Bandgap bowing in Ta-W-O system for efficient solar energy conversion:Insights from density functional theory and X-ray diffractionRamy Nashed, Faisal M. Alamgir, Seung Soon Jang, Yehea Ismail, Mostafa A. El-Sayed et al. Citation: Appl. Phys. Lett. 103, 133905 (2013); doi: 10.1063/1.4823543 View online: http://dx.doi.org/10.1063/1.4823543 View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v103/i13 Published by the AIP Publishing LLC. Additional information on Appl. Phys. Lett.Journal Homepage: http://apl.aip.org/ Journal Information: http://apl.aip.org/about/about_the_journal Top downloads: http://apl.aip.org/features/most_downloaded Information for Authors: http://apl.aip.org/authors

Bandgap bowing in Ta-W-O system for efficient solar energy conversion:Insights from density functional theory and X-ray diffraction

Ramy Nashed,1,2 Faisal M. Alamgir,3 Seung Soon Jang,3 Yehea Ismail,2

Mostafa A. El-Sayed,1 and Nageh K. Allam2,a)

1Laser Dynamics Laboratory, School of Chemistry and Biochemistry, Georgia Institute of Technology,Atlanta, Georgia 30332, USA2Energy Materials Laboratory, Physics Department, School of Sciences and Engineering,The American University in Cairo, New Cairo 11835, Egypt3School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA

(Received 25 May 2013; accepted 12 September 2013; published online 27 September 2013)

The electronic properties of Ta-W-O system have been studied using density functional theory

with PBE0 hybrid functional. The bandgap calculations showed a large and composition-dependent

bowing parameter. While the large bowing parameter at low W content (<25%) is related to the

charge exchange between the localized W 5d state and the extended states in the conduction band,

the volume change is considered the main reason for the large bowing parameter at high W content

(>25%). The electron excitation from the Ta2O5 valence band to WO3 conduction band at high W

content may contribute to the pronounced decrease in the conduction band energy. The staggered

bandgap type between Ta2O5 and WO3, as revealed from the energy band diagram, resulted in

efficient charge carriers’ separation. The minimum hole effective mass occurs along the y-direction

and decreases monotonically with increasing W content. Combining the wide tunability of bandgap

with the small effective mass, it is suggested that Ta-W-O alloys can replace the various

III-V materials for high efficiency solar cells as well as other optoelectronic devices. VC 2013AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4823543]

Hydrogen production by photoelectrochemical (PEC)

water splitting represents an attractive alternative to fossil

fuels as it is renewable, clean, and relatively cheap.1

However, the discovery of new semiconducting materials

and/or engineering the existing materials for commercially

viable PEC technology have been tremendously challeng-

ing.2 To this end, scientists tried to mix materials together,

in an attempt to develop new materials with enhanced PEC

performance. Density Functional Theory (DFT) is a power-

ful tool in this regard.3 Thimsen et al.4 provided an

approach, using Gradient Approximation of Perdew, Burke,

and Ernzerhof (GGA-PBE) functional, to predict the elec-

tronic band structure of mixed metal oxides by combining

DFT calculations with experiments. However, they were

unable to find a difference in the electronic structures of

TiFeO3, Ti-doped a-Fe2O3, and pristine a-Fe2O3, rendering

the study practically ineffective. Also, Huda et al.5 studied

the effect of doping WO3 with Mo using Local Density

Approximation (LDA) functional and showed that the band

structure is kept intact, a result contradicting experiments.6

The inability of GGA and LDA functionals to accurately

predict the band structure of materials stems from their

underestimation of the exchange-correlation energy

between electrons.7 To this end, hybrid functionals can

overcome this underestimation problem by incorporating a

certain fraction of the exact non-local Hartree-Fock

exchange. Using B3LYP hybrid functional, Wang et al.8

were able to reproduce the experimental data given in

Ref. 6 for Mo-doped WO3. Also, the use of PBE0 hybrid

functional enables the reduction in the bandgap calculation

error of Ta2O5 from 75% using GGA-PBE functional to

only 5%.9 For this reason, we base all the calculations of

the present work on hybrid functionals.

Doping Ta2O5 (�3.9 eV) with 5d materials, such as W,

is expected to red shift its absorption to the visible region

and guarantee high carrier mobility, due to the relatively

higher delocalization of 5d orbitals compared with the 3d

and 4d counterparts. Pristine WO3 is unfavorable for water

photolysis as its conduction band minimum is 0.4 eV more

positive than hydrogen evolution potential.10 Herein, we

studied the effect of increasing the W content on the

bandgap, structural properties, and the hole effective mass in

Ta-W-O system.

