electroconductive properties in doped spinel oxides

Optical Materials xxx (2014) xxx–xxx

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Optical Materials

journal homepage: www.elsevier .com/locate /optmat

Electroconductive properties in doped spinel oxides

http://dx.doi.org/10.1016/j.optmat.2014.08.0100925-3467/� 2014 Elsevier B.V. All rights reserved.

⇑ Corresponding author. Tel.: +91 9415117955.E-mail address: [email protected] (Y. Sharma).

Please cite this article in press as: S. Dwivedi et al., Opt. Mater. (2014), http://dx.doi.org/10.1016/j.optmat.2014.08.010

Shalini Dwivedi a, Ramesh Sharma b, Yamini Sharma a,⇑a Dept. of Physics Feroze Gandhi College, Raebareli 229001, U.P., Indiab Dept. of Physics, Feroze Gandhi Institute of Engineering and Technology, Raebareli 229001, U.P., India

a r t i c l e i n f o

Article history:Received 20 April 2014Received in revised form 22 July 2014Accepted 18 August 2014Available online xxxx

Keywords:Spinel oxidesElectronic structureOptical propertiesThermoelectric propertiesVibrational properties

a b s t r a c t

The application of spinel oxides as transparent conducting oxides (TCOs) in optoelectronic devices as asubstitute for ZnO is attracting attention in the recent years. Despite attractive photo-luminescence prop-erties of zinc aluminate and zinc gallate, relatively little work has been done to interpret the opticalresponse of spinel oxides on the basis of energy band structures. We present the electronic propertiesof ZnX2O4 (X = Al, Ga, In) calculated by the full potential linearized augmented plane wave method. Opti-cal properties such as absorption coefficient and reflectivity are calculated and interpreted in terms ofenergy bands and density of states. Enhancement in optical properties was studied for Li and Mn ionsdoped in the ZnGa2O4 matrix. The main features in the experimentally observed photoluminescencespectra for doped and undoped ZnGa2O4 have been verified through the optical parameters.

The transparence of spinel oxides to UV radiations is also clearly illustrated in the reflectivity vs. energycurves. At very small wavelengths the oxides may be used as reflective coating materials. Transport prop-erties of the zinc spinel oxides have been investigated for the first time, and are found to have high See-beck coefficients, high electrical conductivity and low thermal conductivity, with high value of figure ofmerit ZT � 0.8. The study of vibrational and thermodynamic properties by the projector augmented wavemethod confirms the dynamic stability of the doped and undoped spinel oxides. Zinc spinel oxides arefound to be p-type semiconductors with an optimum value of band gap �2–3 eV and appear to meetthe conditions of low resistivity and high transparency (>80%) for state-of-art TCOs.

� 2014 Elsevier B.V. All rights reserved.

1. Introduction

A switch from indium based transparent conducting oxide(TCO) such as indium-tin-oxide (ITO) to zinc based TCOs couldreduce cost as well as toxicity and yield better devices, assumingthat the optical and electrical properties of ZnO become compara-ble to those of ITOs. Al and Ga-doped ZnO seem to be most prom-ising candidates where improvement in the electrical conductivityand optical transparency can be modeled according to solid statedevice requirement. Intensive investigations have been recentlytargeted at improving the electrical and optical properties of ZnOby doping with Al/Ga/In or Al2O3/Ga2O3/In2O3 [1–8]. Literaturesuggests that in ZnO–Al2O3 composite materials system, Al-dopedZnO (AZO) and zinc aluminate spinel were formed, which are wellknown for their applications in optoelectronic devices [2]. Amongstthe oxide phosphors, ZnGa2O4 have been prepared by many meth-ods by doping ZnO with Ga or Ga2O3. These oxides not only showedgreat improvement in electrical conductivity compared to ZnO, buthave possible applications for field emission displays [3–7]. The

ZnkIn2O3 + k oxide system is a promising material with good lumi-nescence, however formation of ZnIn2O4 is not reported [8].

The electronic structure of normal, inverse and partially inversespinel oxides have been studied by density functional theory (DFT)within the local density approximation (LDA) using the linear com-bination of atomic orbitals (LCAO) [9] and tight-binding linearizedmuffin-tin orbital method (TB-LMTO) within the atomic sphereapproximation (ASA) [10]. Although there is an overall agreementbetween the calculations by both the methods regarding the com-position of valence and conduction bands, the band gap were sub-stantially underestimated compared to experimental band gap.Elastic properties under high pressure were studied by plane-wavepseudo potentials. The exchange correlations were treated underthe LDA parameterized by Perdew-Zunger (PZ) as well as general-ized gradient approximation (GGA) with Perdew-Burke-Ernzerhof(PBE) functions [11,12]. The calculated lattice constants and inter-nal parameters were found to be in good agreement with experi-ment. It is observed that DFT with LDA for the various theoreticalmethods underestimates the parameters such as band gappressure coefficients etc. To overcome the problem, Dixit et al. cal-culated the electronic structure of some spinel oxides by using DFTplane wave pseudopotential (PP) based ABINIT code [13]. It was

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2 S. Dwivedi et al. / Optical Materials xxx (2014) xxx–xxx

found that the band gap increased with the application of quasi-particle GW approximation along with PP, and were closer to theexperimental gaps. Similarly, the authors in Ref. [14] computedthe electronic density functions using the DFT based Vienna ab ini-tio simulation package (VASP). The GGA of PBE (Perdew et al.) andhybrid functional (HSE06) was used. The authors concluded thatthe HSE band curvatures were much more accurate than theDFT-GGA values. The various band structure calculation methodsthus describe the properties of materials with varying degrees ofaccuracy and the overall band profiles were found to be in fairlygood agreement with each other, at the same time these methodsalso reproduced the experimental trends quite well.

Amongst the spinel oxides, the photoluminescence and cathod-oluminescent characteristics of ZnGa2O4 exhibited intense blueemission [15,16]. Further, a significant enhancement of the photoresponse has led to fabrication of ZnGa2O4 doped with Mn atoms[17–20]. Lee et al. [21] also investigated the conductivity andphotoconductivity response of undoped and Li-doped ZnGa2O4 epi-taxial films. Similarly, the effect of Li, Cu and Zn doping on theluminance and conductivity of ZnGa2O4 phosphor was studied byYang and Yokoyama [22].

