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First Principles Study of the Transport Properties in Bulk and Monolayer MX (M = Ti, Zr, Hf and X = S, Se) Compounds 3
Yasir Saeed, Ali Kachmar, and Marcelo Andrés Carignano J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b08067 • Publication Date (Web): 30 Dec 2016 Downloaded from http://pubs.acs.org on December 31, 2016
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The Journal of Physical Chemistry
First Principles Study of the Transport Properties in Bulk and Monolayer MX3 (M = Ti, Zr, Hf and X = S, Se) Compounds. Yasir Saeed,⇤ Ali Kachmar, and Marcelo A. Carignano Qatar Environment and Energy Research Institute (QEERI), Hamad Bin Khalifa University (HBKU), Qatar Foundation, P.O. Box 5825, Doha, Qatar Layered materials are the best candidates for thermoelectric application due to their in-plane low thermal conductivity that is a key property to achieve high efficiency. Owing to that, here we present our investigations on electronic as well as thermal transport of bulk and monolayer MX3 compounds (M = Ti, Zr, and Hf and X = S and Se) based on density functional and semi-classical Boltzmann theories. The values of the bandgap is rather similar for bulk and the monolayer, with only a slight change in the shape of bands near the Fermi level that results in a di↵erent e↵ective mass. We found that the monolayer MX3 compounds are better thermoelectric materials than bulk. Also, the p-type monolayer of TiS3 has a high power factor at 600 K that is the double of its room temperature value. The monolayer of the Zr/HfSe3 compounds show a promising behavior as a n-type thermoelectric materials at 600 K. In-plane tensile strain could be used to further tune the TE properties of the monolayers in order to obtain high performance TE materials.
INTRODUCTION (a)
Thermoelectric (TE) materials have been extensively studied for key applications such as the conversion of waste heat into electricity and they have an important potential to contribute to the solution of the energy and environment crises. The efficiency of TE devices is determined by the dimensionless figure of merit ZT = S 2 T /, where is the electrical conductivity, S is the Seebeck coefficient, T is the absolute temperature, and is the thermal conductivity. The latter comprises lattice (l ) and electronic (e ) contributions: = l +e . In order to achieve a high efficiency a TE material has to be a good electrical and poor thermal conductor and at the same time it has to possess a high Seebeck coefficient, see Ref. [1] and the references therein. Nanostructuring, alloying, and application of strain are e↵ective and frequently used approaches [2–4] to improve TE properties, because these processes enhance the phonon scattering and therefore the thermal conductivity is reduced. Bi2 Te3 is known to be the best TE material with an optimum ZT value close to 1 at 400 K [2, 5–7]. However, tellurium (Te) is an expensive, toxic element and of limited availability and then its use for large scale application is prohibitively expensive. Thus, one of the current main interests in TE research is to develop alternative materials (Te free, for example based on S and Se) with higher efficiency for operation between room temperature and 900 K, approximately. Recently, WSe2 among the other transition metal dichalcogenides shows high ZT in nanotube and nonoribbon than its monolayer case [8, 9]. Moreover, exfoliation methods have been proven to work well to extract monolayers from bulk provided that the structure has the proper van der Waals (vdW) gap [10] and therefore 2D materials should be included in the search for the best TE candidates. Transition metal trichalcogenides MX3 , where M is transition metal Ti, Zr or Hf and X is a chalcogenide
z
y x
(b)
FIG. 1. Crystal structures of bulk (a) and monolayer (b) MX3 , where M = Ti, Zr, or Hf and X = S or Se. M atoms are shown in blue and X atoms in red.
