Dual-Emission Origins in Bi3+-Doped M2O3 Sesquioxides (M = Sc, Y, Gd and Lu): A First-Principles Study

Bi3+-doped sesquioxides exhibit dual emissions, marked by distinct Stokes shift and bandwidth, meaning unraveling their underlying origins is particularly intriguing. In this study, we employ first-principles calculations to investigate the luminescence mechanisms within the M2O3:Bi3+ (M = Sc, Y, Gd, Lu) series, with the goal of addressing the posed inquiry. Our investigation commences with the analysis of the site occupancy and charge state of bismuth ions in the two cationic sites through formation energy calculations. Additionally, we examine the local coordination environments for various excited states of Bi3+ dopants, including the 3P0,1 state and two types of charge transfer states, by evaluating their equilibrium geometric structures. The utilization of the hybrid functional enables us to obtain results of electronic structures and optical properties comparable with experiments. Importantly, the calculated energies for the 6s-6p transitions of Bi3+ dopants in the M2O3 series align well with the observed dual-emission energies. This alignment challenges the conventional spectroscopic sense that emission bands with large Stokes shifts can be exclusively ascribed to charge transfer transitions. Consequently, the integration of experimental and theoretical approaches emerges as the optimal strategy for designing novel Bi3+-doped phosphors.


Introduction
Due to the presence of the 6s 2 lone pair, the photoluminescence of Bi 3+ is sensitive to the ligand environment and ranges from ultraviolent to infrared in different matrices, making bismuth an excellent activator [1,2].In particular, some single Bi 3+ -doped phosphors exhibit an extra red-shifted emission band in addition to the commonly observed green or blue emission [3][4][5].This dual-mode emission characteristic is attractive for anti-counterfeiting, temperature sensing and healthcare lighting, e.g., the MgGa 2 O 4 :Bi 3+ material exhibits dynamic luminescence evolution from near-infrared or green light to bluish-white light, showing excellent multi-mode dynamic anti-counterfeiting and encryption performances [6].In order to improve the performance of the dual-mode emission in Bi 3+ -doped phosphors and to push their application boundaries, great efforts have been made to reveal the origin of emission bands and understand the luminescence mechanism.Several potential mechanisms have been proposed in different materials, including the site-selective occupancy of dopants [5,6], the influence of bismuth ions with lower valence states [7], the formation of Bi pairs or clusters [8] and the Jahn-Teller distortion of the Materials 2024, 17, 2039 2 of 11 local environment [9].However, the spectra assignments of the Bi 3+ -doped phosphors were generally judged by the full-width at half maximum (FWHM) and the Stokes shift properties, where the emission bands with larger Stokes shift were always assigned to the charge transfer transitions in experiment.Obviously, such experiential spectra assignment methods were not explicit enough for understanding and developing dual-mode emission phosphors.
Bi 3+ -doped sesquioxides, such as the series of M 2 O 3 :Bi 3+ (M = Sc, Y, Gd and Lu), are promising hosts that exhibit dual-mode emission.In M 2 O 3 hosts, the M 3+ cations have two different ligand sites, namely S 6 and C 2 sites, both of which are hexacoordinated, and the six O 2− ions form highly symmetric octahedral coordination in the S 6 site [10].Previous research has focused on elucidating the assignment of the narrow-band emission and the broad-band emission with larger Stokes shift to the two Bi 3+ sites in the M 2 O 3 :Bi 3+ series.It has been found that Bi 3+ ions mainly occupy the central position of the highly symmetric octahedron, which contributes to the stable narrow-band emission with small Stokes shift, e.g., the emission of Lu 2 O 3 and Gd 2 O 3 with 35 and 40 nm FWHM, respectively, as reported by Z. Zhang [11].However, the detailed geometric and electronic properties have hardly been studied to understand the remarkable difference in the Stokes shift of the two cation sites, and the possibility of the charge transfer transition has not been completely ruled out.First-principles calculations have been widely used as a powerful tool to investigate and elucidate the excitation, relaxation and emission processes of a large number of bismuthdoped phosphors [12].Density functional theory (DFT) can effectively simulate the energy of the ground state and excited states of Bi ions with different valence states in activated phosphors, as well as the optical transitions of Bi 3+ dopants in phosphors, including the 1 S 0 → 3 P 0,1 inner Bi 3+ , the charge transfer transitions including the valence band to Bi 3+ charge transfer (CT) transitions or the Bi 3+ to conduction band, i.e., the metal-to-metal charge transfer (MMCT) transition.
Here, the luminescence mechanism of the dual-mode emission of Bi 3+ ions in M 2 O 3 (M = Sc, Y, Gd and Lu) matrices was investigated using the first-principles methods.The site occupancy and the valence state of the bismuth ions were confirmed by formation energy studies.The geometric and electronic properties of the ground and excited states were calculated to obtain the excitation, relaxation and emission processes of the series of phosphors, which provides insight into the origin of the dual-mode emission.Furthermore, the variation in the (BiO 6 ) 3− ligand environment from the ground states to the excited states was studied for the two cation sites to help explain the remarkable difference in Stokes shift between the two emission bands.

