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Structural Stability and Electronic Properties of InAs Nanowires and Nanotubes: Effects of Surface and Size Haibo Shu, Xiaoshuang Chen,* Huxian Zhao, Xiaohao Zhou, and Wei Lu National Laboratory for Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Science, 200083 Shanghai, People’s Republic of China ReceiVed: June 28, 2010; ReVised Manuscript ReceiVed: September 4, 2010
The surface and size effects on the structural stability and electronic properties of InAs one-dimensional nanostructures are investigated by first-principles calculations within density functional theory. No matter what the diameters, the nanowires are more energetically favorable than the nanotubes due to the preferable sp3 hybridization for In and As atoms in the InAs nanostructures. The formation energies of these nanostructures satisfy a linear dependence relationship with the surface atom ratio. The calculated band structures reveal that the band gaps of InAs nanostructures are determined by two competition mechanisms. One is the quantum confinement effect, which favors the increase of the band gaps with the decreasing diameter or wall thickness. Another is the effect of surface dangling bonds, which induces the decrease of the band gaps with the decreasing diameter or wall thickness. With the same diameter, the band gaps of InAs nanowires are still less than those of the nanotubes. The result indicates that the quantum confinement effect in one-dimensional structures can be enhanced by the formation of tubes instead of wires. I. Introduction One-dimensional semiconductor nanomaterials, such as nanowires (NWs) and nanotubes (NTs), have attracted much attention due to their superiority as the building blocks for the fabrication of nanoscale devices.1,2 Many applications of semiconductor nanomaterials to nanodevices have been demonstrated, such as nanowire diodes,3 field-effect transistors,4,5 photodiodes,6 sensors,7 and solar cells.8 InAs is an important semiconductor material with narrow band gap, high electron mobility (20 times higher than that of Si at room temperature), small electron effective mass, and high-saturation drift velocity.9 In recent years, one-dimensional InAs nanowires have been fabricated by different growth approaches.10-12 Compared to the properties of bulk phase, the InAs nanowires exhibit novel and enhanced electrical and optical functions due to the surface and quantum confinement effects, which make them extremely attractive building blocks for the applications in nanoscale devices.13,14 Since the advent and applications of carbon nanotubes, the nanoscale tubular structures based on InAs are also expected to be synthesized for applications in nanoelectronics. The confinement effect in one-dimensional structures can be enhanced by the formation of tubes instead of wires. It is wellknown that the accessible nanotubes in experiment have bulk phases with the layered crystal structure, such as BN,15 MoS2,16 TiS2,17 ZrS2 and HfS2,18 and NiCl2,19 and with the wurtzite structure, such as SiC,20 AlN,21 GaN,22 ZnO,23 and ZnS,24 respectively. For cubic III-V semiconductor materials with the zinc-blende structure, such as GaAs, InP, and InAs, it is generally thought that their tubular nanostructures are very difficult to be fabricated due to the strong bonding interactions among atoms in the tetrahedral configurations. With the progress in synthesis and fabrication of low-dimensional nanomaterials, InP nanotubes have been first synthesized by using the vapor-liquid-solid (VLS) method.25,26 Recently, Mohan et al. * To whom correspondence should be addressed. E-mail: xschen@ mail.sitp.ac.cn. Phone: +86-21-65420850-24309. Fax: +86-21-65830734.
