Defect Complexes and Non-Equilibrium Processes Underlying the P-Type Doping of GaN
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Mg incorporationin electrically inactiveforms. When H is present, all these complexes are passivated, forming direct Ga-H and Mg-H bonds. The calculated vibrational frequencies of these bonds are in the 2000-cm" range and provide an identification for infrared and Raman lines that have remained unexplained.[3] Finally, our analysis yields a testable prediction: For samples that show the vibrational signatures of hydrogenated SI complexes, a pre-anneal in an atmosphere of N and H followed by annealing in a N atmosphere would significantly enhance Mg activation.
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b)
Fig. 1 Schematic representation of some complexes studied in this work: a) MgGa•-N-H complex; b) MgiH 2; c) MgGa-N-Gai-H 2; and d) Mgca-N-Mgi-H. METHOD The calculations were performed in the framework of density functional theory and the local density approximation for exchange and correlation, using ultrasoft pseudopotentials and a
plane-wave basis set[8] The Ga 3d electrons and the Mg 2p electrons were treated as valence electrons. Additional details for the pseudopotentials can be found in Ref. 9. The energy cutoff for the basis set was chosen at 25 Ry after studies showed convergent results. Supercells of 32 atoms where used in general but some key results were tested in a 64 cubic cell to ensure convergence with supercell size. Such supercells were also found to be well converged in similar cases by earlier investigators.[9,10] We used three special k points corresponding to the hexagonal symmetry[ 11] in the wurtzite phase and the {.5,.5,.5 } special k point in the cubic structure. Results for cubic and wurtzite GaN are generally the same (within 0.1 eV) except in some cases where topology matters. Those cases will be discussed explicitly. All atoms in the supercell were relaxed until the force on each atom was less than 0.15 eV/A. The calculation of the H-related normal modes involved a partial dynamical matrix that included the H atoms and their neighbors. The normal modes were calculated in the harmonic approximation. In a second step, the anharmonic corrections for the transition from the ground to the first excited state of the stretch modes were calculated in a standard way[ 12] using the coefficients of the polynomial that fits the energy as a function of the amplitude along the normal mode trajectory. RESULTS Much of the theoretical literature on defects and impurities in GaN has so far focused on formation energies. However, in a compound semiconductor the formation energies of point defects are functions of the chemical potential of one of the host atoms and the Fermi energy. In the
presence of impurities, formation energies of defect complexes are also functions of the impurity chemical potentials. To avoid much of this complexity, we carried out our analysis by examining key sequences of defect reactions that can be studied by using the same supercell containing identical atomic species and excess charges. The resulting reaction energies are more accurate than absolute formation energies of individual defects, especially charged o
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