Journal of Crystal Growth 195 (1998) 34—40
An X-ray standing wave study of ultrathin InAs films in
GaAs(0 0 1) grown by atomic layer epitaxy
J.A. Gupta , J.C. Woicik, S.P. Watkins *, K.E. Miyano, J.G. Pellegrino, E.D. Crozier
Department of Physics, Simon Fraser University, Burnaby, BC, Canada V5A 1S6
National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
Department of Physics, Brooklyn College, New York, NY 11210, USA
Abstract
X-ray standing wave and X-ray diffraction measurements were used to determine the structure of nominal 1 monolayer
and 1/2 monolayer InAs films buried in GaAs(0 0 1). The films were grown by atomic layer epitaxy using trimethylgallium, tertiarybutylarsine and trimethylindium. For the full monolayer sample the standing wave measurement shows that
the indium atoms reside 1.577$0.014 A> above the GaAs(0 0 4) substrate planes. A calculation based on the macroscopic
elastic theory suggests that this corresponds to a single In Ga As layer with x"0.794$0.068. The coherent fraction
V \V
of 0.766$0.051 indicates a reasonably abrupt interface, as confirmed by the In-excitonic photoluminescence full width
at half maximum of 5.74$0.01 meV. The half monolayer sample is less strained, as expected, with the indium atoms at
1.502$0.030 A> above the substrate planes, corresponding to an In Ga As layer with x"0.446$0.145, and a
V \V
coherent fraction of 0.88$0.12. This study exemplifies the complimentary nature of XSW and XRD. 1998 Elsevier
Science B.V. All rights reserved.
PACS: 81.15Gh; 81.05.Ea; 68.65.#g; 61.10.Yh
Keywords: InAs; GaAs; XSW; ALE; MOCVD; Diffraction
1. Introduction
Advances in semiconductor growth techniques
such as metalorganic chemical vapour deposition
(MOCVD), the related technique of atomic layer
* Corresponding author. Tel.: #1 604 291 5763; fax: #1 604
291 3592; e-mail: [email protected].
epitaxy (ALE), and molecular beam epitaxy (MBE)
have allowed the growth and study of indium
isoelectronic d-doping layers in GaAs(0 0 1). With
In depositions of only fractions of a monolayer
(ML), sharp and intense In-excitonic photoluminescence (PL) emission has been observed
[1—5]. However, for these InAs layers buried beneath a GaAs capping layer, the determination of
the In local structure is a non-trivial task. For
0022-0248/98/$ — see front matter 1998 Elsevier Science B.V. All rights reserved.
PII: S 0 0 2 2 - 0 2 4 8 ( 9 8 ) 0 0 6 3 6 - 8
J.A. Gupta et al. / Journal of Crystal Growth 195 (1998) 34–40
submonolayers of InAs, there has been much work
aimed at determining whether zero-dimensional or
one-dimensional confinement occurs at InAs islands or wires [1—3]. There remains considerable
interest in determining the effect of the InAs distribution on the optical properties.
The synchrotron X-ray standing wave (XSW)
technique [6] has previously been applied in the
study of InAs monolayers embedded in GaAs
grown by MBE. From the standing wave data it is
possible to determine the location of the In atoms
relative to the GaAs(0 0 4) planes, and to obtain
a precise measurement of the InAs layer perfection
(i.e. the d-like nature of the distribution). Results
with MBE-grown films [7—10] have been consistent with predictions of the macroscopic elastic
theory (MET) [11]. Here the lattice mismatch between InAs and GaAs (&7.2%) is accommodated
by a tetragonal distortion of the InAs unit cell,
resulting from pseudomorphic growth.
In this study we have measured the strain in
nominal 1 and 1/2 ML films of InAs in GaAs
grown by the gas phase technique of ALE. X-ray
standing waves were used to measure the In position relative to the underlying GaAs substrate unit
cell, and the perfection of the layers. From the
positional measurement and the MET we have
deduced an In atomic distribution in the plane of
each sample, which we find to be consistent with
the results of X-ray diffraction (XRD) and PL
measurements.
