Band gap engineering of ZnO substituted with nitrogen and fluorine, ZnO_1−3xN_2xF_x: a hybrid density functional study

Abstract

A series of first principles calculations within density functional theory (DFT) have been performed for ZnO, co-doped with N and F with the aim of engineering the band gap and improving its application to photo-absorption activity. A reliable hybrid functional of Heyd, Scuseria and Ernzerhof (HSE) has been used in order to predict the properties of ZnO_1−3xN_2xF_x. We describe a site disordered solid based on the consideration of configurational ensembles and statistical mechanics. The co-doped ZnO energy band gap shrinks and hence the photo absorption activity is enhanced by a considerable amount. The valence band maxima (VBM) of ZnO is dominated by O-2p orbitals with a considerable contribution from Zn-3d states. In co-doped ZnO_1−3xN_2xF_x just above the VBM a new band appears which is mainly composed of N-2p orbitals. The calculated formation energy ΔH_f for ZnO, in zinc rich and oxygen rich conditions are in good agreement with previous results. The calculated binding energies suggest that the stability of ZnO_1−3xN_2xF_x deteriorates at very dilute concentrations suggesting the use of heavy doping is desirable. Our results are helpful in understanding the growth conditions, electronic and optical properties of co-doped ZnO.

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1 Introduction

Earth abundant ZnO with a wide direct band gap (3.37 eV)¹ and a large exciton binding energy (60 meV) at room temperature is a very promising material for electronic and optoelectronic applications^2,3 such as in blue and UV lasers, light emitting diodes, solid state lighting and transparent conductors. For the realization of ZnO based optoelectronic devices, there is great effort in recent years by both theoreticians and experimentalists to achieve stable and p-type ZnO. Great efforts have been made by several authors by doping acceptors such as N,^4,5 P⁶ As,⁷ Sb,⁸ etc. to achieve p-type ZnO. Detailed strain induced optical and photo-catalytic properties of ZnO have been studied by Thanayut et al.⁹ However, it is well established that the donor–acceptor co-doping/cluster doping method is promising in terms of enhancing the acceptor concentration and lowering the acceptor level.^10,11 Co-doping with group 15 elements and N, such as As–N¹² and P–N¹³ have also realized p-type ZnO. There are two main factors which could limit doping. One is low dopant solubility and the other is high defect ionization energy. Wen et al.¹⁴ performed calculations on a N and F co-doped 32 atom supercell using the CASTEP code to show that an N and F complex can lead to a more shallow acceptor level than that of N. In the above study, the generalized gradient approximation (GGA) was used which underestimates the band gap and total energy, and hence the results cannot be compared directly with the experimental data. Therefore, a more advanced scheme has to be used for the study of the ZnO co-doped system. Saha et al.¹⁵ prepared N and F co-doped ZnO samples, and performed X-ray photoelectron spectroscopy along with the ab initio calculations, to understand the electronic properties imparted by heavy co-doping of N and F.

Looking at the available experimental and theoretical results there is an immediate need to address the following points: (a) impact of the presence of N and F dopant on the electronic structure, (b) influence of N and F co-doped ZnO on the optical spectrum and (c) understanding thermodynamic stability of defects in ZnO. In order to explain the above, we performed detailed calculations to describe structural, thermodynamic, electronic and optical properties. The stability of co-doped systems has been assessed by calculating the formation energy and defect pair binding energy. The characteristic changes due to the co-dopants have been explained by an analysis of the partial density of states (PDOS). Special attention has been paid to understand the role of impurity bands on the optical properties. The structure of the paper is organized as follows. Section 2 concerns the computational details used in present study. In Section 3, we present the results and discussion of undoped and co-doped ZnO. Finally the concluding remarks based on our results are summarized in Section 4.

