Computations of RHEED intensities for growing surfaces of GaAs

Computations of RHEED intensities for growing surfaces of GaAs

Zbigniew Mitura

AGH University of Science and Technology,al. A. Mickiewicza 30, 30-059 Kraków, Poland.

DOI:

https://doi.org/10.7494/cmms.2015.4.0550

Abstract:

A novel and practical algorithm for the determination of intensities in reflection high-energy electron diffraction (RHEED) for off-symmetry azimuths is presented. The usefulness of the algorithm is demonstrated for calculations of rocking curves for GaAs. Then the problem of RHEED oscillations that appear during regular growth of nanolayers is discussed. A calculated plot of the oscillation phase is compared with experimental data taken from the literature. Only the unreconstructed surface of GaAs is considered in this analysis, however, even for such a simplified case, the plot of the theoretical phase reproduces the experimental results reasonably well.

Cite as:

Mitura, Z. (2015). Computations of RHEED intensities for growing surfaces of GaAs. Computer Methods in Materials Science, 15(4), 447-458. https://doi.org/10.7494/cmms.2015.4.0550

Article (PDF):

Keywords:

Dynamical diffraction theory, Nanolayers, RHEED intensity oscillations

Publication dates:

Received: 08.08.2015, accepted: 15.12.2015, published:

Publication type:

Original scientific paper

References:

Benenson, W., Harris, J.W., Stocker H., Lutz, H., eds., 2002, Handbook of Physics, Springer-Verlag, New York.

Bojarski, Z., Gigla, M., Stróż, K., Surowiec, M., 2014, Krystalografia, third edition, PWN, Warsaw (in Polish).

Braun, W., Däweritz, L., Ploog, K.H., 1998, New model for reflection high-energy electron diffraction intensity os- cillations, J. Vac. Sci. Technol. B, 16, 2404-2412.

Castaño, F.J., Stobiecki, T., Gibbs, M.R.J., Czapkiewicz, M., Kopcewicz, M., Gacem, V., Speakman, J., Cowlam, N., Blythe, H.J., 1997, Structural and magnetic properties of amorphous Fe/Zr multilayers, J. Phys.: Condens. Matter, 9, 10603-10614.

Chapra, S. C., Canale, R.P., 2010, Numerical Methods for Engineers, sixth edition, McGraw–Hill, New York.

Crook, G. E., Eyink, K. G., Campbell, A. C., Hinson, D. R.,

Streetman, B. G. (1989), Effects of Kikuchi scattering on reflection high-energy electron diffraction intensities during molecular-beam epitaxy GaAs growth, J. Vac. Sci. Technol. A, 7, 2549-2553.

Cullity, B.D., 1978, Elements of X-Ray Diffraction, second edition, Addison-Wesley, Reading.

Dabrowska-Szata, M., 2004, RHEED study of reconstructed GaAs(001) surfaces, eds. Morawiec, H., Stróż, D., Applied Crystallography, Proceedings of XIX Conference, World Scientific, Singapore, 316-319.

Doyle, P.A., Turner, P.S., 1968, Relativistic Hartree-Fock X-ray and electron scattering factors, Acta Cryst. A, 24, 390- 397.

Herman, M.A., Sitter, H., 1996, Molecular Beam Epitaxy: Fundamentals and Current Status, second edition, Springer- Verlag, Berlin.

Holmes, D.M., Sudijono, J.L., McConville, C.F., Jones, T.S.,

Joyce, B.A., 1997, Direct evidence for the step density model in the initial stages of the layer-by-layer homoepitaxial growth of GaAs(111)A, Surface Sci., 370, L173- L178.

Ichimiya, A., 1987, RHEED intensity analysis of Si(111)7×7 at one-beam condition, Surface Sci., 192, L893-L898.

Ichimiya, A., 1991, One-beam RHEED for surface structure analysis, eds., Tong, S.Y., Van Hove, M.A., Takayanagi, K., Xie, X.D., The Structures of Surfaces III, Springer– Verlag, Berlin, 162-167.

Ichimiya, A., 1992, Reflection high-energy positron diffraction (RHEPD), Solid State Phenomena, 28-29, 143-148.

Ichimiya, A., Cohen, P.I., 2004, Reflection High Energy Electron Diffraction, Cambridge University Press, Cambridge.

Inumaru, K., Ohara, T., Yamanaka, S., 2000, Pulsed laser depo- sition of epitaxial titanium nitride on MgO(001) monitored by RHEED oscillation, Appl. Surface Sci., 158, 375-377.

