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Effect of Doping in Controlling Reactivity, Electronic and Optical Properties of Pristine and Ca(II) Intercalated Layered Silicene Tamiru Teshome, and Ayan Datta J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b03002 • Publication Date (Web): 29 Jun 2017 Downloaded from http://pubs.acs.org on July 5, 2017

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The Journal of Physical Chemistry

Effect of Doping in Controlling Structure, Reactivity and Electronic Properties of Pristine and Ca(II) Intercalated Layered Silicene Tamiru Teshome and Ayan Datta* Department of Spectroscopy, Indian Association for the Cultivation of Science, 2A and 2B Raja S. C. Mullick Road, Jadavpur – 700032, Kolkata, WestBengal, India. Email: [email protected]

Abstract

Hybrid two-dimensional (2D) materials composed of carbon and germanium doped silicene monolayers, Si1xCx,

Si1-xGex and Si1-2xCxGex (0 ≤ x ≤ 1) are investigated on the basis of first-principles calculations. Their

structural features can be understood on the basis of the Vegard’s Law. The lattice parameters are shown to correlate well with the arithmetic mean of the percentage doping of individual constituents. The electronic band gap show interesting bell-shaped behavior for Si1-xCx with respect to doping wherein Eg increases from 0 (for x = 0) to a maxima (for x = 0.5) and eventually again decrease to 0 (for x = 1). Clearly controlled carbon doping of silicene monolayer opens up the band-gaps and also provide a tool to harvest solar energy for semiconductor and photovoltaic applications. Apart from pristine monolayer silicene, the effect of Ca(II) intercalated multilayer silicene/germanene as available in the van der Waals mineral phases of CaSi2 and CaGe2 are also investigated. The stability and reaction energies for hydrogenation, fluorination and mixed hydrogenationfluorination for these Ca(II) intercalated structures are compared vis-a-vis pristine and doped monolayer silicene. Optical absorption calculations demonstrate that doping monolayers as well as Ca(II) intercalated multilayer silicene/germanene have strong photo-absorption in visible light region. The presence of Ca(II) stabilizes the silicene/germanene layers and also the Ca(II) is affecting the electronic structure of these 2D materials. 1 ACS Paragon Plus Environment


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Introduction Graphene, a 2D honeycomb structure of atomic carbon, has attracted attention due to its remarkable electronic and magnetic properties for potential advanced technology applications.1, 2,

3, 4

In connection with, there has

been an active interest to study the honeycomb lattices of other group-IV elements. Silicene, the all Si analogue of graphene, that has recently become extremely popular5, is a single silicon monolayer with buckled honeycomb structure6 and has useful chemical and physical properties7, 8, including ferromagnetism, 10

9,

halfmetallicity, 11quantum hall effect12 and giant magnetoresistance.

Two-Dimensional Honeycomb Structures of Silicon and Germanium13 have been studied. Unlike graphene, two-dimensional Si and Ge layers are buckled due to pseudo Jahn-Teller distortion.14 Recently, experimental synthesis of germanene on metal substrates has been achieved.15,

16

First-principles calculations on silicene,

graphene and germanene indicate that the π and π* bonds linearly cross at the Fermi level, reflecting zero band gap semiconducting character.17 This unfortunately makes both pristine silicene and germanene unsuitable in electronic devices with logic operation. To overcome this, extensive efforts have been devoted to realize controllable band gaps in these materials. Several strategies such as patterning into nanoribbons18 and using chemical functionalization19,

20

have been proposed to effectively open a band gap in silicene, graphene and

germanene. Silicane and germanane (fully hydrogenated silicene and germanene) are predicted to be wide band gap semiconductors, with energy gap values ranging between 2.9-4.0 eV for silicane and between 2.9-3.6 eV for germanane.21, 22 Similarly the band structure and optical properties of layered germanane (a van-der Waals solids) 23 has also been studied. Recently, we have shown that blue phosphorene (an indirect band gap system) can be readily converted into a direct band gap n-type semiconductor based on doping with CT molecules like TTF.24 Although intensive theoretical studies on mono- and multilayer silicene have been reported, isolated freestanding silicene has not been obtained experimentally. This is probably because of the inherent air instability of 2D silicon and high reactivity of Si-Si bonds. Even though the computed freestanding silicene and germanene structures are strongly buckled, it has been shown that this buckling can be significantly reduced by 2 ACS Paragon Plus Environment

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stacked functionalized and confined in bilayer graphene.

25, 26, 27

Recent synthesis of silicene28,

29

and

germanene30 have been a major breakthrough in this area because of their enhanced spin-orbit coupling31, 32 and higher electron correlations.33 However, the underlying metal substrate, which is necessary for the growth of these honeycomb lattices, strongly affects the Dirac electron behavior.34 As a result, there has an interest in layered Ca intercalated silicene/germanene system like CaSi2 and CaGe2 for which strong layer and substrate interactions are circumvented.35

