Natural band alignment of MgO_1−xS_x alloys

Magnesium oxide (MgO) is a non-toxic oxide material commonly used in refractory and medical applications. It has a wide bandgap (∼7.8 eV) and direct transition type electronic band structure, which is a promising material for optical device application.¹ Despite these attractive physical properties, MgO has been utilized only as a barrier material in electronics applications, such as spin-tunneling devices.² This is probably because MgO is considered to be carrier uncontrollable and cannot be used as a semiconductor. However, MgO exhibits a standard semiconducting mechanism where Li doping increases electrical conductivity.³ Furthermore, in recent years, bandgap engineering has been demonstrated by epitaxial growth of rock-salt (RS) structured MgZnO alloys.^4–9 Therefore, MgO and MgZnO alloys are attracting attention as new ultra-wide bandgap (UWBG) semiconductors.^10,11

Among the known UWBG semiconductors, oxide materials, such as Ga₂O₃ and Al₂O₃, in particular, are known to have difficulty with p-type (or ambipolar) doping.¹² According to the modern theory of doping, some UWBG materials (also MgO) are unable to control their Fermi energy to near the valence band maximum (VBM) or conduction band minimum (CBM).^13–15 This dopability trend has been empirically explained by the location of the band edges (i.e., VBM and CBM) relative to the vacuum level (E_vac). The empirical criterion indicates that holes can be doped when the VBM is greater than ∼−6 eV, meaning that a shallower VBM is advantageous for p-type doping in oxide materials.^16–18 P-type wide bandgap oxides, such as NiO,¹⁹ CuAlO₂,²⁰ SrCu₂O₂,²¹ and α-Ir₂O₃,²² have been reported, and hybridized orbitals between O 2p and transition metal d produce shallower VBM than other oxides. Transition metal oxides were found to be suitable for p-type doping, but it is difficult to obtain a UWBG (>4 eV) using these compounds due to the influence of d electrons with low binding energy. Despite this trade-off, the alloying of α-Ga₂O₃ and α-Ir₂O₃ has successfully realized p-type UWBG oxides.^23,24 In the case of VBM for α-(Ir, Ga)₂O₃, the energy positions depend on the Ga (Ir) atom compositions.²³ Thus, attempts to search for p-type UWBG oxides has focused on those containing cation atoms with d-bands.

Another approach to p-type doping involves alloying the semiconductor to raise the host VBM toward E_vac and decrease the acceptor level relative to it.¹³ For example, it was found that when zinc oxide (ZnO) is alloyed with the effect of sulfur (S), the nitrogen (N_O) acceptor ionization energy is reduced for pure ZnO.²⁵ These results indicated that a large VBM shift occurs when oxygen that predominantly forms the VBM of ZnO is replaced with another anion atom (S). Therefore, the VBM of oxide semiconductors can be better modulated by substituting anion atoms rather than cation atoms. Unfortunately, only a small number of experimental investigations have been conducted on doped p-type ZnO_1−xS_x because of the strong unintentional n-type doping of ZnO.^26,27 Thus, there are well-established studies of cation-substituted II-VI semiconductor alloys, while there are few reports on the anion-substituted ones.²⁸ Therefore, the common-cation systems, such as MgO_1−xS_x alloys, should be investigated not only for p-type doping of UWBG materials but also for future oxysulfide (or oxychalcogenides) applications.²⁹ 

In this paper, we address to analyze the effect of sulfur incorporation on MgO by using first-principles calculation based on density functional theory (DFT). The formation enthalpies and bandgap of MgO_1−xS_x alloys were investigated, and the natural band alignment of the alloys was also derived from the calculations to predict doping tendency. Moreover, we proposed to combine MgO_1−xS_x alloys with high electron affinity (EA) materials that could induce hole carriers by surface charge transfer doping (SCTD).

Figure 1(a) shows the formation enthalpy per atom of MgO_1−xS_x alloys based on the use of all nonequivalent atomic substitution models. In this calculation, we did not consider the wurtzite structure or the alloy mixing enthalpy. We have estimated critical formation enthalpy (ΔH₀ = 227 meV) by Eq. (2) parabola fitting. The growth temperatures of MgO_1−xS_x alloys using ΔH₀ and Eq. (3) are depicted in Fig. 1(b). The liquidus line was plotted by a straight line between the melting points of end members, which was reported to be 3250 K for MgO⁴³ and around (or above) 2273 K for MgS.⁴⁴ The critical temperatures of the miscibility gap (T_MG) are analytically estimated at ∼5270 K (≃2ΔH₀/k_b). This value is above the melting temperature, and the trend is consistent with previous DFT calculations.⁴⁵ Note that the calculated T_MG value may be overestimated and may require a decreasing correction factor, such as about 0.8.⁴⁶ Although it is difficult to evaluate the absolute value of the temperature scale, we can understand the overall trend of the solid solution limit of S in MgO. These results show that MgO_1−xS_x alloy’s single crystal growth is difficult in thermal equilibrium conditions.⁴⁵ However, metastable regions exist in S concentrations less than 18% and S more than 87% below the liquidus line. Therefore, we believe that the crystal growth of MgO_1−xS_x alloys can be achieved by the mist chemical vapor deposition (CVD) method, which is suitable for the growth of oxide metastable structures and their alloys.^47–64 Indeed, mist CVD has succeeded in synthesizing sulfides, such as ZnS^65–68 and Cu₂SnS₃,⁶⁹ and the growth of metastable MgO_1−xS_x alloys is a future challenge. Note that the S compositions outside of metastable regions in Fig. 1(b), and MgO_1−xS_x alloys may grow in an amorphous phase.⁷⁰ 

