DFT characterization of cadmium doped zinc oxide for photovoltaicand solar cell applications

Bakhtiar Ul Haq a, Rashid Ahmed a,n, Souraya Goumri-Said b,nn

a Department of Physics, Faculty of Science, Universiti Teknologi Malaysia, UTM Skudai, 81310 Johor, Malaysiab School of Chemistry and Biochemistry and Center for Organic Photonics and Electronics, Georgia Institute of Technology, Atlanta, Georgia 30332-0400,United States

a r t i c l e i n f o

Article history:Received 17 February 2014Received in revised form2 June 2014Accepted 4 June 2014

Keywords:ZnOWurtziteZincblendeDFTFP-LAPWmBJElectronic structureAbsorption spectra

a b s t r a c t

Tailoring the energy gap of ZnO through Cd doping renders Cd:ZnO an intriguing material forphotovoltaic and solar cell applications. Unfortunately, the Cd:ZnO blend is unstable, a feature attributedto the structural differences between the parent hexagonal ZnO and cubic CdO. We here report acomparative density functional theory (DFT) study of zinc-blend (ZB) and wurtzite (WZ) ZnO doped withCd – upto 37.5% of the Zn atoms were substituted by an isovalent Cd. Interestingly, the nearly equivalenttotal energy of the ZB and WZ Cd:ZnO blends reflects the relative stability of the cubic phase. Theformation enthalpies increase linearly with increasing Cd concentration. Cd insertion into ZnO is foundto have an insignificant effect on the ZnO structure, with only a slight increase of the lattice constantsthat follow Vegard's formulation. Cd dopants efficiently reduce the electronic band gap of ZnO and inturn the absorption edge and optical energy gap are red-shifted. The Cd:ZnO blends exhibit a lowerenergy gap in the cubic phase as compared to the hexagonal phase, suggesting that a specific energy gapcan be achieved at relatively lower Cd contents in the ZB. The lighter effective free-carrier masses inWZ-Cd:ZnO suggest a higher conductivity and mobility as compared to ZB and the parent ZnO. Thenarrow energy gaps indicate that both hexagonal and cubic Cd:ZnO systems have potential as materialfor solar energy applications.

& 2014 Elsevier B.V. All rights reserved.

1. Introduction

ZnO is an interesting and multifunctional semiconductor thatplays a leading role in II–VI semiconductor family. The wide anddirect band gap of 3.44 eV, intrinsically transparent nature overthe whole visible range, abundant availability, low cost, highchemical and thermal stability make ZnO particularly attractivefor photovoltaic (PV) and solar cell applications. ZnO is oftenhighly doped with atomic impurities, and their now exists con-siderable academic research efforts to control ZnO doping to bothimprove existing physical properties and add new materialdimensionalities, including varying the optoelectronic, magnetic,magneto-optic, electromagnetic, thermoelectric and piezoelectricproperties [1–5]. The current ZnO application range includes manytransparent electronic and photonic devices, such as solar cells,blue and ultraviolet light-emitting diodes, flat panel displays,among many others [1–5]. ZnO based transparent conducting

oxides (TCOs) meet the stringent requirements for thin-film solarcells as it has both appropriate optoelectronic properties andhigh resistance to hydrogen rich plasmas [6–8]. Hence, dopedZnOs are considered as interesting alternatives to Sn-dopedindium oxide (ITO).

The ability to engineer the energy gap of ZnO for photovoltaic/optoelectronic applications strongly depends on the nature of thedopant. The most studied dopant in this regard is Al [9–14].Although Al-doped ZnO have shown some intriguing features,there remains an unresolved problem concerning the environ-mental stability. Therefore, considerable recent research hasfocused on alternative doping schemes. In this regard Cd:ZnOhas been shown to be an interesting option [15–20]. Cd and Zn areisoelectronic transition metals, and hence CdO alloying with ZnOcould manifest interesting features in fused CdO–ZnO structures[21]. Importantly, Cd doping reduces the energy band gap andresults in a red-shift of absorption edge [15–17,22]; hence, one canenvision varying the Cd-doping concentration to tailor the elec-tronic gaps to produce materials of interest for photovoltaicapplications. In addition, incorporation of Cd into ZnO producesa material with increased conductivity [22,23] and increasedcarrier concentration (upto 2.69�1020 cm�3) versus the parentZnO [24].

