Theoretical investigation of electronic structure and thermoelectric properties of MX2 (M=Zr, Hf; X=S, Se) van der Waals heterostructures

Accepted Manuscript Theoretical investigation of electronic structure and thermoelectric properties of MX2 (M=Zr, Hf; X=S, Se) van der Waals heterostructures Fawad Khan, H.U. Din, S.A. Khan, G. Rehman, M. Bilal, Chuong V. Nguyen, Iftikhar Ahmad, Li-Yong Gan, B. Amin PII:

S0022-3697(18)32576-9

DOI:

https://doi.org/10.1016/j.jpcs.2018.11.021

Reference:

PCS 8807

To appear in:

Journal of Physics and Chemistry of Solids

Received Date: 25 September 2018 Revised Date:

21 October 2018

Accepted Date: 27 November 2018

Please cite this article as: F. Khan, H.U. Din, S.A. Khan, G. Rehman, M. Bilal, C.V. Nguyen, I. Ahmad, L.-Y. Gan, B. Amin, Theoretical investigation of electronic structure and thermoelectric properties of MX2 (M=Zr, Hf; X=S, Se) van der Waals heterostructures, Journal of Physics and Chemistry of Solids (2019), doi: https://doi.org/10.1016/j.jpcs.2018.11.021. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT Theoretical investigation of electronic structure and thermoelectric properties of MX2 (M=Zr, Hf; X=S, Se) van der Waals heterostructures Fawad Khan1,2, H. U. Din3, S. A. Khan3, G. Rehman1,2, M. Bilal4,

Center for Computational Materials Science, University of Malakand, Pakistan Department of Physics, University of Malakand, Pakistan 3

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Department of Physics, Hazara University, Pakistan

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2

Abbottabad University of Science and Technology, Pakistan 5

Department of Materials Science and Engineering,

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Chuong V. Nguyen5, Iftikhar Ahmad1,4* , Li-Yong Gan6* , B. Amin3*

Le Quy Don Technical University, Ha Noi 100000, Vietnam 6

School of Materials Science and Engineering,

Key Laboratory of Advanced Energy Storage Materials of Guangdong Province,

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South China University of Technology, Guangzhou 510641, China. Abstract

In this paper, van der Waals heterostructures consisting of MX2 (M= Zr, Hf and X= S, Se) monolayers are modeled. The favorable stacking and stability of the modeled monolayer

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heterostructures are confirmed through binding energy and phonon dispersion calculations. After confirming stability, the electronic and thermoelectric properties of these compounds are

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explored using the first-principles calculations combined with semiclassical Boltzmann transport theory. It is found that type-II band alignment in ZrS2-HfSe2 facilitates charge separation for optoelectronics and solar energy conversion. All studied heterostructures show remarkably higher electrical conductivity than corresponding monolayers, responsible for large power factor values, especially at 1200 K. These findings indicate that the creation of van der Waals heterostructures from MX2 may be promising for efficient optoelectronic and thermoelectric devices.

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I.

INTRODUCTION

Control of dimensionality has proven to be an effective way to manipulate the electronic

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properties of materials, which can further be tuned by doping [1], alloying [2], strain engineering [3, 4], stacking [5–7], and the formation of superlattices [8]. Stacking of monolayers in the form of van der Waals heterostructures have recently emerged as a new class of materials, where quantum coupling between stacked atomically thin two-dimensional (2D) layers give rise to

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fascinating new phenomena. These heterostructures play a significant role in modern semiconductor technologies and leading to revolutionary devices such as tunneling transistors, barristors, flexible electronics, and optoelectronic devices as well as double heterostructure

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semiconductor lasers operational at room temperature and heterostructures bipolar transistors [9, 10]. In these heterostructures, type-II band alignment has been demonstrated that reduces the overlap between the electron and hole wave functions by slowing down the charge recombination, which in fact is expected to be an efficient way for light detection and harvesting [11, 12]. Band gap engineering and strong light-matter interaction enable the development of

