Improved thermoelectric performance of CuGaTe₂ with convergence of band valleys: a first-principles study

Abstract

A high value (1.4) of figure of merit (ZT) of CuGaTe₂ has been experimentally discovered by T. Plirdpring et al. [Adv. Mater. 24, 3622 (2012)]. In order to further enhance its thermoelectric properties, we investigated its electronic structure and thermoelectric properties by first-principles study. Large band-valley number and high convergence of the bottom conduction bands induced a large Seebeck coefficient and a high electrical conductivity of n-type CuGaTe₂. So, for n-type CuGaTe₂, the maximum ZT values 2.1 may be found at 950 K by suitable carrier concentration tuning, which results in a 25% increment in the ZT value compared with p-type CuGaTe₂. Band decomposed charge density calculations indicate that the transport properties are mainly determined by the Cu and Te atoms at the valence-band maximum, in contrast, transport properties are simultaneously affected by the three kind of atoms at the conduction-band minimum. At high temperature, ab initio molecular dynamics calculations demonstrate that Cu atoms precipitated from their crystal matrices lead to a decrease in thermopower. Along the high symmetry point M, the charge density of all atoms is centrosymmetric. Maybe this centrosymmetric electronic structure leads to the conduction band valley convergence at the M point.

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I. Introduction

Thermoelectric materials transform waste heat into electric energy based on thermoelectric effects with low noise, high stability and reliability because there are no moving parts. The widespread applications of thermoelectric devices are limited now mainly due to their lower transforming efficiency.

The efficiency of a thermoelectric device can be improved generally by increasing its thermoelectric figure of merit , where S is thermopower or Seebeck coefficient, T is the temperature, σ is the electrical conductivity, and κ is the thermal conductivity, which written as the sum of lattice and electronic contributions, is κ = κ_l + κ_e. For degenerate semiconductors, the thermopower is proportional to temperature, effective mass m*, and inversely proportional to charge carrier concentration n. In the approximation of energy independent scattering, the relationship is given by:¹

where k_B is the Boltzmann constant, e is the charge of an electron, and h is the Planck constant. So, large thermopower is relative to large effective mass. High electrical conductivity requires a large mobility μ and large carrier concentration n according to the formula below:

σ = neμ. (2)

It is difficult to obtain a high ZT because ZT is a strongly internally contradictory transport property, which requires a combination of a large thermopower found in insulators or semiconductors and a low electric resistivity found in metals. This can be typically only achieved in heavily doped semiconductors combining high electron density of states (DOS) with high carrier concentration, and high mobility.² In addition to high thermopower S and electrical conductivity σ, decreasing thermal conductivity κ is another means to enhance ZT. As κ = κ_l + κ_e, κ_e = LσT (Lorenz number L = π²k_B²/3e²), so increasing σ would increase κ_e, consequently increasing κ, leading to a decrease of ZT. Therefore, the value of electrical conductivity is also a contradictory factor for increasing ZT. These criteria have led to the concept that the ideal material has the electronic structure of a compound semiconductor with the atomic structure of an ‘electron-crystal, phonon-glass’, i.e. high carrier mobility at the same time as low thermal conductivity, suggesting a weak scattering of charge carriers, but a strong scattering of phonons.³ In recent years, high ZT materials have been discovered in oxides,⁴ nanostructured materials,^5,6 skutterudites,^7–9 clathrates,¹⁰ chalcogenides,¹¹ and Zintl phases,¹² indicating that there are many areas yet to research.

