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Electronic Properties of Rutile TiO2 with Nonmetal Dopants from First Principles Xiaoping Han and Guosheng Shao* Institute for Materials Research and Innovation, University of Bolton, Bolton, BL3 5AB, United Kingdom ABSTRACT: The electronic properties of rutile TiO2 with nonmetal dopants are investigated using the first-principles density functional theory. Four types of doping are considered: N doping (substituting N for O), C doping (substituting C for O), N þ H codoping (substitutional N and interstitial H), and C þ H codoping (substitutional C and interstitial H). The results show that N(C) doping of TiO2 leads to intermediate bands owing to N(C) 2p orbitals and there is no overlapping of these intermediate bands with the valence band to narrow the band gap. These bands are of evident curvatures, and they, acting as stepping stones, are expected to help to relay valence electrons to the conduction band and thus result in a red shift in the optical absorption edges. C þ H codoping to TiO2 also gives rise to similar intermediate bands, and N þ H codoping induces significant band-gap reduction without inducing any bands/states within the forbidden gap. The presence of interstitial H next to a C or N dopant helps to eliminate intermediate states arising from the N(C) 2p orbitals. Also, the CH and NH bond lengths in C þ H- and N þ H-codoped TiO2 are comparable with those in CH4 and NH3 molecules, respectively. It is probable to make use of NH3 and CH4 gases to dope TiO2 for significant optical absorption of visible light for enhanced photovoltaic and photocatalytic functionalities.
1. INTRODUCTION Titanium dioxide phases (rutile and anatase TiO2) have been extensively studied both experimentally and theoretically, owing to their great potential for a wide range of applications, such as photocatalysis14 and low-cost solar cells.5,6 However, the potential for various applications is seriously limited by the wide band gaps of TiO2 phases (3.2 eV for anatase and 3.0 eV for rutile), which confines them to absorb only the ultraviolet (UV) part (about 4% of the solar energy) of the solar spectrum to activate their useful functionalities by photoinduced charge carriers. Effective utilization of visible light, which constitutes over 45% of the solar irradiance, is highly desirable so as to deliver a significantly widened avenue to use TiO2 as a multifunctional material. To overcome the UV limitation and extend the optical absorption of TiO2 to the visible-light region, great efforts have been made to reduce the band gap by incorporating transition-metal716 and nonmetal1738 dopants into TiO2. As a result, nonmetal dopants, such as N,17,2230,3234 C,1719,31 F,17,20,3537 S,17,21,38 and P17,38, have been extensively investigated. In particular, N or C doping has attracted great attention recently. Experimental study showed that doping anatase TiO2 with the substitutional N to the O sites in TiO2 improved the optical absorption in the visible-light region.30 The same phenomenon was observed in the N-doped materials of mixed anatase and rutile phases, in the forms of thin films,17,28 powders,17,22,29 or nanoparticles.39 However, the origin underlying the phenomenon has been a debatable subject. Reference 17 concluded that the band-gap narrowing of anatase TiO2 is due to the mixing of the r 2011 American Chemical Society
valence band (VB) with the N 2p states. However, two other theoretical studies on anatase TiO231,40 concluded that the mixing of N 2p with O 2p states is too weak to produce significant band narrowing and that the optical absorption in the visible region was due to the presence of localized gap states (mainly N 2p) above the valence band maximum (VBM). The latter were supported by some photoelectrochemical measurements.22,2830 It should be emphasized that the localized gap states are undesirable for the photovoltaic applications (where the carrier mobility plays a critical role), although they may be useful to the photocatalytic applications. To date, most previous studies on N doping were related to the photocatalytic properties of anatase or mixed anataserutile phases, with little on a single rutile phase. It is well known that the rutile phase is the stable form in TiO2 and, unlike anatase, which has an indirect band gap, rutile has a direct band gap10,38,4147 that is desirable for a semiconductor. It is, therefore, of fundamental importance to understand the effects of N doping on the rutile phase. Compared to N doping, few studies of C-doped TiO2 were reported. Some experimental studies of the C-doped anatase TiO218,19,48 demonstrated enhanced optical absorption and associated photocatalytic properties in the visible-light region. Modeling using the density functional theory (DFT)31 indicated that the observed red shift of optical absorption for C-doped
Received: November 8, 2010 Revised: March 15, 2011 Published: April 04, 2011 8274
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Table 1. Structural Parameters, Bulk Modulus (B0), and Energy Gap (Eg) of Rutile TiO2 in Comparison with Experimental Data and Other Theoretical Results a (Å) this work
a
Figure 1. (a) Unit cell of rutile TiO2 (oxygen and titanium atoms are represented by red and light blue spheres, respectively). The relative positions are (0,0,0) and (1/2,1/2,1/2) for Ti atoms and (u,u,0), (1 u, 1 u,0), (1/2 þ u,1/2 u,1/2), and (1/2 u,1/2 þ u,1/2) for O atoms. (b) N þ H-codoped 2 2 2 TiO2 (the substitutional N and interstitial H are represented by the brown and green spheres, respectively).
