PHYSICAL REVIEW B 84, 165201 (2011)

Configurations, electronic properties, and diffusion of carbon and nitrogen dopants in rutile TiO2:A density functional theory study

Leonidas TsetserisDepartment of Physics, National Technical University of Athens, GR-15780 Athens, Greece

(Received 2 August 2011; revised manuscript received 5 September 2011; published 3 October 2011)

Doping of TiO2 with nonmetal atoms is known to improve the photoconversion efficiency of the material. Here,we use first-principles calculations to describe the atomic-scale details of migration and configurational changesof typical dopants and oxygen-related native defects in rutile TiO2. The complex pathways for transformationsof carbon and nitrogen dopants include structures, which, though very close in energy, have different effects onthe electronic properties of the host system in terms of impurity-related gap states. We also find that, because ofrelatively low diffusion barriers, moderate annealing can activate the migration of impurities and native defectsand lead to defect-induced transformations of dopants. Overall, the results are relevant to the dynamics of C andN dopants in rutile TiO2 and to the performance of the material in photocatalytic and photovoltaic applications.

DOI: 10.1103/PhysRevB.84.165201 PACS number(s): 66.30.J−, 61.72.up

I. INTRODUCTION

Titanium dioxide (TiO2) is one of the most promisingmaterials for solar-cell systems and catalysis. Titania accel-erates the dissociation of various pollutants1–6 and efficientlyconverts light to electrical power.7,8 However, its efficiency asa photo-active material is limited by the fact that it absorbs onlya small percentage of visible light. A possible remedy is to usedoping and improve the optoelectronic properties of TiO2 bysubstituting Ti or O atoms with certain impurities.1,4,5,8–20

The most common crystal forms of TiO2 are the anataseand rutile lattices. In either case, substitution of a smallnumber of oxygen species by carbon or nitrogen atoms hasbeen proposed as a possible mechanism to increase lightabsorption4,9 and, concomitantly, enhance the photocatalyticand photo-conversion efficiency of TiO2. Two explanations forthis improvement have been suggested based on computationalstudies. One scenario attributes the enhancement of absorptionto a decrease of the TiO2 energy band gap following doping.9,18

Alternatively, doping may increase the absorptivity of titaniathrough the creation of dopant-related states within theenergy band gap.11,12,15–17 Clearly, the elucidation of theseissues requires the identification of the most stable dopantconfigurations and their effect on the electronic properties ofthe host system. Moreover, a comprehensive understanding ofthe behavior of doped titania calls for an examination of otheraspects of dopant dynamics, such as migration processes andtransformations that can change the numbers and nature ofimpurities in TiO2.

In a recent study,21 we described the atomic-scale detailsfor the incorporation of carbon and nitrogen dopants in anataseTiO2. In addition to identifying stable dopant structures, weobtained the activation energies for transformations between Cand N dopant configurations and for the migration of these im-purities. Here, we use first-principles calculations to probe thestability and dynamics of C and N dopants in rutile TiO2. Weidentify the lowest-energy configurations of substitutional andinterstitial impurities and their effect on the electronic proper-ties of the oxide. We also describe the minimum-energy path-ways for diffusion of dopants. As in the case of anatase TiO2,our results specify C and N impurity geometries and electroniceffects that differ from those reported in previous studies.

II. METHOD

The results were obtained with the density functionaltheory (DFT) code VASP.22 We used a generalized-gradientcorrected (GGA) exchange-correlation functional,23 projector-augmented-wave potentials,24 and a plane-wave basis withan energy cutoff of 400 eV. Most of the results we presentin the following were based on supercells with 32 Ti and64 O atoms in the impurity-free case. The dimensions ofthe 96-atom supercells were fixed at 9.188, 9.188, and11.836 A, determined by the experimental lattice constants ofrutile TiO2.25 Use of supercells with theoretically optimizeddimensions did not change the main findings on the relativestability of impurity configurations. Sampling26 of k spacefor the calculation of total energy differences employed3 × 3 × 3 k grids. The electronic density of states (DOS)calculations employed the tetrahedron method27 and a finer7 × 7 × 7 k grid. The dependence of the relative stability ofimpurity configurations on dopant concentration was testedfor selected structures using also larger supercells with 64 Tiand 128 O atoms.

Activation energies were obtained with the nudged elasticband method (NEB).28 The method simulates the so-calledminimum energy pathway (MEP) of a reaction with a string ofintermediate configurations that passes through the transitionstate. Previous application of the method provided activationenergies in satisfactory agreement with experimental data onvarious systems,29–31 including Ti-based materials.32–34 In allNEB calculations described below, we used 16 images for eachMEP segment between two metastable configurations. Usingthe calculated barriers and a simple Arrhenius expression, wecan estimate the temperature required for certain processes tobecome activated.