CuGaTe₂ is a well-known semiconductor as a promising candidate for thin film solar cells, photovoltaic devices, and so on. In 1997, B. Kuhn and his co-workers first studied the thermoelectric properties of CuGaTe₂.¹³ They found that the thermopower of CuGaTe₂ is relatively low. In 2012, there were three other papers which discussed the thermoelectric properties of CuGaTe₂.^14–16 In ref. 14, CuGaTe₂ exhibits prominent thermoelectric property, not only is the thermopower increased markedly, but also the value of ZT achieved is 1.4. But a lower thermopower was later acquired by Li et al. and Cui et al.^15,16 These experimental results demonstrated rather different thermoelectric properties of CuGaTe₂ because of different carrier concentrations induced by intrinsic defects under different synthetic conditions. How do we improve further its thermoelectric properties? Although Zou et al. studied thermoelectric and lattice vibrational properties of CuGaTe₂ with first-principles calculation,¹⁷ some important thermoelectric properties remain to be carefully studied. We acquired a more accurate band gap with a different exchange potential and different simulation software. At the same time we found that n-type CuGaTe₂ displays better thermoelectric properties due to the convergence of band valleys and no bipolar effect was observed. There was also no bipolar effect in ref. 18 for n-type AgGaTe₂, which has a similar crystal structure and band gap compared to CuGaTe₂. However, in ref. 17, the power factors of n-type and p-type CuGaTe₂ appear similar because of an inaccurate band gap and bipolar effects.

II. Computational details

The structure of CuGaTe₂ was optimized using the Vienna ab initio simulation package (VASP) based on density functional theory (DFT).¹⁹ The local-density approximation (LDA),²⁰ Perdew–Burke–Ernzerhof (PBE) generalized-gradient approximation (GGA)²¹ and projector-augmented-wave (PAW) potentials of Blöchl²² in the implementation of Kresse and Joubert²³ were used. The electronic structure of CuGaTe₂ was calculated by the full-potential linearized augmented plane waves (FLAPW) approach as implemented in the WIEN2k package.^24,25 Since first-principles methods often significantly underestimate the band gap, after the first self-consistency, we employed a modified Becke–Johnso (TB-mBJ) semilocal exchange potential²⁶ which has been known to give much more accurate band gaps than the standard generalized-gradient approximation (GGA). We included the spin–orbit coupling effects (SO) to account for Cu, Ga and Te. The SO effect leads to band splitting and an increase in band number compared with bands in ref. 17.

Ab initio molecular dynamics (MD) calculations on VASP are achieved by the velocity Verlet algorithm with a time step of 3 fs. A 2 × 2 × 2 super cell was built and a 3 × 3 × 1 Gamma centered special k points grid was used. The initial and final temperatures were set at 300 K and 1000 K, respectively.

III. Results and discussions

A. Crystal structure and electronic properties

Compared with the experimental volume of CuGaTe₂ (V = 430.16 ų) in ref. 15, the GGA tends to overestimate the equilibrium volume (V_GGA = 453.85 ų), and the LDA tends to underestimate the equilibrium volume (V_LDA = 417.15 ų). With the different lattice constants optimized by GGA and LDA, different band gaps (0.75 and 1.03 eV, respectively) were obtained, by self-consistent calculation on WIEN2K package with TB-mBJ semilocal exchange potential. Accurate band gap is important for obtaining reliable thermoelectric properties. So, the optimized lattice parameters by LDA, a = 5.934 Å, c = 11.847 Å were chosen to calculate the band structure and transport properties.

Fig. 1(b) shows that the calculated band gap is 1.03 eV, which is close to the experimental value 1.24 eV.¹³ The valence-band maximum (VBM) is located at the Γ point. This is a characteristic common to a number of chalcopyrite materials, which generally show a fair degree of isotropy. The light-band and heavy-band combination can be seen at the VBM. This has been shown to be good for thermoelectric performance. According to the formula , multiple degenerate valleys can produce large DOS effective mass m^*_DOS without explicitly reducing the mobility μ.²⁷ For p-type CuGaTe₂, band valleys appeared only at the Γ point at the VBM. However, for n-type CuGaTe₂, band valleys appeared at the M and Γ points near the conduction-band minimum (CBM) simultaneously, and these band valleys nearly converged. These converged band valleys would be beneficial for improving the thermoelectric properties of n-type CuGaTe₂. Thus, n-type CuGaTe₂ should have a larger m^*_DOS. For example, the effective mass of hole m* = 0.9 m_e and electron effective mass m* = 1.1 m_e were obtained from eqn (1) when the carrier concentration was n = 1 × 10²⁰ cm⁻³ at 800 K.

