PHYSICAL REVIEW MATERIALS 2, 011601(R) (2018)
Rapid Communications Editors’ Suggestion
Elastically frustrated rehybridization: Origin of chemical order
and compositional limits in InGaN quantum wells
L. Lymperakis,1,*T. Schulz,2,†C. Freysoldt,1M. Anikeeva,2Z. Chen,3X. Zheng,3B. Shen,3C. Chèze,4M. Siekacz,5
X. Q. Wang,3,6,‡M. Albrecht,2and J. Neugebauer1
1Max-Planck-Institut für Eisenforschung GmbH, Max-Planck-Straße 1, 40237 Düsseldorf, Germany
2Leibniz-Institute for Crystal Growth, Max-Born-Straße 2, 12489 Berlin, Germany
3State Key Laboratory of Artiﬁcial Microstructure and Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
4Paul Drude Institute für Festkörperelektronik, Hausvogteiplatz 5-7, 10117, Berlin, Germany
5Institute of High Pressure Physics, Polish Academy of Sciences, Sokolowska 29/37, 01-142 Warsaw, Poland
6Collaborative Innovation Center of Quantum Matter, Beijing, China
(Received 16 May 2017; revised manuscript received 14 July 2017; published 8 January 2018)
Nominal InN monolayers grown by molecular beam epitaxy on GaN(0001) are investigated combining in
situ reﬂection high-energy electron diffraction (RHEED), transmission electron microscopy (TEM), and density
functional theory (DFT). TEM reveals a chemical intraplane ordering never observed before. Employing DFT,
we identify a novel surface stabilization mechanism elastically frustrated rehybridization, which is responsible
for the observed chemical ordering. The mechanism also sets an incorporation barrier for indium concentrations
above 25% and thus fundamentally limits the indium content in coherently strained layers.
Modern optoelectronic devices rely on our ability to tune the
electronic band structure of ultrathin heteroepitaxial structures
via the chemical composition [1–3]. A prime challenge often
encountered when designing and optimizing such devices
is the failure to achieve the targeted chemical composition.
This is related to the fact that the speciﬁc composition is
thermodynamically or kinetically unstable. InxGa1−xN alloys
are a prime example where such thermodynamic limitations
have a severe impact on device features and performances. If
the In composition in these alloys could be controlled from
x=0 (GaN; band gap 3.5 eV) all the way up to x=1 (InN;
band gap 0.7 eV), light emitting devices from the infrared to
the ultraviolet region could be realized. However, so far, the
uppermost In concentrations in coherently grown 2D (In,Ga)N
layers were reported to be around 30% [4–6], which severely
narrows the tunability of InGaN-based emitters.
Such stoichiometric limits may be overcome if the thermo-
dynamic stability for a given composition is more favourable
at the surface than in bulk. In coherently grown heteroepitaxial
layers, the loss of translation symmetry at the growth surface as
well as the strain introduced by the lattice mismatch may shift
the thermodynamic potential of the system, stabilizing alloys
that are unstable in the bulk state [7–11]. Important phenomena
related to this mechanism are compositional latching [12,13],
strain enhanced solubility via suppression of phase separation
or spinodal decomposition [14–16], or increased miscibility
of compounds at the surface, which are unstable in the bulk
[11,17,18]. While these aspects have been discussed in detail
in the past, less attention has been paid to the effects of
*Corresponding author: firstname.lastname@example.org
†Corresponding author: email@example.com
‡Corresponding author: firstname.lastname@example.org
surface termination and surface reconstructions on thermal
decomposition of the constituents and its role in controlling
alloy composition or chemical ordering. Motivated by this, we
have studied stoichiometric limitations in the (In,Ga)N system
in samples grown by means of plasma assisted molecular beam
epitaxy (PAMBE). For this purpose, we have combined in situ
RHEED, high-resolution TEM, and ab initio calculations.
