First-principle study on the effect of S/Se/Te doping and V_Zn-H_i coexistence on ZnO electrical conductivity

This paper is based on the hexagonal wurtzite structure of ZnO with symmetry C6V4 C_{6V}^4 . The construction of pure Zn₃₆O₃₆ supercell is shown in Figure 1A. This paper considered the unipolarity of ZnO in the z-axis direction and is thus asymmetric. Therefore, the selected doping atomic positions are different, and the stability of the ZnO system is also different. Therefore, a Zn₃₅RO₃₅ (R = S/Se/Te) model was constructed, in which the R (R = S/Se/Te) atoms that replaced O atoms and Zn vacancies coexisted, three different substitution positions of R (R = S/Se/Te) atoms were selected from near to far with the relative V_Zn as the center and were denoted by a1, a2, and a3, respectively, and the fixed V_Zn positions were (0.444, 0.556, 0.500) as shown in Figure 1B. The influence of H_i at different positions on the stability of the ZnO system was studied with consideration of practical factors. From the relative V_Zn center from near to far, three doping positions of H_i were considered using b1 (0.700, 0.500, 0.400), b2 (0.763, 0.532, 0.289), and b3 (0.879, 0.591, 0.162), respectively. Then the model of Zn₃₅RH_iO₃₅ (R = S/Se/Te) was constructed, as shown in Figure 1C. The doping amounts of S/Se/Te in the model constructed in this paper (1.39 mol%) are lower than the doping amount without phase transition used in the experiments carried out in several comparable studies in the literature [18,19,20]. The V_Zn content in this paper is 2.78 mol%, which is much lower than the V_Zn content of 9 mol% used in the experiments comprised in the studies of Wu et al. [21] and Ghosh et al. [22], and does not cause a phase change in the system. Therefore, the doping amount used in this study is feasible.

Fig. 1

This paper uses the CASTEP (8.0) module in MS for calculations. Based on density functional theory (DFT) [23], generalized gradient approximation (GGA) was adopted [24], and the plane wave supersoft pseudopotential method based on Perdew–Burke–Ernzerhof (PBE) functional was selected [25]. The plane wave cutoff energy was set to 340 eV. The effect of different cutoff energies on the energy convergence of undoped Zn₃₆O₃₆ was tested. Figure 2 indicates that when the cutoff energy reaches 340 eV, the energy of the system converges and tends to be stable, and so the choice of a cutoff energy of 340 eV used in this paper may be said to be reasonable. This is consistent with previous calculations of the energy cutoff radius [26, 27]. The k point sampling of the first Brillouin zone was 4×4×2. The maximum interatomic force, maximum internal stress, and tolerance shift convergence accuracy were 0.01 eV·Å⁻¹, 0.02 GPa, and 0.0005 Å, respectively. The electron density is not spin polarized, and the charge was set to values adapted to a given case. The valence electron configuration of each atom is: S–3s²3p⁴, Se–4s²4p⁴, Te–5s²5p⁴, Zn–3d¹⁰4s², O–2s²2p⁴, and H–1s¹.

Fig. 2

The doped Zn₃₆O₃₆, Zn₃₅RO₃₅ (R = S/Se/Te), and Zn₃₅RH_iO₃₅ (R = S/Se/Te) systems were geometrically optimized, and the optimized results are listed in Table 1. The calculated lattice constants of the Zn₃₆O₃₆ system are in good agreement with the experimental values of a = b = 3.258 Å and c = 5.220 Å [28]. The rationality underlying the choice of parameters employed in this study is verified.

Table 1 showed that the a, c, and V of Zn₃₅RO₃₅ (R = S/Se/Te) and Zn₃₅RH_iO₃₅ (R = S/Se/Te) were larger than those of Zn₃₆O₃₆. One reason for this finding is attributable to the radius effect: the S/Se/Te ionic radius (2.14/2.24/2.42 Å) [29] is larger than the O ionic radius (1.71 Å) [29]. The second reason is the interionic force: the repulsive force between V_Zn and O, R (R = S/Se/Te) is greater than the attractive force between V_Zn and Zn in the Zn₃₅RO₃₅ (R = S/Se/Te) systems; the repulsive forces between H and V_Zn, between V_Zn and O, and between V_Zn and R (R = S/Se/Te) are greater than the attraction force between O and H, V_Zn and H, and H and R (R = S/Se/Te) in the Zn₃₅RH_iO₃₅ (R = S/Se/Te) systems. Therefore, the volume of the Zn₃₅RO₃₅ (R = S/Se/Te) and Zn₃₅RH_iO₃₅ (R = S/Se/Te) systems increases. Table 1 shows that compared with the Zn35RO35a2−a3 {\rm{Zn}_{35}}{\rm{RO}}_{35}^{a2 - a3} (R = S/Se/Te) and Zn35RHiO35a2−a3 {\rm{Zn}_{35}}{\rm{RH}_{\rm{i}}}{\rm{O}}_{35}^{a2 - a3} (R = S/Se/Te) systems, when the relative distance between the R (R = S/Se/Te) substitution atom and V_Zn is closest to 1.992 Å, the increase in the equivalent unit cell volume caused by doping can be reduced, improving the stability of the structure. This outcome was further confirmed by the formation energies.

