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Two-Dimensional Layered Complex Nitrides as a New Class of Thermoelectric Materials Isao Ohkubo* and Takao Mori WPI Research Center, International Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan S Supporting Information *

ABSTRACT: Two-dimensional layered materials are promising candidates for highperformance thermoelectric materials. We focus on AMN2 layered complex metal nitrides as a new class of two-dimensional materials. Density-functional theory and Boltzmann transport theory calculations of the electronic band structures and electronic transport coefficients for AMN2 (A = Sr, Ba; M = Ti, Zr, Hf) with a KCoO2 crystal structure showed that the electronic band structures and electronic transport properties were highly anisotropic. Large in-plane electronic transport and small electronic transport perpendicular to the layers along the c-axis arose from reduced electronic dispersion along the c-axis compared with other in-plane directions. A cylindrical constant-energy surface with an axis in the kz-direction perpendicular to the layer was found, indicating a two-dimensional electronic structure. The results suggest that excellent thermoelectric properties arise from the two-dimensional electronic structures in AMN2 layered complex metal nitrides.

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INTRODUCTION

Layered compounds tend to have superior electronic properties to those of conventional metals and semiconductors. For example, cuprate1 and iron pnictide2 superconductors have high critical temperatures and cobaltates exhibit a high thermoelectric effect.3,4 There are several complex metal nitrides with layered crystal structures, and they exhibit diverse properties.5 Interest has grown in layered complex metal nitrides, such as MNX (M = Ti, Zr, Hf; X = Cl, Br, I)6 and ternary transition metal dinitrides AMN2 (A = alkaline earth metal; M = Ti, Zr, Hf),5 some of which are superconductors. In this paper, we propose two-dimensional layered complex nitrides, AMN2 (A = Sr, Ba; M = Ti, Zr, Hf)7−9 as a new class of thermoelectric materials with a high thermoelectric effect, using electronic structure and transport calculations based on density-functional theory (DFT) and Boltzmann theory. We compare the chemical and crystal structure and the thermoelectric properties of the nitrides with those of a threedimensional perovskite oxide, SrTiO3 (Figure 1a), for which the electronic band structure and good thermoelectric properties have been well characterized. AMN2 compounds crystallize in the tetragonal space group P4/nmm, of which KCoO2 is a typical example (Figure 1b). Figure 1b shows the two inequivalent N sites, which are denoted N1 (nearly in the M-site plane) and N2 (nearly in the A-site plane), that is, AN2-MN1. Because the N−M−N bonds are disconnected by the AN layers along the c-axis, and expanded in the a-b plane, two-dimensional electronic structures and anisotropic transport properties might be expected. © 2014 American Chemical Society

Figure 1. Crystal structures of (a) perovskite SrTiO3 and (b) SrTiN2. The xx and zz labels indicate the directions of the transport coefficients.

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COMPUTATIONAL METHODS

Our calculations are based on DFT using the full-potential linearized augmented plane wave approach as implemented in the WIEN2k package.10 The modified Becke−Johnson (mBJ)11 potential was used, because the energy gaps calculated using the mBJ potential are substantially better than the generalized gradient approximation/ Perdew−Burke−Ernzerhof and local density approximation with respect to experimental values.12,13 The transport properties were calculated by semiclassical Boltzmann theory in the constant scattering approximation and the rigid band approach14,15 implemented in the BoltzTraP code.16 The relaxation time, τ, was taken to be constant in Received: November 19, 2013 Revised: March 28, 2014 Published: March 30, 2014 2532

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this work. The electrical conductivity and power factor are calculated with respect to τ, whereas the Seebeck coefficient is independent of τ. This approach has been employed successfully by several groups in evaluating the electrical transport properties of thermoelectric compounds, in addition to the rigid band approach.14,15 In this calculation, experimental structural coordinates and lattice parameters were employed. The measured lattice constants are a = 3.905 Å for SrTiO3;17 a = 3.882 Å, c = 7.700 Å for SrTiN2;7 a = 4.161 Å, c = 8.392 Å for BaZrN2;8 a = 4.128 Å, c = 8.382 Å for BaHfN2.9 We used 100 (AMN2) and 1000 (SrTiO3) k-points in the Brillouin zone for calculating the electronic band structure. For the transport calculations, 20 000 (AMN2) and 100 000 (SrTiO3) k-points were used. Convergence tests for SrTiO3 and SrTiN2 with different numbers of k-points were carried out. Convergence was achieved with k-point sampling of 1000 for SrTiO3, and 100 for SrTiN2. For details, see the Supporting Information.

