Thermoelectric Properties of Sn-Containing Mg2Si Nanostructures

Jul 14, 2015 - Very high ZT have been reported for superlattices and nanowires;(2) however, for large-scale applications, thin films and nanocomposite...
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Thermoelectric Properties of Sn-Containing Mg2Si Nanostructures Hilal Balout,† Pascal Boulet,*,† and Marie-Christine Record‡ †

MADIREL and ‡IM2NP, Aix-Marseille University and CNRS, Avenue Normandie-Niemen, F-13397 Marseille cedex 20, France ABSTRACT: The thermoelectric performance of Mg2Sicontaining nanomaterials are predicted based on densityfunctional and Boltzmann’s transport theories. The investigated materials are Mg2Si1−xSnx thin films with x = 0.125 and x = 0.625, and (Mg2Si)1−x (Mg2Sn)x (x = 0.4 and x = 0.6) in the form of either superlattices or assembled nanosticks. The calculated properties (Seebeck coefficient S, electrical conductivity σ, and power factor S2σ) are compared with those of bulk Mg2Si1−xSnx. It is shown that the thin films outperform the bulk materials at low temperature (350 K) as they exhibit a higher Seebeck coefficient and comparable electrical conductivity. A low electrical conductivity at 900 K is responsible for the counter-performance of the films. Superlattices are attractive structures as p-doped materials at both low charge carrier concentration/high temperature and high charge carrier concentration/high temperature. The assembled nanosticks are interesting materials at low carrier concentration/low temperature only.

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INTRODUCTION When a direct energy conversion from heat into electricity is involved, thermoelectricity can be used to recover useful power from waste thermal energies. The efficiency of the thermoelectric devices is related to that of their constitutive materials and the performance of the thermoelectric materials is evaluated through the dimensionless figure of merit ZT = S2σ/κ, where S denotes the Seebeck coefficient, σ is the electrical conductivity, κ is the thermal conductivity, and T is the absolute temperature.1 As a consequence, good thermoelectric materials must have a high Seebeck coefficient, high electrical conductivity, and low thermal conductivity. The interdependency of the TE parameters makes the enhancement efforts of ZT very challenging. The currently recognized ways of optimizing TE materials are to increase the power factor S2σ by optimizing the carrier concentration n and/or to reduce the lattice thermal conductivity by introducing scattering centers. In low dimensional materials, the quantum confinement effects increase power factors and the nanostructures introduce many internal interfaces that scatter phonons. Very high ZT have been reported for superlattices and nanowires;2 however, for large-scale applications, thin films and nanocomposites seem to be more appropriate. In the present paper, we report a theoretical investigation of the thermoelectric properties of Sncontaining Mg2Si nanostructures. Both Mg2Si1−xSnx thin films with x = 0.125 and x = 0.625 and (Mg2Si)1−x(Mg2Sn)x nanocomposites with x = 0.4 and x = 0.6 have been explored. Even though the range of miscibility gap between Mg2Si and Mg2Sn is still a question of debate (see refs 3−7), it is usually accepted to be 0.4 < x < 0.6; hence we modeled the thin films as solid solutions for two compositions outside this range. The paper is composed of two main parts that describe the models © 2015 American Chemical Society

and methodology used and a detailed description and discussion of the results.

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COMPUTATIONAL PROCEDURE In this section we present how the model structures are built and the theoretical approach used to calculate the properties. Model Structures. Mg2Si and Mg2Sn crystallize in an antifluorite FCC structure; they belong to the Fm3m space group. The primitive unit cell of Mg2Si (Mg2Sn) is composed of three atoms, namely Si (Sn) at position (0, 0, 0) and Mg at positions (1/4, 1/4, 1/4) and (3/4, 3/4, 3/4). The bulk Mg2Si1−xSnx structure with x = 0.125 and x = 0.625 is built from a 1 × 1 × 2 supercell of Mg2Si comprising 24 atoms/cell with appropriate Sn to Si substitutions. The Mg2Si1−xSnx thin film structure has been designed from the following procedure. A (110)-oriented thin film is built by cleaving the Mg2Si bulk structure. The film consists of 8 atomic layers (24 atoms/cell), and an on-top vacuum is added to avoid the spurious interaction of the slab with its periodic images. The vacuum thickness is of 15 Å. The method for determining the vacuum size is based on the convergence of both the total energy and the surface energy of the film. Some Sn atoms are then substituted for Si ones so as to obtain the tin compositions x = 0.125 and x = 0.625. Two compositions of the superlattice and assembled nanosticks materials, namely, (Mg2Si) 0.6(Mg2 Sn) 0.4 and (Mg2Si)0.4(Mg2Sn)0.6, are investigated. The corresponding structures are depicted in Figure 1. A small model (Figure Received: April 7, 2015 Revised: July 9, 2015 Published: July 14, 2015 17515

