How to predict the location of the defect levels induced by 3d transition metal ions at octahedral sites of aluminate phosphors

Abstract

How the 3d transition metal (TM) ions induce defect levels in wide band gap compounds and how these defect levels evolve from compound to compound is very important in understanding and predicting the luminescent properties of TM activated phosphors. This issue is discussed by studying the ground state 3dⁿ level locations of the TM impurity ions (Sc–Zn) incorporated at the octahedral sites of many oxides. These ground state 3dⁿ level locations are obtained by collecting the CT bands from the literature of the past 50 years and also by first-principles calculations. By taking the vacuum level as the reference, we scaled all the locations of the TM ion in 3+ and 2+ states and constructed a zig-zag-curve scheme in α-Al₂O₃ through connecting the 3dⁿ ground state energies of Sc to Zn. The scheme can be extended to other aluminates easily and so offers a first estimate on where TM levels are located in compounds without complicated theoretical calculations. The estimate can be improved to a higher accuracy if the position of the valence band is known. Our work provides new insights for understanding the luminescent behavior of 3d-TM doped phosphors and may aid in developing 3d ion doped functional materials further.

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Introduction

In the past few decades, phosphors have been intensively investigated because of their applications in laser materials,¹ displays,² light emitting diodes (LED),^3–5 persistent luminescent materials,^6–9etc. In these phosphors, the lanthanide (Ln) ions and 3d transition metal (3d-TM) ions are the most common luminescent centers. The locations of the electronic levels of these ions with respect to the host bands, e.g. conduction band (CB) and valence band (VB), are imperative for understanding the optical properties of phosphors and their relevant performance. For example, significant quenching would happen for the d orbitals if the excitation states locate in the CB,¹⁰ or the ground states in the VB.⁵ In the persistent luminescent process, if the ground states are just above the VB, the corresponding ions could act as hole trapping centers,¹¹ and if the ground states are close to the CB, the corresponding ions may serve as the electron trapping centers.⁹ The energy transfer might happen if the defect levels of different ions are matched, typically Mn⁴⁺ and Fe³⁺.⁵ But determination or prediction of these level locations in compounds has always remained difficult.

The location of a lanthanide ion electronic ground state 4fⁿ level in different compounds with respect to the VB may vary strongly. However, if the vacuum level is taken as the reference energy, these level locations show small and predictable variation with the type of compound. The above finding is a result of the chemical shift model developed in 2012 by Dorenbos.¹² The level location with respect to the vacuum level is defined as the vacuum referred binding energy (VRBE). The double zigzag like shape of the VRBE curve that connects the 4fⁿ ground state energies for La to Lu appears remarkably invariant with the type of compound. This is very useful in predicting the lanthanide impurity level locations in a given compound.¹³ Whether the 3dⁿ-TMs follow a similar invariance and predictive curve therewith is still an open question. Once the systematics is known it will aid in understanding and developing new 3d-TM doped phosphors further.^14–16

The 3d orbital electrons are more sensitive to the crystal field than the 4f orbital electrons, because the 3d orbitals extend to the outside of the ion while the 4f orbitals are screened by the outer shell 5s and 5p orbitals. Both the strength (depending on the type of the anion and bond lengths between the TM ion and the anion) and type (depending on the anion coordination configuration) of the crystal field in the phosphors have a large influence on the defect level energies. So, obtaining a universal rule for the VRBE of 3d-TM ions is expected to be a more difficult task than for the lanthanides. Luckily, in most of the 3d-TM doped phosphors, the crystal field experienced by the 3d-TM ions can be mainly classified into an octahedral, or a tetrahedral crystal field. So, if we limit our consideration to one type of crystal field and to one type of anion, a common systematics of the VRBE may be revealed.

In this work, we focus our attention on the VRBEs of the 3d-TM ion doped aluminates with an octahedral crystal field. The compounds selected are α-Al₂O₃ and Y₃Al₅O₁₂ (YAG), since experimental data for 3d-TM ions in these compounds are relatively abundant. Both the experimental data collection from the literature and first-principles calculations are carried out. The results show that a common systematics of the VRBEs in the 3dⁿ ground state of 3d-TM in the octahedral crystal field of those aluminates indeed exists. Finally, we attempt to extend these two curves to other aluminates with an octahedral crystal field. The obtained zigzag like curve scheme provides us a tool to predict the 3d-TM level locations in compounds and so offers a guideline value for understanding and developing new phosphors with target properties.

