Band structure, thermoelectric properties, effective mass and electronic fitness function of two newly discovered 18 valence electrons stable half-Heusler TaX(X=Co,Ir)Sn semiconductors: A density functional theory approach

Journal Pre-proof Band structure, thermoelectric properties, effective mass and electronic fitness function of two newly discovered 18 valence electrons stable half-Heusler TaX(X=Co,Ir)Sn semiconductors: A density functional theory approach Paul O. Adebambo, Ridwan O. Agbaoye, Abolore A. Musari, Bamidele I. Adetunji, Gboyega A. Adebayo PII:

S1293-2558(19)31158-6

DOI:

https://doi.org/10.1016/j.solidstatesciences.2019.106096

Reference:

SSSCIE 106096

To appear in:

Solid State Sciences

Received Date: 4 October 2019 Revised Date:

4 December 2019

Accepted Date: 10 December 2019

Please cite this article as: P.O. Adebambo, R.O. Agbaoye, A.A. Musari, B.I. Adetunji, G.A. Adebayo, Band structure, thermoelectric properties, effective mass and electronic fitness function of two newly discovered 18 valence electrons stable half-Heusler TaX(X=Co,Ir)Sn semiconductors: A density functional theory approach, Solid State Sciences (2020), doi: https://doi.org/10.1016/ j.solidstatesciences.2019.106096. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. 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. © 2019 Published by Elsevier Masson SAS.

Band structure, thermoelectric properties, effective mass and electronic fitness function of two newly discovered 18 valence electrons stable half-Heusler TaX(X=Co,Ir)Sn semiconductors: A Density Functional Theory approach Paul O. Adebamboa Ridwan O. Agbaoyea , Abolore A. Musarib Bamidele I. Adetunjic and Gboyega A. Adebayoa a

Department of Physics, Federal University of Agriculture, Alabata Road, PMB 2240, Abeokuta, Nigeria b Physics with Electronics unit, Department of Science Laboratory Technology, Moshood Abiola Polytechnic, Abeokuta, Nigeria and c Department of Physics, Bells University of Technology, Ota, Nigeria (Dated: December 18, 2019) We performed detailed first-principles Density Functional Theory (DFT) Calculations of electronic 2 )− 3 band structure and predict the effective mass as well as the electronic fitness function S 2 στ ( N V in the valence and conduction band edges of two Tantalum-Tin based Half-Heusler Alloys. Implementation of a generalized gradient approximation based DFT coupled with Boltzmann’s transport theory allows us to determine the power factor at an appropriate chemical potential ( and consequently, an optimum carrier concentration) at which other transport properties were determined. In the pure compounds, the electronic fatbands, both in the valence and conduction bands revealed the great influence of the 3-d orbitals of Cobalt atoms in lowering of the energy band gap of compound, while the 5-d Iridium orbitals contribute very little to energy gap lowering. The Seebeck coefficient is found to be hole dependent as well as having a strong dependence on temperature as it decreases with increasing electron carrier concentration in both compounds. At some high temperatures, the Seebeck coefficient developed high shoulders in the Ir-based compound at high hole concentrations close to 1022 cm−3 . We found the Co-based compound to be a better thermoelectric, since the Seebeck coefficient shows a heavy-doped traits, while the Ir-based compound demonstrates a parabolic-shaped Seebeck coefficient (which is a sign of a lightly-doped thermoelectric). From the effective mass calculations, we found that an increase in carrier concentrations results in lowering of the effective mass in the conduction band. PACS numbers: 71.15.-m; 71.15.Mb; 71.20.-b; 71.20.Be; 71.20.Nr Keywords: Electronic structure; DFT; Alloys; Band structure; Heusler Alloys

