2D Li2S monolayer: A global minimum lithium sulfide sandwich

Chemical Physics Letters 722 (2019) 58–63

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Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett

Research paper

2D Li2S monolayer: A global minimum lithium sulfide sandwich a,⁎

Mosayeb Naseri , Shiru Lin a b

b,⁎

T

Department of Physics, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran Department of Chemistry, University of Puerto Rico, Rio Piedras, San Juan, PR 00931, USA

H I GH L IG H T S

global minimum structure of Lithium Sulfide (Li S) is predicted. • ALi 2DS monolayer direct semiconductor with a wide band gap. • Li S monolayer isis astable temperatures. • The electronic propertiesatofhigh Li S monolayer can be effectively modulated by strain effects. • 2

2 2

2

A R T I C LE I N FO

A B S T R A C T

Keywords: 2D material Li2S monolayer Global minimum Direct band gap

In this paper, by employing first principles calculations, a two dimensional global minimum structure of Lithium Sulfide (Li2S) was predicted with a wide direct band gap and an inversed sandwich structure 1T-MoS2. The electronic properties investigations reveal that the predicted Li2S monolayer has a strain tunable direct band gap of 3.20 (4.05 eV) computed by PBE (HSE06) theory. As a wide band gap (WBG) semiconductor that is stable at high temperatures, this monolayer may have many applications in electronics and optoelectronics devices. Furthermore, the presence of a narrow phonon band gap between acoustic and optical modes suggests its application in opto-mechanical resonators.

1. Introduction Wide band gap (WBG) semiconductors exhibit band gaps greater than 3 eV such as GaN, SiC, ZnO, and diamond can be considered as key materials in efficient optoelectronic and electronic devices [1–3]. These kind of materials have two major advantages: Their WBG makes them suitable materials to absorb or emit ultraviolet (UV) light in practical devices. They also provide a higher electric breakdown field lets electronic devices to possess higher breakdown voltages [4,5]. Electronic devices based on WBG semiconductors, for instance light emitting, sensing, and high power devices [6] have been widely studied. Especially, Lithium sulfide (Li2S) as a typical alkali-metal sulfide with a wide band gap crystallizes in the face-centered cubic (FCC) antifluorite (anti-CaF2) structure (space group number 225) has been recently attracted considerable attention due to its potential technological applications; it has been used in solid state ionic batteries [7,8], fuel cells and gas detectors [9], and so on. Theoretical calculation methods have reported that bulk Li2S is semiconducting with a direct band gap of 3.29 eV [10]. Two-dimensional (2D) materials exhibit extraordinarily

⁎

different properties compared with conventional bulk materials. Since the first discovery of graphene [11], two-dimensional materials have been the frontiers of material science, many 2D materials such as graphyne [12], silicene [13,14], boron nitride [15,16], and phosphorene [17], arsenene, antimonene, and bismuthene [18–22], penta-graphene [23], penta structures [24–30] have been theoretically predicted. Furthermore, until now, many applications of 2D materials are in practical uses such as transistors, optical devices, energy storage devices. Despite the wide range of reported applications for bulk Li2S, no experimental or theoretical studies have explored the structural stability, electronic, and optical properties of the potential Li2S monolayer. Herein, by density functional theory (DFT), the first two-dimensional Lithium Sulfide (Li2S) with a similar structure to 1T-MoS2 is predicted with inversed positions for metal and sulfur atoms. The stability of the predicted monolayer is confirmed by cohesive energy computation, phonon modes calculation, first principles molecular dynamic simulations, and global minimal searches. Investigation in electronic properties reveal that the predicted Li2S is semiconducting with an easy-tunable direct band gap of 3.29 eV at PBE level of theory, while 4.05 eV at HSE06 level. As a WBG semiconductor which stables in high

Corresponding authors. E-mail addresses: [email protected] (M. Naseri), [email protected] (S. Lin).

https://doi.org/10.1016/j.cplett.2019.02.047 Received 14 January 2019; Received in revised form 21 February 2019; Accepted 22 February 2019 Available online 05 March 2019 0009-2614/ © 2019 Elsevier B.V. All rights reserved.

