Theory of Carbon Doping of Titanium Dioxide

Theory of Carbon Doping of Titanium Dioxide

Cristiana Di Valentin,*,†,‡ Gianfranco Pacchioni,† and Annabella Selloni‡

Dipartimento di Scienza dei Materiali, UniVersita di Milano-Bicocca, Via R. Cozzi 53, 20125 Milano,Italy, and Department of Chemistry, Princeton UniVersity, Princeton, New Jersey 08540

ReceiVed August 25, 2005. ReVised Manuscript ReceiVed October 26, 2005

Recent experimental studies have determined that carbon doping dramatically improves the photocatalyticactivity of TiO2 in the visible-light region. Using density functional theory (DFT) calculations within thegeneralized gradient corrected approximation, we investigate various structural models of carbon impuritiesin both the anatase and rutile polymorphs of TiO2 and analyze the associated modifications of the electronicband structure. We compare the stability of all these diverse species on the basis of their energy offormation as a function of the oxygen chemical potential, which determines whether the system is in anoxidizing or reducing environment. At low carbon concentrations, we find that, under oxygen-poorconditions, substitutional (to oxygen) carbon and oxygen vacancies are favored, whereas, under oxygen-rich conditions, interstitial and substitutional (to Ti) C atoms are preferred. Higher carbon concentrationsundergo an unexpected stabilization caused by multidoping effects, interpreted as inter-species redoxprocesses. Carbon impurities result in modest variations of the band gap but induce several localizedoccupied states in the gap, which may account for the experimentally observed red shift of the absorptionedge toward the visible. Our results also indicate that carbon doping may favor the formation of oxygenvacancies in bulk TiO2.

1. Introduction

The doping of TiO2 is currently attracting considerableinterest as a promising route to extend the optical absorptionof this material to the visible spectral region.1 This wouldallow the use of sunlight in photochemistry and photo-catalysis, with important and beneficial fallout on theenvironment and economy. Doping with nonmetal atoms2,3

has been determined to be more effective than transition-metal doping,4,5 which has the drawback of yielding sampleswith poor photostability. Among nonmetal elements, nitrogenhas been extensively studied in the past few years.2,6 Avariety of nitrogen-doped TiO2 powders,2,6a-c films,2,6e

nanoparticles,6f and single crystals6d have been synthesized,and the photoactivity and photochemical properties of thesesamples have been investigated.2,6 Theoretical studies havebeen performed to clarify the origin of the observed red shiftof the optical absorption edge. In particular, our recent

calculations7,8 provide evidence that nitrogen impuritiesinduce localized electronic states lying just above the O 2pvalence band, in agreement with several experimentalresults.6b,9-11

Carbon-doped TiO2 has not received the same attention,even though a carbon-doped powder recently was determinedto be five times more active than nitrogen-doped titaniumdioxide in the degradation of 4-chlorophenol by artificial light(λ g 455 nm).12 Various experimental studies report carbon-doped TiO2 absorption properties in the visible spectrum.In particular, two works3,12have commented on the presenceof two optical absorption thresholds, one in the ultraviolet(UV) region (at∼3.0 eV) and one in the visible region (at∼2.0 eV). Carbon impurities in TiO2 might induce new andunexpected features, with respect to nitrogen doping. Nitro-gen is definitely more similar to oxygen, and, except for afew cases where the presence of interstitial nitrogen specieswas proposed,6a,b,8,13it is generally found in substitutionalposition in TiO2. Carbon-doped anatase powders,12,14-16 rutilefilms,3 and nanostructured films17 have been obtained through

* Author to whom correspondence should be addressed. Tel.: 39-02-6448-5235. Fax: 39-02-6448-5400. E-mail: [email protected].

† Dipartimento di Scienza dei Materiali, Universita` di Milano-Bicocca.‡ Department of Chemistry, Princeton University.

(1) Kisch, H.; Macyk, W.ChemPhysChem2002, 3, 399.(2) Asahi, R.; Morikawa, T.; Ohwaki, T.; Aoki, K.; Taga, Y.Science2001,

293, 269.(3) Khan, S. U. M.; Al-Shahry, M.; Ingler, W. B., Jr.Science2002, 297,

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(7) Di Valentin, C.; Pacchioni, G.; Selloni, A.Phys. ReV. B 2004, 70,085116.

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2005, 498.(14) Choi, Y.; Umebayashi, T.; Yoshikawa, M.J. Mater. Sci.2004, 39,

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T.; Nishijima, K.; Miyamoto, Z.; Majima, T.J. Phys. Chem. B2004,108, 19299.

6656 Chem. Mater.2005,17, 6656-6665

10.1021/cm051921h CCC: $30.25 © 2005 American Chemical SocietyPublished on Web 11/25/2005

different synthetic routes. Correspondingly, different inter-pretations of the nature of the carbon doping species havebeen proposed. On the basis of X-ray photoelectron (XPS)and infrared (IR) spectroscopies, either substitutional carbon(replacing oxygen)3,14,17-19 or carbonate species12,15,16havebeen suggested, with the oxidation state of the C atomranging from being negative in the substitutional form tobeing highly positive in the carbonate species. The valenceshell of the C atom contains four electrons (2s2 2p2), as doesthe Ti atom (4s2 3d2), but can also host up to four excesselectrons, as is formally the case in TiC. Thus, the most basicquestion about the character of carbon impurities, i.e.,whether carbon is oxidized or reduced when introduced in aTiO2 matrix, is still open.

