Revisiting the Formulation of Charged Defects in Solids*

Defects are at the heart of microelectronics. However, calculating their properties has long been challenging due to errors associated with the use of supercell + compensating background charge. Starting with the original work on total energy of periodic system [1] and the recent work on innate vacuum level [2], we show that the popular correction on reference Fermi level amounts to a double counting. Next, we reveal the proper definition of defect charge such that, in a multipole expansion, the third-order quadrupole correction can be unambiguously defined. These allow us classify point defects into 3 categories: (i) those that maintain the bulk electron bonding network, such as a substitutional defect, for which first-order Madelung correction is sufficient, (ii) those, such as an interstitial or vacancy, for which the quadrupole correction is necessary, and (iii) those, such as a vacancy in diamond, for which even supercells of thousands of atoms are not sufficient due to a slow inverse-cell-size dependence of dielectric screening. All things considered, however, even the result of a 64-atom supercell converges to within 90 meV.

*In collaboration with Hanzhi Shang, Zeyu Jiang, Yiyang, Sun, and Damien West and work is supported by the U.S. DOE Grant No. DE-SC0002623.

[1] J. Ihm, A. Zunger, and M. L. Cohen, J. Phys. C 12, 4409 (1979).

[2] D.-H. Choe, D. West, and S. Zhang, Phys. Rev. B 103, 235202 (2021).