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SrTi0.8Nb0.2O3 superlattices
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Thin Solid Films 516 (2008) 5916 – 5920 www.elsevier.com/locate/tsf
Critical thickness for giant thermoelectric Seebeck coefficient of 2DEG confined in SrTiO3/SrTi0.8Nb0.2O3 superlattices Hiromichi Ohta a,b,⁎, Yoriko Mune a , Kunihito Koumoto a,b , Teruyasu Mizoguchi c , Yuichi Ikuhara c a
c
Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa, Nagoya 464-8603, Japan b CREST, JST, 4-1-8 Honcho, Kawaguchi 332-0012, Japan Institute of Engineering Innovation, The University of Tokyo, 2-11-16 Yayoi, Bunkyo, Tokyo 113-8656, Japan Available online 13 October 2007
Abstract Seebeck coefficient (|S|) of two-dimensional electron gas (2DEG) confined within (SrTiO3)LB/(SrTi0.8Nb0.2O3)LW superlattices were measured at room temperature to clarify the critical thicknesses of barrier SrTiO3 (LB) and well SrTi0.8Nb0.2O3 (LW) for giant |S| [H. Ohta et al., Nat. Mater. − 1/2 6, 129 (2007)]. The |S| values of the superlattices increased proportionally to LW due to increasing of the density of states near the conduction −1 band edge (quantum size effect), and reached 300 μV K at LW = 1 unit cell SrTi0.8Nb0.2O3 (0.39 nm), which is ∼ 5 times larger than that of the SrTi0.8Nb0.2O3 bulk (60 μV K− 1). The critical thickness of LB and LW for giant |S| was clarified to be 16 unit cells (6.25 nm). The best thermoelectric performance can be obtained at (LB, LW) = (16, 1). © 2007 Elsevier B.V. All rights reserved. Keywords: Thermoelectric energy conversion; Seebeck coefficient; Two-dimensional electron gas (2DEG); SrTiO3; Superlattices
1. Thermoelectric materials Thermoelectric devices can convert waste heat originating from various sources, e.g., electric power plants, factories, automobiles, computers, and even human bodies, to electric power by utilizing the Seebeck effect, in addition to being able to refrigerate various devices by means of the Peltier effect [1,2]. The performance of thermoelectric materials is evaluated in terms of a dimensionless figure of merit, ZT = S2σTκ− 1, where Z, T, S, σ and κ are, respectively, a figure of merit, the absolute temperature, the thermopower or Seebeck coefficient, the electrical conductivity, and the thermal conductivity. Typical Z−T curves for conventional thermoelectric materials are shown in Fig. 1. For the practical application, high ZT material, at least exceeding 1 is demanded. Although the ZT values of these heavy-metal-based materials such as Bi2Te3 and PbTe exceed 1 (Fig. 1, blue curves), enough ⁎ Corresponding author. Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa, Nagoya 464-8603, Japan. Tel.: +81 52 789 3202; fax: +81 52 789 3201. E-mail address: [email protected] (H. Ohta). 0040-6090/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2007.10.034
for practical applications, these materials are not attractive, particularly operating at high temperatures (T ∼ 1000 K), because decomposition, vaporization or melting of the constituents can easily occur at high temperatures. Further, the use of these heavy metals should be limited to specific environments such as space because they are mostly toxic, low in abundance as natural resources (see Table 1), and thus not environmentally benign. 2. Nb-doped SrTiO3: a candidate thermoelectric material Based on this background, several metal oxides such as Na0.75CoO2 (p-type, ZT300 K ∼ 0.1) [3], Ca3Co4O9 (p-type, ZT300 K ∼ 0.07) [4] and SrTiO3 (n-type, ZT300 K ∼ 0.08) [5] have attracted growing attention for the thermoelectric power generation at high temperatures on the basis of their potential advantages over heavy metallic alloys in chemical and thermal robustness. We chose strontium titanate, SrTiO3, as a candidate of thermoelectric material because Clarke number of the constituents is high, thus rich in natural resources. Further, the electrical conductivity of SrTiO3 can be easily controlled from insulator to metal by the substitutional doping of La3+ or Nb5+.
H. Ohta et al. / Thin Solid Films 516 (2008) 5916–5920
Fig. 1. Thermoelectric figure of merit, Z vs. temperature for conventional heavymetal-based materials and SrTi0.8Nb0.2O3 (3D). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
In addition, heavily-doped SrTiO3 exhibits rather large |S| due to that the large density of states (DOS) effective mass (md⁎ = 6 ∼ 10 m0 [6,7]) leads to large |S|. In 2005, we clarified that the 20% (≈4 × 1021 cm− 3) Nb-doped SrTiO3 epitaxial film (SrTi0.8Nb0.2O3 hereafter) exhibits ZT ∼ 0.37 at 1000 K [8,9] (Fig. 1, red curve), which is the largest value among n-type metal oxides ever reported. However, the realization of ZT values exceeding that of heavy-metal-based materials is a great challenge, primarily because of the much larger κ value (κ300 K = 12 W m− 1 K− 1) compared with those of the heavy metallic alloys (0.5–2 W m− 1 K− 1), which are mostly due to higher phonon frequencies of O2− ions [10]. In order to improve the thermoelectric performance of SrTi0.8Nb0.2O3, therefore, the S2σ value must be enhanced according to the commonly observed trade-off relationship between two material parameters in terms of carrier electron concentration (ne): σ increases almost linearly with increasing ne until ionized impurity scattering or electron–electron scattering becomes dominant, while |S| decreases with ne. Thus, further improvement of the ZT value of SrTi0.8Nb0.2O3 is almost impossible at conventional three dimensional (3D) bulk state.