Chemical Physics Letters 722 (2019) 58–63

M. Naseri and S. Lin

ofa = b = 3.974Å is obtained for this monolayer (please see Fig. 1(b)). In the network of Li2S monolayer, there are three different planes, i.e., the sulfur atoms are located at the middle plane, while, the lithium atoms are distributed in two different planes with a vertical distance of Δ = 1.45Å (0.725 Å above and below the sulfur plane), where each sulfur binds to its six neighboring lithium atoms, and each lithium atom is shared by three neighboring sulfurs. 2D Li2S shows similar geometry to 1 T-MoS2, but with special inversed positions of metal and sulfur atoms. Li-S bond length is 2.39Å , which is shorter than that for bulk Li2S (1.88Å ) and longer than that for free Li2S molecule (2.11Å ) [10]. ̇ , 111.145 ̇ Li − S − Li and And, the values of68.86 are obtained for   S − Li − S angles respectively.

temperatures this monolayer is promising candidates for application in electronics and optoelectronics devices. Moreover, the presence of a narrow phonon band gap between acoustic and optical modes suggests its application in opto-mechanical resonators. 2. Computational methods 2D Li2S structures were optimized at the generalized gradient approximation (GGA) functional in the form of Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional as implemented in the Wien2k code [31]. For the Brillouin zone integration, the Monkhorst-Pack scheme [32] with the k-point meshes of 10×10×1, and 20×20×1 were used for the electronic and optical properties calculations respectively. Also the input parameters of RMTKmax = 7, Gmax = 14 Ry1/2 and lmax = 10 were set and to avoid interactions between different layers, a vacuum layer of 15 Å in the non-periodic direction was utilized. To investigate the electronic properties, both GGA and HSE06 hybrid functional in the form of the PBE [33] were employed. Moreover, the Kohn-Sham wave functions, are expanded by using the full potential linear augmented plane waves plus local orbital (FPLAPW + lo). The dynamic stability was evaluated by phonon modes computation, which was performed by using density functional perturbation theory implemented in QUANTUM ESPRESSO package [34]. To treat the core electrons, the Martin-Troullier norm-conserving psedupotential [35] is used, while the energy cutoff of 60 Ry was considered. When evaluating the thermal stability, MD simulations based on the PBE functional and DNP basis set implemented in DMol3 program [36] were used. In our MD simulations, the Nose Hoover method [37,38] was used to control the temperature. 4×4×1 super cells (48 atoms) was annealed at 400, 700, and 1000 K, and each MD simulation in the NVT canonical ensemble was done for 10 ps with a time step of 2 fs. The particle-swarm optimization (PSO) multidimensional method by using CALYPSO code was employed to search for potential stable Li2S 2D structures [39]. In our PSO computations, the population size was set to 50, and the number of generations was set to 30, and unit cell was composited of two lithium atoms and one sulfur atom. VASP program was used for original optimizations at PBE functional level of theory [40]. A 600 eV cutoff for the plane-wave basis set and a 5 × 5 × 1 Gamma centered k-points mesh were adopted.

3.2. Stability evaluation Theoretical prediction methods can give deep insights and offer promising candidates for the experimental researchers to explore new materials. In recent years by using first principles calculations based on density functional theory, many new nano materials have been theoretically inestigated [42–46]. To propose a new stable structure, typically one may evaluate;

• The thermodynamic stability (by computing the cohesive energies), • kinetic stability (by computing phonon dispersion) • Thermal stability (by employing first principles molecular dynamic (MD) simulations) • Preferably, global minimum search To confirm the stability of the proposed 2D monolayer we followed the above mentioned steps. First, the thermodynamic stability is examined by calculating the cohesive energies (Ecoh) of the crystal unit cell. For the Li2S monolayer the cohesive energy can be given as Ecoh =(∑i Ei ) − Et n , whereEt , Ei , and n refer to the total energy of 2D Li2S monolayer, the energy of the i-th atom in the cell, and the number of atoms in the cell. The high cohesive energy of 6.92 eV/atom is obtained for the predicted Li2S monolayer. For comparison, the cohesive energy of Li2S monolayer is higher than those for BeC monolayer (5.39 eV/atom) [47], Be2C-I monolayer (4.84 eV/atom) [48], silicone (3.94 eV/atom) [13,14] and phosphorene (3.44 eV/atom) [17] at the same level of theory. The high cohesive energy for the predicted Li2S monolayer confirms that it indicates strong bonding interactions and structural stability. Then, to verify the dynamic stability of the Li2S monolayer, we calculated its phonon modes along high symmetric path. As seen in Fig. 2(a), there is no imaginary mode in the calculated phonon spectra shows that Li2S monolayer is dynamically stable. To be more precise, the maximum phonon frequency for the Li2S monolayer reaches up to 485 cm−1. Furthermore by closer look at the phonon dispersion curve, one can see a narrow phonon band gap of about 11 cm−1 between the acoustic and the optical phonon branches which suggests the proposed monolayer for using in opto-mechanical resonator applications. Thirdly, the thermal stability of the new designed monolayer was evaluated by first-principles molecular dynamics (FPMD) simulations. In our molecular dynamic simulations, a 3×3×1 super-cell was considered. We preformed three individual MD simulations at temperatures of 400, 700, 1000 K. According to our MD simulations, after 10 ps heating the predicted designed monolayer retains its structure at the temperatures of 400, and 700 K. However, at the temperature of 1000 K the structure is seriously disrupted which shows that its melting point is between 700, and 1000 K. Therefore, one can conclude that the Li2S monolayer exhibits good thermal stability. Finally, since a global minimum structure has more potential to be experimentally realized, we performed a global search for the Li2S monolayer structure with the lowest-energy and check if our designed

