Strain relaxation in InAs heteroepitaxy on lattice-mismatched substrates

Abstract

Abstract Strain relaxation processes in InAs heteroepitaxy have been studied. While InAs grows in a layer-by-layer mode on lattice-mismatched substrates of GaAs(111)A, Si(111), and GaSb(111)A, the strain relaxation process strongly depends on the lattice mismatch. The density of threading defects in the InAs film increases with lattice mismatch. We found that the peak width in x-ray diffraction is insensitive to the defect density, but critically depends on the residual lattice strain in InAs films.

Full text

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Strain relaxation in InAs
heteroepitaxy on lattice-
mismatched substrates
Akihiro Ohtake*, Takaaki Mano & Yoshiki Sakuma
Strain relaxation processes in InAs heteroepitaxy have been studied. While InAs grows in a layer-by-
layer mode on lattice-mismatched substrates of GaAs(111)A, Si(111), and GaSb(111)A, the strain
relaxation process strongly depends on the lattice mismatch. The density of threading defects in the
InAs lm increases with lattice mismatch. We found that the peak width in x-ray diraction is insensitive
to the defect density, but critically depends on the residual lattice strain in InAs lms.
Heteroepitaxy of semiconductors has opened up new possibilities for band-structure engineering and novel
devices, including strained-layer structures. e exibility in the choice of materials for the formation of het-
erostructures is oen limited by lattice mismatch. Heteroepitaxy in lattice-mismatched systems usually follows
a Stranski-Krastanov (SK) growth mode: a pseudomorphic two-dimensional layer is formed below a certain
critical thickness, and is followed by the formation of three-dimensional islands. A prototypical example of such
a system is Ge on Si (lattice mismatch ≈4.2%), in which layer-by-layer growth is limited to 3–4 monolayer (ML).
e island formation is highly undesirable, because it prevents the growth of smooth lms and introduces nucle-
ation centers for defects. us, signicant eorts have been devoted to suppress the strain-induced islanding and
strain-relieving defects. It has been reported that the islanding in the Ge/Si system is eectively suppressed by
introducing As and Sb as surfactant species1–3.
e SK growth occurs also in the InAs/GaAs(001) system having lattice mismatch of 7.2%: InAs islands are
formed at the lm thickness of 1.6 ML4. On the other hand, the use of the (111)A-oriented GaAs substrates forces
the InAs lm to grow in a layer-by-layer mode5–7. e layer-by-layer growth of the (111)A-oriented InAs lm is
accompanied by the formation of a mist dislocation network at the InAs/GaAs interface6, so that the generation
of defects in the lm is strongly suppressed. Similar strain relaxation has been reported for GaSb/GaAs(001) het-
eroepitaxy, which is known for so-called interfacial mist array growth8.
e novel growth technique has been successfully applied to the layer-by-layer growth of InAs on Si(111)9,
GaSb growth on InAs/Si(111)10, and to the improvement of the crystalline quality of InGaAs11 and GaSb12
on InAs/GaAs(111)A. is technique has a great advantage, especially for the growth on Si(111), because the
formation of antiphase domain boundaries in InAs films is suppressed, in contrast with the growth on the
(001)-oriented substrate. However, strain relaxation processes of InAs are far from being completely understood,
and the crystalline quality of InAs has not been studied in detail.
is paper reports the strain relaxation processes and structural properties of InAs lms heteroepitaxially
grown on the lattice-mismatched substrates of GaAs(111)A, Si(111), and GaSb(111)A. While the InAs(111)A
lm grows in a layer-by-layer mode on all substrates irrespective of the lattice mismatch, the strain relaxation
process behaves dierently depending on the lattice mismatch. Fully-strained pseudomorphic InAs layers con-
tinue to grow above ~50 ML on the nearly lattice matched GaSb substrates (lattice mismatch of −0.61%), while
in the InAs/Si system with the largest lattice mismatch of 11.4%, mostly-relaxed InAs lms are formed even at
the very initial stage of the growth. e in-plane compressive strain in InAs on GaAs (lattice mismatch of 7.2%)
gradually relaxed as the growth proceeds, but the strain is not fully relaxed even in the 100nm-thick InAs lm.
Our x-ray diraction (XRD) measurements revealed that the residual strain in InAs lm is responsible for the
peak broadening in XRD proles. On the other hand, the peak width of x-ray rocking curve is insensitive to the
density of threading defects.
