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Theoretical investigation of the effects of doping on the electronic structure and thermoelectric properties of ZnO nanowires Chao Wang, Yuanxu Wang,* Guangbiao Zhang, Chengxiao Peng and Gui Yang The effects of doping ZnO nanowires with Al, Ga and Sb on their electronic structure and thermoelectric properties are investigated by first-principles calculations. We find that the band gap of ZnO nanowires is narrowed after doping with Al and Ga, while band gap broadening is observed in Sb doped ZnO nanowires. The lattice thermal conductivity of ZnO nanowires is obtained based on the Debye–Callaway model. The thermoelectric properties of ZnO nanowires were calculated using the BoltzTraP code. The results show that there exists an optimal carrier concentration yielding the maximum value of ZT for Al, Ga and Sb doped ZnO nanowires at room temperature. The maximum
Received 10th October 2013, Accepted 7th December 2013
value of ZT, 0.147, is obtained for Ga doped ZnO nanowires, when the carrier concentration is
DOI: 10.1039/c3cp54289k
ZnO nanowires when the temperature is between 400 K and 1200 K. We also find that Al doped ZnO
3.62 1019 cm3. The figure of merit ZT of Sb doped ZnO nanowires is higher than that of Ga doped nanowires always have poor thermoelectric properties, which means that the Al dopant may not be the
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optimal choice for ZnO nanowires in thermoelectric applications.
1 Introduction Interest in thermoelectric materials has gained momentum in recent years due to their potential to play an important role in energy conservation and generation. The performance of a thermoelectric material is quantified via the dimensionless figure of merit ZT = sS2T/k, where s is the electrical conductivity, S the Seebeck coefficient, and k the thermal conductivity. The thermal conductivity k is composed of the electronic thermal conductivity kel and the lattice thermal conductivity kph. Generally, it is difficult to achieve high ZT values due to the interdependency of the electronic terms (s, S, and kel). For instance, an increase in s concomitantly leads to an increase in kel, through the Wiedemann–Franz law. Many different strategies have been presented in the search for thermoelectric materials with high ZT values.1,2 The most important approach to improve the ZT values is managed to reduce kph by using nanostructures.3 This has been evidenced by experiments on nanostructured thermoelectric materials. For example, Si nanowires possess a 100-fold improved thermoelectric performance over bulk Si near room temperature.4 Zinc oxide (ZnO) has attracted attention as a candidate for use in thermoelectric applications due to its high melting point, high electrical conductivity and Seebeck coefficient.5 Institute for Computational Materials Science, School of Physics and Electronics, Henan University, Kaifeng, 475004, China. E-mail: [email protected]
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Unfortunately, ZnO materials possess high lattice thermal conductivity due to noncomplex wurtzite structure, which heavily limits the interest in ZnO for thermoelectric application. As mentioned above, nanostructures could effectively decrease kph. Additionally, the electronic thermal conductivity kel is 10- to 100-fold lower than kph in ZnO.6 Hence, decreases in kph would directly lead to a decrease in k. Recently, more efforts in experiments were made to investigate the thermoelectric performance of ZnO nanostructures.5,7 ZnO nanowires are one of the most important nanostructures and have been widely studied for their electrical and optical properties in last few years. However, there are only a few reports on the thermoelectric properties of ZnO nanowires.8,9 Moreover, as thermoelectric materials, ZnO nanowires should be doped in order to achieve excellent carrier transport properties.10 Recently, Shi and his coworkers have investigated the effect of Ga contents on the thermoelectric property of [0001] zinc oxide nanowires.11 However, to the best of our knowledge, there have been no systematic reports on the influence of different doping elements on the thermoelectric properties of ZnO nanowires. In this paper, we investigate the electronic structures of ZnO nanowires doped with Al, Ga, Sb elements, using firstprinciples calculations. Meanwhile, within the framework of Boltzmann theory, the influence of different doping elements on the thermoelectric properties of ZnO nanowires are discussed using the constant relaxation time approximation and rigid band model.
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2 Methods The first-principles calculations on the atomistic relaxation and electronic structure of ZnO nanowires were performed using density functional theory (DFT) within projector augmented wave pseudopotentials as implemented in the VASP program package.12,13 Generalized gradient approximation (GGA) given by Perdew–Burke–Ernzerhof (PBE) was used to treat the electron– electron exchange interaction. All the coordinates of atoms and the lattice parameters of ZnO nanowires were fully relaxed before calculating the electronic structures. The plane-wave energy cutoff was chosen to be 400 eV throughout the calculation. For the sampling of the Brillouin zone, the electronic structures used a 1 1 9 k-point grid generated according to the Monkhorst– Pack scheme. Geometry optimization was achieved using convergence thresholds of 1 105 eV per atom for total energy, 0.04 eV Å1 for maximum force. The tolerance in the selfconsistent field (SCF) calculation was 1 106 eV per atom. All chosen parameters have been tested and accepted due to the balance between the calculation accuracy and the time spent. The ZnO nanowires were created from a 9 9 2 supercell of ZnO having the wurtzite crystal structure, and each ZnO nanowire supercell contained 48 Zn and 48 O atoms. The details of building nanowires is described elsewhere.14 ZnO nanowires extends to infinity along the [0001] direction through the periodic repetition of the supercell. The vaccum region along the [101% 0] and [011% 0] direction in the structures ZnO nanowires is over 10 Å, which ensures that nanowires in neighbouring supercells do not interact with each other. One Zn atom in the supercell is replaced by an impurity atom (Al, Ga, Sb) in order to produce the doped ZnO nanowires. This corresponds to an impurity concentration of 2.1%. The diameters of the doped ZnO nanowires and pure ZnO nanowire are fixed at about 9.80 Å. The ZnO nanowires supercell is shown in Fig. 1. The thermoelectric properties of ZnO nanowires were calculated using the BoltzTraP code.15 This method is based on Boltzmann transport theory and makes use of the electronic
Fig. 1 Side view of the ZnO nanowires supercell along [0001] direction. The red and gray spheres represent Zn and O atoms, respectively. Blue spheres indicate impurity atoms (Al, Ga, and Sb).
