Resolving the Metastable Si-XIII Structure through Convergent Theory and Experiment

Abstract

Silicon is the undisputed cornerstone of modern technology, with applications ranging from micro- and opto-electronics to quantum technologies. Recently, the exploration of its allotropes has emerged as a pivotal frontier for engineering materials with tailored optical and electronic functionalities. High-pressure experiments have revealed several metastable silicon phases, among which is Si-XIII. First observed more than 20 years ago, this phase has remained structurally unidentified, representing a significant gap in our understanding of elemental silicon allotropy. In this work, a convergent methodology is employed combining advanced theoretical modeling with experimental characterization to finally resolve the long-standing structural assignment of Si-XIII. Guided by careful experimental observations, a structural model validated through first-principles optimization and systematically tested against multiple experimental signatures is constructed. All the fingerprints of this phase are rationalized by our proposed crystal structure: interplanar spacings, Raman frequencies, thermodynamic stability, and kinetic pathways. These findings provide a crucial missing piece in the high-pressure phase diagram of silicon and demonstrate the power of integrating computational predictions with experimental validation to resolve complex structural problems in materials science.

Figures (5)

• Figure 1: (a) Schematic representation of the experimental procedure employed to identify the crystal structure of the Si-XIII phase. One grain of the SI-XIII phase was selected inside the transformed region in the annealed pit. This grain was observed along multiple zone axis with mutual rotation of specific angles $\alpha$. (b) SAED pattern of the transformed region in the pit (c) Dark Field TEM obtained from the reflection marked by the green circle in (b). The green circle highlights the selected Si-XIII crystal. (d),(e),(f) and (g) SAED patterns acquired from the same crystalline grain, marked by the green circle in (c), across multiple zone axes, with indicated mutual rotation angles. In these experimental patterns, the corresponding plane spacing distance is reported in Å, for the main reflections. The sequence shows the systematic tilting procedure used to map the reciprocal lattice and the very good agreement with the proposed cell structure, as demonstrated by the corresponding simulated SAED (h),(i),(j), and (k), in which the pattern indexing is also reported.
• Figure 2: Raman spectroscopic analysis of silicon phases under nanoindentation and post-annealing. Panel (a) shows the crystal structures of the analyzed phases: dc-Si (orange), R8 (red), BC8 (blue), and Si-XIII (purple). Their formation energies and volumes are reported in panel (b). Fitted experimental polarized Raman spectra acquired in perpendicular configuration of 10 $\mu$m tip indented silicon are shown for (c) as-indented and (d) post-annealed samples. Peak positions, intensities, and widths were treated as free parameters in the fitting procedure. Raman-active mode frequencies for the different phases, as reported in Table \ref{['tab:Raman']}, were used as references. Experimental peaks are represented by Lorentzian functions colored according to the respective crystal structures shown in panel (a). DFT-calculated non-resonant Raman frequencies, shown as vertical lines in panels (c) and (d), have been rigidly shifted upward by 12 cm$^{-1}$ to align the main R8 peak to the experimental one and facilitate comparison across all phases.
• Figure 3: Transition Pathway Network showing the interconnection between the SI-XIII phase and the main known phases of silicon. The nodes of the network represent metastable minima while the edges connecting them represent the transition barrier found by the SS-Dimer method. The two colorbars represent the formation energy $\Delta E$ relative to the Si-XIII phase and the Barrier height for the transition connecting the two nodes. The relative length of the connection is proportional to the energy barriers of the transitions following the Kamada-Kawai representation.
• Figure 4: Minimum Energy Paths as calculated by Solid State Nudged Elastic Band connecting the Si-XIII phase to the main metastable phases of silicon. (a) Energy paths connecting the BC8 and R8 phases to the Si-XIII. (b) Energy paths connecting the Si-XIII phase to the dc and hd phases. The multiple paths found for the Si-XIII to dc transition are colored in shades of blue.
• Figure 5: Analysis of the evolution of the Si-XIII phase before and after a second oven annealing. Fitted experimental polarized Raman spectra in perpendicular scattering geometry of 20 $\mu$m tip indented silicon are shown for a sample after a first stage annealing up to $220^{\circ}\text{C}$ (a) and the same sample after a successive oven annealing up to $250^{\circ}\text{C}$ (b). Peak positions, intensities, and widths were treated as free parameters in the fitting procedure. Raman-active mode frequencies for the different phases, as reported in Table \ref{['tab:Raman']} are used as references. Fitted peaks are represented by Lorentzian functions colored according to the respective crystal structures as in Figure \ref{['fig:Raman10']}. AFM maps for the same pit taken right after the indentaiton (c), after the first stage annealing (d) and after the final oven annealing (e).