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experimentally with the use of a PbTe (1.5 nm)/Pb0.927Eu0.073Te (45 nm) multiple quantum well (MQW) [13], which exhibited an |S| value ∼ 2.5 times larger than that of the corresponding 3Dbulk. We have examined SrTiO3-based two-dimensional electron gas (2DEG) with the expectation of attaining a much larger enhancement of ZT. We expected that the conduction carrier electrons are localized more strongly in SrTiO3 than in the heavy metal materials, because the energy states near the Fermi level are composed predominantly of d-orbitals of the Ti4+ ions. Very recently, we briefly reported that a high density 2DEG, which confined within a unit cell layer thickness (0.3905 nm) in SrTiO3, exhibit giant |S| that is about 5 times larger than that of the bulk SrTiO3, whereas the 2DEG system retains the rather high σ2D value [14]. In the optimized case, Z2DT value of ∼ 2.4 can be obtained at room temperature. In order to design thermoelectric devices based on the 2DEGSrTiO3, the critical thickness of barrier & well layers for giant |S| must be clarified because insulating barrier layer negatively affect thermoelectric performance. We fabricated a number of (SrTiO3)LB/(SrTi0.8Nb0.2O3)LW superlattices, where LB and LW are number of unit cells for SrTiO3 barrier layer and SrTi0.8Nb0.2O3 well layer, respectively. The |S| values of the superlattices − 1/2 increased proportionally to LW due to quantum size effect, −1 and reached 300 μV K at (LB, LW) = (16, 1) which is ∼5 times larger than that of the SrTi0.8Nb0.2O3 bulk (60 μV K− 1). The critical thickness for quantum confinement was clarified to be 16 unit cells of SrTiO3 (6.25 nm). 4. Superlattice film growth and characterization Superlattices of [(SrTiO3)LB/(SrTi0.8Nb0.2O3)LW]20 (LB = 0–60, LW = 1–20) were fabricated on the (001)-face of a stepped LaAlO3 substrate [15] by pulsed laser deposition (PLD, Pascal) at 950 °C using a KrF excimer laser (Lambda Physik COMPex 102, 20 ns, ∼1 J cm− 2 pulse− 1, 10 Hz) as an ablation light source. A SrTiO3 single crystal plate and a SrTi0.8Nb0.2O3 ceramic were used as targets. During film growth of the superlattices, the intensity oscillation of reflection high-energy electron diffraction
3. Seebeck coefficient of superlattices Two-dimensionally (2D) confined electrons in extremely narrow quantum wells (thickness ≪ ∼ 10 nm, which depends on the DeBroglie wavelength), which are composed of well (electron pocket) and barrier, exhibit exotic electron transport properties as compared to the bulk materials due to the fact that the DOS near the bottom of the conduction band and/or top of the valence band increases with decreasing the well thickness [11]. In 1993, Hicks and Dresselhaus theoretically predicted that thermoelectric figure of merit, Z2DT of thermoelectric semiconductors (well region) can dramatically be enhanced by using superlattices because only S value increases with DOS [12]. This model is based on the assumption that the enhancement of S2 arises mainly from an increase in the DOS near the conduction band edge when the carrier electrons are confined in such a narrow space. Their prediction has been partly confirmed
Table 1 Clarke number of constituent for typical thermoelectric materials Rank
Element
Clarke number
1 2 10 21 28 29 33 35 38 42 60 66 68 77
O Si Ti Sr Co Sn Nb Pb Ga Ge Sb Bi Ag Te
49.5 25.8 0.46 0.02 0.004 0.004 0.002 0.0015 0.001 0.00065 0.00005 0.00002 0.00001 0.0000002
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Fig. 2. Topographic AFM images of (a) (001)-face of LaAlO3 substrate, which was obtained after ultrasonically cleaning of as-polished substrate in conc. HCl solution for 10 min, and (b) the [(SrTiO3)17/(SrTi0.8Nb0.2O3)1]24 superlattice grown on the stepped LaAlO3 substrate at 950 °C. Atomically flat terraces and steps (∼0.4 nm) are clearly seen.
Fig. 3. (a) Out-of-plane XRD Bragg diffraction pattern of [(SrTiO3)17/ (SrTi0.8Nb0.2O3)1]24 superlattice film grown on (001)-face of LaAlO3 substrate. Satellite peaks (±1 and ±2) of superlattice are clearly seen. (b) Cross sectional Z-contrast HAADF-STEM image of [(SrTiO 3 ) 24 /(SrTi 0.8 Nb 0.2 O 3 ) 1 ] 24 superlattice.