Intercalated layered materials are of significant interest due to wide tunability of their conducting properties regulated by the interface states.36, 37, 38 Experimental progresses in recent times enables the synthesis of a wide range of layered materials with subsequent intercalations having precise control over the stoichiometry and number of layers.39 For multilayer silicene, strong Si-Si interactions (interlayer bonding) destroy the sp2 nature of the electrons.40 These limitations may be avoided by means of intercalation in a multilayer system wherein the substrate effects and interlayer sp3 bonding are absent41. Therefore the 2D sp2 electrons might be preserved. Although freestanding silicene probably cannot exist in nature, the material has been successfully deposited on metallic substrates such as ZrB2 (0001), Ir(111), and Ag(111).28, 42- 45 On the other hand, several semiconductors have been explored theoretically to overcome the strong interaction characteristic for metallic substrates. For example, Ding and Wang have reported that GaS nanosheets could preserve the linearly dispersing bands with a gap of 0.17 eV, but the lattice mismatch would amount to 7.5% .46 GaS preserves the Dirac cone of silicene but a large lattice mismatch of 7.5% is a major drawback. Although the lattice mismatch is smaller (2.3 %) for ZnS(0001) the substrate also perturbs the band structure.47 Bhattacharya and co-workers have investigated IIVII and III-VI semiconductor substrates such as AlAs(111) and ZnSe(111).48 They reported that the stability and electronic properties of these systems depend largely on the topmost atoms of the substrate. WSe2 would fit much better (lattice mismatch of 0.6%) but the silicene monolayer develops a large band gap of 0.3 eV.49 The excellent electronic properties and low thermal conductivity make silicene very promising for thermoelectric devices.50,

51

The structural and electronic properties of silicene on MgX2(X = Cl, Br and I) combines a 3 ACS Paragon Plus Environment


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reasonably small lattice mismatch with an almost gapless Dirac cone and a Fermi velocity comparable to freestanding silicene as reported by Jiajie Zhu and Schwingenschögl.52 Recently, Noguchi et al. reported the existence of Dirac dispersion in the Ca(II) intercalated multilayer silicene system CaSi2 using angle resolved photo emission spectroscopy (ARPES). 53

In this article, we propose an effective method to improve the electronic properties of silicene/germanene doping with C atom at different concentration ratio increases and decreases the band gap of the monolayer. Alloying Si with C and Ge atoms in such 2D monolayers systems will be particularly interesting as it promises composition controlled modulation of electronic and optical properties. We report a systematic study of monolayer silicene/germanene along with their Ca(II) intercalated multilayer employing first-principles calculations within the framework of DFT. To the best of our knowledge, there has been no previous report for the reactivity of Ca(II) intercalated silicene/germanene towards hydrogenation/fluorination or mixed hydrofluorination and their optical properties. This work is very significant for the silicene field as it suggests alternative bilayer, tri-layer and multilayer compounds that expand ones imagination to go and synthesize them.

Computational Details In this work, all the calculations are performed within the framework of density functional theory (DFT) using the project-augmented plane-wave method, as implemented in Vienna ab-initio simulation package (VASP). 54, 55

The generalized gradient approximation of Perdew, Burke and Ernzerhof (GGA-PBE) is selected for the

exchange correlation potentials56, and the DFT is employed. The cutoff energy for the plane-wave basis is set to 500 eV and the structures are relaxed until the residual forces on the atoms become smaller than 0.01 eV/ Å. Brillouin zone integration are carried out with 5 x 5 x 1 k meshes for the structure optimization and 7 x 7 x 1 k meshes for optical spectra and band structure calculations. We analyze Dirac dispersion in several possible stacking sequences of AA and AB silicene/germanene intercalated compounds along with their bilayer, tri-layer sandwich and multilayer structures.57 The optical properties were computed utilizing the time-dependent (TD) 4 ACS Paragon Plus Environment

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DFT scheme for the inclusion of electron-hole interactions58 within the random phase approximation (RPA) approach for which the local field effects are included at Hartree level. Only inter-band transitions are taken into account. For a transitionally invariant system, the Fourier transform of the frequency dependent symmetric dielectric matrix in the RPA is given by.59

ε, q, ω = δ, q, ω − |||

χ q, ω | ,

(1)

Where G and G’ are reciprocal lattice vectors and q stands for the Bloch vector of the incident wave. The matrix χ q, ω is the irreducible polarizability matrix in case of the independent particle derived by Adler and Wiser60, 61 in the context of the self-consistent field approach. Optical properties of any system are in general calculated with the help of a frequency dependent complex dielectric function ɛ ω = ɛ ω + iɛ ω . The imaginary part is determined by a summation over empty states using the equation: ɛ ω =

4! e 1 lim ) 2ω+ δ E,/ − E./ − ω × 〈34+ + 56& 738+ 〉〈34+ + 5:& 738+ 〉 ∗ Ω &→ ( ,.../

where ω, the frequency of electromagnetic (EM) radiation in energy unit is Ω represents the volume of the primitive cell, q is the electron momentum operator, c and v are the conduction band and valance state, respectively,ω+ , is the k point weight E,/ , E./ and 34+ , 38+ are the eigenvalues and wave function at the k point, respectively and 56 , 5: are unit vectors for the three Cartesian direction. The phonon calculations are carried out using the PHONOPY code combined with density functional perturbation theory (DFPT) method in VASP.