2 Computational details

We have performed DFT based calculations using the projector augmented wave (PAW) to describe the frozen core electrons and their interaction with valence electrons as implemented in the Vienna Ab initio Simulation Package (VASP).¹⁶ The cutoff energy for all calculated systems was kept constant at 400 eV for a plane wave basis set expansion. The valence states considered during the calculations are Zn(3d, 4s), O(2s, 2p), N(2s, 2p) and F(2s, 2p). We have employed the Monkhorst and Pack¹⁷ scheme to generate Γ-centered K point sets. The Gaussian smearing method with smearing width of 0.1 eV has been adopted to account for partial occupancies. The atomic positions were relaxed until the forces on each atom became smaller than 0.01 eV Å⁻¹ and the total energy converged within 10⁻⁶ eV. The local density approximation (LDA) as given by Ceperley and Alder¹⁸ and GGA as parameterized by Perdew, Burke and Ernzerhof (PBE)¹⁹ has been used to calculate the structural parameters. It is known that LDA/GGA (local/semi-local) functions underestimate energy band gaps and can give zero gaps for small energy gap semiconductors. There are several reasons for this, such as lack of derivative discontinuity and an incomplete self-interaction cancellation in the GGA exchange correlation (xc) functional. To reach the final conclusion, we have also performed HSE calculation to obtain the lattice constants.

The mixing of a certain amount of non-local Hartree–Fock (HF) exchange interaction in the PBE scheme,²⁰ the so-called hybrid functional, has proven to improve the description of the electronic structure (including energy band gap). However, there are practical computational difficulties in this approach arising from the evaluation of the slowly decaying Hartree–Fock exchange E^HF_x with distance. To solve this problem Heyd et al.²¹ proposed a more tractable hybrid functional scheme for supercell calculation as follows:

E^HSE_xc = αE^HF,SR_x(μ) + (1 − α)E^PBE_x(μ) + E^PBE,LR_x(μ) + E^PBE_c (1)

where α represents the percentage of HF exchange included and μ is the controlling parameter for the range separation of the exchange interaction into short-range (SR) and long-range (LR) components, E_c is the correlation energy which remains unchanged relative to PBE functional. We have found that a value of α = 0.37 and μ = 0.20 Å⁻¹ can reproduce the experimental energy band gap of ZnO (3.37 eV). However, in standard calculation of HSE06 the values of α and μ are 0.25 and 0.20 Å⁻¹, respectively. Therefore we denote our calculation as HSE instead of HSE06. These parameters are fixed for all subsequent calculations. In the present calculations, we have used three different sizes of supercells (2 × 2 × 1, 2 × 2 × 2 and 3 × 3 × 2) each doped with N (2x) and F (x), with the corresponding concentrations x = 12.50, 6.25 and 2.78%. The concentration of N is twice that of F in each supercell. The distribution of dopant N and F was investigated by generating all symmetrically inequivalent configurations in the different supercells. The distribution of N and F in the 2 × 2 × 1 supercell is shown in Fig. 1.

Fig. 1 The crystal structure of a 2 × 2 × 2 atomic supercell. The Zn, O, N and F atoms are shown in brown, magenta, blue and light green colour, respectively.

In order to find the inequivalent configurations, we follow the procedure implemented in the Site Occupancy Disorder (SOD) program.²² In this approach all possible configurations (C_Total) in a given supercell are generated under the assumption that each configuration can be uniquely described by the enumeration of the substitution site in a parent structure. The number of inequivalent configurations (C) are 13, 31 and 136 for 2 × 2 × 1, 2 × 2 × 2 and 3 × 3 × 2 supercells, respectively. As shown in Table 1, the total number of configurations is quite high but this number is drastically reduced when the symmetry of the lattice is taken into account. SOD has been employed in a previous study in the description of species distribution over crystal sites in other materials.^23,24 We studied all the inequivalent configurations given in Fig. 2. The calculated energy range of each spectrum is significant with energy differences of approximately 0.88 eV between the most and the least stable configuration. As shown in Fig. 2, the energy difference between inequivalent configurations is reduced considerably for the 3 × 3 × 2 supercell. In the high energy end of the spectra, the density of configurations increases with supercell size and it is largest for the 3 × 3 × 2 supercell. For the calculation of electronic and optical properties, we have used only the most stable configuration for each composition, which is partially justified by the Boltzmann probability analysis. For example, for the 2 × 2 × 1 supercell with composition x = 12.50%, we obtained that the lowest energy configuration (Fig. 1) has a probability of 0.64 at 300 K and 0.32 at 1100 K while all other configurations have much lower probabilities. Therefore the configuration in Fig. 1 is the dominant pattern in the ion distribution. Further, for x = 6.25 and 2.78%, we obtain the lowest energy configuration at probability equal to 0.99 and 0.56 at 300 K, which is lowered to 0.66 and 0.10 at 1100 K. Our approach ignores, as a first approximation, the effect that departure from that ordered pattern has on the electronic structure, which would require further investigation.

