⇦Chinese Physics Letters, 2020, Vol. 37, No. 1, Article code 017102 Electronic Structures and Thermoelectric Properties of ZnSb Doped with Cd and In from First Principles Calculations * Kai Zhou (周凯)**, Ting Zhang (章婷), Bin Liu (刘斌), Yi-Jun Yao (姚义俊) Affiliations School of Physics and Optoelectronic Engineering, Nanjing University of Information Science and Technology, Nanjing 210044 Received 7 September 2019, online 23 December 2019 *Supported by the National Natural Science Foundation of China under Grant No 11605091, and the Scientific Research Foundation of Nanjing University of Information Science and Technology under Grant No 2243141701009.
**Corresponding author. Email: kaizhou@aliyun.com Citation Text: Zhou K, Zhang T, Liu B and Yao Y J 2020 Chin. Phys. Lett. 37 017102    Abstract Thermoelectric properties of pure, Cd- and In-doped ZnSb are studied by first principles calculations of electronic structures and the semi-classical Boltzmann transport theory. The doping of Cd or In at the Zn lattice site slightly increases the lattice parameters due to the larger atomic radii of Cd and In compared with that of Zn. Cd or In doping also apparently increases the interatomic distances between the dopant atoms and the surrounding atoms. The power factor of n-type ZnSb is much larger than that of p-type ZnSb, indicating that n-type ZnSb has better thermoelectric performance than p-type ZnSb. After the doping of Cd or In, the power factor reduces mainly due to the decrease of the electrical conductivity. The temperature dependences of the Seebeck coefficient and the power factor of pure, Cd- and In-doped ZnSb are related to carrier concentrations. DOI:10.1088/0256-307X/37/1/017102 PACS:71.15.Mb, 72.20.Pa, 85.80.Fi © 2020 Chinese Physics Society Article Text The binary compounds Zn$_{4}$Sb$_{3}$ and ZnSb are highly promising thermoelectric materials in the temperature range of about 473–673 K due to their good thermoelectric performance[1,2] and abundance of raw materials. The thermoelectric performance is related to the figure of merit ${\rm ZT}={S^{2}\sigma T} / \kappa$, where $S$ is the Seebeck coefficient, $\sigma$ is the electrical conductivity, $T$ is the absolute temperature, and $\kappa$ is the thermal conductivity. The ZT values of Zn$_{4}$Sb$_{3}$ were reported to be 1.3 at about 670 K[3,4] and 1.4 at about 740 K.[5] The ZT values of ZnSb were reported to be 0.6–0.8 at 573 K for the samples prepared by quenching and mechanical grinding methods[6] and to be 0.63 at 573 K for the samples prepared by mechanical alloying method.[7] By doping with Cu and containing Zn$_{3}$P$_{2}$, the ZT value of ZnSb increased up to greater than 0.9.[8] An even higher value of 1.15 was achieved by doping with Ag and containing in situ formed Ag$_{3}$Sb.[9] Although Zn$_{4}$Sb$_{3}$ has higher ZT values than ZnSb, the thermal stability of Zn$_{4}$Sb$_{3}$ is a problem for its practical use. Zn$_{4}$Sb$_{3}$ tends to decompose to Zn and Sb or ZnSb and Zn during thermal cycling.[10–13] In contrast, ZnSb is stable in a large temperature range. Furthermore, the thermoelectric performance of ZnSb can be improved by doping and nanostructuring.[7–9,14] These advantages have increased the application prospects of ZnSb as a promising thermoelectric material in the intermediate temperature range.[15,16] ZnSb is a stoichiometric compound which is unlike Zn$_{4}$Sb$_{3}$. Zn$_{4}$Sb$_{3}$ has Zn vacancies and interstitials in its lattice framework,[1,11] whereas ZnSb crystallizes in an orthorhombic Pbca framework without inherent vacancies or interstitials. Several first principles calculations have been performed on ZnSb. Benson et al.[17] proposed a covalent bonding scenario with a weak ionicity for ZnSb based on their first principles calculations. Bjerg et al.[18] carried out first principles calculations to investigate intrinsic point defects in ZnSb and found negatively charged Zn defects responsible for its p-type conductivity. The influence of the exchange-correlation functional on the electronic properties of ZnSb was studied by Niedziółka et al.