An Accurate Alternative to Hybrid Functionals for Germanium: DFT+α.

Area of Science:

• Computational Materials Science
• Condensed Matter Physics
• Quantum Chemistry

Background:

• Accurate prediction of material properties using Density Functional Theory (DFT) relies heavily on the chosen exchange-correlation functional.
• Standard functionals like Perdew-Burke-Ernzerhof (PBE) often exhibit systematic errors, overestimating lattice parameters and underestimating electronic band gaps.
• Hybrid functionals, such as Heyd-Scuseria-Ernzerhof (HSE), offer improved accuracy but come with higher computational costs.

Purpose of the Study:

• To evaluate the performance of PBE and HSE functionals in predicting the electronic and structural properties of germanium.
• To address the limitations of existing DFT functionals in accurately capturing semiconductor properties.
• To introduce and validate a novel semiempirical correction scheme, DFT+α, for improved accuracy and efficiency.

Main Methods:

• Comparative analysis of Perdew-Burke-Ernzerhof (PBE) and Heyd-Scuseria-Ernzerhof (HSE) functionals for germanium.
• Development and application of a selective semiempirical correction scheme (DFT+α) targeting 4s-like orbitals.
• Validation of DFT+α by comparing its predictions for lattice constants, band gaps, bulk modulus, elastic constants, and phonon frequencies against experimental data and other DFT methods.

Main Results:

• HSE functional improves upon PBE's band gap error but fails to simultaneously reproduce both indirect (Γ-L) and direct (Γ-Γ) band gaps accurately for germanium.
• The PBE functional's underestimation of the energy difference between 4p and 4s orbitals leads to unphysical sp mixing.
• DFT+α successfully corrects the band edge ordering and orbital character, yielding accurate predictions for germanium's structural and electronic properties.

Conclusions:

• Existing DFT functionals have limitations in accurately describing semiconductor properties, even with hybrid functionals.
• The proposed DFT+α method offers a computationally efficient and accurate alternative for predicting bulk properties of semiconductors.
• DFT+α provides a promising approach to overcome common DFT inaccuracies, particularly concerning orbital interactions and band edge characteristics.