S, Se or Te, are typical vdW stacked layered materials [11]. The M element is sandwiched between sheets of X atoms. These X-M-X layers are bound to one another by vdW forces and therefore, it is possible to extract monolayers of MX3 by exfoliation. MX3 compounds crystallize in a monoclinic structure belonging to space group P 21 /m with Z = 2 [12]. The M atom occupy the center of a trigonal prism with X atoms at the corners. An illustration of the bulk and the monolayer structures of MX3 compounds is given in Fig. 1. Experimentally, the electronic properties of bulk MX3 have been determined [13, 14] while nanosheets and nanoribbons of TiS3 composed of several monolayers have been successfully isolated and show a direct band gap of 1.1 eV [15, 16]. The
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value of the bandgap can be further tuned by applying an external strain [17, 18]. Recently, several first principles studies have been carried out to investigate the electronic properties of bulk [19] and monolayered [20, 21] MX3 . It was found that all the compounds, with the exception of MTe3 that behaves as a metal, are semiconductors with bandgaps in a range of 0.2 2 eV. TiS3 has been found to have interesting properties that makes it a promising candidate for electrode material for rechargeable batteries [22]. This material does not show good properties for TE in bulk shape, since its ZT=0.007 [23] and doping with Nb results in a reduction of the thermal conductivity [24]. The other MX3 compounds are still largely unexplored and a comprehensive TE study is due in order to assess their potential for real world applications. In this context, we investigate the TE properties of bulk and monolayer MX3 compounds except X=Te (because Te based MX3 compounds are showing metallic behavior). Hereafter, X will refer only to S or Se. Changes in interlayer coupling due to vdW, degree of quantum confinement, and symmetry elements lead to dramatic di↵erences in the electronic structure of monolayer with respect to its bulk counterparts. In this paper we demonstrate the TE properties of MX3 in terms of the p and n doped carrier concentration at 300 K for the bulk and for an isolated monolayer. Since the TE properties for device applications are relevant at higher temperatures, we also predict the TE properties of monolayer compounds at 600 K.
METHODOLOGY
Our calculations are based on density functional theory (DFT), using the full-potential linearized augmented plane wave approach as implemented in the WIEN2k code [25]. We employed the generalized gradient approximation of the exchange correlation potential in the Perdew-Burke-Ernzerhof flavor for the calculation of the electronic and transport properties. The transport is calculated by the semi-classical Boltzmann theory within the constant scattering approximation after
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FIG. 2. Band structures of bulk MX3 compounds: (a) TiS3 , (b) ZrS3 , (c) HfS3 , (d) TiSe3 , (e) ZrSe3 and (f) HfSe3 .
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TABLE I. Summary of structural parameters and bandgaps obtained for bulk and monolayered MX3 compounds. TiS3 TiSe3 ZrS3 ZrSe3 HfS3 HfSe3 a (˚ A) 4.90 5.24 5.14 5.33 5.16 5.40 Bulk b (˚ A) 3.37 3.53 3.36 3.67 3.60 3.71 c (˚ A) 8.91 9.40 9.15 9.47 9.24 9.62 96.74 96.69 96.94 96.82 96.66 96.78 Eg (eV) 0.20 0.11 1.19 0.50 1.22 0.37 a (˚ A) 4.95 5.32 5.19 5.45 5.09 5.35 Monolayer b (˚ A) 3.40 3.58 3.44 3.61 3.72 3.77 96.56 96.49 96.55 96.34 96.68 96.74 Eg (eV) 0.20 0.32 1.23 0.55 1.25 0.48
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FIG. 3. Band structures of monolayer MX3 compounds: (a) TiS3 , (b) ZrS3 , (c) HfS3 , (d) TiSe3 , (e) ZrSe3 and (f) HfSe3 .
self-consistency is achieved in the first principles calculations, as implemented in the BoltzTraP code [26]. This approach yields accurate results for various types of TE materials [27–32]. Electronic calculations are performed with MonkhorstPack 6⇥6⇥4 (bulk) and 12⇥12⇥1 (monolayer) k-meshes for the Brillouin zone integrations. Furthermore, we employ finer 24 ⇥ 24 ⇥ 12 (bulk) and 50 ⇥ 50 ⇥ 1 (monolayer) k-meshes for calculating the transport properties. All structures are optimized with a tolerance of 10 5 Ry and a force convergence tolerance of 0.025 eV/˚ A. A 15 ˚ A vacuum slab is used to prevent artificial interaction with periodic images due to the employed periodic boundary conditions for monolayer.
