Structural, Electronic, and Thermoelectric Properties of InSe

Article pubs.acs.org/JPCC

Structural, Electronic, and Thermoelectric Properties of InSe Nanotubes: First-Principles Calculations Hai Gang Si, Yuan Xu Wang,* Yu Li Yan, and Guang Biao Zhang Institute for Computational Materials Science, School of Physics and Electronics, Henan University, Kaifeng 475004, People’s Republic of China ABSTRACT: The structural, electronic, and thermoelectric properties of InSe nanotubes (InSeNTs) are investigated using first-principle calculations based on density functional theory (DFT). The thermoelectric transport coefficients of InSeNTs at room temperature are calculated within the semiclassical Boltzmann theory. Calculated total energies show that (2,2) InSeNT is more stable than other ones. As a consequence of high Seebeck coefficient and reasonable electrical conductivity, its thermoelectric powerfactor with respect to relaxation time is much larger than those of other studied InSeNTs and is nearly 10 times larger than that of BiSb nanotube. The light and heavily bands appear together around the Fermi level in (2,2) InSeNT, inducing its high Seebeck coefficient and reasonable electrical conductivity. (2,2), (4,0), and (6,0) InSeNTs are metallic. (3,3), (4,4), (6,6), and (8,0) InSeNTs are semiconducting. It is found that each Se atom in the semiconducting InSeNTs is coordinated by two In atoms, and that in the metallic InSeNTs is coordinated by three In atoms. The current research proposes a new type of nanotubes to design high-performance thermoelectric materials.

I. INTRODUCTION Thermoelectric materials can convert energy between heat and electricity without moving parts and carbon dioxide production. For the current energy challenges and environmental crisis, thermoelectric materials have recently attracted increasing interest. The thermoelectric performance of a given material is characterized by the materials’ dimensionless figure of merit ZT defined as ZT = S 2 σT /(κ e + κ l)

necessary for a desired goal. In fact, so far, ZT in bulk materials has remained stuck in the range of 0−1 at low temperature (⩽300 K).5 Since the three physical parameters S, σ, and κ are coupled with each other, it remains a major difficulty to further enhance the ZT value in bulk thermoelectric materials. In 1993, Hicks et al. theoretically predicated that two- and one-dimensional structures could have much larger ZT values than the corresponding bulk materials.6−8 High ZT has been achieved in many thermoelectric nanocomposites. For example, peak ZT is increased from 1.0 in bulk to 1.4 in p-type BixSb2−xTe3 nanocomposites, from 0.65 in bulk to 0.95 in ptype Si80Ge20 nanocomposites, and from 0.9 in bulk to 1.3 in ntype Si80Ge20 nanocomposites.9 Bi-based low-dimensional materials such as Bi1−xSbx thin film,10−12 nanowires,13−16 and nanotubes17 have been successfully produced, and enhanced thermoelectric performances have been found in them. Chen et al. theoretically predicted that a ZT value higher than 1 at 300 K is achievable for 1.7 nm diameter Si/Ge superlattice nanowires in the case of a 3-order reduction on lattice thermal conductivity with respect to bulk Si.18 It was found that the ZT value of the Ge/Si core shell nanowire with p-type doping can reach 0.85 at 300 K.19 The improvement of thermoelectric efficiency in low-dimensional systems can be attributed to the enhanced power factor caused by a sharp density of states (DOS) near the Fermi level, as well as the reduced lattice

(1)

where S is the Seebeck coefficient (thermopower), σ (σ = 1/ρ, ρ is the electrical resistivity) is the electrical conductivity, T is the absolute temperature, κe is the electronic thermal conductivity, which is linked to the electrical conductivity by the Wiedemann−Franz law, and κl is the lattice thermal conductivity.1 High performance of a thermoelectric material requires a high ZT with an effort to maximize the power factor S2σ and minimize κ (κ = κe + κl). Recently, Rhyee et al. have successfully synthesized a binary crystalline n-type material, In4Se3−δ, and found that its ZT is 1.48 at 705 K, which is very high for a bulk material.2 They also pointed out that the charge density wave instability and the anisotropic electronic band structure are responsible for the large anisotropy observed in the electric and thermal transport.3 Its high ZT value is the result of the high Seebeck coefficient and low thermal conductivity in the plane of charge density wave. Polycrystalline In4Se3 was also reported by Shi et al. with a maximum ZT of less than 0.6 at 700 K, which comes from its small power factor.4 It is believed that a ZT value exceeding 3 is © 2012 American Chemical Society