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structures calculated by VASP. The rigid band model is applied in BoltzTraP package in order to obtain thermoelectric properties at different carrier concentrations. A Monkhorst–Pack special k-point grid 1 1 15 was used to integrate in the Brillouin zone for the calculations of transport coefficients of ZnO nanowires.
3 Results and discussions 3.1
Electronic structure
The transport properties are closely related to the electronic structure. The effects of the impurity atom on the thermoelectric properties of ZnO nanowires can be understood by analyzing the band structure, band gap and density of states (DOS). The band structures of Al, Ga, Sb doped ZnO nanowires are shown in Fig. 2. For comparison, the band structure of undoped ZnO nanowires is also given in Fig. 2. In order to clearly show the difference of band structures between undoped ZnO nanowires and doped ZnO nanowires, we aligned the single-particle eigenvalues according to 1s core level of the farthest atom away from the impurity. All the band structures presented in Fig. 2 are along the growth direction of ZnO nanowires. The calculated band gaps of ZnO nanowires are listed in Table 1. It can be seen that the band gap of the undoped ZnO nanowire is 1.47 eV, close to the other calculated value of 1.42 eV.16 We also calculated the band gap of bulk wurtzite ZnO using GGA and found it to be only 0.75 eV, which is well below the experimental value of 3.4 eV.17 It is well known that the GGA results usually significantly underestimate the band gap for semiconductors. However, the trend of the band gaps predicted from GGA calculations are expected to be correct. Our results show that the band gaps of undoped and doped ZnO nanowires are larger than that of bulk ZnO, which is the result of the quantum confinement effect. From Table 1 we could find that the band gaps of ZnO nanowires doped with Al and Ga are narrowed, compared with that of undoped ZnO nanowires. In contrast, band gap broadening is found in Sb doped ZnO
Fig. 2 Band structures of undoped ZnO nanowires (a) and Al (b), Ga (c), Sb (d) doped ZnO nanowires. The red horizontal dashed lines denote the Fermi level in undoped ZnO nanowires and doped ZnO nanowires.
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Table 1 Band gaps, effective masses of undoped ZnO nanowires and Al, Ga, Sb doped ZnO nanowires. me in the table is the rest mass of the electrons
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Eg (eV) m* (me)
Undoped
Al-doped
Ga-doped
Sb-doped
1.47 0.593
1.41 0.605
1.37 0.603
1.53 0.693
nanowires. These results are also observed in experiments.18 The origin of these results will be discussed later. As shown in Fig. 2, the band structures of ZnO nanowires change distinctly due to the introduction of impurity atoms. It is clearly seen that the Fermi level shifts to the conduction band after doping. At a sufficiently high doping level, the donor atoms become so close to each other that forms a degenerate semiconductor in which the Fermi level lies within the conduction band similar to the case of metals.19 The semimetallic band characters of doped ZnO nanowires are favorable for their transport properties. Additionally, we could find in Fig. 2 that the impurity band is completely hybridized with the host bands, which is in agreement with a previous study.20 From Fig. 2(b), we note that doping with Al affects slightly the band structures of ZnO nanowires. However, in the case of Ga doping, there evidently appears band splitting in the conduction bands. As to Sb doped ZnO nanowires, the band structure shows a more significant modification and the stronger band splitting could be observed in Fig. 2(d). To illustrate the change of band structures after doping, we investigate the partial density of states (PDOS) near conduction band minimum (CBM) and valence band maximum (VBM) of ZnO nanowires. The calculation results are given in Fig. 3. To align the PDOS of different ZnO nanowires, we use the same method applied to the band structure. In Fig. 3(a), it is noticeable that the top of the valence band is mostly formed by O 2p and Zn 3d. The bottom of the conduction band is dominated by Zn 4s. Some contributions of the O 2s state can also be seen. Similar results were reported by the other group.21 For the Al doped ZnO nanowire, there appears Al 3s
state at the bottom of conduction band, which we can observe in Fig. 3(b). The electrons belonging to Al 3s give 3% of the total DOS.22 We also could observe the downward movement of CBM in Fig. 3(b), which leads to a reduction of the band gap of Al doped ZnO nanowires. According to the experimental results reported by Cong and coworkers, Al doping may induce the enhancement of p–d coupling in ZnO and it will reduce the bandgap.23 Additionally, the new unoccupied DOS caused by strong s–p hybridization of Al–O bonds is incorporated into the conduction band. The PDOS of Ga doped ZnO nanowires is mostly similar to that of Al doped ZnO nanowires, except that Ga 4s is highly delocalized in the conduction band and CBM moves to lower energy. The PDOS of Sb doped ZnO nanowires is quite different from the other cases. First, Sb 5p has stronger delocalization in the entire conduction band, which will affect a lot the shape of the conduction band. This is consistent with the results observed in Fig. 2(d). Furthermore, we could find that Sb 5p orbitals and Zn 4s orbitals are strongly hybridized via O p orbitals in Fig. 3(d). The Cu dxy orbital and Ir 5d orbitals in CaCu3Ir4O12 exhibit similar results observed by Cheng and his coworkers.24 This hybridization would lead to the upward shifting of Zn 4s states at the bottom of the conduction band, which results in bandgap broadening in Sb doped ZnO nanowires. Electron localization function (ELF) can serve as a tool for describing the degree of electron localization and understanding the nature of chemical bonding.25 ELF has its upper limit value of 1, corresponding to perfect localization of electrons. On the other hand, electrons are hardly found in the region where ELF is close to zero. The value ELF = 0.5 represents the situation in a homogeneous electron gas. ELF for undoped ZnO nanowires and Al, Ga, Sb doped ZnO nanowires are shown in Fig. 4. It can be seen from Fig. 4(a) that the maximum value of ELF is around the O atom and the ELF value is very low around the Zn atom. This indicates that the electrons mainly gather around the O atom and the Zn–O chemical bond has obvious character of ionic bonding in undoped ZnO nanowires. The key difference in the ELF plot between undoped and doped ZnO nanowires is the localization of electrons around the doping atom. From Fig. 4(b), we could find that electrons only localized around the O atom now tend to appear around the Al atom. This situation is quiet clear in Fig. 4(c) and (d). There appears homogeneous electron gas around Ga and Sb atoms. The results of ELF coincide with characteristics evident in the PDOS. Effective mass (m*) is one of the fundamental quantities which determine the transport properties of a material, so the effective masses are also calculated in our work. Al, Ga and Sb doped ZnO nanowires are n-type, thus only the effective masses of electrons are considered. m* can be evaluated by m ¼ h2
Fig. 3 PDOS near CBM and VBM of undoped ZnO nanowires (a) and Al (b), Ga (c), Sb (d) doped ZnO nanowires. The zoom-in near the bottom of conduction bands are shown in the insets. The red vertical lines in the insets indicate the Fermi level in doped ZnO nanowires.