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The experimental lattice constants of the MX3 compounds are used as a starting point for the relaxation runs and the obtained optimized lattice parameters for bulk and monolayer are summarized in Table 1. Our results for the optimized structural parameters are in good agreement with other reported theoretical and experimental values for bulk and monolayers given in Refs. [19–21] and references there in. Next, we study the electronic properties by calculating the band structures. The results are plotted in Fig. 2 and 3 for the bulk and monolayer MX3 compounds, respectively. Although previously reported bandgap values [19–21] based on pseudopotentials (VASP) studies that are in good agreement with the experimental results, the nature of bandgap is still unclear. Namely, the direct or indirect character of the bandgap has to be further investigated. The pseudo-potential based studies find an indirect bandgap for the bulk and the monolayer of all the MX3 compounds with the exception of monolayer TiS3 , which is found to be direct [19–21]. Our calculations in Fig. 2 (a) and 3 (a) based on a full-potential study indicate an indirect bandgap for TiS3 in the bulk and monolayer cases, although in the later case the o↵set is very small. For the monolayer, our results are di↵erent than the reported ones using pseudo-potentials. The indirect gap of the TiS3 monolayer can be appreciated by looking along the -B symmetry direction. It is worth noting a recent calculation based on pseudo-potentials [18] that finds that by applying a 5 % compressive strain the bandgap become indirect, as in our all electron calculation shows for the relaxed structure. The ZrS3 and TiSe3 compounds, which are cases b) and d) in Figures 2 and 3, show an indirect to direct bandgap transition between the bulk and the monolayer cases. Both materials in their bulk phase have a indirect bandgap from to Z. The remaining compounds of our study, namely HfS3 (case c), ZrSe3 (case e) and HfSe3 (case f) show no change in the character of the bandgap between the bulk and the monolayer. For HfS3 the bandgap is direct and for Zr/HfSe3 the bandgap is indirect. The values for the bandgap that we calculated are systematically smaller than the experimental values for the cases where they are available, and also smaller than the bandgap calculated with HSE06. It is known that by increasing the level of PBE calculations to HSE the bandgap are significantly improved, but the character of the bands is preserved. Namely, HSE calculations result in an increased bandgap with respect to PBE without a↵ecting the nature of bands near the conduction band minima (CBM) or valence band maxima (VBM). Then, in order to correctly estimate the Seebeck coefficient we use the values of the bandgap resulting from the
pseudo-potential hybrid study of Refs [19–21] to correct the bandgap of our band structure results calculated with full electron approach. We now turn our attention to the room temperature (RT) TE properties (along the in-plane and averaged) of the MX3 compounds in bulk and monolayer. In Figs. 4 and 5, we plot the results for the Seebeck coefficient (S), electronic conductivity ( /⌧ ) and power factor (PF) (= S 2 /⌧ ) as a function of carrier concentration (p and n-type) ranging from 1018 to 1021 cm 3 for bulk and monolayer, respectively. It is convenient to recall the figure of merit ZT depends on S 2 . In p-doped bulk the S coefficient is larger for the sulfide than for the selenide compounds. The former take values around 500 µV/K for our lowest carrier concentration and decreases monotonically, reaching ⇠ 100 µV/K at a concentration ⇠ 1020 cm 3 . In n-doped