SUPPLEMENTARY INFORMATION

Transcription

1 Supplementary Methods Materials Synthesis The In 4 Se 3-δ crystal ingots were grown by the Bridgeman method. The In and Se elements were placed in an evacuated quartz ampoule with an excess of In (5-10 at.%) for Se-deficiency control. Heat treatment was followed by the melting and crystallizing at 550 o C and 590 o C for δ = 0.65 and 0.22 compounds, respectively, during a week with a growth rate of 1.5 mm/hour. Higher growth rate than 2 mm/hour was not good for the sample homogeneity. By comparing the initial and final In/Se concentrations, we found that the excess In about 4 at.% does not incorporate the crystallization at this concentration range during the crystal growth as shown in Suppl. Fig. 1. Because excess In was floated in the upper part of the crystal during the crystal growth, we eliminated the upper part (» 2 mm) of the grown crystals. Characterization and Sample Preparation The chemical inhomogeneity was examined by the inductively coupled plasma spectroscopy (ICP) and electron dispersive spectroscopy (EDS) measurements. The variations of chemical concentration of three different slices of one crystal ingot from top to bottom were about ±2 at.%. The EDS measurements at several different points of a slice of the sample showed the chemical homogeneity within an experimental error. Supp. Fig. 2a and 2b show the crystal structure of In 4 Se 3 in the ab- and bc-planes, respectively. We employed Se-deficiency in order to reduce energy gap. The Se-deficiency has an effect on the creation of electronic charge. The relative formation energy calculation of Se-deficiency for various Se-deficient configurations confirmed that configuration with vacant Se1 sites (Suppl. Fig. 1) are more stable than those with vacant Se2 and Se3 sites. The x-ray diffraction (XRD) pattern on the cross-sectional plane (perpendicular to the growth direction) (Suppl. Fig. 2c) of In 4 Se 3-δ (δ = 0.22) crystal ingot (Suppl. Fig. 1d) revealed that growth direction of the crystal was mainly perpendicular to the c-axis whereas minor random orientation peaks of {h31}, {h11}, and 1

2 {h01} planes were observed. The growth direction (GD) contains the ab-plane whereas the outof-gd has the bc- (in-plane) and ac-planes. We prepared disk-shaped and bar-type samples to measure the thermal conductivity κ and electrical transport properties (S and ρ), respectively. For anisotropic measurements, we cut the samples for two directions: along the growth direction and perpendicular to the growth direction. Typical sample sizes for thermal conductivity and electrical transport properties (S and ρ) measurements are of 10 mmφ diameter with 2 mm thickness and 10 mm long with (2 5)~(2 5) mm 2 cross-sectional area, respectively. Measurements High temperature thermal conductivity κ was obtained by the measurements of sample density ρ s, thermal diffusivity λ (by the laser flash method), and heat capacity C p (ULVAC, Japan); κ=ρ s λc p, where heat capacity C p was used the results from the Dulong-Petit fitting at high temperatures (T 300 K). The high temperature electrical resistivity ρ and Seebeck coefficient S were measured by the four-probe method (ZEM-2, ULVAC, Japan). The orthorhombic bar was placed in the hot and cold side plate and the voltage leads were contacted at the sample surface. By applying the heat and electric pulse, the Seebeck coefficient S = ΔV/ΔT and electrical resistivity ρ = ΔV/ΔI were measured simultaneously. The Hall resistivity ρ xy measurement was carried out by the five-contact AC-transport technique by the physical property measurement system (Quantum Design, USA). The Hall carrier concentration was calculated by the one-band model as following relation: n H = -1/(R H e), where Hall coefficient R H = ρ xy /H and e = C. Theoretical calculation methods The first-principles calculation was performed by the pseudopotential plane wave method using the Vienna Ab initio Simulation Package (VASP). We adopted the generalized gradient approximation (GGA) implemented by Perdew, Burke, and Ernzerhof (PBE) for the exchange 2