2. Experiment
The samples were grown in a Thomas Swan
vertical MOCVD reactor at 50 Torr. Semi-insulating vertical gradient freeze GaAs(0 0 1) epi-ready
substrates were used with no additional cleaning.
Following annealing under tertiarybutylarsine
(TBAs) at 580°C for 300 s, a GaAs buffer layer of
thickness 0.625 lm was grown by conventional
MOCVD using triethylgallium (TEGa) and TBAs.
ALE growth was performed at 390°C. GaAs barrier
layers (of thickness &1.3 ML) above and below
the InAs layer were grown by ALE in four 4-step
cycles each consisting of a 3 s hydrogen purge, 8 s
of trimethylgallium (TMGa), another 3 s hydrogen
35
purge, and finally 6 s of TBAs. The InAs layer was
deposited in a single cycle as above, with a 3 or 1.5 s
trimethylindium pulse, for the single and half
monolayers, respectively. The InAs growth rate was
based on XRD thickness measurements of InAs
homoepitaxial films deposited by ALE [12]. After
the top GaAs ALE layer, the temperature was
raised to 500°C and a thicker GaAs layer was
deposited by conventional MOCVD using TEGa
and TBAs. This growth sequence was also employed in a previous PL study of samples with
several InAs coverages [4].
In the present study three samples were produced. For the XRD and XSW measurements, two
samples were grown with nominal In depositions of
1 and 1/2 ML, and GaAs caps (ALE#MOCVD)
of approximately 100 A> . Actual cap thicknesses
were determined by XRD, as will be discussed.
A third sample was grown for PL characterization
with 1 ML of InAs and a total GaAs cap thickness
of 2550$25 A> , also determined by XRD. During
each growth the sample surface was monitored by
reflectance difference spectroscopy using the arrangement described elsewhere [13].
XSW measurements were made at the National
Institute of Standards and Technology beamline
X24A at the National Synchrotron Light Source,
Brookhaven National Laboratory. The monochromator consisted of a pair of Si(2 2 0) crystals.
Standing waves were produced within the GaAs
crystals and modulated in phase by scanning in
energy through the GaAs(0 0 4) back-reflection at
normal incidence. Indium fluorescence yield data
were obtained using a single-element Li-drifted Ge
detector. Reflectivity measurements were made by
recording the back-reflected photon intensity with
a Ni mesh upstream from the sample.
X-ray diffraction measurements were obtained in
a standard h/2h geometry with a BEDE-D3 apparatus. An asymmetric double crystal channel-cut
monochromator was used with Cu K X-rays of
a
wavelength j"1.54 A> . Rocking-curve measurements were obtained by scanning in angle, h,
through the GaAs(0 0 4) symmetric reflection, near
the Bragg angle, h , given by j"2d sin h , where
1
d is the spacing of the GaAs(0 0 4) planes.
1
Low-temperature photoluminescence measurements were performed at 4.2 K using the 514.5 nm
36
J.A. Gupta et al. / Journal of Crystal Growth 195 (1998) 34–40
line of an Ar-ion laser. Spectra were recorded using
a double-grating 0.85 m spectrometer and GaAs
photocathode photomultiplier tube.
3. Results and discussion
In the XSW experiments, the X-ray reflectivity
and resulting X-ray standing wave pattern are recorded simultaneously [6,14] as shown in Figs. 1
and 2. In each case the bottom curve depicts the
reflectivity results obtained as the incident X-ray
energy is scanned through the GaAs(0 0 4) backreflection condition. The standing wave pattern
results from the superposition of the incident and
back-reflected travelling waves and has the periodicity of the crystal lattice planes with diffraction
vector, H. At the low energy side of the Bragg
Fig. 1. Photon-energy dependence of the reflectivity (lower) and
the In-L fluorescence yield (upper) near the GaAs(0 0 4) Bragg
backreflection condition for the nominally 1 ML sample. The
solid lines are the best fits to the data points.
reflection the nodes of the standing wave lie on the
substrate planes. As the phase changes in the region
of the Bragg peak the wavefield moves continuously until the antinodes lie on the substrate planes
at the high energy side. Indium fluorescence
spectra, shown in the top curves of Figs. 1 and 2,
are proportional to the absorption of the In atoms
in the field of the standing wave. From this response the spatial distribution of the In atoms may
be deduced.
