Site Dependence of Electronic Structure of Gd Impurities in GaN
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Site Dependence of Electronic Structure of Gd Impurities in GaN Tawinan Cheiwchanchamnangij, Atchara Punya, and Walter R. L. Lambrecht Department of Physics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH-44106-7079 ABSTRACT Electronic structure calculations are reported for Gd in GaN on Ga as well as on N site and for pairs of Gd on neighboring Ga and N sites, using the full-potential linearized muffin-tin orbital method in the local spin density approximation with Hubbard U corrections (LSDA+U). The energy of formation for the N site is found to be much higher than for the Ga site even after relaxations are included. The GdN configuration is found to be at best metastable (in ZB). In WZ and in the pair configurations, the Gd is found to move toward an interstitial site leaving a nitrogen vacancy behind. The electronic structure of these structures and their magnetic moments are discussed. INTRODUCTION The origin of ferromagnetism in Gd doped GaN [1,2] is still unclear. The role of defects has been highlighted in several experimental studies [3,4] and both Ga vacancies [5-7] and N or O interstitials [8] have been proposed as additional sources of magnetic moment, which moreover are expected to have longer range coupling than isolated substitutional Gd. On the other hand, some degree of clustering of Gd atoms has also been suggested [9]. Analysis of Xray Linear Dichroism (XLD) studies by Ney et al. [10,11] suggested a fraction of Gd (up to 15 %) to reside on N sites or in pairs of Gd atoms on neighboring Ga and N substitutional sites. The electronic and magnetic properties of such Gd pairs have not yet been studied theoretically. Here we present calculations of the energy of formation and electronic structure of Gd on both N and Ga substitutional sites, including their structural relaxation. Nearest neighbor pairs are also investigated. COMPUTATIONAL METHOD We use the full-potential linearized muffin-tin orbital method [12] in the local spin density approximation including Hubbard U corrections, the so-called LSDA+U method [13]. The Gd 4f electrons experience a strong Coulomb interaction which is modeled by the Uf = 9.19 eV and Jf=1.20 eV parameters, taken from previous work on GdN. [14] In addition, a Ud= 6.39 eV parameter is used to describe the small upward shift of the empty Gd-d states introduced to fix the band gap of GdN. Supercells of 64 atoms size in the zincblende structure are used with one Gd placed at a Ga or N site or two Gd atoms at nearest neighbor Ga and N sites. The structures are fully relaxed and the Brillouin zone integrals are carried out with a 2 × 2 × 2 mesh. The wurtzite structure defects are modeled with a cell of 96 atoms and 2 × 2 × 2 k-mesh. A well converged basis set
with two κ values (for the smoothed Hankel envelope function decay parameters) Gd(spdf, spdf), N(spd,spd), Ga(spd,spd) including Gd 5p semicore states as local orbitals and augmentation lmax=5 is used. The Gibbs energy of formation (at zero temperature and pressure) of the defect is calculated as ΔG f
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