Absorption and Mid-IR SHG in Two-Dimensional Halogen and

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Absorption and Mid-IR SHG in Two-Dimensional Halogen and Hydrogen Saturated Silicene Series Guoyu Yang, and Kechen Wu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b08810 • Publication Date (Web): 14 Nov 2017 Downloaded from http://pubs.acs.org on November 17, 2017

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Absorption and Mid-IR SHG in Two-Dimensional Halogen and Hydrogen Saturated Silicene Series Guoyu Yang†,‡ and Kechen Wu∗,† †

State Key Laboratory of Structural Chemistry, Fujian Institute of Research on the Structure of

Matter, Chinese Academy of Sciences, Fuzhou 350002, People’s Republic of China , and ‡

University of Chinese Academy of Sciences, Beijing 100049,People’s Republic of China

E-mail: [email protected]

*To whom correspondence should be addressed †Fujian Institute of Research on the Structure of Matter ‡University of Chinese Academy of Sciences

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ABSTRACT

Developing nonlinear optical nano-devices compatible to current silicon chip industry is of great interests. Modified silicene, as its single atomic silicon thickness, has become a rising material. Here, based on first-principle calculations, two-dimentional Halogen and Hydrogen saturated silicene is proposed to be competing candidates for strong second harmonic gener ation (SHG) material working in mid-IR range. The SHG coefficient is more than ten times larger than KDP with high electron cloud deformability around halogen atoms. And the Si-H absorption peak is within the range of 2102 - 2140 cm-1 (4673 - 4757 nm), red shifted com pared to 3300 cm-1 (3030 nm) of C-H in graphane. In addition, the two-dimensional material construction method can be extended to other novel two-dimensional single-element materials including borophene, phosphorene, germanene, arsenene, antimonene and bismuthene.

Introduction The nonlinear opitcal (NLO) effect in IR region is crucial with wide application including bio and medical system1 , encrypted communication2 , high energy laser device3. However, corresponding high performance material has yet been well developed as failing to meet the five requirements at the same time, i.e. phase matching behavior, low absorption in working optical wavelength area, high laser induced damage thresholds(LIDTs), stable chemical and mechanic properties, large Second Harmonic Generation (SHG) coefficient4,5. Therefore, exploring new crystalline IR NLO material is of broad scientific and technological importance. If in crystalline NLO material6, the cations can be considered as frameworks mainly to stabilize the material, while the anions as building blocks to exhibit large electron cloud deformability and

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strong SHG effect5,7. Frequently discussed IR NLO material can be categorized into three groups based on their anions: chalcogenide (S group), including AgGaS2,AgGaSe28–12, VA group (P group), including ZnGeP28,13,14, halogen (X group), including Cs2Hg3I8 15–17,and HgBr218. Some recent work implies central symmetric material can exhibit NLO effect after special preparation into nano size19, even though, as a natural result of phase mismatching, the SHG coefficient di jk decreases as the crystal size going down into micrometer for most three dimensional (3D) NLO materials18,20,21. This defect, together with the requirement of equipment miniaturization, inspires scientists to search low dimension (LD) NLO materials. Among those LD materials investigated, two dimension (2D) single/few layer(s), such as MoS222–25, WSe226,27, h-BN22, and GaSe 28 , with their relatively low-cost top-down preparation technique, (i.e. exfoliation from the bulk) is more reported. However probably due to the limitation of laser generation and detection, most work is done in the visible and near-IR region. Silicene, with its atomic thickness 29–31 and compatibility with other electronics material32,33, was expected to be a promising nano material in silicon based chip industry34,35. It is one of the analogues of graphene36 has been synthesized and/or proposed, including borophene 37,38 , phosphorene 39 , germanene 40–42 , arsenene43,44, stanene 45–47 , antimonene 43 and bismuthene48.These single-element systems correspond to elements that are akin to carbon on periodic table of elements, and usually, as perfect 2D crystal, is central symmetric thus no strong SHG effect. To break central symmetry, methods like stacking 22,32 , charge accumulation 26 and electric field 27

, adding substrate 49,50 , strain and stress 33 has been adopted. Here, based on first principle

calculation, Si2XH (X refers to Halogen), a new 2D crystal, halogen and hydrogen saturated

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silicene, or halogen substituted silicane51 , is proposed to be a promising 2D SHG material in IR region fulfilling the five requirements mentioned in paragraph one. The calculation results reveals that the silicon backbone plays the role of ’cation’ in the functional motif theory5,6, including stabilizing the material, red shifting the absorption away from mid-IR area, while the halogen atomsas ’anion’ to generate large SHG signal by offering highly deformable electron cloud.