In this Rapid Communication, we show that deposition of
a nominal InN monolayer (ML, i.e., switching off the Ga-ﬂux)
forms a chemically ordered InxGa1−xN ML, exhibiting a mean
In content of 25%, even a systematic wide-range variation of
the growth parameters did not succeed in overcoming this com-
positional limit. Employing DFT calculations in combination
with thermodynamic concepts we show that a novel surface
mechanism—elastically frustrated rehybridization—leads to
surface geometries that defy our present understanding of sur-
face stabilizing mechanisms, as well as to severe stoichiometric
We targeted to grow short period superlattices consisting of
InN MLs separated by GaN barriers on GaN (0001) surfaces
for band gap tuning via changing the width of the barrier .
Using only binary compounds supposedly avoids strong local
compositional inhomogeneities as present in conventional
pseudobinary InGaN alloys with high indium contents .
After growth of a GaN buffer layer at 800°C on a GaN
(0001) template on sapphire substrate, we start the deposition
of the superlattice. For this purpose, the growth temperature
is reduced to 550 °C–650 °C, the Ga ﬂux is switched off and
the surface is kept under N ﬂux to remove metallic Ga from
the surface. Then the Ga shutter is closed and the In shutter
is opened for depositing a ML of nominal InN on the GaN
surface. Finally, the In ﬂux is switched off and the nominal InN
layer is capped by a GaN barrier. The short period superlattices
typically consist of 10 periods. The GaN barriers are deposited
2475-9953/2018/2(1)/011601(6) 011601-1 ©2018 American Physical Society
L. LYMPERAKIS et al. PHYSICAL REVIEW MATERIALS 2, 011601(R) (2018)
FIG. 1. (a) Experimental images of the (In,Ga)N ML region using negative Cs imaging conditions in (a) the 1100and (b) the 1120zone
axis. TEM image simulations of an (In,Ga)N ML with an In content of 25% in the (c) 1100and (d) 1120zone axis. 90% of the In atoms are
arranged in a (2√3×2√3)R30◦conﬁguration and 10% are randomly distributed. Specimen thickness for the 1100was 7 nm; for the 1120
at a ﬁxed III/V ratio of 1.1 adopting the growth temperature
of the respective InN layer. Descriptions of the generic growth
processes can be found in Refs. [21–24]. Structural and com-
positional analyses were performed in an aberration corrected
transmission electron microscope (TEM) FEI Titan 80-300,
operated at 300 keV and equipped with an on-axis mounted
EAGLE charge coupled device (CCD) camera.
Systematically varying the growth parameters for the
(In,Ga)N deposition, such as temperature (550 °C–650 °C),
III/V ratio (0.8–1.5), N ﬂux (6–14 nm/min) or growth time
(4–64 s, corresponding to nominal thicknesses of 2–32 MLs
of InN) neither resulted in a layer thickness exceeding a
single ML nor a change in the observed composition in
the TEM micrographs. Figure 1(a) displays a typical TEM
image of the (In,Ga)N ML recorded in the 1100zone axis.
The (In,Ga)N ML is characterized by a periodic intensity
variation, with each third atomic column appearing darker than
the surrounding GaN matrix. Under the imaging conditions
used, these darker spots indicate atomic columns with a high
In content, while the bright spots refer to atomic columns
composed of GaN. The ordering occurs in patches extending
several nanometers within the ML plane. In the 1120zone
axis [see Fig. 1(b)], the ML is practically indistinguishable by
means of contrast from the surrounding GaN matrix. While
the 3×periodicity has been observed earlier by RHEED as a
transient phenomenon , the persistence after overgrowth
demonstrated by TEM (and invisible to RHEED) has to our
knowledge never been observed before.
