1. Introduction

Zinc oxide (ZnO) is well known as a fascinating semiconductor with a wide direct band gap of 3.37 eV and a large exciton binding energy of 60 meV at room temperature^{[1, 2]}. The study of ZnO has attracted increasing attention in the past few decades due to its potential applications in short wavelength optoelectronics devices^[3-6]. It is well known that both n-type conduction and p-type conduction of ZnO are imperative in optoelectronics devices^[7]. However, to date, most ZnO, which exist in nature or have been synthesized in the laboratory, are n-type semiconductors due to the low acceptor solubility, deeper acceptor levels and various self-compensating effect forming native defects^{[8, 9]}. There are a few reports about p-type ZnO^[10-15]. Zhang et al.^[12] predicted theoretically that Na substitutes Zn in ZnO has a shallow acceptor level on 170 meV. Ye et al.^{[13, 14]} achieved experimentally reliable p-type ZnO thin films and nanorod doped with Na. Recently, Pandey et al.^[15] demonstrated reliable fabrication of ZnMgO thin films doped with Na by dual ion beam sputtering, the p-type conduction in thin films has been confirmed by Hall measurement and band structure. In a physical picture, the upper valence band ($-4.0$ to 0 eV) is contributed mainly by the O-2p orbitals with some mixing of the Zn-3p and Zn-3d orbitals. Thus, Na substitutes for Zn only lead to small perturbations at the valence band maximum (VBM). Furthermore, because the d orbitals of Na do not have any electrons, the weakened p-d coupling also lowers the energy levels^[12]. However, it is still difficult to fabricate high-quality p-type ZnO because the Na atoms tend to occupy the interstitial sites, which lead to the self-compensation^{[8, 9]}. On the other hand, Persson et al.^[16] reported that the level of VBM of ZnO would shift-up due to a strong valence band offset bowing of S doped in ZnO. The shift-up may lower the acceptor energy level and heighten the doping efficiency of the p-type ZnO. Xu et al.^[17] realized p-type conduction in Ag-S codoped ZnO thin films. Yao et al.^[18] also observed stable p-type conduction in the Ag-S codoped ZnO thin films, the physical mechanism of this was attributed to the formation of the Ag$_{\mathrm{Zn}}^{+}$-S$_{\mathrm{O}}$ complex acceptor. Recently, Niu et al.^[19] did an experimental and theoretical research on the S-N co-doped ZnO, and the results show that the S impurity plays a significance role in forming the p-type conductivity. However, to the best of our knowledge, there has been very little research performed on the p-type conduction of Na-S co-doping ZnO. In this work, Na/S mono-doping and Na-S co-doping in ZnO are studied by first-principles calculations, and it is found that Na-S could be a candidate of p-type conduction.

2. Computational methods

ZnO has a hexagonal structure with a P63mc space group, and each unit cell contains two O atoms and two Zn atoms. In this work, a 72 atoms supercell, which consists of 3 $\times$ 3 $\times$ 2 primitive cells is used, as shown in Fig. 1(a). Fig. 1(b) shows the Na-doped structure of ZnO (Na$_{\mathrm{Zn}})$. For S-Na co-doped structures, we took two configurations into consideration. Fig. 1(c) shows that the Na and S atoms substituted Zn and O atoms, respectively, denoted as Na$_{\mathrm{Zn}}$-S$_{\mathrm{O}}$. Fig. 1(d) shows that one S atom substituted an O atom, while the Na atom occupied the interstitial site, denoted by Na$_{\mathrm{in}}$-S$_{\mathrm{O}}$. In the present work, all the structural geometrical optimization, electronic properties are performed using the density function theory (DFT) approach based on pseudo-potential technology. The exchange and correlation interactions were modeled using the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) functional^[20]. The ionic cores were represented by ultrasoft pseudopotentials for Zn, O, Na and S atoms. The zinc 3d$^{10}$4s$^{2}$ electrons, the oxygen 2s$^{2}$2p$^{4}$ electrons, the sulfur 3s$^{2}$3p$^{4}$electrons and the sodium 2s$^{2}$2p$^{6}$3s$^{1}$ electrons were treated as a part of the valence states. The Brillouin zone integration was performed over the 3 $\times$ 3 $\times$ 3 grid sizes using the Monkorst-Pack method, the plane-wave cutoff energy was set as 450 eV. In the structural geometrical optimization processes, the force on each atom was converged to less than 0.1 eV/nm, the maximum ionic displacement was within 0.002 Å, and the total stress tensor was not greater than 0.1 GPa. All the calculations were performed in the reciprocal space.