Fig. 4. Seebeck coefficient (|S|) of the [(SrTiO3)LB/(SrTi0.8Nb0.2O3)LW]20 superlattices. (a) |S|−LW plots. The Log |S| − Log LW plots is also shown in the inset (b) |S| − LB plots.
H. Ohta et al. / Thin Solid Films 516 (2008) 5916–5920
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gives rise to a brighter image than the lighter Ti4+ ion (Z = 22) in the Z-contrast HAADF-STEM image, the clear stripe-shaped contrast indicates that the superlattice structure was successfully fabricated. From these results, we conclude that the film quality is sufficient to evaluate thermoelectric properties. 5. Thermoelectric response of the superlattices
Fig. 5. |S| − Log ne plots for the 2DEGs and the SrTiO3-bulk samples. Data from Ref. [14] are plotted together with present data. The slope of |S| for 2DEGs is − 1000 μV K− 1, which is five times larger than those for the SrTiO3-bulks (− 200 μV K− 1).
(RHEED) spots was monitored to count the number of SrTiO3 or SrTi0.8Nb0.2O3 layers. The surface morphologies of the films were analyzed by an atomic force microscope (AFM, Nanoscope E, Digital Instruments). Atomically flat terraces and steps, which correspond to a unit cell height of SrTiO3, are clearly seen in the topographic AFM image (Fig. 2), indicating that 2D step-flow growth occurred. Film thickness, crystallographic orientation, and lattice parameters of the resultant films were evaluated by high-resolution X-ray diffraction (HR-XRD, CuKα1, ATX-G, Rigaku Co.). Fig. 3(a) shows out-of-plane Bragg diffraction pattern of [(SrTiO3)17/(SrTi0.8Nb0.2O3)1]24 superlattice film grown on (001)-face of LaAlO3 substrate. Intense Bragg diffraction peak of 002 SrTiO3 (0) is seen together with 002 LaAlO3. In addition, satellite peaks (± 1 and ± 2) are clearly observed around 002 SrTiO3 (0). The superlattice period was calculated to be 7.1 nm (≈ 18 unit cells of SrTiO3), indicating that [(SrTiO3)17/(SrTi0.8Nb0.2O3)1]24 superlattice film was successfully fabricated. Further, stripe-shaped contrast is clearly seen in the Cscorrected high-angle angular dark-field scanning transmission electron microscope (HAADF-STEM, JEOL-2100F) image (Fig. 3(b)). Since the heavier Nb5+ ion (atomic number, Z = 41)
Carrier concentration (ne) and Hall mobility (μHall) of the superlattice films were measured by d.c. four probe method with van der Pauw configuration. All the electrical measurements were performed at room temperature in air. Since the ne of SrTiO3 barrier layer is very low (ne ≪ 1015 cm− 3), the ne of SrTi0.8Nb0.2O3 layer of [(SrTiO3)LB/(SrTi0.8Nb0.2O3)LW]20 is estimated as ne obs. · (LB +LW) /LW. Calculated ne of SrTi0.8Nb0.2O3 layer for the superlattices were ∼4 × 1021 cm− 3 agreeing well with that of the SrTi0.8Nb0.2O3 film [8]. The μHall value of the superlattices was ∼5 cm2 V− 1 s− 1 in all samples. Seebeck coefficient (S) was measured by conventional steady state method in the in-plane direction. Generally, |S| value of multilayered film is given by Σ |S|i σxxi /Σσxxi, where |S|i and σxxi are Seebeck coefficient and sheet conductivity of the i layer, respectively. In the present case, we directly measured |S| of the SrTi0.8Nb0.2O3 layer since the σxxi of the SrTi0.8Nb0.2O3 layer is at least six orders of magnitude larger than that of the SrTiO3 barrier layer. Fig. 4(a) shows |S|−LW plots for [(SrTiO3)15/ (SrTi0.8Nb0.2O3)LW]20 superlattices. A dramatic increase of |S| is seen with decreasing LW value. When LW is 1 unit cell (u.c.), the |S| value reaches 300 μV K− 1, which is ∼5 times larger than that of the SrTi0.8Nb0.2O3 bulk (60 μV K− 1). Slope for the Log |S| − Log LW plots is −1/2 as shown in the inset, indicating that the DOS −1 near the conduction band edge increases proportionally to LW . This is so-called “quantum size effect” [11]. Threshold LW for the quantum confinement is ∼16 u.c. (6.25 nm). Fig. 4(b) shows |S|−LB plots for [(SrTiO3)LB/(SrTi0.8Nb0.2O3)1]20 superlattices. The |S| value gradually increases with LB value and is saturated at 320 μV K− 1 when the LB value reached 16 u.c. (6.25 nm). From these results, we judged that the critical thickness for the 2D-electron confinement is 16 unit cell layers of SrTiO3. When the LB is thinner than 16, conduction electrons at the SrTi0.8Nb0.2O3 can move through the SrTiO3 barrier layer and,
Fig. 6. Direct heating test of [(SrTiO3)15/(SrTi0.8Nb0.2O3)1]100 superlattice. One end of the superlattice sample was heated by a lighter to introduce temperature difference of ∼90 K. The thermo-electromotive force of 32.6 mV was obtained.