Despite spinel oxides having good optical properties, especiallyMn-doped zinc gallate phosphor, relatively little work has beendone to elucidate the effects of doping on the electronic structure.Further, effective work to investigate the electrical and thermalproperties of doped spinel oxides has not been carried out so far.We have therefore undertaken the study of ground state electronicproperties by full potential linearized augmented plane wavemethod.

Few studies of vibrational properties of spinel oxides are avail-able in literature [23–25]. 1st principle calculations of phononfrequency and eigenvectors are of great relevance for predictionand interpretation of Raman and infrared spectra. In addition,unstable modes computed in high symmetry reference structureare a valuable guide to the ground state structure and properties.The dynamic stability and the effect of changing mass of thecations in spinel oxides were studied through the vibrational prop-erties which are calculated by the projector augmented wave(PAW) method.

2. Methodology

In these calculations we have studied the properties of variousmodifications of zinc spinel oxides. We adopt the method of fullpotential linearized augmented plane waves (FP-LAPW) and localorbitals (lo) [26], which are based on the density functional theorywith the modification of the exchange correlation energy by thegeneralized gradient approximation (GGA) proposed by Wu andCohen [27]. The computer code of WIEN2k, which is one of themost accurate ab initio methods, is employed to numerically calcu-late the self consistent energy and charge distributions, and thensubsequently calculate the electronic and optical properties fromthe converged configuration. The calculations are performed for47 k-points in the case of spinel oxides, whereas for doped oxidesthe calculations were carried out for 231 k-points in the irreducibleBrillouin zone (IBZ). The total energy of convergence increases withchanging cation and has a value of �10327.01 Ry for ZnAl2O4,�23934.71 Ry for ZnGa2O4 and �55445.96 Ry for ZnIn2O4. In thecase of ZnAl2O4 crystal, the RMT for Zn = 1.7, Al = 1.86, O = 1.51 Å;for ZnGa2O4, RMT for Zn = 1.78, Ga = 1.94, O = 1.58 Å and forZnIn2O4, RMT for Zn = 1.91, In = 2.08, O = 1.69 Å. A 2 � 1 � 1 supercell was constructed which contained 112 atoms in the unit cell.Zn ion is replaced by alkali metal Li to get 1.7% atom dopedmaterials. In the case of Zn1�xLixGa2O4 crystal, the RMT forZn = 1.78, Li = 1.00, Ga = 1.94 and O = 1.58 Å. Zinc gallate was

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doped by transition metal ion Mn to get Zn1�xMnxGa2O4

(x = 0.035); here, RMT for Zn = 1.78, Mn = 1.78, Ga = 1.9, O = 1.58 Å.The calculations for vibrational properties were carried out with

the molecular-dynamics program VASP (Vienna ab initio simula-tion program) [28]. The program calculates the interatomic forcesvia the Hellmann–Feynman theorem. The direct method used inthe calculation of phonon spectrum utilizes the interatomic forceconstant matrix which is derived from a set of calculations on aperiodically repeated supercell of 3 � 3 � 3 mesh [29]. All theatoms are put in their equilibrium position initially, and then dis-placed slightly by +/�0.02 Angstrom. The calculations explore thefull BZ for an interaction range of 10.0 Å. A total of 6 single pointenergy calculations were run on the supercell containing 56 atoms.The calculations use a plane wave cutoff energy of 400.0 eV with aconvergence criterion of 1.00 � 10–5 eV. The formation energies are�1785.96 and �1210.47 kJ/mol for ZnAl2O4 and ZnGa2O4 respec-tively. The negative sign indicates that the reaction is exothermicwhich implies stability of spinel oxides. The positive pressure of1.142 and 2.457 GPa causes expansion during full geometry opti-mization respectively. On doping ZnGa2O4 by Li/Mn, the formationenergy increases to �9604.61 and �9352.77 kJ/mol respectively,with applied pressure reducing to 1.617 GPa for doping by Li,and increasing to 2.876 GPa on doping by Mn. The optimized lat-tice parameters for ZnAl2O4 change from 7.996 to 8.0844 Å,whereas the parameters for ZnGa2O4 do not change on structureoptimization.

3. Result and discussion

3.1. Structure

The spinel structure AB2O4 with space groupFm�3m, is highlystable and allows different types of cations to be located on twosublattices. The spinel structure where A = Zn, B = Al, Ga and In,can be described as an ordered defect fluorite structure. To picturethe structure, one starts with a cubic close-packed array, a face-centered-cubic lattice of oxygen atoms. This fcc lattice containsempty sites with octahedral and tetrahedral coordination by oxy-gen (one and two sites per oxygen atom, respectively). One-eighthof the tetrahedral sites are filled (A sites), and half of the octahedralsites are filled (B sites). The A sites are located at 8a (1/81/81/8), Bsites at 16e (½½½) and oxygen at 32e (uuu) with ideal u = 0.25[10]. Thus, for the cubic spinel structure, there is only one freestructural parameter u aside from the lattice constant. Variationof this parameter changes the relative sizes of the oxygen tetrahe-dra and octahedra without changing the crystal symmetry (Fig. 1).

In the spinel oxide ZnGa2O4, the octahedral Ga3+ ions(RVI = 0.062 nm) are slightly larger than Zn2+ ions (RIV = 0.060 nm).The dopant atom (Li or Mn) can potentially occupy two differentsites i.e. tetrahedral and octahedral sites, as well as the interstitialsites in the spinel lattice. Since Li (R = 0.059 nm) possesses ionicradius similar to that for Zn (R = 0.060 nm), it may substitute onthe tetrahedral zinc site, giving rise to Zn1�xLixGa2O4. Similarly,Mn also has small ionization potential and suitable ionic radiusand is also substituted at this site.

The bond lengths follow the trend Zn-Al < Zn-Ga < Zn-In andAl-O < Ga-O < In-O due to increase in ion-size while going downthe group. The systematic changes in the bond lengths are respon-sible for modifications in the band structure of spinel oxides. Theaverage bond length between Zn-O and cation X-O in ZnAl2O4

increases by 4.5% in ZnGa2O4, which further increases by 6.2% inZnIn2O4. On doping ZnGa2O4 with Li and Mn atoms, the bondlengths do not change except for the increase in Mn-Zn lengthcompared to Li-Zn bond length. The calculated bond lengths arein good agreement with experimental bond lengths (Table 1) [12].

dx.doi.org/10.1016/j.optmat.2014.08.010


W

L

Γ X

WK

(a)

(b)

Fig. 1. Crystal structure of (a) ZnGa2O4 and (b) Brillouin zone (BZ).

