A First Principles Analysis of Electronic Structure of InGaZnO4 with
Modified Becke-Johnson Exchange Potential
Takashi Masuhara, Satofumi Souma, and Matsuto Ogawa
Graduate School of Engineering, Kobe University, Japan

1Introduction

Recently transparent conductive oxides (TCO) or transparent amorphous oxide semiconductors (TAOS) havebeen gathering much attention, since they are applicableto the thin-film transistors, thin-film light-emitting diodes,
large scale liquid crystal displays, and other wide rangeof information and communication technology (ICT) related devices. Amorphous In-Ga-Zn-O (a-IGZO) is representative of TAOS and especially attracting attention. aIGZO is well known for high electron mobility, wide bandgap etc., and these properties are similar to crystalline
IGZO (c-IGZO). It is also known that because density ofstates (DOS) of oxygen occupy the conduction band minimum (CBM) and valence band maximum (VBM), DOS
can be strongly influenced by oxygen defect. Additionally, a-IGZO thin film transistor (TFT) can be made on aresin substrate at room temperature. Therefore, a-IGZO
is expected to be applied to flexible devices.
In a first principles analysis of electronic structure basedon density functional theory (DFT), exchange-correlation
potential such as local density approximation (LDA) orgeneralized gradient approximation (GGA) tends to underestimate bandgap of semiconductors. In order to improve this issue, advanced methods such as the GW approximation or L(S)DA+U have been proposed. The GW
approximation shows good reproducibility of experimental
data, but it requires a huge computational effort. Moreover, the calculation of IGZO needs supercell methods
which require much computational time. In our study,
we calculate electronic structure with Modified BeckeJohnson (MBJ) potential [1] instead of the GW approximation. MBJ potential has a high precision which is similar in degree of the GW with a low computational time.
We analyze bulk c-InGaZnO4 as a first step and compare
MBJ results of bulk c-InGaZnO4 with those of GGA.
2Models and Calcilation

We choose c-InGaZnO4 as the calculation object because of the simple composition ratio 1:1:1:4.
cInGaZnO4 has a rhombohedral unitcell and hexagonallattice (a=b=3.295Å, c=26.071Å, α=β=90◦ , γ=120◦ [2]).
This unitcell is YbFe2 O4 -type structure and belongs to thespace group 166(R3̄m). Figure 1.(a) shows the 2 × 2 × 1
supercell of InGaZnO4 whose atomic positions are citedfrom Ref. [3]. This supercell has a layered structurecomposed of InO1.5 layers and ZnGaO1.5 layers, respectively. We calculate bulk c-InGaZnO4 using a first principles calculation package WIEN2k [4], which is using density functional theory (DFT) based on the full-potential(linearized) augmented plane-wave ((L)APW)+local or-(a)(b)
new unitcellOIn} InOlayer
GaZnO} layer
1.5

2.5ZnGa

View of IGZO supercell
from aboveabc

Fig. 1. (a)The supercell model of InGaZnO4 which contains (InGaZnO4 )12 , (b)New model suggested by WIEN2k
which contains (InGaZnO4 )6 .

bitals (lo) method (F(L)APW+lo). In practice, we calculate new monoclinic structure (a=26.071Å, a=5.707Å,
c=3.295Å, α=β=γ=90◦ ) suggested by WIEN2k shown inFig.1.(b). Note: The new model belongs to the spacegroup 10(P2/m), and axes of coordinate are changed because of unique axis c in 10(P2/m).
In the calculations, at first we optimize internal structural parameters with PBE-GGA using the calculated
forces on the nuclei. As regards volume optimization using total Energy, because the original structure is close torelaxed and the structure is relaxed in which case volume
increases about 3%, we do not optimize throughout thispaper. As for the MBJ potential, MBJ exchange potential and LSDA correlation potential (PW92) are used(seeRef.[1]). MBJ exchange potential is a modified potential oforiginal Becke-Johnson exchange potential in order to fit
bandgaps of typical semiconductors. We choose this MBJ
potential and PBE-GGA for the exchange-correlation potential and compare the results of two, with the calculation condition, 500 k-point in the 1st BZ, muffin-tin ra−1−1
dius: RIn, RGa, RZn
mt = 2.02 bohr
mt = 1.76 bohr
mt =−1O−1
1.96 bohr , Rmt = 1.74 bohr , RKMAX=6.0, energy toseparate core and valence states: −7.5Ry.
3Results and Discussion