anatase TiO2 is related to the presence of gap states, while there was little on the electronic origin of the gap states. It has been recognized that nonmetal species, such as C, N, and H, are usually present in the processing or application environment, and the effects of their copresence in the TiO2 materials need to be investigated. N þ H codoping on anatase TiO2 has been investigated experimentally,25,4954 and the results showed that the codoping effect is responsible for the enhanced photoactivity of doped TiO2 materials in the range of visible light. Such a codoping effect was backed by a theoretical study of the N þ H-doped anatase phase.55 No such theoretical modeling on the rutile phase has yet been carried out. To the authors’ knowledge, neither experimental nor theoretical research has been reported on the C þ H codoping of TiO2. This work is dedicated to obtain a fundamental insight into the effects of N(þH) and C(þH) doping of the rutile TiO2, using the first-principles method in the framework of the DFT(þU), aiming at self-consistent interpretation and prediction of the interplay of the codopants on the energy band structure of rutile TiO2.
2. METHOD The rutile TiO2 phase has a tetrahedral lattice (P42/mnm) with two Ti atoms and four O atoms per unit cell, as shown in Figure 1a. To avoid direct impurityimpurity interaction between two neighboring cells, we used 2 2 2 supercells with eight unit cells (Ti16O32) to construct the N(C)-doped and N þ H(C þ H)-doped structures, where an O atom was replaced by a N(C) atom or a NH(CH) species, which corresponded
c (Å)
u
Eg (eV)
B (GPa)
LDA
4.576
2.929
0.304
1.68
241
GGA
4.663
2.971
0.305
1.82
250
theorya
4.653
2.965
0.305
2.0
240
theoryb
4.536
2.965
0.304
1.87
experimentc
4.594
2.959
0.305
3.0
216
Reference 47. b Reference 46. c References 5961.
to 3.1% of N(C) or NH(CH). As an example, Figure 1b shows the N þ H-codoped 2 2 2 supercell. DFT calculations were carried out using the Vienna Ab-initio Simulation Package (VASP).56,57 The projector-augmented wave (PAW) pseudopotentials58 were used to describe the ionelectron interactions. The generalized gradient approximation (GGA) was chosen to describe the exchange-correlation interactions (by comparing the results of GGA and local density approximation (LDA), as presented in section 3.1). The planewave basis was generated with valence configurations of Ti-3s23p63d24s2, O-2s22p4, N-2s22p3, C-2s22p2, and H-1s1. The Brillouin zone (BZ) integration was performed on a wellconverged MonkhostPack k-point grid. Extensive tests were carried out to ensure convergence with respect to the number of k-points and energy cutoffs. For the k-point integration, we used a 4 4 6 mesh for the unit cell and a 2 2 3 mesh for the 2 2 2 supercell, respectively. A plane-wave energy cutoff of 400 eV was used in all calculations. All doped structures were geometrically relaxed until the total force on each ion was reduced below 0.01 eV/Å.