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

Solar Energy Materials & Solar Cells

http://dx.doi.org/10.1016/j.solmat.2014.06.0140927-0248/& 2014 Elsevier B.V. All rights reserved.

n Corresponding author.nn Corresponding author.E-mail addresses: rashidahmed@utm.my (R. Ahmed),

Souraya.Goumri-Said@kaust.edu.sa,Souraya.Goumri-Said@chemistry.gatech.edu (S. Goumri-Said).

Solar Energy Materials & Solar Cells 130 (2014) 6–14

Although, Cd:ZnO exhibits interesting features for PV applica-tions, the difference in the stable structural geometries of theparent compounds (i.e. ZnO and CdO) might impede its usefulness.At ambient conditions, CdO is cubic, whereas ZnO is stable in thewurtzite (WZ) phase. This difference in structural phases is amajor issue for practical applications as the resulting material haslow thermal stability – the Cd ions in hexagonal ZnO matrixinduce tension in the lattice of Cd:ZnO, producing tensile strainthat makes it difficult to conserve the hexagonal phase [20]. Theseinternal strains cause distortion in crystal lattice, and reduce thecrystallinity of Cd:ZnO [25]. These problems might be overcome,however, through incorporation of Cd dopants into the zinc-blende (ZB) phase of ZnO. Synthesis of the ZnO in ZB phase hasbeen reported on the cubic GaAs substrate [26,27]. To the best ofour knowledge, the doping of Cd into ZB-ZnO has yet to beexplored.

In this work, we employ density functional theory (DFT)methods to investigate the effect of Cd substitution in both thecubic and hexagonal phases of ZnO; the latter is expected to be amore favorable situation to accommodate a high concentration ofCd atoms with comparatively lower internal strains. Our DFTinvestigations employ the full potential linearized augmentedplane wave (FP-LAPW) method, and make use of the mBJ func-tional to evaluate the electronic gap. Of particular emphasis in thisstudy is the electronic properties of these blend materials as afunction of structure so as to evaluate the potential of Cd:ZnOmaterials for photovoltaic (PV) and solar cell applications.

2. Computational details

FP-LAPW approach as implemented in the WIEN2k code [28]was employed. Though GGA-based DFT calculations provide perti-nent results for many physical properties of conducting oxides, themethods tend to underestimate the energy gap. To overcome thisdifficulty a proper choice of the exchange and correlation (XC)potential functional is crucial. Tran-Blaha modified Becke Johnson(mBJ) functional [29,30], in particular, has been reported in severalstudies of semiconductors and insulators to calculate energy gapwith high accuracy approaching the experimental value [31,32],and will be used here. In order to calculate the structural proper-ties GGA proposed by Perdew et al. (PBE-GGA) is employed [33].Whereas to predict electronic and optical properties, in addition toPBE-GGA, mBJ exchange potential is incorporated [29,30].

To expand the wave functions inside the Muffin-Tin (MT)spheres lmax¼10 and in the interstitial region, an energy cutoffKmax¼8.0/RMT (Ryd)1/2 was used. Radius of MT spheres, RMT werechosen for Zn and Cd as 1. 81 a.u, and for O as 1.55 a.u. Fourierexpanded charge density was truncated at Gmax¼16 au�1. Bril-louin zone (BZ) integration has been performed using Monkhorst–Pack special k-points approach [34]. To ensure convergence of theenergy, the integrals over the special BZ are preformed up to 203(9�9�5) k-points for WZ and 216(6�6�12) k-points for ZBphases. Total energy convergence was ensured to 10�5 Ryd/unit cell.

To investigate how the substitution of Cd impacts the structuraland electronic properties of ZnO, supercells of 32 atoms wereconstructed; supercells for WZ-ZnO and ZB-ZnO were 2�2�2and 2�2�1, respectively. Substitution of Cd atoms has a stronginfluence on the structural symmetry, with the symmetryimpacted by the sites of substitution; see Fig. 1 and Tables 1 and2 for the WZ and ZB geometries, respectively. Such symmetrybreaking for WZ-Cd:ZnO is consistent with previous literaturereports [17]. It is of interest that the total energies of the Cd:ZnOstructures in the WZ and ZB phases are only marginally different,with the minor differences reflecting the equivalent stability of ZBCd:ZnO to that of WZ. The two structures present similar localtetrahedral bonding, with the main difference being their stackingdirection (111). Both the structures carry the same atomic coordi-nation through the second nearest neighbor.