Methods
The first-principles calculations were performed utilizing the Vienna ab initio simulation package [13], employing the projector augmented-wave method in conjunction with density functional theory (DFT).The Perdew-Burke-Ernzerof (PBE) functional [14] was adopted in the geometric structure relaxation, along with the consideration of the spin-orbit coupling interaction for Bismuth dopants.Semicore electrons were explicitly treated with the recommended projector augment-wave (PAW) pseudopotentials [15], including 4s 2 4p 6 5s 2 4d 1 , 2s 2 2p 6 3d 1 4s 2 , 5p 6 5d 1 6s 2 , 5p 6 6s 2 5d 1 , 2s 2 2p 4 and 5d 10 6s 2 6p 3 for Y, Sc, Lu, Gd, O and Bi elements, respectively.The supercell, containing 80 atoms, was employed in modeling the defect-doped systems, and one k point Γ was used in sampling the Brillouin zone.The cutoff energy of the plane-wave basis was set to 520 eV, and the convergent criteria were 10 −5 eV for electronic energy minimization and 0.02 eV/Å for Hellman-Feynman forces on each atom.Based on the relaxed equilibrium geometric structures, the standard PBE0 functionals [16] were utilized to obtain better electronic structure and photoluminescence properties.
The formation energy of a defect X in the charge state of q can be derived as follows [17]: where E tot is the total energy of the optimized supercells, n i is the number of atoms in elements i, which are added to (n i > 0) and or removed from (n i < 0) the perfect supercell, and µ i corresponds to chemical potentials of these species.The Fermi energy level E F represents the chemical potential of the electrons in the host.The thermodynamic charge transition level ϵ(q 1 /q 2 ) was utilized to predict the positions of defect levels.It is defined as the Fermi level at which the defect formation energies of X q 1 and X q 2 equal each other.
It can be deduced from Equation (1) as: where post hoc corrections to the total energy of the charged defects are employed following the method proposed in Ref. [18].For Bi 3+ ion-doped system, the dominant emission can originate from the equilibrium structure of the 6s 1 6p 1 ( 3 P 0,1 ) excited state and the charge transfer state, e.g., Bi 4+ +e and Bi 2+ +h, where the Bi 4+ +e is the excited state of charge transfer from Bi 3+ ions to the bottom of the condition band and always denoted as MMCT, whereas the Bi 2+ +h is the excited state of charge transfer from the top of the valance band to Bi 3+ dopants and always denoted as CT.As in our previous work [8], the equilibrium geometric structure of the MMCT excited state was approximated as M 2 O 3 : Bi 4+ by the geometric relaxation of the supercell that one cation was substituted by Bi 4+ ions.Similarly, the CT excited state was approximated as M 2 O 3 : Bi 2+ .The 3 P 0,1 excited state was approximated by constraining the electron occupancy to (6s 1/2 ) 1 (6p 1/2 ) 1 for M 2 O 3 : Bi 3+ , where the 6s 1/2 and 6p 1/2 are Kohn-Sham orbitals obtained with PBE+ SOC functional.Based on the relaxed equilibrium geometric structures, the peak energy of excitation or emission for a given transition can be obtained approximately by the differences of the total energies of the excited and ground electronic state following the Franck-Condon principle.