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@2E @kz2
1 :
(1)
We calculate m* of undoped ZnO nanowires and doped ZnO nanowires along the growth direction by choosing a small region around the conduction band extrema. The results are given in Table 1. The effective mass of undoped ZnO nanowires is 0.593 me, which is larger than that of bulk ZnO (0.24 me).26
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depends mainly on the phonons scattering, which is closely related to the diameter of nanowires, the doping level and temperature. Here, we use the Debye–Callaway model to calculate kph.29 In this model, kph can be expressed as: ð kB kB T 3 y=T x4 ex kph ¼ 2 tp dx; (2) x h 2p u ðe 1Þ2 0 where kB is the Boltzmann constant, u is the average sound velocity of phonons, T is the absolute temperature, y is the Debye temperature (399.5 K for ZnO),30 x = ho/kBT, o is the phonon frequency, and tp is the combined relaxation time of phonons. The form of the combined relaxation time used here is: y þ B2 o2 T; (3) tp1 ¼ tb1 þ Ao4 þ B1 exp aT
Fig. 4 Electron localization function for undoped ZnO nanowires (a) and Al (b), Ga (c), Sb (d) doped ZnO nanowires. The slices are parallel to the (101% 0) plane and pass through the center of impurity atoms. In Sb doped ZnO nanowires (d), one of nearest-neighbor O atoms is out of the slice plane due to the larger atomic radius of Sb.
Generally, compared with bulk, nanostructures tend to exhibit larger effective masses due to the strong quantum confinement effect. From Table 1, we also note that the electron effective masses of ZnO nanowires increase after being doped with Al, Ga and Sb, which is similar to the reported experimental results.27 This increase is mainly due to the interaction or admixture of host states and impurity states at the conduction band minimum. 3.2
Thermoelectric properties
In the calculations of thermoelectric properties, the electron relaxation time te is a necessary parameter. From the BoltzTraP code, we can only obtain the ratio of electrical conductivity s to electron relaxation time te. In this work, the value of te is obtained by fitting the ratio s/te to measured electrical conductivity data of ZnO nanowires. However, there is lack of the experimental data for 9.80 Å doped ZnO nanowires. Recently, the electrical properties of Al doped ZnO nanowires with the diameter of 20–80 nm were explored by Noriega and coworkers.28 Here, we use their data to estimate the electron relaxation time te of doped ZnO nanowires (r = 1/s = 2.6 103 Ocm, n = 8.8 1019 cm3, T = 300 K). Additionally, te varies with different atomic structure, carrier concentrations and temperature. For simplicity and convenience, we only consider the influence of carrier concentrations and temperature on the electron relaxation time te in our calculation. We use a standard electron–phonon dependence on n and T for te, namely, te = CT1n1/3, where C is a constant. C can be obtained by inserting the value of te. Finally, we have the relationship of te with n and T. Another parameter that needs to be determined in calculating the figure of merit ZT is the lattice thermal conductivity kph. kph
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where tb is the phonon-boundary scattering relaxation time, Ao4 approximates the impurity scattering and the third term o2T describes the phonon–phonon scattering. Here the relaxation time parameters A, B1 and B2 are 1.7 1044 s3, 4.7 1019 s K1, 2.8 1020 s K1, respectively.29 The phonon-boundary scattering relaxation time tb is described by tb1 = u/d based on the Casimir model (d is the diameter of ZnO nanowires). The average sound velocity of the phonons, u, can be calculated from the equation: 3 1 2 ¼ þ ; u3 uL3 uT 3
(4)
where uL = 6365 ms1 and uT = 2735 ms1 are the longitudinal and transverse sound velocities in bulk ZnO, respectively.30 The lattice thermal conductivity of ZnO nanowires calculated by this method agrees well with the experiment data.31,32 Fig. 5 shows the temperature dependence of kph for doped ZnO nanowires in our calculations. At low temperatures (less than 400 K), boundary scattering predominates. In the Debye–Callaway model, the phonon-boundary scattering is frequency independent and temperature independent. Therefore, the thermal conductivity basically goes as T3. As the temperature increases further, the impurity scattering and the phonon–phonon
Fig. 5 Temperature dependence of the thermal conductivity for the ZnO nanowires.