Method

Experimentally, we do not have tools to determine the VRBE of an electron in an impurity level routinely. We do have tools to determine energies with respect to the host bands. The energy of charge (electron) transfer (CT) between TMs and host bands can be probed by optical spectroscopy, and thermoluminescence may provide the depth of an electron or hole trapped in a TM.¹⁷ The CT band energy E^CT(M,n) of Mⁿ⁺ (M represents one of the 3d-TM ions) in oxides is the energy needed for an electron to optically transfer from O²⁻ to Mⁿ⁺, reducing Mⁿ⁺ to M⁽ⁿ⁻¹⁾⁺. Our calculated electronic structures for Al₂O₃ and YAG show that the VBs are dominated by the O²⁻ 2p orbitals (see Fig. S1 in ESI†). E^CT(M,n) describes the energy difference between the acceptor level of Mⁿ⁺ (denoted as M^n+/(n−1)+) and the valence band maximum (VBM).¹⁷ Thus, the VRBE E(M,n − 1) of an electron when in the acceptor level of M^n+/(n−1)+ and E^CT(M,n) satisfies the following formula:

E(M,n − 1) = E_V + E^CT(M,n) (1)

where E_V is the energy of the VBM (the vacuum level is taken as the reference). Note that here we use a notation that is equivalent to what is often used for the lanthanides.

Theoretically, we calculate the total energies and electronic structures of M doped α-Al₂O₃ and YAG by using the VASP 5.3 code,^18,19 where the projector augment wave (PAW)²⁰ pseudopotentials are adopted to describe the interactions of atoms. The generalized gradient approximation (GGA)¹⁸ with an exchange–correlation functional following the Perdew–Burke–Ernzerhof (PBE) approach²⁰ is selected. In order to describe the valence electrons of Ti, V, Cr, Mn and Fe more accurately, the semi core p states are treated as valence. For Sc, both the semi core s and p states are treated as valence. A set of plane wave functions with an energy cut-off of 400 eV is used to describe the electronic wave functions.

The Al ions in α-Al₂O₃ are coordinated by six O ions, while in YAG both six- and four-coordinated Al sites are present. In our calculation, a supercell containing 2 × 2 × 2 unit cells of α-Al₂O₃ with the stoichiometry of Al₃₂O₄₈ and a primitive unit cell (Y₁₂Al₂₀O₄₈) of YAG is adopted. A Γ-centered 4 × 4 × 4 k-mesh is selected for k-point sampling. The defective structural models of α-Al₂O₃ and YAG are constructed by substituting one of the six-coordinated Al ions by an M ion. This M ion should be in the 3+ state in the neutral structural models. To obtain the M ion in the 4+ or 2+ state, an additional electron is taken from or added to the defective structural models. The formation energy E_F of M ion in these charge states is obtained, based on the following formula:²¹

E_F(Mⁿ⁺) = Eⁿ⁻³(M) − E(undoped) + μ_Al + μ_M + (n − 3)ε_f, (2)

where E(undoped) represents the total energy of the undoped compound and E⁽ⁿ⁻³⁾(M) stands for the energy of the Mⁿ⁺-doped compound. n − 3 is the net charge of the defective structural model. In the case of Mn⁴⁺-doped α-Al₂O₃, the net charge of the system n − 3 is 1+ and the charge state of Mn ion is 4+. μ_M and μ_Al are the chemical potentials of bulk M and Al, respectively. ε_f is the chemical potential of the electron and here equal to the Fermi level. The optical transition level energy (OTL) from Mⁿ⁺ (denoted as initial state) to M⁽ⁿ⁻¹⁾⁺ (denoted as final state) is defined as:²¹

ε_f(M^n+/(n−1)+) = [Eⁿ⁻⁴(M) − Eⁿ⁻³(M)] − E_VBM. (3)

E _VBM is the energy at the VBM as is offered by VASP, where the vacuum level is not the reference energy. This OTL energy describes the energy needed for an electron to transfer from the VBM to Mⁿ⁺, resulting in the M ion in the (n − 1)+ state. So, the process underlying OTL ε_f(M^n+/(n−1)+) from first principles calculation should be physically the same as that for E^CT(M,n) from optical spectroscopy. In the calculations of OTL ε_f(M^n+/(n−1)+), the structure of the initial state Mⁿ⁺-doped compound is fully relaxed, and the final state M⁽ⁿ⁻¹⁾⁺-doped compound is calculated with the same structure as that of the Mⁿ⁺-doped compound.²¹

