J. Nig. Soc. Phys. Sci. 1 (2019) 131–137 Journal of the Nigerian Society of Physical Sciences Original Research First-principles calculations of Fluorine-doped Titanium dioxide: A prospective material for solar cells application A. Shamsudeenb, A. Shuaibua,∗, S. G. Abdua, M. S. Abubakara, Abdullahi lawalb aDepartment of Physics, Kaduna State University, P. M. B. 2339, Kaduna, Nigeria bDepartment of Physics, Federal College of Education Zaria, Nigeria Abstract This study focuses on the anatase TiO2 doped Fluorine to investigate their structural and electronics properties using Density Functional Theory (DFT) within generalized gradient approximation (GGA) as implemented in Quantum ESPRESSO (QE). For the anatase TiO2 phase the calculated electronic band structures of pureTiO2 and TiO2 doped Fluorine nanocrystals are displayed along a high symmetry directions and the energy range of band structure is plotted from 0.0 eV to 3.9 eV , the energy separation between the bottom of the conduction band and the top of valence band occurred at the Γ and N points, indicating that anatase T iO2 is an indirect band gap material with an approximate value of 2.30 eV energy gap, this value is consistent with previous DFT result. When F is added the band structure did not change much because fluorine element doping is conducive to the generation of Oxygen holes and enhances the mobility of effective electrons which can enhance the conductivity of the adsorbent substrate and improve the solar cell performance of the fluorine-doped TiO2. The band gap value obtained for F doped TiO2 was found to be 2.11 eV . The dopant formation energy of Fluorine is calculated to be −55.6 Ry which is equivalent to −756.5 eV . Keywords: DFT, T iO2, Fluorine, electronic properties, solar cells Article History : Received: 26 August 2019 Received in revised form: 10 October 2019 Accepted for publication: 11 October 2019 Published: 17 December 2019 c©2019 Journal of the Nigerian Society of Physical Sciences. All rights reserved. Communicated by: B. J. Falaye 1. Introduction Engineers and scientists show so much interest in compounds made of transition metal oxides which have wide band gap, very good light absorption capability, very good value of heat formation and other various fascinating properties. This is be- cause these properties present the potential of use in advanced applications such as solar cells [1, 2, 3]. Nowadays a lot of investigations are carried out on oxide materials, especially to meet industry requirements. This is because material oxides are used in a lot of art technologies such as magnetic disks, ICs and solar cells and their likes. A lot of properties sought ∗Corresponding author tel. no: +2348179931945 Email address: alhazikara@gmail.com (A. Shuaibu ) by researchers and the industry, which is driving more research into the area, include need for economical alternative to current materials, non-toxic and environmentally friendly, wide avail- ability and good electrical, magnetic and or optical properties for use as base materials or doping in optical fibers and sim- ilar uses. These demands are partly driven by need to meet energy demand in the future [3, 4, 5]. One of the oxides which attracted a lot of theoretical and experimental research effort is TiO2 [6]. This is in order to better understand the optoelectronic properties of TiO2. Many naturally occurring and engineered polymorphs of T iO2 exist. These include anatase, baddeleyite, pyrite, columbite, brookite, fluorite, cotunnite and rutile. Three of these (i.e. anatase, brookite and rutile) exist naturally while the rest are manufactured. Due to popular demand and remark- 131 Shamsudeen et al. / J. Nig. Soc. Phys. Sci. 1 (2019) 131–137 132 able properties of the naturally occurring polymorphs such as rutile, for use in production of catalyst, flat panel displays, op- toelectronic devices, sensors, and solar cell technology and so on, many of them are often artificially synthesized. Rutile, as a result of its structure, possesses one of the high- est stabilities that can be found as compared to others. Anatase is also thermodynamically stable up to a temperature of about 800 oC. On another hand brookite has a structure that resem- bles that of rutile, though with less stability at high tempera- tures [7, 8]. The structure of anatase is the most suitable for photo catalytic applications. It is one of the reasons for attract- ing a lot of research interest into the properties of T iO2. Other properties of T iO2, for which it is held in high regards is its use in many ceramic materials to add features and capabilities such as being hydrophilic, photo catalytic, hydrophobic and having antibacterial features [9], this is aside its good chemical stabil- ity, nontoxicity and reduced cost. T iO2 is also used for air and water purification by taking advantage of its antibacterial capa- bilities. It is used in PVC fabrics, used to make materials with self-cleaning effects, used for preservation of glass and cultural heritage [10]. It is also used in de-synthesizing photo cells as a common photocathode. The history of T iO2 went as far back as 1971 when the work of Fushijima and Honda revealed the photo electrochemistry of the material while using it as an anode in an electrochemical cell. This application is what gave rise to all the interest that was generated over the years which led to discovery of a lot of its other properties [11]. Wang et al.[12] reported that T iO2, when used to fabricate ultra-violet (UV) photo-detector, shows more energy efficient operation than other material such as Gallium Nitride (GaN), Silicon (S i) and Zinc Oxide (ZnO). Its wide band gap is what limits the usage of T iO2 as a semiconductor directly used for semiconductor component. This is why it is mostly used as a substrate for other semiconductor materials especially in a thin film solar cell technology. Because of these multiple uses and benefits that can be de- rived from T iO2, it is obviously of paramount importance, to areas of harnessing solar energy, optoelectronics, capturing vis- ible and near visible light, to unveil the full potentials of this compound and its various forms. This should be done through tuning the properties of the oxides such as its band gap and so on. This need is the drive for theoretical and experimen- tal researches in order to have the comprehensive knowledge regarding its structure, properties and their relationship to its performance. A lot of work, especially experimental work is now available in the research community regarding T iO2, but theoretical results of research related to the compilation that are adequate to characterize it are still scarce. Currently most of the theoretical works are at the level of investigations which were performed via Density Function Theory (DFT). Since it gives a simple basis to characterized the quantum properties of various materials and plays an important role in designing many new materials. In addition to many experimental studies of T iO2, is seen by many as a favorable material for many important high technological applications, a few important first principle DFT studies are reported in previous work. Furthermore, the studies discussed and many others, the band gap values of the materials are either over- or under-estimated. This results in de- ducting contradictory nature of the band gaps which highlights the need for more studies. In addition, a lot of the work was done at different side by side of GGA and LDA, a technique which underestimate the band gap. Thus, to better understand the optoelectronic properties of T iO2 such as strong light ab- sorption, photocurrent sensitivity to the polarization of light it is essential to use reliable XC approximations to determine its electronic properties. To utilize the maximum spectral range in the solar spectrum, the band gap of T iO2 should be tuned, which will broaden the operational optical window of the T iO2 -based optoelectronic devices. Nowadays, doping is one of the well-approaches to improve the properties of materials. Doping can dramatically modify physical and chemical properties of materials [13]. Therefore, T iO2 is repeatedly doped with different metals and transition elements to tune its band gap and enhance its optical, electrical, and magnetic properties [14, 15, 16, 17, 18]. Non-metal doping is another approach used to narrow the band gap; in comparison to metal doping that often forms a donor level in the forbidden band, non-metal doping usually shifts the valence band edge upward [18]. Doping with non-metal