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Fig. 6 Room temperature thermoelectric properties of Al, Ga and Sb doped ZnO nanowires as a function of carrier concentration: (a) electrical conductivity s, (b) Seebeck coefficient S, (c) power factor P(sS2), (d) figure of merit ZT.
scattering become important and the thermal conductivity first increases to a maximum then decreases. The electrical conductivity s, Seebeck coefficient S, power factor P and figure of merit ZT at room-temperature are shown in Fig. 6 as a function of carrier concentration. In this study, the impurity concentration is fixed at 2.1%. Given the impurities are fully ionized, the carrier concentration should be about 1.3 1021 cm3. However, according to the amphoteric defect model (ADM), native defects would be generated in semiconductor materials in response to extrinsic doping.33 Based on ADM and quantum confinement effects, Khanal and his coworkers suggest that the maximum electron concentration that can be achieved in ZnO nanowires with the diameter under 60 nm via doping method is 9 1019 cm3.34 Thus the maximum carrier concentration we consider in this paper is 9 1019 cm3. Using the rigid band model, we manually adjust the Fermi level in order to change the carrier concentration. It is well known that the electrical conductivity s is directly proportional to the carrier concentration. As shown in Fig. 6(a), s of doped ZnO nanowires increases when the carrier concentration increases. However, there is a trade off if we look at the Seebeck coefficient S shown in Fig. 6(b). S monotonically decreases with the carrier concentration increasing. The Seebeck coefficient S can be expressed as k Nc S ¼ ln ; (5) n e where n is the carrier concentration, and Nc is the effective state for the conduction band, which is given by Nc = 2(2pm*kT/h2)3/2. Therefore, the trend of S with carrier concentration could be explained by eqn (5). From eqn (5), we also could find that m* determines S through the parameter Nc. Although the difference in the Seebeck coefficient for Al, Ga and Sb doped ZnO nanowires is not significant in Fig. 6(b), we still could see that Sb doped ZnO nanowires have a larger Seebeck coefficient at the same carrier concentration. This result can be attributed to the higher effective
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mass of Sb doped ZnO nanowires. The power factor P(sS2) as a function of carrier concentration is shown in Fig. 6(c). Clearly, there is an optimal carrier concentration yielding the maximum value of P. The Ga doped ZnO nanowire has higher maximum value of P compared with Al, Sb doped ZnO nanowires. We show the figure merit ZT of doped ZnO nanowires at 300 K in Fig. 6(d). Similar to the power factor, ZT of doped ZnO nanowires also has the optimal carrier concentration. The physical reason for this phenomenon could be explained as follows. The electronic thermal conductivity kel can be estimated by the Wiedemann–Franz law, kel = LsT. L, known as the Lorenz number, is about 2.44 108 W O K2. The maximum value of kel calculated from Fig. 6(a) is about 0.33 W mK1. We can find that the electronic thermal conductivity is far smaller than the lattice thermal conductivity kph, which implies k E kph. Thus, with the carrier concentration increasing, the opposite trend could be observed between the electrical conductivity s and Seebeck coefficient S. Meanwhile, the thermal conductivity k would nearly be constant. Based on the reasons mentioned above, ZT should have a maximum value which corresponds to the optimal carrier concentration. The maximum value of ZT, 0.147, is obtained for Ga doped ZnO nanowires, when the carrier concentration is 3.62 1019 cm3. In the figure we also observe that ZT of Ga doped ZnO nanowires is always larger than that of Sb, Al doped ZnO nanowires. This phenomenon arises from the higher electrical conductivity of Ga doped ZnO nanowires due to low effective mass. Furthermore, we investigate the thermoelectric properties of Al, Ga and Sb doped ZnO nanowires with increasing temperature. In this study, we selected the doping level at which ZT achieves the maximum value at room temperature. The calculated results are shown in Fig. 7. In Fig. 7(a), we can see that the electrical conductivity first increases, then decreases when the temperature increases. This can be understood from a competition between carrier concentration and electron relaxation time. In Fig. 7(b), we can clearly observe that Sb doped ZnO nanowires have a higher Seebeck coefficient at higher temperature. This leads to a larger increase of ZT for Sb doped ZnO
Fig. 7 (a) The electrical conductivity s, (b) Seebeck coefficient S, (c) power factor P(sS2), and (d) figure of merit ZT of Al, Ga, Sb doped ZnO nanowires with the change in temperature.
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nanowire between 400 K to 1200 K compared with Ga doped ZnO nanowires, which can be seen in Fig. 7(d). In other words, Sb doped ZnO nanowires have a higher ZT value in this temperature range. From Fig. 6 and 7, we can find that Al doped ZnO nanowires always have poor thermoelectric properties. It means that the Al dopant may not be the optimal choice when we want to enhance the thermoelectric properties of ZnO nanowires by the doping method.
4 Conclusion The electronic structure and thermoelectric properties of Al, Ga and Sb doped ZnO nanowires are calculated in this paper. The electronic structure results show that band gaps of ZnO nanowires are narrowed after doping with Al and Ga, while band gap broadening is observed in Sb doped ZnO nanowires. Additionally, Sb doped ZnO nanowires have a higher effective mass. Furthermore, there exists an optimal carrier concentration yielding the maximum value of ZT for Al, Ga and Sb doped ZnO nanowires at room temperature. The maximum value of ZT, 0.147, is obtained for Ga doped ZnO nanowires, when the carrier concentration is 3.62 1019 cm3. The figure of merit ZT of Sb doped ZnO nanowires is higher than that of Ga doped ZnO nanowires when the temperature is between 400 K and 1200 K. We also find that Al doped ZnO nanowires always have poor thermoelectric properties, which means that the Al dopant may not be the optimal choice for ZnO nanowires in thermoelectric applications.
Acknowledgements This research was sponsored by the National Natural Science Fundation of China (No. 51371036, 21071045 and 11305046), the Program for New Century Excellent Talents in University (No. NCET-10-0132), Program for Innovative Research Team (in Science and Technology) in University of Henan Province (No. 13IRTSTHN017), and Foundation of Henan Educational Committee (13A1470076 and 14A430029).