The experimentally observed 3×periodicity could be
explained by recent theoretical ﬁndings according to which
a√3×√3 In ordered ML with a 33% In concentration
is a T=0 K thermodynamic ground state . However,
this previously identiﬁed ordered structure is not stable at
our experimental growth temperatures (see Ref. ). We
performed extensive DFT and Monte Carlo calculations for
a variety of bulk and surface alloys, which will be reported
elsewhere, and the key outcome was that single (In,Ga)N
MLs embedded in a GaN matrix always undergo an order-
disorder transition well below the actual growth tempera-
ture. We therefore conclude that the experimentally observed
ordering cannot be explained by the thermodynamic stability
of the embedded ordered InxGa1−xN quantum well. Rather, it
must be the result of an ordered surface structure, different
from the In-adlayer structure studied in Ref.  that is
stable only under In-rich growth conditions. Furthermore, it
is thermodynamically stable at growth temperature and keeps
stable even if overgrown by GaN.
In order to test this hypothesis, we systematically varied
surface reconstruction, total In concentrations, and chemical
ordering of (0001) (In,Ga)N surfaces. The surface energy of
these structures were computed by DFT calculations within
the local density approximation (LDA). The surfaces were
modeled with a slab geometry with various surface unit cells:
(n√3×n√3)R30◦(n=1,2), n×n(n=1,2,3,4), as well
as orthogonal (n×n)R90◦(n=2,4).
We ﬁrst focus on surface geometries that can be rationalized
by well-established principles. (1) For N-rich conditions,
group-III-nitride surfaces are expected to obey the electron
counting rule (ECR), i.e., all N/metal dangling bonds should
be doubly occupied/empty, respectively [28,29]. This rule
restricts severely the number of possible conﬁgurations. (2) For
a given reconstruction, Ga/In distribution tends to maximize
the number of Ga-N bonds at the expense of In-N bonds,
because the latter ones have a signiﬁcantly weaker bond energy.
In consequence, undercoordinated sites, where the cation has
not four but only three or two nitrogen neighbors, will be
preferentially occupied by In since this minimizes the number
of weak In-N bonds. This highly intuitive picture has been
successfully used to explain various phenomena on (In,Ga)N
surfaces [30,31]. (3) In atoms tend to stay away from each other
to minimize dilatational stress at short distances. The stress is
a consequence of the larger atomic radius of In compared to
Ga, which makes the In-N bond length ≈11% longer than the
It turned out that none of the energetically preferred
structures constructed from these principles could explain the
experimentally observed (√3×√3)R30◦like structure or a
multiple thereof. We therefore extended our search to non-
conventional structures that disobey some or all of the above
criteria. This search revealed that, although the ECR is valid
ELASTICALLY FRUSTRATED REHYBRIDIZATION: … PHYSICAL REVIEW MATERIALS 2, 011601(R) (2018)
x in InxGa1-xN
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
FIG. 2. Chemical potential μ =Etot
nas a function of
nis the total energy of a (2√3×2√3)R30◦slab
with nIn atoms in the top surface layer. Green/blue and red dots
correspond to the lowest- and higher-energy conﬁguration/s for each
x, respectively. The dashed lines are guidelines for the eye. (Inset)
Top view of the lowest-energy (2√3×2√3)R30◦In0.25Ga0.75N
conﬁguration. Small/black dots denote the N adatoms and small/open
balls the N atoms. Blues balls indicate the In atoms and red and green
balls distinguish the coordination inequivalent Ga atoms. Group-III
atoms at the red sites are triply coordinated, while at the green sites
they are fourfold coordinated. The energy required to incorporate In
at the red sites is more than 0.87 eV higher than at the green position.
under N-rich conditions, In prefers surface sites that according
to our present understanding should be highly unfavorable.
The representative model sketched in Fig. 2allows us to
visualize all the identiﬁed low-energy structures. It consists
of a metal-polar (2√3×2√3)R30◦surface with three triply
coordinated N adatoms on top. This structure obeys the ECR by
construction, independent of the speciﬁc distribution of the In
and Ga atoms in the metal layer. The blue and green colors mark
fourfold coordinated and the red one threefold coordinated
metal atoms. To account for the elastic repulsion between
two neighboring In atoms, the four-fold coordinated sites are
split into two colors: considering that an In atom occupies a
blue site, it should be energetically unfavorable for another
In atom to occupy a neighboring green site. Starting from an
In-free 2 ×2 N adatom surface, we systematically replace Ga
by In atoms. In each step, we compute the energy for a single
substitution on all symmetry inequivalent sites. To proceed
to more In, we then keep the lowest energy conﬁguration
found at this stage, and compute the substitution energies when
adding one more In atom. The corresponding Ga-In exchange
energies, relative to the substitution of a single In, are plotted
in Fig. 2and show a clear gap in the order of an eV between
the three- and fourfold coordinated sites in favor of the latter.
