An Efficient Algorithm for Automatic Structure Optimization in X-ray Standing-Wave Experiments

Abstract X-ray standing-wave photoemission experiments involving multilayered samples are emerging as unique probes of the buried interfaces that are ubiquitous in current device and materials research. Such data require for their analysis a structure optimization process comparing experiment to theory that is not straightforward. In this work, we present a new computer program for optimizing the analysis of standing-wave data, called SWOPT, that automates this trial-and-error optimization process. The program includes an algorithm that has been developed for computationally expensive problems: so-called black-box simulation optimizations. It also includes a more efficient version of the Yang X-ray Optics Program (YXRO) [Yang, S.-H., Gray, A.X., Kaiser, A.M., Mun, B.S., Sell, B.C., Kortright, J.B., Fadley, C.S., J. Appl. Phys. 113, 1 (2013)] which is about an order of magnitude faster than the original version. Human interaction is not required during optimization. We tested our optimization algorithm on real and hypothetical problems and show that it finds better solutions significantly faster than a random search approach. The total optimization time ranges, depending on the sample structure, from minutes to a few hours on a modern computer, and can be up to 100x faster than a corresponding manual optimization. These speeds make the SWOPT program a valuable tool for real-time analyses of data during synchrotron experiments.

[1]  G. Materlik,et al.  X‐ray standing waves and x‐ray photoemission measurements in the energy range 2.7–7 keV , 1992 .

[2]  M. L. Ng,et al.  Aqueous solution/metal interfaces investigated in operando by photoelectron spectroscopy. , 2015, Faraday discussions.

[3]  A. Janotti,et al.  Insulating state of ultrathin epitaxial LaNiO{sub 3} thin films detected by hard x-ray photoemission , 2011 .

[4]  Robert Piché,et al.  Mixture surrogate models based on Dempster-Shafer theory for global optimization problems , 2011, J. Glob. Optim..

[5]  F. Salmassi,et al.  Concentration and chemical-state profiles at heterogeneous interfaces with sub-nm accuracy from standing-wave ambient-pressure photoemission , 2014, Nature Communications.

[6]  C. Buess-Herman,et al.  Effect of urea on the stability of ferric oxide hydrosols , 1997 .

[7]  J. Freidman,et al.  Multivariate adaptive regression splines , 1991 .

[8]  H. Ebert,et al.  Element- and momentum- resolved electronic structure of the dilute magnetic semiconductor Ga$_{1-x}$Mn$_x$As , 2018 .

[9]  G. Matheron.  Principles of geostatistics , 1963 .

[10]  D. Vaknin,et al.  Ion distributions at charged aqueous surfaces by near-resonance X-ray spectroscopy. , 2006, Journal of synchrotron radiation.

[11]  Douglas C. Montgomery,et al.  Response Surface Methodology: Process and Product Optimization Using Designed Experiments , 1995 .

[12]  B. Batterman.  Detection of Foreign Atom Sites by Their X-Ray Fluorescence Scattering , 1969 .

[13]  J. Kortright,et al.  Depth-resolved resonant inelastic x-ray scattering at a superconductor/half-metallic-ferromagnet interface through standing wave excitation , 2018, Physical Review B.

[14]  H. Allen,et al.  Cation effects on interfacial water organization of aqueous chloride solutions. I. Monovalent cations: Li+, Na+, K+, and NH4(+). , 2014, The journal of physical chemistry. B.

[15]  J. Kortright,et al.  Making use of x-ray optical effects in photoelectron-, Auger electron-, and x-ray emission spectroscopies: Total reflection, standing-wave excitation, and resonant effects , 2013 .

[16]  G. Mercurio,et al.  Torricelli: A software to determine atomic spatial distributions from normal incidence x-ray standing wave data , 2019, Comput. Phys. Commun..

[17]  Jeffrey B. Kortright,et al.  Standing wave enhanced scattering in multilayer structures , 1987 .

[18]  B. Batterman.  Effect of Dynamical Diffraction in X-Ray Fluorescence Scattering , 1964 .

[19]  P. Fawell,et al.  An in situ FTIR-ATR study of polyacrylate adsorbed onto hematite at high pH and high ionic strength. , 2004, Langmuir : the ACS journal of surfaces and colloids.

[20]  A. Gray,et al.  Standing-Wave and Resonant Soft- and Hard-X-ray Photoelectron Spectroscopy of Oxide Interfaces , 2018 .

[21]  H. Ebert,et al.  Element- and momentum-resolved electronic structure of the dilute magnetic semiconductor manganese doped gallium arsenide , 2018, Nature Communications.

[22]  A. J. Booker,et al.  A rigorous framework for optimization of expensive functions by surrogates , 1998 .

[23]  Energetic, spatial, and momentum character of the electronic structure at a buried interface: The two-dimensional electron gas between two metal oxides , 2015, 1508.01832.

[24]  J. R. Patel,et al.  Solution to the surface registration problem using X-ray standing waves , 1982 .

[25]  M. Powell.  Recent research at Cambridge on radial basis functions , 1999 .

[26]  S. Tear,et al.  A comparison of reliability (R) factors in a LEED structural analysis of the copper (111) surface , 1981 .

[27]  John B. Pendry,et al.  Reliability factors for LEED calculations , 1980 .

[28]  Christine A. Shoemaker,et al.  A Stochastic Radial Basis Function Method for the Global Optimization of Expensive Functions , 2007, INFORMS J. Comput..

[29]  J. Kortright,et al.  Depth-resolved photoemission spectroscopy from surface and buried layers with soft X-ray standing waves , 2000 .

[30]  Christine A. Shoemaker,et al.  SO-I: a surrogate model algorithm for expensive nonlinear integer programming problems including global optimization applications , 2014, J. Glob. Optim..