Density functional theory investigation of the electronic structure and thermoelectric properties of layered MoS2, MoSe2 and their mixed-layer compound

Journal of Solid State Chemistry 211 (2014) 113–119

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Journal of Solid State Chemistry journal homepage: www.elsevier.com/locate/jssc

Density functional theory investigation of the electronic structure and thermoelectric properties of layered MoS2, MoSe2 and their mixed-layer compound Changhoon Lee a, Jisook Hong a, Wang Ro Lee c, Dae Yeon Kim d, Ji Hoon Shim a,b,n a

Department of Chemistry, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea Divisions of Advanced Nuclear Engineering, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea c Faculty of Liberal Education, Chonbuk National University, Jeonju, Jeonbuk 561-756, Republic of Korea d Agency for Defense Development (ADD), Chinhae, Kyungnam 645-600, Republic of Korea b

art ic l e i nf o

a b s t r a c t

Article history: Received 16 September 2013 Received in revised form 10 December 2013 Accepted 15 December 2013 Available online 21 December 2013

First principles density functional theory calculations were carried out for the 2H-MoQ2 (Q ¼S and Se) and their hypothetical mixed-layer compound. Due to the different electronegativities of S and Se atoms on MoQ2, the band gap size could be adjusted in mixed-layer compound MoS2/MoSe2. Also, the indirect band gap in pure MoQ2 compounds is changed to the pseudo direct band gap in mixed-layer MoS2/MoSe2 which is similar to the monolayer compound. The layer mixing enhances the thermoelectric properties because of the increased density of states around the Fermi level and the decreased band gap size. Therefore, we suggest that this layer mixing approach should be regarded as a useful way to modulate their electronic structures and to improve their thermoelectric properties. & 2014 Published by Elsevier Inc.

Keywords: MoS2 MoSe2 MoS2/MoSe2 Electronic structure Thermoelectric property DFT

1. Introduction The 2H-MoQ2 (Q¼S and Se) compounds are crystallizing in a hexagonal structure with space group P63/mmc corresponding to space group number 194 [1]. In detail, their crystal structures result from the layer of hexagonal stacking in Q–Mo–Q sequence. These Q–Mo–Q layers are connected by van der Waals (vdW) interactions. Each of these stable units is referred to as a monolayer, consisting of two hexagonal plane of chalcogen atoms and intermediate hexagonal plane of transition metal atoms coordinated through ionic-covalent bonding, with the Q atoms in trigonal prismatic arrangement as shown in Fig. 1. Semiconducting layered transition metal dichalcogenides have attracted much interest in their applications due to their wide variety of unique physical and chemical properties such as high anisotropic, optical and thermoelectric properties [2,3]. The weak interaction between the layers and strong bonding within the layers are associated with the charge density wave [4] and superconductivity [5–9]. Also the weak interlayer interaction allows the

n Corresponding author at: Department of Chemistry, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea. E-mail address: [email protected] (J.H. Shim).

0022-4596/$ - see front matter & 2014 Published by Elsevier Inc. http://dx.doi.org/10.1016/j.jssc.2013.12.012

intercalation of a wide variety of metal atoms and interlayer impurities to control the optical and electrical properties of MQ2 compounds [10]. The electrical properties of MQ2 compounds usually show semiconducting behavior [11]. MoS2 is a semiconducting material with a room temperature conductivity of 0.0012 Ω/cm and activation energy of 0.124 eV in the temperature range 150–300 K [12]. It also shows n- and p-type Seebeck coefficient (S¼  275 and 400 μV/K) and diamagnetic behavior. MoSe2 compound was reported [13] to be n-type with the Seebeck coefficient and resistivity values being  900 μV/K and 1.0 Ω/cm at room temperature, respectively. Although the transition metal dichalcogenides MoQ2 (Q¼S, Se) are a good candidate for thermoelectric applications because of their high Seebeck coefficients (S) and low thermal conductivities (k), the MQ2 show large band gap size and low electron density near Fermi level. Therefore, in order to improve thermoelectric properties of MoQ2 (Q¼S and Se), it is necessary decreasing of band gap and increasing of carrier concentration near Fermi level. In this study, we search for a way to modulate the electronic structures and to enhance thermoelectric properties of layered MoQ2 compounds. In order to achieve this purpose, hypothetically constructed mixed-layer system of MoS2 and MoSe2 is considered as shown in Fig. 1c. Because the electronic structures near the band gap