DOI: 10.1021/acs.jpcc.5b03351 J. Phys. Chem. C 2015, 119, 17515−17521

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The Journal of Physical Chemistry C

necessary for transport calculations. From our DFT calculations the nanostructures are found to behave as metals. We have no experimental information about the gap of Mg2Si−Mg2Sn superlattices or assembled nanosticks. However, we know that the gap of Mg2Si1−xSnx varies between about 0.8 and 0.65 eV, depending on the value of x for 0 ≤ x ≤ 1. Therefore, it is unlikely that our nanostructures are metallic materials. The metallic character of the superlattices and assembled nanosticks as found in our calculations could be explained by the wellknown deficiency of DFT to reproduce properly gaps in general. Hence, we set the gap to an intermediate value of 0.74 eV by rigidly shifting the electronic bands. For the sake of comparison, we also set the gap of Mg2Si to this value, although it is found to be 0.22 eV from DFT calculations). The density-functional theory calculations are performed with the Quantum Espresso program (version 4.3.1)13 and the BoltzTraP14 package is used for the transport properties calculations (electrical conductivity and Seebeck coefficient). Because the transport properties involve the derivative of the Fermi function, which is significant only in a small energy window around the Fermi level where τ usually does not change much over this interval (see ref 15 and references therein), τ is assumed to be constant in BoltzTraP. This approximation allows for the direct calculation of the Seebeck coefficient as a function of temperature and doping levels, with no adjustable parameters. As to the thermal conductivity, which is important for evaluating thermoelectric performance of materials, it is composed of two contributions, an electronic one and a lattice one, the latter contribution being largest in semiconductors. In principle, the lattice thermal conductivity can be evaluated from ab initio methods through the calculation of phonon spectra. In practice though, the large size and low symmetry of our models prevent the calculation of phonon band structure from being tractable. Hence, we only investigate the electronic properties in this work.

Figure 1. Models constructed to calculate the properties of the (Mg2Si)x(Mg2Sn)1−x nanostructures. The small nanostructure is viewed along the y axis (b parameter) and the z axis is vertical (c parameter) whereas for the large nanostructure the z axis is horizontal and the y axis is vertical. Key: yellow, Si; mauve, Sn; ice blue, Mg.

1i) made of 30 atoms is built from the superposition of Mg2Si and Mg2Sn structures with overall composition adjusted to obtain exactly either 40%Mg2Si−60%Mg2Sn (as depicted in Figure 1i) or 60%Mg2Si−40%Mg2Sn (where Si and Sn would be inverted in Figure 1i). This type of structure corresponds to a superlattice. A larger model (Figure 1ii) comprising 60 atoms is built from the small one by doubling the b parameter of the unit cell and by vertically shifting the newly added atoms by c/ 2. The so-obtained structure consists of infinite nanosticks of either Mg2Si or Mg2Sn bundled together. The overall compositions are 40%Mg2Si−60%Mg2Sn (corresponding to Figure 1ii) and 60%Mg2Si−40%Mg2Sn. In the superlattice model, the patterns (Mg2Si and Mg2Sn) of the same type share two faces with their period images in the [100] and [010] directions. In the assembled nanosticks model, the patterns of the same type share one face only in [100] direction and an edge in the [011] direction. Property Calculations. The structure optimizations are performed using the Perdew−Burke−Ernzerhof8 (PBE) exchange−correlation functional of the density-functional theory9,10 (DFT). To reduce the number of plane waves, chemically inactive core electrons are replaced with Vanderbilt ultrasoft pseudopotentials.11 Only the Mg-2p63s2, Si-3s23p2, and Sn-4d105s25p2 orbitals are treated as valence ones. The two parameters that affect the accuracy of the calculations are the kinetic energy cutoff which determines the number of plane waves in the wave function expansion and the number of special k-points used for the integration of the properties in the Brillouin zone. The cutoff energy is fixed at 410 eV on the basis of the results of convergence tests. The selection of the k-point mesh is based on the Monkhorst−Pack scheme.12 For the structure optimizations the k-point mesh (kx × ky × kz) used is 4 × 4 × 4 for the bulk Mg2Si1−xSnx structures, 4 × 4 × 1 for the Mg 2 Si 1 − x Sn x thin films, 20 × 20 × 10 for the (Mg2Si)x(Mg2Sn)1−x superlattices, and 10 × 10 × 5 for the (Mg2Si)x(Mg2Sn)1−x assembled nanosticks. The structures are optimized until the following criteria are met: 10−9 Ry for the energy convergence and 10−5 Ry bohr−1 for the energy gradient one. A subsequent self-consistent field calculation is performed for all the structures using a very thin k-point mesh with at least 6000 k-points in the irreducible Brillouin zone so as to obtain a very detailed description of the band structure, which is