3. RESULTS AND DISCUSSION 3.1. Bulk Properties of Rutile TiO2. As shown in Figure 1, the unit cell lattice of rutile TiO2 consists of hexagonally closepacked oxygen atoms, with half of the octahedral sites occupied by titanium atoms. The parameter u is an oxygen fractional coordinate used to define the crystal structure. Computational results of LDA and GGA functionals for its structural parameters a, c, and u; the band gap Eg; and the bulk modulus B0 are summarized in Table 1 together with reported theoretical results and experimental values. It is clear from this table that the GGA functional provides a better overall description than the LDA one. Especially, the GGA band gap is improved by 0.14 eV compared to the LDA one. Therefore, the GGA functional has been employed throughout this work. As is seen in Table 1, the GGA band gap (1.82 eV) is still well below the experimental value of 3.0 eV. It is well recognized now that DFT alone may underestimate the band-gap values of transition-metal oxides significantly, wherein a considerable nonlocal effect due to strong Coulomb repulsion etc, may exist. In this work, we have considered the nonlocal effect via the inclusion of a Hubbard U parameter to the Ti 3d electrons for improved band structure calculations (DFT þ U method).6264 The DFT þ U method combines the standard DFT with a Hubbard Hamiltonian for the Coulomb repulsion U and exchange interaction J. Here, the DFT þ U approach of Dudarev et al.64 was used, for which the local part is described by the CeperleyAlder functional65 and the Coulomb and exchange 8275
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The Journal of Physical Chemistry C interactions are treated by a single effective parameter Ueff = U J. Using this method, we calculated the band gaps of rutile with the range of Ueff from 0 to 10, and the result is shown in Figure 2. It is clear that the band gap of rutile can be linearly widened by increasing Ueff from 0 to 7 eV. A further increment of Ueff is less effective. Beyond 7 eV, the extent to open up the band gap gradually reduces, and the maximal band-gap value corresponds to Ueff = 8 eV, over which the band gap starts to decrease. Our results are different from those of ref 66 (where the band gap of rutile TiO2 linearly opens up with increasing Ueff), but similar to the results obtained using the CASTEP code16 (where the band gap reaches the maximum also at Ueff = 8 eV, beyond which it begins to narrow). As was discussed in ref 16, the appearance of a
Figure 2. Effect of Ueff (U J) on the rutile band gap. The Hubbard correction is applied to the 3d electrons. The dotted line represents the experimental value of the rutile band gap.
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maximum in the chart of band gap against the Hubbard parameter is likely to suggest additional mechanisms for the nonlocal effect, and it is thus reasonable to limit the Hubbard correction for Ueff e 7 eV. The band gap for Ueff = 7 eV is 2.71 eV (only 0.29 eV less than the experimental value 3.0 eV), which significantly improves the accuracy in predicting the band gap with respect to the GGA result (1.82 eV). The band structures and partial densities of states (PDOS) of rutile TiO2 using GGA and GGA þ U formalisms are shown in Figure 3. Both calculated valence band (VB) widths are about 6 eV, being in good agreement with the experimental values.6769 It is seen from Figure 3b,d that both valence bands are mainly composed of O 2p states, with some hybridization with Ti 3d orbitals. Both conduction bands (CBs) are mainly composed of the Ti 3d states, agreeing well with the experimental finding from TEY spectroscopy.70 Figure 3a,c shows that the GGA þ U valence band is nearly the same as the GGA one, but there is an evident difference between the GGA and GGA þ U conduction bands. In the GGA case, as shown in Figure 3a, the upper conduction band is almost completely separated from the lower conduction band at 3.3 eV. However, in the GGA þ U case (Figure 3c), the upper and lower conduction bands are overlapped with each other, owing to the upward shift of the lower conduction band. Apparently, it is the upward shift of the lower conduction band that contributed to the improved band-gap prediction using the Hubbard U correction to Ti 3d electrons. 3.2. N and N þ H Doping of Rutile TiO2. N-doped TiO2 was studied using a N atom to substitute an O atom in a 2 2 2 TiO2 supercell. The optimization of the atomic structures showed that the atomic displacements are slight, implying that the incorporation of N atoms in the O sites yields little strain to the neighboring Ti atoms. The calculated TiN bonds are between
Figure 3. Band structures and PDOS of the unit cell of rutile TiO2 using GGA (a, b) and GGA þ U (c, d) formalisms. The dotted-dashed line at energy zero represents the Fermi level. 8276
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Figure 4. Total charge densities of pure (a) and N-doped (b) TiO2. The plane (110) that cuts substitutional N was chosen.
