Electronic Structure and Thermoelectric Properties of ZnO Single

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Electronic Structure and Thermoelectric Properties of ZnO Single-Walled Nanotubes and Nanowires Chao Wang, Yuanxu Wang, Guangbiao Zhang, and ChengXiao Peng J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp403827n • Publication Date (Web): 18 Sep 2013 Downloaded from http://pubs.acs.org on September 27, 2013

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The Journal of Physical Chemistry

Electronic Structure and Thermoelectric Properties of ZnO Single-Walled Nanotubes and Nanowires Chao Wang, Yuanxu Wang,∗ Guangbiao Zhang, and Chengxiao Peng Institute for Computational Materials Science,School of Physics and Electronics, Henan University,Kaifeng,475004,China E-mail: [email protected]

∗ To

whom correspondence should be addressed

1 ACS Paragon Plus Environment


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Abstract Based on ab initio electronic structure calculations and Boltzmann transport theory, the size dependence of thermoelectric properties of ZnO single-walled nanotubes (SWNTs) and nanowires was investigated. There is an optimal carrier concentration yielding the maximum value of ZT at room-temperature. The optimal carrier concentration and the maximum value of ZT depend on the diameters and structure of ZnO. The maximum value of ZT for ZnO SWNTs are remarkably higher than that of ZnO nanowires. The 9.60 Å ZnO SWNT possess the highest ZT value, 0.322, which is nearly 3-fold higher than that of best experimental samples at roomtemperature. Keywords: thermoelectricity; nanostructures; zinc oxide; density functional theory

Introduction Thermoelectric materials could generate electrical power from waste heat, for example, the engine of automobiles, power plants, and are regarded as promising candidates in solving the energy crisis. However, traditional thermoelectric materials have not been widespread due to their low energy conversion efficiency. The conversion efficiency of a thermoelectric material is evaluated by the dimensionless figure of merit ZT = S2 σ T /κ , where S, σ , T and κ are the Seebeck coefficient, electrical conductivity, absolute temperature and thermal conductivity, respectively. Large ZT materials may have either higher thermoelectric power factor S2 σ , or lower thermal conductivity κ . However, S, σ , and κ are interdependent and cannot be controlled independently in bulk materials. 1 Therefore, it is difficult to increase the value of ZT. As first proposed by Hicks and Dresselhaus, large improvements in figure of merit could be achieved in nanostructured systems due to the large reduction of κ arising from phonon scattering and keeping high electron mobility. 2 The prediction has been evidenced by recent experiments in nanostructured thermoelectric materials. For example, Si nanowires possess a 100-fold improved thermoelectric performance over bulk Si near room temperature. 3,4 This thus opens up a new strategy on the search of thermoelectric materials with high ZT value. 2 ACS Paragon Plus Environment

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Zinc oxide (ZnO) is promising for the thermoelectric applications because it is low cost, nontoxic, stable in high temperature, especially its excellent charge carrier transport properties are tunable via doping. 5–7 Al-doped ZnO (Al0.02 Zn0.95 O) shows reasonably good thermoelectric performance (ZT ≈ 0.3 at 1000K). 8 Unfortunately, ZnO materials possess high lattice thermal conductivity due to noncomplex wurtzite structure, 9 which heavily limits the interests of ZnO materials in thermoelectric application. Based on Hicks and Dresselhaus’s theory, it is believed that nanostructured ZnO materials could overcome the problem of high thermal conductivity in ZnO bulk materials. Recently, more efforts in theory and experiments were made to investigate thermoelectric performance of nanostructured ZnO materials 10–14 and some exciting progress has been made. 15 However, most of previous research has focused on ZnO nanowires, there is little work about thermoelectric performance of the other important ZnO nanostructures, such as ZnO nanotubes. In last few years, multiwalled ZnO nanotubes have been successfully synthesized. 16,17 Although ZnO SWNTs have not been synthesized until now, the theoretical studies have suggested that ZnO SWNTs might be synthesized through solid-vapor phase processes. 18 Especially, Xiao et al. pointed out that for one-dimensional ZnO nanostructures, SWNTs could be more stable than wires. 19 Additionally, the wall of ZnO SWNTs is only one atom layer, which would dramatically reduce κ arising from phonon scattering and increase ZT value. However, to the best of our knowledge, there have been no systematical theoretical reports about thermoelectric properties of ZnO SWNTs. In this paper, we present some theoretical results about thermoelectric properties of ZnO SWNTs oriented along the [0001] direction, which is the commonest growth direction of multiwalled ZnO nanotubes fabricated in experiments. Meanwhile, the results of ZnO nanowires are also given for comparison purpose. The influence of the size of ZnO SWNTs and nanowires on thermoelectric performance has been discussed in our work.



