Self-regulation of charged defect compensation and formation energy pinning in semiconductors

Current theoretical analyses of defect properties without solving the detailed balance equations often estimate Fermi-level pinning position by omitting free carriers and assume defect concentrations can be always tuned by atomic chemical potentials. This could be misleading in some circumstance. Here we clarify that: (1) Because the Fermi-level pinning is determined not only by defect states but also by free carriers from band-edge states, band-edge states should be treated explicitly in the same footing as the defect states in practice; (2) defect formation energy, thus defect density, could be pinned and independent on atomic chemical potentials due to the entanglement of atomic chemical potentials and Fermi energy, in contrast to the usual expectation that defect formation energy can always be tuned by varying the atomic chemical potentials; and (3) the charged defect compensation behavior, i.e., most of donors are compensated by acceptors or vice versa, is self-regulated when defect formation energies are pinned. The last two phenomena are more dominant in wide-gap semiconductors or when the defect formation energies are small. Using NaCl and CH3NH3PbI3 as examples, we illustrate these unexpected behaviors. Our analysis thus provides new insights that enrich the understanding of the defect physics in semiconductors and insulators.