Figure 5. Band structures and DOS of N-doped TiO2 using GGA (a, b) and GGA þ U (c, d) formalisms. The dotted-dashed line at energy zero represents the Fermi level.
1.989 and 2.059 Å, being slightly stretched with respect to the TiO bonds in pure rutile (1.956 and 1.988 Å). This is due to the
slightly larger ionic radius of N than that of O. Therefore, replacing an O atom with a N atom only induces slight structural changes. 8277
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The Journal of Physical Chemistry C To study the charge transfer brought about by N doping, we plotted the total charge densities of TiO2 with and without N doping, as shown in Figure 4. The comparison between panels a and b in Figure 4 reveals that N doping hardly gives rise to any variations in the charge densities of Ti and O, indicating negligible charge transfer. Furthermore, we calculated the electronic population at each atomic site by integrating the total electronic charges inside a sphere centered on each atom with effective ionic radii, the so-called ShannonPrewitt radii.71 They are 0.605, 1.36, and 1.42 Å for Ti, O, and N atoms. Through comparing the cases with and without N doping, we find that the electron population of N atom is 0.94e less than that of the substituted O atom without N doping, while those of other atoms keep nearly the same. This is in agreement with the number of valence electrons for N and O atoms and means that each N dopant offers a hole as charge carrier in TiO2. Further orbital decomposition shows that the hole is mostly due to 2p states. Similar results can be obtained from the Mulliken populations with and without N doping, which also indicate that N doping hardly induces any charge transfer. The GGA band structure and DOS of N-doped TiO2 are shown in Figure 5a,b. Comparing to the band structure of pure TiO2 in Figure 3a, N doping causes the Fermi level to shift downward to the VB, meaning it is a p-type dopant. We see from Figure 5a that a narrow isolated band of gap states, or an intermediate band, appears above the top of the VB (VBM) at the Fermi level, which is mainly owing to the N 2p orbitals according to the PDOS analysis shown in Figure 5b. This N-induced intermediate band can act as an acceptor level to result in p characteristics for TiO2, which is in line with the above electronic population analysis. The band gap between the highest O 2p band and the lowest Ti 3d band is 1.97 eV (as shown in Figure 5a), indicating that N doping causes the overall band gap to be broadened by 0.15 eV compared with that of pure TiO2 (1.82 eV). This is consistent with the measurements of ref 72 on N-doped rutile TiO2 single crystals, and with another theoretical result.73 The electron mobility in the intermediate band can be calculated using the equation μ = eτ/m* (here, τ is the mean free time and m* is effective mass, both being associated with the curvature of the relevant band),74 resulting in an electron mobility of 239 cm2/V 3 s. Such high electron mobility can assist the dissociation of electronhole pairs to effectively reduce the probability for their recombination. Electrons in such an acceptor-like intermediate band can be further excited to the CB bottom. Because of the much narrower lower subgap, it is easy to achieve the excitation of valence electrons from the VB to the intermediate band, which makes the wider upper subgap the controlling factor for electron excitation. As shown in Figure 5a, the upper subgap is 1.57 eV, which is 0.25 eV (14%) narrower than the band gap of pure TiO2 (1.82 eV), leading to improved optical absorption. The GGA þ U method was also used to investigate the N-doped TiO2, where Ueff for 3d electrons was set as 7 eV. The calculated band structure and DOS are shown in Figure 5c,d. Being consistent with the GGA results, one curved intermediate band (mainly due to N 2p according to the PDOS analysis in Figure 5d) appears above the valence band to divide the band gap into two subgaps. Its upper subgap (the controlling factor of electron excitation) is 2.37 eV, being 0.34 eV (13%) narrower than the band gap of pure TiO2 (2.71 eV). It is clear that the relative differences between the upper subgap and overall gap for
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Figure 6. Band structure of TiO2 with N þ H codoping. The dotteddashed line at energy zero represents the Fermi level.