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therefore, bandwidth broadening or formation of mini-band may occur. On the other hand, two-dimensionality of the conduction electrons decreases with increasing the LW. When the LW is thicker than 16, the conduction electrons behave three-dimensionally. Thus, optimum composition to obtain giant |S| of (SrTiO3)LB/ (SrTi0.8Nb0.2O3)LW is (LB, LW) =(16, 1). The |S| − Log ne plots are shown in Fig. 5, which verify that the experimental data points for the 2DEGs and the SrTiO3-bulk samples form two straight lines with different slopes. The slope for the SrTiO3-bulk samples is −200 μV K− 1, corresponds with the value of −kB / e ln 10 (−198 μV K− 1), indicating that the DOS near the Fermi surface is parabolic. On the other hand, the slope of the |S| − Log ne line for the 2DEGs (LW = 1) is −1000 μV K− 1, suggesting a stepped cumulative DOS is formed as a result of the quantum size effect. Finally, we performed direct heating test of [(SrTiO3)15/ (SrTi0.8Nb0.2O3)1]100 superlattice (Fig. 6) at room temperature in air. A lighter was used to introduce a temperature difference between both ends of the sample. Since SrTiO3 is basically stable at high temperatures as described above, large voltage (thermo-electromotive force) can be obtained by using high temperature (∼1000 K) waste heat from electric power plants, factories and automobiles. 6. Summary Seebeck coefficient (|S|) of (SrTiO3)LB/(SrTi0.8Nb0.2O3)LW superlattices, where LB and LW are number of unit cells for SrTiO3 barrier layer and SrTi0.8Nb0.2O3 well layer, respectively, were measured at room temperature. The |S| values of the − 1/2 superlattices increased proportionally to LW due to quantum −1 size effect, and reached 320 μV K at (LB, LW) = (16, 1) which is ∼5 times larger than that of the SrTi0.8Nb0.2O3 bulk (60 μV K− 1). The critical thickness for quantum confinement was 16 unit cells of SrTiO3 (6.25 nm). The present results provide useful information to design future 2DEG-SrTiO3-based thermoelectric materials.
Acknowledgements This work was financially supported by the Industrial Technology Research Grant Program in 2005 from the New Energy and Industrial Technology Development Organization (NEDO), and Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology (no. 18686054). References [1] T.M. Tritt, M.A. Subramanian, H. Bottner, T. Caillat, G. Chen, R. Funahashi, X. Ji, M. Kanatzidis, K. Koumoto, G.S. Nolas, J. Poon, A.M. Rao, I. Terasaki, R. Venkatasubramanian, J. Yang, MRS Bull. (special issue on harvesting energy through thermoelectrics: power generation and cooling) 31 (2006) 188 articles therein. [2] F.J. DiSalvo, Science 285 (1999) 703. [3] I. Terasaki, Y. Sasago, K. Uchinokura, Phys. Rev. B 56 (1997) R12685. [4] M. Shikano, R. Funahashi, Appl. Phys. Lett. 82 (2003) 1851. [5] T. Okuda, K. Nakanishi, S. Miyasaka, Y. Tokura, Phys. Rev. B 63 (2001) 113104. [6] H.P.R. Frederikse, W.R. Thurber, W.R. Hosler, Phys. Rev. 134 (1964) A442. [7] S. Ohta, T. Nomura, H. Ohta, K. Koumoto, J. Appl. Phys. 97 (2005) 034106. [8] S. Ohta, T. Nomura, H. Ohta, M. Hirano, H. Hosono, K. Koumoto, Appl. Phys. Lett. 87 (2005) 092108. [9] S. Ohta, H. Ohta, K. Koumoto, J. Ceram. Soc. Japan 114 (2006) 102. [10] Y.S. Touloukian, R.W. Powell, C.Y. Ho, P.G. Klemens, Thermophysical Properties of Matter Volume 2, Thermal Conductivity: Nonmetallic Solids, IFI/Plenum, New York, 1970. [11] M.A. Meyers, O.T. Inal (Eds.), Frontiers in Materials Technologies, Elsevier, Amsterdam, 1985. [12] L.D. Hicks, M.S. Dresselhaus, Phys. Rev. B 47 (1993) 12727. [13] L.D. Hicks, T.C. Harman, X. Sun, M.S. Dresselhaus, Phys. Rev. B 53 (1996) R10493. [14] H. Ohta, S-W. Kim, Y. Mune, T. Mizoguchi, K. Nomura, S. Ohta, T. Nomura, Y. Nakanishi, Y. Ikuhara, M. Hirano, H. Hosono, K. Koumoto, Nat. Mater. 6 (2007) 129. [15] T. Ohnishi, K. Takahashi, M. Nakamura, M. Kawasaki, M. Yoshimoto, H. Koinuma, Appl. Phys. Lett. 74 (1999) 2531.