Properties of the M 2 O 3 Hosts
The M 2 O 3 (M = Sc, Y, Gd and Lu) matrices are attributed to the cubic crystal system and Ia-3 (No. 206) space group.There are two different cation crystallographic sites, C 2 and S 6 , which can be replaced with Bi 3+ ions, as shown in Figure 1.The crystal structure of cubic M 2 O 3 is composed of regular and asymmetric octahedra of M and O atoms, with M atoms filling the interstitial sites of the octahedra.The band structures of four pristine M 2 O 3 are plotted in Figure 2.
The results show that Sc 2 O 3 is a direct band gap material, with the conduction band minimum (CBM) and valance band maximum (VBM) located at the high-symmetry k-point of Γ.For the remaining three hosts, Y 2 O 3 , Gd 2 O 3 and Lu 2 O 3 , their VBM was located at the k-path from the high-symmetry k-point of Γ to H, implying indirect gap semiconductors.The Kohn-Sham band gaps calculated with the PBE functional are 3.83 eV, 3.87 eV, 4.02 eV and 4.12 eV for M = Sc, Gd, Lu and Y, respectively, which are seriously underestimated compared to the experimentally reported optical band gaps.Since the excitation and emission processes of the CT and MMCT states involve the orbitals of the band edges, the accuracy of the band gap values can greatly influence the spectral assignments and mechanism studies.Hybrid DFT has been widely used to improve the description of electronic structures.With the standard PBE0 functional, the band gap energy (E g ) was improved to be 6.49eV, 6.16 eV, 6.21 eV and 6.39 eV for M = Sc, Gd, Lu and Y, respectively.The PBE0 calculated band gap values are consistent with those estimated in the vacuumreferred binding energy diagram, reported by P. Dorenbos [19], which are about 6.50 and 6.40 eV for Sc 2 O 3 and Y 2 O 3 , respectively.Furthermore, the choice of the PBE0 functional aligns well with the nonempirical hybrid functionals, characterized by a Fock exchange fraction inversely correlated with the material's dielectric constant (ϵ ∞ ) [20], showing promise in achieving more uniform accuracy in band gap prediction, as well as in predicting other electronic and optical properties of semiconductors [21].In Figure 2, the PBE0 calculated density of states (DOSs) exhibit the composition of the band edges.For all four hosts, the tops of the valence bands are dominated by the O-p orbitals, partially contributed by the orbitals of cations.For Sc 2 O 3 hosts, the bottom of the conduction band was dominated by the Sc-d orbital.However, the bottom of the conduction band of the other three hosts was dominated by the M-s orbitals and partially mixed with M-p, M-d and O-p orbitals.

The Defect Properties of M 2 O 3 :Bi 3+
As shown in Figure 3, the formation energy calculations were performed for studying the properties of the intrinsic and Bi-doped defects in M 2 O 3 (M = Sc, Y, Gd and Lu), including the intrinsic defects of cation vacancies at the C 2 and S 6 sites, e.g., V M (C 2 ) and V M (S 6 ), oxygen vacancies (V O ) and oxygen interstitial defects (O i ), as well as those of bismuth ions substituting the C 2 and S 6 cation sites.
at the k-path from the high-symmetry k-point of Γ to H, implying indirect gap semiconductors.The Kohn-Sham band gaps calculated with the PBE functional are 3.83 eV, 3.87 eV, 4.02 eV and 4.12 eV for M = Sc, Gd, Lu and Y, respectively, which are seriously underestimated compared to the experimentally reported optical band gaps.Since the excitation and emission processes of the CT and MMCT states involve the orbitals of the band edges, the accuracy of the band gap values can greatly influence the spectral assignments and mechanism studies.Hybrid DFT has been widely used to improve the description of electronic structures.With the standard PBE0 functional, the band gap energy (Eg) was improved to be 6.49eV, 6.16 eV, 6.21 eV and 6.39 eV for M = Sc, Gd, Lu and Y, respectively.The PBE0 calculated band gap values are consistent with those estimated in the vacuumreferred binding energy diagram, reported by P. Dorenbos [19], which are about 6.50 and 6.40 eV for Sc2O3 and Y2O3, respectively.Furthermore, the choice of the PBE0 functional aligns well with the nonempirical hybrid functionals, characterized by a Fock exchange fraction inversely correlated with the material's dielectric constant ( ) [20], showing promise in achieving more uniform accuracy in band gap prediction, as well as in predicting other electronic and optical properties of semiconductors [21].In Figure 2, the PBE0 calculated density of states (DOSs) exhibit the composition of the band edges.For all four hosts, the tops of the valence bands are dominated by the O-p orbitals, partially contributed by the orbitals of cations.For Sc2O3 hosts, the bottom of the conduction band was dominated by the Sc-d orbital.However, the bottom of the conduction band of the other three hosts was dominated by the M-s orbitals and partially mixed with M-p, M-d and Op orbitals.

