Local-Strain-Induced Charge Carrier Separation and Electronic

Jan 19, 2011 - Department of Physics and Astronomy and High Pressure, Science and Engineering Center, University of Nevada, Las Vegas,. Nevada ... §S...
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Local-Strain-Induced Charge Carrier Separation and Electronic Structure Modulation in Zigzag ZnO Nanotubes: Role of Built-In Polarization Electric Field Liangzhi Kou,*,†,‡ Yi Zhang,*,† Chun Li,§ Wanlin Guo,‡ and Changfeng Chen† †

Department of Physics and Astronomy and High Pressure, Science and Engineering Center, University of Nevada, Las Vegas, Nevada 89154, United States ‡ Institute of Nano Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China § School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi'an 710072, China ABSTRACT: By use of first-principles calculations, we examine the effects of uniaxial strain and radial deformation on electronic properties of zigzag ZnO nanotubes. Our results show that local strain or deformation can cause significant reduction of the band gap owing to quantum-confined Stark effect induced by the built-in electric polarization. Driven by this polarization field, the charge carriers are separated with hole and electron states localized on the opposite ends of the tube. In sharp contrast, uniform tensile strain tends to widen the band gap while compressive strain and radial deformation have negligible effects on the band gap, although they can produce considerable shifts in edge-state energies. The present results reveal the key role of local strain as an effective tool in tuning the properties of zigzag ZnO nanotubes. Such local-strain-induced electronic structure modulation suggests an effective approach to design and implementation of ZnO nanotubes in nanoscale devices.

’ INTRODUCTION Zinc oxide (ZnO) is a prototypical II-VI semiconductor and piezoelectric material that holds great promise for wide-ranging applications in electronics, optoelectronics, sensors, and energy conversions.1-4 In particular, one-dimensional (1D) ZnO nanostructures such as nanowires, nanorods, nanotubes, etc., possess unique physical and chemical properties arising from surface and quantum confinement effects, which make them excellent candidates as fundamental building blocks for field effect transistors, gas sensors, resonators, transducers, actuators, cantilevers, and electric nanogenerator.5-8 In recent years, intensive efforts have been directed toward synthesizing, characterizing, and understanding these material systems. Among them, ZnO nanotubes (NTs) have been regarded as a promising material for advanced photovoltaic applications owing to their high surface area, crystalline quality, and piezoelectric effect. Successful syntheses of ZnO NTs with hollow centers and thick walls have been reported in recent years.9-12 From a fundamental point of view, it is highly desirable to first examine and understand the essential single-walled ZnO NTs as basic building units of such systems. Although their experimental synthesis remains a challenge, recent demonstration of growing sheetlike planar ZnO may enable the realization of theoretically predicted single-walled ZnO NTs in practice.13,14 It has been suggested that the single-walled ZnO NTs conformations are energetically possible and might be synthesized through solid-vapor phase processes.15 The structural stability, electronic, optical, and r 2011 American Chemical Society

magnetic properties of single-walled ZnO NTs also have been studied using first-principles methods.16-21 Recent investigation has demonstrated that ZnO NTs exhibit strong piezoelectric properties and can effectively convert nanoscale mechanical energy into electrical energy.22 Meanwhile, owing to their outstanding optical property and large exciton binding energy, ZnO NTs have been used to fabricate dyesensitized solar cells with high conversion efficiency.23 These technological advancements rely heavily on the strong mechanical-electric and optical-electric couplings in ZnO NTs. However, a comprehensive understanding of the effects of mechanical strain and deformation on the electronic property of ZnO NTs remains to be explored. In this work, we report a systematic investigation of the effects of uniaxial or radial strain on electronic properties of zigzag ZnO NTs using first-principles calculations based on density functional theory. We reveal that uniform uniaxial tensile strain widens the band gap while compressive or uniform radial strain has little effect on the gap regardless of the tube diameter. Most interestingly, our calculations show that local axial or radial strain can induce significant reduction in band gap. Analysis indicates that the built-in piezoelectric polarization electric-field induced by local strain drives the separation of different charge carriers Received: September 8, 2010 Revised: November 29, 2010 Published: January 19, 2011 2381

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Figure 1. (a) Band gap variation of zigzag ZnO NTs under axial strain. The inset shows energy shift of the band edge states. (b) Band structures of the (10,0) zigzag ZnO nanotube under unstrained and (3% strained states. The wave function distributions of CBM (upper) and VBM (lower) states are presented in the insets.

toward opposite ends of the tube. The ensuing quantumconfined Stark effect leads to the reduced electronic band gap in ZnO NTs. These results provide insights into the underlying physical mechanism for effective tuning of electronic structure via nanomechanical manipulation of ZnO NTs, which may prove useful for their applications in nanoscale functional devices.

