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Coherent X-ray spectroscopy reveals the persistence of island arrangements during layer-by-layer growth

Abstract

Understanding surface dynamics during epitaxial film growth is key to growing high-quality materials with controllable properties. X-ray photon correlation spectroscopy (XPCS) using coherent X-rays opens new opportunities for in situ observation of atomic-scale fluctuation dynamics during crystal growth. Here, we present XPCS measurements of two-dimensional island dynamics during homoepitaxial growth in the layer-by-layer mode. Analysis of the results using two-time correlations reveals a new phenomenon—a memory effect in the arrangement of islands formed on successive crystal layers. Simulations indicate that this persistence in the island arrangements arises from communication between islands on different layers via adatoms. With the worldwide advent of new coherent X-ray sources, the experimental and analysis methods pioneered here will enable broad application of XPCS to observe atomic-scale processes on surfaces.

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Fig. 1: Experimental schematic and diffuse scattering from islands.
Fig. 2: Measured two-time correlations.
Fig. 3: Simulated two-time correlations.
Fig. 4: Correlations of island positions.
Fig. 5: Persistence times of island arrangements.

Data availability

Raw X-ray data were generated at the Advanced Photon Source large-scale facility. The data that support the plots within this paper and other findings of this study are available from the corresponding authors on reasonable request.

References

  1. Song, Y., Chen, X., Dabade, V., Shield, T. W. & James, R. D. Enhanced reversibility and unusual microstructure of a phase-transforming material. Nature 502, 85–88 (2013).

    Article  ADS  Google Scholar 

  2. Ogawa, Y., Ando, D., Sutou, Y. & Koike, J. A lightweight shape-memory magnesium alloy. Science 353, 368–370 (2016).

    Article  ADS  Google Scholar 

  3. Gornostyrev, Yu. N. & Katsnelson, M. I. Misfit stabilized embedded nanoparticles in metallic alloys. Phys. Chem. Chem. Phys. 17, 27249–27257 (2015).

    Article  Google Scholar 

  4. Mikhailov, A. S. & Showalter, K. Control of waves, patterns and turbulence in chemical systems. Phys. Rep. 425, 79–194 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  5. Jiang, F. et al. Spontaneous oscillations and waves during chemical vapor deposition of InN. Phys. Rev. Lett. 101, 086102 (2008).

    Article  ADS  Google Scholar 

  6. McLeod, A. S. et al. Nanotextured phase coexistence in the correlated insulator V2O3. Nat. Phys. 13, 80–86 (2016).

    Article  Google Scholar 

  7. Huang, F.-T. & Cheong, S.-W. Aperiodic topological order in the domain configurations of functional materials. Nat. Rev. Mater. 2, 17004 (2017).

    Article  ADS  Google Scholar 

  8. Shpyrko, O. G. X-ray photon correlation spectroscopy. J. Synchrotron Radiat. 21, 1057–1064 (2014).

    Article  Google Scholar 

  9. Pierce, M. S. et al. Surface X-ray speckles: coherent surface diffraction from Au (001). Phys. Rev. Lett. 103, 165501 (2009).

    Article  ADS  Google Scholar 

  10. Kim, H. et al. Surface dynamics of polymer films. Phys. Rev. Lett. 90, 068302 (2003).

    Article  ADS  Google Scholar 

  11. Ruta, B. et al. Revealing the fast atomic motion of network glasses. Nat. Commun. 5, 3939 (2014).

    Article  Google Scholar 

  12. Roseker, W. et al. Towards ultrafast dynamics with split-pulse X-ray photon correlation spectroscopy at free electron laser sources. Nat. Commun. 9, 1704 (2018).

    Article  ADS  Google Scholar 

  13. Ulbrandt, J. G. et al. Direct measurement of the propagation velocity of defects using coherent X-rays. Nat. Phys. 12, 794–799 (2016).

    Article  Google Scholar 

  14. Pierce, M. S. et al. Quasistatic X-ray speckle metrology of microscopic mag-netic return-point memory. Phys. Rev. Lett. 90, 175502 (2003).

    Article  ADS  Google Scholar 

  15. Sanborn, C., Ludwig, K. F., Rogers, M. C. & Sutton, M. Direct measurement of microstructural avalanches during the martensitic transition of cobalt using coherent X-ray scattering. Phys. Rev. Lett. 107, 015702 (2011).