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Computational methods The atomistic relaxation and electronic structure calculation were performed using density functional theory (DFT) within projector augmented wave pseudopotentials as implemented in the VASP program package. 20,21 We used local density approximation (LDA) to treat the electronelectron exchange interaction. We chose the LDA instead of the PBE in this work since the PBE catastrophically overestimates both equilibrium volume and the strain for the binary semiconductors. 22–24 Before calculating the electronic structures, all the coordinates of atoms and the lattice parameters of ZnO SWNTs and nanowires were fully relaxed by a conjugate gradient technique. The kinetic energy cutoff of 400 eV was used to expand the electronic wave functions 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 × 10−5 eV/atom for total energy, 0.04 eV/Å for maximum force. The tolerance in the self-consistent field (SCF) calculation was 1 × 10−6 ev/atom. We also performed the spin-polarized calculations to evaluate the effect of spin in ZnO nanowires and SWNTs. No magnetism was found. This result is consistent with the published references. 25,26 The thermoelectric properties of ZnO SWNTs and nanowires were calculated based on Boltzmann transport theory, using BoltzTraP code. 27 This method used the electronic structures of ZnO SWNTs and nanowires calculated by VASP. Monkhorst-Pack special k-point grid 1 × 1 × 15 was used to integrate in Brillouin zone for the calculations of transport coefficients. In the BoltzTraP code, the electron scattering time is assumed independent of energy. The scattering time drops out of the expression for the Seebeck coefficient so we need not even know its magnitude when we calculate the Seebeck coefficient. In general, it is a good approximation as long as the scattering rate does not vary radically on an energy scale of a few kT . It has been used with quantitative accuracy in calculating thermopowers of ZnO and other materials. 28–30 However, when we calculate the electrical conductivity, we need the explicit treatment of electronic relaxation time τ . Recent results suggest that the electrical conductivity is less sensitive to a decrease in nanostructure size. 3,31,32 From the point of conductivity, we can consider nanotubes as the nanostructure with the 4 ACS Paragon Plus Environment

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further reduction of featured size of nanowires. Thus, we can treat τ as a constant and adopt the relaxation time of ZnO nanowires with average diameters of 150 nm for simplicity and convenience (τ = 28 f s). 33 This approximation has been successfully employed in previous works. 14,34

Results and discussion Geometry optizomization The ZnO SWNTs and nanowires have been created from a 9 × 9 × 1 supercell of ZnO having the wurtzite crystal structure. The process of building the SWNTs and nanowires is described as follows: ZnO nanowires are constructed by removing all atoms outside the big circle area in Figure Figure 1(a). ZnO nanotubes are obtained by removing the atoms from the outside and inside area of the two circles in Figure Figure 1(a). The diameter of the ZnO SWNTs and nanowires is varied ¯ and [0110] ¯ direction by changing the diameter of the circles. The vaccum region along the [1010] in the structures of ZnO SWNTs and nanowires is over 10Å, which ensures that nanowires and SWNTs in neighbouring supercells do not interact with each other. The optimized atomic structures of ZnO SWNTs and nanowires are shown in Figure Figure 1(b)-(e). The relaxation of ZnO SWNT ( nanowires ) with different diameters exhibit similar trend. Herein, we take 9.60Å ZnO SWNT and 9.51Å ZnO nanowire for example to analyze the results of relaxation. We could find that the initial polygon structure of ZnO nanotube transform into a perfect cylindrical tube after relaxation. The distance between Zn and O atoms approximately ¯ direction in initial polygon structure changes from 1.973 to 1.853Å, amounting along the [0110] to a contraction of -6.08%. The length of relaxed Zn-O bond along [0001] direction is found to be 1.850Å, which corresponds to a contraction of -7.04% from bulk value. For ZnO nanowire, the relaxed Zn-O bond length on the outmost surface layer along the [0001] direction is 1.835Å, while that in the inner sites is 1.968Å. It is obvious that the relaxation of the atoms in the inner sites is much smaller as compared to that in the outermost surface layer.