DFT and DFT þ U are similar (14% vs 13%). We can also see from Figure 5a,c that the lower subgaps from the GGA and GGA þ U calculations are very close as well (0.40 and 0.42 eV, respectively). It is apparent that the Hubbard U correction in N-doped TiO2 opens up the band gap mainly by widening the upper subgap and hardly influences the position of the intermediate band with respect to the VBM. This is consistent with the theoretical observation for Mn-doped rutile.16 Actually, similar cases can be obtained through comparing the GGA and GGA þ U results of the N þ H-, C-, and C þ H-doped rutile TiO2, suggesting that it is rather generic that gap widening of TiO2 due to the Hubbard correction is mainly induced in the upper subgap. This allows one to perform a reliable study of the intermediate bands/states without using the Hubbard correction, so long as they are referred to the VBM. In the following discussion, we only focus on presenting the results from GGA calculations. N þ H doping of TiO2 was studied through introducing one interstitial H into the N-doped TiO2. Due to the very small radius of H, we only consider interstitial sites for the H codopant. Three distinctly different ways exist in distributing the substitutional N together with the interstitial H, with the H atom being placed in the interstitial sites as nearest or second-nearest neighbor to N, or being placed far away from it. Total energy calculations on these configurations show that the nearest neighboring configuration (as shown in Figure 1b) is most stable. Thus, in the following, the nearest neighboring configuration will be used for investigating the effect of N þ H codoping on TiO2. It shows to compare the electronic populations with and without N þ H doping that N þ H doping causes no evident charge variation on the surrounding Ti and O atoms. This is not difficult to understand, because a N dopant at an O site introduces a hole and an interstitial H offers an electron to achieve local charge neutrality. We see from Figure 6 that there are no gap states due to the N þ H codoping, and the resulted band gap is 1.68 eV, about 8.3% narrower than that of pure TiO2 (1.82 eV). Obviously, H doping (as donor) lowers the energy level of N 2p (as acceptor), making the N 2p states mix with the VB. Therefore, the intermediate band in N-doped TiO2 disappears via donoracceptor annihilation, and an alloy with intrinsic characteristics is induced via codoping (as shown in Figure 6). This shows that it is the mixing of the O states in the VB with the N states that leads to the band-gap narrowing and, consequently, a red shift of the optical absorption edge. This 8278
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Figure 7. Total charge density of N þ H-doped TiO2. A plane that cuts through N and H was chosen. The atoms circled with the dotted line are not in the chosen plane.
effect is similar to the experimentally observed72,75 and theoretically supported55 effects of the N þ H codoping on the anatase phase, where the red shift of the optical absorption edge resulted from band-gap narrowing. It is worth stressing that the removal of gap states would be helpful to avoid electronhole recombination due to gap states, making the TiO2 materials more efficient for optoelectronic devices. The thermodynamic stability of doped rutile can be studied on the basis of doping energy (Ef), which is the energy required to incorporate the dopant/s in the pure rutile lattice. The lower the value, the easier it is to create such doping. As an example, the N-doping energy in a 2 2 2 supercell can be calculated using the following equation:
Figure 8. Band structure (a) and DOS (b) of C-doped TiO2. The dotted-dashed line at energy zero represents the Fermi level.