2 I.

INTRODUCTION

The tremendous achievements of the last two decades in computational materials science and physics are largely due to the availability of sophisticated high-performance clusters as well as developments of highly efficient simulation packages which can handle several atoms or molecules. These and other factors have made possible, contributions to materials engineering from groups around the globe and provide the opportunities to conduct multi-field interrelated researches. The trend in simulation has always been to test theories, stand-alone experiment lab or to compare with experiments. However, the first-principles method and other simulation techniques continue to push further, the horizon of discoveries farther than experiments. Among the various first-principles or ab-initio methods, the Plane-Wave Self-Consistent Field (PWSCF) calculations allow determining very accurately, the electronic band structure and other properties using basic sets1 and pseudopotentials. Using the PWSCF within the Density Functional Theory (DFT), make possible the calculations of other important properties of systems and recently, thermoelectric and thermodynamic properties are included/adapted in the various PWSCF and other packages6–9 . The good thing about these add-ons is that almost all of the physics theories involved the determination of property is embedded in the script/package developments; in many instances, there are improvements in calculated properties when compared with experiments. The special class of compounds known as Heusler Alloys2 has found advantageous applications in photovoltaic, spintronic, thermoelectric and other devices3 . In fact, in the last ten years, Heusler alloys have dominated the terrain of materials engineering and technology4 . However, the much attention given to Heusler alloys is not commensurate with the research output and expectations probably these are due to various reasons among which are slow realizations of techniques6 required to carry out novel computations and certain attributes of the Heusler alloys which may limit the efficiency of the alloys. For example among other attributes, half-Heusler alloys are known to have 18 valence electrons and C1b structure (space group number and symbol 216 &F ¯43m respectively) which can be tuned appropriately by doping such that there can be crossover from semiconductor to magnetic metal10 or half-metallic ferromagnetic; indeed, the valence electron count in half-Heusler Alloys are responsible for the magnetic and transport properties. Although doping half-Heusler Alloys may result in better functional materials, many properties of the emerging materials are yet to be understood. The elemental combination of Heusler Alloys are well understood in the Periodic Table of elements, however, it is also known that not all combinations are stable12–14,35 , therefore, the gains from efficient DFT calculations will only make sense if applied to stable phases of Half-Heusler Alloys, otherwise such effort will only amount to academic exercise with no practical applications. Out of the over 480 possible combinations, only less than 90 have been identified out of which only about 53 compounds have been discovered to be stable15 . As mentioned above, availability of efficient computational facilities/tools will result in more human capabilities to predict previously unknown materials, as well as enhance the prediction of properties of already discovered compounds16–18 . In predicting new materials, important properties are sometimes overlooked as emphases are usually placed only on structural properties. It is, therefore, necessary to perform rigorous calculations of several other properties and test the results against those of known materials (see for example, Ref.15 ). The 18-valence-electron attribute of many half-Heusler compounds makes these compounds to be multi-functional in nature19,20 , while the crystal structures21 , as well as other properties of some multi-functional, have been known22–26 . It is known that increasing the power factor or decreasing the lattice thermal conductivity leads to an increased figure of merit (ZT ), so the main aim of adding impurities to a thermoelectric material is to gain on ZT . Besides, finding ways to increase the effective mass and therefore, the Seebeck coefficient, may also lead to more efficient thermoelectric material at the expense of carrier mobility in the case of compounds with flat bands. Information on transport properties, effective mass, and electronic fitness function are lacking or not adequate in many of the calculations on the recently discovered multi-functional materials15 , this work, therefore, aims at filling the gaps on the structural, thermoelectric and transport properties of two T a − Sn based half-Heusler. As the information on effective mass and electronic fitness function complement other properties in determining the usefulness of materials as a semiconductor or optoelectronic devices, it is our belief that the present work will provide the needed data for useful applications of the compounds. In this work, detailed first-principles DFT calculations were carried out to determine the Structures as well as predicting some transport properties and the effective mass as well as the electronic fitness function of recently predicted15 pure T aXSn(X = Ir, Co) based on Boltzmann’s transport theory. The effective masses are calculated at Γ point where the transition occurred in the pure compounds. In Section II, detailed theory and computational methods are stated, while in Section III, the main results of the calculations are highlighted and discussed. In Section IV, the major conclusions of our findings are stated.