have synthesized InAs nanotubes based on lattice-mismatched InP/InAs core-shell nanowires.27 Their transmission electron microcopy observation has shown the single-crystalline InAs nanotubes with wurtzite structure, in agreement with the extensive experimental studies that the low-dimensional InAs nanostructures often exhibit a wurtzite crystal structure.28,29 Although InAs nanotubes are fabricated successfully in experiment, the fundamental structural and electronic properties of the nanotubes with different sizes and configurations remain unclear. Theoretical investigations of InAs nanowires have been performed extensively in the past few years. Persson and Xu30 performed a tight-binding approach to investigate wave functions and band structures of InAs and InP nanowires, and they found the parabolic-like conduction-band structures. Galicka et al.31 investigated the structural trends of InAs nanowires with zincblende and wurtzite structures using first-principles calculations. They found that the wurtzite structure is stable for diameter of wires less than 50 nm, while the zinc-blende and wurtzite structure nanowires have similar formation energies for the large diameters. The mechanical, structural, and electronic properties of [111] zinc-blende InAs and InP nanowires have been studied by Santos and Piquini.32 They have shown that the properties of nanowires can be tailored by changing the diameter of wires and external pressure. Recent theoretical study from firstprinciples calculations have shown that the hole mobilities of InAs nanowires exceed the bulk value up to five times, while the electorn mobilities remain comparable to the bulk one.33 However, to the best of our knowledge, theoretical studies on the stabilization mechanism and characteristics of electronic structures of InAs nanotubes have not yet been reported. Therefore, it is necessary to compare the energetics and electronic properties of InAs nanowires and nanotubes at the same theoretical level. It is of great importance for the applications of these InAs nanomaterials. In this work, we perform the first-principles calculations within density functional theory (DFT) by focusing on the
10.1021/jp105949z 2010 American Chemical Society Published on Web 09/27/2010
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Figure 2. Evolution of formation energy of InAs nanowires and faceted nanotubes as a function of wire/tube diameters. Figure 1. Top view of atomic configurations of InAs nanowires (W0-W4) and faceted nanotubes (T1-T6). Blue and red spheres represent In and As atoms, respectively.
structural stability and electronic properties of various onedimensional InAs nanostructures, including nanowires and faceted nanotubes. The diameters of the InAs nanowires and nanotubes considered are up to 3.7 nm. Our results demonstrate that the surface and size effects play an important role in determining the structural and electronic properties of InAs nanostructures. II. Models and Computational Methods Our calculations are performed within DFT as implemented by the Vienna ab initio simulation package (VASP).34,35 The exchange-correlation energy is described in the generalizedgradient approximation (GGA) using the PW91 functional.36 The energy cutoff for the plane-wave expansion is set to 360 eV, using the projector augmented wave (PAW) potentials37 to describe the electron-ion interaction. Periodic boundary conditions are employed in the xy plane with a supercell large enough to eliminate the interaction between neighboring wires or tubes. The Monkhorst-Pack k-point mesh of 1 × 1 × 8 is found to provide sufficient accuracy in the Brillouin-zone integation. The convergence in energy and force is set as 10-4 eV and 10-3 eV/Å, respectively. InAs nanowires and faceted nanotubes are created on the basis of the optimized wurtzite crystal structure and oriented along the [0001] direction. The optimized lattice parameters of wurtzite InAs (a ) 4.327 Å and c/a ) 1.639) are in agreement with the experimental values (a ) 4.284 Å and c/a ) 1.633).38 Based on the experimental and theoretical studies, all of the nanowires and faceted nanotubes under consideration have approximately a cylindrical shape. We consider nanowires W0, W1, W2, W3, and W4 with 12, 48, 108, 192, and 300 atoms per unit cell (see Figure 1), respectively. Six faceted nanotubes are considered as T1, T2, T3, T4, T5, and T6 with 96, 144, 180, 192, 252, 288 atoms per unit cell, respectively. Figure 1 shows the planar atomic configurations of all calculated InAs nanostructures. III. Results and Discussion We first optimize the atomic positions and lattice parameters along the axial direction for all InAs nanowires and nanotubes (see Figure 1). Surface passivation is not considered in present calculations because these InAs nanostructures are often fabricated at high temperature. For InAs nanowires, there are no
