Zero-point lattice expansion and band gap renormalization: Grüneisen approach versus free energy minimization

Brousseau-Couture, Véronique; Godbout, Émile; Côté, Michel; Gonze, Xavier

doi:10.1103/physrevb.106.085137

Cited by 6 publications

(5 citation statements)

References 106 publications

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“…These corrections may vary depending on the wavevector, e.g., for the indirect band gap of diamond the GW correction is around 0.02 eV while it is about 0.2 eV for the direct band gap. 21,63 We also ignored thermal expansion, zeropoint lattice expansion, 64,65 and further anharmonic effects. Other calculations including these phenomena are detailed in Table 2.…”

Section: Resultsmentioning

confidence: 99%

Spectroscopic signatures of nonpolarons: the case of diamond

Abreu

Nery

Giantomassi

et al. 2022

Phys. Chem. Chem. Phys.

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Section: Resultsmentioning

confidence: 99%

Spectroscopic signatures of nonpolarons: the case of diamond

Abreu

Nery

Giantomassi

et al. 2022

Phys. Chem. Chem. Phys.

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“…To compute the effect of thermal expansion, the volumetric quasi-harmonic approximation (QHA) is used, neglecting deviatoric thermal stresses and internal forces (v-ZSISA approximation). − The only contributions to the thermal expansion of the crystal are the coupling between phonons and the change in unit cell volume, with cell parameters and internal coordinates relaxed at fixed volumes. We obtain the temperature versus volume curve of the undoped SLA by minimizing the Helmholtz free energy (FE) ,, F false( V , T false) = E false( V false) + F vib false( V , T false) where F vib false( V , T false) = ∑ q ν ℏ ω boldq ν ( V ) 2 + k B T ln false( 1 − normale − ℏ ω boldq ν ( V ) / k normalB T false) Here, E ( V ) is the static DFT energy versus volume curve, with all non-volumetric degrees of freedom relaxed, and F vib ( V , T ) is the vibration energy with the same cell and atomic geometry. The FE curve is constructed using seven configurations within a [−2%, +4%] volume change with respect to the static equilibrium volume.…”

Section: Methodsmentioning

confidence: 99%

A First-Principles Explanation of the Luminescent Line Shape of SrLiAl₃N₄:Eu²⁺ Phosphor for Light-Emitting Diode Applications

et al. 2023

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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 SrLiAl3N4:Eu2+ 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 ΔSCF-constrained occupation method, and a generalized Huang–Rhys theory are used to provide an accurate description of the vibronic processes occurring at the two Sr2+ sites that the Eu2+ 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 UCr4C4-type phosphors. Furthermore, these results highlight the importance of the Sr channel in shaping the narrow emission of SrLiAl3N4:Eu2+, and they shed new light on the structure–property relations of such phosphors.

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“…To make a fair comparison with experimental data, the first-principles data shown in Fig. 4 include the theoretical contribution of the zero-point expansion of the lattice [78,79]. This term originates from the phonon contribution to the total free energy of the crystal, which increases the T = 0 K lattice parameter compared to the static equilibrium value and, in turn, affects the band gap energy (see Appendix D for more details).…”

Section: Experiments Vs First Principlesmentioning

confidence: 99%

“…For a more thorough discussion of the zero-point lattice expansion and its effect on the band gap ZPR, see Ref. [79].…”

Section: Appendix D: Zero-point Expansion Of the Latticementioning

confidence: 99%

Effect of spin-orbit coupling on the zero-point renormalization of the electronic band gap in cubic materials: First-principles calculations and generalized Fröhlich model

2023

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The electronic structure of semiconductors and insulators is affected by ionic motion through electron-phonon interaction, yielding temperature-dependent band gap energies and zero-point renormalization (ZPR) at absolute zero temperature. For polar materials, the most significant contribution to the band gap ZPR can be understood in terms of the Fröhlich model, which focuses on the non-adiabatic interaction between an electron and the macroscopic electrical polarization created by a long-wavelength optical longitudinal phonon mode. On the other hand, spin-orbit interaction (SOC) modifies the bare electronic structure, which will, in turn, affect the electron-phonon interaction and the ZPR. We present a comparative investigation of the effect of SOC on the band gap ZPR of twenty semiconductors and insulators with cubic symmetry using first-principles calculations. We observe a SOC-induced decrease of the ZPR, up to 30%, driven by the valence band edge, which almost entirely originates from the modification of the bare electronic eigenenergies and the decrease of the hole effective masses near the Γ point. We also incorporate SOC into a generalized Fröhlich model, addressing the Dresselhaus splitting which occurs in non-centrosymmetric materials, and confirm that the predominance of non-adiabatic effects on the band gap ZPR of polar materials is unchanged when including SOC. Our generalized Fröhlich model with SOC provides a reliable estimate of the SOC-induced decrease of the polaron formation energy obtained from first principles and brings to light some fundamental subtleties in the numerical evaluation of the effective masses with SOC for non-centrosymmetric materials. We finally warn about a possible breakdown of the parabolic approximation, one of the most fundamental assumptions of the Fröhlich model, within the physically relevant energy range of the Fröhlich interaction for materials with high phonon frequencies treated with SOC. This is a post-peer-review version of the article published in Physical Review B, which includes the Supplemental Material in the main file.

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Zero-point lattice expansion and band gap renormalization: Grüneisen approach versus free energy minimization

Cited by 6 publications

References 106 publications

Spectroscopic signatures of nonpolarons: the case of diamond

Spectroscopic signatures of nonpolarons: the case of diamond

A First-Principles Explanation of the Luminescent Line Shape of SrLiAl₃N₄:Eu²⁺ Phosphor for Light-Emitting Diode Applications

Effect of spin-orbit coupling on the zero-point renormalization of the electronic band gap in cubic materials: First-principles calculations and generalized Fröhlich model

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Zero-point lattice expansion and band gap renormalization: Grüneisen approach versus free energy minimization

Cited by 6 publications

References 106 publications

Spectroscopic signatures of nonpolarons: the case of diamond

Spectroscopic signatures of nonpolarons: the case of diamond

A First-Principles Explanation of the Luminescent Line Shape of SrLiAl3N4:Eu2+ Phosphor for Light-Emitting Diode Applications

Effect of spin-orbit coupling on the zero-point renormalization of the electronic band gap in cubic materials: First-principles calculations and generalized Fröhlich model

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A First-Principles Explanation of the Luminescent Line Shape of SrLiAl₃N₄:Eu²⁺ Phosphor for Light-Emitting Diode Applications