First principles study of silicene symmetrically and asymmetrically functionalized with halogen atoms

Abstract

Using first principles calculations with the hybrid exchange–correlation functional, we systematically investigated the structural and electronic properties of silicene symmetrically and asymmetrically (Janus) decorated with halogen elements. The calculations show that all the functionalized systems are direct-band-gap semiconductors. Even more remarkable, by carefully selecting the adsorption adatoms on silicene and applying elastic tensile strain, a direct-band-gap semiconductor with any value between 0.98 and 2.13 eV can be obtained. The formation energies indicate that all the silicene derivatives should be formed experimentally. The present study suggests a rather practical way for gap opening and modulation of silicene.

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1 Introduction

Silicene is a two-dimensional (2D) graphene-like material that has been synthesized in the laboratory recently.^1–3 Similar to graphene, silicene is gifted with many fascinating characters, such as the presence of Dirac cone, quantum spin Hall effect and ultrahigh mobility.^4–8 These properties make silicene very suitable for electronic applications.^9,10 Indeed, the successful application of silicene will be favorable news considering the silicon-based modern semiconductor industry. However, silicene has a small intrinsic electronic band gap of only 1.55 meV,¹¹ which considerably impedes its use in several applications. For example, conventional field effect transistor (FET) requires semiconducting channels with a sizeable band gap to achieve a high on/off ratio.¹² Moreover, for the development of 2D-semiconductor-based optoelectronic devices, particularly to response photons with long wave-lengths, such as red-light-emitting diodes (LEDs) and photodetectors, a direct band gap of less than 3 eV is essential. Accordingly, for the requirement of most applications in nanodevices such as electronics and optoelectronics, a tunable direct band gap must be opened in silicene.

The most conventional way to open a band gap is applying uniaxial strain,¹³ external electric field¹⁴ and interlayer interaction,^15,16 but the band gaps reported in literature^13–15 are still too small for many applications. Alternatively, fabricating silicene nanoribbon^17,18 can open a band gap, but it is very difficult to control the width precisely and edge structure of the nanoribbon during fabrication. It is generally believed that chemical functionalization is an efficient method to tune the electronic and magnetic properties of 2D materials. For instance, the fully hydrogenated silicene exhibits nonmagnetic semiconducting properties, while half-hydrogenation on one side induces ferromagnetic semiconducting properties.^19,20 Moreover, many investigations predicted that chemical functionalized 2D materials can be excellent candidates for large-gap quantum spin Hall insulators.^21–27 In particular, chemical functionalization is also an efficient method to open a band gap for several 2D materials. For example, the adsorption of hydrogen on graphene (graphane) turned semimetal into insulators,²⁸ which has been verified experimentally.²⁹ Similarly, another fully saturated graphene derivative is fully fluorinated graphene (fluorographene), which has been realized by numerous groups.^30–34 Experimental measurements have shown that fluorographene is an insulator (resistivity > 10¹² Ω) with a band gap greater than 3.0 eV (from optical spectra).³² The photoluminescence spectra of fluorographene also confirms that it is an insulator with a band gap of 3.8 eV.³³ Intrigued by the interesting electronic properties found in graphene derivatives shown above, chemical functionalizations have also been used to tailor the electronic properties of silicene. Among the different functionalization strategies, halogenations are attracting increasing attention. Several studies have investigated the electronic structures of symmetrically functionalized monolayer silicene sheets.^35,36 These silicene derivatives always show a moderate band gap with a small carrier effective mass, which suggests that chemical functionalization is a very effective way to open a band gap in silicene.

Materials that comprise two types of radicals are named after the mythological Roman god of gates, Janus. Most Janus materials exhibit unique properties and have stimulated people to investigate and fabricate various Janus nanostructures. For example, Li et al.³⁷ studied the band gap modulation of Janus graphene monolayer by interlayer hydrogen bonding and the external electric field. Zhang et al.³⁸ presented the first experimental realisation of nonsymmetrically modified single-layer graphene—Janus graphene. Bissett et al.³⁹ presented the effects of covalent functionalisation on the Raman spectrum in terms of monofacial (one-sided) and bifacial (two-sided) functionalisation using both monolayer and bilayer graphene. The intensive studies of Janus graphene inspired us to address an interesting question whether we can efficiently tailor the electronic properties of the silicene layer using Janus functionalization. Very recently, calculations on Janus functionalized silicene with radicals and organic groups proved to be very effective to open a band gap in silicene.⁴⁰ However, the investigation of asymmetrically (Janus) functionalized monolayer silicene sheets with different halogen atoms is still absent.