3. Geometric configuration and stabilities 3.1. Geometric configuration of 2D Li2S monolayer Our designed two-dimensional Li2S structure possesses a hexagonal atomic configuration with the space group number 164 (P-3 ml) (Fig. 1 (a)), possess a sandwich structure, similar to 1T-MoS2, but with lithium atoms at outside layers while sulfur at the inside layer. To find the ground state of the structure, joint atomic relaxation and lattice optimization procedures were performed. For the aim of lattice optimization, by employing the Brich-Murnaghan thermodynamic equation state [41] the variation of the unit cell total energy versus unit cell volume was calculated. According to Brich-Murnaghan thermodynamic equation state;

E (V ) = E0 +

+

9B0 V0 ⎧ ⎡ V0 2 ⎛ ⎞ 16 ⎨ ⎢ V ⎩⎣⎝ ⎠

9B0 V0 ⎧ ⎡ V0 2 ⎛ ⎞ 16 ⎨ ⎢ V ⎩⎣⎝ ⎠

3

3

3

Ấ ⎫ − 1⎤ B0 ⎥ ⎬ ⎦ ⎭ 2

2 3

V − 1⎤ ⎡6 − 4 ⎛ 0 ⎞ ⎥ ⎢ ⎝V ⎠ ⎦ ⎣

⎤ ⎫, ⎥⎬ ⎦⎭

Ấ

where V0 , V , B0 , B0 are the volume of the initial considered unit cell, deformed volume, bulk modulus, and derivative of the bulk modulus with respect to pressure. Using this view, the minimum point of the E-V curve presents the ground state of the crystal. According to our calculation an optimized lattice constants 59

Chemical Physics Letters 722 (2019) 58–63

M. Naseri and S. Lin

Fig. 1. (a) Structure of the predicted Li2S monolayer. (b) 2D charge density of the Li2S monolayer. (c) The energy vs lattice parameter of the Li2S monolayer. (d) A unit cell of the Li2S monolayer from top and side views.

would not continue the properties computations on them.

Li2S is the global minimum by CALYPSO code. During our global minimum search we obtained three structures for Li2S monolayer, namely Li2S-I, Li2S-II, Li2S-III (Fig. 3). Li2S-I is the same as what we designed above. However, when the structures were fully optimized, it was found that the Li2S-II and Li2S-III are dynamically unstable, so we

4. Electronic and optical properties To investigate the electronic properties of the stable 2D Li2S

Fig. 2. Phonon spectra of 2D Li2S monolayer (left); the top and side views of the Li2S monolayer at the end of 10 ps MD simulations at 400, and 700 K (right). 60

Chemical Physics Letters 722 (2019) 58–63

M. Naseri and S. Lin

Fig. 3. The optimized Li2S-I, Li2S-II, and Li2S-III monolayers, which are found with lowest three energy.

Fig. 4. Band structures of 2D Li2S monolayer by PBE (blue dash lines) and HSE06 functional (red lines)(left). The energy change of 2D Li2S monolayer versus strains (right up), and band gaps change versus strains (right down). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

strain coefficients are presented by ε = 0%, ± 3%, ± 6%, ± 9%, in which the ε with positive and the negative values is corresponded to the tensile and compressive strains respectively. The variation of the band structures for the designed Li2S monolayer semiconductor under different in-plane biaxial strain conditions are plotted in Fig. 4 (right panel). The electronic properties of the predicted 2D monolayer under different strain conditions are summarized in Table 1. As a wide band gap semiconductor (band gap larger than 3.0 eV),