[19] First principles calculations were also used to predict novel ZnSb polymorphs with improved thermoelectric properties by Amsler et al.[16] In this work, we carry out first principles calculations to investigate the electronic structures and thermoelectric properties of pure, Cd- and In-doped ZnSb. The calculated results can give some guidance on improving the thermoelectric properties of ZnSb via doping. The calculations of electronic structures were carried out using the ABINIT package[20] with the projector augmented wave (PAW) method.[21] The exchange-correlation function was described in the Perdew–Burke–Ernzerhof (PBE) scheme with generalized gradient approximation (GGA).[22] A cutoff energy of 30 Ha was adopted for the plane-wave basis expansion. The Brillouin zone was sampled using Monkhorst–Pack[23] k-point meshes of $2\times 4\times 4$. The cutoff energy and k-point meshes can ensure the convergence of the total energy to 1 mHa. A $2\times 1\times 1$ supercell containing 32 atoms with 16 Zn atoms and 16 Sb atoms was used for pure ZnSb. Cd- and In-doped ZnSb structures were constructed by replacing one Zn atom with the corresponding dopant atoms in the supercell. All the structures were fully optimized by the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm[24] until the forces acting on all atoms are less than $2.0\times 10^{-4}$ Ha/Bohr. A tolerance of $5.0\times 10^{-6}$ Ha/Bohr for the difference of forces was set to be the convergence limit in the calculations. The BoltzTrap code[25] was used to calculate Seebeck coefficient and electrical conductivity based on the semi-classical Boltzmann theory with the constant relaxation time approximation.
cpl-37-1-017102-fig1.png
Fig. 1. The interatomic distances in and around a rhomboid ring for (a) pure, (b) Cd- and (c) In-doped ZnSb.
The calculated lattice parameters for pure, Cd- and In-doped ZnSb are listed in Table 1. The calculated results for pure ZnSb are in good agreement with the experimental[11] and other theoretical calculation data.[17,18] After the substitution of one Zn atom with a Cd or In atom, the lattice parameters slightly increase due to the larger atomic radius of Cd or In compared with that of Zn. Figure 1 shows the interatomic distances in and around a rhomboid ring for pure, Cd- and In-doped ZnSb. The interatomic distances for pure ZnSb shown in Fig. 1(a) are very close to the results of previous theoretical calculations.[17] After Cd or In doping, the interatomic distances around the Cd or In atom apparently increase, which can be seen in Fig. 1. For example, the Cd–Zn interatomic distance is about 2.87 Å and the In–Zn interatomic distance is about 2.96 Å. They are clearly larger than the Zn–Zn interatomic distance of about 2.72 Å in pure ZnSb. However, the Zn–Sb interatomic distances far from the Cd or In atom are nearly unchanged.
Table 1. The calculated lattice parameters ($a$, $b$ and $c$) for pure, Cd- and In-doped ZnSb (the experimental data[11] are given in parentheses).
$a$ (Å) $b$ (Å) $c$ (Å)
ZnSb 6.274 (6.204) 7.819 (7.741) 8.214 (8.098)
CdZn$_{15}$Sb$_{16}$ 6.300 7.851 8.248
InZn$_{15}$Sb$_{16}$ 6.316 7.871 8.269
The calculated band structures of pure, Cd- and In-doped ZnSb are shown in Fig. 2. It is well known that density functional theory systematically underestimates the value of the bandgap of semiconductors. The calculated band structure for pure ZnSb (Fig. 2(a)) shows an indirect bandgap of about 0.03 eV, which is in good agreement with previous theoretical calculation results.[17,19] However, the experimental result indicates that pure ZnSb has an indirect bandgap of 0.5 eV.[26] For pure ZnSb, the maximum of the valence band is along the ${\it\Gamma}$–$X$ direction and the minimum of the conduction band is along the ${\it\Gamma}$–$Z$ direction, which are in good agreement with the previous calculations.[17,19,27] The value of the bandgap is nearly unchanged after Cd or In doping, but the Fermi level shifts down for Cd doping and up for In doping.
cpl-37-1-017102-fig2.png
Fig. 2. Band structures for (a) pure, (b) Cd- and (c) In-doped ZnSb.