To address this issue, in this study, we aim to investigate the electronic properties of Janus silicene, the silicene decorated with halogen elements on the opposite faces, by first principles calculations. We only consider the so-called ‘chair’ geometry for simplicity like previous work.⁴¹ We explore the influence of elastic strain on the gap. The reason for the band gap varying under strain was also investigated. These results would provide a new route to tune the electronic properties of silicene toward novel 2D electronic and optoelectronic devices.

2 Computational details

In this research, first-principles calculations were performed using the Vienna ab initio simulation package (VASP),⁴² which is based on the DFT in a plane-wave basis set with the projector-augmented wave (PAW) method.⁴³ The exchange–correlation functional was approximated by spin-restricted generalized gradient approximation of Perdew–Burke–Ernzerhof (GGA-PBE) functional⁴⁴ to optimize the structures and obtain the initial electronic structures. The DFT-D2 method of Grimme⁴⁵ was considered for all simulations. We employed the valence electron configurations as 3s²3p², 2s²2p⁵, 3s²3p⁵, 4s²4p⁵ and 5s²5p⁵ for Si, F, Cl, Br and I, respectively. The energy cutoff for plane-wave expansion was set to 550 eV. For the silicene unit cell, the first Brillouin zone (BZ) sampling was done using a 25 × 25 × 1 and 41 × 41 × 1 Monkhorst–Pack⁴⁶ k-points grid for relax and static calculations, respectively. The convergence with respect to the number of k-points in BZ was carefully tested. The tetrahedron methodology with Blöchl corrections⁴⁷ was employed for all the calculations, except for the band calculations, which employed the Gaussian smearing methodology⁴⁸ with a smearing of 0.05 eV. All the results presented herein were obtained by adopting primitive cells. A large vacuum space of 20 Å was placed to avoid the interaction between adjacent images. All the structures were fully relaxed using the conjugated gradient method until the Hellmann–Feynman force on each atom was less than 0.001 eV Å⁻¹.

The Heyd–Scuseria–Ernzerhof (HSE06) hybrid functional⁴⁹ is useful for accurately describing the electronic structure of periodic systems. Very recently, Bianco et al.⁵⁰ predicted the band gap of germanane to be 1.53 eV using the HSE06 functional, which is in excellent agreement with the diffuse reflectance absorption measurement. In addition, previous studies also showed that the geometry is insensitive to the functional choice.⁵¹ Consequently, in the present study, we chose the PBE functional to obtain the best parameters for each system and PBE as well as HSE06 functional to obtain the electronic structure information. The mixing parameter of 0.25 and a screening parameter of 0.2 Å⁻¹ were set for the Hartree–Fock exchange.

3 Results and discussion

3.1 Symmetrically functionalized silicene

First, we investigated the geometric and electronic structure of symmetrically functionalized silicene (denoted as Si₂X₂). As shown in Fig. 1(a), for Si₂X₂ systems (X = F, Cl, Br and I), halogen adatoms adsorbed on each Si atom were placed alternatively above or below the Si atoms. Structural parameters, such as the formation energies (E^f), Si–Si–Si angle (Ф_Si) and X–Si–X angle (Ф_X), lattice constants (a), buckling height between two Si plane (Δ), Si–Si bond length (l_Si–Si), Si–X bond length (l_Si–X), band gap by PBE and HSE06 functionals are given in Table 1.

Fig. 1 Schematic illustrating the crystal structure of (a) Si₂X₂ and (b) Si₂XY (Janus) systems. The blue, red and green balls represent Si, X and Y (X = F, Cl, Br and I; Y = F, Cl, Br, I and ≠ X) atoms, respectively.

Table 1 Geometrical and electronic structure data for all systems studied. The formation energies (eV per atom), Si–Si–Si angle (deg), X–Si–Y angle (deg), lattice constants (Å), buckling height between two Si planes (Å), Si–Si, Si–X and Si–Y bond lengths (Å), band gap (eV) by PBE and HSE06 are given

Si2XY	E^f	ФSi	ФX	a	Δ	lSi–Si	lSi–X	lSi–Y	Gap (PBE)	Gap (HSE06)
Si2F2	−2.10	111.48	107.38	3.92	0.71	2.37	1.63	—	0.64	1.57
Si2Cl2	−1.14	110.81	108.09	3.89	0.73	2.36	2.07	—	1.27	2.13
Si2Br2	−0.98	111.21	107.67	3.91	0.72	2.37	2.24	—	1.29	2.07
Si2I2	−0.75	111.29	106.48	4.00	0.68	2.41	2.46	—	0.67	1.47
Si2FCl	−1.62	111.11	107.77	3.90	0.72	2.36	1.63	2.07	0.97	1.86
Si2FBr	−1.54	111.33	107.54	3.91	0.71	2.37	1.63	2.24	0.95	1.83
Si2FI	−1.43	112.07	106.72	3.97	0.69	2.39	1.63	2.46	0.65	1.48
Si2ClBr	−1.06	111.99	107.91	3.90	0.73	2.37	2.07	2.24	1.24	2.10
Si2ClI	−0.94	111.73	107.10	3.96	0.70	2.39	2.08	2.46	0.86	1.69
Si2BrI	−0.86	111.83	107.00	3.96	0.70	2.39	2.24	2.46	0.87	1.69