To address this question, in the present work, we usedensity functional theory (DFT) calculations within thegeneralized gradient approximation (GGA) to study variouspossible carbon doping species in both the anatase and rutilepolymorphs of TiO2. We examine carbon substituting eitherO or Ti atoms, or lying in interstitial TiO2 positions andconsider various carbon concentrations, to account forpossible multi-atom doping effects. Also, we investigate theinterplay between carbon impurities and oxygen vacancies,because this may result in interesting and unexpectedconsequences.16 The stability of all these diverse species hasbeen compared on the basis of their energy of formation, asa function of the oxygen chemical potential, which deter-mines whether the system is in an oxidizing or reducingenvironment.

The nature of the carbon-induced modifications of the TiO2

electronic band structure is also controversial. Band gapnarrowing3,17or the formation of localized midgap states12,14,15

have been alternatively proposed. To obtain insight into thisissue, we have performed a careful analysis of the carbonimpurity states and their influence on the TiO2 band structure.Our results indicate that localized gap states are indeedformed, the character and density of which are dependenton both the concentration of doping C atoms and the oxygenpressure/temperature conditions during preparation.

2. Computational Details

DFT calculations have been performed using theν-ESPRESSOpackage,20 within the plane-wave-pseudo-potential approach, to-gether with the Perdew-Burke-Ernzerhof (PBE)21 exchange-correlation functional and ultrasoft pseudo-potentials22 (with kineticenergy cutoffs of 25 and 200 Ry for the smooth part of the electronicwave functions and augmented electron density, respectively). TheCar-Parrinello (CP) approach23,24was used for geometry optimiza-tions, with the Brillouin zone sampling limited to theΓ point,whereas the PWSCF code20 was used to perform calculations at alow-symmetry k-point, to obtain the electronic band structure,accurate reaction energies, and the density maps for the electronicstates. The computational setup is the same as that used in ref 7.To model the doped material, we considered almost cubic 2x2 ×2x2 × 1 and 2 × 2 × 3 supercells for anatase and rutile,respectively (see Figure 1). The optimized bulk lattice parametersare taken from previous calculations, in which the same approxima-tions of this work were used.25 Various levels of substitutionalcarbon doping were modeled by replacing one or three O atoms inthe 96-atom anatase (72-atom rutile) cell. This corresponds to apercentage contribution in weight from 0.47% (0.63%) to 1.41%(1.89%) of carbon in anatase (rutile), comparable to those used insome of the experiments. The procedure of including more C atomsin the same supercell allows a more direct comparison of theinfluence of the doping concentration on the electronic bandstructure of the system. Interstitial doping was modeled by addingone C atom to the pure or substitutionally carbon-doped TiO2

supercells. The role of oxygen vacancies was investigated byremoving one O atom of the cell where substitutional or interstitialC atoms are present. Finally, we also performed calculations inwhich one Ti atom in the supercell was replaced by a C atom.Atomic relaxations were conducted, using second-order dampeddynamics until all components of the residual forces were<0.025eV/Å.

3. Results and Discussion

The anatase and rutile polymorphs of TiO2 (see Figure 1)exhibit several differences.26-28 From the structural point ofview, the main differences are that anatase is 9% less densethan rutile and is characterized by longer Ti-Ti distances;from the electronic structure point of view, anatase shows aslightly larger band gap (3.2 eV)29 than rutile (3.0 eV).30 Asusual, the band gaps are underestimated by DFT calculations,which give 2.19 eV (2.61 eV) and 1.81 eV (2.14 eV) atΓ (alow-symmetryk-point) for anatase and rutile, respectively.7

(16) Li, Y.; Hwang, D.-S.; Lee, N. H.; Kim, S.-J.Chem. Phys. Lett.2005,404, 25.

(17) Barborini, E.; Conti, A. M.; Kholmanov, I. N.; Miseri, P.; Podesta`,A.; Milani, P.; Cepek, C.; Sakho, O.; Macovez, R.; Sancrotti, M.AdV.Mater. 2005, 17, 1842.

(18) Wang, H.; Lewis, J. P.J. Phys.: Condens. Matter2005, 17, L209.(19) Lee, J.-Y.; Park, J.; Cho, J. H.Appl. Phys. Lett.2005, 87, 011904.

(20) Baroni, S.; Dal Corso, A.; de Gironcoli, S.; Giannozzi, P.; Cavazzoni,C.; Ballabio, G.; Scandolo, S.; Chiaretti, G.; Focher, P.; Pasquarello,A.; Laasonen, K.; Trave, A.; Car, R.; Marzari, N.; Kokalj, A. Plane-Wave Self-Consistent Field (PWscf), http://www.pwscf.org.

(21) Perdew, J. P.; Burke, K.; Ernzerhof, M.Phys. ReV. Lett. 1996, 77,3865.

(22) Vanderbilt, D.Phys. ReV. B 1990, 41, 7892.(23) Car, R.; Parrinello, M.Phys. ReV. Lett. 1985, 55, 2471.(24) Laasonen, K.; Pasquarello, A.; Car, R.; Lee, C.; Vanderbilt, D.Phys.

ReV. B 1993, 47, 10142.(25) Lazzeri, M.; Vittadini, A.; Selloni, A.Phys. ReV. B 2001, 63, 155409.(26) Asahi, R.; Taga, Y.; Mannstadt, W.; Freeman, A. J.Phys. ReV. B 2000,

61, 7459.(27) Muscat, J.; Swamy, V.; Harrison, N. M.Phys. ReV. B 2002, 65, 224112.(28) Woicik, J. C.; Nelson, E. J.; Kronik, L.; Jain, M.; Chelikowsky, J. R.;

Heskett, D.; Berman, L. E.; Herman, G. S.Phys. ReV. Lett.2002, 89,077401.

(29) Tang, H.; Berger, H.; Schmid, P. E.; Le´vy, F.; Burri, G.Solid StateCommun.1977, 23, 161.