For better prediction of thermoelectric properties, we shift the bandgap to the experimental value of 0.5 eV when use the BoltzTraP code with constant relaxation time approximation to calculate the thermoelectric properties of pure, Cd- and In-doped ZnSb. Figure 3 presents the Seebeck coefficient $S$, power factor with respect to scattering time $S^{2}\sigma /\tau$ and electronic thermal conductivity with respect to scattering time $\kappa_{\rm e}/\tau$ for pure ZnSb as a function of carrier concentration at temperatures of 300–700 K. The peak values of $S$ for p-type and n-type ZnSb appear at carrier concentrations of about $+3\times 10^{17}$ cm$^{-3}$ and $-3\times 10^{17}$ cm$^{-3}$, respectively. The maximum absolute value of $S$ of n-type ZnSb is always larger than that of p-type ZnSb for each temperature investigated in the present work. The power factor of n-type ZnSb is also much larger than that of p-type ZnSb. These results indicate that n-type ZnSb has better thermoelectric performance than p-type ZnSb. For n-type ZnSb, the power factor increases with increasing temperature and carrier concentration. The electronic thermal conductivity increases with increasing temperature and carrier concentration for both n- and p-type ZnSb. The increase of the electronic thermal conductivity will decrease the ZT value at elevated temperature. However, the electronic thermal conductivity is only one part of the total thermal conductivity. The other part is the lattice thermal conductivity. The contribution of the electronic part to the total thermal conductivity is very small for lightly doped semiconductors.[15,28]
cpl-37-1-017102-fig3.png
Fig. 3. (a) Seebeck coefficient $S$, (b) power factor $S^{2}\sigma$ divided by relaxation time $\tau$, (c) electrical conductivity $\sigma$ divided by $\tau$, and (d) electronic thermal conductivity $\kappa_{\rm e}$ divided by $\tau$ for pure ZnSb as a function of carrier concentration at temperatures of 300–700 K.
The experimental $S$ value of undoped ZnSb was reported to be $+196$ µV/K with a charge carrier concentration of $2\times 10^{16}$ holes/cm$^{3}$ to $4\times 10^{16}$ holes/cm$^{3}$ at about 300 K.[29] Our calculated result at the carrier concentration of $3.7\times 10^{16}$ holes/cm$^{3}$ and 300 K is about $+187$ µV/K, which is in agreement with the experimental value. However, at the carrier concentration of $1.2\times 10^{18}$ holes/cm$^{3}$ the experimental $S$ value was reported to be $+340$ µV/K,[30] which is much smaller than our calculated $S$ value of $+620$ µV/K. This difference can be attributed to Zn vacancies or other defects in the experimental samples. The ab initio calculations carried out by Bjerg et al.[18] indicated that Zn vacancies have lower formation energies and that the negative charge of these defects induces intrinsic ZnSb to be p-type conductivity. Lund et al.[27] also showed that Zn vacancies are the most stable intrinsic defects in ZnSb. Furthermore, by performing first-principles calculations on ZnSb supercells with a Zn vacancy, Niedziółka et al.