Results and discussions

Table 1 lists the experimental data relevant to the CT bands of M ions with both trivalent and tetravalent charge states in α-Al₂O₃. These data are collected from the relevant literature of the past 50 years. Table 1 shows that for an M ion usually more than one value is listed. The overlap between CT bands with inter-configurational transitions observed in the absorption/excitation spectra often complicates proper assignment. Such experimental limitations result in different reported values with large uncertainty. We list most of those experimental data for reference. For Mn³⁺, the experiment provides the onset or threshold of the CT band (4.15 eV),²² while values for other TMs refer to the energy at the peak of the CT bands. Considering that the widths of the CT bands are typically 1 eV, the CT peak energy of Mn³⁺ is estimated to be about 4.65 eV. We adopt the symbol * to distinguish such estimated values. Ref. 23 describes two different CT data for Co³⁺, one is 3.1 eV measured at 1000 K and the other is 3.7 eV at 77 K. For Cu³⁺ and Zn³⁺, unfortunately, we did not find CT data. For the tetravalent ions, only the experimental CT band energies for Ti⁴⁺, V⁴⁺ and Mn⁴⁺ could be found in the literature.

Table 1 The CT data for M ions incorporated into Al₂O₃ and YAG. All energies are in eV

	Al2O3		Y3Al5O12
	3+	4+	3+	4+
a Estimated from the threshold energy of the CT band. b Estimated from defect levels of Cr^3+ obtained through TL measurements.
Sc	8.1^24	—	6.67^25	—
Ti	7.04,^26 7.67,^26 7.0^22	4.4,^27 4.56,^28 5.4^29	—	4.8 ± 0.3^30
V	5.75^22	3.76^31	—	3.28,^31 >3.1^32
Cr	6.94,^22 6.90^33	—	6.66^16^b	2.76^34
Mn	4.65^22 ^a	3.91^35	—	4.20,^36 4.0^37
Fe	4.80,^22,38 4.60^39	—	4.86,^40 4.88^41 5.04,^42 4.75^42	—
Co	3.10^23, 3.7^23	—	—	—
Ni	3.16,^22 4.13^23	—	3.50^43,44	—

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For CT data of M doped YAG, only those for Sc, Cr, Fe and Ni in the trivalent charge state and Ti, V, Cr and Mn in the tetravalent state are available (Table 1). In YAG, the M ions may be at lattice sites with either octahedral or tetrahedral crystal fields. In Table 1, all the data pertain to octahedral sites except possibly for V⁴⁺, for which the site occupied has not been specified in experiments.^31,45 The CT energy of Sc^{3+ 16,46,47} may be underestimated, since there is considerable mixing of the 3d-orbital with the orbitals at the nearby lying YAG band edge. The CT data of Cr³⁺ are not clear, and the value of 6.66 eV is indirectly estimated from thermoluminescence (TL) glow peak analysis by Ueda et al.¹⁶ Combining the CT energies with the VRBE at the VBM of Al₂O₃ (−9.6 eV) and YAG (−9.38 eV⁴⁸), the VRBE in the ground state of the M⁽ⁿ⁻¹⁾⁺ ions in Al₂O₃ and YAG are obtained.

These data are not enough to construct the complete VRBE curve of the 3d-TM electrons in the octahedral crystal field in α-Al₂O₃. We therefore calculate the OTL of Mⁿ⁺ doped α-Al₂O₃ using first-principles calculations. The calculated OTL together with the experimental acceptor level energies extracted from the CT values are shown in Fig. 1. All the calculated electronic structures of M doped α-Al₂O₃ can be found in part B of the ESI.† The charge state of Zn will be discussed at the end of this section.

Fig. 1 The OTL and VRBE of M ions in α-Al₂O₃. The circle and square symbols represent the OTL of ε_f(M^3+/2+) and ε_f(M^4+/3+), respectively. The plus and cross symbols represent experimental acceptor levels of M³⁺ and M⁴⁺ in α-Al₂O₃. The triangle is the OTL ε_f(Co^3+/2+) with a low-spin state (see below). The arrows indicate the CT process.

In Fig. 1, the data from the OTL of ε_f(M^3+/2+) and ε_f(M^4+/3+) are represented by circle and square symbols, respectively, while the data for the experimental acceptor levels of M³⁺ and M⁴⁺ are denoted as plus (+) and cross (×) symbols. In order to compare the OTL data of ε_f(M^3+/2+) with the experimental data, the calculated results have been shifted upwards by about 0.77 eV. Although this calculation systematically underestimates the experimental values, the GGA-PBE calculation can work well in predicting the trend of the CT energies of the 3d-TM ions from Sc to Zn.