Predictably, the valence and conduction bands of SrTiN2 are anisotropic, with much less dispersion along the Γ-Z direction (corresponding to the c-axis), than along the other in-plane directions. The lowest conduction band in SrTiN2 has primarily Ti 3dxy character with a width of 2 eV. The highest valence band has N 2p character. Because these Ti 3d states are empty, Ti is in the formal 4+ state, and the rest of the electronic structure is indicative of a closed-shell ionic insulator with some mixing of the N 2p states and Ti 3d states, analogous to SrTiO3. The Ti 3d character extends over 8 eV from the conduction band minimum, partially because of the crystal-field splitting of the 3d orbitals. The band characters of BaZrN2 and BaHfN2 also show a similar trend to SrTiN2 (Figure S1, Supporting Information). Figure 3 shows several calculated properties for SrTiO3 and SrTiN2 at 300 K, plotted as a function of chemical potential (μ). To estimate thermoelectric efficiency, we have used a specific measure, namely, the electronic part of the dimensionless thermoelectric figure of merit, S2σT/κe (=ZeT),22 because the lattice thermal conductivity cannot be calculated by the usual DFT calculations. The doping levels over the entire range of the plots may be unattainable; however, it allows a complete analysis of what produces good electronic and thermoelectric properties.14,23 Within the rigid-band approach, the positive and negative chemical potentials correspond to n-type and ptype doping, respectively. Seebeck coefficients reach a maximum near the middle of the energy band gaps (Eg) because the Seebeck coefficient in semiconductors is inversely proportional to the carrier density. However, the carrier density in n-type semiconductors should be controlled around the bottom of the conduction band. Experimentally, SrTiO3 is an ntype semiconductor, in which the electron carrier density can be controlled by substituting a La3+ ion into the Sr2+ site and a Nb5+ ion into the Ti4+ site.24,25 The Fermi level in nondoped SrTiO3 is located about 0.1 eV below the bottom of the conduction band.26 Under the rigid band approximation, the chemical potential varies in addition to the carrier density. The chemical potentials should be near the bottom of the conduction band to achieve the maximum power factor. In general, the power factor (S2σ) depends on the carrier density. The maximum power factor of SrTiO3 is 0.04 electrons per Ti site, corresponding to 6.7 × 1020 cm−3, which is at 0.055 eV in the conduction band for SrTiO3 (arrow in Figure 3f). SrTiN2, BaZrN2, and BaHfN2 may become n-type semiconductors because most compounds containing Ti4+, Zr4+, or Hf4+ (d0) ions are n-type semiconductors.26 Similarly, the maximum power factor of SrTiN2 is 0.003 electrons per Ti site, corresponding to 5.2 × 1019 cm−3, which is at 0.025 eV below the bottom of the conduction band. The calculated carrier density of SrTiO3 agrees well with the experimental values24,25 and the values calculated using DFT or semiclassical Boltzmann transport theory.27,28 The experimental carrier density for the maximum power factor is 3−10 × 1020 cm−3 at room temperature,24,25 which agrees well with our calculations and previously reported calculations.27,28 Our calculated Seebeck coefficient for SrTiO3 at the same carrier density with the maximum power factor around the bottom of the conduction band is −120 μV K−1 at 300 K, which is similar to experimentally determined (−100 to −300 μV K−1) and previously reported calculation values (−100 to −172 μV K−1). A relaxation time, τ, of 3−10 fs, obtained by fitting to experimental results, has been reported. Our calculation results indicate that the electrical conductivity, σ, at 300 K for SrTiO3