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The formation energy E^f for per atom in Table 1 was calculated using the following equation:

where E_total, E_silicene and E_X2 are the total energies of halogenated silicene, silicene and singlet halogen molecule, respectively.

A study of graphene derivatives involving Group IA or Group VIIA elements was done by Klintenberg, et al.⁴¹ They predicted that the C₂F₂ system has a negative E^f, whereas C₂Cl₂, C₂Br₂ and C₂I₂ systems have positive values, which indicate the latter three systems are difficult to be synthesized. To date, only fully fluorinated graphene derivatives have been reported.⁵² However, in our study, all Si₂X₂ systems should be formed experimentally because they all have negative formation energies, as can be seen from Table 1. Note that our results of E^f for Si₂X₂ systems are in excellent agreement with those described in a recent study performed by Zhang, et al.³⁶

Stability is vitally important for the application of 2D materials. To verify the stability of Si₂X₂ systems, phonon calculations were performed and are shown in Fig. 2. No imaginary frequencies are found except for the Si₂I₂ system, whereas negative frequencies appear at the Γ points. Furthermore, these results for phonon calculations are consistent with previous results.³⁶

Fig. 2 Phonon dispersion relations of (a) Si₂F₂, (b) Si₂Cl₂, (c) Si₂Br₂ and (d) Si₂I₂ systems.

We now turn to investigate the geometric properties of Si₂X₂ systems. The Ф_Si for Si₂F₂, Si₂Cl₂, Si₂Br₂ and Si₂I₂ systems are 111.48°, 110.81°, 111.21° and 111.29°, respectively. The Ф_X for Si₂F₂, Si₂Cl₂, Si₂Br₂ and Si₂I₂ systems are 107.38°, 108.09°, 107.67° and 106.48°, respectively. For one extreme limit, where all the bonds are sp² hybridized, the Ф_Si and Ф_X are 120° and 90°, respectively. For another extreme limit, where all the bonds are sp³ hybridized, both Ф_Si and Ф_X are 109.5°.⁴¹ The Ф_Si and Ф_X for Si₂X₂ systems indicate a mix of sp² and sp³ hybridization.

The lattice constants are 3.92, 3.89, 3.91 and 4.00 Å for Si₂F₂, Si₂Cl₂, Si₂Br₂ and Si₂I₂ systems, respectively. Compared with pristine silicene (a = 3.87 Å, computed at the same level), these lattice constants are found to increase. Moreover, these systems also addressed a more buckled structure (Δ = 0.71, 0.73, 0.72 and 0.68 Å for Si₂F₂, Si₂Cl₂, Si₂Br₂ and Si₂I₂ systems, respectively) than silicene (Δ = 0.44 Å). The Si–Si bond lengths in Si₂F₂, Si₂Cl₂, Si₂Br₂, and Si₂I₂ systems are 2.37, 2.36, 2.37 and 2.41 Å, respectively. The Si–X bond lengths in Si₂F₂, Si₂Cl₂, Si₂Br₂ and Si₂I₂ systems are 1.63, 2.07, 2.24 and 2.46 Å, respectively. The Si–Si and Si–X bond lengths are found to increase monotonically with periodic number. Our results are consistent with previous reports,^36,53 which validates the accuracy of our calculations. It should also be noted that the results of Gao et al. are different because of the different functional used in their calculations.³⁵

The band gaps of Si₂X₂ systems calculated using PBE and HSE06 functional are listed in Table 1. The gap of Si₂F₂, Si₂Cl₂, Si₂Br₂ and Si₂I₂ systems are 0.64 (1.57), 1.27 (2.13), 1.29 (2.07) and 0.67 eV (1.47 eV) by the PBE (HSE06) functional. The results in the present study agree well with previous literature. For example, these values by the PBE functional are in agreement with ref. 36, and the value of Si₂F₂ system by the HSE06 functional is also in excellent agreement with ref. 40, although the values of all Si₂X₂ systems by the HSE06 functional are slightly larger than those obtained by the sX-LDA functional.³⁵

The band structures of Si₂X₂ systems calculated using the PBE functional are shown in Fig. 3. For all the systems, both the valence band maximum (VBM) and conduction band minimum (CBM) are located at the Γ point in BZ, hence they are all direct band gap semiconductors. We also investigated the band structures of Si₂X₂ systems using the HSE06 functional (see Fig. 3). The HSE06 functional yields a larger gap and a comparable profile of the band structure, which demonstrates the necessity of hybrid functional calculations.

