Research on Molecular Structure and Electronic Properties of Ln3+ (Ce3+, Tb3+, Pr3+)/Li+ and Eu2+ Co-Doped Sr2Si5N8 via DFT Calculation

We use density functional theory (DFT) to study the molecular structure and electronic band structure of Sr2Si5N8:Eu2+ doped with trivalent lanthanides (Ln3+ = Ce3+, Tb3+, Pr3+). Li+ was used as a charge compensator for the charge imbalance caused by the partial replacement of Sr2+ by Ln3+. The doping of Ln lanthanide atom causes the structure of Sr2Si5N8 lattice to shrink due to the smaller atomic radius of Ln3+ and Li+ compared to Sr2+. The doped structure’s formation energy indicates that the formation energy of Li+, which is used to compensate for the charge imbalance, is the lowest when the Sr2 site is doped. Thus, a suitable Li+ doping site for double-doped lanthanide ions can be provided. In Sr2Si5N8:Eu2+, the doped Ce3+ can occupy partly the site of Sr12+ ([SrN8]), while Eu2+ accounts for Sr12+ and Sr22+ ([SrN10]). When the Pr3+ ion is selected as the dopant in Sr2Si5N8:Eu2+, Pr3+ and Eu2+ would replace Sr22+ simultaneously. In this theoretical model, the replacement of Sr2+ by Tb3+ cannot exist reasonably. For the electronic structure, the energy level of Sr2Si5N8:Eu2+/Li+ doped with Ce3+ and Pr3+ appears at the bottom of the conduction band or in the forbidden band, which reduces the energy bandgap of Sr2Si5N8. We use DFT+U to adjust the lanthanide ion 4f energy level. The adjusted 4f-CBM of CeSr1LiSr1-Sr2Si5N8 is from 2.42 to 2.85 eV. The energy range of 4f-CBM in PrSr1LiSr1-Sr2Si5N8 is 2.75–2.99 eV and its peak is 2.90 eV; the addition of Ce3+ in EuSr1CeSr1LiSr1 made the 4f energy level of Eu2+ blue shift. The addition of Pr3+ in EuSr2PrSr2LiSr1 makes part of the Eu2+ 4f energy level blue shift. Eu2+ 4f energy level in EuSr2CeSr1LiSr1 is not in the forbidden band, so Eu2+ is not used as the emission center.


Introduction
Red fluorescent materials are essential parts of improving the color rendering index in phosphor-converted WLEDs (pc-WLEDs) and have high application value. With rareearth ions as activating ions, as a representative of the matrix of red phosphors, Sr 2 Si 5 N 8 alkaline earth metal silicon nitride has been extensively studied in recent years [1][2][3]. When Eu 2+ is used as the activating ion, the luminous intensity is the highest. Simultaneously, Sr 2 Si 5 N 8 :Eu 2+ has become the representative of commercial red fluorescent materials because of its outstanding fluorescence performance in all aspects [4]. However, the main problem is that Sr 2 Si 5 N 8 :Eu 2+ is sensitive to temperature, and Sr 2 Si 5 N 8 :Eu 2+ luminous intensity is significantly reduced when the temperature is higher. Considering that M 2 Si 5 N 8 is a layered or similar layered structure, its openness is relatively high so that the above problems can be solved through component engineering [5].
The coordination environment, electronic structure, and morphological characteristics of the Eu 2+ ion are several vital factors that affect phosphors' luminescence performance.