monolayer, its band structure was calculated. We found that Li2S monolayer is a semiconductor with a direct wide band gap of about 3.29 eV (Fig. 4). Both valence band maximum (VBM) and conduction band minimum (CBM) are located at the Γ point. Since PBE functional theory usually underestimates the electronic band gap, the band gap of 2D Li2S monolayer was also computed by the Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional [49] theory. The shape of band structures from HSE06 are similar to that of PBE, while the bad gap of 2D Li2S from HSE06 level of theory is 4.05 eV (Fig. 4). It is well-known that different effects such as applying an electric field, substrate effect, and exerting strain may tune the electronic and optical properties of materials [50-55]. To know more about the electronic properties of the designed 2D semiconductors and to its potential applications, the band structures of the designed monolayer semiconductor under different biaxial strain conditions were calculated. In our calculation the strain effects are defined by the variation of the lattice constants, i.e., the strained lattice constants are given bya = a0 (1 + ε ) , wherea 0 is the unstrained lattice constant and the

Table 1 The variations of the structural properties and the electronic band gap of the Li2S at the PBE, and HSE06 level of theories under strain conditions.

61

Strain values

−9%

−6%

−3

0

+3%

+6%

+9%

Lattice constant (Å) Gap-PBE (eV) Gap-HSE06 (eV) Strain energy (eV/atom)

3.61 1.71 2.82 0.11

3.73 2.32 3.11 0.04

3.85 2.81 3.63 0.01

3.97 3.29 4.05 0.00

4.09 3.41 4.25 0.01

4.21 3.54 4.45 0.04

4.33 3.44 4.32 0.08

Chemical Physics Letters 722 (2019) 58–63

M. Naseri and S. Lin

and the reflectivity spectrum of 2D Li2S monolayer (Fig. 5), this monolayer presents almost negligible absorption and a bit reflection (∼2.5%) in visible range of light, which suggests this monolayer acts as a transparent layer for visible lights, however, as seen in Fig. 5, this monolayer shows a high absorption in UV field region. Therefore, the 2D Li2S monolayer has good potential for applications in UV field as a wide band gap semiconductor. 5. Conclusions By using first principles calculations based on the density functional theory, a new Lithium sulfide, 2D Li2S monolayer is predicted. The predicted Li2S monolayer possess a sandwich structure, similar to 1 TMoS2, but with lithium atoms at outside layers while sulfur at the inside layer. 2D Li2S has good thermodynamic, dynamic and thermal stabilities, also 2D Li2S is the global minimum, which make it feasible to be realized experimentally and promising for applications at high temperatures. The electronic properties investigations demonstrated that Li2S monolayer is a semiconductor with a wide direct band gap of 3.29 (at PBE level of theory, while 4.05 eV at HSE06 level). Moreover, this monolayer exhibit not only very small absorption ratio but also it has low reflectivity in the visible range of the electromagnetic spectra suggests it as antireflection window in solar cell applications. These excellent electronic and optical properties make Li2S monolayer as a good candidate for using in new nano-optoelectronics devices.

Fig. 5. The absorption and the reflectivity of 2D Li2S monolayer.

Li2S monolayer may have good potential applications in UV-light shielding, solar cell applications (antireflection layer) and other wide band gap semiconductor devices. Thus, for deeper investigation of 2D Li2S monolayer, we calculated its corresponding complex dielectric constants ε (ω) = ε1 (ω) + iε2 (ω) at a given frequency for its optical properties. The complex dielectric constant is defined as ε (ω) = ε1 (ω) + iε2 (ω) , where ε1 and ε2 refer to the real and imaginary part of the complex dielectric function, respectively. The value of ε1 (ω) refers to the absorption at a given frequency of ω. The imaginary part of this function can be described by random phase approximation (RPA), which presents the inter-band optical transitions between occupied and unoccupied electron states, 2 εαβ (ω) =

