The explanation of InN bandgap discrepancy based on experiments and first-principle calculations

Article abstract of DOI:10.1016/j.physleta.2011.01.024

Indium nitride (InN) films with different free electron concentration and optical bandgap were grown either directly on sapphire substrate or on pre-covered gallium nitride (GaN) buffer through metal-organic chemical vapor deposition (MOCVD) method. Based on first-principle calculations, we confirm that the widening of InN optical bandgap reported before is caused by high density of free electrons. To find the contributor of the free electrons, the characteristic energetic levels of O_N, V_N and Si _In are investigated. We find that they are all high enough to uplift the optical bandgap from about 0.78 eV to 1.9 eV, which almost can't be enlarged further when it reaches 2.09 eV.

Full text of DOI:10.1016/j.physleta.2011.01.024

Physics Letters A 375 (2011) 1152–1155
Contents lists available at ScienceDirect
Physics Letters A
www.elsevier.com/locate/pla
The explanation of InN bandgap discrepancy based on experiments and
first-principle calculations
∗
Chaoren Liu , Jingbo Li
State Key Laboratory for Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing 100083, China
a r t i c l e i n f o
a b s t r a c t
Article history:
Indium nitride (InN) films with different free electron concentration and optical bandgap were grown
either directly on sapphire substrate or on pre-covered gallium nitride (GaN) buffer through metal-
organic chemical vapor deposition (MOCVD) method. Based on first-principle calculations, we confirm
that the widening of InN optical bandgap reported before is caused by high density of free electrons.
To find the contributor of the free electrons, the characteristic energetic levels of ON, VN and SiIn are
investigated. We find that they are all high enough to uplift the optical bandgap from about 0.78 eV to
1.9 eV, which almost can’t be enlarged further when it reaches 2.09 eV.
Received 26 November 2010
Received in revised form 7 January 2011
Accepted 12 January 2011
Available online 14 January 2011
Communicated by R. Wu
Keywords:
© 2011 Elsevier B.V. All rights reserved.
First principle calculation
Indium nitride
Band gap
Defect
1. Introduction
the main contributors of free elections in InN. However, the con-
duction band structure and the position of defect levels, essential
to interpret the blueshift of absorption edge, haven’t been dealt
Indium nitride has been attracting researchers for the fact that
it has relatively a narrow bandgap and a high electronic mobility
among III–V compounds. However, experimentally the discrepancy
of temperature requirement [1,2] and the scarcity of well-matching
substrates impede the improvement of material quality. Theoreti-
cally, the well-known error of conventional local density approxi-
mation (LDA) leads to a negative gap for InN which brings troubles
to the investigation of primary prosperities. For example, resorting
to optical measurements, some groups asserted a wide bandgap
(∼ 1.9 eV) [3–5] while others proposed that InN has a narrower
bandgap (∼ 0.8 eV) [6–10]. On the basis that InN films which
have wide bandgap are usually polycrystal and have a high density
of unintentionally doped free electrons (∼ 1020 cm−3), narrower
bandgap supporters believed that Burstein–Moss shift [11] enlarges
the optical bandgap. Afterwards, it was found that there is a strong
electron accumulation layer on InN surface [12] and that strains
also contribute to the variation of the bandgap [13,14], all of which
further confuse the problem. Van de Walle [15–17] has done a sys-
tematic research to the formation energy of intrinsic defects and
impurity defects in InN. It is confirmed that the formation energy
of all the intrinsic defects except N vacancy is too high to gener-
ate in a considerable amount under room temperature in n-type
InN. Comparatively, impurity defects (ON, SiIn) have lower forma-
tion energies, so they supposed that impurities and N vacancy are
with as far as my knowledge, which is the emphasis in our work.