’ MODELS AND TECHNIQUE DETAILS The single-walled ZnO NT models investigated here are created in analogy with single-walled boron nitride NTs (BNNTs) with B and N replaced by Zn and O, respectively. We mainly focus on the zigzag NTs in this work, because they have atomic arrangements much closer to wurtzite ZnO and are more stable than armchair ones.16,21 For the tubes under uniform axial or radial strain, only one unit cell along c axis is used to investigate the effect on electronic properties. However, to model the effect of local uniaxial strain and radial deformation, a large supercell containing ten ZnO NT unitcells is constructed. Similar to the index representation in carbon or BNNTs, the zigzag ZnO NTs are also labeled with (n, 0). Calculations are carried out with the linear combination of atomic orbital basis implemented in the SIESTA package,24 using the Perdew-Burke-Ernzerh (PBE)25 of generalized gradient approximation (GGA) for the exchange correlation energy and norm-conserving pseudopotentials for the core-valence interactions. The double-ζ polarized numerical atomic-orbital basis sets for Zn and O are used. A 1 1  10 Monkhorst-Pack k-point grid is used in the energy calculations. An energy cutoff of 300 Ry is sufficient to converge the grid integration of the charge density, and atomic positions are fully relaxed under applied strain using a conjugate gradient method so that the force on each atom is less than 0.02 eV/Å. The above structures are placed in a periodically repeating supercell, separated by a vacuum region of >10 Å in radial directions, so that the interaction between the tubes can be negligible. All these pseudopotentials and parameters adopted here have been successfully used in ZnO nanostructures in our previous work,26,27 and their validity has been well established. ’ RESULTS AND DISCUSSIONS 1. Electronic Structure Modulation via Uniform Strain. Before exploring the effects of local strain on electronic properties, we first examine the effects of uniform uniaxial or radial

Figure 2. Shifts of CBM, VBM, and energy gap induced by uniform radial deformations in the (10,0) ZnO nanotube.

strain. Consistent with previous results, the (10,0) zigzag ZnO NT exhibits semiconducting nature, the electronic structure always displays a direct band gap of about 1.94 eV at Γ point, which shows a small variation with increasing diameter.16,17 The calculated electronic band gap variations within the strain range of 5% are shown in Figure 1a. Here the strain is defined as ε = (c - c0)/c0  100%, where c and c0 are the deformed and initial lattice lengths along c axis, respectively. It is found that the gap increases almost linearly with tensile strain while it remains nearly unchanged under compressive strain. However, it should be noted that this conclusion is only valid within a small strain range; when the compressive strain reaches up to ∼30%, structural transition and direct-indirect band gap transition will occur.28 To reveal the underlying mechanism for this straininduced band gap variation, we have plotted the electronic band structures of (10,0) zigzag ZnO nanotube under different strain states as shown in Figure 1b, where the wave function distributions of band-edge states in the strain-free state are also presented. It is seen that the conduction band minimum (CBM) states mainly originated from the Zn 4s orbital are insensitive to applied strain, thus the energy remains unchanged. In contrast, the energy of valence band maximum (VBM) states that mostly come from the O 2p orbital is shifted downward under tensile strain owing to the electron orbital overlap caused by variation in bond length (indicated by the red dashed rectangle in the lower inset of Figure 1b). The different energy shifts of edge states in response to strain (see inset of Figure 1a, ΔECBM and ΔEVBM) result in the interesting gap modulation. We also studied the gap variation with strain for the (15,0) tube and found that the obtained results are very similar to those of the (10,0) tube, suggesting that the general behavior of electronic structure modulation is insensitive to tube diameter. Another common strain pattern besides uniaxial strain is radial deformation, which has been demonstrated to have a significant effect on electronic properties of nanotubes.29 We have examined the effects of uniform radial deformation on electronic properties in zigzag ZnO NTs. Here the cross-sectional deformation is quantified by the dimensionless parameter η = (d0 - d)/d0, where d0 is the diameter of the undeformed tube and d is the minor diameter of the deformed tube (see inset of Figure 2). The geometries of deformed tubes were relaxed by constraining the 2382

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Figure 3. Band gap of the (10, 0) ZnO NT as a function of uniaxial local strain.