Fig. 1 (a) The crystal structure of CuGaTe₂, a = 5.93 Å, c = 11.85 Å; (b) the energy band of CuGaTe₂. Top of the valence band is set to zero.

According to the formula σ = neμ, σ is proportional to the carrier concentration n. At the same temperature 670 K, although the carrier concentration of CuGaTe₂ is lower, n = 1.4 × 10¹⁹ cm⁻³, in ref. 14, its electrical conductivity is higher, σ = 1.35 × 10⁴ S m⁻¹, compared with BiCuSeO, n = 1.77 × 10²⁰ cm⁻³, σ = 2.9 × 10³ S m⁻¹.²⁸ In order to discover the inherent character of the high electrical conductivity of CuGaTe₂, the electron localization function (ELF) was used to calculate the bonding properties between Te, Ga and Te, Cu atoms. The calculated isosurfaces of charge are displayed in Fig. 2(a) with the isosurfaces value of 0.75. As can be seen in this figure, the Te and Ga atoms are connected by covalent bonds. These covalent bonds extend along the Te and Ga direction and are connected to all the Te and Ga atoms together. So a covalent bond net is formed in the CuGaTe₂ crystal. This is favorable for electron mobility. The ionic bonds between Cu and Te atoms enable the Cu atoms to provide a larger DOS near the VBM. The sharp DOS shape near the VBM provides an opportunity to generate a larger DOS effective mass for electrical holes and this is beneficial for acquiring a larger Seebeck coefficient.

Fig. 2 (a) ELF graph of CuGaTe₂, isosurface value 0.75; (b) band decomposed charge density from −1 to 0 eV, isosurface value 0.0057; (c) band decomposed charge density from 0 to 1 eV, isosurface value 0.0007.

Bands near the Fermi level strongly affect the transport properties. So band decomposed charge densities near the Fermi level were calculated separately with VASP from −1 to 0 eV and 0 to 1 eV, which are shown in Fig. 2(b) and (c). For Fig. 2(b), the isosurface value varies from F_min = −0.0073 to F_max = 0.0999, and the displayed isosurface level is 0.0057 (F_min and F_max representing the minimum and maximum isosurface values, respectively). In this isosurface level, the charge density is concentrated around the Cu and Te atoms. The charge on both sides of the Te atom is paralleled with the connecting line direction of the two nearest Cu atoms. These indicate that the transport properties of p-type CuGaTe₂ are mainly determined by the interaction between Cu and Te atoms at the VBM. On the other hand, for Fig. 2(c), the isosurface value varies from F_min = −0.00043 to F_max = 0.00237, and the displayed isosurface level is 0.00066. The charge density is distributed around Te, Ga and Cu atoms at the CBM. So the transport properties of n-type CuGaTe₂ are simultaneously affected by the three kinds of atoms at the CBM. This provides more options for engineering conduction bands near the Fermi level.

Conduction band valleys near the Fermi level at the M point are approximately converged. This is attractive for conduction band engineering. So the band decomposed charge density for these bands was calculated with VASP. Looking along the high symmetry points from the A to M direction, i.e., the direction along the central Ga atom in Fig. 3(a) which is perpendicular to the plane of the paper and inwards, the charge density of all the atoms is centrosymmetric. Maybe this centrosymmetric electronic structure leads to the conduction band valley convergence at the M point. Fig. 3(b) gives the two-dimensional representation of the charge density at the M point of the CBM. The two-dimensional charge density is composed of the anti-bonding state between Te, Cu and between Te, Ga atoms. The charge density of Te atoms was mainly distributed on the side away from the two near Cu atoms because of the anti-bonding state. The charge density distributed on the two side of the Te atoms when the Te atoms were between the Ga and Cu atoms. This further confirmed that the transport properties are simultaneously affected by the three kinds of atom at the CBM.

Fig. 3 (a) Band decomposed charge density of conduction bands near the Fermi level at the M point, isosurface value 0.008; (b) two-dimensional representation.

