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Stabilities, Electronic and Optical Properties of SnSe S Alloys: A First Principles Study 2(1-x)

2x

Yucheng Huang, Xi Chen, Danmei Zhou, Hai Liu, Chan Wang, Jinyan Du, Lixin Ning, and Sufan Wang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b00794 • Publication Date (Web): 18 Feb 2016 Downloaded from http://pubs.acs.org on March 1, 2016

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The Journal of Physical Chemistry

Stabilities, Electronic and Optical Properties of SnSe2(1-x)S2x Alloys: A First Principles Study †

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Yucheng Huang*, ,‡, Xi Chen ,‡, Danmei Zhou ,‡, Hai Liu ,‡, Chan Wang ,‡, Jinyan Du ,‡, Lixin †

†

Ning*, ,§, Sufan Wang ,‡ †

Center for Nano Science and Technology, ‡College of Chemistry and Material Science, The Key

Laboratory of Functional Molecular Solids, Ministry of Education, Anhui Laboratory of Molecule-Based Materials, Anhui Normal University, §Department of Physics, Anhui Normal University, Wuhu, 241000, Peoples’ Republic of China

ABSTRACT First principles investigations are performed on the stabilities, electronic and optical properties of SnSe2(1-x)S2x (x = 0.0625, 0.25, 0.5, 0.625, 0.8125 and 1.0) monolayer alloys by using density functional theory (DFT) calculations. It is found that, above a critical temperature of 702 K, the mixing of SnSe2 and SnS2 is likely to form random alloys. The calculated negative substitution energy of S at the Se site of SnSe2 suggests an alternative strategy for the synthesis of the alloys, i.e., by the substitution S for Se in SnSe2 monolayers. It is also shown that, due to the lattice mismatch and the pronounced charge transfer between SnSe2 and SnS2, the bandgap values of the alloys deviate strongly from the concentration-averaged values of the constituents. Moreover, the dielectric functions of the alloys are determined to be anisotropic, with optical properties along the xy plane being more susceptible to the S content than those along the z direction, and the alloying enhances the absorption strength in the visible spectral region. We hope that these insights will be useful for future applications of SnSe2(1-x)S2x alloys. *

E-mail: [email protected], [email protected].

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1. Introduction In the past few years, the surge in graphene research1 has stimulated numerous studies on novel low-dimensional materials.2 As an important class of two-dimensional (2D) materials, layered chalcogenide materials (LCMs) have become a new hotspot in material science because of their excellent electronic and photonic properties.3 Analogous to the graphene, these 2D LCMs, such as MoSe2,4 WS2,5 MoS2,6 MoTe2,7 NbSe28 and NbS2,9 can be easily fabricated by a new method of synthesis of liquid exfoliation 10 Among the 2D LCMs, tin dichalcogenides SnX2 (X = S, Se) have recently attracted intensive attention.11-20 The materials crystallize in hexagonal symmetry and are isostructural with CdI2.21 Each layer has a X-Sn-X sandwich-like structure, and the layers are weakly coupled by van der Waals interactions. Similar to other 2D layer materials, single-layer and multi-layer nanosheets of SnX2 can be easily isolated from their bulk counterparts by mechanical exfoliation.22 These SnX2 nanosheets are expected to have wide applications in the fields of film electrodes, infrared optoelectronic devices, thermoelectric refrigerators, solar cells and next-generation atomic electronics, etc.,16-18, 20 due to their low cost, superior electronic and optical properties. Numerous studies23-31 have reported that properties of LCM-based composite materials can be tuned from those of one constituent to another, and are superior or complementary to those of the constituents, which hold promise for designing opto- and nanoelectronic trial devices with unique properties. For example, Komsa29 et al. have reported the stability and electronic properties of single layers of MoS2xSe2(1-x) and demonstrated that such materials can be exfoliated from the bulk mixed materials, and the bandgap can be continuously tuned. Tongay23 et al. have investigated the experimental fabrications of monolayer Mo1-xWxSe2 and produced monolayer alloys with