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efficient photovoltaic, optoelectronic and thermoelectric devices based on 2D transition metal dichalcogenides (TMDs) heterostructures [5, 13]. The most strikingly highlighted 2D graphene, exhibiting superior properties than graphite, has been extensively studied over the past few years. Rapid progress in graphene and

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methods used to prepare ultrathin layers, have inspired great enthusiasm to explore new 2D materials. TMDs monolayers are emerging as promising materials for a wide range of applications, e.g., in energy storage [14], gas sensors [15], catalysis [16], field-effect transistors

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[17], logic circuits [18], optoelectronic/photonic [19], memory devices [20] and potential thermoelectric applications [21–23]. Extremely strong light-matter interactions in TMDs monolayers make them fascinating for constructing MX2 heterostructure, which are exciting for novel optoelectronic and photovoltaic applications [24]. Very recently, an intrinsic type-I band alignment with an indirect band gap is demonstrated in ZrS2/HfS2 van der Waals heterostructure, which can be tuned to become type-II by applying an electric field [25]. Indeed, similar lattice parameters allow the creation of a variety of TMDs heterostructures with very few structural defects, but lattice mismatch also induce strain across the interface which plays a crucial role in electronic properties of heterostructures and can improve the device performance [9]. 2

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In the present work, a comprehensive insight is gained into the electronic structures of two types of heterostructures. One type includes ZrS2-HfS2 and ZrSe2-HfSe2, showing very small lattice mismatch (<1%). While ZrS2-HfSe2 and ZrSe2-HfS2 heterostructures show lattice mismatch about 2%, which is experimentally achievable [26]. For comparison, we have also

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investigated electronic structure of MX2 (M= Zr, Hf and X= S, Se) monolayers of corresponding heterostructures. Thermoelectricity has also been proposed to be favorably controllable by reducing the dimensionality [27]. While these monolayers have shown to be of moderate gaps together with high S, σ and low κ, and thus are promising candidates for thermoelectric

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applications [28, 29]. Therefore, we have also investigated the thermoelectric performance in terms of the Seebeck coefficient (S), electrical conductivity (σ) and power factor (PF) of

II. COMPUTATIONAL DETAILS

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corresponding heterostructures.

We employ density functional theory in the PWSCF code [30] using ultrasoft pseudopotentials and exchange correlation functional in the form of Perdew-Burke-Ernzerhof

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(PBE) functional and taking into account the van der Waals interaction by the empirical dispersion correction using the method of Grimme (DFT (PBE)-D2) [31]. Lattice constants are optimized and the atomic positions are relaxed until the forces have converged to 10−4 eV/Å while total energy convergence criterion is set at 10−4 eV. A plane wave cut-off energy of 816 eV

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is used together with a 50×50×1 k-grid for the Brillouin zone integration. A vacuum layer thicker than 16 Å is added along the c-axis in both monolayers and heterostructures to prevent artifacts of the periodic boundary conditions and interlayer distance larger than 3.5 Å is considered in all

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heterostructures.

The Boltzmann semi-classical theory and constant relaxation time approximation

(CRTA) as implemented in BoltzTrap code, is used to examine the electronic transport properties (Seebeck coefficient (S), electrical conductivity (σ) and power factor (PF)) [32, 33]. The electrical conductivity as a coefficient of temperature (σα,β(T,µ)) and chemical potential (µ) can be written as:
, ,  =

Ω


,   −

3

,, 

 d

(1)

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,   =





∑,  , k , kδ − ",# 

(2)

where α and β are tensor indices, Ω, e and f(T,ε,µ) represent volume of unit cell, the

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electron charge and Fermi-Dirac distribution, respectively, N is the number of k-points sampled and να(i,k) is αth component of the group velocity of carriers with wave vector k . The Seebeck coefficient (S), also known as thermoelectric power, is obtained as '

$, = %
, , & , , 

(3)




,   −  − (Ω

,,

 d

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, ,  =

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In equation 3, , (T,µ) denotes the group velocity and may be given by



(4)

Generally, the relaxation time τ = τk is dependent upon both the k vector direction and the band index. However, it has been widely reported that τ is independent of electron momentum k or energy [34] therefore, one may assume that Seebeck coefficient is independent of relaxation time

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(τ) and hence, may be written as S = σ−1ν. In present work, the CTRA comprising universal τ = 10−14s, independent of the material’s choice, is adopted. Furthermore, τ used to determine the electrical conductivity, does not considerably vary at the energy scale of kBT [35]. The calculated values of Seebeck coefficient and electrical conductivity are further used to demonstrate the

RESULTS AND DISCUSSION

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III.