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Figure 1: (a) Top view of a 9 × 9 × 1 ZnO supercell with wurtzite structure. (b)-(e) The relaxed atomic structure of ZnO SWNTs and nanowires with diameters of 9.60, 15.70, 9.51 and 15.84 Å, respectively. (b)-(e) are central projection of the structures viewed along [0001] direction. Grey and red spheres represent the Zn and O atoms, respectively.

Electronic structures The thermoelectric properties of materials would be affected by the band structure. Therefor, we calculated the band structures of ZnO SWNTs and nanowires, and the results are presented in Figure Figure 2. The band structures are shown along the growth direction of nanowires and nanotubes. The band gaps of ZnO SWNTs and nanowires are listed in Table Table 1. We could find that the calculated band gaps of ZnO nanostructures are well bellow the experimental value of ZnO. It is well known that the LDA usually underestimate the band gap, but the trend of the band gaps of ZnO nanostructures predicted from the LDA calculations are expected to be correct. Moreover, the obtained band gaps of ZnO nanowires are in agreement with the other calculated results. 12,14 It is easy to notice that the band gap of ZnO nanowire decreases as the diameter increases, showing a result of quantum confinement. However, there appears to be little variation in the band gaps of ZnO SWNTs with the diameters increasing. Our results of the band gaps of ZnO nanotubes are very similar with earlier reported results. 35 Elizondo and Mintmire also reported that the band gaps of ZnO nanotubes remain fairly constant despite different radii and geometries. 36 The same trend, band gap is insensitive to the nanotube diameter, was discovered in other nanotubes (for example, InN nanotubes 37 ). This can be understood from a competition between two different 6 ACS Paragon Plus Environment

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mechanisms. The quantum confinement effect favors the increase of the band gaps with reduction of diameters. However, the surface dangling bonds would lead to the decrease of the band gaps as the diameters decrease. The reason is that the dangling bonds are responsible for the distribution of surface states at the top of the valence band and bottom of the conduction band. For ZnO SWNT, the high-density surface states counteract the increasing bandgap value from the contribution of the quantum confinement effect, which result in nearly constant band gaps.

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Γ

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Figure 2: Electronic band structures of ZnO SWNTs and nanowires. (a) and (b) are the band structures of ZnO SWNTs with diameters of 9.60 and 15.70Å, respectively. (c) and (d) are corresponding to the band structures of 9.51 and 15.84 Å nanowires, respectively. Of the three factors comprising Z, Seebeck coefficient S and electrical conductivity σ are closely related to effective masses m∗ . S can be expressed as k Nc S = ln( ), e n 7 ACS Paragon Plus Environment

(1)


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Table 1: Band gaps (Eg ), electron effective masses (m∗e ), hole effective masses (m∗h ) and lattice thermal conductivity (κl ) of ZnO SWNTs and nanowires diameter(Å) Eg (eV) m∗e (me ) m∗h (me ) κl (Wm−1 K−1 ) a Data given in Ref 38–42

SWNTs 9.60 15.70 1.55 1.61 0.605 0.596 -0.586 -0.559 0.44 0.47

nanowires 9.51 15.84 1.51 1.16 0.580 0.522 -3.466 -3.657 2.84 4.55

bulka 3.4 0.29 -0.31,-1.98 54

n is the carrier concentration, and Nc is the effective density of states for conduction band, which is given by Nc = 2(2π m∗ kT /h2 )3/2 . It could be found that m∗ determines S through the parameter Nc . σ can be given by

σ = ne2 τ /m∗ ,

(2)

Hence, an increase of m∗ leads to a significant decrease in electrical conductivity and increase in Seebeck coefficient. In fact, the net effect of high effective mass is a lower thermoelectric figure of merit, zT , when the carriers are predominantly scattered by phonons according to the deformation potential theory of Bardeen-Shockley. 43 m∗ at the minimum of conduction bands and the maximum of valence bands can be evaluated by

m∗ = h¯ 2 (

∂ 2 E −1 ) . ∂ kz2

(3)