Surprisingly, the actually observed energetic trends defy our
previous understanding that the surface tries to minimize the
number of weak In-N bonds. Rather, In has a strong tendency
to go onto a four-fold coordinated site leaving a Ga atom on
the threefold site. Furthermore, bringing two In atoms onto
FIG. 3. On-site projected density of states (pDOS) of a 2 ×2N
adatom (0001) GaN surface with 25% InN at the topmost surface
layer. (a) and (b) The In atom sits at a fourfold/triply coordinated site,
respectively. The blue curves indicate the pDOS on the N adatom and
on the ﬁrst surface layer atoms. The gray shaded area denotes the
pDOS from the fourth surface layer and the yellow shaded area the
highest occupied surface state. The arrows indicate the onset of
the lowest unoccupied surface states and the horizontal solid lines
the position of the highest occupied states. (Insets) Yellow, red, and
green colored density plots indicate the partial charge density of
the states in the energy range shaded in yellow, red, and green in
the pDOS, respectively. (Insets bottom) Schematic representation
of the tetrahedra formed by the triply coordinated metal atoms and
the three N atoms bound to them. The red/green isocontour surface
shows the corresponding dangling bond state. Dark/light small balls
denote the N adatom/atoms, respectively. Red/green balls are the
In/Ga atoms, respectively. The dark green in the left inset denote
the triply coordinated Ga atom.
nearest neighbor sites (blue and green) costs a small energy
penalty (50–150 meV per pair). As the total In concentration
increases, the number of such pairs inevitably grows when the
In is put outside the sublattice depicted in blue, creating an
increasing gap between the next low-energy site (blue) and the
less favorable ones (green).
The trends in the computed chemical potential for the
various sites immediately explains the observed experimental
limitations in achieving higher In concentrations as well as
chemical ordering. Substituting In on only the blue sites leaves
the chemical potential essentially ﬂat, i.e., adding one, two,
or three In atoms costs essentially the same energy. However,
adding a fourth In atom and thus increasing the In concentration
from 1/4 to 1/3 increases the In potential by ≈0.3eV. To
realize this increase in the In chemical potential in our MBE
would require to raise the In ﬂux by a factor of ≈5. Such
a huge increase in the In ﬂux would eventually switch the
growth conditions to In-rich, which will either stabilize two
MLs of In on the surface or ﬂood the surface with In, resulting
in In droplets and poor growth morphology. The challenge
to realize such a huge increase in the chemical potential
becomes even more evident when comparing this value with
the heat of formation of InN (0.2 eV) which corresponds
L. LYMPERAKIS et al. PHYSICAL REVIEW MATERIALS 2, 011601(R) (2018)
FIG. 4. In situ RHEED pattern after deposition of (a) and (b) GaN, as well as (c) and (d) InN along the 1100and the 1120azimuth,
to the maximum interval the potential can have when in
thermodynamic equilibrium with InN.
The question remains which mechanism stabilizes a struc-
ture that violates the established principles. In order to address
this question, we compare the electronic density of states
(DOS) of a surface where the In atom occupies one of the
low-energy fourfold coordinated (blue) sites with that of the
conﬁguration where the In atom is sitting on one of the triply
coordinated (red) sites (see Fig. 3). The latter conﬁguration
should be the preferred conﬁguration, following the established
chemical bond-strength principle. As can be seen in the DOS,
the large energy gain of the fourfold coordinated site is a direct
consequence of a sizable downward-shift of a doubly occupied
surface band (marked by the yellow color). An inspection of the
corresponding wave function reveals that this doubly occupied
surface band for both structures is related to the dangling bond
state of the neighboring surface N adatom (yellow isocontour
surface in Fig. 3).