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power factor (PF = S2σ).

Bulk MX2 (M= Zr, Hf and X= S, Se) crystallize in 1T-CdI2 structure [36], where Zr/Hf

atom forms a two-dimensional hexagonal close packed plane and each of them is octahedrally coordinated by six chalcogen atoms. Total energy difference of 1T and 2H phase (∆E = E1T − E2H) in Table I show that monolayers of these materials in 1T phase (see Fig. 1 (i)) are more stable than in 2H phase. Atomic positions and lattice constants of 1T-MX2 monolayers are optimized and the results agree well with experiments and previous theoretical findings [37–40]. In heterostructures, one monolayer is stacked on top of other monolayer and re-optimized the average in-plane lattice constants of involved systems. Since, the electronic structure is very sensitive to the layer stacking [41], different choices are investigated, presented in Fig.1; (ii): Hf 4

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atom of HfS2 monolayer is located on chalcogen atom (top-layer) of ZrS2 monolayer; (iii): Hf atom of HfS2 monolayer is located on chalcogen atom (bottom-layer) of ZrS2 monolayer; (iv): Hf atom of HfS2 monolayer is located on top of Zr atom of ZrS2 monolayer; (v): where two monolayers shifted laterally so that on-top positions are avoided, is also analyzed. Binding

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energy, defined as the difference of total energy of heterostructure and corresponding two isolated monolayer systems [6, 8, 42], E = EZrX2−HfX2 −EZrX2 −EHfX2, show that the third stacking is most favorable; see Table I. Therefore, this situation is studied in the following. Furthermore, the interlayer distance is approximately 3.0 Å, indicates there is no bonding between the chalcogen

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atoms and reveals the van der Waals interaction between two layers of the heterostructures. A small variation in bond-length is due to the lattice mismatch between corresponding monolayers in heterostructures, presented in Table I. Variation in bond-length of monolayers in

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heterostructures not only modulates the electronic band structure but also alters phonon stiffness. Therefore, we have also investigated the phonon dispersion to further confirm the stability of third stacking of these monolayers, see Fig. 2. Phonon dispersion for all heterostructures exhibit no imaginary frequency, which confirms their stability. Fig. 2 also shows 15 optical modes and 3 acoustic modes at the Γ-point of the Brillouin zone due to the six atoms in the cell. The general behavior of all these systems is same. It is clear from Fig.2 that optical modes in the frequency

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range (30-40 cm−1), above acoustic modes at Γ-point indicate weak vdW interaction between constituent monolayers of these heterostructures. Similar low frequency optical modes are also experimentally observed in MoS2/WSe2 and MoSe2/MoS2 heterostructures [43] and theoretically

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demonstrated in MoSe2/Zr2CO2, WSe2/Zr2CO2, MoSe2/Zr2CF2, WSe2/Zr2FO2 and SiC-TMDs heterobilayers [44, 45] . Moreover, the phonon spectra of these heterostructures, simply a sum of phonon vibrational modes of their parent monolayers, also indicate the weak van der Waals

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interaction across the interface. Changes in the frequencies of the optical modes from ZrS2-HfS2 and ZrSe2-HfSe2 to ZrSe2-HfS2 and ZrS2-HfSe2 show substantial hardening and softening of the phonon frequencies due to the lattice mismatch. Band structures show that MX2 (M= Zr, Hf and X= S, Se) monolayers are indirect band

gap semiconductors with valence band maximum (VBM) at Γ-point and conduction band minimum (CBM) at M-point, see Fig. 3. VBM is mainly due to the chalcogen atom p state, while CBM is mainly due to the transition metal d state see Fig.4. As the electronic configuration of Zr:[Kr]4d25s2 and Hf:[Xe] 4f145d26s2, where 4d,5s (Zr) and 5d,6s (Hf) states are the valence state located near the Fermi level and actively involved in physical behavior. However, the 4f orbital, as completely occupied in Hf, is not mainly involved to affect the electronic states in valence 5