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RESULTS AND DISCUSSION The electronic band structures of SrTiO3 and SrTiN2 are shown in Figure 2. SrTiN2, BaZrN2, and BaHfN2 are band

Figure 2. Electronic band structures of (a) SrTiO3 and (b) SrTiN2. The labels in the Brillouin zone, Γ, X, R, and M, for SrTiO3 correspond to 0,0,0; 0,1/2,0; 0,0,1/2; 1/2,1/2,0 in lattice constant units, respectively. Γ, X, M, Z, R, and A for SrTiN2 correspond to 0,0,0; 0,1/2,0; 1/2,1/2,0; 0,0,1/2; 0,1/2,1/2; 1/2,1/2,1/2, respectively.

insulators with calculated band gaps of 1.55, 1.59, and 1.68 eV, respectively (Figure S1, Supporting Information). The calculated band gap of SrTiO3 is 2.75 eV, which is the same as the values previously calculated using the mBJ exchange and correlation functional.12,13 The experimental band gap is 3.2 eV.18 Because band gaps are usually underestimated, the true values for AMN2 may be much larger. Farault et al. reported the synthesis of SrTiN2, which showed a metallic behavior.7 This metallic behavior could be due to a metallic TiN impurity phase in the SrTiN2 samples. However, single-phase SrTiN2 epitaxial films have been prepared by Luo et al.19 The epitaxial SrTiN2 showed a band insulator behavior. This is in good agreement with our calculations. Luo et al. also successfully fabricated epitaxial BaZrN2 and BaHfN2 films, which show a metallic behavior.20 However, our calculations and previous electronic structure calculations reported by Kaur et al.21 indicate that BaZrN2 and BaHfN2 are band insulators. Further research is necessary to explain this inconsistency. 2533

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Figure 3. Absolute values of carrier densities (|n|), density of states (DOS), and transport coefficients versus the chemical potential (μ), for SrTiO3 and SrTiN2 (xx-direction and zz-direction) at 300 K. (a) (h) Absolute values of carrier densities, (b) (i) DOS, (c) (j) (o) electronic conductivities (σ/τ), (d) (k) (p) electronic part of the thermal conductivities (κe /τ), (e) (l) (q) Seebeck coefficients (S), (f) (m) (r) power factors (S2σ/τ), and (g) (n) (s) electronic figures of merit (ZeT). Left and right panels show the valence band side (V.B.) and conduction band side (C.B.), respectively. The units for carrier density, DOS, σ/τ, κe/τ, S, power factor (S2σ/τ), are f.u.−1, states eV−1 f.u.−1, Ω−1 cm−1 s−1, W cm−1 K−1 s−1, μV K−1, and W cm−1 K−2 s−1, respectively.

is 0.6−2.1 × 103 S cm−1. Experimental electronic conductivities of 0.1−1.0 × 103 S cm−1 have been reported.24,25 The electronic conductivity and electronic part of the thermal conductivity in the c-axis direction (zz-direction) of SrTiN2 are considerably lower than those in the xx-direction over the entire chemical potential range (Figure 3j,k,o,p) because the electronic and electronic thermal conductivities occur along the in-plane Ti−N networks. Ti−N bonds are formed in the direction of the a- and b-axes, which correspond to the xx- and yy-directions, respectively. Therefore, twodimensional electronic structures and anisotropic transport properties are expected. In SrTiN2, along the zz-direction, large power factors around the conduction band minimum are not desirable because of the poor electronic conductivity. The electronic figures of merit for SrTiO3 and SrTiN2 are 0.4 and 0.6, respectively, when the power factors reach a maximum near the conduction band edges. Experimental figures of merit for SrTiO3 are less than 0.1 at room temperature.24,25 The large values of the electronic figures of merit in our calculations are caused by the lattice thermal conductivity, which is not considered. The values of experimental dimensionless thermoelectric figures of merit for AMN2 should be much smaller. The transport properties were evaluated on the basis of rigid band approximation, in which the electronic structure of the material is expected to remain unchanged in the doped regions. To express the results using a more tangible quantity, it is necessary to obtain the chemical potential from the carrier density. This can be obtained via solving for the inverse of the following distribution equation at the corresponding chemical potential and temperature.