The indium fluorescence yield from the standing
wave measurement is written [6] in terms of the
coherent fraction, F&, and the coherent position,
P&, which measures the position of the indium
atoms relative to the substrate planes, normalized
by the diffraction plane spacing, d . (For a single
atom in bulk P&"1.) The yield, ½&, is
½&"½(1#R#2(RF& cos(a!2pP&)).
(1)
Fig. 2. Photon-energy dependence of the reflectivity (lower) and
the In-L fluorescence yield (upper) near the GaAs(0 0 4) Bragg
backreflection condition for the nominally 1/2 ML sample. The
solid lines are the best fits to the data points.
J.A. Gupta et al. / Journal of Crystal Growth 195 (1998) 34–40
Here R and a denote the reflectivity and phase as
given by the dynamical theory of X-ray diffraction
[6,14], and ½ is proportional to the beam flux
which depends linearly on energy. Detailed discussions of the relationship between F&, P&, and
Fourier analysis of the positional distributions
have been published by other authors [6,15].
The coherent fraction provides a measure of the
perfection of the deposited In layer. While an ideal,
perfect interface would yield a coherent fraction of
1.0, corresponding to a perfect, d-like distribution
of In atoms, thermal effects reduce the maximum
value obtainable during an XSW measurement.
Consideration of the Debye—Waller factor for the
GaAs substrate suggests that for a structurally perfect layer the measured value would be approximately 0.9 [16].
In Figs. 1 and 2 the solid lines represent the fits
to the experimental data. The reflectivity curves
were fitted using the dynamical theory [6,14], and
the fitting includes a Gaussian broadening function
which accounts for the monochromator resolution.
Using the reflectivity, phase and broadening determined from the reflectivity curves, the In-fluorescence spectra were fitted using Eq. (1) to determine
the adjustable parameters F& and P&. The results
are given in Table 1. Positions of the In atoms
relative to the GaAs(0 0 4) planes with spacing
d "1.4133 A> are then given by P&d and also
1
1
appear in Table 1.
It is instructive to compare the results for the
1 ML sample with results obtained in similar samples produced by MBE. Table 1 shows the values of
P& and F& which have been reported previously
[7—10]. It should be noted that the coherent position is determined modulo d , so that a coherent
1
37
position of 0.116 is equivalent to 1.116 (allowing
a more direct comparison with the other results)
[6].
In Ref. [8], the XSW positional result was compared with the predictions of MET [11]. Taking
account of the InAs lattice strains parallel, e , and
,
perpendicular, e , to the InAs/GaAs interface,
,
where
C
(2)
e "!2 e ,
,
,
C
the strained lattice constants may be determined.
The unstrained InAs lattice constant is a "
'
6.0584 A> , while for pseudomorphic growth the coherency condition is a "a
"5.6532 A> . Since
,
% e "(a !a )/a ,
(3)
,
,
' '
e "(a !a )/a ,
(4)
,
,
' '
the MET predicts that the In atoms should reside
1.6247 A> above the last As layer of the substrate.
Comparing the positional result from our ALE
monolayer with the MBE results, it appears that
our sample is not as highly strained as the MBE
samples. At the same time, the coherent fraction of
0.766$0.051 is among the best measured, but still
somewhat lower than the ideal value of 0.9 which
would be measured for a structurally perfect layer.
Without the thermal effects, our result would be
&0.851, which suggests that the quantum well
interface in our sample is quite smooth; reduction
from ideality likely reflects a combination of
compositional variation at the interface, interface
roughness, or a strain-induced spread in the In
positions perpendicular to the plane. Processes
such as In segregation have been observed for this
Table 1
XSW parameters for ALE samples determined from the In L-fluorescence data compared with results reported for MBE-grown films.