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different gap values, which was believed to open avenue for broadening the materials library and applications of 2D semiconductors. Klee27 et al. have reported the optoelectric characteristics of monolayer alloys with the composition ranging from MoS2 to MoSe2, and observed a photoconductive response of the photocurrent on the illumination intensity, which has potential applications in optoelectronics. Zheng25 et al. have fabricated the single-crystal monolayer WxMo1-xS2 alloy triangles using chemical vapor deposition method and found that the photoluminescence peak shifts continuously from 687.4 nm at the triangle center to 633.6 nm at the edge, which indicates that this composition-graded alloy may have interesting functions in broadband photodetection and multi-color light emission. Therefore, intriguing properties can be readily obtained by alloying two or more 2D materials. Since both SnSe2 and SnS2 are isostructural with the hexagonal CdI2 type crystal, they would become soluble in each other beyond a certain temperature. Thus, synthesizing SnSe2-SnS2 heterostructures might allow one to engineer optical and physical properties with minimum structural defects. Very recently, Pan et al.32 have fabricated the field-effect devices using thin crystals of SnS2-xSex with varying Se-content. Through a thorough characterization, the authors found that, with the increase of Se composition, the bandgap decreases and the drain-source current modulation is suppressed. To our best knowledge, however, theoretical investigations related to this system have not been reported yet. Some open issues, such as the mixing/segregation behavior and soluble temperature of the alloy, the variation of electronic and optical properties from SnSe2 to SnS2 as well as the underlying reasons, are still unclear from a theoretical point of view. To address the above mentioned issues, in this work we have carried out DFT calculations on 2D SnSe2(1-x)S2x alloys with different constituent concentrations. Results show that “random”



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alloys can be favorably formed through mixing two separated constituents beyond the critical solubility temperature of 702 K. Bandgap of the alloy can be continuously tuned from pure SnSe2 to SnS2, but does not scale linearly with the S concentration. Moreover, optical anisotropy is observed and the absorption strength is obviously enhanced in the visible spectral region by alloying. We expect this study may shed light on the future applications of SnX2 in opto- and nanoelectronics. 2. Computational Methods All the DFT calculations described in this work were performed by using the projector augmented wave (PAW)33 formalism as implemented in the Vienna ab initio Simulation Package (VASP).34-35 The PBE exchange-correlation functional36-37 in the generalized gradient approximation (GGA) was selected, and the cutoff energy for the plane wave basis was set to 350 eV. In order to make the calculated bandgap values closer to the experimental ones, the inner 4d electrons were treated as valence electrons, and the effect of the on-site Coulomb repulsion of 4d electrons were corrected by the GGA+U approach.38 The value of U = 9.0 eV has been employed as it can reproduce the experimental bandgap of SnSe2.26 In this work, the calculated bandgap for pure SnSe2 and SnS2 are 1.14 and 2.08 eV, respectively, which are in good agreement with the corresponding experimental values.39 The Monkhorst-Pack k-point grid was used to sample the Brillouin zone.40 By minimizing the quantum mechanical stresses and forces, the lattice vectors and atomic positions were fully relaxed for all the considered structures. The convergence threshold was 10-5 eV for energy and 10-2 eV/A for force. To remove spurious interactions between neighboring structures in periodic calculations, a vacuum layer of no less than 15 Å was constructed in the perpendicular direction. The DFT method has been proven to be one of the most accurate methods for the computation of the electronic structure of solids.41-46


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Figure 1. Top view and side view of models of Sn16Se32 (a) and Sn16Se12S20 (b).

3. Results and Discussion 3.1 Structural Properties and Stabilities of SnSe2(1-x)S2x Alloys The model of SnSe2 monolayer was cleaved from its bulk along (001) direction, which contains a Se-Sn-Se triple layer (Fig. 1a). A supercell was constructed, consisting of a 4×4 unit cell. The S atoms were imported into the monolayer with different concentrations, i.e., x = 0.0625 for Sn16Se30S2, x = 0.25 for Sn16Se24S8, x = 0.5 for Sn16Se16S16, x = 0.625 for Sn16Se12S20, x = 0.8125 for Sn16Se6S26 and x = 1.0 for pure SnS2. To determine whether the S atoms prefer separation or aggregation, we first selected Sn16Se12S20 as a porotype to investigate the alloying behavior of SnSe2 and SnS2 (Fig. 1b). The free energy of mixing is defined as ∆F x ∆H x T∆S x

(1),

where ∆H x is the internal energy of mixing, and is expressed



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∆H x EA B xE 1 xE

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(2).

Here, A and B are the constituent of binary compounds (i.e., A = SnS2 and B = SnSe2), and 0 ≤ x ≤ 1, as usual. The mixing entropy per cell is evaluated according to 47 ∆S x 2xlnx 1 x ln1 xk

(3).

To find the most favorable structure, the S composition between the upper and down layer (xdown and xup) was allowed to interchange, with the constraint x = (xdown + xup)/2.