elements such as F shows an enhancement in the electronic, optical, and magnetic proper- ties of narrow-band gap semiconductor materials [19, 20, 21]. The doping by F has also shown higher thermal stability and conductivity in graphene [22]. The aforesaid reasons motivated us to study the doping by Fluorine atom, which can significantly modify/tune the electronic properties T iO2. To the best of our knowledge, no theoretical studies on F-doped T iO2 exist in lit- erature. The Fluorine doping approach in T iO2 may open new paths to non-metal elements doping for various other potential applications such as infrared detectors, infrared LEDs, lasers, transistors, and thermo-photovoltaic systems. 2. COMPUTATIONAL DETAILS 2.1. Computational method The calculations are performed on the 2 × 2 × 2 supercells relative to the standard primitive unit cell of Fluorine doped anatase T iO2 within first principle calculation using Quantum ESPRESSO simulation package [23]. Perdew-Burke-Ernzerhof generalized gradient approximation (PBE-GGA) exchange-correlation potential [24] were used for treating electron-electron effects. For integrals, smearing has been adopted and to be specific Maxfessel-Paxton smearing method. The brillouin zone inte- gration is performed using Monkhorst-Pack scheme [25] with 3 × 3 × 2 k-points grids for all the materials. For fluorine doped T iO2 structure 2 × 2 × 2 supercells relative to the stan- dard conventional unit cell were used. The supercell consists of twelve numbers of atoms: four Titanium atom and eight Oxy- gen atoms. One O atom was replaced by Fluorine atom making 0.25 % occupancy by the dopant. The super cell dimensions are kept fixed throughout the calculations, while the atomic positions are fully relaxed for all calculations using Broyden- Fletcher-Golfarb-Shannon (BFGS) algorithm, until the forces acting on the atoms are below 0.001 eV/Å. 132 Shamsudeen et al. / J. Nig. Soc. Phys. Sci. 1 (2019) 131–137 133 3. RESULTS AND DISCUSSION 3.1. Convergence Test In any DFT calculation using DFT code, it is of paramount importance to perform a convergence test calculation before commencing the actual calculation. The results presented be- low represent the convergence test with respect to plane wave kinetic energy cut-off and k-points mesh for undoped anatase T iO2 and Fluorine atom doped T iO2. 3.1.1. Convergence Test Results of undoped T iO2 Figure 1: (A) the convergence of total energy with respect to the kinetic energy cut-off. (B) The convergence of the total energy with respect to the k-points grids. 3.1.2. Convergence Test Results of doped Fluorine atom. It could be seen from Figure 1 that the total energy changes considerably with the kinetic energy cut-off, until at some en- ergy cut-off where it becomes almost stable. In all the two cases, as the total energy decreases, the kinetic energy cut-off increases from 10 Ry to 40 Ry and becomes almost stable at 40 Ry. That is to say, the total energy remains constant with any further increases in the kinetic energy cut-off from 40 Ry. This indicates a well-converged energy cut-off. That is why; Figure 2: (A) NO HEADING. (B) NO HEADING. 40 Ry was used as the plane wave basis set for the kinetic en- ergy cut-off of the two cases. However, Figure 2B and Figure 5B show the variations of the total energy with respect to the k-points grids. The total energy changes considerably with the number of k-points at a certain points, showing a well-converged value. In all the two cases, the total energy increases from 1×1×2 to 3×3×2 k-point grids and become almost stable at 3 × 3 × 2. As such, 3 × 3 × 2 k-points have been adopted for the three cases. Furthermore, Monkhorst and Pack method of selecting k-points is commonly used in most DFT calculations [25]. Most of the DFT codes provide ways of choosing k-points using Monkhorst and Pack method. 