Thin Solid Films 516 (2008) 5916 – 5920 www.elsevier.com/locate/tsf
Critical thickness for giant thermoelectric Seebeck coefficient of 2DEG confined in SrTiO3/SrTi0.8Nb0.2O3 superlattices Hiromichi Ohta a,b,⁎, Yoriko Mune a , Kunihito Koumoto a,b , Teruyasu Mizoguchi c , Yuichi Ikuhara c a
c
Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa, Nagoya 464-8603, Japan b CREST, JST, 4-1-8 Honcho, Kawaguchi 332-0012, Japan Institute of Engineering Innovation, The University of Tokyo, 2-11-16 Yayoi, Bunkyo, Tokyo 113-8656, Japan Available online 13 October 2007
Abstract Seebeck coefficient (|S|) of two-dimensional electron gas (2DEG) confined within (SrTiO3)LB/(SrTi0.8Nb0.2O3)LW superlattices were measured at room temperature to clarify the critical thicknesses of barrier SrTiO3 (LB) and well SrTi0.8Nb0.2O3 (LW) for giant |S| [H. Ohta et al., Nat. Mater. − 1/2 6, 129 (2007)]. The |S| values of the superlattices increased proportionally to LW due to increasing of the density of states near the conduction −1 band edge (quantum size effect), and reached 300 μV K at LW = 1 unit cell SrTi0.8Nb0.2O3 (0.39 nm), which is ∼ 5 times larger than that of the SrTi0.8Nb0.2O3 bulk (60 μV K− 1). The critical thickness of LB and LW for giant |S| was clarified to be 16 unit cells (6.25 nm). The best thermoelectric performance can be obtained at (LB, LW) = (16, 1). © 2007 Elsevier B.V. All rights reserved. Keywords: Thermoelectric energy conversion; Seebeck coefficient; Two-dimensional electron gas (2DEG); SrTiO3; Superlattices
1. Thermoelectric materials Thermoelectric devices can convert waste heat originating from various sources, e.g., electric power plants, factories, automobiles, computers, and even human bodies, to electric power by utilizing the Seebeck effect, in addition to being able to refrigerate various devices by means of the Peltier effect [1,2]. The performance of thermoelectric materials is evaluated in terms of a dimensionless figure of merit, ZT = S2σTκ− 1, where Z, T, S, σ and κ are, respectively, a figure of merit, the absolute temperature, the thermopower or Seebeck coefficient, the electrical conductivity, and the thermal conductivity. Typical Z−T curves for conventional thermoelectric materials are shown in Fig. 1. For the practical application, high ZT material, at least exceeding 1 is demanded. Although the ZT values of these heavy-metal-based materials such as Bi2Te3 and PbTe exceed 1 (Fig. 1, blue curves), enough ⁎ Corresponding author. Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa, Nagoya 464-8603, Japan. Tel.: +81 52 789 3202; fax: +81 52 789 3201. E-mail address: [email protected] (H. Ohta). 0040-6090/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2007.10.034
for practical applications, these materials are not attractive, particularly operating at high temperatures (T ∼ 1000 K), because decomposition, vaporization or melting of the constituents can easily occur at high temperatures. Further, the use of these heavy metals should be limited to specific environments such as space because they are mostly toxic, low in abundance as natural resources (see Table 1), and thus not environmentally benign. 2. Nb-doped SrTiO3: a candidate thermoelectric material Based on this background, several metal oxides such as Na0.75CoO2 (p-type, ZT300 K ∼ 0.1) [3], Ca3Co4O9 (p-type, ZT300 K ∼ 0.07) [4] and SrTiO3 (n-type, ZT300 K ∼ 0.08) [5] have attracted growing attention for the thermoelectric power generation at high temperatures on the basis of their potential advantages over heavy metallic alloys in chemical and thermal robustness. We chose strontium titanate, SrTiO3, as a candidate of thermoelectric material because Clarke number of the constituents is high, thus rich in natural resources. Further, the electrical conductivity of SrTiO3 can be easily controlled from insulator to metal by the substitutional doping of La3+ or Nb5+.
H. Ohta et al. / Thin Solid Films 516 (2008) 5916–5920
Fig. 1. Thermoelectric figure of merit, Z vs. temperature for conventional heavymetal-based materials and SrTi0.8Nb0.2O3 (3D). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
In addition, heavily-doped SrTiO3 exhibits rather large |S| due to that the large density of states (DOS) effective mass (md⁎ = 6 ∼ 10 m0 [6,7]) leads to large |S|. In 2005, we clarified that the 20% (≈4 × 1021 cm− 3) Nb-doped SrTiO3 epitaxial film (SrTi0.8Nb0.2O3 hereafter) exhibits ZT ∼ 0.37 at 1000 K [8,9] (Fig. 1, red curve), which is the largest value among n-type metal oxides ever reported. However, the realization of ZT values exceeding that of heavy-metal-based materials is a great challenge, primarily because of the much larger κ value (κ300 K = 12 W m− 1 K− 1) compared with those of the heavy metallic alloys (0.5–2 W m− 1 K− 1), which are mostly due to higher phonon frequencies of O2− ions [10]. In order to improve the thermoelectric performance of SrTi0.8Nb0.2O3, therefore, the S2σ value must be enhanced according to the commonly observed trade-off relationship between two material parameters in terms of carrier electron concentration (ne): σ increases almost linearly with increasing ne until ionized impurity scattering or electron–electron scattering becomes dominant, while |S| decreases with ne. Thus, further improvement of the ZT value of SrTi0.8Nb0.2O3 is almost impossible at conventional three dimensional (3D) bulk state.