In this Letter, we have grown high-quality InN films under dif-
ferent conditions using MOCVD, and afterwards X-ray diffraction
(XRD) and absorption spectroscopy analysis are applied to charac-
terize them. Simulation results combined with experimental data
from this work and some previous works support the narrower
gap in InN and attribute the origin of blueshift to Burstein–Moss
shift. Based on the results given by Van de Walle, we choose three
defects in InN with relatively low formation energy (ON, VN and
SiIn) and calculate their energetic positions from which it can be
seen that they are all high enough to push the absorption edge as
high as about 1.1 eV.
2. Calculation details
The band structure is calculated using the density functional
theory with local density approximation as implemented in VASP
code [18]. In self-consistent calculation, the little region around Γ
point, where LDA gives negative band gap, is excluded when in-
tegrating in reciprocal space. In this case, the occupying-sequence
remains correct, so the convergent result will not influenced by the
negative band gap. Frozen-core projected augmented wave meth-
ods [19] is utilized to describe the ion–electron interactions. The
In4d electrons are explicitly treated as valence electrons. The cut-
off energy of the plane wave is set to 400 eV. In doped system,
a point defect is placed into a 96-atom cuboid superlattice sug-
gested by Van de Walle [17]. Monkhorst–Pack special k-point grid
Corresponding author. Tel.: +86 0 15811043227; fax: +86 10 82305056.
*
E-mail addresses: supermanliu5@semi.ac.cn (C. Liu), jbli@semi.ac.cn (J. Li).
0375-9601/$ – see front matter © 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.physleta.2011.01.024

C. Liu, J. Li / Physics Letters A 375 (2011) 1152–1155
1153
(2 × 2 × 2) is used to integrate in Brillouin zone. Ion relaxation
continues until Hellmann–Feynman forces acting on each atom are
smaller than 0.01 eV/Å. The optimized wurtzite InN lattice con-
stant are a = 3.527 Å, c/a = 1.61, u = 0.375 in good agreement
with experimental values (a = 3.5446 Å, c/a = 1.609) [20].
In the calculation of absorption edge as the function of free
electron density, we treat absorption edge as the energetic distance
between valence band maximum (VBM) and Fermi level assuming
the bandgap of perfect InN to be 0.78 eV. The free electron concen-
tration is given out by dividing integrated DOS of conduction band
under the given Fermi level by the volume of the superlattice. To
get the energetic position of defects and impurities, we calculate
the partial density of states (PDOS) of atoms nearest to them. In
the case of ON, the PDOS of the four nearest indium atoms (5s or-
bit) is plotted. We also give out the PDOS of the same four indium
atoms (5s orbit) in pure InN for comparison. In the first plot, there
is a significant peak comparing to the second one which indicates
the defect level position of ON. The method for VN and SiIn is the
same.
Fig. 1. X-ray diffraction (XRD) patterns of as-grown InN sample I and sample II. GaN
buffer layer in sample II is detected.
3. Experiments
InN samples were grown by MOCVD method either directly
on c-plane (0001) sapphire substrates (sample I) or on sapphires
which were pre-deposited with GaN buffers (sample II). Trimethyl-
indium (TMIn), trimethyl-gallium (TMGa) and ammonia (NH3)
were used as precursors. High-purity nitrogen was used as carrier
gas. Before growth, sapphire wafers were heated under a hydro-
◦
gen flow at 1050 C for 20 min, followed by 3-min-nitridization
under a flow of NH3 and H2 mixture. For sample I, InN films
◦
were deposited subsequently for 40 min under 580 C and atmo-
spheric pressure with the flow rate of TMIn and NH3–H2 mixture
to be 200 SCCM (standard cubic centimeter per minute) and 3 SLM
(standard liter per minute) respectively. For sample II, a 120 nm
GaN buffer layer was deposited before the growth of InN. The pa-
rameters in the preparation of samples I and II are the same except
for GaN buffer layer. High quality of crystallization of the samples
was confirmed by XRD measurements. Each sample was also ex-
amined by Hall and absorption spectroscopy.
Fig. 2. Absorption spectrum of the two samples in this work where hν is photon
energy and α is absorption coefficient. Dot lines guide eyes to the intercepts on
abscissa which indicate the absorption bandgap.
