pubs.acs.org/NanoLett
Mass Transportation Mechanism in Electric-Biased Carbon Nanotubes Jiong Zhao,† Jia-Qi Huang,‡ Fei Wei,‡ and Jing Zhu*,† †
Beijing National Center for Electron Microscopy, The State Key Laboratory of New Ceramics and Fine Processing, Laboratory of Advanced Materials, Department of Materials Science and Engineering and ‡ Beijing Key Laboratory of Green Chemical Reaction Engineering and Technology, Department of Chemical Engineering, Tsinghua University, Beijing 100084, China ABSTRACT The mass transportation mechanism in electric-biased carbon nanotubes (CNTs) is investigated experimentally. Except for the widely accepted electromigration mechanism, we find out the thermal effect can also induce the mass transportation in the form of thermomigration or thermal evaporation. Moreover, the convincing in situ transmission electron microscope experiment results show the thermal gradient force overrides the electromigration force in most conditions, according to specific parameters of the CNTs and “cargos”. A full analysis on the thermal gradient force and electromigration force imposed on the cargos is given, thus our experimental results are well explained and understood. KEYWORDS Carbon nanotubes, Fe cargo, in situ TEM, evaporation, electromigration, thermomigration.
C
ontrolled mass transportation in nanoscale is a key issue in nanotechnology. The inherent hollow pipe structured carbon nanotubes (CNTs) have been employed to transport gas and liquid atoms or ions, large molecules like DNA, solid particles, etc.1-11 Recently, chemical potential difference,1 mechanical force,2,3 and acoustic waves4 have been demonstrated to drive the transportation in CNTs, and most reported experimental works used the approach of electric bias imposed directly on two ends of the CNTs.5-10 The mechanism of the electric bias actuated transportation is arguing at present,5-11 electromigration force and thermal gradient are two competitive driving forces. Current understanding favors the electromigration mechanism.5-9,11 However, here we show the thermal gradient force overrides the electromigration force in most conditions by means of in situ transmission electron microscopy (TEM) studies. The length of the CNTs, the location and size of the “cargos”, as well as the magnitude of the bias can affect the transportation mechanism apparently. Generally, for a two terminal connected MWCNT, when applied with an electric bias there are mainly three mass transportation mechanisms. One is thermal evaporation, which means the cargo changes its size; one is thermomigration, which means temperature gradient pushes the cargo; the third is electromigration, which means the current pushes the cargo. Joule heating of such 1D diffusive conductor can be analytically analyzed.12 Assuming the thermal and electrical conductivities of the CNTs are temperature independent and a symmetric boundary condition,13 the tem-
* To whom correspondence should mail.tsinghua.edu.cn. Received for review: 03/12/2010 Published on Web: 10/19/2010 © 2010 American Chemical Society
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perature distribution over the CNT is parabolic with midpoint of the CNT as the hottest position. Therefore the temperature gradients are larger near the two ends. Thermal gradient force comes from the momentum transfer from the phonons of CNTs to the cargos, pointing from hotter place to colder place. This thermal gradient force (per volume) can be determined by the size, position, and local temperature of the cargo, and its relationship with the current density passing through the CNT can be derived as
( )
Fthermo ) α exp -
2βl2 l dT L2j2 L4j4 dx
(1)
where l is the size of the cargo, L is the CNT length, j is the current density, dT/dx is the temperature gradient along the CNT, and R and β are two constants. The derivation of eq 1 and full analysis will be presented after the discussion of our experimental results. On the other hand, electromigration force is caused by the electronic scattering of impurities or local defects in the crystal lattice. The main character of electromigration force is direction dependent on the current, apparently different from the thermal gradient force. The magnitude of the force (per atom) is proportional to the current density,14
Felectro ) eF(Zd + Zw)j
(2)
where e is electron elementary charge, F is electrical resistivity, and Zd and Zw are effective valences for the direct and the wind force mediated processes, respectively. The direction of the electromigration force is still under debate,11,15
jzhu@
4309
DOI: 10.1021/nl1008713 | Nano Lett. 2010, 10, 4309–4315
FIGURE 1. (a) Scheme of the in situ TEM nanomanipulator and scanning tunneling microscope (STM) facility. (b) Analysis of the forces imposed on the cargo when the cargo is near one end of the CNT. (c) Diagram of the mass transportation mechanisms with respect to different conditions and the absolute value of two competitive forces, Fthermo and Felectro. The Four colored force-current density curves corresponds to small cargo condition (red), end position of the cargo (purple), electromigration condition (green), and short CNT condition (blue). Specially, the small cargo condition (red) does not include condition that the cargo is at the zero temperature gradient location( i.e., at middle point of CNT). The black line corresponds to the invariant electromigration force. The onset migration current density refers to the extreme points of Fthermo.
highly dependent on the materials chosen and the electronic property of the MWCNTs. For Fe cargo, more reports support the electron wind force domination.6-9 The third force imposed on the cargo is the binding force, the binding force decreases when the temperature rises. The three forces are schematically presented in Figure 1b. When the cargo is thermally excited, binding force is ignorable. The absolute values of thermomigration force and electromigration force with respect to current density under different conditions are shown in Figure 1c. Multiwall carbon nanotubes (MWCNTs) synthesized by a chemical vapor deposition (CVD) method employing Fe as the catalyst16 are used in our experiments. The two ends of the CNTs are contacted with a static gold (Au) electrode and a tungsten (W) tip connected with a piezo driven nanomanipulator, respectively (Figure 1a). A dc bias can be applied between the Au electrode and W tip with I-V curves taken simultaneously (see Supporting Information, Figure S1). Fe nanoparticles encapsulated in the CNTs act as cargos transported (see Supporting Information, Figure S2). All experiments are carried out within a few minutes and only limited damage of very few outer walls of the sample can be found; also, heating is approximately homogeneous in the illuminated area, so radiation damage effect and electron beam heating effect can be neglected in our analysis. Our experiment starts with a top-closed MWCNT, contacted with the W tip (Figure 2a,b). When a bias of 1.3 V is applied17 with a current of 123 µA, the end near W tip accumulates more and more Fe substances (Figure 2c) that come from the midway places of the MWCNT. Three minutes later, when we reverse the bias at -1.3 V and -122 µA this phenomenon persists (Figure 2d). The current direction independence rules out the possibility of electromigration. © 2010 American Chemical Society
It is just like vapor deposition in the tube furnace without carrying gas. This part by part transportation is probably thermal evaporation. The atoms and clusters (
