Quasiparticle electronic structure of barium-silicon oxynitrides for white-LED application

Ba${}_3$Si${}_6$O${}_{12}$N${}_2$:Eu${}^{2+}$ and Ba${}_3$Si${}_6$O${}_9$N${}_4$:Eu${}^{2+}$ have strikingly similar atomistic structures, but the former is an efficient green phosphor at working temperature while the latter is a bluish-green phosphor whose luminescence decreases quite fast with temperature. Aiming at the understanding of such different behavior, we compute the quasiparticle electronic band structure of the two hosts, Ba${}_3$Si${}_6$O${}_{12}$N${}_2$ and Ba${}_3$Si${}_6$O${}_9$N${}_4$, thanks to many-body perturbation theory in the $G_0{W}_0$ approximation. The gap differs by about 0.43 eV. We analyze the eigenfunctions at the top of the valence band, at the bottom of the conduction band, and also the chemical shifts for the Ba site in the two hosts. The valence bands, directly impacted by the different stoichiometric ratio, are not thought to play a large role in the luminescence. Deceivingly, the dispersive bottom of the conduction band, directly related to luminescent properties, is similar in both compounds. The spatial topology of the probability density of the bottom of the conduction bands differs, as well as the location of the 5d peak, with a much higher energy than the bottom of the conduction band in Ba${}_3$Si${}_6$O${}_{12}$N${}_2$ than in Ba${}_3$Si${}_6$O${}_9$N${}_4$. Electromagnetic absorption spectra are also computed for both compounds.

Figure 1

(a) Crystal structure of Ba${}_3$Si${}_6$O${}_{12}$N${}_2$ after structural relaxation. There are two inequivalent barium atoms. The first one is labeled Ba${}_1$ and occupies the 1a Wyckoff position and the other labeled Ba${}_2$ is in the 2d Wyckoff position. Figure (b) shows the crystal structure of Ba${}_3$Si${}_6$O${}_9$N${}_4$ after structural relaxation. There are three inequivalent barium atoms. The first one is labeled Ba${}_1$ and occupies the 1c Wyckoff position, the second one labeled Ba${}_2$ is in the 1a Wyckoff position, and the last one named Ba${}_3$ is in the 1b Wyckoff position.

Figure 2

(a) and (b) show the crystalline environment of the two inequivalent barium atoms in Ba${}_3$Si${}_6$O${}_{12}$N${}_2$. (c)–(e) show the crystalline environment of the three inequivalent barium atoms in Ba${}_3$Si${}_6$O${}_9$N${}_4$. Bond lengths are reported in Table .

Figure 3

On the left side: the $G_0{W}_0$ Ba${}_3$Si${}_6$O${}_{12}$N${}_2$ quasiparticle band structure and on the right side: the $G_0{W}_0$ Ba${}_3$Si${}_6$O${}_9$N${}_4$ quasiparticle band structure. The red line is the partial density of state (PDOS) of the Ba${}_{\mathrm{d}}$ level, the blue line is the PDOS of the Ba${}_{\mathrm{s}}$ level, the green line is the PDOS of the O${}_{\mathrm{p}}$ level, and the black line is the PDOS of the N${}_{\mathrm{p}}$ level. The gray area is the total density of states (DOS).

Figure 4

Magnitude of $G_0{W}_0$ corrections to the DFT eigenenergies for Ba${}_3$Si${}_6$O${}_{12}$N${}_2$ on the left side and Ba${}_3$Si${}_6$O${}_9$N${}_4$ on the right side. The negative corrections (blue crosses) are for the occupied states and the positive (red dots) for the unoccupied states. The full line shows the energy polyfit that was used to generate the quasiparticle band structure in Fig. 3.

Figure 5

(a) Density of the first unoccupied band (84th band) of Ba${}_3$Si${}_6$O${}_{12}$N${}_2$ at the $\Gamma$ point, that is ${\Psi }_{84\Gamma }^{*}{\Psi }_{84\Gamma }$. The channel density corresponds mainly to the 6s state of barium. (b) Density of the first unoccupied band (80th band) of Ba${}_3$Si${}_6$O${}_9$N${}_4$ at the $\Gamma$ point, that is ${\Psi }_{80\Gamma }^{*}{\Psi }_{80\Gamma }$. Both isodensity are at 10% of the maximum density of that state. Large values are located around nitrogen and oxygen atoms.

Figure 6

(a) Density of the first unoccupied band (84th band) of Ba${}_3$Si${}_6$O${}_{12}$N${}_2$ at the $\Gamma$ point seen from the top. (b) Density of the first unoccupied band (80th band) of Ba${}_3$Si${}_6$O${}_9$N${}_4$ at the $\Gamma$ point seen from the top. Both isodensity are at 10% of the maximum density of that state.

Figure 7

(a) Density of the sum of the 85 to 90th bands of Ba${}_3$Si${}_6$O${}_{12}$N${}_2$ at the $\Gamma$ point that corresponds mainly to the 5d states of barium. (b) Density of the sum of the 81 to 83rd bands of Ba${}_3$Si${}_6$O${}_9$N${}_4$ at the $\Gamma$ point that corresponds mainly to the 5d states of barium. Both isodensity are at 10% of the maximum density of that state.

Figure 8

Comparison of the Ba${}_3$Si${}_6$O${}_{12}$N${}_2$ and Ba${}_3$Si${}_6$O${}_9$N${}_4$ electromagnetic absorption spectra at the RPA level for electric field polarization in the two nontrivial directions.