For OTL ε_f(M^3+/2+) (the upper curve in Fig. 1), we find that except for Cr, the OTL decreases with the increase of the atomic number from Sc to Zn. This result is reasonable, since OTL is related to the defect levels, which may be inherited from the 3d orbitals of 3d-TM atoms. Like the 3rd ionization potentials of the free TM atoms, the binding energy of the 3d electron in 3d-TM atoms decreases with the growing number of nuclear charge. For Cr^3+/2+, the OTL is about 1.2 eV higher than that of V^3+/2+. As shown in Fig. S4 in the ESI,† V³⁺ has two valence electrons in the spin-up low triplet states. The OTL ε_f(V^3+/2+) describes the energy needed to transfer an electron from VBM to V³⁺ ion. This electron should be accommodated in the spin-up low triplet states. However, Cr³⁺ (Fig. S5, ESI†) has three valence electrons that already fully occupy the spin-up low triplet states, and so the electron from the VBM has to occupy either the spin-up high doublet states or the spin-down triplet states (the OTL in these two cases are different by 0.043 eV). Obviously, this needs much more energy than in the case of V³⁺. This is why ε_f(Cr^3+/2+) is about 1.2 eV larger than that of ε_f(V^3+/2+).

The good agreement of OTL ε_f(M^3+/2+) with the experimental CT band energies E^CT(M,3) of trivalent TMs gives us the confidence that the CT band energies E^CT(M,4) of tetravalent TM ions can also be predicted by the GGA-PBE calculations. From the experimental side, we only found CT data for Ti⁴⁺, V⁴⁺ and Mn⁴⁺ in Al₂O₃. The OTL ε_f(M^4+/3+) curve reproduces those CT data, if it is lifted by 1.566 eV. The overall trend is that the ε_f(M^4+/3+) decreases from Ti to Zn. The ε_f(Mn^4+/3+) is more than 1 eV larger than ε_f(Cr^4+/3+). The Mn⁴⁺ ion is like Cr³⁺ with three valence electrons, and the added electron has to occupy the higher energy doublet state. Also ε_f(Ni^4+/3+) is higher than that of its neighbors. This can also be explained from the filling of the 3d-orbitals. As shown in Fig. S9 (ESI†), the Ni⁴⁺ ion has six valence electrons which fully occupy the low triplet states with both spin-up and spin-down. The added electron has to occupy the higher energy doublet states.

Comparing the two OTL curves, one observes that when the lower curve is shifted leftwards by one element these two curves run nearly parallel, except for the data points of ε_f(Ni^4+/3+) and ε_f(Co^3+/2+). The reason is that similar 3dⁿ configurations are now compared. For two M ions with the same electron configuration, the value for the lower curve is about 2.5 eV lower than that for the upper curve. This difference is a direct consequence of the higher ionic charge. Although both Ni⁴⁺ and Co³⁺ have six valence electrons, their electronic configurations are different. As shown in Fig. S8 and S9 in ESI,† five valence electrons of Co³⁺ occupy the spin-up states with one valence electron located at the low spin-down triplet states, resulting in a local magnetic moment of 4 μ_B at Co³⁺. This state is consistent with the experimental ground state of t⁴e².²³ We denote this state as the high-spin state. For Ni⁴⁺, six valence electrons occupy the lower triplet states with both spin orientations, and thus the local magnetic moment of Ni⁴⁺ is 0 μ_B. So this state is labeled as the low-spin state. The OTL of Co³⁺ in the low-spin state has also been calculated, which is about 1.626 eV higher than that of the high-spin state as shown in Fig. 1 (the triangle).

Considering the similarity of OTL ε_f(M^n+/(n−1)+) and CT band energies E^CT(M,n), the VRBE E(M,n − 1) is also computed from the OTL ε_f(M^n+/(n−1)+). The results are shown in Fig. 1 with the right side y-axis. By connecting these OTL or VRBE values, we obtain the zig-zag like curves of OTL (VRBE) of the M ions in α-Al₂O₃.