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C. Lee et al. / Journal of Solid State Chemistry 211 (2014) 113–119

c

A

a

B b

DOS

A

B

A

B

Energy Fig. 1. ((a) and (b)) The top and side views of the crystal structure of 2H-MoQ2, where Q ¼ S, Se. The scarlet and yellow circles represent Mo and chalcogen atoms, respectively. (c) The side view of the mixed-layer MoS2/MoSe2 in which two different layers MoS2 (A) and MoSe2 (B) alternate along the stacking direction. (d) Schematic diagram illustrating of rearrangement of electronic structure. Here, A and B are DOS of different layer of mixed-layer MoS2/MoSe2 and the layer A (MoS2) is having a more electronegative chalcogen atom than does the layer B (MoSe2). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

are sensitively affected by the interlayer Q…Q vdW interaction [14], the interlayer S…Se vdW interactions in the mixed layer compound could modify its the band gap properties. The thermoelectric properties of a semiconductor MoQ2 are strongly connected with its electronic structure around the band gap and hence on the interlayer vdW interactions. Thus, one might expect that the thermoelectric properties of MoS2/MoSe2 can be considerably changed from those of pure MoQ2. It is of interest and importance to explore if the construction of a mixed-layer system MoS2/MoSe2 is a way of improving the thermoelectric property of a layered MQ2. In understanding the structures and physical properties of solid state compounds in general, it is essential to know their bonding and the nature of their frontier energy levels. For covalent bonding character compounds, it is generally difficult to predict the nature of their frontier energy levels in the absence of first principles electronic structure calculations. Furthermore, for such compounds, it is often difficult to put forward a simple bonding picture with which to describe the essential features of their calculated electronic structures. It is important to carry out systematic electronic structure studies on closely related systems to gain the insight into the band gap properties. In the present work, we examine the electronic structures of the MQ2 and its mixed-layer MoS2/MoSe2 compound on the basis of first principles density functional theory (DFT) calculations to find the effect of layer mixing in their geometrical and electronic structure, by expansion, to seek way of the possibility of the improving their electric properties, especially thermoelectric properties.

2. Computational details In our density functional calculations, we employed the frozencore projector augmented wave method [15,16] encoded in the Vienna ab initio simulation package (VASP) [17], and the generalized-gradient approximation (GGA) of Perdew et al. [18] for the exchange–correlation functional with the plane-wave-cutoff energy of 450 eV and a set of 200 k-point in the irreducible

Table 1 The structural parameters a, c and zQ of MQ2 (space group P63/mmc) and their calculated electronic band gaps Eg (eV) obtained by the GGA calculations. Here zQ refers to the z-coordinate of the chalcogen Q (4h site). a (Å)

c (Å)

zQ

M–Q (Å)

Eg

MoS2 MoSe2

3.169 3.289

12.324 12.927

0.6230 0.6210

2.408 2.527

0.89 0.83

a

3.1922 3.3290

12.5100 13.1547

0.6245 0.6227

2.422 2.550

0.96 0.92

a

MoS2 MoSe2

a The structural parameters of optimized MQ2 (space group P63/mmc) and their calculated electronic band gaps Eg (eV) obtained from the J. Klimes0 s vdW-DF calculations.

