Electronic Properties of Zn2V(1–x)NbxN3 Alloys to Model Novel Materials for Light-Emitting Diodes

We propose the Zn2V(1–x)NbxN3 alloy as a new promising material for optoelectronic applications, in particular for light-emitting diodes (LEDs). We perform accurate electronic-structure calculations of the alloy for several concentrations x using density-functional theory with meta-GGA exchange–correlation functional TB09. The band gap is found to vary between 2.2 and 2.9 eV with varying V/Nb concentration. This range is suitable for developing bright LEDs with tunable band gap as potential replacements for the more expensive Ga(1–x)In(x)N systems. Effects of configurational disorder are taken into account by explicitly considering all possible distributions of the metal ions within the metal sublattice for the chosen supercells. We have evaluated the band gap’s nonlinear behavior (bowing) with variation of V/Nb concentration for two possible scenarios: (i) only the structure with the lowest total energy is present at each concentration and (ii) the structure with minimum band gap is present at each concentration, which corresponds to experimental conditions when also metastable structures are presents. We found that the bowing is about twice larger in the latter case. However, in both cases, the bowing parameter is found to be lower than 1 eV, which is about twice smaller than that in the widely used Ga(1–x)In(x)N alloy. Furthermore, we found that both crystal volume changes due to alloying and local effects (atomic relaxation and the V–N/Nb–N bonding difference) have important contributions to the band gap bowing in Zn2V(1–x)NbxN3.

L ight-emitting diodes (LEDs) are used in devices where brightness, low power consumption, and reliability are needed, including automotive, mobile, and display applications.Most bright LEDs are based on group III−V semiconductors or their alloys.−13 In particular, III−N alloys exhibit an ultrawide band gap due to the quantum confinement effect. 14Therefore, III−N alloys find applications in blue LEDs and ultraviolet optoelectronic devices 15−17 and in high-power electronic devices. 17Currently, InGa-N alloys are mostly used in industry due to their favorable electronic properties and established synthetic routes.However, these materials and their syntheses are expensive.It is also difficult to produce p-type doped GaN, which is needed for blue LEDs.Therefore, there is an active search for semiconductors that could replace InGa-N/GaN materials 1,18 in electronic devices.
A class of promising nitride compounds for LEDs are polyvalent ternary compounds, which are based on Zn or Mg nitrides with crystal structures derived from parent compounds of wurtzite or rock-salt structures.−21 Zn 2 PN 3 (i.e., II−V−N) alloy is characterized by wide gap (higher than 4 eV) and a low electronic effective mass, which makes it suitable for power electronics, where wider gaps allow higher breakdown voltages. 22Examples of experimentally synthesized wurtzite materials of the II−V−N family include Zn 2 VN 3 with a predicted fundamental band gap of 2.23 eV and a direct gap of 2.35 eV. 23Zn 2 VN 3 is a weakly doped p-type semiconductor that exhibits broadband room-temperature photoluminescence spanning the range between 2 and 3 eV.Its electronic properties can be tuned over a wide range via isostructural alloying on the cation site, making this a promising material for optoelectronic applications. 23he effect of vanadium doping on the electronic and optical properties of various semiconductors is far from trivial.−26 Furthermore, vanadium at high concentration is seen to differently affect the band gap in GaN depending on the magnetic order of vanadium defects: in the case of ferromagnetic ordering, vanadium doping narrows the band gap, while in the case of antiferromagnetic ordering, vanadium increases the band gap. 27Another metal dopant that has a nontrivial effect on the band gap of mixed semiconductors is niobium.In ZnS, it causes the band gap reduction in the spin-minority channel. 28t has been shown experimentally that Zn 2 NbN 3 crystallizes in a cation-disordered wurtzite (ZG) structure with an optical band gap of 2.1 eV. 29This study presents wurtzite Zn 2 NbN 3 as a promising new ternary semiconductor for optoelectronic and ferroelectric applications and suggests the possibility of synthesizing quaternary nitride semiconductors by exchanging Nb with V.It is therefore very interesting, both from a practical and fundamental standpoint, to systematically study the electronic structure of Zn 2 V (1−x) Nb x N 3 alloys incorporating Zn (s-element) and V and Nb (d-elements).
