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Elastically frustrated rehybridization: Origin of chemical order and compositional limits in InGaN quantum wells


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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.
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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.
DOI: 10.1103/PhysRevMaterials.2.011601
Modern optoelectronic devices rely on our ability to tune the
electronic band structure of ultrathin heteroepitaxial structures
via the chemical composition [13]. 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. InxGa1xN 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% [46], 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 [711]. Important phenomena
related to this mechanism are compositional latching [12,13],
strain enhanced solubility via suppression of phase separation
or spinodal decomposition [1416], 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:
Corresponding author:
Corresponding author:
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 InxGa1xN 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 [19].
Using only binary compounds supposedly avoids strong local
compositional inhomogeneities as present in conventional
pseudobinary InGaN alloys with high indium contents [20].
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
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 (23×23)R30configuration and 10% are randomly distributed. Specimen thickness for the 1100was 7 nm; for the 1120
14 nm.
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. [2124]. 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 [25], 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
a3×3 In ordered ML with a 33% In concentration
is a T=0 K thermodynamic ground state [26]. However,
this previously identified ordered structure is not stable at
our experimental growth temperatures (see Ref. [27]). 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 InxGa1xN quantum well. Rather, it
must be the result of an ordered surface structure, different
from the In-adlayer structure studied in Ref. [26] 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:
(n3×n3)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
Ga-N one.
It turned out that none of the energetically preferred
structures constructed from these principles could explain the
experimentally observed (3×3)R30like 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
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
composition x.Etot
nis the total energy of a (23×23)R30slab
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 (23×23)R30In0.25Ga0.75N
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 (23×23)R30surface 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
pDOS (a.u)
0.33 eV
0.37 eV
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
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 (23×23)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)R30structure in perfect agreement with the
ab initio predictions.
To further verify that the ab initio predicted (23×
23)R30surface with 25% In content is indeed the source
110% of the In atoms were randomly distributed.
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. [32]. 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. [25], which the authors
interpreted as a (3×3)R30reconstruction. However,
the differences between a (23×23)R30and a (3×
3)R30N-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 [21].
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. [27]). This is a
remarkably high temperature when compared against typical
growth temperatures for (In,Ga)N alloys with a high In content
[6]. 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
(No. U1630109).
L.L. and T.S. contributed equally to this work.
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... The stacking structures of AlInN and InGaN were observed by TEM [63][64][65]. For InGaN, a faint image of repeated (In-Ga-Ga), indicating the configuration of In and Ga atoms in the c(0001) plane, was observed [65]. ...
... The stacking structures of AlInN and InGaN were observed by TEM [63][64][65]. For InGaN, a faint image of repeated (In-Ga-Ga), indicating the configuration of In and Ga atoms in the c(0001) plane, was observed [65]. However, no atomic images showed the ordered configuration of Al and Ga atoms. ...
The metastability of Al n /12 Ga 1- n /12N ( n =2, 3, and 4) was investigated by the statistical analysis of electroluminescence (EL) spectra having dual peaks with a peak-to-peak distance ( pp ) of > 10 nm generated from nonflat Al x Ga 1- x N ( x ~0.2) quantum wells (QWs) fabricated on c (0001) sapphire substrates with a miscut of 1.0° towards the m [1-100] axis. To explain the origins of the dual-peak EL (DPEL) spectra, which are often observed for AlGaN-QWs with Ga content of greater than 0.7, a nonflat QW model incorporating two metastable compositions, Al ( n -1)/12 Ga 1-( n -1)/12 N and Al n /12 Ga 1- n /12 N ( n : integer), is proposed. By the statistical analysis of peak wavelengths in DPEL spectra and the verification of EL spectral shapes, two series of featured EL peak wavelengths with intervals of 2–3 nm were obtained from five out of six LED wafers. The two series of featured EL peak wavelengths were assigned by comparison with the calculated EL wavelengths. Then, Al 2/12 Ga 10/12 N and Al 3/12 Ga 9/12 N were determined to be the origins of peaks with the longer and shorter wavelengths in the DPEL, respectively, in addition to the metastable Al n /12 Ga 1- n /12 N ( n =4–9) compositions observed in our previous studies. When DPEL ( pp > 10 nm) appeared, the difference in QW thickness between Al 2/12 Ga 10/12 N and Al 3/12 Ga 9/12 N tended to be larger than one monolayer (ML), indicating a significant amount of Ga or GaN mass transport. Furthermore, the Al 2/12 Ga 10/12 N and Al 3/12 Ga 9/12 N QWs are considered to have thicknesses of m ML ( m : consecutive integers), suggesting the 1 ML configuration of Al and Ga atoms on the c (0001) plane. In addition, the DPEL obtained from nonflat Al x Ga 1- x N ( x ~0.25) QWs by another research group was shown to be related to two metastable Al n /12 Ga 1- n /12 N ( n =3, 4), similarly to our one exceptional LED wafer, which also agreed with the model proposed in this work.