National Institute for Materials Science (NIMS), Tsukuba, 305-0044, Japan. *email: OHTAKE.Akihiro@nims.go.jp
OPEN
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Results and discussion
 Figure1(a) shows the variation in the in-plane lattice constant (d110) of the InAs lm growing on the GaAs(111)
A substrate. e d110 values were measured from the distance between the 11 and
1
1
reections in reection
high-energy electron diraction (RHEED) patterns along the [
1
1
2] direction. e data clearly shows that InAs
pseudomorphically grows below ~2 ML, and that the in-plane lattice constant gradually increases with lm thick-
ness above ~2 ML, in good agreement with earlier results6,7. e strain in the InAs lm has relaxed by only ~80%,
even aer the 50 ML-growth.
Similarly to the case for InAs/GaAs(111)A, the InAs lm is two-dimensionally grown on the In-terminated
Si(111) substrate9. However, the strain relaxation processes between the two systems are quite dierent. Shown
in Fig.1(b) is the variation in the d110 value for the InAs growth on the Si(111) substrate. A new set of streaks
from the InAs lm appeared in the RHEED patterns at the very early stage of the growth (~0.6 ML), in addition
to those from the Si substrate. e spacing of streaks is quite close to the value of bulk InAs, and remains almost
unchanged throughout the growth (<50 ML). is indicates that, on the Si(111) substrate, the InAs lm was
nucleated with its inherent lattice constant, and that pseudomorhic InAs layers are not formed. us, it is likely
that the lattice mismatch of InAs/Si (11.5%) is too large to be accommodated by elastic deformation of thin InAs
lms.
In the nearly lattice-matched system of InAs on GaSb(111)A (lattice mismatch ≈0.61%), as shown in Fig.1(c),
no signicant change in the d110 value is observed below 50 ML (17.5 nm). us, it is plausible that 50 ML-InAs
lms are coherently strained to the GaSb substrate. is is consistent with the critical thickness (~20 nm) for
the onset of mist dislocations in InAs on GaSb estimated on the basis of the model proposed by Matthews and
Blakeslee13.
Figure 1. e variation of the in-plane lattice constant (d110) of InAs lms grown on the GaAs(111)A (a),
Si(111) (b), and GaSb(111)A (c) substrates. e values were measured from the distance between the 11 and
1
1
reections in the RHEED patterns.
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Figure2(a,b) show the two-dimensional reciprocal-space maps (RSMs) for the asymmetric 115 reection of
100 nm-thick InAs lms grown on the GaAs(111)A and In-terminated Si(111) substrates, respectively. e verti-
cal and horizontal axes correspond to the indices along the [111] and [
1
1
2] directions, respectively. e in-plane
lattice constant of InAs grown on GaAs is 0.4236 nm, and is quite smaller than that of bulk InAs (0.4284 nm). e
residual strain in the InAs lm (d110 (lm)−d110(bulk))/d110(bulk)) is −1.124%. According to classical elastic
theory, the in-plane compressive strain causes the expansion of the lattice constant, d111, in the direction normal
to the surface. Poisson’s ratio σ of the strained InAs(111)A layer is σ=(c11+2c12+4c44)/
(2c11+4c12−4c44)=1.75, where c11=8.33,c12=4.53, and c44=3.96 (×106 Pa) are the elastic stiness coe-
cients of InAs14,15. us, using the measured d110 value, the d111 value is estimated to be 0.3520 nm, in good agree-
ment with the measured value of 0.3511 nm.
e d110 and d111 values of InAs grown on Si(111) are 0.4281 and 0.3499 nm, which are quite close to those
of bulk InAs (0.4284 nm and 0.3498 nm), as seen in Fig.2(b). The residual in-plane strain is estimated to
be −0.089%, indicating that the InAs lm is mostly relaxed.
In contrast to the case for the compressively strained systems of InAs/GaAs and InAs/Si, InAs lms are tensile
strained on GaSb. e measured d110 (0.4303 nm) and d111 (0.3489 nm) values of the InAs lm are slightly larger
and smaller, respectively, than those of bulk values. e tensile in-plane strain in InAs is relaxed by ~30%, indicat-
ing that the strain begins to relax in the InAs lm below 100 nm. is is broadly consistent with the mechanical
equilibrium model13, from which the critical thickness is estimated to be 20 nm, as mentioned earlier. On the other
hand, the growth experiments on the (001)-oriented GaSb substrate showed that InAs lms as thick as 200 nm are
fully strained16. It is suggested that the strain relaxation mechanism is a strong function of substrate orientation.