4. Results and analysis
4.2. Explanation of bandgap discrepancy through ab-initio band
structure calculations
4.1. Samples characterization
To explain the discrepancy between larger bandgap of InN in
previous literatures and recently-proposed narrower bandgap us-
ing Burstein–Moss shift, we have calculated the absorption edge as
the function of free electron concentration as shown in Fig. 3. The
band structure is also drawn in Fig. 4. In good agreement with
results in previous literatures [22], there is a negative bandgap
(−0.0013 eV), nearly equal to zero, in the small region around Γ
point where should be excluded in k-sampling. VBM is a p-like
state which couples strongly with In4d states because they share
the same symmetry. As shown in Fig. 4, the energetic distance
from In4d to VBM amounts to 13.4 eV, much smaller than the
experimental value (14.9 eV [23]). So the overestimated p–d cou-
pling pushes VBM upwards and decreases the calculated bandgap.
In Fig. 3, it can be seen that data of InN films in this work and from
other previous works distribute approximately along the calculated
line, indicating that Burstein–Moss shift is the essential cause of
bandgap blueshift. From structure of conduction band (Fig. 4), the
curve is sharp below 1.31 eV-meaning a small DOS while smooth
above 1.31 eV-meaning a large DOS. So, when Fermi level reaches
upto 1.31 eV, the absorption edge is 2.09 eV (1.31 eV + 0.78 eV)
in our model and becomes less sensitive to further increase of
free electrons, in consistency with the fact that there are scarce
XRD patterns (Fig. 1) tell that samples are well-oriented in
(0001) direction. The free electron concentration and electronic
−3
mobility are 1.49 × 1020 cm
and 128 cm2/V s for sample I while
−3
the values for sample II are 1.9 × 1019 cm
and 595 cm2/V s
determined by Hall measurement. Although Hall measurements
overestimate the free electron concentration due to the contribu-
tion of the electron accumulation layer (1013 cm
as indicated by
−2
Mahboob [12] and Chang [21]), taking into account the thickness
(∼ 400 nm) and the free electron concentration of our sample, it
is reliable to regard the values given by Hall measurements as the
values for the bulk because the amounts of free electrons on the
surface layer are less than the total amounts by at least one order
of magnitude. We fit the absorption spectroscopy to (hνα)2 ∼ hν
plot where α is absorption coefficient, hν is photon energy. As
shown in Fig. 2, extrapolations of the linear part to abscissa give a
wider optical bandgap (1.27 eV) for sample I and a narrower one
(0.85 eV) for sample II. The positions of the XRD peaks for sample I
and sample II are almost the same, indicating similar crystalliza-
tion. We neglect the influence of strains to bandgap due to the
fact that it is minor (∼ tens of meV) [14] in the energetic range of
our interest (∼ eV).

1154
C. Liu, J. Li / Physics Letters A 375 (2011) 1152–1155
Fig. 5. (Color online.) Partial density of states for ON, VN and SiIn. For ON, blue line
is 5s orbit of four indium atoms nearest to oxygen. For VN, blue line is 5s orbit of
four indium atoms nearest to nitrogen vacancy. For SiIn, blue line is 3s orbit of four
nitrogen atoms nearest to silicon. The black lines are presented for comparison. In
ON and VN, black lines are 5s orbit of four indium atoms nearest to one nitrogen in
pure InN. In SiIn, black line is 3s orbit of four nitrogen atoms nearest to one indium
in pure InN.
Fig. 3. (Color online.) Absorption bandgap of InN as a function of free electron con-
centration with an assumption of 0.78 eV for the bandgap of perfect InN. Solid line
travels the DFT-LDA calculated result and red circles indicate the values of samples
in this work. Some previous data is shown in the figure as a reference.