Table 1 Total number of configurations (C_Total) and number of symmetrically inequivalent configurations (C) calculated for ZnO_1−3xN_2xF_x

Supercell	Conc. (x) (%)	CTotal	C
2 × 2 × 1	12.50	168	13
2 × 2 × 2	6.25	1680	31
3 × 3 × 2	2.78	19 040	136

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Fig. 2 The calculated configurational energies (relative to lowest energy for each composition) of inequivalent configuration generated by SOD.

The HSE approach overcomes the deficiency of the underestimation of the band gap. However such calculations are computationally too expensive to be carried out for large number of k-points as needed for the computation of optical spectra. Therefore, we have adopted the following procedure to calculate the optical spectra. First, we compute ab initio the HSE band structure and PDOS. Second, we calculate the dielectric function with dense k mesh (10 × 10 × 10 Γ centered) using semi-local GGA method.²⁰ Finally the calculated optical spectra are shifted by a scissor’s operator (Δ) so as to match the energy band gap calculated by HSE. The value of Δ = 2.38, 0.87, 1.26, 1.21 eV for x = 0.00, 2.78, 6.25 and 12.50%, respectively. This approach requires less computer time. On the other hand, it allows the inclusion of a dense k mesh and bands, which is necessary for the computation of optical properties.

3 Results and discussion

3.1 Structural parameters

Once we figure out the most stable configuration, this configuration was relaxed using conjugate gradient minimization until the Hellmann Feynman forces acting on each ion are less than 0.01 eV Å⁻¹. The minimum of the total energy with respect to the volume is obtained by the fitting to the Murnaghan equation of state.²⁵ The best results are obtained within HSE. The estimated lattice constant shows very good agreement with measured values^1,15 and previous calculations,^14,15,26 presented in Table 2. There is a common feature in calculated lattice constants, that a increases with increasing concentration (x), while c shows very minor change irrespective of XC. The optimized lattice parameters for different structures of co-doped ZnO are not significantly different from bulk ZnO, presented in Table 2.

Table 2 Calculated lattice constants (Å) and energy band gap E_g (= Γ_ν − Γ_c) (in eV) for the ZnO_1−3xN_2xF_x system along with other calculations and available experimental value

Conc. (x)		Present			Other			Experimental
		LDA	GGA	HSE	LDA	GGA	HSE
a Ref. 14.b Ref. 13.c Ref. 25.d Ref. 1.
0.00%	a	3.172	3.277	3.246	3.181^a	3.22^b	3.249^c	3.248^a
	c/a	1.614	1.626	1.600	1.600^a	1.60^b	1.599^c	1.601^a
	Eg	0.72	0.79	3.37		0.73^b	3.43^c	3.37^d
12.50%	a	3.223	3.310	3.295
	c/a	1.614	1.615	1.634
	Eg	0.44	0.48	2.79
6.25%	a	3.212	3.292	3.257		3.31^b
	c/a	1.603	1.606	1.606		1.61^b
	Eg	0.61	0.66	3.09
2.78%	a	3.207	3.289	3.249
	c/a	1.608	1.602	1.613
	Eg	0.62	0.66	3.10