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band or conduction band. The electronic structure and the band gap value depend upon the electronegativity and the distance apart the component atoms, in the crystal lattice. Large band gaps are associated with small interatomic spacing and large differences of electronegativity [46]. Moreover, 5d elements contain both d and f subshells, due to which it possesses poor

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shielding effect, making it less reactive than 4d elements. Hence, band gap value decreases (increases) in monolayer from S(Zr) to Se(Hf), presented in Table I.

Magnitude of the monolayers band gap presented in Table I is better than other PBE calculations [25, 47]. The difference may be due to the pseudopotentials used in our calculations.

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Although, the band gap values are further improved by using HSE06 functional, presented in Fig. 3 and the values are given in Table I, but there is no experimental data for comparison. It is reported in DFT that hybrid functionals lead to better agreement with experiments than other

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semilocal functionals. But this approach is not generalized and depends upon the material’s choice [48]. For MoS2 monolayer, PBE(HSE06) band gap underestimates(overestimates) the experimental value by 0.12(0.45) eV [48–51].The above results and the qualitatively consistent nature of HSE06 and PBE band structures encourage us to choose PBE for the investigation of these materials.

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Similar to corresponding monolayers, all heterostructures are indirect band gap semiconductors with VBM at Γ-point and CBM at M-point, see Fig. 3. Here, we emphasize that intrinsic strain may result in different electronic properties of 2D TMDs [52]. For instance, the heterobilayer ZrS2-HfS2 with a small intrinsic tensile strain in HfS2 and compressive strain in

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ZrS2, shows a comparatively smaller band gap than corresponding monolayers, presented in Table I. This is due to the fact that compressive strain is more effective in band gap modulation than a tensile strain [53] because the potential energy between atoms increases more rapidly

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when atoms are brought closer (compression) than in equilibrium rather than pulled further away (tension) from equilibrium [54]. In a similar fashion, the band gap of other heterostructures is also smaller than the corresponding monolayers. Electronic structure in terms of partial density of states (PDOS) of heterostructures is

presented in Fig. 4. In case of ZrS2-HfS2, ZrSe2-HfSe2 and ZrSe2-HfS2 both the CBM and VBM are dominated by Zr-4d and chalcogen atom p states of ZrS2(ZrSe2) layer of heterostructure. This kind of localization of the VBM and CBM in similar regions of the heterostructure is known as type-I band alignment. Hence, these three heterostructures belong to type-I band alignment. Recently, intrinsic type-I band alignment with an indirect band gap in ZrS2-HfS2 has been reported [25], which is tuned to type-II by applying an external electric field. Surprisingly, the 6

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density of states (DOS) of ZrS2-HfSe2 show that VBM is due to the Se-p state with contribution of Hf-5d state from the layer of HfSe2, while CBM is due to the Zr-4d state of ZrS2. This type of alignment is known as type-II band alignment (spatially separate electron-hole pairs) [55]. TypeII band alignment in ZrS2-HfSe2 heterostructure without application of external electric field may

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be due to the high electron affinity difference in corresponding monolayers [56]. To further investigate type-II band alignment, orbitally weighted band structures for ZrS2-HfSe2 heterostructure in Fig. 5 show that CBM is mainly due to the Zr-dxz and Zr-dz2 states with small contribution of Zr-dxy state at M-point of Brillouin zone, while Zr-dx2−y2 and Zr-dxy states are

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contributing mainly at Γ-point. Aforementioned all states of Hf are not contributing at the CBM. Similarly, VBM is mainly due to the Se-p state of HfSe2. This kind of localization of the VBM and CBM in different layers of the heterostructure spatially separates electron-hole pairs (type-II

material is needed for this purpose.