Figure 1 shows the band structure of pristine and

W-doped Ta2O5. For the 8.3%W case, the effect of W

appears as an impurity state near the conduction band.

However, as the W content increases, the band structure is

significantly modified and the conduction band edge moves

downwards, in agreement with the findings of Wang et al.8

The bandgap monotonically decreases from 3.53 eV in pris-

tine Ta2O5 to 2.77, 2.07, and 1.04 eV for 8.3%, 25%, and

50% of W content, respectively, which can be understood

from the density of states plotted in Figure 2. The valence

band maximum (VBM) is dominated by O 2p orbitals,

whereas the conduction band minimum (CBM) is dominated

by Ta 5d orbitals.9,11 Therefore, substituting Ta with W is

expected to modify the conduction band (CB) while keeping

the valence band (VB) intact. Figure 2(c) shows that the total

density of states of the doped Ta2O5 near the CBM agrees

very well with the partial density of states of W 5d shown

in Figure 2(d). This asserts that the reduction in the bandgap

a)Author to whom correspondence should be addressed. Electronic mail:

nageh.allam@aucegypt.edu

0003-6951/2013/103(13)/133905/5/$30.00 VC 2013 AIP Publishing LLC103, 133905-1

APPLIED PHYSICS LETTERS 103, 133905 (2013)

is due to the incorporation of W. The CBM is shifted down-

wards because W 5d orbital has lower energy than Ta 5d

orbital.3 Note that the energy of the VBM remains nearly

constant for all doped structures. However, its k-position

seems to shift towards point B as the W content increases.

The shift of the VBM towards B point is accompanied by a

lowering of the CB states at points B and X. This also sug-

gests another transition between the VBM and the CB state

at point B, which has a larger energy gap but lower momen-

tum change and hence high probability of transition.

FIG. 1. Band structure of (a) pristine

Ta2O5, (b) 8.3%W, (c) 25%W, and (d)

50%W-doped Ta2O5 under PBE0

calculations.

FIG. 2. (a) and (b) Partial and total

density of states in pristine Ta2O5, (c)

total density of states in pristine and

Ta-W-O, and (d) partial density of

states due to W 5d for different Ta-W-

O alloys.

133905-2 Nashed et al. Appl. Phys. Lett. 103, 133905 (2013)

The change in the VBM and CBM positions upon the

incorporation of W results in the formation of indirect

bandgap. The material becomes highly indirect upon the

addition of a small amount of W, with the phonon momen-

tum, required for the electron excitation, increasing by more

than six times at 8.3% W compared with pristine Ta2O5.

However, as the W content increases, the material becomes

less indirect, returning to its initial state at 50% W. Table SI

(in the supporting information12) and Figure 3 summarize

the effect of W content on the band structure of Ta2O5. Both

the bandgap and the phonon momentum decrease with

increasing the W content. Although the electronic transition

between VBM and CBM is highly indirect at 25% W, there

exists another possible transition between VBM and point B

in the CB. This transition is more direct and hence have

larger absorption coefficient, requiring a phonon momentum

of 0.75 nm�1, which is 35% less in momentum than that

required for the transition between VBM and CBM, with a

photon energy of around 2.4 eV that is still very close to the

optimum value.

In conventional mixed metal oxide systems, the bandgap

decreases till it reaches the value of the constituent metal ox-

ide with the lower bandgap. However, Figure 3(a) shows that

at W content greater than 17%, the bandgap of the Ta-W-O

system falls below 2.4 eV (the bandgap of pristine WO3).

This phenomenon can be understood from the expression for

the bandgap of any semiconductor alloy, AxB1�x, where the

alloy bandgap can be determined as the weighted average of

its components14

EABg ðxÞ ¼ xEA

g þ ð1� xÞEBg (1)

where x denotes composition, EABg is the bandgap of the

alloy, EAg and EB

g are the bandgaps of components A and B,

respectively. However, some semiconductor alloys deviate

from such linear relationship to have a quadratic form15

DEABg ðxÞ ¼ bxðx� 1Þ (2)

where b is known as the bowing parameter and is generally

composition independent. It is thought that the bowing

parameter is originated from three distinct physical contribu-

tions: (i) volume change due to the change in the lattice

constants of the alloy constituents when they form the alloy;