Brillouin zone. The interlayer interactions in MQ2 and mixed-layer compound are vdW interactions in nature, which are not correctly treated in the simple GGA method. Thus, in our study, we employed the vdW-DF scheme [19] to describe their interlayer interactions. The structures of the pure MoQ2 (Q¼ S, Se) as well as the mixed-layer MoS2/MoSe2 compounds were fully optimized, and the self-consistent-field convergence thresholds of 10  5 eV and 0.001 eV/Å for the total electronic energy and force, respectively. The optimized structural parameters are listed Table 1, and those of the mixed-layer compound MoS2/MoSe2 in Table 2. In general, the DFT calculation with the PBE functional underestimates a band gap, we carried out the calculations with the hybrid functional HSE06 [20–22] resulting in band gaps of 1.18 eV for MoS2, 1.15 eV for MoSe2, and 0.74 eV for MoS2/MoSe2. The thermoelectric transport coefficients are calculated within the Boltztrap code [23] which solves the semi-classical Boltzmann equation and the rigid band approach [24]. The rigid band approach to conductivity is based on the transport distribution

sαβ ðεÞ ¼

! 1 ∑ s ði; k Þ N ! αβ i; K

δ ðε  ε ! Þ dε

i;

k ;

ð1Þ

C. Lee et al. / Journal of Solid State Chemistry 211 (2014) 113–119

Table 2 The structural parameters a, c, zS, zSe, Mo–S and Mo–Se as well as the band gaps Eg (eV) of the mixed-layer compound MoS2/MoSe2 with space group P-6m2 obtained from the J. Klimes0 s vdW-DFT calculations. Here zS and zSe refer to the z-coordinates of chanlcogen atoms S and Se, respectively. We note that the Mo of MoS2 layer occupied 1e site (2/3, 1/3, 0) and the Mo atom of MoSe2 layer occupied 1d site (1/3, 2/3, 0.5).

MoS2/MoSe2

a (Å)

c (Å)

zS (2h)

zSe (2i)

Mo–S (Å)

M–Se (Å)

Eg

3.2575

12.8090

0.8789

0.3673

2.438

2.535

0.63

where N is the number of the k points, i is the energy band index ! and k is the reciprocal lattice vector, ε ! is the band structure and i; K the K-dependent transport tensor is given as !

!

!

sαβ ði; k Þ ¼ e2 τ !υα ði; k Þυβ ði; k Þ; i;

k

ð2Þ

!

τ ! is the relaxation time, υα ði; k Þ is the a component of the group

k velocity. The transport coefficients as a function of chemical potential and temperature can be calculated by integrating the transport distribution function over energy.   Z ∂f ðT; εÞ 1 sαβ ðT; μÞ ¼ sαβ ðεÞ  μ ð3Þ dε; ∂ε Ω i;

vαβ ðT; μÞ ¼

Rijk ¼

1 eT Ω

Eind j jappl Bappl i k

Z



sαβ ðεÞðε  μÞ 

 ∂f μ ðT; εÞ dε; ∂ε

¼ ðs  1 Þαj sαβk ðs  1 Þiβ ;

Sij ¼ Ei ð∇j TÞ  1 ¼ ðs  1 Þαi vβj ; where f is the Fermi–Dirac distribution function,

ð4Þ

ð5Þ ð6Þ

μ is the chemical

potential, s is the electric conductivity, ν is the thermoelectric conductivity, R is the Hall coefficient, and S is the Seebeck coefficient. The band structure ε ! is regarded as rigid band and the relaxation i; k time is considered as a constant which is a good approximation for the carrier scattering processes independent of the reciprocal lattice vector and temperature. The method has been successfully used to calculate transport properties and to predict the optimal doping levels of the thermoelectric materials [25–28]. In order to give converged results of the transport properties, dense 8000 k points in the irreducible zone is used to calculate the electronic thermoelectric properties.

3. Electronic structures Fig. 2 shows the density of states (DOS) and band dispersion plots of MoS2 and MoSe2 with experimental crystal structures. Similar electronic structures are obtained with the optimized crystal structures using vdW-DF scheme (see Supporting information). We also carried out the calculation with hybrid functional HSE06 to estimate more accurate band gap. The DOS with hybrid HSE06 functional are summarized in S2 of SI. Electronic structure getting from HSE06 is very similar to those getting from GGA and vdW-DF scheme. All the compounds show clear insulating behavior and the calculated band gaps are listed in Table 1. The metal d blocks are strongly hybridized with chalcogen p blocks as shown in the typical electronic structure containing covalent bond character. Because of the wide overlap between metal d block and chalcogen p block, the spin density on transition metal is suppressed to be non-spin polarized electronic structure of MoS2 and MoSe2.

