Designing substrates for silicene and germanene: First-principles calculations

We propose a guideline for exploring substrates that stabilize the monolayer honeycomb structure of silicene and germanene while simultaneously preserving the Dirac states: in addition to having a strong binding energy to the monolayer, a suitable substrate should be a large-gap semiconductor with a proper work function such that the Dirac point lies in the gap and far from the substrate states when their bands align. We illustrate our idea by performing first-principles calculations for silicene and germanene on the Al-terminated (0001) surface of ${\mathrm{Al}}_2{\mathrm{O}}_3$. The overlaid monolayers on Al-terminated ${\mathrm{Al}}_2{\mathrm{O}}_3$(0001) retain the main structural profile of the low-buckled honeycomb structure via a binding energy comparable to the one between silicene and Ag(111). An unfolded band structure derived from the $k$-projection method reveals that a gapped Dirac cone is formed at the K point due to the structural distortion and the interaction with the substrate. The gaps of 0.4 and 0.3 eV, respectively, for the supported silicene and germanene suggest that they may have potential applications in nanoelectronics.

Figure 1

Schematic illustration of the interaction between a semiconducting substrate and a monolayer with Dirac states. $W_{\text{sub}} \left(W_{\text{mono}}\right)$ represents the work function of the substrate (the monolayer). $\mathrm{\Delta }{E}_i$ denote the energy differences between the substrate states and the Dirac point. $V_{\text{int}}$ stands for the interaction between the substrate and the monolayer. VBM and CBM represent the valence-band maximum and conduction-band minimum, respectively.

Figure 2

Structure of $\left(\sqrt{13}\times \sqrt{13}\right)$ silicene on $\left(3\times 3\right)$ Al-terminated ${\mathrm{Al}}_2{\mathrm{O}}_3$(0001). (a) Perspective view and (b) top view of the relaxed S1 structure. Top view of the relaxed (c) S2 and (d) S3 structures. Si atoms are represented by blue, green (buckling away from the substrate), and yellow (buckling towards) balls.

Figure 3

Electronic bands of silicene. (a)–(c) $k$-projected bands in the $\left(1\times 1\right)$ BZ for isolated silicene in the S1, S2, and S3 structures, respectively. (e)–(g) Corresponding bands for supported silicene on Al-terminated ${\mathrm{Al}}_2{\mathrm{O}}_3$(0001). (d) and (h) $k$-projected bands for isolated and supported silicene on O-terminated ${\mathrm{Al}}_2{\mathrm{O}}_3$(0001), respectively. Bands of ideal $\left(1\times 1\right)$ silicene are shown as solid white lines overlaid for comparison. The inset in (a) shows bands about K in the range $\pm 0.04$ Å${}^{-1}$. The Fermi level is set to be zero.

Figure 4

Interaction between silicene and ${\mathrm{Al}}_2{\mathrm{O}}_3$(0001). (a) BZs of silicene/${\mathrm{Al}}_2{\mathrm{O}}_3$(0001), $\left(1\times 1\right)$ silicene, and ${\mathrm{Al}}_2{\mathrm{O}}_3$(0001) shown in green, blue, and red, respectively. ${\mathbf{B}}_{\mathbf{1}}$ and ${\mathbf{B}}_{\mathbf{2}}$ represent the reciprocal-lattice vectors of $\left(1\times 1\right) {\mathrm{Al}}_2{\mathrm{O}}_3$(0001). (b), (c) Band alignment of the isolated silicene and O-terminated and Al-terminated (0001) surfaces of ${\mathrm{Al}}_2{\mathrm{O}}_3$, respectively. In the case of Al-terminated ${\mathrm{Al}}_2{\mathrm{O}}_3$(0001), the isolated systems are obtained from configuration S1. The calculated work functions and the gaps of ${\mathrm{Al}}_2{\mathrm{O}}_3$(0001) are shown. VBM and CBM represent the valence-band maximum and conduction-band minimum, respectively.

Figure 5

DFT calculations of germanene on Au(111) and ${\mathrm{Al}}_2{\mathrm{O}}_3$(0001). (a) Relaxed structure of $\left(3\times 3\right)$ germanene on $\left(\sqrt{19}\times \sqrt{19}\right)$ Au(111). (b) and (c) $k$-projected bands for isolated and supported germanene, respectively. (d)–(f) Corresponding results for $\left(2\times 2\right)$ germanene on $\left(\sqrt{3}\times \sqrt{3}\right) {\mathrm{Al}}_2{\mathrm{O}}_3$(0001). Buckled Ge atoms are shown in green balls.

Figure 6

Band structure with SOC about the K point for germanene/${\mathrm{Al}}_2{\mathrm{O}}_3$(0001). The bands without SOC (in white) are overlaid for comparison.

Figure 7

$k$-projected bands for isolated silicene in the structure calculated for (a) $\left(\sqrt{12}\times \sqrt{12}\right)$ and (b) $\left(\sqrt{13}\times \sqrt{13}\right)$ Ag(111). Bands for ideal silicene are shown as white lines for comparison.