The DOS and partial DOS (PDOS) of atoms, Cu, Ga, Te, are shown in Fig. 4. There are high peaks given by the Cu atoms just below the VBM, which apparently show the impact of heavy valence bands. Increasing DOS near the Fermi level is an effective means of achieving large thermopower. This can be proved by the formula below:²⁹

where n(E) and μ(E) are energy dependent carrier density and mobility, respectively. Forming localized resonant states through doping³⁰ or by increasing band degeneracy via temperature assisted band convergence²⁷ can increase DOS near the Fermi level. There is high DOS near the Fermi level, so CuGaTe₂ is one of the good p-type thermoelectric materials. Fig. 4(a) demonstrates that the valence band edge is composed primarily of Cu atoms, and the PDOS in Fig. 4(b) shows that the valence band is composed primarily of Cu d-orbital character, which indicates that Cu atoms play an important role in increasing DOS near the Fermi level. Te and Ga atoms are hybridized clearly, so they are composed of covalent bonds. This would be beneficial to electron transport, however, it would also lead to high thermal conductivity. When Cu precipitates out of the matrix CuGaTe₂ phase at high temperature above 800 K,¹⁴ the thermal conductivity of CuGaTe₂ decreased markedly due to the scattering of phonons and electrons. Thus, if we need to adjust the hole carrier concentrations to enhance the thermopower of CuGaTe₂, an effective way would be to adjust the contents of Ga, not the Cu atoms.¹⁴ In contrast, the DOS of the conduction band edge is composed primarily of gallium and telluride atoms, PDOS of the conduction band is mainly composed of Ga s-, Te p- and Cu d-orbital characters, yet the role of the Cu d-orbital character is the least important among these three kinds of atom. So, for n-type CuGaTe₂, Cu atoms no longer play an important role in increasing the DOS near the Fermi level. Thus, for this reason, Cu atoms could be substituted by other atoms for band engineering and increasing DOS near the edge of the conduction band to achieve higher thermopower. So CuGaTe₂ can form good thermoelectric materials by both n- and p-type doping. This means that there are more options for enhancing the thermoelectric performance of CuGaTe₂. We can choose appropriate doping atoms to tune its carrier concentration, to increase the local DOS near the Fermi level and the effective mass of the valence or conduction bands, meanwhile reducing the thermal conductivity κ by phonon scattering due to atomic mismatch.¹⁶

Fig. 4 (a) DOS and (b) PDOS for CuGaTe₂. The Fermi level is at zero.

Thermal conductivity is another important factor which can affected the ZT value significantly. Cu atoms can become fast ions in some materials at high temperature, leading to liquid-like thermoelectrics, and decreasing thermal transportation enormously, such as Cu₂Se.³¹ CuGaTe₂ crystal shows high thermal conductivity at low and medium temperature ranges, 24 W m⁻¹ K⁻¹ up to around 50 K, 6.7 W m⁻¹ K⁻¹ at room temperature, and 2.0 W m⁻¹ K⁻¹ at about 670 K. However, above 800 K, the decrease in κ_l is much larger than that based on a 1/T law.¹⁴ At the same time, electrical conductivity in ref. 14 also abnormally decreased at 900 K. In order to find the reasons for the above two phenomena, we simulated the atomic positional changing of CuGaTe₂ with ab initio molecular dynamics from 300 K to 1000 K. Fig. 5 demonstrates snapshots of the ionic positions of Cu, Ga, and Te between layers consisting of Te ions or Cu and Ga ions in the crystal CuGaTe₂. The ions labeled as 0 represent the initial positions; 1 and 2 represent the positions at 891 K and 1000 K, respectively. For the sake of showing the ionic positional changes clearly, ions in the layers around the central ions are all placed in their initial positions. At Fig. 5(a), the Cu ion vibrated to the top-left corner relative to its initial position at 891 K. However, it moved to the bottom-right corner at 1000 K, and almost arrived at the nearest Te-layer below it. Like the Cu ions, the Ga ion vibrated from the top-right to the bottom-left positions between Te-layers as shown in Fig. 5(b). Thus, the Cu ions deviated heavily from their equilibrium positions when they vibrated out-of-order in a large scale between Te-layers. This enables the Cu atoms to precipitate from their crystal matrices and led to the decrease in thermopower.

