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The origin of the pronounced and composition-dependent band-gap bowing in Sn/Pb mixed perovskite alloys has been under debate for a long time. Previous studies reported conflicting results on whether the chemical or structural effect is the dominant mechanism. In this paper, the band-gap bowing effect and its possible origins in recently synthesized two-dimensional (2D) ${\mathrm{Cs}}_{2}{\mathrm{Pb}}_{x}{\mathrm{Sn}}_{1\text{\ensuremath{-}}x}{\mathrm{I}}_{2}{\mathrm{Cl}}_{2}$ alloys are investigated from first-principles calculations. In agreement with experiments, a large and composition-dependent bowing coefficient is observed. By analyzing the contribution from volume deformation, charge exchange, structural relaxation, and short-range order, it is found that the dominant mechanism causing the anomalous gap bowing is the structural relaxation-induced wave-function localization, forming isovalent-defect-like states, despite the negligible octahedral distortion and small lattice mismatch between the two end compounds. This is understood by the s-p repulsion-induced strong antibonding character of the valence-band maximum which leads to a large deformation potential, thus even a small atomic displacement can result in a large shift of the energy level. These results thus highlight the critical role of strong deformation potential and structural relaxation effect in unusual band evolution of 2D Sn/Pb perovskite alloys, and can be helpful to the modulation of their band gap for optoelectronic applications.

Germanium is crystalized in the cubic diamond structure, but its high energy hexagonal Ge (lonsdaleite) phase has many novel properties such as direct band gap. Using first-principles calculations, we show that the hexagonal lonsdaleite phase of Ge can be stabilized by introducing carriers, either electrons or holes, because Ge in the cubic and hexagonal phases form a type-I band alignment with both electrons and holes localized at the hexagonal site. This result is distinct from that in zinc-blende compounds such as ZnSe, because due to the lack of inversion symmetry, the crystal-field splitting, zone folding, and symmetry-controlled level repulsion between valence and conduction band states lead to a type-II band alignment between its cubic and hexagonal phases, so the hexagonal (wurtzite) phase of ZnSe can only be stabilized, in principle, by holes. This distinction reveals that, due to the symmetry differences, the well-investigated understanding of band structure differences between zinc-blende and wurtzite phases should not be simply extended to that of diamond and lonsdaleite phases despite the remarkable structure resemblance between the two cases.

Magnetic dipole (MD) spontaneous emission plays a vital role in the field of optical magnetism, which has been observed in trivalent lanthanide ions. In this case, the luminescence properties of the MD are largely affected by the crystal field symmetry at the embedding trivalent lanthanide ion site, but the correlation between the doping properties and the MD emission has not been fully understood. Here, we systematically investigate the doping properties of Eu in $\mathrm{Sr}M{\mathrm{O}}_{3}$ ($M=\mathrm{Ti},\mathrm{Zr},\mathrm{Hf}$) using first-principles calculations, in order to maximize the MD emission efficiency of the Eu-doped perovskites. By analyzing the formation energies under the accessible growth conditions, we determine the ideal conditions for Eu-doped perovskites that could maximize the MD emission. We also theoretically demonstrate the spin flipping emission mechanism of ${\mathrm{Eu}}^{3+}$. Our study thus provides a guideline for the design of highly efficient MD emission materials.

$P$-type doping in oxides is usually difficult due to their low valence-band energy. In order to make them $p$ type, the electronic structure of the oxides should be fundamentally changed; that is, the occupied valence band should be raised significantly. Here, using first-principles calculations, we propose that by adding a small amount of ${\mathrm{Bi}}_{2}{\mathrm{O}}_{3}$ into ${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ to form dilute ${({\mathrm{Bi}}_{x}{\mathrm{Ga}}_{1--x})}_{2}{\mathrm{O}}_{3}$ alloys and, more importantly, with properly chosen dopants, we can achieve efficient $p$-type doping in a transparent oxide. We show that adding a few percent of Bi to ${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ leads to an intermediate valence band that is sufficiently high in energy to facilitate $p$-type doping; however, the commonly expected shallow acceptors, Mg and Zn substitution on the Ga site (${\mathrm{Mg}}_{\mathrm{Ga}}$ and ${\mathrm{Zn}}_{\mathrm{Ga}}$), are still deep acceptors, whereas the expected deep acceptor, ${\mathrm{Cu}}_{\mathrm{Ga}}$, actually creates a relatively shallow level in ${({\mathrm{Bi}}_{x}{\mathrm{Ga}}_{1--x})}_{2}{\mathrm{O}}_{3}$ alloys. This trend is opposite to what is found in pure ${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$. The puzzling behavior of the acceptor levels in the ${({\mathrm{Bi}}_{x}{\mathrm{Ga}}_{1--x})}_{2}{\mathrm{O}}_{3}$ alloys is attributed to the polaronic character of the holes in the Zn- and Mg-doped cases, and the decoupling of the hole state and the valence-band edge in the Cu-doped case. This understanding provides insights into the realization of $p$-type doping in dilute ${({\mathrm{Bi}}_{x}{\mathrm{Ga}}_{1--x})}_{2}{\mathrm{O}}_{3}$ alloys and paves a way to dope semiconductor materials with a strongly correlated band edge state, i.e., materials with a tendency to form polaronic acceptor or donor states.

Cu is usually considered as an effective dopant to introduce shallow acceptors in Zn chalcogenides because it is on the left-hand side of Zn in the Periodic Table. Here, using first-principles calculations based on the hybrid functional with spin polarization, we show that contrary to the common expectation, Cu substituting Zn ($\mathrm{C}{\mathrm{u}}_{\mathrm{Zn}}$) in bulk Zn chalcogenides actually generates rather deep acceptor levels in ZnO, ZnS, and ZnSe, i.e., 2.91, 1.03, and 0.53 eV above the valence-band maximum (VBM), respectively, except in ZnTe (0.13 eV). More interestingly, the absolute Cu impurity energy level does not follow the variation of the VBM, decreasing from ZnTe to ZnSe to ZnS to ZnO, instead, it is the highest in ZnO. The abnormal behavior of $\mathrm{C}{\mathrm{u}}_{\mathrm{Zn}}$ in ZnO is attributed to the fact that, due to the very low O $2p$-orbital energy, the $\mathrm{C}{\mathrm{u}}_{\mathrm{Zn}}$ defect wave function has dominantly localized the Cu $3d$-orbital component, whereas in other Zn chalcogenides, anion $p$ states are dominant. The localized Cu $3d$ state leads to the enhanced exchange energy that elevates the acceptor level, which explains why the Cu impurity level is abnormally deep in ZnO. This finding provides insight in designing shallow acceptor levels in II--VI semiconductors.