n=

∫ De(E) e(μ−E)/1k T + 1 dE B

Here, n is the carrier density, E is the energy, De is the density of states obtained from the electronic structure calculation, kB is the Boltzmann’s constant, and T is the temperature. Figure 4 shows the calculated chemical potential. The chemical potential of SrTiO3 is located in the band gap for low carrier densities of less than 1020 cm−3. At carrier densities greater than 1020 cm−3,

Figure 4. Variation of chemical potential, μ, as a function of temperature for (a) SrTiO3 and (b) SrTiN2. The gray regions indicate the conduction band (C.B.). The solid lines indicate conduction band minimum (C.B.M.). 2534

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anisotropic transport and Seebeck coefficient are enhanced in layered compounds, such as layered copper oxide superconductors30 and layered cobaltate thermoelectric materials (NaxCoO2, Ca3Co4O9−δ).3,31−33 The calculated conductivity ratio (σxx/σzz) of SrTiN2 reaches about 7300 at 10 K. This is a large value compared with that of La2−xSrxCuO4 (100−200) and NaxCoO2 (200 at 4.2 K). The perpendicular conductivity across the layers along the c-axis is reduced as the distance between conductive layers increases.34 The distance between conductive TiN layers in SrTiN2 is 7.7 Å, which is longer than that in layered oxides, such as La2−xSrxCuO4 (distance between CuO2 planes of 6.6 Å) and NaxCoO2 (distance between CoO2 planes of 5.4 Å). The two-dimensionality is enhanced by isolated conductive TiN layers separated by thick SrN spacer layers. Anisotropy is also observed for the Seebeck coefficients. A sharp change in the slope of Seebeck coefficient for SrTiN2 in the zz-direction was observed around 900 K. The Seebeck coefficient (S) is given by the Mott formula, S = (π2KB2T/3e) [d ln(σ)/dμ],29 and is related to the logarithmic derivative of the conductivity. The zz-direction logarithmic derivative of the conductivity at 1200 K is much larger than that at 800 K (see the Supporting Information). However, the xx-direction logarithmic derivative of the conductivity is unchanged. Therefore, the zz-direction Seebeck coefficient increases dramatically above 900 K. The constant-energy surface, which the Ti 3dxy orbitals contribute to, is anisotropic and is considered as open in the kzdirection perpendicular to the layer, indicating a strong quasitwo-dimensional electronic structure (Figure 6). This cylin-

the chemical potential is located in the conduction band, which indicates that SrTiO3 behaves as a degenerate semiconductor. This agrees well with experimental results24,25 and previous calculations.27,28 The chemical potential of SrTiN2 is located in the band gap when the carrier density is lower than 1020 cm−3. Figure 5 shows the temperature dependences of several transport coefficients calculated for carrier densities of 0.04 per

Figure 5. Temperature dependence of transport properties of SrTiO3 (dashed blue line) and SrTiN2 (two solid green lines) calculated for carrier densities of 0.04 per Ti site and 0.003 per Ti site for SrTiO3 and SrTiN2, which correspond to 6.7 × 1020 and 5.2 × 1019 cm−3, respectively. (a) Electronic conductivities, (b) electronic part of the thermal conductivities, (c) Seebeck coefficients, (d) power factors, and (e) electronic figures of merit (ZeT). Labels xx and zz indicate the inplane and out-of-plane transport properties along the c-axis, respectively. Figure 6. Constant-energy surfaces for (a) SrTiO3 and (b) SrTiN2. The constant-energy surfaces were calculated at the chemical potential with the maximum power factor. The electron carrier densities of SrTiO3 and SrTiN2 are 0.04 and 0.003 per Ti site, corresponding to 6.7 × 1020 and 5.2 × 1019 cm−3, respectively.