We calculate electron effective masses m∗e and hole effective masses m∗h of ZnO SWNTs and nanowires along the growth direction by choosing a small region around the band extrema. The results are shown in Table Table 1 accompanied with experimental values. First, our calculations show that the effective masses of ZnO SWNTs and nanowires are larger than that of bulk ZnO. Generally, compared with bulk, nanostructurs tend to exhibit a larger effective masses due to strong quantum confinement effect. In addition, we note that the smaller the diameter of SWNTs/nanowires the larger the electron effective mass, which is consistent with other reports. 12,44 We also find that the electron effective masses of ZnO SWNTs are larger than that of


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ZnO nanowires at similar diameters. Now we discuss the change of hole effective masses. There are topmost three bands around Γ in the conduction bands of bulk ZnO. 28 Baskoutas and Bester found that the hole state of ZnO exhibit a size dependence, which could lead to band crossings. 45 This phenomenon also could be observed in Figure Figure 2. In fact, the hole effective masses listed in Table Table 1 correspond to two different bands. With the decrease of featured size, the light band would shift upward. The hole effective masses of ZnO SWNTs correspond to the light band, while the hole effective masses of ZnO nanowires correspond to the heavy band.

Thermoelectric properties As mentioned above, the figure of merit ZT could be calculated when the electronic conductivity

σ , Seebeck coefficient S and thermal conductivity κ are known. σ and S could be evaluated from the electronic structure. The thermal conductivity contains electronic and lattice contributions,

κ = κe + κl . The electronic thermal conductivity κe depends on the electronic band structure and also could be obtained by the Wiedemann-Franz law, κe = Lσ T ( L is the Lorentz number). The lattice thermal conductivity κl depends mainly on the phonons scattering, which are closely related to the diameter and wall thickness of nanotubes or nanowires. Here, we use the Debye-Callaway model to calculate κl . 46 In this model, the lattice thermal conductivity κl can be expressed as: kB κl = 2 2π υ

kB T h¯

3 Z

0

θ /T

τp

x 4 ex dx, (ex − 1)2

(4)

where kB is the Boltzmann constant, υ is the average sound velocity of phonon (3100 ms−1 ), 47 T is the absolute temperature, θ is the Debye temperature (399.5 K for ZnO), 48 x = h¯ ω /kB T , and τ p is the combined relaxation time of phonons. The form of the combined relaxation time used here is:

τ p−1

= τb−1 + Aω 4 +

θ B1 exp − + B2 ω 2 T, aT

(5)

where τb is the phonon-boundary scattering relaxation time, Aω 4 approximates the impurity scattering and the third term ω 2 T describes the phonon-phonon scattering. Here the relaxation time 9 ACS Paragon Plus Environment


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parameters A, B1 and B2 are 1.7 × 10−44 s3 , 4.7 × 10−19 sK−1 , 2.8 × 10−20 sK−1 , respectively. 46 The phonon-boundary scattering relaxation time τb can be described by τb−1 = υ /d based on the Casimir model (d is the featured size). However, for ZnO nanotubes, we have to consider the specular scattering at the boundary. We now introduce the parameter p when we calculate the phonon-boundary scattering relaxation time of nanotubes. The value of p represents the probability that the phonon is undergoing a specular scattering event at the boundary. Then the expression of τb could be adjusted to τb−1 = υ (1 − p)/d. A large p value, 0.8, which corresponds to a great probability of specular scattering is used in our calculations. Finally, we can calculate the lattice thermal conductivity κl of ZnO nanowires and nanotubes by combining Equation Eq. (4) and Equation Eq. (5). The calculation results of κl for ZnO SWNTs and nanowires at room-temperature are listed in Table Table 1. We could find that thermal conductivity of ZnO nanostructures show significant decrease compared with bulk ZnO, which is mainly due to enhancement of phonon boundary scattering. The calculated thermoelectric properties of ZnO SWNTs and nanowires at room-temperature are shown in Figure Figure 3 as a function of carrier concentration. The rigid band model is employed in order to calculate the thermoelectric coefficients for different carrier concentrations. According to equation (Eq. (2)), the electrical conductivity σ is directly proportional to the carrier concentration. As shown in Figure Figure 3(a), σ of ZnO SWNTs and nanowires increases when the carrier concentration increases. However, there is a trade off if we look at the Seebeck coefficient S shown in Figure Figure 3(b). When the carrier concentration increases, S monotonically decreases, which also could be concluded from equation (Eq. (1)). As mentioned earlier,