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experimentally with the use of a PbTe (1.5 nm)/Pb0.927Eu0.073Te (45 nm) multiple quantum well (MQW) [13], which exhibited an |S| value ∼ 2.5 times larger than that of the corresponding 3Dbulk. We have examined SrTiO3-based two-dimensional electron gas (2DEG) with the expectation of attaining a much larger enhancement of ZT. We expected that the conduction carrier electrons are localized more strongly in SrTiO3 than in the heavy metal materials, because the energy states near the Fermi level are composed predominantly of d-orbitals of the Ti4+ ions. Very recently, we briefly reported that a high density 2DEG, which confined within a unit cell layer thickness (0.3905 nm) in SrTiO3, exhibit giant |S| that is about 5 times larger than that of the bulk SrTiO3, whereas the 2DEG system retains the rather high σ2D value [14]. In the optimized case, Z2DT value of ∼ 2.4 can be obtained at room temperature. In order to design thermoelectric devices based on the 2DEGSrTiO3, the critical thickness of barrier & well layers for giant |S| must be clarified because insulating barrier layer negatively affect thermoelectric performance. We fabricated a number of (SrTiO3)LB/(SrTi0.8Nb0.2O3)LW superlattices, where LB and LW are number of unit cells for SrTiO3 barrier layer and SrTi0.8Nb0.2O3 well layer, respectively. The |S| values of the superlattices − 1/2 increased proportionally to LW due to quantum size effect, −1 and reached 300 μV K at (LB, LW) = (16, 1) which is ∼5 times larger than that of the SrTi0.8Nb0.2O3 bulk (60 μV K− 1). The critical thickness for quantum confinement was clarified to be 16 unit cells of SrTiO3 (6.25 nm). 4. Superlattice film growth and characterization Superlattices of [(SrTiO3)LB/(SrTi0.8Nb0.2O3)LW]20 (LB = 0–60, LW = 1–20) were fabricated on the (001)-face of a stepped LaAlO3 substrate [15] by pulsed laser deposition (PLD, Pascal) at 950 °C using a KrF excimer laser (Lambda Physik COMPex 102, 20 ns, ∼1 J cm− 2 pulse− 1, 10 Hz) as an ablation light source. A SrTiO3 single crystal plate and a SrTi0.8Nb0.2O3 ceramic were used as targets. During film growth of the superlattices, the intensity oscillation of reflection high-energy electron diffraction
3. Seebeck coefficient of superlattices Two-dimensionally (2D) confined electrons in extremely narrow quantum wells (thickness ≪ ∼ 10 nm, which depends on the DeBroglie wavelength), which are composed of well (electron pocket) and barrier, exhibit exotic electron transport properties as compared to the bulk materials due to the fact that the DOS near the bottom of the conduction band and/or top of the valence band increases with decreasing the well thickness [11]. In 1993, Hicks and Dresselhaus theoretically predicted that thermoelectric figure of merit, Z2DT of thermoelectric semiconductors (well region) can dramatically be enhanced by using superlattices because only S value increases with DOS [12]. This model is based on the assumption that the enhancement of S2 arises mainly from an increase in the DOS near the conduction band edge when the carrier electrons are confined in such a narrow space. Their prediction has been partly confirmed
Table 1 Clarke number of constituent for typical thermoelectric materials Rank
Element
Clarke number
1 2 10 21 28 29 33 35 38 42 60 66 68 77
O Si Ti Sr Co Sn Nb Pb Ga Ge Sb Bi Ag Te
49.5 25.8 0.46 0.02 0.004 0.004 0.002 0.0015 0.001 0.00065 0.00005 0.00002 0.00001 0.0000002
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Fig. 2. Topographic AFM images of (a) (001)-face of LaAlO3 substrate, which was obtained after ultrasonically cleaning of as-polished substrate in conc. HCl solution for 10 min, and (b) the [(SrTiO3)17/(SrTi0.8Nb0.2O3)1]24 superlattice grown on the stepped LaAlO3 substrate at 950 °C. Atomically flat terraces and steps (∼0.4 nm) are clearly seen.
Fig. 3. (a) Out-of-plane XRD Bragg diffraction pattern of [(SrTiO3)17/ (SrTi0.8Nb0.2O3)1]24 superlattice film grown on (001)-face of LaAlO3 substrate. Satellite peaks (±1 and ±2) of superlattice are clearly seen. (b) Cross sectional Z-contrast HAADF-STEM image of [(SrTiO 3 ) 24 /(SrTi 0.8 Nb 0.2 O 3 ) 1 ] 24 superlattice.