III. RESULTS

In the next sections, we report results on the stability anddynamics of carbon and nitrogen dopants in rutile TiO2. Westart with the case of substitutional carbon dopants and thendiscuss results on carbon interstitial impurities. In the secondpart, we present the findings of calculations on substitutionaland interstitial nitrogen impurities.

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FIG. 1. (Color online) Configurations of substitutional C dopants(shown with arrows) in rutile TiO2. Compared to the most stablestructure (a), the energies of (b), (c), and (d) are 0.08, 0.13, and0.07 eV higher, respectively. [Ti: light gray, O: dark gray (red), C:gray spheres.]

A. Substitutional carbon dopants

Figure 1 depicts the most stable configurations of a carbonimpurity in the vicinity of an oxygen vacancy inside rutileTiO2. The energies of all these structures are almost equalto each other. In particular, the energy difference betweenthe most stable structure of Fig. 1(a) and the geometries ofFigs. 1(b)–1(d) are 0.08, 0.14, and 0.07 eV, respectively. Theconfiguration of Fig. 1(c) is spin-polarized with a magneticmoment of 2.64μB . Table I summarizes the total energies andmagnetic moments for the most stable configurations of C- andN-doped rutile TiO2. Other first-principles studies17,35,36 haveinvoked a substitutional configuration (C-O) with a C atom atan O vacancy site. Compared to the lowest-energy structureof Fig. 1(a), however, the C-O geometry is less stable by0.50 eV.

TABLE I. Energies and magnetic moments (M) for the moststable configurations of substitutional C (Cs), interstitial C (Ci),substitutional N (Ns), and interstitial N (Ni) impurities in rutile TiO2.In each case, the energies are referenced with respect to the moststable structure.

Impurity type Configuration Energy (eV) M (μB )

Cs Fig. 1(a) 0.00 0.00Cs Fig. 1(b) 0.08 0.00Cs Fig. 1(c) 0.14 2.64Cs Fig. 1(d) 0.07 0.00Ci Fig. 4(a) 0.00 3.81Ci Fig. 4(b) 0.70 0.00Ci Fig. 4(c) 0.74 0.00Ci Fig. 4(d) 0.37 0.00Ns substitutional 0.00 1.00Ni Fig. 9(a) 0.00 1.00Ni Fig. 9(b) 0.14 1.00

FIG. 2. (Color online) Energy variation and structures (insets)during migration of a substitutional C dopant in rutile TiO2. TS isthe transition state of the rate-limiting step. The activation energy is1.4 eV. [Ti: light gray, O: dark gray (red), C: gray spheres.]

The 0.5 eV value is close to the 0.6 eV energy differenceobtained in the DFT studies16 of di Valentin et al. for the C-Oconfiguration and the structure of Fig. 1(d). Moreover, thereis agreement between these two sets of DFT investigations inidentifying the geometry of Fig. 1(d) as a stable C impurityconfiguration. The results of the present study, however, showthat this stable structure competes in terms of stability withthe other geometries shown in Fig. 1. Likewise, the energiesof the structures of Figs. 1(b)–1(d) lie within 0.08 eV from themost stable configuration of Fig. 1(a) when a larger supercellwith a total of 192 atoms is employed. For this lower dopantconcentration of x = 0.8%, the energy of a C-O configurationis 0.45 eV higher than that of the structure of Fig. 1(a).

In the most stable configuration of Fig. 1(a), the C atomis in an off-site position with respect to the oxygen vacancy.Diffusion of the impurity comprises transformations betweenstructures of the types shown in Fig. 1 and hopping of aneighboring oxygen atom to the vacancy site. The latterhopping event is the rate-limiting step for the overall diffusionprocess. Figure 2 shows the energy variation during themultistep process that allows diffusion of the dopant. Based onthese results, the effective activation energy for the migrationof a substitutional C impurity is 1.4 eV. Transformationsbetween the configurations of Fig. 1 have lower barriers of0.5–0.6 eV. Hence, low-energy structures change from oneto another even at low temperatures, while diffusion requiresannealing at moderate temperatures of about 100–150 ◦C.

