities in the
optical response of the wavelength selective detection
system.7,8 In each of these cases a shift in the position of the
knee toward lower ~higher! energies is accompanied by an
increase ~decrease! in the width of the knee.
In Eq. ~3!, l 2k E 0 /hc and 3.6l cal
a are linear functions of
l k , and are approximately equal. The linearity of these two
functions arises from the fact that the width and the position
of the band edge are linear functions of temperature above
room temperature.9 Therefore, to first order in l a and E 0 ,

~4!

for GaAs and InP l 1 and l 2 are on the order of 1 mm, and
A 1 and A 2 are on the order of 0.05.
In practice, the interpretation of band-edge spectra is further complicated if the spectrometer used to record the spectra fails to fully resolve the shape of the spectrum in the
region of the knee, as is the case with commercially available
band-edge thermometers. Artificial broadening of the spectra
reduces the ability of the third term of Eqs. ~3! and ~4! to
adjust for spurious shifts in the position of the knee. Therefore, in order to extend the correction term in Eq. ~3! to
instruments with less than ideal resolution, an adjustable
multiplicative constant, C s , is used to scale the correction
@see Eq. ~4!#. C s 51 in the ideal case and it can be increased
to compensate for any reduction in coupling between the
width of the knee and the position of the knee when the
instrument resolution is below the critical value needed to
resolve the band edge of the substrate.
Equation ~4! relates the position and the width of the knee
of the measured substrate to the position of the knee of the
calibration wafer. Using this relationship, substrate temperature can be obtained directly from the previously determined
calibration curve, as follows:
cal 2
T5T 1 1T 2 l cal
k 1T 3 ~ l k ! .

~5!

In Eq. ~5!, T 1 , T 2 , and T 3 are fitting parameters that are
determined experimentally. Since the energy shift in the
band gap is proportional to the phonon occupation, which is
typically linear in temperature for temperatures above room
temperature,9,10 a linear fit is usually sufficient when the position of the knee is given in terms of energy. Similarly, in
terms of wavelength, a second-order fit is usually sufficient.
Higher-order fitting parameters can be added to Eq. ~5! when
the shift of the band edge is less than ideal.
III. SUBSTRATE TEMPERATURE DURING THE
GROWTH OF A 930 NM RESONANT CAVITY
In structures such as quarter-wave mirror stacks, thin-film
interference can have a large effect on the shape of the spectrum. To test the validity of the correction algorithm derived
above, a l5930 nm distributed Bragg reflector ~DBR! resonant cavity, comprising a ten period 65.4 nm thick GaAs by
77.8 nm thick Al0.98Ga0.02As quarter-wave stack on each side
of a 261.6 nm thick GaAs cavity is grown. This structure is
grown on a radiatively heated 50 mm diam semi-insulating
GaAs substrate, in a Vacuum Generators ~VG! V80H MBE
system. Substrate temperature is controlled by holding constant the temperature ~766 °C! of the thermocouple located
between the substrate heater and the substrate in the V80H
sample manipulator.

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Johnson et al.: In situ temperature control of MBE growth

FIG. 2. Oscillations in the position and the width of the knee of the diffuse
reflectance spectrum during the growth of a ten-period distributed Bragg
reflector pair with a l5930 nm resonant cavity. For clarity, the cavity structure is drawn behind the data.