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Theoretical investigation of the effects of doping on the electronic structure and thermoelectric properties of ZnO nanowires Chao Wang, Yuanxu Wang,* Guangbiao Zhang, Chengxiao Peng and Gui Yang The effects of doping ZnO nanowires with Al, Ga and Sb on their electronic structure and thermoelectric properties are investigated by first-principles calculations. We find that the band gap of ZnO nanowires is narrowed after doping with Al and Ga, while band gap broadening is observed in Sb doped ZnO nanowires. The lattice thermal conductivity of ZnO nanowires is obtained based on the Debye–Callaway model. The thermoelectric properties of ZnO nanowires were calculated using the BoltzTraP code. The results show that there exists an optimal carrier concentration yielding the maximum value of ZT for Al, Ga and Sb doped ZnO nanowires at room temperature. The maximum
Received 10th October 2013, Accepted 7th December 2013
value of ZT, 0.147, is obtained for Ga doped ZnO nanowires, when the carrier concentration is
DOI: 10.1039/c3cp54289k
ZnO nanowires when the temperature is between 400 K and 1200 K. We also find that Al doped ZnO
3.62 1019 cm3. The figure of merit ZT of Sb doped ZnO nanowires is higher than that of Ga doped nanowires always have poor thermoelectric properties, which means that the Al dopant may not be the
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optimal choice for ZnO nanowires in thermoelectric applications.
1 Introduction Interest in thermoelectric materials has gained momentum in recent years due to their potential to play an important role in energy conservation and generation. The performance of a thermoelectric material is quantified via the dimensionless figure of merit ZT = sS2T/k, where s is the electrical conductivity, S the Seebeck coefficient, and k the thermal conductivity. The thermal conductivity k is composed of the electronic thermal conductivity kel and the lattice thermal conductivity kph. Generally, it is difficult to achieve high ZT values due to the interdependency of the electronic terms (s, S, and kel). For instance, an increase in s concomitantly leads to an increase in kel, through the Wiedemann–Franz law. Many different strategies have been presented in the search for thermoelectric materials with high ZT values.1,2 The most important approach to improve the ZT values is managed to reduce kph by using nanostructures.3 This has been evidenced by experiments on nanostructured thermoelectric materials. For example, Si nanowires possess a 100-fold improved thermoelectric performance over bulk Si near room temperature.4 Zinc oxide (ZnO) has attracted attention as a candidate for use in thermoelectric applications due to its high melting point, high electrical conductivity and Seebeck coefficient.5 Institute for Computational Materials Science, School of Physics and Electronics, Henan University, Kaifeng, 475004, China. E-mail: [email protected]
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Unfortunately, ZnO materials possess high lattice thermal conductivity due to noncomplex wurtzite structure, which heavily limits the interest in ZnO for thermoelectric application. As mentioned above, nanostructures could effectively decrease kph. Additionally, the electronic thermal conductivity kel is 10- to 100-fold lower than kph in ZnO.6 Hence, decreases in kph would directly lead to a decrease in k. Recently, more efforts in experiments were made to investigate the thermoelectric performance of ZnO nanostructures.5,7 ZnO nanowires are one of the most important nanostructures and have been widely studied for their electrical and optical properties in last few years. However, there are only a few reports on the thermoelectric properties of ZnO nanowires.8,9 Moreover, as thermoelectric materials, ZnO nanowires should be doped in order to achieve excellent carrier transport properties.10 Recently, Shi and his coworkers have investigated the effect of Ga contents on the thermoelectric property of [0001] zinc oxide nanowires.11 However, to the best of our knowledge, there have been no systematic reports on the influence of different doping elements on the thermoelectric properties of ZnO nanowires. In this paper, we investigate the electronic structures of ZnO nanowires doped with Al, Ga, Sb elements, using firstprinciples calculations. Meanwhile, within the framework of Boltzmann theory, the influence of different doping elements on the thermoelectric properties of ZnO nanowires are discussed using the constant relaxation time approximation and rigid band model.
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2 Methods The first-principles calculations on the atomistic relaxation and electronic structure of ZnO nanowires were performed using density functional theory (DFT) within projector augmented wave pseudopotentials as implemented in the VASP program package.12,13 Generalized gradient approximation (GGA) given by Perdew–Burke–Ernzerhof (PBE) was used to treat the electron– electron exchange interaction. All the coordinates of atoms and the lattice parameters of ZnO nanowires were fully relaxed before calculating the electronic structures. The plane-wave energy cutoff was chosen to be 400 eV throughout the calculation. For the sampling of the Brillouin zone, the electronic structures used a 1 1 9 k-point grid generated according to the Monkhorst– Pack scheme. Geometry optimization was achieved using convergence thresholds of 1 105 eV per atom for total energy, 0.04 eV Å1 for maximum force. The tolerance in the selfconsistent field (SCF) calculation was 1 106 eV per atom. All chosen parameters have been tested and accepted due to the balance between the calculation accuracy and the time spent. The ZnO nanowires were created from a 9 9 2 supercell of ZnO having the wurtzite crystal structure, and each ZnO nanowire supercell contained 48 Zn and 48 O atoms. The details of building nanowires is described elsewhere.14 ZnO nanowires extends to infinity along the [0001] direction through the periodic repetition of the supercell. The vaccum region along the [101% 0] and [011% 0] direction in the structures ZnO nanowires is over 10 Å, which ensures that nanowires in neighbouring supercells do not interact with each other. One Zn atom in the supercell is replaced by an impurity atom (Al, Ga, Sb) in order to produce the doped ZnO nanowires. This corresponds to an impurity concentration of 2.1%. The diameters of the doped ZnO nanowires and pure ZnO nanowire are fixed at about 9.80 Å. The ZnO nanowires supercell is shown in Fig. 1. The thermoelectric properties of ZnO nanowires were calculated using the BoltzTraP code.15 This method is based on Boltzmann transport theory and makes use of the electronic
Fig. 1 Side view of the ZnO nanowires supercell along [0001] direction. The red and gray spheres represent Zn and O atoms, respectively. Blue spheres indicate impurity atoms (Al, Ga, and Sb).