Figure 3 compares the electronic DOS of pristine rutile TiO2

and of the same system with one substitutional C impurityper 64 oxygen atoms. The DFT-GGA result for the bandgap of rutile TiO2 is 1.7 eV, about 0.2 eV lower than thecorresponding value in the case of anatase TiO2.21 The 0.2 eVvalue is consistent with the difference between measured theband gaps of anatase (3.2 eV) and rutile (3.0 eV) titania.37,38

As absolute values, the calculated band gaps are significantlysmaller than experimental data due to a well-known limitationof DFT-GGA approaches. The incorporation of a substitutionalC impurity has a pronounced effect on the electronic propertiesof rutile titania. The associated DOS data of Fig. 3 show thatthe C-doped system has a larger band gap (by 0.22 eV) thanthe pristine crystal. The results of Fig. 3 also make clear thatimpurities of the types of Figs. 1(a)–1(c) create one distinctlevel in the energy band gap of the system. The position of this

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FIG. 3. (Color online) Electronic density of states (DOS) ofpristine rutile TiO2 (shaded) and TiO2 with substitutional C impuritiesof the type of Fig. 1(a) (black line), Fig. 1(b) (red line), and Fig. 1(c)(blue line). Zero of energy is set at the valence band (VB) maximum.CB is the conduction band. The arrows show impurity-related levelsin the band gap of rutile TiO2. The DOS data (a)–(c) show smalldifferences at the top of the VB and the bottom of the CB.

level depends on the nature of the impurity configuration. Forthe structures on Figs. 1(a)–1(b), the gap state lies close to theconduction band minimum, while for the geometry of Fig. 1(c),the gap level is located about 0.6 eV above the valence bandmaximum.

B. Interstitial carbon impurities

Figure 4 shows the most stable configurations for interstitialcarbon impurities in rutile TiO2. In the lowest-energy structurein Fig. 4(a), the impurity forms four chemical bonds withsurrounding oxygen atoms. This tetrahedral bond arrangementis spin-polarized with a magnetic moment of 3.81μB . For alower dopant concentration of x = 0.8% the magnetic momentis 3.94μB . When the C-O bonds are broken, the energyincreases. In particular, the energies of impurity structureswith three, two, and one C-O bonds are higher than that

FIG. 4. (Color online) Configurations of interstitial C impurities(shown with arrows) in rutile TiO2. The most stable structure is (a),while the energies of (b), (c), and (d) are 0.70, 0.74, and 0.37 eVhigher, respectively. [Ti: light gray, O: dark gray (red), C: grayspheres.]

FIG. 5. (Color online) Energy variation during migration of aninterstitial C impurity in rutile TiO2. Indexes (a)–(d) refer to structuresof Fig. 4. TS is the transition state of the rate-limiting step. Theactivation energy is 1.94 eV.

of the structure of Fig. 1(a) by 0.70, 1.16, and 1.75 eV,respectively. The energy difference between four-fold andthree-fold coordinated C structures is 0.48 eV for x = 0.8%.We should note that in previous DFT studies16 the C interstitialconfiguration contained only one single C-O bond. As shownhere, this structure is considerably less stable than thetetrahedral geometry of Fig. 4(a).

The C interstitial geometry with three C-O bonds is shownin Fig. 4(b). Other local-energy minima structures are depictedin Figs. 4(c)–4(d). These configurations are intermediategeometries for the migration of a C interstitial in rutileTiO2. Their energies are 0.74 and 0.37 eV higher than thatof the structure of Fig. 4(a). The second energy differencebecomes 0.43 eV when the impurity concentration drops tox = 0.8%. The NEB results of Fig. 5 show that consecutivetransformations between the configurations of Fig. 4 allowmigration of a C interstitial with an effective activation energyof 1.94 eV. The formation of four C-O bonds stabilizes theimpurity and does not allow its hopping unless the system isheated at high temperatures.

As shown in the DOS data of Fig. 6, in the presence of a Cinterstitial impurity, the band gap of the host system increasesby 0.18 eV. We have seen that substitutional carbon impuritiescause a comparable increase of the band gap of rutile TiO2.This effect is consistent with the experimental observation6 of a

FIG. 6. (Color online) Electronic density of states (DOS) ofpristine rutile TiO2 (shaded) and TiO2 with an interstitial C impurityof the type of Fig. 4(a) (red line). Zero of energy is set at the valenceband (VB) maximum. CB is the conduction band.