Fig. 4. Seebeck coefficient (|S|) of the [(SrTiO3)LB/(SrTi0.8Nb0.2O3)LW]20 superlattices. (a) |S|−LW plots. The Log |S| − Log LW plots is also shown in the inset (b) |S| − LB plots.
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gives rise to a brighter image than the lighter Ti4+ ion (Z = 22) in the Z-contrast HAADF-STEM image, the clear stripe-shaped contrast indicates that the superlattice structure was successfully fabricated. From these results, we conclude that the film quality is sufficient to evaluate thermoelectric properties. 5. Thermoelectric response of the superlattices
Fig. 5. |S| − Log ne plots for the 2DEGs and the SrTiO3-bulk samples. Data from Ref. [14] are plotted together with present data. The slope of |S| for 2DEGs is − 1000 μV K− 1, which is five times larger than those for the SrTiO3-bulks (− 200 μV K− 1).
(RHEED) spots was monitored to count the number of SrTiO3 or SrTi0.8Nb0.2O3 layers. The surface morphologies of the films were analyzed by an atomic force microscope (AFM, Nanoscope E, Digital Instruments). Atomically flat terraces and steps, which correspond to a unit cell height of SrTiO3, are clearly seen in the topographic AFM image (Fig. 2), indicating that 2D step-flow growth occurred. Film thickness, crystallographic orientation, and lattice parameters of the resultant films were evaluated by high-resolution X-ray diffraction (HR-XRD, CuKα1, ATX-G, Rigaku Co.). Fig. 3(a) shows out-of-plane Bragg diffraction pattern of [(SrTiO3)17/(SrTi0.8Nb0.2O3)1]24 superlattice film grown on (001)-face of LaAlO3 substrate. Intense Bragg diffraction peak of 002 SrTiO3 (0) is seen together with 002 LaAlO3. In addition, satellite peaks (± 1 and ± 2) are clearly observed around 002 SrTiO3 (0). The superlattice period was calculated to be 7.1 nm (≈ 18 unit cells of SrTiO3), indicating that [(SrTiO3)17/(SrTi0.8Nb0.2O3)1]24 superlattice film was successfully fabricated. Further, stripe-shaped contrast is clearly seen in the Cscorrected high-angle angular dark-field scanning transmission electron microscope (HAADF-STEM, JEOL-2100F) image (Fig. 3(b)). Since the heavier Nb5+ ion (atomic number, Z = 41)
Carrier concentration (ne) and Hall mobility (μHall) of the superlattice films were measured by d.c. four probe method with van der Pauw configuration. All the electrical measurements were performed at room temperature in air. Since the ne of SrTiO3 barrier layer is very low (ne ≪ 1015 cm− 3), the ne of SrTi0.8Nb0.2O3 layer of [(SrTiO3)LB/(SrTi0.8Nb0.2O3)LW]20 is estimated as ne obs. · (LB +LW) /LW. Calculated ne of SrTi0.8Nb0.2O3 layer for the superlattices were ∼4 × 1021 cm− 3 agreeing well with that of the SrTi0.8Nb0.2O3 film [8]. The μHall value of the superlattices was ∼5 cm2 V− 1 s− 1 in all samples. Seebeck coefficient (S) was measured by conventional steady state method in the in-plane direction. Generally, |S| value of multilayered film is given by Σ |S|i σxxi /Σσxxi, where |S|i and σxxi are Seebeck coefficient and sheet conductivity of the i layer, respectively. In the present case, we directly measured |S| of the SrTi0.8Nb0.2O3 layer since the σxxi of the SrTi0.8Nb0.2O3 layer is at least six orders of magnitude larger than that of the SrTiO3 barrier layer. Fig. 4(a) shows |S|−LW plots for [(SrTiO3)15/ (SrTi0.8Nb0.2O3)LW]20 superlattices. A dramatic increase of |S| is seen with decreasing LW value. When LW is 1 unit cell (u.c.), the |S| value reaches 300 μV K− 1, which is ∼5 times larger than that of the SrTi0.8Nb0.2O3 bulk (60 μV K− 1). Slope for the Log |S| − Log LW plots is −1/2 as shown in the inset, indicating that the DOS −1 near the conduction band edge increases proportionally to LW . This is so-called “quantum size effect” [11]. Threshold LW for the quantum confinement is ∼16 u.c. (6.25 nm). Fig. 4(b) shows |S|−LB plots for [(SrTiO3)LB/(SrTi0.8Nb0.2O3)1]20 superlattices. The |S| value gradually increases with LB value and is saturated at 320 μV K− 1 when the LB value reached 16 u.c. (6.25 nm). From these results, we judged that the critical thickness for the 2D-electron confinement is 16 unit cell layers of SrTiO3. When the LB is thinner than 16, conduction electrons at the SrTi0.8Nb0.2O3 can move through the SrTiO3 barrier layer and,
Fig. 6. Direct heating test of [(SrTiO3)15/(SrTi0.8Nb0.2O3)1]100 superlattice. One end of the superlattice sample was heated by a lighter to introduce temperature difference of ∼90 K. The thermo-electromotive force of 32.6 mV was obtained.