bulk the picture is just the opposite: S is larger (its absolute value) for Ti/Zr/HfSe3 than for the sulfides. /⌧ shows a mixed behavior with respect to p and n type bulk compounds, but the highest values are for HfSe3 in the two doping types at the relevant concentration range, which is 1019 1020 cm 3 . At 1020 cm 3 Ti/Zr/HfS3 has a /⌧ value of around 1019 /⌦ms for p-type that increases to 7.5 ⇥ 1019 /⌦ms in n-type for HfSe3 . Hence, in the p-type bulk case, HfSe3 has double /⌧ than Ti/Zr/HfS3 due to small S value at 1020 cm 3 for the HfSe3 . Consequently, the HfSe3 has a high PF of 13 ⇥ 1010 W/mK2 s at a p-type carrier concentration of 1019 cm 3 , which is the ideal concentration in most cases. Also Zr/HfS3 gives slightly higher PF 14 ⇥ 1010 W/mK2 s at a carrier concentration of 3 ⇥ 1019 cm 3 . We conclude that Zr/HfS3 are also good candidates for bulk p-type TE materials, similarly to TiS3 [23, 24]. The PF in the n-type bulk is clearly dominated by HfSe3 with value of 120 ⇥ 1010 W/mK2 s at carrier concentration of 2.5 ⇥ 1020 cm 3 . In Fig. 5, the MX3 monolayer compounds are analyzed as a function of the p-type and n-type carrier
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RESULTS AND DISCUSSION
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Since TE materials are usually operated at temperatures higher than RT, we studied the response of these systems at 600 K for the monolayer case. In Fig. 6, we present the Seebeck coefficient (S), electronic conductivity ( /⌧ ) and power factor (PF) (= S 2 /⌧ ) as a function of carrier concentration (p and n-type). The S value for all the MX3 monolayers decreases from ⇠ 350 µV/K to ⇠ 250 µV/K as the p-type carrier concentration increases from 1019 cm 3 to 1020 cm 3 . The corresponding n-type results go from ⇠ 400 µV/K to ⇠ 200 µV/K for Ti/Zr/HfSe3 , and from ⇠ 300 µV/K to ⇠ 100 µV/K for Ti/Zr/HfS3 . Similarly to the 300 K results, the monolayer of TiS3 is the best candidate material for TE applications under p-type doping conditions, as it reaches a PF of 27 ⇥ 1010 W/mK2 s at carrier concentration of 6.5 ⇥ 1019 cm 3 . This value is 55% higher than the bulk value and 40% higher than its monolayer value at 300 K. For n-type doping, HfSe3 and ZrSe3 monolayers have the highest PF among the entire family, reaching 160 ⇥ 1010 W/mK2 s at carrier concentration of 1.5 ⇥ 1020 cm 3 . Therefore, these two materials are good candidates for n-type TE materials at the typical operational temperature.
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concentrations at RT. The S value for ZrSe3 reaches ⇠ 500 µV/K while the other MX3 compounds reach ⇠ 450 µV/K at p-type carrier concentration of 1018 cm 3 . On the other hand, the (absolute value) S value for n-type ZrSe3 reaches ⇠ 550 µV/K and decreases with increasing carrier concentration. The reason for the similitude in the S values for the bulk and monolayer cases is the proximity of their bandgap values. This is indeed quite surprising. For example, in other 2D TE materials like Bi2 Te3 [2, 5–7] and MoS2 [33], the bandgap always increases by decreasing the dimension. The TiS3 monolayer is clearly the best candidate for TE applications among all the members of the MX3 family of compounds under p-type doping conditions. The TiS3 monolayer reaches a PF of 16 ⇥ 1010 W/mK2 s at an ideal carrier concentration, which is 25% higher than the bulk value of 12 ⇥ 1010 W/mK2 s. For the n-type case, the monolayers of HfSe3 and ZrSe3 show the highest PF, reaching 90 ⇥ 1010 W/mK2 s at a carrier concentration of 7 ⇥ 1019 cm 3 and 1.5 ⇥ 1020 cm 3 , respectively. We conclude that monolayer MX3 compounds are in general preferable than the bulk phase for TE applications at RT.