Figure  1.  (Color online) Supercell of ZnO for (a) ZnO, (b) Na$_{\mathrm{Zn}}$, (c) Na$_{\mathrm{Zn}}$-S$_{\mathrm{O}}$, and (d) Na$_{\mathrm{in}}$-S$_{\mathrm{O}}$.

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3. Results and discussion

The formation energy ($E_{\mathrm{f}})$ is an important physical factor when it turns to the solubility property and the energy stability of dopants. The formation energy of the doped ZnO supercells in neutral charge state is defined as^{[21, 22]}

where $E^{\rm tot}[X]$ is the total energy of the supercell with doping, $E^{\rm tot}[\text{bulk}]$ is the total energy of the same supercell without doping, $n_{i}$ is the number of atoms added to ($n_{i} >0)$, or removed out ($n_{i} <0)$ of the supercell, and $\mu_{i}$ is the chemical potential. We took the two extreme conditions of O-rich and Zn-rich into consideration because the growth environments influence the chemical potential. Under extreme O-rich conditions, $\mu_{\rm Zn} =\mu_{\rm Zn} (\text{bulk})+\Delta H_{\rm f}$, $\mu_{\rm O} =\frac{1}{2}\mu_{\rm O_{2} } =\frac{1}{2}E_{\rm O_{2} }$, while extreme Zn-rich conditions, $\mu_{\rm Zn} =\mu_{\rm Zn} (\text{bulk})=E_{\rm Zn} (\text{bulk}), \mu_{\rm O} =\frac{1}{2}\mu_{\rm O_{2} } +\Delta H_{\rm f},$ where $\Delta H_{\rm f}$ is the formation enthalpy of ZnO, and our calculated value ($-3.53$ eV) is in good agreement with the experimental value of $-3.6$ eV^[23] and the theoretical value of $-3.59$ eV^[24]. Fig. 2 shows the formation energies as a function of $\mu_{\rm O}$ for Na$_{\mathrm{Zn}}$-S$_{\mathrm{O}}$ and Na$_{\mathrm{in}}$-S$_{\mathrm{O}}$. According to the results, with increasing $\mu_{\rm O}$, it becomes difficult to obtain Na$_{\mathrm{Zn}}$-S$_{\mathrm{O}}$ and Na$_{\mathrm{in}}$-S$_{\mathrm{O}}$. However, the Na$_{\mathrm{Zn}}$-S$_{\mathrm{O}}$ have smaller formation energy than Na$_{\mathrm{in}}$-S$_{\mathrm{O}}$ in energy ranges from -3.10 to 0 eV of $\mu_{\mathrm{O}}$, indicating that the density of interstitial impurity of Na is effectively lower using the Na-S co-doping method. This result means a new opportunity for growth of the p-type ZnO has opened up.

Figure  2.  Calculated impurity formation energies as a function of the chemical potential $\mu_{\mathrm{O}}$ for Na$_{\mathrm{in}}$-S$_{\mathrm{O\thinspace }}$and Na$_{\mathrm{Zn}}$-S$_{\mathrm{O}}$.