Ti site (SrTiO3) and 0.003 per Ti site (SrTiN2), which corresponds to 6.7 × 1020 and 5.2 × 1019 cm−3, respectively. The variation of chemical potential as a function of temperature obtained in Figure 4 was used for this calculation of temperature dependences of transport coefficients. The temperature dependence of the conductivities includes the effect of the constant scattering approximation. The electronic conductivity and electronic part of thermal conductivity in the xx-direction of SrTiN2 are lower than those of SrTiO3. Anisotropic transport properties were obtained for the layered AMN2 compounds, except for the three-dimensional perovskite, SrTiO3. The electronic and thermal conductivities and the Seebeck coefficients were anisotropic, which indicates a much lower conductivity in the c-axis direction (zz-direction) than in the in-plane directions (xxdirection). These anisotropic transports are consistent with the electronic structure shown in Figure 2b. Electron and electronic thermal conductivities occur through Ti 3dxy orbitals in the inplane direction (xx-direction). The SrN layers prevent the electronic transport along the c-axis, which greatly reduces the dispersion of the Ti 3dxy band along the Γ-Z direction. This

drical constant-energy surface causes the anisotropic transport and Seebeck coefficient. In addition to the transport and Seebeck coefficient behaviors, the temperature dependences of the power factors and electronic figures of merit vary. The xx-direction Seebeck coefficients are higher for AMN2 than for SrTiO3 above 200 K (Figure 5c). At 1200 K, the xxdirection Seebeck coefficient of SrTiN2 reaches −300 μV K−1. The power factor of the xx-direction in SrTiN2 is slightly lower than that of SrTiO3. The electronic figure of merit in the xxdirection for SrTiN2 is larger than that for SrTiO3 above 200 K. The temperature-dependent behavior of each transport coefficient of SrTiO3 tends to be similar to that in previous calculations27,28 and experimental results.24,25 In normal electronic structure calculations, the lattice thermal conductivity cannot be calculated. For semiconductors, the lattice thermal conductivity usually cannot be ignored because it can be as 2535

