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Stacking effect on electronic, photocatalytic and optical properties: A comparison between bilayer and monolayer SnS
Computational Materials Science 158 (2019) 272–281
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Stacking effect on electronic, photocatalytic and optical properties: A comparison between bilayer and monolayer SnS
T
Qiang Zhanga, Xuanyu Chena, Wing-Chung Liub, Yuexia Wanga,
⁎
a b
Key Laboratory of Nuclear Physics and Ion-beam Application (MOH), Institute of Modern Physics, Fudan University, Shanghai 200433, China Kong Cheong Enterprise Development LTD, Trans Asia Center, 18 Kin Hong Street, Kwai Chung, Hong Kong, China
ARTICLE INFO
ABSTRACT
Keywords: Density functional theory Stacking models Electronic properties Photocatalytic properties Optical properties
In this work, the stacking-dependent optoelectronic performances of a bilayer SnS were explored based on density functional theory (DFT). The results demonstrated that an AB-stacking induces an indirect-to-direct transition, a feature that is capable of vanquishing electron transition impediment from an intrinsic indirect monolayer SnS. An anisotropic and small carrier effective mass exists in all the stacking models, among which the AB-stacking with the lowest value favors high carrier mobility. Calculated band alignments are indicative of acceptable and adjustable photocatalytic activity for all the stacking models, unlike the monolayer SnS. The ABstacking configuration possesses the strongest redox power, which facilitates it to be a potential candidate for photocatalytic water splitting. Additionally, the AB-stacking does effectively improve optoelectronic properties. The study demonstrated that layer-stacking is an availably adjustable method in the fields of sunlight-driven photocatalysis for nano-optoelectronic devices.
1. Introduction In the last two decades, two-dimensional (2D) layered materials have aroused tremendous research interest having its origin rooted in the unique electronic, mechanical and optical properties for splendiferous prospects of applications in next generation optoelectronic and photonic devices [1–4]. Among them, the layered group-IV chalcogenides have attracted enormous attentions recently in light of their earth abundant, environmental friendship, low cost and unique potential applications in fields such as solar energy conversion, optoelectronics and thermoelectric devices [5–8]. The most representative group-IV chalcogenide is SnSe, which is well known as high-performance thermoelectric material with ultralow thermal conductivity [9,10]. Furthermore, bulk and monolayer group-IV monochalcogenides MX (M = Ge, Sn; X = S, Se) possess many merits, such as stability, flexibility and high-performance as piezoelectric materials. In stark contrast to MoS2 and AlN, the anisotropic piezoelectric coefficients of MX families are fairly large [5,11–13]. Moreover, atomically thin group-IV monochalcogenides are interesting in spin physics as desirable spin-transport devices. For example, the absence of inversion symmetry and the generation of dipole moment due to the interaction of spin-orbit coupling in the SnSe and GeSe sheets induce spin splitting of the energy bands with anisotropic feature, and make the sheets unprecedented potential in direction-dependent spin-transport devices [14]. ⁎
Among group-IV monochalcogenide families, tin sulfide (SnS) also possesses prominently high absorption efficiency since its absorption approaches the optical absorption threshold of ∼1.3 eV [15], an optimal band gap. Additionally, SnS has a p-type conductivity with a large intrinsic hole concentration of 1017 cm−3 [16]. Hence, it was widely accepted that layered SnS is considerably suitable for photovoltaic (PV) absorbers. Currently, the conversion efficiency of SnS-based cells just approaches to 2%, indicating that large improvement can be done in the design of the photoelectric conversion devices. The ideas to improve the properties usually involve in adopting atomic thickness [17,18] and imposing strain upon the compounds [19]. For instance, the optoelectronic properties of few-layer SnS can be effectively adjusted through controlling layer number and strain along the stacking direction [20]. It’s worthy of noting that very recently, high quality and large-size monolayer SnS flakes were fabricated successfully based on liquid exfoliation method [21]. So, researches on 2D layered SnS will continue to be on the rise in the foreseeable future. It is well known that multi-layered structures can be synthesized by stacking with an accurate steerability. The strong covalent bonds knitting skeletons guarantee the in-plane stability, at the same time, the interlayer interactions establish the stacking SnS multi-layers. Although reassembled by stacking few-layered sheets with well-known skeletons, a novel 2D material much possibly shows us unacquainted phenomena in physical or chemical properties, which may facilitate the design in
Corresponding author. E-mail address: [email protected] (Y. Wang).
https://doi.org/10.1016/j.commatsci.2018.11.035 Received 16 August 2018; Received in revised form 26 October 2018; Accepted 19 November 2018 0927-0256/ © 2018 Published by Elsevier B.V.
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PV devices [22,23]. Therefore, stacking is anticipated to act as a new physical dimension to discover and modulate novel optoelectronic properties [20,24,25]. It was reported that the power conversion efficiency of AA- and AB-stacking bilayer phosphorene can approach ∼18 and 16%, much higher than the reported efficiencies in cutting-edge optoelectronic or photonic devices (trilayer graphene/transition metal dichalcogenides) [22]. To date, the research on the stacking behaviors of layered SnS is far from abundant, especially on the stacking-dependent electronic, photocatalytic and optical properties. In this work, we investigated the structural parameters, stability, photocatalysis and optoelectronic properties of the bilayer SnS for the four various layer-stacking cases to explore the staking effect based on density functional theory (DFT) calculations together with van der Waals (vdW)-corrected exchange-correlation function. The results showed that the AB-stacking with stable structure is superior to the other three stacking models: only the AB-stacking can induce an indirect-to-direct band gap transition; the effective mass of the ABstacking is the smallest, favoring high mobility of carriers; the ABstacking has acceptable and adjustable photocatalytic activity, and the strongest redox power for photocatalytic water splitting. Most importantly, it was found that the AB-stacking does effectively improve the photoelectric properties in comparison with the monolayer SnS. The underlying mechanisms governing the optical properties were thoroughly discussed. Our work evidenced that the layer-stacking is an available method to design 2D-materials with advanced photoelectric and photocatalytic properties.
