Electronic structure and optical properties of ZnSiO3 and Zn2SiO4

S. Zh. Karazhanov,1, 2 P. Ravindran,1 P. Vajeeston,1 A. Ulyashin,3 H. Fjellvag,1 and B. G. Svensson3

1Centre for Material Science and Nanotechnology, Department of Chemistry,University of Oslo, PO Box 1033 Blindern, N-0315, Oslo, Norway

2Physical-Technical Institute, 2B Mavlyanov St., Tashkent, 700084, Uzbekistan3Department of Physics, University of Oslo, PO Box 1048 Blindern, N-0316, Oslo, Norway

(Dated: August 25, 2006)

The electronic structure and optical properties of orthorhombic, monoclinic, ilmenite and corun-dum modifications of ZnSiO3, and rhombohedral and tetragonal modifications of Zn2SiO4 are stud-ied using ab initio density functional calculation. From the structural optimization the equilibriumstructural parameters are calculated and compared with available experimental studies. All thesephases are found to be wide-band-gap insulators at 0 K. The lowest part of the conduction bandis more dispersive than the topmost part of the valence band. The conduction-band minimum isformed by s states where the major contribution comes from the Zn-4s electrons. From the site- andorbital-projected density of states, charge-density and electron localization function analyses it isfound that these compounds are ionic. From the calculated linear optical spectra we found that theoptical properties of tetragonal Zn2SiO4 is almost isotropic, while those of the three other phasesare anisotropic. The magnitude of the absorption and reflection coefficients for all the ZnSiO3 andZn2SiO4 phases are so small in the energy range 0−5 eV and hence these materials can be regardedand classified as transparent.

PACS numbers: 71.15.-m; 71.22.+iKeywords: ZnSiO3, Zn2SiO4, transparent oxides

I. INTRODUCTION

Investigation of ZnSiO3 deserves attention because ithas special properties such as excellent adhesion to steelsurfaces, high heat resistance, high hardness, abrasionresistance, inertness to crude and refined oils, greases,and solvents, resistance to radiation (including nuclearradiation), weather resistance etc.1 ZnSiO3 phases arepredominantly used for buildings, offshore constructions,and bridges. They can be used as abrasion-resistant coat-ing with controlled electrical conductivity. ZnSiO3 isvery inert and, with exception of exposure to strong acidsand alkalides, do not degrade in most industrial and ma-rine environments. It was shown in Ref. 2 that nanodis-persed ZnSiO3 co-deposited on nickel-phosphorous alloysare also corrosion resistant as well as high-temperatureoxidation resistant. Recently, formation of a new crys-talline phase of ZnSiO3 is reported3 upon irradiation ofthe nanocomposite films ZnS-SiO2 with ultraviolet light.The crystalline phase is found to be formed in the amor-phous media as a result of the photoinduced reactionsbetween ZnO and SiO2.

Phase transitions of ZnSiO3 at high pressures and tem-peratures were studied experimentally.4 ZnSiO3 in theform of ilmenite mineral was synthesized4,5 at 17 GPaand 1000 oC. Cell parameters for the ilmenite phase weremeasured using the X-ray diffraction method under hy-drostatic conditions.6 This phase is not stable at atmo-spheric pressure and is formed as a result of transforma-tion of clinopyroxene ZnSiO3 with monoclinic structureat 10–12 GPa. The latter is formed from the reaction ofwillemite with quartz at about 3 GPa.7 It is found thatZnSiO3 transformed into an ilmenite structure at 15 GPa

and 1000 oC. The temperature and pressure dependenceof this phase transition reaction was studied in Refs. 7,8.

Zn2SiO4 in the phenacite-structure is well known un-der mineralogical name willemite. As mineral, willemiteZn2SiO4 belongs to a large family of naturally occurringorthosilicates.23 It has numerous technological applica-tions such as phosphor host, crystalline phase in glassceramics, electrical insulators, glazes, and pigments (see,e.g., Ref. 9). Because of its unique luminescent proper-ties, wide energy band gap (5.5 eV) and excellent chemi-cal stability, Zn2SiO4 is one of the promising candidatesfor flat panel displays,10–15 X-ray or nuclear medical im-age receptors, X-ray to light converters coupled to opticaldetectors,16 etc. Zn2SiO4 is formed in the heterostruc-ture ZnO/Si because the Zn and O atoms diffuse intoSi.17–19 ZnO deposited on silicate glass is used as a trans-parent conducting oxide (TCO) buffer in photovoltaicsolar cells.20 Zn2SiO4 is found to form a large band off-set [Fig. 1],19 which can be one of the reasons of lowefficiency 8.5 % of the crystalline Si-ZnO solar cells.21By secondary ion mass spectroscopy vast interdiffusionis found between the ZnO film and the Si substrate.18Cathodoluminescence and glancing-angle X-ray diffrac-tion analysis allowed to establish the existance of tetrag-onal modification of Zn2SiO4. By XRD measurements anew rhombohedral modification of Zn2SiO4 was found22

at the boundary between ZnO particles and SiO2 matrix.The usual temperature for the formation of Zn2SiO4

is in the range from 700 to 1300 oC (see, e.g., Refs. 15,22,24–27). Zn2SiO4 nanoparticles are prepared by solid-phase reaction methods.26,27 However, this method doesnot give products with high-luminescence efficiency.26Alternative synthetic routes have been proposed, suchas hydrothermal, polymer pyrolysis, and sol-gel meth-

2

FIG. 1: Band diagram from Ref. 19 for the Si-ZnO hetero-junction with Zn2SiO4 state located in between Si and ZnO.

ods. The properties of coatings and mixtures of Zn2SiO4

powders depend on the shapes and sizes of the pow-der particles. So, fabrication of Zn2SiO4 particles withprecisely-controlled morphologies is an important chal-lenge. Ref. 28 describes synthesis of zinc-silicate-coatedmicroparticles with biologically controlled 3D-shapes.

Due to preference of Zn for tetrahedral ratherthan octahedral coordination by oxygen at low pres-sures, the zinc silicates crystallize into the phenacite-structure Zn2SiO4. At pressures above 3 GPa themixture of Zn2SiO4 and SiO2 is transformed intoZnSiO3 with Zn atoms located in distorted octahedralcoordination.4,5,8,29

Despite many functional useful properties of ZnSiO3

and Zn2SiO4 no proper theoretical study has yet beenreported. Indeed, Refs. 10 and 30 have studiedZn2SiO4 by the self-consistent-field multiple-scatteringXα cluster method, Ref. 31 has investigated fayalitesM2SiO4 (M=Fe and Co) by GGA+U approximation, andRef. 32 has examined the related compounds Zn2SnO4,Cd2SnO4, and In2CdO4 by the VASP package. However,by the Xα cluster method it is not possible to extract thesolid-state band structure and at the time the study wascarried out it was not possible to perform such calcula-tions, because the unit cells contained too many formulaunits. Nowadays this problem can be solved by availableab initio packages and modern supercomputers. Study ofthe zinc silicates present much interest for semiconductordevice technology, because they are formed at the inter-face of the ZnO–Si and ZnO–SiO2 systems, and thereforestrongly influence optical and photoelectric properties.The aim of the present work is to study the electronicstructure and optical properties of the zinc silicates anddizinc orthosilicates.