The formation energies of all the doped systems were calculated to analyze the stability of doped systems. The calculation formula is expressed as the following in the literature [30, 31]: (1) Ef(R+VZn)=EZnO:R+VZn − EZnO−μR+μO+μZn \matrix{ {{E_f}\left( {R + {V_{Zn}}} \right) = {E_{ZnO:R + {V_{Zn}}}}} \hfill \cr {\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; - \;{E_{ZnO}} - {\mu _R} + {\mu _O} + {\mu _{Zn}}} \hfill \cr } (2) Ef(R+VZn+Hi)=EZnO:R+VZn+Hi − EZnO−μR−μHi+μO+μZn \matrix{ {{E_f}\left( {R + {V_{Zn}} + {H_i}} \right) = {E_{ZnO:R + {V_{Zn}} + {H_i}}}} \hfill \cr {\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\,\,\;\;\; - \;{E_{ZnO}} - {\mu _R} - {\mu _{{H_i}}} + {\mu _O} + {\mu _{Zn}}} \hfill \cr } where E_ZnOR+VZn represents the total energy of the ZnO:V_Zn+R (R = S/Se/Te) system; E_ZnOR+VZn+Hi is the total energy of the ZnO:V_Zn+H_i+R (R = S/Se/Te) system; E_ZnO represents the total energy of the pure Zn₃₆O₃₆ system; and μ_R, μ_Hi, μ_O, and μ_Zn are the chemical potentials of S/Se/Te atom, H atom, O atom, and Zn atom, respectively. μ_ZnO(bulk) = μ_O + μ_Zn; thus, μ_O and μ_Zn were included in the calculation formula of the E_f of the doped system. The E_f of the system were the same in O- and Zn-rich conditions; hence, this paper did not separately calculate the E_f in O- and Zn-rich conditions. The E_f calculation results are shown in Figure 3. According to Figure 3, among the Zn₃₅RO₃₅ (R = S/Se/Te) systems, the Zn₃₅SO₃₅ system had the lowest formation energy and was relatively stable. This result is attributable to the fact that among the three dopant atoms of S, Se, and Te, the radii of S and O atoms were the closest, the lattice distortion caused by the substitution of S atom for O atom was the smallest, and the structure was the most stable. In Zn35RO35a1−a3 {\rm{Zn}_{35}}{\rm{RO}}_{35}^{a1 - a3} (R = S/Se/Te), when the R replacement atom was closest to V_Zn (1.992 Å), the E_f of the Zn35RO35a1 {\rm{Zn}_{35}}{\rm{RO}}_{35}^{a1} (R = S/Se/Te) was the most stable system.

Fig. 3

The system with the lowest formation energy in the Zn₃₅RH_iO₃₅ (R = S/Se/Te) system was selected, and the formation energies of the b1, b2, and b3 positions of the H_i were calculated to explore the effect of the H_i position on the stability of the ZnO. The results are shown in Figure 4. The figure shows that the E_f of the Zn₃₅RH_iO₃₅ (R = S/Se/Te) system also increased gradually with the increase in the distance between H_i and V_Zn. The formation energy of the Zn35RHib1O35a1 {\rm{Zn}_{35}}{\rm{RH}_{\rm{i}}}^{b1}{\rm{O}}_{35}^{a1} (R = S/Se/Te) system was the lowest when H_i was located at the b1 position, which is the nearest neighbor center position, because V_Zn was the acceptor, and a Coulomb attraction was present between it and the donor H_i. A closer distance corresponds to a more stable system. This result is consistent with a similar research [32].

Fig. 4

Considering the structural stability of the system, the most stable Zn35RO35a1 {\rm{Zn}_{35}}{\rm{RO}}_{35}^{a1} (R = S/Se/Te) and Zn35Rb1HiO35a1 {\rm{Zn}_{35}}{{\rm{R}}^{b1}{\rm H}_{\rm{i}}}{\rm{O}}_{35}^{a1} (R = S/Se/Te) systems were selected as the research objects. The superscripts of the above systems were omitted to facilitate subsequent research.