Fig. 3 Calculated electronic band structures along the Γ → M → K → Γ direction (left) and partial charge densities of the CBM (right upper) and VBM (right lower) for (a) Si₂F₂, (b) Si₂Cl₂, (c) Si₂Br₂ and (d) Si₂I₂ systems by both PBE (blue solid line) and HSE06 (green solid line) functionals. The zero energy value corresponds to the Fermi level and the isosurface value was set to 0.0015 e Å⁻³. The blue, orange, green, brown, and violet balls represent Si, F, Cl, Br, and I atoms, respectively.

3.2 Asymmetrically (Janus) functionalized silicene

Next, we investigated the geometric and electronic structure of asymmetrically (Janus) functionalized silicene (denoted as Si₂XY). The model of Si₂XY systems (X = F, Cl, Br and I; Y = F, Cl, Br, I and ≠ X) are shown in Fig. 1(b). The formation energies (E^f), Si–Si–Si angle (Ф_Si), X–Si–Y angle (Ф_X), lattice constants (a), buckling height between two Si planes (Δ), Si–Si (l_Si–Si), Si–X (l_Si–X) and Si–Y (l_Si–Y) bond lengths and band gap by PBE and by HSE06 functionals are given in Table 1.

The formation energy E^f for per atom in Table 1 is calculated using the following equation:

where E_total, E_silicene, E_X2 and E_Y2 are the total energies of halogenated silicene, silicene, singlet halogen X₂ and Y₂ molecule. It can be seen from Table 1 that all Si₂XY systems have negative formation energies; this means that exothermic reactions and all the systems should be formed experimentally. Note that the formation energy of the Si₂XY system also always lies between the formation energy of Si₂X₂ and Si₂Y₂.

The phonon dispersion relations of the Si₂XY systems were calculated to verify the stability, as shown in Fig. 4. Among these systems, no evident imaginary frequencies were found in Si₂FCl, Si₂FBr, Si₂ClBr, and Si₂ClI systems, indicating good stability. For Si₂FI and Si₂BrI systems, small negative frequencies appear at the Γ points suggesting a less stable structure.

Fig. 4 Phonon dispersion relations of (a) Si₂FCl, (b) Si₂FBr, (c) Si₂FI, (d) Si₂ClBr, (e) Si₂ClI and (f) Si₂BrI systems.

The Ф_Si of Si₂FCl, Si₂FBr, Si₂FI, Si₂ClBr, Si₂ClI and Si₂BrI systems are 111.11°, 111.33°, 112.07°, 111.99°, 111.73° and 111.83°, respectively. In addition, the Ф_X of Si₂FCl, Si₂FBr, Si₂FI, Si₂ClBr, Si₂ClI and Si₂BrI systems are 107.77°, 107.54°, 106.72°, 107.91°, 107.10° and 107.00°, respectively. Again, we found a mix of sp² and sp³ hybridization in Si₂XY systems.

It is interesting to find that the lattice constant of the Si₂XY system always lies between the lattice constants of Si₂X₂ and Si₂Y₂, just like the case of the formation energy. For example, the lattice constant of the Si₂BrI (3.96 Å) system is larger than that in Si₂Br₂ (3.91 Å) system but smaller than that in Si₂I₂ (4.00 Å) system. It is even more promising to tailor the properties if other properties, particularly the band gap, have a similar trend.

Next, we investigated the electronic structure of the asymmetrically functionalized silicene. The band gap calculated by both PBE and HSE06 functionals are given in Table 1. The gaps ranged from 0.65 (1.48) to 1.24 eV (2.10 eV) by the PBE (HSE06) functional. The band gap of Si₂XY is always between the Si₂X₂ and Si₂Y₂ systems. For example, for the Si₂FCl system, the gap (0.97 eV in PBE and 1.86 eV in HSE06) is between Si₂F₂ (0.64 eV within PBE and 1.57 eV within HSE06) and Si₂Cl₂ (1.27 eV within PBE and 2.13 eV within HSE06) systems. This rule is also suitable for other Janus systems.

