Bandgap engineering in an epitaxial two-dimensional honeycomb Si$_{6-x}$Ge$_x$ alloy

In this Letter, we demonstrate that it is possible to form a two-dimensional (2D) silicene-like Si$_5$Ge compound by replacing the Si atoms occupying on-top sites in the planar-like structure of epitaxial silicene on ZrB$_2$(0001) by deposited Ge atoms. For coverages below 1/6 ML, the Ge deposition gives rise to a Si$_{6-x}$Ge$_{x}$ alloy (with $x$ between 0 and 1) in which the on-top sites are randomly occupied by Si or Ge atoms. The progressive increase of the valence band maximum with $x$ observed experimentally originates from a selective charge transfer from Ge atoms to Si atoms. These achievements provide evidence for the possibility of engineering the bandgap in 2D SiGe alloys in a way that is similar for their bulk counterpart.

Alloying materials with similar structures and miscible elements is of great interest for a wide range of applications as it allows for adjusting various parameters to values which can not be achieved with elemental materials or compounds. This versatility is well exemplified by the engineering of the bandgap of semiconducting alloys which makes possible the fine tuning of the wavelength of solid-state lightings by controlling the alloys composition. With the continuous efforts to scale down the dimension of elementary bricks of electronic devices, the fabrication of low-dimensional alloys, including two-dimensional (2D) materials, became a technologically important challenge [1] as it was for bulk semiconducting materials in the past. Alloying semimetallic graphene, with its isomorphic wide-bandgap analogue h-BN which would have permitted to set the value of the bandgap of a 2D h-BNC alloy in a wide energy range, was however found to be hindered by the low miscibility of the two materials resulting in a phase segregation [2]. In contrast, ternary and quaternary alloys of transition metal dichalcogenide could be synthethized successfully [3][4][5][6][7] and the tunability of the optical bandgap was demonstrated. Among the 2D materials experimentally fabricated, silicene, a 2D honeycomb latttice of Si atoms, has the particularity to allow for continuing scaling down the Si-based nanoelectronics [8]. Thorough efforts were put into evaluating methods for tuning the electronic properties of silicene including doping [9,10], or the adsorbtion of adatoms or molecules [11][12][13]. Alloying free-standing forms of silicene and germanene, its Ge analogue, investigated by first principles calculations [14][15][16] suggested that such 2D hexagonal SiGe alloys are stable and various parameters including the lattice parameter or the spin-orbit gap open in the Dirac cones were found to be tunable with the Si:Ge ratio while the non-triviality of the band structure is preserved.
In this Letter, we report the realization of a 2D SiGe epitaxial alloy fabricated by depositing Ge on silicene on zirconium diboride (ZrB 2 ) films grown on Si(111) [17]. Furthermore, we investigated the possibility of engineering its bandgap in a way similar to bulk SiGe alloys.
Epitaxial silicene sheets were prepared by annealing ZrB 2 thin films epitaxially grown on Si(111) [18,19] in ultrahigh vacuum (UHV). The deposition of Ge on silicene was realized by means of a Knudsen cell implemented in each of the UHV systems used for these experiments. The Ge flux, calibrated in each of these systems by depositing Ge on a Si(111) substrate, was in the 0.09 -0.12 ML.min −1 range (1 monolayer (ML) refer to the density of atoms in epitaxial silicene on ZrB 2 (0001): 1.73 × 10 15 at.cm −2 ). Scanning tunneling microscopy (STM) was performed at room temperature. Photoemission spectroscopy exper-iments were conducted at beamline BU06 of UVSOR. Core-level spectra in normal emission and angle-resolved photoemission spectroscopy (ARPES) spectra were recorded at room temperature and at 20 K, respectively. The respective energy resolutions as estimated from the broadening of the Fermi edge are 35 and 10 meV.
DFT calculations within a generalized gradient approximation (GGA) [20,21] were performed using the OPENMX code [22] based on norm-conserving pseudopotentials generated with multireference energies [21] and optimized pseudoatomic basis functions [22]. The two input structures consist of (2 × 2) ZrB 2 (0001) slabs made of 8 Zr and 7 B layers terminated on both face respectively by silicene or Si 5 Ge layers. A 42Å vacuum space is separating the slabs. For Zr atoms, a s3p2d2 basis function i.e. including three, two, and two optimized radial functions allocated respectively to the s, p, and d orbitals. For Si, Ge and B atoms, s2p2d1 basis functions were adopted. A cutoff radius of 7 Bohr was chosen for all the basis functions. A regular mesh of 220 Ry in real space was used for the numerical integrations and for the solution of the Poisson equation. A (5×5×1) mesh of k points was used. For geometrical optimization, the force on each atom was relaxed to be less than 0.0001 Hartree/Bohr. In order to take into account the strength of translational symmetry breaking, the spectral weight as derived from the imaginary part of the one-particle Kohn-Sham Green function, was unfolded to the Brillouin zone of the "one-Si-atom unit cell" [23] following a method described in Ref. [24].
Silicene crystallises spontaneously on ZrB 2 (0001) in a so called "planar-like" ( [23,25] adopted by several forms of epitaxial silicene [26][27][28]. This structure fits with the (2 × 2) unitcell of ZrB 2 (0001) in such a way that a Si = 2  [18,29] into a single domain in a way similar to the deposition of silicon [30]. However, in contrast to silicon atoms, the deposition of Ge atoms results in a contrast between the protrusions, observed for all scanning conditions, and most visible for a bias voltage of 1.0 V, which suggests that some Ge atoms substituted Si protruding atoms. As this Ge coverage is beyond that required to fully turn the domain structure of silicene into a single-domain (0.03 ML) [30], the excess of atoms results locally in the formation of bilayer silicon islands [31] like the one shown in the inset of Fig. 1.(c).
These islands are rare and distant (few hundreds of nanometers from each others).
The The Fig. 1.(d) presents such a planar-like structure after optimization by DFT, which appears to be essentially similar to that shown in Fig. 1.(a). The main difference is the length of the bonds between atoms of the on-top and bridges sites which increases from 2.37Å to 2.47Å. This distance is longer than that of the Si-Ge bonds measured in bulk SiGe alloys [32] or calculated for 2D hexagonal SiGe alloys [15]. The Ge atom is located 1.74Å above the bottom Si atoms instead of 1.58Å for the on-top Si atom in silicene which confirms that the taller protrusions must be assigned to Ge atoms. Si atoms of the bottom layers were forced to remain in the same plane. In contrast to the slight increase of the equilibrium lattice parameter found for free-standing 2D hexagonal SiGe alloy [15], the planar-like structures of silicene and Si 5 Ge have the same equilibrium lattice parameter of 3.89Å (Fig. 4.(c)), corresponding to a compressive strain of 6.2 % which suggests that any strain-induced effect on evolution of the band structure is negligible.