Table 1Electronic properties of Zinc spinel oxides.

ZnAl2O4 ZnGa2O4 ZnIn2O4

Lattice parameter (Å) 7.91(8.09 [21])

8.275 [13]8.334 [22]

8.842

Fermi energy (eV) 0.49928 0.38132 0.33263Convergence energy (Ry) �10327.01 �23934.71 �55445.96Band gap (eV) Direct 3.81 – –

Indirect – 1.85 –Optical 3.85 1.98 1.03Exp. 4.11[10],

4.35[13],3.9 [10]

2.79 [10] 1.43

m⁄/mo 0.14 0.27 0.2880.35 [12] 0.25 [12] 0.22 [12]

Bond length (Å) Al–O = 1.981.98 [13]1.88 [12]

Zn–O = 1.711.92 [13]

Zn–Al = 3.27

Zn–Zn = 3.43

Al–Al = 2.79

O–O = 2.792.66 [12]

Ga–O = 2.071.95 [13]1.89 [12]

Zn–O = 1.791.88 [13]

Zn–Ga = 3.43

Zn–Zn = 3.58

Ga–Ga = 2.93

O–O = 2.922.68 [12]

In–O = 2.212.17 [12]

Zn–O = 1.91

Zn–In = 3.67

Zn–Zn = 3.83

In–In = 3.13

O–O = 3.123.07 [12]

S. Dwivedi et al. / Optical Materials xxx (2014) xxx–xxx 3

3.2. Energy bands and density of states

The energy bands for ZnX2O4 are plotted along high symmetrydirections W-L-C-X-W-K as shown in Fig. 2(a–c). The nature ofdispersion of bands is characteristic of spinel oxides, with lessdispersive bands at top of valence region compared to bottomregion.

A direct band gap of 3.81 eV is observed in ZnAl2O4 at theC-point at the centre of BZ. Both ZnGa2O4 and ZnIn2O4 have anindirect band gap of 1.85 and 1.03 eV respectively, along the C-Ldirection. The lowering of band gap in the zinc spinel oxides is inaccordance with substitution of heavier cations in ZnX2O4 spinels.The band gap of ZnAl2O4 and ZnGa2O4 calculated by TB-LMTO-ASAmethod were also underestimated compared to the experimentalband gap of 4.11 and 2.79 eV respectively [10]. The calculated bandgap are underestimated compared to experimental values due towell known exchange–correlation effects in DFT based calcula-tions. Stoica and Lo calculated the electronic structure of zincspinel oxides by DFT-GGA-PBE and DFT-HSE and concluded thatHSE gives better agreement of band gap with experimental mea-surement [14] (Table 1).

It is observed from Figs. 2(a, b, c), that the conduction band min-imum shows a parabolic nature at C-point and the depth of thiscurve appears to increase with substitution of heavier cation inthe zinc spinel oxide ZnX2O4. This band appears to allow opticaltransitions from valence (VB) to the conduction band (CB), andimparts the semiconducting properties to the spinel oxides, other-wise these oxides would have a very high indirect gap at W-point.From the band structure it is also observed that the valence-bandmaximum is quite flat which implies that the effective mass is


rather large. The calculated effective masses are 0.14, 0.27 and0.288 m0 for ZnAl2O4, ZnGa2O4 and ZnIn2O4 respectively.

The energy bands can be interpreted in terms of the contribu-tion to density of states by the various atoms. We make the follow-ing observations from the partial and total density of states (PDOSand TDOS) for ZnAl2O4, doped and undoped ZnGa2O4 and ZnIn2O4

(Fig. 3).

(i) Both cations Zn and Ga/In contain filled d-shell, Al does notcontain d-electrons. The O s-states contribute to the energybands at lower energies and p-states contribute in thevalence band region in vicinity of Fermi energy level.

(ii) From the band manifold it is observed that the states invalence band region lie between Fermi energy level EF at0 eV to �7.17 eV for ZnAl2O4, which decreases to�6.516 eV in ZnGa2O4 and reduces further to �5.30 eV forZnIn2O4. At the valence band edge p-states of O give maxi-mum contribution for all the three spinel oxides. It isobserved that ZnIn2O4 has maximum number of states clos-est to the EF. Similarly, amongst cation Al/Ga/In, the s- and p-states contribute the most at EF, although contributions fromZn remain nearly constant.

(iii) The band gap in the oxides originate due to hybridization ofmetal atoms with oxygen ions. With increase in weight ofcation X (=Al, Ga, In), there is greater p-d interaction invalence band of ZnGa2O4 and ZnIn2O4, which leads todecrease in extent of band manifold compared to ZnAl2O4.The increase in atomic size of the X cation leads to a greaterspatial overlap, which can be observed in TDOS in Fig. 3.

(iv) For slightly doped Zn1�xLixGa2O4 (x = 0.017), the energyband gap is found to increase to 2.07 eV. The projectedDOS is modified to some extent due to substitution of Zn2+

by Li1+ ions, Li s-states contribute at lower energies andhybridize with neighboring O states.

(v) In Zn1�xMnxGa2O4 the size of the band gap increases to2.58 eV, although the contribution of Zn and Ga states tothe total DOS remains nearly same. Since Mn2+ is substitutedinto the Zn2+ site, which is surrounded by a tetrahedral



Fig. 2. Selected energy bands along high symmetry directions of first Brillouin zone (BZ) using FP-LAPW method. Here, R (1/2, 1/2, 1/2), C (0, 0, 0), X (1/2, 0, 0) and M (1/2, 1/2,0) are featured k-point in the BZ (a) ZnAl2O4, (b) ZnGa2O4 and (c) ZnIn2O4.