3 II.

THEORY AND COMPUTATIONAL TECHNIQUES

The structural signature of T aXSn(X = Ir, Co) in stable phase are given in Figure 1 with atomic positions Sn(0 0 0), X(0.25 0.25 0.25) and T a(0.5 0.5 0.5). Self-Consistent Field, SCF calculations were carried out on a set of three configurations (primitive cell and two supercells along the unit lengths 1 × 1 × 1 and 2 × 2 × 2 ). All calculations were carried out in accordance with PWSCF5 using ultrasoft pseudopotentials27,28 which uses scalar relativistic as well as fully relativistic projected augumented wave (PAW) data sets. The Density Functional Theory used in the work relies on PAW Pseudopotential method of Perdew-Burke-Erzenhoff (PBE) exchange-correlation functional in the frame work of Generalized Gradient Approximation (GGA)29 implemented in Quantum espresso Package1,5 . In the determination of the stable structure, the lattice positions were optimized and the minimum energy in each configuration calculated; the energy difference of the supercells and the primitive cell is insignificant. Wavefunction cut-off of 50 and 40Ry were use respectively in the TaCoSn and TaIrSn, all structural calculations are done using the Quantum Espresso5 package. In the SCF calculations, we use 22×22×22 and 23×23×23 Monkhorst-Pack grids30 respectively in the primitive cell calculations for both the Co and Ir-based alloys. In the supercell configurations and preceding all calculations, the Ta and Co atom were assigned initial magnetization of 0.5 with 24 symmetry operations having no inversion. Convergence of the SCF calculations was attained after 15 iterations with an estimated accuracy in SCF less than 8.6 × 10−7 Ry. The thermoelectric transport properties, inverse effective mass and electronic fitness function were determined using the output from an SCF-relax calculations and Non-Self-Consistent Field (NSCF) calculations as well as the BoltzTraP7–9 package. In order to determine the transport properties, Boltzmann transport theory was employed in accordance with the method of Zhang and Singh7 , however, we first calculated the Power Factor (PF) S 2 σ of the materials in order to determine appropriately, the energies at which transport properties are to be calculated. Our approach is to locate the peak in the PF closest to the Fermi energy in the conduction bands and use the corresponding energy to determine other transport properties of the alloys. This allows to fine tune the energy close to the Fermi level where important physics are not missed. It should be emphasized however, that the calculated PF is in unit of time, i.e. one gets στ from the transport properties calculations. As a starting point in determining the transport properties, we performed a two-step plane-wave sets calculations involving a relax-scf calculation followed by a dense k-points, high verbosity nscf calculation in the supercells in which 82 Kohn-Sham states and a convergence threshold of 1.0 × 10−10 were employed. In the SCF relax calculations, a fast convergence after 14 iterations with convergence accuracy of 4.7 × 10−7 Ry was attained. At the end of the SCF calculations, the total magnetization was 0.03 Bohr mag/cell while the absolute magnetization was 0.03 Bohr mag/cell. The calculations above were followed by high verbosity, dense k-points non self-consistent field calculations in order for the transport properties to be calculated using Boltzmann transport theory. The method by Ref9 in which Fourier transformation is used to obtain semi-classical transport coefficient by interpolating the energy bands is adopted in the calculations of transport properties in this work. One needs a knowledge of the effective mass around the band edges to accurately determine some useful applications of the compounds. Therefore, to determine the effective mass as well as the Electronic Fitness Function (EFF) in the valence and conduction bands edges, the approach of Singh and co-workers6,7 was employed.

III. A.

RESULTS AND DISCUSSION Structure of T aCoSn and T aIrSn

From literature on both experiments and theoretical calculations, there are few reports on the structural properties of TaCoSn and TaIrSn compounds in pristine states. In the present work, using Density Functional Theory (DFT) calculations, the electronic structure and transport properties of two half-Heusler compounds are presented in pure states. The effective masses and the EFF of the compounds are also determined. The 5d orbitals of Tantalum atoms have very strong effects on the band structure of both TaCoSn and TaIrSn compounds with Co − 3d and T a − 5d orbitals dominating the highest valence bands (see Figure 2a to d) with indirect transitions at Γ → X in both compounds. The lattice parameters for both Half-Heusler compounds are optimized in both non-magnetic and ferromagnetic states, as presented in Figures 1c and d. Although the minimum energy for these two states appeared to be equal, the real state of these Half-Heusler compounds is the non-magnetic state. This conclusion was attributed to the fact when we did the spin-polarised calculation for these materials, both their total and absolute magnetizations are equal to 0.00 Bohr mag/cell. This implied that they are non-magnetic Half-Heusler compounds. The expression