Computational Methods Here, using Vienna ab initio simulation package (VASP)52 , density functional theory (DFT) based first principle calculation is performed. Projector augmented-wave (PAW) pseudopotential 53

is used at the general gradient approximation (GGA) level in the scheme of Perdew-Burke-

Ernzerhof (PBE) functional54. A vacuum layer of 50 Å along the z-direction is employed in order to avoid interactions between two Si2XH images in nearest-neighbor unit cell. The structure optimization is performed with 3x3x1 supercell, cutoff energy 550 eV, unitcell energy difference smaller than 10-4 eV. The atom position is relaxed with fixed lattice parameters until the force is less than 10-3 eV/Å and the lattice constant scanned to the accuracy of 0.01 Å. A Gammacentered Monkhorst-Pack scheme55 with k-point mesh of 7x7x1 is used. For static calculation, the convergence criterion of total energy is 10-6 eV, cutoff energy 750 eV. The k-point mesh is 7x7x1 for density of state (DOS) and optical properties. And for band calculation, 20 k points are intercepted between two symmetric points. The SHG coefficient was calculated using length gauge method56–58 without scissor operator correction.59 And the absorption spectrum is also confirmed by using many-body perturbation theory including quasiparticle GW0 and the Bethe-Salpeter equation (BSE).60,61 The total energy cutoff

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was set to 550 eV, and for the response function was set to 200 eV. A k-mesh of 5x5x1 with unit cell was used. A total of 160 bands and 96 frequency points were included in the GW0 calculation which was followed by the BSE spectrum calculation using the GW0 quasiparticle results. The 32 highest valence and 32 lowest conduction bands were included in the calculation of the excitonic states. The IR absorption wavenumber is calculated on crystal unit cell using the VASP Density Functional Perturbation Theory (DFPT), and intensity calculated by summing up the dipole derivative of rectified coordinate.62–65 The phonon dispersion spectrum is calculated using PHONOPY package66 with finite displacement method on supercell as or larger than 3x3x1.

Results and discussion Structure Monolayer Silicene, though well known as single layer (111) cut of fcc Si31, has rarely been prepared by liquid or mechanical exfoliation from the bulk like graphene36, antimonene67, MoS2 and h-BN22. Instead, reported synthesyzing methods is mainly bottom-up vacuum deposition31,68– 70

, like borophene37. To further saturize silicene, soft chemical synthesis hydrolization71,72,

followed by functional group substitution73–75 is a promising strategy. And substrate could be used to control which side to be covered or exposed for reaction109, 110. Though, possibly because that normal halogenated reagents (such as CCl4, Cl2 gas, PCl5) are highly toxic, to the best of our knowledge, Si2XH (Figure 1)has not been really synthesized by now. Therefore, first-principle based principle calculation should be serving as a very useful tool here.76

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Figure 1: Structure of Si2XH (X = F, Cl, Br, I) Here the X;Y;Z directions were defined in this way: the Z direction was perpendicular to the Si2XH plane; X is the zigzag direction in the plane; Y is the armchair direction in the plane.

As seen from our phonon calculation result (See Supporting Information, Phonon Spectra), among the four Si2XH (X=F, Cl, Br, I) models, Si2FH and Si2IH are both stable with small imaginary frequency within the acceptable range compared with borophene77–79 and bismuthene80, while Si2ClH and Si2BrH has no imaginary frequency. The binding energy of each model (defined in (Eq. 1)) is respectively -0.29, -0.49, -0.42, -0.42, -0.58 eV/atom(Si2H2, Si2FH, Si2ClH, Si2BrH, Si2IH), which is consistent with previous calculation result in literature.81,82 (1)

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Where

and

crystal.

are respectively the total energy per atom of silicene and that of Si 2XH

is the total energy per atom in XH molecular.

and

denote the molar

fractions of the corresponding atoms.

For the structure, the Si2XH crystals belong to P3M1 symmetric group (group 156), and Si2H2 to P3-M1 symmetric group (group 164), with the Si sp3 hybrid orbital remains three fold symmetry (Figure 1).

