Elsevier

Materials Research Bulletin

Volume 98, February 2018, Pages 206-212
Materials Research Bulletin

Prediction of perovskite and other ternary oxide multilayers as mirrors for soft X-rays

https://doi.org/10.1016/j.materresbull.2017.10.018Get rights and content

Highlights

  • Theoretical framework to identify optimal multilayers for high x-ray reflectivity.

  • Perovskite oxide multilayers are proposed as soft x-ray mirrors.

  • High soft x-ray reflectivity up to 33% are expected in perovskite multilayers.

Abstract

We propose multilayers of perovskite and related ternary oxides with a general formula of ABO3 as high reflectivity mirrors, especially for use in water window region (2.3–4.4 nm). The high reflectivity combinations of oxide multilayers were deduced using evolutionary search algorithms such as genetic algorithms, and the calculation speed was accelerated via parallel computing methods We also propose a figure of merit for X-ray reflectivity in periodic multilayers systems, which can simplify the future efforts on identifying material combinations, and the search through this multi-dimensional parameter space. The highest reflectivity value was found to be over 33% at 3.1 nm in the water window region. The effect of interface roughness was simulated and the decrease in reflectivity was found to be modest for practically achievable roughness values. This work establishes the foundation for future experimental and theoretical studies towards achieving high reflectivity x-ray mirrors of complex oxide multilayers.

Introduction

X-ray mirrors are widely used in biological imaging [1], next generation lithography [2], atto-second spectroscopy [3], [4], X-ray telescopes [5], [6], [7] etc. Biological imaging using X-rays provides several advantages such as operation in ambient conditions, wide range of excitation conditions (energy, incident photon flux), high spatial resolution, and the ability to deduce wide range of structural and chemical information using element specific excitations [8]. Particularly, imaging and spectroscopy in the K absorption edges of carbon and oxygen encompassing the X-ray wavelength of 2.3 nm–4.4 nm, also known as water window region, is ideal to study a wide range of biological systems [9]. Despite these obvious advantages, the development of X-ray optics in this wavelength regime for a full-fledged microscope has remained challenging.

Section snippets

Background

As the refractive index contrast between all the elements, and hence, the materials are small, multilayers of materials, with large index mismatch, are required to create constructive interference between many reflections to achieve sizeable reflectivity. To this end, the absorption edges of elements in the desired wavelength of operation is used to maximize the index mismatch between layers [6], [10], [11]. In the past, metallic multilayers have been successfully used as X-ray condenser

Methods

The interaction between electromagnetic radiation and matter is dictated by the complex refractive index n = 1  δ + . Within the X-ray region, the real part of the refractive index is close to unity for most materials and air, and the imaginary part is vanishingly small, except at the absorption edge, as noted earlier. This causes very weak reflections of X-ray at the air/material or any material/material interface under most wavelength and incidence angles. This problem can be solved by employing

Results and discussions

Following the analysis procedure described above, we identified the figure of merit function (ϕ) for a pair of ternary oxides with the potential for high maximum x-ray reflectivity as ϕ=|δ1δ2|(β1+β2)Z2Z1λ, where δ1 and δ2 are the real part of refractive index, β1 and β2 are the imaginary part of refractive index, Z1 and Z2 are atomic weights for the two materials respectively, and λ is the incident wavelength. The figure of merit and the calculated maximum X-ray reflectivity for 30 candidate

Conclusion

In conclusion, we have proposed perovskite and related ternary oxide multilayers for high reflectivity X-ray mirrors in the water window region. We have used evolutionary search methods to establish a figure of merit for obtaining ternary oxide material combinations and their relevant multilayer parameters to achieve high X-ray reflectivity. The reflectivity values were obtained by solving the Fresnel’s equation in an iterative manner. Based on this procedure, we have identified ScVO3/NdCoO3

Acknowledgements

The authors gratefully acknowledge the technical contributions of Jamshid Kavosi and Shiyang Zhang during the early stages of this project. This work was supported by the startup grant from USC Viterbi School of Engineering. The authors acknowledge partial support from Air Force Office of Scientific Research (AFOSR) under grant number FA9550-16-1-0335. Computational infrastructure for the work described in this paper was supported by the University of Southern California’s Center for

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