Strain engineering of antimonene by a first-principles study: Mechanical and electronic properties

Recent success in the experimental isolation and synthesis of highly stable atomically thin antimonene has triggered great interest into examining its potential role in nanoelectronic applications. In this work, we investigate the mechanical and electronic properties of monolayer antimonene in its most stable $\beta$-phase using first-principles calculations. The upper region of its valence band is found to solely consist of lone pair $p$-orbital states, which are by nature more delocalized than the $d$-orbital states in transition metal dichalcogenides, implying superior transport performance of antimonene. The Young's and shear moduli of $\beta$-antimonene are observed to be $\sim 25\%$ higher than those of bulk antimony, while the hexagonal lattice constant of the monolayer reduces significantly ($\sim 5\%$) from that in bulk, indicative of strong interlayer coupling. The ideal tensile test of $\beta$-antimonene under applied uniaxial strain highlights ideal strengths of 6 and 8 GPa, corresponding to critical strains of 15% and 17% in the zigzag and armchair directions, respectively. During the deformation process, the structural integrity of the material is shown to be better preserved, albeit moderately, in the armchair direction. Interestingly, the application of uniaxial strain in the zigzag and armchair directions unveil direction-dependent trends in the electronic band structure. We find that the nature of the band gap remains insensitive to strain in the zigzag direction, while strain in the armchair direction activates an indirect-direct band gap transition at a critical strain of 4%, owing to a band switching mechanism. The curvature of the conduction band minimum increases during the transition, which suggests a lighter effective mass of electrons in the direct-gap configuration than in the free-standing state of equilibrium. The work function of free-standing $\beta$-antimonene is 4.59 eV, and it attains a maximum value of 5.07 eV under an applied biaxial strain of 4%. The findings reported in this work provide fundamental insights into the mechanical behavior and strain-tunable nature of the electronic properties of monolayer $\beta$-antimonene, in support of its promising role for future nanoelectromechanical systems and optoelectronic applications.

Figure 1

The structural configuration of monolayer antimonene in its $\beta$-phase.

Figure 2

(a) The structural configuration of bulk antimony and (b) its directional bulk modulus under hydrostatic pressure, represented on the orthogonal axes B${}_i^{*}$, where B${}_i^{*}$ = B${}_{\mathbf{u}}{l}_i$. The contour lines projected on the translated B${}_i^{*}$B${}_j^{*}$ planes illustrate the directional bulk modulus for the special cases of B${}_k^{*}$ = 0 (i.e., $l_k$ = 0).

Figure 3

(a) A schematic atomic model of monolayer $\beta$-antimonene being subjected to in-plane uniaxial strain in the zigzag and armchair directions (left panel). The stress-strain relationship (right panel), (b) in-plane transverse strain response, and (c) normal strain response for monolayer $\beta$-antimonene under applied uniaxial tensile strain in the zigzag (red line) and armchair (blue line) directions. The dash-dotted lines indicate the fitted values of the elastic constants (see Table 1).

Figure 4

(a) The variation of the structural geometry of monolayer $\beta$-antimonene under applied uniaxial tensile strain in the zigzag (red line) and armchair (blue line) directions. The bond lengths and angles are normalized with respect to their respective equilibrium values calculated in Table 1. (b) A schematic view of the rigid zones (shaded) and dominant structural response (arrows) during uniaxial tensile deformation in the zigzag and armchair directions. Note: (abc) $\equiv$ (xyz).

Figure 5

(a) The electronic band structure of monolayer $\beta$-antimonene in its equilibrium configuration. The bands are calculated at the PBE level of theory (black lines) and corrected to include the effect of SOC (red lines). A separate comparison along the Y-$\mathrm{\Gamma }$ path is also made using the HSE06 functional (blue lines) to obtain a more accurate estimate of the band gap $E_{\mathrm{gap}}$. (b) The planar-averaged potential along the normal direction, where $E_{\mathrm{f}}$ and $E_{\mathrm{vac}}$ are the energy values at the Fermi and vacuum levels, respectively. (c) The total and orbital projected density of states of monolayer $\beta$-antimonene in its equilibrium configuration. The dashed line indicates the Fermi level.

Figure 6

(a) A schematic atomic model of monolayer $\beta$-antimonene being subjected to in-plane biaxial strain in both the zigzag and armchair directions. (b) The electronic band structure of monolayer $\beta$-antimonene under various applied uniaxial (zigzag and armchair) and biaxial strain configurations. (c) The variation of the electronic band gap under applied uniaxial and biaxial tensile strain. (d) The variation of the work function under applied biaxial tensile strain.