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band alignment), which is useful for light detection and harvesting, because no additional

Transport coefficients as a function of chemical potential (µ) are investigated by solving the Boltzmann transport equation using BoltzTraP code as implemented in PWSCF code [32], see Fig. 6. Chemical potential indicating doping level of a compound; for n-type doping, µ has

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positive value and responsible for shifting up the Fermi level while for p-type doping, µ has negative value and shifts downward the Fermi level, which mainly influence the Seebeck coefficient and conductivity.

A remarkable value of Seebeck (S) around µ = 0 confirms that an enhanced S can be

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obtained through small p-type or n-type doping. Increasing band gap from ZrS2(ZrSe2) to HfS2(HfSe2) results in a considerable shift of maximum S towards the gap edges. For promising thermoelectric devices and ZT values, the Seebeck coefficient has usually larger value than

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200µV/K [57, 58]. At 300K, peak value of Seebeck coefficient for HfS2, HfSe2, ZrS2 and ZrSe2 monolayers, in p-type region is 2430, 1121, 1999, and 856µV/K, while in n-type region, is 2513, 1210, 2070 and 934 µV/K, respectively. Large Seebeck coefficient in n-type region for these monolayers is attributed to large contrast of DOS particularly near band gap edges (see Fig. 4) [59–61]. Similarly, large contrast of DOS in conduction band is responsible for large S values in n-type region of ZrS2-HfS2, ZrS2-HfSe2, ZrSe2-HfS2 and ZrSe2-HfSe2 heterostructures (see Fig. 4). Both ZrS2-HfSe2 and ZrSe2-HfSe2 heterobilayers have almost the same maximum S value attributed to the small difference in their energy gap. At 1200K, the S value decreases exponentially and almost one-fourth of that obtained at 300 K for both monolayers and heterobilayers. The maximum S moves towards the band edges from ZrS2-HfS2(ZrSe2-HfS2) to 7

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ZrS2-HfSe2(ZrSe2-HfSe2) as confirmed by the decrease of their respective band gap values. The heterobilayer ZrS2-HfS2 attains larger S than the others and hence are promising for efficient thermoelectric applications. Smaller S in heterobilayer than that in monolayer, is ascribed to the decreased band gap.

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Electrical conductivity divided by constant relaxation time (σ/τ) demonstrates larger value in p-type region than n-type region at both 300 and 1200 K which may be attributed to the considerable difference in the dispersion of conduction and valence bands found along high symmetry directions. At 300 K, a larger (smaller) value of electrical conductivity observed for

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HfSe2(HfS2) is due to smaller(greater) band gap nature. Further, a small decrease in electrical conductivity as compared to Seebeck coefficient is found at 1200 K, indicating that the electrical conductivity is less sensitive to temperature. One can clearly observe almost the same trend in

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maximum σ/τ around chemical potential at both temperature 300 and 1200K. Moreover, the electrical conductivity (Seebeck coefficient) decreases (increases) as µ approach to 0. Sharp increase (decrease) in electrical conductivity (Seebeck coefficient) is observed at higher chemical potential in both p-type and n-type regions. Similar trend is observed in electrical conductivity for all heterobilayers. At 300 K (1200K), the peak value of electrical conductivity lying in p-type region is 2.37×1020(2.20×1020), 2.39×1020 (2.22×1020), 2.01×1020 (1.87×1020) and

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2.89×1020 (2.65×1020) (1/Ω.m.s) for ZrS2-HfS2, ZrS2-HfSe2, ZrSe2-HfS2 and ZrSe2-HfSe2 heterobilayers, respectively. It is noted that at both temperatures, σ/τ for heterobilayers attains considerable peak values as compared to that observed in monolayers which will effect the

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thermopower of the thermoelectric materials. This variation in σ/τ from monolayer to heterobilayer is due to the band gap engineering. To optimize thermoelectric performance, power factor (PF) as a function of chemical