Although the direct or indirect nature of the bandgap transition is an essential parameter of semiconductors for optoelectronic applications, the understanding why some of the conventional semiconductors have direct or indirect bandgaps remains ambiguous. In this Letter, we revealed that the existence of the occupied cation d bands is a prime element in determining the directness of the bandgap of semiconductors through the s-d and p-d couplings, which push the conduction band energy levels at the X- and L-valley up, but leaves the {\Gamma}-valley conduction state unchanged. This unified theory unambiguously explains why Diamond, Si, Ge, and Al-containing group III-V semiconductors, which do not have active occupied d bands, have indirect bandgaps and remaining common semiconductors, except GaP, have direct bandgaps. Besides s-d and p-d couplings, bond length and electronegativity of anions are two remaining factors regulating the energy ordering of the {\Gamma}-, X-, and L-valley of the conduction band, and are responsible for the anomalous bandgap behaviors in GaN, GaP, and GaAs that have direct, indirect, and direct bandgaps, respectively, despite the fact that N, P, and As are in ascending order of the atomic number. This understanding will shed light on the design of new direct bandgap light-emitting materials., Comment: 15 pages, 4 figures

SnSe has emerged as an efficient and fascinating thermoelectric material. A fundamental understanding of the effects and nature of intrinsic defects and dopants in SnSe is crucial to optimize its thermoelectric performance. In this paper, we perform first-principles calculations to examine the native and extrinsic point-defect properties in SnSe. We show that the easy formation of acceptorlike Sn vacancy (${\mathrm{V}}_{\mathrm{Sn}}$) is responsible for the $p$-type conductivity in intrinsic SnSe. We also propose a mechanism and explain the anomalous temperature dependence of the carrier concentration in intrinsic SnSe crystals. Concerning the extrinsic defects, we focus on the dopants used in experiments. We find that Na (Ag) substitution on Sn site, ${\mathrm{Na}}_{\mathrm{Sn}}$ (${\mathrm{Ag}}_{\mathrm{Sn}}$), acts as acceptor, whereas, substitutional ${\mathrm{Br}}_{\text{Se}}, {\mathrm{I}}_{\text{Se}}$, and ${\mathrm{Bi}}_{\text{Sn}}$ dopants act as donor. It is shown that for Ag doping, its carrier concentration will be saturated with increasing doping concentration due to the coexistence of compensated defects (${\mathrm{Ag}}_{\mathrm{i}}$ and ${\mathrm{Ag}}_{\text{Sn}}$). Furthermore, we analyze how this doping introduced carrier impact on their thermoelectric characteristics. It is found that the more efficient doping of Na, Br, and I can realize higher $ZT$.

Unlike other two-dimensional (2D) isovalent materials, the 2D group IV monochalcogenides, $MX$ ($M\phantom{\rule{0.28em}{0ex}}=\phantom{\rule{0.28em}{0ex}}\mathrm{Si}$, Ge, Sn, and Pb; $X\phantom{\rule{0.28em}{0ex}}=\phantom{\rule{0.28em}{0ex}}\mathrm{S}$, Se, and Te), are found to be either in a black phosphorene-derived distorted NaCl-type ($d$-NaCl) structure or a recently predicted $Pma2$ structure. Both $M$ and $X$ atoms in the $d$-NaCl structure are threefold coordinated, whereas $M$ and $X$ in the $Pma2$ structure are fourfold and twofold coordinated, respectively. Using first-principles total energy and electronic structure calculations and a global structural search technique, we systematically investigated the mechanism underlying the polymorphism of the 2D group-IV monochalcogenides. Our analysis show that the relative stability of the two distinct crystallographic phases depends on the strength of the $M\ensuremath{-}M$ covalent bond and the electronegativity difference between the constituent elements $M$ and $X$. For small cations, the covalency plays more important role, whereas for large cations the Coulomb interaction becomes more dominant. Therefore, the $\mathrm{Si}X$ and $\mathrm{Ge}X$ compounds assume the $Pma2$ structure, whereas the $MX$ compounds with heavy cation elements ($M\phantom{\rule{0.28em}{0ex}}=\phantom{\rule{0.28em}{0ex}}\mathrm{Sn}$ and Pb) tend to adopt the $d$-NaCl structure.

Nonequilibrium growth of Si-III-V or Si-II-VI alloys is a promising approach to obtaining optically more active Si-based materials. We propose a new class of nonisovalent $\mathrm{S}{\mathrm{i}}_{2}\mathrm{AlP}$ (or $\mathrm{S}{\mathrm{i}}_{2}\mathrm{ZnS}$) alloys in which the Al-P (or Zn-S) atomic chains are as densely packed as possible in the host Si matrix. As a hybrid of the lattice-matched parent phases, $\mathrm{S}{\mathrm{i}}_{2}\mathrm{AlP}$ (or $\mathrm{S}{\mathrm{i}}_{2}\mathrm{ZnS}$) provides an ideal material system with tunable local chemical orders around Si atoms within the same composition and structural motif. Here, using first-principles hybrid functional calculations, we discuss how the local chemical orders affect the electronic and optical properties of the nonisovalent alloys.

It is well known that ternary zinc-blende semiconductors are always more stable in the chalcopyrite (CH) structure than the Cu-Au (CA) structure because the CH structure has a large Coulomb interaction and a reduced strain energy. Surprisingly, an experimental study showed that the $\mathrm{ZnFeS}{\mathrm{e}}_{2}$ alloy takes the CA order as the ground-state structure, which is consistent with our density functional theory calculations showing that the CA order has lower energy than the CH order for $\mathrm{ZnFeS}{\mathrm{e}}_{2}$. We reveal that the orbital degree of freedom of a high-spin $\mathrm{F}{\mathrm{e}}^{2+}$ ion $({d}^{6})$ in the tetrahedral crystal field plays a key role in stabilizing the CA order. First, the spin-minority $d$ electron of the $\mathrm{F}{\mathrm{e}}^{2+}$ ion tends to occupy the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-like orbital instead of the ${d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$-like orbital because of its large negative Coulomb energy. Second, for a nearest-neighboring $\mathrm{F}{\mathrm{e}}^{2+}$ pair, two spin-minority $d$ electrons with occupied ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-like orbitals on the plane containing the Fe-Fe bond have lower electronic kinetic energies. Both conditions can be satisfied in the CA ordered $\mathrm{ZnFeS}{\mathrm{e}}_{2}$ alloy, whereas there is an orbital frustration in the CH structure. Our results suggest that the orbital degree of freedom provides a new way to manipulate the structure and properties of alloys.