The knowledge of the relaxation time (⌧ ) and thermal conductivity () allows the calculation of the figure of merit ZT. Recently Guilmeau et al. [23, 24] measured for pristine TiS3 and with a slight Nb doping in bulk phase and found that the doping induces a reduction in from 3.6 W/Km to 2.0 W/Km at RT and 1.4 W/Km at a temperature of 523 K, which is the temperature corresponding to the highest ZT. One could speculate that doping the n-type TiS3 bulk with Hf may result in a similar e↵ect. Namely, the e↵ect of Hf would be to reduce to ⇠ 1 W/Km while keeping the PF of the bulk TiS3 . This later assertion is based on that both bulk materials, i.e. TiS3 and HfS3 , have the same room temperature PF at carrier concentrations of the order 1020 cm 3 . A similar argument could be risen for the monolayer cases of n-type Ti/Zr/HfSe3 at 600 K. We are currently performing a study on systems with mixed cations and strain e↵ects to verify these predictions. In conclusion, we have established the dependence of the TE properties of bulk and monolayer MX3 compounds with carrier consternation and temperature. Our study is based on density functional theory to establish the electron structure properties and semiclassical Boltzmann theory to determine the transport properties. A careful description of the structural and electronic properties are essential to understand the TE properties. We demonstrated that monolayer MX3 compounds are better TE materials than the bulk. Also, p-type monolayer TiS3 has PF of 16 ⇥ 1010 W/mK2 s at 300 K that increases by a factor of two at 600 K. The monolayer HfSe3 and ZrSe3 compounds show a promis-
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ing behavior as a n-type TE materials with a high PF of 90 ⇥ 1010 W/mK2 s at 300 K and 160 ⇥ 1010 W/mK2 s at 600 K. We speculate that the figure of merit ZT could be further enhanced by inter mixing of cations (Ti/Zr/Hf) in monolayer at high temperature by reducing while keeping the PF constant. In-plane tensile strain is also a possibility to tune the bandgap in order to increase S and disorder the monolayer lattice to reduce , both favorable e↵ects to achieve high performance TE materials.
[6] Tritt, T. M. Holey and Unholey Semiconductors. Science 1999, 283, 804-805. [7] Poudel, B.; Hao, Q.; Ma, Y.; Lan, Y.; Minnich, A.; Yu, B.; Yan, X.; Wang, D.; Muto, A.; Vashaee, D.; Chen, X.; Liu, J.; Dresselhaus, M. S.; Chen, G.; Ren, Z. HighThermoelectric Performance of Nanostructured Bismuth Antimony Telluride Bulk Alloys. Science 2008, 320, 634638. [8] Chen, K. X.; Luo, Z. Y.; Mo, D. C.; Lyu, S. S. WSe2 Nanoribbons: New High-Performance Thermoelectric Materials. Phys Chem Chem Phys. 2006, 18, 1633716344. [9] Chen, K. X.; Wang X. M.; Mo, D. C.; Lyu, S. S. Thermoelectric Properties of Transition Metal Dichalcogenides: AUTHOR INFORMATION From Monolayers to Nanotubes. J. Phys. Chem. C 2015, 119, 26706-26711. [10] Nicolosi, V.; Chhowalla, M.; Kanatzidis, M. G.; Strano, Corresponding Author M. S.; Soleman, J. N. Liquid Exfoliation of Layered Ma⇤Phone:+(974)-55165815. E mail:
[email protected]; terials. Science 2013, 340, 1226419.
