Kriti Tyagiab,
Bhasker Gahtori*a,
Sivaiah Bathulaa,
Niraj Kumar Singha,
Swati Bishnoiab,
S. Aulucka,
A. K. Srivastavaa and
Ajay Dhar*a
aCSIR-Network for Solar Energy, CSIR-National Physical Laboratory, Physics of Energy Harvesting Division, Dr K. S. Krishnan Road, New Delhi-110012, India. E-mail: adhar@nplindia.org; bhasker@nplindia.org; Fax: +91 11 4560 9310; Tel: +91 11 4560 9455 Tel: +91 11 4560 9456
bAcademy of Scientific and Innovative Research (AcSIR), CSIR-NPL Campus, New Delhi-110012, India
First published on 18th January 2016
Motivated by the unprecedented thermoelectric performance of SnSe, we report its band structure calculations, based on density functional theory using the full potential linearized augmented plane wave. These calculations were further extended to evaluate the electrical transport properties using Boltzmann transport theory and the results were compared with the as-synthesized polycrystalline counterpart, which was synthesized employing conventional vacuum melting technique followed by consolidation employing spark plasma sintering. The as-synthesized SnSe was thoroughly characterized employing XRD, FESEM and TEM for phase purity, morphology and structure. The theoretically predicted band gap values and the temperature dependence of the electrical transport properties of SnSe were in reasonable agreement with the experimental results, within the approximations employed in our theoretical calculations. These theoretical calculations suggested that the optimum thermoelectric performance in SnSe is expected to occur at a hole doping concentration of ∼3 to 5 × 1021 cm−3. The measured fracture toughness and hardness of SnSe were found to be ∼0.76 ± 0.05 MPa √m and 0.27 ± 0.05 GPa, respectively, which are comparable with other state-of-the-art thermoelectric materials. The high value of thermal shock resistance ∼252 ± 9 W m−1, coupled with its good mechanical properties suggests SnSe to be a potential material for thermoelectric device applications.
The anisotropy in TE properties has been well documented on several alloys and compounds and originates primarily due to a variation in their electrical and thermal transport properties when measured along different crystallographic axes.4–6 It manifests itself in terms of different TE performance, when ZT is measured in different directions in a TE sample. This anisotropy in polycrystalline materials mostly arises by using the secondary material processing techniques such as the hot pressing,7,8 spark plasma sintering4,9,10 and extrusion11 of powdered TE material. An example of this kind of large anisotropy has recently been reported in a simple binary compound, SnSe, by Zhao et al.,5 where a vastly different ZT has been observed along the different crystallographic directions. These authors have reported a very high ZT of 2.6 along the b-axis in SnSe single crystals and 2.3 and 0.8 along the c and a-axis, respectively. Although these authors report a large ZT in single crystalline SnSe along its b-axis, but its value in polycrystalline SnSe has been reported to be only 0.3.12
SnSe has a layered structure and crystallizes in orthorhombic symmetry with a space group Pnma (space group no. 63) and undergoes a phase transition above a temperature of 750 K, where it possesses a lower symmetry (Cmcm space group no. 62). Recently, there has been a resurgence in the interest on the TE properties of SnSe5,12–14 ever since Zhao et al.5 reported an unprecedented ZT ∼ 2.62 at 923 K along its b-axis. These authors have experimentally found its electrical and thermal transport properties to be highly anisotropic along all the crystallographic directions. Later, Sassi et al.,14 reported a ZT of 0.5 at 823 K in polycrystalline SnSe, synthesized employing vacuum encapsulation followed by spark plasma sintering. Recently, Chen et al.,12 have reported an enhanced ZT value of 0.6 at 750 K in melt-grown Ag doped polycrystalline SnSe.