-10 -5 0 5 100

7

14

21

EF

Energy (eV)

Total Zn Al O

Den

sity

of

Stat

es/e

V p

er u

nit

cell

Total Zn Ga O

0

612

18 ZnGa2O

4

ZnAl2O

4

0

8

16 LixZn

1-xGa

2O

4

Total Li Zn Ga O

0

9

18Mn

xZn

1-xGa

2O

4 Total Mn Zn Ga O

0

9

18

27

36ZnIn

2O

4 Total Zn In O

Fig. 3. Partial density of states (PDOS) and total density of states (TDOS) of (a)ZnAl2O4, (b) ZnGa2O4, (c) Zn1�xLixGa2O4, (d) Zn1�xMnxGa2O4 and (e) ZnIn2O4.


environment of oxygen atoms, the Mn d-levels split energet-ically into lower eg and upper t2g states in the tetrahedralcrystal field and are found to be located in the band gap ofthe ZnGa2O4 matrix. The electronic structure is modifiedslightly since the O p-states hybridize with Mn d-states,which pushes the states from Fermi level EF to lower ener-gies at �3.22 eV.

Since the spinel oxides have band gaps�3–4 eV, these materialsmay have potential applications as TCOs. It was thought pertinentto investigate the optical response and transport phenomenonsince these semiconductors may have important optoelectronicand thermoelectric properties.

3.3. Optical properties

Zinc spinel oxides have been studied by researchers as attrac-tive phosphor host candidate material for flat panel displaysbecause of their favorable photo-luminescence and cathode-


luminescence properties, excellent mechanical and thermalstability. Due to good optical characteristics, ZnGa2O4 films areused as reflective optical coatings in aerospace applications,however ZnAl2O4 and ZnIn2O4 are not widely used due to absenceof complete information on optical constants. From diffuse reflec-tance spectra, ZnGa2O4 was found to have a wider band gap thanITO and may serve as a good replacement if the optical propertiesof zinc spinel oxides could be enhanced [1,5].

The optical response of the spinel oxides can be described by acomplex frequency dependent dielectric function ½eðxÞ ¼ e1ðxÞþie2ðxÞ� [30]. The imaginary part e2ðxÞ, which arises from intrabandand interband transitions, depends on the DOS and momentummatrix p, and is calculated by considering all the possible transi-tions from occupied to unoccupied states (with fixed k-vectors)over the Brillouin zone (BZ).

emm2 ¼ 8p2e2=m2x2

Xunocc

n

Xocc

n0

ZBZ

Pvnn0 ðkÞ

�� 2f knð1� f kn0 Þ

� dðEkn � Ek

n0 � �hxÞ � d3k=ð2pÞ3 ð1Þ

In Eq. (1), m is mass of electron and X is the volume of unit cell.The function f kn is the Fermi distribution and knj i is related tocrystal wave functions corresponding to the nth eigenvalue withcrystal momentum k.

The real part of the dielectric function e1ðxÞcan be calculatedfrom e2ðxÞ using the Kramers–Kronig relation as given below,

e1ðxÞ ¼ 1þ ð2=pÞPZ 1

0e2ðx0Þx0dx0=ðx02 �x2Þ ð2Þ

Semiconductors are known to have absorption up to 105 cm�1

for photons with energies above the band gap, and very lowabsorption for photons having energy below the band gap. Theabsorption edge peaks in the optical region corresponds to bothdirect and indirect band transitions from the valence band to theconduction band. Relatively little work has been done to interpretthe optical response of doped and undoped spinel oxides on thebasis of energy band structures. Optical properties such as absorp-tion coefficient a(hm) is calculated from the dielectric functionsgiven in Eq. (1).

aðxÞ ¼ 2x e21ðxÞ þ e2

2ðxÞ� �1=2 � e1ðxÞ=2� �1=2

ð3Þ



0 2 4 6 8 100

2

4

6

80

50

100

150 σ

(1/Ω

Ω

cm

)x10

4

Energy (eV)

ZnIn2O4 ZnGa2O4 LixZn1-xGa2O4 MnxZn1-xGa2O4 ZnAl2O4

(b)

α (1

04 / cm

)

(a)

Fig. 4. Optical properties of ZnAl2O4, ZnGa2O4, Zn1�xLixGa2O4, Zn1�xMnxGa2O4,ZnIn2O4 (a) absorption coefficient a(ht) and (b) optical conductivity r(ht).


The a(hm) vs. hm curves for undoped and Mn/Li-doped ZnGa2O4

along with ZnAl2O4 and ZnIn2O4 are plotted in Fig. 4(a). The opticalband gap can be determined from the plots of a(hm) vs. hm curvesby extrapolating the linear portions of the curve to hm. The opticalband gaps are 3.85, 1.98 and 1.43 eV for ZnAl2O4, ZnGa2O4 andZnIn2O4 respectively.

Absorption is a process reverse to photoluminescence, which isthe creation of electron–hole pair when photon absorbed by asemiconductor undergoes recombination and emits a photon withrandom phase, polarization and direction. From the various posi-tions of peaks in the curves of absorption coefficient, we can obtainsufficient information about the photoluminescence spectra of spi-nel oxides. In zinc aluminate, the absorption begins at 3.85 eV,which is the optical band gap in the near UV region and corre-sponds to interband transitions from the valence to conductionbands i.e. from O p ? Al s-states and Zn d ? Al p-states. The peaksat 4.5 eV (278.8 nm) with absorbance of 8.06 � 104 cm�1 and7.66 eV in UV region may be due to excitation from Al p ? Os-states and Zn d ? O p-states.

Zinc gallate is known as a blue-emitting phosphor and showsblue emission with relatively low efficiency. In zinc gallate, theexcitation features start from 1.98 eV (623 nm) in the red/orangeregion which corresponds to the optical band gap. The absorptionpeak at 2.6 eV (463 nm) for the blue region with an absorbance of8.07 � 104 cm�1 may be due to the interband transitions fromstates in VB i.e. O p ? to Ga s-states in CB, and also from Znd ? Ga p-states. The cathodoluminescence characteristic ofZnGa2O4 which exhibits a blue peak at 470 nm [17,20] confirmsthe calculated excitation feature. Enhancement in absorptionbegins at 4.76 eV (278 nm) in the UV region with a high value ofabsorbance of 31.45 � 104 cm�1. This increase in absorbance canbe correlated to the experimentally measured photocurrentobtained for 254 nm (4.88 eV) irradiation of ZnGa2O4 films [21].