Linear Optical Properties (Absorption) Since the three fold symmetry were kept in the Si2XH series, the relationship (Eq. 2,Eq. 3) in linear dielectric function hold. (2)

(3)

Also, the optical absorption in monolayer structure in different direction varies:83,84 in the direction perpendicular to the 2D surface is principally excitonic absorption, but the parallel com ponent not affected by that. The absorption coefficient is obtained by using Eq. 4:83,84

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(4)

First, the electronic absorption calculated with DFT (Figure 2), (A.1) (A.2)) and GW0 (Figure 2), (B.1) (B.2)) was discussed. DFT calculation, though neglect many-body effect and exciton effect (which is usually illegible in bulk semiconductor material), was sometimes used to estimate the electronic optical absorption gap for being affordable.85 Here the DFT calculated absorption low energy limit is about 1 eV (1240 nm), which is without the mid-IR range (1500-6000nm).

Figure 2: Electronic and Vibrational Absorbtion of Si2H2 and Si2XH (A.1) (A.2): Electronic absorption coefficient calculated with DFT in the unit of eV and nm; (B.1) (B.2): Electronic absorption coefficient calculated with GW0 in the unit of eV and nm; (C.1) (C.2): Vibration Absorbtion in IR in the unit of cm-1 and nm.

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Here, the IR absorption was plotted both in wavenumber (cm-1) and wavelength (nm) with the Lorentz broadening of FWHM=100 cm-1 using Multiwfn.86

And for GW0, previous work usually stressed on two gaps in semiconductor: fundamental (or quasi-particle) and optical gaps, which were each calculated by ab initio GW0 to include electron-electron interaction, and by GW0 approach plus the Bethe-Salpeter equation (BSE) to include electron-hole interaction (excitonic effect).85 The GW calculated absorption result (Figure 2), (B.1) (B.2)) shares the same low-energy limit with DFT result (Figure 2), (A.1) (A.2)) (1 eV, 1240 nm), especially for Si2H2, the absorption low limit is consistent with previous work.87,88 However, the relative absorption strength of in-plane and perpendicular differs in these two methods. These result is in accordance with the conclusion proved in several groups that the perpendicular direction was principally affected by exciton, but the parallel was not83,84, so our calculation result should be considered as reliable in this aspect. Also, this validated our accuracy parameter choices in GW0 method. As the result, the electronic absorption in mid-IR range is eligible, so we turn attention to the vibration absorption in IR range. The IR region absorption is dominated by vibration. Comparison between the IR spectrum of Si2XH and Si2H2 (Figure 2), (C.1) (C.2)) gives two points: every model shares a small peak in the place about 2100 cm-1 (4761 nm), the peaks were assigned to Si-H bond vibration (see Supporting Information, IR Absorption); while in the broad and strong peak groups around 500 nm, every Si2XH has multiple/shoulder peaks, while Si2H2 does not. In Si2XH, part of these peaks corresponds to Si-X bond vibration, some were significantly coupled with Si-Si bond vibration, so the peak groups would be complex; while for Si2H2, for the structure is simpler with central symmetry, the peaks’ shape is plain. Concentrated on the absorption range,

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elaboration on vibration (Figure 2), (C.1) (C.2)) reveals that on 1000-4000 nm, the Si2XH material could be considered as transparent, which takes a large part on mid-IR region (15006000 nm). So, the low absorption makes Si2XH series of strong candidates as SHG material in mid-IR.

Nonlinear Optical Properties Just like dielectric function, symmetry also simplifies the SHG coefficient analysis. In Si 2XH (P3M1, group 156) and Si2H2 (P3-M1, group 164), Si sp3 hybrid orbital remains three fold symmetry (Figure 1). So among the 10 reduced SHG coefficients di jk (i, j,k = X,Y,Z), with X,Y,Z in Figure 1 also denoting the direction of dielectric constant coordinate system,89 only four (showing in (Eq. 7) and (Eq. 8)) need to be paid attention to when calculating effective SHG coefficient de f f (Eq. 5) (Eq. 6).90 (5)

(6)

Where de f f (ooe) and de f f (eeo) denotes de f f in ooe and eeo mode (here o means ordinary and e means extraordinary ). And

and

are defined by optic polarization vector in polar

coordinates. group1 :

-dXXY = dYYY (7)

group2 :

dXXZ = dYYZ (8)

Nonlinear Optical Result. How to quantitatively evaluate the SHG effect of 2D monolayer (ML) material is another important issue to be considered. In previous literature, two methods were proposed: (i) to

