Fundamental Resolution of Difficulties in the Theory of Charged Point Defects in Semiconductors

A defect’s formation energy is a key theoretical quantity that allows the calculation of equilibrium defect concentrations in solids and aids in the identification of defects that control the properties of materials and device performance, efficiency, and reliability. The theory of formation energies is rigorous only for neutral defects, but the Coulomb potentials of charged defects require additional ad hoc numerical procedures. Here we invoke statistical mechanics to derive a revised theory of charged-defect formation energies, which eliminates the need for ad hoc numerical procedures. Calculations become straightforward and transparent. We present calculations demonstrating the significance of the revised theory for defect formation energies and thermodynamic transition levels.

Figure 1

Formation energies as functions of the supercell size for different charge states. Solid lines are calculations using the present theory (screening by band electrons); dashed lines are calculations using the conventional approach based on a compensating uniform charged background (jellium).

Figure 2

Formation energy of an oxygen vacancy in ZnO under oxygen-poor conditions. The $+2/0$ transition occurs at 1.5 eV above the valence band maximum.