Fig. 4. DFT-LDA calculated band structure of pure wurtzite InN including several
In4d bands. The dash line points out the position of VBM which, for simplicity,
is set at 0 eV. The energetic distance between In4d level and VBM is 13.4 eV as
indicated in the figure.
Fig. 6. Defect levels of ON, VN and SiIn which are possible electron contributors in
as-grown InN films with VBM at 0 eV. We assume that fundamental bandgap of
InN is 0.78 eV as proposed in recent works and the absorption bandgap of highly-
degenerated InN samples is 1.9 eV grown mainly before 2003. The units (eV) are
omitted in this figure.
works reporting an optical bandgap higher than 2.09 eV except
the situations where InNO alloy forms. There might be a correc-
tion to the value 1.31 eV due to the influence of negative bandgap.
We ignore it in this Letter because the region around Γ point
where LDA gives negative bandgap is very small, which is shown
in Fig. 4. Wu et al. [24] dealt with the InN bandgap issue using
Kane’s two band k · p model [25], but their model includes too
many hypotheses and simplifications which weaken its reliability.
Difference between their model and experimental data enlarges as
free electron concentration increases.
(1.9 eV − 0.78 eV) higher than conduction band maximum (CBM).
Because only defects whose energetic levels locate above Fermi
level are able to ionize, we then calculate the energetic positions
of ON, VN and SiIn. In Fig. 5, we give the PDOS (s orbit) of atoms
nearest to the defects (blue lines) as well as that in pure InN (black
lines). We can see that there are distinct peaks in blue curves
which mark the positions of defect levels. To illustrate clearly, we
abstract them and put into Fig. 6 from which we find the defect
levels of them are all higher than 1.9 eV. That is to say, all of
the three defects can ionize when the Fermi level is as high as
1.9 eV and contribute to Burstein Moss shift. It is well known that
LDA method usually underestimates the positions of defect levels
in conduction band. That is to say the actual positions are higher
than the calculated ones. Still, our conclusions will not be changed.
Duan et al. [26] have investigated N vacancy and they found that
the defect levels are well above the CBM, in agreement with our
results. This might be due to the fact that InN have the lowest
CBM among III–V compounds [27].
4.3. Find the contributors of free electrons
As discussed above, perfect InN has
a narrower bandgap
(∼ 0.8 eV) and the wider absorption edge (∼ 1.9 eV) found in
previous works results from high density of free electrons in these
samples whose crystallization quality was confined by the grow-
ing methods at that time. The work followed will be engaged
to find the origin of the unintentionally doped free electrons. In
wider bandgap samples, the absorption edge is as high as 1.9 eV
which is the approximate position of Fermi level. If we suppose
that InN has a bandgap of 0.78 eV, the Fermi level is about 1.12 eV

C. Liu, J. Li / Physics Letters A 375 (2011) 1152–1155
1155
5. Conclusions
[2] Y. Nanishi, Y. Saito, T. Yamaguchi, Jpn. J. Appl. Phys. 42 (2003) 2549.
[3] C.P. Foley, T.L. Tansley, Phys. Rev. B 33 (1986) 1430.
[4] Motlan, E.M. Goldys, T.L. Tansley, J. Cryst. Growth 241 (2002) 165.
[5] K.L. Westra, M.J. Brett, Thin Solid Films 192 (1990) 227.
[6] J. Wu, W. Walukiewicz, W. Shan, K.M. Yu, J.W. Ager, S.X. Li, E.E. Haller, H. Lu,
W.J. Schaff, J. Appl. Phys. 94 (2003) 4457.
[7] M. Yoshimoto, H. Yamamoto, W. Huang, H. Harima, J. Saraie, Appl. Phys. Lett. 83
(2003) 3480.
[8] S.H. Wei, X.L. Nie, I.G. Batyrev, S.B. Zhang, Phys. Rev. B 67 (2003) 165209.
[9] V.Y. Davydov, et al., Phys. Status Solidi B 229 (2002) R1.
