Tuning the carrier concentration to improve the thermoelectric performance of CuInTe2 compound

The electronic and transport properties of CuInTe2 chalcopyrite are investigated using density functional calculations combined with Boltzmann theory. The band gap predicted from hybrid functional is 0.92 eV, which agrees well with experimental data and leads to relatively larger Seebeck coefficient compared with those of narrow-gap thermoelectric materials. By fine tuning the carrier concentration, the electrical conductivity and power factor of the system can be significantly optimized. Together with the inherent low thermal conductivity, the ZT values of CuInTe2 compound can be enhanced to as high as 1.72 at 850 K, which is obviously larger than those measured experimentally and suggests there is still room to improve the thermoelectric performance of this chalcopyrite compound.

The electronic and transport properties of CuInTe 2 chalcopyrite are investigated using density functional calculations combined with Boltzmann theory. The band gap predicted from hybrid functional is 0.92 eV, which agrees well with experimental data and leads to relatively larger Seebeck coefficient compared with those of narrow-gap thermoelectric materials. By fine tuning the carrier concentration, the electrical conductivity and power factor of the system can be significantly optimized. Together with the inherent low thermal conductivity, the ZT values of CuInTe 2 compound can be enhanced to as high as 1.72 at 850 K, which is obviously larger than those measured experimentally and suggests there is still room to improve the thermoelectric performance of this chalcopyrite compound.
which includes the Seebeck coefficient S , the electrical conductivity σ , the electronic thermal conductivity e κ , and the lattice thermal conductivity L κ . In principle, the ZT value can be improved by utilizing some strategies to increase the power factor ( 2 S σ ) and/or decrease the thermal conductivity ( ) e L κ κ + . However, it is usually very challenging to do so because of strong interdependence of these transport coefficients. Over the past several decades, major effort has been directed towards the optimization of current TE materials such as Bi 2 Te 3 , SiGe alloy, PbTe and their doped compounds, as well as the exploration of novel high-performance compounds [1,2,3,4,5,6,7,8]. Usually, the state-of-the-art TE materials with higher ZT values are limited to only a few narrow-gap semiconductors and most of them were developed in the 1960s [9]. In order to further improve the TE performance, we need to explore new materials such as chalcopyrites CuGaTe 2 [10,11] and AgGaTe 2 [12,13]. This kind of compounds were found to exhibit larger ZT value at high temperature region, which can be explained by significant decrease in the thermal conductivity at increased temperature.
As a typical chalcopyrite compound, the thermoelectric performance of CuInTe 2 has attracted much attention recently since it inherently has larger Seebeck coefficients and lower thermal conductivity. Liu et al. [14] reported that CuInTe 2 is a promising thermoelectric material with a larger  [15]. The measured band gap is 1.04 eV, which is much larger than those of traditional thermoelectric materials (for example, 0.11 eV for Bi 2 Te 3 [16] and 0.14 eV for Sb 2 Te 3 [17]). It should be mentioned that larger band gap usually leads to relatively small electrical conductivity compared with those of state-of-the-art materials. In this regard, tuning carrier concentration through element doping could be an effective way to optimize both the electrical conductivity (σ ) and the power factor ( 2 S σ ). Cheng et al. [18] reported that the carrier concentration of CuInTe 2 is greatly enhanced by doping the system with Cd, which leads to an enhancement of ZT value by more than 100% at room temperature and around 20% at 600 K. In addition, Kosuga et al. [19] found that the reduction in the Cu content acts as hole doping and the sample of Cu Our theoretical approach combines the first-principles calculations and Boltzmann transport theory. The structure optimization and electronic properties of CuInTe 2 are calculated by using projector augmented-wave (PAW) method [20] as implemented in the Vienna ab initio simulation package (VASP) [21,22,23]. We use the hybrid functional in the form of Heyd-Scuseria-Ernzerhof (HSE). The Brillouin zone is sampled by a 7 × 7 × 4 k-mesh and a plane wave cutoff energy of 350 eV is adopted in the calculations. The system is fully relaxed until the magnitude of the forces acting on all the atoms become less than 0.01 eV/Å. The electronic transport coefficients are derived by using the semi-classical Boltzmann theory [ 24 ], where the carrier concentration and temperature dependence of relaxation time is obtained by fitting the existing experimental data.