(ii) charge exchange occurring when a highly electronegative

atom substitutes a less electronegative atom, which creates

localized energy levels close to the CBM that interacts with

the extended states and lowers the conduction band; (iii)

structural relaxation due to the relaxation of the cation-anion

bond lengths in the alloy.14,15

Using Eqs. (1) and (2) and the data given in Figure 3,

the calculated bowing parameter for Ta-W-O system shows

a very large and composition dependent bowing parameter

of �8.6, �6.1, and �7.7 for the materials containing 8.3%

W, 25% W, and 50% W, respectively. A similar phenom-

enon was reported for GaAsN alloys.15 While for GaAsN

system the bowing parameter monotonically decreased with

increasing N concentration, for Ta-W-O system, the bowing

parameter shows a minimum value at �25% of W content

before it increases again at 50% W. In the GaAsN system,

the bowing parameter decreases with increasing the N con-

tent because the N 2p orbital is merged with the extended

states in the CB at higher N concentration and thus it is no

longer localized. Therefore, the charge exchange effect is no

longer valid. This suggests that for Ta-W-O system, there

would be different mechanisms causing the bowing parame-

ter at different W contents. We believe at 8.3%W, the domi-

nant contribution to the bowing parameter is charge

exchange, similar to GaAsN system. This is asserted by

Figure 1(b), which shows a localized W 5d state close to the

extended states that strengthens charge exchange. Also, the

band structure for 8.3%W is significantly different from pris-

tine Ta2O5 (Figures 1(a) and 1(b)) where the bandgap

becomes considerably indirect indicating a strong interaction

between W and Ta2O5 orbitals. At 25% W, the bowing pa-

rameter is still high but it is less than the 8.3% W case, indi-

cating that the contribution of charge exchange is reduced,

as confirmed by the decreased phonon momentum closer to

that of pristine Ta2O5. For 50%W, the indirect bandgap is

exactly the same as pristine Ta2O5, which infers a minimum

interaction between W and Ta2O5 orbitals. However, the

bowing parameter for 50% W is higher than its 25% W coun-

terpart, indicating another mechanism. At this high W con-

tent, the W atoms tend to cause volume change in the crystal

lattice due to the different ionic radii of Ta2O5 and WO3 as

observed via the X-Ray Diffraction (XRD) investigation

(Figure 4(a)). The peak positions and their corresponding d-

spacing for pure Ta2O5 as well as 2.5%W and 10%W alloys

are given in Table SII.12 As the W content increases, the

XRD peaks are consistently shifted towards lower 2H values

for peaks II and III, whereas it remains almost constant

for peak I, indicating the lattice expansion upon the addition

of W. From the (h,k,l) values and their corresponding

d-spacing, the lattice parameters were determined at each

d-value simultaneously. The lattice parameters for pristine

Ta2O5 are a¼ 6.42 A�, b¼ 3.78 A�, and c¼ 3.48 A�, whereas

they are a¼ 6.46 A�, b¼ 3.82 A�, c¼ 3.52 A�, and

a¼ 6.45 A�, b¼ 3.85 A�, c¼ 3.53 A�, for 2.5%W and 10%W

alloys, respectively. This shows a lattice expansion in a- and

b-directions and a volume expansion by 2.9% and 3.8% for

2.5%W and 10%W alloys, respectively. Moreover, this indi-

cates that W is preferably incorporated in planes that have

projections in yz- and/or xz-planes, such as (100), (010),FIG. 3. The bandgap (diamond) and phonon momentum (circle) required for

electron transition in Ta-W-O system as a function of W content.

133905-3 Nashed et al. Appl. Phys. Lett. 103, 133905 (2013)

(110), and (101). This is very useful in designing more effi-

cient one-dimensional (1D) photoanodes for solar water

splitting, where the charge separation occurs perpendicular

to the light absorption direction.16 Therefore, the 1D struc-

tures should be oriented such that the W-containing planes

are aligned perpendicular to light absorption.

Furthermore, we believe that with W content of 10% or

greater, small precipitation of WO3-rich phases may start

forming within the matrix of the (Ta,W)2O5, leading to

micro-scale heterojunctions. This is asserted by the peak

shoulder in Figure 4(c) occurring at 2H¼ 53�, which corre-

sponds to (331) plane of WO3.17 A similar phenomenon was

reported for Ti-Fe-O system,18 with a maximum reported ef-

ficiency of only 1.2% under Air Mass (AM) 1.5 illumination

at 0.7 V bias. This modest efficiency can be understood from

Figure 5(a), where the bandgap of TiO2 brackets that of

Fe2O3 (straddling bandgap). Upon illumination, an electron

is excited from the VB of Fe2O3 to its CB. Due to the band

bending, the excited electrons are imposed to move leftwards

where they get trapped and afterwards recombine with a pho-

togenerated hole and hence decreasing the total current. To

assess the efficiency of the Ta-W-O system, we compare it

to the Ti-Fe-O system, see Figure 5(b). The position of the

CBM of WO3 occurs in the bandgap of Ta2O5 leading to a

staggered bandgap configuration. Upon illumination, an

electron may be excited from the VB of Ta2O5 to the CB of

WO3 and hence decreasing the energy required for the elec-

tron excitation. Figure 5(b) also shows that there is an energy

barrier for both excited holes and electrons, imposing holes,

and electrons to move in opposite directions and hence maxi-

mizing the total current. Based on this comparison, Ta-W-O

may be considered as an efficient alternative photoanode ma-

terial in water splitting systems or as the active layer in solar

cells.

