Berlin 2005 – scientific programme

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O: Oberflächenphysik

O 28: Methodisches (Exp. und Theorie)

O 28.6: Talk

Saturday, March 5, 2005, 16:15–16:30, TU EB407

The multipole compensation method for slab geometry — •Ferenc Tasnadi — IFW Dresden, ITF Group Numerical Solid State Physics and Simulation

The multipole compensation method developed by M. Weinert¹ to solve the Poisson equation for 3-dimensional periodic crystalline systems is extended for slabs, layer symmetric² structures. Unlike in Ref.¹ the presented method assumes localized (compact support), overlapping original charge distributions as introduced in Ref.³ and non-local (no compact support) Ewald density distributions. The Poisson equation is solved with periodic boundary conditions in the plane and with finite voltage boundary condition in the perpendicular (z) direction. For the K_||≠ 0 case a Fourier transformation helps to calculate the solution in a three dimensional periodic sense. While for the K_||=0 case, the required charge neutrality is the starting point to find the solution. The K_||=0 solution connects the z directional potential step with the surface density of the dipole z component. For both cases suitable representations of the spherical harmonics are needed to arrive at expressions that are convenient for numerical implementation.
¹M.Weinert, J. Math. Phys. 22,11 (1981).
²V. Kopsky and D.B. Litvin, eds., Subperiodic Groups, vol. E of International Tables for Crystallography (Kluwer Academic Publisher, Dordrecht/Boston/London, 2002).
³K. Koepernik and H. Eschrig, Phys. Rev. B. 59, 1743 (1999).