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compare with a known freshly cleaved bulk surface (say, alpha-quartz22). This method is experimentally convenient, and the theory of bulk surface is well established91, yet it ignored the difference of thickness between the two models, ((sub)nano vs. (semi)infinite), thus hindered further analyzation. (ii) to compare with 3D bulk result92. This method adds a ’thickness’ (l) to define the ’volume’ of 2D ML material. Here l is decided by the layer distance of corresponding 3D crystals92, or microscope image of several-layer structure24. In this paper, SHG coefficient was defined within the first principle calculation scheme. To compare with the first method, the SHG coefficient direct calculation result in 3D vacuum layer d(vac) was multiplied with the vacuum layer height, (i.e. h = 50 Å here) (Eq. 9). The result d(2D) means SHG effect per unit area. (Figure 3, left Y axis). While to compare with the second method, as corresponding Si2XH 3D crystals do not actually exist, thickness l has to be newly defined. Here four two-layer (2L) models were built to include different stacking modes93. The layer distance of the four varied within 5%, so the average was used in (Eq. 10)(See Supporting Information, Geometry). The d(3D) here means the SHG coefficient per ’volume’. d(2D) = d(vac) ·h d(3D) = d(vac) ·h / l

(9) (10)

Here, d(2D) and d(3D) are ML SHG coefficients presented in 2D (per area) and 3D (per volume), and d(vac) is the result calculated with vacuum layer in models.

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Figure 3: SHG Coefficient of Si2H2 and Si2XH Here, the black square, red dot, green up triangle, and blue down triangle is respectively for -dXXY , dYYY , dXXZ, dYYZ. And the solid characters are for d(2D) (left Y-axis), hollow for d(3D) (right Y-axis). The five horizontal lines, as the notation, denotes several large SHG 3D crystal in IR range, respectively: HgBrI, HgI2 21,94 in X group; AgGaS2, AgGaSe2 8–12 in S group; ZnGeP2 8,13,14 in P group.

The result of di jk is plotted in Figure 3. First, the SHG of Si2H2, a central symmetric structure, is very close to zero, which is consistent with the second order nonlinear optics principle.90 Second, it is shown that the two doubles -dXXY and dYYY , dXXZ and dYYZ data matched well, which is in accordance with previous symmetry analysis (Eq. 7) (Eq. 8). Thirdly, the corrected di jk (3D), is comparable with, if not stronger than, previous IR crystal material HgBrI,HgI2

21,94

(X group) ,

AgGaS2, AgGaSe2 8–12 (S group) ; and ZnGeP2 8,13,14 (P group) (Figure 3, right Y axis). Fourthly, the di jk increases as the X atom goes heavier, following the sequence of F, Cl, Br, I. This can be explained by two sides, heavier X makes the two sides of silicene more asymmetric, thus larger hyper-polarizabiliy90 (here hyper-polarizabiliy equals half of di jk 95); and halogen electron cloud d formability increases as the atoms go heavier96.

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Nonlinear Optical Band and DOS Analysis. To further specify the structure - property - function relationships, detailed band, density of state and partial charge analysis is performed. Since SHG means electron hopping from valence bands (VB) to conductive bands (CB), band analysis should be a good starting point. By adjusting the upper and lower boundary of the bands (Supporting Information, Define SHG of a Single Band) in NLO calculation, the contribution to SHG coefficient in certain direction from each band can be specified. For any di jk among the four discussed, it is found that the sum of the five most contributing VBs’ makes more than 80% of the total di jk, and that also applies to CB. Here Si2ClH is taken as an example; others are shown in (Supporting Information, Band and DOS). As shown in Figure 4, the five VBs and five CBs with most contribution of the each four effective di jk of Si2ClH were highlighted in the total bands. The ten bands are near Fermi level but not the closest ten, which means that the two-electron process selectivity is not just energy dependent. Careful investigation into the VB shows that the group -dXXY =dYYY share the same important five VBs and five CBs, while the dXXZ=dYYZ makes another group, which is in accordance with the P3M1 symmetry. And for the convenience of discussion, the bands were sorted by the energy at Gamma point and numbered. The criteria is that the top VB is numbered half the total number of the valence shell electrons (for example, 3x3 model Si2XH top VB corresponds to

× 3×

3×(2× 4 + 7 + 1) = 72). So here, as shown in Figure 4 Si2ClH, band No.71, 72 are important only for -dXXY and dYYY ; band No.49, 50 are for dXXZ and dYYZ; band No.52, 53 and 54 are important for both groups of di jk.