(30) Henrich, V. H.; Kurtz, R. L.Phys. ReV. B 1981, 23, 6280.

Figure 1. Supercell models for bulk anatase (96 atoms) and rutile (72atoms) used in all the calculations of this work. The yellow and small brownspheres represent O and Ti atoms, respectively.

Theory of Carbon Doping of Titanium Dioxide Chem. Mater., Vol. 17, No. 26, 20056657

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A different behavior of the two phases upon doping with Natoms has been also observed.7 Therefore, in the following,anatase and rutile will be analyzed and discussed separately.

3.1. Anatase.3.1.1. Model Structures for Carbon Dopingand RelatiVe Stability.In principle, there are three possibleways to include C atoms into the lattice. The first one is toreplace a lattice oxygen with a carbon; the second is toreplace a Ti atom with a C atom. Both these mechanismsimply the rupture of Ti-O bonds that must be replaced byTi-C or by C-O bonds. The third possibility is that carbonis stabilized at an interstitial position. Given the relativelysmall size of the C atom, this may occur without inducingtoo much strain in the structure. The relative stability of thesediverse species varies as a function of the oxygen chemicalpotential (µO), which is a parameter that characterizes theoxygen environment during synthesis. The environment actsas a reservoir, which can give or take any amount of oxygenwithout changing its temperature and pressure.31,32Oxygen-poor conditions correspond to a low value ofµO, and,conversely, oxygen-rich conditions correspond to a highvalue ofµO. By referencingµO to the energy of an O atomin the O2 molecule (µO ) 1/2µ(O2) + µ′O), we take-4 eV eµ′O e 0, where the valueµ′O ) 0 corresponds to the oxygen-rich limit at which oxygen condensation will occur,31,32

whereasµ′O ) -4 eV is approximately one-half the en-thalpy of formation of anatase TiO2 (computed as 9.25 eVwith the present computational setup, to be compared to theexperimental value of 9.8 eV).33 In Figure 2 we report theenergies of formation of all the carbon-doped models

considered in this work as a function ofµ′O, according tothe formula

wheren is the number of C atoms andm is the number ofoxygen vacancies per supercell in the model considered. Forcarbon, we use a fixed value of the chemical potentialµC,and take the value at which the formation energy of CO2 iszero: µC ) µ(CO2) - µ(O2). The calculations in thefollowing assume that CO2 is an independent reservoir, notin equilibrium with O2.32 However, this is not a crucialassumption, because the relative stability of the differentspecies is observed to remain the same if CO2 and O2 areconsidered to be in equilibrium. Also, to translate the rangeof µO considered into a more usual measure of oxygenconcentration, we convertedµ′O to oxygen pressure at afixed temperature of 700 K (topx-axis),31 the typicalannealing temperature used for anatase carbon-doped TiO2.Note that theµO values of<2 eV correspond to oxygenpartial pressures that cannot be reached experimentally.

We start by analyzing low carbon concentrations, corre-sponding to a single carbon impurity per supercell. Weconsidered five different models, which are identified by fivelines in the stability diagram of Figure 2: black, red, blue,green, and magenta. The black line represents the formationenergy (Eform) for the species in which one O atom is replacedby one C atom (CS-O) in the anatase supercell (see Figure3a). For this species,Eform increases asµO increases (positiveslope), indicating that oxygen-poor conditions are morefavorable for implanting substitutional carbon. This substitu-tion leads to significantly longer (and, thus, weaker) Ti-Cbonds (2.008 and 2.217 Å), with respect to the original Ti-Obonds (1.942 and 2.002 Å), as indicated in Table 1. In thissubstitutional configuration, the C atom is reduced. This isconfirmed by the population analysis of the C 2p states,which become more populated (see also below).

The addition of one C atom in an interstitial position ofthe 96-atom anatase supercell (CI) results in the formation

(31) Reuter, K.; Scheffler, M.Phys. ReV. B 2001, 65, 035406.(32) Reuter, K.; Scheffler, M.Phys. ReV. B 2003, 68, 045407.(33) Lide, D. R., Ed.CRC Handbook of Chemistry and Physics; CRC

Press: Boca Raton, FL, 2000.

Figure 2. Formation energies (Eform, in eV) as a function of the oxygenchemical potential (µO) or asa function of the oxygen pressure at fixedtemperature (T ) 700 K) (topx-axis) for different carbon species in anatase.

Figure 3. Partial geometry of the models for (a) one substitutional C atomto O (CS-O), (b) one substitutional C atom to Ti (CS-Ti), (c) one interstitialC atom (CI), and (d) one interstitial C atom nearby an oxygen vacancy (CI

+ VO) in the anatase TiO2 supercell reported in Figure 1. The yellow spheresrepresent O atoms, the small brown spheres represent Ti atoms, and theblack sphere represents the carbon impurity.

Eform ) 1nEtot(C-doped)- 1

n[Etot(Pure)+ nµC - mµO]

6658 Chem. Mater., Vol. 17, No. 26, 2005 Di Valentin et al.



of three C-O bonds that involve the carbon dopant and threelattice oxygens (see Figure 3c). In this configuration, carbonis formally oxidized and forms strong covalent bonds withthe O atoms, as indicated by the electronic states analysis(see below). The C-O distances are in the range of 1.416-1.432 Å (see Table 1). The formation energy of CI (the redline in Figure 2) shows no dependence onµO. Thus, underoxygen-rich conditions, interstitial carbon becomes morestable than any oxygen-substitutional (S-O) species.