Good transparent conducting oxides (TCOs), such as ${\mathrm{In}}_{2}{\mathrm{O}}_{3}$:Sn (ITO), usually combine large optical band gaps, essential for high transparency, with relatively small fundamental band gaps due to low conduction-band minima, which favor $n$-type doping and enhance the electrical conductivity. It has been understood that the optical band gaps are wider than the fundamental band gaps because optical transitions between the band-edge states are forbidden. The mechanism blocking such transitions, which can play a crucial role in the designing of alternative TCOs, nonetheless remains obscure. Here, based on first-principles density functional theory calculations and symmetry analysis of three oxides, ${M}_{2}{\mathrm{O}}_{3}$ $(M=\mathrm{Al},\mathrm{Ga},\mathrm{In})$, we identify the physical origin of the gap disparities. Three conditions are necessary: (1) the crystal structure must have global inversion symmetry; (2) in order to belong to the ${A}_{g}$ or ${A}_{1g}$ irreducible representations, the states at the conduction-band minimum must have cation and oxygen $s$ character; (3) in order to have $g$ parity, the oxygen $p$ orbitals constituting the states near the valence-band maximum must be strongly coupled to the cation $d$ orbitals. Under these conditions, optical excitations across the fundamental gap will be forbidden. The three criteria explain the trends in the ${M}_{2}{\mathrm{O}}_{3}$ $(M=\text{Al},\text{Ga},\text{In})$ sequence, in particular, explaining why ${\mathrm{In}}_{2}{\mathrm{O}}_{3}$ in the bixbyite structure yields the highest figure of merit. Our study provides guidelines expected to be instrumental in the search for new TCO materials.

We report that the discovery of stable two-dimensional, earth-abundant, semiconducting materials is of great interest and may impact future electronic technologies. By combining global structural prediction and first-principles calculations, we have theoretically discovered several previously unknown semiconducting silicon phosphides (SixPy) monolayers, which could be formed stably at the stoichiometries of y/x ≥1. Unexpectedly, some of these compounds, i.e., P-6m2 Si1P1 and Pm Si1P2, have comparable or even lower formation enthalpies than their previously known bulk allotropes. The band gaps (Eg) of SixPy compounds can be dramatically tuned in an extremely wide range (0< Eg < 3 eV) by simply changing the number of layers or applying an in-plane strain. Furthermore, we find that carrier doping can drive the ground state of C2/m Si1P3 from a nonmagnetic state into a robust half-metallic spin-polarized state, originating from its unique valence band structure, which can extend the use of Si-related compounds for spintronics.

Using first-principles calculations and symmetry analysis, we show that as cation atoms in a zinc blende--based semiconductor are replaced through atomic mutation (e.g., evolve from ZnSe to $\mathrm{CuGaS}{\mathrm{e}}_{2}$ to $\mathrm{C}{\mathrm{u}}_{2}\mathrm{ZnGeS}{\mathrm{e}}_{4}$), the band gaps of the semiconductors will become more and more indirect because of the band splitting at the zone boundary, and in some cases will even form the segregating states. For example, although ZnSe is a direct band gap semiconductor, quaternary compounds $\mathrm{C}{\mathrm{u}}_{2}\mathrm{ZnGeS}{\mathrm{e}}_{4}$ and $\mathrm{C}{\mathrm{u}}_{2}\mathrm{ZnSnS}{\mathrm{e}}_{4}$ can be indirect band gap semiconductors if they form the primitive mixed CuAu ordered structures. We also find that the stability and the electronic structure of the quaternary polytypes with different atomic ordering are almost negative-linearly correlated. We suggest that these intrinsic properties of the multication semiconductors can have a large influence on the design and device performance of these materials.

The diffusion of particles in solid-state materials generally involves several sequential thermal-activation processes. However, presently, diffusion coefficient theory only deals with a single barrier, i.e., it lacks an accurate description to deal with multiple-barrier diffusion. Here, we develop a general diffusion coefficient theory for multiple-barrier diffusion. Using our diffusion theory and first-principles calculated hopping rates for each barrier, we calculate the diffusion coefficients of Cd, Cu, Te, and Cl interstitials in CdTe for their full multiple-barrier diffusion pathways. As a result, we found that the calculated diffusivity agrees well with the experimental measurement, thus justifying our theory, which is general for many other systems.

The Fermi level of a material is a fundamental quantity that determines its electronic properties. Thus, the ability to tune Fermi levels is important for developing electronic device materials. However, for most materials, the Fermi level is limited to a certain range in the band gap due to the existence of certain intrinsic compensating defects. Here we demonstrate that quenching can be used as an effective way to overcome this limit, allowing the Fermi levels to be tuned in a much wider range. Taking a photovoltaic material CdTe as a prototype example, we analyzed the physical origin of Fermi level pinning and explained why growing the sample at high temperature followed by rapid quenching to room temperature can overcome the self-compensation limit. We further show that for CdTe, quenching can increase the Fermi level range from about 0.6 to 1.1 eV, which has a great potential in improving CdTe solar cell performance. Our proposed strategy of tuning Fermi level positions beyond the intrinsic equilibrium doping limit is general and can be applied to other semiconductor systems.

Using first-principles calculations, we study the diffusions of interstitial defects Cd, Cu, Te, and Cl in CdTe. We find that the diffusion behavior is strongly correlated with the electronic structure of the interstitial diffuser. For Cd and Cu, because the defect state is the non-degenerated slike state under Td symmetry, the diffusions are almost along the [111] directions between the tetrahedral sites, although the diffusion of Cu shows some deviation due to the s - d coupling. The diffusions of the neutral and charged Cd and Cu follow similar paths. However, for Te and Cl atoms, because the defect state is the degenerated p-like state under Td symmetry, large distortions occur. Therefore, the diffusion paths are very different from those of Cd and Cu interstitials, and depend strongly on the charge states of the interstitial atoms. For Te, we find that the distortion is mostly stabilized by the crystal-field splitting, but for Cl, the exchange splitting plays a more important role.