[email protected] (Y.S.). [11] Kr¨ onert, W.; Plieth, K. Z. Die Struktur des ZirkontriseNotes lenids ZrSe3 . Anorg. Allg. Chem. 1965, 336, 207-218. [12] Furuseth, S.; Brattas, L.; Kjekshus, A. Crystal StrucThe authors declare no competing financial interest. tures of TiS3 , ZrS3 , ZrSe3 , ZrTe3 , HfS3 and HfSe3 . Acta Chemica Scandinavisa A 1975, 29, 623-631. [13] Gorlova, I.; Pokrovskii, V. Y.; Zybtsev, S.; Titov, A.; ACKNOWLEDGMENT Timofeev, V. Features of the Conductivity of the QuasiOne-Dimensional Compound TiS3 . J. Exp.Theor. Phys. 2010, 111, 298-303. This publication was made possible by PDRA grant [14] Hoesch, M.; Cui, X.; Shimada, K.; Battaglia, C.; Fuji(PDRA1-0119-14119) from the Qatar National Research mori, S.-i.; Berger, H. Splitting in the Fermi Surface of Fund (a member of Qatar Foundation). The findings ZrTe3 : A Surface Charge Density Wave System. Phys. achieved herein are solely the responsibility of the auRev. B, 2009, 80, 075423-075431. thors. The HPC resources and services used in this work [15] Molina-Mendoza, A. J.; Barawi, M.; Biele, R.; Flores, were provided by the Research Computing group in Texas E.; Ram¨ on Ares, J.; S´ anchez, C.; Rubio-Bollinger, G.; Agra¨ıt, N.; D’Agosta, R.; Ferrer, I. J.; CastellanosA&M University at Qatar. We also acknowledge the Gomez, A. Electronic Bandgap and Exciton Binding helpful discussion with Dr. Nirpendra Singh (KAUST). Energy of Layered Semiconductor TiS3 . Adv. Electron. Mater. 2015, 1, 1500126. [16] Pawbake,A. S.; Island, J. O.; Flores, E.; Ram¨ on Ares, J.; Sanchez, C.; Ferrer, I. J.; Jadkar, S. R.; van der Zant, H. S. J.; Castellanos-Gomez, A.; Late, D. J. Temperature⇤
[email protected],
[email protected], +974 Dependent Raman Spectroscopy of Titanium Trisulfide 55165815 (TiS3 ) Nanoribbons and Nanosheets. ACS Appl. Mater. Interfaces 2015, 7, 24185-24190. [17] Li,M.; Dai, J.; Zeng, X. C. Tuning the Electronic PropREFERENCES erties of Transition-Metal Trichalcogenides via Tensile Strain. Nanoscale 2015, 7, 15385-15391. [18] Biele, R.; Flores, E.; Ram¨ on Ares, J.; S´ anchez, C.; Fer[1] Bell, L. E. Cooling, Heating, Generating Power, and Rerer, I. J.; Rubio-Bollinger, G.; Castellanos-Gomez, A.; covering Waste Heat with Thermoelectric Systems. SciD’Agosta, R. Strain Induced Bandgap Engineering in ence 2008, 321, 1457-1461. Layered TiS3 . arXive:1509.00532v1 2015. [2] Venkatasubramanian, R.; Siivola, E.; Colpitts, T.; [19] Abdulsalam, M.; Joubert, D. P. Structural and ElecO’Quinn, B. Thin-Film Thermoelectric Devices with tronic Properties of MX3 (M= Ti, Zr and Hf; X= S, High Room-Temperature Figures of Merit. Nature 2001, Se, Te) From First Principles Calculations. Eur. Phys. J. 413, 597. B 2015, 88, 177. [3] Harman, T. C.; Taylor, P. J.; Walsh, M. P.; LaForge, B. [20] Dai, J.; Zeng, X. C. Titanium Trisulfide Monolayer: E. Quantum Dot Superlattice Thermoelectric Materials Theoretical Prediction of a New DirectGap Semiconducand Devices. Science 2002, 297, 2229-2232. tor with High and Anisotropic Carrier Mobility. Angew. [4] Soni A.; Shen, Y.; Yin, M.; Zhao, Y.; Yu, L.; Hu, X.; Chem. Int. Ed. 2015, 54, 7572-7576. Dong, Z.; Khor, K. A.; Dresselhaus, M. S.; Xiong, Q. In[21] Jin, Y.; Li, X.; Yang, J. Single Layer of MX3 (M = Ti, terface Driven Energy Filtering of Thermoelectric Power Zr; X= S, Se, Te): a New Platform for Nano-Electronics in Spark Plasma Sintered Bi2 Te2.7 Se0.3 Nanoplatelet and Optics. Phys. Chem. Chem. Phys. 2015, 17, 18665Composites. Nano Lett. 2012, 12, 4305-4310. 18669. [5] Snyder, G. J.; Toberer, E. S. Complex Thermoelectric Materials. Nat. Mater. 2008, 7, 105-114.
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