To transform CS-O to CI, we can imagine the displacementof a C atom occupying a lattice oxygen position (substitu-tional) to an interstitial position and, at the same time, fillthe oxygen vacancy that is formed with an O atom. Thisformally corresponds to an oxidation reaction, which mayoccur under oxygen-rich conditions (µ′O f 0). The processis exothermic:

Direct comparison of the stability of substitutional andinterstitial carbon dopants can be achieved by consideringtwo systems with the same stoichiometry: the substitutionalmodel (Figure 3a) and a model in which the displacementof one C atom to the interstitial position leaves a vacantoxygen site (CI + VO in Figure 3d). The new species is aninterstitial C atom bound to only two lattice O atoms (C-Obond lengths are 1.394 Å); the third O-site being vacant.This configuration is 0.4 eV more stable than the substitu-tional one over the entire range ofµO considered (the blueline versus the black line in Figure 2). This indicates thatthere is a remarkable preference for carbon to be oxidizedin anatase, by binding to O lattice ions, rather than beingreduced by binding to Ti lattice ions. This is caused by thefact that the C-O bonds are stronger than the C-Ti bonds.However, under oxygen-poor conditions, a substitutionalcarbon species may be stabilized by excess electrons broughtby a lattice oxygen vacancy (CS-O + VO), as indicated bythe larger slope of the green line in Figure 2, with respect tothe black line for CS-O. At very low values ofµ′O, the CS-O

+ VO species (the green line in Figure 2) is even more stablethan the interstitial CI species (the red line in Figure 2). Theobservable structural consequence of this stabilization is theshortening of the Ti-C bond lengths from 2.008 Å to 2.217Å to 1.926-1.957 Å. Thus, according to the specific

stoichiometry of the TiO2 sample, substitutional or interstitialcarbon species may be present in different amounts. Areduced TiO2 sample, rich in oxygen vacancies, can favorthe inclusion of carbon in positions normally occupied bylattice oxygens (substitutional); a stoichiometric TiO2 sample,obtained in an oxidizing environment, favors the inclusionof C atoms in interstitial positions.

We also considered the possibility that a C atom replacesone Ti atom (CS-Ti in Figure 3b). This does not change thevalence electron counting, because the two atoms areisovalent. However, although the number of valence electronsis the same, the possibility for Ti atom to hybridize the 3d,4s, and 4p orbitals leads to different coordination numbers.In particular, while the Ti atom is six-coordinated in anatase,we found that substitutional C is four-coordinated, which isusual for this atom. This causes a strong distortion of theanatase structure: the carbon impurity assumes a tetrahedralgeometry, where the C-O bonds are much shorter than theTi-O bonds (see Table 1). The two remaining O atoms,which were 3-fold coordinated before substitution, reducetheir coordination to two. The oxidation state of the C atomis positive, because it is replacing a Ti atom and formallydonates the four electrons to the lattice oxygens (actuallythe bond is partly covalent). To calculate the formationenergy of the CS-Ti species, we assumed the system to be inthermodynamic equilibrium not only with a reservoir ofoxygen, as in all previous cases, but also with a reservoir ofbulk TiO2 (in practice, this corresponds to assuming the Tichemical potential to beµTi ) µTiO2 - 2µO).31,32Within theseideal conditions, CS-Ti seems to be very stable, under oxygen-rich conditions. A similar conclusion is also observed whena somewhat different approach (see ref 34) is used tocalculate the formation energies of impurities, in whichµTi

and µO are treated on similar footing. With respect to thelatter approach, the one used in the present paper seems toprovide a theoretical picture that is more similar to theexperimental procedure: we consider CO2 as the carbonsource and we investigate defect stability as a function ofoxygen content in the atmosphere under working conditions.

3.1.2. Higher Carbon Concentration.Higher dopantconcentrations have been modeled by substituting threelattice O atoms of the 96-atom anatase supercell with threeC atoms (see Figure 4). Their positions have been chosen tobe as far apart as possible, to avoid any clustering of the Catoms. Indeed, we have found that when two C atoms aresitting in two neighboring lattice positions, they have atendency to form direct multiple bonds, leading to a verystable complex. Because no experimental evidence for suchcarbon species is available, we did not consider it any further,and, instead, tried to avoid the formation of direct C-Cbonds by keeping the C atoms in the unit cell as separatedas possible.

When three substitutional C atoms are initially present inthe anatase supercell (corresponding to an impurity concen-tration of 3%), important rearrangements occur during thestructural relaxation. Although two C atoms preserve theinitial substitutional character (CS-O) and remain bound to

(34) Northrup, J. E.; Zhang, S. B.Phys. ReV. B 1993, 47, 6791.

Table 1. Bond Lengths in Carbon-Doped Anatase TiO2a

bond length (Å)C-dopedTiO2 Ti-Ceq

b Ti-Caxc C-O1 C-O2 C-O3 C-O4

CS-O 2.008 2.217CI 2.228 1.416 1.417 1.432CI + VO 2.168 1.394 1.394CS-O + VO 1.926 1.936 1.957CS-Ti 1.393 1.394 1.451 1.4513C

CS-O 1.876 1.899 1.919CS-O 1.932 1.949 1.915CI + VO 2.878 1.284 1.308CS-O 1.889 1.871 1.917CS-O 1.938 1.935 1.919CI 2.977 1.275 1.290 1.320

a In pure TiO2: Ti-Oeq ) 1.942 Å and Ti-Oax ) 2.002 Å.b EquatorialTi-C bond.c Axial Ti-C bond.

