ARTICLE pubs.acs.org/JPCC
Electrical Transport Study of Single-Walled ZnO Nanotubes: A First-Principles Study of the Length Dependence Qin Han,†,* Bing Cao,‡ Liping Zhou,† Guiju Zhang,‡ and Zhenghui Liu§ †
Jiangsu Key Laboratory of Thin Films, School of Physical Science and Technology, Soochow University, Suzhou, China, 215006 Institute of Modern Optical Technologies and Key Lab of Modern Optical Technologies of Jiangsu Province, Soochow University, Suzhou, China, 215006 § Suzhou Institute of Nano-tech and Nano-bionics, CAS, Ruoshui Road 398, Dushu Lake Higher Education Town, Suzhou Industrial Park, Suzhou, China, 215125 ‡
bS Supporting Information ABSTRACT: The electronic transport properties are characterized for single-walled zigzag (9, 0) ZnO nanotubes sandwiched between two lithium electrodes using a combined nonequilibrium Green’s function and DFT-based formalism. By applying different bias voltages, the current-voltage characteristics are calculated for nanotubes of different lengths. The results indicate that the conductance of the system decreases exponentially with the increased length of the nanotubes. Metallic behavior is predicted for very short nanotubes, which is caused by the interface states from the metal-nanotubes interface. For longer nanotubes, the effect of the interface becomes smaller with the increased lengths. And semiconductor-like behaviors are observed, which are mainly determined by the ZnO nanotubes themselves. In addition, a peculiar phenomenon is observed that the values of the current at high bias are insensitive to the lengths. The behaviors can be understood in terms of the transmission spectrum, which shows that the transport properties are dominated by the electron states above the Fermi energy.
1. INTRODUCTION ZnO is a unique material that exhibits a wide bandgap (3.37 eV), large exciton binding energy (60 meV), and low lasing threshold, which is applicable to optoelectronics, sensors, transducers, and nanogenerators.1-4 In recent years, ZnO nanostructures of different morphologies, such as nanowires, nanotubes, nanoribbons, nanohelixes, and nanocages, have been fabricated.5-9 In view of attractive physical properties of ZnO nanostructures, tubular structures of ZnO have gained great interest, which may possess novel electronic properties and provide more prominent advantages. Several groups have synthesized ZnO nanotubes with bulk-related geometries.10,11 For example, Xing et al. observed that ZnO nanotubular structures with geometries related to the hexagonal structure of the ZnO crystal. The diameters of these tubes are ranging from 30 to 100 nm with wall thicknesses as small as 4 nm.10 Recently, double-walled ZnO nanotubes with a round wall shape have been synthesized.11 Although single-walled ZnO nanotubes with a round wall shape have not been synthesized until now, the theoretical studies discussed by Tu and Hu using a first-principles approach have suggested that the single-wall nanotubes conformations are energetically possible and might be synthesized through solidvapor phase processes.12 The as-synthesized ZnO nanotubes are expected to be used as blocks of nano-electromechanical system (NEMS) such as transistors, diodes, and switches and ultrasensitive detectors. So it is very important to know the transport r 2011 American Chemical Society
properties of nanotubes/blocks for device design and system integration. However, to the best of our knowledge, there have been no systematical theoretical reports about the electronic transport properties of ZnO nanotubes. In this article, we use the nonequilibrium Green’s functions (NEGF) technique and DFT to obtain a full ab initio selfconsistent description of the transport properties. We investigate the conductance of single-walled ZnO nanotubes of different lengths coupled to lithium electrodes. The transport properties of such coupled systems are determined by the electronic structures of nanotubes and electrodes. The results show two behaviors of electronic transport: a linear behavior for very short nanotubes, and a semiconducting-like behavior for long nanotubes. In addition, an interesting phenomenon is observed that the values of the current at high bias are insensitive to the lengths, which can be understood in terms of transmission spectrum.