Fig. 2 shows the VRBE curves of 3d-TM ions in YAG by using the experimental data listed in Table 1 and first-principles calculations. All the electronic structures are shown in ESI.† In Fig. 2, the OTL of ε_f(M^3+/2+) and ε_f(M^4+/3+) in YAG are represented by circle and square symbols, respectively, while the corresponding experimental acceptor levels are denoted as plus (+) and cross symbols (×). The VRBE is shown in Fig. 2 on the right side y-axis. The resulting ε_f(Sc^3+/2+), ε_f(Ti^3+/2+) and ε_f(Cr^3+/2+) are inaccurate and the reason is discussed in part C of the ESI.† In Fig. 2, we adopt open symbols to distinguish ε_f(Sc^3+/2+), ε_f(Ti^3+/2+) and ε_f(Cr^3+/2+) from other OTLs. For the upper curve, the energy difference between the OTL of ε_f(Fe^3+/2+) and ε_f(Ni^3+/2+) agrees well with the experiments after the calculated OTL are shifted upwards by 0.656 eV. For more evidence, we also calculate the OTL of Fe ions in tetrahedral site and the difference of ε_f(Fe^3+/2+) at tetrahedral and octahedral sites is only −0.14 eV, while the CT of Fe ions in these two sites is experimentally the same.⁴⁰ For the lower curve, the calculated results are shifted upwards by 1.357 eV.

Fig. 2 The OTL and VRBE of M ions in YAG. The circle and square symbols represent OTL of ε_f(M^3+/2+) and ε_f(M^4+/3+), respectively, where the open and full symbols denote the accurate and inaccurate results. The plus and cross symbols represent acceptor levels of 3d-TM ions with 3+ and 4+ in YAG extracted from the CT data. Note, the coordination of V^4+/3+ is not specified in the literature.

Comparing Fig. 2 with Fig. 1, we find that the VRBE curves are very similar to each other. So, we replot these VRBE curves in Fig. 3 for comparison. Here, the VRBE of ε_f(M^3+/2+) and ε_f(M^4+/3+) in α-Al₂O₃ is represented by the circle and square symbols, while in YAG by up and down triangles. The VRBE curves of M in both YAG and α-Al₂O₃ are almost parallel, respectively, except the underestimated values for Sc^3+/2+, Ti^3+/2+ and Cr^3+/2+ in YAG.

Fig. 3 The VRBE of M ions in α-Al₂O₃ and YAG. The circle and square symbols represent VRBE of ε_f(M^3+/2+) and ε_f(M^4+/3+) in α-Al₂O₃, while the up and down triangle represent VRBE of ε_f(M^3+/2+) and ε_f(M^4+/3+) in YAG. The horizontal lines represent experimental VBM (lower) and conduction band minimum (upper) of Al₂O₃ (solid line) and YAG (dash line).

The similarity in the VRBE curves of α-Al₂O₃ and YAG can be understood from molecular orbital theory. As shown in Fig. 4, the 3d orbitals of the M ion couple with the ligand bonds. The ligand bonds are fully occupied and are from the bonding orbitals of O ions and cations, such as Al³⁺ in α-Al₂O₃ or Y³⁺ and Al³⁺ in YAG. The combination of the ligand bonds with d_x²−y² or d_z² orbital forms a σ bonding orbital with the lowest energy (denoted as e) and σ antibonding orbital (e*) with the highest energy. Between these orbitals are t and t*, which are π bonding and antibonding orbitals originating from the coupling of d_xy, d_xz or d_yz with the ligand bonds. The e and t orbitals are lower in energy than the ligand bonds and are fully occupied by the electrons from the ligand bonds. (Theoretically, the electrons are indistinguishable, but we notionally indicate the electrons as being derived from the ligands or 3d-TM for the purpose of filling the energy-level diagram.) The t* and e* orbitals have higher energies, and appear in the band gap as defect levels. The 3d-electrons from the M ion will go to fill the t* and e* orbitals. So the energies of t* or e* dominate 3d-TM VRBE. As we limited M ions to the octahedral site, the factors that affect VRBE are the size of AlO₆ and the energies of ligand bonds. The average Al–O bond length is 191.5 pm in α-Al₂O₃ and 192 pm for the octahedral Al site in YAG. The ligand bonds in the crystal form the VB. As shown in Fig. S1 in the ESI,† the VB of both compounds have a width of about 7 eV with the VBM at about −9.6 eV for α-Al₂O₃ and −9.38 eV for YAG (here the reference energy is the vacuum level). Thus, the defect levels of M ions in these two compounds are similar to each other and then also to the VRBE of 3d-TM.

Fig. 4 Schematic energy level diagram for transition metal in the octahedral site of α-Al₂O₃ and YAG. Not drawn to scale.