4 for the exchange Murnaghan equation of state (EOS) is given as:       1 Vn Vn + + δE(V ) = E − E0 = BV0 B0 (1 − B 0 ) B 0 (B 0 − 1)

(1)

Where Vo is the equilibrium volume at zero pressure, Eo is the equilibrium energy, B, and B 0 are respectively the bulk modulus and its derivative. This expression in equation 1 was used to obtain the EOS parameters. However, the results of the structural calculations for these materials in the non-magnetic state were presented in Table 1. We found agreements in the present structural calculations with the predictions of Alex Zunger and co-workers15 . In Figure 2, we observed that the T a − 5d orbitals dominate the CBM in the pure compounds, while the Ir − 5d and Co − 3d are responsible for the VBM. TABLE I. Lattice constant a, bulk modulus B0 , and pressure derivatives B00 TaIrSn and TaCoSn Half-Heusler alloys. Alloys Methods a0 ( ˚ A) B0 (GP a) B00 TaCoSn (space group F ¯ 43m (216)) Present Work 5.967 165.4 4.48 Experiment 5.9431 others 5.97415 , 5.9532 TaIrSn (space group F ¯ 43m (216)) Present Work 6.236 181.0 4.33 Experiment Others 6.23315 , 6.25133 175.5033 4.4533

B.

Thermoelectric transport properties

In order to reduce the influence of opposing Seebeck effect, the electron carrier concentration is separated from hole carrier concentration, this separation allows a large net Seebeck effect in both the n-type and p-type conduction. In the Co-based compound, the Seebeck coefficient decreases as electron carrier concentration increases at different temperature, with optimum carrier concentration towards the 1019 cm−3 in the electron carrier, while in the hole carriers, the optimum carrier concentration value of about 1020 cm−3 was observed. Although, in the case of Ir-based compound the Seebeck coefficient also decreases with carrier concentrations, the increase is parabolic (Figures 3a and 4a(top plot))suggesting TaIrSn is already a form of a lightly-doped thermoelectric. The above statement is contrary to what obtains in TaCoSn which shows the compound is already an heavy-doped thermoelectric (3a) and hence will make a better thermoelectric material than the Ir-based compound. In addition, TaCoSn is expected to have a higher conductivity that TaIrSn. The Seebeck coefficient of Figure 4b shows an increasing value with hole carrier concentrations up to 1021 cm−3 . The Iridium atom, been a heavy element is responsible for the high conductivity value in both the electron and hole carrier concentrations. At different temperature, the conductivity essentially increases with increasing electron carriers in both compounds. However, since the Power factor is slightly higher in the Co-based compound at each temperature, it is expected to possess a higher figure of merit than the Ir-base compound provided the ratio κCo : κIr < 1, where κ is the total thermal conductivity. Results of thermoelectric transport properties are presented in Figures 3 and 4. In Figure 3, we show the carrier concentration and temperature dependent Power factor, PF (bottom figure) both for electrons (3a) and holes (3b) in the Co-based compound where an obvious nonlinear dependent is visible at all temperature. In the hole carrier concentrations, the highest PF was observed at 800K with the least PF occurring at 100K. The hole carrier concentration of ≈ 1020 cm−3 is a good value at 800K (upper red color), while at all other temperature, the value remains the same. Overall, the Power factor increases with increasing electron carrier concentration with highest peaks located farther to the right of 1021 cm3 and decreases beyond this value. Electronic fitness function is a transport function which helps detect prospective high performing materials for thermoelectric applications based on electronic band structure and transport properties35 . Machine learning has been deployed recently to predict the electronic fitness function, with the aid of Gaussian process regression model and the Bayesian optimization −2 method36 . The calculation of electronic fitness function, which is defined as S 2 (σ/τ )(N/V ) 3 help to determine the band that decouples conductivity, as well as the Seebeck coefficient. This helps in predicting semiconductors as a possible candidate for thermoelectric materials. Electronic fitness function and Boltzmann transport theory are highly dependent on the electronic band structure. The complexity in the band structure plays a role in the magnitude of both quantities. A low value of electronic fitness function is recorded in materials with isotropic parabolic band structure while a significant value is recorded for materials that decouple the electrical conductivity and the Seebeck coefficient35,36 . Conventionally the performance of thermoelectric materials are optimized by increasing the power

