The InTe has intrinsically low lattice thermal conductivity κL originating from the anharmonic bonding of In1+ ion in the lattice, which scatters the phonons. Here we report the enhancement of thermoelectric properties in Te-deficient InTe1−δ (δ = 0, 0.01, 0.1, and 0.2) polycrystalline compounds by lattice softening and energy band gap opening. Te-deficiency gives rise to more weak chemical bonding between In1+ atoms and In3+Te2− clusters than those of pristine InTe, resulting in the reduction of κL near the room temperature. The weak ionic bonding is confirmed by the increase of lattice volume from the X-ray diffraction and lattice softening by the decrease of Debye temperature with increasing Te-deficiency. We observed the low lattice thermal conductivity κL of 0.53 W m−1 K−1 at 300 K for InTe0.99, which is about 25 % decreased value than those of InTe. The Te-deficiency also induces energy band gap so that the electrical resistivity and Seebeck coefficient are increased due to the decrease of carrier concentration. Temperature-dependent thermoelectric properties shows the high Seebeck coefficient at high temperature and high electrical conductivity near room temperature, resulting in the temperature-insensitive high power factor S2σ over a wide temperature range. Owing to the temperature-insensitive high power factor and intrinsic low lattice thermal conductivity by Te-deficiency, the thermoelectric performances of figure-of-merit ZT and engineering ZTeng are enhanced at mild temperature range (≤550 K).
Thermoelectricity is very promising technology for an energy harvesting and environmentally friendly cooling technology because thermoelectric materials can directly convert waste heat into electricity and drive temperature difference at two ends of thermoelectric materials that is applied to the solid state cooling. The performance of thermoelectric (TE) materials is defined by the dimensionless figure-of-merit ZT = S2σT/(κel + κL), where S, T, σ, κel, and κL are the Seebeck coefficient, absolute temperature, electrical conductivity, electronic thermal conductivity, and lattice thermal conductivity, respectively. In order to achieve the high performance, it needs to be increased the power factor PF = S2σ as well as to be decreased the lattice thermal conductivity κL.
The enhancement in PF has been reported through the formation of resonant level,1 the band convergence,2 and the carrier filtering effect.3 The effective way to reduce κL is to induce phonon scattering by nano-structuring,4 anharmonicity of phonons,5 and nano-scale grain boundary,6 nano-precipitation,7 and point defects.8 The optimization of carrier concentration for materials with intrinsically low κL are good approach for high efficiency of TE materials. Recent investigation shows that the phonon interaction with lone pair electrons results in low lattice thermal conductivity due to lattice anharmonicity. For example, the cubic I-V-VI2 (where I = Cu, Ag, Au or alkali metal; V = As, Sb, Bi; and VI = Se, Te) compounds have intrinsically low κL due to strong anharmonicity originating from the lone-pair electrons of the group V atoms.9,10 The s2 electrons on the group V atoms do not form sp3 hybridized bonds and are isolated, which can be easily distorted by lattice vibrations leading to the lattice anharmonicity.10 The enhancement in TE properties of AgSbSe2-based compounds have been mainly focused on the carrier concentration optimization by various dopants such as Ge,11 Zn,12 Sb-deficient13 and other doping materials.14,15
InTe exhibits the ultra low κL due to rattling vibrations of In1+ atoms with the 5s2 lone pair electrons.16 The structure of InTe is the tetragonal with the space group I4/mcm composed of In+-In3+-Te2−.17 The In3+ and Te2− ions form sp3 hybridized bonding but the In1+ ions are loosely bonded ionically to the In3+-Te2− chains. Here, we investigated the thermoelectric properties on the Te-deficiency effect in p-type InTe1−δ (δ = 0.0, 0.01, 0.1, and 0.2) compounds. We observed the enhancement of power factor over a wide temperature range due to the increase in Hall mobility, while the compounds maintain intrinsically low κL of 0.53 W m−1 K−1 at 300 K for InTe0.99 which is about 25 % lower value than those of pristine InTe. The low κL in Te-deficient compounds may come from the weak bonding strength, confirmed by the Debye temperature and lattice parameters. Owing to the improved power factor and decreased lattice thermal conductivity, the Te-deficient compounds of InTe1−δ enhances ZT and engineering ZTeng values over a wide temperature range.