We studied systematically the structural and electronic properties of binary $\mathrm{Cd}X$ $(X=\mathrm{S},$ Se, and Te) semiconductors in both zinc-blende (ZB) and wurtzite (WZ) structures, the band alignment on the ZB/WZ interfaces, and carrier localization induced by the band offsets. We show, by first-principles band-structure calculation that at low temperature, CdS is stable in the wurtzite structure, while CdSe and CdTe are stable in the zinc-blende structure. However, coherent substrate strain can change CdTe to be more stable in the wurtzite form. We find that $\mathrm{Cd}X$ in the wurtzite structure has a larger band gap than the one in the zinc-blende structure. The band alignment on the ZB/WZ interface is found to be type II with holes localized on the wurtzite side and electrons on the zinc-blende side.

The electronic structure in nitrogen-poor ${\mathrm{GaAs}}_{1\ensuremath{-}x}{\mathrm{N}}_{x}$ alloys is investigated using a plane-wave pseudopotential method and large supercells. Our calculations give a detailed description of the complex perturbation of the lowest conduction band states induced by nitrogen substitution in GaAs. The two principal physical effects are (i) a resonant impurity state ${a}_{1}(N)$ above the ${a}_{1}({\ensuremath{\Gamma}}_{1c})$ conduction band minimum (important at ``impurity'' concentrations, $x\ensuremath{\sim}{10}^{17} {\mathrm{cm}}^{\ensuremath{-}3})$ and (ii) the creation of ${a}_{1}{(L}_{1c}),$ and ${a}_{1}{(X}_{1c})$ states due to the splitting of the degenerate ${L}_{1c}$ and ${X}_{1c}$ GaAs levels (important at alloy concentrations, $x\ensuremath{\sim}1%$ or $\ensuremath{\sim}{10}^{21} {\mathrm{cm}}^{\ensuremath{-}3}).$ We show how the interaction of ${a}_{1}(N),$ ${a}_{1}({\ensuremath{\Gamma}}_{1c}),$ ${a}_{1}{(L}_{1c}),$ and ${a}_{1}{(X}_{1c})$ provides a microscopic explanation for the origin of the experimentally observed anomalous alloy phenomena.

We have studied systematically the chemical trends of the band-gap pressure coefficients of all group IV, III-V, and II-VI semiconductors using first-principles band-structure method. We have also calculated the individual ``absolute'' deformation potentials of the valence-band maximum (VBM) and conduction-band minimum (CBM). We find that (1) the volume deformation potentials of the ${\ensuremath{\Gamma}}_{6c}$ CBM are usually large and always negative, while (2) the volume deformation potentials of the ${\ensuremath{\Gamma}}_{8v}$ VBM state are usually small and negative for compounds containing occupied valence d state but positive for compounds without occupied valence d orbitals. Regarding the chemical trends of the band-gap pressure coefficients, we find that (3) ${a}_{p}^{\ensuremath{\Gamma}\ensuremath{-}\ensuremath{\Gamma}}$ decreases as the ionicity increases (e.g., from $\mathrm{G}\stackrel{\ensuremath{\rightarrow}}{e}\mathrm{GaA}\stackrel{\ensuremath{\rightarrow}}{s}\mathrm{ZnSe}),$ (4) ${a}_{p}^{\ensuremath{\Gamma}\ensuremath{-}\ensuremath{\Gamma}}$ increases significantly as anion atomic number increases (e.g., from $\mathrm{Ga}\stackrel{\ensuremath{\rightarrow}}{N}\mathrm{Ga}\stackrel{\ensuremath{\rightarrow}}{P}\mathrm{GaA}\stackrel{\ensuremath{\rightarrow}}{s}\mathrm{GaSb}),$ (5) ${a}_{p}^{\ensuremath{\Gamma}\ensuremath{-}\ensuremath{\Gamma}}$ decreases slightly as cation atomic number increases (e.g., from $\mathrm{AlA}\stackrel{\ensuremath{\rightarrow}}{s}\mathrm{GaA}\stackrel{\ensuremath{\rightarrow}}{s}\mathrm{InAs}),$ (6) the variation of ${a}_{p}^{\ensuremath{\Gamma}\ensuremath{-}L}$ are relatively small and follow similar trends as ${a}_{p}^{\ensuremath{\Gamma}\ensuremath{-}\ensuremath{\Gamma}},$ and (7) the magnitude of ${a}_{p}^{\ensuremath{\Gamma}\ensuremath{-}X}$ are small and usually negative, but are sometimes slightly positive for compounds containing first-row elements. Our calculated chemical trends are explained in terms of the energy levels of the atomic valence orbitals and coupling between these orbital. In light of the above, we suggest that ``empirical rule'' of the pressure coefficients should be modified.

The electronic structure of abrupt $(\mathrm{InAs}{)}_{n}/(\mathrm{GaSb}{)}_{n}$ superlattices is calculated using a plane wave pseudopotential method and the more approximate eight band $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ method. The $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ parameters are extracted from the pseudopotential band structures of the zinc-blende constituents near the $\ensuremath{\Gamma}$ point. We find, in general, good agreement between pseudopotential results and $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ results, except as follows. (1) The eight band $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ significantly underestimates the electron confinement energies for $nl~20.$ (2) While the pseudopotential calculation exhibits (a) a zone center electron-heavy hole coupling manifested by band anticrossing at $n=28,$ and (b) a light hole--heavy hole coupling and anticrossing around $n=13,$ these features are absent in the $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ model. (3) As $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ misses atomistic features, it does not distinguish the ${C}_{2v}$ symmetry of a superlattice with no-common-atom such as InAs/GaSb from the ${D}_{2d}$ symmetry of a superlattice that has a common atom, e.g., InAs/GaAs. Consequently, $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ lacks the strong in-plane polarization anisotropy of the interband transition evident in the pseudopotential calculation. Since the pseudopotential band gap is larger than the $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ values, and most experimental band gaps are even smaller than the $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ band gap, we conclude that to understand the experimental results one must consider physical mechanisms beyond what is included here (e.g., interdiffusing, rough interfaces, and internal electric fields), rather than readjust the $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ parameters.

