Hyperuniform Monocrystalline Structures by Spinodal Solid-State Dewetting

Marco Salvalaglio, Mohammed Bouabdellaoui, Monica Bollani, Abdennacer Benali, Luc Favre, Jean-Benoit Claude, Jerome Wenger, Pietro de Anna, Francesca Intonti, Axel Voigt, and Marco Abbarchi

Phys. Rev. Lett. 125, 126101 – Published 15 September 2020

Abstract

Materials featuring anomalous suppression of density fluctuations over large length scales are emerging systems known as disordered hyperuniform. The underlying hidden order renders them appealing for several applications, such as light management and topologically protected electronic states. These applications require scalable fabrication, which is hard to achieve with available top-down approaches. Theoretically, it is known that spinodal decomposition can lead to disordered hyperuniform architectures. Spontaneous formation of stable patterns could thus be a viable path for the bottom-up fabrication of these materials. Here, we show that monocrystalline semiconductor-based structures, in particular ${Si}_{1 - x} {Ge}_{x}$ layers deposited on silicon-on-insulator substrates, can undergo spinodal solid-state dewetting featuring correlated disorder with an effective hyperuniform character. Nano- to micrometric sized structures targeting specific morphologies and hyperuniform character can be obtained, proving the generality of the approach and paving the way for technological applications of disordered hyperuniform metamaterials. Phase-field simulations explain the underlying nonlinear dynamics and the physical origin of the emerging patterns.

Received 3 March 2020
Accepted 7 August 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.126101

Physics Subject Headings (PhySH)

Spinodal decomposition Surface instabilities

Disordered systems Random & disordered media

Phase-field modeling

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Marco Salvalaglio ^1,2,*, Mohammed Bouabdellaoui ³, Monica Bollani^4,†, Abdennacer Benali³, Luc Favre³, Jean-Benoit Claude ⁵, Jerome Wenger⁵, Pietro de Anna ⁶, Francesca Intonti⁷, Axel Voigt ^1,2, and Marco Abbarchi ^3,‡

¹Institute of Scientific Computing, TU Dresden, 01062 Dresden, Germany
²Dresden Center for Computational Materials Science (DCMS), TU Dresden, 01062 Dresden, Germany
³Aix Marseille Univ, Université de Toulon, CNRS, IM2NP 13397, Marseille, France
⁴Istituto di Fotonica e Nanotecnologie-Consiglio Nazionale delle Ricerche, Laboratory for Nanostructure Epitaxy and Spintronics on Silicon, Via Anzani 42, 22100 Como, Italy
⁵Aix Marseille Université, CNRS, Centrale Marseille, Institut Fresnel, 13013 Marseille, France
⁶Institut des Sciences de la Terre, University of Lausanne, Lausanne 1015, Switzerland
⁷LENS, University of Florence, Sesto Fiorentino 50019, Italy

^*marco.salvalaglio@tu-dresden.de
^†monica.bollani@ifn.cnr.it
^‡marco.abbarchi@im2np.fr

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Vol. 125, Iss. 12 — 18 September 2020

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Images

Figure 1
Spinodal solid-state dewetting. (a) Scheme of the samples: ultrathin silicon on insulator substrates (14 nm thick Si on 25 nm thick ${SiO}_{2}$ BOX) followed by epitaxial deposition of ${Si}_{1 - x} {Ge}_{x}$ alloys and high-temperature annealing in a MBE. (b) Left panel: transmission electron micrograph (TEM) of a dewetted island. Right panel: high-resolution TEM highlighting the interface between BOX, some pristine UT SOI, and ${Si}_{0.7} {Ge}_{0.3}$ . (c) Scanning electron micrographs (SEM) of 150 nm ${Si}_{0.7} {Ge}_{0.3}$ on UT SOI after 4 h annealing at a nominal temperature of $800 ° C$ (measured with a pyrometer at the center of the sample). Left to right: morphologies observed from the edge to the center of the sample, respectively taken at 150, 500, 920, 1800, and $7500 μ m$ from the sample edge (the latter being unchanged up to the center and starting at $\sim 3 mm$ from the edge). They account for a temperature gradient of about $50 ° C$ and allow to monitor a smooth change in a single experiment.
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Figure 2
Simulations and pattern analysis. (a) Breakup of a perturbed film ( $h = 0.25 ℓ$ , $L = 4 ℓ$ , details on $ℓ$ in the text). (b) Simulated sample for pattern analysis ( $h = 0.5 ℓ$ , $L = 20 ℓ$ ). (c) Analysis by Minkowski functionals [ $m_{1} (\bar{ρ})$ and $m_{2} (\bar{ρ})$ vs $m_{0} (\bar{ρ})$ ] for the pattern of (b) (open squares) and experimental data (filled dots), corresponding to 25 nm Ge deposited on UT SOI and annealed at $470 ° C$ for 45 min. The inset shows a $1 / 10 \times 1 / 10$ portion of the full image (reported in the Supplemental Material, SM [52]). The error bars show the variability of $m_{1} (m_{0})$ and $m_{2} (m_{0})$ with different spinodal-like patterns (not shown). Solid lines correspond to the expected values for a Gaussian random field (GRF) [39].
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Figure 3
Hyperuniformity and tuning of the disorder: (a) Radial spectral density $ψ^{*} (| k |)$ for the pattern of Fig. 2 [ $ψ_{H}^{*} (| k |)$ ] and a numerically generated GRF [ $ψ_{G}^{*} (| k |)$ ], with the inset showing $ψ_{H}^{*} (k_{x}, k_{y})$ . (b) Logarithmic plot of data in panel (a) highlighting the decay of $ψ^{*} (| k |)$ for $| k | \to 0$ . Dashed and dotted lines are the trend of $| k |^{4}$ and $| k |^{6}$ , respectively. (c) AFM images of Ge ( $h = 50 nm$ and 25 nm) deposited on UT SOI and annealed at different temperature. (d) Logarithmic plot of experimental $ψ_{Z}^{*} (| k |)$ for similar samples annealed at different temperature [see panel (c), corresponding large view $40 μ m \times 40 μ m$ AFM images have been used]. (e) Comparison of $ψ_{Z}^{*} (| k |)$ of the patterns in the two last panels of (c).
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