... However, although the fabrication of InN/GaN SPSLs was demonstrated, more recent studies have concluded that (Ga,In)N/GaN SLs with maximum In content of 0.3 instead of 1 formed [18]- [21]. This effect possibly results from strain and give rise to a reconstruction of In on GaN(0001) surface that strictly limits the maximum In coverage in (Ga,In)N layers, and in turn, restricts their emission range considerably [20], [22]. leakage current [23]- [25]. ...
... For this LED sample, the structure was inverted (p-type layer at the bottom, n-type layer on top) and the delta-doped SL (sample H) was implemented at the bottom of this inverted structure. Also, no (Al,Ga)N EBL was inserted in this sample, as it has been shown that for an inverted LED structure, this layer is not mandatory to suppress the electron overflow [22]. The final (Ga,In)N cap was doped with Si with a nominal concentration of 3 × 10 17 cm -3 to improve the n-type conductivity. ...
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In dieser Arbeit wurden die komplexen Mechanismen für den Einbau von Mg und In in (Ga,In)N/GaN(0001)-Heterostrukturen, die mittels PA-MBE hergestellt wurden, mit morphologischen, optischen und elektrischen Charakterisierungsmethoden untersucht. Darüber hinaus wurde die Verwendung von (Ga,In)N/GaN SPSLs als HIL oder als aktiver Bereich in herkömmlichen LED-Strukturen untersucht. In-situ-Messungen zeigten, dass die Desorption von In in Gegenwart von N und Mg auf der GaN(0001)-Oberfläche zunimmt. Ferner wurden Mg-dotierte (Ga,In)N/GaN-SLs mittels PAMBE gezüchtet und mittels QMS, XRD und SIMS charakterisiert. Die (Ga,In)N/GaN-SLs zeigten eine bessere Oberflächenmorphologie als die (Ga,In)N-Schichten, die homogen mit Mg dotiert wurden. Jedoch wurde eine deutliche Abnahme des In-Gehalts in der (Ga,In)N ML festgestellt, wenn Mg gleichzeitig mit In zugeführt wurde. Gleichzeitig nahm die Mg-Konzentration in Gegenwart von In zu, was möglicherweise auf eine Wirkung als oberflächenaktive Substanz zurückzuführen ist. Für das SL, bei dem nur die (Ga,In)N-QWs mit Mg dotiert waren, wurde vom Messergebnis von SIMS eine maximale Mg-Konzentration von 2,6 × 1022 cm-3 für eine 1 ML dicke (Ga,In)N:Mg-Schicht deduziert. Zusätzlich haben andere Experimente ähnliche Ergebnisse aufgezeigt. Thermoleistung-Studien zeigten, dass das Delta-dotierte SL und die SL-Strukturen mit Mg-Dotierung in 20% der QB p-leitfähig sind. Zusätzlich wurde ein Gleichrichterverhalten der (Ga,In)N/GaN SL-Strukturen mit einem Idealitätsfaktor von weniger als 10 für die QW-dotierten SLs demonstriert. Ausgehend von der elektrischen Charakterisierung wurden drei verschiedene LED-Strukturen, die auf den vielver-sprechendsten Mg-dotierten (Ga,In)N SL-Strukturen (Delta-dotiertes SL und 20% QB-dotiertes SL) basierten, hergestellt und charakterisiert.