5 factor and reducing the thermal conductivity, increase in effective mass and reduction in carrier density produce increase in Seebeck coefficient but does not favour the electrical conductivity35,36 , hence the electronic fitness function become a tool to search for materials with improved figure of merit.35 recorded an increase in experimental figure of merit with the electronic fitness function especially for Binary semiconductors, alternatively the figure of merit can be increased by reducing the lattice thermal conductivity. The relationship between the band structure and thermoelectric behavior of these compounds are established by calculating the electronic fitness function which dependent on doping level and temperature as shown in Fig.6. As mentioned by Singh and Co-workers35 , the decoupling between the electrical conductivity and Seebeck coefficient can determined via EFF. Using the calculated Fermi Level to determine the Power Factor at room temperature, we were able to estimate the energy levels in both the conduction and valence bands at which it is possible to calculate, appropriately the effective mass as well as the electronic fitness function. A fixed doping level with six (Co-based) and ten (Ir-based) concentrations were used to determine both the electronic fitness function and the effective mass in the two compounds (Figures 5 and 6). In Fig.5, the only peak occurred at ≈ −2.79E + 19cm−3 with a valley occurring around −1.309E + 20cm−3 . Similarly, in Fig.5b, a major pronounced high peak was observed close to zero carrier concentration in the Ir-based compound with a disappeared valley (present in Fig.5a) and an appearance of a shoulder at ≈ 2.843E + 19cm−3 .

IV.

CONCLUSION

We have shown and highlighted bands contributions in the electronic band structures of stable half-Heusler TaCoSn and TaIrSn compounds using Plane wave self-consistent field density functional theory. The effective masses of the compounds are predicted in both conduction and valence bands. The behaviour of the compounds under fixed-doping was also predicted. In TaCoSn, the 3d-orbitals of Cobalt as well as the Tantalum orbitals are responsible for the low band gap while the Tantalum orbitals are mainly responsible for the small gap in the Ir-based compounds. In the TaIrSn compounds, since Irridium is an heavy element, it is expected that doping the compound with a 5datom will results the band-crossing between the doping element and Tantalum atom. On the other hand, doping TaCoSn with a similar element will make the Cobalt orbitals to dominate both the valence and conduction bands. The Seebeck coefficient is found to be hole dependent as well as having a strong dependence on temperature as it decreases with increasing electron carrier concentration in both compounds. At some high temperatures, the Seebeck coefficient developed high shoulders in the Ir-based compound at high hole concentrations close to 1022 cm−3 . We found the Co-based compound to be a better thermoelectric, since the Seebeck coefficient shows a heavy-doped traits, while the Ir-based compound demonstrates a parabolic-shaped Seebeck coefficient (which is a sign of a lightly-doped thermoelectric). From the effective mass calculations, we found that an increase in carrier concentrations results in lowering of the effective mass in the conduction band.

ACKNOWLEDGMENTS

Work was supported by the DAAD under its Reinvitation Programme and carried out mainly using computational resources at the University of Duisburg. GA is grateful to Prof. P. Kratzer and Dr. D. Ceresoli for useful discussion. †Visiting under the DAAD Reinvitation Programme 2018 at the Faculty of Physics, University of Duisburg-Essen, Lotharstrasse 1, D-47057 Germany

1

2

3

P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau, M. Buongiorno Nardelli, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, M. Cococcioni, N. Colonna, I. Carnimeo, A. Dal Corso, S. de Gironcoli, P. Delugas, R. A. DiStasio Jr, A. Ferretti, A. Floris, G. Fratesi, G. Fugallo, R. Gebauer, U. Gerstmann, F. Giustino, T. Gorni, J Jia, M. Kawamura, H.-Y. Ko, A. Kokalj, E. Kucukbenli, M .Lazzeri, M. Marsili, N. Marzari, F. Mauri, N. L. Nguyen, H.-V. Nguyen, A. Otero-de-la-Roza, L. Paulatto, S. Ponce, D. Rocca, R. Sabatini, B. Santra, M. Schlipf, A. P. Seitsonen, A. Smogunov, I. Timrov, T. Thonhauser, P. Umari, N. Vast, X. Wu, S. Baroni J.Phys.: Condens.Matter 29, 465901 (2017) ¨ F. Heusler (1903). ”Uber magnetische Manganlegierungen”. Verhandlungen der Deutschen Physikalischen Gesellschaft (in German). 12: 219. R. L. Zhang, L. Damewood, Y. J. Zeng, H. Z. Xing, C. Y. Fong, L. H. Yang, R. W. Peng and C. Felser, JOURNAL OF APPLIED PHYSICS 122, 013901 (2017)