115

The conduction band minimums (CBM) are lying in the middle of

Γ–K symmetry lines, and the valence band maximums (VBM) are on the Γ point indicating the indirect band gap of MoQ2 compounds. Fig. 2(c–e) shows contributions of Mo 4d orbitals with the fat-band representation. As shown in Fig. 2(e), CBM and VBM bands are mainly contributed by inplane component orbital dx2  y2 and dxy at K–M region. In order to understand the origin of the band dispersion at CBM and VBM, we have performed the extended Hückel tight-binding calculation for trigonal prism dimer MoQ6/MoQ6 and MoS6/MoSe6 clusters [29]. Fig. 3(a) shows the simplified orbital shape of the lowest lying unoccupied molecular orbitals (LUMO) of MoQ6/MoQ6 cluster. The single trigonal prism MoQ6 unit produces a hybridized orbital of Mo dx2  y2 /dxy orbital and Q px =py orbitals (Fig. 3a) within the layer. The interlayer Q…Q vdW interaction induces the LUMO, and it is the main characteristic of the lowest conduction band. The bonding type overlap between two p orbital tails of trigonal prisms along the c-direction (interlayer interaction) leads its energy lowing in the ab plane (Γ–M and K–Γ). In doing so, the lowest conduction band is push down at Γ–M and K–Γ points. As a consequence, the CBM is developed at the middle of Γ–K points and the indirect band gap appears on MoQ2 system. Band gap size of Se compound is slightly smaller than that of S compound about 0.06, 0.04, and 0.03 for GGA, and vdW-DF, and HSE06 functional, respectively. The MoS2 bands are all slightly wider than MoSe2 bands because of smaller unit cell size and shorter Mo–Q bond length. Also, as moving from the S to the Se atom, the effect of the chalcogen ligand field on metal d block grows and leads wide bands near the Fermi level. As a result, the band gap size of MoSe2 is smaller than that of MoS2. We have constructed the hypothetical mixed-layer MoS2/ MoSe2 in which different MoS2 and MoSe2 layers are stacking alternatively along the c direction (see Fig. 1(c)). Their electronic structure would be reconstructed as shown in Fig. 1(d). One can speculate that the electronic structures of each layer are not largely changed by the layer mixing because of the weak vdW interlayer interaction. This means that the electronic structure of each layer would keep its pure electronic structure. However, the electronic structure around Fermi level could be rearranged by the layer mixing. When the layer A has a more electronegative chalcogen atom than does the layer B, the VBM and CBM of the layer A are lowered in energy with respect to those of the layer B. Thus, the band gap Eg of a mixed-layer structure is smaller than those of its pure components. The MoSe2 layer having less electronegative Se atom is newly interposed at higher valence band region, while the MoS2 layer with more electronegative S atom is contributed lower conduction level (see Fig. 1(d)). The calculated DOS of the mixed layer system clearly shows this feature as shown in Fig. 4(a). As a result, the band gap size is decreased by the layer mixing. Calculated band gaps for the layer mixed MoS2/MoSe2 compound is much smaller than those of their pure compounds (see Tables 1 and 2). As we expected, VBM is mainly contributed by MoSe2 layer and the contribution near CBM come from MoS2 layer as shown in the DOS plot of Fig. 4. Although our optimized structure of layer mixed MoS2/MoSe2 compounds shows that the c-axis length is about the same with average c-axis length of MoS2 and MoSe2 and interlayer S–Se distances are practically same with average of S–S and Se–Se distances along the c-direction as listed in Tables 1 and 2, the interlayer interaction between MoSe2 layer and MoS2 layer would be weakened because the orbital energies of S 3p and Se 4p are different. In general, orbital interaction between identical levels is stronger than orbital interaction between different levels. This mean the vdW interaction along the c-direction are weaken on layer-mixed MoS2/MoSe2 compound. This would lead the weakening of the interlayer S…Se interactions, which results in the suppression of the bonding between layers in MoS2/MoSe2 compound as shown in Fig. 3(b).