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3.2 The formation energy

The formation energy of bulk ZnO is evaluated using HSE XC assuming equilibrium with a reservoir of Zn and O. Under thermal equilibrium:

μ_Zn + μ_O = ΔH_ZnO (2)

where ΔH_ZnO is the formation energy of ZnO and μ_i represents the chemical potential of the element i. Here μ_Zn and μ_O were varied between the oxygen poor (zinc rich) limit (μ_Zn = μ^bulk_Zn and ) and the oxygen rich (zinc poor) limit (μ_Zn = μ^bulk_Zn + ΔH_ZnO). Depending upon growth conditions μ_Zn could vary in the energy range ΔH_ZnO ≤ μ_Zn ≤ 0. Our calculated value of ΔH_ZnO = −3.43 eV per ZnO molecule or per pair of Zn and O, compared to the experimental value −3.6 eV,²⁷ indicates that the energy calculated from first principles is quite promising.

The calculated formation energy tells us about the thermodynamic stability and its equilibrium concentration. It also explores the optimum growth conditions and their stability. The defect formation energy ΔH_f depends on the chemical potential of the host and the defect element. The formation energy of co-doped ZnO in the neutral state is defined as follows:

ΔH_f = E_TOT(D) − E_TOT(bulk) + Δn_Znμ_Zn + Δn_Oμ_O + ΣΔn_iμ_i (3)

where E_TOT(D) is the total energy obtained from the supercell calculation with impurity N and F and E_TOT(bulk) is the total energy of the equivalent perfect supercell. n_i indicate the number of atoms of the type i that has been added (n_i < 0) or removed (n_i > 0) from the supercell and μ_i is the chemical potential of the corresponding species. The quantities Δn_i and μ_i are the number of species i (Zn, O, N and F) removed from the perfect cell to its respective reservoir to form a defective cell and the corresponding reservoir chemical potential, respectively. The value of chemical potential of μ_Zn, μ_O, μ_N and μ_F should not exceed the energy of hcp Zn, gaseous O₂, N₂ and F₂. Our calculations give an upper limit μ^bulk_Zn = −2.44 eV, μ^gas_O = −16.20 eV, μ^gas_F = −7.57 eV and μ^gas_N = −22.42 eV, respectively. For the calculation of the chemical potential, we have used HSE XC which gives relatively better results than LDA/GGA. At the equilibrium condition between the reservoir of Zn, O and ZnO, eqn (2) must be satisfied. The chemical potential of the element cannot exceed that of the respective bulk or gaseous state i.e. μ_Zn ≤ μ^bulk_Zn and μ_O ≤ μ^gas_O. Our calculations of the formation energies suggests that x = 2.78% in all the three cases of substitutional doping is energetically favored. The variation of the formation energy for co-doped ZnO (2 × 2 × 1, 2 × 2 × 2 and 3 × 3 × 2 supercell) along with the change in chemical potential (Δμ) from Zn-rich to O-rich condition is shown in Fig. 3. Our calculations show that the O-rich condition has a positive value of the formation energy which shows a decreasing trend as we proceed towards O-poor condition. The formation energy is highly negative under Zn-rich condition. This indicates that the solubility of N is effectively enhanced by using N and F co-doping method. The present calculation also shows that Zn-rich condition is more suitable than the O-rich condition for the growth of N and F co-doped ZnO.

Fig. 3 The variation of defect formation energy with change in chemical potential (Δμ) from Zn-rich to O-rich conditions for 2 × 2 × 1, 2 × 2 × 2, 3 × 3 × 2 supercells.

3.3 Binding energy

We have also calculated the binding energy (E_b), which is equal to the energy difference between the total energy of the complex compound and the sum of the total energies of the isolated constituents, defined as follows

E_b = E^f_N–ZnO + E^f_F–ZnO − E^f_NF–ZnO − E^f_ZnO (4)

where E^f_N–ZnO, E^f_F–ZnO, E^f_NF–ZnO and E^f_ZnO represents the energy of N doped, F doped, N and F co-doped and undoped ZnO in same supercell, respectively.