FIG. 2: Crystal structures of (a) orthorhombic ZnSiO3-o, (b) ilmenite ZnSiO3, (c) corundum ZnSiO3, (d) mono-clinic ZnSiO3, (e) rhombohedral Zn2SiO4, and (f) tetragonalZn2SiO4.

II. STRUCTURAL ASPECTS ANDCOMPUTATIONAL DETAILS

A. Crystal structures

The crystal structures of different modifications of Zn-SiO3 and Zn2SiO4 are given in Fig. 2. The optimizedlattice parameters for orthorhombic (o), monoclinic (m),rhombohedral, corundum (c)and ilmenite (i) modifica-tions of ZnSiO3, and tetragonal (t) as well as rhombo-hedral (r) modifications of Zn2SiO4 are compared withavailable experimental values in Table I.

Two polymorphs of ZnSiO3 have been synthesized athigh pressures and temperatures (see, e.g., Ref. 34).Monoclinic ZnSiO3 is reported to be stable above 30 kbarand 850 oC, while orthorhombic ZnSiO3 appears to bemetastable under all conditions. These characteristicsare considered to be due to a peculiar behavior of Znatoms in structures where tetrahedral coordinations pre-dominate. In monoclinic ZnSiO3 [Fig. 2 (d)], Zn arecoordinated both octahedrally (M1) and tetrahedrally

3

TABLE I: Unit-cell volumes, structural parameters, bulk modulus (B0), as well as the derivative of bulk modulus (B′0) for

ZnSiO3-o, -m, -i, c, and Zn2Si4-r and -t derived from the present DFT calculations by a search of the total energy minimum.Values given in parentheses refer to experimental data quoted33 and xxxx

Compound Unit Cell (A) Atom Site x y z B0 (GPa) B′0Space groupZnSiO3-o a=17.9844(18.2040)a Zn1 8c 0.1256(0.1255) 0.3542(0.3559) 0.5037(0.4039) 79.89 9.42Pbca b=9.0714(9.0870)a Zn2 8c 0.3764(0.3761) 0.5143(0.5092) 0.3989(0.4005)

c=5.2723(5.2780)a Si1 8c 0.2246(0.2741) 0.3366(0.3363) 0.0891(0.0867)V=860.14(873.09)a A3 Si2 8c 0.4709(0.4730) 0.1667(0.1656) 0.2119(0.2839)

O1 8c 0.1846(0.1853) 0.3317(0.3346) 0.0855(0.0820)O2 8c 0.3113(0.3115) 0.4996(0.4966) 0.1094(0.1040)O3 8c 0.3058(0.3039) 0.2476(0.2521) 0.3428(0.3400)O4 8c 0.5618(0.5621) 0.3368(0.3389) 0.7147(0.7800)O5 8c 0.4305(0.4327) 0.4847(0.4853) 0.7039(0.7040)O6 8c 0.4462(0.4488) 0.2064(0.2100) 0.4194(0.5710)

ZnSiO3-m 9.6400(9.787)a Zn1 4e 0.5000(0.5000) 0.3946(0.3919) 0.2500(0.2500) 61.45 12.73C2/c 9.1024(9.161)a Zn2 4e 0.0000(0.0000) 0.2323(0.2361) 0.2500(0.2500)

5.2629(5.296)a Si1 8f 0.3052(0.3016) 0.0845(0.0849) 0.2647(0.2668)430.53(442.04)a A3 O1 8f 0.1233(0.1241) 0.0835(0.0868) 0.1442(0.1473)β = 111.22(111.42)ao O2 8f 0.3807(0.3787) 0.2413(0.2393) 0.3778(0.3719)

O3 8f 0.3591(0.3533) 0.0316(0.0238) 0.0193(0.0273)

ZnSiO3-i xxxx a=4.8557(4.7469)b Zn 3a 0.0000(0.0000) 0.0000(0.0000) 0.6471(0.3599) 127.20 4.85

R3 b=4.8557(4.7469)b Si 3a 0.0000(0.0000) 0.0000(0.0000) 0.1469(0.1556)

c=7.9167(13.7536)b O 9b 0.9908(0.9867) 0.3330(0.3688) 0.4801(0.5729)

V=161.65(268.39)b A3

a=(4.7460)c Znb=(4.7460)c Sic=(13.7550)c OV=(268.3000)c A3

a=(5.3413)d Zn

b=(5.3413)d Si

c=(5.3413)d O

V=(89.4600)d A3

ZnSiO3-c a=4.7560 Zn 6c 0.0000 0.0000 0.3679 211.10 5.74R3 b=4.7560 Si 6c 0.0000 0.0000 0.1599

c=13.6633 O 18f 0.9904 0.3714 0.5726V=267.65 A3

Zn2SiO4-t a=6.9562(7.0069)e Zn 8d 0.1549(0.1570) 0.2500(0.2500) 0.1250(0.1250) 71.11 1.37I42d b=6.9562(7.0069)e Si 4b 0.0000(0.0000) 0.0000(0.0000) 0.5000(0.5000)

c=6.3533(6.4637)e O 16e 0.3054(0.3079) 0.4832(0.4890) 0.1070(0.1376)V=307.43(317.53)e A3

Zn2SiO4-r a=8.5553(8.6454)f Zn1 18f 0.7762(0.7760) 0.6019(0.6015) 0.3741(0.3757) 142.38 3.13

R3 c=8.5553(8.6454)f Zn2 18f 0.1103(0.1106) 0.9405(0.9419) 0.7038(0.7030)

V=508.04(525.94)f A3 Si 18f 0.4460(0.4473) 0.2663(0.2665) 0.0383(0.0392)O1 18f 0.2306(0.2349) 0.1884(0.1900) 0.8970(0.8997)O2 18f 0.5254(0.5250) 0.4760(0.4719) 0.1908(0.1896)O3 18f 0.8607(0.8596) 0.8546(0.8571) 0.5344(0.5321)O4 18f 0.5679(0.5658) 0.2518(0.2543) 0.9256(0.9278)

aExperimental values from Ref. 34.bExperimental values from Ref. 8.cExperimental values from Ref. 4.dExperimental values from Ref. 4,6.eExperimental values from Ref. 35.fExperimental values from Ref. 36.

4

(M2).34 The Zn atoms at the M2 sites are not coor-dinated to the bridging O atoms of the SiO4 chains.In orthorhombic ZnSiO3 [Fig. 2 (a)], Zn atoms at theM1 sites have irregular octahedral coordination to the Oatoms. The shape of the SiO4 chains in monoclinic andorthorhombic ZnSiO3 is also not the same, a distinctionthat results the different linking of O to Zn in the twostructures.

ZnSiO3 in ilmenite and corundum phases have trigo-nal (R3 ) symmetry and consists of a slightly distortedhexagonal close-packing array of O atoms with Zn andSi atoms in the interstices. Structural properties ofthese compounds have been analyzed more in detail inRefs. 7,8 and 29.

