Ab initio Study of Luminescence in Ce-doped Lu2_2SiO5_5: The Role of Oxygen Vacancies on Emission Color and Thermal Quenching Behavior

We study from first principles the luminescence of Lu$_2$SiO$_5$:Ce$^{3+}$ (LSO:Ce), a scintillator widely used in medical imaging applications, and establish the crucial role of oxygen vacancies (V$_O$) in the generated spectrum. The excitation energy, emission energy and Stokes shift of its luminescent centers are simulated through a constrained density-functional theory method coupled with a ${\Delta}$SCF analysis of total energies, and compared with experimental spectra. We show that the high-energy emission band comes from a single Ce-based luminescent center, while the large experimental spread of the low-energy emission band originates from a whole set of different Ce-V$_O$ complexes together with the other Ce-based luminescent center. Further, the luminescence thermal quenching behavior is analyzed. The $4f-5d$ crossover mechanism is found to be very unlikely, with a large crossing energy barrier (E$_{fd}$) in the one-dimensional model. The alternative mechanism usually considered, namely the electron auto-ionization, is also shown to be unlikely. In this respect, we introduce a new methodology in which the time-consuming accurate computation of the band gap for such models is bypassed. We emphasize the usually overlooked role of the differing geometry relaxation in the excited neutral electronic state Ce$^{3+,*}$ and in the ionized electronic state Ce$^{4+}$. The results indicate that such electron auto-ionization cannot explain the thermal stability difference between the high- and low-energy emission bands. Finally, a hole auto-ionization process is proposed as a plausible alternative. With the already well-established excited state characterization methodology, the approach to color center identification and thermal quenching analysis proposed here can be applied to other luminescent materials in the presence of intrinsic defects.Comment: 13 pages, 8 figures, accepted by Phys. Rev. Material

First-principles Study of the Luminescence of Eu2+-doped Phosphors

The luminescence of fifteen representative Eu$^{2+}$-doped phosphors used for white-LED and scintillation applications is studied through a Constrained Density Functional Theory. Transition energies and Stokes shift are deduced from differences of total energies between the ground and excited states of the systems, in the absorption and emission geometries. The general applicability of such methodology is first assessed: for this representative set, the calculated absolute error with respect to experiment on absorption and emission energies is within 0.3 eV. This set of compounds covers a wide range of transition energies that extents from 1.7 to 3.5 eV. The information gained from the relaxed geometries and total energies is further used to evaluate the thermal barrier for the $4f-5d$ crossover, the full width at half-maximum of the emission spectrum and the temperature shift of the emission peak, using a one-dimensional configuration-coordinate model. The former results indicate that the $4f-5d$ crossover cannot be the dominant mechanism for the thermal quenching behavior of Eu$^{2+}$-doped phosphors and the latter results are compared to available experimental data and yield a 30$\%$ mean absolute relative error. Finally, a semi-empirical model used previously for Ce$^{3+}$-doped hosts is adapted to Eu$^{2+}$-doped hosts and gives the absorption and emission energies within 0.9 eV of experiment, underperforming compared to the first-principles calculation.Comment: 17 pages, 13 figures, (Phys. Rev. B 2017 Accept

Assessment of First-Principles and Semiempirical Methodologies for Absorption and Emission Energies of Ce3+^{3+}-Doped Luminescent Materials

In search of a reliable methodology for the prediction of light absorption and emission of Ce$^{3+}$-doped luminescent materials, 13 representative materials are studied with first-principles and semiempirical approaches. In the first-principles approach, that combines constrained density-functional theory and $\Delta$SCF, the atomic positions are obtained for both ground and excited states of the Ce$^{3+}$ ion. The structural information is fed into Dorenbos' semiempirical model. Absorption and emission energies are calculated with both methods and compared with experiment. The first-principles approach matches experiment within 0.3 eV, with two exceptions at 0.5 eV. In contrast, the semiempirical approach does not perform as well (usually more than 0.5 eV error). The general applicability of the present first-principles scheme, with an encouraging predictive power, opens a novel avenue for crystal site engineering and high-throughput search for new phosphors and scintillators.Comment: 12 pages, 3 figure

First-principles study of Ce3+^{3+} doped lanthanum silicate nitride phosphors: Neutral excitation, Stokes shift, and luminescent center identification

We study from first principles two lanthanum silicate nitride compounds, LaSi$_{3}$N$_{5}$ and La$_{3}$Si$_{6}$N$_{11}$, pristine as well as doped with Ce$^{3+}$ ion, in view of explaining their different emission color, and characterising the luminescent center. The electronic structures of the two undoped hosts are similar, and do not give a hint to quantitatively describe such difference. The $4f\rightarrow 5d$ neutral excitation of the Ce$^{3+}$ ions is simulated through a constrained density-functional theory method coupled with a ${\Delta}$SCF analysis of total energies, yielding absorption energies. Afterwards, atomic positions in the excited state are relaxed, yielding the emission energies and Stokes shifts. Based on these results, the luminescent centers in LaSi$_{3}$N$_{5}$:Ce and La$_{3}$Si$_{6}$N$_{11}$:Ce are identified. The agreement with the experimental data for the computed quantities is quite reasonable and explains the different color of the emitted light. Also, the Stokes shifts are obtained within 20\% difference relative to experimental data.Comment: 12 pages, 10 figure