The Defect Properties of M2O3:Bi 3+
As shown in Figure 3, the formation energy calculations were performed for studying the properties of the intrinsic and Bi-doped defects in M2O3 (M = Sc, Y, Gd and Lu), including the intrinsic defects of cation vacancies at the C2 and S6 sites, e.g., VM(C2) and VM(S6), oxygen vacancies (VO) and oxygen interstitial defects (Oi), as well as those of bismuth ions substituting the C2 and S6 cation sites.It should be noted that the formation energy lines of Bi 3+ dopants will be slightly shifted according to the actual doping concentration.
By considering the synthesis conditions, the referenced chemical potentials of the O, M and Bi elements were set as follows: By considering the synthesis conditions, the referenced chemical potentials of the O, M and Bi elements were set as follows: where is the room temperature and partial-pressure-corrected chemical potential of oxygen gas.In our calculation, ∆µ O was set as 0 eV to simulate the oxygen-rich environment [22,23].
By studying the formation energies, the site occupancy and charge state of the intrinsic defects and bismuth dopants can be well determined.According to the formation energy diagrams, the electric neutrality of the four M 2 O 3 (M = Sc, Gd, Lu and Y) hosts is maintained by the charge balance between the cation vacancies V 3− M and anion vacancies V 2+ O .The energy positions of the Fermi levels were obtained to be around the middle of the band gap but close to the VBM, which is consistent with the O-rich environment in our calculations.Compared with the intrinsic defects, including V O , V M (S 6 ), V M (C 2 ) and O i defects, whose formation energies are all around 2.0 eV in the M 2 O 3 series, the bismuth dopants show remarkably lower formation energies.The bismuth dopants are expected to be the dominant defects in M 2 O 3 :Bi 3+ phosphors.It is noted that the doped bismuth ions are mainly in the trivalent charge state; thus, the energy positions of the Fermi levels are hardly influenced by the doping concentration of Bi 3+ ions.Furthermore, Figure 3 shows that the formation energies of Bi 3+ dopants in the cation sites with S 6 symmetry are slightly lower (−0.1~−0.2eV) than those with C 2 symmetry.This is similar to the formation energy properties of the two cation vacancies, V M (S 6 ) and V M (C 2 ).
M2O3 and Bi2O3, respectively, and  is the room temperature and partial-pressurecorrected chemical potential of oxygen gas.In our calculation, Δ was set as 0 eV to simulate the oxygen-rich environment [22,23].
By studying the formation energies, the site occupancy and charge state of the intrinsic defects and bismuth dopants can be well determined.According to the formation energy diagrams, the electric neutrality of the four M2O3 (M = Sc, Gd, Lu and Y) hosts is maintained by the charge balance between the cation vacancies  and anion vacancies  .The energy positions of the Fermi levels were obtained to be around the middle of the band gap but close to the VBM, which is consistent with the O-rich environment in our calculations.Compared with the intrinsic defects, including VO, VM(S6), VM(C2) and O defects, whose formation energies are all around 2.0 eV in the M2O3 series, the bismuth dopants show remarkably lower formation energies.The bismuth dopants are expected to be the dominant defects in M2O3:Bi 3+ phosphors.It is noted that the doped bismuth ions are mainly in the trivalent charge state; thus, the energy positions of the Fermi levels are hardly influenced by the doping concentration of Bi 3+ ions.Furthermore, Figure 3 shows that the formation energies of Bi 3+ dopants in the cation sites with S6 symmetry are slightly lower (−0.1~−0.2eV) than those with C2 symmetry.This is similar to the formation energy properties of the two cation vacancies, VM(S6) and VM(C2).
In Figure 4, the thermodynamic charge transition levels ε(+1/0) and ε(0/−1) of Bi dopants were plotted to investigate the trap properties of M2O3:Bi 3+ in the four M2O3 states (M = Sc, Y, Gd and Lu).The Bi 3+ dopants can act as both the electron and hole trap in the four M2O3 hosts.The hole trap positions provided by the Bi 3+ dopants in the C2 sites are 2.36 eV, 2.11 eV, 2.10 eV and 2.11 eV for M = Sc, Y, Gd and Lu, respectively.For the S6 cation sites with higher symmetry, the corresponding hole trap positions are 2.21 eV, 2.09 eV, 2.09 eV and 2.04 eV for M = Sc, Y, Gd and Lu referring to the VBM, respectively.The electron trap positions provided by the Bi 3+ dopants are 1.24 eV, 1.60 eV, 1.45 eV and 1.42 eV at the C2 site for M = Sc, Y, Gd and Lu, respectively, while they are 1.45 eV, 1.78 eV, 1.65 eV and 1.67 eV at the The Bi 3+ dopants can act as both the electron and hole trap in the four M 2 O 3 hosts.The hole trap positions provided by the Bi 3+ dopants in the C 2 sites are 2.36 eV, 2.11 eV, 2.10 eV and 2.11 eV for M = Sc, Y, Gd and Lu, respectively.For the S 6 cation