There are five high pressure polymorphs of Zn2SiO4

have been identified and they are designated as modifi-cations I to V in order of increasing pressure.29 Phase Icorresponding to willemite, phase I transforms into phaseII at about 30 kbar, which is unstable above 80 kbarwhere it is believed to partially decompose into phaseIII and small amounts of ZnO. This results in some-what non-stoichiometric composition in samples and con-sequently phase III as well as phases IV and V are non-stoichiometric. Phase V is obtained35 at pressures above130 kbar at 900 oC.

In the Zn2SiO4-t structure [Fig. 2 (c)] oxygen atomsjoin together to Si and Zn so that each oxygen of the SiO4

tetrahedra is bonded to Zn atoms thus forming an inte-grated part of a Zn-O-Si network. The oxygen atoms arelocated approximately body-centered cubic arrangementin Zn2SiO4-t, while the Zn and Si atoms are in tetrahedracoordination to the O atoms. In the Zn2SiO4-r structure[Fig. 2 (d)] the Zn and Si atoms are tetrahedrally co-ordinated to oxygen atoms. The Zn atoms occupy twocrystallographically different sites, but the environmentsaround these sites differ only slightly.

B. Density-functional calculations

The electronic structures of ZnSiO3 and Zn2SiO4 werestudied using the VASP-PAW package,37 which calcu-lates the Kohn–Sham eigenvalues in the framework of thedensity-functional theory (DFT)38 within the local den-sity approximation (LDA).39 The exchange and correla-tion energy per electron were described by the Perdew-Zunger parametrization40 of the quantum Monte Carloresults of Ceperley-Alder.41 The interaction between elec-trons and atomic cores was described by means of non-norm-conserving pseudopotentials implemented in theVASP package. The pseudopotentials are generated inaccordance with the projector-augmented wave (PAW)method.42,43 The use of the PAW pseudopotentials ad-dresses the problem of the inadequate description of thewave functions in the core region - a problem commonto all pseudopotential approaches.44 The application ofthe pseudopotentials allow us to construct orthonormal-ized all-electron-like wave functions for the Zn-3d and

-4s, Si-3s and -3p, and O-2s and -3p valence electrons.Spin-orbit coupling was not included in the present cal-culations.

Effective masses of conduction band (CB) electrons arecalculated by:

1mc(k)

=1~2

∂2E(k)∂k2

(1)

for a direction k in the vicinity of the Γ point, sincethe CB minimum of the band dispersions of all the com-pounds considered [Sec. III B] were located at the Γ pointof the Brillouin zone. The band edge energies E(k) havebeen extracted from DFT calculations and polynomialfitting has been performed. From the fitted polynomialsecond order derivative was calculated, which was usedfor the effective mass calculations in Eq. 1.

C. Calculation of optical properties

The imaginary part of the dielectric function ε2(ω) hasbeen derived from DFT results by summing all the al-lowed transitions from occupied to unoccupied states forenergies much larger than those of the phonons:

εij2 (ω) =

V e2

2π~m2ω2

∫d3k

∑

nn′〈kn|pi|kn′〉〈kn′|pj |kn〉 ×

fkn(1− fkn′)δ(εkn′ − εkn − ~ω). (2)

Here (px, py, pz) = p is the momentum operator, fkn isthe Fermi distribution, and |kn〉 is the crystal wave func-tion, corresponding to the energy εkn with momentumk.

The real part of the dielectric function ε1(ω) is cal-culated using the Kramer-Kronig transformation. Theknowledge of both the real and imaginary parts of thedielectric tensor allows one to calculate other importantoptical spectra. In this paper we present and analyzethe reflectivity R(ω) and the absorption coefficient α(ω)calculated using the following expressions:

R(ω) =

∣∣∣∣∣

√ε(ω)− 1√ε(ω) + 1

∣∣∣∣∣

2

, (3)

α(ω) =√

2ω

√√ε21(ω) + ε22(ω)− ε1(ω). (4)

Here ε(ω) = ε1(ω)+ iε2(ω) is the complex dielectric func-tion. The optical spectra are calculated for the energyrange from 0 to 20 eV.

The thus obtained optical spectra yield unbroadenedfunctions, and consequently they exhibit more structurethan the corresponding experimental spectra. To repro-duce the experimental conditions correctly, it is necessaryto broaden the calculated spectra. The exact form of thebroadening function is unknown, although comparisonwith measurements suggests that the broadening usually

5

increases with increasing excitation energy. Also, the in-strumental resolution smears out many fine features. Tosimulate these effects the lifetime broadening was simu-lated by convoluting the absorptive part of the dielectricfunction with a Lorentzian, whose full width at half maxi-mum (FWHM) is equal to 0.01 eV at the photon energy 1eV, and increasing quadratically with the photon energy.The experimental resolution was simulated by broaden-ing the final spectra with a Gaussian, where the FWHMis equal to 0.02 eV.

III. RESULTS AND DISCUSSION

A. Ground-state properties

The crystal structures studied were optimized usingforce as well as stress minimization and then total energyhas been calculated for different volumes, which was thenfitted by a cubic spline [Fig. 3] and its minimum (Emin

tot )was taken as the equilibrium volume. The symmetriesof all phases considered remain the same for both re-laxed and unrelaxed lattices. Lattice parameters derivedfrom the DFT calculations are given in Table I togetherwith experimentally determined values. Analysis of theTable I shows that accuracy of the calculated and ex-perimentally determined lattice parameters for ZnSiO3-o, −m, Zn2SiO4-r, and Zn2SiO4-t are almost the same.Lattice parameters for ZnSiO3-i determined experimen-tally in Refs. 8 and Ref. 4,6 are equivalent and differ fromcalculated values significantly.xxxx However, calculatedlattice parameters for ZnSiO3-cxxx are almost the sameas those determined experimentally4,6 for ZnSiO3-ixxx.

Calculated magnitude of Emintot for ZnSiO3-i is found to

be considerably higher in energy than that of the otherZnSiO3 phases. However, Emin

tot for ZnSiO3-c, -m, and-o are energetically closer to each other. Among themZnSiO3-c and -o are less stable than ZnSiO3-mxxx. Anal-ysis of the Fig. 3 shows that Emin

tot for ZnSiO3-c and -oare located very close to each other indicating that thesetwo phases can easily transform from one to another.

Analysis of Fig. 3(b) shows that among the Zn2SiO4

compounds considered Zn2SiO4-r is more stable thanideal and defective Zn2SiO4-t. A defective Zn2SiO4-t lat-tice (we call it Zn2SiO4-d) was created by shifting one ofthe Zn atoms into an interstitial position. and then thelattice was relaxed. From Fig. 3(b) it is clear that sucha defective lattice is not stable.

By the results from the structural optimization studiesit is concluded that for analysis of the electronic structureand optical spectra major attention should be focusedinto the following phases ZnSiO3-o, ZnSiO3-m, Zn2SiO4-r, and Zn2SiO4-t, which are more stable than the others.