    Article  ADS  Google Scholar 

  16. Chesnel, K., Nelson, J. A., Kevan, S. D., Carey, M. J. & Fullerton, E. E. Oscillating spatial dependence of domain memory in ferromagnetic films mapped via X-ray speckle correlation. Phys. Rev. B 83, 054436 (2011).

    Article  ADS  Google Scholar 

  17. Chesnel, K., Wilcken, B., Rytting, M., Kevan, S. D. & Fullerton, E. E. Field mapping and temperature dependence of magnetic domain memory induced by exchange couplings. New J. Phys. 15, 023016 (2013).

    Article  ADS  Google Scholar 

  18. Chesnel, K., Safsten, A., Rytting, M. & Fullerton, E. E. Shaping nanoscale magnetic domain memory in exchange-coupled ferromagnets by field cooling. Nat. Commun. 7, 11648 (2016).

    Article  ADS  Google Scholar 

  19. Pierce, M. S. et al. Disorder-induced microscopic magnetic memory. Phys. Rev. Lett. 94, 017202 (2005).

    Article  ADS  Google Scholar 

  20. Gorfman, S. et al. Ferroelectric domain wall dynamics characterized with X-ray photon correlation spectroscopy. Proc. Natl Acad. Sci. USA 115, E6680–E6689 (2018).

    Article  Google Scholar 

  21. Malik, A. et al. Coherent X-ray study of fluctuations during domain coarsening. Phys. Rev. Lett. 81, 5832–5835 (1998).

    Article  ADS  Google Scholar 

  22. Livet, F. et al. Kinetic evolution of unmixing in an AlLi alloy using X-ray intensity fluctuation spectroscopy. Phys. Rev. E 63, 036108 (2001).

    Article  ADS  Google Scholar 

  23. Fluerasu, A., Sutton, M. & Dufresne, E. M. X-ray intensity fluctuation spectroscopy studies on phase-ordering systems. Phys. Rev. Lett. 94, 055501 (2005).

    Article  ADS  Google Scholar 

  24. Kim, Y. Y. et al. Synchrotron X-ray scattering and photon correlation spectroscopy studies on thin film morphology details and structural changes of an amorphous-crystalline brush diblock copolymer. Polymer 105, 472–486 (2016).

    Article  Google Scholar 

  25. Wang, X. D. et al. Free-volume dependent atomic dynamics in beta relaxation pronounced La-based metallic glasses. Acta Mater. 99, 290–296 (2015).

    Article  Google Scholar 

  26. Ruta, B. et al. Hard X-rays as pump and probe of atomic motion in oxide glasses. Sci. Rep. 7, 3962 (2017).

    Article  ADS  Google Scholar 

  27. Bikondoa, O. On the use of two-time correlation functions for X-ray photon correlation spectroscopy data analysis. J. Appl. Crystallogr. 50, 357–368 (2017).

    Article  Google Scholar 

  28. Brown, G., Rikvold, P. A., Sutton, M. & Grant, M. Speckle from phase-ordering systems. Phys. Rev. E 56, 6601 (1997).

    Article  ADS  Google Scholar 

  29. Brown, G., Rikvold, P. A., Sutton, M. & Grant, M. Evolution of speckle during spinodal decomposition. Phys. Rev. E 60, 5151–5162 (1999).

    Article  ADS  Google Scholar 

  30. Neave, J. H., Joyce, B. A., Dobson, P. J. & Norton, N. Dynamics of film growth of GaAs by MBE from RHEED observations. Appl. Phys. A 31, 1–8 (1983).

    Article  ADS  Google Scholar 

  31. Tsao, J. Y. Materials Fundamentals of Molecular Beam Epitaxy (Academic, Cambridge, 1993).

  32. Kaufmann, N. A. K., Lahourcade, L., Hourahine, B., Martin, D. & Grandjean, N. Critical impact of Ehrlich–Schwobel barrier on GaN surface morphology during homoepitaxial growth. J. Cryst. Growth 433, 36–42 (2016).

    Article  ADS  Google Scholar 

  33. DenBaars, S. P. et al. Development of gallium-nitride-based light-emitting diodes (LEDs) and laser diodes for energy-efficient lighting and displays. Acta Mater. 61, 945–951 (2013).

    Article  Google Scholar 

  34. Perret, E. et al. Island dynamics and anisotropy during vapor phase epitaxy of m-plane GaN. Appl. Phys. Lett. 111, 232102 (2017).

    Article  ADS  Google Scholar 

  35. Pierce, M. S. et al. Dynamics of the Au (001) surface in electrolytes: in situ coherent X-ray scattering. Phys. Rev. B 86, 085410 (2012).