3. Results and discussions

3.1. Structure and energy: ZB versus WZ phase

Fig. 2(a) depicts the influence of Cd concentration on the Etotand ΔE(WZ/ZB). The linear increase in Etot with increasing Cdconcentration reflects the stability of Cd:ZnO for high Cd content.The material stability can be estimated by Helmholtz free energy,which is simply the sum of formation enthalpy (mixing energy,ΔH(x, T)) and product of temperature and entropy (ΔS(x, T)). Theformation enthalpy, which is difference between the energy of thealloy and the weighted sum of its constituents, solely determinesthe relative stability of Cd:ZnO system and is calculated asΔH(x)¼E(Zn1�xCdxO)�xE(CdO)�(1�x)E(ZnO), see Table 3. Fig. 2(b) showsthat ΔH increases as a function of the Cd content, obeyingVegard's law. The linear fit for ΔH is ΔH ¼ 2:56x�0:062.

Fig. 1. The schematic structures of Cd:ZnO in WZ and ZB geometries. The numbers labeled spheres show the Cd/Zn substitutional sites. The purple colored big spheres andthe red colored small spheres represent Zinc and oxygen atoms respectively. (For interpretation of the references to color in this figure legend, the reader is referred to theweb version of this article).

B. Ul Haq et al. / Solar Energy Materials & Solar Cells 130 (2014) 6–14 7

Positive ΔH is due to the volumetric changes caused by themismatch in atomic radii of Zn and Cd, consistent with previouscalculations [18,35]. The large value of ΔH that corresponds to highcritical temperature reflects the immiscibility approach of Cd:ZnO

in a wide compositional range at a specific epitaxial growthtemperature. On the basis of the calculated enthalpies for theinvestigated constituents i.e. 0.0625oxo0.375, we investigatedthe T–x phase diagram [32,36,37], see Fig. 3. This result suggeststhat the critical temperature is expected to be in the compositionrange 0.45oxo0.55.

Understanding the impact of the Cd dopants on the ZnO latticeparameters is important as minor variations in the lattice para-meters might suggest high solubility of Cd in ZnO (and vice versa).Lattice constants of two structural geometries are collected inTable 4. Lattice volume experiences linear expansion in thepresence of Cd atoms in both WZ and ZB phases, a trend inagreement with the experimental observations [38,39]. Theincrease in lattice volume is due to the difference in Cd (0.97 Å)and Zn (0.74 Å) atomic radii. Due to the expanded volume of Cd:ZnO, the lattice constants of both WZ Cd:ZnO and ZB Cd:ZnO arelarger than pure ZnO. However, the calculated c/a ratio for WZphase does not reveal any change [35]. The increase in latticeparameters is fitted by the following equations:

aðwzÞ ¼ 3:27xþ0:5 ð1Þ

c ðwzÞ ¼ 5:25xþ0:67 ð2Þ

aðzbÞ ¼ 4:63xþ0:60 ð3ÞFig. 4 depicts the variation in lattice parameters as a function of

Cd composition. A nearly linear increase can be observed for bothstructural geometries that agrees well with Vegard's law [40], andreveals the high solubility of Cd in both WZ and ZB matrices ofZnO. Variation in lattice constant values in the ZB geometry ismore significant than in WZ. In the WZ case, lattice constants aand c increase by 0.35 Å and 0.55 Å, respectively, between 6.25%and 37.5% of Cd compositions, while the difference in a betweenthe two compositions for ZB phase is 0.18 Å.

To evaluate the fabrication of morphologically stable devices,we examine the deviation in lattice parameters of Cd:ZnO in termsof Vegard's formalism using the following formulas:

aðxÞ ¼ xaCdOþð1�xÞaZnO�δaxð1�xÞ ð4Þ

cðxÞ ¼ xcCdOþð1�xÞcZnO�δcxð1�xÞ ð5Þwhere δ denotes the deviation in lattice constants a and c fromVegards law; a(x), c(x) are the lattice parameters of Cd:ZnOfor various compositions; aCdO, cCdO and aZnO, cZnO are thelattice constants of the parent CdO and ZnO, respectively. Thesame approach has been adapted to determine the deviationin the lattice constants for ZB phase. The negative values of δindicate that the calculated lattice constants slightly overestimateVegard's values. Deviation of lattice parameters is possibly due tothe difference in the bond length of Zn–O and Cd–O bonds.Overall, the deviation in the lattice parameters is small for theconsidered Cd:ZnO compositions, revealing their structural stabi-lity. Furthermore, we observe varied Zn–O and Cd–O bond lengthsin WZ and ZB geometries: calculated Zn–O bond length in WZ is1.93 Å and 1.06 Å in ZB, which are smaller than the Cd–O bondlengths of 2.16 Å in WZ and 1.23 Å in ZB. The calculated bond-lengths are in good agreement to the findings of Bai et al. [17], andreflect the difference in the atomic radii.