Several authors15–19 have reported the band structure of SnSe based on ab initio electronic structure calculations, employing different approximations. He et al.13 have calculated the band structure of SnSe using the generalized gradient approximation (GGA + U) method, as applied in Vienna ab initio Simulation Package (VASP), and reported an indirect band gap of 0.8 eV. Shi and Kioupakis15 have also performed the band structure calculations of SnSe and obtained a gap of 0.829 eV. Employing the first principle calculations using local density approximations (LDA), Kutorasinski et al. have reposted a band gap of 0.465 eV,16 however, Ding et al.17 have obtained a lower band gap of 0.69 eV, calculated using the GGA approximations.
In the present work, we report the theoretically derived electrical transport properties of SnSe, calculated using density functional theory (DFT), which has been compared with those measured experimentally on as-synthesized polycrystalline SnSe. The band structure calculations have been performed using full-potential linearized augmented plane wave (FP-LAPW) as implemented in WIEN2K code, based on DFT and a band gap value of 0.89 for Cmcm-phase has been realized, which is in closest agreement thus far with the reported optical band gap.5,18 The band structure calculations were then extended to theoretically evaluate the electrical transport properties of SnSe, employing the Boltzmann transport theory. The results suggest that the experimentally determined temperature dependent electrical transport behavior agrees well with that predicted theoretically using density-functional theory calculations, employing Engel-Vosko Generalized Gradient Approximation (EVGGA). In addition to the TE performance, the mechanical properties of TE materials are equally important especially during actual device operation. Thus, in the current study, we also report the hardness, fracture toughness and thermal shock resistance of as-synthesized polycrystalline SnSe.
The theoretical calculation were performed using the DFT within the FP-LAPW method in a scalar relativistic version as embodied in the WIEN2K code.16,21 The exchange–correlation (XC) potential was solved using three different possible approximations. The XC was described by the LDA and the GGA, which is based on exchange–correlation energy optimization to calculate the total energy.22,23 In addition, we have also used EVGGA,24 which optimizes the corresponding potential for electronic band structure calculations.
It is well-known that in calculating the self-consistent band structure within DFT, the LDA approximation generally underestimates the band gap.25 This is mainly due to the fact that LDA has relatively simple forms that are not sufficiently flexible to accurately reproduce both the exchange–correlation energy and its charge derivative. Engel and Vosko24 considered this shortcoming and constructed a new functional form of GGA that is able to better reproduce the exchange potential at the expense of lesser agreement in with the exchange energy. This approach yields better band splitting and some other properties that mainly depend on the accuracy of the exchange–correlation potential.
The Kohn–Sham equations were solved using a basis of linear augmented plane wave. The potential and charge density in the muffin-tin (MT) spheres are expanded in spherical harmonics with lmax = 10 and non-spherical components up to lmax = 4. We have used RKm = 7.0. In the interstitial region the potential and the charge density are represented by Fourier series. Self-consistency is obtained using 360 k points in the irreducible Brillouin zone (IBZ). The self-consistent calculations converge since the total energy of the system is stable within 0.00001 Ry. We extended our DFT studies to calculate the transport properties using 9900 k points in IBZ, which were calculated employing Boltzmann theory with constant scattering time approximation (CSTA) as implemented in the BoltzTraP code.26–28 The CSTA was used to directly calculate the Seebeck coefficient as a function of doping level and temperature, with no adjustable parameters.29,30
Fig. 1 As-synthesized polycrystalline SnSe (a) X-ray diffraction data (b) FESEM micrograph showing inherent nanoscale microstructure. Inset in (b) showing the crystalline size distribution. |
A detailed electron microscopy in real and reciprocal space led to important information pertaining to ultra-fine microstructural evolution in the material. Fig. 2(a) shows an illustrative micrograph of fine grains with uniform distribution and densely packed throughout in the microstructure. A corresponding selected area electron diffraction pattern (SAEDP, inset A in Fig. 2(a)) exhibits a polycrystalline nature of the material with the Debye rings, revealing three important atomic planes of the interplanar spacings of 0.293, 0.287, 0.183 nm with respective hkl indices of 111, 400, 511, of an orthorhombic crystal structure (space group: Pnma, lattice parameters: a = 1.15, b = 0.42, c = 0.44 nm, reference: ICDD, 00-014-0159). The ultrafine crystallites of nano-grained microstructure further exhibits that these in most of the instances the thin crystals are overlapping and