Stochastic models and Monte Carlo simulations of x-ray diffraction from relaxed epitaxial films

• Applicant: Dr. Vladimir Kaganer
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2010 to 2014
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 182722588

• Final Report Year: 2014

Final Report Abstract

Stochastic models for realistic dislocation arrangements in relaxed epitaxial films have been developed and verified by quantitative comparison with the x-ray diffraction experiments on diverse epitaxial systems. Dislocation arrangements and the x-ray diffraction patterns from the following epitaxial systems have been analyzed in collaboration with several experimental groups: misfit dislocations of different types and with different correlations at the interfaces of SiGe/Ge/Si heteroepitaxial multilayers; simultaneously present misfit and threading dislocations in GaN epitaxial films grown by molecular beam and by vapor phase epitaxy; distorted honeycomb structures of misfit dislocations at the interfaces with threefold symmetry, particularly InN/ZnO interface. The Monte Carlo methods have been developed for a direct simulation of the x-ray diffraction patterns from these dislocation structures. Approximate analytical methods have been developed to describe the diffraction profiles. A detailed quantitative comparison of the experimental peak profiles and reciprocal space maps, Monte Carlo simulations, and the analytical approximations has been performed for each epitaxial system. These results allow to propose reliable advanced methods of x-ray analysis of relaxed heteroepitaxial systems. X-ray diffraction from non-periodic films consisting of random layers with different thicknesses has been described in application to the epitaxial sodium bismuth titanate films. The results are applicable to a broad class of epitaxial systems with one-dimensional disorder. The theory of x-ray diffraction peak broadening due to strain fluctuation has been extended to the case of inhomogeneous fluctuations and applied to describe the diffraction peak profiles from self-induced GaN nanowires. The spatial distribution of mean-squared strain in the nanowires has been obtained. A stochastic model explaining the height equilibration in dense nanowire arrays has been proposed and applied to self-induced GaN nanowires. Summarizing, a set of theoretical tools for a comprehensive analytical and numerical description of the x-ray diffraction profiles and reciprocal space maps from various epitaxial systems has been developed and verified in collaboration with several experimental groups.

Publications

• Inhomogeneous strain in GaN nanowires determined from x-ray diffraction peak profiles. Physical Review B 86, 115325 (2012)
  V. M. Kaganer, B. Jenichen, O. Brandt, S. Fernández-Garrido, P. Dogan, L. Geelhaar, and H. Riechert
  
• X-ray diffraction from nonperiodic layered structures with correlations: analytical calculation and experiment on mixed Aurivillius films. Acta Crystallographica A 68, 148–155 (2012)
  V. S. Kopp, V. M. Kaganer, J. Schwarzkopf, F. Waidick, T. Remmele, A. Kwasniewski, and M. Schmidbauer
  
• X-ray diffraction study of plastic relaxation in Ge-rich SiGe virtual substrates. Physical Review B 85, 245311 (2012)
  V. S. Kopp, V. M. Kaganer, G. Capellini, M. De Seta, and P. Zaumseil
  
• Analysis of reciprocal space maps of GaN(0001) films grown by molecular beam epitaxy. Journal of Applied Crystallography 47, 256–263 (2013)
  V. S. Kopp, V. M. Kaganer, B. Jenichen, and O. Brandt
  
• Height self-equilibration during the growth of dense nanowire ensembles: Order emerging from disorder. Applied Physics Letters 103, 133105 (2013)
  K. K. Sabelfeld, V. M. Kaganer, F. Limbach, P. Dogan, O. Brandt, L. Geelhaar, and H. Riechert
  
• Self-regulated radius of spontaneously formed GaN nanowires in molecular beam epitaxy. Nano Letters 13, 3274–3280 (2013)
  S. Fernández-Garrido, V. M. Kaganer, Karl K. Sabelfeld, T. Gotschke, J. Grandal, E. Calleja, L. Geelhaar, and O. Brandt
  
• Strain distributions and diffraction peak profiles from crystals with dislocations. Acta Crystallographica A, Foundations and Advances. Volume 70, Issue 5, September 2014, Pages 457-471
  V. M. Kaganer and K. K. Sabelfeld
  
• X-ray determination of threading dislocation densities in GaN/Al2 O3 (0001) films grown by metalorganic vapor phase epitaxy. Journal of Applied Physics 115, 073507 (2014)
  V. S. Kopp, V. M. Kaganer, M. V. Baidakova, W. V. Lundin, A. E. Nikolaev, E. V. Verkhovtceva, M. A. Yagovkina, and N. Cherkashin
  
• X-ray diffraction from hexagonal dislocation networks. Philosophical Magazine, Volume 94, 2014 - Issue 28, Pages 3247-3258
  V. S. Kopp and V. M. Kaganer