Figure 5. Theoretical defect energetics in Ca₂ZnN₂, CaZn₂N₂ and CaMg₂N₂.

The formation energies of native point defects as a function of the Fermi level for (a) Ca₂ZnN₂, (b) CaZn₂N₂ and (c) CaMg₂N₂ under N-rich and N-poor chemical potential conditions, corresponding to I–VI indicated in Fig. 2a and Supplementary Fig. 13. The range of the Fermi level is given by the valence band maximum, which is set to zero, and the conduction band minimum. V in defect species denotes vacancies. The subscripts designate defect sites, where i means interstitial sites. The results for two interstitial sites in Ca₂ZnN₂ are shown with solid and broken lines (Supplementary Fig. 14). The charge states of defects, which correspond to the gradients as defined by equation (1) in the Methods section, are described; only the most energetically favourable charge state at a given Fermi level is shown for each defect. Positive and negative charge states mean donor and acceptor behaviour of defects, respectively. The Fermi level at which the favourable charge state changes corresponds to the positions of donor or acceptor levels, which are designated by filled circles; shallow donor or acceptor levels associated with electronic states inheriting host orbital characteristics are designated by open circles. The controllable ranges of the Fermi level, in which carrier compensation by spontaneous formation of native defects is avoidable, are indicated by arrows.