Received: November 3, 2011 Revised: January 12, 2012 Published: January 18, 2012 3956

dx.doi.org/10.1021/jp210583f | J. Phys. Chem. C 2012, 116, 3956−3961

The Journal of Physical Chemistry C

Article

Figure 1. Crystal structure of In4Se3 (a) and the model of planar InSe sheet (b). Red and purple spheres represent In and Se atoms, respectively.

thermal conductivity owing to the increased phonon scattering. InSe nanotubes (InSeNTs) extracted from corresponding bulk In4Se3 may also have high thermoelectric performance. In this work, we aim to achieve a better thermoelectric performance for InSeNTs by contacting the low-dimensional system of In4Se3. In this work, we investigate the structural, electronic, and thermoelectric properties of InSeNTs. First, the structural stabilities and electronic properties are studied by using the first-principles method. Then, the thermoelectric transport properties are calculated by using the semiclassical Boltzmann theory and rigid-band approximation. Figure 2. Side and top views of initial InSeNTs cut from crystal In4Se3 (a,b) and optimized (2,2) InSeNT (c,d). Purple and red spheres represent In and Se atoms, respectively.

II. COMPUTATIONAL DETAILS The geometry optimization has been carried out within the projector augmented wave (PAW) method as implemented in the Vienna ab initio simulation package (VASP).20−22 The plane-wave cutoff energy of 500 eV and 2 × 2 × 8 Monkhorst− Pack k-points are chosen to ensure that the total energies of all structures are well converged to be less than 1 meV. The closest distance between InSeNTs is set to be 12 Å, so that they can be treated as independent entities. Electronic structure calculations are performed using the self-consistent full-potential linearized augmented plane waves (FP-LAPW) method based on density functional theory (DFT), using the Perdew−Burke−Ernzerhof of generalized gradient approximation (PBE−GGA)23 for the exchange and correlation potential. The calculations are performed by using WIEN2k.24−26 The Seebeck coefficient S and electrical conductivity are obtained by using the semiclassical Boltzmann theory and the rigid-band approach.27 Within this method, the Seebeck coefficient S is independent of the relaxation time (τ), while the electrical conductivity σ and the electronic component of thermal conductivity κe can only be evaluated with respect to the parameter (τ).

carbon nanotubes as shown in Figure 1b. We investigate the armchair (2,2), (3,3), (4,4), (6,6) and zigzag (4,0), (6,0), (8,0) InSeNTs. After full relaxation, (3,3), (4,4), and (6,6) InSeNTs become buckled with large difference between maximal diameter and minimal diameter as shown in Figure 3b, whereas (2,2), (4,0), and (6,0) InSeNTs basically keep their initial configuration, and (8,0) InSeNT has a gear-like configuration. The structures of the initial nanotube cut from In4Se3 crystal and optimized (2,2) InSeNT are plotted in Figure 2. After relaxation, the In−Se bond perpendicular to the InSeNT axial direction slightly shrinks (from 2.78 Å (B1) to 2.62 Å (B3)). Another type of In−Se bond also contracts a little (from 2.73 Å (B2) to 2.62 Å (B4)). Therefore, the decreased length of the In−Se bond during relaxation means that (2,2) InSeNT becomes more stable. In order to further investigate the stability of these InSeNTs, the binding energy (Eb) of each InSeNT is calculated and is listed in Table 1. The Eb is defined as Eb= Etotal/n − (μIn + μSe), where Etotal is the total energy of each InSeNT, n is the number of In(Se) atoms, μIn is the chemical potential of In in a vacuum, and μSe is the chemical potential of Se in a vacuum. As shown in Table 1, (2,2) InSeNT is the most stable in nearly freestanding conditions because it has the lowest lowest Eb, −6.94 eV. The Eb of armchair InSeNTs increases monotonically with increasing diameters. For the zigzag structure, (8,0) InSeNT is more stable than (4,0) and (6,0) ones, which may be related to its gear-like structure. The Eb of armchair InSeNT is lower than that of zigzag InSeNT with similar diameter, indicating that armchair InSeNTs are more stable than zigzag ones. The buckled and gear-like InSeNTs have a much larger difference between the maximal In−Se bond length and the minimal In−