A positive binding energy implies that the energy to create isolated defects is higher than for forming the complex compound, i.e. the interaction between defects is attractive and complex formation becomes thermodynamically advantageous. The calculated binding energies for 2 × 2 × 1, 2 × 2 × 2 and 3 × 3 × 2 supercells are equal to 2.41, 2.72 and 0.29 eV, respectively. These positive values of E_b suggest that the stability of N and F co-doped system deteriorates at very dilute concentration which clearly suggests that the doping of the system must be heavy.

3.4 Electronic properties of ZnO

The calculated band structure (BS) and projected density of states (PDOS) for ZnO is presented in Fig. 4a. These figures show a direct band gap of 3.37 eV for ZnO which is in good agreement with experiment.¹ This shows that HSE hybrid function successfully overcomes the limitation of the conventional LDA/GGA which underestimates energy band gaps. Therefore it is justified to use HSE for the co-doped systems also. Analysis of the PDOS (Fig. 4a) indicates that the VBM is composed of mainly O-2p and an appreciable amount of Zn-3d, while conduction band minima (CBM) is dominated by mainly Zn-4s, with a relatively small amount of Zn-4p. As shown in Fig. 4a, the lower part of the valence band ∼−5.5 to −3.8 eV shows a broad structure in the PDOS which is attributed to the strong hybridization between O-2p and Zn-3d orbitals. The upper part of VBM ∼−4.0 to 0 eV is dominated by the O-2p orbitals with a small contribution of Zn-3d orbitals. The conduction band is located above ∼3.4 eV with gradually increasing density of states (DOS). The main components of the conduction bands are the Zn-4s and O-2p orbitals.

Fig. 4 The calculated band structure and partial density of states of ZnO_1−3xN_2xF_x for (a) x = 0.00% (b) x = 2.78% (c) x = 6.25% and (d) x = 12.50%.

3.5 Electronic properties of N and F co-doped ZnO

In this section, we will discuss how the presence of n-type (F) and p-type (N) dopant can reduce the energy band gap which is useful for optoelectronic devices. Both N and F are simultaneously introduced into the supercell to model the co-doped system. The normalized total density of states (TDOS) for x = 0.00, 2.78, 6.25 and 12.50% are presented in Fig. 5. There is no acceptor level for x = 0.00% while three distinguished structures appear at ∼−1.5, −2.2 and −2.9 eV in the upper valence band dominated by O-2p for ZnO. For x = 2.78 and 6.25% the states at ∼−2.2 and −2.9 eV get broader, however, the main structure at ∼−1.5 eV remains distinguished because O-2p with appreciable amount of Zn-3d still dominates the VBM. When the concentration of N and F increases to x = 12.50%, a strong acceptor level appears just above the VBM dominated by N-2p instead of O-2p and Zn-3d. This happens because the energy of N-2p is higher than O-2p. Since the N atom has five valence electrons compared to six electrons of O, two N atoms provide two holes and one F provides one electron. We choose two N and one F atoms as double acceptors in order to avoid the repulsion interaction between acceptors. On the other hand, we used F to substitute for O atom in order to reduce the anion and cation p–d coupling. Our findings are in good agreement with previous calculations performed for co-doped TiO₂²⁸ and BiNbO₄.²⁹ Gai et al.³⁰ had suggested that by substituting an isovalent elements of N as acceptor, could reduced the transition. The doping of isovalent elements in the CaO ordered structure has been studied by Naeemullah et al.³¹ Calculations predict reduction in energy band gap with increasing size of anion, however no localized states appear in this gap.

Fig. 5 The calculated normalised total density of states of Zn_1−3xN_2xF_x for x = 0.00%, 2.78%, 6.25% and 12.50%.