3.2. Structural Properties of the Undoped T iO2 and T iO2 doped F. In order to explore the structural properties of the anatase T iO2 with space group 14/amd was simulated in Figure 3. The anatase structure exhibit tetragonal geometry and have a high symmetry in which six Oxygen atoms is surrounded to each T i atom. From Table 5, it can be observed that, for 12.5 % substitu- tional doping case, there are eight symmetrically different ap- proach in which Oxygen (O) atom can be replaced by Fluorine (F) atom(s). But for this particular study, as shown in tables above, one configuration (D8 0.125) is considered. No struc- tural transition is seen; as such the crystal parameters remained 133 Shamsudeen et al. / J. Nig. Soc. Phys. Sci. 1 (2019) 131–137 134 Table 1: Convergence test of T iO2 total energy with respect to kinetic energy cut-off of the plane wave of undoped T iO2. S/N Kinetic Energy Cut-Off (Ry) Total Energy (Ry) 1 10 -680.917 2 20 -740.466 3 30 -747.717 4 40 -747.374 5 50 -748.413 6 60 -748.421 7 70 -748.429 Table 2: Convergence of the total energy with respect to the k-points grids of undoped T iO2. S/N NUMBER OF K-POINTS Total Energy (Ry) 1 1 × 1 × 2 -749.018 2 3 × 3 × 2 -747.670 3 5 × 5 × 2 -747.673 4 7 × 7 × 2 -747.673 5 9 × 9 × 2 -747.672 6 11 × 11 × 2 -747.673 7 13 × 13 × 2 -747.674 Table 3: Convergence test of total energy with respect to the kinetic energy cut-off. S/N KINETIC ENERGY CUT-OFF (Ry) TOTAL ENERGY (Ry) 1 10 -694.517 2 20 -756.204 3 30 -763.468 4 40 -764.135 5 50 -764.174 6 60 -764.183 7 70 -764.191 Table 4: Convergence of the total energy with respect to the k-points grids of undoped T iO2. S/N NUMBER OF K-POINTS TOTAL ENERGY (Ry) 1 1 × 1 × 2 -764.697 2 3 × 3 × 2 -763.468 3 5 × 5 × 2 -763.481 4 7 × 7 × 2 -763.478 5 9 × 9 × 2 -763.478 6 11 × 11 × 2 -763.479 7 13 × 13 × 2 -763.480 Table 5: Configurations for substitutional doping of O by F anatase T iO2 material. Undoped O O O O O O O O D1 0.125 F O O O O O O O D2 0.125 O F O O O O O O D3 0.125 O O F O O O O O D4 0.125 O O O F O O O O D5 0.125 O O O O F O O O D6 0.125 O O O O O F O O D7 0.125 O O O O O O F O D8 0.125 O O O O O O O F 134 Shamsudeen et al. / J. Nig. Soc. Phys. Sci. 1 (2019) 131–137 135 Figure 3: (A): Anatase Structure for undoped T iO2 and (B) T iO2 doped F. the same as that for the undoped system. To find the stability of the structure after Fluorine doping, the dopant formation en- ergy of the Fluorine atom is estimated using Equation 1 [26]. The dopant formation energy in this context simply refers to the energy needed to insert one Fluorine atom with a chemical potential µF into the supercell after removing one Oxygen atom with chemical potential µF from the same position [27]. E f = Edoped − Eundoped + µo −µF (1) where, Edoped is the total energy of the anatase T iO2 material; Eundoped is the total energy of the anatase undoped T iO2 system; µo is the chemical potential per atom of Oxygen bulk crystal; µF is the chemical potential per atom of Fluorine bulk crystal. Following common practice, the chemical potentials were found as the DFT total energy per atom in the bulk systems. The dopant formation energy of Fluorine is calculated to be −55.6 Ry which is equivalent to −756.5 eV . This serves as the measure of the stability of the doped structure, the lower value of the formation energy signifies the most stable struc- ture. From this value of dopant formation energy, this shows that, the Fluorine doped T iO2 is stable. 3.3. Electronic Properties Electronic properties calculations are very crucial for de- scribing the optoelectronic properties of solids. The electronic properties investigations of T iO2, doped Fluorine covers the electronic band structure, density of state (DOS) and partial density of state (PDOS). The main purpose of the ground state, electronic band structure, DOS and PDOS calculations in this work is to obtain KS eigenvalues and eigenfunctions as well as useful information about the electronic properties of the con- cerned materials. To understand the effect of doping on T iO2, Fluorine (F) was added in the calculations. The calculated elec- tronic band structures of pure T iO2 and T iO2 doped Fluorine thin film are displayed along the eight symmetry (Γ → H → N → P → Γ → X → M → R) directions and the energy range of band structure is plotted from 0.0 eV to 3.9 eV . The Fermi level position on the band structure of these crystals is shown by the zero on the energy scale. PBE exchange correlation poten- tials is chosen over LDA, because in several cases GGA-PBE gives more reliable and accurate results for DFT electronic cal- culation. The energy separation between the bottom of the con- duction band and the top of valence band occurred at the Γ and N