2. CALCULATION METHOD AND SIMULATION MODEL To calculate the transport properties of the ZnO nanotubebased two-probe devices, we use a first-principles nonequilibrium Green’s function-based electronic transport package, Atomistix, developed by Brandbyge and co-workers.13-16 The method is Received: September 20, 2010 Revised: January 9, 2011 Published: February 10, 2011 3447
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Figure 1. Typical structure of two-probe device with a ZnO nanotube sandwiched between two Li (001) electrodes (L, R). Note that the central area C also contains a considerable portion of the electrodes. Unit cells used in the analysis are indicated. This particular finite-sized tube consists of 8 unit cells with 18 O and 18 Zn atoms in each cell.
based on DFT and can treat the two-probe system self-consistently under finite bias conditions. The two-probe system consists of a scattering region coupled between two macroscopic bulk electrodes. The simulation procedure is described briefly as follows. First, the electronic structures of the two electrodes are calculated to get a self-consistent potential, which provides the real space boundary conditions for the Kohn-Sham effective potential of the central scattering region. Then from the Green’s function of the scattering region, the density matrix is obtained and hence the electron density. Thus, the DFT Hamiltonian matrix can be calculated using above boundary conditions and the electron density. This procedure is iterated until self-consistency is achieved. Moreover, the current that passes through the scattering region can be calculated from the corresponding Green’s function and self-energies using the Landauer-B€uttiker formula:16 Z 2e μR IðVb Þ ¼ dEðfL ðE, Vb Þ - fR ðE, Vb ÞÞTðE, Vb Þ ð1Þ h μL where μL and μR are chemical potentials of the left and right electrodes respectively, fL(E, Vb) and fR(E, Vb) are the FermiDirac functions of the two electrodes at energy E under the bias voltage Vb, T(E, Vb) is the bias-dependent transmission coefficient. When the bias voltage Vb is applied, the chemical potential in the left/right electrode will be shifted and their difference is equal to eVb: eVb ¼ μL ðVb Þ - μR ðVb Þ
ð2Þ
where μL = Ef - eVb/2 and μR = Ef þ eVb/2, in which Ef is the Fermi energy. For the two-probe device, the equilibrium conductance G is evaluated by the transmission coefficients T(E,Vb) at the Fermi energy Ef of the system under zero bias voltage G ¼
2e2 TðEf , Vb ¼ 0V Þ h
ð3Þ
Details about this methodology can be found in ref 16. We assume a two-probe device with a single-walled zigzag (9, 0) ZnO nanotube17 connected to two semi-infinite Li (001) electrodes, shown in Figure 1. This two-probe device is an open system, which consists of three parts: the left/right electrode and the scattering region. The left and right regions all consist of four layers of Li (001)-6 6 surface atoms, repeated periodically, which could form the infinite electrode. The scattering region includes a portion of the semi-infinite electrodes where all the screening effects take place, thus the charge distributions in the
electrodes correspond to the bulk phases of the same material to a prescribed numerical accuracy. Figure 1 shows an 8-cell nanotube sandwiched between the electrodes, where each unit cell in the ZnO nanotube consists of 18 O and 18 Zn atoms. The nanotube-electrode distance is fixed to be a constant for all the systems: the distance between the last plane of atoms in the left electrode and the plane containing the left terminal O-atom ring of the nanotube is 1.5 Å, and the distance between the right electrode and the right terminal Zn atom plane of the nanotube is 2.3 Å. The values are obtained from total energy optimization: the axial distances of Li-O and that of Li-Zn are varied from 1 to 4 Å respectively with a minimal step of 0.1 Å. The total energies of the whole scattering region for a 4-cell system are evaluated and the minimal value is achieved at 1.5 and 2.3 Å for the left and right side, respectively. Then a constant interaction by fixing the distances between nanotubes and electrodes is kept in the study of electronic transport characteristics with length of nanotubes. The methods are same as those used in literature,18-20 which took fixed distances to compare the transport properties of differentlengthed 1D nanostructures including carbon nanotubes, boron nitride nanotubes, and OPVn molecules. The binding energy between the ZnO nanotube and Li surface can be defined as: Ebinding ¼ Etotal ½tube þ Li - Etotal ½tube - Etotal ½Li
ð4Þ
and the calculated value with above optimized distances is -35.0 eV for the 4-cell system. Although the absolute value may be overestimated by the local density approximation (LDA) method used in our DFT electronic structure description, the negative Ebinding denotes an exothermic process, which indicates a reasonably strongly coupled contact and a stable connection between nanotubes and electrodes. The reliability of LDA methods for our calculations and the comparisons to other DFT methods21-23 are discussed in Supporting Information. The core electrons of all the atoms were modeled with Troullier-Martins nonlocal pseudopotentials, whereas the valence electrons were expanded in a double-ζ basis set.