The width and the position of the knee of the diffuse
reflectance spectra taken during this growth are shown in
Fig. 2. To put this data in perspective, the resonant cavity
structure is superimposed over the data, where the shaded
layers are GaAs. Growth began at 0 min and ended at 208.4
min. During this time, interference effects cause the position
and the width of the knee of the spectrum to oscillate. During
growth, the peaks and valleys of the interference fringe spectrum move through the knee region of the band-edge spectrum, broadening and narrowing this region of the spectrum.
As the structure thickens, the interference fringes get closer
together, increasing the distortion of the knee region of the
spectrum. The result is a general increase in the amplitude of
the oscillations with structure thickness. Initially, the interference fringes are broad, and affect the knee region of the
spectrum in a linear manner. Consequently, the position and
the width of the knee oscillate in phase. However, during the
latter part of the growth the fringes become narrow, and
affect the knee region of the spectrum in a nonlinear manner,
which causes the position and the width of the knee to oscillate out of phase. This eventually reduces the effectiveness of
the correction algorithm in Eq. ~4!.
The temperature of the substrate as determined using DRS
during the growth of the resonant cavity is shown in Fig. 3.
The curve labeled ‘‘uncorrected’’ is the temperature given by
the calibration curve @Eq. ~5!# when using the position of the
knee in the measured spectrum. The curve labeled ‘‘corrected’’ is the temperature given by the calibration curve
when the position of the knee is adjusted for variations in the
width of the knee @see Eq. ~4!#. For clarity, the DBR cavity
structure is drawn in the background of Fig. 3 ~shaded areas
are GaAs!. The oscillations in the uncorrected temperature
are a result of thin-film interference distortion of the bandedge spectrum, and to a lesser extent, are a result of periodic
variations in emission properties of the substrate. In the corrected temperature, most of the spurious temperature shifts
caused by thin-film interference have been successfully removed by the correction algorithm.

1504

FIG. 3. Substrate temperature inferred from the knee region of the diffuse
reflectance spectrum during the growth of a l5930 nm resonant cavity
structure on semi-insulating GaAs. In the uncorrected curve, temperature is
inferred from the position of the knee of the spectrum. In the corrected
curve, temperature is inferred from both the position and the width of the
knee of the spectrum.

The substrate temperature increases abruptly by about
6 °C at the start of growth, when two Ga cells are opened.
The first cell ~Ga1! contributes a GaAs growth rate of 14.7
nm/min, while the second cell ~Ga2! contributes a GaAs
growth rate of 0.3 nm/min. The Ga2 cell remains open during the entire growth and supplies the Ga component of the
Al0.98Ga0.02As layers. The initial sharp rise in temperature is
caused by the additional heat load on the substrate due to
radiant energy from the Ga cells. Since the growth is done
under constant thermocouple temperature, it appears that the
thermocouple is insensitive to this additional heat load.
The substrate temperature stays constant during the
growth of the first GaAs layer. At the end of the GaAs layer
growth, the Ga1 shutter is closed and the Al shutter is
opened ~AlAs growth rate of 14.7 nm/min!. It is interesting
to note that since no sudden temperature changes are observed at the GaAs–AlGaAs interfaces, the heat load of the
Al cell and the heat load of the Ga1 cell are roughly the
same. During the growth of the first AlGaAs layer the substrate cools as the emittance of the substrate increases with
the addition of the lower-index AlGaAs layer. The thermocouple appears to be insensitive to these changes, however,
DRS correctly senses the drop in the true substrate temperature. During the growth of the remainder of the first mirror
stack the substrate temperature fluctuates around an average
temperature of about 613 °C.
During the growth of the 261.6 nm GaAs cavity the substrate temperature increases significantly, and at the end of
the GaAs cavity the temperature is about 3 °C higher than
the initial GaAs growth temperature. During the growth of
the top mirror stack the substrate again cools, reaching an
average temperature of about 615 °C for the rest of the
growth. This new average temperature is about 2 °C higher
than that of the first mirror stack. During the growth of the

