APPLIED PHYSICS LETTERS 102, 102103 (2013)
Electronic structure of a single-layer InN quantum well in a GaN matrix
M. S. Miao, Q. M. Yan, and C. G. Van de Walle
Materials Department, University of California, Santa Barbara, California 93106-5050, USA
(Received 9 January 2013; accepted 26 February 2013; published online 11 March 2013)
Using first-principles methods and 8-band k p simulations, we study the electronic structure of an
ultrathin quantum-well system consisting of a single layer of InN inserted in GaN matrix.
Experimental photoluminescence and electroluminescence emission peaks for such structures have
been reported in the wavelength region between 380 to 450 nm. In contrast, our calculations show
an energy difference between the electron and hole states around 2.17 eV (573 nm). Possible
origins of the experimental light emission are examined. We suggest that the experimental
emission may be due to recombination of electrons (holes) in GaN with holes (electrons) in the
C 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4794986]
quantum well. V
InN has been attracting attention as an important nitride
semiconductor because of its low band gap (less than
0.7 eV).1,2 Combined with the large gaps of GaN and AlN, it
enables the band gaps of nitride alloys to cover the entire visible spectrum and reach well into the infrared. Compared to
GaN, InN is more difficult to grow due to its low dissociation
temperature.3,4 To date, the most important applications are
ultraviolet (UV) to green light emitting diodes (LED) and
lasers that use InGaN alloys with fairly low In concentrations.
Growing high-quality InGaN layers with high In content on
GaN is difficult due to the large lattice mismatch between InN
and GaN and the tendency for phase separation.
One proposal to overcome these problems is to use ultrathin layers of InN sandwiched between GaN. Yoshikawa
et al. reported that high quality InN layers with an atomically
sharp and flat interface could be fabricated at growth temperatures as high as 650 C.5–8 Light emission from the recombination of electrons and holes in such InN/GaN monolayer
quantum wells (MLQWs) was observed in both photoluminescence (PL)5 and electroluminescence (EL).9 The emission
peak ranged from 380 nm to 425 nm, corresponding to
recombination energies between 3.26 and 2.92 eV. This large
value, relative to the low gap of bulk InN, could potentially
be caused by quantum confinement in the MLQW. However,
there is no direct experimental evidence that the emission
indeed results from the recombination of electrons and holes
within the quantum well. In addition, it is difficult to determine whether the inserted layer actually consists of pure binary InN; partial evaporation might result in less than 100%
In being present in the layer, or interdiffusion might occur
that leads to InGaN alloy formation.
In this Letter, we study the atomic and electronic structure
of this InN/GaN MLQW using first-principles as well as semiempirical methods. We use density functional theory with projector augmented wave (PAW) potentials10 as implemented in
the VASP code.11 The calculations (including atomic relaxations)
were performed using the Heyd-Scuseria-Ernzerhof (HSE)
hybrid functional,12 which has been found to yield band-gap
values that are much closer to experiment than those obtained
with local or semi-local functionals. We used a mixing parameter corresponding to 28% of Hartree-Fock exchange, which
yields lattice parameters a ¼ 3.182 Å, c ¼ 5.175 Å for GaN and
a ¼ 3.548 Å, c ¼ 5.751 Å for InN, and band gaps of 3.42 eV for
0003-6951/2013/102(10)/102103/3/$30.00
GaN and 0.83 eV for InN. We have also performed simulations
of quantum-well structures using the 8-band k p method.13,14
The parameters for the k p Hamiltonian, including Luttinger
parameters, band gaps, band offsets, and deformation potentials
were all taken from previous first-principles calculations.15–18
Linear interpolation was used to obtain the parameters for
InGaN.
The quantum well consists of a single layer of InN
embedded within 23 atomic layers of GaN [Fig. 1], and
the whole structure is periodically repeated in the growth
direction (c axis). A cutoff energy of 300 eV and a k mesh of
4 4 1 centered at the C point are used. The InN layer is
assumed to be pseudomorphically grown on GaN, i.e., the
lattice constant in the plane of the interface is that of GaN,
while the lattice constant along the c direction is allowed to
relax.