... Indium content x In (at%) The possibility of alloy ordering in our QWs was checked by aberration-corrected high resolution TEM (HRTEM) observations along the [ 1100 ] zone axis in thinner foil areas, as required to show this phenomenon 23 . We did not obtain experimental indications of ordering in our samples except for the high temperature sample A1 which exhibited few sparse patches (≈1 nm in length) but not a continuous ordered structure. ...
... abrupt interfaces. Moreover, growth from an In-Ga intermetallic is in contrast to recent reports on nitrogen-rich realization of In x Ga 1−x N/GaN MQWs 21,23,45 , whereby it was reported that such In x Ga 1−x N QWs are restricted to x In = 25% and 1 ML thickness accompanied by a characteristic × 3 RHEED (reflection high-energy electron diffraction) pattern. Although the single ML thickness and its indium content could be attributed to In x Ga 1−x N growth from a 2 × 2 indium adatom reconstruction 46 i.e., 0.25 ML indium adatom surface content at the beginning of the GaN deposition stage, this is in contrast to the observed × 3 RHEED pattern. ...
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InGaN/GaN quantum wells (QWs) with sub-nanometer thickness can be employed in short-period superlattices for bandgap engineering of efficient optoelectronic devices, as well as for exploiting topological insulator behavior in III-nitride semiconductors. However, it had been argued that the highest indium content in such ultra-thin QWs is kinetically limited to a maximum of 33%, narrowing down the potential range of applications. Here, it is demonstrated that quasi two-dimensional (quasi-2D) QWs with thickness of one atomic monolayer can be deposited with indium contents far exceeding this limit, under certain growth conditions. Multi-QW heterostructures were grown by plasma-assisted molecular beam epitaxy, and their composition and strain were determined with monolayer-scale spatial resolution using quantitative scanning transmission electron microscopy in combination with atomistic calculations. Key findings such as the self-limited QW thickness and the non-monotonic dependence of the QW composition on the growth temperature under metal-rich growth conditions suggest the existence of a substitutional synthesis mechanism, involving the exchange between indium and gallium atoms at surface sites. The highest indium content in this work approached 50%, in agreement with photoluminescence measurements, surpassing by far the previously regarded compositional limit. The proposed synthesis mechanism can guide growth efforts towards binary InN/GaN quasi-2D QWs.
... 18,19) The metastability structure of AlGaN is still unclarified due to the lack of atomic images of ordered AlGaN. [20][21][22] Atomic ordering reduces entropy, and the formation enthalpy of ordered AlGaN has been computed using primitive cell sizes with 4, 8, 12, and 16 atoms, and the inplane atomic configurations in the c(0001) plane have been predicted. 23) Computations are restricted by the number of atoms in a single primitive cell, and the results of computation using a cell incorporating 16 atoms including N atoms showed the possible metastability of n/8 (n: integer). ...
Energy-dispersive X-ray signals calibrated by Rutherford backscattering indicated the generation of Al13/24Ga11/24N in Ga-rich stripes in a nonflat Al0.58Ga0.42N layer. Also, the CL peak wavelengths of ~259 and 272 nm also showed the generation of Al15/24Ga9/24N and Al13/24Ga11/24N in Al-rich zones and Ga-rich stripes, respectively. The wavelength of a strong CL peak at ~246 nm, which was observed from the Al0.7Ga0.3N layer in our previous study, is also considered to correspond to the near-band-emission wavelengths of Al17/24Ga7/24N. In particular, the stronger reproducibility of metastable Al15/24Ga9/24N generation was confirmed, in agreement with the computed predictions by other research groups.
... One approach for growing high quality InGaN films with higher In content is to reduce the mismatch strain which is a result of pseudomorphic growth on GaN substrates and the larger covalent radius of In compared to Ga. It has been shown for such strained films that a preference of In to occupy fourfold coordinated surface sites poses a limit to the indium concentration to 0.25 [30]. The large mismatch also results in mechanical stress at the interface and may result in additional defects like dislocations or V-pits as the film thickness increases [31]. ...