The band structure and PDOS of ZnO_1−3xN_2xF_x for x = 0.00, 2.78, 6.25 and 12.50% presented in Fig. 4a–d, shows that there is a significant reduction of the direct energy band gap by N and F co-doping, which is an important outcome of the present study. The direct energy band gaps for x = 0.00, 2.78, 6.25 and 12.50% are found to be 3.37, 3.10, 3.09 and 2.79 eV, respectively. The calculated band structure gives rise to sub-bands at the top of the valence band originating from N and F co-substitution. The band width of the sub-bands for x = 2.78, 6.25 and 12.50% are equal to ∼0.52, ∼1.82 and ∼1.36 eV, respectively. There is a substantial increase in band width of sub-bands with increasing concentration of N and F. We can also conclude that electrons are more delocalized for light to heavy doping of N and F. For x = 2.78% (Fig. 4b) the defect sub-band shows two minima along the L → M and H → K directions of the Brillouin zone. Both minima have the same energy equal to ∼0.5 eV, resulting in a sharp structure in the PDOS contributed mainly by N-2p, as presented in Fig. 4b. Further with the increasing N and F co-doped concentration, the energy difference between the band present along L → M and H → K increases, causing two distinguished structures to appear in the PDOS for x = 6.25%, as presented in Fig. 4c and dominated by N-2p orbitals. The sharp peaks in the valence bands of ZnO become broadened and diffused due to disorder upon the substitution of N and F atoms at the anion site. With further increase of N and F concentration, i.e. x = 12.50%, the lower sub-band shows a substantial contribution arising from Zn-3d orbitals. From Fig. 4b–d, we find that the F-2p states lie deep relative to the N-2p states. Thus the reduction in energy band gap is a consequence of the co-substitution of N and F, as F enhances the effect of N substitution. On the other hand the CBM remains unaffected by the substitution of N and F. A detailed investigation of co-doping of N–N, P–P and N–P in SrTiO₃ has been presented by Liu et al.³² The presented results shows an acceptor level appearing at the valence band edge which causes a reduction in the energy band gap.

3.6 Optical properties of N and F co-doped ZnO

We have calculated the imaginary part of the frequency dependent dielectric function ε(ω) for x = 0.00, 2.78, 6.25 and 12.50%. A Gaussian broadening of 0.10 eV has been used for all the four cases. Since ZnO_1−3xN_2xF_x has hexagonal crystal symmetry, one can distinguish between ordinary (E ⊥ C) and extraordinary (E ∥ C) light polarizations. The exciton effect causes a redistribution of the spectral strength at lower photon energies which is not included in the present paper. Schleife et al.³³ computed optical spectra including excitonic effect using a GGA + U + scissor operator (Δ). The parameter Δ is used to match the calculated energy band gap with the more accurate ab initio quasiparticles approach.

ZnO_1−3xN_2xF_x possesses hexagonal symmetry which results in anisotropic optical properties as shown in Fig. 6. The calculated ordinary/extraordinary part of the dielectric function for x = 0.00, 2.78, 6.25 and 12.50% are presented in Fig. 6a–d along with available ellipsometry spectra for ZnO.³⁴ As we can see from Fig. 6a, substantial optical absorption for bulk ZnO as well as co-doped materials is restricted to photon energies below 20 eV. In terms of energy positions of the peaks, the agreement with the measured³⁴ imaginary part of ZnO is very good except near the absorption edge. The absorption is dominated by bound excitonic states which is independent of the light polarization. It has become possible to compute two-particle excitonic effect excitations in the framework of Bethe–Salpeter-Equation (BSE).³³ However, such calculations are very time consuming and would take us away from the main theme of this work.

Fig. 6 The calculated imaginary part of dielectric function ε₂(ω) of ZnO_1−3xN_2xF_x for (a) x = 0.00%, (b) x = 2.78%, (c) x = 6.25% and (d) x = 12.50%.