ZnGa2O4 is also well known as phosphor matrix for Mn2+/Cr3+

activators with efficient green emission for field emission display(FED) and is emerging as a potential substitute to the presentliquid crystal display technology [16,18–20]. Doping effects of Li,Cu, Zn and SnO2 on luminescence and conductivity of ZnGa2O4

phosphor was found to enhance conductivity [8,20]. An intensegreen emission from 501–506 nm (2.475 eV) is reported in thephotoluminescence spectra of ZnGa2O4 doped with Mn2+ ions,which corresponds to absorption peak at 2.685 eV (462.6 nm) inthe figure [17,19,20]. The absorption curve also shows a prominentpeak (a = 25.95 � 104 cm�1) at 1.137 eV (1090.5 nm) in the far IR


region followed by a structure at 1.91 eV (649.1 nm) in additionto absorption peak in green region. From the energy bands andPDOS it is clear that the luminescence in Zn1�xMnxGa2O4 may becaused by interband transitions from O p-states to Mn d-statespresent in the vicinity of Fermi energy level EF. Similarly, on dopingZnGa2O4 with Li, it is observed that there is appearance of anabsorbance peak of intensity of 8.07 � 104 cm�1 at 0.373 eV(3.324 lm) in the mid-IR region, further the value of blueabsorbance of the peak in visible region at 2.66 eV increasesslightly to 8.29 � 104 cm�1. Similar increase in absorbance at278 nm (4.76 eV) is observed on Li doping, although the peakintensity does not show appreciable change compared to ZnGa2O4,which is probably due to light doping levels.

Interestingly, in the yet-to-be-fabricated ZnIn2O4 which has anoptical band gap of 1.43 eV, which falls in the red region, theabsorption spectra shows structure similar to ZnGa2O4 at 2.6 eV(blue) and an enhanced value of absorbance of 45.91 � 104 cm�1

at 4.879 eV (254.1 nm) in UV region. Thus, ZnIn2O4 has all therequired features without doping, and may find potential applica-tions similar to ZnGa2O4.

Only interband transitions that imply a change Dl = ±1 in theangular momentum are allowed. The main optical structures aredue to presence of oxygen vacancies. Some forbidden transitionswithin the valence band may also take place such as d ? d transi-tions in the Mn2+ tetrahedral sites. The optical structure in the blueregion in ZnGa2O4 is due to transfer between Ga3+ ions at the octa-hedral sites which are surrounded by O2� ions. Presence of Li1+ orMn2+ at Zn2+ site provides new levels for transitions, giving rise toadditional peaks in doped oxides. Thus both ZnGa2O4 and ZnIn2O4

have minimum loss in IR region due to the band gap and also exhi-bit very good absorbance in visible and UV regions. The absorbancecurves show additional losses in the IR, red and green regions ondoping ZnGa2O4 with Mn.

The dielectric function is directly related to the optical conduc-tivity, which is a measure of electrical conductivity in the presenceof an alternating electric field. There are mainly three wavelengthregions of interest in the photoconductivity response of undopedand Li/Mn doped ZnGa2O4, i.e. visible, long wavelength UV andshort wavelength UV. In the optical conductivity curve for ZnAl2O4

shown in Fig. 4(b), conductivity begins at 3.85 eV with other majorstructures corresponding to 4.315 and 7.66 eV in UV region. In thecase of ZnGa2O4 and ZnIn2O4, the excitation features start from1.98 and 1.43 eV in the visible region respectively. The Li dopedZnGa2O4 shows a new conductivity feature of 0.99 � 103 (X cm)�1

at 0.09 eV (13.776 lm) and Zn1�xMnxGa2O4 also shows additionalfeatures in the IR region. The conductivity spectra of all the oxidesshow several intense peaks in visible as well as UV regions. Athigher energies >8.5 eV there is rapid change in shape of spectra,the conductivity of ZnAl2O4 increases and shows very high excita-tion peaks. The features in ZnIn2O4 for photon energy >7.5 eV arefound to show lower values compared to ZnGa2O4, thereafter theconductivity falls rapidly in high UV region for all the oxides. Thiscould be explained on the basis of coupling of phonons with indi-rect transitions.

The application of the spinel oxides as TCOs in optoelectronicdevices as a substitute for ZnO is attracting attention in the recentyears. The reflectivity in the spinel oxides can be calculated fromthe dielectric functions,

RðxÞ ¼ ðeðxÞ1=2 � 1Þ=ðeðxÞ1=2 þ 1Þ�� 2 ð4Þ

The plot of reflectivity vs. energy for the spinel oxides is shownin Fig. 5. ZnO is known to be completely transparent (98%) at500 nm, and transparency decreases with increasing wavelengths.ZnAl2O4 shows a reflectance of 0.06 i.e. 92% transparency in the UV,visible and IR regions due to its wide band gap, at smaller



0 2000 4000 6000 80000.0

0.2

0.4

0.6

0.8

0 400 800 1200 1600 20000.0

0.2

0.4

0.6

0.8

Ref

lect

ivity

λ (nm)

λ (nm)

Ref

lect

ivity

ZnIn2O4 ZnGa2O4 LixZn1-xGa2O4 MnxZn1-xGa2O4 ZnAl2O4

Fig. 5. Reflectivity function R(x) of ZnAl2O4, ZnGa2O4, Zn1�xLixGa2O4, Zn1�xMnx

Ga2O4 and ZnIn2O4.


wavelengths the reflectivity is seen to increase anomalously.Undoped ZnGa2O4 exhibits about 86–87% transparency throughoutthe UV to near IR regions, doped zinc gallate is found to bemarginally more transparent. Zn1�xMnxGa2O4 shows 93%transparency for a very narrow wavelength region �400 nm, thematerial is highly reflective (60%) for other wavelengths, andmay be used as reflective coating for IR radiations. ZnIn2O4 has atransparent nature similar to ZnGa2O4. The rapid increase inreflectance of spinel oxides in UV regions is probably becausevibrational optical modes are setup in the ZnX2O4 matrix, therebythe hybridized O and Al/Ga/In states get modulated.

Thus the ZnX2O4 spinel oxides exhibit excellent transparency inIR, visible and UV regions which confirms the experimental obser-vations. The photoluminescence is correlated well with structuresin absorption coefficient and optical conductivity curves.