TiO2-xCx(s) + x2O2(g) f TiO2Cx(s) (∆E ) -3.8 eV)


Ti atoms, the third C atom is displaced from the substitutionalposition and binds to two neighboring O atoms, forming a(CO2)n- species. This results in the formation of an interstitialcarbon and an oxygen vacancy, (CI + VO), confirming thatC prefers to bind to lattice oxygens rather than to titanium.The 2CS-O + CI + VO complex is more stable than the singlesubstitutional CS-O impurity (the brown line versus the blackline in Figure 2). This multi-atom effect is effective instabilizing substitutional species under oxygen-poor condi-tions, but it is not sufficient under oxygen-rich conditions,where interstitial C impurities are still favored (see the redline in Figure 2).

The bond lengths of the new complex provide insight intothe nature of the binding. The Ti-C bonds of the twosubstitutional species are quite short (see Table 1), muchshorter than for one isolated substitutional carbon, and evenshorter than the original Ti-O distance of pure anatase. TheC-O bond lengths formed by the third interstitial C atom(1.284-1.308 Å) are much shorter than those of theinterstitial C atom in the presence of a neighboring oxygenvacancy (1.394 Å). This suggests that the two substitutionalC atoms are reduced by excess electrons that originate fromthe third C atom, which is concomitantly oxidized in theinterstitial position. This redox process can explain theremarkable shortening of the Ti-C bonds for the substitu-tional species and the formation of an interstitial carbonspecies. The tendency of the carbon species to be oxidizedwhen implanted in the anatase TiO2 matrix becomes thedriving force for the formation of stable reduced substitu-tional CS-O species. The oxygen vacancy, which is left behindafter the displacement of the C atom from the substitutionalsite to the interstitial site, does not seem to have any signifi-cant role in this process. Indeed, we have also performed acalculation in which this vacancy is healed by adding anextra O atom and the interstitial C is bound to three latticeoxygens (CI). This corresponds to a sample where two Catoms are substituting for lattice oxygens, and one is inter-stitial. The effect on the structural parameters is negligible,suggesting that the redox process is not related to theformation of the oxygen vacancy but is only determined bythe simultaneous presence of substitutional and interstitialC atoms. However, healing the oxygen vacancy with an extraO atom, from 2CS-O + CI + VO to 2CS-O + CI, produces a

stabilization whose extent is a function of the oxygenconcentration (compare the orange line to the brown line inFigure 2), going from roughly zero at very lowµO to ∼1 eVunder oxygen-rich conditions (µ′O ) 0).

3.1.3. Oxygen Vacancies in the Presence of CarbonDoping.The effect of carbon doping on the formation energyof oxygen vacancies is illustrated by the following reactions:

The first of these reactions represents the formation of anoxygen vacancy in undoped TiO2. With our supercell, thecorresponding energy (computed with respect to1/2O2) isEf_Vo ) 4.2 eV. In the presence of interstitial carbon (secondreaction), the same process costs 3.4 eV: this is the sum ofthe energies needed to break both the C-O and Ti-O bonds.Even more remarkable, the presence of substitutional carbon(third reaction) reducesEf_Vo to 1.9 eV, which is less thanhalf the value computed for the nondefective bulk oxide.This effect might be ascribed to the tendency of substitutionalC atoms to accept excess electrons from the oxygen vacancy.This means that substitutional carbon is a deep electron trapthat competes with the Ti 3d states to accommodate extracharge generated by doping (e.g., via the addition of alkalimetals) or by the formation of substoichiometric oxides.

3.1.4. Electronic Band Structure.The carbon-inducedchanges on the band structure are summarized in Scheme 1.The calculations refer to a low-symmetryk-point. Onesubstitutional C atom (CS-O in Figure 3a) produces twooccupied and one empty localized states in the semiconductorband gap. Notice that this is unaffected by the doping process(2.59 vs 2.61 eV in undoped bulk anatase TiO2). The gapstates lie 0.7, 1.1, and 1.8 eV above the top of the O 2pvalence band and can be assigned to the C 2p states.

Interstitial carbon (CI in Figure 3c) induces more complexfeatures. In addition to the C 2s state, there are three bondingC-O states that lie below the bottom of the O 2p valenceband. The corresponding antibonding C-O states are veryhigh in energy and fall within the TiO2 conduction band.As a consequence, the excess electrons introduced by the(oxidized) interstitial carbon impurity are transferred to Ti3d states at the bottom of the conduction band, and not tothe C-O antibonding states. In this way, two new occupiedstates are formed in the band gap (2.79 eV), at 0.9 and 0.1eV, respectively, below the bottom of the conduction band.The former is a state strongly localized on a Ti atom nearthe interstitial C atom, whereas the latter is a more delocal-ized state with conduction band character (see Scheme 1).Therefore, the interstitial C atom causes states in the gapthat have Ti 3d character rather than C character.

The presence of an oxygen vacancy further modifies thepicture. For the CS-O + VO species, the excess electrons

Figure 4. Partial geometry of the model for three carbon impurities in theanatase supercell of Figure 1. The yellow spheres represent O atoms, thesmall brown spheres represent Ti atoms, and the black spheres representthe carbon impurities.

TiO2(s) f TiO2-x(s) + xVo + x2O2(g) (Ef_Vo

) 4.2 eV)

TiO2Cx(s) f TiO2-xCx(s) + xVo + x2O2(g)

(Ef_Vo) 3.4 eV)

TiO2-xCx(s) f TiO2-2xCx(s) + xVo + x2O2(g)

(Ef_Vo) 1.9 eV)



generated by oxygen removal are trapped by the empty 2pstates of the substitutional C impurity, resulting in three, well-localized, occupied C 2p states, located at 0.6, 1.1, and 1.3eV above the top of the O 2p valence band (see Scheme 1).The band gap (2.68 eV) does not change significantly. Inthe case of interstitial carbon (CI + VO in Figure 3d), theexcess electrons from the oxygen vacancy occupy anantibonding C-O state that lies only 0.2 eV above the topof the valence band. The other two impurity states in theband gap correspond to those of the interstitial CI speciesand lie just below the conduction band (0.3 and 0.1 eV,respectively, with a band gap of 2.79 eV; see Scheme 1).