Results and Discussion A. Structures and Stability The necessary and sufficient condition for dynamical stability of a crystal at low temperature is phonon stability. We have examined dynamical stability of silicene, germanene, graphene, and CaSi2 and CaGe2 phonon dispersion along the high symmetry lines ᴦ-K-M-ᴦ as shown in Fig. 1 (a-e), respectively. The absence of soft modes within the entire Brillouin zone clearly indicating that silicene, germanene, graphene, CaSi2 and CaGe2 are indeed stable. 5 ACS Paragon Plus Environment


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We considered 2D Si-C and Si-Ge hybrids with different Si concentrations. First, we produced a 3 x 3 unit cell of silicene, in which silicon atoms are gradually substituted by carbon/germanium atoms to obtain different Si/C and Si/Ge ratios. After carefully considering the possible structures of all of these configurations for Si1-xCx, Ge1-xCx and Si1-xGex including isomeric forms (different structures with the same composition), the energies are compared to obtain the most stable configuration. The suitability of our level of theory might be gauged from the reproducible band gap of SiC and Dirac cones for pristine monolayer silicene and germanene. Therefore, we employed our method to investigate the effect of doping and optical properties of the 2D monolayers.

The well-known Vegard’s law (Eqn. 2) was utilized to understand the qualitative hybrid structures. According to Vegard’s law, unit cell parameters should vary linearly with composition for a continuous and constant temperature substitution in a solid solution for which the substituted atoms/ions are randomly distributed. The lattice parameters are controlled by the relative size of the atoms or species exchanged.62, 63 Table 1: Doping ratio (x), lattice constant “a” (Å), Energy gap Eg (eV) and optical excitation energy Ee (eV) for Si1-xCx,Si1-xGex and Ge1-xCx. doping Ratio(x)

C-doping silicene

Ge-doping silicene

C-doping germanene

a

Eg

Ee

a

Eg

Ee

a

Eg

Ee

0

3.86

0

4.0

3.86

0

4.0

4.06

0

4.0

0.111

3.69

0.32

4.0

3.88

0.02

3.75

3.77

0.27

1.95

0.222

3.52

0.51

5.14

3.90

0.02

3.06

3.65

0.36

2.01

0.333

3.15

1.99

5.31

3.92

0.04

3.70

3.53

0.49

2.5

0.5

3.09

2.55

5.35

3.95

0.05

1.69

3.26

2.07

3.5

0.556

3.03

1.38

2.63

3.96

0.03

0.86

3.14

1.02

3.65

0.778

2.73

0.65

1.75

4.01

0.03

0.75

2.69

0.80

2.1

1.0

2.46

0

4.0

4.06

0

0.61

2.46

0

4.0

The simplest mathematical expression for Vegard’s law for a binary solid solution A-B is: 6 ACS Paragon Plus Environment

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< = a> 1 − ? + a@ ?

(2)

where x = ?A is the mole fraction of component B a = a> and a = a@ are the lattice parameters of pure components A and B, respectively. The doping silicene sheets were generated without prior bias or preference for any structure by replacing the Si atoms by C/Ge and C-Ge. The concentration of individual C and Ge doping were varied from 0 ≤ x ≤ 1 where x is the relative composition of one type of atom with respect to the total number of atoms in the unit cell. Positions of the doping have also been varied for the different concentration of substitution doping to analyses the effect of doping. Note that, for multiple configurations at the same doping concentration, the most stable structure was chosen (supporting information Fig. S1and S2). Graphene is a pure planar monolayer as shown in Fig. 2 (I(i)) while silicene and germanene undergo slight out-of-plane buckling with buckling height, dH = 0.45 Å and 0.69 Å, respectively as consequence of pseudo Jahn-Teller distortion as discussed above. The optimized structures of 2D Si1-xCx, Si1-xGex, Ge1-xCx and Si1-2xCxGex and doping at different ratio are listed in Fig. 2 (I-IV). The isotropic silicene-graphene (Si0.5C0.5) hybrid is stable in a planar hexagonal lattice with Si-C bond length of 1.78 Å. With the increases of the substitution ratio-of C, the buckling of the planar structure also decreases. In Fig. 2(II and III), the optimized structures of 2D Si1-xGex and Ge1-xCx monolayers at different doping ratios are shown. The Ge0.5C0.5 (GeC) monolayer in planar or lower buckled structure obtained germanene doping carbon due to the symmetry destroyed and electronegativity difference between the C and Ge atoms; hence, GeC has a polar structure. In contrast, with the increases of Ge doping silicene, the buckling height increases in between silicene-germanene (dH=0.45-0.69 Å). As shown that in Fig. 2(IV), for Si1-2xCxGex we have C and Ge co-doping silicene as obtained by increasing the concentration ratios from x = 0.06 to x = 0.5.

The variation of the lattice constants and average Si-X (X = C, Ge) bond lengths for Si1-xCx, Si1-xGex and Ge1xCx

with respect to doping are shown in Fig. 3((b), (d) and (f)), respectively. The x=0 (un-doping) substitution

ratios correspond to pristine silicene sheet, while 1(100%) substitution ratio graphene (germanene) monolayer. For Si1-xCx and Ge1-xCx, increasing x leads to shrinkage of the lattice constants as shown in Fig. 3(a) and Fig. 7 ACS Paragon Plus Environment


