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White light-emitting diodes are gaining popularity and are set to become themost common light source in the U.S. by 2025. However, their performance isstill limited by the lack of an efficient red-emitting component with a narrowband emission. The red phosphor SrLiAl$_3$N$_4$:Eu$^{2+}$ is among the firstpromising phosphors with a small bandwidth for next-generation lighting, butthe microscopic origin of this narrow emission remains elusive. In the presentwork, density functional theory, the $\Delta$SCF-constrained occupation method,and a generalized Huang-Rhys theory are used to provide an accurate descriptionof the vibronic processes occurring at the two Sr$^{2+}$ sites that theEu$^{2+}$ activator can occupy. The emission band shape of Eu(Sr1), with azero-phonon line at 1.906 eV and a high luminescence intensity, is shown to becontrolled by the coupling between the 5d$_{z^2}$-4f electronic transition andthe low-frequency phonon modes associated with the Sr and Eu displacementsalong the Sr channel. The good agreement between our computations andexperimental results allows us to provide a structural assignment of theobserved total spectrum. By computing explicitly the effect of the thermalexpansion on zero-phonon line energies, the agreement is extended to thetemperature-dependent spectrum. These results provide insight into theelectron-phonon coupling that accompanies the 5d-4f transition in similarUCr$_4$C$_4$-type phosphors. Furthermore, these results highlight theimportance of the Sr channel in shaping the narrow emission ofSrLiAl$_3$N$_4$:Eu$^{2+}$, and they shed new light on the structure-propertyrelations of such phosphors.

A First-Principles Explanation of the Luminescent Line Shape of SrLiAl$_3$N$_4$:Eu$^{2+}$ Phosphor for Light-Emitting Diode Applications