VOLUME 87, NUMBER 20 PHYSICAL REVIEW LETTERS 12 NOVEMBER 2001 Entropy-Driven Stabilization of a Novel Configuration for Acceptor-Hydrogen Complexes in GaN Sukit Limpijumnong,* John E. Northrup, and Chris G. Van de Walle Xerox Palo Alto Research Center, 3333 Coyote Hill Road, Palo Alto, California 94304 (Received 13 July 2001; published 29 October 2001) We present a model for the microscopic structure of Mg-H complexes in GaN, explaining the unusual bond angle observed in recent vibrational spectroscopy studies. The structure is not the lowest-energy configuration at T  0, but it is stabilized at elevated temperatures due to the large entropy associated with a set of low-energy rotational excitations. The rotational excitation spectrum is calculated using a quantum-mechanical model in which the hydrogen atom moves in a weak corrugation potential. Conse- quences for experiment are discussed. DOI: 10.1103/PhysRevLett.87.205505 PACS numbers: 61.72.Bb, 61.72.Vv, 63.20.Pw It is well known that hydrogen can passivate dopants in semiconductors, resulting in the formation of electrically inactive dopant-hydrogen complexes [1]. This process plays a critical role during the growth of acceptor-doped GaN, where incorporation of H results in complete neutral- ization of the acceptors. A post-growth anneal is required to remove H from the vicinity of the acceptors, yielding the desired p-type conductivity. A thorough understand- ing of complex formation and dissociation is deemed es- sential for optimizing the activation process and enhancing the conductivity. Experimentally, vibrational spectroscopy has proven an excellent tool for monitoring the presence of acceptor-hydrogen complexes [2]. Identification of the complex responsible for a particular line, however, is pos- sible only in conjunction with first-principles theory. For instance, the local vibrational mode (LVM) at 3125 cm 21 observed in Mg-doped GaN [3,4] occurs at a much higher frequency than expected for Mg-H bonds. Computations have shown, however, that the hydrogen atom in the Mg-H complex is strongly bonded to a nitrogen neighbor of the Mg atom [see Fig. 1(a)], explaining the high frequency of the observed vibrational mode [5]. Recently, infrared spectroscopy using polarized light produced additional information about the Mg-H complex: Clerjaud et al. [4] found that the electric dipole induced by the vibration (which should roughly correspond to the ori- entation of the N-H bond) formed an angle of 130 ± with the c axis of the GaN wurtzite crystal. This large deviation from the expected angle of 109 ± in the AB N, (antibond- ing) configuration [see Fig. 1(a)] is very puzzling. Our calculations show that a distorted AB N, configuration in which the N-H bond forms an angle of 130 ± with the c axis (as shown in Ref. [4]) is unstable and immediately relaxes back to the regular configuration with u  109 ± . The first goal of this Letter is to propose a new model for the configuration of the Mg-H complex, illustrated in Fig. 1(b): in this structure (which we label OA k ), the N-H bond is not aligned in the same direction as the Mg-N bond [as in Fig. 1(a)]; rather, the Mg-N bond is oriented (roughly) along [0001], and the interaction between H and the Mg atom changes the angle u to approximately 130 ± . Both this angle and the calculated vibrational frequency for this structure (reported below) are in very good agreement with experiment [4]. However, one mystery remains: the calculated total energy of this configuration is higher (by 0.19 eV) than the energy of the AB N, configuration. The magnitude of this energy difference would render experi- mental observation of OA k very unlikely. The second goal of this Letter is to provide an expla- nation for the stabilization of the 130 ± configuration. The relative occupation of the two configurations is determined at high temperatures, where the H atom is sufficiently mo- bile to explore various local minima. The stability of the candidate configurations is thus determined by their free energy. It turns out the 130 ± configuration gives rise to a set of low-energy excitations, which contribute signifi- cantly to the entropy of the complex. At sufficiently high temperatures the entropy term lowers the free energy of the FIG. 1. Schematic representation of atomic positions in the (11-20) plane for a Mg-H complex in wurtzite GaN, with H at the (a) AB N, site and (b) OA k site. Large circles represent Ga atoms, medium circles N atoms, shaded circle the Mg atom, and the small circle the H atom. Dashed circles indicate ideal atomic positions, dashed lines bonds in the ideal lattice. Changes in Mg-N bond lengths are given as a percentage of change from the bulk Ga-N bond lengths. 205505-1 0031-9007 01 87(20) 205505(4)$15.00 © 2001 The American Physical Society 205505-1