This result may come as a surprise, since the N adatom has
in both structures the same three-fold coordination. Inspecting
the unoccupied states reveals the underlying mechanism: As
shown in Fig. 3the unoccupied orbitals of the energetically
preferred structure with the fourfold coordinated In atom are
shifted upwards. While the unoccupied states have no direct
impact on the energetics and thus the thermodynamic stability
of the surface, according to the bond orbital picture an upward
shift of the antibonding orbital is accompanied by a downshift
of the occupied bonding orbital, which effectively reduces the
energy of the system. The downshift of the occupied orbital
though cannot be observed directly, because it hybridizes with
the valence-band manifold below the band gap.
Let us now consider the triply coordinated cation. The triply
coordinated cation at the free surface (red color in Fig. 3)
can relax by shifting its position along the surface normal.
In case of Ga this ﬂexibility allows the cation dangling bond to
rehybridize from the bulklike sp3dangling bond conﬁgurations
to a more p-like conﬁguration (raising the energy as seen in
Fig. 3) while the back bonds rehybridize from sp3to a planar
sp2conﬁguration. The sp 2conﬁguration lowers the bond
energy with the N atoms and leads to an inward displacement
of the triply coordinated cation. While a Ga atom, which ﬁts to
the underlying lattice, gains energy through this energetically
favorable rehybridization, this is not the case for an In. The
inward displacement of the atom in this case would be inhibited
by the too large atomic radius of the In atom. The necessary
strain energy exceeds the gain due to rehybridization and thus
causes a large elastic frustration. We call this new mechanism,
which causes the technologically well-known stoichiometric
limitations in (In,Ga)N alloys, elastically frustrated rehy-
Comparing our experimental TEM images against image
simulations based on the above identiﬁed (2√3×2√3)R30◦
conﬁguration and considering a residual chemical disorder,1
we ﬁnd excellent agreement on the near atomic level between
simulation and experiment [see Figs. 1(c) and 1(d) for the
1100and the 1120zone axis, respectively]. Even ﬁne
details such as the slightly increased intensity below the
darker intensity spots (corresponding to the In-rich atomic
columns) in the 1100projection can be identiﬁed in the
experiment. However, an unequivocal identiﬁcation of the
atomic conﬁguration solely by contrast analyses would require
larger areas of ordered patches (see supplemental material).
To distinguish between the two structures, we determined the
In concentration in the ML by a lattice parameter analysis
which is discussed in the supplemental material. This analysis
yields an In concentration of 25%, allowing to rule out
the (√3×√3)R30◦structure in perfect agreement with the
ab initio predictions.
To further verify that the ab initio predicted (2√3×
2√3)R30◦surface with 25% In content is indeed the source
110% of the In atoms were randomly distributed.
ELASTICALLY FRUSTRATED REHYBRIDIZATION: … PHYSICAL REVIEW MATERIALS 2, 011601(R) (2018)
of the observed chemical ordering and the compositional lim-
itations we investigated the respective reconstructions during
growth by RHEED. At the end of the GaN barrier growth, the
RHEED exhibits a 2 ×2 surface reconstruction, as displayed
in Figs. 4(a) and 4(b) for the 1100and the 1120azimuth,
respectively. This reconstruction is the expected one for N-rich
conditions of GaN and agrees with surface calculations of
Northrup et al. . Subsequent deposition of InN leads
to a 3×periodicity along the 1100azimuth, while a 1×
periodicity persists along the 1120azimuth, as shown in
Figs. 4(c) and 4(d), respectively. These observations are con-
sistent with those described in Ref. , which the authors
interpreted as a (√3×√3)R30◦reconstruction. However,
the differences between a (2√3×2√3)R30◦and a (√3×
√3)R30◦N-adatom reconstruction in RHEED are negligible
(see supplemental material). A previous in situ RHEED study
estimated that the 3×streak intensity along the 1100azimuth
maximizes for a nominal In coverage of around 0.33 .