According to the macroscopic theory of elasticity, within
the linear regime, the strain in the perpendicular direction is
xx , in which C13
related to the biaxial strain by zz ¼ 2 CC13
33
and C33 are the elastic constants. Using 2 CC13
¼ 0:821 (Ref.
33
19), we plot zz as a function of xx , together with the calculated strains in a MLQW and in bulk InN subject to the same
in-plane biaxial strain as the MLQW. As shown in Fig. 2, the
calculated zz for bulk InN is lower than that predicted from
macroscopic elasticity, which is due to the nonlinearity at
FIG. 1. Calculated atomic structure of an InN single layer inserted in a GaN
matrix. Large (green) balls represent Ga, large darker (purple) balls In, and
the small (grey) balls N. Bond lengths (in Å) are indicated.
102, 102103-1
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Appl. Phys. Lett. 102, 102103 (2013)
FIG. 2. Relation between imposed in-plane biaxial strain and strain in the
perpendicular direction for InN, calculated based on elastic constants (black
line). The strain in a MLQW (delineated by the planes of the N atoms on either side of the In) obtained by HSE calculations is indicated with a red dot,
and the calculated strain in bulk InN subject to the same in-plane biaxial
strain is indicated by an orange triangle.
FIG. 3. Band gaps of InGaN MLQWs. Open circles show results from
8-band k p simulations; the red filled square shows the result from firstprinciples hybrid density functional theory; the crosses correspond to the experimental PL peak energies reported for 1 ML and 2 ML InN layers (see
Ref. 5), and the triangle to the EL peak energy (see Ref. 9).
such a large strain. However, the strain in the very thin
MLQW is quite different from that in strained bulk InN and
actually compares remarkably well with the macroscopic
theory.
Figure 1 shows the optimized structure of the InN layer
embedded in a GaN matrix. The In-N bonds are severely distorted, resulting in very different bond lengths for bonds
between In and N in the same bilayer (2.056 Å) versus In
and N in adjacent bilayers (2.182 Å). For comparison, the
bond lengths in bulk InN are 2.155 Å and 2.161 Å. There are
also two different N-In-N angles, one formed by N atoms in
the same bilayer and the other by N atoms in adjacent
bilayers (½N-In-N0 ). These two angles are very close in value
in bulk InN (110:2 and 108:7 ), but in the MLQW, the
0
N-In-N angle decreases to 101:4 while the N-In-N angle
increases to 116:7 . The distortion is partially due to the
large strains that are present in the MLQW, but also to the
different bonding features of the N atoms bonded to In in different layers: the N atoms in the same bilayer as In bond to
three In and to one Ga, while N atoms in the adjacent bilayer
bond to three Ga and one In. To provide insight in these contributions, we performed a calculation for bulk InN strained
with the same xx and zz as the MLQW. We found In-N
bond lengths of 2.093 Å in-plane and 2.125 Å along c. This
bond-length difference is significantly smaller than the difference in bond lengths found for the MLQW, showing the
important impact of the specific bonding environment (partial bonding to Ga atoms).
Accurate results for the electronic band structure of the
InN/GaN MLQW are obtained here by employing a hybrid
functional.12 The calculated energy difference between the
electron state (lowest unoccupied orbital) and the hole state
(highest occupied orbital) is 2.17 eV. This energy (corresponding to a wavelength of 573 nm) is much higher than the
fundamental gap of InN, indicating that quantum confinement is significant. However, the energy is much below the
emission peaks (above 2.92 eV) observed in PL5 or EL9
experiments.
One potential explanation for this discrepancy is that the
inserted layer is not pure InN but actually consists of InGaN.
In order to examine this hypothesis, we simulated the electronic structure of GaN/InGaN/GaN quantum wells using the
8-band k p method, as shown in Fig. 3. Reassuringly, we
found that the k p simulation yields a band gap for the pure
InN MLQW of 1.97 eV, close to the first-principles result.
The recombination energy increases with decreasing In concentration, but reaches the values that are observed in PL
and EL experiments only when the In concentration is less
than about 35% In. If the QW is actually more than one ML
thick (which would result from interdiffusion), then even
lower In concentrations would be required to produce the experimental emission peaks. Assuming that the experimental
growth indeed results in high-In layers on a monolayer scale,
we cannot attribute the emission to recombination within an
InGaN QW.