3.2. Electronic band gap and related properties

To investigate the influence of Cd dopants on the electronicproperties of ZnO, the electronic structures for all the consideredcompositions were determined (Fig. 5). The electronic band-structures of Cd:ZnO resemble that of pure ZnO rather than theenergy band gap. The direct band gap nature is preserved in thepresence of Cd due to the similar electronic structures of the

Table 1The symmetry breaking of Cd:ZnO in WZ geometry for different Cd substitutionalsites (Fig. 1) and their corresponding energies are shown.

Composition Zn/Cd positions Symmetry Energy/formula unit

Zn15Cd1O16 10 P3m1 �4217.7888

Zn14Cd2O16 10,11 Pm �4692.823810,14 Cm �4692.770210,16 P3m1 �4692.7377

Zn13Cd3O16 5,10,14 P1 �5167.75221,10,16 Cm �5167.750110,11,12 P3m1 �5167.7190

Zn12Cd4O16 1,6,9,13 Cc �5642.73182,6,10,14 Cmc21 �5642.72105,6,7,10 P3m1 �5642.69915,6,11,12 Pm �5642.78605,6,15,16 Cm �5642.64166,10,13,14 P1 �5642.7318

Zn11Cd5O16 2,6,10,13,14, P1 �6117.71252,5,6,11,12 P1 �6117.71244,5,6,15,16 Cm �6117.71281,3,6,9,13 P1 �6117.71252,4,6,10,14 Cm �6117.71294,5,6,7,10 Cm �6117.7116

Zn10Cd6O16 1,2,5,6,11,12 Pm �6592.74821,2,6,10,13,14, P1 �6592.69351,3,5,6,15,16 P1 �6592.69281,3,6,8,9,13 Cm �6592.69322,4,6,10,12,14 Cm �6592.68064,5,6,12,13,15 P1 �6592.6938

Table 2The symmetry breaking of Cd:ZnO in ZB geometry for different Cd substitutionalsites (Fig. 1) and their corresponding energies are shown.

Composition Zn/Cd positions Symmetry Energy/formula unit

Zn15Cd1O16 10 P-42m �4217.7818

Zn14Cd2O16 10,12 P-42m �4692.744410,15 Cmm2 �4692.7599

Zn13Cd3O16 7,10,12 P2 �5167.73767,10,15 P2 �5167.736110,11,12 P222 �5167.7348

Zn12Cd4O16 2,7,10,12 P2 �5642.71336,7,8,12 P1 �5642.71326,7,10,12 P1 �5642.71464,7,10,16 P2 �5642.71346,7,14,15 P2221 �5642.70186,11,14,16 Cm �5642.71527,10,12,15 P-42m �5642.7120

Zn11Cd5O16 2,6,8,10,12 P2 �6117.69052,6,8,14,15 P1 �6117.69042,7,9,10,15 P2 �6117.69052,6,11,14,16 P2 �6117.69033,4,6,8,11 P2 �6117.69053,4,10,11,12 P222 �6117.69054,7,10,12,15 P2 �6117.6903

Zn10Cd6O16 2,3,4,6,7,8 P2221 �6592.66703,4,6,8,10,12 P222 �6592.65623,4,9,10,11,12 P-42m �6592.65684,6,10,3,8,12 P222 �6592.65626,7,8,10,11,12 P2221 �6592.65626,8,10,12,14,16 P222 �6592.6562

B. Ul Haq et al. / Solar Energy Materials & Solar Cells 130 (2014) 6–148

parent compounds [41–46]. The energy gaps of WZ and ZB Cd:ZnOcalculated with GGA and mBJ are listed in Table 5. As expected, theelectronic gap values calculated with GGA are smaller than that ofmBJ. Electronic gaps experience a nearly linear decrease as afunction of composition in both structural phases. For each phase,the variation in the energy gap can be fit by the followingquadratic equations:

for the WZ phase:

EgðGGAÞ ¼ 0:8094�1:4624x�0:40229x2 ð6Þ

EgðmBJÞ ¼ 2:70644�2:37698xþ1:69509x2 ð7ÞFor ZB phase:

EgðGGAÞ ¼ 0:68454�0:91418x�1:2096x2 ð8Þ

EgðmBJÞ ¼ 2:5438�1:39166xþ0:28343x2 ð9ÞAn important result may be deduced from Eqs. (8) and (9), is

the reduced energy gap as a function of Cd concentration, which isprincipally due to the different energy gaps of parent compoundsCdO (2.29 eV) and ZnO (3.44 eV) [39,47]. ZB phase of the parentcompounds bear narrower gaps [46] that lead to narrower gap forZB Cd:ZnO vs. WZ Cd:ZnO. Narrower gap of ZB Cd:ZnO suggeststhat smaller energy gaps can be obtained at lower Cd concentra-tions in ZB phase than in WZ. This also show that the reducedenergy band gap of Cd:ZnO might be favorable for the photo-catalytic activities [48].

Fig. 6 depicts the variation in energy gap as a function of Cdcomposition. The energy gap reduction in WZ Cd:ZnO for higherCd content has been reported in several other theoretical andexperimental studies [16,38,39,49,50]. For example, Zheng et al.experimentally measured an energy gap for WZ Cd:ZnO of 2.6 eVat 23% Cd concentration [39]. Our energy gap of 2.22 eV for 25%reflects a matching impression to the experimental value. We notethat for the same concentration, however, PBE-GGA provides asignificantly smaller value of 0.42 eV. Similarly, the PBE-GGAcalculated energy gaps for other compositions are underestimated,

in agreement with other GGA-based results [50]. This severelyunderestimated band gap values with GGA is because of the well-known self-interaction correction (SIC) problem with commonexchange correlation functionals. GGA underestimated energygaps are improved with the mBJ potential, as reported in Table 5.

It is evident from Fig. 5 that the impurity leads to a decreasedenergy gap, which is mainly caused by a reduced conduction band(C.B) minimum. The valence band (V.B) maximum, located at theFermi level, remains fixed for all the compositions. The trend issimilar for both phases and holds well with the previous reportedinvestigations [50]. V.B bandwidth, though, is affected by the Cddopants, showing an expansion with increasing Cd content, seeTable 6. Moreover, the Cd content reduces the radius of the CBminima curvature. Consequently, the inverse proportion betweenthe effective masses of free charge carriers and the energy bandcurvature might lead to a higher values of the effective masses ofelectrons in Cd:ZnO. Calculated values of the effective masses ofelectrons in the Cd:ZnO system for WZ and ZB phases are0.30470.004m0 and 0.33570.002m0, respectively (m0 presentsthe rest mass of electrons). The effective masses of free carriers inZnO in the presence of Cd dopant are heavier than that in pureZnO (0.24 m0) [51]. This can be attributed to the smaller curvatureof the C.B minima in the Cd:ZnO than pure ZnO. However variationin Cd content shows no significant change in effective mass. Thecomparatively heavier effective charge-carrier masses in the ZBphase can lead to lower conductivities and carrier mobilities.

The composition-dependent energy gap narrowing due to Cddoping suggests that Cd:ZnO could be a desirable system for solarcells and other optoelectronic devices. However, for profitable andproductive optoelectronic applications, further qualitative and quanti-tative analysis of the nearly-linear or so called non-linear decrease ingap energy, as depicted in Fig. 6, is needed. The deviation of gapenergies for alloys from the linear average can be determined bydefining the band gap bowing coefficient bE using the quadraticfunction of impurity content as proposed in [52] and given by

EgðAxB1�xCÞ ¼ xEACðaACÞþð1�xÞEBCðaBCÞ�bExð1�xÞ ð10ÞbE mainly originates from the changes that take place in dopingprocess. For instance, the volume deformation (bVD) that occurs due tochanges in the lattice parameters of the parent compounds, the chargeexchange in the alloy that results in chemical electronegativity (bCE),the structural relaxation (bSR) due to the relaxation of anion–cationbond lengths. Hence, the total bowing in the energy gap is:b¼bVDþbCEþbSR. The calculated bowing parameters are listed inTable 7 for PBE-GGA and mBJ exchange potential. Our analysis ofenergy gap bowing parameter reflects the major contribution from thecharge exchange where the bowing parameters are small, correspond-ing well with previous studies [50].

To further understand the electronic structure, we determinedthe total and partial density of state (DOS) of Cd:ZnO. DOS of

Fig. 2. (a)The blue line shows the variation in the WZ/ZB energy difference and red lines shows the variation in the total energies with increase in Cd contents. (b) Theincrease in the enthalpies of WZ and ZB Cd:ZnO with increase in Cd concenteration. (For interpretation of the references to color in this figure legend, the reader is referredto the web version of this article).

