PHYSICAL REVIEW B VOLUME 50, NUMBER 23 15 DECEMBER 1994-I Ab initio calculation of structural and lattice-dynamical properties of silicon carbide K. Karch, ' P. Pavone, W. Mindi, O. Schutt, and D. Strauch Theoretische Physih, Universitat Regensburg, D 9M-$0 Regensburg, Germany (Received 11 April 1994; revised manuscript received 8 August 1994) The plane-wave pseudopotential approach to density-functional theory (DFT) in the local-density approximation has been applied to investigate a variety of ground-state properties of the 3C, 2H, and 4H polytypes of silicon carbide. The linear-response theory within DFT has been used to obtain lattice-dynamical properties of cubic Sic such as the phonon-dispersion curves, phonon eigenvectors, elastic and Griineisen constants, as well as the thermal expansion coefFicient and specific heat within the quasiharmonic approximation. Finally, we present some results for phonon-dispersion curves in the hexagonal 2K (wurtzite) and 4K structure. These results are analyzed and discussed in view of further applications to temperature-dependent properties. I. INTRODUCTION Silicon carbide (SiC) is considered to be a promising material for electronic and optical devices due to its out- standing mechanical, chemical, thermal, and electronic properties. Microelectronic devices made of SiC can be used in high-power, high-speed, high-temperature, high- &equency, and even hard-radiation applications. ~'2 Yet, before a wide use of SiC in the production of electronic devices can be possible, a series of technological problems has to be solved, such as the growing of monocrystalline large-size and high-quality SiC samples or the doping with donors and acceptors. The overcoming of these tech- nological problems requires a deep understanding of the physical properties peculiar to SiC. Furthermore, SiC is the only IV-IV compound which occurs not only in cubic (3C) but also in complex, long-range ordered hexagonal (nH) and rhombohedral (mR) structures. However, to date SiC has not been the subject of the same thorough theoretical and experimental investigations as, e.g. , the group-IV crystals or the III-V semiconductors. In recent years, 6rst-principles investigations of the structural and electronic properties of SiC have been per- formed by many groups. Further studies went deep into the high-pressure behavior6' and the eEects of atomic relaxation on structural properties ' of SiC. Some attempts to explain the phenomenon of the poly- typism of SiC have also been undertaken. However, up to now only a few ab initio calculations of the lattice- dynamical properties of SiC are available. ' Moreover, the thermal properties of SiC have not yet been investi- gated &om 6rst principles. Since the electronic energies of the diferent phases of SiC are very close, inclusion of the phonon contri- butions to the &ee energy may become important and in this case these contributions must be calculated reli- ably. Thus the purpose of this work is a study of lattice- dynamical and therxnal properties of some of the diferent phases of SiC, which need the structural properties as a prerequisite. Therefore, we have investigated various ground-state properties of the 3C, 2H, and 4H poly- types of SiC. We have calculated the equilibrium lattice parameters, the bulk modulus, the pressure derivative of the bulk modulus, the Born e6'ective charges, and the high-&equency dielectric tensor. For cubic SiC, we have also calculated phonon-dispersion curves, phonon eigen- vectors, elastic constants, and the internal-strain param- eter. Concerning the hexagonal 2H and 4H phases, we have determined the phonon-dispersion curves along se- lected high-symmetry directions and the I' point &equen- cies, respectively. Finally, we have evaluated the mode Gruneisen parameters, the thermal expansion coeKcient, and the specific heat at constant volume and at constant pressure of 3C SiC within the &amework of the quasi- harmonic approximation. The results for all calculated quantities are in excellent agreement with the available experimental data. The structure of the paper is the following: After this introduction a short outline of the theory and a brief de- scription of the investigated physical quantities are given in Sec. II. In Sec. III the results of our calculation are presented and compared with the available experimental data. Finally, the conclusions are summarized in Sec. IV. II. THEORETICAL FRAMEWORK A. Method The plane-wave pseudopotential total-energy scheme within the local-density approximation (LDA) of the density-functional theory is used to obtain the energy differences between the various structural phases of SiC. For the exchange and correlation energy the Perdew and Zunger parametrization is used. The evaluation of in- tegrals over the irreducible wedge of the Brillouin zone (BZ) has been performed using sets of Chadi-Cohen spe- cial points. Soft norm-conserving pseudopotentials for carbon and silicon have been generated using the method proposed by Troullier and Martins. 8 DiHerent potentials 0163-1S29/94/50{23)/17054(10}/$06.00 50 Qc 1994 The American Physical Society