1 1 Ef ¼ Edoped þ EO2 EN2 Epure 2 2 Here, Edoped and Epure are the total energies of the supercells with and without N doping and EO2 and EN2 refer to the total energies of oxygen and nitrogen molecules, respectively. The calculated energies for the N doping and N þ H codoping in the rutile phase are 0.13 and 0.076 eV/atom, respectively. The slightly positive value of doping energy is indicative of the metastable nature for the formation of the N- or NH-doped structures of TiO2, which are thermodynamically allowed owing to the overall negative energy of formation of the doped phase with respect to the ground-state energy of the constituent species. The positive doping energy for the N-doped phase is understandable as the OTi bonding is indeed stronger than the NTi bonding. The lower doping energy for the NH-codoped structure indicates that formation of a pair of N and H is energetically preferred with respect to N doping. In fact, a doped nitrogen atom in the O site introduces an unpaired electron, which tends to attract a H atom also with an unpaired electron to form covalent NH bonding, as shown in the charge density map shown Figure 7. It is especially worth mentioning that the optimized NH bond length in N þ H-doped TiO2 is 1.06 Å, comparable to that in a NH3 molecule (1.05 Å). This result is similar to that for anatase,55 suggesting that it is likely to make use of NH3 to dope TiO2 for an effectively narrowed band gap. This can be realized, for example, by introducing NH3 into the gas flux for magnetron sputtering deposition. 3.3. C and C þ H Doping of Rutile TiO2. C-doped TiO2 was studied using a C atom to substitute an O atom in a 2 2 2
Figure 9. Charge density difference between the pure and C-doped TiO2. A plane (110) that cuts through C was chosen.
TiO2 supercell. The optimized structures showed that their atomic displacements are greater than those for the N-doped phase. This is consistent with the fact that the ionic radius of C is larger than that of N. Thus, compared with N doping, substitution of a C atom for an O site exerts larger strain to the neighboring Ti atoms. This is bound to give rise to evident charge redistribution about ions around the C ion. Analyses of electronic populations of the C and its surrounding ions show that three Ti ions nearest to C have 0.12e more charge than those of Ti ions in the pure phase and that the second-nearest O ions to C have about 0.1e more than those in the pure phase. This indicates that C doping leads to weaker ionicity in TiO2. 8279
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Figure 11. Total charge density of C þ H-doped TiO2. A plane that cuts through C and H was chosen. The atoms circled with the dotted line are not in the chosen plane.
Figure 10. Band structure (a) and DOS (b) of TiO2 with C þ H codoping. The dotted-dashed line at energy zero represents the Fermi level.
We see from Figure 8a that there are three isolated intermediate bands due to C doping. To better characterize these impurity states, we map the charge density difference between pure and C-doped TiO2. This can be done by subtracting the charge density of the structure with C substitution from that of pure TiO2, as shown in Figure 9. The most evident charge density change occurs around the C atom, with some minor characteristics attributable to the O 2p orbitals. This is in line with the PDOS chart shown in Figure 8b, where the isolated states are mainly composed of C 2p orbitals. Similar to N doping, these C-induced isolated states do not contribute to narrowing the band gap, and the band gap between the highest O 2p band and the lowest Ti 3d band is 1.87 eV (slightly more than that of pure TiO2). All three isolated intermediate bands have considerable curvatures to indicate good carrier mobilities (the calculated electron mobility values are 235, 371, and 279 cm2/V 3 s for the lowest, middle, and highest states, respectively). Compared to N-doped TiO2, the C-doped material has more intermediate bands with greater curvatures, leading to easier excitation of valence electrons to CB, and thus contributing to extended optical absorption in the longer-wavelength range of light. TiO2 with C þ H doping was studied through introducing an interstitial H into C-doped TiO2. Only the configuration with H being in the interstitial sites nearest to the substitutional C was investigated because it is the most stable. Only two intermediate bands were present in the forbidden gap (Figure 10a), which are mainly owing to C 2p, as shown in Figure 10b. The above results indicate that, similar to N þ H doping, introducing one H into C-doped TiO2 also causes one intermediate band/state to disappear. When we introduce another interstitial H near C,