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Strain and composition play a fundamental role in semiconductor physics, since they are means to tune the electronic and optical properties of a material and hence develop new devices. Today it is still a challenge to measure strain in epitaxial systems in a non-destructive manner which becomes especially important in strain-engineered devices that often are subjected to intense stress. In this work, we demonstrate a microscopic mapping of the full tensors of strain and lattice orientation by means of scanning X-ray diffraction microscopy. We develope a formalism to extract all components of strain and orientation from a set of scanning diffraction measurements and apply the technique to a patterned In$_x$Ga$_{1-x}$N double layer to study strain relaxation and indium incorporation phenomena. The contributions due to varying indium content and threading dislocations are separated and analyzed.
... Researchers encountered several challenges for InGaN ternary alloys, such as the growth of high-quality, thick, and p-type In-rich InGaN. For instance, the development of InGaN/GaN-based devices with coherently grown 2D InGaN layers is limited to around 30% In composition due to thermodynamic or kinetic instability [10]. Moreover, the lattice mismatch between InGaN and GaN always causes a compressive strain and induces strong internal polarization fields in these materials. ...
This article discusses the key challenges and the recent breakthroughs in realizing high-quality indium (In)-rich indium gallium nitride (InGaN) epilayers and InGaN/GaN multiple quantum wells (QWs) by using the metal–organic chemical vapor deposition (MOCVD) technique. The main challenges such as the difficulties in growing high-quality In-rich and p-type InGaN are identified. The issues related to compressive strain and piezoelectric polarization induced by the large lattice mismatch between GaN and InGaN, and the degradation of InGaN QW quality due to In-rich clusters are also reviewed.
... 11) A strong In incorporation is expected in these MQWs with the increase of the in-plane lattice parameter compared to what is possible on GaN. 12,13) This should be accompanied with a reduction of the internal electric field in the QWs compared to QWs with the same In content on GaN. 14,15) Red electroluminescence (EL) was reached with LED chip sizes from 300 × 300 μm 2 to 50 × 50 μm 2 . ...
The full InGaN structure was grown on two different InGaNOS substrates from Soitec. An electron blocking layer was inserted in the full InGaN light emitting diode (LED). Enhanced internal quantum efficiency of red emitting InGaN/InGaN quantum wells was measured with a value above 10% at 640 nm. 10 μm diameter circular micro-LEDs are emitted at 625 nm with an external quantum efficiency of 0.14% at 8 A cm−2 with an estimated light extraction efficiency below 4%. With a a lattice parameter of 3.210 Å, InGaN based red LED can also emit up to 650 nm.
... FIG. 6. Configurations of the ordering of (a) Al 2/3 Ga 1/3 N and (b) Al 1/3 Ga 2/3 N on the c(0001) plane based on the analogy to InGaN presented by Neugebauer and co-workers. 43,45 (c) (left) Configuration of Al 1/2 Ga 1/2 N on the c(0001) plane and (right) view from a red arrow, which were proposed by Strunk and co-workers. 37,38 (XRD), 32 selective-area diffraction (SAD), [33][34][35][36][37][38] or calculation. ...