4π 2e 2 1 lim Ω q → 0 q2

∑

⇀

2w ⇀δ (ε ⇀ − ε k

ck

Acknowledgement This work is supported by Kermanshah Branch, Islamic Azad University, Kermanshah, Iran. References [1] F. Roccaforte, F. Giannazzo, F. Iucolano, J. Eriksson, M.H. Weng, V. Raineri, Appl. Surf. Sci. 256 (2010) 5727–5735. [2] F. Roccaforte, P. Fiorenza, G. Greco, R. Lo Nigro, F. Giannazzo, A. Patti, M. Saggio, Phys. Status Solidi A 211 (2014) 2063–2071. [3] Joint Conferences SEMTHERM 2017 (Smart Engineering of New Materials) & MICROTHERM 2017 (Microthechnology and Thermal Problems in Electronics) Lodz, Poland26th–30th June 2017 (http://www.micro.semtherm.eu). [4] S.-H. Ryu, S. Dhar, S. Haney, A. Agarwal, A. Lelis, B. Geil, C. Scozzie, Mater. Sci. Forum 743 (2009) 615–617. [5] M.K. Das, Mater. Sci. Forum 1275 (2004) 457–460. [6] S.-H. Ryu, S. Krishnaswami, B. Hull, J. Richmond, A. Agarwal, A. Hefner, in: Proc. of the 18th International Symposium on Power Semiconductor Devices & IC's (ISPSD2006), Naples, Italy, June 4–8, 2006 (pag. 265). [7] P.G. Bruce, S.A. Freunberger, L.J. Hardwick, J.M. Tarascon, Nat. Mater. 11 (2012) 19–29. [8] J. Guo, Z. Yang, Y. Yu, H.C.D. Abruña, L.A. Archer, J. Am. Chem. Soc. 135 (2012) 763–767. [9] H. Khachai, R. Khenata, A. Bouhemadou, A.H. Reshak, A. Haddou, M. Rabah, B. Soudini, Solid State Commun. 147 (2008) 178–182. [10] Z. Liu, D. Hubble, P.B. Balbuena, P.P. Mukherjee, Phys. Chem. Chem. Phys. 17 (2015) 9032–9039. [11] K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov, Science 306 (2004) 666–669. [12] D. Malko, C. Neiss, F. Vines, A. Gorling, Phys. Rev. Lett. 108 (2012) 086804. [13] C.C. Liu, W.X. Feng, Y. Yao, Phys. Rev. Lett. 107 (2011) 076802. [14] P. Vogt, P.D. Padova, C. Quaresima, J. Avila, E. Frantzeskakis, M.C. Asensio, A. Resta, B. Ealet, G.L. Lay, Phys. Rev. Lett. 108 (2012) 155501. [15] K. Watanabe, T. Taniguchi, H. Kanda, Nat. Mater. 3 (2004) 404–409. [16] G. Giovannetti, P.A. Khomyakov, G. Brocks, P.J. Kelly, J. van den Brink, Phys. Rev. B. 76 (2007) 073103. [17] S. Balendhran, S. Walia, H. Nili, S. Sriram, M. Bhaskaran, Small 11 (2015) 640–652. [18] S. Zhang, Z. Yan, Y. Li, Z. Chen, H. Zeng, Angew. Chem. In. Ed. 54 (2015) 3112–3115. [19] S. Zhang, M. Xie, F. Li, Z. Yan, Y. Li, E. Kan, W. Liu, Z. Chen, H. Zeng, Angew. Chem. Int. Ed. 55 (2016) 1666–1669. [20] S. Zhang, W. Zhou, Y. Ma, J. Ji, B. Cai, S.A. Yang, Z. Zhu, Z. Chen, H. Zeng, Nano Lett. 17 (2017) 3434–3440. [21] S. Zhang, S. Guo, Z. Chen, Y. Wang, H. Gao, J. Gómez-Herrero, P. Ares, F. Zamora, Z. Zhu, H. Zeng, Chem. Soc. Rev. 47 (2018) 982–1021. [22] W. Zhou, S. Guo, S. Shang, Z. Zhu, X. Song, T. Niu, K. Zhang, X. Liu, Y. Zhu, H. Zeng, Nanoscale 10 (2018) 3350–3355. [23] S. Zhang, J. Zhou, Q. Wang, X. Chen, Y. Kawazoe, P. Jena, Proc. Natl. Acad. Sci. 112

⇀

vk

c , v, k ∗

− ω) ×

u⇀

u

⇀

ck + eα q

⇀

vk

u⇀

⇀

ck + eβ q

u

⇀

vk

In the above relation the indices c and υ refer to the conduction and valence band states, anduc→ refers to the cell periodic part of the ork bitals at the k-point. Using the complex dielectric function all optical parameters of a matter can be simply calculated. Here the reflectivity and the absorption coefficient are analyzed. The reflectivity is defined as:

R (ω) =

(n − 1)2 + k 2 ' (n + 1)2 + k 2

where n and k are the real and imaginary parts of the complex refractive index given by:

(ε12 + ε22)1 2

2

n (ω) =

(ε12 + ε22)1 2

2

k (ω) =

+ ε1

− ε1

'

'

Also, The absorption coefficient α(ω) is defined by;

α (ω) =

2 ω [(ε12 + ε22)2 − ε1 ]1 2 ,

The optical absorption and the reflectivity spectrum of 2D Li2S monolayer are presented in Fig. 5. Considering the optical absorption 62

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