Mobility is an important parameter used to measure the conductivity of a system. The p-type conductivity of the system is proportional to the hole mobility. A higher hole mobility indicates that the p-type conductivity of a system is better. The hole mobility formula [33, 34] is: (3) μh3D=23/2π1/23c3Dh¯4eEI2mh*5/2(kBT) \mu _h^{3D} = {{{2^{3/2}}{\pi ^{1/2}}} \over 3}{{{c^{3D}}{{\overline h }^4}e} \over {E_I^2m_h^{*5/2}\left( {{k_B}T} \right)}} where c^3D is the elastic modulus, defined as c3D=[∂2E∂δ2]V0 {c^{3D}} = {{\left[ {{{{\partial ^2}E} \over {\partial {\delta ^2}}}} \right]} \over {{V_0}}} [35], E is the total energy of the system, and V₀ is the total volume of the system at equilibrium. E_I is the deformation potential energy, defined as EI=ΔEδ {E_I} = {{\Delta E} \over \delta } [34], where δ is the deformation amount, and ΔE is the energy change at the top of the valence band along the transport direction. mh* m_h^* is the effective mass of the hole, defined as m*=h¯2(d2Edk2)−1 {m^*} = {\bar h^2}{\left( {{{{d^2}E} \over {d{k^2}}}} \right)^{ - 1}} , where m^* is the effective mass of the carrier, h¯ \bar h is Planck's constant, k is the direction of the wave vector, and E is the energy of the carrier in the wave vector k. T is the temperature, which was set to 300 K. The smaller the mh* m_h^* of the holes and the smaller the E_I, the greater the system mobility and the better the electrical conductivity. The calculated data of each system according to Eq. (3) are shown in Table 2. The calculated effective mass of pure Zn₃₆O₃₆ was consistent with the experimental value ascertained in the study of Janotti et al. [36], which shows that the data in this paper are reliable.

Table 2 shows that the hole mobilities of the Zn₃₅RO₃₅ (R = S/Se/Te) and Zn₃₅RH_iO₃₅ (R = S/Se/Te) systems are anisotropic. This result is attributable to the fact that ZnO has unipolarity, and therefore, the mobility of the system is different along different transport directions. In the Zn₃₅RO₃₅ (R = S/Se/Te) and Zn₃₅RH_iO₃₅ (R = S/Se/Te) systems, the hole mobilitiy of the Zn₃₅SO₃₅ system along the a-axis was the highest, and the hole mobilities of the Zn₃₅SeH_iO₃₅ system along the c-axis were the highest. Table 2 displays that in tandem with the unintentional incorporation of H_i, the hole mobility of the doped system decreases along the a direction and increases along the c direction. The results showed that the unintentional incorporation of the H_i can greatly increase the mobility of the doping system along the c direction, but it is not conducive to the mobility along the a direction.

The calculated band structure of pure Zn₃₆O₃₆ system is shown in Figure 5. The bandgap of the pure Zn₃₆O₃₆ system is 0.73 eV, which is close to the calculated result available from the literature [37], but inconsistent with the experimental value (3.37 eV). This is because the energy of Zn–3d is overestimated when the architecture is calculated using GGA, resulting in an underestimation of the bandgap [38]. However, this error has little effect on the analysis of the relative physical quantities of the ZnO system.

Fig. 5

The calculated band structures of the Zn₃₅RO₃₅ (R = S/Se/Te) and Zn₃₅RH_iO₃₅ (R = S/Se/Te) systems are shown in Figures 6A–6F.

Fig. 6

According to Figures 6A–6F, the valence band maximum (VBM) and conduction band minimum (CBM) of the doped systems correspond to the same high symmetry point, which indicates that they are all direct bandgap semiconductors. The figures indicate that R (R = S/Se/Te) and H_i lead to remarkable changes in the valence and conduction bands of the system. Among them, the VBM and CBM of the Zn₃₅SO₃₅, Zn₃₅SeO₃₅, and Zn₃₅SH_iO₃₅ systems moved up, the Fermi level entered the valence band, and the systems were the p-type semiconductor. However, the VBM and CBM of the Zn₃₅TeO₃₅, Zn₃₅SeH_iO₃₅, and Zn₃₅TeH_iO₃₅ systems moved down, and the Fermi level was located between the valence and conduction bands, indicating that no p-type degeneracy had occurred. Therefore, studying the electrical conductivities of the Zn₃₅TeO₃₅, Zn₃₅SeH_iO₃₅, and Zn₃₅TeH_iO₃₅ systems will be meaningless; accordingly, these three systems were not further studied.