II. EXPERIMENTAL AND THEORETICAL DETAILS
The Te-deficient InTe1−δ compounds were prepared by direct melting and hot press sintering. Stoichiometric elements of In (99.999 %) and Te (99.999 %) shots of InTe1−δ (δ = 0.0, 0.01, 0.1, and 0.2) were loaded in quartz ampoules and sealed under a high vacuum 10−5 torr environment. The quartz ampoules were heat treated in a rocking furnace at 850°C over 24 hours and slowly cooled to room temperature for 30 hours. The ingots were pulverized into fine powders in an agate mortar and the powders were sintered by a vacuum hot-press sintering machine in a graphite mold at 510 °C for 1 h under a uniaxial pressure of 50 MPa. The sample densities of the sintered compounds have a range from 6.19 g/cm3 to 6.23 g/cm,3 which is close to the theoretical density (6.29 g/cm3) with high relative densities (98 ∼99 %). The sintered samples were cut and polished for thermoelectric properties measurement. We measured the samples along the parallel direction to the uniaxial direction of the hot-press.
The structural properties were identified by the powder X-ray diffraction (XRD) using a Cu Kα radiation (D8 Advance, Bruker, Germany). The heat capacity Cp measurements for the estimation of Debye temperature ΘD were conducted by a physical property measurement system (PPMS, Dynacool-14T, Quantum Design, U.S.A.). The electrical resistivity ρ and Seebeck coefficient S measurement were carried out by a ZEM-3 (ULVAC, Japan) under 5N helium environment. The thermal diffusivity λ was measured by a laser flash method (LFA-456, Netzsch, Germany) and thermal conductivity κ was obtained by the relation κ = dsλCp, where ds, λ, and Cp are the sample density, thermal diffusivity, and specific heat, respectively. The Hall coefficient RH for carrier concentration and Hall mobility μH were measured by a PPMS using a four-probe contact method with the magnetic field sweeping from to 5 T.
C. Theoretical details
In order to investigate the electronic band structure, we used the VASP code18–20 and the projector-augmented plane wave (PAW) method21 within the Perdew-Burke-Ernzerhof generalized gradient approximation (GGA)22 for the exchange-correlation functional. For structural relaxations, the reciprocal-space energy integration was performed by the Methfessel-Paxton technique.23 We used a 9×9×9 k-points mesh and a 520 eV energy cutoff of the wave function. The convergence criterions of the electronic self-consistency for energy and forces set were chosen as 10−6 eV and 10−2 eV/Å, respectively. Magnetism was included by considering spin-polarized calculations. The calculations of the total energies with structure relaxations were performed by the tetrahedron method incorporating a Blöchl correction.24 The electronic band structure was obtained from Kohn-Sham eigenvalues estimated by a static selfconsistent calculation along high symmetry lines in the Brillouin zone.25
III. RESULTS AND DISCUSSION
The X-ray diffraction (XRD) patterns and lattice volumes of Te-deficient InTe1−δ (δ = 0.0, 0.01, 0.1, and 0.2) compounds are presented in Fig. 1(a) and (b), respectively. The diffraction peaks of all the compounds represent single phase with the tetragonal structure (space group I4/mcm) with no other impurity peaks. The lattice parameters are listed in Table I. The a-axis lattice parameters are monotonically increased with increasing Te-deficiency. The c-axis lattice parameters are also increased except the case of δ = 0.01 compound. Inset of Fig. 1(b) presents the crystal structure of stoichiometric InTe (upper left) and InTe1−δ (lower right) compounds, where the Te-defect is indicated as sky blue ball. In many cases, self-defect structure shrinks crystal lattice resulting in the decrease of lattice parameters. On the other hand, the increasing of lattice parameters and lattice volume indicates that the Te-deficiency itself decreases c-axis lattice parameter in δ = 0.01 but the bond strength becomes weak with increasing Te-deficiency.
|δ .||a (Å) .||c (Å) .||V (Å) .|
|δ .||a (Å) .||c (Å) .||V (Å) .|
The weak bond strength or lattice softening decreases Debye temperature ΘD. The temperature-dependent specific heat Cp is presented in Fig. 2. It rapidly saturates at high temperature region which follows Dulong-Petit law. The Debye temperatures are estimated from the Debye T3 law. The Cp is represented by Cp = γT + βT3 where .26 The Debye temperature ΘD of the compounds are listed in Table II. The ΘD of stoichiometric InTe is 101 K is decreased down to 92 K for δ = 0.1 and 0.2 compounds, which reveals the strengths of chemical bonding of Te-deficient compound become weaker than those of stoichiometric InTe. Both the decrease in ΘD and the increase in lattice volume of Te-deficient compounds are originated from the weakening of bonding strength between In+ atoms and In3+Te2− clusters.