Dans un micro-écran, chaque pixel est composé de trois diodes électroluminescentes (LEDs) émettant respectivement dans le bleu, le vert et le rouge. Pour les applications de réalité augmentée et de réalité virtuelle auxquelles sont destinées ces technologies d’affichage, les tailles de ces LEDs nécessitent d’être réduites à moins d’une dizaine de μm, ce qui restreint l’utilisation commune de plusieurs familles de matériau. Une approche monolithique est ainsi nécessaire. Les LEDs à base de nitrures d’éléments III pourraient théoriquement couvrir tout le spectre visible mais leur efficacité chute au-delà de 460 nm. Afin d’obtenir des LEDs efficaces à base de (Ga,In)N émettant à grande longueur d’onde, l’un des points clefs est l’augmentation de la concentration en In des puits quantiques à base d’In- GaN, tout en gardant une bonne qualité cristalline. Une des solutions envisagées, et probablement la plus efficace, est de disposer d’un substrat InGaN relaxé, c’est-à-dire un substrat plus en accord de maille avec l’InGaN de forte composition constituant les puits quantiques de la zone active. Ce désaccord de maille est en effet à l’origine d’une forte contrainte compressive dans ceux-ci, dont les répercussions sur le rendement radiatif et le taux d’incorporation d’indium sont préjudiciables. Ces travaux de thèse proposent d’explorer, en détail, les caractéristiques des structures émettrices à grande longueur d’onde à base d’InGaN crues sur ces pseudo-substrats InGaN relaxés et la possibilité de fabrication et d’amélioration de tels substrats. Sur les pseudo-substrats InGaN appelés InGaNOS fabriqués par Soitec, une structure adaptée à ce type de substrat permet d’émettre à une longueur d’onde de 624 nm, avec une efficacité quantique interne (IQE) optique de 6.5%, à température ambiante. L’estimation par des cartographies de déformation d’une teneur en indium de 39% dans ces puits quantiques à base d’InGaN, soit au-delà de la limite théorique de 25% sur GaN, est une première et atteste la pertinence de notre approche. Néanmoins, l’émission des puits quantiques demeure inhomogène et une couche d’InGaN donneur à forte teneur en indium a été développée en vue de la fabrication de pseudo-substrats InGaN de meilleure qualité cristalline et avec un plus grand paramètre de maille a. Finalement, un pseudo-substrat InGaN relaxé a été conçu. La couche d’InGaN relaxée en surface dispose d’un paramètre de maille de 3.209°A, obtenue au moyen d’un procédé de relaxation en trois étapes : la structuration des échantillons en mésas, la porosification du n-GaN sous-jacent et un recuit à haute température.
Carbon impurities in GaN form both acceptors and donors. Donor-to-acceptor ratios (DARs) determine the semi-insulating behavior of carbon-doped GaN (GaN:C) layers and are still debated. Two models are discussed; both can theoretically achieve semi-insulating behavior: the dominant acceptor model (DAM, DAR<1) and the auto-compensation model (ACM, DAR=1). We perform a capacitance–voltage analysis on metal/GaN:C/nGaN (n-doped GaN) structures, exhibiting Fermi-level pinning in GaN:C, 0.7 eV above the valence band maximum. This observation coupled with further interpretation clearly supports the DAM and contradicts the ACM. Furthermore, we reveal a finite depletion width of a transition region in GaN:C next to nGaN, where carbon acceptors drop below the Fermi level becoming fully ionized. Calculation of the potential drop in this region exhibits DAR values of 0.5–0.67 for GaN:C with total carbon concentrations of 1018 cm−3 and 1019 cm−3. Based on those results, we re-evaluate formerly published density functional theory (DFT)-calculated formation energies of point defects in GaN. Unexpectedly, growth in thermodynamic equilibrium with the bulk carbon phase contradicts our experimental analysis. Therefore, we propose the consideration of extreme carbon-rich growth conditions. As bulk carbon and carbon cluster formation are not reported to date, we consider a metastable GaN:C solid solution with the competing carbon bulk phase being kinetically hindered. DFT and experimental results agree, confirming the role of carbon at nitrogen sites as dominant acceptors. Under N-rich conditions, carbon at gallium sites is the dominant donor, whereas additional nitrogen vacancies are generated under Ga-rich conditions.
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We investigate designed InN/GaN superlattices (SLs) grown by plasma-assisted molecular beam epitaxy on c-plane GaN templates in situ by line-of-sight quadrupole mass spectroscopy and laser reflectivity, and ex situ by scanning transmission electron microscopy, X-ray diffraction, and photoluminescence (PL). The structural methods reveal concordantly the different interface abruptness of SLs resulting from growth processes with different parameters. Particularly crucial for the formation of abrupt interfaces is the Ga to N ratio that has to be bigger than 1 during the growth of the GaN barriers, as Ga-excess GaN growth aims at preventing the unintentional incorporation of In accumulated on the growth surface after the supply of InN, that extends the (In,Ga)N quantum well (QW) thickness. Essentially, even with GaN barriers grown under Ga-excess yielding to 1 monolayer (ML) thick QWs, there is a real discrepancy between the designed binary InN and the actual ternary (In,Ga)N ML thick QWs revealed by the above methods. The PL emission line of the sample with atomically abrupt interfaces peaks at 366 nm, which is consistent with the In content measured to be less than 10%.