Using a first-principles generalized one-dimensional Ising model we have studied the band structure and stability of two types of zinc-blende-based polytype series: type-a GaInP{sub 2} and type-b CuInSe{sub 2}. The interaction parameters for the formation energy are found to be short range, while the convergence is slower for the band-gap and conduction-band energies of the type-a GaInP{sub 2} polytypes. We predict that the CuAu-like phase can coexist in nominally chalcopyrite CuInSe{sub 2} and CuInS{sub 2}, while such coexistence is less likely in CuGaSe{sub 2}. We also predict that type-II band alignment can exist between different ordered type-a GaInP{sub 2} polytypes, despite that the band alignment between ordered and disordered GaInP{sub 2} are predicted to be type I. {copyright} {ital 1999} {ital The American Physical Society}

We present the results of a first-principles calculation of the direct band-gap pressure coefficient a{sub g} for a series of Ga and In semiconductor compounds with both the chalcopyrite (e.g., CuGaSe{sub 2} and CuInSe{sub 2}) and the zinc-blende structures (e.g., GaAs and InAs). We found good agreement between the calculated and experimental pressure coefficients. We found that a{sub g} in chalcopyrites are dramatically reduced relative to zinc-blende compounds, and that the Ga{r_arrow}In substitution lowers a{sub g} in chalcopyrites more than in zinc-blende compounds. As a result, the empirical rule suggested for zinc-blende compounds, stating that for a given transition (e.g., {Gamma}{sub 15v}{r_arrow}{Gamma}{sub 1c}) a{sub g} does not depend on substitutions, has to be modified for chalcopyrites. Based on our results we question the currently accepted experimental value for CuInTe{sub 2} (2.2 meV/kbar); we calculate this value to be close to 5.9 meV/kbar. {copyright} {ital 1998} {ital The American Physical Society}

Spontaneous CuPt ordering induces a band-gap reduction $\ensuremath{\Delta}{E}_{g}$ relative to the random alloy, a crystal field splitting ${\ensuremath{\Delta}}_{\mathrm{CF}}$ at valence-band maximum, as well as an increase of spin-orbit splitting ${\ensuremath{\Delta}}_{\mathrm{SO}}.$ We calculate these quantities for ${\mathrm{Al}}_{x}{\mathrm{In}}_{1\ensuremath{-}x}\mathrm{P},$ ${\mathrm{Al}}_{x}{\mathrm{In}}_{1\ensuremath{-}x}\mathrm{As},$ ${\mathrm{Ga}}_{x}{\mathrm{In}}_{1\ensuremath{-}x}\mathrm{P},$ and ${\mathrm{Ga}}_{x}{\mathrm{In}}_{1\ensuremath{-}x}\mathrm{As}$ using the local density approximation (LDA), as well as the more reliable LDA-corrected formalism. We further provide these values and the valence-band splittings $\ensuremath{\Delta}{E}_{12}$ (between ${\overline{\ensuremath{\Gamma}}}_{4,5v}$ and ${\overline{\ensuremath{\Gamma}}}_{6v}^{(1)}$) and $\ensuremath{\Delta}{E}_{13}$ (between ${\overline{\ensuremath{\Gamma}}}_{4,5v}$ and ${\overline{\ensuremath{\Gamma}}}_{6v}^{(2)}$) for these materials as a function of the degree \ensuremath{\eta} of long range order. In the absence of an independent measurement of \ensuremath{\eta}, experiment is currently able to deduce only the ratio $\ensuremath{\Delta}{E}_{g}/{\ensuremath{\Delta}}_{\mathrm{CF}}.$ Our LDA-corrected results for this quantity compare favorably with recent experiments for ${\mathrm{Ga}}_{x}{\mathrm{In}}_{1\ensuremath{-}x}\mathrm{P}$ and ${\mathrm{Ga}}_{x}{\mathrm{In}}_{1\ensuremath{-}x}\mathrm{As},$ but not for ${\mathrm{Al}}_{x}{\mathrm{In}}_{1\ensuremath{-}x}\mathrm{P},$ where our calculation does not support the experimental assignment. The ``optical LRO parameter \ensuremath{\eta}'' can be obtained by fitting our calculated $\ensuremath{\Delta}{E}_{g}(\ensuremath{\eta})$ to the measured $\ensuremath{\Delta}{E}_{g}(\ensuremath{\eta}),$ and by expressing the measured $\ensuremath{\Delta}{E}_{12}(\ensuremath{\eta})$ and $\ensuremath{\Delta}{E}_{13}(\ensuremath{\eta})$ in terms of our calculated ${\ensuremath{\Delta}}_{\mathrm{CF}}(\ensuremath{\eta})$ and ${\ensuremath{\Delta}}_{\mathrm{SO}}(\ensuremath{\eta}).$ We also provide the calculated x-ray structure factors for ordered alloys that can be used experimentally to deduce \ensuremath{\eta} independently.

We studied the defect physics in ${\mathrm{CuInSe}}_{2},$ a prototype chalcopyrite semiconductor. We showed that (i) it takes much less energy to form a Cu vacancy in ${\mathrm{CuInSe}}_{2}$ than to form cation vacancies in II-VI compounds (ii) defect formation energies vary considerably both with the Fermi energy and with the chemical potential of the atomic species, and (iii) the defect pairs such as $({2\mathrm{V}}_{\mathrm{Cu}}^{\mathrm{\ensuremath{-}}}{+\mathrm{I}\mathrm{n}}_{\mathrm{Cu}}^{2+})$ and $({2\mathrm{C}\mathrm{u}}_{\mathrm{In}}^{2\mathrm{\ensuremath{-}}}{+\mathrm{I}\mathrm{n}}_{\mathrm{Cu}}^{2+})$ have particularly low formation energies (under certain conditions, even exothermic). Using (i)--(iii), we (a) explain the existence of unusual ordered compounds ${\mathrm{CuIn}}_{5}{\mathrm{Se}}_{8},$ ${\mathrm{CuIn}}_{3}{\mathrm{Se}}_{5},$ ${\mathrm{Cu}}_{2}{\mathrm{In}}_{4}{\mathrm{Se}}_{7},$ and ${\mathrm{Cu}}_{3}{\mathrm{In}}_{5}{\mathrm{Se}}_{9}$ as a repeat of a single unit of $({2\mathrm{V}}_{\mathrm{Cu}}^{\mathrm{\ensuremath{-}}}{+\mathrm{I}\mathrm{n}}_{\mathrm{Cu}}^{2+})$ pairs for each $n=4,$ 5, 7, and 9 units, respectively, of ${\mathrm{CuInSe}}_{2};$ (b) attribute the very efficient $p$-type self-doping ability of ${\mathrm{CuInSe}}_{2}$ to the exceptionally low formation energy of the shallow defect Cu vacancies; (c) explained in terms of an electronic passivation of the ${\mathrm{In}}_{\mathrm{Cu}}^{2+}$ by ${2\mathrm{V}}_{\mathrm{Cu}}^{\mathrm{\ensuremath{-}}}$ the electrically benign character of the large defect population in ${\mathrm{CuInSe}}_{2}.$ Our calculation leads to a set of new assignment of the observed defect transition energy levels in the band gap. The calculated level positions agree rather well with available experimental data.