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3(e) which is concomitant with increasing the fraction of the shorter Si-C and Ge-C bonds at the expense of the longer Si-Si and Ge-Ge bonds. Thus, evidences from reduced average bond-length in the hybrid 2D monolayers (Si1-xCx and Ge1-xCx). The lattice constant decreases linearly from 3.86 Å for pure silicene (x=0) to 2.47 Å for pure graphene (x=1) and lattice constant decreases from germanene 4.06 Å to graphene 2.47 Å as shown in Fig. 3(a) and Fig. 3(e), respectively. Similar trend is also observed for Si1-xGex for which sequential substitution of Si by Ge leads to an expanded lattice constant in Fig. 3(c) which again correlates well with an increasing fraction of the longer Si-Ge bonds within a shorter Si-Si silicene monolayer in Fig. 3(d). Here again, the lattice constant monotonically increases from 3.86 Å from pure silicene to 4.06 Å for pure germanene (x=1). Within the hybrid layers, the bond lengths of Si-C and Si-Ge are in the ranges of 1.75 Å - 1.84 Å and 2.34 Å - 2.40 Å which are in the fraction of x=0.111 - 0.778. Clearly, the effect of doping carbon and germanium on silicene element is specific as C doping reduces the lattice constant while it is vice-versa for Ge. Nevertheless, for both the cases, an increment or decrement of lattice constants is correlated linearly with doping concentration in harmony with the Vegard’s law.

We further investigate the bilayer sandwiched compound silicene-Ca-silicene. Although this compound has not yet been synthesized experimentally, it represents an intercalated bilayer exfoliated from bulk CaSi2. In fact recently, based on molecular dynamics simulations, we have shown that liquid-phase exfoliation provides an excellent synthetic route to produce mono to few layer 2D materials 64. The atomic structures for several of Ca intercalated silicene/germanene multilayer where in buckled silicene/germanene layers and trigonal Ca layers are alternatively stacked (supporting information Fig. S5-S9). Here, we choose to present the electronic properties of bilayer, tri-layer sandwich together with multilayer CaSi2 and CaGe2 with AA and AB stacking sequences. For further confirmation of momentum shifts of Dirac cones, we show the two-dimensional dispersion in both shifted the ᴦ-k-M plane and A-H-L plane of the Brillouin zone. This happens actually due to the enhanced hopping within the silicene/germanene layers, which further increases in the presence of intercalated Ca atoms. Furthermore, A sublattice points of one silicene/germanene layer and B sublattice points 8 ACS Paragon Plus Environment

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of the adjacent silicene/germanene layer in CaSi2 and CaGe2 come closer with enhanced buckling, breaking the in-plane sublattice symmetry and making the interlayer hopping within different sublattice points asymmetric. This is evident from the appearance of the Dirac cone on high symmetric point in the case of AA stacked CaSi2 and CaGe2 systems, in spite of the fact that, the hopping does not break the sublattice symmetry. The AB staking does not show the shift of the Dirac cone. This can be attributed to the in-plane sublattice symmetry breaking. We further investigate the bilayer sandwich compound of Si2-Ca-Si2 and Ge2-Ca-Ge2. That geometry also indicates the enhanced coupling induced interaction of individual Dirac dispersions that leads to the shift of Dirac cone. This makes the next-next-neighbor electron hopping within A sublattice points and within B sublattice points different. Because of the buckled geometry of silicene/germanene layers, only one kind of sublattice points in each layer is close proximity to the intercalated Ca atoms.

The reactivity of freestanding silicene/germanene towards hydrogenation, fluorination and mixed hydrogenation-fluorination (H-silicene-F and H-germanene-F) was studied by computing their binding energies. The binding energies, Eb are calculated as:

EB = C ED − EEFB − EGH

(3)

Where ET is the total energy of system, Esub is the energy of substrate, ESi is the energy of silicene and N is the number of Si, Ge, F and H atoms in the unit cells. The binding energy of H-Silicene-F and H-Germanene-F are -4.01 eV and -4.74 eV per HF, respectively. The band gap of freestanding H-silicene-F and H-germanene-F are 1.65 eV and 0.60 eV, respectively. Interestingly, on mixed functionalization of the top-layer of germanene (Hgermanene-F) in CaGe2 multilayer, the Ge-monolayer becomes planar. This is in marked contrast to freestanding H-germanene-F (hydrofluro-germanene) which is strongly buckled. To understand this effect, the total charge associated with each atom and the zero flux surfaces’ defining the Bader volumes was computed as: ∆ρ = ρD − ρEFB − ρGH

(4)

where ρD refers to total charge, ρEFB is the charge of substrate and ρSi, Ge= silicane, germanane, fluorosilicene, fluorogermanene, half hydrogenated and half fluorinated silicene/germanene charge densities, respectively. The 9 ACS Paragon Plus Environment


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charge density differences as displayed in Fig. 4(a) highlight that, the charge transfer occurs mainly within the silicene lower lying layer. Fig. 4(b) shows that the fluorine atoms accept 1.09 electrons while the Ca atoms donate 1.97 electrons. Fig. 4(c) indicates the mixed hydrogenated-fluorinated structure of CaSi2 multilayer wherein a charge density difference of 1.24 and 0.96 electrons exist for F and H, respectively. As shown in Fig. 5(a) for hydrogenation of the topmost germanene sheet in CaGe2, hydrogen accepts 0.76 electrons and which are donated by the Ge-atoms. The topmost germanane layer and the CaGe2 substrate show weak van der Waals interaction between the two systems with the binding energy -2.03 eV per H atoms. Such phase-separated state was reported for graphene and graphane to maximize/minimize the boundary length between graphenegraphane.65 Fig. 5(b) refers to the fluorinated CaGe2 multilayer which shows a charge density difference of 1.11, 1.09 and 1.97 electrons for F, Ge and Ca atoms, respectively. Extremely, the lower F atoms interacts with Ca atoms which results in almost doubling of the binding energy (-4.31 eV) vis-a-vis hydrogenated CaGe2. In case of mixed hydrogenated-fluorinated germanene, the Ge-monolayer becomes planar due to the strong binding of F-atoms with Ca(II) ions (-6.47 eV) as shown in Fig. 5(c).