3.4. Thermoelectric properties

Thermoelectric oxide materials are strong candidates for hightemperature power generation from waste heat. NanostructuredAl-doped ZnO exhibited a high figure of merit ZT � 0.44, whichshowed the possibility of using ZnO for low cost practical wasteheat harvesting. Intensive investigations have recently been tar-geted at improving the thermoelectric properties of ZnO by dopingwith Al/Ga/In. Further, for application of spinel oxides as TCOs, theelectrical conductivity should show an improvement over the elec-trical conductivity of ZnO which has a value of 9.63 � 103 (X m)�1.

Several properties can be calculated from the band energiesobtained from the FP-LAPW method. The thermoelectric propertieshave been investigated using the program BoltzTraP [31] inter-faced with WIEN2k which calculates the semi classic transportcoefficients. Derivatives such as group velocities are required fordetermination of some of the material properties. In the BoltzTraPcode, Fourier expansion of band energies is carried out to

Table 2Transport properties of zinc spinel oxides (at 300�K).

ZnAl2O4 ZnGa2O4

S (lV/K) 258 240r (1/X m) 3.04 � 104 9.41 � 104

RH (m3/C) 4.05 � 10–8 6.81 � 10–9

k (W/m K) 0.775 2.05c (J/mol K) 0.880 3.54ZT 0.783 0.792n (1/cm3) 1.54 � 1021 9.81 � 1020


determine the gradient along the energy bands to obtain the groupvelocities. For Fourier expansion of the band energies, the codeuses star functions for maintaining the space group symmetry.The bulk semi classical properties such as electrical and thermalconductivities, can be obtained from the Boltzmann theory. Theseproperties are calculated as a function of temperature T andchemical potential l, and are determined by some micro quantitiessuch as degeneracy of the energy bands near the Fermi level, theeffective mass of the charge carriers, the mobility of the chargecarriers and the thermal conductivity of phonons.

The group velocity mk which is the derivative of the band energyek with respect to the wave vector is a key quantity for the calcu-lation of transport properties and is evaluated numerically. Theelectrical conductivity r(T) is obtained from the group velocity asshown in the equation

r ¼ e2X

k

� @f 0

@e

� �skvk!

mk!

ð5Þ

where sk and f0 denotes the relaxation time and the Fermi functionrespectively; e denotes the electronic charge. The Seebeck and Hallcoefficients, thermal conductivities and other transport parametersare derived from the electrical conductivity. The calculated trans-port parameters at 300 K are given in Table 2.

One of the most important charge transport property, theelectrical conductivity r(T) for ZnAl2O4, ZnGa2O4, Zn1�xLixGa2O4,Zn1�xMnxGa2O4 and ZnIn2O4 are 3.04 � 104, 9.41 � 104

(1.06 � 10–3 X cm), 4.93 � 104, 5.78 � 104 and 1.4 � 105 (X m)�1

respectively. The ZnGa2O4 films have a resistivity of 100 mX cm,which is higher than the calculated value for bulk ZnGa2O4. Simi-larly, room temperature conductivity of ZnO film doped with 5%Ga2O3 is 8.7 � 103 (X m)�1 [21], and ZnO doped with c-Al2O3 hasa conductivity of �104 (X m)�1 at high temperatures [1]. Our cal-culated values fall within the range of experimental values.

The inherent problem of the spinel oxides for phosphorapplications is its poor electrical conductivity, which accumulateselectrons on the phosphor screen and leads to degradation of lumi-nous efficiency. Moderate improvement in conductivity wasobserved in the case of Sn-doped (5%) ZnGa2O4 [8]. In the case ofLi and Mn-doped ZnGa2O4, appreciable change is not observed,probably due to low levels of doping.

Since the calculation of the Hall coefficient (RH) depends on thesecond derivatives of the bands, it is an important test for thetheoretical method. The Hall coefficients for the spinel oxides arefound to be of the order of 10�9 m3/C. Since the Hall effect canbe used for determination of carrier density and its nature usingthe relation n = 1/RHe, the ambient temperature charge densitywas found to be 1.54 � 1021, 9.81 � 1020, 1.44 � 1021 cm�3 forZnAl2O4, ZnGa2O4 and ZnIn2O4 respectively. On doping ZnGa2O4

with Li, the charge density increases slightly to 1.15 � 1021 cm�3.Mn-doped zinc gallate has a charge density of �1.8 � 1021 cm�3,the negative sign indicates that the charge carriers are electrons.

Charge mobilities (le) can also be written in terms of electricalconductivity and Hall coefficients,

le ¼ �reRHe or lh ¼ �rhRHh ð6Þ

Zn1�x LixGa2O4 Zn1�x MnxGa2O4 ZnIn2O4

240 �20.7 1644.92 � 104 5.78 � 104 1.4 � 105

5.44 � 10–9 �3.47 � 10–9 4.35 � 10–9

1.04 0.248 1.9330.7 17.8 1.810.8174 0.029 0.5851.15 � 1021 1.8 � 1021 1.44 � 1021



0 200 400 600 8000

2

4

6

8

0 200 400 600 800-3

-2

-1

0

10

20

40

60

80

T (K)

(b)S

(V/K

)*10-5

S (V

/K)*

10-4

T (K)

MnxZn

1-xGa

2O

4

(a)

c p (J/

(mol

K))

ZnIn2O

4

ZnGa2O

4

LixZn

1-xGa

2O

4

MnZnGa2O

4

ZnAl2O

4

Fig. 6. Variation of ZnAl2O4, ZnGa2O4, Zn1�xLixGa2O4 and Zn1�xMnxGa2O4, ZnIn2O4

(a) specific heats and (b) Seebeck coefficient with temperature.

0.30 0.35 0.40 0.450.0

0.2

0.4

0.6

0.8

1.0

ZT

μ (Ry)0.0

0.2

0.4

0.6

0.8

1.0

0

1

2

3

4

InGaAl

ZT

Band Gap

ZT

Band G

ap (eV)

(2.07)LixZn1-xGa2O4

(0.82)LixZn1-xGa2O4

Fig. 7. ZT and band gaps of spinel oxides. Inset shows the variation of ZT with l (Ry)for ZnGa2O4.


By substituting the values of Hall coefficient and electrical con-ductivity in Eq. (6), the charge mobilities at room temperature arefound to have values of 12, 6.408, 6.097 cm2/V s for ZnAl2O4,ZnGa2O4 and ZnIn2O4 respectively. Mobility is reduced to 2.6 and2.005 cm2/V s for Li and Mn-doped ZnGa2O4 respectively. Smallereffective mass for zinc gallate as compared to that for zinc alumi-nate, suggested a higher mobility of charges in gallate, howevercalculations are contrary to expectation due to lowering of valueto Hall coefficient.