[10] V.Y. Davydov, A.A. Klochikhin, V.V. Emtsev, Phys. Status Solidi B 230 (2002) R4.
[11] T.S. Moss, Proc. Phys. Soc. London, Sect. B 67 (1954) 775;
E. Burstein, Phys. Rev. 93 (1954) 632.
[12] I. Mahboob, T.D. Veal, L.F.J. Piper, C.F. McConville, H. Lu, W.J. Schaff, J. Furth-
muller, F. Bechstedt, Phys. Rev. B 69 (2004) 201307.
[13] X.Q. Wang, S.B. Che, Y. Ishitani, A. Yoshikawa, J. Appl. Phys. 99 (2006) 073512.
[14] P. Schley, R. Goldhahn, G. Gobsch, M. Feneberg, K. Thonke, X. Wang, A.
Yoshikawa, Phys. Status Solidi B 246 (2009) 1177.
In summary, inspired by the concept of Burstein–Moss shift, we
simulate the relation between absorption edge and free electron
concentration based on DFT-LDA methods, which is in good agree-
ment with experimental data. This verifies that the band gap of
InN is around 0.78 eV, not the widely accepted value of 1.9 eV.
High density of free electrons is the cause of blue shift of InN
absorption edge which is usually used to determine band gap ap-
proximately. We also give a schematic in which energetic positions
of the four n-type defects with low formation energies are shown.
We can see that they are all high enough to ionize when Fermi
level is lifted upto 1.9 eV and in turn help to widen absorption
edge. Hence, they are the potential contributors of free electron
density in InN because of their low formation energy and low ion-
ization energy. However, DOS of conduction band starts to increase
sharply from the energy of 2.09 eV above VBM, determining that
absorption edge can rarely reach higher than 2.09 eV.
[15] C. Stampfl, C.G. Van de Walle, D. Vogel, P. Krüger, J. Pollmann, Phys. Rev. B 61
(2000) R7846.
[16] C.G. Van de Walle, Phys. Status Solidi B 235 (2002) 89.
[17] C.G. Van de Walle, J. Neugebauer, J. Appl. Phys. 95 (2004) 3851.
[18] G. Kresse, J. Hafner, Phys. Rev. B 47 (1993) 558;
G. Kresse, J. Hafner, Phys. Rev. B 48 (1993) 13115.
[19] P.E. Blöchl, Phys. Rev. B 50 (1994) 17953;
Acknowledgements
G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758.
J.L. gratefully acknowledges financial support from the “One-
Hundred Talent Plan” of the Chinese Academy of Sciences and
National Science Fund for Distinguished Young Scholar (Grant
No. 60925016). This work is supported by the National High Tech-
nology Research and Development program of China under con-
tract No. 2009AA034101.
[20] I.G. Pichugin, M. Tiachala, Izv. Akad. Nauk SSSR, Neorg. Mater. 14 (1978) 175.
[21] Y.H. Chang, Y.S. Lu, Y.L. Hong, C.T. Kuo, S. Gwo, J.A. Yeh, J. Appl. Phys. 107 (2010)
043710.
[22] F. Bechstedt, J. Furthmüller, J. Cryst. Growth 246 (2002) 315.
[23] Q.X. Guo, M. Nishio, H. Ogawa, A. Wakahara, A. Yoshida, Phys. Rev. B 58 (1998)
15304.
[24] J. Wu, W. Walukiewicz, Appl. Phys. Lett. 84 (2004) 2805.
[25] J. Wu, W. Walukiewicz, W. Shan, K.M. Yu, J.W. Ager III, E.E. Haller, H. Lu, W.J.
Schaff, Phys. Rev. B 66 (2002) 201403.
References
[26] X.M. Duan, C. Stampfl, Phys. Rev. B 77 (2008) 115207.
[27] T. Dietl, H. Ohno, MRS Bulletin 28 (2003) 714.
[1] A.G. Bhuiyan, A. Hashimoto, A. Yamamoto, J. Appl. Phys. 94 (2003) 2779.