As shown in Fig. 5(a), the Al–O bonds in α-Al₂O₃ are about 186 pm and 197 pm (calculated result) with O–Al–O angles of about 79.71°, 90.736°, and 101.17°, which have large deviations from the perfect Al–O octahedron. For the octahedron in YAG, the O–Al–O angles are 93.20° and 86.80° (Fig. 5(b)) and close to perfect. However, the VRBE of 3d-TM in these two compounds is very similar. These results imply that the distortion of crystal field has little influence on the VRBE.

Fig. 5 The Al–O octahedron in (a) α-Al₂O₃ and (b) YAG with different crystal field distortions. The data present the angle of adjacent O–Al bonding.

Although the VRBE curve of 3d-TMs in YAG is similar to that in α-Al₂O₃, they are not exactly the same as seen in Fig. 3. The question then arises how to predict the VRBE of 3d-TMs in other aluminates with octahedral sites. Considering the relatively scarce CT data of 3d-TM in a specific aluminate, it is difficult to obtain a complete VRBE curve similar to α-Al₂O₃ and YAG. Yet, to obtain the VRBE of a given 3d-TM ion at an octahedral site in different aluminates seems to be feasible. Rogers and Dorenbos reported that the VRBEs of Ti^4+/3+ in many different oxides fall within ±1 eV from the mean value of −3.95 eV.⁴⁹ For Mn⁴⁺, Fe³⁺ and Cr³⁺ oxides, we collected in Table 2 the CT band energies, and the corresponding VRBEs for Mn^4+/3+, Fe^3+/2+ and Cr^3+/2+ are shown in Fig. 6. For Mn^4+/3+, the compounds covered include aluminates plus the zirconate CaZrO₃. The average acceptor VRBE value is −4.82 eV with a spread of ±0.8 eV. Since the O²⁻–Mn⁴⁺ CT band is very broad and there is often a strong overlap between the ⁴A_2g → ⁴T_1g band and the CT band, it is difficult to determine the precise CT peak position.

Table 2 Experimental data for CT energies of O²⁻ to Mn⁴⁺, Fe³⁺ and Cr³⁺ (E^CT) in different compounds and the corresponding VRBE values. The VRBEs of the conduction band minimum and valence bands maximum (E_C and E_V), found from Rogers and Dorenbos^49,52 or obtained from Dorenbos's Chemical Shift Model,¹² are also listed. All energies are in eV

Ions	Host	E ^CT	E V	E C	VRBE
a Here, the bandgap of MgO at room temperature is about 7.6 eV^74 and the Ev can be deduced from the data in the literature.^75 Its impurity level is about 0.8 eV below the conduction band of MgO.^76 So the VRBE of Cr^3+ in MgO would be about −2.02 eV. Its CT value is about 6.8 eV, which is also listed in the table for completeness. b See the experimental data in ESI. c This value is obtained from TL results.^16
Mn^4+	LaAlO3	3.69,^53 3.54^54	−7.83	−1.45	−4.14, −4.29
	GdAlO3	3.80^55	−8.66	−0.67	−4.86
	SrAl12O19	3.69^56	−8.23	−0.30	−4.54
	CaAl12O19	3.67^57	−8.13	−0.40	−4.46
	YAlO3	4.13^58	−9.04	−0.44	−4.91
	SrMgAl10O17	3.84^59	−8.63	−2.43	−4.79
	Y3Al5O12	4.20,^36 4.0^37	−9.38	−1.71	−5.18, −5.38
	Sr4A114O25	3.79^60	−8.03	−0.74	−4.24
	α-LiAlO2	3.88^61	−8.88	−0.4	−5.00
	CaYAlO4	3.70^62	−8.56	−2.32	−4.86
	SrAl4O7	3.81^63	−8.41	−1.93	−4.60
	α-Al2O3	3.91^35	−9.60	−0.08	−5.69
	CaZrO3	3.25^64	−8.35	−2.46	−5.10
Fe^3+	LiAl5O8	4.35^65	−8.6	0.4	−4.25
	Y3Al5O12	4.86,^40 4.88,^41 5.04,^42 4.75^42	−9.38	−1.71	−4.52, −4.50, −4.34, −4.63
	Y3Ga5O12	4.64^66	−9.01	−2.42	−4.37
	α-Al2O3	4.80,^22,38 4.60^39	−9.60	−0.08	−4.8, −5.0
	MgO	4.27,^67 4.30,^68 4.43,^69 4.02^69	−8.60	−0.80	−4.33, −4.30, −4.17, −4.58
	α-Ga2O3	3.59^70	−8.17	−3.63	−4.58
	GdAlO3	4.20^b	−8.66	−0.67	−4.30
	BaTiO3	2.3^71	−7.25	−3.59	−4.95
Cr^3+	α-Al2O3	6.94,^22 6.90^33	−9.6	−0.08	−2.66, −2.70
	β-Ga2O3	4.10^50	−8.17	−3.63	−4.07
	ZnGa2O4	4.56^51	−8.40	−3.50	−3.84
	Y3Al5O12	6.66^c	−9.38	−1.71	−2.72^c
	MgO^a	6.80	−8.82	−1.22	−2.02
	LaAlO3	5.28^72	−7.82	−1.22	−2.54
	GdAlO3	6.36^73	−8.66	−0.92	−2.30