They determine the luminescence characteristics by indirectly changing the degree of crystal field splitting (CFS) [6], nephelauxetic effect (NE), the highest and lowest 5d energy level splitting [7,8]. For example, from both experiments and calculations Li [9] and Bulloni [10] proved that Ca 2+ partially replaced Eu 2+ in Sr 2 Si 5 N 8 matrix's emission peaks, which tended to appear red-shifted in Eu 2+ occupied eight coordination sites, though its stability was reduced. Liu used Ba 2+ to replace partial Sr 2+ in Sr 2 Si 5 N 8 , after the substitution, the emission peak was blue-shifted. As Eu 2+ in the ten-coordinate structure is more stable than the eight-coordinate structure, its thermal stability is improved. Chen [11] performed a doping modification based on Sr 2 Si 5 N 8 :Eu 2+ . In Sr 2 Si 5 N 8 :Eu 2+ , part of Al 3+ is used to replace Si 4+ . As the Al-N bond length is longer than that of Si-N, the bond length between Eu 2+ and surrounding N 3− is shorter, the crystal field intensity increases, and the emission peak position is red-shifted. Wang [12] used partial AlO + instead of SiN + , and the effects of the increase in the crystal field and the increase in electronegativity cancelled each other out, rendering the peak position unchanged, but the thermal stability and strength increased. In Rb 3 Ysi 2 O 7 :Eu 2+ system, the weak covalent interaction of Eu 2+ and O 2− prevented Eu 2+ from showing red emission [13]. The above-mentioned previous studies had found that different activating ions and ligand sites affected the energy level distribution of the activated ions and f orbitals, thereby affecting the luminescence performance.
Doping with more than one lanthanide ion can make up for the deficiency of one lanthanide ion doping. For example, Li [14] successfully introduced Gd 3+ /Er 3+ /Lu 3+ into Bi 2 Mo 6 to enhance its photocatalytic performance. Tang [15] introduced Ce 3+ and Tb 3+ into Na 3 SrMg 11 (PO 4 ) 9 . There are relatively few reports on the lanthanide Eu 2+ doped with M 2 Si 5 N 8 as the base material and further doped with another lanthanide. The study found that Tb 3+ and Eu 2+ co-doped Sr 2 Si 5 N 8 has a 20% increase in emission intensity [16]. Therefore, we want to systematically study the changes in the molecular structure and luminescence properties of Eu 2+ and other Ln 3+ co-doped systems. Among many lanthanides, the excitation spectrum of Pr 3+ 4f-5d is relatively simple [8]. In the [Xe] (near nuclear pseudopotential electron) 4f 1 5d 1 configuration during the excitation, Pr 3+ has only one 4f energy level, which can occupy two different electrons. Tb's advantage is that in 4f 7 5d, the 4f 7 [ 8 S 7/2 ] energy level is relatively stable, and the next higher 4f 7 [ 6 P J ]5d 1 energy level is about 3.5-4.0 eV higher. Therefore, it can be observed that 4f 8 -4f 7 ( 8 S 7/2 )5di turns into an isolated state. Ce 3+ is widely used as an activating ion in various fluorescent systems: Lu 3 Al 5 O 12 :Ce 3+ [17], LaSi 6 N 11 :Ce 3+ [18], Tb 3 Al 5 O 12 :Ce 3+ [19], In summary, so we prefer to use any one of Ce 3+ , Pr 3+ , Tb 3+ and Eu 2+ doping for the Sr 2 Si 5 N 8 matrix to explore the changes in molecular structure and properties.
To realize the fundamental principal research on the luminescence characteristics, Fang [24] used the first principles to calculate the molecular structure and energy band structure of M 2 Si 5 N 8 (M = Ca, Sr). Shen [25] studied the band structure of Sr 2 Si 5 N 8 :Eu 2+ through first-principles calculations and combined experiments to reveal the mechanism of luminescence. Density functional theory (DFT) based on first-principles ideas has been successfully applied to the study of microscopic particle systems. In this paper, combined with previous studies, first-principles calculations are used to study the model of Ce 3+ , Pr 3+ , Tb 3+ , respectively, with Li + co-doped Sr 2 Si 5 N 8 matrix system and Ce 3+ /Pr 3+ /Tb 3+ , respectively, with Eu 2+ , Li + three types of ions co-doped Sr 2 Si 5 N 8 matrix. The optimized structural parameters of the co-doping model for different ion species and sites are presented. We calculate the energy band and density of states of varying doping systems to analyze the electronic structure.