The crystal structure of CuInTe 2 is shown in Figure 1, which exhibits typical chalcopyrite structure (space group I-42d) with 16 atoms per unit cell. Each Cu and In atom is connected by 4 Te atoms, forming diamond-like structure. The experimentally measured lattice constants of CuInTe 2 are a = b = 6.20 Å and c = 12.44 Å [15], which are exclusively used in the following calculations. It is found that the Cu and In atoms form ordered long-range cubic framework while the Te atoms form localized short-range non-cubic lattice distortions. Such special structure characteristic can block the heat transport while has less effect on the electron conduction, which may be very beneficial to the thermoelectric performance of CuInTe 2 , as well as other chalcopyrite compounds [25].
Since the standard density functional theory (DFT) with the local-density approximation (LDA) or generalized gradient approximation (GGA) underestimates the band gap of chalcopyrite compounds [11,26], we use the HSE hybrid functional to calculate the electronic properties of CuInTe 2 compound. Indeed, Cheng et al. [18] reported that due to the substitution of Cd at In sites, the carrier concentration is greatly increased, leading to greatly enhanced electrical conductivity and power factor.
Based on the band structure, we are able to evaluate the transport coefficients by using the semi-classical Boltzmann theory [24] and the rigid-band approach [30]. values of them (~1600 µV/K) are much larger than those of most conventional thermoelectric materials due to relatively larger band gap of CuInTe 2 . Unlike the Seebeck coefficient which is independent of the relaxation time τ , the electrical conductivity σ can only be calculated with respect to τ . The room temperature σ τ as a function of chemical potential µ is plotted in Figure 3(b). We see there is a sharp increase of σ τ around the band edge and it is more pronounced for the p-type system, which may be benefited from the band degeneracy at the VBM. In order to evaluate the particular value of σ , we need to know the relaxation time which is usually very complicated to calculate since it depends on the detailed scattering mechanism involved. For simplicity, here the relaxation time is obtained by fitting the experimentally measured electrical conductivity [19,31], and its carrier concentration and temperature dependence can be expressed as: Note such treatment of relaxation time has been generally used for other thermoelectric materials such as CuGaTe 2 , AgGaTe 2 and ZnO system [11,13,32].
For the CuInTe 2 compound, the averaged value of constant A in Equation (2) where the Lorenz number L can be expressed as: Here η is the reduced Fermi energy, and r is the scattering parameter which is 1 2 − for acoustic-phonon scattering. The Fermi integral given by: The calculated Lorenz number of CuInTe 2 is 1.52 ~ 1.71×10 −8 V 2 /K 2 in the carrier concentration range from 1.0×10 19 to 1.0×10 20 cm −3 , which is basically a constant and indicates that the electronic thermal conductivity should exhibit similar behavior as that of electrical conductivity and thus is not shown here. Inserting all these transport coefficients into Equation (1) and using a room temperature lattice thermal conductivity of 4.50 W/mK fitted from experimental data [33], we are now able to evaluate the thermoelectric performance of CuInTe 2 compound. Figure 3(d) plots the room temperature ZT value as a function of chemical potential. We see there are two remarkable peaks around the Fermi level, which is 0.15 at optimized concentration of 2.69×10 19 cm −3 for the p-type CuInTe 2 , and 0.10 for the n-type system at carrier concentration of 9.96×10 17 cm −3 . The relatively larger ZT value of p-type CuInTe 2 is due to the fact that p-type system has larger electrical conductivity compared with n-type system while the Seebeck coefficients and electronic thermal conductivities of them are similar at optimized carrier concentration.
We now discuss the temperature dependence of the thermoelectric performance. Figure 4 plots the lattice thermal conductivity of CuInTe 2 as a function of temperature (solid line), which is obtained by fitting the available experimental data [33] at different temperatures (black squares) and can be expressed by: 1729.14 1.27 It can be seen that the L κ of CuInTe 2 decreases quickly from 4.0 to 0.94 W/mK as the temperature increases from 300 to 700 K. The extremely low thermal conductivity at higher temperature shows its great potential as TE material. In Figure 4, we also plot the calculated ZT value of n-type and p-type CuInTe 2 as a function of temperature