The band structures of Si₂XY systems calculated using the PBE functional are shown in Fig. 5. Like Si₂X₂ systems, for all the Si₂XY systems, both the valence band maximum (VBM) and conduction band minimum (CBM) are located at the Γ point in BZ, indicating that they are all direct band gap semiconductors. We also investigated the band structures of Si₂XY systems using the HSE06 functional as implemented in the VASP software package (see Fig. 5). Again, the HSE06 functional predicted a significantly larger band gap and a comparable profile of the band structure.

Fig. 5 Calculated electronic band structures along the Γ → M → K → Γ direction (left) and partial charge densities of the CBM (right upper) and VBM (right lower) for (a) Si₂FCl, (b) Si₂FBr, (c) Si₂FI, (d) Si₂ClBr, (e) Si₂ClI and (f) Si₂BrI systems by both PBE (blue solid line) and HSE06 (green solid line) functionals. The zero energy value corresponds to the Fermi level and the isosurface value is set to be 0.0015 e Å⁻³. The blue, orange, green, brown and violet balls represent Si, F, Cl, Br and I atoms, respectively.

The above results suggest that asymmetrical functionalisations are effective in opening the band gap. This fact, together with the observation that the band gap of the Si₂XY system always lies between the band gap of Si₂X₂ and Si₂Y₂, leads to an expectation that the gap of an Janus silicene system is determined by the influence of X and Y elements. If we assume that the gap values of these Si₂XY systems by HSE06 functional are accurate, or at least close to their real values, the gap of these silicene derivatives appears comparable to conventional semiconductor devices. As shown in Table 1, the gap values of Si₂ClI (1.69 eV) are close to bulk GaAs (1.5 eV), which can be used as a channel material of field effect transistors (FETs). In addition, the gap values for Si₂FCl, Si₂FBr and Si₂ClBr are 1.86, 1.83 and 2.10 eV, respectively. Moreover, they are all direct band gap semiconductors, which is vital for optoelectronic applications. Thus, Si₂FCl and Si₂FBr can have potential applications in red-light-emitting diodes, whereas Si₂ClBr have potential applications in orange-light-emitting diodes.

As discussed above, we examined two cases of functionalisation: saturated silicene with one type of adatom and two types of adatoms. However, the doubt was whether we could even go further using not only two types of adatoms but three or even four. For example, if we alloyed Si₂FBr with 50% I (100% F on one side, 50% Br and 50% I on the other side, see Fig. 6(a)), could this system also exhibit direct semiconducting behavior? We calculated the band structure of the Si₂FBr_0.5I_0.5 system by PBE functional (see Fig. 6(b)). It is also a direct band gap semiconductor, and a gap of 0.78 eV by PBE functional is obtained. Interestingly, we found that the band gap of Si₂FBr_0.5I_0.5 system also lies between the band gap of Si₂FBr (0.95 eV) and Si₂FI (0.65 eV) system (see inset in Fig. 6(b)). We also computed the band structures of Si₂FBr_0.25I_0.75 and Si₂FBr_0.75I_0.25 systems. The direct gap of 0.91 and 0.74 eV by the PBE functional for Si₂FBr_0.25I_0.75 and Si₂FBr_0.75I_0.25 systems are obtained, respectively. Thus, the band gaps of these systems also lay between the band gap of the Si₂FBr and Si₂FI system. This rule is also solid for the other Si₂XY_xZ_1−x systems, such as Si₂FCl_0.5Br_0.5 system. Therefore, the desired value for the direct band gap from 1.57 to 2.13 eV can be achieved in silicene by carefully alloying different adsorption adatoms on two sides, which has the evident technical merit of using silicene in electronic devices.

Fig. 6 (a) Schematic of alloying Si₂FBr with 50% I atoms. The blue, orange, brown and violet balls represent Si, F, Br and I atoms, respectively. (b) Calculated electronic band structures along the Γ → M → K → Γ direction for the Si₂FBr_0.5I_0.5 system by PBE functional. The zero energy value corresponds to the Fermi level. Inset: relation between the band gap in Si₂FBr, Si₂FBr_0.5I_0.5 and Si₂FI systems.