Kohmoto, S., Mizuno, S., Ichimiya, A., 1989, RHEED intensity analysis of Li/Si(111) structures, Appl. Surface Sci., 41- 42, 107-111.

Maksym, P.A., 2001, Investigation of iterative RHEED calculations, Surface Sci., 493, 1-14.

Maksym, P.A., Korte, U., McCoy, M., Gotsis, H.J., 1998, Calculation of RHEED intensities for imperfect surfaces, Surf. Rev. Lett., 5, 873-880.

McCoy, J.M., Korte, U., Maksym, P.A., Meyer-Ehmsen, G., 1992, Analysis of RHEED data from the GaAs(001)2×4 surface, Surface Sci., 261, 29-47.

Mitura, Z., 1999a, Iterative method of calculating reflection- high-energy-electron-diffraction intensities, Phys. Rev. B, 59, 4642-4645.

Mitura, Z., 1999b, RHEED from epitaxially grown thin films, Surf. Rev. and Lett., 6, 497-516.

Mitura, Z. Dudarev, S.L., Whelan, M.J., 1998, Phase of RHEED oscillations, Phys. Rev. B, 57, 6309-6312.

Mitura, Z., Dudarev, S.L., Whelan, M.J., 1999, Interpretation of reflection high-energy electron diffraction oscillation phase, J. Cryst. Growth, 198/199, 905-910.

Mitura, Z., 2013, Computer studies on reflection high-energy electron diffraction from the growing surface of Ge(001), J. Appl. Cryst., 46, 1024-1030.

Mitura, Z., 2015, Theoretical analysis of reflection high-energy electron diffraction (RHEED) and reflection high-energy positron diffraction (RHEPD) intensity oscillations expected for the perfect layer-by-layer growth, Acta Cryst. A, 71, 513-518.

Mitura, Z., Dudarev, S.L., 2015, Algorithms for determining the phase of RHEED oscillations, J. Appl. Cryst., 48, 1927- 1934.

Ohtake, A., 2008, Surface reconstructions on GaAs(001), Surface Sci. Rep., 63, 295-327.

Ohtake, A., Ozeki, M., Yasuda, T., Hanada T., 2002, Atomic structure of the GaAs(001)-(2×4) surface under As flux, Phys. Rev. B, 65, 165315.

Olligs, D., Bürgler, D.E., Wang, Y.G., Kentzinger, E., Rücker, U., Schreiber, R., Brückel, Th., Grünberg, P., 2002, Roughness-induced enhancement of giant magnetoresistance in epitaxial Fe/Cr/Fe(001) trilayers, Europhys. Lett., 59, 458-464 .

Peng, L.-M., Whelan, M.J., 1990, Dynamical RHEED from MBE growing surfaces, Surface Sci., 238, L446-L452.

Peng, L.-M. , Dudarev, S.L., Whelan, M.J., 2004, High-Energy Electron Diffraction and Microscopy, Oxford University Press, Oxford.

Pukite, P.R., Cohen, P.I., Batra, S., 1988, The contribution of atomic steps to reflection high energy electron diffrac- tion from semiconductor surfaces, eds, Larsen, P.K.,

Dobson, P.J., Reflection High Energy Electron Diffrac- tion and Reflection Electron Imaging of Surfaces, Plenum Press, New York, 427-447.

Radi, G., 1970, Complex lattice potentials in electron diffraction calculated for a number of crystals, Acta Cryst. A, 26, 41-56.

Reid, J.S., 1983, Debye-Waller factors of zinc-blende-structure materials – a lattice dynamical comparison, Acta Cryst. A, 39, 1-13.

Sadowski, J., Dłużewski, P., Kret, S., Janik, E., Łusakowska, E.,

Kanski, J., Presz, A., Terki, F., Charar, S., Tang, D., 2007, GaAs:Mn nanowires grown by molecular beam epitaxy of (Ga,Mn)As at MnAs segregation conditions, Nano Letters, 7, 2724-2728.

Schowalter, M., Rosenauer, A., Titantah, J.T., Lamoen, D., 2009, Computation and parametrization of the temperature dependence of Debye–Waller factors for group IV, III–V and II–VI semiconductors, Acta Cryst. A, 65, 5- 17.

Zhao, T.C., Poon, H.C., Tong, S.Y., 1988, Invariant-embedding R-matrix scheme for reflection high-energy electron dif- fraction, Phys. Rev. B, 38, 1172-1182.

Zhang, J., Neave, J.H., Dobson, P.J., Joyce, B.A., 1987, Effects C N of diffraction conditions and processes on RHEED intensity oscillations during the MBE growth of GaAs, C Appl. Phys. A, 42, 317-326.