The total density of states (DOS) and partial density of states (PDOS) of the Zn₃₆O₃₆, Zn₃₅SO₃₅, Zn₃₅SeO₃₅, and Zn₃₅SH_iO₃₅ systems were calculated to study the effect of doping defects on the hole concentration of the ZnO system (Figures 7A–7D).

Fig. 7

Figures 7A–7D illustrate that the O–2p state in the Zn₃₆O₃₆ system determines the VBM, and the Zn–4s state determines the CBM. Its Fermi level did not enter the valence band and was not a p-type degeneracy semiconductor. The Fermi levels of the Zn₃₅SO₃₅, Zn₃₅SeO₃₅, and Zn₃₅SH_iO₃₅ systems entered the valence band, which indicates that they are all p-type semiconductors. This is consistent with the analysis results in Section 3.3.

Figures 7B and 7C indicate that the upper valence bands of the Zn₃₅SO₃₅ and Zn₃₅SeO₃₅ systems in the range of −3 eV to 0 eV were formed by the hybridization of O–2p and a small amount of Zn–3d state orbital. The lower valence band from −6 eV to −3 eV was formed by the hybridization of Zn–3d and a small amount of O–2p orbitals. The electrons in the O–2p and S–3p/Se–4p states occupy the vicinity of the Fermi level, and p–p state coupling occurs and the VBM moves up. This is because the atomic number of O group elements increases, which leads to the rise of the p-state energy level and the rise of the VBM. The carriers were degenerated, and the system exhibited p-type conductivity. The calculation results showed that S/Se doping is beneficial to the transition of the ZnO system from a natural n-type semiconductor to a p-type semiconductor.

Figure 7D shows that the valence band of the Zn₃₅SH_iO₃₅ system was formed by the coupling of O–2p, Zn–3d, and S–2p state orbits. Near the Fermi level, p–p state coupling occurs between the p-state orbital of S and the p-state orbital of O, the VBM moves up, and the Fermi level enters the valence band. The reason is the same as above. Notably, Figure 7D shows that the H–1s state contributes to the DOS near −7 eV. This result indicates that the doping of H_i affects the low-valence band region and does not contribute much to the electronic states near the Fermi level.

Another reference factor that cannot be ignored when exploring the conductivity of p-type semiconductors is the hole concentration. In this paper, as shown in Figures 7B–7D, Origin 8.5 software was used to integrate the part of the DOS beyond the Fermi level, and the hole concentration P_i is equal to the integral value divided by the total volume of the doped system. The calculation results are shown in Table 3.

Table 3 shows that the hole concentrations of the Zn₃₅SO₃₅ and Zn₃₅SeO₃₅ systems were considerably higher than that of the Zn₃₅SH_iO₃₅ system. The result was due to V_Zn as the acceptor, and the donor H_i needs to suppress and compensate for V_Zn. Therefore, the hole concentration of the Zn₃₅SH_iO₃₅ system decreased. Among the doped systems, the Zn₃₅SO₃₅ system had the highest hole concentration of 2.80×10²¹ cm⁻³ and the best conductivity.

The conductivity calculation formula of a p-type semiconductor is expressed in the literature [39] as the following: (4) σi=piμhe {\sigma _i} = {p_i}{\mu _h}e where μ_h and e represent the hole mobility and the amount of elementary charge, respectively. The calculated hole conductivities of all the doped systems along different transport directions are shown in Table 4.

Table 4 shows that the conductivity of the pure Zn₃₆O₃₆ system is 0. Compared with the conductivity of the Zn₃₆O₃₆ system, the conductivities of the Zn₃₅SO₃₅, Zn₃₅SeO₃₅, and Zn₃₅SH_iO₃₅ systems were remarkably higher. The calculation results showed that the Zn₃₅SO₃₅, Zn₃₅SeO₃₅, and Zn₃₅SH_iO₃₅ systems were all beneficial in terms of improving the conductivity of the ZnO. The comparison of the Zn₃₅SO₃₅ and Zn₃₅SeO₃₅ systems showed that the conductivity of the S-doped system is remarkably larger than that of the Se-doped system, indicating that S doping is more beneficial in terms of improving the p-type conductivity of ZnO. The comparison of the Zn₃₅SO₃₅ and Zn₃₅SH_iO₃₅ systems revealed that H_i doping reduces the conductivity of the doped system along the G→ F direction and increases the conductivity of the doped system along the G→ Z direction, indicating that H_i doping can effectively improve the transport performance of the system along the G→ Z direction. Interestingly, in all the doped systems, the conductivities of the Zn₃₅SO₃₅ and Zn₃₅SH_iO₃₅ systems were the largest along the G→ F and G→ Z directions, respectively.