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potential for monolayers and heterobilayers at temperature 300 K and 1200K are shown in Fig. 6. Obviously, the peak values of PF at both 300 K and 1200 K in n-type region are greater than in p-type due to the larger S in n-type region. At 300 K, the optimized power factor with maximum values of 1.525×1011, 1.594×1011, 1.340×1011, and 1.433×1011 W/K2ms are found in n-type region, while at 1200 K in the same region these values are 5.126×1011, 5.054×1011, 4.726×1011 and 4.599×1011 W/K2ms for HfS2, HfSe2, ZrS2 and ZrSe2 respectively. More interestingly, the peak values of S for all monolayer and heterobilayer systems at 300 K are greater than at 1200 K, however, a higher value of PF at 1200K is caused by the higher values of electrical conductivity. Further, it can be seen that HfS2 has larger PF (at 1200 K) than HfSe2, ZrS2 and ZrSe2, making it more suitable for thermoelectric applications. A similar behavior can 8

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be observed in heterobilayers. Among these heterobilayers, ZrS2-HfSe2 has comparatively greater PF in n-type region at 300 K devising better performance for TE materials. At 1200 K, highest PF values in n-type region for ZrS2-HfS2, ZrS2-HfSe2, ZrSe2-HfS2 and ZrSe2-HfSe2 are 7.737×1011, 9.755×1011, 7.419×1011 and 8.217×1011 W/K2ms, respectively. The optimized PF at K

for

ZrS2-HfSe2

is

comparatively

larger

than

other

studied

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1200

MX2

heterobilayers/monolayers. Interestingly, remarkable larger values of PF calculated (at 300 and 1200 K) for both monolayers and heterobilayers, is obtained as compared to other investigated low-dimensional materials [62], which indicate their potential applications in thermoelectric

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devices.

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IV. CONCLUSION

In summary, we explore structural, vibrational, electronic and thermoelectric properties of MX2 (M= Zr, Hf and X= S, Se) monolayers and their out-of-plane heterostructures by first principles density functional theory and Boltzmann transport calculations. The structural properties reveal that all MX2 monolayers are stable in 1T-phase. The stacking order of

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minimum energy is determined for all heterostructures, which is further confirmed by calculations of phonon dispersion. Both monolayers and their heterostructures show indirect semiconducting band gap nature. Type-II band alignment in ZrS2-HfSe2 without application of external electric field, enhances its performance for light detection. Transport coefficients such as

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Seebeck coefficient, electrical conductivity and power factor as a function of chemical potential at 300 K and 1200 K are investigated and reveal that Seebeck coefficient (electrical conductivity) attains large values in n-type(p-type) doping. At high temperature (1200 K), owing to large PF

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values in n-type region of all heterostructures than corresponding monolayers emerge these materials as potential candidates for efficient thermoelectric applications. ACKNOWLEDGEMENT

The authors acknowledge financial support from Higher Education Commission of

Pakistan

(HEC),

Project

No.

20-3959/NRPU/R&D/HEC2014/234,

5727/KPK/NRPU/R&D/HEC/2016, and National Natural Science Foundation of China (No.11504303). The authors are also thankful to Center for Computational Materials Science, University of Malakand Chakdara, Pakistan and the National Supercomputing Center in Guangzhou (Tianhe II supercomputer) for computing and technical support.

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∗Authors

to

whom

correspondence

should

be

addressed:

[email protected],

[email protected], [email protected]

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ZrS2

HfS2

ZrSe2

HfSe2

∆E (eV)

-0.55

-0.68

-0.45

-0.56

a (Å)

3.67

3.65

3.78

3.75

M-X (Å)

2.58

2.55

2.71

2.68

Eg-PBE (eV)

1.28

1.56

0.58

0.77

Eg-HSE (eV)

1.85

2.14

1.01

1.15

hetero-bilayer

ZrS2- HfS2

ZrSe2- HfSe2

ZrSe2- HfS2

ZrS2- HfSe2

Eii (eV)

-0.19

-0.257

-0.23

-0.21

Eiii (eV)

-0.187

-0.254

-0.22

-0.21

Eiv (eV)

-0.20

-0.272

-0.25

-0.23

Ev (eV)