[29,30]. A DFT-D2 semiempirical dispersion-correction method, which has taken the vdW interactions into account and reasonably predicted the interlayers distance, was used to calculate the interlayer distance for stacking models [23,31]. A vacuum space of 18 Å was adopted to avoid the interactions of image interlayers. In the calculation of structural optimization and relevant properties, the convergence criterion for total force on each atom was less than 10−2 eV/Å, and for energy, 10−6 eV. It is well known that traditional exchange-correlation functional, such as GGA-PBE, underestimates the band gap by about 30% [32,33], which will result in incorrect optoelectronic calculations. Therefore, based on well-PBE-optimized structures, we adopted the state-of-the-art HSE06 function [34–36] to further calculate optoelectronic properties. A 41 × 31 × 1 and 41 × 31 × 3 k-points generated by the Monkhorste-Pack scheme were used to sample Brillouin zone (BZ) for the monolayer and the bilayer SnS, respectively. For optical spectra calculations, unoccupied states should be considered as more as possible in order to meet the accuracy, meanwhile, the integral in the irreducible BZ with a grid containing more k points was done by means of the modified tetrahedron method. 3. Results and discussions 3.1. Geometric structure Here, monolayer SnS motif was adopted from a well-characterized configuration by experiments [21], which belongs to the space group Pmn21 (No. 31, C27V ) and possesses the analogue puckered structure as black phosphorene (BP) [25]. Fig. 1 is well-optimized structure, where zigzag and armchair directions are along a and b vectors, respectively. Relaxed structural parameters are summarized in Table 1, which are consistent with those by other works [25,34,37,38]. The lattice lengths of a and b in its primitive cell are very close, 4.07 Å and 4.30 Å, respectively. Thus, it can be regarded as square structure approximately, as shown in Fig. 1(c). Distinct from SnS, BP exhibits more disparity of length between a and b lattice parameters [39]. Obviously, the square
2. Computational details All first-principle calculations on the basis of DFT [26,27] have been implemented using Vienna ab initio simulation package (VASP) [28]. A method under the framework of the projector augmented wave (PAW) and a plane wave basis set with a cutoff energy of 400 eV were used. The generalized gradient approximation (GGA) was expressed by Perdew-Burke-Ernzerhof (PBE) as the exchange-correlation functional
Fig. 1. The structure of monolayer SnS in (a) top and (b) side view. d1 and d2 are the in-plane and out-of-plane bond lengths, respectively. θ1 and θ4 are the in-plane bond angles and θ2 and θ3 are the out-of-plane bond angles. (c) The unit cell of monolayer SnS. (d) Brillouin zone with high-symmetry points labeled. 273
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Table 1 The structural parameters for the monolayer and bilayer SnS are given. Type
Mono AA AB AB′ AC
Binding energy (meV/atom)
/ −48.1 −55.65 −38.02 −46.56
Equilibrium distance
Lattice constant (in Å)
Bond length (in Ǻ)
Bond angle (in degree)
de-in
a
b
d1
d2
θ1 = θ4
θ2
θ3
/ 3.28 Å 3.06 Å 3.17 Å 3.64 Å
4.07 4.063 4.061 4.081 4.072
4.30 4.203 4.205 4.103 4.204
2.74 2.72 2.71 2.72 2.72
2.59 2.67 2.67 2.66 2.67
95.99 94.9 94.96 94.62 94.59
88.95 85.9 86.01 86.21 86.27
101.03 103.17 103.54 102.81 102.74
structure of SnS with almost in-plane feature stems from relatively weaker sp3 hybridization, contrasting with even more puckered structure of BP which presents a stronger sp3 hybridization [25]. Then we systematically investigated the layer-stacking behaviors for the bilayer SnS. Four main high symmetry stacking orders were considered in this study, namely, AA-, AB-, AB′- and AC-stacking, which are similar to the bilayer phosphorene [40] and the arsenene [23], as shown in Fig. 2. In the AA-stacking configuration (see Fig. 2(a)), the upper layer is accurately matched with the under layer in the xy-plane. For the AB-stacking, the upper layer of the AA-stacking is shifted by a half of the unit cell along the a-direction with respect to the under layer (Fig. 2(b)). For the case of the AB′-stacking (Fig. 2(c)), it is derived from shifting the upper layer of the AA-stacking by a half of the unit cell along the b-direction, which makes the two constituent stacking skeletons form mirror images each other, as seen in the side view. The space group of the AB′-stacking is not the same as that of the ABstacking, since a-axis and b-axis are not equivalent. The AC-stacking is constructed when the upper layer is shifted by a half of the unit cell both along the a- and b-directions with respect to the AA-stacking (Fig. 2(d)). In order to explore optoelectronic properties in response to stacking models, we firstly evaluated the interlayer binding energy for the bilayer SnS, which is defined as Eb = (Ebi 2 × Emono)/ N , where Ebi (Emono ) represents the total energy of the relaxed bilayer (monolayer) SnS, and N, the total number of atoms in the bilayer SnS. Fig. 3 is the binding energy (Eb ) as a function of interlayer distance din, with which we obtained well-optimized equilibrium interlayer distance (de-in) listed in Table 1. The lowest value in a binding energy curve corresponds to the stable configuration of the bilayer. Thus, structural parameters (see Table 1) for each stacking model can be measured base on these stable configurations. The results are fairly consistent with previous calculations [41]. It’s well known that KBT reflects average thermal energy of single atoms, here KB is the Boltzman constant and T is temperature. The value is close to 26 meV at 300 K. So, the binding energies for the AA-, AB- AB′- and AC-stacking structures exceed the average thermal energy of single atom at the temperature of 300 K, which means that the four stacking models considered here are energetically favorable for survival at the room temperature. For the AB-stacking, the binding energy is the lowest, and it is thus the energetic top-priority configuration with respect to other three stacking systems. Such case is similar to bilayer stacking BP [40]. Table 1 shows that de-in is sensitive to the stacking models. Since the atoms of the top layer point directly to those of the under layer for the AA- and AC-stacking models, it causes somewhat large interlayer distance. By contrast, the upper layer does not directly stack over the under layer for the AB- and AB′-configurations, and thus the interlayer distance is smaller. For the most compatible AB-stacking, d1 reduces slightly to 2.71 Å, while d2 significantly extends to around 2.67 Å utilizing the PBE scheme with vdW interaction. This means that the vdW interaction compresses the in-plane bonds d1 and stretches the out-of-plane bonds d2 by stacking, which causes decrease of θ2 and increase of θ3, as shown in Table 1. Subsequently, the bond angles θ1 and θ4 synchronously adjust themselves to the environment variation. The angles of θ1(θ4), θ2 and θ3 are closer to the bulk values [20].
3.2. Electronic properties To explore the effect of stacking on electronic performances of the bilayer SnS, the band structures, density of states (DOS) and partial charge density of conduction band minimum (CBM) and valence band maximum (VBM) are presented in Fig. 4 based on HSE06 scheme. Table 2 summarizes the band gaps, both from PBE and HSE06 calculations, in which a strongly stacking-order-dependent band gap has been observed and stacking decreases the band gap, compared to the monolayer. The results are in good agreement with existing theoretical values [41]. What's more, DOS for the monolayer indicates that the states of conduction bands (CBs) near the Fermi level are primarily governed by 5p states of Sn, while those of valence bands (VBs) are predominantly rooted in 3p states of S, with slight weight of Sn 5p states. After stacking, the position of CBM determined by 5p states of Sn moves prominently, which is mutually supported by the variation of the partial charge density of CBM as shown in Fig. 4. Although partial charge density and the intensity of DOS of S 3p states adjusted accordingly, the position of VBM from 3p states of S is basically kept in the Γ-Y zone. This may be correlated with the electronegativity of atom species. Sn has lower electronegativity, and thus its charge distribution is reshaped more than that of S. Actually, a series of variations in electronic structure originate from the changed bond lengths and bond angles after stacking [42]. Combining with Table 2, we found that CBM of the AB-stacking moving into the Γ-Y zone, directly changes the intrinsic characteristic of monolayer SnS from indirect band gap to direct band gap. The AB′- and AC-stacking bilayers still keep indirect band gap although the CBM positions also go into the Γ-Y zone. In any case, stacking increases electron excitation probability for the two stacking models since a phonon momentum, which is required to guarantee momentum conservation in the indirect interband transition, becomes smaller. VBM in the Γ-Y direction and CBM along the Γ-X direction determine that AA-stacking is indirect band gap. Considering that the AB-stacking is the most stable stacking configuration, and causes an indirect-to-direct transition with the bandgap (1.63 eV) in a range of the optimal bandgap of solar cells, which is vigorous in boosting optical activity. As such we kept a close watch on its electronic structure. It was found from Fig. 4 that below Fermi level, the electronic state distribution is almost independent on stacking: in the deep energy level (about −15 eV), the bands and states distributing mainly come from 3s orbitals of S atoms; just below Fermi energy and above −12.5 eV, S 3p states strongly hybridize Sn 5p states, forming valence bonds, which is usually observed in group IV-VI compounds [43]. Also, it can be seen that the majority of valence states near the Fermi level come from p states of group VI atoms. This should be due to more valence electrons rooted in group VI elements with respect to group IV elements. Discrepancy between the AB-stacking bilayer and the monolayer emerges above the Fermi level, where the variation of band edge stems from 5p orbitals of Sn atoms. This means that the vdW interaction cannot substantially influence the electronic states in deep energy levels, but does disturb the band edge near Fermi level. This convinces us that the stacking is feasible to finely tune the band structure near Fermi level, which is advantageous to scissor the photoelectric or photocatalytic properties of materials. Moreover, as can be 274
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Fig. 2. Four high-symmetric stacking structures: (a) AA-, (b) AB-, (c) AB′-, and (d) AC-stacking, where top and side views are shown. din denotes the interlayer distance. Solid and hollow circles present atoms of upper and under layers, respectively.
seen from partial densities of states (PDOS) in Fig. 4, abundant electronic states distribute near the band edges, i.e., approaches the VBM and CBM in SnS, indicative of an extraordinary capability for electronic transitions and facility for desirable absorption. The feature of the band structure is similar to that of the organometallic perovskites [44] with excellent performance as optoelectronic and photonic devices. Apart from electronic band gap, charge carrier effective mass is another important parameter to evaluate the transition behaviors of
electrons in nano-electronic devices. The effective mass of electrons/ holes is defined by the curvature of the energy bands near CBM/VBM, which can be calculated using: m = 2/( 2E / k 2) , where , E and k represent Planck constant, energy and momentum, respectively. The effective masses of carriers along armchair and zigzag directions are summarized in Table 2. For the monolayer SnS, the effective masses of me = 0.303(me = 0.166 ) electrons and holes are and mh = 0.258(mh = 0.193) along the zigzag direction (armchair direction), 275
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which ( ) reflects the response of medium to electromagnetic waves [47]. 2 ( ) represents the imaginary part of ( ) , which is in close relation with band structure and can be expressed as follows [36]: 2(
)=
4 e2 m2 2
2d 3k | ik|P|fk |2 Fik (1 (2 )3
i, f ,
F fk ) (E fk
Eik
E)
(1)
where P, |ik , and |fk represent the transition matrix, conduction band states, and valence band states, respectively. F denotes the Fermi function. E and are the energy and frequency of the incident photon, respectively. The other symbols are kept their usual meanings. All optical properties have been calculated rooting in the consequence of 2 ( ) at the level of HSE06. The real part 1 ( ) can be characterized by means of the Kramerse-Kronig equation [48]: 1(
Fig. 3. The binding energy of four different stacking structures as a function of the interlayer distance, din.