σ is in inverse proportion to effective mass. In Figure Figure 3(a), it is easily find that at the same carrier concentration, the order of σ values from highest to lowest are 9.60 Å SWNT, 9.51 Å nanowire, 15.70 Å SWNT and 15.84 Å nanowire. The Seebeck coefficient S in Figure Figure 3(b) follows the inverse trend. In thermoelectric application, the power factor P (σ S2 ) is an important factor influencing the thermoelectric performance directly. The power factor as a function of carrier concentration is given in Figure Figure 3(c). There is an optimal carrier concentration


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2500 9.60 Å SWNT 15.70 Å SWNT 9.51 Å nanowire 15.84 Å nanowire

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Figure 3: Room-temperature thermoelectric properties of ZnO SWNTs and nanowires as a function of carrier concentration: (a) electrical conductivity σ ; (b) Seebeck coefficient S; (c) power factor P(σ S2 ); (d) figure of merit ZT



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yielding the maximum value of P. As the diameter of ZnO SWNT/nanowire increases, the maximum value of P decreases and optimal carrier concentration shifts to lower carrier concentration. Furthermore, ZnO SWNTs have higher maximum value of P comparing with ZnO nanowires at similiar diameters. Combined the calculations of the power factor and the lattice thermal conductivity, we show the figure merit ZT in Figure Figure 3(d). The ZT value firstly increases with the carrier concentration, reaches a maximum value and then decreases. Similar to power factor, the smaller the diameter of ZnO SWNT/nanowire the higher the maximum value of P. However, we could find that the maximum value of ZT for ZnO SWNTs are remarkably higher than that of ZnO nanowires. This phenomenon arises from significant decrease of the lattice thermal conductivity in ZnO SWNTs. In the case of 9.60 Å ZnO SWNT, the maximum value of ZT is 0.322 when the carrier concentration is 4.3 × 1019 cm−3 . This result is nearly 3-fold higher than that of best experimental samples ( non-nanostructured Al-doped ZnO) at room-temperature. 49

Conclusion In summary, we have investigated the structural, electronic and thermoelectric properties of ZnO SWNTs and nanowires. ZnO SWNTs with different diameters would transform into perfect cylindrical tubes after relaxation. For ZnO nanowires, band gap increases as the diameter decreases due to quantum confinement effect. However, we find that band gap is insensitive to the diameter of ZnO SWNT, which is very interesting from the point of view of applications. Additionally, we also note that the electron effective masses of ZnO SWNTs are larger than that of ZnO nanowires at similar diameters. There is an optimal carrier concentration yielding the maximum value of ZT at room-temperature. The optimal carrier concentration and the maximum value of ZT depend on the diameters and structure of ZnO. The maximum value of ZT for ZnO SWNTs are remarkably higher than that of ZnO nanowires. The 9.60 Å ZnO SWNT possess the highest ZT value, 0.322, which is nearly 3-fold higher than that of best experimental samples at room-temperature.


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Acknowledgement This research was sponsored by the National Natural Science Foundation of China (No. 51371036 and 21071045), Program for Innovative Research Team (in Science and Technology) in University of Henan Province (No. 13IRTSTHN017), the Program for New Century Excellent Talents in University(No. NCET-10-0132), the Technological Cooperation Project between the Academy of Sciences and Henan Province (No. 092106000033).

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Table of Contents 0.4

0.3

ZT

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

9.60 Å SWNT 15.70 Å SWNT 9.51 Å nanowire 15.84 Å nanowire

0.2

0.1

0 18 10

10

20

19

10 -3



Page 18 of 18

Electronic Structure and Thermoelectric Properties of ZnO Single

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