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1505

Johnson et al.: In situ temperature control of MBE growth

second mirror, the temperature oscillations ~after correction!
are larger than in the first stack. In this case, the increase is
not real, as the effectiveness of the correction algorithm is
reduced by the fact that the position and width of the knee
are now slightly out of phase. At the end of the growth, the
substrate temperature abruptly drops by about 5 °C when the
two Ga shutters are closed.
The two major trends observed in the substrate temperature during the growth of the DBR cavity structure are the
decrease in temperature with the growth of AlGaAs on thick
GaAs layers and the increase of temperature with the growth
of the GaAs cavity on the mirror stack. In both cases the
temperature decrease ~or increase! is due to the increase ~or
decrease! in the emittance of the substrate, which is caused
by the deposition of a layer whose index of refraction is
lower ~or higher! than that of the underlying material.
In order to better understand the effect the optical properties of the growing structure have on substrate temperature, a
mathematical model for radiant energy transfer between the
heater and substrate11 is used to simulate substrate temperature variation during the growth of the structure at constant
thermocouple temperature. The result of this simulation is
labeled the ‘‘substrate thermal model’’ in Fig. 3. This model
does a remarkably good job of reproducing key features of
the substrate temperature variation during the growth of the
DBR cavity. For example, it correctly predicts: ~1! the higher
average temperature during the growth of the second mirror
stack; ~2! the peak temperature during the growth of the
GaAs cavity; and ~3! the decrease in temperature during the
first AlGaAs–GaAs period of each mirror stack.
The substrate thermal model also predicts small temperature oscillations that have the same period as the mirror
stack. In comparison, the period of the DRS temperature oscillations is about 1.2 times larger. The longer period for
DRS is due to the interference distortion of the band-edge
spectrum in the vicinity of the knee wavelength, which is
about 20% longer than the wavelength of the resonant cavity.
These two different periods result in a beating in the DRS
temperature that is particularly noticeable in the first mirror
stack. The fact that the period for interference dominates the
DRS temperature during the growth of the mirror stacks indicates that the temperature displacement of the diffuse reflectance spectrum is smaller that the interference displacement, even after correction.
The substrate temperature oscillations during the growth
of the mirror stacks have maxima in the AlGaAs layers and
minima in the GaAs layers. At first this behavior appears to
be out of phase with the more prominent features of the
temperature curve, namely, that the temperature decreases
during AlGaAs growth and increases during GaAs growth.
The explanation for this is as follows: Superimposed over the
broad subgap emission spectrum of GaAs–AlGaAs materials
is a narrow emission peak where the band gap of the material
overlaps the tail of the blackbody spectrum. The combination
of band-gap changes and interference effects cause the integrated intensity of the emission peak to vary with the same
period as the quarter-wave mirror stacks. Because of this,

1505

FIG. 4. Feedback control of substrate temperature during the growth of
near-lattice-matched InGaAs on semi-insulating InP, using diffuse reflectance spectroscopy ~DRS!. The substrate setpoint ~460 °C!, the DRS temperature, the thermocouple temperature and setpoint, and the heater power
are shown.

substrate emission goes through a maximum in the 65.4 nm
GaAs layers and a minimum in the 77.8 nm AlGaAs layers.
IV. TEMPERATURE CONTROL DURING THE
GROWTH OF ABSORBING OVERLAYERS
During the growth of absorbing overlayers, such as nearlattice-matched InGaAs on InP, radiatively heated substrates
are known to heat up dramatically as the layer becomes
thicker, and this occurs with either constant heater power or
constant thermocouple temperature.12 Under these growth
conditions it is imperative that one has an alternative in situ
method of determining substrate temperature. Band-edge
thermometry is a suitable method, with the limitation that the
opaque overlayer will eventually obscure the band edge of
the substrate.
In the following experiment a near-lattice-matched, 400
nm thick, InGaAs layer is grown on a radiatively heated 50
mm semi-insulating InP substrate in a DCA MBE system.
The substrate ~i.e., DRS! temperature, thermocouple temperature, and heater power recorded during the growth of this
layer are shown in Fig. 4. The DRS temperature is used to
control the setpoint of the thermocouple, which in turn controls the output power of the heater. The supervisory computer checks the DRS temperature every 30 s, and if the DRS
temperature has deviated more than 61 °C from the substrate setpoint of 460 °C, the computer adds the difference to
the thermocouple setpoint. In addition, at the start of growth
the thermocouple setpoint is reduced by 6 °C to adjust for the
additional radiant heat load of the In and Ga effusion cells.
Using this control algorithm, the substrate temperature
tends to stay about 1 °C above its setpoint throughout most
of the growth. Decreasing the update time ~from 30 to 10 s!
and the deviation threshold ~from 1.0 to 0.5 °C! would bring
the substrate temperature closer to the setpoint. Also, there
are small oscillations in the substrate temperature at the start
and stop points that are caused by the abrupt changes in the
thermal load on the substrate when the In and Ga cells are

