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).