Stability, diffusion, and complex formation of beryllium in wurtzite GaN
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Stability, diffusion, and complex formation of beryllium in wurtzite GaN Sukit Limpijumnong, Chris G. Van de Walle, and Jörg Neugebauer1 Xerox PARC, Palo Alto, CA 94304, U.S.A. 1 Fritz-Haber-Institut, Berlin, Germany. ABSTRACT We have studied the properties of Be dopants in GaN using first principles calculations. Substitutional Be on a Ga site acts as an acceptor, but interstitial Be poses a potential problem because of its low formation energy and donor character. We study the diffusion of interstitial Be and find it to be highly anisotropic. We also study the formation of complexes between substitutional and interstitial Be, and between substitutional Be and hydrogen. We have calculated the Be-H vibrational modes to aid in experimental identification of such complexes. INTRODUCTION Acceptor doping of nitride semiconductors still poses serious challenges. Magnesium can be incorporated up to about 1020 cm-3 before a saturation and subsequent decrease of the hole concentration sets in [1]. But Mg has a large ionization energy (210 meV, Ref. [2]), resulting in a low hole concentration at room temperature since only ~1% of Mg are ionized. Previous computational studies that explored various candidate acceptors showed that Be is a viable acceptor due to its high solubility and low ionization energy compared to Mg [3,4]. However, the small size of Be renders incorporation on interstitial sites (Beint, which acts as a donor) almost as favorable as on the substitutional Ga site (BeGa), where Be needs to reside in order to act as an acceptor. In order to assess the consequences of this behavior, we have carried out a comprehensive study of the stability and diffusivity of Be interstitials. In addition, we have examined complex formation, both between BeGa and Beint, and between BeGa and hydrogen; the latter is known to play an important role in p-type doping of GaN. In the next sections, we will briefly discuss the theoretical approach and summarize our main results for stability and diffusivity of Beint. We will then focus on the details of vibrational modes of BeGa-H complexes, which we hope will serve as a signature for probing this complex experimentally. THEORETICAL APPROACH We use density-functional theory (DFT) in the local density approximation and ab initio norm-conserving pseudopotentials, with a plane-wave basis set. The effect of Ga 3d states was included through the “nonlinear core correction” (nlcc), allowing us to use an energy cutoff of 40 Ry. The theoretical lattice constant of bulk GaN is used throughout, in order to avoid any spurious relaxations. We use a supercell geometry, consisting of several primitive unit cells of wurtzite GaN and containing one impurity. 32-, 72-, and 96-atom cells were used in this study. Convergence tests indicate that 96-atom cells yield formation energies converged to better than 0.1 eV. Such large supercells are computationally very demanding. In order to be able to perform calculations for a large number of configurations, particularly in the course of mapping out total-ene
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