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therefore, bandwidth broadening or formation of mini-band may occur. On the other hand, two-dimensionality of the conduction electrons decreases with increasing the LW. When the LW is thicker than 16, the conduction electrons behave three-dimensionally. Thus, optimum composition to obtain giant |S| of (SrTiO3)LB/ (SrTi0.8Nb0.2O3)LW is (LB, LW) =(16, 1). The |S| − Log ne plots are shown in Fig. 5, which verify that the experimental data points for the 2DEGs and the SrTiO3-bulk samples form two straight lines with different slopes. The slope for the SrTiO3-bulk samples is −200 μV K− 1, corresponds with the value of −kB / e ln 10 (−198 μV K− 1), indicating that the DOS near the Fermi surface is parabolic. On the other hand, the slope of the |S| − Log ne line for the 2DEGs (LW = 1) is −1000 μV K− 1, suggesting a stepped cumulative DOS is formed as a result of the quantum size effect. Finally, we performed direct heating test of [(SrTiO3)15/ (SrTi0.8Nb0.2O3)1]100 superlattice (Fig. 6) at room temperature in air. A lighter was used to introduce a temperature difference between both ends of the sample. Since SrTiO3 is basically stable at high temperatures as described above, large voltage (thermo-electromotive force) can be obtained by using high temperature (∼1000 K) waste heat from electric power plants, factories and automobiles. 6. Summary Seebeck coefficient (|S|) of (SrTiO3)LB/(SrTi0.8Nb0.2O3)LW superlattices, where LB and LW are number of unit cells for SrTiO3 barrier layer and SrTi0.8Nb0.2O3 well layer, respectively, were measured at room temperature. The |S| values of the − 1/2 superlattices increased proportionally to LW due to quantum −1 size effect, and reached 320 μV K at (LB, LW) = (16, 1) which is ∼5 times larger than that of the SrTi0.8Nb0.2O3 bulk (60 μV K− 1). The critical thickness for quantum confinement was 16 unit cells of SrTiO3 (6.25 nm). The present results provide useful information to design future 2DEG-SrTiO3-based thermoelectric materials.
Acknowledgements This work was financially supported by the Industrial Technology Research Grant Program in 2005 from the New Energy and Industrial Technology Development Organization (NEDO), and Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology (no. 18686054). References [1] T.M. Tritt, M.A. Subramanian, H. Bottner, T. Caillat, G. Chen, R. Funahashi, X. Ji, M. Kanatzidis, K. Koumoto, G.S. Nolas, J. Poon, A.M. Rao, I. Terasaki, R. Venkatasubramanian, J. Yang, MRS Bull. (special issue on harvesting energy through thermoelectrics: power generation and cooling) 31 (2006) 188 articles therein. [2] F.J. DiSalvo, Science 285 (1999) 703. [3] I. Terasaki, Y. Sasago, K. Uchinokura, Phys. Rev. B 56 (1997) R12685. [4] M. Shikano, R. Funahashi, Appl. Phys. Lett. 82 (2003) 1851. [5] T. Okuda, K. Nakanishi, S. Miyasaka, Y. Tokura, Phys. Rev. B 63 (2001) 113104. [6] H.P.R. Frederikse, W.R. Thurber, W.R. Hosler, Phys. Rev. 134 (1964) A442. [7] S. Ohta, T. Nomura, H. Ohta, K. Koumoto, J. Appl. Phys. 97 (2005) 034106. [8] S. Ohta, T. Nomura, H. Ohta, M. Hirano, H. Hosono, K. Koumoto, Appl. Phys. Lett. 87 (2005) 092108. [9] S. Ohta, H. Ohta, K. Koumoto, J. Ceram. Soc. Japan 114 (2006) 102. [10] Y.S. Touloukian, R.W. Powell, C.Y. Ho, P.G. Klemens, Thermophysical Properties of Matter Volume 2, Thermal Conductivity: Nonmetallic Solids, IFI/Plenum, New York, 1970. [11] M.A. Meyers, O.T. Inal (Eds.), Frontiers in Materials Technologies, Elsevier, Amsterdam, 1985. [12] L.D. Hicks, M.S. Dresselhaus, Phys. Rev. B 47 (1993) 12727. [13] L.D. Hicks, T.C. Harman, X. Sun, M.S. Dresselhaus, Phys. Rev. B 53 (1996) R10493. [14] H. Ohta, S-W. Kim, Y. Mune, T. Mizoguchi, K. Nomura, S. Ohta, T. Nomura, Y. Nakanishi, Y. Ikuhara, M. Hirano, H. Hosono, K. Koumoto, Nat. Mater. 6 (2007) 129. [15] T. Ohnishi, K. Takahashi, M. Nakamura, M. Kawasaki, M. Yoshimoto, H. Koinuma, Appl. Phys. Lett. 74 (1999) 2531.