III. RESULTS AND DISCUSSION The layered structure of In4Se3 crystal is shown in Figure 1a. As seen in this figure, covalently bonded In−Se layers are stacked along the x-axis direction by relatively strong van der Waals interaction. The two-dimensional In−Se crystalline layer is really like parallel nanotubes connecting with each other, and it is reasonable to expect that the nanotube in such layered structure can be stable in freestanding conditions. Since the initial nanotube has the hexagonal basic units displayed in Figure 2a, which are similar to the hexagonal basic unit of graphene, it is natural to construct InSeNTs through rolling an InSe sheet in a manner similar to that for rolling graphene to 3957



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(labeled as band 2 in Figure 4) moves downward more than the lowest conduction band (band 1). The band gap of (8,0) InSeNT is much larger than other semiconducting InSeNTs. From Table 1, we can see that all semiconducting InSeNTs have large ΔB, indicating the strong sensibility of electronic structure to the atomic configuration. Compared with (4,0) InSeNT, the degeneracy of band 3 and band 4 disappears in (6,0) InSeNT, and they split to four bands with other bands around the Fermi level unchanged. In addition, the split bands 3a, 4a, and bands 3b, 4b move upward and downward from the Fermi level, respectively. In order to investigate the origin of the different electronic behavior for the studied InSeNTs, it is valuable to analyze their difference in structural configuration. It is found that the metallic and semiconducting InSeNTs have different atomic configuration. In the metallic InSeNTs, each In atom is coordinated by three Se atoms with bond lengths from 2.52 to 2.71 Å. However, the In atom in the semiconducting InSeNTs is coordinated by four Se atoms with bond lengths from 2.64 to 2.73 Å. Furthermore, each Se atom in the semiconducting InSeNTs and metallic InSeNTs is coordinated by two and three In atoms with bond lengths of about 2.7 Å, respectively. Therefore, the semiconducting and metallic InSeNTs have very different atomic configurations. The valence electronic configuration of the Se atom is 4s24p4. That is to say, there are two half-filling p orbital in each Se atom. In the semiconducting InSeNTs, the Se atom is coordinated by two In atoms, and, consequently, the partially filled p orbital of the Se atom will be fully filled during constructing these semiconducting InSeNTs. However, the Se atom in the metallic InSeNTs is coordinated by three In atoms, which will result in their metallic characteristic. Hence, the filling degree of the out-most p orbital for the Se atom should play a key role in determining whether these InSeNTs are semiconducting or metallic. Since the electron states around the Fermi level have an important effect on the thermoelectric transport properties of these studied InSeNTs, we calculated their total and partial density of states (TDOS and PDOS) and draw them in Figure 5. As seen in this figure, the DOSs on the Fermi level of (2,2) and (6,0) InSeNTs are equally attributed to the In s, In p, and Se p states. From −3.5 to −1 eV, the In s states have a weak contribution to their TDOS. The similar DOS shape around the Fermi level of In s, In p, and Se p shows a strong hybridization between these orbitals. In order to clearly show the bonding properties in these InSeNTs, we calculated their electron density difference (EDD) and plotted them in Figure

Figure 3. Three kinds of atomic configurations of InSeNTs: (a) buckled nanotubes (b-NTs) including (3,3), (4,4), (6,6) InSeNTs, (b) hexagonal nanotubes (h-NTs), which keep the initial configurations including (2,2), (4,0), (6,0), and (c) gear-like nanotubes (g-NTs) including (8,0) InSeNT. Both the top and side views are shown. Purple and red spheres represent In and Se atoms, respectively.

Se bond length (ΔB) than those InSeNTs keeping the initial configuration. Therefore, the chirality and diameter are important to the stability of these studied InSeNTs. To study thermoelectric properties, an accurate electronic structure is required. We calculated the band structures of these studied InSeNTs and plotted them in Figure 4. As seen in this figure, (2,2), (4,0), and (6,0) InSeNTs are metallic, and other ones are semiconducting with indirect band gaps. Moreover, the band gaps of b-NTs ((3,3), (4,4), and (6,6)) decrease with increasing diameters. This decrease in band gaps is mainly due to the downward motion of the bottom two conduction bands. With the increasing diameters, the low-lying conduction band