B. Band gaps The band gaps of 2D Si1-xCx and Si1-xGex monolayers are related not only with the substitution ratio of C and Ge but also on the detailed Si-C and Si-Ge order. As observed in Fig. 6(a) for Si1-xCx at a given composition, several possible structures exist and they have different band gaps. This leads to a rich variation in the band gaps when the composition of the hybrid is changed. This is also shown in Fig. 6(a) for which different structure at the same composition creates different gaps and hence, a spread in the band-gap versus composition plots. The band gap first increases with increasing x and reaches a peak of 2.55 eV at x = 0.5 (Si:C = 1:1). Beyond this, the band gap starts to decrease and eventually collapses to 0 for x=0. Interestingly, the band gap of Si1-xCx shows a non-monotonic bell-shaped relationship with doping. For less than 50% doping of C in silicene, the band gap increases with increase in doping then it reaches a maxima at x = 0.5 and eventually again decays to zero for 100% doping. The same band gap trend is observed in Ge1-xCx in Fig. 6(b). In other words, 10 ACS Paragon Plus Environment

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intermediate doping connects the two zero-gap semiconductors pair namely silicene-graphene and germanenegraphene forms new gap opened semiconductors. Our studies of the electronic properties results agree with previous result reported.66 Due to the difference in electronegativity between Si and C atoms (silicon: 1.90 and carbon: 2.55 at the Pauling’s scale), the valence electrons of Si tend to transfer towards the nearest C atoms for 2D Si0.5C0.5 sheet creating charge-transfer states and electron localizations. This is evident from the partial charge density of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) for Si0.5C0.5 (supporting Information Fig. S4). Such localized electron distribution, consequently opens up a band gap of 2.55 eV in Si0.5C0.5 which is also in agreement with the previous reports.67, 68 The SiC and GeC monolayer structure have large band gaps as shown in Fig. 6(a) and 6(b) at x=0.5. The valance band width of the Si1-xCx and Ge1-xCx decreases with the increase in the electronegativity difference between Si/Ge and the C atom. A different situation arises in the case of Si1-xGex for which the band gap remains constant (zero band gap) with increasing x as shown in Table 1.

Obviously, the energy bands of the silicene, graphene and germanene without doping present the expected zerogap character, with π and π* bands both cross the Fermi level at the K-point, as displayed in Fig. 7(I(a-c)), respectively. The Dirac point is found at the symmetric K point in the hexagonal Brillouin zone. Therefore, it is expected that doping will mainly affect the occupation of the π and π* bands. Fig. 7(II(a)) and Fig. 7 (II(b)) shows the band structures of CaSi2 and CaGe2, respectively. This can be understood from the analyses along the high

symmetry

points

of

the

first

Brillouin

zone.

It

is

evident

that

unlike

freestanding

silicene/germanene/graphene which shows a Dirac cone at K-point at the Fermi energy as shown Fig. 7(I (a-c)) respectively the same cannot be detected for CaSi2 and CaGe2. According to our calculations, the two Dirac cones at K and H lie at 2.11 eV and 2.71 eV for CaSi2, respectively below the Fermi energy. In case of CaGe2 Dirac cones found at 2.06 eV at K-point and 2.92 eV at H-point below the Fermi energy. As a result, a large band gap of 4.29 eV and 4.05 eV open up at the K and H points respectively. As a consequence of the electron transfer from Ca atoms to the silicene/germanene layers, the conical dispersion is shifted below the Fermi 11 ACS Paragon Plus Environment


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energy. These observations clearly indicate that the buckling silicene/germanene layers plays an important role in introducing sub-lattice symmetry breaking and consequent asymmetric interlayer hopping within different sublattice points. That makes the individual Dirac dispersions of individual buckled layers interact with each other, thus shifting the Dirac cone from the high symmetric points. Their similar behavior have been observed experimentally and theoretically.35, 42, 69