2 ) = 1 + ( )p
( )2 2 ( ) ( )2 ( )2
d
0
(2)
where the capital P is the integral principal value. The electron energy loss function L ( ) can be obtained by converting the complex dielectric function as the following equation:
respectively. These results match well with other works [45]. In principle, the size of effective mass is insensitive to the stacking, i.e., the bilayer structure still remains small effective mass like the monolayer, which indeed facilitates high mobility. Detailed analysis reveals that the effective masses of carriers along armchair and zigzag directions of the AA-, AB′- and AC-stacking models increase slightly. Instead, the effective masses of carriers decrease slightly in the AB-stacking structure, which is largely desirable for light-emitting device.
L ( ) = Im
1 = ( )
2(
1
2( ) ) + 22 ( )
(3)
1 ( ) and 2 ( ) acting as the basic parameters can also deduce other optical performances, such as the refractive index n ( ) , extinction coefficient ( ) , absorption coefficient ( ) and the reflectivity R ( ) as follows:
3.3. Photocatalytic properties
n( ) =
As a preferred photocatalyst material, it should possess appropriate band gap (1.23–3 eV), efficient visible light absorption and suitable band edge positions bestriding the oxidation and reduction potentials of water. Table 2 lists band gaps for all structures studied here. Fig. 5 also shows the aligned band edge positions of the monolayer and the bilayers with regard to the vacuum level, where redox potentials of water (dashed line) at pH = 0 and 7 are also plotted for referring. It is found that at pH = 0, CBMs for all the structures are above the reduction potential of water, which facilitates hydrogen evolution reaction, while VBMs still above the oxidation potential of water depress oxygen evolution reaction. Therefore, imposing an additional bias potential is indispensable to fulfil redox process spontaneously. Fortunately, such bias potentials can be desirably obtained by adjusting the pH value of medium [46]. As shown in Fig. 5, the water redox potentials (magenta dashed lines) prominently rise when the pH value of medium is adjusted to pH = 7. In this way, the band edge positions for all the bilayers successfully bestride the oxidation and reduction potentials of water at pH = 7, favorable for photocatalytic water splitting in a neutral solution, except the monolayer SnS. The monolayer is thus not appropriate as a photocatalyst either in pH = 0 or in pH = 7 medium, which agrees reasonably with previous work [46]. The CBMs (VBMs) are positioned at −3.79 eV (−5.35 eV), −3.75 eV (−5.38), −3.86 eV (−5.29 eV) and −3.91 eV (−5.26 eV) for the AA-, AB-, AB′- and ABstacking models, respectively. This indicates that the AB-stacking configuration possesses the strongest oxidizing and reducing power for photocatalytic water splitting among all the stacking models. What's more, a balance between the reduction and oxidation abilities inherent in the AB-stacking, will promote redox reactions spontaneously and inhibit the recombination of carriers. The results indicate that stacking efficiently lows the band edges of SnS, which makes the band edges bestride the redox potentials of water and facilitates hydrogen evolution reaction at pH = 7.
( )= ( )= R( ) =
2 1 (
)+
2
2(
)+
1(
)
(4)
2
( 1 ( )2 +
2 [
2 1 (
2(
) 2)1/2 2
)+
(n 1) 2 + (n + 1) 2 + xx ( ) + yy ( )
2 2(
1(
)
1(
)
(5)
)]1/2
(6)
2
(7)
2
) represent the vertical and and zz ( ) = xy ( ) = 2 parallel components with regard to z-axis, respectively, where xx ( ) , yy ( ) and zz ( ) are diagonal elements of the dielectric matrix ij ( ). zz (
3.4.1. Interband transitions and dielectric function Fig. 6 displays the dielectric functions in the directions normal to the z-axis and parallel to the z-axis. One can see that the dielectric functions display obviously anisotropy below 7.5 eV photon energy region. In high-energy region, electronic transition probabilities both along in-plane and out-of-plane directions are very small, in the near of zero, which makes the dielectric function look like isotropy in the monolayer and the AB-stacking. Such phenomenon is also in common in other 2D-materials [49,50]. The peaks of imaginary part ( 2xy ( ) and 2zz ( ) ) in the monolayer (pinpointed as A, B, C and D) and the ABstacking (pinpointed as A, B and D) are presented in Fig. 4(a) and (c), respectively, with the corresponding energies listed in Table 3. After AB-stacking, Peak C at 4.69 eV disappears. Peaks in Fig. 6 arising from the possible interband transitions are correspondingly denoted in Fig. 4. These interband transitions have their origins rooted in the contribution from S 3p states in the VBs to the Sn 5p states in the CBs. It should be noted that multiple interband transitions from different bands along different BZ directions probably point at the same energy position in the 2 ( ) curve. This means that the interband transitions denoted in Fig. 4(a) and (c) may not cover all electronic transitions. Table 3 shows that the static dielectric constants of AB-stacking are larger than that of the monolayer, which is ascribed to the existence of a narrower band gap in the AB-stacking [51]. In this work, 1xy (0) for the AB-stacking is underestimated by 25% with respect to the experimental
3.4. Optical properties The investigation on typical optical characteristics of materials generally relies on the dielectric function ( ) = 1 ( ) + i 2 ( ), in 276
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Fig. 4. Electronic band structure, corresponding total and partial density of states (DOS), and partial charge densities (yellow) of CBM and VBM with the isosurface value 0.035 eÅ−3 for the monolayer and the bilayers of different stacking models. Possible optical interband transitions are marked by the guiding arrow in (a) and (c), which are in line with structure peaks in the imaginary part of dielectric function. The Fermi level is set to zero. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Table 2 Calculated electronic bandgaps at the levels of PBE and HSE. The effective masses of hole (mh ) and electron (me ) with regard to the free electron mass (me ). Type
PBE gap (eV) (type)
HSE gap (eV) (type)
mh /me Zigzag direction
mh /me Armchair direction
me / me Zigzag direction
me / me Armchair direction
Monolayer AA-Stacking AB-Stacking AB′-Stacking AC-Stacking
1.47 (Indirect) 0.917 (Indirect) 1.033 (Direct) 0.884 (Indirect) 0.789 (Indirect)
1.97 1.56 1.63 1.43 1.35
0.258 0.875 0.232 0.923 1.059
0.193 0.553 0.196 0.212 0.436
0.303 0.632 0.263 0.565 0.872
0.166 0.173 0.162 0.458 0.551
(Indirect) (Indirect) (Direct) (Indirect) (Indirect)
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same as the monolayer, but also the intensity of the peaks is enhanced largely. Moreover, the main peak width of 2 ( ) in Fig. 6 increases after AB-stacking, and correspondingly, the frequency scope of optical absorption increases and the optical transmittance decreases on the whole with respect to the monolayer. The enhanced peaks in 2 ( ) and the broadened optical absorption scope may be due to the increased occupied states of electronics near the Fermi level. All of those variations indicate that UV-light response of the AB-stacking bilayer is improved by the interface vdW-interaction. 3.4.2. Electron energy loss spectra Electron energy loss spectra (L ( ) ) function as Eq. (3) reflects the energy losses by a rapid electron penetrating the medium [47]. The well-defined abrupt loss peaks, corresponding energy named plasma energy, are associated with the frequency of the plasma resonance [53]. For the monolayer, Fig. 7(a) shows that a remarkable peak of L ( ) function in the xy plane locates at 8.23 eV (Peak 1), which is closely related to a dip in 2xy ( ) at the same energy position (see Fig. 6). Just at this position, the 1xy ( ) curve crosses the horizontal line (zero level) to be positive. A somewhat abrupt loss peak in the xy plane (Peak 2) is also found at 12.24 eV. The peak 1 and 2 are associated with the surface plasmons. Another peak (Peak 4) in the xy plane is evident at 9.65 eV in the monolayer, but it is not found in the AB-stacking. For the AB-
Fig. 5. The calculated band edge positions for the monolayer and the bilayers with respect to the vacuum level. The black and magenta dashed lines denote the water redox potentials of pH = 0 and pH = 7 for water splitting. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
value [52]. The difference can be attributed to the factors: our model is perfect 2D material, without considering any effects from phonon-, defect-, or disorder-induced. It is noteworthy that after AB-stacking, not only all peaks of 2 ( ) are positioned in the ultraviolet (UV) regions,
Fig. 6. Photon energy dependent real part ( 1 ( ) ) and imaginary part ( 2 ( ) ) of dielectric function. The the monolayer (a) and the AB-stacking (b).