3.3 Strain engineering

Elastic strain is a powerful tool that can turn the band gap in a continuous way⁵⁴ and has been realized experimentally.⁵⁵ Generally, 2D materials have always been addressed with superior mechanical properties. In particular, silicane, the full hydrogenated silicene, possesses great mechanical flexibility and can bear a large biaxial tensile strain up to 24%.⁵⁶ A previous study also predicted the Poisson's ratio of the Si₂F₂, Si₂Cl₂, Si₂Br₂ and Si₂I₂ systems are 0.22, 0.23, 0.25, and 0.24, respectively, indicating the potential of Si₂X₂ systems as flexible electronics.³⁶ Therefore, we examined the effects of biaxial tensile strain up to a magnitude of +10% on the electronic properties of Si₂X₂ and Si₂XY systems afterward. Fig. 7 shows the band gaps of Si₂X₂ and Si₂XY systems as a function of the biaxial tensile strain. Note that only the results for stable structure are presented here. With increasing tensile strain, the band gap of Si₂X₂ and Si₂XY systems decreased monotonically (see Fig. 7(a) and (b)). This trend is very similar to the case of single and bilayer germanane because Li et al.⁵⁴ demonstrated that the band gaps of monolayer and bilayer germanane decrease with increasing biaxial tensile strain up to 12% and 9%, respectively. More interestingly, unlike the case of the MoS₂ monolayer,^57–59 all the systems in our study, the tensile strain does not result in a direct–indirect band gap transition. This is vital for their potential applications in optoelectronics. The GGA method may underestimate the value of the band gap. We also computed the band gaps of Si₂X₂ and Si₂XY systems as a function of the biaxial tensile strain using the HSE06 functional (see Fig. 7(c) and (d)). Indeed, the GGA method may underestimate the band gap. However, the general trend should be solid. Moreover, we found that the direct band gap of the Si₂X₂ and Si₂XY systems can vary from 0.98 to 2.13 eV. Therefore, combining the asymmetrically functionalisation with biaxial tensile strain, the band gap of halogenated silicene can be tuned in a relatively wide range, increasing the tenability for their potential application in both nanoelectronics and optoelectronics.

Fig. 7 Variation of the band gap with respect to strain: computed using PBE functional for the (a) Si₂X₂ and (b) Si₂XY systems and computed using HSE06 functional for the (c) Si₂X₂ and (d) Si₂XY systems.

We further investigated the reason for the varying band gap. We calculated the conduction band minimum (CBM) and valence band maximum (VBM) for all the systems. As shown in the right panel of the Fig. 3 and 5, for all the systems, the CBM of Si₂X₂ and Si₂XY systems is mainly an anti-bonding state of Si sp orbitals, whereas the VBM is a mix of Si p orbitals and X (Y) p orbitals. The effects of biaxial tensile strain on CBM are considerable. As the Si–Si bond length increases, the anti-bonding interaction is weakened, which results in the downward shift of CBM. In addition, the effect of the biaxial tensile strain on VBM is vanishingly small. Overall, the downward shift of CBM results in a decrease in band gap.

4 Conclusions

In conclusion, we systematically investigated the geometric and electronic properties of silicene symmetrically and asymmetrically (Janus) functionalized with halogen atoms in this paper, which may be of great technological interest. All the systems are direct band gap semiconductors. The gap value of the Janus system, Si₂XY, is between the Si₂X₂ and Si₂Y₂ systems. Furthermore, after alloying 50% Z atoms, we found that the gap value of Si₂XY_xZ_1−x system is also between the Si₂XY and Si₂YZ systems. In addition, the gap of the Si₂X₂ and Si₂XY systems can be turned continuously under biaxial strain, denoting a rather flexible way toward tailoring the electronic properties of silicene. Therefore, we can obtain a direct band gap semiconductor based on silicene with any value between 0.98 and 2.13 eV by carefully selecting the adsorption adatoms on two sides and applying elastic strain. Recently, several groups have successfully synthesized fluorinated, chlorinated and brominated graphene.⁵² Because of the rich semiconducting properties in combination with the experiment development, the symmetrically and asymmetrically (Janus) functionalized silicene have potential applications in silicon-based electronics and optoelectronic nanodevices.

Acknowledgements

The author would like to thank Dr Jyh-Pin Chou and Dr Chaoping Liang for many valuable discussions. This research was supported by the National Science and Technology Major Project of the Ministry of Science and Technology of China (2013ZX04008011). It was also supported by the Scientific Research Foundation of Graduate School of Southeast University (YBPY1602).