significant changes in the structures after the structural optimization, except the change of bond lengths and angles in the lateral surface. Most of the surface atoms are found to relax inward, but the relaxation degree of In atoms is different from that of As atoms. The inward relaxation of In atoms is much larger than that of As atoms. The surface atomic relaxation leads to 0-3% contraction of In-As bonds in the zigzag side and about 2% contraction of In-As bonds along the axial direction. The In-As-In and As-In-As bond angles in the nanowires are deviated from the tetrahedral bond angles in the wurtzite InAs bulk. For examples, for the nanowire W2 (see Figure 1), the In-As-In and As-In-As bond angles become 105.3° and 113.7°, respectively. In addition, it is found that the radial compression of the wires induces about 1% elongation of the axial lattice parameters when compared to that of the bulk InAs unit cell. For the faceted InAs nanotubes, the surface relaxation in the inner lateral surface is similar to that of the outer surface, except that the atomic displacement is just the reverse. The contraction degree of the In-As bonds in the inner and outer surfaces of the faceted nanotubes is very close to that of the surface of the nanowires. To determine the structural stability of InAs nanowires and nanotubes, we calculate their formation energies. The formation energy (Ef) is defined by the expression
Ef ) (nEInAs - Etot)/n
(1)
where EInAs is the total energy of wurtzite InAs bulk, Etot is the total energies of InAs nanostructures, and n is the number of InAs pairs in InAs nanostructures. Thus, the formation energy of InAs bulk is corresponding to the energy zero. The Ef values of InAs nanowires and nanotubes as a function of diameter are summarized in Figure 2. The formation energies of the nanowires decrease with the increase of wire diameters (d) (see Figure 2). Moreover, we find that the formation energies of the nanowires do not decrease linearly with the increase of wire diameters. They satisfy an inverse relationship of diameter, namely, Ef ) k/d. By fitting the DFT data points, we obtain the formation energy, Ef ≈ 0.359/d. The decreasing formation energies with the wire diameters suggest that the InAs nanowires have higher stability in the larger sizes. Figure 2 also gives the formation energy Ef of the faceted nanotubes as a function of tube diameters, respectively. It is found that the Ef of the nanotubes is not only determined by the diameter of tubes but also controlled by the wall thickness of tubes. The comparison
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Figure 3. Variation of formation energy with surface atom ratios for various InAs nanowires and nanotubes.
of Ef of the nanowires and nanotubes with the same diameters shows Ef(FNTs) > Ef(NWs). The result can be understood by the following reasons. The In and As atoms prefer to form sp3hybridized bonds in the wurtzite InAs bulk. However, all In and As atoms in the surface of InAs nanowires and nanotubes are sp2 hybridized. They are energetically unfavorable and result in the increase of system energy. The small nanowires and thinwalled nanotubes have large Ef due to the high-density dangling sp2 bonds. Thus, they are very difficult to be synthesized in experiment. In addition, we can find that the Ef of some faceted nanotubes closes to that of some nanowires due to the same surface atom ratio (surface atom ratio is defined as the ratio of the numbers of surface and total atoms). The result gives the possibility of the fabrication of the faceted nanotubes under proper growth conditions. For example, we can fabricate InAs nanotubes with the small surface atom ratio by adding the size of catalyst and reducing the core composition (e.g., InP). The above results suggest that the surface atom ratio is an important factor for determining the stability of the InAs nanowires and nanotubes. The evolution of Ef as a function of surface atom ratio is plotted in Figure 3. It is found that the Ef of the nanowires and nanotubes increases linearly with the surface atom ratio (λ). By fitting the data of Ef, the linear relation between the Ef and λ can be described by the expression Ef ) 0.76λ. The relationship also can be obtained by a physical model. The formation energy of an InAs nanostructure can be approximated as
Ef ) λEs + (1 - λ)Ei
(2)
where Es and Ei are the formation energies from the contribution of surface atoms and inner atoms, respectively. Due to the inner In and As atoms with the perfect sp3 bonds, the inner atoms almost are not responsible for the total formation energy. Thus, the Ef can be simplified as Ef ) λEs. For nanowire W0 (λ ) 1), Ef ) Es ) 0.76 eV/InAs. Taking Es ) 0.76, we get the relationship between Ef and λ, Ef ) 0.76λ, in agreement with the fitting expression. Let us consider now the electronic structures of InAs nanostructures. It is useful to promote the applications of these materials in developing the nanoscale electronic and optoelectronic devices. Figure 4 shows the typical band structures of the InAs nanowire W3 and the faceted nanotube T3. The band gaps Eg of all structures are direct band gap at the Γ point. The
Figure 4. Electronic band structures of (a) InAs nanowire (W3) and (b) faceted InAs nanotube (T3). The dashed lines denote the positions of the Fermi level.