-0.18

-0.24

-0.22

-0.20

a (Å)

3.66

3.75

3.71

3.70

d (Å)

2.90

2.98

2.93

2.95

2.57

2.70

2.69

2.59

2.56

2.69

2.57

2.67

1.26

0.52

0.38

0.53

1.80

0.85

0.58

0.76

Hf-X (Å)

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Eg-PBE (eV)

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Eg-HSE (eV)

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Zr-X (Å)

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monolayer

TABLE I. Difference of ground state energy (∆E), lattice constant (a), bond length (M-X), band gap (Eg−PBE, Eg−HSE), binding energy (Eii, Eiii, Eiv, Ev), interlayer distances (d) for monolayers and heterostructures.

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FIG. 1. (i): ZrS2 monolayer; (ii): Hf atom of HfS2 monolayer is located on chalcogen atom (toplayer) of ZrS2 monolayer; (iii): Hf atom of HfS2 monolayer is located on chalcogen atom (bottom-layer) of ZrS2 monolayer; (iv): Hf atom of HfS2 monolayer is located on top of Zr atom

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avoided.

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of ZrS2 monolayer; (v): where two monolayers shifted laterally so that on-top positions are

FIG. 2. Phonon spectra of heterostructures, first row (i) ZrS2-HfS2, (ii) ZrSe2-HfSe2, second row (i) ZrS2-HfSe2, (ii) ZrSe2-HfS2. 14

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FIG. 3. Band structures, first row i) ZrS2, ii) HfS2, iii) ZrSe2 and iv) HfSe2 monolayers and second row i) ZrS2-HfS2, ii) ZrSe2-HfSe2, iii) ZrSe2-HfS2 and iv) ZrS2-HfSe2, heterostructures of

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monolayers.

FIG. 4. Partial density of states, first row i) ZrS2, ii) HfS2, iii) ZrSe2 and iv) HfSe2 monolayers and second and third row d and p states of corresponding layer in i) ZrS2-HfS2, ii) ZrSe2-HfSe2, iii) ZrSe2-HfS2 and iv) ZrS2-HfSe2, heterostructures.

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FIG. 5. Orbitally weighted band structures of the ZrS2-HfSe2 out-of-plane heterostructures for Zr (red), Hf (green), S(brown) and Se (blue). First row (a)Zr/Hf-dxy (b) Zr/Hf-dxz (c) Zr/Hf-dz2,

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second row (a) S/Se-px (b) S/Se-py (c) S/Se-pz.

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FIG. 6. Transport coefficients as a function of chemical potential of MX2 monolayers and their

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corresponding heterostructures.

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Stacking of monolayers in the form of Van der Waals heterostructures have recently emerged as a new class of materials, where quantum coupling between stacked atomically thin two-dimensional layers gives rise to fascinating new phenomena. Band gap engineering and strong light-matter interaction enable the development of efficient photovoltaic, opto-

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electronic and thermoelectric devices based on 2D TMDC heterostructures.

In this paper, we focused on the structural, electronic and thermoelectric performance of novel van der Waals heterostructures consisting of MX2 (M= Zr, Hf and X= S, Se) monolayers. The favorable stacking and stability of the modelled monolayer heterostructures are

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confirmed through formation energy and phonon dispersion calculations. After confirming stability, the electronic and thermoelectric properties of the compounds are explored by

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using the first-principles calculations combined with semiclassical Boltzmann transport theory. It is found that Type-II band alignment in ZrS2 -HfSe2 facilitates charge separation for optoelectronics and solar energy conversion. All studied heterostructures show remarkably higher electrical conductivity than corresponding monolayers, responsible for large power factor values, especially at 1200 K. These findings indicate that the creation of van der Waals heterostrucutres from MX2 (M= Zr, Hf and X= S, Se) may be promising for efficient

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optoelectronic and thermoelectric devices.

The work in this paper is significantly based on new results and emphasize understanding of the physics of new emerging low-dimensional systems in the form of Van der Waals

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heterostructures for energy conversion and storage in modern technologies.

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