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RESULTS In this part we present the structural features of the models obtained after geometry optimization, the band structures and the transport properties, namely, the electrical conductivity σ, the Seebeck coefficient S, and the power factor S2σ, with respect to the doping levels. Structural Properties. The optimized cell parameter a of Mg2Si is 6.369 Å, which is in good agreement with both the experimental value (6.35 Å)16 and other theoretical predictions (6.24−6.51 Å).17 The change in the cell parameters when the dimensionality of the materials is reduced from 3D (bulk Mg2Si1−xSnx) to 2D (thin film) can be observed in Table 1. For x = 0.125 and x = 0.625 the a parameters of the bulk Mg2Si0.875Sn0.125 and bulk Mg2Si0.375Sn0.625 are 6.243 and 6.640 Å, respectively, whereas that of the thin film, for the same fractions, are 6.439 and 6.633 Å. It can be noticed that the relaxation of the slab with respect to bulk is particularly small for the high fraction of tin. Table 1. Optimized Cell Parameter a of the Bulk and Thin Films Mg2Si1−xSnx (Å) x = 0.125 x = 0.625 17516

bulk structures

thin films

6.243 6.640

6.439 6.633 DOI: 10.1021/acs.jpcc.5b03351 J. Phys. Chem. C 2015, 119, 17515−17521

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Mg2Si the Sn−Sn distance (4.645 Å) is increased compared to that with 60%-Mg2Si (4.575 Å). Two Si−Si distances are found at 4.525 and 4.645 Å for the former and three at 4.515, 4.525, and 4.575 Å for the latter. The Mg−Mg and Si−Mg distances spread between 3.15−3.70 Å and 2.75−2.90 Å, respectively. Hence, we notice that the interatomic distances are longer in the SL than in the Mg2Si bulk structure. In the ANS (Figure 2ii) the Sn−Sn distances shorten (4.615 Å for 40%-Mg2Si and 4.515 Å for 60%-Mg2Si) compared to that in the SL. In addition, the distribution of all the other interatomic distances is more spread, which reveals that more degrees of freedom are available in the large structure for relaxing. Quite surprisingly, a short Si−Si distance is observed at 3.505 Å in the 60%-Mg2Si structure (panel a), which confirms the structural flexibility. Electronic Band Structures. The band structures of the Mg2Si1−xSnx thin films with compositions x = 0.125 and x = 0.625 show a direct band gap at the Γ-point (Figure 3). The

The evolution of the optimized lattice parameters of the (Mg2Si)x(Mg2Sn)1−x superlattices (SL) and assembled nanosticks (ANS) shows that they increase with the tin content (Table 2). The increase in the a parameter with Sn content can be explained by the enlargement of the interatomic distances when substituting Sn for Si. Table 2. Optimized Cell Parameters of the (Mg2Si)x(Mg2Sn)1−x Nanostructures (Å) superlattices

assembled nanosticks

cell parameter

40% Mg2Si

60% Mg2Si

40% Mg2Si

60% Mg2Si

a b c

6.571 6.571 17.084

6.473 6.473 16.912

6.521 13.804 16.691

6.446 13.485 16.557

The radial distribution functions (RDF) allow for revealing the detailed structural features. The RDFs are presented in Figure 2. It can be seen that for the SL (Figure 2i) with 40%-

Figure 3. Electronic band structure of the Mg2Si1−xSnx thin films: (a) x = 0.625; (b) x = 0.125.

