Lattice dynamics of GaN: Effects of 3d electrons K. Karch and F. Bechstedt Institut fu ¨r Festko ¨rpertheorie und Theoretische Optik, Friedrich-Schiller-Universita ¨t, D-07743 Jena, Germany T. Pletl Institut fu ¨r Theoretische Physik, Universita ¨t Regensburg, D-93040 Regensburg, Germany Received 23 January 1997; revised manuscript received 29 April 1997 We perform first-principles calculations of structural, dielectric, and lattice-dynamical properties of cubic GaN. The equilibrium structure is obtained using the plane-wave pseudopotential approach within the density- functional theory and local-density approximation. The dielectric and vibrational properties are computed within the density-functional perturbation theory. The effect of the Ga 3 d electrons is treated by taking into account the nonlinear core corrections for the exchange and correlation energy. The importance of 3d electrons for the bonding strength is determined, and their influence on the dielectric and dynamical properties of GaN is analyzed and discussed. S0163-18299700231-2 The group-III nitrides AlN, GaN, and InN are regarded as promising wide-band gap semiconductors for optoelectronic applications in the short-wavelength range as well as for high-temperature, high-power, and high-frequency electronic devices. In particular, GaN is a basic material for the real- ization of light-emitting diodes and lasers in the blue and UV range of the spectrum. Under ambient conditions, GaN crystallizes in the wurtzite 2H ) structure. However, in the past few years molecular-beam epitaxy techniques have en- abled the growth of GaN films of zinc-blende 3C ) structure. 1 In the 3 C and 2 H structures each atom of one kind is tetrahedrally surrounded by four atoms of the other kind; both phases have the same nearest-neighbor shell, the first difference occurs with the second neighbors. Therefore, the physical properties of both structures are quite similar, but the zinc-blende nitrides are expected to show improved elec- tronic properties due to the reduced phonon scattering. 2 Moreover, the zinc-blende phase is hoped to be more ame- nable to doping than the wurtzite phase, since all of the III-V compounds which can be efficiently doped are cubic. There- fore, it is meaningful to characterize theoretically the physi- cal properties of 3 C GaN. Despite the technological interest in GaN, little is known about its lattice dynamics from the theoretical point of view. Moreover, phonons are important as elementary excitations for standard characterization of the sample quality by means of first-order Raman spectroscopy. 3–7 Accurate first- principles calculations have been performed only for nonpo- lar zone-center phonons using either a mixed-basis 8 or the linear muffin-tin orbital LMTO method 9,10 within the frozen-phonon approach. A particular problem of first- principles calculations concerns the semicore Ga 3d elec- trons. The Ga 3d shell in GaN is not as inert as in the other Ga compounds and affects both the electronic and structural properties. 11 The breakdown of the frozen-core approxima- tion for the Ga 3 d states is related to the energetical reso- nance of Ga 3d and N 2s levels 11 and the significant overlap of Ga 3d with the Ga 4s and 4p charge density. 12 The com- putational effort for an accurate description of the strongly localized 3d wave functions within the plane-wave pseudo- potential approach is rather extensive. 13 On the other hand, the significant overlap of the Ga 3d electrons with the Ga valence states can be treated within the frozen-core approxi- mation, if the nonlinear core correction NLCC of Louie, Froyen, and Cohen 14 is taken into account. The NLCC both enhances the transferability of pseudopotentials and reduces considerably the computational effort. Wright and Nelson 13 showed that the structural and electronic properties of GaN can be correctly described within the plane-wave pseudopo- tential method and the NLCC approach. Moreover, the NLCC approach of shallow d electrons of group-II atoms has been already successfully applied to the description of the structural as well as of the lattice-dynamical properties of II-VI compounds. 15 In this report we present a first-principles study of the structural properties, i.e., lattice constant a , bulk modulus B 0 , and its pressure derivative B 0 ' , of the dielectric, i.e., Born effective charge Z B and dielectric constant   , and of the lattice-dynamical properties, i.e., the phonon frequencies, of 3C GaN. The ground-state properties are obtained within the local-density approximation LDA by minimizing the static total energy using the Vinet equation of state. 16 For the exchange-correlation potential the parametrization of Perdew and Zunger is used. 17 The Ga and N pseudopoten- tials are generated according to the scheme of Troullier and Martins 18 including the NLCC for the 3d states of Ga. The basic quantities in lattice dynamics, i.e., the harmonic interatomic force constants are computed within density- functional perturbation theory 19 generalized to the framework of NLCC. 15 The plane-wave expansion of the electronic wave functions is limited by an energy cutoff of 60 Ry to ensure the convergence of the phonon frequen- cies to within 3 cm -1 . The Brillouin zone BZ summations are performed using a set of 28 Chadi-Cohen special points. 20 The resulting values of the equilibrium structural param- eters and of the dielectric quantities are reported in Table I. To characterize the accompanying lattice-dynamical proper PHYSICAL REVIEW B 15 AUGUST 1997-I VOLUME 56, NUMBER 7 56 0163-1829/97/567/35604/$10.00 3560 © 1997 The American Physical Society