3. RESULTS AND DISCUSSIONS The equilibrium conductance G is studied for different number n of unit cells. The conductance at Fermi energy Ef (shifted to Ef = 0) decreases as the tube length increases: 1.425 G0 (G0 = 2e2/h, conductance quantum) for 1 cell, 0.3499 G0 for 2 cells, 0.1104 G0 for 3 cells, and so forth. For clarity, log of the conductance versus the number n of unit cells is presented in Figure 2, which shows that the equilibrium conductance decreases exponentially with the length increase of ZnO nanotubes. The exponential decrease of conductance with the increased length has been also found in the literature.24 It is related to the nonresonance transmission through these tubes. Very roughly, one may view the nonresonant transmission process as tunneling through an insulating barrier. The transmission value goes down exponentially with the thickness of the barrier. Figure 3 shows the current-voltage (I-V) curves of five nanotube-based devices of increasing length. The shortest nanotube including one unit cell displays a linear behavior characteristic at the calculated bias range. For longer nanotubes, the I-V curves show a slow increase of the current with the bias 3448
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Figure 2. Logarithmic plot of equilibrium conductance (the transmission value at the Fermi energy) versus length of ZnO nanotubes defined by the number of unit cells.
Figure 3. Current-voltage (I-V) curves of the two-probe system shown in Figure 1 as a function of the varied length of ZnO nanotubes. Here, square, circles, upper triangles, lower triangles, and rhombuses represent data for length 1, 2, 4, 6, and 8 units, respectively.
voltage up to a certain bias and then a steep increase at a point, which indicates that the nanotubes possesses semiconductor characteristics. To gain insight into the basic physics of transport through the nanotubes, we carefully estimate contributions of electrodes, interfaces, and nanotubes for two-probe systems with different tube lengths. First, we consider the direct tunneling from one electrode to the other. In other words, we take away the ZnO nanotubes from the two-probe systems while keeping the distance between the left and right electrodes unvaried, then perform calculations on these systems to investigate the direct tunneling from one electrode to the other. For the 1-cell clearance the equilibrium conductance is 0.0337 G0, which is substantially smaller than that of the 1-cell nanotubes (1.425 G0). When the gap between the two electrodes exceeds 2 unit cells, the magnitude of the transmission is 10 -10, that is, close to zero in a large energy region. So the direct tunneling could be ignored for such systems. Then we consider the effect of the interface lying between the electrodes and nanotubes. The electrode/nanotube junction is characterized by charge transfer. For an isolated nanotube such as the 4-cell length nanotube, the Mulliken charge is 0.89e for O atom on the left terminal and -0.80e for Zn atom on the right terminal, whereas the charge far away from the terminal is about 1.19e for O atom and -1.19e for Zn atom. When Li electrodes are added to both terminals of
Figure 4. (a) Density of states (DOS) of an infinitely long (9,0) ZnO nanotube; (b-f) density of states (DOS) of the scattering regions including the nanotube and a portion of Li atoms and the projected density of states (PDOS) of the central nanotube including only Zn and O atoms for different-lengthed devices at equilibrium.
nanotubes, the charge is 0.99e for O atom on the left interface and -1.05e for Zn atom on the right interface, whereas the charge far away from the interface is about 1.19e for the O atom and -1.19e for the Zn atom. In contrast to the isolated nanotubes, the charge lying on the middle atoms almost does not change, whereas a significant charge transfer happens at interfaces between electrodes and nanotubes. The negative binding energy of -35.0 eV for the 4 cell system means that there exist strong bonds between nanotubes and electrodes. These strong couplings will influence interface states and greatly affect density of electronic states. Figure 4 shows the 3449
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Figure 5. Transmission spectra for the devices consisting of 1, 2, 4, 6, and 8 unit cells, respectively.