C. Lee et al. / Journal of Solid State Chemistry 211 (2014) 113–119

State (/eV, /2FU)

116

Total Mo S

10

Total Mo Se

5

0

-8

-4

0

4

-8

0

-4

-8

0

4

4

Energy

Energy

4

-4

0

-4

Γ

Μ Κ

Γ

Ζ

-8

Γ

Μ Κ

Γ

Ζ

Fig. 2. DOS (upper panel) and band dispersion (lower panel) plots calculated for MoQ2: (a) MoS2, and (b) MoSe2. The fattened band dispersion relations of MoQ2: (c) dz2 , (d) dxz þ dyz , and (e) dx2  y2 þ dxy . Γ, M, K, and Z represent the wave vector points (0, 0, 0), (1/2, 0, 0), (1/3, 1/3, 0), and (0, 0, 1/2) in the first Brillouin zone.

Consequently, the K point becomes the CBM and pseudo direct band gap is opened on mixed-layer MoS2/MoSe2 compound. This situation is very similar to the case of the monolayer MoQ2 [30]. The indirect band gap of bulk MoQ2 compound is changed to direct band gap in monolayer MoQ2 compound. Thus, one can suggest that the two dimensional electronic structure can be realized with the layer mixing instead of the manipulation of the MoQ2 monolayer system.

4. Thermoelectric properties High efficiency of a thermoelectric material is determined by the figure of merit, ZT ¼S2sT/κ, where S is the Seebeck coefficient, s is the electrical conductivity, and κ is the thermal conductivity at a given temperature T. Due to high S and low κ, MoQ2 system is a good candidate for the thermoelectric application [31]. However, it is reported that the ZT value is small in this system due to small conductivity induced by the large band gap energy. Here, we suggest that the reduced band gap in the mixed layer MoQ2 can provide the high efficient thermoelectric materials with large ZT.

The calculated Seebeck coefficients and power factor are shown in Fig. 5. The doping effect is reflected by the change of the chemical potential μ within the rigid-band approximation. In addition, we also assume the relaxation time τ to be energy independent. Because the Seebeck coefficient is independent of τ, the T dependence of the Seebeck coefficients should be reasonably realistic. In the absence of the detail information of τ for the MoQ2 and mixed-layer MoS2/MoSe2 compounds, we calculate the power factor in units of τ. The chemical potential dependence of the Seebeck coefficients for MoS2 and MoSe2, given in Fig. 5(a and b), show two peaks in the profile which are located at chemical potential  70.1 eV. The maximum Seebeck coefficients are  1400 and  1000 μV/K for MoS2 and MoSe2, respectively. The Seebeck coefficient of MoS2 is larger than that of MoSe2 because of the larger band gap size of MoS2. The Seebeck coefficient of mixedlayer MoS2/MoSe2 is much smaller than that of their pure MoQ2 system as shown in Fig. 5(c). The band gap narrowing and increased electron density around the Fermi level causes the small Seebeck coefficient on the mixed layer system. As the temperature increase, Seebeck coefficients for all systems are gradually decreased because of the increase of electrons and holes

C. Lee et al. / Journal of Solid State Chemistry 211 (2014) 113–119

117

Fig. 3. (a) Shapes of the molecular orbital of Mo2S12 cluster. (b) Shapes of the molecular orbital of MoS6MoSe6 cluster. Here, Mo, S, and Se atoms are represented by cyan, yellow, and red circles, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

MoSe2 4

2 0 4

0

MoS2

Energy

State (/atom)

4

State (/2FU)

2

-4

0 10

Total 5 0 -8

-4 0 Energy (eV)

-8

Γ

Μ

Κ

Γ

Ζ

4

Fig. 4. ((a) and (b)) DOS and band dispersion plots calculated for mixed-layer MoS2/MoSe2.

conductivity by increasing of thermal energy. The negative Seebeck coefficients is slightly dominant in pure MQ2 compounds, while the positive Seebeck coefficients is slightly larger than negative one in mixed-layer MoS2/MoSe2 system. However Seebeck coefficients difference between hold and electron doping case is much small, it is almost negligible.