|δ .||ΘD (K) .||S (μV/K) .||nH (1019 cm−3) .||μH (cm2 V−1 s−1) .||m* (me) .||PF (mW m−1 K−2) .|
|δ .||ΘD (K) .||S (μV/K) .||nH (1019 cm−3) .||μH (cm2 V−1 s−1) .||m* (me) .||PF (mW m−1 K−2) .|
Figure 3 presents the temperature-dependent thermoelectric properties of electrical resistivity ρ, electrical conductivity σ, Seebeck coefficient S, and power factor PF = S2/ρ of the InTe1−δ (δ = 0.0, 0.01, 0.1, and 0.2) compounds. The ρ(T) in Fig. 3(a) reveals the metallic behavior with temperature; decreasing with decreasing temperature. The S(T) of the compounds also shows the metallic behavior with positive p-type conduction of carriers, as shown in Fig. 3(c). The ρ(T) and S(T) are systemically increased with increasing Te-deficiency concentrations. From the Hall resistivity measurement ρxy, we obtained the Hall carrier concentration nH = −1/(RHe) and Hall mobility μH = RH/ρ, where RH is the Hall coefficient RH = ρxy/H (H = magnetic field), as listed in Table II. For increasing Te-deficiency, the room temperature Hall carrier concentration nH is decreased for about 5 ∼6 times than those of pristine InTe. The increase of electrical resistivity and Seebeck coefficient for Te-deficient compounds is attributed from the decrease of Hall carrier concentration. Because of the decrease of Hall carrier concentration, the Hall mobility μH is increased for about 2 times due to the suppression of electron-electron scattering in Te-deficient compounds.
Interestingly, the slope of the ρ(T) for the Te-deficient compounds changes near 470 K in Fig. 3(a). When we examine the temperature exponent of the resistivity by σ = sigma0 + ATn, the temperature exponent n is abruptly changed as shown in Fig. 3(b). For pristine InTe compound, σ ∝ T−0.28 at T ≤ 420 K and the exponent is decreased to σ ∝ T−1.36 at T ≥ 420 K. It is known that the temperature exponent of electrical conductivity should have n ≃1.5 for ionization scattering and n ≃−1.5 for acoustic phonon scattering.27 Small critical exponent n = −0.28 implies the mixed scattering of ionization and acoustic phonon scattering. Abrupt increase of critical exponent n = −1.36 at 420 K indicates the different scattering process for enhancement of acoustic phonon scattering.
For increasing Te-deficiency concentration, the critical exponents are decreased as n = −0.88 (δ = 0.01), and respectively, implying that the acoustic scattering is increased with increasing Te-deficiency. In addition, the crossover temperature from ionization to acoustic scattering is increased to 470 K from 420 K (InTe). Comparing to the pristine compound, the acoustic phonon scattering becomes dominant in Te-deficient compounds (n ≃−1.97 ∼−2.1) at high temperature. The enhancement of acoustic scattering process can be understood by the lattice softening as we discussed in the above. The weak bond strength by Te-deficiency gives rise to increase of carrier scattering by lattice vibration.
Within the parabolic band assumption, we estimated the effective mass of carrier as following relation:28
where kB, h, e, m*, T, and n are the Boltzmann constant, Plank constant, elementary charge, effective mass of carrier, absolute temperature, and carrier concentration, respectively. The effective masses m* of the Te-deficient compounds are decreased (∼0.55 me) comparing with the pristine compound (0.78 me) but do not show systematic behavior with Te-deficient concentrations.
Owing to the enhancement of Seebeck coefficient at high temperature and high electrical conductivity at room temperature, the power factor showed improved value below 500 K for Te-deficient compounds, as presented in Fig. 3(d). When we compare the power factor with the Hall mobility in Table II, the enhancement in PF of Te-deficient compounds below 500 K can be attributed to the increase in the carrier mobility μH.
In order to understand the transport properties, we performed theoretical electronic band structures of stoichiometric InTe and InTe1−δ (δ = 0.25) in Fig. 4(a) and 4(b), respectively. The stoichiometric InTe exhibits band touching between conduction and valence bands at the M- and Z-points. The band touching at the points is topologically trivial because small perturbation of Te-vacancy opens energy band gap as shown in Fig. 4(b). There is a direct band gap 0.15 eV at the M-point while in-direct zero-gap is observed along the Γ-Z direction. The semimetallic zero-gap energy is consistent with the metallic behavior of ρ(T). The increase of electrical resistivity and decrease Hall carrier concentration in Te-deficient compounds than those of InTe are understood by the band gap opening at the M-point. Small Seebeck coefficient in InTe at room temperature can be ascribed by the semimetallic band character. The energy band gap opening attributes to the increase of Seebeck coefficient in Te-deficient compounds.
