Revisiting the Formulation of Charged Defect in Solids

Area of Science:

• Solid State Physics
• Materials Science
• Computational Materials Science

Background:

• Defect physics is crucial for understanding microelectronic material properties.
• Accurate calculation of defect formation energies is essential for predicting material behavior.
• Existing methods for calculating defect formation energies often require complex corrections.

Purpose of the Study:

• To re-evaluate and simplify corrections in total energy calculations for defect physics.
• To formulate an accurate expression for quadrupole corrections using linear response theory.
• To demonstrate accurate formation energy calculations for various defects, including those in anisotropic materials.

Main Methods:

• Utilizing total energy calculations with careful tracking of reference energy.
• Applying linear response theory to derive quadrupole corrections.
• Testing the methods on diverse defects, including the 2+ diamond vacancy.

Main Results:

• The "potential alignment" correction in total energy calculations was shown to vanish.
• The classic Makov-Payne correction was confirmed to yield accurate results.
• An accurate expression for the quadrupole correction was formulated.
• Accurate formation energies were obtained for numerous defects in small supercells.
• The slow convergence for the 2+ diamond vacancy was attributed to size-dependent dielectric constants arising from slowly varying gap levels.

Conclusions:

• Refined total energy calculations simplify defect physics.
• The Makov-Payne correction and a new quadrupole correction provide accurate defect formation energies.
• Understanding defect-induced dielectric constant variations is key for convergence in specific cases.