Substitutional C replacing a Ti atom (CS-Ti in Figure 3b)causes a reduction of the band gap by 0.1 eV, because of ashift of the top of valence band, but does not introduce newstates in the gap. The top of the valence band is essentiallycomposed of the O 2p lone pairs of the four O atoms bondedto the tetrahedrally coordinated C atom.

For the case of three carbon impurities in the supercell(see Figure 4), corresponding to higher dopant concentration,the number of electronic states in the gap is, of course, larger(see Scheme 1). The nature of these states is of two types:the two substitutional carbons (CS-O) accept the fourelectrons from the third oxidized interstitial carbon (CI +VO), and thus results in six (three+ three) occupied 2p stateswhich lie in a range of 0.3-1.3 eV above the top of thevalence band, whereas the band gap is reduced to 2.46 eV.The states of interstitial carbon lie below the bottom of thevalence band.

3.2. Rutile. 3.2.1. Model Structures for Carbon Dopingand RelatiVe Stability. The formation energies of theinvestigated carbon species in rutile are reported in Figure5, as a function ofµ′O. This diagram largely resembles thatobtained for anatase in Figure 2. Substitutional carbonimpurities (CS-O, represented by the black line in Figure 5)become energetically less stable in an oxidizing environment.In contrast, interstitial species (CI, red line) are favored athigher oxygen concentrations. The conversion from oxygenchemical potential to oxygen pressure in Figure 5 (the top

x-axis) has been obtained at the fixed temperature of 1000K. Annealing above this temperature is required to obtainrutile carbon-doped TiO2. At 1000 K, evenµO values lowerthan 2 eV correspond to oxygen pressures that can be reachedexperimentally.

As in the case of anatase, the replacement of one latticeO atom with one C atom to form a substitutional C impurityin the rutile supercell (CS-O in Figure 6a) causes someexpansion of the coordination sphere around the Ti atoms(the Ti-C bonds are∼2.109 and 2.075 Å, whereas the Ti-Obonds in rutile are 1.956 and 1.999 Å; see Table 2). On theother hand, the addition of one C atom in the 72-atom rutilesupercell leads to the formation of an interstitial C impurity

Scheme 1

Figure 5. Formation energies (Eform, in eV), as a function of the oxygenchemical potential (µO) or as oxygen pressure at fixed temperature (T )1000 K) (topx-axis), for different carbon species in rutile.




(CI in Figure 6c) tightly bound to just one lattice oxygen,(CO)n-, and weakly interacting with two nearby Ti atoms(see Figure 6c). The C-O distance is 1.287 Å, whereas theC-Ti distances are 2.047 and 2.152 Å. Thus, the interstitialC species in rutile has a different structure, with respect tothe anatase counterpart. This is most likely due to structuraldifferences in the two polymorphs but could also reflect somedifferences in their oxidative properties. Note, indeed, that,in the case of anatase, the interstitial C atom is coordinatedto three O atoms, forming (CO3)n- species, whereas, in rutile,there is a single C-O bond.

As for anatase, in rutile, the transformation of substitutionalto interstitial C also is an exothermic oxidation reaction,which may occur under oxygen-rich conditions (µ′O f 0):

This is not surprising if we consider that, in the formationof interstitial C atoms, no bonds are broken, which contraststhe substitutional case. By creating an oxygen vacancy inthe presence of interstitial C atoms (CI + VO in Figure 6d),the C impurity is still tightly bound to one lattice O atom(1.398 Å); however, at the same time, it is also weakly boundto the two Ti atoms, which are oxygen-deficient (the Ti-Cbond lengths are 1.968 and 2.030 Å). This configuration is0.6 eV more stable than a substitutional C atom over theentire range ofµO considered (see the blue line versus the

black line in Figure 5). Again, the substitutional CS-O speciesmay be stabilized by the localization of the excess electronsassociated with the formation of an oxygen vacancy (CS-O

+ VO) (see the green line versus the black line in Figure 5).This stabilization leads to a shortening of the Ti-C bondlengths from 2.075 to 2.109 Å to 1.885-1.956 Å (see Table2). The larger positive slope of the green line in Figure 5makes the CS-O + VO species more stable than CS-O underoxygen-poor conditions.

The replacement of one Ti atom by a C atom in rutile(CS-Ti in Figure 6b) leads to a planar CO3 species (bondlengths are reported in Table 2). The three remaining Oatoms, which are not coordinated to the C impurity, become2-fold coordinated. We again notice that the rutile polymorphseems to be less effective in oxidizing the C impurities, withrespect to anatase, where the CS-Ti atom is tetrahedrallycoordinated to four lattice O atoms. As in anatase, theformation energy of CS-Ti impurities, calculated under theassumption that the system is in equilibrium with a TiO2

reservoir, shows the strong stabilization of these speciesunder oxygen-rich conditions.

3.2.2. Higher Dopant Concentration.Higher dopantconcentrations have been modeled by replacing three latticeO atoms of the 72-atom rutile supercell. The lattice undergoesa considerable rearrangement upon relaxation (see Figure 7and Table 2). Only one C atom preserves the substitutionalconfiguration (CS-O); a second C atom (CI) remains coor-dinated to three Ti atoms but also forms one C-O bond(1.427 Å), and the third C atom forms a short C-O bond(1.268 Å) and only two Ti-C bonds (CI). Notice that,although the Ti-C bonds of the CI species are rather long(>2 Å), the Ti-C bond of the substitutional C species (CS-O)are shortened to 1.924, 1.935, and 1.955 Å (i.e., they areeven shorter than both the Ti-C bonds of the isolatedsubstitutional species and the Ti-O bonds of pure rutileTiO2).