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Johnson et al.: In situ temperature control of MBE growth

opened or closed. In order to improve the feedback control of
the substrate temperature, a more sophisticated computer
control algorithm such as a proportional–integral–derivative
loop could be implemented. In this case the deviation of the
substrate temperature from its setpoint would be limited by
the noise in the DRS measurement.
As can be seen in Fig. 4, each time the thermocouple
setpoint is updated, there is a sharp drop in the heater power
and the thermocouple temperature quickly moves to its new
setpoint. The thermal response of the thermocouple–heater
system is fast compared to the thermal response of the
substrate—this is why the nested control loop we are using
works so well.
By the end of the growth, the thick InGaAs layer has
reduced the DRS signal by a factor of 5. This is indicated by
the increase in the noise of the DRS temperature measurement ~see Fig. 4!. In our experience the DRS technique is
limited to the growth of InGaAs layers that are less than 1
mm thick. Also, by the end of the growth the thermocouple
temperature is lower than the substrate temperature. 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, and this reduces both
the heater power output and the thermocouple temperature.
If only absorption in the InGaAs layer was important, one
would expect the slope of the thermocouple temperature
curve to decrease monotonically with thickness. However, a
closer look at the thermocouple curve in Fig. 4 shows a
slight dip in the slope at a 160 nm layer thickness. This dip is
the result of the thin-film interference effects on the emission
spectrum in the InGaAs layer. This thin-film interference
feature was verified in simulation using the thermal substrate
model. It is also interesting to note that for a bare substrate,
the initial substrate–thermocouple offset is much lower here
than in the previous experiment ~30 °C instead of 150 °C!.
The emission–absorption properties of the thermocouple–
heater system of the DCA chamber are very different from
those of the VG system used to grow the resonant cavity.
Finally, the spectral dependence of the absorption coefficient of the InGaAs overlayer distorts the shape of the bandedge spectrum. Again, the apparent temperature shift caused
by this distortion is corrected using the technique described
in Eq. ~4!. Simulations show that the error is about 2 °C for

1506

a 400 nm thick InGaAs layer and that this apparent temperature shift can be reduced to less than 0.5 °C by using Eq. ~4!.
V. CONCLUSIONS
A substrate temperature measurement method is presented
wherein temperature is inferred from the position of the knee
of the band-edge spectrum of the substrate. The width of the
knee of the band-edge spectrum is used to correct for spurious shifts in the position of the knee caused by differences in
the properties of the substrate and the measurement conditions from those of a reference substrate. Spurious temperature shifts caused by thin-film interference during the growth
of a distributed Bragg reflector cavity structure are significantly reduced when using both the position and the width of
the knee of the spectrum to determine the temperature. A
substrate thermal model is used to predict the key features of
the real temperature variations of a radiatively heated substrate during the growth of a l5930 nm resonant cavity under constant thermocouple control. Diffuse reflectance spectroscopy is used to control substrate temperature to within
62 °C during the growth of the InGaAs on InP. Conventional constant-thermocouple control during the same growth
results in substrate temperature variations of more than
50 °C.
ACKNOWLEDGMENTS
This work is part of a DARPA-funded program entitled
‘‘Integrated MultiSensor Control of Molecular Beam Epitaxy’’ under Agreement No. MDA972-95-1-0016, monitored
by Lt. Col. Gernot S. Pomrenke.
1

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3
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7
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8
S. R. Johnson, Ph.D. thesis, University of British Columbia, 1996.
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