References

1. C.-L. Lin, R. Arafune, K. Kawahara, N. Tsukahara, E. Minamitani, Y. Kim, N. Takagi and M. Kawai, Appl. Phys. Express, 2012, 5, 045802.
2. B. Feng, Z. Ding, S. Meng, Y. Yao, X. He, P. Cheng, L. Chen and K. Wu, Nano Lett., 2012, 12, 3507–3511.
3. A. Resta, T. Leoni, C. Barth, A. Ranguis, C. Becker, T. Bruhn, P. Vogt and G. Le Lay, Sci. Rep., 2013, 3, 2399.
4. S. Cahangirov, M. Topsakal, E. Aktürk, H. Şahin and S. Ciraci, Phys. Rev. Lett., 2009, 102, 236804.
5. D. Jose and A. Datta, Acc. Chem. Res., 2014, 47, 593–602.
6. H. Oughaddou, H. Enriquez, M. R. Tchalala, H. Yildirim, A. J. Mayne, A. Bendounan, G. Dujardin, M. Ait Ali and A. Kara, Prog. Surf. Sci., 2015, 90, 46–83.
7. Z.-G. Shao, X.-S. Ye, L. Yang and C.-L. Wang, J. Appl. Phys., 2013, 114, 093712.
8. J. Zhao, H. Liu, Z. Yu, R. Quhe, S. Zhou, Y. Wang, C. C. Liu, H. Zhong, N. Han, J. Lu, Y. Yao and K. Wu, Prog. Mater. Sci., 2016, 83, 24–151.
9. G. Le Lay, Nat. Nanotechnol., 2015, 10, 202–203.
10. L. Tao, E. Cinquanta, D. Chiappe, C. Grazianetti, M. Fanciulli, M. Dubey, A. Molle and D. Akinwande, Nat. Nanotechnol., 2015, 10, 227–231.
11. C.-C. Liu, W. Feng and Y. Yao, Phys. Rev. Lett., 2011, 107, 076802.
12. F. Schwierz, Nat. Nanotechnol., 2010, 5, 487–496.
13. H. Zhao, Phys. Lett. A, 2012, 376, 3546–3550.
14. Z. Ni, Q. Liu, K. Tang, J. Zheng, J. Zhou, R. Qin, Z. Gao, D. Yu and J. Lu, Nano Lett., 2012, 12, 113–118.
15. R.-w. Zhang, C.-w. Zhang, W.-x. Ji, S.-j. Hu, S.-s. Yan, S.-s. Li, P. Li, P.-j. Wang and Y.-s. Liu, J. Phys. Chem. C, 2014, 118, 25278–25283.
16. Y. Li and Z. Chen, J. Phys. Chem. Lett., 2013, 4, 269–275.
17. Y. Ding and J. Ni, Appl. Phys. Lett., 2009, 95, 083115.
18. F.-b. Zheng, C.-w. Zhang, S.-s. Yan and F. Li, J. Mater. Chem. C, 2013, 1, 2735.
19. C.-w. Zhang and S.-s. Yan, J. Phys. Chem. C, 2012, 116, 4163–4166.
20. F.-b. Zheng and C.-w. Zhang, Nanoscale Res. Lett., 2012, 7, 1–5.
21. Z. Song, C.-C. Liu, J. Yang, J. Han, M. Ye, B. Fu, Y. Yang, Q. Niu, J. Lu and Y. Yao, NPG Asia Mater., 2014, 6, e147.
22. Z. Run-Wu, Z. Chang-Wen, J. Wei-Xiao, L. Sheng-Shi, H. Shu-Jun, Y. Shi-Shen, L. Ping, W. Pei-Ji and L. Feng, New J. Phys., 2015, 17, 083036.
23. Y.-p. Wang, W.-x. Ji, C.-w. Zhang, P. Li, F. Li, P.-j. Wang, S.-s. Li and S.-s. Yan, Appl. Phys. Lett., 2016, 108, 073104.
24. R.-w. Zhang, W.-x. Ji, C.-w. Zhang, S.-s. Li, P. Li and P.-j. Wang, J. Mater. Chem. C, 2016, 4, 2088–2094.
25. R.-w. Zhang, C.-w. Zhang, W.-x. Ji, S.-s. Li, S.-s. Yan, S.-j. Hu, P. Li, P.-j. Wang and F. Li, Sci. Rep., 2016, 6, 18879.
26. R.-w. Zhang, C.-w. Zhang, W.-x. Ji, S.-s. Li, S.-s. Yan, P. Li and P.-j. Wang, Sci. Rep., 2016, 6, 21351.
27. H. Zhao, C.-w. Zhang, W.-x. Ji, R.-w. Zhang, S.-s. Li, S.-s. Yan, B.-m. Zhang, P. Li and P.-j. Wang, Sci. Rep., 2016, 6, 20152.
28. J. O. Sofo, A. S. Chaudhari and G. D. Barber, Phys. Rev. B: Condens. Matter Mater. Phys., 2007, 75, 153401.
29. D. C. Elias, R. R. Nair, T. M. G. Mohiuddin, S. V. Morozov, P. Blake, M. P. Halsall, A. C. Ferrari, D. W. Boukhvalov, M. I. Katsnelson, A. K. Geim and K. S. Novoselov, Science, 2009, 323, 610–613.