    Article  ADS  Google Scholar 

  36. Ju, G. et al. An instrument for in situ coherent X-ray studies of metal–organic vapor phase epitaxy of III-nitrides. Rev. Sci. Instrum. 88, 035113 (2017).

    Article  ADS  Google Scholar 

  37. Xu, D., Zapol, P., Stephenson, G. B. & Thompson, C. Kinetic Monte Carlo simulations of GaN homoepitaxy on c-and m-plane surfaces. J. Chem. Phys. 146, 144702 (2017).

    Article  ADS  Google Scholar 

  38. Martín-García, L. et al. Memory effect and magnetocrystalline anisotropy impact on the surface magnetic domains of magnetite(001). Sci. Rep. 8, 5991 (2018).

    Article  ADS  Google Scholar 

  39. Sinha, S. K., Jiang, Z. & Lurio, L. B. X-ray photon correlation spectroscopy studies of surfaces and thin films. Adv. Mater. 26, 7764–7785 (2014).

    Article  Google Scholar 

  40. Sutton, M., Laaziri, K., Livet, F. & Bley, F. Using coherence to measure two-time correlation functions. Opt. Express 11, 2268–2277 (2003).

    Article  ADS  Google Scholar 

  41. Tersoff, J., Denier van der Gon, A. W. & Tromp, R. M. Critical island size for layer-by-layer growth. Phys. Rev. Lett. 72, 266–269 (1994).

    Article  ADS  Google Scholar 

  42. Castellano, C. & Politi, P. Spatiotemporal distribution of nucleation events during crystal growth. Phys. Rev. Lett. 87, 056102 (2001).

    Article  ADS  Google Scholar 

  43. Ratsch, C. et al. Level-set method for island dynamics in epitaxial growth. Phys. Rev. B 65, 195403 (2002).

    Article  ADS  Google Scholar 

  44. Theis, W. & Tromp, R. M. Nucleation in Si(001) homoepitaxial growth. Phys. Rev. Lett. 76, 2770–2773 (1996).

    Article  ADS  Google Scholar 

  45. Thompson, C. et al. Imaging and alignment of nanoscale 180° stripe domains in ferroelectric thin films. Appl. Phys. Lett. 93, 182901 (2008).

    Article  ADS  Google Scholar 

  46. Mattoni, G. et al. Striped nanoscale phase separation at the metal-insulator transition of heteroepitaxial nickelates. Nat. Commun. 7, 13141 (2016).

    Article  ADS  Google Scholar 

  47. Ravy, S. Homometry in the light of coherent beams. Acta Crystallogr. A 69, 543–548 (2013).

    Article  MathSciNet  Google Scholar 

  48. Hettel, R. DLSR design and plans: an international overview. J. Synchrotron Radiat. 21, 843–855 (2014).

    Article  Google Scholar 

  49. Ju, G. et al. Characterization of the X-ray coherence properties of an undulator beamline at the Advanced Photon Source. J. Synchrotron Radiat. 25, 1036–1047 (2018).

    Article  Google Scholar 

  50. Plimpton, S. et al. Crossing the Mesoscale No-mans Land via Parallel Kinetic Monte Carlo Tech. Rep. SAND20096226 (Sandia National Laboratories, 2009).

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Acknowledgements

We thank M. Sutton for suggesting the smoothing method used in the speckle analysis, and D. Byelov of ASI and R. Woods of the APS Detector Pool for expert assistance with the area detector. Support was provided by the Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering (XPCS measurements and analysis) and Scientific User Facilities (KMC model development). Measurements were carried out at the Advanced Photon Source, a DOE Office of Science user facility operated by Argonne National Laboratory. Computing resources were provided on Blues and Fusion, high-performance computing clusters operated by the Laboratory Computing Resource Center at Argonne National Laboratory.

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G.J., M.J.H., J.A.E, P.H.F., G.B.S., C.T., H.Z. and H.K. developed the pink beam XPCS set-up and carried out the measurements. D.X., P.Z., G.B.S. and C.T. developed and carried out the simulations. G.J. and G.B.S. analysed the results. All coauthors contributed to drafting and editing the manuscript.

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Correspondence to Guangxu Ju or G. Brian Stephenson.

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Ju, G., Xu, D., Highland, M.J. et al. Coherent X-ray spectroscopy reveals the persistence of island arrangements during layer-by-layer growth. Nat. Phys. 15, 589–594 (2019). https://doi.org/10.1038/s41567-019-0448-1

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