xy (
) and
zz (
) are perpendicular and parallel to z-axis for
Table 3 Peak positions in imaginary part of dielectric function ( 2 ( ) ), value of real part of dielectric function ( 1 (0) ), refractive index (n (0) ), reflectivity (R (0) ) at zero energy and plasma energy (Ep ) for monolayer and AB-stacking are given. System
Peaks position (eV)
Monolayer
A = 3.16
Plasma energy Ep (eV)
n (0)
R (0)
1xy (0)
=4
Epxy = 8.23, 9.65, 12.24
nxy = 1.99
Rxy = 0.11
B = 3.89
1zz (0)
= 2.48
Epzz = 12.05
nzz = 1.57
Rzz = 0.05
A = 3.33
1xy (0)
= 9.57
Epxy = 8.54, 12.76
nxy = 2.19
Rxy = 0.14
1zz (0)
= 7.04
Epzz = 12.73
nzz = 1.88
Rzz = 0.09
C = 4.69 D = 6.44 AB-stacking
1 (0)
B = 4.07
C = 5.42
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For both the monolayer and the AB-stacking, ( ) steeply raises at first. After climbing the maximum, it keeps descending in a large range of UV energy (∼10 eV) until zero. Since ( ) is always above zero, the scattering and absorbing for the light occur in quite a large energy range. Similar behaviors of n ( ) and ( ) were also reported in the measured optical properties of SnS films [55]. The minimum values of n ( ) in the xy plane, 7.5 eV for the monolayer and 10.7 eV for the AB-stacking just correspond to the peaks of ( ) . Besides, they are also in accordance with those peaks of the absorption spectra shown in Fig. 9. It is not surprising because ( ) presents the utilization of incident light, according with the light absorption in the medium when the incident light enters the medium. The optical spectra along the z-axis also display a similar phenomenon. 3.4.4. Absorption coefficient and reflectivity coefficient The absorption coefficient ( ( ) ) and the reflectivity (R ( ) ) can trace back to 1 ( ) and 2 ( ) in the Eqs. (6) and (7). The calculated absorption coefficient of the AB-stacking in Fig. 9 is fairly consistent with the experimental results [32,56]. The optical absorption coefficient is remarkably elevated after AB-stacking. Obviously, the ABstacking may possess a higher light-harvesting efficiency, and stronger resonance absorption in a large range from the visible region to the UV with respect to the monolayer SnS. This is due to the fact that the interlayer coupling generates new band states and leads to new optical transitions, which increases imaginary part of dielectric function, and therefore, enhances the absorption efficiency [49,50]. We used the linear extrapolation method to fit the absorption threshold, which accords with the optical band gap in 2 ( ) . The results show that the absorption threshold is 2.15 eV for the monolayer and 1.8 eV for the AB-stacking. An appreciable red-shift of the absorption threshold means that the photo-generated electrons just require small photon energy to directly excite from the VBs to CBs in the AB-stacking, which effectively raises the harvest rate of visible light for 2D SnS as a PV material. The appreciable augment of absorption peak intensity, the extension of energy region for the resonance absorption, and also a boosted visiblelight response, all move the AB-stacking SnS toward practical applications in sunlight-driven photocatalysis as nano-optoelectronic devices to harvest the visible light and UV-light.
Fig. 7. Electron energy loss function (L ( ) ) in the xy plane and along the z-axis for the monolayer (a) and the AB-stacking (b).
stacking (Fig. 7(b)), Peak 1 and Peak 2 arouse at 8.54 eV and 12.76 eV, being the counterparts of the monolayer. Along the z-axis, one peak (Peak 3) at the energy of 12.05 eV for the monolayer (12.73 eV for the AB-stacking) is also most likely derived from the surface plasmons. The intensity enhancement of the peaks in the AB-stacking may be attributed to the collective plasmonic oscillations caused by the stacking effect. 3.4.3. Refractive index and extinction coefficient The refractive index (n ( ) ) and extinction coefficient ( ( ) ) correspond to the real and imaginary parts of the complex refractive index N = n i , respectively. As a criterion of judgement, the two parameters assist researchers to measure the transparency of nano-optoelectronic and photonic devices [54]. As can be seen from Fig. 8, the maximum value of n ( ) slightly moves towards lower energy after stacking. In Table 3, the value of the refractive index at 0 eV (n (0) ) increases. This is undesirable since lower n (0) is required for optical materials in applications of antireflection coating, photovoltaic devices, nano-optoelectronic diodes, and so on.
Fig. 8. Calculated electron refractive index (n ( ) ) and extinction coefficient ( ( ) ) in the xy plane and along the z-axis for the monolayer (a) and the AB-stacking (b). 279
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Fig. 9. Calculated absorption coefficient ( ( ) ) and reflectivity (R ( ) ) in the xy plane and along the z-axis for the monolayer (a) and the AB-stacking (b).
structures, photocatalytic and optical properties of SnS. Evaluations from experiments are expected to evidence our results.
The reflectivity coefficients are depicted in Fig. 9. The major peaks of the AB-stacking locate in higher energy region and its maximal intensity increases almost 29% of the monolayer. Since the light reflectivity is positively associated with the light absorption in the medium, an overall red-shift is also generated in the reflectivity spectra of the AB-stacking. The red-shift is the result of the narrowed bandgap induced by stacking effect.
CRediT authorship contribution statement Qiang Zhang: Investigation, Methodology, Writing - original draft, Writing - review & editing. Xuanyu Chen: Software. Wing-Chung Liu: Formal analysis. Yuexia Wang: Funding acquisition, Investigation, Writing - review & editing.