Table 3The mixing enthalpies of Cd:ZnO in WZ and ZB geometries.

Enthalpy (ΔH) (kcal/mol)

WZ ZB

Zn15Cd1O16 0.110 �0.214Zn14Cd2O16 0.261 �0.053Zn13Cd3O16 0.403 0.401Zn12Cd4O16 0.566 0.575Zn11Cd5O16 0.732 0.764Zn10Cd6O16 0.917 0.930

B. Ul Haq et al. / Solar Energy Materials & Solar Cells 130 (2014) 6–14 9

Cd:ZnO is similar for all compositions. Therefore, DOS determinedfor Zn15Cd1O16 with the mBJ potential will be considered as anarchetype for both WZ and ZB phases. It is evident from Fig. 7that the DOS are mainly comprised of Zn-d, Cd-d, and O-pelectrons. Though the effects of Zn-(s,p), Cd-(s,p) and O-s electronsare weak, their contributions to DOS are important and could beresponsible for certain novel features in the electronic, opticalproperties and PV applications of the system. Cd d-electrons arelocalized mostly in the deep V.B energy regime about �7.0 to�6.37 eV (�6.93 to �6.26 eV for ZB). These electrons mainlydefine the bottom edge of the V.B. Cd-d electrons are shifted toeven deeper in V.B with increase in Cd contents, and are posi-tioned at �7.84 eV to �6.46 eV (�7.53 to �6.38 eV for ZB) for0.375 of Cd contents. Increase in V.B width as a function of Cddopant concentration is possibly attributed to the shifting of Cd

d-electrons to deep V.B with changing Cd content. Zn-d electronsexhibit comparable density to Cd-d electrons and appear in theenergy regime of �5.64 eV to the Fermi level (�5.52 eV to Fermilevel for ZB). The Zn d-band expands as the Cd content increases.Additionally, the Zn-d electrons are located at higher energy withrespect to Fermi level in the blend compared to pure ZnO [45,46].Table 6 reveals that the binding energies increases as the Cdcontent increases. C.B minima is intrinsically originated from O-s, pand Zn-s characters. In addition, Cd-s electrons also appear in theC.B minima, adding to its s-character. The increase in Cd concen-tration results in enrichment of s-electrons in CB minima thatdrive a down shift of the C.B continuum, and consequentlynarrows the energy gap.

3.3. Optical properties

To investigate the optical transitions in Cd:ZnO and its possibleapplications in optoelectronics and solar cell applications, weinvestigated the optical properties of the WZ and ZB phases. Thedielectric function describes the excitations between the occupiedand unoccupied states caused by interaction of electrons andphotons. Imaginary part of the dielectric function is consideredas pandect for optical properties as once it determined, the realpart can be evaluated using well-known Kramers – Kronig rela-tions [53]. Consequently, the other optical observable can bederived from the complex dielectric function. The spectra definedby these excitations can be described as joint density of statesbetween the V.B and C.B. As with the DOS, we only present theoptical parameters determined for Zn15Cd1O16 with mBJ potentialas prototype.

Fig. 8 depicts the real and imaginary parts of the dielectricfunction for Cd:ZnO for both cubic and hexagonal phases. Inter-estingly, the optical spectra of these two phases are very similar,which can be linked to their similar band structures. First majorstructure in the imaginary part for WZ Cd:ZnO appears at 3.42 eV(3.20 eV for ZB). As it is the low-energy, it must account to theoptical transition between the V.B maxima and C.B minima.Position of first structure in ZB phase at slightly lower energythan WZ is due to its narrower band gap than in WZ phase.Referring to the DOS, it can be assigned a transition between theO-2p and Zn-4s electrons. For the remaining compositions, thistransition occurs at energies of 3.02 eV (3.02 eV ZB), 3.02 (2.92 eVZB), 3.01 (2.89 eV ZB), 2.77 (2.66 eV ZB), 2.64 (2.41 eV ZB), 2.52(2.40 eV ZB) for the 0.125, 01875, 0.25, 0.3125, and 0.375 composi-tions, respectively. This trend reveals that the first optical transi-tion occurs at lower energies for higher Cd content, directly

Fig. 3. T–x phase diagram are shown for Cd:ZnO in WZ and ZB geometries against the increase in the Cd concentration. The black and red lines show the binodal andspinodal curves respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).