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Fig. 6 Stacked VRBE schemes for acceptor levels of Mn^4+/3+, Fe^3+/2+ and Cr^3+/2+ in different phosphors. The valence and conduction bands are represented by the bottom and top bars, respectively. The solid data point is the VRBE of those acceptor levels in a specific compound. Horizontal dashed line denotes the average VRBE for those acceptor levels.

Fig. 6(b) shows that the average VRBE of Fe^3+/2+ is −4.50 eV in aluminates with a spread ±0.4 eV. We also collected the VRBEs of Fe^3+/2+ in other oxides, like Y₃Ga₅O₁₂, MgO, α-Ga₂O₃ and the titanate BaTiO₃, and find that those values are quite well consistent with that average value. We take the average value (−4.58 eV) covering all the Fe³⁺-doped oxides listed in Table 2 as the VRBE of Fe^3+/2+ with a spread of about ±0.4 eV.

The VRBE of Cr^3+/2+ locates at about −2.45 eV with a range of ±0.3 eV, as shown in Fig. 6(c). This value does not cover β-Ga₂O₃ and ZnGa₂O₄, since the acceptor level of Cr³⁺ is very close to their conduction bands. So, it is difficult to distinguish the CT bands of Cr³⁺ from the host absorption. In the literature,^50,51 the host band absorptions of β-Ga₂O₃ and ZnGa₂O₄ were regarded as the CT bands as shown in Fig. 6(c). In these cases, the actual VRBE value could be largely underestimated. A similar situation may occur for Sc³⁺-doped compounds.¹⁴

Although the VRBEs of Ti^4+/3+, Mn^4+/3+, Cr^3+/2+ and Fe^3+/2+ in the listed compounds show a spread of about ±1 eV, their mean values still can offer a first estimate on the location of TM acceptor levels in compounds. For the average VRBEs of other 3d-TM ions, we could not obtain enough CT data to extract them. An alternative approach is to shift our OTL curves until the VRBEs of Fe^3+/2+ and Mn^4+/3+ evaluated from our calculation are consistent with the average values in Fig. 6(a and b), respectively. The results are shown in Fig. 7 and Table 3. The VRBEs of Ti^4+/3+ and Cr^3+/2+ predicted from our VRBE curves are about −3.792 eV and −2.468 eV, and the corresponding experimental mean values are about −3.95 eV⁴⁹ and −2.49 eV. The VRBEs of Cr³⁺ impurity levels in GdAlO₃ and LaAlO₃ obtained through the Cr³⁺-CB electron transfer process are about −6.2 ± 0.2 eV and −6.3 ± 0.2 eV, respectively,⁷³ which are also very close to our Cr^4+/3+ data of −6.235 eV. Such good agreement demonstrates that our VRBE curves in Fig. 7 also fit well with other 3d-TM ions in octahedral aluminates. Thus, the VRBE curves in Fig. 6 can be used to roughly predict the acceptor levels of 3d-TM ions at octahedral sites in a given aluminate.

Fig. 7 The average VRBE of 3d-TM ions in aluminates predicted by combining the calculated OTL energies with the experimental CT-energies.

Table 3 The average VRBE of 3d-TM ions in aluminates predicted in this work. All energies are in eV

	TM^3+/2+	TM^4+/3+
Sc	−1.679	—
Ti	−2.626	−3.792
V	−3.709	−5.221
Cr	−2.468	−6.235
Mn	−4.360	−4.820
Fe	−4.580	−6.464
Co	−5.904	−6.962
Ni	−5.853	−6.214
Cu	−5.924	−7.494
Zn	−7.566	−7.885

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In an attempt to arrive at a more accurate prediction of VRBE, we studied the fluctuation of the 3d-TM VRBE in different aluminates. The dashed line in Fig. 8 shows that when the VRBE at the VBM increases, the VRBE of the Mn^4+/3+ acceptor level increases linearly with a slope of about 0.74. The maximum deviation of the experimental VRBE of Mn^4+/3+ from the dashed line is 0.19 eV. So, the estimation of the VRBE of Mn^4+/3+ in an aluminate might be more accurately made if the VRBE of the VBM is known.