[19] demonstrated that Zn vacancies have a large influence on the Seebeck coefficient. The undoped ZnSb with higher carrier concentrations should have more Zn vacancies because p-type conductivity is induced by these vacancies according to the above discussion. In this case the influence of Zn vacancies on Seebeck coefficient will be more significant, and therefore the difference between the experimental data and the calculated results will be more noticeable. Figure 4 presents the transport properties of Cd-doped ZnSb as a function of carrier concentration at temperatures of 300–700 K. The maximum absolute values of $S$ for n- and p-type Cd-doped ZnSb are about 521 µV/K at the carrier concentration of $-3.8\times 10^{18}$ cm$^{-3}$ and 460 µV/K at the carrier concentration of $1.6\times 10^{18}$ cm$^{-3}$. These maximum values are smaller than those of pure ZnSb. Beyond the maximum points the absolute value of $S$ decreases with increasing charge carrier concentration. The absolute value of $S$ and the power factor of n-type Cd-doped ZnSb decrease with increasing temperature in a large carrier concentration range. The difference of the power factor between of n- and p-type Cd-doped ZnSb is smaller than that between of n- and p-type pure ZnSb. The power factor of Cd-doped ZnSb is generally smaller than that of pure ZnSb due to Cd doping which reduces the electrical conductivity (see Fig. 4(c)). The maximum values of the power factor of p-type Cd-doped ZnSb appear at different carrier concentrations for different temperatures as shown in Fig. 4(b). For example, the best power factor for p-type Cd-doped ZnSb can be achieved at the carrier concentration of about $5.0\times 10^{19}$ cm$^{-3}$ for 500 K, whereas for 300 K the best power factor appears at the carrier concentration of about $4.0\times 10^{19}$ cm$^{-3}$. The electronic thermal conductivity of Cd-doped ZnSb also decreases compared with that of pure ZnSb due to Cd doping which increases the scattering possibility of charge carriers. The electronic thermal conductivity of p-type Cd-doped ZnSb increases faster with increasing carrier concentration in comparison with that of n-type Cd-doped ZnSb.
cpl-37-1-017102-fig4.png
Fig. 4. (a) Seebeck coefficient $S$, (b) power factor $S^{2}\sigma$ divided by relaxation time $\tau$, (c) electrical conductivity $\sigma$ divided by $\tau$, and (d) electronic thermal conductivity $\kappa_{\rm e}$ divided by $\tau$ for Cd-doped ZnSb as a function of carrier concentration at temperatures of 300–700 K.
Figure 5 shows the transport properties of In-doped ZnSb as a function of carrier concentration at temperatures of 300–700 K. The maximum absolute values of $S$ for n- and p-type In-doped ZnSb are about 515 µV/K at the carrier concentration of $-1.1\times 10^{18}$ cm$^{-3}$ and 445 µV/K at the carrier concentration of $2.6\times 10^{18}$ cm$^{-3}$. These maximum values are also smaller than those of pure ZnSb. The maximum values of the power factor of p-type In-doped ZnSb are larger than those of the n-type In-doped ZnSb in the temperature range of 300–500 K, indicating that p-type In-doped ZnSb may have better thermoelectric performance than the n-type one in this temperature range. The power factor of n-type In-doped ZnSb increases with the increase of the charge carrier concentration in the temperature range of 500–700 K. However, the power factor of p-type In-doped ZnSb first increases with increasing carrier concentration and then reaches peak values at different carrier concentrations for different temperatures as shown in Fig. 5(b). The electronic thermal conductivity of p-type In-doped ZnSb increases faster with increasing carrier concentration in comparison with that of the n-type one.
cpl-37-1-017102-fig5.png
Fig. 5. (a) Seebeck coefficient $S$, (b) power factor $S^{2}\sigma$ divided by relaxation time $\tau$, (c) electrical conductivity $\sigma$ divided by $\tau$, and (d) electronic thermal conductivity $\kappa_{\rm e}$ divided by $\tau$ for In-doped ZnSb as a function of carrier concentration at temperatures of 300–700 K.