sites with higher symmetry, the corresponding hole trap positions are 2.21 eV, 2.09 eV, 2.09 eV and 2.04 eV for M = Sc, Y, Gd and Lu referring to the VBM, respectively.The electron trap positions provided by the Bi 3+ dopants are 1.24 eV, 1.60 eV, 1.45 eV and 1.42 eV at the C 2 site for M = Sc, Y, Gd and Lu, respectively, while they are 1.45 eV, 1.78 eV, 1.65 eV and 1.67 eV at the S 6 site for M = Sc, Y, Gd and Lu, respectively.For all four M 2 O 3 hosts, the thermodynamic charge transition levels of Bi 3+ dopants at S 6 cation sites are slightly lower than those in the C 2 cation sites; however, the energy difference between ε(+1/0) and ε(0/−1) levels is similar for Bi 3+ in the two cation sites of sesquioxide and is hardly influenced by the local symmetry.Our calculation results are in great agreement with the vacuum-referred binding energy diagram provided by P. Dorenbos, where the MMCT transition energies are used to locate the Bi 3+ 6s ground state relative to the CBM.It is reported that the Bi 3+ dopants provide the hole trap and electron trap with depths around 2.0 eV and 1.0 eV, respectively, in both Y 2 O 3 :Bi 3+ and Sc 2 O 3 :Bi 3+ .
In order to investigate the electronic structure properties of Bi 3+ dopants at the two cation sites, the PBE0+SOC calculated partial DOSs and the charge density distribution of 6s and 6p orbitals are plotted in Figure 5.
C2 cation sites; however, the energy difference between ε(+1/0) and ε(0/−1) levels is similar for Bi 3+ in the two cation sites of sesquioxide and is hardly influenced by the local symmetry.Our calculation results are in great agreement with the vacuum-referred binding energy diagram provided by P. Dorenbos, where the MMCT transition energies are used to locate the Bi 3+ 6s ground state relative to the CBM.It is reported that the Bi 3+ dopants provide the hole trap and electron trap with depths around 2.0 eV and 1.0 eV, respectively, in both Y2O3:Bi 3+ and Sc2O3:Bi 3+ .
In order to investigate the electronic structure properties of Bi 3+ dopants at the two cation sites, the PBE0+SOC calculated partial DOSs and the charge density distribution of 6s and 6p orbitals are plotted in Figure 5.As the selected series of materials have similar structural environments and similar luminescent properties, only the DOSs of Y2O3:Bi 3+ phosphors were provided.For the M2O3:Bi 3+ series, the 6s and 6p orbitals of Bi 3+ dopants are always in the band gap, regardless of Bi 3+ substituting the S6 or C2 cation sites.Due to the stronger crystal filed environment at the S6 lattice site, the Bi 3+ 6p orbital shows larger energy splitting than that at the C2 lattice site.As shown in the charge density profile, the Bi 3+ -6s orbital contains substantial contributions from the p orbitals of the six oxygen ligands, and the corresponding distributions are similar for Bi 3+ -6s orbitals at both the C2 and S6 sites.The charge density distributions of Bi 3+ -6p orbitals are quite different.The Bi 3+ -6p orbitals mainly distribute along the one axis for the Bi 3+ ions at C2 sites; however, the charge density distributions of Bi 3+ -6p orbitals remain similar with the Bi 3+ -6s orbitals at S6 sites, where the six oxygen ligands contribute uniformly to the Bi 3+ -6p orbitals due to the high symmetry.The geometric structure relaxation and the Stokes shift properties of Bi dopants are correlated with the electronic structure of the Bi 6s and 6p orbitals, which results in the different luminescence properties of the 3 P0,1 excited state at the two cation sites.As the selected series of materials have similar structural environments and similar luminescent properties, only the DOSs of Y 2 O 3 :Bi 3+ phosphors were provided.For the M 2 O 3 :Bi 3+ series, the 6s and 6p orbitals of Bi 3+ dopants are always in the band gap, regardless of Bi 3+ substituting the S 6 or C 2 cation sites.Due to the stronger crystal filed environment at the S 6 lattice site, the Bi 3+ 6p orbital shows larger energy splitting than that at the C 2 lattice site.As shown in the charge density profile, the Bi 3+ -6s orbital contains substantial contributions from the p orbitals of the six oxygen ligands, and the corresponding distributions are similar for Bi 3+ -6s orbitals at both the C 2 and S 6 sites.The charge density distributions of Bi 3+ -6p orbitals are quite different.The Bi 3+ -6p orbitals mainly distribute along the one axis for the Bi 3+ ions at C 2 sites; however, the charge density distributions of Bi 3+ -6p orbitals remain similar with the Bi 3+ -6s orbitals at S 6 sites, where the six oxygen ligands contribute uniformly to the Bi 3+ -6p orbitals due to the high symmetry.The geometric structure relaxation and the Stokes shift properties of Bi dopants are correlated with the electronic structure of the Bi 6s and 6p orbitals, which results in the different luminescence properties of the 3 P 0,1 excited state at the two cation sites.

