Self-Consistent Electronic-Structure Calculations for Interface Geometries
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SELF-CONSISTENT ELECTRONIC-STRUCTURE CALCULATIONS FOR INTERFACE GEOMETRIES Erik C. Sowa* , J. M. MacLaren** , X. -G. Zhangt and A. Gonis t *Department of Chemistry and Materials Science, Lawrence Livermore National Laboratory, Livermore, CA 94551 **Department of Physics, Tulane University, New Orleans, LA 70018 t Center for Computational Sciences, University of Kentucky, Lexington, KY 40506-0045 IDepartment of Chemistry and Materials Science, Lawrence Livermore National Laboratory, Livermore, CA 94551
ABSTRACT We describe a technique for computing self-consistent electronic structures and total energies of planar defects, such as interfaces, which are embedded in an otherwise perfect crystal. As in the Layer Korringa-Kohn-Rostoker approach, the solid is treated as a set of coupled layers of atoms, using Bloch's theorem to take advantage of the two-dimensional periodicity of the individual layers. The layers are coupled using the techniques of the RealSpace Multiple-Scattering Theory, avoiding artificial slab or supercell boundary conditions. A total-energy calculation on a Cu crystal, which has been split apart at a (111) plane, is used to illustrate the method. INTRODUCTION Interfaces strongly affect materials properties. They may either enhance or limit desirable materials characteristics. A basic understanding of structure-property relationships in materials with interfaces is clearly desirable; however, the standard electronic-structure tools of the theoretical solid-state physicist are designed with pure single crystals in mind. The breaking of translational symmetry by the presence of an interface is an important conceptual and technical challenge to the electronic-structure theorist. Bloch's theorem, which reduces the size of the problem from a macroscopic number of atoms to the number of atoms in the unit cell of the crystal, no longer applies. In order to recover translational invariance, an isolated interface may be approximated by a periodic array of repeating slabs of finite thickness, i.e., a supercell; standard reciprocal-space techniques may then be used. If, however, one is interested in an isolated interface, care must be taken to ensure that the results are independent of slab thickness. Large repeat distances parallel to the interface, in combination with slabs thick enough to avoid interference between adjacent interfaces, can result in a unit cell with too many atoms for current techniques using current computers. Approximating the isolated interface with a free cluster of atoms also suffers from slow convergence with respect to size. Neither method uses the natural boundary conditions for a bicrystal. One of the few techniques available which does not assume a perfect crystal from the very beginning is the Green function method, originally developed by Korringa [1] and Kohn and Rostoker [2] (KKR). When cast in the language of multiple-scattering theory (MST), it does not require translational invariance explicitly, although Bloch's theorem may still be used when appropriate. One still has to
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