Structures Distortion of Doped Models
In Table 1, a (Å), b (Å), c (Å) are the three sets of edge lengths of the unit cell. α, β, γ/( • ) are, respectively, the angle between b and c; a and c; a and b. Polyhedral volume (Å 3 ) is the coordination polyhedron volume of Ln and N. Distortion index (Å) is the distance a ligand moves after the d/f orbital energy level splits and stabilizes, which reflects distortion effect. Distortion effect: For transition element/rare earth element ions with a high coordination number (>6), high-spin d/f orbitals and low-spin d/f orbitals are unstable in regular polyhedrons, which will cause these d/f orbits to undergo further splitting in energy, in order to stabilize the ion, causing the coordination relationship to deviate from the symmetry of the regular polyhedron. Effective coordination number means that due to the regular coordination polyhedron's structural distortion, the bond length between the ligand and the central atom changes, resulting in non-integer coordination.  [26] (regardless of the coordination number) decreases from left to right; Eu 2+ , Ce 3+ /Li + , Pr 3+ /Li + replace Sr 2+ in turn. Due to the cationic ligand's volume coarctation, the lattice constant and unit cell volume will be slightly smaller. The volume of the doped system is smaller than that of undoped lanthanide ions. Sr 2 Si 5 N 8 volume, unit cell volume and doped ion radius are positively correlated. The average bond length between the lanthanide ion and N becomes shorter, making the bond between the lanthanide ion and the surrounding N stronger. The structure is more compact, the crystal field strength increases, and there will be a redshift tendency. Comparing the system in which the same lanthanide ion replaces eight-coordinate Sr 2+ and ten-coordinate Sr 2+ , we find that the distortion degree of eight-coordinate Sr 2+ is greater than that of ten-coordinate Sr 2+ . The formation of an eight-coordinate structure will produce a stronger electron cloud. The nephelauxetic effect (NE) produces a centroid shift, which has a synergistic effect with the above redshift. However, for trivalent lanthanide ions doped with the same coordination number, the different Li + sites have almost no effect on the structure, which is only used to balance the charge. Figure 1a shows  In the Sr 2 Si 5 N 8 matrix, the selected doping (Sr) site is the same distance as Sr 1 -Sr 1 and Sr 2 -Sr 2 , before being replaced by Ln 3+ /Li + , which has a distance of 5.748 Å; the distance is 3.467 Å between Sr 1 -Sr 2 . When Ln 3+ and Li + are doped to replace Sr 1 , in the order of Pr 3+ , Ce 3+ , Tb 3+ , the Ln-Li distances increased by 0.06 Å, 0.066 Å, 0.037 Å, respectively, and the degree of distortion was 1.05%, 1.14% and 0.64%. The overall deviation is not significant. When Ln 3+ /Li replaces different sites, the degree of distortion is always above 7.56%. From the perspective of the degree of lattice distortion, it is unlikely to occur in actual situations. When Ln 3+ /Li + is doped to replace Sr 2 , the distortion degree of Pr Sr2 Li Sr2 -Sr 2 Si 5 N 8 and Ce Sr2 Li Sr2 -Sr 2 Si 5 N 8 is about 2.40%. After Ln Sr1 Li Sr -Sr 2 Si 5 N 81 and Ln Sr2 Li Sr2 -Sr 2 Si 5 N 8 are doped to replace the Sr site, the distance between Ln-Li becomes longer, while Ln Sr1 Li Sr2 and Ln Sr2 Li Sr1 have shorter distances than that before doping.    In Table 3, Ln 3+ /Eu 2+ is the coordination polyhedron information of the ion and N. Except for the six ligand structures with three double lanthanide ions substituted for the Sr site, the other structures are not below the theoretical values. Only the following three doping models are Eu 2+ and Ce 3+ to replace Sr 1 , Eu 2+ to replace Sr 2 , and Ce 3+ to replace Sr 1 , Eu 2+ replaces Sr 2 , Pr 3+ replaces Sr 2 in line with the actual structure. Neither Tb 3+ nor Eu 2+ co-doped systems are desirable. The unit cell volume and ligand structure of the co-doped system did not change significantly from the single-doped system. After screening more than 30 models, a total of three models may exist stably after structure optimization. According to the order of Figure 4a-c, the distances before optimization of Ln-Li, Ln-Eu and Eu-Li are 5.748 