The In—As planar distances were calculated from the measured coherent positions
1 ML (Present work)
1/2 ML (Present work)
1 ML (MBE) [7]
1 ML (MBE) [8]
1 ML (MBE) [9]
1 ML In
Ga
As (MBE) [10]
Coherent position
Coherent fraction
In—As planar distance (A> )
1.116$0.010
1.063$0.021
1.17$0.02
0.16$0.02
1.154$0.01
0.053$0.02
0.766$0.051
0.88$0.12
0.58$0.07
0.73$0.1
0.43$0.03
0.53$0.1
1.577$0.014
1.502$0.030
1.65$0.03
1.64$0.03
1.63$0.01
1.488$0.028
38
J.A. Gupta et al. / Journal of Crystal Growth 195 (1998) 34–40
used to predict the concentration of the layer in
a similar fashion to the XRD determination of alloy
concentration by the measurement of lattice constant in thicker films [17].
Assume that the XSW position is correct, and
that the In atoms are arranged in a single layer.
Based on our experimental result this layer cannot
be completely covered by In. If the layer actually
consists of an alloyed distribution, In Ga As,
V \V
then we can solve for x based on the MET.
From Vegard’s law, the unstrained lattice constant of the layer, a , is
a "xa #(1!x)a
.
(5)
'
% The elastic constants for the alloyed layer are given
by the concentration-weighted values for InAs and
GaAs [18], as
C "xC'#(1!x)C% ,
C "xC'#(1!x)C% .
From MET
Fig. 3. Photoluminescence emission from a nominally 1 ML
InAs film on GaAs(0 0 1), buried beneath a 2550$25 A> GaAs
cap.
system [13], although we cannot resolve details of
such a process with an XSW measurement using
only one set of substrate diffraction planes. For the
1/2 ML sample we have measured a coherent fraction of 0.88$0.12, which corresponds to &0.98
after accounting for the thermal effects.
Fig. 3 shows a photoluminescence spectrum obtained at 4.2 K for a nominally 1 ML sample, with
a 2550$25 A> cap as described previously. The
peak location is found to be 1.459 eV, with a full
width at half maximum of 5.74$0.01 meV. The
location of the peak is close to the expected position for excitonic emission from an InAs monolayer
[4], while the linewidth is as narrow as the best
results reported elsewhere [2,4,5] and is indicative
of satisfactory growth conditions.
What is the significance of our positional
measurement? XSW measurements of samples
grown by MBE [7—10] support the macroscopic
description of this interface. Our results may be
(6)
a "a (e #1),
,
,
or
(7)
xC'#(1!x)C% (a
a "a !2
!a ).
,
xC'#(1!x)C% % (8)
The value of x can now be determined by substituting equation Eq. (5) into Eq. (8), and using the
standing wave result a "P&a
. Our measured
,
% values of a "6.309$0.057 A> and a "6.009$
,
,
0.119 A> lead to x"0.794$0.068 and x"0.446$
0.149, for the 1 and 1/2 ML films, respectively.
If this same approach is applied to the results of
Woicik et al. [10], in which XSW measurements
were made for a single In Ga As layer with
V \V
a nominal x value of 0.48, it is found that the
measured coherent position of 1.053$0.02 is indicative of an alloy composition x"0.378$0.142.
This is quite reasonable, since the input Ga : In
ratio and growth rates were determined from
The values for InAs are C'"8.329;10 N m\,
C'"4.526;10 N m\, and for GaAs C% "11.9;
10 N m\, C% "5.38;10 N m\.
J.A. Gupta et al. / Journal of Crystal Growth 195 (1998) 34–40
Fig. 4. X-ray rocking curve data obtained near the GaAs(0 0 4)
symmetric substrate reflection, for *h"h!h . Data for the
1 and 1/2 ML samples (upper and lower curves, respectively) are
indicated by points. Solid lines indicate the results of dynamical
simulations as described in the text.
growths with much thicker layers. Because the indium and gallium shutters were open simultaneously during the MBE growth, the alloy-like
distribution is to be expected. In contrast, for our
ALE films no Ga-source molecules were incident
on the substrate during the InAs layer growth.
Fig. 4 shows the XRD data for the 1 and 1/2 ML
samples. It is interesting to note that the Pendellösung fringes are clearly visible out to 7200 arcsec
on either side of the main substrate reflection. This
is somewhat remarkable for such thin layers of
InAs capped by nominally 100 A> of GaAs. Highresolution XRD studies of thin InAs layers have
been reported previously [2,7], in which cases the
GaAs caps typically exceeded &275 A> .