Having established the favorable structures of 2D Si1-xCx, Si1-xGex, Ge1-xCx and Si1-2xCxGex sheets, we proceed to explore their novel properties. We found that the band gaps could be direct or indirect, which also depends on the detailed configurations. For further understanding the change in the band gaps, we plotted the energies band structures for 2D Si1-xCx, Si1-xGex, Ge1-xCx and Si1-2xCxGex monolayer systems, respectively (supporting information Fig.S3 (I-IV)). There are indirect band gaps for x=0.111, x=0.222, and x=0.333 in C doping silicene (Si1-xCx) and for x=0.111, x=333 and x=0.778 in C doping germanene (Ge1-xCx). Similarly, for codoping C-Ge silicene (Si1-2xCxGex) at x=0.278, x=0.333, 0.389 and 0.444 have indirect band gaps. Their indirect and direct band structures are illustrated in (supporting information Table S3). Overall, the energy and type of the band gaps are closely related with the concentration ratio of C atoms and the Si-C and Ge-C order. For small doping (x=0.111) in Si1-xCx, the valence band maximum (VBM) and conduction band minima (CBM) almost meet at the Fermi energy at ᴦ-point. As doping increases, both VB and CB flatten out considerably to create the largest band gap for Si0.5C0.5 in the Si1-xCx family. On further increase in the mole fraction of C atoms in silicene, the CBM starts to come closer to the Fermi-energy and becomes almost a semi-metal at x=0.889. The same properties observed for Ge1-xCx monolayer. In case of Si1-xGex for all doping concentrations, VBM and CBM are always close to the Fermi level which results in direct and negligible band gap (Eg= 0.02 eV) at the ᴦpoint. When C and Ge are co-doped within silicene, the band-gaps increase as we increase the fraction of C-Ge. For x=0.06 the VB and CB touch the Fermi level creating semimetalic state. As we increase the doping ratio of x (C-Ge) the band gap starts to open and both VB and CB are far from the Fermi level. Since Ge-doping alone does not affect the band-gap in silicene, the remarkable opening of the band gaps on co-doping C arises entirely 12 ACS Paragon Plus Environment

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from carbon atoms. As seen from Table 1, Si1-xCx and Ge1-xCx shows the discussed bell-shaped behavior, Si1xGex

shows zero band gaps and Si1-2xCxGex shows an energy gap ranging from 0.04 eV to 2.07 eV depending

upon the doping and their ratio. Generally, silicene/germanene monolayer doping with C atom concentration open up the band gap. This can be understood from the band gap flexible by increasing or decreasing the concentration ratio. Thus, evidences are the monolayer silicene and germanene doping with C atom at different concentration ratio increases (from x=0.111 to x=0.5) and decreases (from x=0.5 to x=1) the band gap of the monolayer. On the other hand, hydrogenation and fluorination freestanding silicene/germanene obtained open up band gap. In opposition to, silicene doping with Ge atom and silicene/germanene intercalated Ca layers functionalized with H, F and mixed H and F together with bilayer sandwiched and multilayer does not open up the band gap. The energy shift of Dirac dispersion below the Fermi energy in CaSi2 and CaGe2 in AA stacking sequence systems are expected due to electron transfer from Ca atom to silicene/germanene layers (supporting information S5).

C. Optical properties To explain origin of the peaks, contributions of specific transitions between the bands along the high-symmetry ᴦ-K-M-ᴦ direction as displayed in Fig. 7(I (a-c)) were calculated. In the optical spectra, one can expect only π to π* and σ to σ* transitions as allowed if the light is polarized parallel to the silicene/germanene/doping-silicene monolayer. In contrast, only π to σ* and σ to π* transitions are allowed if the light is polarized perpendicular to the sheets. The absorption spectrum of pure silicene, graphene and germanene are shown in Fig. 7(I (d-f)). We found that silicene due to the low-buckled structure exhibits two prominent absorption peaks: the π to π* at photon energy 1.65 eV and 4 eV for E⊥c and 6.5 eV for the polarization of light E∥c as shown in Fig. 7(I(d)). The absorption spectra of graphene the π to π* transition along the K-M direction was found from two peaks at 2.0 eV and 4.0 eV for the polarization of light E⊥c. In the energy range from 7 eV to 11 eV the imaginary part of dielectric function is negligible in the polarization of light E∥c. The main feature in the region from 12 to 24 eV is an intense resonance at 14 eV which arises from σ to σ* transitions around the M points in both ᴦ-M and 13 ACS Paragon Plus Environment


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M-ᴦ direction. For germanene, the π to π* absorption spectra was found to be near-infrared at 0.56 eV along the K-M direction when the light is polarized along E⊥c. The σ to σ* transitions are around the ᴦ-M and M-ᴦ points at energy 3.85 eV in the near UV when the polarization of light E∥c as shown in Fig. 7(I(e)). The excitonic effects in 2D silicene and germanene are significant and stronger than that in graphene. Those are due to the fact that the Si-Si and Ge-Ge bond are weaker than the C-C bond. The results found were in agreement with previous calculations.70

In Fig. 7(II (c and d)) we list all bound excited states in the absorption spectra of CaSi2 and CaGe2, respectively. The top of σ-band is situated closer to Fermi energy than the crossing point of π and π* bands at the K and H points. This suggests that electrons from Ca atoms are pre-dominantly donated to π* band in CaSi2 and CaGe2 with a maximum absorption frequency of 3.15 eV and 2.75 eV, respectively. The first exciton peak of CaSi2 for E⊥c was found to be located at 0.5 eV, the second exciton peak lies at 1.25 eV for E⊥c and the third exciton peak exists at 2 eV. The most intense peak in the absorption spectrum exists at 2.75 eV for CaSi2 which begins in the near-infrared region and gradually increases to the visible frequency as shown in Fig. 7(II(c)). More interestingly, the first exciton is observed at 1.85 eV for E∥c in CaGe2 and an intense peak exists at photon energy of 2.85 eV as shown in Fig. 7(II(d)). The optical absorption spectra of freestanding silicene and germanene functionalized with H, F and mixed H-F were also calculated (supporting information Fig. S12 and Fig. S13). The optical absorption shows maxima at 3.82 eV for E⊥c and 7.35 eV for E∥c in silicane. Vertical transitions from the top of the valance band to the bottom of the conduction band close to ᴦ-point contribute towards the absorption spectrum. For germanene, the optical absorption spectra begins in the near infrared region (0.95 eV) and is observed in visible region at photon energy 3.36 eV for E⊥c and peaks at 7.46 eV for E∥c. In case fluorine functionalized silicene, the optical absorption spectrum peaks a 4.00 eV and 8.75 eV for E⊥c and E∥c, respectively. For F-germanene, the optical absorption spectrum shows maxima 3.04 eV and 7.12 eV for E⊥c and E∥c, respectively. For H-Silicene-F and H-Germanene-F, the maximum exciton peak lies around 3.32 eV and 3.01 eV for E⊥c, respectively. In general, for freestanding silicene functionalized with H 14 ACS Paragon Plus Environment