gap energy is much larger when the content in tin is small; it amounts to about 0.25 and 0.1 eV when x = 0.125 and 0.625, respectively. The overall shape of the band structure is very similar in both thin films. Nonetheless, some differences can clearly be evidenced. In the valence band the two uppermost bands at the Γ-point are well separated when x = 0.125 (Figure 3b) whereas they are much closer to each other when x = 0.625 (Figure 3a). Hence, the electron density at the vicinity of the Fermi level seems to increase with x. In the conduction band the two lowest bands at the Γ-point are close to each other for x = 0.125 whereas they are more distant for x = 0.625. Hence, contrary to the valence band, the density of states is much weaker next to the Fermi level for x = 0.625. The difference in density of states of the valence and conduction bands in the region of the Fermi level between both films should be reflected in the Seebeck coefficient. When comparing the band structures of the bulk and thin film Mg2Si1−xSnx (Figure 4), one can see that, at equal fraction of tin, the gaps of both materials are about the same. However, the densities of states are different. The degeneracy of the states at the Γ-point in the valence band of the bulk materials increases the density of states at both x = 0.125 and x = 0.625 (Figure 4b,a). This is less evident in the conduction band for x = 0.125. In effect, for both materials, only one band is located near the Fermi level. However, the asymmetry of the band in the case of the thin film (Figure 4d) makes itself flatter near the Fermi level than the band of the bulk. It can then be suggested that the density of states of the band conduction of the thin film is higher than that of the bulk. This should also lead to differences in the Seebeck coefficient of both structures. The band structures of the SL and ANS materials are depicted in Figure 5. For the (Mg2Si)0.4(Mg2Sn)0.6 SL (panel a)

Figure 2. Radial distribution functions of the (Mg2Si)x(Mg2Sn)1−x nanostructures: (a) and (d) 60% Si; (b) and (e) 40% Si; (c), (f) bulk Mg2Si. 17517

DOI: 10.1021/acs.jpcc.5b03351 J. Phys. Chem. C 2015, 119, 17515−17521

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Hence in the following the values of the electrical conductivity σ are given relative to τ (σ/τ). For the bulk Mg2Si and Mg2Si1−xSnx bulk and thin film structures, at low and moderate doping levels (up to 1020 cm−3) and irrespective of the type of doping and temperature, the electrical conductivity σ increases very slowly with increasing doping level, which is characteristic of semiconductors (Figure 6a,d). At high doping levels (>1020) σ of the thin films increases

Figure 4. Electronic band structure of the thin films of Mg2Si1−xSnx (right panels) compared to that of the bulk Mg2Si1−xSnx (left panels): (a) and (c) x = 0.625; (b) and (d) x = 0.125.

Figure 5. Electronic band structures of the (Mg2Si)x(Mg2Sn)1−x nanostructures: (a) SL with 40%-Mg2Si; (b) ANS with 40%-Mg2Si; (c) SL with 60%-Mg2Si; (d) ANS with 60%-Mg2Si.

Figure 6. Transport properties of the bulk Mg2Si and Mg2Si1−xSnx bulk and thin film structures at 350 and 900 K: (a) and (d) electrical conductivity; (b) and (e) Seebeck coefficient; (c) and (f) power factor.

the bottom of the conduction band is located at the Γ-point, and the same applies for (Mg2Si)0.6(Mg2Sn)0.4 (panel c). By contrast, the top of the valence band shifts from between the Γ−R line for the former structure to between the A − Γ line for the latter one. We note, however, that, in the case of (Mg2Si)0.4(Mg2Sn)0.6 (panel a) the energy of the highest orbital along the Γ−R line is very similar to that of the highest orbital along the A−Γ line. For (Mg2Si)0.4(Mg2Sn)0.6 and (Mg2Si)0.6(Mg2Sn)0.4 ANS (Figure 5 panels b and d, respectively) the bottom of the conduction band is located on the Γ−U line whereas the top of the valence band is near the U k−point. Transport Properties. The electrical conductivity, Seebeck coefficient, and power factor of the various structures are described for hole and electron types of charge carriers with concentrations in the range 1018−1022 cm−3. Electrical Conductivity. As mentioned in the computational section, the calculation of the thermoelectric properties are performed within the constant scattering-time approximation τ.