60 90 120

-36

-34

-32 ZnSiO3-(c)

ZnSiO3-(i)

ZnSiO3-(o)

ZnSiO3-(m)

80 120 160

Volume (Å3)

-47

-46

-45Tot

al e

nerg

y (e

V)

Zn2SiO

4-(t)

Zn2SiO

4-(d)

Zn2SiO

4-(r)

(a)

(b)

FIG. 3: Total energy (Etot) vs cell volume per formula unitfor (a) ZnSiO3 and (b) Zn2SiO4.

B. Results from band structure analysis

For studies of the optical properties knowledge aboutthe interband optical transitions are needed. From thispoint of view a detailed studies on the electronic struc-ture of different phases of zinc silicates are needed. Bandstructures along the high-symmetry directions in theBrillouin zone are presented in Fig. 4. The interesting as-pect of the electronic structure at the valence band (VB)of ZnSiO3-o, ZnSiO3-m, ZnSiO3-c, and Zn2SiO4-r is thepresence of a flat band in the topmost VB, whereas thebottommost CB separated from the VB by a wide gap isfound to be more dispersive. This feature is typical forTCO of n-type conductivity (see, e.g., Refs. 10,30–32,45–47). The overall features of the electronic structure indi-cate predominant ionic type of chemical bonding in thesecompounds and also the valence electrons located at thetopmost VB are tightly bounded to the O atoms. Con-sequently, holes are almost immobile and their contribu-tion to current transport is expected to be considerablysmaller than that of CB electrons. However, the statesat the CB minimum are much more dispersive than thetopmost VB states. Consequently, small carrier effectivemasses, high electron mobility and, respectively, high n-

6

FIG. 4: Band dispersion for (a) ZnSiO3-o, (b) ZnSiO3-m, (c)Zn2SiO4-r and (d) Zn2SiO4-t. The Fermi level is set to zero.

type conductivity, and the Burstein-Moss shift or shiftof the optical absorption edge with doping are expected.The high dispersion comes out from a strong hoppingbetween neighboring Zn sites. This statement shall bejustified in Subsection III C by detailed analysis of thepartial DOS in the CB minimum. This is one of themost important electronic band structure features46,47 ofa host TCO material. Hence these materials can be re-garded as very promising candidates for TCO.

The valence band (VB) states for ZnSiO3-i andZn2SiO4-t are more dispersive compared to other com-pounds considered. It indicates that hybridization in-teractions plays an important role in chemical bondingof ZnSiO3-i and Zn2SiO4-t. Furthermore, it is expectedthat the contribution of holes to current transport can besignificant in these phases. However, as discussed aboveabout the studies of the structural properties, ZnSiO3-iis less stable compared to other ZnSiO3 phases.

It should be noted that the bands at the topmost VBof ZnSiO3-o, ZnSiO3-m, Zn2SiO4-r and Zn2SiO4-t arevery close to each other and are very flat [Fig. 4]. Con-sequently, it is hard for the eye to identify the maximumin the VB. Therefore, we have displayed the band dis-persion in the vicinity of band gap in Fig. 5. From thisfigure it is clear that for all the considered phases of zincsilicates the CB minimum is located at the Γ point. How-ever, the VB maximum is located at different k points.The band dispersion of ZnSiO3-o is complicated, wherethe VB maximum is located in the range from Γ pointto a location between the X and S points. ZnSiO3-m,ZnSiO3-i, ZnSiO3-c and Zn2SiO4-r are found to be in-direct band gap compounds with the VB maximum lo-cated around Z point (ZnSiO3-m), X, P and N point(ZnSiO3-i and ZnSiO3-c)xxxx. Zn2SiO4-r has a directband gap with CB minimum and VB maximum located

ΓX SY Γ WU KT Z

0

2

4

6

Ene

rgy

(eV

)

V Z Γ A X L

0

2

4

6

F Γ Z F L Γ

0

2

4

6

Ene

rgy

(eV

)

Z Γ X P N Γ

0

2

4

6

(a) (b)

(d)(c)

FIG. 5: Band structure of the topmost VB and lowest CB(dotted lines) for (a) ZnSiO3-o, (b) ZnSiO3-m, (c) Zn2SiO4-r, and (d) Zn2SiO4-t. The Fermi level (solid lines) is set tozero.

around the Γ point. Topmost VB of Zn2SiO4-t is almostdispersionless in the whole Brillouin zone. The large in-direct band gap for ZnSiO3-m, ZnSiO3-i, and ZnSiO3-cindicates that small absorption is to be expected. Thisresult has been confirmed by studies of optical spectrafor these compounds.

Band gap values (Eg) for all the compounds studied arelisted in Table II. The experimental Eg value is widelyavailable only for Zn2SiO4-r. It is in the range from5.50 to 6.26 eV. The band gap 4.36 eV estimated fromthe band diagram for Si-ZnO heterojunction derived fromthe XPS studies19 is probably that of Zn2SiO4-t. Exper-imentally measured band gap for the other ZnSiO3 andZn2SiO4 phases are not yet available for comparison.

TABLE II: Band gaps (in eV) for the zinc silicates ZnSiO3

and Zn2SiO4 calculated from DFT within the GGA. The cal-culated Eg value for Zn2SiO4-r is compared with availableexperimental values.

Compound Eg EExptg Ref.

ZnSiO3-o 3.5006ZnSiO3-m 3.6762ZnSiO3-c 4.1751ZnSiO3-i 2.2166Zn2SiO4-r 2.8299 5.5 Ref. 12

5.3 Ref. 486.15 Ref. 226.262 Ref. 22

Zn2SiO4-t 2.7950 4.36 Ref. 19

The value of Eg calculated in the present DFT studiesfor ZnSiO3-o and -m phases exceeds 3.5 eV, while that forZn2SiO4-r is only 2.83 eV. Since the band gaps calculatedby DFT within LDA are likely to be about 50 % smaller

7

2

4

2

4

2

4

Tot

al D

OS

(sta

tes/

(eV

f.u

.))

-15 -10 -5 0 5Energy (eV)

2

4

2

4

-15 -10 -5 0 5Energy (eV)

2

4

(a)

(b)

(c)

(d)

(e)

(f)

ZnSiO3

ZnSiO3

ZnSiO3

ZnSiO3

Zn2SiO

4

Zn2SiO

4

(-r)

(-t)

(-o)

(-m)

(-i)

(-c)

FIG. 6: Total DOS for (a) ZnSiO3-o, (b) ZnSiO3-m, (c)ZnSiO3-i, (d) ZnSiO3-c, (e) Zn2SiO4-r, and (f) Zn2SiO4-t.The Fermi level is set to zero.

than actual experimental values, the real band gaps forthese zinc silicates may be around 5.0 eV, which in turnwould imply that the materials are transparent acrossthe entire visible spectrum. Hence, these materials carryone of the most desirable properties for the TCO’s.45,46Although the calculated direct band gap of ZnSiO3-i issmall (2.22 eV), it can surely be increased upon doping(Burstein-Moss shift) or by structural defects as it shallbe demonstrated in Subsection IIIH.

