Solving the Phase Problem of Diffraction: X-ray Standing Waves Imaging on Bismuthene/SiC(0001)

TL;DR

Diffraction data lack phase information, limiting direct 3D structural reconstruction. The authors apply Normal Incidence X-ray Standing Wave (NIXSW) imaging to retrieve both amplitudes and phases of Bragg reflections and reconstruct the 3D atomic density within the unit cell via a Fourier sum of complex structure factors $F_{oldsymbol{H}}$. In a graphene-protected Bi intercalation system on 4H-SiC(0001), hydrogenation triggers a Bi adsorption-site switch from $T_4$ hollow to $T_1$ on-top, enabling a honeycomb Bi layer that constitutes 2D bismuthene. This work demonstrates a model-free, element-specific 3D imaging technique for surfaces and 2D heterostructures, linking atomic-scale structural changes to the emergence of a quantum spin Hall insulator phase.

Abstract

The phase retrieval problem is a fundamental shortcoming of all diffraction-based methods, arising from the inability to measure the phase of scattered waves. The (normal incidence) X-ray standing wave (NIXSW) technique circumvents this issue by introducing a (Bragg-generated) X-ray standing wave field throughout the sample, relative to which any atomic species can be localized by probing its fluorescence or photoelectron yield. In essence, in a single measurement the complex scattering factor (i.e., its amplitude \textit{and} phase) corresponding to the used Bragg reflection is determined. Performing this for multiple Bragg reflections enables one to reconstruct the scattering density of the sample in three dimensions, straightforwardly as the Fourier sum of all measured (complex) scattering factors. Here, we utilize this technique to reveal the structural key features involved in the formation of the quantum spin Hall insulator bismuthene on silicon carbide. In this prominent example, the two-dimensional Bi layer is confined between a 4H-SiC substrate crystal and an epitaxial graphene layer. The key finding is a change in the adsorption site of the Bi atoms underneath the graphene upon hydrogenation, caused by the H-saturation of one (out of three) Si dangling bonds per unit cell. This structural change, clearly revealed by our NIXSW imaging experiment, is the key feature leading to the formation of the characteristic band structure of the 2D bismuthene honeycomb.

Figures (5)

• Figure 1: (a,b) and (c,d) Representative XP spectra of C 1s, Si 2s and Bi 4f$_\text{7/2}$ of the phase before, and the bismuthene phase after hydrogenation ( +H), respectively. The spectra were measured at a photon energy $\sim$5eV below the the Bragg energy of the 4H-SiC(0004) reflection ($h\nu_{\text{Bragg}} = \text{\qty{2.4634}{keV}}$). All peaks relevant for the NIXSW analysis are labeled, and further details on the fitting models discussed in the Supplementary Information. (e,f) Corresponding absorption yield curves and typical reflectivity curves of the (0004) reflection for both phases.
• Figure 2: (a) Argand representation of the NIXSW results for the phase (before hydrogenation), obtained for the (0004) reflection. Each data point represents a complex number with modulus $F_\textrm{c}^{\boldsymbol{H}}$ and phase $P_\textrm{c}^{\boldsymbol{H}}$. Individual data points for each species correspond to several measurements on different sample positions, their average is shown as polar vectors with error bars. (b) Corresponding ball-and-stick model illustrating the vertical distances between the relevant species, derived from the coherent positions. (c,d) Same like (a,b), but for the bismuthene phase after hydrogenation. In (d), bismuthene and QFG regions are illustrated in the left and right, respectively.
• Figure 3: Density distribution maps (2D cuts in the (11$\overline{\text{2}}$0) plane) of selected individual Fourier terms for bulk Si. The distributions correspond to single, one-dimensional cosine functions, the amplitudes and phases of which are given by the coherent fractions and positions obtained for the respective Bragg reflection. The period of the cosine corresponds to the Bragg plane spacing. High (low) densities are shown bright (dark).
• Figure 4: Geometric structure of 4H-SiC as determined by NIXSW imaging. In (a) and (b) selected cross-sectional views of the determined atomic distribution for Si and C, respectively, are shown. The main image (bottom right) displays the (1$\overline{\text{2}}$10) plane, whereas the left and top image show cuts in perpendicular directions as indicated by the orange dashed lines. The superimposed ball-and-stick models demonstrate an excellent agreement between the expected atomic positions and the maxima of the determined atomic distribution. In (c) a combined illustration of the maxima from (a) and (b), color coded as red and black for Si and C, is presented. Note that for the lower image, maxima of an additional plane offset by $a/2$ were included, to resemble the typical side view of 4H-SiC often shown in ball-and-stick models.
• Figure 5: Comparison of the Bi adsorbate structure for both phases, as determined by NIXSW imaging. In (a) and (b) the atomic distributions for Bi are shown for the phase and bismuthene, respectively (same cross-sectional views as in \ref{['fig:XSWI_cuts']}(a) and (b)). S2 and S2* terminations of the bulk are indicated by orange dashed lines. In (c) and (d) the combined bulk and surface structure is shown for a S2* terminated surface, with Si, C, and Bi color coded in red, black, and blue, respectively. The change from the $\text{T}_\text{4}$ to the $\text{T}_\text{1}$ adsorption site due to hydrogenation is clearly visible. For the topmost graphene layer no lateral atomic positions can be determined since it is incommensurate with the substrate.