therefore elucidating the presence of moiré fringes. Inset B in Fig. 2(a) shows a set of almost parallel translational – moiré patterns with a fringe spacing of about 1.13 nm between them. Underneath of these moiré fringes a stacking of high index atomic planes with interplanar spacing of about 0.183 nm (hkl: 511) are also depicted in the inset B of Fig. 2(a). Fig. 2(b) clearly displays that the intrinsically formed individual nanograins are faceted and ultrafine with the size approximately between 30 to 60 nm. At the atomic scale, a grain with size about 40 nm (Fig. 2(b)), shows a distinct stacking of planes with the interplanar spacing of about 0.287 nm of corresponding hkl: 400 (inset C in Fig. 2(b)), in correspondence with XRD and FESEM data. The interfaces between these nanograins were also examined under the electron beam to look into the microstructure. Inset A in Fig. 3 shows an interface (marked with a set of arrows) constituted between the two grains I and II. A further magnified area of encircled region in inset A of Fig. 3 with white dotted line reveal the thickness of the interface about 2 nm stacked between grains I and II (inset B of Fig. 3). Moreover, at the apex of the interface, the microstructure was mixed with the existence of both distorted atomic planes and amorphous phase (inset B of Fig. 3). However the high resolution images of either sides of interface shows single crystalline nature. As an illustrative example, in Fig. 3, a single grain II shows the presence of well stacked atomic planes with the interplanar spacing of 0.293 nm of hkl indices 111.
Fig. 4(b) shows the contribution of each atom to the density of states (DOS) for the Cmcm phase, via partial-DOS, which clearly shows a finite gap between valance and conduction band (ESI51 Fig. S1(b)† for Pnma phase). The valence band comprises of peaks at around −7.5 eV and between 0 and −5 eV. The peak around −7 eV arises from the s-state of Sn. The top of the valence band has major contributions from Sn-p, Se-p and Sn-s while the bottom of the conduction band arises from Sn-p and Se-p states. We find a significant hybridization between Sn-p, Se-p and Se-d from −5.0 eV to top of valence bands. Conduction band mainly comprises of Sn-p and Se-d states. The inset of Fig. 4(b) shows an enlarged axial view of the partial DOS for Cmcm phase of SnSe, within a few eV from the Fermi level.
Fig. 5 Temperature dependence of theoretically calculated transport properties along the crystallographic axes for SnSe (a) Seebeck coefficient (b) electrical conductivity and (c) power factor. |
Fig. 5(a) shows comparison between the experimentally determined Seebeck coefficient for polycrystalline SnSe with those calculated theoretically along the three crystallographic axes. The experimentally determined positive values of Seebeck coefficient (Fig. 5(a)) indicates a p-type conductivity its temperature dependence is reasonably in close agreement to those calculated theoretically, in the Pnma phase of SnSe. The discontinuity at ∼450 K is accounted to the thermal activation of the carriers5 while at ∼750 K corresponds to the phase transition from Pnma to Cmcm space group.5 This temperature dependence of Seebeck coefficient (Fig. 5(a)) is also similar to those reported experimentally by Sassi et al.14 and Zhao et al.5 However, for Cmcm phase, a mixture of light and heavy conduction bands could explain a nearly temperature independent thermopower owing to bipolar conduction.19
Fig. 5(b) shows that the experimental electrical conductivity increases with temperature although this increase is much sharper in Cmcm phase. In contrast, the theoretically estimated temperature dependence of conductivity of SnSe (p-type) reveals nearly a linear behaviour with a negative slope. This could be attributed to the fact that a constant scattering time (τ) approximation has been used to theoretically evaluate the electrical conductivity using DFT, while in practice τ varies with temperature, hence the observed deviation in experimental and theoretical behaviour of electrical conductivity. Moreover, DFT is known to underestimate the band gap of semiconductors and insulators when using local and semi-local approximation. Hence, SnSe, with a band gap of ∼0.8 eV behaves as metal while performing transport properties calculations using DFT, which is clearly reflected in temperature dependence of electrical conductivity as the theoretically calculated values decrease continuously with temperature in the entire temperature. Despite these limitations, both the calculated and experimental electrical conductivity values lie in same range. In view of various approximations that have been applied in the theoretical calculations, the agreement between experiment and theoretical behaviour of electrical properties of SnSe is quite reasonable. The dependence of power factor (PF) with temperature is also depicted in Fig. 5(c). A strong variation along y-axis as compared to x- and z-axis, in the entire temperature range is observed, which is well in accordance with the results shown in Fig. 5(a) and (b). A slope change at ∼750 K in the experimental results and theoretical calculations indicates the discussed phase transition.