4. Conclusions
Acknowledgements
Our calculations on the basis of PBE + vdW first-principles provided fundamental insights into the interlayer stacking of the bilayer SnS, where the AB-stacking is the most stable in energy among the four diverse stacking orders. For the stable AB-stacking bilayer, interlayer coupling more deeply reshapes 5p states of Sn governing CBM, while not S, since Sn has lower electronegativity. This evoked delicate-adjustment in CBM directly changes the intrinsic characteristic of the monolayer SnS, such as transition from indirect band gap to direct band gap, and decreases the band gap, which facilitated the electronic transition. Also, stacking decreases the carrier effective mass, facilitating high mobility for carriers, and thus being beneficial in the application of light-emitting diodes. Moreover, stacking efficiently declines the band edges of CBM and VBM, especially the edge of CBM. This makes the reaction (photocatalytic water splitting) possible after adjusting the pH value of the medium. In particular, the AB-stacking bilayer possesses the strongest redox power. Typical optical parameters calculated here, such as dielectric function, electron energy loss spectra, refractive index, extinction coefficient, reflectivity coefficient and absorption coefficient, can be tuned through interlayer coupling. Stacking remarkably enhances the peak of dielectric function, narrows the region of electron energy loss, broadens the energy scope and increases the intensity for absorbing photons. On the other hand, refractive index and extinction coefficient are somewhat increased. The detailed analysis concerned with the dependence of electronic and optical properties on the stacking contributes to understanding the electronic characteristics of the bilayer SnS, and confirms that layer-stacking is a feasible pathway to tune the electronic
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Stacking effect on electronic, photocatalytic and optical properties: A comparison between bilayer and monolayer SnS
T
Qiang Zhanga, Xuanyu Chena, Wing-Chung Liub, Yuexia Wanga,
⁎
a b
Key Laboratory of Nuclear Physics and Ion-beam Application (MOH), Institute of Modern Physics, Fudan University, Shanghai 200433, China Kong Cheong Enterprise Development LTD, Trans Asia Center, 18 Kin Hong Street, Kwai Chung, Hong Kong, China
ARTICLE INFO
ABSTRACT
Keywords: Density functional theory Stacking models Electronic properties Photocatalytic properties Optical properties
In this work, the stacking-dependent optoelectronic performances of a bilayer SnS were explored based on density functional theory (DFT). The results demonstrated that an AB-stacking induces an indirect-to-direct transition, a feature that is capable of vanquishing electron transition impediment from an intrinsic indirect monolayer SnS. An anisotropic and small carrier effective mass exists in all the stacking models, among which the AB-stacking with the lowest value favors high carrier mobility. Calculated band alignments are indicative of acceptable and adjustable photocatalytic activity for all the stacking models, unlike the monolayer SnS. The ABstacking configuration possesses the strongest redox power, which facilitates it to be a potential candidate for photocatalytic water splitting. Additionally, the AB-stacking does effectively improve optoelectronic properties. The study demonstrated that layer-stacking is an availably adjustable method in the fields of sunlight-driven photocatalysis for nano-optoelectronic devices.
1. Introduction In the last two decades, two-dimensional (2D) layered materials have aroused tremendous research interest having its origin rooted in the unique electronic, mechanical and optical properties for splendiferous prospects of applications in next generation optoelectronic and photonic devices [1–4]. Among them, the layered group-IV chalcogenides have attracted enormous attentions recently in light of their earth abundant, environmental friendship, low cost and unique potential applications in fields such as solar energy conversion, optoelectronics and thermoelectric devices [5–8]. The most representative group-IV chalcogenide is SnSe, which is well known as high-performance thermoelectric material with ultralow thermal conductivity [9,10]. Furthermore, bulk and monolayer group-IV monochalcogenides MX (M = Ge, Sn; X = S, Se) possess many merits, such as stability, flexibility and high-performance as piezoelectric materials. In stark contrast to MoS2 and AlN, the anisotropic piezoelectric coefficients of MX families are fairly large [5,11–13]. Moreover, atomically thin group-IV monochalcogenides are interesting in spin physics as desirable spin-transport devices. For example, the absence of inversion symmetry and the generation of dipole moment due to the interaction of spin-orbit coupling in the SnSe and GeSe sheets induce spin splitting of the energy bands with anisotropic feature, and make the sheets unprecedented potential in direction-dependent spin-transport devices [14]. ⁎
Among group-IV monochalcogenide families, tin sulfide (SnS) also possesses prominently high absorption efficiency since its absorption approaches the optical absorption threshold of ∼1.3 eV [15], an optimal band gap. Additionally, SnS has a p-type conductivity with a large intrinsic hole concentration of 1017 cm−3 [16]. Hence, it was widely accepted that layered SnS is considerably suitable for photovoltaic (PV) absorbers. Currently, the conversion efficiency of SnS-based cells just approaches to 2%, indicating that large improvement can be done in the design of the photoelectric conversion devices. The ideas to improve the properties usually involve in adopting atomic thickness [17,18] and imposing strain upon the compounds [19]. For instance, the optoelectronic properties of few-layer SnS can be effectively adjusted through controlling layer number and strain along the stacking direction [20]. It’s worthy of noting that very recently, high quality and large-size monolayer SnS flakes were fabricated successfully based on liquid exfoliation method [21]. So, researches on 2D layered SnS will continue to be on the rise in the foreseeable future. It is well known that multi-layered structures can be synthesized by stacking with an accurate steerability. The strong covalent bonds knitting skeletons guarantee the in-plane stability, at the same time, the interlayer interactions establish the stacking SnS multi-layers. Although reassembled by stacking few-layered sheets with well-known skeletons, a novel 2D material much possibly shows us unacquainted phenomena in physical or chemical properties, which may facilitate the design in
Corresponding author. E-mail address: [email protected] (Y. Wang).
https://doi.org/10.1016/j.commatsci.2018.11.035 Received 16 August 2018; Received in revised form 26 October 2018; Accepted 19 November 2018 0927-0256/ © 2018 Published by Elsevier B.V.
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PV devices [22,23]. Therefore, stacking is anticipated to act as a new physical dimension to discover and modulate novel optoelectronic properties [20,24,25]. It was reported that the power conversion efficiency of AA- and AB-stacking bilayer phosphorene can approach ∼18 and 16%, much higher than the reported efficiencies in cutting-edge optoelectronic or photonic devices (trilayer graphene/transition metal dichalcogenides) [22]. To date, the research on the stacking behaviors of layered SnS is far from abundant, especially on the stacking-dependent electronic, photocatalytic and optical properties. In this work, we investigated the structural parameters, stability, photocatalysis and optoelectronic properties of the bilayer SnS for the four various layer-stacking cases to explore the staking effect based on density functional theory (DFT) calculations together with van der Waals (vdW)-corrected exchange-correlation function. The results showed that the AB-stacking with stable structure is superior to the other three stacking models: only the AB-stacking can induce an indirect-to-direct band gap transition; the effective mass of the ABstacking is the smallest, favoring high mobility of carriers; the ABstacking has acceptable and adjustable photocatalytic activity, and the strongest redox power for photocatalytic water splitting. Most importantly, it was found that the AB-stacking does effectively improve the photoelectric properties in comparison with the monolayer SnS. The underlying mechanisms governing the optical properties were thoroughly discussed. Our work evidenced that the layer-stacking is an available method to design 2D-materials with advanced photoelectric and photocatalytic properties.