It should be mentioned that in the above discussion the relaxation time $\tau$ is supposed to be constant for pure, Cd- and In-doped ZnSb. However, with the doping of Cd or In, the scattering rates of charge carriers will increase, and thus the relaxation time $\tau$ will decrease. In the BoltzTrap code, the calculated electrical conductivity is related to the relaxation time (i.e., $\sigma /\tau $). Therefore, the calculated power factor is also related to the relaxation time (i.e., $S^{2}\sigma /\tau $). The decrease of the relaxation time $\tau$ induced by the doping of Cd or In will reduce the power factor ($S^{2}\sigma $). However, the dopant atoms will also increase the scattering rates of phonons, and thus decrease the lattice thermal conductivity, which may compensate for the reduction of the power factor ($S^{2}\sigma $). Therefore, it is still possible to maintain ZT at a high level for Cd- and In-doped ZnSb. In summary, the electronic structures and thermoelectric properties of ZnSb doped with Cd and In have been investigated by first principles calculations and Boltzmann transport equations. After Cd or In doping at the Zn lattice site, the lattice parameters slightly increase due to the larger atomic radius of Cd or In in comparison with that of Zn, and the interatomic distances around the Cd or In atom apparently increase as well. The power factor of n-type ZnSb is much larger than that of p-type ZnSb, indicating that n-type ZnSb has better thermoelectric performance than p-type ZnSb. After Cd or In doping, the power factor of ZnSb reduces mainly due to the decrease in the electrical conductivity, and the maximum absolute values of the Seebeck coefficient are also smaller than those of pure ZnSb. The p-type In-doped ZnSb has a larger power factor than the n-type In-doped ZnSb in the temperature range of 300–500 K, indicating that p-type In-doped ZnSb may have better thermoelectric performance than n-type In-doped ZnSb in this temperature range. The variation of the Seebeck coefficient and power factor of pure, Cd- and In-doped ZnSb with temperature is related to the carrier concentration. References Disordered zinc in Zn4Sb3 with phonon-glass and electron-crystal thermoelectric propertiesFulfilling thermoelectric promises: β-Zn4Sb3 from materials research to power generationPreparation and thermoelectric properties of semiconducting Zn4Sb3Thermoelectric properties of Zn4Sb3 prepared by hot pressingUnexpected High-Temperature Stability of β-Zn 4 Sb 3 Opens the Door to Enhanced Thermoelectric PerformancePreparation of Single-Phase ZnSb Thermoelectric Materials Using a Mechanical Grinding ProcessPreparation and properties of ZnSb thermoelectric material through mechanical-alloying and Spark Plasma SinteringThermoelectric properties of Cu doped ZnSb containing Zn 3 P 2 particlesEnhanced thermoelectric figure of merit in p-type Ag-doped ZnSb nanostructured with Ag3SbThermally stable thermoelectric Zn4Sb3 by zone-melting synthesisA Promising Thermoelectric Material: Zn 4 Sb 3 or Zn 6 - δ Sb 5 . Its Composition, Structure, Stability, and Polymorphs. Structure and Stability of Zn 1 - δ SbThermoelectric Characterization of Zone-Melted and Quenched Zn4Sb3Thermal Stability of Thermoelectric Zn4Sb3New Interest in Intermetallic Compound ZnSbTransport properties of the II–V semiconductor ZnSbZnSb Polymorphs with Improved Thermoelectric PropertiesElectronic structure and chemical bonding of the electron-poor II-V semiconductors ZnSb and ZnAsAb initio Calculations of Intrinsic Point Defects in ZnSbInfluence of the Exchange–Correlation Functional on the Electronic Properties of ZnSb as a Promising Thermoelectric MaterialABINIT: First-principles approach to material and nanosystem propertiesImplementation of the projector augmented-wave method in the ABINIT code: Application to the study of iron under pressureGeneralized Gradient Approximation Made SimpleSpecial points for Brillouin-zone integrationsGeneral methods for geometry and wave function optimizationBoltzTraP. A code for calculating band-structure dependent quantitiesOptical and Electrical Properties and Energy Band Structure of ZnSbPhysical properties of thermoelectric zinc antimonide using first-principles calculationsFirst-principles study of anisotropic thermoelectric transport properties of IV-VI semiconductor compounds SnSe and SnSThermal and Electronic Transport Properties of p -Type ZnSbA study of transport properties in Cu and P doped ZnSb
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