Figure 6. (a) Ttransmissions of different bias voltage for 1 cell system, (b) 3D plot of the bias dependence of the transmission spectra for 4 cells. Regions between the dashed lines are the bias window.
density of states (DOS) of the scattering regions including the nanotube and a portion of Li atoms and the projected density of states (PDOS) of the central nanotube including only Zn and O atoms for different-lengthed devices at equilibrium. It can be observed that shapes of DOS are similar with PDOS of nanotubes. However, the PDOS near Ef of nanotubes are much smaller than DOS, which means the states near Ef of the devices are mainly contributed by interface states and Li electrodes and not by central nanotubes. Figure 5 indicates the transmission spectra T(E) of nanotubes with different lengths at equilibrium. It can be observed that T(E) near Ef is nonzero for short tubes with less than 2 cells and is almost zero for long tubes with more than 4 cells. Because the electronic states near Ef are mainly contributed by interface states and Li electrodes, the drastic decrease of the transmission values near Ef with increased lengths can be explained by overlapping of interface states. For short nanotubes, the interface states on both terminals of nanotubes will overlap and help electrons transfer from one electrode to the other. These states contribute to the conductance significantly and result in the high conductance at equilibrium. So the short system indicates metal-like behavior. For longer nanotubes that have the same interface conformation, the overlapping of the interface states decreases quickly with increased tube lengths. The effect of interfaces could be ignored and electronic properties of interconnect nanotubes will play main roles for electron transport. Comparing T(E) spectra and PDOS of the 4-cell system, the first peak below Ef in T(E) spectrum is corresponding to the same position of PDOS, which is called the highest occupied molecular orbital (HOMO). Similarly, the first peak above Ef is
called the lowest unoccupied molecular orbital (LUMO). In inorganic semiconductors the energy difference between the HOMO and LUMO level can be regarded as the band gap. Part a of Figure 4 indicates the DOS of an infinitely long ZnO nanotube, which gives the bandgap of about 1.2 eV. With increasing length the gap between HOMO and LUMO, which are marked by the down arrows in parts b-f of Figure 4, becomes narrower and close to the bandgap of the infinite nanotube. The band gaps could determine the electrical transport properties of long-tube systems. The current in the two-probe devices is calculated by the Landauer-B€uttiker formula expressed by eq 1, in which the integral region between μL and μR is referred to the bias window, as indicated by the two dotted lines in Figure 6. Part a of Figure 6 shows the transmissions of different bias voltage for the 1-cell system. Although the transmission spectrum of the system shows considerable variations, no resonance peak enters the range of the integration, which leads to the linear increase of the current for 1-cell system. The voltage dependent transmission spectra T(E, Vb) for the 4-cell two-probe device is plotted in part b of Figure 6. The spectra show considerable variations as a function of E, but relatively little as a function of Vb for small bias voltages. First, the peak position above the Fermi energy (LUMO) moves toward the Fermi energy as the voltage bias increases. This shift is related to changes in electronic levels due to the influence of an external bias potential. For Vb < 0.9 V the energy level of the transmission does not shift much. When the applied voltage is more than 1.2 V which corresponds to energy gap, ELUMO is lower than the chemical potential of the right electrode, 3450
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the equilibrium conductance and results in the linear behavior of the electrical transport. As the tube length is increased the transmission spectrum T(E) develops a gap around the Fermi level and the equilibrium conductance decreases exponentially. The reason for the gap formation is that the longer nanotubes suffer less influence from the coupling to the electrodes and thereby the transmission spectrum is mainly determined by density of states of interconnect nanotubes. Our results indicate that the long nanotubes act largely as quantum wires, whose I-V characteristics depend weakly on the length of tube. The features explored here may be applicable to other NEMS systems and have important implications in the design of small electronic devices.
’ ASSOCIATED CONTENT
bS
Supporting Information. Comparisons between the LDA and GGA method. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*Tel: 86-512-69157059. Fax: 86-512-65112232. E-mail: hanqin@ suda.edu.cn.