[29,30]. A DFT-D2 semiempirical dispersion-correction method, which has taken the vdW interactions into account and reasonably predicted the interlayers distance, was used to calculate the interlayer distance for stacking models [23,31]. A vacuum space of 18 Å was adopted to avoid the interactions of image interlayers. In the calculation of structural optimization and relevant properties, the convergence criterion for total force on each atom was less than 10−2 eV/Å, and for energy, 10−6 eV. It is well known that traditional exchange-correlation functional, such as GGA-PBE, underestimates the band gap by about 30% [32,33], which will result in incorrect optoelectronic calculations. Therefore, based on well-PBE-optimized structures, we adopted the state-of-the-art HSE06 function [34–36] to further calculate optoelectronic properties. A 41 × 31 × 1 and 41 × 31 × 3 k-points generated by the Monkhorste-Pack scheme were used to sample Brillouin zone (BZ) for the monolayer and the bilayer SnS, respectively. For optical spectra calculations, unoccupied states should be considered as more as possible in order to meet the accuracy, meanwhile, the integral in the irreducible BZ with a grid containing more k points was done by means of the modified tetrahedron method. 3. Results and discussions 3.1. Geometric structure Here, monolayer SnS motif was adopted from a well-characterized configuration by experiments [21], which belongs to the space group Pmn21 (No. 31, C27V ) and possesses the analogue puckered structure as black phosphorene (BP) [25]. Fig. 1 is well-optimized structure, where zigzag and armchair directions are along a and b vectors, respectively. Relaxed structural parameters are summarized in Table 1, which are consistent with those by other works [25,34,37,38]. The lattice lengths of a and b in its primitive cell are very close, 4.07 Å and 4.30 Å, respectively. Thus, it can be regarded as square structure approximately, as shown in Fig. 1(c). Distinct from SnS, BP exhibits more disparity of length between a and b lattice parameters [39]. Obviously, the square
2. Computational details All first-principle calculations on the basis of DFT [26,27] have been implemented using Vienna ab initio simulation package (VASP) [28]. A method under the framework of the projector augmented wave (PAW) and a plane wave basis set with a cutoff energy of 400 eV were used. The generalized gradient approximation (GGA) was expressed by Perdew-Burke-Ernzerhof (PBE) as the exchange-correlation functional
Fig. 1. The structure of monolayer SnS in (a) top and (b) side view. d1 and d2 are the in-plane and out-of-plane bond lengths, respectively. θ1 and θ4 are the in-plane bond angles and θ2 and θ3 are the out-of-plane bond angles. (c) The unit cell of monolayer SnS. (d) Brillouin zone with high-symmetry points labeled. 273
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Table 1 The structural parameters for the monolayer and bilayer SnS are given. Type
Mono AA AB AB′ AC
Binding energy (meV/atom)
/ −48.1 −55.65 −38.02 −46.56
Equilibrium distance
Lattice constant (in Å)
Bond length (in Ǻ)
Bond angle (in degree)
de-in
a
b
d1
d2
θ1 = θ4
θ2
θ3
/ 3.28 Å 3.06 Å 3.17 Å 3.64 Å
4.07 4.063 4.061 4.081 4.072
4.30 4.203 4.205 4.103 4.204
2.74 2.72 2.71 2.72 2.72
2.59 2.67 2.67 2.66 2.67
95.99 94.9 94.96 94.62 94.59
88.95 85.9 86.01 86.21 86.27
101.03 103.17 103.54 102.81 102.74
structure of SnS with almost in-plane feature stems from relatively weaker sp3 hybridization, contrasting with even more puckered structure of BP which presents a stronger sp3 hybridization [25]. Then we systematically investigated the layer-stacking behaviors for the bilayer SnS. Four main high symmetry stacking orders were considered in this study, namely, AA-, AB-, AB′- and AC-stacking, which are similar to the bilayer phosphorene [40] and the arsenene [23], as shown in Fig. 2. In the AA-stacking configuration (see Fig. 2(a)), the upper layer is accurately matched with the under layer in the xy-plane. For the AB-stacking, the upper layer of the AA-stacking is shifted by a half of the unit cell along the a-direction with respect to the under layer (Fig. 2(b)). For the case of the AB′-stacking (Fig. 2(c)), it is derived from shifting the upper layer of the AA-stacking by a half of the unit cell along the b-direction, which makes the two constituent stacking skeletons form mirror images each other, as seen in the side view. The space group of the AB′-stacking is not the same as that of the ABstacking, since a-axis and b-axis are not equivalent. The AC-stacking is constructed when the upper layer is shifted by a half of the unit cell both along the a- and b-directions with respect to the AA-stacking (Fig. 2(d)). In order to explore optoelectronic properties in response to stacking models, we firstly evaluated the interlayer binding energy for the bilayer SnS, which is defined as Eb = (Ebi 2 × Emono)/ N , where Ebi (Emono ) represents the total energy of the relaxed bilayer (monolayer) SnS, and N, the total number of atoms in the bilayer SnS. Fig. 3 is the binding energy (Eb ) as a function of interlayer distance din, with which we obtained well-optimized equilibrium interlayer distance (de-in) listed in Table 1. The lowest value in a binding energy curve corresponds to the stable configuration of the bilayer. Thus, structural parameters (see Table 1) for each stacking model can be measured base on these stable configurations. The results are fairly consistent with previous calculations [41]. It’s well known that KBT reflects average thermal energy of single atoms, here KB is the Boltzman constant and T is temperature. The value is close to 26 meV at 300 K. So, the binding energies for the AA-, AB- AB′- and AC-stacking structures exceed the average thermal energy of single atom at the temperature of 300 K, which means that the four stacking models considered here are energetically favorable for survival at the room temperature. For the AB-stacking, the binding energy is the lowest, and it is thus the energetic top-priority configuration with respect to other three stacking systems. Such case is similar to bilayer stacking BP [40]. Table 1 shows that de-in is sensitive to the stacking models. Since the atoms of the top layer point directly to those of the under layer for the AA- and AC-stacking models, it causes somewhat large interlayer distance. By contrast, the upper layer does not directly stack over the under layer for the AB- and AB′-configurations, and thus the interlayer distance is smaller. For the most compatible AB-stacking, d1 reduces slightly to 2.71 Å, while d2 significantly extends to around 2.67 Å utilizing the PBE scheme with vdW interaction. This means that the vdW interaction compresses the in-plane bonds d1 and stretches the out-of-plane bonds d2 by stacking, which causes decrease of θ2 and increase of θ3, as shown in Table 1. Subsequently, the bond angles θ1 and θ4 synchronously adjust themselves to the environment variation. The angles of θ1(θ4), θ2 and θ3 are closer to the bulk values [20].
3.2. Electronic properties To explore the effect of stacking on electronic performances of the bilayer SnS, the band structures, density of states (DOS) and partial charge density of conduction band minimum (CBM) and valence band maximum (VBM) are presented in Fig. 4 based on HSE06 scheme. Table 2 summarizes the band gaps, both from PBE and HSE06 calculations, in which a strongly stacking-order-dependent band gap has been observed and stacking decreases the band gap, compared to the monolayer. The results are in good agreement with existing theoretical values [41]. What's more, DOS for the monolayer indicates that the states of conduction bands (CBs) near the Fermi level are primarily governed by 5p states of Sn, while those of valence bands (VBs) are predominantly rooted in 3p states of S, with slight weight of Sn 5p states. After stacking, the position of CBM determined by 5p states of Sn moves prominently, which is mutually supported by the variation of the partial charge density of CBM as shown in Fig. 4. Although partial charge density and the intensity of DOS of S 3p states adjusted accordingly, the position of VBM from 3p states of S is basically kept in the Γ-Y zone. This may be correlated with the electronegativity of atom species. Sn has lower electronegativity, and thus its charge distribution is reshaped more than that of S. Actually, a series of variations in electronic structure originate from the changed bond lengths and bond angles after stacking [42]. Combining with Table 2, we found that CBM of the AB-stacking moving into the Γ-Y zone, directly changes the intrinsic characteristic of monolayer SnS from indirect band gap to direct band gap. The AB′- and AC-stacking bilayers still keep indirect band gap although the CBM positions also go into the Γ-Y zone. In any case, stacking increases electron excitation probability for the two stacking models since a phonon momentum, which is required to guarantee momentum conservation in the indirect interband transition, becomes smaller. VBM in the Γ-Y direction and CBM along the Γ-X direction determine that AA-stacking is indirect band gap. Considering that the AB-stacking is the most stable stacking configuration, and causes an indirect-to-direct transition with the bandgap (1.63 eV) in a range of the optimal bandgap of solar cells, which is vigorous in boosting optical activity. As such we kept a close watch on its electronic structure. It was found from Fig. 4 that below Fermi level, the electronic state distribution is almost independent on stacking: in the deep energy level (about −15 eV), the bands and states distributing mainly come from 3s orbitals of S atoms; just below Fermi energy and above −12.5 eV, S 3p states strongly hybridize Sn 5p states, forming valence bonds, which is usually observed in group IV-VI compounds [43]. Also, it can be seen that the majority of valence states near the Fermi level come from p states of group VI atoms. This should be due to more valence electrons rooted in group VI elements with respect to group IV elements. Discrepancy between the AB-stacking bilayer and the monolayer emerges above the Fermi level, where the variation of band edge stems from 5p orbitals of Sn atoms. This means that the vdW interaction cannot substantially influence the electronic states in deep energy levels, but does disturb the band edge near Fermi level. This convinces us that the stacking is feasible to finely tune the band structure near Fermi level, which is advantageous to scissor the photoelectric or photocatalytic properties of materials. Moreover, as can be 274
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Fig. 2. Four high-symmetric stacking structures: (a) AA-, (b) AB-, (c) AB′-, and (d) AC-stacking, where top and side views are shown. din denotes the interlayer distance. Solid and hollow circles present atoms of upper and under layers, respectively.
seen from partial densities of states (PDOS) in Fig. 4, abundant electronic states distribute near the band edges, i.e., approaches the VBM and CBM in SnS, indicative of an extraordinary capability for electronic transitions and facility for desirable absorption. The feature of the band structure is similar to that of the organometallic perovskites [44] with excellent performance as optoelectronic and photonic devices. Apart from electronic band gap, charge carrier effective mass is another important parameter to evaluate the transition behaviors of
electrons in nano-electronic devices. The effective mass of electrons/ holes is defined by the curvature of the energy bands near CBM/VBM, which can be calculated using: m = 2/( 2E / k 2) , where , E and k represent Planck constant, energy and momentum, respectively. The effective masses of carriers along armchair and zigzag directions are summarized in Table 2. For the monolayer SnS, the effective masses of me = 0.303(me = 0.166 ) electrons and holes are and mh = 0.258(mh = 0.193) along the zigzag direction (armchair direction), 275
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which ( ) reflects the response of medium to electromagnetic waves [47]. 2 ( ) represents the imaginary part of ( ) , which is in close relation with band structure and can be expressed as follows [36]: 2(
)=
4 e2 m2 2
2d 3k | ik|P|fk |2 Fik (1 (2 )3
i, f ,
F fk ) (E fk
Eik
E)
(1)
where P, |ik , and |fk represent the transition matrix, conduction band states, and valence band states, respectively. F denotes the Fermi function. E and are the energy and frequency of the incident photon, respectively. The other symbols are kept their usual meanings. All optical properties have been calculated rooting in the consequence of 2 ( ) at the level of HSE06. The real part 1 ( ) can be characterized by means of the Kramerse-Kronig equation [48]: 1(
Fig. 3. The binding energy of four different stacking structures as a function of the interlayer distance, din.