tubes to lie between two planes separated by a distance d. Variations of the band gaps together with the energy shift of band-edge states as a function of η for the (10,0) tube are displayed in Figure 2. The gap stays nearly constant over a large range of the deformation parameter η(0-0.5). Our analysis of the energy variations of band edge states shows that both the energies of CBM and VBM states have been shifted downward almost linearly with radial deformation by nearly the same amount, thus leading to a constant gap. 2. Electronic Structure Modulation via Applied Local Strain. In practical applications of nanotubes, applied strain or deformation is usually nonuniform. For example, in experimental measurement for electrical/mechanical properties, one or two ends of the nanostructures need to be fixed.30 Therefore, the study of effects of strain or deformation on electronic structure modulation needs to be extended to situations involving nonuniform strain or deformation. Previous investigations have found a rich variety of phenomena, such as local-strain-induced confinement of charge carriers in a localized region to form a quantum well,31 charge separations that are very useful in solar cell applications,32,33 and reduced band gap as a result of band offset.29 These properties are very different from the results obtained under uniform strain conditions. It is thus desirable to study the electronic structure modulation via local strain or deformation in ZnO NTs. To this end, we have constructed a supercell containing ten unit cells of the (10,0) zigzag ZnO NTs, in which three unit cells at each of the two ends remain unstrained and the four unit cells in the middle part are stretched/compressed. Our calculated results show that the band gap of the (10,0) ZnO NT is reduced considerably with uniaxial local tensile or compressive strain as indicated in Figure 3, in sharp contrast to the increase (unchanged) of gap under uniform axial tensile (compressive) strain. Here, we take the nanotube under the 5% partial strain as a representative example to reveal underlying physics mechanism of gap reduction in local strained condition. We first apply a band arrangement analysis, which has been successfully used in understanding nanostructures with applied local strain.31-34 The analysis indicates that the energies of both band-edge states in the strained region (middle section) are shifted downward while those in strain-free regions (two ends) remain unchanged. It thus leads to a staggered band-edge arrangement and a gap reduction originating from the band

Figure 4. The charge separation induced by stretching the middle part of the (10,0) ZnO NT. (a) The PDOS for different sections along the axial direction as indicated in the inset. These three sections with the same number of atoms are encompassed by shaded rectangles, where the shade colors are consistent with those of corresponding lines. The stretching part is indicated by black dashed lines. The charge carrier spatial distribution of CBM (b) and VBM (c) states are presented.

offset and consequent charge separation with the electrons confined in the deformed region while the holes in the undeformed region. However, a close examination of the situation in the partially deformed ZnO NT tells a quite different story. As shown in Figure 4a, the projected density of state (PDOS) of the nanotube under 5% local strain indicates a relative shift between the energies of the right and left segments of the tube, instead of remaining unchanged for both segments as predicted by the band arrangement analysis. It results in a local concentration of the CBM and VBM states on the two opposite ends of the tube, which can be clearly visualized in the distributions of edge states shown in parts b and c of Figure 4. Such nonuniform energy shift and charge separation characterized by the confinement of electrons and holes on the opposite ends of the tube can be attributed to the strong piezoelectricity of the ZnO, which lacks symmetry along its c axis with the Zn2þ cations and O2- anions tetrahedrally coordinated. In the absence of strain, the centers of positive and negative charges overlap, yielding zero dipole moment. When a local strain is applied along the c axis, the center of the cations and that of the anions are relatively displaced, resulting in a net dipole moment. A constructive addition of the dipole moments created by all of the units in the crystal results in a macroscopic polarization electric-field along the strain direction in the crystal.35 Such a field is generated by the nonmobile, nonannihilable ionic charges, which remains in the crystal as long as the strain remains and vanishes upon unloading. As a result, the positive/negative charge carrier (VBM/CBM state) will be driven to the low/high electric potential end by this built-in electric field induced by polarization in piezoelectric material. The charge redistribution due to the breaking of electric potential symmetry, which is known as 2383

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Figure 5. Electrostatic potential distribution in a partially stretched zigzag (10, 0) ZnO NT under 5% local tensile strain.

Figure 7. Side (a) and top (b) view of the partially radial deformed model of the (10,0) ZnO nanotube. Some of the bond lengths along axial direction are presented (Å) to indicate the variation of strain. Also presented are the CBM (c) and VBM (d) distributions induced by the partial radial deformation.