−50 The bowing parameter (b) determines how far from linear the band gap dependence on alloy composition is.In the general case of a binary alloy α (1−x) β x N, b is defined as the coefficient of the nonlinear term in the phenomenological expression 51 where E g αN and E g βN are the band gaps for the pure α and β nitrides, respectively.In general, the parameter b can also depend on x, accounting for higher-order deviations from linearity.Moreover, for each concentration x the band gap of an alloy E g (x) depends on the atomic configuration c (distribution of the metal atoms in the sublattice).This dependence is called an alloy broadening.In the presence of broadening, b will depend on the abundance of various configurations in the synthesized materials depending on the synthesis method and relative thermodynamic stability of configurations.The parameter b indicates whether the band gap is smaller (b > 0) or larger (b < 0) than the linear combination of end-point band gaps.Hence, to design LEDs with specific optical properties, knowledge of the bowing parameter is of fundamental importance.
A class of promising nitride compounds for LEDs are polyvalent ternary compounds, which are based on Zn or Mg nitrides with crystal structures derived from parent compounds of wurtzite or rock-salt structures.These nitrides can be combined with GaN and related III−N wurtzite semiconductors, which are amenable to p-type doping upon contact formation. 19−21 Zn 2 PN 3 (i.e., II−V−N) alloy is characterized by a wide gap (higher than 4 eV) and a low electronic effective mass, which makes it suitable for power electronics, where wider gaps allow higher breakdown voltages. 22Examples of experimentally synthesized wurtzite materials of II−V−N family include Zn 2 VN 3 with a predicted fundamental band gap of 2.23 eV and a direct gap of 2.35 eV. 23n 2 VN 3 is a weakly doped p-type semiconductor that exhibits broadband room-temperature photoluminescence spanning the range between 2 and 3 eV.Its electronic properties can be tuned over a wide range via isostructural alloying on the cation site, making this a promising material for optoelectronic applications. 23e effect of vanadium doping on the electronic and optical properties of various semiconductors is far from trivial.−26 Furthermore, vanadium at high concentration is seen to differently affect the band gap in GaN depending on the magnetic order of vanadium defects: in the case of ferromagnetic ordering, vanadium doping narrows the band gap, while in the case of antiferromagnetic ordering, vanadium increases the band gap. 27Another metal dopant that has a nontrivial effect on the band gap of mixed semiconductors is niobium.In ZnS, it causes the band gap reduction in the spin-minority channel. 28t has been shown experimentally that Zn 2 NbN 3 crystallizes in a cation-disordered wurtzite (ZG) structure with an optical band gap of 2.1 eV. 29This study presents wurtzite Zn 2 NbN 3 as a promising new ternary semiconductor for optoelectronic and ferroelectric applications and suggests the possibility of synthesizing quaternary nitride semiconductors by exchanging Nb with V.It is therefore very interesting, both from a practical and fundamental standpoint, to systematically study the electronic structure of Zn 2 V (1−x) Nb x N 3 alloys incorporating Zn (s-element) and V and Nb (d-elements).
−55 Changes in alloy composition produce a near-linear volume variation which is well-known as Vegard's law. 56In order to separate the effect of this volume change on the band gap from the electronic effects of varying concentration, we will study the behavior of the band gap at constant volume but varying concentration.Since the disorder plays a role in the broadening of the emission, we will investigate this as well.Furthermore, we will distinguish the nonlinearity of the band gap dependence on concentration for two specific cases: (i) considering only the band gap coming from the structures with lowest total energy at each concentration (as approximate indicator of thermodynamic stability) and (ii) considering only the minimum band gap among all possible structures at each concentration.
Zn 2 VN 3 and Zn 2 NbN 3 are seen experimentally in previous works 20,23 to adopt orthogonal structures.Thus, we have chosen to consider only this polymorph at different concentrations.These alloys contain cation sites occupied by Zn in the oxidation state (+II) and two different possible oxidation states for V or Nb: (i) low oxidation state (+II) or (ii) high oxidation state (+V), depending on the oxidation state of N [(−II) in the first case or (−III) in the second case].