2 ) = 1 + ( )p
( )2 2 ( ) ( )2 ( )2
d
0
(2)
where the capital P is the integral principal value. The electron energy loss function L ( ) can be obtained by converting the complex dielectric function as the following equation:
respectively. These results match well with other works [45]. In principle, the size of effective mass is insensitive to the stacking, i.e., the bilayer structure still remains small effective mass like the monolayer, which indeed facilitates high mobility. Detailed analysis reveals that the effective masses of carriers along armchair and zigzag directions of the AA-, AB′- and AC-stacking models increase slightly. Instead, the effective masses of carriers decrease slightly in the AB-stacking structure, which is largely desirable for light-emitting device.
L ( ) = Im
1 = ( )
2(
1
2( ) ) + 22 ( )
(3)
1 ( ) and 2 ( ) acting as the basic parameters can also deduce other optical performances, such as the refractive index n ( ) , extinction coefficient ( ) , absorption coefficient ( ) and the reflectivity R ( ) as follows:
3.3. Photocatalytic properties
n( ) =
As a preferred photocatalyst material, it should possess appropriate band gap (1.23–3 eV), efficient visible light absorption and suitable band edge positions bestriding the oxidation and reduction potentials of water. Table 2 lists band gaps for all structures studied here. Fig. 5 also shows the aligned band edge positions of the monolayer and the bilayers with regard to the vacuum level, where redox potentials of water (dashed line) at pH = 0 and 7 are also plotted for referring. It is found that at pH = 0, CBMs for all the structures are above the reduction potential of water, which facilitates hydrogen evolution reaction, while VBMs still above the oxidation potential of water depress oxygen evolution reaction. Therefore, imposing an additional bias potential is indispensable to fulfil redox process spontaneously. Fortunately, such bias potentials can be desirably obtained by adjusting the pH value of medium [46]. As shown in Fig. 5, the water redox potentials (magenta dashed lines) prominently rise when the pH value of medium is adjusted to pH = 7. In this way, the band edge positions for all the bilayers successfully bestride the oxidation and reduction potentials of water at pH = 7, favorable for photocatalytic water splitting in a neutral solution, except the monolayer SnS. The monolayer is thus not appropriate as a photocatalyst either in pH = 0 or in pH = 7 medium, which agrees reasonably with previous work [46]. The CBMs (VBMs) are positioned at −3.79 eV (−5.35 eV), −3.75 eV (−5.38), −3.86 eV (−5.29 eV) and −3.91 eV (−5.26 eV) for the AA-, AB-, AB′- and ABstacking models, respectively. This indicates that the AB-stacking configuration possesses the strongest oxidizing and reducing power for photocatalytic water splitting among all the stacking models. What's more, a balance between the reduction and oxidation abilities inherent in the AB-stacking, will promote redox reactions spontaneously and inhibit the recombination of carriers. The results indicate that stacking efficiently lows the band edges of SnS, which makes the band edges bestride the redox potentials of water and facilitates hydrogen evolution reaction at pH = 7.
( )= ( )= R( ) =
2 1 (
)+
2
2(
)+
1(
)
(4)
2
( 1 ( )2 +
2 [
2 1 (
2(
) 2)1/2 2
)+
(n 1) 2 + (n + 1) 2 + xx ( ) + yy ( )
2 2(
1(
)
1(
)
(5)
)]1/2
(6)
2
(7)
2
) represent the vertical and and zz ( ) = xy ( ) = 2 parallel components with regard to z-axis, respectively, where xx ( ) , yy ( ) and zz ( ) are diagonal elements of the dielectric matrix ij ( ). zz (
3.4.1. Interband transitions and dielectric function Fig. 6 displays the dielectric functions in the directions normal to the z-axis and parallel to the z-axis. One can see that the dielectric functions display obviously anisotropy below 7.5 eV photon energy region. In high-energy region, electronic transition probabilities both along in-plane and out-of-plane directions are very small, in the near of zero, which makes the dielectric function look like isotropy in the monolayer and the AB-stacking. Such phenomenon is also in common in other 2D-materials [49,50]. The peaks of imaginary part ( 2xy ( ) and 2zz ( ) ) in the monolayer (pinpointed as A, B, C and D) and the ABstacking (pinpointed as A, B and D) are presented in Fig. 4(a) and (c), respectively, with the corresponding energies listed in Table 3. After AB-stacking, Peak C at 4.69 eV disappears. Peaks in Fig. 6 arising from the possible interband transitions are correspondingly denoted in Fig. 4. These interband transitions have their origins rooted in the contribution from S 3p states in the VBs to the Sn 5p states in the CBs. It should be noted that multiple interband transitions from different bands along different BZ directions probably point at the same energy position in the 2 ( ) curve. This means that the interband transitions denoted in Fig. 4(a) and (c) may not cover all electronic transitions. Table 3 shows that the static dielectric constants of AB-stacking are larger than that of the monolayer, which is ascribed to the existence of a narrower band gap in the AB-stacking [51]. In this work, 1xy (0) for the AB-stacking is underestimated by 25% with respect to the experimental
3.4. Optical properties The investigation on typical optical characteristics of materials generally relies on the dielectric function ( ) = 1 ( ) + i 2 ( ), in 276
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Fig. 4. Electronic band structure, corresponding total and partial density of states (DOS), and partial charge densities (yellow) of CBM and VBM with the isosurface value 0.035 eÅ−3 for the monolayer and the bilayers of different stacking models. Possible optical interband transitions are marked by the guiding arrow in (a) and (c), which are in line with structure peaks in the imaginary part of dielectric function. The Fermi level is set to zero. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Table 2 Calculated electronic bandgaps at the levels of PBE and HSE. The effective masses of hole (mh ) and electron (me ) with regard to the free electron mass (me ). Type
PBE gap (eV) (type)
HSE gap (eV) (type)
mh /me Zigzag direction
mh /me Armchair direction
me / me Zigzag direction
me / me Armchair direction
Monolayer AA-Stacking AB-Stacking AB′-Stacking AC-Stacking
1.47 (Indirect) 0.917 (Indirect) 1.033 (Direct) 0.884 (Indirect) 0.789 (Indirect)
1.97 1.56 1.63 1.43 1.35
0.258 0.875 0.232 0.923 1.059
0.193 0.553 0.196 0.212 0.436
0.303 0.632 0.263 0.565 0.872
0.166 0.173 0.162 0.458 0.551
(Indirect) (Indirect) (Direct) (Indirect) (Indirect)
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same as the monolayer, but also the intensity of the peaks is enhanced largely. Moreover, the main peak width of 2 ( ) in Fig. 6 increases after AB-stacking, and correspondingly, the frequency scope of optical absorption increases and the optical transmittance decreases on the whole with respect to the monolayer. The enhanced peaks in 2 ( ) and the broadened optical absorption scope may be due to the increased occupied states of electronics near the Fermi level. All of those variations indicate that UV-light response of the AB-stacking bilayer is improved by the interface vdW-interaction. 3.4.2. Electron energy loss spectra Electron energy loss spectra (L ( ) ) function as Eq. (3) reflects the energy losses by a rapid electron penetrating the medium [47]. The well-defined abrupt loss peaks, corresponding energy named plasma energy, are associated with the frequency of the plasma resonance [53]. For the monolayer, Fig. 7(a) shows that a remarkable peak of L ( ) function in the xy plane locates at 8.23 eV (Peak 1), which is closely related to a dip in 2xy ( ) at the same energy position (see Fig. 6). Just at this position, the 1xy ( ) curve crosses the horizontal line (zero level) to be positive. A somewhat abrupt loss peak in the xy plane (Peak 2) is also found at 12.24 eV. The peak 1 and 2 are associated with the surface plasmons. Another peak (Peak 4) in the xy plane is evident at 9.65 eV in the monolayer, but it is not found in the AB-stacking. For the AB-
Fig. 5. The calculated band edge positions for the monolayer and the bilayers with respect to the vacuum level. The black and magenta dashed lines denote the water redox potentials of pH = 0 and pH = 7 for water splitting. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
value [52]. The difference can be attributed to the factors: our model is perfect 2D material, without considering any effects from phonon-, defect-, or disorder-induced. It is noteworthy that after AB-stacking, not only all peaks of 2 ( ) are positioned in the ultraviolet (UV) regions,
Fig. 6. Photon energy dependent real part ( 1 ( ) ) and imaginary part ( 2 ( ) ) of dielectric function. The the monolayer (a) and the AB-stacking (b).