C. Density of states

To explore the origin of the states in the band struc-ture of zinc silicates the density of states (DOS) has beenanalyzed. Figure 6 presents total DOS for ZnSiO3-o,ZnSiO3-m, ZnSiO3-i, ZnSiO3-c, Zn2SiO4-r and Zn2SiO4-t phases. It is seen that the VB consists of two major re-gions. Upper one is very broad and located in the energyrange around -9.5–0.0 eV. The lower region is located inthe energy range from -20 to -17 eV. It is narrow and issplit into two sharp subbands.

To have more insight into the origin of VB and CBspectra and chemical bonding, orbital and site projectedDOS have been plotted in Fig. 7. It is seen that thestates at the lowest energy are contributed mainly fromthe O-2s. Smaller contribution comes from hybridized Si-3s and -3p orbitals. The topmost VB can be divided intothree parts: The lowest part is basically contributed fromthe Si-3s-orbitals. This result shows strong hybridizationof the Si-3s and 3p orbitals. This feature is the prop-erty of the Si atoms only. The sharp and high-intensitystates located around -5 eV originate from the Zn-3d elec-trons. The third, topmost part of the VB is the hybrid

246 s

pd

2468

0.2

0.4

0.6

0.51.01.5

DO

S (s

tate

s eV

-1 at

om-1

)

123

-20 -15 -10 -5 0 5Energy (eV)

0.5

1.0

1.5

Zn1

Zn2

Si

O1

O2

O3

EF(a)

0.5

1.0

1.5 spd

0.3

0.6

0.9

DO

S (s

tate

s at

om-1

eV

-1)

-20 -15 -10 -5 0 5Energy (eV)

0.3

0.6

0.9O1-O4

Zn1-Zn2

Si

(b)

FIG. 7: The orbital and site-projected DOS for (a) monoclinicZnSiO3-m, and (b) Zn2SiO4-r. The Fermi level is set to zero.

of the Zn-3d and the O-2p states, while contribution ofthe Si 3p states is negligible. Consequently, deviation ofZn and/or O atoms from stoichiometry is expected tochange the topmost region of the band structure dras-tically. This result is consistent with band dispersionanalysis for ideal and defective lattices of Zn2SiO4-t (Sec-tion III H) where we observed intermediate band formeddue to Zn interstitials. DOS at the minimum of CB isfound to be too small. Hence, absorption around thefundamental bandgap is also expected to be very small,which is the desirable feature for TCO’s. This feature isalso in agreement with the analysis of the band dispersion(Section III B) and optical spectra (Section IIIG).

ZnSiO3-o, -m, -c, Zn2SiO4-t and -r have two types ofZn atoms, Zn1 and Zn2. However, contribution of Zn1and Zn2 of each of the above silicates to topmost VBis almost the same. Similar result is valid for Si1 andSi2 atoms of ZnSiO3-o and ZnSiO3-c. ZnSiO3-o has sixdifferent types of O atoms, O1−O6. However, contri-bution of O3 and O6 to the topmost VB is almost thesame. The band dispersion originating from O1, O2, O4,and O5 atoms are also almost the same. Similarly, onecan say that ZnSiO3-m has also two types of O atoms,whereas Zn2SiO4-r and Zn2SiO4-t have just one type ofO atom. These results are consistent with Bader andVoronoi charge analysis discussed in the following sec-tions.

Analysis of the Fig. 7 shows that the magnitude of theangular momentum and site-projected DOS at the CBminimum is considerably smaller than those of VB andhence it is difficult to analysis in detail. So, for closerinspection of the origin of the CB states, fine structureof the lowest CB edge is plotted in Fig. 8 for ZnSiO3-o,

8

3.5 4.0 4.5Energy (eV)

0.01

0.02

0.03D

OS

(sta

tes/

(eV

f.u

.)) Zn-4s

Si-3sO-2s

(a) ZnSiO3-o

3.5 4.0 4.5Energy (eV)

0.01

0.02

0.03 Zn-4sSi-3sO-2s

(b) ZnSiO3-m

2.7 3.0 3.3Energy (eV)

0.01

0.02

DO

S (s

tate

s/(e

V f

.u.)

)

Zn-3sSi-3sO-2s

(c) Zn2SiO

4-(r)

1.2 1.4 1.6 1.8Energy (eV)

0.02

0.04

0.06 Zn-4sSi-3sO-2sO-3p

(d) Zn2SiO

4-(t)

FIG. 8: The orbital and site-projected DOS in the CB mini-mum of (a) ZnSiO3-o and (b) ZnSiO3-m, and (c) Zn2SiO4-rand (d) Zn2SiO4-t . The Fermi energy is set to zero.

ZnSiO3-m, Zn2SiO4-r, and Zn2SiO4-t. Analysis showsthat maximum in the DOS at the CB minimum is con-tributed by Zn, O, and Si and this result is same for allthe compounds considered. The edge of CB is formed bythe s states. As is well known,45,46 the s-type characterof the CB edge is one of the most important features ofthe TCO materials in order to give the electrons high mo-bility and conductivity.47 Major contribution to the CBedge comes from the Zn-4s orbitals. It shows to stronghopping between two neighboring Zn sitesxxx. Contribu-tion of the O-2s orbitals to the DOS is smaller than thoseof the Zn-4s. The smallest contribution comes from theSi-3s orbitals. These analysis shows that all these ele-ments can provide a path for electrical conductivity inthe crystal. Among them, the Zn-4s orbitals play an im-portant role in the electrical conductivity of all the zincsilicates considered. Based on smaller contribution ofthe Si-3s and O-2s orbitals to the CB edge than the Zn-4s orbitals it is thought that the SiO2 layers may playlittle role in scattering electrons that move within theZnO layer. So, in the zinc silicates heavily doped by ionssubstituting one of the elements of the SiO2 layer, thereduction in mobility can be restrained. Experimentalresearch is required to verify this suggestion by estab-lishing the relationship between the electrical propertiesand concentration of dopant ions.

D. Conduction band effective masses

As noted in the analysis of the band dispersions [Fig. 4]the lowest CB states are much more dispersive thanthe topmost VB states. Consequently, CB electrons are

lighter than holes and the influence of latter can be ruledout from conductivity. The reason is that the valenceelectrons are tightly bound into O atoms resulting in al-most flat VB states. So, we have not calculated holeeffective masses.

The calculated CB electron effective masses are pre-sented in Table III. Analysis shows that the masses forZnSiO3-o and Zn2SiO4-r are almost isotropic, while thosefor the other zinc silicates considered are anisotropic.Hence, electron mobility and conductivity of ZnSiO3-oand Zn2SiO4-r are expected to be isotropic, while thosefor ZnSiO3-m and Zn2SiO4-t are anisotropic. At presentthere are no experimental data to compare the theoreti-cal results.

The CB electron masses of ZnSiO3-o, ZnSiO3-m andZn2SiO4-t are of the same magnitude, whereas those ofZn2SiO4-r are considerably larger. Hence, Zn2SiO4-r isless suitable for TCO compared to the formers. The CBelectron masses computed in the present work are al-most two times larger than those of Zn2SnO4, Cd2SnO4,and CdIn2O4 (Ref. 32). It shows that mobility of CBelectrons and, consequently, conductivity of the silicatesconsidered are also expected to be small.