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FIG. 7. (Color online) Energy variation and structures (insets)during migration of a substitutional N dopant (shown with arrows)in rutile TiO2. The activation energy is larger than 3.5 eV. [Ti: lightgray, O: dark gray (red), N: gray spheres.]

blue shift in the absorptivity of rutile TiO2 upon carbon doping.Unlike the case of substitutional C impurities, interstitial Catoms do not generate levels in the band gap of the material.The increase of the band gap and the dependence of gapstate formation on the nature of C impurities (substitutionalor interstitial) are qualitatively similar to findings on carbondoping of anatase TiO2.21

C. Substitutional nitrogen dopants

As in previous studies on N-doped rutile TiO2,39–41 wefind that the lowest-energy structure for substitutional N hasthe dopant at the position of a missing oxygen atom. Thissubstitutional geometry is spin-polarized with a magneticmoment of 1.0μB . Other impurity configurations have theN atom at an off-vacancy position and with one bond to aneighboring O atom. The off-site geometries are considerablyless stable (by at least 1.3 eV) than the lowest-energysubstitutional structure. Diffusion of the impurity requiresexchange of positions between the N dopant and a vicinal Oatom, as shown in Fig. 7. The activation energy of the processis so high (about 3.5 eV) that migration of substitutional Ndopants requires annealing at extreme temperatures.

Nitrogen doping of rutile TiO2 does not modify the energyband gap of the host system, at least for the concentration of oneN atom per 64 O atoms. A substitutional N impurity introducesa single level inside the gap, about 0.5 eV higher than thevalence band maximum (VBM). The associated DOS data areshown in Fig. 8. The appearance of an N-related gap state andthe small change of the band gap upon substitutional N dopingare in agreement with other DFT studies39,40 and experimentaldata.14,42 Substitutional N doping introduces a level at aboutthe same energy position also in the case of anatase TiO2.21 Anotable difference between rutile and anatase N-doped titaniais that in the latter case substitutional N impurities decreasethe energy band gap of the system by introducing a band tail21

at the VBM.

D. Interstitial nitrogen impurities

Nitrogen impurities bind with oxygen atoms in stablesplit-interstitial configurations of the type shown in Fig. 9.

FIG. 8. Electronic density of states (DOS) of pristine rutile TiO2

(shaded) and TiO2 with a substitutional N dopant at an oxygenvacancy site (solid line). Zero of energy is set at the valence band(VB) maximum. CB is the conduction band.

Several, nearly degenerate N interstitial structures exist withvariations in the orientation of the N-O bond. For example,the largest energy difference between the structures depictedin Fig. 9 is 0.14 eV. Previous studies39,41,43 identified similarstable N structures, without explicit reference to near energydegeneracy among different geometries. As shown in Fig. 10,intrasite transformations between split-interstitial geometrieshave small barriers of less than 0.2 eV. Intersite hopping ofthe nitrogen impurity between neighboring oxygen atoms hasa larger barrier of 1.14 eV. This value represents the activationenergy for diffusion of an interstitial N atom in rutile TiO2.The process is thus activated at moderate temperatures ofabout 100 ◦C. We should note that interstitial and substitutionalN configurations are spin-polarized with magnetic momentsof 1.00μB . They can thus play a role in the observedferromagnetism of rutile titania following N implantation.44,45

DFT calculations39,43 have shown that interstitial N struc-tures of the type of Fig. 9(d) generate levels inside the bandgap of rutile TiO2. Indeed, this property is seen also in Fig. 11,which presents the electronic DOS for pristine rutile titaniaand for the same system with one N interstitial per 64 Oatoms. Two types of interstitial structures are considered,

FIG. 9. (Color online) Configurations of interstitial N impurities(shown with arrows) in rutile TiO2. The diffusion barrier is 1.14 eV.[Ti: light gray, O: dark gray (red), N: gray (cyan) spheres.]

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FIG. 10. (Color online) Energy variation during migration ofan interstitial N impurity in rutile TiO2. TS corresponds to thetransition state of the rate-limiting step, related to N hoppingbetween neighboring O sites. ITS is the transition state for intrasitetransformations between configurations depicted in Fig. 9.

those of Fig. 9(a) and Fig. 9(d). For the former configuration,the most important impurity effect is the appearance of fourdistinct levels within the rutile band gap. One of these levelslies at a mid-gap position, while the other three are locatedwithin 0.3 eV from the VBM. With respect to the size ofthe band gap, there is only a small difference between theimpurity-free and impurity-laden systems. The other impuritystructure of Fig. 9(d) also generates levels in the gap. However,the number and position of the gap states differ with respect tothe geometry of Fig. 9(a), even though the energy differencebetween the two configurations is only 0.05 eV. The existenceof impurity-related gap states and the small increase of the gapupon loading with N interstitials are common features betweenrutile and anatase21 TiO2.