steadily, though much more slowly than in the case of the bulk materials. This is caused by the negligibly small increase of the σzz component of the σ tensor for the thin film. Despite the difference in the energy gap between the films with different tin fractions, their electrical conductivities are nearly identical on the whole range of doping levels, irrespective of the doping type. The electrical conductivity of the SL and ANS structures shows features characteristic of semiconducting materials; at low and moderate doping levels (up to 1020 cm−3) and irrespective of the type of doping and temperature, σ increases slowly with increasing doping level, whereas at higher doping levels σ sensibly increases (Figure 7a,d). Interestingly, a small difference can be noticed at high concentrations between the SL and the ANS. Indeed, irrespective of the temperature the electrical conductivity of the ANS is smaller than that of the SL. This has a sizable effect on the power factor as we will see below. 17518

DOI: 10.1021/acs.jpcc.5b03351 J. Phys. Chem. C 2015, 119, 17515−17521

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Figure 7. Transport properties of the bulk Mg2Si and the (Mg2Si)0.4(Mg2Sn)0.6 and (Mg2Si)0.6(Mg2Sn)0.4 superlattices and assembled nanosticks structures with respect to holes and electrons carrier concentrations: (a) and (d) electrical conductivity; (b) and (e) Seebeck coefficient; (c) and (f) power factor.

1098 μV K−1 (n = 1.54 × 1015 h cm−3) for p-type and 1012 μV K−1 (n = 1.23 × 1015 e cm−3) for n-type at 350 K. At this temperature (Mg2Si)0.6(Mg2Sn)0.4 and (Mg2Si)0.4(Mg2Sn)0.6 SL show S of about 900 μV K−1 at n = 4 × 1015 h cm−3 and 850 μV K−1 at n = 2.5 × 1015 h cm−3. As the temperature increases, the maximum value of S decreases to about 460 μV K−1 (n = 9.28 × 1018 h cm−3) and 450 μV K−1 (n = 7.18 × 1018 e cm−3) at 900 K for bulk Mg2Si and 400 μV K−1 (n = 2 × 1019 h cm−3) and 375 μV K−1 (n = 2 × 1019 e cm−3) for (Mg2Si)x(Mg2Sn)1−x SL. It can be seen that the position of the maximum of S shifts up with increasing temperature from low doping level (∼1015 cm−3) at 350 K to the high one (∼1019 cm−3) at 900 K. At 350 and 900 K the p-doped SL exhibits systematically higher maximal values of S than does the ANS. By contrast, for n-doped SL the maxima are the same at 350 K, and at 900 K the ANS exhibits a slightly larger Seebeck coefficient. The differences are not huge, though, and both structures show high Seebeck coefficients, irrespective of their compositions (around 800−1000 μV K−1 at 350 K and 300−400 μV K−1 at 900 K). Power Factor. A high Seebeck coefficient or electrical conductivity does not systematically lead to good power factor (PF = S2σ). Indeed, the PF is proportional to S2 and σ, and in the linearized equation of the Boltzmann transport theory S and σ are inversely proportional to each other, so high values of PF result from a compromise between S and σ. The maximum of PF for the Mg2Si1−xSnx thin films is systematically located in the range (1−3) × 1020 cm−3 of carrier concentration, irrespective of the nature of carrier and temperature. At low temperature of 350 K and for p-doping type the power factor of the Mg2Si0.375Sn0.625 thin film (6.5 × 10 11 W m −1 K−2 s −1 ) markedly outperforms that of Mg2Si0.875Sn0.125 (2.5 × 1011 W m−1 K−2 s−1). For n-doping type both films perform about equally [(4−4.5) × 1011 W m−1 K−2 s−1]. As the temperature increases to 900 K, the difference in performance between the p-doped films tends to vanish, whereas that between the n-doped films tends to slightly increase. As it turns out, for n-doped materials, Mg2Si0.875Sn0.125 performs better than Mg2Si0.375Sn0.625 at 900 K, but not at 350 K, whereas for p-doped materials, Mg2Si0.375Sn0.625 performs better on the whole range of temperature. As an overall trend, it can be stated that the thin films perform equally well or better