Although the band structure calculations using GGA-

PBE functional underestimate the bandgap of systems with

strongly correlated electrons, they can still give a qualitative

estimation of the effective mass because the effective mass

depends on the curvature of the VBM and CBM rather than

on their absolute values. Figure S212 shows the band struc-

tures using GGA-PBE functional, asserting the fact that

VBM and CBM still preserve their curvature under GGA

calculations. Herein, we consider the effective mass of holes

only because the water splitting device is a minority carrier

device and the Ta-W-O system is an n-type semiconductor.

A low effective mass is a desirable property providing a high

charge carrier mobility and a high solar-to-hydrogen conver-

sion efficiency.13

The procedure used to calculate the effective mass is

given in the supplementary information.12 The numbers for

PBE0 and GGA-PBE show the same trend (Table SIII12),

with the effective mass showing an anisotropic direction

dependency. The smallest value is in the y-direction, the

direction perpendicular to the (010) plane in the crystal lat-

tice, which is the most favorable direction for the hole trans-

port. As the W content increases, the effective mass in the

FIG. 4. X-ray diffraction (XRD) pat-

terns of pristine Ta2O5, 2.5%W, and

10%W.

FIG. 5. Energy band diagrams of

(a) Ti-Fe-O and (b) Ta-W-O illustrat-

ing the charge carrier transport for

both systems.

133905-4 Nashed et al. Appl. Phys. Lett. 103, 133905 (2013)

y-direction becomes smaller compared with other directions,

making the hole transport in the y-direction more favorable.

The monotonic decrease in the effective mass as a function

of the W content can be attributed to the delocalization of

the W electron energy levels. At 25% and 50% of W con-

tents, the effective mass in the y-direction is approximately

0.5 me and 0.25 me, respectively, where me is the electron

rest mass. Note that the effective mass of holes in TiO2 is

0.8 6 0.2me.19 The comparable effective mass of holes in

Ta-W-O system to that in III-V semiconductors, and the high

dielectric constant of Ta2O5 ensure a higher diffusion

length.20 A large diffusion length indicates less recombina-

tion of charge carriers, resulting in higher overall conversion

efficiency. This suggests that Ta-W-O alloys can be an

excellent candidate in hydrogen production systems and

replacing expensive III-V semiconductors17 for high effi-

ciency solar cells.

In conclusion, we demonstrate that Ta-W-O alloys have

widely tunable bandgaps from 3.7 eV to 1 eV. The bandgap

monotonically decreases with increasing W content, showing

a large composition-dependent bowing parameter. At low W

content, a high bowing parameter of �8.6 originates from

charge exchange due to the interaction of the localized elec-

tron energy level in W with the extended states of the CB.

The charge exchange decreases with increasing W content

due to the merging of the delocalized electron energy level

in W with the extended states of the CB, decreasing the bow-

ing parameter to �6.1 at 25% of W content. At 50%W, the

bowing parameter increases again to �7.7 due to the volume

change as observed by XRD. At W content higher than 10%,

Ta2O5 and WO3 tend to form microscopic heterostructures

such that electrons are excited from the VB of Ta2O5 to the

CB of WO3. The created electron-hole pair is well extracted

due to the staggered bandgap nature of Ta-W-O alloy. The

effective mass of holes in pristine Ta2O5 as well as Ta-W-O

alloys has minimum value along the y-direction, which

decreases monotonically with increasing W content. At suffi-

ciently large W content (>25%), the effective mass is com-

parable with that of III-V semiconductors.

Based on our study, we recommend using 25% W sys-

tem as a photoanode for water splitting due to the staggered

bandgap effect. Furthermore, the hole effective mass at this

W content is half that of pristine Ta2O5 and TiO2, suggesting

a large hole mobility and hence a minimum carriers recombi-

nation. For solar cells, the 50% W system would be most

suitable. However, the practical feasibility of producing

alloys with such high content of mixing ratios needs to be

validated.

This research was partially funded by The American

University in Cairo. F.M.A. would like to acknowledge the

support of the American Chemical Society’s Petroleum

Research Fund Grant No. 50934-DNI10. M.A.E. acknowl-

edges the financial support from DOE Grant No. DE-FG02-

97ER14799.

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