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The effect of elastic strain in epitaxial InGaN layers coherently grown on GaN wafers on spinodal decomposition of the ternary compound is examined. The effect results in considerable suppression of phase separation in the strained InGaN layers. To predict correctly the position of the miscibility gap in the T-x diagram it is important to take into account the compositional dependence of the elastic constants of the ternary compound. The contribution of the elastic strain to the Gibbs free energy of InGaN is calculated assuming uniform compression of the epitaxial layer with respect to the underlying GaN wafer. The interaction of binary constituents in the solid phase is accounted for on the base of regular solution model. The enthalpy of mixing is estimated using the Valence Force Field approximation. The strain effect becomes stronger with increasing In content in the InGaN. As a result the miscibility gap shifts remarkably into the area of higher InN concentration and becomes of asymmetrical shape. Various growth surface orientations and the type of crystalline structure (wurtzite or sphalerite) provide different effects of the elastic strain on phase separation in ternary compounds.
We explore an alternative way to fabricate (In, Ga)N/GaN short-period superlattices on GaN(0001) by plasma-assisted molecular beam epitaxy. We exploit the existence of an In adsorbate structure manifesting itself by a (3×3)R30° surface reconstruction observed in-situ by reflection high-energy electron diffraction. This In adlayer accommodates a maximum of 1/3 monolayer of In on the GaNsurface and, under suitable conditions, can be embedded into GaN to form an In0.33Ga0.67N quantum sheet whose width is naturally limited to a single monolayer. Periodically inserting these quantum sheets, we synthesize (In,Ga)N/GaN short-period superlattices with abrupt interfaces and high periodicity as demonstrated by x-ray diffractometry and scanning transmission electron microscopy. The embedded quantum sheets are found to consist of single monolayers with an In content of 0.25–0.29. For a barrier thickness of 6 monolayers, the superlattice gives rise to a photoluminescence band at 3.16 eV, close to the theoretically predicted values for these structures.
We study the impact that local strain effects have on the spatial distribution of In in coherent InxGa1−xN grown epitaxially on GaN(0001) using an effective crystal growth modeling technique that combines a semi-grand-canonical Monte Carlo simulation with an ab initio parametrized empirical force field. Our calculations show that InxGa1−xN epitaxial layers exhibit a strong tendency towards ordering, as highlighted by the formation of a vertical stack of the 3×3 patterned layers along the 〈c〉 direction. The ordering phenomena are identified as a key factor that determines lateral phase separation in InxGa1−xN epitaxial layers at the nanometer scale. Consequences of this nanophase separation for the enhanced radiative emission through carrier localization in InxGa1−xN of x<1/3 are discussed.
The results of the growth of thin (∼3 nm) InGaN/GaN single quantum wells (SQWs) with emission wavelengths in the green region by plasma-assisted molecular beam epitaxy are present. An improved two-step growth method using a high growth temperature up to 650 °C is developed to increase the In content of the InGaN SQW to 30% while maintaining a strong luminescence intensity near a wavelength of 506 nm. The indium composition in InGaN/GaN SQW grown under group-III-rich condition increases with increasing growth temperature following the growth model of liquid phase epitaxy. Further increase in the growth temperature to 670 °C does not improve the photoluminescence property of the material due to rapid loss of indium from the surface and, under certain growth conditions, the onset of phase separation.