Seebeck Coefficient. The Seebeck coefficient S of bulk Mg2Si and Mg2Si1−xSnx bulk and thin film materials is depicted in panels b and e of Figure 6. In the following, when we mention the maximum of S, it stands for the maximum of the absolute value of S. Irrespective of the nature of the dopants, the maximum of S decreases when the temperature increases, and it shifts toward higher doping concentration. When comparing the Mg2Si1−xSnx films and the bulk Mg2Si, one can observe that from low temperatures to high ones an inversion of the maxima of S between the bulk structure and the films is operated. In effect, at low temperatures the bulk Mg2Si exhibits a maximum of S at carrier concentrations lower than those for the films whereas at high temperatures the opposite is observed. Therefore, at 350 K (Figure 6i(b,e)) the p- and n-doped films bear largest Seebeck coefficients around 1020 and 1019 h cm−3, respectively, with values around +250 and −350 μV K−1. In this region of doping the thin film outperforms the bulk. This is essentially due to the high value of the Szz. At 900 K for x = 0.125 the Seebeck coefficients amount to 223 μV K−1, which is about the same value as for the bulk, and −280 μV K−1, which is much larger than the bulk value (−225 μV K−1). When comparing the Seebeck coefficient of the Mg2Si1−xSnx film with that of the bulk Mg2Si1−xSnx structures, one sees that S evolves at low temperature in accordance with the predictions made in the previous section from the densities of states. That is, for the p-doped film S is lower than that of bulk (180 μV K−1 for x = 0.125 vs 350 μV K−1 at 350 K), which corresponds to a larger valence band DOS of the bulk. On the contrary, for the n-doped film S is larger (in absolute value) than that of bulk (−375 μV K−1 for x = 0.125 vs −150 μV K−1), which corresponds to a larger valence band DOS of the film. As the temperature is raising, S of both the p- and n-doped films still outperforms that of the bulk with a maximum difference observed for the n-doped films (e.g., −280 μV K−1 vs −200 μV K−1 for x = 0.125). The Seebeck coefficients of p- and n-doped (Mg2Si)x(Mg2Sn)1−x SL and ANS materials are depicted in Figure 7i,ii (panels b and e) with respect to the doping level. Irrespective of the temperature and doping type the bulk Mg2Si exhibits the highest values of S, with a maximum value of about 17519

DOI: 10.1021/acs.jpcc.5b03351 J. Phys. Chem. C 2015, 119, 17515−17521

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Table 3. Comparison of the Maximum Power Factor between the (110)-Oriented Monocrystalline Mg2Si and Mg2Si1−xSnx Thin Films for 1018 and 1.2 × 1020 Electrons and Holes per cm3 (Units 1011 W m−1 K−2 s−1) at 350 and 900 K Mg2Si

Mg2Si1−xSnx

electrons concentration power factor temperature (K)

1018 0.14 350

1.2 × 1020 3.5 900

holes 1018 0.28 350

electrons

1.2 × 1020 4.0 900

1018 1.0 350

1.2 × 1020 4.0 900

holes 1018 1.0 350

1.2 × 1020 4.0 900

bulk Mg2Si1−xSnx are small, and (2) comparable values of σ for all the materials. As for the n-doped film, this can be explained by the high Seebeck coefficient. At 900 K, the counterperformance of the Mg2Si1−xSnx film is caused by a very low electrical conductivity compared to the other materials. As we compare Mg2Si1−xSnx and Mg2Si films, the alloying with Sn improves significantly the thermoelectric performances at low temperature and carrier concentration only, whereas at high temperature and carrier concentration, the power factors are about the same for both films. The superlattice type of structure is very appealing as a pdoped material both at low carrier concentration/low temperature, where it remarkably outperforms the bulk, and high carrier concentration/high temperature where its PF is about the same as that of bulk Mg2Si, though at a slightly lower carrier concentration. The stick assemblage is interesting as a n-doping material at low carrier concentration/low temperature only where its PF is almost twice as high as that of bulk Mg2Si.