3 correlation energy functional with the spin-orbit interaction. The Monkhorst and Pack scheme of k-point sampling is used for integration over the first Brillouin zone. The energy cutoff is chosen to be 240 ev and atomic positions are fully relaxed until all force components are smaller than 0.02 ev/å. The unit cell is composed of 28 atoms with seven different sites (four sites for indiums and three sites for seleniums) and each site occupies four equivalent atomic positions. The calculated lattice parameters are of a = Å, b = Å and c = Å, respectively, which are similar to the experimental values. For Se-deficient In 4 Se 3-δ (δ = 0.25) crystal, single Se atom was eliminated from the twelve Se atoms that occupied three crystallographically nonequivalent sites in the unit cell. We found that the configuration with vacant Se1 site is lower in energy than other configurations with Se2 and Se3 sites by 0.14 ev and 0.19 ev per unit cell, respectively (Fig. 1 in the text). The thermoelectric properties are calculated by using BoltzTraP program. Dense mesh of k-points in full Brilloun zone is used for the calculation. Exchange correlation energy functional is calculated using Engel-Vosko (EV) GGA for the Boltzmann transport calculation. Although PBE-GGA has been widely used for the self-consistent charge consistent calculation, it is known to underestimate the band gap. For a calculation of thermoelectric properties, a correct estimation of band gap is important. The EV-GGA has shown good agreement with experimental band gap. Indeed, PBE-GGA gives a band gap of 0.17 ev, but the EV-GGA gives a band gap of 0.57 ev, which is similar to the experimental value of 0.64 ev (Ref. 14 in the text). We have used a rigid band approximation in the doping effect. In order to obtain the temperature dependent transport properties, we fix the chemical potential at μ = 0.22 ev, and use a constant time relaxation parameter τ = sec. Supplementary Discussion Thermoelectric properties of In 4 Se 3-δ (δ = 0.22 and 0.65) Suppl. Fig. 3 shows the thermoelectric properties of In 4 Se 2.78 (δ = 0.22, black square) and In 4 Se 2.35 (δ = 0.65, red circle) for both orientations of the growth direction (ab-plane, open symbol) and perpendicular to the growth direction (bc-plane, closed symbol). The thermal conductivity κ(t) of In 4 Se 3-δ is very low (1.5 W m -1 K -1 at 300 K) along the c-direction, and it 3

4 decreases with increasing the Se-deficiency: 0.94 W m -1 K -1 for δ = 0.22 and 0.74 W m -1 K -1 for δ = 0.65 at T = 705 K, which is due to the disorders induced by the Se-defect. The low thermal conductivity in the ab-plane for the δ = 0.65 crystal is caused by the van der Waals interaction between the In-Se layers. The Seebeck coefficient S(T) and electrical resistivity ρ(t) are presented in Suppl. Fig. 3b and 3c, respectively. The temperature-dependent behavior of S(T) for the δ = 0.22 crystal increases with temperature up to 450 K and saturates at higher temperatures (~ μv/k), while the S(T) for the δ = 0.65 crystal along the c-axis monotonically decreases with increasing temperature, reaching ~ 295 μv/k at 705 K. The ρ(t) shows a gap-like increase with decreasing temperature as shown in Suppl. Fig. 3c. At temperatures lower than 400 K, in the case of the δ = 0.65 crystal, ρ(t) in the ab-plane is smaller than that measured in the bc-plane. The power factor S 2 σ for these compounds, which is depicted in the inset of Suppl. Fig. 3c, increases with temperature. The power factor reaches about 1.5 mw m -1 K -2 at 705 K for δ = 0.65 compound. The materials dimensionless figure of merit ZT is presented in Suppl. Fig.3d. The value of ZT reaches remarkably high values of 1.48 and 1.10 for In 4 Se 2.35 (δ = 0.65) and In 4 Se 2.78 (δ = 0.22), respectively, at 705 K along the bc-plane. The Hall carrier concentration n Hall of the In 4 Se 2.78 (δ = 0.22) crystal in the ab-plane, which is determined by Hall resistivity measurements, estimated to be cm -3, as shown in the inset of Suppl. Fig. 3d. Boltzman transport calculation Suppl. Fig. 4 represents the anisotropic Boltzman transport calculation results of electrical conductivity σ, Seebeck coefficient S, and power factor S 2 σ with respect to chemical potential μ of the In 4 Se 3 compound. The positive (negative) chemical potential indicates the electron (hole) doping, respectively. With increasing chemical potential by electron doping, the electrical conductivity significantly increases at high chemical potential range (μ 0.5 ev) and the absolute Seebeck coefficient shows maximum at μ = 0.1 ev with saturation value of S at μ 0.5 ev. The power factor is maximum near μ = 0.8 ev due to significantly increase of the electrical conductivity at high electron doping range. The Boltzman transport result as shown in Fig. 2 of the main text used the chemical potential of μ=0.22 ev which is comparable to the experimental properties. Because it is not an optimum value for high power factor, the power factor of the 4