Figure 5. Variation of band gap values with surface atom ratios for various InAs nanowires and nanotubes. The inset indicates the band gaps as a function of diameter for various InAs nanostructures.
computed band gap of the wurtzite InAs bulk is 0 eV, consistent with the previous DFT results, but is lower than the experimental value (0.667 eV).38 It is a well-known fact that the DFT approach underestimates band gaps, but the trends elucidated by the computational results based on the same calculated accuracy for different InAs nanostructures should still be valid. Figure 5 summarizes the result of our calculations for the band gaps of InAs nanostructures as the functions of the surface atom ratio λ and diameter d, respectively. The variation of band gaps with the surface atom ratio for the nanostructures is divided into two parts (see Figure 5). For λ e 50%, the band gaps exhibit a good linear relation of the surface atom ratio, whereas the band gaps shows little dependence upon the surface atom ratio for λ ) 1. This can be understood from a competition between two different mechanisms. The first is the quantum confinement effect, which favors the increase of the band gaps with the reduction of wire/tube sizes. For example, the band gap of InAs nanowire is 0.30 eV at the wire diameter of 3.7 nm (W4) and increases to 1.04 eV at the wire diameter of 1.3 nm (W1), as shown in Figure 5. A similar phenomenon also can be observed in the InAs nanotubes. The second is the effect of the surface dangling bonds, which favors the decrease of the band gaps with the reduction of wire/tube sizes. 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 λ e 50%, the quantum confinement effect
InAs Nanowires and Nanotubes
J. Phys. Chem. C, Vol. 114, No. 41, 2010 17517 the relation of the band gaps in the nanostructures with the same diameters, Eg(FNTs) > Eg(NWs). IV. Conclusions In summary, we have performed detailed investigations on the effects of the surface and size on the structural stability and electronic properties of InAs nanowires and nanotubes by using first-principles calculations. Comparison of the calculated formation energies of InAs nanostructures suggests that the nanowires are more energetically favorable than the faceted nanotubes. Moreover, the formation energies of these InAs nanostructures are proportional to the surface atom ratio. Thus, the fabrication of the ultrathin nanowires and the thin-walled nanotubes remains a large challenge in experiment. The calculated band structures show that the band gaps of InAs nanostructures are determined by two different competition mechanisms. One is the quantum confinement effect, and the other is the effect of the surface dangling bonds. With the reduction of the diameter or wall thickness, the former causes the increase of band gaps and the latter leads to the decrease of band gaps. These results provide important information for the fabrication and utilization of InAs nanomaterials as the building blocks in nanoscale electronic and optoelectronic devices.
Figure 6. Isosurface plots of the squared wave functions of the valence maximum (VBM) and the conduction band minimum (CBM) of InAs nanowire (W3) and nanotube (T3) at the Γ point. The isovalue is 0.0002 e/Å3.
is dominated, and the band gaps of the nanostructures show a linear dependence upon the surface atom ratio. In contrast, for λ ) 1 the high-density surface states counteract the increasing band gap value from the contribution of the quantum confinement effect. Thus, the surface passivation is a good way to restrain the surface states and increase band gap of the nanostructures, such as hydrogen passivation. In addition, we find that the band gaps of the InAs nanostructures decrease with the increase of size when they have the same surface atom ratios. With the same size, the band gaps of the nanowires and nanotubes satisfy the relation Eg(FNTs) > Eg(NWs). It indicates