another intermediate band disappears. As a result, only one intermediate band is left within the forbidden gap. The calculated formation energies for C, C þ H, and C þ 2H doping are 0.16, 0.12, and 0.09 eV/atom, respectively (C is referred to graphite). This indicates that the C þ H- or C þ 2Hcodoped structures are energetically favored with respect to the C-doped phase. Considering that a substitutional C atom at the O site provides two unpaired electrons, it is easy to understand why one or two H atoms tend to present in the interstitial sites nearest to the substitutional C atom to form covalent CH bonding (as shown in Figure 11). Especially, the optimized CH bond length in C þ H doping is 1.12 Å, and both of the optimized CH bond lengths in C þ 2H doping are 1.11 Å. All these bond lengths are close to that in a CH4 molecule (1.09 Å). To the authors’ knowledge, neither experimental nor theoretical work has been reported on the C þ H doping of TiO2. Such theoretical and experimental studies are necessary, as TiO2-based materials are often used or processed in atmospheres that contain both C and H. Interestingly, the present work shows that it is likely to make use of CH4, for example, mixing CH4 in the sputtering gas for thin film deposition, to achieve cost-effective C þ H codoping of TiO2 for significant enhancement in optical absorption in the visible-light region. Overall, either C or N doping induces intermediate band/s in the forbidden gap of TiO2, and the introduction of each H next to a N or C dopant helps to remove one intermediate band via donoracceptor annihilation. Even though the intermediate bands in the doped TiO2 may not always contribute to the band-gap narrowing, they do contribute to extending the optical absorption edge into the longer wavelength region of the solar spectrum via the role as stepping stones to relay valence electrons into the conduction band. The moderate widths and evident curvatures of these intermediate bands are helpful to provide adequate density of states and charge carrier mobility. This offers sufficient capacity for a large number of electrons from the valence band to be energetically pumped into them, from where they can be further relayed into the conduction band. The electron mobility associated with the evident curvature of the intermediate band/s is helpful for enhanced electronhole separation to lower the probability for carrier recombination. These curved intermediate bands are fundamentally different from flat midgap defect states whose limited number of quantum 8280
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The Journal of Physical Chemistry C states limits their role as stepping stones, with the pinned electrons at the defect state/s to be readily annihilated via recombination with holes waiting below. This is helpful to both photonic and photocatalytic applications and offers great promise for practical applications of TiO2 under the illumination of visible or even infrared light, for either photovoltaic solar-cell cells or visible-light photocatalysis. As is well-known, there has been great endeavor to induce curved intermediate band/s via quantum dots/wells in single-crystal semiconductors so that a new class of “intermediate band” solar cells can be realized in order to permit multiwavelength absorption of solar light without energy waste due to the intraband relaxation of high-energy electrons in the conduction band.16 The spin DFT calculations for Ti atoms was also used for the calculations of all the above systems, and the results showed that all spin moments are nearly zero, suggesting that there is little tendency for spin polarization for the doped materials of interest to this work.
4. CONCLUSIONS DFT calculations have been carried out to study the effects of anion doping and codoping on the electronic structure of rutile TiO2, with the doping schemes covering N, N þ H, C, and C þ H. It is shown that nonmetal doping with N or C induces intermediate bands of evident curvatures, which mainly originate from N(C) 2p orbitals and are expected to facilitate optical absorption in the visible-light region. C þ H and C þ 2H codoping to TiO2 also gives rise to similar intermediate bands, and N þ H codoping induces significant band-gap reduction. The CH and NH bond lengths in C þ H- and N þ Hcodoped phases are comparable with those in CH4 and NH3 molecules, respectively. The presence of H next to the C or N dopant helps to eliminate intermediate states arising from the N(C) 2p orbitals via donoracceptor anihilation. The outcome of this work suggests that it is probable to utilize NH3 and CH4 gases to dope TiO2 for extending optical absorption into the long wavelength regions of solar irradiance for enhanced photovoltaic and photocatalytic functionalities. For example, one can readily mix one of these gases with Ar as an ionized energetic flux for plasma sputtering deposition to codope TiO2. ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. Telephone: þ44 (0)1204 903592. Fax: þ44 (0)1204 399074.
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