LAUSR

In Ref [1], Wu, Zhang, and Pantelides challenged the existing calculation methods of charged defects in crystals using first-principles supercell approaches. They argue that to calculate the formation energy of a charged defect, the added electrons or holes should be kept in the supercell occupying statistically distributed states, so the supercell is neutral. First, we want to point out that in standard supercell calculations of charged defects [2,3], the added electrons or holes are kept in the supercell. The only difference between Ref. [1] and Refs. [2,3] is that, in the latter case, the charge is added to a virtual state with an average energy EF and a plane-wave-like jellium state in the supercell. The added jellium state, which is a good approximation for the delocalized states, is treated the same way as the other eigenstates in the system, i.e., they are included in calculating the total potential and total energy of the system, so the defect formation energy is naturally a linear function of EF. Therefore, the concept proposed in Ref. [1] is similar to that employed in Refs. [2,3]. Second, in Ref. [1], the transition from defect state to the statistically averaged state is further simplified by the conduction band minimum (CBM) state for donors [valence band maximum (VBM) state for acceptors]. However, in current supercell defect calculations (with a couple of hundred or even thousand atoms), such as those used in Ref. [1], the CBM and VBM states do not exist in the defect cell. To demonstrate this, we repeated the calculations of Ref. [1] using the VASP code [4] and analyzed the wave function characters of the states claimed to be the CBM or VBM states in Ref. [1]. As shown in Fig. 1, the results obtained using the same procedure used in Ref. [1] are different from the jellium model calculation. This is because (i) in the calculation of Wu, Zhang, and Pantelides [1], instead of putting the electron (hole) to the CBM (VBM) state, the electrons (holes) are put into a perturbed state Ei that is just above (below) the defect level. So, an error equal to qðEi-ECBMðVBMÞÞ occurred in Ref. [1]. For VSi in Si, after correcting this error, the calculated results become close to those obtained using the jellium model because for VSi in Si, the perturbated states are relatively delocalized [Fig. 1(c)]. However, for VO in ZnO, the difference is still quite large, even with the correction [Fig. 1(b)]. This is because the state just above the defect level (EDþ1) is not the delocalized host CBM state. Instead, it is a defectlike folded-in localized state [Fig. 1(d)]. Hence, the electron transition between the ED and EDþ1 states is not the one from the defect state to the host CBM state, as claimed in Ref. [1]. This explains why the results obtained in Ref. [1] for charged VO are very different from that obtained in the jellium model [Fig. 1(b)]. Therefore, their result is clearly not the one intended to be calculated through the supercell approach.