Using large (512-atom) pseudopotential supercell calculations, we have investigated the composition dependence of the momentum matrix element ${M}_{v,c}$ for transitions between the valence-band maximum and the conduction-band minimum of three semiconductor alloys: ${\mathrm{GaP}}_{1\ensuremath{-}x}{\mathrm{N}}_{x}$ and ${\mathrm{GaAs}}_{1\ensuremath{-}x}{\mathrm{N}}_{x},$ exhibiting large chemical and size differences between their alloyed elements, and ${\mathrm{GaP}}_{1\ensuremath{-}x}{\mathrm{As}}_{x},$ which is a weakly perturbed alloy. In the composition ranges where these alloys have a direct band gap, we find that (i) in ${\mathrm{GaP}}_{1\ensuremath{-}x}{\mathrm{As}}_{x},$ ${M}_{v,c}$ is large (like the virtual-crystal value) and nearly composition independent; (ii) in ${\mathrm{GaAs}}_{1\ensuremath{-}x}{\mathrm{N}}_{x},$ ${M}_{v,c}$ is strongly composition dependent: large for small $x$ and small for large $x;$ and (iii) in ${\mathrm{GaP}}_{1\ensuremath{-}x}{\mathrm{N}}_{x},$ ${M}_{v,c}$ is only slightly composition dependent and is significantly reduced relative to the virtual-crystal value. The different behavior of ${\mathrm{GaP}}_{1\ensuremath{-}x}{\mathrm{As}}_{x},$ ${\mathrm{GaP}}_{1\ensuremath{-}x}{\mathrm{N}}_{x},$ and ${\mathrm{GaAs}}_{1\ensuremath{-}x}{\mathrm{N}}_{x}$ is traced to the existence/absence of impurity levels at the dilute alloy limits: (a) there are no gap-level impurity states at the $x\ensuremath{\rightarrow}1$ or $x\ensuremath{\rightarrow}0$ limits of ${\mathrm{GaP}}_{1\ensuremath{-}x}{\mathrm{As}}_{x},$ (b) an isolated As impurity in GaN ($\mathrm{GaN}:\mathrm{A}\mathrm{s}$) has a deep band gap impurity level but no deep impurity state is found for N in GaAs, and (c) $\mathrm{GaN}:\mathrm{P}$ exhibits a P-localized deep band-gap impurity state and $\mathrm{GaP}:\mathrm{N}$ has an N-localized resonant state. The existence of deep levels leads to wave-function localization in real space, thus to a spectral spread in momentum space and to a reduction of ${M}_{v,c}.$ These impurity levels are facilitated by atomic relaxations, as evident by the fact that unrelaxed $\mathrm{GaN}:\mathrm{A}\mathrm{s}$ and $\mathrm{GaN}:\mathrm{P}$, show no deep levels, have extended wave functions, and have large interband transition elements.

The rocksalt-structure PbS, PbSe, and PbTe semiconductors and their alloys exhibit a series of electronic-structure anomalies relative to the II-VI system, including the occurrence of direct gaps at the L point, anomalous order of band gaps and valence-band maximum energies versus anions, negative optical bowing, and negative band-gap pressure coefficients. We show that these anomalies result from the occurrence of the Pb s band below the top of the valence band, setting up coupling and level repulsion at the L point. Furthermore, we find that the topology of the frustrated octahedral structure leads to the occurrence in the random alloy of two distinct bonds for each anion-cation pair and to the predicted stabilization of {ital bulk} ordered Pb{sub 2}STe CuPt-like phase. {copyright} {ital 1997} {ital The American Physical Society}

Currently little is known about the atomic and electronic structure of Cu${}_{2}$ZnSnS${}_{4}$ (CZTS) surfaces, although the efficiency of kesterite-based solar cells has been increased to over 11$%$. Through the first-principles calculations, we studied the possible surface structures of the frequently observed cation-terminated (112) and anion-terminated ($\overline{1}\overline{1}\overline{2}$) surfaces, and found that the polar surfaces are stabilized by the charge-compensating defects, such as vacancies (V${}_{\mathrm{Cu}}$, V${}_{\mathrm{Zn}}$), antisites (Zn${}_{\mathrm{Cu}}$, Zn${}_{\mathrm{Sn}}$, Sn${}_{\mathrm{Zn}}$), and defect clusters (Cu${}_{\mathrm{Zn}}$+Cu${}_{\mathrm{Sn}}$, 2Zn${}_{\mathrm{Cu}}$+V${}_{\mathrm{Sn}}$). In stoichiometric single-phase CZTS samples, Cu-enriched defects are favored on (112) surfaces and Cu-depleted defects are favored on ($\overline{1}\overline{1}\overline{2}$) surfaces, while in non-stoichiometric samples grown under Cu poor and Zn rich conditions both surfaces favor the Cu-depleted defects, which explains the observed Cu deficiency on the surfaces of the synthesized CZTS thin films. The electronic structure analysis shows that Cu-enriched surfaces produce detrimental states in the band gap, while Cu-depleted surfaces produce no gap states and are thus benign to the solar cell performance. The calculated surface properties are consistent with experimental observation that Cu-poor and Zn-rich CZTS solar cells have higher efficiency.

Using the first-principles method and special quasirandom structure approach, we have studied the formation energies of two prototype defects in alloys, Ge${}_{\mathrm{As}}$ in Al${}_{x}$Ga${}_{1\ensuremath{-}x}$As and Cu${}_{\mathrm{Cd}}$ in CdS${}_{x}$Te${}_{1\ensuremath{-}x}$. We find that giant bowing effects for the defect formation energy can exist in semiconductor alloys. The bowing effect originates from the concentrated distribution of defects at low energy sites caused by the defect wave-function localization and the size-mismatch-induced strain effect. Because the bowing effect can drastically reduce the defect formation energy---even in dilute semiconductor alloys---it can have wide applications, such as alloy-enhanced defect solubility in semiconductors.

The physical properties and chemical trends of defects in GaAs under the hyperdoping situation are investigated and found to be very different from those in the impurity limit. We show that at high dopant concentrations, a defect complex denoted as the $DDX$ center becomes the dominant ``killer'' to limit the electron carrier concentration, whereas in the impurity limit, the electron carrier concentration is usually limited by the well-known $DX$ center. The $DDX$ center shows some opposite chemical trends compared to the $DX$ center. For example, to avoid the $DX$ center, anion site donors are preferred, but to avoid the $DDX$ center, cation site donors are better. Our proposed mechanism is able to explain some puzzling experimental observations.

