Modular Design via Multiple Anion Chemistry of the High Mobility van der Waals Semiconductor Bi4O4SeCl2

Making new van der Waals materials with electronic or magnetic functionality is a chemical design challenge for the development of two-dimensional nanoelectronic and energy conversion devices. We present the synthesis and properties of the van der Waals material Bi4O4SeCl2, which is a 1:1 superlattice of the structural units present in the van der Waals insulator BiOCl and the three-dimensionally connected semiconductor Bi2O2Se. The presence of three anions gives the new structure both the bridging selenide anion sites that connect pairs of Bi2O2 layers in Bi2O2Se and the terminal chloride sites that produce the van der Waals gap in BiOCl. This retains the electronic properties of Bi2O2Se while reducing the dimensionality of the bonding network connecting the Bi2O2Se units to allow exfoliation of Bi4O4SeCl2 to 1.4 nm height. The superlattice structure is stabilized by the configurational entropy of anion disorder across the terminal and bridging sites. The reduction in connective dimensionality with retention of electronic functionality stems from the expanded anion compositional diversity.


Crystal Structure Solution
Single crystals of Bi4O4SeCl2 were mounted in Parabar oil. A suitable crystal was selected and placed on a MiTeGen tip (20 micron) and data were collect via a Rigaku XtaLAB AFC11 (RINC): quarter-chi single diffractometer. The crystal was kept at 100 K during data collection. The crystal was kept at 100 K during data collection. Using Olex2 1 , the structure was solved with the ShelXT 2 structure solution program using Intrinsic Phasing and refined (Supplementary Fig. 4) with the XL refinement package 3 using Least Squares minimisation.
Alert A, B & C found in the checkcif report are due to the strong absorption of Bi in the crystal. Face indexing was attempted, but the crystal proved too small and empirical absorption corrections using spherical harmonics were employed.
The resulting crystal data refinement parameters are summarized in Tables 1-6 below. Figure 4. Thermal ellipsoid plot for the asymmetric unit of Bi4O4SeCl2, as solved using ShelXT. Ellipsoids are drawn at 50%.

Disorder and Entropy Stabilization
In order to calculate the change in enthalpy as a function of disorder parameter x for the reaction (1) in the main text, supercells with Cl/Se defects were created for the VASP calculations. The defect distribution was chosen such that the same number of total defects were present in each slab, thus maintaining an even distribution of charge. Within each slab, the defect sites were chosen at random by a Python algorithm in order to generate a random configuration, consistent with the use of a configurational entropy term that assumes that all local configurations are interchangeable at the temperatures considered. Each supercell was allowed to relax in VASP before the energy was calculated. It is notable that after relaxation, S14 the Bi-Cl bond lengths are slightly longer than the Bi-Se bond lengths in the same layer. For example, for x = 3/8 the Bi-Se and Bi-Cl bond lengths in the Bi2O2Se type slab are 3.22689 Å and 3.37054 Å, respectively, while in the BiOCl type slab they are 2.945 Å and 3.02573 Å respectively. This is expected for these bond chemistries; for example, in BiSeCl, the two anions occupy chemically similar sites with Bi-Cl and Bi-Se bond lengths of 2.910(3) Å and 2.8545(9) Å respectively. The Bi-anion bonds are still overall longer in the Bi2O2Se(Cl) (bridging) slab than in the Bi2O2Cl(Se)2 (terminal) slab, due to the difference in terminal and bridging environments.
Supplementary Figure 6. The configurations of atoms for the supercells used in the calculations as shown in Figure 3 of the main text. Arrangements were chosen such that each layer hosted the same total number of defect sites, with the atoms selected as defect sites chosen at random via a Python algorithm.