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Fig. 3(a) shows the band structures of pure ZnO. The conduction band minimum and the valence band maximum are at the same G $k$-point, suggesting a direct gap semiconductor. The calculated band gap (0.74 eV) is smaller than the experimental value (3.37 eV)^[1], which is underestimated by GGA, but in good agreement with other calculations using the same method^[24]. Figs. 3(b) and 3(c) show the band structures of Na-mono doped ZnO and Na-S codoped ZnO, respectively. The conduction band minimum and the valence band maximum are also at a highly symmetric G $k$-point, suggesting a direct gap semiconductor. The calculated band gaps are 0.84 eV and 0.80 eV for Na-mono doped ZnO and Na-S codoped ZnO, respectively. The effective hole masses of Na-mono doped ZnO are larger than the effective hole masses of Na-S codoped ZnO because the effective hole masses are proportional to their band gaps based on Zhang's report^[25]. Fig. 4(b) displays the total density of states (TDOS) of ZnO, as well as the partial density of states (PDOS) of the Zn and O atoms. It can be observed that the valence band of ZnO can be divided into two parts. The lower valence band ($-6.0$ to $-4.0$ eV) is composed mainly of Zn-3d states, the upper valence band ($-4.0$ to 0 eV) is contributed by O-2p states, in addition, the conduction band is dominated by O-2p and Zn-3d states, which are supported by previous works^[26]. The calculated TDOS and PDOS of the Zn, O and Na atoms are plotted in Fig. 4(c). The Fermi level shifts downward into the valence band, exhibiting p-type behavior, and an impurity state is delocalized at the Fermi level. This localized state stems mainly from the O-2p and a small portion of Na-2p states. The localized state from the O-2p is attributed to small perturbations at the valence band maximum. The calculated results demonstrated that p-type ZnO can be obtained by Na-mono doping. The calculated TDOS and PDOS of the Zn, O, S and Na atoms are shown in Fig. 4(c). A similar change trend of Na-mono doped ZnO appeared in Na-S codoped ZnO. The DOS near the Fermi-level increases and originates mainly from O 2p states with a little contribution from Zn 4s, Zn 3p, Zn 3d, Na 2s, Na 2p and S 3p states. It is showed that the contribution to the acceptor level is mainly from Na 2s, Na 2p states and S 3p states. It is therefore illuminated that the level of VBM of ZnO would shift-up due to a strong valence band offset bowing of S doped in ZnO. The shift-up may lower the acceptor energy level and enhance doping efficiency of the p-type ZnO^[12]. As a result, p-type ZnO can be achieved by Na-S co-doping. To study the holes generated around the VBM, the areas from the Fermi-levels to the VBMs of Na-mono doped ZnO and Na-S codoped ZnO are integrated. The calculated results are 1.82 and 1.93 for Na-mono doped ZnO and Na-S codoped ZnO, respectively. These results reveal that the Na-S codoped ZnO possesses more hole carriers than Na-mono doped ZnO, which is helpful for p-type ZnO.

Figure  3.  Band structures of ZnO for (a) ZnO, (b) Na$_{\rm Zn}$, (c) Na$_{\rm Zn}$-So.

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Figure  4.  Density of states of ZnO for (a) ZnO, (b) Na$_{\rm Zn}$, (c) Na$_{\rm Zn}$-So.

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4. Conclusions

The calculations regarding the defect formation energies, the electronic structures and the properties of hole carriers of pure, Na-mono, and Na-S co-doped ZnO, were performed using the first-principle method. The calculated results show that Na$_{\mathrm{Zn}}$-S$_{\mathrm{O}}$ have smaller formation energy than Na$_{\mathrm{in}}$-S$_{\mathrm{O\thinspace }}$in energy ranges from -3.10 to 0 eV of $\mu_{\mathrm{O}}$, indicating that it opens up a new opportunity for growth of the p-type ZnO. The Fermi-levels of doped structures moved to lower energy directions, showing p-type conductivities compared to pure ZnO. Subsequent conductivity analyses indicated that Na-S codoped ZnO had a better p-type transportation behavior. We concluded that the Na-S co-doped ZnO structure would be favorable for a p-type ZnO realization.