TABLE III: Effective masses of CB electrons (in units of thefree-electron mass m0) for ZnSiO3-o, ZnSiO3-m, Zn2SiO4-rand Zn2SiO4-t.

ZnSiO3-o ZnSiO3-m Zn2SiO4-r Zn2SiO4-t

0.3723 (Γ−X) 0.3351 (Γ− A) 1.2257 (Γ− F ) 0.3162 (Γ−N)0.3533 (Γ−W ) 0.4304 (Γ− Z) 1.2398 (Γ− L) 0.3778 (Γ−X)0.3904 (Γ− Y ) 1.2400 (Γ− Z) 0.4695 (Γ− Z)

E. Charge-density and electron localizationfunction analysis

More detailed understanding of the bonding nature canbe obtained from charge-density and electron localizationfunction (ELF) analysis.49–51 Figure 9 (a) presents chargedensity analysis for Zn-O and Si-O bonds of Zn2SiO4-r.The other compounds Zn2SiO4-t, ZnSiO3-o, ZnSiO3-m,ZnSiO3-i, and ZnSiO3-c exhibit the features similar toZn2SiO4-r. It follows from the charge-distribution anal-ysis that the highest charge density is residing in theimmediate vicinity of the nuclei of Zn and O atoms. Thelarge amount of charge around Zn is because Zn 3d semi-core electrons are included into the computations. Nocharge is seen in the center of the Si atoms. This resultis in agreement with Bader charge analysis discussed inthe following section and it can be related to absence ofcore charge in the Si pseudopotential used in the presentcalculations. Character of the Si-O bonds coming outfrom the calculations seems to be much more ionic com-pared to that of the Zn-O bonds. The bonds between Siand O atoms are stronger than those between Zn and O.Analysis of Fig. 9 (a) shows that the charge around O

9

FIG. 9: Charge density for (a) Zn2SiO4-r and (b) ZnO.

atoms is too small. This is because the O atoms are notlocated in that particular plane for which the charge den-sity is plotted. In the Zn2SiO4-r structure there are twodifferent Zn atoms and four different O atoms. However,as is seen in Fig. 7 (b) contribution of the different Znand O atoms into DOS is almost the same. The chargedensity distribution in Fig. 9 (a) is in good agreementwith this result.

In order to have more insights into the chemical bond-ing in zinc silicates, Zn-O bonding of ZnO in the wurtzitestructure is analyzed in Figures 9 (b). It is seen that thecharges around Zn and O atoms of ZnO are distributedalmost spherical in shape, while those of zinc silicatesare nonspherical. It is hard to quantify the differences ofthe charge located around Zn and O atoms between zincsilicates and ZnO. Quantitative analysis are needed todiscuss the problem and this question shall be discussedin the following section based on quantitative Bader andVoronoi charge analysis.

The ELF is one of the useful tools to characterize chem-ical bonding in solids. It is a measure for the prob-ability distribution of paired electrons. Compared tocharge distribution, it is able to better distinguish dif-ferent bonding situations for electrons from ELF analy-sis. For more information about capabilities of this toolsee, e.g. Refs. 49–51 and references therein. Figures 10present the calculated ELF plot. Analysis shows thatthe ELF value is very low at the Si and Zn. Higher valueof ELF is available around O atoms. Around Zn atomsof Zn2SiO4-4 lattice narrow regions are seen which seemto be isolatedxxx. However, these regions are connectedto each other and not isolated.xxx ELF value in theseregions are < 0.2. In ZnO similar spot is located in be-tween two O atoms and ELF indicates a maximum valuearound 0.52 ([Fig. 10 (b)]). Consequently, the electronsin this spot are more or less well paired in nature.51 Ex-trapolating the site preference rule of hydrogen in metal,alloy, and intermetallic frameworks51 to dielectrics thesesites are suggested to be the candidates for locating aH, Li, Cu, or Na atomxxxx. However, according to therule, the site should be isolated, i.e. there should be noatom, but there should be some amount of charge. Inour case, the space is not completely isolated. There isZn atom located closer to this more or less isolated space

FIG. 10: ELF for (a) Zn2SiO4-r and (b) ZnO.

with high value of ELF. The charge of this space, should,in principle, participate in forming the stable 1s2 pairedelectron, thus completing the valence shell of H atom.The high ELF value in the interstitial region exceeding0.5 can be the indicator that the site has enough poten-tial to complete the valence shell of the incorporated Hatom. No interstitial site with high ELF value was foundaround Si-O bonding.

F. Bader and Voronoi charge analysis

Further insight into chemical properties of materialscan be obtained from quantitative analysis of chargetransfer between constituents of the material. Such kindof methods require knowledge of the space around eachatom, which contains the charge of the atom. Nowa-days, several schemes are available for partitioning thespace around atoms. In this work we shall use Baderand Voronoi charge analysis.52–54 According to topolog-ical analysis by Bader each atom of a compound is sur-rounded by a surface that run through minima of thecharge density. These regions are known as Bader re-gions. This way allows to estimate the total chargearound each atom by integrating the electronic den-sity within the Bader region where an atom’s nucleusis located, and possibly adding the electronic charge innearby. According to the other tool known as Voronoieach grid point of charge density is assigned to the near-est atom, but each of these distances are not scaled bythe radius of each atom, So, the Voronoi charges in thepresent article is just for a sanity check.

The results of the Bader and Voronoi charge analysisfor the zinc silicates have been presented in Table IV.As expected, Zn and Si atoms donate electrons, while Oatoms are acceptors. The amount of the donated chargeindicates to ionic type of chemical bonding. However,Bader charge of Si atoms are more than > +4.0 sup-plied in the pseudopotential for the Si atom, becauseof the absence of Bader maximum at the Si atomxxxx.Consequently, one should expect more charge around O

10

atoms. This result indicates that according to Badercharge analysis the ionic type of chemical bonding is wellpronounced. The problem arises because of the missingthe core charge in the pseudopoentials. At the momentit is not safe to say that the Bader analysis predicts acharge of > +4.0 on Si and the failure can be ascribed tothe missing core in the pseudopotential for the Si atom-xxx.

TABLE IV: Atomic charges (in units of the electron chargee−) within the atomic basins of Zn, Si, and O calculated ac-cording to Bader’s topological analysis and Voronoi deforma-tion density in ZnSiO3-o, ZnSiO3-m, Zn2SiO4-r and Zn2SiO4-t.