Fig. 5 Snapshots of ab initio simulated ionic positions of Cu, Ga, and Te by molecular dynamics at initial positions (labeled as 0), 891 K (labeled as 1), and 1000 K (labeled as 2): (a) Cu ion in the center; (b) Ga ion in the center; (c) Te ion in the center.

Along with the increase of random thermal motion, the thermal conductivity should be reduced markedly. This was confirmed by the experimental work in ref. 14, the lattice thermal conductivity κ_l reduced from 6.7 W m⁻¹ K⁻¹ at room temperature to 0.7 W m⁻¹ K⁻¹ at 900 K. Furious random thermal motions would weaken the covalent bonds between Ga and Te atoms at high temperature. This possibly leads to a phase transition and further decrease of the thermal and electrical conductivities.³² The abnormally increased electric resistivity and Seebeck coefficient from 900 K to 950 K in ref. 14 may possibly be induced by such phase transition. The reduced thermal conductivity is another important reason for so high a ZT value in the experimental work.¹⁴ However, at the same time, the increased electrical resistivity from 900 K to 950 K in ref. 14 is a negative factor for further enhancing the thermoelectric performance of CuGaTe₂.

B. Transport properties

The anisotropic transport properties of CuGaTe₂ were calculated based on the calculated electronic structure using the Boltzmann theory. Carrier concentration affects S and σ greatly, so we simulated doping with a rigid band approximation. This method has been used to simulate the transport properties of chalcopyrite materials by Zou et al. and Parker et al.^17,18 The simulated and experimental thermopower values in Fig 7(b) are pretty consistent. Thus, the rigid band approximation should be valid for studying CuGaTe₂ doping. Different structures along different directions can lead to anisotropic properties. The transport properties along the X and Z directions are shown in Fig. 6. Fig. 6(a) shows the anisotropy of at different temperatures. The anisotropy of n-type CuGaTe₂ is moderately effected by carrier concentration, but for the p-type CuGaTe₂, the effect is almost negligible. The electric conductivity is given by eqn (2). The carrier mobility is strongly effected by the band-mass of a single valley:where m^*_b is the band-mass of a single valley. The relationship between the DOS effective mass and the band-mass of a single valley is given by:^27,33,34where C includes orbital degeneracy imposed by the symmetry of the Brillouin zone. Eqn (2) demonstrates that electric conductivity is proportional to the carrier concentration and mobility. Combining eqn (2)–(5), we find, when the carrier concentrations are equal, σ is determined by μ. As the DOS effective mass of the valence band is almost equal along the Γ–X and Γ–Z directions (Fig. 1(b)), so the anisotropy for p-type CuGaTe₂ is almost negligible. For the conduction band, the dispersion along the Γ–X direction is weaker than that along the Γ–Z direction, so is large along the x direction. Regardless of n-type or p-type CuGaTe₂, electric conductivity increases with increasing carrier concentration, which is in agreement with electric conductivity proportional to the carrier concentration. In contrast to , the anisotropy of the thermopower is little effected by changes in the temperature and carrier concentration. The thermopower is more sensitive to carrier concentration at low doping concentration range. Fig. 6(c) shows the anisotropy of the power factor with respect to the relaxation time . The anisotropy of for n-type CuGaTe₂ is larger than that for p-type CuGaTe₂ at higher temperature, and the anisotropy of is mainly due to the anisotropy of . The power factor of n-type CuGaTe₂ is larger than p-type CuGaTe₂, which indicates that the thermoelectric properties for n-type CuGaTe₂ are better than p-type CuGaTe₂. The highest appears along the x direction, which is consistent with crystal anisotropy.

Fig. 6 Transport coefficients of CuGaTe₂ as a function of carrier concentration: (a) electric conductivities relative to relaxation time, (units in 10¹⁹ S m⁻¹ s⁻¹); (b) thermopower, S (units in μV K⁻¹); (c) power factors with respect to relaxation time, (units in 10¹¹ W K⁻² m⁻¹ s⁻¹).