Depending on the oxidation state of V and Nb, the electronic correlation in the localized d-orbitals of the transition metal cations can be different and the calculated electronic structure may be more or less sensitive to the approximations in the computational methods.Moreover, Nb/ V−N bonds can have a significant covalent character, which decreases the localization of d-electrons on the Nb/V ions, further reducing on-center electronic correlation.Indeed, such nitrides were previously shown to be weakly correlated materials as confirmed by combined experimental and theoretical studies. 23,57Thus, using on-site models such as the Hubbard U model, which is often used to account for strong on-site electronic correlation in ionic transition-metal compounds, is not well-justified for these materials, as it may not fully capture the physics of Nb/V−N bonding.To evaluate the oxidation state, we have performed Bader charge analysis The Journal of Physical Chemistry Letters for both extreme concentrations Zn 2 VN 3 and Zn 2 NbN 3 within the primitive cell.
The Bader charges for V and Nb are equal to 1.80 and 2.24 au, respectively (see Supporting Information, Table ST.1).Thus, V and Nb are in the low oxidation state (II versus the maximum possible V), and increasing Nb concentration results in a slight increase of the oxidation state of d-element present in the structure.At the same time, the oxidation state of nitrogen decreases from −1.38 to −1.52 au.These values seem to indicate that there is a high occupation of d-shells of the transition-metal ions.Taking into account the analysis in the earlier work, 23,57 we conclude that there is indeed a high degree of covalency in V/Nb−N bonding in these materials, which makes them weakly correlated despite the high occupation of the d-states.
It is well-known that even for weakly correlated compounds standard local-density and generalized-gradient approximations (GGA) to the DFT functional can significantly underestimate the band gap of semiconductors.−60 This functional was recently demonstrated to yield accurate band gaps of a wide range of semiconductors, 61 including nitrides. 1 Fundamental and direct band gaps calculated with TB09 for Zn 2 VN 3 are in good agreement with previous hybrid functional (HSE06) calculations (2.21 and 2.28 eV with TB09 versus 2.23 and 2.35 eV with HSE06 23 ).For Zn 2 NbN 3 TB09 direct band gap is 2.87 eV, which is in a very good agreement with the experimental value 3.00 eV. 29Considering that the functional works well for the alloy end-points and that the alloying atoms belong to the same group in the periodic table, TB09 will yield accurate band gaps for Zn 2 V (1−x) Nb x N 3 , comparable to significantly more computationally expensive hybrid functional HSE06, preventing its systematic use for larger supercells.
To model the new ternary nitride semiconductors, we use an approach in which the formula unit of the three-component semiconductors is doubled, and one of the identical cations in

The Journal of Physical Chemistry Letters
the supercell is replaced by a different cation with the same total charge, resulting in a new four-component compound with a similar crystal structure. 29,62,63In this way, we have built 24-atom primitive orthogonal cells of Zn 2 V (1−x) Nb x N 3 alloy with all possible arrangements of V and Nb atoms in the β sublattice, as shown in Figure 4. We consider different volumes for the same concentrations and quantify the alloy broadening in this set of models.
Next, we have generated 1 × 1 × 2 and 1 × 2 × 1 48-atom supercells of Zn 2 V (1−x) Nb x N 3 alloys with all possible atomic arrangements of V and Nb for each concentration x.In this study, we do not consider supercells with random atomic positions.In disordered alloys the concept of band dispersion and therefore the difference between direct and fundamental gaps need careful consideration. 64However, a detailed analysis of effective band structure using a spectral decomposition 64 is beyond the scope of this study.
For the fully optimized supercells, the band gap bowing parameter b in eq 1 is calculated in this work as a function of concentration 0 < x < 1 for each configuration as follows: g

Zn NbN g
Zn VN g Zn V Nb N Subsequently, we have calculated the average bowing parameter b avg as follows: where the sum is over concentration j and N is the total number of b values.