The specific heat vs. temperature curves for spinel oxidesshow similar behavior and cp of zinc aluminate is the lowestamongst the spinel oxides (Fig. 6a). On doping ZnGa2O4, the spe-cific heat increases rapidly beyond 100 K and has a value of 30.7and 18.106 J/mol K at 300 K for Li and Mn-doped ZnGa2O4

respectively.In terms of their thermoelectric properties, thermal devices are

characterized by the parameter figure of merit (Z):

Z ¼ S2rj

ð7Þ

Good thermoelectric materials have high values of Seebeckcoefficient (S) and electrical conductivities along with low thermalconductivities (j). The normal state thermopower (Seebeck coeffi-cient) depends highly sensitively on the electronic structure, and alarge value of the power factor (S2r) is desired for high figure ofmerit. The Seebeck coefficient of spinel oxides is found to increaseswith increasing temperature and attains a constant value beyond�200 K (Fig. 6(b)). For Mn-doped ZnGa2O4, the Seebeck coefficientchanges sign, and its value also decreases by an order. At roomtemperature, the spinel oxides have a high value of Seebeck coeffi-cient 258, 240 and 164 lV/K for ZnAl2O4, ZnGa2O4 and ZnIn2O4

respectively. The positive values of Seebeck and Hall coefficientsin the entire temperature range indicate that the majority carriersare holes, thus the spinel oxides are found to have p-type semicon-ducting properties (Table 2).

Thermal conductivity is one of the key factors in thermoelec-trics which is highly sensitive to material disorder. At room tem-perature the thermal conductivity values are 0.775, 2.05 and1.93 W/m K for ZnAl2O4, ZnGa2O4 and ZnIn2O4 respectively. Wehave plotted ZT i.e. figure of merit and band gap of the variousspinel oxides (Fig. 7). Zinc gallate has the highest figure of merit(0.792) compared to ZnAl2O4 and ZnIn2O4. The ZT is found toincrease to 0.8174 on doping ZnGa2O4 with Li, it howeverdecreases on doping with Mn (Table 2). Substitution of Zn2+ by


Li1+ in ZnGa2O4 gives rise to vacancies at tetrahedral sites, whichmay cause reduction in lattice contribution to thermal conductiv-ity, further the number of charge carriers have also increasedslightly on doping with Li. The inset shows the dependence ofZT on chemical potential l. From the graph, it can be seen thata maximum of ZT � 1 can be achieved for a chemical potentialcorresponding to 0.4–0.45 Ry. Since, increase in chemical poten-tial can be achieved by creating vacancies or doping or substitu-tion by atoms/ions at Zn2+, Ga3+ or O2� sites, it may be possibleto enhance the figure of merit as is seen in the case of Li dopingof ZnGa2O4. Bi2Te3 which is regarded a good thermoelectric mate-rial has a Seebeck coefficient of 267 lV/K, electrical conductivityvalue 0.09 � 105 1/X m and low thermal conductivity value of0.5 W/m K, which yields a figure of merit ZT = 0.58 [32]. On com-paring, it is clear that the spinel oxides have better figure of meritand thus can have potential applications as thermoelectricmaterials.

3.5. Vibrational properties

Due to the structural complexity of the spinel structure, the1st principle’s study of phonon frequency, structural instabilitiesand effect of varying cations as a function of temperature and pres-sure is a very useful complement to experimental investigations aswell as to ground state electronic properties. Few experimentaldetails of dynamics of spinel oxides are available such as vibra-tional properties of spinel MgAl2O4 which have been studied withRaman and IR spectroscopy along with inelastic neutron scatteringand by 1st principles molecular dynamic programme [25]. Simi-larly, Sinha and Kim have calculated phonon modes of MgAl2O4

and ZnAl2O4 by applying angular force constant model [24]. Infra-red and Raman spectra of ZnGa2O4 was measured by VanGordanet al. [23]. To achieve a better understanding of the mass effecton the vibrational modes at the zone center, we perform the pho-non calculations of zinc aluminate and gallate which can help inbetter understanding the dynamics of other spinel systems withsimilar structures.

From standard symmetry analysis of cubic spinel structurewhich belongs to the crystal point group O_h (m3m), both Ramanactive and infrared active modes are obtained. The calculated pho-non spectrum of ZnAl2O4 and ZnGa2O4 are presented along specialsymmetry directions W–L–C–X–W–K (Fig. 8). All frequencies arepositive, which indicate that the spinel structures are dynamicallystable. It is seen that ZnAl2O4 has states at higher frequencies com-pared to ZnGa2O4. The frequencies of the Raman active A1g, eg andT2g modes and T1u infrared active modes are given in Table 3. The



Table 3Vibrational modes of ZnAl2O4 and ZnGa2O4.

ZnAl2O4 ZnGa2O4

Modes Frequency (1/cm) Modes Frequency (1/cm)

T1u(I) �11.87 T1u(I) 10.3T2g(R) 198.7, 196 [24] T2u 120.5T1u(I) 223.2, 220 [24] T1u(I) 168.8, 175 [23]T2u 247.5 T2g(R) 183.9T1g 361.01 Eu 209.6Eu 390.6 T1g 331.1Eg(R) 415.3, 417 [24] T1u(I) 333.3, 328 [23]T2u 476.7 Eg(R) 367.5T1u(I) 487.3, 440 [24] T1u(I) 393.7, 420 [23]T2g(R) 512.3, 509 [24] A2u 401.6T1u(I) 544.8, 543 [24] T2u 420.2,Eu 602.6 T2g(R) 475.3, 467 [23]T2g(R) 655.5, 658 [24] Eu 548.5T1u(I) 660.6, 641 [24] T1u(I) 571.8, 570 [23]A2u 668.6 T2g(R) 606.1, 611 [23]A2u 769.3 A2u 699.3A1g(R) 783.1, 758 [24] A1g(R) 701.4, 714 [23]


cations Zn and Al/Ga occupy the tetrahedral and octahedral sitesrespectively, the replacement of Al by Ga leads to change in bandfrequency due to change in Al-O/Ga-O bond lengths. The higherinfrared active modes 660.6 and 487.64 cm�1 are due to Zn-Ostretching and bending modes in ZnO4 tetrahedra, and the vibra-tional modes 544.8 and 223.2 cm�1 correspond to the Al-O stretch-ing and bending modes in ZnO6 octahedra in ZnAl2O4. Similarly, forZnGa2O4, the infrared active modes 571.8 and 393.7 cm�1 are dueto Zn-O stretching and bending modes in ZnO4 tetrahedra; vibra-tional modes 420.2 and 168.8 cm�1 corresponds to the Ga-Ostretching and bending modes in ZnO6 octahedra.