The resulting natural band lineups to E_BP are plotted in Fig. 3; they are aligned with respect to the red dotted line. The E_BP represents a charge neutrality level (CNL), which marks the energy where defect states change their character from predominantly donor-like (acceptor-like). Unintentional heavy p-type doping is expected to occur when the E_BP line overlaps or below the VBM.⁸⁰ This shows that the energy formation of the acceptor-type defects becomes smaller than that of the donor-type defects.⁸¹ According to this simple classification concept, we can infer that the closer the E_BP is to the VBM of the alloys, the higher the potential will be for p-type doping. The lowest E_BP (1.67 eV) occurred for the MgO_0.5S_0.5 case; this value is significantly lower than that of MgO (E_BP = 5.34 eV). However, the tunability of the VBM position with the S content is lost at ∼2 eV below the E_BP. The natural band lineup result indicates that S incorporation enhances the possibility of p-type doping, although the modified Tersoff method does not provide band edge positions on an absolute energy scale. Therefore, we employed the atomic SSE approach to evaluate the band discontinuities of MgO_1−xS_x alloys. The natural band alignment relative to the E_vac of the MgO_1−xS_x alloys is illustrated in Fig. 4. The different trends of each band edge position as a function of the S content were found to be consistent with Fig. 3. Here, we estimated the possibility of achieving p-type doping of MgO_1−xS_x alloys using several doping limitation indicators. Some works have presented universal CNLs,⁸² such as the hydrogen ϵ(±) level,⁸³ limiting Fermi level (F_lim),⁸⁴ and Fermi level stabilization energy (E_FS).⁸⁵ The ϵ(±) level, F_lim, and E_FS are located at about −4.5, −4.7 ± 0.2,⁸⁶ and −4.9 eV below E_vac, respectively. These CNLs are indicators used to discriminate whether extrinsic defects or hydrogen are donors or acceptors depending on the Fermi level in a material. However, in this work, we focus only on the deepest E_FS level from E_vac. Moreover, following the empirical rule, hole doping of oxide is possible when the VBM is located above ∼−6 eV.^16–18 These different indicators originate from different approaches; they all seem to indicate the intrinsic doping criteria for semiconductors. According to the empirical rule $(Elimp)$⁠, our calculated band lineup of the MgO_1−xS_x alloys shows that hole doping becomes possible when x exceeds 0.25. Such a trend is understandable given the E_FS using the amphoteric native defect model.⁸⁵ As shown in Fig. 4, the VBM of MgO_1−xS_x (0.5 ≤ x ≤ 0.875) is located almost at the E_FS, which explains the strong possibility for p-type doping at these S compositions. Since the smaller the energy difference |E_FS − VBM|, the larger the maximum hole carrier concentration, MgO_1−xS_x alloys are expected to exhibit enhanced p-type conduction with respect to MgO.⁸⁷ Therefore, the empirical rule and the E_FS trends are consistent as p-type dopability indicators. We note that finding suitable dopants for an alloy is difficult with the current DFT calculation framework.

Although Fig. 4 shows a trend similar to the VBM change obtained via the E_BP result, it reveals a larger hole-doping possibility than Fig. 3. Note that in several recent studies, the modified Tersoff method (E_BP) has not correctly predicted the p-type dopability trend.^88–90 Consequently, we expect the E_FS value and the empirical rule $(Elimp)$ to be better predictors of p-type doping criteria. These band alignment results indicate that doping MgO with both electrons and holes is extremely difficult. For example, lithium (Li) is a deep acceptor level in MgO, and its activation energy has been reported to be about 0.7 eV³. However, the Li acceptor activation energy is expected to decrease as the VBM moves upward upon S alloying.⁹¹ Furthermore, since the defect and impurity levels are determined by the host material,⁹² S concentrations of about 25% or less for MgO_1−xS_x alloys can be expected to lower the Li acceptor levels by increasing the energy position of the VBM, as in the case of ZnO_1−xS_x alloys.²⁵ Additionally, universal levels of oxygen⁹³ and transition metal impurities^94,95 have been reported, and these could become shallow acceptor levels through VBM modulation. This experimental evidence is not yet available; however, a theoretical result based on defect formation energy calculations suggested that MgS is a p-type transparent conducting material candidate.^96,97 This result is consistent with those based on the empirical rule and the E_FS predictions, and we thus believe that our calculations can correctly predict the p-type dopability criteria.