The obtained fundamental and direct band gaps for the two scenarios (lowest-energy configuration for each concentration and lowest band gap for each concentration) are shown in Figures 1 and 2, respectively.In both cases the band gap varies between 2.2 and 2.9 eV.This is within the range of band gaps for InGa-N alloys (1−3.5 eV). 1 When only configurations with the lowest total energy are considered (Figures 1a and 2a), the band gap dependence on concentration shows a low bowing of 0.306 eV for fundamental and 0.326 eV for direct band gaps.
When metastable structures are present, we observe (see Figures 1b and 2b) about twice larger bowing (0.637 and 0.711 eV for fundamental and direct band gap, respectively).This is explained by generally smaller band gaps for metastable alloy configurations.
The obtained bowing parameters for Zn 2 V (1−x) Nb x N 3 are a factor of 2 smaller than for Ga (1−x) In (x) N alloys, calculated by some of us earlier. 1 Smaller bowing is beneficial because of a more predictable band gap in synthesized materials in the whole concentration range.This confirms the potential advantage of Zn 2 V (1−x) Nb x N 3 over Ga (1−x) In (x) N alloy as alternative materials for LEDs.
To disentangle effects of volume change from local relaxation/electronic effects of alloying on band gap bowing, we have analyzed the fundamental band gap as a function of the concentration x for strained crystals by fixing the volume V a of 24-atom orthorhombic primitive cells and optimized only the atomic positions for each configuration.In Figure 3a, the volume per atom for all configurations at each concentration x in Zn 2 V (1−x) Nb x N 3 alloy supercells (i.e., 1 × 2 × 1 and 1 × 1 × 2) is shown.The increase of Nb concentration for a stoichiometric compound causes a near linear increase in atomic volume, with the root-mean-square deviation (RMSD) from Vegard's law equal to 0.2 Å/atom.We found that different configurations at the same concentration have very similar equilibrium volumes, barely distinguishable in Figure 3a.
Figure 3b shows the fundamental band gap variation with concentration x for fixed cell volumes: Zn 2 VN 3 , Zn 2 V (0.5) Nb 0.5 N 3 , and Zn 2 NbN 3 .The atoms within each fixed-volume cell are fully relaxed.For Zn 2 V (0.5) Nb 0.5 N 3 , the volume was fixed to that of the lowest-energy configuration at this concentration.
Interestingly, although the band gap at fixed stoichiometry decreases with increasing volume and the cell volume increases upon adding Nb, the band gap increases with Nb concentration, even at small Nb concentrations (12.5%).This is explained by the character of the valence band maximum (VBM) and conduction band minimum (CBM), which can be seen in the projected density of states (pDOS) 3).The VBM in these materials is mainly composed of N 2p orbitals, while CBM states are d states of transition metal atoms.According to the Bader charge analysis (see Supporting Information Table ST.1), each metal atom loses about two electrons, which should go to the N 2p band, and transition-metal atoms also form N 2p−d bonds with predominantly covalent character as showed by the same population of these bands by pDOS (see Supporting Information Figures SF.1−SF.3).Thus, 2/3 of electrons in the N 2p band are mainly localized on N anions.However, slightly more electron density is transferred from Nb to N 2p relative to V. The resulting electron repulsion in the N 2p band is reduced when the cell volume is increased, which results in lowering of the VBM.Although the CBM also lowers, the VBM lowering is more pronounced due to stronger repulsion in the case of Nb-doping.
Figure 4 shows the atomic structures for different concentrations and configurations of Zn 2 V (1−x) Nb x N 3 24atom supercells, which were used to calculate band gaps in Figure 3b.The analysis of the relative energies of different configurations of Nb and V at a concentration x = 0.5 shows that the structure with Nb and V forming mixed layers (Figure 4c) is the most unstable one.It has the smallest fundamental band gap of 2.42 eV among the three symmetrically nonequivalent configurations in this unit cell.The config-urations d (Figure 4d) and e (Figure 4e) have very close fundamental band gaps of 2.510 and 2.514 eV, respectively.The configuration e is the most stable one (see Tables ST.1 and ST.2 in the Supporting Information).The volume of configuration e was chosen for the fixed volume at x = 0.5.
