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

Abdulgaffar Abdurrazaq1,2, Ruggero Lot1,3, Antoine Jay1

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Density functional theory (DFT) calculations for materials properties are improved by a new DFT+α method. This approach accurately predicts germanium

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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.