Fig. 8 The VRBE of Cr^3+/2+, Fe^3+/2+ and Mn^4+/3+ as a function of the VBM of different aluminates with octahedral sites derived from Table 2.

The relationship between the VRBE of Mn^4+/3+ and VBM could be understood from molecular orbital theory. As mentioned above, the VRBE of the Mn ion is dominated by the antibonding orbitals t* and e*. On raising the energies of ligand bonds, the t* and e* orbitals increase in energy and so does the VRBE of the Mn ion. Since the VB is mainly formed by ligand bonds, the increase of the energies of ligand bonds can cause the VBM to shift upwards. So, the VRBE of Mn^4+/3+ increases with the increase of VBM. This rule can also be applied for the VRBEs of other 3d-TM ions. So, we fitted the VRBE of Cr^3+/2+ or Fe^3+/2+ to a straight line as shown by the solid or dotted line in Fig. 8. Their slopes are about 0.13 and 0.59 with the largest data deviations of about 0.23 eV and 0.18 eV, respectively. When more data are available these seemingly linear relationships can be tested further. Here we used the VBM as a variable but other aspects like the crystal field splitting of the 3dⁿ level can also be important.

Finally, we will elaborate somewhat further on the charge states of the M ions in compounds. When the energies of the 3d orbitals are higher than those of the ligand bonds, t* and e* are mainly contributed by the 3d orbitals. Sc, Ti, V, Cr, Mn, Fe and Co ions belong to this category, which can be proved by the PDOS in Fig. S2–S8 of the ESI.† So, the electrons in the t* and e* can be roughly regarded as the 3d electrons of the M ions. The OTL and CT energies then reflect the location of the acceptor levels induced by the t* or e* orbitals and thus approximately reflect the VRBE of the 3d orbitals of M ions. So, we denote them, for example, as OTL(M^3+/2+) or E^CT(M,3). When the atomic number increases from Sc to Zn, the energies in the 3d orbitals decrease and the contribution of ligand bonds (which are mostly O 2p orbitals) to the t* or e* orbitals increases. Especially, in the case of Zn, the defect levels are mostly contributed by O 2p orbitals, while the contribution of 3d orbitals concentrates on the bonding t and e orbitals, which are about 3–6.0 eV below the VBM. Now, the electrons in the t* and e* should be roughly regarded as the p electrons of O ions. Thus, the charge state of the Zn ion is nearly unrelated to the defect levels in the band gap. In other words, the Zn ion should be approximately in the 2+ state in all the calculations, as two 4s electrons of Zn atom are delocalized when doped. However, the OTL and CT energies still reflect the locations of acceptor levels induced by t* or e* orbitals. Although the contribution of the 3d orbitals of Zn to the t* and e* orbitals is negligibly small, the energies of 3d orbitals still can be considered as part of the e* orbitals. So, we adopted OTL(Zn^3+/2+) or E^CT(Zn,3) to denote the corresponding OTL or CT bands, nominally.

Conclusion

In this work, we offer a method to predict the acceptor levels of 3d-TM ions in octahedral aluminates by constructing zig-zag like VRBE curves employing the experimental CT band energies of 3d-TM ions and by first-principles calculation. These curves offer a rough estimate about the acceptor level energies of 3d-TM ions with a spread of about ±1 eV. The estimation can be more accurate if we take the molecular orbital theory into consideration without complicated calculations. Our work gives a vivid and quantitative explanation of how binding energy varies with the increase of n for the 3d orbital electrons, and makes it easier to estimate their doping levels in a specific compound. Those predictable levels are very useful in engineering the luminescent properties of 3d-TM activated phosphors. For the phosphors with tetrahedral sites, such as silicates, (oxy)nitrides, we speculate that similar rules may exist from the view of the molecular orbital theory, but the shape of the zig-zag-curve should be different from that in octahedral sites as shown in Fig. 7. We need more experimental data to extract and verify them. This work is under way.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No: 51302059 and 11404085), NSAF (Grant No: U1630118), China Scholarship Council (201406695020) and the Natural Science Foundation of Anhui Province (Grant 1708085ME121). Calculations were carried out at the Supercomputing Center of University of Science and Technology of China.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c8tc05401k

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