The bowing parameters b avg calculated from data shown in Figure 3b are summarized in Table 1.When the volume is not fixed for the 24-atom unit cell, the calculated b avg is 0.382 eV for the most stable structures (i.e., the band gap of the most stable configuration of Zn 2 V 0.5 Nb 0.5 N 3 is considered), and 0.495 eV when the configuration of Zn 2 V 0.5 Nb 0.5 N 3 with the lowest band gap is considered.The data show that fixing the volume does not remove bowing but noticeably reduces it.This means that both volume change and local effects (atomic relaxation and the V−N/Nb-N bonding difference) make important contributions to the band gap bowing.
We calculated the band gap dependence on Nb concentration in Zn 2 V (1−x) Nb x N 3 alloys.A full range of concentrations (0 ≤ x ≤ 1) was considered.The band gap is found to vary between 2.2 and 2.9 eV with varying V/Nb concentration.Thus, these novel materials are promising alternatives to the widely used but expensive GaN and InGa-N alloys used for blue LEDs and other optoelectronic applications.The effects of alloy broadening were investigated.The alloy broadening was found to significantly increase the average band gap bowing (from 0.306 to 0.637 eV for fundamental gap, and from 0.326 to 0.711 eV for direct gap) if metastable structures are present in synthesized alloys.In all cases, the bowing parameter is smaller than 1 eV.
The analysis of Bader charges and bonding character revealed that alloying does not change noticeably the nature of bonding in the material.For the whole range of concentrations, VBM is composed mainly of N 2p states, while CBM is formed by transition metal d-orbitals (3d or 4d depending on the Nb concentration).Increasing Nb concentration results in near-linear atomic volume increase.Although volume increase is found to reduce the band gap at fixed composition, the band gap increases even at small concentrations of Nb.This is explained by a slightly more ionic character of Nb−N bonds relative to V−N, which results in a more pronounced lowering of the VBM relative to CBM due to the higher electron−electron repulsion in the localized N 2p band.Increasing the volume leads to a more pronounced decrease of the energy of the band with larger electronic density.The band gap is indirect for Nb concentrations x < 0.5 but becomes direct from x = 0.5.

Figure 1 .
Figure 1.Calculated TB09 fundamental band gap as a function of concentration for (a) the structures with lowest total energy and (b) structures with the lowest band gap among the different V/Nb arrangements in Zn 2 V (1−x) Nb x N 3 1 × 2 × 1 and 1 × 1 × 2 supercells.The red dashed line in both panels shows the band gap calculated using eq 1 with bowing parameter b equal to b avg obtained by averaging over the whole range of concentrations.

Figure 2 .
Figure 2. Calculated TB09 direct band gap as a function of concentration for (a) the structures with the lowest total energy and (b) structures with the lowest band gap among the different V/Nb arrangements in Zn 2 V (1−x) Nb x N 3 1 × 2 × 1 and 1 × 1 × 2 supercells.The red dashed line in both panels shows the band gap calculated using eq 1 with bowing parameter b equal to b avg obtained by averaging over the whole range of concentrations.

Figure 3 .
Figure 3. (a) Volume per atom as a function of concentration x, calculated by TB09 for orthorhombic 1 × 2 × 1 and 1 × 1 × 2 supercells of Zn 2 V (1−x) Nb x N 3 alloys.(b) Fundamental band gap calculated with TB09 as a function of concentration x for fixed volume of 1 × 1 × 1 primitive cells of Zn 2 VN 3 (cyan), Zn 2 V (0.5) Nb 0.5 N 3 (green), and Zn 2 NbN 3 (red).The volume is fixed to that of the structure shown in the Figure 4e.Letter labels in panel b correspond to the labels of specific configurations in Figure 4.

Table 1 .
Values of b avg (in eV) Calculated from Data Shown in Figure3b