Figure3(a–c) compare x-ray rocking curves (XRCs) measured from 100nm-InAs on GaAs(111)A, Si(111),
and GaSb(111)A. e FWHM values are 1627.7 arcsec (a), 230.05 arcsec (b), and 496.83 arcsec (c). It is well
known that crystal imperfections, such as mosaic domains, threading defects, structural inhomogeneities, and
lattice distortions, cause a broadening of XRD proles. However, it is dicult to specify the origin of the peak
broadening from the rocking curves of the symmetric 111 reection alone. On the other hand, RSMs of asymmet-
ric reections provides important information of the structural quality of the InAs lm; as can be seen in Fig.3(a),
the 115 reection has an elliptical shape, which is elongated along the direction perpendicular to the [115] azi-
muth. is means that the broadening of XRD peaks arises from the misorientation of InAs lattice planes. While a
slight broadening is observed in Fig.2(c), such a broadening is not observed in Fig.2(b). In Fig.3(d), the FWHM
values are plotted as a function of the absolute value of residual strain: the FWHM value increases with the abso-
lute value of residual strain. In general, uniformly-strained at layers are unstable against the modulation of the
surface prole, which allows a partial relaxation of the strain by elastic deformation17–19. us, it is likely that the
strained InAs lm on the GaAs(111)A substrate is elastically deformed to accommodate the residual strain. Such
elastic deformation is accompanied by the misorientation of the InAs lattice planes, resulting in the broadening
perpendicular to the reciprocal lattice vector of the corresponding diraction spot.
Figure4(a) shows a representative plan-view transmission electron microscopy (TEM) image of InAs on
Si(111). A high density of threading defects, such as threading dislocations, stacking faults, and stacking-fault
tetrahedra, is clearly observed. e densitiesof these defects are listed in Table1. Similar TEM images were
obtained for InAs on GaAs(111)A and GaSb(111)A with lower densities of threading defects. On the other hand,
Figure 2. Reciprocal-space maps (RSMs) of the asymmetric 115 reection measured from 100 nm-InAs lms
on GaAs (a), Si (b), and GaSb (c) substrates. e dashed lines show the position of bulk InAs. e RSMs were
generated using the Bruker DIFFRAC.LEPTOS soware package ver. 7.7, and were assembled using the Adobe
Illustrator CS6.
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as mentioned earlier, the FWHM value of XRC for InAs/Si is much smaller than that for InAs/GaAs. e FWHM
value of XRC is oen cited as a measure of structural quality: it has been generally believed that the existence of
high densities of threading defects causes the broadening of XRC width. However, the present results show that
narrower (broader) peaks in XRCs are not necessarily an indication of lower (higher) density of threading defects
in heteroepitaxial layers.
Previous studies have shown that the two-dimensional growth of InAs on GaAs(111)A and Si(111) substrates
is accompanied by the formation of a mist dislocation network at the interfaces to accommodate the strain6,7. In
the ideal case, perfect dislocation arrays are formed covering all the interface area, leaving the growing lms free
of threading dislocations. However, as shown in Fig.4(b), the actual mist dislocation arrays are not perfect; it is
likely that the disorder in the mist dislocation network acts as the source of the threading defects (arrows). e
averaged period of mist-dislocation network pmd is given by pmd=b/f, where b is the Burgers vector and f is the
lattice mist. For partially-relaxed 100 nm-InAs on GaAs(111)A, the pmd value is estimated to be 6.7 nm, which
is twice as large as that for the fully-relaxed interface of InAs/Si(111) (3.3 nm). If we assume that the nucleation
probability of threading defects increases with the density of mist dislocations, we can explain why the defect
density is higher in the InAs lm on Si(111).
In the nearly lattice-matched InAs/GaSb system, the densities of threading defects are slightly lower than
those for InAs/GaAs, as shown in Table1. On the other hand, since the lattice mismatch of InAs/GaSb is more
than an order of magnitude smaller than that for InAs/GaAs, one may expect a much lower density of mist dis-
locations. Figure4(c) shows the plan-view TEM image of 100nm-InAs/GaSb(111)A; since the sample contains
both the InAs lm and the GaSb substrate, mist dislocations at the interface are imaged (yellow dashed lines), as
well as threading defects (red arrows). We note that only threading defects in the InAs lms are imaged at thinner
(<100 nm) regions (See Supplementary Fig. S1). As compared with InAs on GaAs (Fig.4(b)), the distribution
of the mist dislocations is highly irregular; such an irregular conguration is likely to be responsible for the
increase of threading defects: as indicated by arrows in Fig.4(c), threading dislocations are oen observed at
the end of mist dislocations. us, it is reasonable to consider that the extremely large critical thickness for the
generation of mist dislocation makes it dicult to rearrage highly separated mist dislocations to an ordered
periodic network at the buried interface beneath thick InAs layers.
Figure 3. 111 XRCs of 100 nm-InAs lms grown on GaAs(111)A (a), Si(111) (b), and GaSb(111)A (c).