Quasiparticles and phonon satellites in spectral functions of semiconductors and insulators: Cumulants applied to full first principles theory and Fr\"ohlich polaron

The electron-phonon interaction causes thermal and zero-point motion shifts of electron quasiparticle (QP) energies $\epsilon_k(T)$. Other consequences of interactions, visible in angle-resolved photoemission spectroscopy (ARPES) experiments, are broadening of QP peaks and appearance of sidebands, contained in the electron spectral function $A(k,\omega)=-{\Im m}G_R(k,\omega) /\pi$, where $G_R$ is the retarded Green's function. Electronic structure codes (e.g. using density-functional theory) are now available that compute the shifts and start to address broadening and sidebands. Here we consider MgO and LiF, and determine their nonadiabatic Migdal self energy. The spectral function obtained from the Dyson equation makes errors in the weight and energy of the QP peak and the position and weight of the phonon-induced sidebands. Only one phonon satellite appears, with an unphysically large energy difference (larger than the highest phonon energy) with respect to the QP peak. By contrast, the spectral function from a cumulant treatment of the same self energy is physically better, giving a quite accurate QP energy and several satellites approximately spaced by the LO phonon energy. In particular, the positions of the QP peak and first satellite agree closely with those found for the Fr\"ohlich Hamiltonian by Mishchenko $\textit{et al.}$ (2000) using diagrammatic Monte Carlo. We provide a detailed comparison between the first-principles MgO and LiF results and those of the Fr\"ohlich Hamiltonian. Such an analysis applies widely to materials with infra-red active phonons. We also compare the retarded and time-ordered cumulant treatments: they are equivalent for the Fr\"ohlich Hamiltonian, and only slightly differ in first-principles electron-phonon results for wide-band gap materials.Comment: 21 pages, 19 figure

Band widths and gaps from the Tran-Blaha functional : Comparison with many-body perturbation theory

For a set of ten crystalline materials (oxides and semiconductors), we compute the electronic band structures using the Tran-Blaha [Phys. Rev. Lett. 102, 226401 (2009)] (TB09) functional. The band widths and gaps are compared with those from the local-density approximation (LDA) functional, many-body perturbation theory (MBPT), and experiments. At the density-functional theory (DFT) level, TB09 leads to band gaps in much better agreement with experiments than LDA. However, we observe that it globally underestimates, often strongly, the valence (and conduction) band widths (more than LDA). MBPT corrections are calculated starting from both LDA and TB09 eigenenergies and wavefunctions. They lead to a much better agreement with experimental data for band widths. The band gaps obtained starting from TB09 are close to those from quasi-particle self-consistent GW calculations, at a much reduced cost. Finally, we explore the possibility to tune one of the semi-empirical parameters of the TB09 functional in order to obtain simultaneously better band gaps and widths. We find that these requirements are conflicting.Comment: 18 pages, 16 figure

A First-Principles Explanation of the Luminescent Line Shape of SrLiAl3_3N4_4:Eu2+^{2+} Phosphor for Light-Emitting Diode Applications

White light-emitting diodes are gaining popularity and are set to become the most common light source in the U.S. by 2025. However, their performance is still limited by the lack of an efficient red-emitting component with a narrow band emission. The red phosphor SrLiAl$_3$N$_4$:Eu$^{2+}$ is among the first promising phosphors with a small bandwidth for next-generation lighting, but the microscopic origin of this narrow emission remains elusive. In the present work, density functional theory, the $\Delta$SCF-constrained occupation method, and a generalized Huang-Rhys theory are used to provide an accurate description of the vibronic processes occurring at the two Sr$^{2+}$ sites that the Eu$^{2+}$ activator can occupy. The emission band shape of Eu(Sr1), with a zero-phonon line at 1.906 eV and a high luminescence intensity, is shown to be controlled by the coupling between the 5d$_{z^2}$-4f electronic transition and the low-frequency phonon modes associated with the Sr and Eu displacements along the Sr channel. The good agreement between our computations and experimental results allows us to provide a structural assignment of the observed total spectrum. By computing explicitly the effect of the thermal expansion on zero-phonon line energies, the agreement is extended to the temperature-dependent spectrum. These results provide insight into the electron-phonon coupling that accompanies the 5d-4f transition in similar UCr$_4$C$_4$-type phosphors. Furthermore, these results highlight the importance of the Sr channel in shaping the narrow emission of SrLiAl$_3$N$_4$:Eu$^{2+}$, and they shed new light on the structure-property relations of such phosphors.Comment: 10 pages, 6 figure