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structures calculated by VASP. The rigid band model is applied in BoltzTraP package in order to obtain thermoelectric properties at different carrier concentrations. A Monkhorst–Pack special k-point grid 1 1 15 was used to integrate in the Brillouin zone for the calculations of transport coefficients of ZnO nanowires.
3 Results and discussions 3.1
Electronic structure
The transport properties are closely related to the electronic structure. The effects of the impurity atom on the thermoelectric properties of ZnO nanowires can be understood by analyzing the band structure, band gap and density of states (DOS). The band structures of Al, Ga, Sb doped ZnO nanowires are shown in Fig. 2. For comparison, the band structure of undoped ZnO nanowires is also given in Fig. 2. In order to clearly show the difference of band structures between undoped ZnO nanowires and doped ZnO nanowires, we aligned the single-particle eigenvalues according to 1s core level of the farthest atom away from the impurity. All the band structures presented in Fig. 2 are along the growth direction of ZnO nanowires. The calculated band gaps of ZnO nanowires are listed in Table 1. It can be seen that the band gap of the undoped ZnO nanowire is 1.47 eV, close to the other calculated value of 1.42 eV.16 We also calculated the band gap of bulk wurtzite ZnO using GGA and found it to be only 0.75 eV, which is well below the experimental value of 3.4 eV.17 It is well known that the GGA results usually significantly underestimate the band gap for semiconductors. However, the trend of the band gaps predicted from GGA calculations are expected to be correct. Our results show that the band gaps of undoped and doped ZnO nanowires are larger than that of bulk ZnO, which is the result of the quantum confinement effect. From Table 1 we could find that the band gaps of ZnO nanowires doped with Al and Ga are narrowed, compared with that of undoped ZnO nanowires. In contrast, band gap broadening is found in Sb doped ZnO
Fig. 2 Band structures of undoped ZnO nanowires (a) and Al (b), Ga (c), Sb (d) doped ZnO nanowires. The red horizontal dashed lines denote the Fermi level in undoped ZnO nanowires and doped ZnO nanowires.
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Table 1 Band gaps, effective masses of undoped ZnO nanowires and Al, Ga, Sb doped ZnO nanowires. me in the table is the rest mass of the electrons
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Eg (eV) m* (me)
Undoped
Al-doped
Ga-doped
Sb-doped
1.47 0.593
1.41 0.605
1.37 0.603
1.53 0.693
nanowires. These results are also observed in experiments.18 The origin of these results will be discussed later. As shown in Fig. 2, the band structures of ZnO nanowires change distinctly due to the introduction of impurity atoms. It is clearly seen that the Fermi level shifts to the conduction band after doping. At a sufficiently high doping level, the donor atoms become so close to each other that forms a degenerate semiconductor in which the Fermi level lies within the conduction band similar to the case of metals.19 The semimetallic band characters of doped ZnO nanowires are favorable for their transport properties. Additionally, we could find in Fig. 2 that the impurity band is completely hybridized with the host bands, which is in agreement with a previous study.20 From Fig. 2(b), we note that doping with Al affects slightly the band structures of ZnO nanowires. However, in the case of Ga doping, there evidently appears band splitting in the conduction bands. As to Sb doped ZnO nanowires, the band structure shows a more significant modification and the stronger band splitting could be observed in Fig. 2(d). To illustrate the change of band structures after doping, we investigate the partial density of states (PDOS) near conduction band minimum (CBM) and valence band maximum (VBM) of ZnO nanowires. The calculation results are given in Fig. 3. To align the PDOS of different ZnO nanowires, we use the same method applied to the band structure. In Fig. 3(a), it is noticeable that the top of the valence band is mostly formed by O 2p and Zn 3d. The bottom of the conduction band is dominated by Zn 4s. Some contributions of the O 2s state can also be seen. Similar results were reported by the other group.21 For the Al doped ZnO nanowire, there appears Al 3s
state at the bottom of conduction band, which we can observe in Fig. 3(b). The electrons belonging to Al 3s give 3% of the total DOS.22 We also could observe the downward movement of CBM in Fig. 3(b), which leads to a reduction of the band gap of Al doped ZnO nanowires. According to the experimental results reported by Cong and coworkers, Al doping may induce the enhancement of p–d coupling in ZnO and it will reduce the bandgap.23 Additionally, the new unoccupied DOS caused by strong s–p hybridization of Al–O bonds is incorporated into the conduction band. The PDOS of Ga doped ZnO nanowires is mostly similar to that of Al doped ZnO nanowires, except that Ga 4s is highly delocalized in the conduction band and CBM moves to lower energy. The PDOS of Sb doped ZnO nanowires is quite different from the other cases. First, Sb 5p has stronger delocalization in the entire conduction band, which will affect a lot the shape of the conduction band. This is consistent with the results observed in Fig. 2(d). Furthermore, we could find that Sb 5p orbitals and Zn 4s orbitals are strongly hybridized via O p orbitals in Fig. 3(d). The Cu dxy orbital and Ir 5d orbitals in CaCu3Ir4O12 exhibit similar results observed by Cheng and his coworkers.24 This hybridization would lead to the upward shifting of Zn 4s states at the bottom of the conduction band, which results in bandgap broadening in Sb doped ZnO nanowires. Electron localization function (ELF) can serve as a tool for describing the degree of electron localization and understanding the nature of chemical bonding.25 ELF has its upper limit value of 1, corresponding to perfect localization of electrons. On the other hand, electrons are hardly found in the region where ELF is close to zero. The value ELF = 0.5 represents the situation in a homogeneous electron gas. ELF for undoped ZnO nanowires and Al, Ga, Sb doped ZnO nanowires are shown in Fig. 4. It can be seen from Fig. 4(a) that the maximum value of ELF is around the O atom and the ELF value is very low around the Zn atom. This indicates that the electrons mainly gather around the O atom and the Zn–O chemical bond has obvious character of ionic bonding in undoped ZnO nanowires. The key difference in the ELF plot between undoped and doped ZnO nanowires is the localization of electrons around the doping atom. From Fig. 4(b), we could find that electrons only localized around the O atom now tend to appear around the Al atom. This situation is quiet clear in Fig. 4(c) and (d). There appears homogeneous electron gas around Ga and Sb atoms. The results of ELF coincide with characteristics evident in the PDOS. Effective mass (m*) is one of the fundamental quantities which determine the transport properties of a material, so the effective masses are also calculated in our work. Al, Ga and Sb doped ZnO nanowires are n-type, thus only the effective masses of electrons are considered. m* can be evaluated by m ¼ h2
Fig. 3 PDOS near CBM and VBM of undoped ZnO nanowires (a) and Al (b), Ga (c), Sb (d) doped ZnO nanowires. The zoom-in near the bottom of conduction bands are shown in the insets. The red vertical lines in the insets indicate the Fermi level in doped ZnO nanowires.