points or band structure calculations within PBE which in- dicate that anatase T iO2 is an indirect band gap material with value of 2.30 eV energy gap, this value is consistent with pre- vious DFT result. However, the value is smaller than experi- mental result of 3.21 eV [28] and this effect is the limitation of DFT approach due to approximations used in the exchange- correlation functional. On the other hand, the F-doped T iO2 model was established based on the perfect crystal plane model. A fluorine atom replaces one of the O atoms on the surface of the anatase T iO2 perfect crystal plane, and F atom combined with T i atoms to form T i − F bonds. It can be seen that the energy band gap did not change much after the fluorine atom being doped and the value obtained was found to be 2.11 eV . Furthermore, fluorine element doping is conducive to the gen- eration of Oxygen holes and enhances the mobility of effective electrons, which can enhance the conductivity of the adsorbent substrate and improve the solar cell performance of the fluorine- doped T iO2. Figure 4: Band structure of (A) Pure T iO2 (B) F doped T iO2 For more clarification for the nature of the energy gap, we have also study the total density of state (DOS) of anatase T iO2, and F doped anatase T iO2. Figure 5 shows a decomposition of the calculated total DOS of T iO2 and F doped T iO2 in bulk forms. For pure T iO2 the lowest valence states is dominated by T i-s orbital and O-p orbital while in the cased of F doped T iO2 the lowest valence states is dominated by T i-s orbital, O-p orbital and F-p orbital. The T i-d orbital and O-s orbital con- tribute much high in the conduction band for pure T iO2 while T i-d, O-s, O-s orbital as well as F-s orbital contributed slightly higher in the conduction band. The T i-p and O-p orbitals of T iO2 contribute a slightly higher in the valence band near the Fermi level. For F anatase doped T iO2 the main contribution 135 Shamsudeen et al. / J. Nig. Soc. Phys. Sci. 1 (2019) 131–137 136 Table 6: Calculated energy gap of T iO2 and T iO2 doped F with previous first principle calculations and experimental data. Material Work Method Band gap Eg(eV ) Nature Pure T iO2 Our Work PBE-GGA 2.30 Indirect Other Work PBE-GGA[29] 2.14 Indirect EV-GGA[29] 2.32 Indirect PBE-GGA[30] 2.30 Indirect PBE-GGA[31] 2.30 Indirect Experiment[32] 3.21 Indirect F doped T iO2 Our Work PBE-GGA 2.11 Indirect of valence band near the Fermi level is from T i-p orbital and O- p orbital. The T i-s, O-s and O-p orbitals contributed the most near the Fermi level, thus held responsible for the properties of T iO2. Also, s- and p-orbitals of T i atoms, s- and p-orbitals of O atoms and s-orbital of F atoms of F doped T iO2 compound contributed the most near the Fermi level, thus held responsible for the properties. Figure 5: Total and partial density of state (A) Pure T iO2 (B) F doped T iO2. 4. Conclusion A first principle study was used using PBE XC functional in Quantum ESPRESSO code. The available results were com- pared with other experimental values. The electronic properties density of state, partial density of state and band gap values were calculated in the ground state properties. It was found that T iO2 in anatase phase has indirect band gap with a value of 2.30 eV , this value is consistent with previous DFT results. The obtained band gap value is smaller than experimental result of 3.21 eV and this effect is the limitation of DFT approach due to approximations used in the exchange-correlation functional. The Fluorine doped T iO2 model was established based on the perfect crystal plane model. A fluorine atom replaces one of the O atoms on the surface of the anatase T iO2 perfect crys- tal plane, and F atom combined with T i atoms to form T i − F bonds. It can be seen that the energy band gap did not change much after the fluorine atom being doped. Furthermore, fluo- rine element doping is conducive to the generation of Oxygen holes and enhances the mobility of effective electrons which can enhance the conductivity of the adsorbent substrate and im- prove the solar cell performance of the fluorine-doped T iO2. The dopant formation energy of Fluorine is calculated to be −55.6 R which is equivalent to −756.5 eV . 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