The high-doping situation in rutile is more difficult torationalize in detail, with respect to anatase. However,structural variations seem to point again toward some redoxprocesses that occur between the dopant species. Thesubstitutional species is reduced, while the other two, inintermediate configurations between substitutional and in-terstitial, are both oxidized, but to different degrees. The

Figure 6. Partial geometry of the models for (a) one substitutional C atomto O (CS-O), (b) one substitutional C atom to Ti (CS-Ti), (c) one interstitialC atom (CI), and (d) one interstitial C atom nearby an oxygen vacancy (CI

+ VO) in the rutile supercell of Figure 1. The yellow spheres represent Oatoms, the small brown spheres represent Ti atoms, and the black sphererepresents the carbon impurity.

Table 2. Bond Lengths in Carbon-Doped Rutile TiO2a

bond length (Å)C-dopedTiO2 Ti-Ceq

b Ti-Caxc C-O1 C-O2 C-O3

CS-O 2.092 2.109 2.092CI 2.047 2.152 1.287CI + VO 1.968 2.030 1.398CS-O + VO 1.885 1.956 1.933CS-Ti 1.309 1.309 1.2963C

CS-O 1.924 1.935 1.955CI + VO 2.024 2.096 2.063 1.427CI + VO 2.198 2.096 1.268

a In pure TiO2: Ti-Oeq ) 1.942 Å and Ti-Oax ) 2.002 Å.b EquatorialTi-C bond.c Axial Ti-C bond.

TiO2-xCx(s) + x2O2(g) f TiO2Cx(s) (∆E ) -3.0 eV)

Figure 7. Partial geometry of the model for three carbon impurities in therutile supercell of Figure 1. The yellow spheres represent O atoms, thesmall brown spheres represent Ti atoms, and the black spheres representthe carbon impurities.




stabilization induced by this intra-species redox process isless pronounced than in the case of the anatase polymorph,as indicated by the downward shift in energy of the brownline, with respect to the black line in Figure 5 for rutile, tobe compared with the same shift in Figure 2 for anatase.

3.2.3. Oxygen Vacancies in the Presence of CarbonDoping.The effect of carbon doping on the oxygen vacancyformation energy in rutile is somewhat different than inanatase. With the present supercell of 72 atoms, the cost toform an oxygen vacancy in the pure material is 4.4 eV (withrespect to1/2O2), i.e., 0.2 eV higher than in pure anatase.Although for anatase, substitutional C was determined to bemore efficient than the interstitial species in reducing thisenergy cost, in rutile, both substitutional and interstitial Cdoping induce a strong reduction of the oxygen vacancyformation energy, which becomes 2.4 eV.

From these results, we conclude that all types of carbonimpurities in titania should favor the formation of oxygenvacancies. This could be of considerable importance for theunderstanding of the photocatalytic activity of this material.

3.2.4. Electronic Band Structure.The carbon-inducedmodifications of the rutile electronic structure are sum-marized in Scheme 2 (again, the calculations refer to a low-symmetryk-point). The substitutional CS-O species gives riseto two occupied and one empty localized states in the bandgap of TiO2 rutile. The gap becomes 0.3 eV wider, withrespect to the undoped crystal (2.42 eV vs 2.13 eV). Thecarbon-induced localized states lie 0.4, 0.8, and 1.5 eV above

the top of the valence band and are attributable to the threealmost atomic-like C 2p states.

The scenario is more complicated in the case of theinterstitial CI species (see Scheme 2). C-O bonding stateslie deep in energy below the O 2p valence band, and onlyone C 2p state is left in the band gap,∼1.3 eV above thetop of the valence band (the gap is slightly wider, 2.27 eV,than in the undoped material).

In presence of an oxygen vacancy, the excess electronsare trapped at the empty p state of the C atom. For thesubstitutional CS-O + VO species, the positions of theresulting three occupied C 2p localized states are 0.4, 0.8and 1.1 eV above the top of the valence band (band gap of2.38 eV). For the interstitial CI + VO species, two impuritystates in the band gap lie 1.1 and 1.5 eV above the top ofthe valence band and the gap is 2.43 eV.

Finally, a substitutional C atom replacing one Ti atom inthe rutile supercell (CS-Ti) causes a shift of the valence bandtoward lower energies. The concomitant shift of the conduc-tion band is smaller, so that there is a resulting increase ofthe overall band gap from 2.13 eV to 2.38 eV.

The effect of increasing the dopant concentration to threeC atoms per supercell is qualitatively similar to that discussedfor anatase (compare Schemes 1 and 2). Different types ofcarbon-related states are formed: the substitutional C atom(CS-O) shows three 2p states in the band gap, because itaccepts two electrons from the other oxidized C atoms (CI);these form two C-O species whose states lie partially belowthe bottom of the valence band and partially in the band gap.There are six resulting occupied states in the band gap: threefrom the substitutional C atom and three from the interstitialC atoms, which lie in a range of 0.1-1.8 eV above the topof the valence band. The band gap becomes 2.71 eV.