The temperature-dependent transport properties of CuGaTe₂ were calculated to simulate the carrier concentration in ref. 14 based on the calculated electronic structure. However, the calculated includes the scattering rate τ⁻¹. In order to get the particular value of σ, we used the experimental data in ref. 14 to derive the value of τ. At 800 K, the carrier concentration and electrical conductivity are n = 2.4 × 10¹⁹ cm⁻³ and σ = 2.2 × 10⁴ (Ω m)⁻¹. At the same temperature and carrier concentration, the calculated value of is 1.2 × 10¹⁸ (Ω m s)⁻¹. So we can obtain τ = 1.8 × 10⁻¹⁴ s for this sample of CuGaTe₂ at 800 K. In a certain regime, there is an approximate electron–phonon T dependence, σ ∝ T⁻¹. For doping dependence, there is a standard electron–phonon form, τ ∝ n^−1/3.³⁵ This yields τ = 4.2 × 10⁻⁵ T⁻¹ n^−1/3 with τ in s, T in K, and n in cm⁻³. From 900 to 950 K, the experimental results show that the relationship σ ∝ T⁻¹ does not hold. Nevertheless, with the same method, we could yield τ = 3.8 × 10⁻⁵ T⁻¹ n^−1/3 at 950 K with the extrapolated carrier concentration.

For the calculated carrier concentration n, thermopower S as a function of temperature is shown in Fig. 7. Fig. 7(a) shows the simulated (solid line) and experimental (square) temperature dependent values of the carrier concentration n. The simulated and experimental carrier concentrations coincide from 650 K to 800 K. Fig. 7(b) shows the temperature dependent values of the calculated and experimental thermopower. Above all, the calculated band gap 1.03 eV is less than the experimental band gap 1.24 eV, which would result in a small difference between the calculated and experimental thermopower values because we find that the thermopower value calculated with the band structure E_g = 0.75 eV (optimized lattice constants by GGA) is higher than that of the thermopower value calculated with the band structure E_g = 1.03 eV (optimized lattice constants by LDA) at the same carrier concentration. The experimental S values are very close to the simulated values between 430 K and 560 K. Beneath 400 K, the simulated carrier concentration decreased faster than the experimental results, at the same time, the experimental S values decreased distinctly compared with the simulated values, which is possibly due to the increasing ratio of carrier concentration arising from defects (or impurities). At the higher temperature range, the impurity concentration increases because impurity phases exist. Such as, Ga₂Te₅ forms easily as T is elevated to 680 K in the Ga₂Te₃ based alloy systems.³⁶ Cu atoms could precipitate from their matrices,¹⁴ the electron–hole cancellation effect would occur due to thermal excitations at high temperature. All the above factors could be possible reasons for the decreased S values at high temperature.

Fig. 7 Calculated temperature-dependent transport properties of CuGaTe₂: (a) carrier concentration (units in 10¹⁹ cm⁻³); (b) thermopower, S (units in μV K⁻¹).

Electrical conductivity is another important factor which effects the power factor value greatly. Electrical conductivity has an intimate relationship with the carrier concentration. Increasing the carrier concentration of CuGaTe₂ would increase the electrical conductivity, however, the thermopower would decrease along with the increased carrier concentration. Therefore, the power factor could be improved further by adjusting the carrier concentration. In order to derive the maximum values of power factor and ZT, we simulated doping with the rigid band approximation. The carrier-concentration-dependent electrical conductivity, thermopower, power factor, and ZT are shown in Fig. 8. The values of electrical conductivity σ increased with increasing carrier concentration. At the same carrier concentration, the electrical conductivity at 800 K is larger than that at 950 K, and the electrical conductivity of n-type CuGaTe₂ is a little higher than that of p-type CuGaTe₂ at the carrier concentration range from 1 × 10¹⁹ to 1 × 10²¹ cm⁻³. Compared with p-type CuGaTe₂, n-type CuGaTe₂ not only has high electrical conductivity, but also has a large thermopower at the same temperature and carrier concentration (Fig. 8(b)). These lead to much higher power factor values compared with the p-type results (Fig. 8(c)). In order to conveniently compare, the simulated S values were reduced in proportion to their ratio with the experimental values at 800 and 950 K, respectively. The maximum values of n-type power factors were 1.7 times and 1.6 times higher than the p-type maximum results at 800 and 950 K, respectively. This means that the n-type CuGaTe₂ may acquire a higher ZT value.