Fig. 2. shows band structure and density of statesof bulk c-InGaZnO4 with the results of GGA. Fig. 3.
shows these with results of MBJ. In those figures, we define the high-symmetric point as M(0,1/2,0), K(0,1/2,1/2),
Z(0,0,1/2), A(1/2,0,0), respectively. The bandgaps of

(a)

10(b)

(a)

10(b)

tot
In totO tot
Zn totGa tottot
In totO tot
Zn totGa tot5Energy [eV]

Energy [eV]50-5-100-5MKΓ

ZΓ A 0 10 20 30 40 50 60-10MKΓ

DOS [states/eV]Z

Γ A 0 10 20 30 40 50 60

DOS [states/eV]

Fig. 2. (a)Electronic structure and (b) DOS calculatedwith GGA.

Fig. 3. (a)Electronic structure and (b) DOS calculatedwith MBJ.

GGA and MBJ are 1.32eV and 3.07eV, which are respectively underestimated by 62% and 12% compared to theexperimental optical bandgap of 3.5eV [5]. It should be
noted that the underestimation of bandgap is significantlyimproved with using the MBJ potential. While, there isno big difference of DOS between GGA and MBJ. Figure
4 shows an enlarged view of partial DOS with MBJ. Thes state of indium (In(s)), s and p states of oxygen (O(s,p))
at the CBM, and Zn(d), O(p) at the VBM are fairly large,
especially oxygen occupy both the CBM and VBM. Table I. shows the effective masses of electron from Γ point.
These values are calculated by fitting from -5% to 5% of
the CBM in the 1st BZ(e.g. from −0.05(π/a) to 0.05(π/a))to E = ~2 k2 /2m∗ . It is found that c-InGaZnO4 has theisotropic effective mass of an electron: GGA 0.21m0 andMBJ 0.33m0 . It is noteworthy that the result from thepresent MBJ 0.33m0 is quite comparable to the experimental value of 0.32m0 [6].

Acknowledgments

4The authors are grateful to Prof. P. Blaha at Wien
Technical University for his kind reply.
References[1] F. Tran and P. Blaha, Phys. Rev. Lett. 102, 226401 (2009).
[2] N. Kimizuka and T. Mohri, J. Solid State Chem. 60, 382(1985).
[3] H. Omura, H. Kumomi, K. Nomura, T. Kamiya, M. Hirano, and H. Hosono, J. Appl. Phys. 105, 093712 (2009).
[4] K. Schwarz and P. Blaha, Comput. Mater. Sci. 28, 259(2003).
[5] M. Orita, M. Takeuchi, H. Sakai, and H. Tanji, Jpn. J.
Appl. Phys. 34, L1550 (1995).
[6] A. Takagia, K. Nomurab, H. Ohtab, H. Yanagia, T.
Kamiya, M. Hiranob, and H. Hosonoa , Thin Solid Films
486, 38-41 (2005).

Conclusion

We have performed a first principles calculation withmodified Becke-Johnson (MBJ) potential for bulk cInGaZnO4 . As a result, it is found that the underestimations of the bandgap and the effective mass of electron are considerably improved by using MBJ potential ina first principles calculation for c-InGaZnO4 and resultsfrom MBJ were close to experimental values. Such highprecision values are obtained within as much as 10 times
computational time of the GGA calculation. It is also
found that states of oxygen significantly occupy the CBMand VBM.

Table I. The effective mass of electron along each directions
from Γ point.

effective mass (m∗ /m0 )directions

GGAMBJΓ → M ( [010] )Γ → K ( [011] )Γ → Z ( [001] )Γ → A ( [100] )

0.209
0.208
0.207
0.196

0.333
0.326
0.322
0.341

(a)

5(a) In(b) Ga(c) Zn(d) O4(b)2

10-1

00.1 0.2 0.3 0.4

00.1 0.2 0.3 0.4

00.1 0.2 0.3 0.40(c)Energy[eV]Energy[eV]30.1 0.2 0.3 0.4 0.5

Partial DOS[states/eV]

totspdFig. 4. Enlarged partial DOS of (a)In (b)Ga (c)Zn and(d)O calculated with MBJ.

Fig. 5. Energy contours of the CBM in the 1st BZ. (a) a∗ c∗plane, (b) a∗ b∗ plane, (c) b∗ c∗ plane, respectively.