Tuning of electronic and optical properties of a predicted silicon allotrope: Hexagonal silicon $h10$-Si

The indirect band gap of the diamondlike silicon does not allow direct travel of electrons between valence band and conduction band edges, which has limited its application and performance in optoelectronic devices. Searching new silicon allotropes with highly tunable or direct band gap becomes more and more urgent with the increasing demand on clean energy. Here, we predict a silicon allotrope, $h10$-Si, which is an indirect-gap semiconductor with a band gap of about 0.96 eV. Furthermore, the electronic and optical properties exhibit a strong dependence on strain. In particular, the indirect band gap of the predicted silicon allotrope can be switched to a direct band gap at a uniaxial tensile strain of about 8% and the light absorption can be tuned continuously in a wide range of photon energy. Besides, the single-layer counterpart of this allotrope is confirmed to be dynamically stable and more stable in energy than silicene, endowing it with potential applications in nanoscale devices.

Figure 1

(a) Side and (b) top views of $h10$-Si. The Si atoms are connected to form 8-Si and 6-Si channels and the two kinds of channels are perpendicularly connected by hexahedral building blocks. The building blocks are represented by orange polyhedrons and two inequivalent Si atoms are labeled by Si1 and Si2, respectively

Figure 2

(a) Energy-volume curves of $h10$-Si and other siliconallotropes. (b) Fractional bond length compression as a function of pressure. (c) $V/V_0$ and fractional axis compression as a functions of pressure. $V_0$ is the equilibrium volume and ${\mathit{a}}_0$ as well as ${\mathit{c}}_0$ are the corresponding equilibrium lattice parameters.

Figure 3

(a) Band structure of pristine $h10$-Si. Several bands significantly affected by uniaxial strain are numbered as band 1, band 2, and band 3 and the individual energy gaps are represented by arrow lines. (b) Brillouin zone (BZ) and the high-symmetry $\mathit{k}$ points. (c) Schematic diagram of uniaxial compressive and tensile strains. (d) Individual energy gaps of $h10$-Si under different strains. ${\mathrm{\Delta }}_1, {\mathrm{\Delta }}_2, {\mathrm{\Delta }}_3$ denote the energy differences between the CBM at $\xi , \mathrm{\Gamma }, \xi$ points and the VBM at K, A, A points, namely, ($\mathrm{K}\leftrightarrow \xi$), ($\mathrm{A}\leftrightarrow \mathrm{\Gamma }$), ($\mathrm{A}\leftrightarrow \xi$), respectively. The dotted line denotes the band gap. (e) The band structures evolution under the uniaxial strains of $0\%, 1.5\%, 6\%$, and $9\%$.

Figure 4

Characteristic charge density and the corresponding planar average along $c$ axis ($z$) direction at ${\xi }_0$ and A points under (a) $0\%$ and (b) $9\%$ strains, respectively. The orbital compositions are written as superscripts.

Figure 5

(a) Optical absorption spectrum (${\varepsilon }_2$) of pristine $h10$-Si without any uniaxial strains as a function of the photon energy with respect to that of $d$-Si and solar spectral irradiance. (b) The continuous shift of the low-energy peak with a wide range of strains from $-3\%$ to $7.5\%$. The chromatic bars on top of spectra indicate the regions of infrared (IR), visible (VIS), and ultraviolet (UV) light.