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Manuscript Title: Fast LEED intensity calculations for surface crystallography using Tensor LEED.
Authors: V. Blum, K. Heinz
Program title: TensErLEED
Catalogue identifier: ADNI_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 134(2001)392
Programming language: Fortran.
Computer: Digital/Compaq Alpha Workstations PWS433au, XP1000, Pentium PC.
Operating system: Compaq Tru64 Unix, Linux.
RAM: 100M words
Word size: 8
Keywords: Electron-solid diffraction, Low energy electron diffraction (LEED), Structure optimization, Surface crystallography, Surface reconstruction, Surface relaxation, Surface structure, Surface segregation, Tensor LEED (TLEED), Solid state physics.
Classification: 7.2, 8.

Nature of problem:
The quantitative analysis of low energy electron diffraction (LEED) intensity vs. energy I(E) spectra is an important tool to obtain surface crystallographic information [1-4]. Direct methods to extract such information from LEED data work in special cases only. One generally resorts to a trial-and-error technique, comparing calculated I(E)-curves for different surface geometries to spectra measured from a real surface in order to retrieve the correct structural parameters by way of a best fit. Since experimental techniques are continuously refined and the complexity of studied systems grows dramatically, a fast means to calculate I(E) spectra for many different surface structures, compare them to experimental data and identify the best fit is a prime necessity of the field. The TensErLEED computer code aims to satisy this need. Examples studied with previous versions of this code include open metal surfaces [5], reconstructed alloy surfaces [6], and complex reconstructions of thin films [7-9] and semiconductor surfaces [10].

Solution method:
Standard full dynamic LEED calculations [11] are used to obtain the electron wave field diffracted from a reference surface. Using the Tensor LEED approximation [12-14], geometrical, vibrational [15] and chemical [16,17] parameters in a large portion of the parameter space around that reference structure are then varied. A search algorithm [18] allows to retrieve the best fit between measured data and calculated spectra reliably for typically 15 or more parameters.

Restrictions:
The surface is required to be periodic in two dimensions. Aspherical atomic scattering can only be included within the Tensor LEED approximation, not in the full dynamic reference calculation.

Running time:
Running times depend very much on the actual problem. Times of 1-10 hours for systems of intermediate complexity including a structure optimization on a 500 MHz Compaq XP1000 workstation may serve as an estimate.

References:
[1] M.A. Van Hove, W.H. Weinberg, and C.-M. Chan, Low Energy Electron Diffraction (Springer, Berlin, 1986).
[2] K. Heinz, Rep. Prog. Phys. 58 (1995) 637.
[3] M.A. Van Hove, Surf. Rev. Lett. 4 (1997) 479.
[4] K. Heinz, L. Hammer, Z. Kristallogr. 213 (1998) 615.
[5] M. Arnold, A. Fahmi, W. Frie, L. Hammer, K. Heinz, J. Phys. C 11 (1999) 1873.
[6] M. Kottcke, H. Graupner, D.M. Zehner, L. Hammer, K. Heinz, Phys. Rev. B 54 (1996) R5275.
[7] S. Muller, P. Bayer, C. Reischl, K. Heinz, B. Feldmann, H. Zillgen, M. Wuttig, Phys. Rev. Lett. 74 (1995) 765.
[8] K. Heinz, P. Bayer, S. Muller, Surf. Rev. Lett. 2 (1995) 89.
[9] A. Seubert, J. Schardt, W. Weiss, U. Starke, K. Heinz, Appl. Phys. Lett. 76 (2000) 727.
[10] U. Starke, J. Schardt, J. Bernhardt, M. Franke, K. Reuter, H. Wedler, K. Heinz, J. Furthmuller, P. Kackell, F. Bechstedt, Phys. Rev. Lett. 80 (1998) 758.
[11] M. A. Van Hove, S.Y. Tong, Surface Crystallography by LEED (Springer, Berlin, 1979).
[12] P.J. Rous, J.B. Pendry, D.K. Saldin, K. Heinz, K. Muller, N. Bickel, Phys. Rev. Lett. 57 (1986) 2951.
[13] P.J. Rous, J.B. Pendry, Surf. Sci. 219 (1989) 355.
[14] P.J. Rous, Prog. Surf. Sci. 39 (1992) 3.
[15] U. Loffler, R. Doll, K. Heinz, J.B. Pendry, Surf. Sci. 301 (1994) 346.
[16] R. Doll, M. Kottcke, K. Heinz, Phys. Rev. B 48 (1993) 1973.
[17] K. Heinz, R. Doll, M. Kottcke, Surf. Rev. Lett. 3 (1996) 1651.
[18] M. Kottcke, K. Heinz, Surf. Sci. 376 (1997) 352.