Compound Atom Voronoi Bader

ZnSiO3-o Zn1 1.2049 1.3754Zn2 1.1578 1.3322Si1 2.0012 4.0025Si2 1.9790 4.0028O1 −1.0648 −1.6705O2 −1.0613 −1.6786O3 −1.0572 −2.0133O4 −1.0510 −1.6637O5 −1.0503 −1.6769O6 −1.0583 −2.0097

ZnSiO3-m Zn1 1.1860 1.3757Zn2 1.1101 1.3495Si 1.9968 4.0025O1 −1.0375 −1.6848O2 −1.0265 −1.6816O3 −0.9810 −1.9888

ZnSiO3-i Zn 1.1559 1.3723Si 1.8309 4.0031O −0.9956 −1.7923

ZnSiO3-c Zn1 1.3035 1.3597Zn2 1.3133 1.3597Si1 1.7421 4.0018Si1 1.7448 4.0018O −1.0172 −1.7870

Zn2SiO4-r Zn1 1.1520 1.3365Zn2 1.1376 1.3384Si 1.8613 4.0024O1 −1.1152 −1.7021O2 −1.1210 −1.7112O3 −1.0557 −1.6366O4 −0.8592 −1.6275

Zn2SiO4-t Zn1 1.1023 1.3193Zn2 1.2623 1.3408Si 1.7580 4.0025O1 −1.1322 −1.6859O2 −0.7945 −1.6252O3 −0.9896 −1.6479O4 −1.1064 −1.7036

ZnO Zn 1.0516 1.2170O −1.0516 −1.2170

Analysis of the Voronoi charges shows that Si atomsdonate just some part, but not all of its valence electrons.As a result, the Voronoi charge around Zn, Si and Oatoms are smaller than the Bader charge. Consequently,according to Voronoi charge, chemical bonding of zinc sil-icates is not as much ionic as in the case of Bader chargeanalysis. Comparing the Bader and Voronoi charges ofzinc silicates with those of ZnO one can see that the for-mer is more ionic than the latter. So, incorporation of Siinto ZnO matrix leads to modulation of the crystal lat-tice, electronic and optical properties, and also increasesionic degree of the chemical bonding.

ZnSiO3-o, -m, c, Zn2SiO4-t and -r have two different

type of Zn atoms. However, the amount of charge withinthese two Zn sites for all these compounds are almost thesame. Similar result has been obtained for charges of Si1and Si2 atoms of ZnSiO3-o and ZnSiO3-c. ZnSiO3-o hassix different types of oxygen atoms. However, charges atthe O3 and O6 sites are almost the same. The amountof charge at O1, O2, O4, and O5 are also close to eachother. So, instead of considering six different O atoms itis sufficient to consider just two types of O atoms for theanalysis. Similarly, one can say that ZnSiO3-m has alsotwo types of O atoms, whereas Zn2SiO4-r and Zn2SiO4-thave just one type of O atoms. This result is consistentwith orbital and site projected DOS, and charge densityanalysis.

G. Optical properties

Figure 11 displays the real (ε1(ω)) and imaginary(ε2(ω)) part of the dielectric function, absorption coef-ficient (α(ω)) and reflectivity (R(ω)). In order to under-stand the optical anisotropy of the zinc silicates, threecomponents of the dielectric function are calculated forZnSiO3-o, six components for ZnSiO3-m and two com-ponents for Zn2SiO4-t. For simplicity of analysis, onlythree diagonal components of the dielectric function areconsidered for ZnSiO3-m. These three components aredirected along the crystallographic a, b and c axes. Thetwo components for Zn2SiO4-t correspond to the electricfield parallel E‖c and perpendicular E⊥c to the crys-tallographic c axis. There are no published data on theoptical spectra for zinc silicates. We hope that our calcu-lated optical spectra will motivate experimental studieson these materials.

Optical spectra are found to be anisotropic for allthe compounds considered. The anisotropy is well pro-nounced in ZnSiO3-m and Zn2SiO4-rxxx for which allthe optical spectra along the direction E ‖ c are muchsmaller than the other directions. Furthermore, a simi-larity is evident in the absorption and reflectivity spectrabetween these two compounds (Fig. 11). That is the re-flectivity changes non-monotonically with increasing theenergy. It has a maximum at E ≈ 10 eV. For E > 10 eV,R(ω) decreases with increasing of energy. As discussedabove, the optical spectra for E ‖ c is much smaller thanthose for E ‖ a and E ‖ b. Also, along the directionsE ‖ a and E ‖ b all the optical spectra are more or lessisotropic. For the ZnSiO3-o the optical spectra except re-flectivity, are also isotropicxxxx. The reflectivity spectrashows anisotropy at high energies E ≤ 13 eV.

For E ≥ 7.5 eV the absorption coefficient α(ω) in-creases with increasing the energy for all the compoundsconsidered. For ZnSiO3-o, α(ω) has a maximum atE ≈ 12.5 eV and it decreases with increasing the en-ergy at E < 12.5 eV. For the other zinc silicates α(ω)staysxxxx to be almost the same for E ≥ 10.0 eV.

Analysis of the optical spectra shows that the valuesof the real part of the dielectric function, absorption, and

11

2

4

ε 2(ω)

2

4

ε 1(ω)

1

2

α(ω

) (x1

05 cm

-1)

5 10 15

0.1

0.2

0.3

R(ω

)

5 10 15Energy (eV)

E || aE || bE || c

(a) (b) ZnSiO3-(m)ZnSiO

3-(o)

0

2

4

2

4

0

1

2

5 10 15

0.1

0.2

5 10 15Energy (eV)

(c) Zn2SiO

4-(r) (d) Zn

2SiO

4-(t)

FIG. 11: Optical spectra of (a) ZnSiO3-o and (b) ZnSiO3-m, and of (c) Zn2SiO4-rxxxx and (d) Zn2SiO4-t. For the latterthe directions corresponding to the electric field parallel E‖c (dashed lines) and perpendicular E⊥c (thick solid lines) to thecrystallographic c axis are considered. For the other compounds considered the directions along E⊥a (thick solid lines), E⊥b(thin solid lines), and E⊥c (dashed lines) are considered.

reflectivity are too small in the energy range 0–5 eV. Itindicates that the compounds considered in the presentstudies have interest to use as TCO.

H. Electronic structure of Zn2SiO4-t with a Zninterstitial

As demonstrated in Section III C major contributionto the lowest CB of the zinc silicates comes from theZn-4s states. Furthermore, Zn-4dxxxx states contributessignificantly to the topmost VB. Consequently, VB max-imum and CB minimum should change drastically onthe Zn-related structural point defects. Although in Sec-tion IIIA it was shown that the defective structure is less

stable compared to the ideal one [Fig. 3], in this Sectionwe shall discuss electronic structure, charge density andELF analysis, as well as optical spectra of the defectiveZn2SiO4-t structure to demonstrate some interesting fea-tures coming out from structural point defects. For thepresent study one Zn interstitial in a unit cell of Zn2SiO4-t shall be considered.

Figure 12 displays band dispersion for the defectiveZn2SiO4-t with the Zn interstitial. It is seen that thefree-electron-like band at the CB minimum has been splitfrom the CB to 0.60 eV and from VB to 1.31 eV. As itwas shown in Sec. III C upon discussion of the partialDOS, this feature is related to origin of the lowest CBstates originating mainly from the strongly hybridizedZn-4s, Si-3s, and O-2s states. Hence, the structural point

12

Z Γ X P N Γ

-3

0

3

6

Ene

rgy

(eV

)

FIG. 12: Band dispersion for defective Zn2SiO4-t with Zninterstitials. The Fermi level is set at zero of energy.

defects can form an intermediate band. The calculatedwidth of this isolated band is 2.17 eV and it is dispersive.Furthermore, effective mass of electrons in this band isaround 0.46m0xxxx. These features indicate that elec-trons of this band can significantly contribute to conduc-tivity. If by doping the intermediate band shall partiallybe filled with electrons, then it can be regarded as metal-lic band. The present study shows that the intermediatebands can be formed not only by impurities, but also bystructural point defects.