that the increasing quantum confinement effect in onedimensional structures can be enhanced by the formation of tubes instead of wires. Figure 6 shows the spatial distributions of the squared wave functions of the valence band maximum (VBM) and conduction band minimum (CBM) of the InAs nanowire W3 and the faceted nanotube T3. For the InAs nanowire W3 (see Figure 6a and Figure 6b), the VBM and CBM originate from the 4p states of the outer and inner As atoms, respectively. The interactions of these p states in InAs nanowires result in the dispersion of the corresponding energy level, which favors the increase of the band gaps with the reduction of the diameters, as shown in Figure 5. Similar behavior has been found in ZnO and ZnS nanowires.39,40 For the faceted nanotube T3 (shown in Figure 6c and Figure 6d), the VBM also originates from the 4p states of the As atoms, but the CBM consists of the 4p states of the inner and outer edge As atoms and the s states of other atoms. In other words, the VBM of all InAs nanostructures originates from the 4p states of As atoms, but the states in the CBM show a transition from the p-like character to the s-like character when the nanostructures are changed from the nanowires to the nanotubes. The reason is that the interactions between the p and s states in the nanostructures result in the dispersion of the CBM and VBM. Thus, the s and p bands are shifted to lower and higher energies, respectively. The shift is responsible for
Acknowledgment. This work was supported in part by the State Key Program for Basic Research of China (2007CB613206), the National Natural Science Foundation of China (10725418, 10734090, 10990104, and 60976092), the Key Fund of Shanghai Science and Technology Foundation (09DJ1400203, 10JC1416100, and 10510704700), the Creative Group (60221502), and the Knowledge Innovation Program of the Chinese Academy of Sciences (Q-ZY-6). Computational resources from the Shanghai Supercomputer Center are acknowledged. References and Notes (1) Li, Y.; Qian, F.; Xiang, J.; Lieber, C. M. Mater. Today 2006, 9, 18. (2) Pauzauskie, P. J.; Yang, P. Mater. Today. 2006, 9, 36. (3) Agarwal, R.; Lieber, C. M. Appl. Phys. A: Mater. Sci. Process. 2006, 85, 209. (4) Lind, E.; Persson, A. I.; Samuelson, L.; Wernersson, L. E. Nano Lett. 2006, 6, 1842. (5) Dayeh, S. A.; Aplin, D. P. R.; Zhou, X. T.; Yu, P. K. L.; Yu, E. T.; Wang, D. L. Small 2007, 3, 326. (6) Hayden, O.; Agarwal, R.; Lieber, C. M. Nat. Mater. 2006, 5, 352. (7) Heremans, J. Nanometer-scale thermoelectric materials. Springer Handbook of Nanotechnology; Springer: New York, 2007; Vol. 345, p 345. (8) Garnett, E. C.; Yang, P. J. Am. Chem. Soc. 2008, 130, 9224. (9) Tomioka, K.; Motohisa, J.; Hara, S.; Fukui, T. Nano Lett. 2008, 8, 3475. (10) Park, H. D.; Prokes, S. M.; Cammarata, R. C. Appl. Phys. Lett. 2005, 87, 063110. (11) Dick, K. A.; Deppert, K.; Samuelson, L.; Seifert, W. J. Cryst. Growth 2006, 297, 326. (12) Dick, K. A.; Deppert, K.; Mrtensson, T.; Mandl, B.; Samuelson, L.; Seifert, W. Nano Lett. 2005, 5, 761. (13) Roddaro, S.; Nilsson, K.; Astromskas, G.; Samuelson, L.; Wernersson, L.-E.; Karlstro¨m, O.; Wacker, A. Appl. Phys. Lett. 2008, 92, 253509. (14) Nilsson, H. A.; Caroff, P.; Thelander, C.; Lind, E.; Karlstro¨m, O.; Wernersson, L.-E. Appl. Phys. Lett. 2010, 96, 153505. (15) Chopra, N. G.; Luyken, R. J.; Cherrey, K.; Crespi, V. H.; Cohen, M. L.; Louie, S. G.; Zettl, A. Science 1995, 269, 966. (16) Tenne, R.; Margulis, L.; Genut, M.; Hodes, G. Nature (London) 1992, 360, 444. (17) Chen, J.; Li, S.; Tao, Z.; Shen, Y.; Cui, C. J. Am. Chem. Soc. 2003, 125, 5284. (18) Nath, M.; Rao, C. N. R. Angew. Chem., Int. Ed. 2002, 41, 3451. (19) Hacohen, Y. R.; Grunbaum, E.; Tenne, R.; Sloan, J.; Hutchison, J. L. Nature (London) 1998, 395, 336. (20) Wang, H.; Li, X. D.; Kim, T. S.; Kim, D. P. Appl. Phys. Lett. 2005, 86, 173104.
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