5 presented compound In 4 Se 3-δ (δ = 0.64, ZT = 1.48 at T = 705 K) can be further increased by increasing electron doping (up to μ = 0.8 ev) level. Suppl. Fig. 5 shows the temperature-dependent behavior of Hall carrier density n H, anisotropic electrical resistivity ρ, and Seebeck coefficient S. The fixed parameters of chemical potential μ = 0.22 ev and relaxation time τ = sec were determined in order to roughly estimate the experimentally measured carrier density and electrical resistivity. The angle averaged calculation results of Boltzman transport can qualitatively describe the experimental electrical transport and thermoelectric properties (see main text). As described in the main text, the anisotropic properties of electrical resistivity and Seebeck coefficient are so small with respect to crystal orientation because this calculation does not take into account the superzone boundary due to the charge density wave lattice distortion. 5

6 Supplementary Figure 1. Binary phase diagram of In-Se. The starting compositions of grown crystals of In 4 Se 3-δ (δ = 0.65 and 0.22) are of In 67 Se 33 and In 63 Se 37, respectively. Excess In as much as 4 at.% segregated at the top of the crystal ingots. Red horizontal line represents the melting (590 o C) and crystallizing temperature (460 o C) range of δ = 0.22 compound. 6

7 Supplementary Figure 2. a. Crystal structure of In 4 Se 3 : Perspective view of the ab-plane. Covalently bonded In-Se layers are stacked in the a-axis direction. Each covalently bonded layer is bonded to neighboring layers by relatively strong van der Waals interaction. Extra In atoms reside in the interstitial sites between the multivalent In-Se clusters. b. Side view of the bc-plane of In 4 Se 3 crystal. c. XRD pattern of the cross-sectional area of the crystal ingot, In 4 Se 3-δ (δ = 0.22). d. In 4 Se 3-δ (δ = 0.22) crystal ingot grown by the Bridgeman method. Crystallographic c- axis is perpendicular to the growth direction. One grid spacing in the background is 5 5 mm

8 Supplementary Figure 3. Thermoelectric properties of Se-deficient In 4 Se 3-δ crystals of (δ = 0.22 (black squares) and δ = 0.65 (red circles). Open and closed symbols indicate measurements in the ab-plane and along the bc-plane, respectively. a. Temperature-dependent thermal conductivities κ(t). b. Temperature-dependent Seebeck coefficient S(T). c. Temperaturedependent electrical resistivity ρ(t) and power factor defined by S 2 σ (inset). d. Temperaturedependent dimensionless figure-of-merit ZT and effective carrier concentration n Hall (inset). 8

9 Supplementary Figure 4. Boltzmann transport calculation result of the a. electrical conductivity σ, b. Seebeck coefficient S, and c. power factor S 2 σ with respect to chemical potential μ of the In 4 Se 3-δ (δ = 0.25) compound under fixed conditions of temperature T = 600 K and relaxation time of scattering τ = sec. 9

10 Supplementary Figure 5. Temperature-dependent anisotropic transport properties by the Boltzmann transport calculation. a. the carrier density n, b. electrical resistivity σ, and c. Seebeck coefficient S of the In 4 Se 3-δ (δ = 0.25) compound under fixed conditions of chemical potential μ = 0.22 ev and relaxation time of scattering τ = sec. 10