The power factor (S2s) is an important factor for the efficiency of thermoelectric material. In general, the optimum power factor is found for the carrier concentration around nef f  1019  1020 cm  3 in the conventional semiconducting materials [32]. The calculated power factor of the mixed-layer MoS2/MoSe2 system is clearly bigger than that of pure MoQ2 systems (MoS2 and MoSe2), as

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C. Lee et al. / Journal of Solid State Chemistry 211 (2014) 113–119

1400

400K 500K 600K

700

S (μV/K)

700

S (μV/K)

1400

400K 500K 600K

0 -700 -1400

0 -700

MoSe2

-1400

-1.0

-0.5

0.0

0.5

1.0

-1.0

Chemical potential μ (eV)

-0.5

0.0

1.0

MoS2 MoSe2 MoS2/MoSe2

0.9

2

400K 500K 600K

0

0.6

21

S (μV/K)

S σ/τ (10 μW /cm K s)

800

400

0.5

Chemical potential μ (eV)

-400

-800 -1.0

-0.5

0.0

T=400K

0.3

2

MoS2/MoSe2 0.5

1.0

Chemical potential μ (eV)

1E18

1E19

1E20 e

3

Carrier concentration n (1/cm )

Fig. 5. Dependence of the Seebeck coefficients calculated for (a) MoS2 and (b) MoSe2 on the chemical potential at three temperatures. The black, red, green circles refer to 400, 500 and 600 K, respectively. (d) The calculated thermoelectric power factors for MoS2/MoSe2 as a function of carrier concentration at 400 K. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

shown in Fig. 5(d). Although the layer mixing reduces the Seebeck coefficient by the band gap narrowing, the increase of the electric conductivity by the increased electron density near the Fermi level is much more effective. As a consequence, the reduced band gap and weakened interlayer vdW interaction gives the enhanced power factor on the mixed layer system. From our results, we suggest that the layer mixing of MoQ2 system should be considered as a crucial approach to improve their thermoelectric properties and it can be possible to predict the change of thermoelectric properties by the modulation of their electronic structures.

that primary reason for change of electronic structure and improvement of thermoelectric properties on mixed-layer should be increasing chances of meeting between different layers. Perfectly alternating AB structure is not necessary and sufficient condition enhancing thermoelectric properties in our mixedlayer concept, though we were considered perfect AB alternating structure for simplicity of calculation. It is just needed directionality of layered compounds and a lot of meeting chances between different layers. It can be achieved by experimental work and this concept is very similar with misfit layer and interface study.

5. Conclusions

Acknowledgment

We surveyed the electronic structure and thermoelectric properties for MoS2, MoSe2 and their mixed-layer MoS2/MoSe2 by using the DFT approach. Compared to the pure MoS2 or MoSe2 system, the band gap energy of the mixed-layer system is considerably decreased due to the different electronegativity of each layer. The pure MoQ2 system shows the indirect band gap, the CBM in the middle of G and K point and the VBM at the G point, while the mixed layer system shows the direct band gap at K point. All the change of the electronic structures can be understood with the change of the weak interlayer S…Se interaction between layers. We provide that the thermoelectric property would be substantially improved by the layer mixing of MoQ2 systems. Actually, we understand that making perfect AB stacking along the c-axis is not easy in experimental work. When the main difference between pure MoQ2 and mixed-layer MoS2/MoSe2 compounds is interlayer interaction, the improved thermoelectric properties and modulation of electronic should be resulting in change of interlayer interaction. Our suggestion in this study is

This research was supported by the computing resources of the NERSC center and the HPC center of NCSU.

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