First-principles investigation of electronic structural and optical properties of rare earth doped β-Si₃N₄ crystals

Based on the density functional theory within the generalized gradient approximation (GGA) method, the geometric structure, electronic and dielectric properties of rare earth (La and Y) doped β-Si₃N₄ were studied and the origin of the differences and similarities among the rare earths (La and Y) characterized in this work were discussed. The fully relaxed structural parameters of β-Si₃N₄ crystal are found to be in good agreement with experimental data. The formation energy calculations indicate that both La and Y atoms are preferentially doped on the Si sites, which is in agreement with previous experimental observations. Furthermore, the calculated band gap of the doped structures decreases significantly, specifically, the larger La atom results in narrower band gap than that of Y doped β-Si₃N₄. The reason was extensively analyzed by the density of states (DOS). Subsequently, the dielectric function, absorption coefficient of the polycrystalline were compared with these values for plane polarized at[100] and[001] directions. The calculations show that the optical dielectric constant in the rare earth (especially La) doped structures increase remarkably, compared with the undoped β-Si₃N₄.