As noted in Ref. 45 separation of the lowest highly dis-persive CB state is preferable to satisfy one of the impor-tant features of the band structure such that the plasmafrequency should be below the visible range. From thispoint of view separation of the CB minimum and forma-tion of the intermediate band can lead to lowering theplasma frequency, since it is proportional to the largestenergy of the intraband transition.xxxxx

The Zn interstitial has increased width of the topmostregion of VB from 7.5 corresponding to ideal lattice to10.0 eV and split two localized bands of the ideal cellin the lowest VB into three localized bands. For de-tailed knowledge of the defect-induced changes of theband structure comparative analysis of the total DOSand orbital and site projected DOS has been performedfor ideal and defective Zn2SiO4-t [Fig. 13 (a) and (b)].

It is seen that Si-3s and -3p states still contribute sig-nificantly to the lowest VB. However, compared to theideal lattice these bands have been splitted and convertedfrom two narrow high-intensity localized states into threelow-intensity localized states. At the topmost VB theSi-3s and -3p bands are considerably hybridized. Fur-thermore, distinct from the ideal lattice, which at thetopmost VB had some contribution from Zn and no con-tribution from Si, the defective lattice has contributionfrom Si-3p and no contribution from Zn atoms. It meansthat the nature of the Si-O and Zn-O bonds have beenchanged. The Si-O bonds, which in ideal lattice was al-most purely ionic, possessed some covalency, whereas the

2

4

d

-15-10 -5 0 5Energy (eV)

0.5

1.0

1.5

0.2

0.4

DO

S (s

tate

s/(e

V f

u))

-15-10 -5 0 5

EF

Zn

Si

O

sp

(a)

EF

Zn

Si

O

(b)

FIG. 13: Total, orbital and site projected DOS for the (a)defective and (b) ideal Zn2SiO4-t. The Fermi level is set tozero.

Zn-O bonds, which in ideal lattice had some covalencybecome almost purely ionic.

Figure 14 shows the dielectric response functions ε1(ω)and ε1(ω), absorption coefficient α(ω) and reflectivityR(ω) for the defective Zn2SiO4-t. Two peaks at 1.65and 2.47 eV are well defined in the spectral distributionof the dielectric response. These peaks can be ascribedto the optical transition from the VB to the intermedi-ate band. The n peak at around 3.98 eV corresponds tothe VB to CB transitionxxx. In the absorption spectrathe former two peaks are smaller than latter. It showsthat the optical transition from VB to CB is strongerxxx.In the reflectivity spectra magnitude of these peaks arecomparable. Since Zn2SiO4-t is undoped, there are noelectrons in the intermediate band. Furthermore, illu-mination intensity considered in the present calculationscorresponds to one sunxxx. Consequently, the transitionfrom the intermediate band to CB is negligiblexxxx.

As discussed above, the Zn interstitials have changedthe band structure as well as optical properties and hencethey are expected to influence the chemical bonding also.Charge-density and ELF analysis have been performedfor the defective Zn2SiO4-t. Compared to ideal lattice,the bonding interaction between Zn-O has been modi-fied significantly. Figure 15 demonstrates these features.Charge-distribution [Fig. 15(a)] analysis shows that thehighest charge density is residing in the vicinity of theZn site. However, distinct from the ideal lattices, someamount of charge is located in between the two nearestZn atoms when one have Zn interstitials. Analysis of ELF[Fig. 15(b)] shows that in between the two Zn atoms thereis a spot where ELF indicates a maximum value of around0.52. So, one can conclude that the electrons in this spotis paired well enough.51 According to the site preferencerule51 this site can be the candidates for locating a H or

13

0

2

4ε 2(ω

)

5 10 15

2

4

ε 1(ω)

0

1

2

α(ω

)

5 10 15Energy (eV)

0.1

0.2

R(ω

)

FIG. 14: Optical spectra of the defective Zn2SiO4-t for theelectric field directed parallelly E‖c (dashed lines) and per-pendicularly E⊥c (thick solid lines) to the crystallographicc axes. The absorption coefficients are given in [cm−1] di-vided by 105.

FIG. 15: (a) Charge density and (b) ELF for defectiveZn2SiO4-t.

other impurity atom with unpaired electron, which par-ticipates in forming the stable 1s2 paired electron andcompletes the valence shell of the H atom. Knowing theunit cell volume for Zn2SiO4-t [Table I] maximal valueof the hydrogen concentration (NH) is estimated to beequal to NH = 3.2× 1021 cm−3. No interstitial site withhigh ELF value was found between the Si-O bonding.Furthermore, this feature is not found in ideal lattices ofthe compounds considered in this study.

IV. CONCLUSION

This work presents ab initio studies of electronic struc-ture and optical properties of ZnSiO3-o and -m, and

Zn2SiO4-r and -t. By a search of the total energy mini-mum the equilibrium volume is found, which is in goodagreement with experimentally determined one. TheDFT calculations of the electronic structure and opti-cal properties of the zinc silicates have been performedusing the experimentally determined lattice parameters.It is shown that all the compounds considered are wideband gap, lowest CB is dispersive, while the topmost VBis dispersionless. Furthermore, the lowest CB is formedof the valence s orbitals of the Zn, Si, and O atoms andmajor contribution comes from the Zn-4s orbitals. Thelowest one among the peaks in the dependence of the par-tial DOS of the Zn-4s, Si-3s, and O-2s orbitals on energyis located at the same energy. This result is valid for allthe compounds considered in this study. It is found thatthe Si-3p orbitals contribute to the lowest valence band,while the Si 3s-like orbitals contribute to the topmost va-lence band of the compounds. Analysis of the density ofstates, charge-density, Bader and Voronoi charges, andELF shows that the compounds understudied are ionic.It is found that ELF value is high in the interstitial sitesbetween the O-O bond in ZnO and Zn-Zn bond in thedefective Zn2SiO4-t. Optical properties are found to beanisotropic for all other compounds considered. In theenergy range from 0 to 5 eV, absorption and reflectiv-ity coefficients are found to be very small. Based on theabove analysis it is concluded that the zinc silicates canbe regarded as potential candidates for TCO. From DFTcalculations of electronic structure of the Zn interstitialsin Zn2SiO4-t it is concluded that point structural defectscan modulate the band structure, chemical bonding, andoptical properties and form an intermdeiate band. Elec-tronic transitions from the VB to the intermediate bandwas found in the optical spectra.

Acknowledgments

This work has received financial and supercomputingsupport from the Research Council of Norway. SZK hasreceived partial financial support from Academy of Sci-ences of Uzbekistan. SZK thanks R. Vidya, A. Klaveness(University of Oslo, Oslo, Norway), and Dr. K. Knizek(Institute of Physics ASCR, Prague, Czech Republic) fordiscussions and help in computations.

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