Table 4The lattice parameters of Cd:ZnO in WZ and ZB geometries as a function Cdcontents.

Composition WZ ZB

a(Å) δa c(Å) δc a(Å) δa

Zn15Cd1O16 3.30 0.002 5.29 0.1225 4.67 �0.469Zn14Cd2O16 3.33 �0.129 5.33 0.1845 4.70 �0.228Zn13Cd3O16 3.37 �0.186 5.37 0.0113 4.74 �0.213Zn12Cd4O16 3.40 �0.184 5.42 0.0692 4.79 �0.266Zn11Cd5O16 3.44 �0.204 5.46 0.0443 4.82 �0.221Zn10Cd6O16 3.46 �0.182 5.50 0.0331 4.85 �0.192

Fig. 4. The variation in the lattice constants of Cd:ZnO in WZ geometry as afunction of Cd contents. In sent the increase in the Cd:ZnO in ZB geometry has beenshown. The dotted lines shows the variation according to Vegard's law.

B. Ul Haq et al. / Solar Energy Materials & Solar Cells 130 (2014) 6–1410

associated to the narrower electronic gap. The band gap narrowingfor higher dopant concentration reduces the separation betweenO-2p in V.B and Zn-4s states in C.B. Due to lower s/p separation inZB phase, the transition occurs at comparatively lower energies. Inprevious first principles studies with common exchange correla-tion potentials, these excitations were reported at significantlylower energies in ZnO [46] and Cd:ZnO [50]. However, thediscrepancy in our results with previous studies can be assignedto difference in the exchange correlation potential, as our calcu-lated energy gaps with mBJ potential is larger than GGA.

Second major structure is positioned at 12.83 eV (at 12.79 eV forZB), which is shifted to 11.25 (at 11.12 eV for ZB) when theCd dopant concentration reaches 3.75%. This structure can beassigned to the excitations between Zn-3d and O-2p states. Inaddition, a third major structure is located at 19.94 eV (at 19.85 eVfor ZB), and is due to optical excitations between Zn-3d and O-selectrons. These excitations move to higher energy as the Cd contentincreases. For 3.75% of Cd contents, the structure is shifted to 21.33 eV(at 21.21 eV for ZB). This might be attributed to a transfer of Zn-d bandinto deep valence band with higher Cd concentration.

Fig. 5. The electronic structures of Cd:ZnO in WZ and ZB geoetries determined with GGA and mBJ potentials.

Table 5The electronic band gap of Cd:ZnO in WZ and ZB geometries calculated with GGA and mBJ potentials.

Composition Eg(WZ) (eV) Eg(ZB) (eV)

GGA mBJ GGA mBJ

Zn15Cd1O16 0.736 2.57 0.63 2.45Zn14Cd2O16 0.585 2.44 0.54 2.40Zn13Cd3O16 0.525 2.29 0.45 2.29Zn12Cd4O16 0.423 2.22 0.40 2.19Zn11Cd5O16 0.336 2.16 0.30 2.15Zn10Cd6O16 0.189 2.04 0.16 2.06

Fig. 6. The variation in the energy gap Cd:ZnO in WZ and ZB geometries detemined with GGA and mBJ potentials.

B. Ul Haq et al. / Solar Energy Materials & Solar Cells 130 (2014) 6–14 11

To investigate the optical band gap in the presence ofCd dopants, we calculated the absorption spectra of Cd:ZnO. Inconjunction to the energy gap narrowing, the optical gapdecreases as a function of Cd content. The features of the absorp-tion coefficient for various Cd concentrations are the same ratherthan shrinkage in the optical energy gap (see Fig. 9). The reductionin optical gap leads to a red-shift in the absorption edge, whichagrees with previous predictions [17,49]. This feature is similar forboth cubic and hexagonal phases. Our computed optical gap isnarrower than the experimental results [17]. This could be due tothe underestimated band gap within DFT. Optical gap decreasesfrom 2.72 eV for Zn15Cd1O16 to 2.28 eV (2.61 eV to 2.37 eV for ZB)Zn10Cd6O16, which agrees well with previous calculations[19,24,50]. Thus absorption spectra reveal a large absorptionresponse in Cd:ZnO for photon energies equivalent to or above

the energy band gap. Minor absorption below the optical gap canbe linked with the absorption of free carriers.