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and F, the absorption occurs mostly in the visible region while that for germanene it is in the infrared for E∥c. However, when E∥c both silicene/germanene in their pristine together with functionalized forms exhibit UV absorption.

The typical optical spectra of C, Ge and C-Ge doping silicene are shown in Fig. 8(I-IV). With increase of the C doping, the intensity of the main absorption peak (E⊥c) increases in the range of 2.50-5.50 eV and then decrease after x=0.556-0.778 as shown in Fig. 8(I(a-f)). For polarization along E∥c as we increases the Cdoping concentration the intensity of the absorption peak increases and at concentration x=0.778 this peak disappears. As shown in Fig. 8(I-III(a-f)) when the light is polarized E∥c the photon energy increases in the UV region for silicene doped with C/Ge and germanene doped with C. In other cases of mixed C-Ge doped system as shown in Fig. 8(IV(a-f)), with increases of doping concentration, the intense peak vary when the light is polarized E⊥c and for E∥c, the absorption peak is found at 8 eV for x=0.06 as shown in Fig. 8(IV(a)). Therefore, in the presence of C-Ge atoms in the system gives rise in-plane low energy π excitation peak due to polarization along the 2D-plane. For C-doping systems in both silicene and germanene the absorption is redshifted with respect to pristine silicene and graphene. For E∥c polarization the absorption spectrum is blueshifted compared to the pristine systems irrespective of doping.

Conclusion In summary, we have performed a comprehensive structural search on the two-dimensional Si1-xCx, Si1-xGex, Ge1-xCx and Si1-2xCxGex sheet with 0 ≤ x ≤ 1 within density functional theory. The structures of the doping systems are linearly correlated with the structures of their individual atomic constituents as predicted by the Vegard’s law. All the in-plane hybrid structures are semiconductors with widely tunable band gaps on doping. The band gaps increase from 0 eV at x=0 or 1 to 2.55 eV at x=0.5 for 2D Si1-xCx. Furthermore, we obtain the band gap 2.07 eV for monolayer Ge1-xCx at x=0.5. The band gaps for C-Ge co-doping systems are controlled by C atoms as Ge doping alone is insufficient to open up the band gap. Optical properties of 2D Si1-xCx, Si1-xGex, 15 ACS Paragon Plus Environment


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Ge1-xCx and Si1-2xCxGex hybrids indicates that with different C, Ge and C-Ge composition ratios the optical responses can be remarkably different and yet absorb visible light for specific compositions. The optical spectrum of silicene/graphene/germanene/doping-silicene monolayer sheets have been calculated for light polarization parallel and perpendicular to the plane. When C-doping in silicene is small (x=0.111 to x=0.5), the main absorption peak occurs in the range of 2.50-5.50 eV and almost vanishes at higher doping. For Ge-doping silicene, the intensity of the main absorption peak decreases in the visible region from 3.75-0.75 eV. Amongst the four systems studied here (three binary and one ternary), Si1-xCx is expected to be most useful to experimentalist as one might be able to access them by sequential replacement of Si by C or vice-versa and observe a monotonic band gap dependence till x ≤ 0.5. It is important to note that for the same stoichiometric ratio of Si/C, there can be multiple low-energy configurations which would result in a spread across the bellshaped curve of the band-gap with respect to doping. Presence, of such configurations would be all the more important under ambient experimental conditions. Nevertheless, it would be worthwhile to experimentally explore the predicted bell-shaped band gap behavior for C doping silicene/germanene and optical properties of such low-dimensional materials. Clearly controlled C doping of silicene and germanene monolayer opens up the band-gaps and also provide a tool to harvest solar energy for semiconductor and photovoltaic applications. Interestingly, apart from pristine monolayer silicene, Ca(II) intercalated multilayer silicene/germanene to the electronic properties and stability of their hydrogenated and fluorinated as available in the van der Waals mineral phases of CaSi2 and CaGe2 are also investigated. Based on phonon spectra, we showed that silicene, germanene, graphene, CaSi2 and CaGe2 are stable as it does not exhibit imaginary phonon mode. Ca(II) intercalated multilayer silicene/germanene towards hydrogenation, fluorination and mixed hydrogenationfluorination are studied. Optical absorption calculations demonstrate that doping monolayers along with Ca(II) intercalated multilayer silicene/germanene have strong photo-absorption in visible light region. The presence of Ca(II) stabilizes the silicene/germanene layers and also the Ca(II) is affecting the electronic structure of these 2D materials.

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ASSOCIATED CONTENT Supporting Information. AUTHOR INFORMATION Corresponding Author E-mail: [email protected]. Tel.: +91-33-24734971. Notes The authors declare no competing financial interest.