The XRD data were modeled using BEDE dynamical simulation software employing the
Takagi—Taupin equations [19]. In the discussion of
39
the XSW data, we have conjectured that the In
atoms reside in single In Ga As layers, and that
V \V
the group III layer has a distance a /4 from the last
,
As plane of the substrate. Thus the net displacement of the GaAs cap from the substrate is a /2.
,
The solid lines in Fig. 4 show the results of our
simulations with the alloy compositions and layer
thicknesses determined in this way. In addition, the
GaAs cap thicknesses determined from the simulations are 97$3 A> for the 1 ML sample, and
85$3 A> for the 1/2 ML sample. Comparing the
data and the simulations, it appears that our inferences based on the XSW results provide a good
description of the XRD data. It is important to
mention, however, that the XRD data could be
interpreted differently. For instance, a reasonable
simulation for the 1 ML sample rocking curve
could alternatively have been obtained by supposing a single InAs layer and an associated substratecap displacement of approximately 3.0$0.3 A> ,
although this can not be related to a physical
distribution of In atoms.
Two factors may contribute to the lower than
expected coverage in our monolayer sample. Without the benefit of reflection high-energy electron
diffraction (RHEED) oscillations during the In deposition, the ALE process is at a disadvantage
compared with MBE growth. Specifically, we rely
upon ex situ XRD characterization to estimate the
amount of In deposited. The precision in the In
coverage determined in this way is not adequate to
distinguish between a full monolayer and a 79.4%
alloy layer, as illustrated here. Secondly, our
growth process has employed the “flash-off” technique, first suggested by Brandt et al. for MBE
growth of similar structures [20]. It is possible that
raising the growth temperature after the GaAs cap
ALE cycles may result in a greater-than-intended
desorption of segregated In atoms, thus contributing to the lower In coverage. Indeed, a limited
desorption is the goal of the flash-off step.
Our interpretation of an alloyed distribution of
In atoms, particularly in the 1/2 ML case, suggests
that for submonolayer coverages the In atoms do
not form monolayer islands, as proposed in the
past [1—3]. Ideally, such islands would reside at
the ideally strained InAs position (1.6247 A> ),
although edge effects at InAs islands might lower
40
J.A. Gupta et al. / Journal of Crystal Growth 195 (1998) 34–40
the measured position. We must emphasize that
our proposed structure does not constitute
a unique and unambiguous interpretation of the
data. It is well known that segregation of In atoms
is a factor limiting the growth of perfect InAs layers
[13], although our calculations suggest that the
segregation process alone cannot explain the coherent positions we have measured in our samples
[21].
4. Conclusions
We have performed the first X-ray standing wave
study of ultrathin InAs layers buried in GaAs, deposited by ALE. A comparison between the results
for our nominally 1 ML sample and previous studies with MBE samples suggests that our sample
does not consist of a single, highly-strained In
layer. Rather, a calculation based on the macroscopic elastic theory indicates that the In atoms are
distributed within an In Ga As layer, with x"
V \V
0.794$0.068. For the nominally 1/2 ML sample
we find our XSW results to also be consistent with
a single alloy layer, with x"0.446$0.149. Our
simulations show that this interpretation provides
an adequate description of the XRD data. For the
1 ML sample the coherent fraction of 0.766$0.051
is indicative of a fairly uniform In distribution,
giving rise to the narrow PL emission observed.
Factors such as segregation or terrace nucleation
have not been included in the present analysis; with
only one XSW measurement it is not strictly correct to infer any such multiple-location scenario.
Finally, we have only attempted to measure the
location of In atoms relative to the (0 0 4) GaAs
planes. A more detailed, three-dimensional description of the In distribution is required and is the
subject of ongoing experiments.
Acknowledgements
This work was supported by the Natural
Sciences and Engineering Research Council of
Canada. The National Synchrotron Light Source
at Brook-haven National Laboratory, Upton, NY,
is supported by the US Department of Energy
under contract No. DE-AC02-76CH00016.
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