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.
Access optionsAccess options
Subscribe to Journal
Get full journal access for 1 year
only $15.58 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
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.
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).
Ogawa, Y., Ando, D., Sutou, Y. & Koike, J. A lightweight shape-memory magnesium alloy. Science 353, 368–370 (2016).
Gornostyrev, Yu. N. & Katsnelson, M. I. Misfit stabilized embedded nanoparticles in metallic alloys. Phys. Chem. Chem. Phys. 17, 27249–27257 (2015).
Mikhailov, A. S. & Showalter, K. Control of waves, patterns and turbulence in chemical systems. Phys. Rep. 425, 79–194 (2006).
Jiang, F. et al. Spontaneous oscillations and waves during chemical vapor deposition of InN. Phys. Rev. Lett. 101, 086102 (2008).
McLeod, A. S. et al. Nanotextured phase coexistence in the correlated insulator V2O3. Nat. Phys. 13, 80–86 (2016).
Huang, F.-T. & Cheong, S.-W. Aperiodic topological order in the domain configurations of functional materials. Nat. Rev. Mater. 2, 17004 (2017).
Shpyrko, O. G. X-ray photon correlation spectroscopy. J. Synchrotron Radiat. 21, 1057–1064 (2014).
Pierce, M. S. et al. Surface X-ray speckles: coherent surface diffraction from Au (001). Phys. Rev. Lett. 103, 165501 (2009).
Kim, H. et al. Surface dynamics of polymer films. Phys. Rev. Lett. 90, 068302 (2003).
Ruta, B. et al. Revealing the fast atomic motion of network glasses. Nat. Commun. 5, 3939 (2014).
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).
Ulbrandt, J. G. et al. Direct measurement of the propagation velocity of defects using coherent X-rays. Nat. Phys. 12, 794–799 (2016).
Pierce, M. S. et al. Quasistatic X-ray speckle metrology of microscopic mag-netic return-point memory. Phys. Rev. Lett. 90, 175502 (2003).
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).
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).
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).
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).
Pierce, M. S. et al. Disorder-induced microscopic magnetic memory. Phys. Rev. Lett. 94, 017202 (2005).
Gorfman, S. et al. Ferroelectric domain wall dynamics characterized with X-ray photon correlation spectroscopy. Proc. Natl Acad. Sci. USA 115, E6680–E6689 (2018).
Malik, A. et al. Coherent X-ray study of fluctuations during domain coarsening. Phys. Rev. Lett. 81, 5832–5835 (1998).
Livet, F. et al. Kinetic evolution of unmixing in an AlLi alloy using X-ray intensity fluctuation spectroscopy. Phys. Rev. E 63, 036108 (2001).
Fluerasu, A., Sutton, M. & Dufresne, E. M. X-ray intensity fluctuation spectroscopy studies on phase-ordering systems. Phys. Rev. Lett. 94, 055501 (2005).
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).
Wang, X. D. et al. Free-volume dependent atomic dynamics in beta relaxation pronounced La-based metallic glasses. Acta Mater. 99, 290–296 (2015).
Ruta, B. et al. Hard X-rays as pump and probe of atomic motion in oxide glasses. Sci. Rep. 7, 3962 (2017).
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).
Brown, G., Rikvold, P. A., Sutton, M. & Grant, M. Speckle from phase-ordering systems. Phys. Rev. E 56, 6601 (1997).
Brown, G., Rikvold, P. A., Sutton, M. & Grant, M. Evolution of speckle during spinodal decomposition. Phys. Rev. E 60, 5151–5162 (1999).
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).
Tsao, J. Y. Materials Fundamentals of Molecular Beam Epitaxy (Academic, Cambridge, 1993).
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).
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).
Perret, E. et al. Island dynamics and anisotropy during vapor phase epitaxy of m-plane GaN. Appl. Phys. Lett. 111, 232102 (2017).
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).
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).
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).
Martín-García, L. et al. Memory effect and magnetocrystalline anisotropy impact on the surface magnetic domains of magnetite(001). Sci. Rep. 8, 5991 (2018).
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).
Sutton, M., Laaziri, K., Livet, F. & Bley, F. Using coherence to measure two-time correlation functions. Opt. Express 11, 2268–2277 (2003).
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).
Castellano, C. & Politi, P. Spatiotemporal distribution of nucleation events during crystal growth. Phys. Rev. Lett. 87, 056102 (2001).
Ratsch, C. et al. Level-set method for island dynamics in epitaxial growth. Phys. Rev. B 65, 195403 (2002).
Theis, W. & Tromp, R. M. Nucleation in Si(001) homoepitaxial growth. Phys. Rev. Lett. 76, 2770–2773 (1996).
Thompson, C. et al. Imaging and alignment of nanoscale 180° stripe domains in ferroelectric thin films. Appl. Phys. Lett. 93, 182901 (2008).
Mattoni, G. et al. Striped nanoscale phase separation at the metal-insulator transition of heteroepitaxial nickelates. Nat. Commun. 7, 13141 (2016).
Ravy, S. Homometry in the light of coherent beams. Acta Crystallogr. A 69, 543–548 (2013).
Hettel, R. DLSR design and plans: an international overview. J. Synchrotron Radiat. 21, 843–855 (2014).
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).
Plimpton, S. et al. Crossing the Mesoscale No-mans Land via Parallel Kinetic Monte Carlo Tech. Rep. SAND20096226 (Sandia National Laboratories, 2009).
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.
The authors declare no competing interests
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Physical Review B (2019)