To get a better understanding of the transport phenomenon in SnSe, the Boltzmann transport calculations for the Seebeck coefficient (S), electrical conductivity with respect to relaxation time (σ/τ) and power factor with respect to relaxation time (S2σ/τ) as a function of carrier concentration were carried out. The behaviour of S, σ/τ and S2σ/τ, as a function of carrier concentration, along the three crystallographic axes for both the phases of SnSe, are depicted in Fig. 6(a–f). Fig. 6(a) and (b) show that S decreases with increasing carrier concentration in accordance with the “Pisarenko Relation” for both the phases. This decrease in S, for both Pnma and Cmcm phases, is nearly similar along x- and z-axis however in contrast along the y-axis it shows a lower S till a carrier concentration of ∼2 × 1021 cm−3 after which a broad hump is observed. This suggests that the magnitude of the Seebeck coefficient can be tailored suitably by tuning the carrier concentration. The carrier concentration dependence of σ/τ is shown in Fig. 6(c) and (d) for Pnma and Cmcm phases of SnSe, respectively. These figures suggest that the Cmcm phase exhibits higher values of σ/τ as compared to Pnma phase. Although, while for Pnma phase, σ/τ exhibits almost similar behaviour in all the three crystallographic directions, the anisotropy is clearly pronounced in the case of Cmcm phase. Owing to the different trend in variation of S and σ/τ along the three axis, the S2σ/τ values for Pnma phase show a strong variation with carrier concentration, along all the three axes, as compared to Cmcm phase (Fig. 6(e) and (f)). Typically, in the Pnma phase along y-axis, S2σ/τ value decreases till a carrier concentration of ∼2 × 1021 cm−3 (Fig. 6(e)) after which S starts to increase with temperature (Fig. 6(a)) leading to an overall increase of S2σ/τ values. Similar to S and σ/τ, the graph for S2σ/τ Cmcm phase (Fig. 6(f)) shows a strong variation along y-axis as compared to x- and z-axis, in the entire temperature range. The magnitude of S2σ/τ along y-axis is ∼8 times lower than x- and z-axis. For both the phases, a peak value of S2σ/τ occurs at a carrier concentration of ∼3 to 5 × 1021 cm−3, where the bipolar effect is clearly evident. Fig. 6(f) clearly shows that S2σ/τ would show a maximum value at a hole doping concentration of ∼3 to 5 × 1021 cm−3 which qualifies as an optimum condition for ideal TE performance in Cmcm phase of p-type SnSe.
(1) |
(2) |
The magnitude of thermal shock resistance for TE materials is very important parameter during actual operation of the device, owing to the temperature gradient between the hot and cold ends of the TE device legs, which can lead to material failure due to internal mechanical stress induced by the temperature gradients.46–48 The thermal shock resistance parameter (RT), is given by the expression,46
(3) |
Footnote |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5ra23742d |
This journal is © The Royal Society of Chemistry 2016 |