Figure 6. (a) Band arrangement of the armchair (5,5) ZnO NT under local tensile strained condition; the four unitcells in the middle of the tube are sketched by 5%. (b)VBM and (c) CBM state distributions are also presented.

quantum confined Stark effect,36 leads to the splitting of the subband levels and thus the decrease of band gaps of locally strained zigzag ZnO NTs. Therefore, the band gap reduction in a piezoelectric material under local strain originates from the quantum confined Stark effect, which is qualitatively different from the band offset in some other nanostructures, such as SiC and carbon NTs. To estimate the strength of the electric field, we have examined the electrostatic potential distribution along the c axis under 5% local strain. It can be calculated from Figure 5 using the maximum potential difference divided by the length between them; the obtained value of 2.77 MV/cm is comparable to that in ZnO/ZnMgO quantum wells and is large enough to modulate electronic properties.36,37 To contrast the effects of the built-in electric field originated from piezoelectricity of zigzag ZnO NTs, we have examined the charge distributions of band-edge states of the nonpiezoelectric locally strained armchair (5,5) ZnO nanotube, where the tube under 5% tensile strain in the middle part is analyzed as an example. In this case, we find that the energy of the VBM state in the strained region is shifted upward while that of CBM state remains unchanged because of its insensitivity to applied strain, leading to a staggered band arrangement characterized by the local concentration of the VBM state in strained region to form a quantum well (Figure 6a). Because of the absence of piezoelectricity, no polarization electric-filed is induced by the local

Figure 8. Band gap of the (10, 0) ZnO NT as a function of radial local strain.

strain. Consequently, the band arrangement analysis is valid here, the charge separation is featured with the holes confined in the deformed region while the electrons in the whole region (see parts b and c of Figure 6). As a result of band offset, its electronic band gap is reduced to 1.8 eV from 1.92 eV at the unstrained state. Besides local tensile stretching, we also studied the effects of local radial deformation, which is easy to achieve experimentally by pressing radially with an atomic force microscope tip. Here we specify the cross-sectional deformation of the central unit cell in the supercell with a fixed dimensionless parameter η, while the rest of the tube is allowed to relax fully. The final structure with local η = 0.5 is illustrated in parts a and b of Figure 7. It is seen 2384

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The Journal of Physical Chemistry C that while the middle segment of the tube becomes flat, which also influences the adjacent regions, the units far away from the middle region retain the circular cross-sectional shape. Our analysis of bond-length variations along the c axis shows that the Zn-O bond lengths are stretched in the local radial deformation region while those away from the deformed region remain nearly unchanged from the unstrained situation. The resulting built-in polarization electric field also leads to large gap reductions as a function of radial local strain. (See Figure 8; for instance, the gap is reduced to 1.34 eV from 1.94 eV at η = 0 when the middle tube segment undergoes a radial deformation with η = 0.5.) Meanwhile, there is a significant charge separation at two opposite ends of the tube (see parts c and d of Figure 7). Our results show that local strain or deformation leads to distinct physical phenomena compared with those under uniform strain or deformation. Since the obtained charge separation and gap modulation are mainly driven by the polarization electric field induced by local deformation, it is expected that these phenomena may also be present in other piezoelectric nanostructures and could pave a path for design of nanodevices based on piezoelectric nanostructures.

’ CONCLUSION We have presented a first-principles study of the effects of uniform and local strain on electronic properties of zigzag ZnO NTs. We find that uniform tensile strain increases the band gap while compressive or radial deformation has little effect on the band gap in spite of the shift of band-edge energy. In contrast, local strain or radial deformation reduces the band gap as a result of quantum confined Stark effect caused by the polarization electric field, which is induced by relative displacements of cation and anion in such a piezoelectric material. The positive and negative charge carriers are transferred to the opposite ends of the tube due to the built-in polarization electric field. These results unveil fundamentally different behaviors of physical properties of ZnO NTs under various strain conditions. They suggest a wide range of tunability of electronic properties of zigzag ZnO NTs via nanomechanical manipulation, which may find promising applications in nanodevices.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: L.K. [email protected]. Y.Z.: email zhangyi@ physics.unlv.edu.

’ ACKNOWLEDGMENT This work is supported by DOE Cooperative Agreement No. De-FC52-06NA26274 at UNLV and by the 973 Program (No. 2007CB936204), National NSF (No. 10732040) of China and Jiangsu Province NSF (BK2008042) at NUAA. C.L. acknowledges support from National NSF (No. 11002109) of China, Fundamental Research Fund (JC200935), and the Ao-Xiang Star Project of NWPU. ’ REFERENCES (1) Huang, M. H.; Mao, S.; Feick, H.; Yan, H.; Wu, Y.; Kind, H.; Weber, E.; Russo, R.; Yang, P. Science 2001, 292, 1897. (2) Wan, Q.; Li, Q. H.; Chen, Y. J.; Wang, T. H.; He, X. L.; Li, J. P.; Lin, C. L. Appl. Phys. Lett. 2004, 84, 3654. (3) Wang, X.; Zhou, J.; Song, J.; Liu, J.; Xu, N.; Wang, Z. L. Nano Lett. 2006, 6, 2768.

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