E. Interactions between dopants and point defects

In many different types of materials, interactions betweenimpurities and native defects can modify their physicalcharacteristics and their effect on the properties of the hostsystem.46–48 For this reason, the concentration and mobility

FIG. 11. (Color online) Electronic density of states (DOS) ofpristine rutile TiO2 (shaded) and TiO2 and with an interstitial Nimpurity of the type of Fig. 9(a) (solid blue line) or Fig. 9(d) (blackline with squares). Zero of energy is set at the valence band (VB)maximum. CB is the conduction band.

of defects are key factors for the dynamics of dopants intitania and, concomitantly, for their role in photocatalyticand photoconversion activity. Oxygen vacancies and oxygeninterstitials are typical native TiO2 defects. The lowest-energyoxygen interstitial configuration is similar to that of Fig. 9(d)with the nitrogen atom replaced by oxygen. The diffusionbarrier of the defect is only 0.78 eV, while the activationenergy for the migration of oxygen vacancies is moderatelylarger at 1.14 eV. The latter value is in close agreement withthe reported49 barrier of 1.1 eV for O vacancies in rutileTiO2. Hence, both types of native defects are mobile at roomtemperature or at slightly elevated temperatures.

When a migrating oxygen defect arrives at the site of acarbon or nitrogen impurity it reacts with the latter as follows.An oxygen interstitial transforms a substitutional carbon atomto an interstitial impurity in a strongly exothermic reaction thatreleases 6.19 eV. The reaction is energetically favorable, albeitwith a lower energy gain of 2.07 eV, also for a substitutionalnitrogen dopant. Interstitial impurities, on the other hand, aretrapped at oxygen vacancy sites and they are transformed tosubstitutional configurations. The energy gain of this processfor the case of nitrogen is 4.29 eV, while for carbon it issignificantly lower at only 0.31 eV.

IV. DISCUSSION

The performance of doped titania in applications that relyon photo-conversion is certainly a complex issue that involvesmany different processes. Clearly though, the atomic-scaledetails of dopant incorporation and dynamics stand out asone of most important pieces of information if one is toacquire a comprehensive understanding of this performance.In this respect, the identification of dopant structures that differfrom those reported in previous first-principles studies may beregarded as the first key finding of the present study. Onlyafter the most stable dopant configurations have been foundone can make predictions about other significant features, suchas the effect of dopants on the electronic and, ultimately, theabsorption properties of TiO2.

The results of this work show that carbon and nitrogen im-purity effects in rutile TiO2 have a number of similarities withanalogous effects in anatase titania.21 In both cases, the bandgap of C-doped TiO2 is larger than that of the impurity-freematerial. Therefore, the experimentally observed enhancementof photo-induced activity may only be related to the creation oflevels in the band gap of titania upon carbon doping. Formationof gap states seems also to be the dominant mechanism forthe enhancement in rutile N-doped TiO2. Substitutional Nimpurities in anatase TiO2, on the other hand, reduce the bandgap and introduce states in the gap.

As noted above, a number of findings on the stability andelectronic effects of C and N impurities confirm similar resultsreported in previous theoretical studies. By the same token,however, the present study adds key pieces of informationabout the dynamics of C and N dopants in rutile TiO2. First,it shows that there are a number of C and N configurationswhich are very close in energy, but differ in terms of structuraland electronic characteristics. This property is a likely factorfor the use of titania in photocatalytic and photovoltaicapplications. Furthermore, given that dopants and point defects

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become mobile at room or moderate temperatures, variationsin conditions that favor the presence of oxygen vacancies orself-intertstitials may eventually enable dopant-defect interac-tions that lead to transformations between substitutional andinterstitial impurity species. In this way, one may be able toexercise an indirect control on the performance of TiO2-basedsystems.

V. SUMMARY

Using density functional theory calculations, we haveidentified the most stable configurations of carbon and nitrogendopants in rutile TiO2 and the effect of these species on theelectronic properties of the system. Substitutional carbon,

substitutional nitrogen, and interstitial nitrogen impuritiesintroduce levels within the band gap of titania. Carbondoping increases the gap, while nitrogen doping has asmaller effect in this respect. The relatively low barriers fordiffusion of the impurities and native defects suggest thatmigration and interactions between these types of imper-fections are operative at moderate temperatures, leading tochanges in the physical properties of C- and N-doped rutileTiO2.

ACKNOWLEDGMENTS

The calculations used resources of the EGEE and Hellas-Grid infrastructure.

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