Doping behavior in quantum dots (QDs) differs from that in the bulk. Despite many efforts, the doping properties are still not fully understood. Using first-principles methods, we have calculated the formation energies of various group-III acceptors and group-V donors doping at all nonequivalent sites in a Si QD (Si${}_{147}$H${}_{100}$). To analyze the trend of the formation energy, we decompose it into two terms: the unrelaxed formation energy (chemical energy) and the relaxation energy. We find that the unrelaxed formation energy generally increases as the dopant moves from the center of the QD to the surface. The variation of the unrelaxed formation energy in the surface region is explained by the variation of the local potential of the QD and the size effect. The relaxation energy gain increases as the size mismatch between the dopant and Si atom increases. Generally, the relaxation effect becomes more significant as the dopant moves toward the surface of the QD. The trend of the formation energy is determined by the two terms discussed above. If the size mismatch between the dopant and the Si atom is small, the trend of the formation energy generally follows that of the unrelaxed formation energy, increasing as the dopant moves from the center to the surface; thus, these dopants have a better chance of staying in the core region. On the other hand, if the size mismatch is large, the relaxation effect dominates and the formation energy decreases, which indicates these dopants cannot enter the core region under equilibrium growth conditions.

As alternatives to the mixed-anion Cu${}_{2}$ZnSn(S,Se)${}_{4}$ alloys, the mixed-cation Cu${}_{2}$Zn(Sn,Ge)Se${}_{4}$ and Cu${}_{2}$Zn(Sn,Si)Se${}_{4}$ alloys can also span a band gap range that fits the requirement of the solar cell light absorber. However, material properties of these alloys as functions of alloy composition $x$ are not well known. In this paper, using the first-principles calculations, we study the structural and electronic properties of these alloys. We find that (i) the Cu${}_{2}$Zn(Sn,Ge)Se${}_{4}$ alloys are highly miscible with low formation enthalpies, while the Cu${}_{2}$Zn(Sn,Si)Se${}_{4}$ alloys are less miscible; (ii) the band gap of Cu${}_{2}$Zn(Sn,Ge)Se${}_{4}$ increases almost linearly from 1.0 eV to 1.5 eV as the Ge composition $x$ increases from 0 to 1, whereas the band gap of Cu${}_{2}$Zn(Sn,Si)Se${}_{4}$ spans a larger range from 1.0 eV to 2.4 eV and shows a slightly larger bowing; and (iii) the calculated band offsets shows that the band gap increase of the alloys with the addition of Ge or Si results primarily from the conduction band upshift, whereas the valence band shift is less than 0.2 eV. Based on these results, we expect that the component-uniform and band-gap-tunable Cu${}_{2}$Zn(Sn,Ge)Se${}_{4}$ and Cu${}_{2}$Zn(Sn,Si)Se${}_{4}$ alloys can be synthesized and have an improved photovoltaic efficiency.

Amorphous semiconductors are known to give rise to greatly reduced conductivity relative to their crystalline counterparts, which makes the recent development of amorphous oxide semiconductors with high electron mobility unexpected. Using first-principles molecular dynamics and electronic structure simulations, we have analyzed the electronic and optical properties of covalent and ionic oxide amorphous semiconductors. We observe that in covalent systems, amorphization introduces deep defect states inside the gap, resulting in a substantial deterioration of electrical conductivity. In contrast, in ionic systems, such as the transparent conducting oxide ZnO, amorphization does not create deep carrier-recombination centers, so the oxides still exhibit good conductivity and visible transparency relative to the crystalline phases. The origin of the conductivity imbalance between covalent and ionic amorphous semiconductors can be explained using a band coupling mechanism.

Tradition has it that in the absence of structural phase transition, or direct-to-indirect band-gap crossover, the properties of semiconductor alloys (bond lengths, band gaps, elastic constants, etc.) have simple and smooth (often parabolic) dependence on composition. We illustrate two types of violations of this almost universally expected behavior. First, at the percolation composition threshold where a continuous, wall-to-wall chain of given bonds (e.g., Ga-N-Ga-N...) first forms in the alloy (e.g., $\mathrm{Ga}{\mathrm{As}}_{1\ensuremath{-}x}{\mathrm{N}}_{x}$), we find an anomalous behavior in the corresponding bond length (e.g., Ga-N). Second, we show that if the dilute alloy (e.g., $\mathrm{Ga}{\mathrm{As}}_{1\ensuremath{-}x}{\mathrm{N}}_{x}$ for $x\ensuremath{\rightarrow}1$) shows a localized deep impurity level in the gap, then there will be a composition domain in the concentrated alloy where its electronic properties (e.g., optical bowing coefficient) become irregular: unusually large and composition dependent. We contrast $\mathrm{Ga}{\mathrm{As}}_{1\ensuremath{-}x}{\mathrm{N}}_{x}$ with the weakly perturbed alloy system $\mathrm{Ga}{\mathrm{As}}_{1\ensuremath{-}x}{\mathrm{P}}_{x}$ having no deep gap levels in the impurity limits, and find that the concentrated $\mathrm{Ga}{\mathrm{As}}_{1\ensuremath{-}x}{\mathrm{P}}_{x}$ alloy behaves normally in this case.

Using first-principles band structure calculations, we investigate the crystal-field and spin-orbit splittings at the valence-band edge of ZnO and their dependence on the strain. Different from other conventional semiconductors, the variation of the valence-band splitting of ZnO shows a strong nonlinear dependence on the strain and the slope of the crystal-field splitting as a function of strain can even change sign. Our analysis shows that this unusual behavior in ZnO is due to the strong coupling between Zn $3d$ states and oxygen $2p$ states. A mapping of the valence-band ordering in ZnO under different strain levels is provided that will be useful in designing ZnO-based optoelectronic devices.

Graphene magnetism has been proposed but based on thermodynamically unstable zigzag edges and dangling electrons with broken sublattice symmetry. From results of first-principles calculations, we propose a way to realize thermodynamically stable graphene ferromagnetism by seamlessly incorporating transition metals into the graphene honeycomb network. An Fe atom substituting a carbon-carbon dimer of graphene can result in nearly square-planar covalent bonding between the spin-polarized Fe 3$d$ orbitals and graphene dangling bond states. Dangling bond passivation of the divacancy pore with N and O strongly affects the Fe incorporation into the graphene network in terms of energetics and electronic structure. The Fe-N${}_{4}$ or Fe-C${}_{4}$ incorporated graphene is predicted to show long-range ferromagnetism particularly due to carrier mediation when electron doped.