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@2E @kz2
1 :
(1)
We calculate m* of undoped ZnO nanowires and doped ZnO nanowires along the growth direction by choosing a small region around the conduction band extrema. The results are given in Table 1. The effective mass of undoped ZnO nanowires is 0.593 me, which is larger than that of bulk ZnO (0.24 me).26
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depends mainly on the phonons scattering, which is closely related to the diameter of nanowires, the doping level and temperature. Here, we use the Debye–Callaway model to calculate kph.29 In this model, kph can be expressed as: ð kB kB T 3 y=T x4 ex kph ¼ 2 tp dx; (2) x h 2p u ðe 1Þ2 0 where kB is the Boltzmann constant, u is the average sound velocity of phonons, T is the absolute temperature, y is the Debye temperature (399.5 K for ZnO),30 x = ho/kBT, o is the phonon frequency, and tp is the combined relaxation time of phonons. The form of the combined relaxation time used here is: y þ B2 o2 T; (3) tp1 ¼ tb1 þ Ao4 þ B1 exp aT
Fig. 4 Electron localization function for undoped ZnO nanowires (a) and Al (b), Ga (c), Sb (d) doped ZnO nanowires. The slices are parallel to the (101% 0) plane and pass through the center of impurity atoms. In Sb doped ZnO nanowires (d), one of nearest-neighbor O atoms is out of the slice plane due to the larger atomic radius of Sb.
Generally, compared with bulk, nanostructures tend to exhibit larger effective masses due to the strong quantum confinement effect. From Table 1, we also note that the electron effective masses of ZnO nanowires increase after being doped with Al, Ga and Sb, which is similar to the reported experimental results.27 This increase is mainly due to the interaction or admixture of host states and impurity states at the conduction band minimum. 3.2
Thermoelectric properties
In the calculations of thermoelectric properties, the electron relaxation time te is a necessary parameter. From the BoltzTraP code, we can only obtain the ratio of electrical conductivity s to electron relaxation time te. In this work, the value of te is obtained by fitting the ratio s/te to measured electrical conductivity data of ZnO nanowires. However, there is lack of the experimental data for 9.80 Å doped ZnO nanowires. Recently, the electrical properties of Al doped ZnO nanowires with the diameter of 20–80 nm were explored by Noriega and coworkers.28 Here, we use their data to estimate the electron relaxation time te of doped ZnO nanowires (r = 1/s = 2.6 103 Ocm, n = 8.8 1019 cm3, T = 300 K). Additionally, te varies with different atomic structure, carrier concentrations and temperature. For simplicity and convenience, we only consider the influence of carrier concentrations and temperature on the electron relaxation time te in our calculation. We use a standard electron–phonon dependence on n and T for te, namely, te = CT1n1/3, where C is a constant. C can be obtained by inserting the value of te. Finally, we have the relationship of te with n and T. Another parameter that needs to be determined in calculating the figure of merit ZT is the lattice thermal conductivity kph. kph
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where tb is the phonon-boundary scattering relaxation time, Ao4 approximates the impurity scattering and the third term o2T describes the phonon–phonon scattering. Here the relaxation time parameters A, B1 and B2 are 1.7 1044 s3, 4.7 1019 s K1, 2.8 1020 s K1, respectively.29 The phonon-boundary scattering relaxation time tb is described by tb1 = u/d based on the Casimir model (d is the diameter of ZnO nanowires). The average sound velocity of the phonons, u, can be calculated from the equation: 3 1 2 ¼ þ ; u3 uL3 uT 3
(4)
where uL = 6365 ms1 and uT = 2735 ms1 are the longitudinal and transverse sound velocities in bulk ZnO, respectively.30 The lattice thermal conductivity of ZnO nanowires calculated by this method agrees well with the experiment data.31,32 Fig. 5 shows the temperature dependence of kph for doped ZnO nanowires in our calculations. At low temperatures (less than 400 K), boundary scattering predominates. In the Debye–Callaway model, the phonon-boundary scattering is frequency independent and temperature independent. Therefore, the thermal conductivity basically goes as T3. As the temperature increases further, the impurity scattering and the phonon–phonon
Fig. 5 Temperature dependence of the thermal conductivity for the ZnO nanowires.