Fig. 8 Calculated carrier concentration dependent transport properties of CuGaTe₂ with different temperatures: (a) electrical conductivity (units in 10⁴ S m⁻¹); (b) thermopower, S (units in μV K⁻¹); (c) power factors, S²σ (units in mW K⁻² m⁻¹); (d) ZT.

As an estimate of thermoelectric conversion efficiency, the thermoelectric figure of merit can be expressed as , which is shown in Fig. 8(d). The experimental κ values in ref. 14 are used for calculation convenience. As κ = κ_l + κ_e, κ_e = LσT, so increasing σ would increase κ_e, consequently increasing κ, thus leading to a decrease of ZT. In order to achieve more accurate κ values, the value of κ_e used here was increased with increasing electrical conductivity. Under this circumstance, the calculated maximum ZT value is 1.5 for p-type CuGaTe₂ at 950 K, which only increased 0.1 compared with the experimental value (1.4) when the carrier concentration decreased from 4 × 10¹⁹ to 2.3 × 10¹⁹ cm⁻³. When the carrier concentration increased further from 4 × 10¹⁹ cm⁻³, the ZT value decreased gradually. This is consistent with the experimental results. For example, comparing the ZT values in ref. 14 and 15, we find that their ZT values decreased from 0.5 to 0.48 at 700 K when the carrier concentration increased from 1.04 × 10¹⁸ to 2.05 × 10¹⁹ cm⁻³ at room temperature. Comparing ZT and carrier concentration values in ref. 14 and 16, we can see a similar relationship between the carrier concentration and ZT values. However, for the n-type doped CuGaTe₂, the calculated maximum ZT values are 1.2 and 2.1 at 800 and 950 K, respectively, corresponding to carrier concentrations of 4.8 × 10¹⁹ and 2.8 × 10¹⁹ cm⁻³. This shows that the maximum ZT value of CuGaTe₂ could increase from 1.5 to 2.1 by appropriately tuning its carrier concentration with n-type doping, which means a 25% increment in ZT values.

IV. Conclusion

In summary, the electronic structure and transport properties of CuGaTe₂ were studied by first-principles calculations and Boltzmann theory. Several aspects of our work can be generalized below. (1) Band decomposed charge density calculation indicates that the transport properties of p-type CuGaTe₂ are mainly determined by the interaction between Cu and Te atoms at the VBM. However, at the CBM, transport properties of n-type CuGaTe₂ are mainly affected simultaneously by Cu, Ga, and Te, the three kinds of atom. This provides more options to engineer conduction bands near the Fermi level. (2) DOS and PDOS calculation demonstrate that Cu and Te atoms play an important role for large Seebeck coefficients for p-type CuGaTe₂. Ga-s, Te-p and Cu-d electrons are the main components of PDOS near the CBM. This is consistent with the band decomposed charge density calculation. We can choose appropriate doping atoms to tune its carrier concentration, to increase the local DOS near the Fermi level, meanwhile reducing the thermal conductivity κ by phonon scattering. (3) Above 900 K, the covalent bonds between Te and Ga atoms become weakened. This is a two-edged factor for further enhancing thermoelectric performance of CuGaTe₂ because it would lead to both electrical and thermal conductivity being reduced simultaneously. (4) Compared with p-type CuGaTe₂, the ZT value increased by 25% at 950 K for n-type CuGaTe₂.

Acknowledgements

This research was sponsored by the National Natural Science Foundation of China (no. 51371076, no. U1204112), Program for Innovative Research Team (in Science and Technology) in University of Henan Province (no. 13IRTSTHN017), and Foundation of Henan Educational Committee (no. 14A140016, 14A430029, 14B140003).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c4ra02595d

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