With the help of BS and PDOS we will attempt to assign the various peaks to electronic transitions. There are three peaks beyond the absorption edge in the spectrum. The peak A at ∼8.2 eV could arise from the transitions from the top valence band states (VBs) (includes to 0.05 eV below) to the conduction band states (CBs). The peak B has multiple structures between ∼11.5 and 12.0 eV. These could be caused by transitions from O-2p VBs (includes 1.0 eV below the VBM) in the CBs. Furthermore the structure C at 13.0 eV appears to arise from Zn-3d located below (2.5 eV) the VBM. A small structure D at 16 eV may be a mixed transition from Zn-3d and O-2p states and a small contribution from Zn-3s lying below (3.5 eV) the VBM.

There is weak polarization anisotropy in the plateau like region ∼5 to 7 eV, in Fig. 6a. However, it is more visible in the narrow energy range i.e. from the absorption edge to 5 eV and ∼7 and 13 eV. This confirms that anisotropy is mainly contributed from O-2p VBs. For the N and F co-doped system, x = 2.78%, presented in Fig. 6b, anisotropy is lifted and the sharp peaks at A, C and D get broadened. The peak B remains relatively sharp because it is attributed to the Zn-3d states. For x = 6.25%, a strong structure appears at ∼2 eV near the edge of the absorption spectra. This peak is large because of the high defect density. We observe that there is a sharp peak at the edge of absorption for x = 12.50% because the energy band gap has significantly reduced due to the heavy co-doping of N and F as shown in Fig. 6c and d. The reduction in the energy band gap is due to increased attractive forces between ions by the incorporation of F. This pulls down the Zn-4s states of CBM.

Our calculated imaginary part of the dielectric function is compared with the available experimental curve.³⁴ We find good agreement in terms of peak positions. The absorption coefficient α(ω) can be obtained in terms of the real and complex part of the dielectric function ε(ω).³⁵ To make a direct comparison to experiment and absorption coefficient, we use our calculated dielectric function to compute ε(ω) using the following equation.

The results are shown in Fig. 7. The main effect of N and F incorporation is to introduce a red shift of the absorption onset and not a defect related peak in the band gap region. The red shift of the absorption edge is considerable even for inclusion of N and F as low as for x = 2.78% and gives rise to notable absorption in the visible region. For moderate concentrations, x = 6.25 and 12.50%, the absorption edge is not further shifted, however, the magnitude of the absorption in the visible spectral region increases. Our results explicitly show the importance of co-doping in ZnO which is also consistent with previous calculations.^14,15

Fig. 7 The calculated absorption coefficient α(ω) of ZnO_1−3xN_2xF_x for (a) x = 0.00%, (b) x = 2.78%, (c) x = 6.25% and (d) x = 12.50%.

4 Conclusions

To conclude, we performed first principles calculation using HSE to systematically investigate the stabilities, band structure and optical properties of ZnO_1−3xN_2xF_x alloys with varying N and F content. Results suggest that Zn-rich condition is more stable than O-rich condition. The energy band gap of N and F co-doped ZnO decreases with increasing concentrations (x) of N and F. The optical properties of pure ZnO and N and F co-doped ZnO are investigated and our calculations suggest that heavily co-doped N and F enhance the acceptor energy level. The calculated optical properties for x = 6.25 and 12.50% shows a strong absorption peak in the visible region and strongly indicates that heavily N and F co-doped ZnO could be used as materials for optoelectronic devices.

Acknowledgements

One of us (SK) thanks Ricardo Grau-Crespo, J. Furthmüller and R. Goldhahn for helpful discussion and is also grateful to INSA-DFG for the financial support to visit OVGU, Magdburg, Germany. SA thanks IIT Delhi and CSIR-NPL for financial support. He also thanks the use of the HPC at the Intra-University Accelerator Centre (IUAC) in New Delhi, Physics Department IIT Kanpur, Institute of Mathematical Science (IMSc) in Chennai and Fourth Paradigm (CSIR-4PI) in Bangaluru. Furthermore, this work was supported by the Science and Engineering Research Board (SERB), New Delhi vide grant no. SB/S2/CMP-033/2014.

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