On doping ZnGa2O4 with Li and Mn, the possible vibrationalmodes are greatly enhanced from 17 modes in ZnGa2O4 to 67and 69 modes for Li and Mn-doped zinc gallate respectively(Fig. 8(c) and (d)). The lowest frequency mode is at 8.5 cm�1 andhighest mode is at 682.62 cm�1, the lower modes are due to Znions, Li atoms contribution to motion at highest frequency10–15 THz along with O atoms. For Mn-doped ZnGa2O4, the lowestmode occurs at 10.3 cm�1 and highest at 667.3 cm�1, Zn ions againcontribute to lower modes, Mn and Ga ions contribute to modes inthe mid-range 2.5–9 THz, and O atoms vibrate at highest frequen-cies 9–17 THz.

A good agreement between experimental and calculated vibra-tional modes for ZnAl2O4 and ZnGa2O4 justifies our calculations.Even though too many experimental details of microscopic dynam-ics of ZnGa2O4 are not known [23], our understanding of the latticedynamics of ZnAl2O4 and MgAl2O4 [24] can lead to better under-standing of the spectra.

0

20

10

Fre

rque

ncy

(TH

z)

0

20

10

Fre

rque

ncy

(TH

z)

W L G X W K

W L G X W K

(a)

(b)

(c)

(d

Fig. 8. Phonon dispersion relations for (a) ZnAl2O4, (b) Z


3.6. Thermodynamic properties

Thermodynamic functions are calculated from the phonondensity of states within the harmonic approximation [27]. Theformation energy for ZnAl2O4 is �1785.96 kJ/mol and decreasesto �1210.47 kJ/mol for ZnGa2O4. The negative sign shows that thereaction is exothermic and implies that zinc gallate is more stable

0

20

10

Fre

rque

ncy

(TH

z)

0

20

10

Fre

rque

ncy

(TH

z)

R X G M R G

R X G M R G

)

nGa2O4, (c) Zn1�xLixGa2O4 and (d) Zn1�xMnxGa2O4.



0 500 1000 1500 2000 2500 30000

400

800

1200

0

1000

2000

3000

0

1000

2000

3000

0

2000

4000

6000

8000

C v (J/

K/m

ol)

T (K)

ZnGa2O4 LixZn1-xGa2O4 MnxZn1-xGa2O4 ZnAl2O4

S (V,T

) (J/

K/m

ol)

U (

kJ/m

ol)

F (

kJ/m

ol)

Fig. 9. Thermodynamic properties of ZnAl2O4, ZnGa2O4, Zn1�xLixGa2O4 andZn1�xMnxGa2O4.


than zinc aluminate. On doping, the formation energy forZn1�xLixGa2O4 increases to �9604.61 kJ/mol, this indicates thateven slight doping by Li in ZnGa2O4 distorts the spinel structure.On doping with Mn, the formation energy was found to be�9352.77 kJ/mol. However, the doped zinc gallate do not give riseto unstable modes.

To compare the stability of the different spinel oxides at giventhermodynamic conditions (P, V, T), one must go beyond theground state and calculate the free energy, which depend on theentropy and internal energy. The calculated values of entropy(SV,T) and internal energy (UV,T) are plotted in Fig. 9. There is agradual increase in SV,T and UV,T with temperature, which becomesconstant at temperatures >500 K. For stable spinel oxides, theHelmholtz free energy is compared instead of Gibbs free energy.Since F(V, T) = U(V, T) + TS(V, T), both the oxides have same values.The value of F(V, T) for Mn, Li-doped ZnGa2O4 increases marginallyat low temperatures, but at high temperatures the energy increasesrapidly.

The calculated dynamical properties clearly show that dopedand undoped zinc spinel oxides are stable at ambient temperatures.

4. Conclusions

We report the energy band structure and density of states cal-culations based on the density functional theory. From the opticaland transport properties of zinc spinel oxides it is found thatZnGa2O4 and ZnIn2O4 exhibit potential photo-electrochemicalproperties.

The experimentally observed blue photoluminescence inZnGa2O4 and green spectrum for Mn-doped ZnGa2O4 have beenclearly verified through the optical parameters such as absorptioncoefficients, which were mainly associated with interband transi-tions from bands which are contributed mainly by 2p-states of O,3d-states of Zn forming the highest occupied level of valence bandand the bottom of conduction band populated by 4p-states of Zn.Additional peaks in the red region in Zn1�xMnxGa2O4 imply d–dtransition on the Mn ions. The transparence of spinel oxides toUV radiations is also clearly illustrated in the reflectivity vs. energy


curves which narrows down on doping. At very small wavelengthsthe oxides show anomalous behavior and become highly opaque toradiations.

The spinel oxides behave like good thermoelectric materialsand have high values of Seebeck coefficient (160–258 lV/K), elec-trical conductivities (�104 1/X m) and low thermal conductivities(0.7–2.0 W/m K), resulting in figure of merit (ZT) as high as 0.8. Thespinel oxides are p-type semiconductors with an optimum value ofband gap �2–3 eV and appear to meet the conditions of low resis-tivity and high transparency (>80%) for state-of-art TCOs.

The stability of the phosphors is observed from the thermody-namic properties and vibrational studies, which along withchemical stability offers advantage of spinel oxides over sulfidephosphors commonly used for vacuum fluorescent displays. Thefeatures in optical, transport and vibrational spectra show goodcorrespondence with experiments, which means that the bandsand DOS positions are quite accurately described in DFT-GGA.

Acknowledgements

We are thankful to CST (U.P.), Lucknow, India for providingfinancial assistance in form of major research project. We aregrateful to Prof. Blaha and his team for the WIEN2k code and Prof.Kresse and Prof. Hafner and team for VASP code.

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electroconductive properties in doped spinel oxides

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