Å, 5.748 Å, 5.748 Å; 5.748 Å, 3.467 Å, 6.713 Å; 3.467 Å, 5.748 Å, 3.467 Å. Among them, the distance between (a) and (b) does not change obviously before and after convergence, which is less than 0.1% compared with the original Sr-Sr distance. In summary, Combining Figure 5 and Table 4, we can draw the following conclusions: Eu Sr1 Ce Sr1 Li Sr1 and Eu Sr2 Ce Sr1 Li Sr1 can exist stably after Eu 2+ /Ce 3+ /Li + co-doped with Sr 2 Si 5 N 8 , without considering the formation energy conditions. In the Eu Sr2 Pr Sr2 Li Sr1 -model, there are three distance types: Ln-Eu, Ln-Li, and Eu-Li. Compared with the original Sr sites, the distance changes are 5.6%, 8.9%, and 9.7%, respectively. In the Eu 2+ /Tb 3+ /Li + -Sr 2 Si 5 N 8 model, the ionic radius of Tb 3+ is too small, resulting in excessive structural distortion and difficulty in optimization convergence, so its structure cannot exist stably.  Figure 6 is the formation energy diagram of Ce 3+ (Tb 3+ , Pr 3+ )/Li + co-doped Sr 2 Si 5 N 8 with eight-coordinate (Sr 1 ) and ten-coordinate (Sr 2 ). From the definition of formation energy, the lower formation energy value means the target product is easier to form. Among all the values, Ce 3+ and Li + 's formation energy co-doped in eight-coordinate and ten-coordinate systems, respectively, is the lowest. Pr 3+ and Li + co-doped together to replace eight-coordinate Sr has the highest formation energy. For Ce 3+ and Tb 3+ , Ce 3+ (Tb 3+ ) and Li + are, respectively, doped at the same Sr site to form lower energy. Pr and Li co-doped to replace ten-coordinate Sr 2+ has the lower formation energy, and for co-doped to replace eight-coordinate Sr 2+ , the formation energy is the highest. Three kinds of lanthanide ions doping to replace Sr 2 are easier to generate in theory. The formation energy of Li + is lower when it is at the Sr 2 site, so the fixed Li +

Band Structures and Density of States
We first calculated the ground state energy band and state density of Eu 2+ single-doped Sr 2 Si 5 N 8 and Tb 3+ (Ce 3+ , Pr 3+ )/Li + co-doped Sr 2 Si 5 N 8 systems, as shown in Figure 7, for our subsequent calculations of Eu 2+ /Ce 3+ (Tb 3+ , Pr 3+ )/Li + ion co-doping, which provides a basis for comparison. The calculated bandgap of Sr 2 Si 5 N 8 :Eu 2 2+ is 3.21 eV, which is slightly smaller than the experimental bandgap because the approximate processing of the DFT exchange-correlation term causes the bandgap to become narrower [27]. In the (a-l) ground-  The states diagram's density shows that the main components of VBM are 2p of N, 3s, 3p of Si, and CBM is mainly composed of 4f energy level of La, 5d, 5s orbitals of Sr and 3p, 3s of Si. Eu 6s, Eu 5p, Ce 6s, Ce 5p, Pr 6s, Pr 5p, Tb 6s and Tb 5p are minor in their contributions. The (Partial Density of State, PDOS) of Ce, Sr, N, Si in Ce Sr1 Li Sr1 -Sr 2 Si 5 N 8 are the same as the four PDOS in Sikander Azam's calculation about Sr 2 Si 5 N 8 :Ce 3+ [28]. Figure 7a has strong peaks at 2.04 eV and 2.46 eV, Figure S1b has approximately the same values at 2.07 eV, 2.10 eV, 2.25 eV, and 2.34 eV, while Figure S1c has a higher peak at 2.31 eV. Figure S1d has peaks of similar intensity at 2.25 eV, 2.43 eV, and 2.49 eV. The 4f energy level of Figure S1f-h is between 2.28 and 2.52 eV, and the 4f peak value of Pr 3+ in Figure S1e is very high. If Pr 3+ is the luminous center, the luminous intensity is much higher than Figure S1f-h. The 4f of Tb 3+ in Figure S1j has a higher peak intensity at 1.17 eV, which has a good potential for activating ions. Figure 7 shows the energy bands and state density of the three kinds of triple-doped ions systems, Eu Sr1 Ce Sr1 Li Sr2 -Sr 2 Si 5 N 8 , Eu Sr2 Ce Sr1 Li Sr2 -Sr 2 Si 5 N 8 , Pr Sr2 Eu Sr2 Li Sr2 -Sr 2 Si 5 N 8 . In Eu Sr1 Ce Sr1 Li Sr2 -Sr 2 Si 5 N 8 , Eu 2+ is the main component in the forbidden band. Ce 3+ is close to the bottom of the conduction band. Eu Sr2 Ce Sr1 Li Sr2 -Sr 2 Si 5 N 8 is in the conduction band and has low intensity. Therefore, among the lanthanide ions of this system, only Ce 3+ is the luminescence center. For Pr Sr2 Eu Sr2 Li Sr2 -Sr 2 Si 5 N 8 , the band distribution is relatively dense. The 5d electrons in the excited state may produce multi-level transitions [29].