The Luminescence Mechanism of M 2 O 3 :Bi 3+
As reported in experimental research [5.10],Bi 3+ dopants in a series of M 2 O 3 (M = Sc, Y, Gd, Lu) phosphors show similar excitation and emission characteristics, including a narrow-band absorption peak at 340-400 nm, corresponding to a strong emission in the 380-470 nm range, and a second localized band absorption in the 300-360 nm range, corresponding to a broad emission in the 360-600 nm range with low emission intensity.Table 1 shows the optical transition energies of Bi 3+ ions in the four hosts, including the results from DFT calculations and the experimental reports, where the calculated excitation and emission energies are in good agreement with the experimental data [10].For M 2 O 3 :Bi 3+ phosphors, the A band transition dominates both the excitation and emission, and the CT and MMCT transitions require remarkably higher excitation energies.Our results support the A band assignment in previous research [5,10], where the broad excitation and emission bands were attributed to the Bi 3+ dopants at C 2 sites, and the sharp excitation and emission bands originated from the S 6 sites.Except for the dominant A band optical transitions, G. Blasse reported a high-energy excitation band at 4.71 eV for Y 2 O 3 :Bi 3+ [24], and Bordun observed similar excitation bands in Bi 3+ -doped Y 2 O 3 and Sc 2 O 3 ceramics [25].R. K. Datta also reported that these are practically identical in both spectra, namely, a weak broad line around 4.70 eV and a slowly rising structure starting at 5.20 eV in Y 2 O 3 :Bi 3+ [26].Although prior studies assigned these bands to the C-band, P. Dorenbos agreed with the assignment of P. Boutinaud, who both suggested that these excitation bands should be assigned to the MMCT transition [27], and this is confirmed by our calculation results.
As listed in Table 1, there are slight differences (~0.3 eV) between the excitation energies of Bi 3+ dopants being at the C 2 and S 6 sites, including the A band, CT and MMCT transitions.However, the emission properties of the A band transition are quite different for Bi 3+ dopants at the two cation sites.In both of the experimental and calculation results, the Bi 3+ dopants at C 2 sites exhibit a large Stokes shift in the range of 1.2-1.4eV, while such values are remarkably smaller (at around 0.3 eV) for the Bi 3+ dopants at S 6 sites.There were arguments that the main double-peaked green emission band centered around 3.7 eV should correspond to the crystal-field splitting of the low-excited levels in the low-symmetry C 2 luminescent center [28].However, the energy positions of the lowest Bi 3+ 6p levels show slight differences between the two sites, as plotted in Figure 5.And the geometric relaxation difference in the 3 P 0,1 excited state results in a remarkably different Stokes shift at the two sites according to our calculations.Based on the relaxed equilibrium structures of the ground state and various excited states of Y 2 O 3 :Bi 3+ , a schematic configuration coordinate diagram (Figure 6) is constructed to show all the excited states, illustrating the luminescence process.For the M 2 O 3 :Bi 3+ series, the potential energy surface of the Bi 4+ + e CBM state intersects with that of (Bi 3+ ) 3 P 0,1 , and non-radiative relaxation from the former to the latter can be bridged with the cooperation of phonons.
This relaxation also occurs from Bi 2+ + h VBM to Bi 4+ + e CBM and (Bi 3+ ) 3 P 0,1 .The dominant emission is expected to originate from the lowest 3 P 0,1 excited state, and the Bi 3+ dopants at C 2 site exhibit obviously larger geometric relaxation in emission processes.The Stokes shift properties of Bi 3+ -doped phosphors are always considered as an important index to distinguish the emission band from the 3 P 0,1 and charge transfer states, e.g., the broad yellow light of Ba 2 YGaO 5 :Bi 3+ peaking at 587 nm with full-width at half maximum (FWHM) of 135 nm was assigned as the MMCT transition due to the large Stokes shift (1.43 eV) [29].Our calculations on the M 2 O 3 :Bi 3+ series imply that the A band transition can also provide emission with large Stokes shift, and the detailed structure-activity relationship requires further studies.This relaxation also occurs from Bi 2+ + hVBM to Bi 4+ + eCBM and (Bi 3+ ) 3 P0,1.The dominant emission is expected to originate from the lowest 3 P0,1 excited state, and the Bi 3+ dopants at C2 site exhibit obviously larger geometric relaxation in emission processes.The Stokes shift properties of Bi 3+ -doped phosphors are always considered as an important index to distinguish the emission band from the 3 P0,1 and charge transfer states, e.g., the broad yellow light of Ba2YGaO5:Bi 3+ peaking at 587 nm with full-width at half maximum (FWHM) of 135 nm was assigned as the MMCT transition due to the large Stokes shift (1.43 eV) [29].Our calculations on the M2O3:Bi 3+ series imply that the A band transition can also provide emission with large Stokes shift, and the detailed structure-activity relationship requires further studies.