The conventional eight-band {bold k}{center_dot}{bold p} model predicts a {ital decrease} of the electron effective mass and {ital no} {ital dependence} of the (001) strain band-gap deformation potential with the degree {eta} of long-range order in Ga{sub 0.5}In{sub 0.5}P alloys. We show that a complete band-structure approach predicts instead that (i) the electron effective mass in the ordering direction {ital increases} from 0.092{ital m}{sub 0} for {eta}=0 (random alloy) to 0.133{ital m}{sub 0} for {eta}=1 (ordered alloy), and (ii) the strain deformation potential {ital decreases} in magnitude from 8.26 eV for {eta}=0 to 6.34 eV for {eta}=1. These two effects are caused by the mixing of the conduction-band minimum with the {ital L}-derived conduction band, neglected in the standard eight-band model.

Local-density approximation (LDA) band-structure calculations place the 3d band of zinc-blende ZnO, ZnS, ZnSe, and ZnTe at 5.4, 6.4, 6.8, and 7.5 eV below the valence-band maximum (VBM), while photoemission measurements place them at 7.8, 9.0, 9.4, and 9.8 eV below the VBM, respectively. We show that this \ensuremath{\sim}3-eV LDA error can be accounted for using a ``broken symmetry'' band-structure approach. In this approach, a d core hole is placed in an impuritylike splitoff d subband resulting from the creation of the hole on a particular Zn sublattice. Self-consistent solutions to such a constrained LDA problem reveal that the final hole state is sufficiently localized to trigger a self-interaction correction of 3--4 eV, needed to explain the discrepancy with experiment. This 3--4 eV shift is reduced, by screening effects, from the 9.7-eV value in a free Zn atom. Finally, we calculated the binding energy ${\mathit{E}}_{\mathrm{Mn}}$ for Mn 3d states in ZnTe:Mn and the effective Coulomb interaction parameter ${\mathit{U}}_{\mathrm{eff}}$. Significant improvements over the results of local-spin-density calculations were found. The calculated ${\mathit{E}}_{\mathrm{Mn}}$=${\mathit{E}}_{\mathrm{VBM}}$-3.93 eV and ${\mathit{U}}_{\mathrm{eff}}$=6.85 eV are in good agreement with experiments.

We investigated theoretically the ordering-induced change of the {ital E}{sub 1}, {ital E}{sub 2}, and {ital E}{sub 0}{sup {prime}} transitions in Ga{sub 0.5}In{sub 0.5}P using symmetry arguments and first-principles band-structure calculations. We show that upon (111) superlattice ordering these transitions are altered dramatically---some states shift up in energy, some shift down, and new ``ordering-induced`` transitions, absent in the disordered phase, now become allowed. Experimental observation of these changes could serve as new fingerprints of ordering. We have also studied the pressure dependence of the energies of the {ital X}{sub 1{ital c}} and {ital L}{sub 1{ital c}} derived states in the ordered superlattice. The recent experimental observation of the ``{ital X}{sub 1{ital c}}-like`` state at higher pressure is identified as a mixture of the folded {ital L}{sub 1{ital c}} and {ital X}{sub 1{ital c}} states. A microscopic explanation is given.

Theoretical calculation of defect properties, especially transition energy levels, is typically done by first-principles density-functional theory calculation using supercells with finite size. So far, three approaches---band-filling corrections (BFC), band-edge corrections (BEC), and no corrections (NC)---have been applied to deal with the potential inaccuracy caused by the finite size. In this paper, we compare these three approaches by calculating the (0/2$+$ ionization energies of the oxygen vacancy (V${}_{\mathrm{O}}$) in In${}_{2}$O${}_{3}$ and ZnO. We find that a correction must be included whether or not the defect level is deep or shallow, especially when the defect band has a large dispersion. The BFC approach gives the best correction. The BEC approach works well in GGA calculations only for certain systems in which the band gap underestimation is partially corrected by choosing effective band edges.

In theoretical studies of thin film and nanostructured semiconductors, pseudohydrogen (PH) is widely used to passivate the surface dangling bonds. Based on these calculations, it is often believed that nanostructured semiconductors, due to quantum confinement, have a larger band gap than their bulk counterparts. Using first-principles band structure theory calculation and comparing systematically the differences between PH-passivated and real-hydrogen--passivated (RH-passivated) semiconductor surfaces and nanocrystals, we show that, unlike PH passivation that always increases the band gap with respect to the bulk value, RH passivation of the nanostructured semiconductors can either increase or decrease the band gap, depending on the ionicity of the nanocompounds. The differences between PH and RH passivations decreases when the covalency of the semiconductor increases and can be explained using a band coupling model. This observation greatly increases the tunability of nanostructured semiconductor properties, especially for wide-gap ionic semiconductors.

Using band symmetry analysis and density functional theory calculations, we reveal the origin of why oxygen vacancy (${V}_{\mathrm{O}}$) energy levels are shallow in some $AB$O${}_{3}$ perovskites, such as SrTiO${}_{3}$, but are deep in some others, such as LaAlO${}_{3}$. We show that this diverse behavior can be explained by the symmetry of the perovskite structure and the location ($A$ or $B$ site) of the metal atoms with low $d$ orbital energies, such as Ti and La atoms. When the conduction band minimum (CBM) is an antibonding ${\ensuremath{\Gamma}}_{12}$ state, which is usually associated with the metal atom with low $d$ orbital energies at the $A$ site (e.g., LaAlO${}_{3}$), then the ${V}_{\mathrm{O}}$ energy levels are deep inside the gap. Otherwise, if the CBM is the nonbonding ${\ensuremath{\Gamma}}_{{25}^{\ensuremath{'}}}$ state, which is usually associated with metal atoms with low $d$ orbital energies at the $B$ site (e.g., SrTiO${}_{3}$), then the ${V}_{\mathrm{O}}$ energy levels are shallow and often above the CBM. The ${V}_{\mathrm{O}}$ energy level is also deep for some uncommon $AB$O${}_{3}$ perovskite materials that possess a low $s$ orbital, or large-size cations, and an antibonding ${\ensuremath{\Gamma}}_{1}$ state CBM, such as ZnTiO${}_{3}$. Our results, therefore, provide guidelines for designing $AB$O${}_{3}$ perovskite materials with desired functional behaviors.