We further investigated the optical parameters such as energyloss function (L(ω)) of Cd:ZnO, which is the measure of the energyloss by fast moving electrons while traversing in ZnO in thepresence of Cd impurity. The structure in the L(ω) shown inFig. 10 is associated to the plasma resonance at plasma frequency.It is characterized by the transformation of Cd:ZnO from metalliccharacter to an insulating dielectric. Major peak in L(ω) appears at23.11 eV (at 21.49 for ZB). In the presence of Cd atoms, this peakappears at higher energy compared to our previous first principlesand other experimental results [46,54] for pure ZnO. Fig. 10 showsthat the major peak in the WZ phase is blue-shifted compared tothe ZB phase and is positioned at 23.30 eV (at 21.83 eV in ZB),agreeing well with the previous calculations [50].

The application of Cd:ZnO in optoelectronic devices requiresinvestigation of the refraction spectra R(ω). R(ω) spectra of Cd:ZnOhas been depicted in the inset of Fig. 10. The static refractiveindices of Cd:ZnO, listed in Table 8, decreases as the Cd contentincreases, and can be associated to the band gap narrowing withincrease of the Cd concentration. The refractive indices of the ZBphase are smaller than in the WZ phase due to its narrower gap.The refraction spectra reveal no significant variation for visible andnear infrared wavelength, reflecting the optical stability of thesematerials. The lower value of the refractive indices can beattributed to the abrupt absorption in the ultraviolet energyregime. Such characteristics of Cd:ZnO make it desirable for PV

Table 6The V.B width, Cd d-band width and binding energies of Zn 3d-electrons calculatedwith mBJ potentials.

Composition V.B width (eV) Cd d-band width(eV)

Binding energy (eV) of Zn3d-electrons

WZ ZB WZ ZB WZ ZB

Zn15Cd1O16 �7.258 �6.878 0.544 0.699 �3.784 �3.735Zn14Cd2O16 �7.382 �6.966 0.860 0.783 �3.860 �3.788Zn13Cd3O16 �7.500 �7.311 0.954 1.130 �4.081 �3.861Zn12Cd4O16 �7.750 �7.415 1.234 1.384 �4.227 �3.926Zn11Cd5O16 �7.930 �7.724 1.486 1.606 �4.863 �4.227Zn10Cd6O16 �8.210 �7.754 1.567 1.720 �4.983 �4.811

Table 7The energy gap bowing parameters calculated with GGA and mBJ potentials.

Energy gap bowing WZ ZB

GGA mBJ GGA mBJ

bVD �0.15 �0.074 �0.332 �0.188bCE �1.452 �1.058 �3.568 �2.892bSR �0.264 �0.436 0.276 0.176b �1.866 �1.568 �3.624 �2.904

Fig. 7. The DOS of Cd:ZnO at 0.625% of Cd contents in WZ and ZB geometries determined with mBJ potential.

Fig. 8. The complex dielectric function of Cd:ZnO for 6.25% of Cd in WZ and ZBgeometries.

B. Ul Haq et al. / Solar Energy Materials & Solar Cells 130 (2014) 6–1412

applications, including UV sensors, UV LEDs, and UV protectinglayers. The quality of the optical properties of Cd:ZnO can bemodified for devices necessity by varying the Cd concentration.

4. Conclusion

Two forms of Cd:ZnO (cubic and hexagonal phases) have beenstudied to examine a number of physical properties, includingstructural, thermodynamic, electronic, and optical properties viadensity functional theory (DFT) using the FP-LAPW method. mBJpotential approximation provides an energy gap in good agree-ment with experiment. Cubic Cd:ZnO is found equally stable to thehexagonal phase. Smaller values of the effective masses in WZ vsZB suggest a higher mobility and conductivity. The substitution ofZn by Cd has insignificant effect on the structural geometries,suggesting a high solubility of Cd in ZnO. Energy gap of ZnOnarrows in the presence of Cd dopants. This finding suggests thatthe band gap of Cd:ZnO can be efficiently tailored to reach thedesired efficiency for photovoltaic applications.

Acknowledgment

Authors (Bakhtiar Ul Haq and Rashid Ahmed) acknowledgefor the financial support of the Ministry of Education (MOE)/UniversitiTeknologi Malaysia (UTM) through Grant nos. Q.J130000.2526.02H89;R.J130000.7826.4F113 and Q.J130000.2526.04H14.

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Fig. 9. The absorption spectra of Cd:ZnO in WZ and ZB geometries determined with mBJ potential.

Fig. 10. The energy loss function of Cd:ZnO in WZ and ZB geometries have beenshown. The inset shows the Refraction spectra.

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