Table 1. The Binding Energy Per Unit of In−Se Atoms of Seven Kinds of InSeNTs Eb (in eV), and the Average Diameter of Each InSeNT Dave (in Å)a Eb Dave Bmax Bmin ΔB Eg ECBM EVBM

(2,2)

(3,3)

(4,4)

(6,6)

(4,0)

(6,0)

(8,0)

−6.94 5.61 2.702 2.642 0.06

−6.47 5.29/8.33 3.069 2.635 0.434 0.6885 0.6558 −0.03266

−6.42 6.93/10.71 3.067 2.634 0.433 0.5457 0.4727 − 0.07298

−6.34 10.04/13.96 3.125 2.634 0.491 0.2503 0.1583 − 0.10196

−6.09 6.294 2.813 2.726 0.087

−6.03 9.36 2.768 2.734 0.034

−6.22 8.26/11.75 3.173 2.633 0.54 1.8125 1.0738 −0.07428

Maximal and minimal In−Se bond lengths Bmax and Bmin (in Å), and bond length difference ΔB = Bmax − Bmin. Conduction band minimum ECBM, valence band maximum EVBM, and band gaps Eg = ECBM − EVBM (in eV).

a

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Figure 4. Calculated energy band structures of armchair and zigzag InSeNTs. The red arrows indicate that the band gap is direct or indirect.

Figure 6. Calculated EDDs contours for (6,0) InSeNT (left upper), (8,0) InSeNT (left lower), (2,2) InSeNT (right upper), and (3,3) InSeNT (right lower), respectively. Contours plot on the plane including the neighbor In and Se atoms. The value of the contours is from 0 to 0.8 e/Å3 with an increment of 0.01 e/Å3.

Figure 5. Calculated total DOS and partial DOS of (a) (2,2) InSeNT, (b) (3,3) InSeNT, (c) (6,0) InSeNT, and (d) (8,0) InSeNT. The Fermi levels are indicated by dotted lines.

picture, the optimal doping concentration can be obtained by integrating the DOSs of these nanotubes from the Fermi level to the desired chemical potential.31 The peak values for power factors of the studied InSeNTs around the Fermi level are listed in Table 2. As seen in this table, the (2,2) nanotube has the largest peak value of the power factor (1.44 × 1012 W/K2ms) at −0.19 eV, which is nearly 10 times larger than that of BiSb nanotube reported by Lv et al.6 Since the power factor is proportional to the Seebeck coefficient and electrical conductivity, we list our calculated Seebeck coefficient (S) and electrical conductivity of the studied InSeNTs in Table 2. As shown in this table, the absolute values of the Seebeck coefficients for (4,4) and (6,0) InSeNTs are much smaller than those for other InSeNTs. Among these studied InSeNTs, the (2,2) one has the largest S, which makes a large contribution to its high power factor. Another factor for the high power factor of (2,2) InSeNT is its reasonable electrical conductivity. As shown in Table 2, its electrical conductivity is much higher than that of other InSeNTs except for the (6,0) one. Therefore, the high Seebeck coefficient and reasonable electrical conductivity lead to the high power factor of (2,2) InSeNT. The origin of high Seebeck coefficient and reasonable electrical conductivity of (2,2) InSeNT can be explored from its electronic band structure around the Fermi Level. As noted by Zhang et al., a combination of heavy and light bands at the

6. EDD has been generated by subtracting their superpositioned, noninteracting, atomic electron densities (procrystal) from their calculated electron density. EDD is a powerful tool to analyze the bonding properties in a material. Charge accumulation between atoms indicates the formation of a covalent bond. From this figure, it is clearly seen that the neighboring In and Se atoms form strong covalent bonds. We now turn to discuss the thermoelectric transport properties of InSeNTs. Calculated power factors (S2σ) for these studied InSeNTs are plotted as a function of chemical potential (μ) at 300 K in Figure 7, where the relaxation time τ is included as a parameter. Since the electronic relaxation time τ is a complex function of temperature, atomic structure, electron energy, and carrier concentration, it is typically treated as a constant for simplicity and convenience. This method has been used to calculate the transport coefficients of some known thermoelectric materials, and a very good agreement is found with experiment values.28−30 Here we focus on (2,2) InSeNT and b-NTs since they are energetically more favorable than other InSeNTs. We find that for all investigated nanotubes, there exist obviously sharp peaks around the Fermi level, which indicates that the power factors of these nanotubes can be largely optimized by proper doping.6 Within the rigid-band 3959