The Pisarenko relation of Seebeck coefficient S versus Hall carrier density nH is depicted in Fig. 5. It relatively follows well with the single parabolic band assumption with effective mass of 0.6 me. The energy band dispersion at the band touching M- and Z-points can be regarded as quadratic dispersion not Dirac-like linear band dispersion. Therefore, we can apply the single parabolic band assumption for obtaining Lorenz number and lattice thermal conductivity from the Wiedemann-Franz law. In metallic or semi-metallic system, the electronic thermal conductivity follows the Wiedemann-Franz law by κel = L0Tσ, where L0 is the Lorenz number from the Drude model: W Ω K−2. Because the Te-deficient compounds have small band gap and the compounds follows single parabolic band model, we should calculate the Lorenz number within the single parabolic model with acoustic phonon scattering using following formalism:29,30
where Fn(η) is the Fermi integral and the η is the reduced electrochemical potential which is available from the temperature dependent Seebeck coefficient as given by:
The Lorenz number L in terms of temperature and η values can be calculated by fitting with Eq. (3):
where the r = − 1/2 for acoustic phonon contribution. The calculated Lorenz number L(T) are depicted in Fig. 6(a). The L(T) of Te-deficient compounds (δ = 0.01, 0.1, and 0.2) are smaller than those of stoichiometric InTe, indicating different chemical potential energy from the InTe. Using the Lorenz number, we obtained the lattice thermal conductivity κL as shown in Fig. 6(b) (open symbols).
While the electronic contribution of thermal conductivity κel of stoichiometric InTe has 0.13 W m−1 K−1, the κel of Te-deficient compounds is less than 0.05 0.13 W m−1 K−1, indicating that the acoustic phonon contribution is significant in thermal conductivity for Te-deficient compound. When we consider the semimetallic energy band calculation in 4, the κ does not exhibit the bipolar diffusion effect at high temperature. It is caused by dominant contribution of acoustic phonon scattering in thermal conductivity.
Near room temperature, the κL(T) of Te-deficient compounds is lower than the one of stoichiometric InTe. The lowest κL is observed 0.53 W m−1 K−1 at 300K for δ = 0.01, which is about 25 % lower than those of InTe. When the heat conduction is dominated by acoustic phonon scattering, the κL(T) for anharmonic Umklapp processes is represented by following relation:31
where A is a pre-factor, is the average mass of an atom in the crystal, δ3 is the volume per atom, n is the number of atoms in the primitive unit cell, and γ is the high temperature limit of Grüneisen parameter.
The low κL values of Te-deficient InTe1−δ compounds is associated with the decrease in Debye temperature, as listed in Table II because . In addition, as we pointed out, the increase of lattice volume indicates lattice softening in Te-deficient compounds. The weakening of chemical bond strength owing to the Te-vacancy contributes to weak chemical bonding between In1+ atoms and In3+Te2− chains, resulting in the reduction of κL. The acoustic phonon scattering, which is observed in the temperature exponent of σ(T) as presented in Fig. 3(b), also related with the decrease of κL.
Owing to the reduction of lattice thermal conductivity κL and enhancement of power factor at intermediate temperature range (T ≤ 500 K), the thermoelectric figure-of-merits ZT of the Te-deficient compounds are enhanced, as shown in Fig. 7(a). Even though high temperature ZT values of the Te-deficient compounds are lower than the pristine InTe, because of the temperature-insensitive power factor and low thermal conductivity over a wide temperature range, the engineering ZT values of the Te-deficient compounds are enhanced as shown in Fig. 7(b), where the engineering ZTeng is defined by:
In summary, we demonstrate that the Te-deficiency in InTe1−δ decreases lattice thermal conductivity κL. The decrease of Debye temperature ΘD and the increase of lattice volume with increasing Te-deficiency InTe1−δ (δ = 0.01, 0.1, and 0.2) originate from the weakening of chemical bond strengths and lattice softening. The temperature exponent of electrical conductivity σ(T) shows that the acoustic phonon contribution in electrical and phonon transport becomes dominant in Te-deficient compounds. For Te-deficient compounds, the energy band gap is opened while the pristine InTe has semimetallic energy band structure. Opening of small energy band gap increases Seebeck coefficient, thereby the power factor of the Te-deficient compounds are improved below 470 K. The enhancement of power factor is related with the increase of Hall mobility. Owing to the enhancement of power factor at intermediate temperature range and reduction of lattice thermal conductivity over a wide temperature range, the ZT and engineering ZTeng values are increased for Te-deficient compounds. This result suggests that the vacancy control and lattice softening are important criteria to enhance thermoelectric performances.
This research was supported by the Nano-Material Technology Development Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011-0030147) and by the Materials and Components Technology Development Program of MOTIE/KEIT (10063286).