Conclusions
In this study, we employed first-principles calculations to elucidate the luminescence mechanisms underlying the dual emissions in the M2O3:Bi 3+ series (M = Sc, Y, Gd, Lu).Utilizing formation energy calculations, we confirmed the prevalence of trivalent bismuth ions in both cationic sites, with a slight preference for the M 3+ sites with S6 symmetry over the C2 sites.The larger band gap of the M2O3 series, ranging from 6.1 to 6.5 eV, provides enough space to accommodate both the 6s and the lowest 6p orbitals of the Bi 3+ dopants.Our calculated charge transition levels for Bi 3+ dopants exhibit remarkable similarity in the two cationic sites of the M2O3 series, where Bi 3+ ions can serve as deep electron traps (with depths around 1.0 eV) and hole traps (with depths around 2.0 eV).The dominance of the 6s-6p transitions of Bi 3+ dopants in both cationic sites was affirmed, while the observed high-energy excitation band at approximately 4.7 eV was identified as the MMCT transition.Through an exploration of the variations in electronic and geometric structures during the luminescence kinetics processes, our calculations contribute to a comprehensive understanding and provide design principles for novel Bi 3+ -doped phosphors.
Author Contributions: Investigation, data curation and writing-original draft preparation, H.B.;

Conclusions
In this study, we employed first-principles calculations to elucidate the luminescence mechanisms underlying the dual emissions in the M 2 O 3 :Bi 3+ series (M = Sc, Y, Gd, Lu).Utilizing formation energy calculations, we confirmed the prevalence of trivalent bismuth ions in both cationic sites, with a slight preference for the M 3+ sites with S 6 symmetry over the C 2 sites.The larger band gap of the M 2 O 3 series, ranging from 6.1 to 6.5 eV, provides enough space to accommodate both the 6s and the lowest 6p orbitals of the Bi 3+ dopants.Our calculated charge transition levels for Bi 3+ dopants exhibit remarkable similarity in the two cationic sites of the M 2 O 3 series, where Bi 3+ ions can serve as deep electron traps (with depths around 1.0 eV) and hole traps (with depths around 2.0 eV).The dominance of the 6s-6p transitions of Bi 3+ dopants in both cationic sites was affirmed, while the observed high-energy excitation band at approximately 4.7 eV was identified as the MMCT transition.Through an exploration of the variations in electronic and geometric structures during the luminescence kinetics processes, our calculations contribute to a comprehensive understanding and provide design principles for novel Bi 3+ -doped phosphors.

Materials 2024, 17 , 2039 4 of 11 Figure 1 .
Figure 1.The crystal schematic diagram of the (a) M2O3 (M = Sc, Y, Gd and Lu) and the (b) S6 and (c) C2 cation crystallographic sites, where the bond lengths of Gd2O3 material were listed as example.

Figure 1 . 11 Figure 1 .
Figure 1.The crystal schematic diagram of the (a) M 2 O 3 (M = Sc, Y, Gd and Lu) and the (b) S 6 and (c) C 2 cation crystallographic sites, where the bond lengths of Gd 2 O 3 material were listed as example.