S15
In order to understand the effects of the Cl/Se disorder on the electronic structure, electronic structure calculations were performed on the supercell for x = 3/8, as shown in Figure  performed with SCAN + SOC as implemented in VASP. The red lines show the scatter of the electronic states from the supercell, mapped onto the grey lines from the perfectly ordered unit cell. As can be seen, the valence band is smeared, while the bands that form the conduction band minimum (just above 0 eV along the Γ-Z direction) are relatively S16 unchanged. This smearing has the effect of reducing the difference between the indirect and direct band gap.

Computational Details
Unless otherwise stated, calculations of the electronic structures and exfoliation energies of both the bulk solids and the 2D slabs were carried out on fully ordered structures (x = 0). All calculations were performed using periodic, plane-wave based, density functional theory as implemented in VASP 5 . Core electrons were treated using the projector augmented wave approach 6 .
Structural optimization was performed using the meta-GGA functional SCAN+rVV10 7 which includes non-local correlation to better describe van der Waals interactions. A plane-wave cutoff energy of 550 eV was used, and structures optimized until forces fell below 0.01 eV/Å.
Both cell parameters and atomic positions were relaxed for bulk crystal structures, whereas the cell was fixed for slab calculations. The k-point grids used in the calculations are tabulated in Table S7.
The inclusion of spin-orbit coupling with van der Waals functionals is not currently     Figure 9).

Bi2O2Se
BiOCl Bi4O4SeCl  Figure 9. Structural analysis of Bi4O4SeCl2 as compared to its parent systems Bi2O2Se and BiOCl, where X is the Bi2O2 layer thickness, Y is the Se atomic layer thickness, Z is the two Cl atomic layers thickness (see Figure 1). In Bi2O2Se, c = 2X + 2Y; in BiOCl, c = X + Z; in Bi4O4SeCl2, c = 4X + 2Y + 2Z.

Optical Measurements and XPS
Diffuse reflectance measurements were taken on powdered samples of BiOCl, Bi2O2Se and

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The diffuse reflectance data for BiOCl and Bi2O2Se were transformed into Tauc plots in order to determine the indirect band gap, as these materials are previously reported to have indirect gaps of 3.46eV and ~0.8eV respectively 13,14 , as shown in Figure S10. To allow for direct comparison of the experimental XPS data with the calculated DOS, photoionization cross section corrections for individual orbitals were applied. Gaussian broadening of FWHM 0.4 eV was also applied to account for instrumental broadening determined by the full-width half maximum of a polycrystalline silver foil, followed by a further Lorentzian broadening to account for life time of the core holes.

Exfoliation
In order to calculate the binding energy, two methods were used. First, the energy of the (relaxed) slab was compared to that of the bulk material. This energy approaches that of the slab calculations, as shown in Figure 6(a) of the main text. Secondly, the c-axis of the bulk material was elongated by various amounts and the system was allowed to relax and the S29 energy was calculated, in order to investigate the effect on the structure of the layers as they are separated. For BiOCl and Bi4O4SeCl2, the structure of the layer remains intact as the system is elongated, whereas for Bi2O2Se, the layer rearranges and bonds break, as shown in Figure S11. Multiple possible relaxed structures (based on the symmetry of the supercell) were tested for Bi2O2Se to find the one with lowest energy, as shown in Figure S12 below.
The lowest energy structure is consistent with the pattern of surface termination found by and Se are observed, the signal of Cl is too weak to be observed due to its low electron density. d Bi elemental mapping of another selected area, from XPS, along with raw spectra from some noted markers. e Se elemental mapping of another selected area, from XPS, along with raw spectra from some noted markers. As with EDX, the XPS signal of Cl is too weak to be observed.
For the XPS mapping, data were collected on a Kratos Axis Supra instrument using monochromatic Al kα radiation (1486.7 eV). A charge neutralizer was used throughout as the samples were mounted such that they were electrically isolated from the sample bar. The spectra were calibrated to a binding energy of 285.0 eV for the hydrocarbon C 1s peak post acquisition (all samples have adventitious carbon present from atmosphere). The data were processed and analysed using the Kratos ESCApe software and CasaXPS.