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(8) Seeger, O.; Hofmann, M.; Striihle, J.; Lava, J. P.; Frit, B. Z. Anorg. Allg. Chem. 1994, 620, 2008. (9) Gregory, D. H.; Barker, M. G.; Edwards, P. P.; Slaski, M.; Siddons, D. J. J. Solid State Chem. 1998, 137, 62. (10) Blaha, P.; Schwarz, K.; Madsen, G.; Kvasicka, D.; Luitz, J. WIEN2k, An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties; TU Vienna: Vienna, Austria, 2001. (11) Tran, F.; Blaha, P. Phys. Rev. Lett. 2009, 102, 226401. (12) Koller, D.; Tran, F.; Blaha, P. Phys. Rev. B 2011, 83, 195134. (13) Guo, S. D.; Liu, B. G. J. Appl. Phys. 2011, 110, 073525. (14) Scheidemantel, T. J.; Ambrosch-Draxl, C.; Thonhauser, T.; Badding, J. V.; Sofo, J. O. Phys. Rev. B 2003, 68, 125210. (15) Madsen, G. K. H. J. Am. Chem. Soc. 2006, 128, 12140. (16) Madsen, G. K. H.; Singh, D. J. Comput. Phys. Commun. 2006, 175, 67. (17) Mitchell, R. H.; Chakhmouradian, A. R.; Woodward, P. M. Phys. Chem. Miner. 2000, 27, 583. (18) Benthem, K. V.; Elsasser, C.; French, R. H. J. Appl. Phys. 2001, 90, 6156. (19) Luo, H.; Wang, H.; Bi, Z.; Feldmann, D. M.; Wang, Y.; Burrell, A. K.; McCleskey, T. M.; Bauer, E.; Hawley, M. E.; Jia, Q. J. Am. Chem. Soc. 2008, 130, 15224. (20) Luo, H.; Wang, H.; Bi, Z.; Zou, G.; McCleskey, T. M.; Burrell, A. K.; Bauer, E.; Hawley, M. E.; Wang, Y.; Jia, Q. Angew. Chem. 2009, 121, 1518; Angew. Chem., Int. Ed. 2009, 48, 1490. (21) Kaur, A.; Ylvisaker, E. R.; Li, Y.; Galli, G.; Pickett, W. E. Phys. Rev. B 2010, 82, 155125. (22) Sevik, C.; Ç ağın, T. Phys. Rev. B 2010, 82, 045202. (23) Yang, J.; Li, H.; Wu, T.; Zhang, W.; Chen, L.; Yang, J. Adv. Funct. Mater. 2008, 18, 2880. (24) Okuda, T.; Nakanishi, K.; Miyasaka, S.; Tokura, Y. Phys. Rev. B 2001, 63, 113104. (25) Ohta, S.; Nomura, T.; Ohta, H.; Koumoto, K. J. Appl. Phys. 2005, 97, 034106. (26) Robertson, J. J. Vac. Sci. Technol., B: Microelectron. Nanometer Struct.–Process., Meas., Phenom. 2000, 18, 1785. (27) Shirai, K.; Yamanaka, K. J. Appl. Phys. 2013, 113, 053705. (28) Kinaci, A.; Sevik, C.; Ç ağın, T. Phys. Rev. B 2010, 82, 155114. (29) Ziman, J. M. Principle of the Theory of Solids; Cambridge University Press: Cambridge, U.K., 1979. (30) Nakamura, Y.; Uchida, S. Phys. Rev. B 1993, 47, 8369. (31) Tang, G. D.; Guo, H. H.; Yang, T.; Zhang, D. W.; Xu, X. N.; Wang, L. Y.; Wang, Z. H.; Wen, H. H.; Zhang, Z. D.; Du, Y. W. Appl. Phys. Lett. 2011, 98, 202109. (32) Zhao, B. C.; Sun, Y. P.; Lu, W. J.; Zhu, X. B.; Song, W. H. Phys. Rev. B 2006, 74, 144417. (33) Sugiura, K.; Ohta, H.; Nakagawa, S.; Huang, R.; Ikuhara, Y.; Nomura, K.; Hosono, H.; Koumoto, K. Appl. Phys. Lett. 2009, 94, 152105. (34) Honma, T.; Hor, P. H. Solid State Commun. 2010, 150, 2314. (35) Lee, K. H.; Kim, S. W.; Ohta, H.; Koumoto, K. J. Appl. Phys. 2006, 100, 063717.

much as an order of magnitude larger than the electronic thermal conductivity. The successful reduction of the lattice thermal conductivity induced by lower dimensional structures was reported for strontium titanium oxide-based Ruddlesden− Popper phases, which are layered perovskite structures.35 The lattice thermal conductivity in two-dimensional Sr 2TiO4 drastically decreases in comparison with that of threedimensional SrTiO3. Therefore, the lattice thermal conductivity and the electronic part of the thermal conductivity of AMN2 may be sufficiently lower than those of SrTiO3, which suggests that much higher thermoelectric figures of merit can be expected in AMN2.

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CONCLUSION In conclusion, the electronic band structures and thermoelectric transport coefficients were calculated for layered complex nitrides, AMN 2 . The AMN 2 compounds show highly anisotropic transport and thermoelectric coefficients arising from strong quasi-two-dimensional electronic structures. Comparing AMN2 compounds with the three-dimensional perovskite SrTiO3, a well-known compound with good thermoelectric properties, predicted larger in-plane Seebeck coefficients and electronic figures of merit in AMN 2 compounds. The synthesis of complex metal nitrides is often complicated. However, epitaxial film growth techniques have overcome these problems, enabling the synthesis of singlephase samples.19,20 The combination of epitaxial synthesis and electronic structure calculations will be a powerful tool for exploring novel physical properties in layered complex nitrides.

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ASSOCIATED CONTENT

* Supporting Information S

Description of calculations; electronic band structures and transport properties of BaZrN2 and BaHfN2; sharp change in the zz-direction Seebeck coefficient slope for AMN2. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*I. Ohkubo. E-mail: [email protected]. Author Contributions

All authors have approved the final version of the paper. Funding

This work was supported by the Shorai Foundation for Science and Technology. Notes

The authors declare no competing financial interest.

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REFERENCES

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