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Figure 4: Electronic Properties of Si2ClH In the left figure for band, red lines are band No. 71,72,89,90, only important to -dXXY and dYYY; blue lines are band No. 49,50,76,76, only important to dXXZ and dYYZ; green lines are band No. 52,53,54,73,74,75, important to -dXXY and dYYY, dXXZ and dYYZ. This means for -dXXY and dYYY, the bands concerned are No. 52,53,54,71,72,73,74,75,89,90; for dXXZ and dYYZ, the bands concerned are 49, 50, 52, 53, 54, 73, 74, 75, 76, 77. All the bands are sorted and numbered by the energy of Gamma(G) points. The Valence Bands are Band No. 1 to No. 72.

Nonlinear Optical Charge Analysis. Partial charge density of the each seven bands was plotted in 3D real space (Supporting Information, Partial Charge Analysis). Band No.71 and 72 are basically the same situation, with charge distributed on X and Si atoms, but not bonded; No.49 and 50, 52, 53 and 54 are the similar, electron clouds is around X atoms extending towards Si (Figure 5). This comes to the

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conclusion that for -dXXY and dYYY , Cl atoms takes the main contribution, Si atoms are the auxiliary at best; and for dXXZ and dYYZ, the SHG signal is almost attributed to Cl atoms. This is in consistent with the previous analysis on NLO crystals binary and ternary metal halides.96

Figure 5: Partial Charge Analysis of Si2ClH Other Issues in Nonlinear Effect. For NLO crystals, proper transparency usually means low electron absorption and vibration absorption in working region. The Si2XH are semiconductor with band gap >1.8eV, calculated electron absorption is mainly in UV region (Supporting Information, Electronic Absorption) 97,98. And for vibration part in IR region(Supporting Information, IR Absorption), as the mid-IR region is 1500-6000 nm, the Si-H bond absorption peak ranging in 2102 - 2140 cm-1 (4673 4757 nm) indicates that Si2XH is better IR material compared to graphane, where C-H bond vibration is around 3300 cm-1 (3030 nm). The Si-X wavenumber decreases from 700 to 300 cm-1 (14286 nm to 33333 nm, or 14 mm to 33 mm) (Supporting Information, IR absorption). These Si-H and Si-X IR peaks are consistent with previous spectrum results99,100.

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Si2XH, belonging to P3-M1 symmetry, is uniaxial crystal. But for monolayer, phase matching issue is trivial with atomical thickness perpendicular to the plane,24 so birefringence was illegible here. As to the laser damage threshold, many issues should be considered,

4

such as melting

temperature by dynamic simulation101, thermo-conductivity66,102, heat capacity 66 light absorption and heat conversion. These would be further complimented in our future work. To the best of our knowledge, at present, GW approach in low dimension material optical properties were mostly applied in linear optical aspect.85,103,104 In this paper, SHG coefficients were calculated by DFT method, which just include single-electron approximation in the twophoton process, and the actual multi-exciton process was indicated to be more prominent if correlation was taken into consideration. 105 So it is very likely our result could survive future reliable full GW calculation in many-electron process.106–108

Conclusion Si2XH, halogen and hydrogen saturated silicene, was predicted to be 2D monolayer mid-IR nonlinear optical material by first principle calculation. Electron properties analysis revealed that SHG signals mainly attributed to electron cloud of halogen atoms, and the transparency in midIR region attributed to the vibration red shifted by heavier silicon atoms. We expect our work not only inspire optoelectronic device design in silicon-based nano chip technology, but also be generalized to other graphene analogues.

ASSOCIATED CONTENT Supporting Information. Geometry parameters;

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Phonon Spectra; Define SHG of a Single Band; BAND and DOS; Partial Charge Analysis; IR Absorption.

AUTHOR INFORMATION Corresponding Author Kechen Wu, E-mail: [email protected] Author Contributions The manuscript was written with contributions from all authors. All authors have given approval to the final version of the manuscript. Funding Sources This study was supported by the National Natural Science Foundation of China (No. 21673240), Foreign Cooperation Project of Fujian Province (No. 2017I0019), and the Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (the second phase). Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT

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This study was supported by the National Natural Science Foundation of China (No. 21673240), Foreign Cooperation Project of Fujian Province (No. 2017I0019), and the Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (the second phase).

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