6 4

5

6 7 8 9 10 11

12 13

14 15

16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

32

33

34 35 36

T. Tsuchiya, T. Kubota, T. Sugiyama, T. Huminiuc, A. Hirohata and K. Takanashi, J. Phys. D: Appl. Phys. 49 (2016) 235001 P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. Fabris, G. Fratesi, S. de Gironcoli, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A. P. Seitsonen, A. Smogunov, P. Umari, R. M. Wentzcovitch, J.Phys.:Condens.Matter 21, 395502 (2009) http://dx.doi.org/10.1088/0953-8984/21/39/395502 G. Xing, J. Sun, Y. Li, X. Fan, W. Zheng, D. J. Singh, Phys. Rev. Mater. 1, 065405 (2017); erratum ibid 1, 079901 (2017) Y. Li, L. Zhang and D.J. Singh, Phys. Rev. Mater. 1, 055001 (2017). L. Lentz, https://blog.levilentz.com/boltztrap-tutorial-for-quantum-espresso/ G. K. H. Madsena D. J. Singh, Computer Physics Communications, Volume 175, Issue 1, 1 July 2006, Pages 67-71. J. Tobola, J. Pierre, S. Kaprzyk, R. V. Skolozdra and M. A. Kouacou, J. Phys.: Condens. Matter 10 1013, 1998 Xing-Qiu Chena, R. Podloucky and P. Rogl, Journal of Applied Physics 100, 113901 (2006); https://doi.org/10.1063/1.2374672 I. Galanakis, Ph Mavropoulos and P. H. Dederichs, J. Phys. D: Appl. Phys. 39 765, 2006. S. Curtarolo, G. L. W. Hart, M. B. Nardelli, N. Mingo, S. Sanvito and O. Levy, Nature Materials volume 12, pages 191–201 (2013). S. Curtarolo, D. Morgan, K. Persson, J. Rodgers and G. Ceder, Phys. Rev. Lett. 91, 135503 (2003). R. Gautier, X. Zhang, L. Hu, L. Yu, Y. Lin, T. O. L. Sunde, D. Chon, K. R. Poeppelmeier and A. Zunger, NATURE CHEMISTRY, VOL 7, DOI: 10.1038/NCHEM.2207 J. Feng, R.G. Hennig, N.W. Ashcroft and R. Hoffmann, Nature 451, 445–448 (2008). C. J. Pickard and R. J. Needs, Nature Phys. 3, 473–476 (2007). Z. W. Lu, S-H. Wei, A. Zunger, S. Frota-Pessoa and L. G. Ferreira, Phys. Rev. B 44, 512–544 (1991). F. Yan, X. W. Zhang, Y. G. Yu, L. P. Yu, A. Nagaraja, T. O. Mason, and A. Zunger, Nat. Commun 6 (2015). X. W. Zhang, L. P. Yu, A. Zakutayev, and A. Zunger, Adv Funct Mater 22, 1425 (2012). Inorganic Crystal Structure Database, ICSD ( Fachinformationszentrum Karlsruhe, Karlsruhe, Germany 2013). S. Chadov, X. Qi, J. Kubler, G. H. Fecher, C. Felser, and S. C. Zhang, Nature materials 9, 541 (2010). A. Roy, J. W. Bennett, K. M. Rabe, and D. Vanderbilt, Phys Rev Lett 109, 037602 (2012). G. J. Snyder and E. S. Toberer, Nature materials 7, 105 (2008). C. Uher, J. Yang, S. Hu, D. T. Morelli, and G. P. Meisner, Phys Rev B 59, 8615 (1999). Y. G. Yu, X. Zhang and A. Zunger, Phys. Rev. B 95, 085201, DOI: 10.1103/PhysRevB.95.085201 A. Dal Corso, Computational Material Science 95, 337 (2014). P. E. Bl¨ ochl, Phys. Rev. B 50, 17953, (1994). J. P. Perdew and K. Burke and M. Ernzerhof, Phys. Rev. Lett., 77, 3865,(1996) H. J. Monkhorst and J. D. Pack, Physical Review B,13, 5188,(1976) Zakutayev A, Zhang X, Nagaraja A, Yu L, Lany S, Mason TO, et al. Theoretical prediction and experimental realization of new stable inorganic materials using the inverse design approach. J Am Chem Soc 2013;135:10048–54. E. Haque, M.A. Hossain. First-principles study of elastic, electronic, thermodynamic, and thermoelectric transport properties of TaCoSn Results in Physics 10 2018; 458–465. K. Kaur, and R. Kumar. Giant thermoelectric performance of novel TaIrSn Half Heusler compound. Physics Letters A 381 2017; 3760–3765. In a private communication with Davide Ceresoli, February, 2019. G. Xing, J. Sun, Y. Li, X. Fan, W. Zheng and D. J. Singh, J. Appl. Phys. 123, 195105 (2018) L. Bassman, P. Rajak, R. K. Kalia, A. Nakano, F. Sha, J. Sun, D. J. Singh, M. Aykol, P. Huck, and K. Persson and P. Vashishta, npj Computational Materials, 4, 74, 2018.