Figure 7. Transmission spectra for the devices consisting of 4, 6, and 8 unit cells at the bias voltage of 3.0 V, respectively.
resulting in the onset of current flow. At about 1.8 V, the first transmission peak enters the range of the integration and contributes to the integral, which generates the current increased rapidly. This indicates a semiconductor-like behavior, which is also observed in another two-probe devices based on the ZnO nanotubes. A peculiar phenomenon is observed from Figure 3 that the values of the current at high bias are insensitive to the lengths. As indicated above by formula 1, current is obtained by the integration of the transmission spectrum from left chemical potential μL to right chemical potential μR. Figure 7 presents the T(E, Vb = 3.0 v) of the two-probe devices based on the 4-cell, 6-cell, and 8-cell ZnO nanotubes, where it is observed that the current under high bias is mainly contributed by the integration of the transmission function above Ef. The transmission spectra above Ef can be divided into a baseline (as shown with dashed line in Figure 7) and several peaks. The baseline increases rapidly with the energy and becomes the main contributor of the current at high voltage. For nanotubes of different lengths, the background changes little and so the current varies only slightly. Because the difference on the length would not affect their transport properties, less control is need and therefore the features may be explored in the design of small electronic devices.
4. CONCLUSIONS Using the nonequilibrium Green’s functions and DFT we have obtained the current-voltage characteristics of ZnO nanotubes coupled to Li(100) electrodes. For short nanotubes, the metal-nanotube interface states drastically contribute to
’ ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China (Grant Nos. 60776065, 10804080, and 10947107) and the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province, China (Grant No. 09KJB140007). ’ REFERENCES (1) He, J. H.; Chang, P. H.; Chen, C. Y.; Tsai, K. T. Nanotechnology 2009, 20, 135701. (2) Yang, K; She, G. W.; Wang, H; Ou, X. M.; Zhang, X. H.; Lee, C. S.; Lee, S. T. J. Phys. Chem. C 2009, 113, 20169–20172. (3) Gao, P. X.; Ding, Y.; Mai, W. J.; Hughes, W. L.; Lao, C. S.; Wang, Z. L. Science 2005, 309, 1700–1704. (4) Wang, Z. L.; Song, J. H. Science 2006, 312, 242–246. (5) Vayssieres, L. Adv. Mater. 2003, 15, 464–466. (6) Xing, Y. L.; Xi, Z. H.; Xue, Z. Q.; Zhang, X. D.; Song, J. H.; Wang, R. M.; Xu, J.; Song, Y.; Zhang, S. L.; Yu, D. P. Appl. Phys. Lett. 2003, 83, 1689–1691. (7) Yan, H. Q.; Johnson, J.; Law, M.; He, R. R.; Knutsen, K.; McKinney, J. R.; Pham, J.; Saykally, R.; Yang, P. D. Adv. Mater. 2003, 15, 1907–1911. (8) Kong, X. Y.; Wang, Z. L. Appl. Phys. Lett. 2004, 84, 975–977. (9) Snure, M.; Tiwari, A. J. Nanosci. Nanotechnol. 2007, 7, 481–485. (10) Xing, Y. J.; Xi, Z. H.; Zhang, X. D.; Song, J. H.; Wang, R. M.; Xu, J.; Xue, Z. Q.; Yu, D. P. Solid State Commun. 2004, 129, 671–675. (11) Xu, W. Z.; Ye, Z. Z.; Ma, D. W.; Lu, H. M.; Zhu, L. P.; Zhao, B. H.; Yang, X. D.; Xu, Z. Y. Appl. Phys. Lett. 2005, 87, 093110. (12) Tu, Z. C.; Hu, X. Phys. Rev. B 2006, 74, 035434. (13) ATK version 2008. 02; Atomistix A/S (www.atomistix.com). (14) Brandbyge, M.; Mozos, J.-L.; Ordejon, P.; Taylor, J.; Stokbro, K. Phys. Rev. B 2002, 65, 165401. (15) Soler, J. M.; Artacho, E.; Gale, J. D.; García, A.; Junquera, J.; Ordejon, P.; Sanchez-Portal, D. J. Phys.: Condens. Matter 2002, 14, 2745– 2779. (16) Taylor, J.; Guo, H.; Wang., J. Phys. Rev. B 2001, 63, 245407. (17) Elizondo, S. L.; Mintmire, J. W. J. Phys. Chem. C 2007, 111, 17821–17826. 3451
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