Determination of DFT + U Parameters of Each System
In Table 5, as the value of U eff increases from 0 to 8 eV, when Eu 2+ is equal to 6 eV, the 4f electron orbital of Eu 2+ appears at the top of the valence band. When U eff = 8 eV, the filled state 4f orbital has wholly entered the valence band, and the energy level is about −1 eV (set the top of the valence band as the Fermi level, that is, E f = 0 eV). When U eff = 4 eV, Sr 2 Si 5 N 8 :Eu Sr1 2+ and Sr 2 Si 5 N 8 :Eu Sr2 2+ 's 4f-CBM energy difference is 2.22 eV and 2.23 eV, respectively, according to the energy wavelength conversion formula: In the above formula, E (energy)-eV, k (Planck's constant) = 6.63 × 10 −34 J·s, k = 1.6 × 10 −19 J/eV, C (speed of light) = 3 × 10 17 nm/s, λ (wavelength)-nm. The parameters can be obtained in the following formula: The direct bandgaps of Figure 8a  In summary, we add different U eff to the strongest peak of the 4f energy level and the energy distribution range in Figure 8a-k to make it fall within the appropriate range. The energy ranges of 4f-CBM in Figure 8a-d are 2.42-2.85 eV, 2.80-3.03 eV, 2.65-3.13 eV, 2.67-2.91 eV, respectively. In Figure 8a, Ce Sr1 Li Sr1 -Sr 2 Si 5 N 8 is closer to the excitation energy range of Ce 3+ doped Sr 2 Si 5 N 8 from 2.85 to 3.25 eV [30] reported in the experiment, but Figure 8a has a global redshift of 0.43 eV. In Figure 7e-h, the energy ranges of 4f-CBM are 2.75-2.99 eV, 2.28-3.06 eV, 2.27-3.08 eV, 2.37-2.97 eV, respectively. In Figure 8e, Pr Sr1 Li Sr1 -Sr 2 Si 5 N 8 is closer to the excitation energy range of Pr 3+ doped SrAl 2 O 4 from 2.53 to 2.88 eV [30] reported in the experiment. The energy ranges of 4f-CBM in Figure 8i-k are 2.68-3.04 eV, 2.77-3.07 eV, 2.71-3.07 eV, respectively, which is far from the experimental excitation of Sr 2 Si 5 N 8 :Tb 3+ [16]. The U eff values of Eu 2+ and Ce 3+ are 4 eV and 6 eV, respectively, and the energy range is mainly 2.27-2.82 eV, and the peak value is 2.27 eV, 2.39 eV, 2.82 eV. In Figure S2b, the Eu 2+ 4f energy level is not in the forbidden band. When Ce U eff is 5 eV, the energy range of 4f-CBM is from 2.35 to 2.83 eV. The Eu 2+ , Pr 3+ U eff values in Figure S2c are, respectively, 1 eV, 7 eV, and Eu 2+ 4f energy levels have three strong peaks of 2.19 eV, 2.25 eV, and 2.93 eV. Pr 3+ has the highest peak intensity of 2.69 eV in 2.69-2.99 eV.