Since in this estimate desorption and decomposition have not
been included, which both decrease the actual In content, the
lower In content with 25% predicted by our ab initio study
and TEM analyses appears to be consistent. Our RHEED data
show the 3×periodicity along the 1100azimuth to be stable
for temperature as high as 650 °C (see Ref. ). This is a
remarkably high temperature when compared against typical
growth temperatures for (In,Ga)N alloys with a high In content
. Further InN deposition causes a reduction of the 1 ×3
RHEED reﬂex intensity. We trace this back to the fact that once
the In content in the ML reaches 25%, further In incorporation
is inhibited but instead accumulated on the surface. The same
argument also explains our experimental observation that the
thickness of the (In,Ga)N is limited to a single ML.
In summary, by combining TEM, RHEED, and DFT calcu-
lations we have demonstrated that the growth of nominal InN
MLs on GaN (0001) by MBE under slightly N-rich growth
conditions leads to ordered MLs with a mean In content of
25%, irrespective of the amount of In provided to the surface.
The severe limitation of the In concentration is explained by a
novel mechanism, elastically frustrated rehybridization, which
prevents In atoms from occupying low-coordinated surface
sites. The observed preference of In for fourfold coordinated
surface sites reveals not only a novel mechanism, but has
direct consequences for the growth of these technologically
highly relevant ﬁlms: its high thermodynamic stability limits
the maximum In concentration to 25% as well as the thickness
to a single ML when switching off the Ga ﬂux. Our ﬁndings
are the ﬁrst example of a surface induced ordered InGaN
quantum well in the III nitrides and reveal fundamental limi-
tations for extending the compositional range for this material
system via digital alloying. The observed mechanism may also
open the route to growing purposefully ordered ML alloys
in (In,Ga)N/GaN and possibly other alloy systems, which
substantially reduces compositional disorder. Also, it may help
to identify possible strategies that prevent this mechanism thus
allowing to overcome this stoichiometric limit and to achieve
higher In concentrations.
We thank R. Calarco and C. Skierbiszewski for MBE
advice and T. Markurt for TEM imaging. Funding of this
work by the European Union’s Horizon 2020 research and
innovation program (Marie Skłodowska-Curie Actions) under
Grant Agreement “SPRInG” No. 642574 and FP7-NMP-
2013-SMALL-7 program under Grant Agreement No. 604416
(DEEPEN) is gratefully acknowledged. X.Q.W. acknowledges
support from the National Key Research and Development
Program of China (No. 2016YFB0400100), Science Challenge
Project (No. TZ2016003-2), the Sino-German Center for
Science Promotion, NSFC and DFG (GZ1309), and NSAF
L.L. and T.S. contributed equally to this work.
 H. Kroemer, Proc. IEEE 51,1782 (1963).
 R. Dingle, W. Wiegmann, and C. H. Henry, Phys.Rev.Lett.33,
 R. Dupuis and P. D. Dapkus, Appl. Phys. Lett. 31,466 (1977).
 W. C. Yang, C. H. Wu, Y. T. Tseng, S. Y. Chiu, and K. Y. Cheng,
J. Appl. Phys. 117,015306 (2015).
 G. R. Mutta, P. Ruterana, J. L. Doualan, M. P. Chauvat, F. Ivaldi,
S. Kret, N. A. K. Kaufmann, A. Dussaigne, D. Martin, and N.
Grandjean, Phys. Status Solidi B 248,1187 (2011).
 M. Siekacz, M. Sawicka, H. Turski, G. Cywi´nski, A. Khacha-
puridze, P. Perlin, T. Suski, M. Bo´ckowski, J. Smalc-
Koziorowska, M. Kry´sko, R. Kudrawiec, M. Syperek, J.