(d) FWHM values of the 111 XRCs plotted as a function of residual strain.
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Conclusions
e eects of lattice mismatch on the growth mode and strain relaxation process in InAs heteroepitaxy on
GaSb(111)A, GaAs(111)A, and Si(111) substrates have been studied. e highest and lowest defect densities are
identied in the highly lattice-mismatched InAs/Si and the nearly lattice-matched InAs/GaSb systems, respec-
tively. On the other hand, the peak width in XRD is insensitive to the lattice mismatch and is roughly proportional
to the residual strain in InAs lms.
Figure 4. Plan-view TEM images of InAs lms grown on Si(111) (a) and GaSb(111)A (c) substrates. (b) shows
the scanning tunneling microscopy (STM) image of 4 ML-InAs on GaAs(111)A. Image dimensions of (a–c) are
900 nm×1200 nm, 200 nm×150 nm, and 1500 nm×2000 nm, respectively. e STM image was acquired in
the constant current mode with a tunneling current of 0.1 nA and a sample voltage of −3 V. e arrows marked
TD, SF, and SFT, indicate the threading dislocation, stacking fault, and stacking-fault tetrahedron, respectively,
while the position of the mist dislocation (MD) is indicated by the yellow dashed lines. We note that the Si
substrate was completely removed from the sample (a), while the sample (c) consists of the InAs lm and GaSb
substrate.
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Methods
e growth experiments were carried out in a multi-chamber MBE system. e As-doped Si(111) wafer was
cleaned by radiatively heating at 950°C in the MBE chamber20. Clean and well-ordered (7×7) reconstructions
were conrmed by STM, x-ray photoelectron spectroscopy, and RHEED. In-terminated (4×1) reconstruction
was prepared by depositing 1 ML of In on the Si(111)-(7×7) surface at 450°C. e clean surfaces of GaAs(111)
A and GaSb(111)A were prepared by growing undoped homoepitaxial layers at 450°C on the thermally cleaned
substrates21,22. e GaAs (GaSb) layers were grown with an As4/Ga (Sb4/Ga) ux ratio of ~50 (~8). While only a
(2×2) reconstruction is observed on the GaAs(111)A surface under the conventional MBE condition, (2×2)
(2
3
×23
) and (1×5) reconstructions were observed on GaSb(111)A as the surface Sb coverage is increased. In
the present study, GaAs(111)A-(2×2) and GaSb(111)A-(2
3
23×
) surfaces were used as substrates for the InAs
growth.
InAs lms were grown on the GaAs(111)A substrate at 450 °C with an As4/In ux ratio of ~50. On the other
hand, the growth on Si(111) and GaSb(111)A results in the formation of twins and islands under otherwise iden-
tical condition. us, to suppress the growth front roughening, the growth on these substrates were carried out
using As2 molecules having higher reactivity to In adatoms with a higher As2/In ratio of ~150. e growth rate of
InAs was approximately 0.034 ML/s, which was calibrated by RHEED intensity oscillation measurements on the
(001)-oriented InAs substrate. Here, 1 ML of InAs is dened as 6.3×1014 atoms/cm2, which is the site-number
density of unreconstructed InAs(111)A surface. Great care was taken to avoid the possible adsorption of As
molecules on Si(111) substrate for the growth on the In-terminated Si(111) substrate, because the In-terminated
Si surface easily reacts with As molecules to transform itself to the As-terminated one, on which InAs grows in
an island mode9. us, the InAs growth on Si is initiated under the lower As2/In ratio of 30, and the ux ratio is
increased to ~150 aer the 10 ML-growth. e growth process of InAs was monitored by RHEED in real time,
and the structural properties have been characterized using XRD and TEM. High resolution XRD measurements
were carried out using a monochromatic Cu Kα1 radiation. A channel-cut analyzer crystal was used for XRC
measurements. RSM data were obtained using an one-dimensional array detector. e density and type of thread-
ing defects in InAs lms were assessed by TEM operated at 200 keV.
Data availability
e data that support the ndings of this study are available from the corresponding author upon reasonable
request.
Received: 25 November 2019; Accepted: 31 January 2020;
Published: xx xx xxxx
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Acknowledgements
is work was partlysupported by JSPS KAKENHI Grant Number 19K04480.
Author contributions
A.O. conceived and conducted the growth experiments, T.M. and Y.S. carried out the XRD measurements. All
authors reviewed the manuscript.
Competing interests
e authors declare no competing interests.
Additional information
Supplementary information is available for this paper at https://doi.org/10.1038/s41598-020-61527-9.
Correspondence and requests for materials should be addressed to A.O.
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