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Fig. 6 Room temperature thermoelectric properties of Al, Ga and Sb doped ZnO nanowires as a function of carrier concentration: (a) electrical conductivity s, (b) Seebeck coefficient S, (c) power factor P(sS2), (d) figure of merit ZT.
scattering become important and the thermal conductivity first increases to a maximum then decreases. The electrical conductivity s, Seebeck coefficient S, power factor P and figure of merit ZT at room-temperature are shown in Fig. 6 as a function of carrier concentration. In this study, the impurity concentration is fixed at 2.1%. Given the impurities are fully ionized, the carrier concentration should be about 1.3 1021 cm3. However, according to the amphoteric defect model (ADM), native defects would be generated in semiconductor materials in response to extrinsic doping.33 Based on ADM and quantum confinement effects, Khanal and his coworkers suggest that the maximum electron concentration that can be achieved in ZnO nanowires with the diameter under 60 nm via doping method is 9 1019 cm3.34 Thus the maximum carrier concentration we consider in this paper is 9 1019 cm3. Using the rigid band model, we manually adjust the Fermi level in order to change the carrier concentration. It is well known that the electrical conductivity s is directly proportional to the carrier concentration. As shown in Fig. 6(a), s of doped ZnO nanowires increases when the carrier concentration increases. However, there is a trade off if we look at the Seebeck coefficient S shown in Fig. 6(b). S monotonically decreases with the carrier concentration increasing. The Seebeck coefficient S can be expressed as k Nc S ¼ ln ; (5) n e where n is the carrier concentration, and Nc is the effective state for the conduction band, which is given by Nc = 2(2pm*kT/h2)3/2. Therefore, the trend of S with carrier concentration could be explained by eqn (5). From eqn (5), we also could find that m* determines S through the parameter Nc. Although the difference in the Seebeck coefficient for Al, Ga and Sb doped ZnO nanowires is not significant in Fig. 6(b), we still could see that Sb doped ZnO nanowires have a larger Seebeck coefficient at the same carrier concentration. This result can be attributed to the higher effective
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mass of Sb doped ZnO nanowires. The power factor P(sS2) as a function of carrier concentration is shown in Fig. 6(c). Clearly, there is an optimal carrier concentration yielding the maximum value of P. The Ga doped ZnO nanowire has higher maximum value of P compared with Al, Sb doped ZnO nanowires. We show the figure merit ZT of doped ZnO nanowires at 300 K in Fig. 6(d). Similar to the power factor, ZT of doped ZnO nanowires also has the optimal carrier concentration. The physical reason for this phenomenon could be explained as follows. The electronic thermal conductivity kel can be estimated by the Wiedemann–Franz law, kel = LsT. L, known as the Lorenz number, is about 2.44 108 W O K2. The maximum value of kel calculated from Fig. 6(a) is about 0.33 W mK1. We can find that the electronic thermal conductivity is far smaller than the lattice thermal conductivity kph, which implies k E kph. Thus, with the carrier concentration increasing, the opposite trend could be observed between the electrical conductivity s and Seebeck coefficient S. Meanwhile, the thermal conductivity k would nearly be constant. Based on the reasons mentioned above, ZT should have a maximum value which corresponds to the optimal carrier concentration. The maximum value of ZT, 0.147, is obtained for Ga doped ZnO nanowires, when the carrier concentration is 3.62 1019 cm3. In the figure we also observe that ZT of Ga doped ZnO nanowires is always larger than that of Sb, Al doped ZnO nanowires. This phenomenon arises from the higher electrical conductivity of Ga doped ZnO nanowires due to low effective mass. Furthermore, we investigate the thermoelectric properties of Al, Ga and Sb doped ZnO nanowires with increasing temperature. In this study, we selected the doping level at which ZT achieves the maximum value at room temperature. The calculated results are shown in Fig. 7. In Fig. 7(a), we can see that the electrical conductivity first increases, then decreases when the temperature increases. This can be understood from a competition between carrier concentration and electron relaxation time. In Fig. 7(b), we can clearly observe that Sb doped ZnO nanowires have a higher Seebeck coefficient at higher temperature. This leads to a larger increase of ZT for Sb doped ZnO
Fig. 7 (a) The electrical conductivity s, (b) Seebeck coefficient S, (c) power factor P(sS2), and (d) figure of merit ZT of Al, Ga, Sb doped ZnO nanowires with the change in temperature.
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nanowire between 400 K to 1200 K compared with Ga doped ZnO nanowires, which can be seen in Fig. 7(d). In other words, Sb doped ZnO nanowires have a higher ZT value in this temperature range. From Fig. 6 and 7, we can find that Al doped ZnO nanowires always have poor thermoelectric properties. It means that the Al dopant may not be the optimal choice when we want to enhance the thermoelectric properties of ZnO nanowires by the doping method.
4 Conclusion The electronic structure and thermoelectric properties of Al, Ga and Sb doped ZnO nanowires are calculated in this paper. The electronic structure results show that band gaps of ZnO nanowires are narrowed after doping with Al and Ga, while band gap broadening is observed in Sb doped ZnO nanowires. Additionally, Sb doped ZnO nanowires have a higher effective mass. Furthermore, there exists an optimal carrier concentration yielding the maximum value of ZT for Al, Ga and Sb doped ZnO nanowires at room temperature. The maximum value of ZT, 0.147, is obtained for Ga doped ZnO nanowires, when the carrier concentration is 3.62 1019 cm3. The figure of merit ZT of Sb doped ZnO nanowires is higher than that of Ga doped ZnO nanowires when the temperature is between 400 K and 1200 K. We also find that Al doped ZnO nanowires always have poor thermoelectric properties, which means that the Al dopant may not be the optimal choice for ZnO nanowires in thermoelectric applications.
Acknowledgements This research was sponsored by the National Natural Science Fundation of China (No. 51371036, 21071045 and 11305046), the Program for New Century Excellent Talents in University (No. NCET-10-0132), Program for Innovative Research Team (in Science and Technology) in University of Henan Province (No. 13IRTSTHN017), and Foundation of Henan Educational Committee (13A1470076 and 14A430029).
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