7

(1a)

(1b)

(1c)

(1d)

(1e)

(1f)

FIG. 1. Optimized structure of (a) TaCoSn, (b) TaIrSn, optimized lattice parameters of (c) TaCoSn, (d) TaIrSn and Optimized volume of (e) TaCoSn, and (f) TaIrSn.

8

(a)

Pure TaCoSn and TaIrSn Bands 20

DOS (E)

15

10

5

0 −4

−3

−2

−1

(b)

0 1 Energy (eV)

2

3

4

(c)

10

DOS (E)

8

6

4

2

0 −4

−3

−2

−1

0 1 Energy (eV)

2

3

4

(d)

FIG. 2. In (a) Orbital contributions to the band structures of TaCoSn, (b) TaIrSn and Density of state of (c)TaCoSn, and (d) TaIrSn

9

(a)

(b) FIG. 3. Calculated Seebeck coefficient (top), Conductivity(middle) and Power Factor(bottom) with respect to electrons and holes in TaCoSn at different temperatures from 100-800K; in (a), left side are electrons and holes on the right.

10

(a)

(b) FIG. 4. Calculated Seebeck coefficient (top), Conductivity(middle) and Power Factor(bottom) with respect to holes and electrons in TaIrSn at different temperature from 100-800K; in (a), left side are electrons and holes on the right.

11

(a)

(b) FIG. 5. Calculated Inverse Effective mass in the minimum conduction and maximum valence bands in TaCoSn (a) and TaIrSn (b) at 300K

12

(a)

(b) FIG. 6. The average electronic fitness function (conductivity weighted direction) in T aCoSn (a) and T aIrSn (b)at 300K

Properties of TaX(X=Co,Ir)Sn  semiconductors

 

 

Highlights of the Manuscript TaCoSn and TaIrSn are two newly discovered stable half­Heusler compounds, we determined some properties of the compounds using first­principles method. The highlights are: → Presentation of the orbital contributions to the band structure via fat band determination. → Dependence of Seebeck coefficient on holes concentration. → Calculations of effective masses of the compounds. → Determination of electronic fitness function in both compounds.

Authors statement The manuscript is not under consideration for publication by any other journal apart from Solid Sate Sciences. We take responsibility for the contents of the manuscript and assert that the work was  performed by all of the authors. We state below the contribution/s of each author: P.O. Adebambo: Preparation of the input parameters, as well as optimization of the parameters. He  also involed in the preparation of the manuscript. Analysis of data. R.O. Agbaoye: Preparation of graphs, analysis of data and preparation of the manuscript. A.A. Musari: He was involved in the analysis of the data and preparation of the manuscript. B.I. Adetunji: Preparation of the manuscript, analyses of data and results.  G.A. Adebayo: Conceptualize the research, calculations, analyses of data/results. Overall  administration and supervision of the project. All authors are involved in the original writing of the manuscript.