Figure 2. (a) Mixing energy of the SnSe2(1-0.625)S2(0.625) alloys as a function of the S concentration in the upper chalcogen layer xup (xdown = 2*0.625−xup). (b) Mixing energies of 10 configurations of the SnSe2(1-0.625)S2(0.625) with respect to the average number of S-Se nearest-neighbor bonds. The calculated bandgaps (Eg) of 1, 2, 3 configurations are labeled in eV. As shown in Fig. 2a, with the increase of xup, the mixing energy for the SnSe2(1-0.625)S2(0.625) alloy increases. The lowest mixing energy occurs at xup = 0.625, indicating that an average distribution of S atoms in the two layers are thermodynamically most stable. This situation is in line with the result of MoS2(1-x)Se2x system.29 After assuring xup = xdown, we further investigated the distribution of the S atoms in the layers, i.e., forming dissimilar chalcogen pairs or clustering into S-S ensembles. We define n as the fraction of S-Se bond in the nearest-neighbor chalcogen sites


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averaged over all sites,29 n n!6#. The mixing energy for each configuration as a function of n is plotted in Fig. 2b. It can be seen that the mixing energies are scattered disorderly without regularity, but the variation is substantially small (< 0.02 eV). These results indicate that no preferential configuration exists for this system. Thus, a “random” behavior of SnSe2-SnS2 alloy can be verified. On the basis of this finding, other alloys with different S compositions are modeled by random distributing S atoms onto SnSe2 monolayer, only guaranteeing upper and lower layers having the same number of S atoms. In order to further confirm whether the random distribution of the S atoms has effect on electronic properties, we choose three configurations with relative large energy difference to compute their bandgaps (1, 2 and 3 in Fig. 2b). Results show that the bandgaps of 1, 2 and 3 configurations are 0.947, 0.952 and 0.929 eV, respectively. The negligible differences in magnitude indicate that random models can be constructed safely to investigate the variation of physical properties with the S concentration.

Figure 3. (a) Total energy of SnSe2(1-x)S2x alloys as a function of lattice parameter. (b) Calculated values for the parameter a of SnSe2(1-x)S2x alloys with different S contents.



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Since the atomic size of the S atom is smaller than that of Se, the S substitution for Se will introduce lattice strain definitely. We thus adjusted the lattice parameter around its equilibrium value for each model, and then calculated their total energies. The correlations between the lattice constant and the total energy are shown in Fig. 3a, in which the lowest point in each curve corresponds to the optimized lattice parameter. In Fig. 3b, the optimized lattice parameter value as a function of S content is illustrated. A nearly linear relationship appears, which is known as Vegard’s law.48 Such a law has already been experimentally confirmed for other bulk TMD alloys49 or 2D monolayer alloys.29

Figure 4. Mixing enthalpy (a) and quasi-binary phase diagram (b) as a function of the S content for the SnSe2(1-x)S2x alloys. Binodal and spinodal curves are shown in green and rose red lines in Fig. b.

Phase stability of an alloy is important for its designing. Using eq (2), we calculated the mixing enthalpy for different SnSe2(1-x)S2x alloys. As shown in Fig. 4a, binary alloys possess positive mixing enthalpies, indicating that SnSe2(1-x)S2x have a tendency of phase segregation at low


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temperatures. Considering the contribution from mixing entropies, the solubility can be improved by increasing the temperature. One may notice that the magnitude of mixing enthalpies is very small, only on the order of 10 meV per SnSe2 unit. Thus, a complete miscibility can be expected at experimentally achievable temperatures. To obtain this critical temperature, we first fitted the mixing enthalpies as a function of the S composition by a second-order polynomial ∆H Ωx1 x

(4)

based on quasi-chemical model, where Ω is the interaction parameter dependent on the material. Then, the mixing Helmholtz free energies are written as ∆F Ωx1 x RTxlnx 1 x ln1 x

(5),

thereby the bimodal solubility curve and the spinodal decomposition curve can be simply produced through

&'( &

0 and

& * '( &*

0, which are simplified to be

RTln x ln 1 x 1 2xΩ 0

(6)

and RT 2x1 xΩ 0

(7).

The obtained binary phase diagrams are shown in Fig. 4b. The binodal and spinodal curves meet at x = 0.5 at a critical temperature T+ Ω/2R, where the symmetry feature is in agreement with systems such as Mo1-xTxS2 (T=W, Cr and V)31 and TSe2(1-x)Te2x (T=Mo, W)50, but in contrast to the systems of V1-xMoxTe251 and TS2(1-x)Te2x (T=W, Mo)50 with asymmetry features. The difference was attributed to whether the point and triplet effective cluster interaction can be neglected or not in the construction of the cluster expansion for these alloys.50 The calculated value for T+ is 702 K,



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which is higher than MoSe(S)Te and WSe(S)Te alloys owing to the more positive mixing enthalpies.50 Note that the solubility would be underestimated if the entropy contributed by the lattice vibration were taken into account. When the temperature is higher than T+ , the large entropy of solid solutions suppresses the positive mixing enthalpy. Thus, the immiscibility gap begins to disappear and the layered SnSe2(1-x)S2x alloys become stable in the whole range of composition. At a specific temperature below T+ , for example 600 K, the SnSe2(1-x)S2x alloys can still be formed but with lower solubility, i.e., the concentration of S must be within the range of 0

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