Misiewicz, Z. Wasilewski, S. Porowski, and C. Skierbiszewski,
J. Appl. Phys. 110,063110 (2011).
 G. B. Stringfellow, J. Cryst. Growth 27,21 (1974).
 D. M. Wood and A. Zunger, Phys. Rev. Lett. 61,1501 (1988).
 A. Zunger and S. Mahajan, in Handbook on Semiconductors,
edited by S. Mahajan (Elsevier, Amsterdam, 1994), Vol. 3b,
 J. E. Bernard, S. Froyen, and A. Zunger, Phys. Rev. B 44,11178
 J. Tersoff, Phys. Rev. Lett. 74,434 (1995).
 G. Stringfellow, J. Appl. Phys. 43,3455 (1972).
 M. Quillec, H. Launois, and M. C. Joncour, J. Vac. Sci. Technol.
 M. J. Jou, Y. T. Cherng, H. R. Jen, and G. B. Stringfellow, Appl.
Phys. Lett. 52,549 (1988).
 R. M. Cohen, M. J. Cherng, R. E. Benner, and G. B. Stringfellow,
J. Appl. Phys. 57,4817 (1985).
 S. Yu. Karpov, MRS Internet J. Nitride Semicond. Res. 3,
 S. B. Zhang and S. H. Wei, Phys.Rev.Lett.86,1789 (2001).
 M. Albrecht, H. Abu-Farsakh, T. Remmele, I. Hausler, L.
Geelhaar, H. Riechert, R. Fornari, and J. Neugebauer, Phys. Rev.
Lett. 99,206103 (2007).
 I. Gorczyca, T. Suski, N. E. Christensen, and A. Svane, Cryst.
Growth Des. 12,3521 (2012).
 S. Chichibu, T. Azuhata, T. Sota, and S. Nakamura, Appl. Phys.
Lett. 70,2822 (1997).
 C. Chèze, F. Feix, M. Anikeeva, T. Schulz, M. Albrecht, H.
Riechert, O. Brandt, and R. Calarco, Appl. Phys. Lett. 110,
L. LYMPERAKIS et al. PHYSICAL REVIEW MATERIALS 2, 011601(R) (2018)
 C. Chèze, M. Siekacz, F. Isa, B. Jenichen, F. Feix, J. Buller,
T. Schulz, M. Albrecht, C. Skierbiszewski, R. Calarco, and H.
Riechert, J. Appl. Phys. 120,125307 (2016).
 X. Wang, S. Liu, N. Ma, L. Feng, G. Chen, F. Xu, N. Tang, S.
Huang, K. J. Chen, S. Zhou, and B. Shen, Appl. Phys. Express
 S. T. Liu, X. Q. Wang, G. Chen, Y. W. Zhang, L. Feng, C. C.
Huang, F. J. Xu, N. Tang, L. W. Sang, M. Sumiya, and B. Shen,
J. Appl. Phys. 110,113514 (2011).
 H. J. Chen, R. M. Feenstra, J. E. Northrup, T. Zywietz, J.
Neugebauer, and D. W. Greve, J. Vac. Sci. Technol. B 18,2284
 S. Lee, C. Freysoldt, and J. Neugebauer, Phys.Rev.B90,245301
 See Supplemental Material at http://link.aps.org/supplemental/
10.1103/PhysRevMaterials.2.011601 for more details on the
methodology, bulk order-disorder transition temperatures and
 W. A. Harrison, J. Vac. Sci. Technol. 16,1492 (1979).
 M. Himmerlich, L. Lymperakis, R. Gutt, P. Lorenz, J.
Neugebauer, and S. Krischok, Phys. Rev. B 88,125304
 J. E. Northrup, L. T. Romano, and J. Neugebauer, Appl. Phys.
Lett. 74,2319 (1999).
 A. I. Duff, L. Lymperakis, and J. Neugebauer, Phys.Rev.B89,
 J. E. Northrup, J. Neugebauer, R. M. Feenstra, and A. R. Smith,
Phys. Rev. B 61,9932 (2000).