Here, we propose an alternative explanation for the
observed emission peaks. As shown in Fig. 4, the observed
light emission may originate from the recombination of carriers located in different spatial regions, i.e., from the GaN
barrier to the InN quantum well. Our first-principles calculations produce energy differences between the highest occupied state (hole state) and the three lowest unoccupied states
(electron states) at the C point of 2.17, 2.71, and 2.97 eV; the
latter two energies actually correspond to electron states that
are mainly localized in GaN. We also find that the energy differences between the lowest unoccupied state (electron state
in the MLQW) and the second- and third-highest occupied
states (hole states in the GaN region) are 2.57 and 2.71 eV.
In order to examine the likelihood of this mechanism,
we plot the wave functions of the electron and the hole states
in the InN quantum well in Figs. 4(b) and 4(c). Not surprisingly for such a thin QW, the wave functions spread out into
the neighboring GaN barrier layers. The hole state is localized not only on N atoms within the InN layer but also on N
atoms in the underlying GaN layer [Fig. 4(b)]; electrons, on
the other hand, spill over into the GaN overlayer [Fig. 4(b)].
102103-3
Miao, Yan, and Van de Walle
Appl. Phys. Lett. 102, 102103 (2013)
well embedded in GaN, using both first-principles density
functional theory and the 8-band k p method. Our calculations show that recombination between electrons and holes
in the MLQW results in light emission around 573 nm. Such
recombination may be suppressed due to difficulties in carrier capture. We propose that the reported emission peaks in
the blue and UV originate from recombination involving carriers in the neighboring GaN barrier regions.
FIG. 4. (a) Schematic view of energy levels and potential recombinations
between electron and hole states for an InN MLQW with GaN barriers. The
valence-band offset (VBO) and conduction-band offset (CBO) are taken
from our recent HSE calculations (see Ref. 20). The dashed red lines show
the energies of electron and hole states confined within the QW. The energies EReh ; EReb , and ERbh correspond to the recombination of electrons and holes
in the QW, electrons in the QW with holes in the GaN barrier, and electrons
in the GaN barrier with holes in the QW. (b) and (c) HSE wavefunctions of
the hole state at the valence-band maximum and the electron state at the
conduction-band minimum in an InN MLQW. The atomic structure corresponds to that of Fig. 1.
The relative spatial locations of the electron and hole states
are consistent with the polarization field evident in Fig. 4(a).
The spillover of the QW wave functions into the barrier
layers facilitates recombination of carriers in the QW with
carriers in the GaN barrier. Recombination of electrons in
GaN with holes in the QW gives rise to an emission energy
ERbh ¼ 2:71 eV; recombination of electrons in the QW with
holes in GaN emits light at EReb ¼ 2:57 eV. Capture of carriers
in nitride QWs is known to be imperfect; strategies for
addressing electron overshoot, in particular, have been widely
discussed. This illustrates that trapping of carriers in this ultrathin well may be a bottleneck, leading to suppression of the
lowest-energy recombination channel and favoring recombination involving carriers in the barriers. We also note, however, that the energy region corresponding to our calculated
lowest-energy emission (2.17 eV) was not explored in the PL
and EL studies to date. The remaining difference between our
calculated recombination energies (ERbh and EReb ) and the
observed PL energies in the 2.92–3.26 eV range could be due
to the composition of the MLQW, which may not consist of
pure InN as discussed above.
In summary, we have studied the structural relaxation
and the electronic structure of a monolayer InN quantum
M.S.M. was supported by the Center for Energy
Efficient Materials, an Energy Frontier Research Center
funded by the U.S. DOE-BES under Award No. DESC0001009. Additional support was provided by NSF
(DMR-0906805), the UCSB Solid State Lighting and Energy
Center, and the MRSEC Program of the National Science
Foundation under Award No. DMR 1121053. We also
acknowledge NSF-funded XSEDE resources (DMR070072N) and the computing facilities of the Center for
Scientific Computing at the CNSI and MRL (an NSF
MRSEC, DMR-1121053) (NSF CNS-0960316).
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