InN/GaN superlattices offer an important way of band gap engineering in the blue-green range of the spectrum. This approach represents a more controlled method than the band gap tuning in quantum well systems by application of InGaN alloys. The electronic structures of short-period wurtzite InN/GaN(0001) superlattices are investigated, and the variation of the band gap with the thicknesses of the well and the barrier is discussed. Superlattices of the form mInN/nGaN with n ≥ m are simulated using band structure calculations in the Local Density Approximation with a semiempirical correction for the gap error. The calculated band gap shows a strong decrease with the thickness (m) of the InN well. In superlattices containing a single layer of InN (m = 1) the band gap increases weakly with the GaN barrier thickness n, reaching a saturation value around 2 eV. In superlattices with n = m and n > 5 the band gap closes and the systems become “metallic”. These effects are related to the existence of the built-in electric fields that strongly influence valence- and conduction-band profiles and thus determine effective band gap and emission energies of the superlattices. Varying the widths of the quantum wells and barriers one may tune band gaps over a wide spectral range, which provides flexibility in band gap engineering.
The incorporation of In into the technologically relevant (0001) (Ga-polar) and (0001̄) (N-polar) surfaces of In0.25Ga0.75N is investigated using density functional theory. The cases of coherent pseudomorphic growth on GaN and on lattice-matched heterointerfaces are considered. For pseudomorphic growth on GaN, In incorporation into the {0001} surface layers is limited to a tiny growth window corresponding to extreme In-rich growth conditions and at the In-rich/Ga-poor region of the metal chemical potentials. Lattice-matched growth, however, allows for a wider growth window. Surface phase diagrams are constructed as a function of growth conditions and reveal similarities between the two polar growth planes. However, a strong driving force is found for segregation of In atoms to the first III-N layer for Ga-polar growth, but not for N-polar growth. The former was found to be mainly due to chemical effects (stronger Ga-N as compared to In-N bonds), absent in the case of N-polar growth. Furthermore, finite-temperature calculations show that In incorporated into the first III-N layer is stable to ≈150 K higher temperatures in the N-polar surface than in the Ga-polar surface, indicating that for a given level of In incorporation, higher temperatures can be used for N-polar growth as compared to Ga-polar growth.
The surface electronic structure of GaN(0001) surfaces is characterized by photoelectron spectroscopy. Depending on the surface preparation conditions, such as cooldown in nitrogen plasma after growth and additional vacuum annealing or Ga deposition, different surface states are observed at the valence-band edge and inside the band gap of GaN, while the surface Fermi-level position E-F was found to be independent at 2.9-3.0 eV, indicative of unoccupied surface states that pin E-F. The experimental results are combined with band structures of different 2 x 2 reconstructed surfaces calculated by density-functional theory. Comparing the experimental results with the theoretical density of surface states allows an identification of the microscopic origin of these states and an assignment of the related surface structure. The presence of a 2 x 2 nitrogen adatom structure after growth is found that can be identified by its fingerprint surface states approximate to 0.9 eV above and approximate to 0.6 eV below the valence-band maximum (VBM). For Ga vacancy and adatom structures a similar agreement is found, revealing surface states approximate to 0.3 and approximate to 1.4 or approximate to 1.6 eV above the VBM, respectively.
In{sub x}Ga{sub 1-x}N alloys (0 {<=} x {<=} 1) have been grown on GaN/sapphire templates by molecular beam epitaxy. Growth temperature controlled epitaxy was proposed to modulate the In composition so that each In{sub x}Ga{sub 1-x}N layer was grown at a temperature as high as possible and thus their crystalline quality was improved. The bandgap energies of the In{sub x}Ga{sub 1-x}N alloys have been precisely evaluated by optical transmission spectroscopy, where the effect of residual strain and electron concentration (the Burstein-Moss effect) on the bandgap energy shift has been considered. Finally, a bowing parameter of {approx}1.9 {+-} 0.1 eV has been obtained by the well fitting In-composition dependent bandgap energy.
Quantum levels associated with the confinement of carriers in very thin, molecular-beam-grown AlxGa1-xAs-GaAs-AlxGa1-xAs heterostructures result in pronounced structure in the GaAs optical absorption spectrum. Up to eight resolved exciton transitions, associated with different bound-electron and bound-hole states, have been observed. The heterostructure behaves as a simple rectangular potential well with a depth of ~0.88DeltaEg for confining electrons and ~0.12DeltaEg for confining holes, where DeltaEg is the difference in the semiconductor energy gaps.