The calculated relative VBM positions (ΔVBM) concerning MgO are shown in Fig. 5(a). These results indicate that the increasing trends of the natural valence band offset of MgO_1−xS_x with increasing S content obtained using different approaches are consistent. The offset value trend can be explained as a chemical trend by considering the atomic energy of common anions, such as O, S, Se, and Te atoms. Figure 5(b) shows the atomic energy levels, including the configuration energy (CE)⁹⁸ and SSE⁴² for each atom. The energies of these VI-group atoms become closer to E_vac as the atomic number increases, except for the SSE of Te atoms. CE refers to the energy of isolated atoms, whereas SSE refers to the energy of “atoms in a crystal,” such as the Bader charge concept.⁹⁹ Our calculation results can be explained by the SSE more simply than those derived from the CE. For example, a rough estimate of E_g can be obtained by calculating the difference in SSE between cation atoms, such as Mg and Zn, and anion atoms [cf. Fig. 5(b)].⁴¹ The VBM of MgO_1−xS_x can be determined by calculating the difference in the SSE scale between S and O atoms. These findings indicate that the energy levels of atoms in a crystal are determined by the oxidation (or reduction) state.¹⁰⁰ Therefore, the energy position of the VBM of ionic bonded materials can be modulated via anion atom substitutions. We note that the VBM modulation is only possible when anion atoms dominate the top of the valence band of the material (see the supplementary material, Figs. S1–S9). These results clearly show that Mg atoms contribute little to the valence band in the energy range of −5 to 0 eV.

From our band alignment results, we have considered hole doping by SCTD.¹⁰¹ The SCTD technique has been demonstrated for hydrogenated diamonds¹⁰² and several inorganic semiconductors: graphene,¹⁰³ silicon,¹⁰⁴ cubic boron nitride,¹⁰⁵ and perovskite materials.¹⁰⁶ In order to holes doping spontaneously, we have to contact the high electron affinity (EA) or high work function materials with MgO_1−xS_x alloys. Here, we have investigated whether SCTD occurs for metastable MgO_1−xS_x condition (x ≤ 0.18) with E_g over 4 eV shown in Fig. 6. The high EA materials are ∼6.7 eV for MoO₃,¹⁰⁷ V₂O₅,¹⁰⁸ CrO₃,¹⁰⁹ and ∼6.45 eV for WO₃,¹¹⁰ respectively. The results indicated that the surface charge transfer appeared spontaneously at S content above 10% for MgO_1−xS_x alloys in contact with high EA materials except for WO₃. Note that the energetic positions of the VBM for MgO_1−xS_x alloys are calculated by the SSE scale approach, while the CBMs for high EA materials are experimental values. These high EA materials induced sheet hole carrier concentrations greater than 10¹³ cm⁻² with respect to hydrogenated diamond.^102,111 Thus, the sheet hole carrier concentration of MgO_1−xS_x alloys is expected to be the same order of magnitude hydrogenated diamond by SCTD. This is consistent with the number of adsorbed molecules on the MgO (100) or (111) surface,¹¹² and the sheet hole carriers are expected to be tunable around 10¹⁴ cm⁻². Other potential surface charge-induced phenomena include defect modulation doping,¹¹³ formal (or surface) polarization effects,^114,115 and electrochemical doping.^116–119 These phenomena are different from bulk doping but show that holes can be generated by using appropriate surface or interface effects. Therefore, these SCTD schemes must be adopted instead of conventional impurity doping to realize p-type UWBG oxide semiconductors.

We have investigated the S incorporation effect of MgO using a first-principles calculation based on DFT. Our results indicated that the solubility of S content required for the metastable solid phase of the MgO_1−xS_x alloys was estimated to be less than 18% or over 87%, respectively. The bandgap of MgO_1−xS_x alloys became the smallest at 50% S content, and the bowing parameter was estimated to be b ≃ 13 eV. Our calculated natural band alignment indicated that the MgO_1−xS_x alloys tend to be more easily doped to p-type than n-type. Based on the calculated VBM positions, we predicted that metastable MgO_1−xS_x with S content of 10%–18% can be SCTD by high EA materials. We hope that the present work may provide design guidelines for p-type oxysulfide materials.

The details of the DFT calculations and their results are provided in the supplementary material.

This work was supported, in part, by Grants-in-Aid for Scientific Research (Grant No. 20H00246) from MEXT, Japan.

The authors have no conflicts to disclose.

Yuichi Ota: Conceptualization (equal); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Writing – original draft (lead); Writing – review & editing (lead). Kentaro Kaneko: Data curation (equal); Formal analysis (equal); Investigation (equal); Writing – review & editing (equal). Takeyoshi Onuma: Data curation (equal); Formal analysis (equal); Investigation (equal); Writing – review & editing (equal). Shizuo Fujita: Conceptualization (lead); Funding acquisition (lead); Project administration (lead); Supervision (lead); Writing – review & editing (equal).

The data that support the findings of this study are available within the article and its supplementary material.