Electronic structure and hyperfine parameters of substitutional Al and P impurities in silica

The electronic structure of substitutional Al and P impurities in silica is investigated using supercell calculations within the framework of density functional theory (DFT). Evaluation of hyperfine matrices for the magnetic nuclei facilitates comparison to experimental data. It is found that the unpaired spin state of substitutional P is well described by the theory, while the unpaired spin state found for substitutional Al is severely at variance with the experimental data. Cluster calculations using both the DFT and the Hartree-Fock approximation indicate that the problem is not caused by the supercell approach but rather by the residual self-interactions present in the DFT energy functionals. A simple model discussion serves to illustrate why DFT succeeds for P but fails for Al: First, it is argued that DFT self-interactions are larger for holes than for electrons. Second, there is an “asymmetry” between electrons and holes in the electronic states of the silica network: The hole present at the Al impurity goes into a nonbonding O orbital while the extra electron present at the P impurity goes into a P-O antibonding state.