xy (
) and
zz (
) are perpendicular and parallel to z-axis for
Table 3 Peak positions in imaginary part of dielectric function ( 2 ( ) ), value of real part of dielectric function ( 1 (0) ), refractive index (n (0) ), reflectivity (R (0) ) at zero energy and plasma energy (Ep ) for monolayer and AB-stacking are given. System
Peaks position (eV)
Monolayer
A = 3.16
Plasma energy Ep (eV)
n (0)
R (0)
1xy (0)
=4
Epxy = 8.23, 9.65, 12.24
nxy = 1.99
Rxy = 0.11
B = 3.89
1zz (0)
= 2.48
Epzz = 12.05
nzz = 1.57
Rzz = 0.05
A = 3.33
1xy (0)
= 9.57
Epxy = 8.54, 12.76
nxy = 2.19
Rxy = 0.14
1zz (0)
= 7.04
Epzz = 12.73
nzz = 1.88
Rzz = 0.09
C = 4.69 D = 6.44 AB-stacking
1 (0)
B = 4.07
C = 5.42
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For both the monolayer and the AB-stacking, ( ) steeply raises at first. After climbing the maximum, it keeps descending in a large range of UV energy (∼10 eV) until zero. Since ( ) is always above zero, the scattering and absorbing for the light occur in quite a large energy range. Similar behaviors of n ( ) and ( ) were also reported in the measured optical properties of SnS films [55]. The minimum values of n ( ) in the xy plane, 7.5 eV for the monolayer and 10.7 eV for the AB-stacking just correspond to the peaks of ( ) . Besides, they are also in accordance with those peaks of the absorption spectra shown in Fig. 9. It is not surprising because ( ) presents the utilization of incident light, according with the light absorption in the medium when the incident light enters the medium. The optical spectra along the z-axis also display a similar phenomenon. 3.4.4. Absorption coefficient and reflectivity coefficient The absorption coefficient ( ( ) ) and the reflectivity (R ( ) ) can trace back to 1 ( ) and 2 ( ) in the Eqs. (6) and (7). The calculated absorption coefficient of the AB-stacking in Fig. 9 is fairly consistent with the experimental results [32,56]. The optical absorption coefficient is remarkably elevated after AB-stacking. Obviously, the ABstacking may possess a higher light-harvesting efficiency, and stronger resonance absorption in a large range from the visible region to the UV with respect to the monolayer SnS. This is due to the fact that the interlayer coupling generates new band states and leads to new optical transitions, which increases imaginary part of dielectric function, and therefore, enhances the absorption efficiency [49,50]. We used the linear extrapolation method to fit the absorption threshold, which accords with the optical band gap in 2 ( ) . The results show that the absorption threshold is 2.15 eV for the monolayer and 1.8 eV for the AB-stacking. An appreciable red-shift of the absorption threshold means that the photo-generated electrons just require small photon energy to directly excite from the VBs to CBs in the AB-stacking, which effectively raises the harvest rate of visible light for 2D SnS as a PV material. The appreciable augment of absorption peak intensity, the extension of energy region for the resonance absorption, and also a boosted visiblelight response, all move the AB-stacking SnS toward practical applications in sunlight-driven photocatalysis as nano-optoelectronic devices to harvest the visible light and UV-light.
Fig. 7. Electron energy loss function (L ( ) ) in the xy plane and along the z-axis for the monolayer (a) and the AB-stacking (b).
stacking (Fig. 7(b)), Peak 1 and Peak 2 arouse at 8.54 eV and 12.76 eV, being the counterparts of the monolayer. Along the z-axis, one peak (Peak 3) at the energy of 12.05 eV for the monolayer (12.73 eV for the AB-stacking) is also most likely derived from the surface plasmons. The intensity enhancement of the peaks in the AB-stacking may be attributed to the collective plasmonic oscillations caused by the stacking effect. 3.4.3. Refractive index and extinction coefficient The refractive index (n ( ) ) and extinction coefficient ( ( ) ) correspond to the real and imaginary parts of the complex refractive index N = n i , respectively. As a criterion of judgement, the two parameters assist researchers to measure the transparency of nano-optoelectronic and photonic devices [54]. As can be seen from Fig. 8, the maximum value of n ( ) slightly moves towards lower energy after stacking. In Table 3, the value of the refractive index at 0 eV (n (0) ) increases. This is undesirable since lower n (0) is required for optical materials in applications of antireflection coating, photovoltaic devices, nano-optoelectronic diodes, and so on.
Fig. 8. Calculated electron refractive index (n ( ) ) and extinction coefficient ( ( ) ) in the xy plane and along the z-axis for the monolayer (a) and the AB-stacking (b). 279
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Fig. 9. Calculated absorption coefficient ( ( ) ) and reflectivity (R ( ) ) in the xy plane and along the z-axis for the monolayer (a) and the AB-stacking (b).
structures, photocatalytic and optical properties of SnS. Evaluations from experiments are expected to evidence our results.
The reflectivity coefficients are depicted in Fig. 9. The major peaks of the AB-stacking locate in higher energy region and its maximal intensity increases almost 29% of the monolayer. Since the light reflectivity is positively associated with the light absorption in the medium, an overall red-shift is also generated in the reflectivity spectra of the AB-stacking. The red-shift is the result of the narrowed bandgap induced by stacking effect.
CRediT authorship contribution statement Qiang Zhang: Investigation, Methodology, Writing - original draft, Writing - review & editing. Xuanyu Chen: Software. Wing-Chung Liu: Formal analysis. Yuexia Wang: Funding acquisition, Investigation, Writing - review & editing.
4. Conclusions
Acknowledgements
Our calculations on the basis of PBE + vdW first-principles provided fundamental insights into the interlayer stacking of the bilayer SnS, where the AB-stacking is the most stable in energy among the four diverse stacking orders. For the stable AB-stacking bilayer, interlayer coupling more deeply reshapes 5p states of Sn governing CBM, while not S, since Sn has lower electronegativity. This evoked delicate-adjustment in CBM directly changes the intrinsic characteristic of the monolayer SnS, such as transition from indirect band gap to direct band gap, and decreases the band gap, which facilitated the electronic transition. Also, stacking decreases the carrier effective mass, facilitating high mobility for carriers, and thus being beneficial in the application of light-emitting diodes. Moreover, stacking efficiently declines the band edges of CBM and VBM, especially the edge of CBM. This makes the reaction (photocatalytic water splitting) possible after adjusting the pH value of the medium. In particular, the AB-stacking bilayer possesses the strongest redox power. Typical optical parameters calculated here, such as dielectric function, electron energy loss spectra, refractive index, extinction coefficient, reflectivity coefficient and absorption coefficient, can be tuned through interlayer coupling. Stacking remarkably enhances the peak of dielectric function, narrows the region of electron energy loss, broadens the energy scope and increases the intensity for absorbing photons. On the other hand, refractive index and extinction coefficient are somewhat increased. The detailed analysis concerned with the dependence of electronic and optical properties on the stacking contributes to understanding the electronic characteristics of the bilayer SnS, and confirms that layer-stacking is a feasible pathway to tune the electronic
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