Acknowledgements This work was supported by The World Academy of Sciences (TWAS) - for the advancement of science in developing countries (FR number: 3240280472) and Indian Association for the Cultivation of Science (IACS) is gratefully acknowledged. AD thanks DST, INSA and BRNS for partial funding.

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Figure 1: Phonon dispersion of (a) Silicene, (b) Germanene, (c) Graphene, (d) CaSi2 and (e) CaGe2. ᴦ (0, 0, 0), K (2/3, 1/3, 0), M (½, 0, 0) refer to special points in the first Brillouin zone in reciprocal space.



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Figure 2: Lowest energy structures of the most stable structures of: (I) 2D Si1-xCx at different doped ratio of C atoms (a) silicene (x=0.0), (b) x=0.111, (c) x=0.222, (d) x=0.333, (e) x=0.5, (f) x=0.556, (g) x=0.778) (h) x=0.889 and (i) graphene (x=1.0). (II) 2D Si1-xGex at different doped ratio of Ge atoms (a) silicene (x=0.0), (b) x=0.111, (c) x=0.222, (d) x=0.333, (e) x=0.5, (f) x=0.556, (g) x=0.778) (h) x=0.889 and (i) germanene (x=1.0). (III) 2D Ge1-xCx at different doped ratio of C atoms (a) germanene (x=0.0), (b) x=0.111, (c) x=0.222, (d) x=0.333, (e) x=0.5, (f) x=0.556, (g) x=0.778) (h) x=0.889 and (i) graphene (x=1.0). (IV) 2D Si1-2xCxGex at different co-doped ratio of C and Ge atoms (a) silicene (x=0.0), (b) x=0.056, (c) x=0.111, (d) x=0.167, (e) x=0.278, (f) x=0.333, (g) x=0.389, (h) x=0.444 and (i) x=0.5. Blue spheres represent Si atoms, dark gray spheres represent Ge atoms and brown spheres represent C atoms.


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Figure 3: Lattice parameters and bond lengths (both in Å) for (a) Si1-xCx, (b) Si-C, (c) Si1-xGex, (d) Si-Ge (e) Ge1-xCx and (f) Ge-C at different fractions of C and Ge.



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Figure 4: Charge density difference for (a) Hydrogenation of CaSi2, (b) Fluorination of CaSi2 and (c) Mixed hydrogenation-fluorination of CaSi2. Note that all the reactions occur on the topmost silicene layers of CaSi2. Ca, Si, F and H atoms are shown in green, blue, gray and white respectively. Pink/yellow represents charge accumulation/depletion, the isosurfaces refer to isovalues=4.85 x10-3 electrons/bohr3.

Figure 5: Charge density difference for (a) Hydrogenation of CaGe2, (b) Fluorination of CaGe2 and (c) Mixed hydrogenation-fluorination of CaGe2. Note that all the reactions occur on the topmost germanene layers of CaGe2. Ca, Ge, F and H atoms are shown in green, violet, gray and white respectively. Pink/yellow represents charge accumulation/depletion, the isosurfaces refer to isovalues=4.85 x10-3 electrons/bohr3.


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Figure 6: Calculated band gaps in (a) Si1-xCx and (b) Ge1-xCx sheets as the function of doping ratio of C atoms. Note that the spread in the band gaps for intermediate doping arises due to multiple configurations/structures at the same composition. The solid lines connect the band gaps for the most stable configuration at a given doping concentration.



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(I) Silicene-Graphene-Germanene

(II) CaSi2 and CaGe2

Figure 7: (I) Band structure of pure (a) silicene, (b) graphene and (c) germanene and the imaginary part of dielectric function of optical spectra (d) silicene, (e) graphene and (f) germanene. (II) The band structures along the high symmetric points of (a) the intercalated compound CaSi2 with alternatively stacked silicene and Ca in AA stacking sequence, (b) CaGe2 with alternatively stacked germanene and Ca in AA stacking sequence, (c) Optical absorption spectrum of CaSi2 and (d) CaGe2 for light polarization E⊥c and E∥c to the surface plane shown in blue and red respectively. 28 ACS Paragon Plus Environment

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(II) Si1-xGex

(I) Si1-xCx

(III) Ge1-xCx

(IV) Si1-2xCxGex

Figure 8: Imaginary part of dielectric function of 2D for E⊥c and E∥c in (I) 2D Si1-xCx at different doping ratio of C atoms (a) x=0.111, (b) x=0.222, (c) x=0.333, (d) x=0.5, (e) x=0.556 and (f) x=0.778). (II) 2D Si1-xGex at different doping ratio of Ge atoms (a) x=0.111, (b) x=0.222, (c) x=0.333, (d) x=0.5, (e) x=0.556 and (f) x= 0.778). (III) Ge1-xCx at different doping ratio of C atoms (a) x=0.111, (b) x=0.222, (c) x=0.333, (d) x=0.5, (e) x = 0.556 and (f) x=0.778). (IV) 2D Si1-2xCxGex at different co-doping ratio of C and Ge atoms (a) x=0.06, (b) x = 0.111, (c) x=0.167, (d) x=0.25, (e) x=0.278 and (f) x=0.389 monolayer system.



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Effect of Doping in Controlling the Structure ... - ACS Publications

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