4. Concluding Remarks

The density functional theory (DFT) calculations presentedin this work show that doping TiO2 with carbon can lead tothe formation of different species, which strongly affect the

Scheme 2

TiO2(s) f TiO2-x(s) + xVo + x2O2(g) (Ef_Vo

) 4.4 eV)

TiO2Cx(s) f TiO2-xCx(s) + xVo + x2O2(g)

(Ef_Vo) 2.4 eV)

TiO2-xCx(s) f TiO2-2xCx(s) + xVo + x2O2(g)

(Ef_Vo) 2.4 eV)



electronic structure of the material. The relative stability ofall these species, as a function of the oxygen chemicalpotential (partial pressure) during synthesis, have beencalculated. The diagrams show that, under oxygen-poorconditions, substitutional (to oxygen) carbon and oxygenvacancies are favored, whereas under oxygen-rich conditions,interstitial and substitutional (to Ti) C atoms are preferred.Our calculations also predict an unexpected stabilizationinduced by multidoping effects, which are interpreted asinterspecies redox processes.

In the case of carbon-doped anatase, a recent experimentalstudy12 has indicated the formation of two optical absorptionthresholds: one in the UV region (3.0 eV) and one in thevisible region (up to 1.7 eV). According to laser flashphotolysis experiments,15 the holes formed upon visible lightexcitation are less reactive than those formed upon UVexcitation in pure TiO2, because they are trapped at midgaplevels induced by carbon doping. Lesser mobility is expectedonly for the holes but not for the electrons, which are excitedinto the conduction band. This means that carbon-dopedsystems exhibit a decreased direct oxidation ability. On theother hand, reduction properties or indirect oxidation proper-ties (via reactions with surface intermediates of wateroxidation or oxygen reduction) are much improved uponirradiation with visible light, also because the holes trappedat the carbon doping site do not serve as effective chargerecombination centers.15 This feature makes nonmetal dopingof TiO2 much more appealing than transition-metal doping.

Analysis of the computed electronic structure shows thatcarbon doping in anatase results in a series of localizedoccupied states in the band gap whose density and natureare dependent on the interaction with the oxide matrix, thedopant concentration, and the presence of oxygen vacancies.These states can explain the experimentally observed absorp-tion edge shift toward the visible (vis region, up to almost1.7 eV) of carbon-doped anatase TiO2, with respect to theundoped material.12,14-16 The impurity states are attributableto both substitutional C atoms replacing O atoms, and tointerstitial C atoms. These species are likely to be simulta-neously and synergically present in anatase TiO2. The resultsare different when carbon replaces titanium, because no statesare found in the band gap, but only a small band gapshrinking. This could account for the slight reduction of theoptical threshold energy in the ultraviolet (UV) regionobserved experimentally,12 but not for the enhanced absorp-tion in the vis region.

The main conclusions drawn for anatase generally are alsovalid for carbon-doped rutile, although the details aredifferent. Carbon doping of rutile TiO2 (substitutional to Oor interstitial) induces a series of localized occupied statesin the band gap, which can explain the absorption edge shift(up to 2 eV) observed experimentally for thin and nano-structured rutile films.3,17 The replacement of Ti atoms byC atoms does not result in impurity states in the gap but,differently from anatase, does not induce even a modestdecrease of the band gap. The shift in optical absorptionthreshold in the UV region, as reported in ref 3, may beprobably ascribed to a rutile-anatase phase transition thatoccurs upon doping.

Another important result of our study is that carbon dopingfavors the formation of oxygen vacancies. The concomitantpresence of C species and O vacancies has been observedexperimentally (by X-ray photoelectron spectroscopy (XPS)and electron paramagnetic resonance (EPR)) and shown tobe responsible for the improved photocatalytic activity inthe vis region.16 Similar conclusions were drawn, in aprevious theoretical study,8 also for the case of nitrogen-doped TiO2 and corroborated by recent experimental resultsof deep-level optical spectroscopy on nitrogen-doped TiO2

thin films.35 This suggests that the origin of the increasedphotoactivity of carbon- and nitrogen-doped TiO2 may beassociated with more-complex phenomena than the simplepresence of the impurity atoms, such as, for instance,concomitant changes in the stoichiometry of the sample.

Finally, it is interesting to comment briefly on thedifferences between carbon doping and nitrogen doping inTiO2. The results obtained in our previous studies7,8 onnitrogen-doped anatase are summarized by the stabilitydiagram reported in Figure 8. Substitutional nitrogen dopingdoes not present any multi-atom effects, as indicated by theperfect overlapping of the three lines relative to one, two,and three substitutional N atoms per supercell (NS-O).7,8

Substitutional nitrogen doping is stabilized by the presenceof oxygen vacancies (NS-O + VO).8 The latter situation isthe most stable under oxygen-poor conditions. Under oxygen-rich conditions, interstitial nitrogen species (NI)8 becomefavored. Nitrogen-induced electronic states are localized N2p states and lie a few tenths of an eV above the top of thevalence band. By comparing Figure 8 to Figures 2 and 5,

(35) Nakano, Y.; Morikawa, T.; Ohwaki, T.; Taga, Y.Appl. Phys. Lett.2005, 86, 132104.

Figure 8. Formation energies (Eform, in eV) as a function of the oxygenchemical potential (µO) or as a function of the oxygen pressure at fixedtemperature (T ) 700 K) (top x-axis), for different nitrogen species inanatase.



we can see that carbon exhibits a more-complex chemistrythan nitrogen when introduced in TiO2. However, the resultsof our calculations suggest that the ability to control carbonincorporation in TiO2 should make it possible to shift theabsorption threshold of this material to the vis region. Thiswould represent a major advancement for photocatalyticapplications.

Acknowledgment. The calculations were performed on thelemieux supercomputer at the Pittsburgh Supercomputing Centerand on the SGI Origin 2000 at the Princeton Institute for theScience and Technology of Materials. Financial support byCOFIN-2003 is also acknowledged.

CM051921H


Theory of Carbon Doping of Titanium Dioxide

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