Theoretical Models
Three lanthanide ions (Ln 3+ = Ce 3+ , Pr 3+ , Tb 3+ ) were selected as doping ions to dope Sr 2 Si 5 N 8 and Sr 2 Si 5 N 8 :Eu 2+ , respectively. As shown in Figure 9a, there are two kinds of Sr doping sites, namely, eight-coordinate Sr 1 [SrN 8 ] (0.5000, 0.8734, 0.9997) and tencoordinate Sr 2 [SrN 10 ] (0.7500, 0.1158, 0.8683). Since in the doped ions, Ln are all positively trivalent and Sr is bivalent to neutralize the entire system's charge, every time a positive trivalent lanthanide ion is introduced to replace Sr 2+ , a Li + is introduced to replace Sr 2+ to keep the entire system electrically neutral. The chemical formula of Sr 2 Si 5 N 8 doped with Ln 3+ /Li + is Ln Sr1/Sr2 Li Sr1/Sr2 Sr 2 Si 5 N 8 , while the chemical formula of Sr 2 Si 5 N 8 doped with Ln 3+ /Li + /Eu 2+ is Ln Sr1/Sr2 Eu Sr1/Sr2 Li Sr1/Sr2 -Sr 2 Si 5 N 8 . Figure 9b has established a 2 × 2 × 1 supercell (60 atoms) with a doping concentration of 12.5% for Ln 3+ , Eu 2+ , and Li + . If we continue to expand the unit cell to 3 × 2 × 1 to reduce the doping concentration, the calculation requires more K points than 5 × 8 × 6, and it is complicated for the structure to converge. Notably, 2 × 2 × 1 is the largest supercell structure that can be established under the premise that the structure can converge.

Computational Methods
When considering all ground-state calculations, density functional theory (DFT) calculations are performed in the Vienna AB Initio Simulation Package (VASP, Vienna ab initio simulation package) using the projector-augmented wave (PAW) method [31]. Exchangecorrelation (XC, exchange-correlation) energy is described in the Perdew-Burke-Ernzerhof (PBE) method in generalized gradient approximation (GGA) [32]. The cutoff energy of all calculated plane wave bases is set to 500 eV. The energy convergence tolerance of the Sself-Cconsistent Ffield (SCF) is 10 −4 eV. The convergence tolerance of the relaxation force is 0.01 eV/Å per atom. Sr 2 Si 5 N 8 :Eu 2+ original unit cell model removed the energy band calculation.
To solve the problem that DFT cannot handle d and f electrons, the Hubbard model compensates for the strong correlation between d and f electrons by adding additional energy terms. The corrected energy's form is as follows: There are many forms of Hubbard model correction. We choose the simplest Dudarev approximation [33]; the form is as follows: U and J are the critical parameters of Hubbard's correction item, replaced by = (U − J). Different ions have different U eff values in different host environments.
Regarding the calculation method of the effective coordination number, this article adopts Brunner's method [34], which assumes that ionic or covalent bonds connect the central atoms of the surrounding atoms. In the established C.N principle, the energy standard is defined as each coordination. The bond energy between (X i ) and the central atom (M) is different from the bond energy between the nearest ligand (X 0 ) and the central atom. The energy ratio E (M−X i ) : E (M−X 0 ) is defined as the contribution of X i atom to M atom C.N*. If the nearest atom is only affected by the Coulomb force, it is easy to get formula (5) C.N * where Y (M−X i ) is the bond length between the central atom and the ligand. The formation of energy can evaluate the stability of the structure. The model after substitution and doping lattice can be described as the following formula (6) In the above formula E f (Sr 2 Si 5 N 8 :Eu 2+ /Ln 3+ /Li + ) is the formation energy, E(Sr 2 Si 5 N 8 :Eu 2+ /Ln 3+ /Li + ) is the energy calculated by SCF, µ(Sr 2+ ), µ(Eu 2+ ), µ(Li + ) are the chemical potentials of Sr, Eu, Li, and Ln, respectively, and E(Sr 2 Si 5 N 8 ) is the energy calculated by the lattice matrix SCF. For the chemical potential of the element, formula (7) can be used µ(x) = E(Cell of X)/n where µ(x) is the chemical potential of X, E (Cell of X) is the elemental unit cell of element X, and n is the number of X contained in the elemental unit cell.