The relationship between crystal structure and related material properties is discussed for the common 3C, 6H, 4H, and 2H polytypes of SiC. The theoretical results are derived in the framework of well converged density‐functional calculations within the local‐density approximation and the pseudopotential‐plane‐wave approach. In the case of electronic excitations additionally quasiparticle corrections are included. The lattice‐dynamical properties of the noncubic polytypes are described within a bond‐charge model. We focus our attention on the actual atomic structures, the accompanying lattice vibrations, thermodynamical properties, properties of layered combinations of polytypes, optical spectra, and surface equilibrium structures. On the one hand, the influence of the polytype on the material properties is considered. On the other hand, indications for driving forces of the polytypism are extracted.

The SiC͑111͒-͑333͒ phase was analyzed by scanning tunneling microscopy (STM), low-energy electron diffraction (LEED) holography, density functional theory (DFT), and conventional LEED. A single adatom per unit cell found in STM acts as a beam splitter for the holographic inversion of discrete LEED spot intensities. The resulting 3D image guides the detailed analyses by LEED and DFT which find a Si tetramer on a twisted Si adlayer with cloverlike rings. This twist model with one dangling bond left per unit cell represents a novel ͑n3n͒-reconstruction mechanism of group-IV (111) surfaces. [S0031-9007(97)

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A systematic study of ground-state properties of cubic and hexagonal silicon carbide polytypes (3C-, 6H , 4H-, and -2H-SiC) is reported using well converged density-functional calculations within the local-density approximation and norm-conserving, fully separable, soft, ab initio pseudopotentials. Equilibrium results are obtained for the lattice parameters, atomic positions, bond lengths and angles, cohesive energies, and the bulk modulus. The internal degrees of freedom, i.e. , atomic relaxations, are fully taken into account. The results are discussed in comparison with experimental data. We derive trends with the hexagonality for the molecule volume and the energetic ordering of the polytypes. Driving forces for the polytypism and the atomic relaxations are discussed.

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Some years ago Kleinman and Bylander [Phys. Rev. Lett. 48, 1425] proposed a fully nonlocal form of norm-conserving pseudopotentials. Its application reducesif compared to other ab initio pseudopotentialsthe computational effort to calculate potential matrix elements. However, if the procedure is not applied cautiously, it can destroy important chemical properties of the atoms. In this paper we identify the origin of this problem, and we give a theorem which tells if a "ghost" state occurs below the zero-node state of the atom. We also show how the difficulties can be avoided, i.e. , how reliable, fully nonlocal, norm-conserving pseudopotentials can be obtained. Some years ago Kleinman and Bylander' (KB) proposed a fully nonlocal form of norm-conserving pseudopotentials. Its application reducesif compared to other ab initio pseudopotentialsthe computational efFort to calculate potential matrix elements. Although the suggestion is intriguing, it has not been applied widely. The reason is that the calculated chemical binding of molecules and solids [e.g., GaAs (Ref. 2)] is sometimes described incorrectly. These problems arise, although for atomic calculations the wave functions and the logarithmic derivatives Di(E) and dDt(E)ldE at the reference energies E& and for r ) r, equal those of the all-electron calculations. Here r, defines the range of "pseudoization" of the ionic potential, and it roughly equals the range of the core electrons.In this paper we analyze the properties of the KB Hamiltonian and explain why it may cause unphysical results. In short, the problem is due to the fact that the KB Hamiltonian does not obey the Wronskian theorem, which implies that atomic eigenfunctions are energetically ordered such that (for a given quantum number l) the energies increase with the number of nodes. As this theorem is not valid for the KB Hamiltonian, it can have eigenstates with nodes even below the zero-node state. Or, the zero-node states may be followed directly by an n 2 node state. Both possibilities will usually prevent an application of these potentials for a reliable description of chemical binding. Below we show how this problem can be avoided, so that no diSculties arise in actual calculations.We take selenium as an example. In Fig. 1 the highest occupied eigenstates (4s and 4p) of the all-electron calculation, the corresponding states of the norm-conserving pseudopotential of Bachelet, Hamann, and Schluter (BHS), and the corresponding results of the BHS-based KB potential are displayed. The two pseudopotential calculations give exactly identical wave functions, which for r & r, also equal those of the all-electron calculation. Figure 2 shows the logarithmic derivatives of the s, p, and d states of the three calculations. In the d results of the all-electron calculation we also see the Se 3d level at -2.01 hartrees, which in the pseudopotential calculations is treated as a core state. We see that at the refer-1.0 0.5 -0.5-0.5 0~e 1~~L -0.5-/ I 0.5 I I I I I I I 7 -0.5--1.0 0 r (a.u. ) FIG. 1. The 4s (sol...

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