30. J. T. Robinson, J. S. Burgess, C. E. Junkermeier, S. C. Badescu, T. L. Reinecke, F. K. Perkins, M. K. Zalalutdniov, J. W. Baldwin, J. C. Culbertson, P. E. Sheehan and E. S. Snow, Nano Lett., 2010, 10, 3001–3005.
31. R. Zbořil, F. Karlický, A. B. Bourlinos, T. A. Steriotis, A. K. Stubos, V. Georgakilas, K. Šafářová, D. Jančík, C. Trapalis and M. Otyepka, Small, 2010, 6, 2885–2891.
32. R. R. Nair, W. Ren, R. Jalil, I. Riaz, V. G. Kravets, L. Britnell, P. Blake, F. Schedin, A. S. Mayorov, S. Yuan, M. I. Katsnelson, H. M. Cheng, W. Strupinski, L. G. Bulusheva, A. V. Okotrub, I. V. Grigorieva, A. N. Grigorenko, K. S. Novoselov and A. K. Geim, Small, 2010, 6, 2877–2884.
33. K.-J. Jeon, Z. Lee, E. Pollak, L. Moreschini, A. Bostwick, C.-M. Park, R. Mendelsberg, V. Radmilovic, R. Kostecki, T. J. Richardson and E. Rotenberg, ACS Nano, 2011, 5, 1042–1046.
34. D. K. Samarakoon, Z. Chen, C. Nicolas and X.-Q. Wang, Small, 2011, 7, 965–969.
35. N. Gao, W. T. Zheng and Q. Jiang, Phys. Chem. Chem. Phys., 2012, 14, 257–261.
36. W.-B. Zhang, Z.-B. Song and L.-M. Dou, J. Mater. Chem. C, 2015, 3, 3087–3094.
37. F. Li and Y. Li, J. Mater. Chem. C, 2015, 3, 3416–3421.
38. L. Zhang, J. Yu, M. Yang, Q. Xie, H. Peng and Z. Liu, Nat. Commun., 2013, 4, 1443.
39. M. A. Bissett, Y. Takesaki, M. Tsuji and H. Ago, RSC Adv., 2014, 4, 52215–52219.
40. P. A. Denis, Phys. Chem. Chem. Phys., 2015, 17, 5393–5402.
41. M. Klintenberg, S. Lebegue, M. Katsnelson and O. Eriksson, Phys. Rev. B: Condens. Matter Mater. Phys., 2010, 81, 085433.
42. G. Kresse and J. Furthmüller, Comput. Mater. Sci., 1996, 6, 15–50.
43. G. Kresse and D. Joubert, Phys. Rev. B: Condens. Matter Mater. Phys., 1999, 59, 1758–1775.
44. J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865–3868.
45. S. Grimme, J. Comput. Chem., 2006, 27, 1787–1799.
46. H. J. Monkhorst and J. D. Pack, Phys. Rev. B: Solid State, 1976, 13, 5188.
47. P. E. Blöchl, O. Jepsen and O. K. Andersen, Phys. Rev. B: Condens. Matter Mater. Phys., 1994, 49, 16223–16233.
48. C. L. Fu and K. M. Ho, Phys. Rev. B: Condens. Matter Mater. Phys., 1983, 28, 5480–5486.
49. J. Heyd, G. E. Scuseria and M. Ernzerhof, J. Chem. Phys., 2003, 118, 8207–8215.
50. E. Bianco, S. Butler, S. Jiang, O. D. Restrepo, W. Windl and J. E. Goldberger, ACS Nano, 2013, 7, 4414–4421.
51. F. Karlický, R. Zbořil and M. Otyepka, J. Chem. Phys., 2012, 137, 034709.
52. F. Karlický, K. Kumara Ramanatha Datta, M. Otyepka and R. Zbořil, ACS Nano, 2013, 7, 6434–6464 , and references therein.
53. Y. Ding and Y. Wang, Appl. Phys. Lett., 2012, 100, 083102.
54. Y. Li and Z. Chen, J. Phys. Chem. C, 2014, 118, 1148–1154.
55. F. Guinea, M. I. Katsnelson and A. K. Geim, Nat. Phys., 2009, 6, 30–33.
56. Q. Peng and S. De, Nanoscale, 2014, 6, 12071–12079.
57. K. He, C. Poole, K. F. Mak and J. Shan, Nano Lett., 2013, 13, 2931–2936.
58. A. Castellanos-Gomez, R. Roldán, E. Cappelluti, M. Buscema, F. Guinea, H. S. J. van der Zant and G. A. Steele, Nano Lett., 2013, 13, 5361–5366.
59. E. Scalise, M. Houssa, G. Pourtois, V. Afanas'ev and A. Stesmans, Nano Res., 2011, 5, 43–48.

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