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achieve high thermoelectric performance. Moreover, nanostructure always has a lower thermal conductivity than the corresponding bulk system. Therefore, (2,2) InSeNT should have a high thermoelectric performance. A strong increase in the Seebeck coefficient has been observed experimentally in Bi nanowires. As shown in Table 2, the S2σ/τ peak of (4,4) InSeNT is larger than those of (3,3) and (6,6) InSeNTs, which is mainly due to the relative high electrical conductivity of (4,4) InSeNT. (3,3), (4,4), and (6,6) InSeNTs (b−-NTs) have similar electronic band structures with different band gaps, as shown in the Figure 4. The moderate band gap of (4,4) InSeNT among the b-NTs could be appropriate and beneficial to balance between the Seebeck coefficient and the electrical conductivity.

IV. CONCLUSION In summary, we have employed first-principles calculations and Boltzmann transport theory to predict InSeNT structures and explore their thermoelectric properties. After full relaxation, (2,2) InSeNT is the most stable one among the studied InSeNTs. (3,3), (4,4), (6,6), and (8,0) InSeNTs are semiconducting. Other studied InSeNTs are metallic. The filling degree of the Se 4p orbital plays a key role in determining whether these studied InSeNTs are semiconducting or metallic. The Se atom in the semiconducting InSeNTs is coordinated by two In atoms, and that in the metallic InSeNTs is by three In atoms. The S2σ/τ of (2,2) InSeNT is much larger than that of other InSeNTs and is nearly 10 times larger than that of BiSb nanotubes around the Fermi level. It is found that an appearance of light and heavily bands around the Fermi level results in its high Seebeck coefficient and reasonable electrical conductivity. The current research proposes new types of nanotubes to design high-performance thermoelectric materials. Moreover, it is possible to further improve the thermoelectric performance of InSeNTs by optimization of tube sizes, doping, or tuning the surface structure in future work.

Figure 7. Calculated power factors with respect to the relaxation time (S2σ/τ) as a function of chemical potential μ of seven kinds of InSeNTs at 300 K.

Table 2. Peak Value of Power Factors with Respect to Relaxation Time S2σ/τ (in 1011 W/K2 ms), and Their Corresponding Seebeck Coefficients S (in μV/K) and Electrical Conductivity with Respect to Relaxation Time (in 1019/(Ω ms)) at 300 K As a Function of Chemical Potential (μ) around the Fermi Level S σ/τ S σ/τ μ 2

(2,2)

(3,3)

(4,4)

(6,6)

(4,0)

(6,0)

(8,0)

14.4 225 2.9 −0.19

0.48 200 0.12 −0.07

1.08 109 1.0 0

0.23 200 0.06 −0.03

3.96 −200 1.0 −0.067

2.8 87 3.4 −0.01

0.61 208 0.15 −0.02

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valence band edge may lead to both high Seebeck coefficient and reasonable electrical conductivity.32 High Seebeck coefficient is usually found in compounds with heavy band mass. High carrier mobility, on the other hand, needs small carrier effective mass. As seen in Figure 4, both heavy and light bands appear around the Fermi level of (2,2) InSeNT, and, consequently, it can achieve its high thermoelectric performance. The enhancement in S of (2,2) InSeNT also can be explained with the Mahan−Sofo theory, which suggests that a local increase in the TDOS over a narrow energy range around the Fermi level can achieve a high S.7,8,33,34 The high electrical conductivity of (2,2) InSeNT is consistent with its high DOS around the Fermi Level, as depicted in Figure 5a. The large value of TDOS around the Fermi level means more conduction electrons can contribute to electrical conductivity. The electrical conductivity is defined by σ = neμ, where n is the carrier concentration, e is the electronic charge, and μ is the carrier mobility. The electrical conductivity is directly proportional to the carrier concentration. Hence, the high DOS around the Fermi level suggests that (2,2) InSeNT has a relatively high carrier concentration, which results in its high electrical conductivity. The high Seebeck coefficient and reasonable electrical conductivity of (2,2) InSeNT prove that nanostructural engineering can provide the possibility to

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was sponsored by the National Natural Science Fundation of China (No. 21071045), the fund of Henan University (No. SBGJ090508), and the Program for New Century Excellent Talents in University (No. NCET-10-0132).

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Structural, Electronic, and Thermoelectric Properties of InSe

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