Figure 2 .
Figure 2. The PBE calculated band structure (a-d) and the PBE0 calculated DOSs (e-h) of a series of M2O3 (M = Sc, Gd, Lu and Y), respectively.

Figure 2 .
Figure 2. The PBE calculated band structure (a-d) and the PBE0 calculated DOSs (e-h) of a series of M 2 O 3 (M = Sc, Gd, Lu and Y), respectively.

Figure 3 .
Figure 3.The PBE calculated formation energies of intrinsic defects and Bi 3+ dopants in M2O3 sesquioxides (M = Sc (a), Gd (b), Lu (c) and Y (d)) as a function of the Fermi level in O-rich environment.It should be noted that the formation energy lines of Bi 3+ dopants will be slightly shifted according to the actual doping concentration.

Figure 3 .
Figure 3.The PBE calculated formation energies of intrinsic defects and Bi 3+ dopants in M 2 O 3 sesquioxides (M = Sc (a), Gd (b), Lu (c) and Y (d)) as a function of the Fermi level in O-rich environment.It should be noted that the formation energy lines of Bi 3+ dopants will be slightly shifted according to the actual doping concentration.

Figure 5 .
Figure 5.The PBE0+SOC calculated partial DOSs of 6s and 6p orbitals of Bi 3+ dopants in the two cation sites for the ground state of Y2O3:Bi 3+ , and the corresponding charge density distribution profiles.

Figure 5 .
Figure 5.The PBE0+SOC calculated partial DOSs of 6s and 6p orbitals of Bi 3+ dopants in the two cation sites for the ground state of Y 2 O 3 :Bi 3+ , and the corresponding charge density distribution profiles.

039 9 of 11 Figure 6 .
Figure 6.The configuration coordinate diagrams of the potential surfaces of Bi 3+ dopants substituting the cation sites with (a) C2 symmetry and (b) S6 symmetry for M2O3:Bi 3+ phosphors (M = Sc, Y, Gd and Lu), where 1 S0 and 3 P0,1 denote the ground and the lowest triplet 6s6p excited states of Bi 3+ , respectively, Bi 4+ + eCBM simulates Bi 4+ with one electron at CBM, representing the lowest MMCT excited state, and Bi 2+ + hVBM simulates Bi 2+ with a loose hole at VBM, representing the lowest CT excited state.

Figure 6 .
Figure 6.The configuration coordinate diagrams of the potential surfaces of Bi 3+ dopants substituting the cation sites with (a) C 2 symmetry and (b) S 6 symmetry for M 2 O 3 :Bi 3+ phosphors (M = Sc, Y, Gd and Lu), where 1 S 0 and 3 P 0,1 denote the ground and the lowest triplet 6s6p excited states of Bi 3+ , respectively, Bi 4+ + e CBM simulates Bi 4+ with one electron at CBM, representing the lowest MMCT excited state, and Bi 2+ + h VBM simulates Bi 2+ with a loose hole at VBM, representing the lowest CT excited state.

Author Contributions:
Investigation, data curation and writing-original draft preparation, H.B.; conceptualization and methodology, B.L. and C.M.; investigation and data curation, M.S.K.; writingreview and editing, A.S., M.G.B. and J.W. All authors have read and agreed to the published version of the manuscript.Funding: This work was financially supported by the National Natural Science Foundation of China (Grant Nos.52161135110, 12274048 and 12304439).BL acknowledges support from the China Postdoctoral Science Foundation (Grant No. 2023MD744135) and the Scientific and Technological Research Program of Chongqing Municipal Education Commission (Grant No. KJQN202200629).MSK appreciates support from the National Young Foreign Talents Plan (Grant No. QN2023035001L) and the 2021 Chongqing Postdoctoral International Exchange Program of China Postdoctoral Science Foundation (Grant No. YJ20210346).AS and MGB are thankful for support from the Overseas Talents Plan of Chongqing Association for Science and Technology (Grant No. 2022[60]) and the Polish NCN projects 2021/40/Q/ST5/00336.Institutional Review Board Statement: Not applicable.
and E Bi 2 O 3 [bulk] are the calculated total energy per formula unit for M 2 O 3 and Bi 2 O 3 , respectively, and E O 2 [gas]

Table 1 .
The calculated and measured excitation and emission energies of M 2 O 3 :Bi 3+ series.