than bulk Mg2Si at 350 K only. The reverse is observed at 900 K. Table 3 presents a comparison between the power factors of the (110)-oriented monocrystalline Mg2Si (from ref 18) and the Mg2Si1−xSnx thin films. It appears that the best improvement when Mg2Si is alloyed with Sn is obtained at low temperature and low carrier concentration (350 K and 1018 cm−3). In effect, PF increases by factors of 7 and 3.5 for n- and p-doping, respectively. By contrast, at high carrier concentration (1.2 × 1020 cm−3) and high temperature (900 K) there is practically no improvement in PF. For the nanostructures (Figure 7 panels c and f) a clear difference appears in the power factor between the SL and ANS depending on the type of doping. For p-type of doping at low and high temperature, the SL show a better PF than the ANS. In addition, at 350 K the SL, especially that with 40%-Sn, bear a substantially higher value of PF (about twice as high) than the bulk Mg 2 Si whereas at 900 K all three materials ((Mg2Si)x(Mg2Sn)1−x SL with x = 0.4 and 0.6 and bulk Mg2Si) have similar maximal values of about 11 × 1011 W m−1 K2 s at 1021 h cm−3. On the other side, for n-type doping the ANS bear higher PF values than the SL. In the range 1019 to 3 × 1020 e cm−3, all the nanostructures show a PF higher than the bulk Mg2Si at 350 K. The PF of the (Mg2Si)0.4(Mg2Sn)0.6 ANS reaches 4.27 × 1011 W m−1 K2 s at 1020 e cm−3, which is about twice as high as that of bulk Mg2Si. Above 3 × 1020 e cm−3 the bulk Mg2Si shows the highest value of PF with a maximum of about 2.7 × 1011 W m−1 K2 s at 6.6 × 1020 e cm−3. Therefore, these results show that at low temperature biphasic materials perform better and with lower doping requirements than the bulk Mg2Si. By contrast, at high temperature of 900 K, the bulk Mg2Si exhibit the highest values of PF along the whole electron doping range with a maximum peak of about 13 × 1011 W m−1 K2 s at 1021 e cm−3 compared with maximum 6 × 1011 W m−1 K2 s at 3 × 1020 e cm−3 for (Mg2Si)x(Mg2Sn)1−x ANS with x = 0.4. These results tend to show that nanostructured materials perform better at low temperature and low carrier concentration than bulk Mg2Si.

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AUTHOR INFORMATION

Corresponding Author

*P. Boulet. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was granted access to the HPC resources of CINES (Centre Informatique National de l’Enseignement Supérieur, Montpellier, France) under the allocation C2014086881 made by GENCI (Grand Equipement National de Calcul Intensif). This work was also supported by the computing facilities of the CRCMM (Centre regional de Compétences en Modélisation Moléculaire de Marseille) and by the mésocentre d’AixMarseille Université (project 13b020). The foundation EADS is acknowledged for the financial support of Mr. H. Balout’s Ph.D. thesis.

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REFERENCES

(1) Goldsmid, H. J. In Handbook of Thermoelectrics; Rowe, D., Ed.; CRC Press: Boca Raton, FL, 1995; Chapter Conversion Efficiency and Figure-of-Merit. (2) Tritt, T. M. In Thermoelectric Materials - New Directions and Approaches; Tritt, T. M., Kanatzidis, M. G., Lyon, H. B., Mahan, G. D., Eds.; Materials Research Society: Warrendale, PA, 1997; Chapter Measurement and Characterization Techniques for Thermoelectric Materials. (3) Kozlov, A.; Grobner, J.; Schmid-Fetzer, R. Phase formation in Mg-Sn-Si and Mg-Sn-Si-Ca alloys. J. Alloys Compd. 2011, 509, 3326− 3337. (4) Viennois, R.; Colinet, C.; Jund, P.; Tédenac, J. C. Phase stability of ternary antifluorite type compounds in the quasi-binary systems Mg2X-Mg2Y (X, Y = Si, Ge, Sn) via ab-initio calculations. Intermetallics 2012, 31, 145−151. (5) Zaitsev, V.; Fedorov, M. I.; Gurieva, E.; Eremin, I.; Konstantinov, P.; Samunin, A.; Vedernikov, M. Highly effective Mg2Si1−xSnx

CONCLUSION To summarize, the Seebeck coefficient of the n-doped Mg2Si1−xSnx thin films outperforms that of the bulk Mg2Si and bulk Mg2Si1−xSnx materials, irrespective of the temperature. By contrast, the p-doped film is outperformed by the other materials, except anecdotally at low temperature (350 K) and high carrier concentrations (>1020). The improvement of S for the p-doped film can be interpreted as an increase of the electronic band DOS, especially at low temperature. Compared with bulk Mg2Si and bulk Mg2Si1−xSnx the power factor of the Mg2Si1−xSnx films is markedly improved at a low temperature of 350 K only. This can be explained for the pdoped film by the conjunction of (1) a high S of the film in a carrier concentration region where the S of bulk Mg2Si and 17520

DOI: 10.1021/acs.jpcc.5b03351 J. Phys. Chem. C 2015, 119, 17515−17521

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DOI: 10.1021/acs.jpcc.5b03351 J. Phys. Chem. C 2015, 119, 17515−17521