Kinetical faceting of the low index W surfaces under electrical current
Introduction
For the ultra-small cross sections of nanomaterials, the capacity for intensive electrical current will be the bottleneck similar to which was encountered in the microelectronic industry [1]. Electrical current can degrade the materials in the form of electromigration or thermomigration (Soret effects) [1]. Metallic atoms and vacancies located at the grain boundaries are usually easier to be driven by the electrical current and segregated to form voids and hillocks [2], which finally destroy the whole wire. But for nanowires or nanofilms which are single crystalline their surfaces will mostly act as the electromigration paths [3]. Surface electromigration is a process of atomic diffusion or reconstruction by surface atoms under electrical current. It has been mostly studied on semiconductor surfaces with conventional surface analysis techniques like Auger electron microscopy (AEM), low energy electron microscopy (LEEM), scanning tunneling microscopy (STM) or scanning electron microscopy (SEM) [4]. It was proposed that under current the vicinal surfaces of low index planes can behave like step motion [4], [5], step bending [6], and step bunching [7] followed by surface instability which finally form facets. However what if the low index surfaces without steps are electrically stressed? Do they keep stable (peeling off or deposition layer by layer [8]) or become instable? These questions still remain unsolved.
For each specific surface, the surface energy can be uniquely defined, and in equilibrium the exposed surfaces of single crystals are determined by their surface energies (Wulff construction) [9], [10]. The body centered cubic (BCC) structure has two lowest energy surfaces ({110} and {112}), with the surface energy of {110} a little lower than {112} [11]. Nevertheless, as a kinetic process electromigration will make things different, the atomic flux on the surfaces must be involved. Krug et al. have developed continuum models describing surface behaviors under electrical field (current) [12], [13]. One of the key findings is the instability condition, μ'(0) > 0(μ'(0) = dμ/dm|m = 0, where μ is the atomic mobility in current direction, m is the slope of the surface) [12]. The key point is electromigration induced surface mass flux causes mass accumulation or consumption and hence induces surface instabilities. If the local flux import is larger than export, the accumulated mass will continue to build up the slopes and finally make small facets, and vice versa. The difference between import and export rate of mass is caused by the different surface diffusivities on different surfaces. Meanwhile, the instability can also be caused by the variation of migration force [14] as flux is the product of mobility and force. However, the electromigration force variation on metals is relatively smaller than the surface diffusivity (mobility) variations.
Some studies have shown the electromigration can effectively influence the step meandering or step bunching [14]. The evolution of the surface morphologies during electromigration was also used to be investigated experimentally on many kinds of surfaces, like W [15], Au [8], Ag [4], [16], Cu [5], Si [17], [18] etc. There were also some observations about the initial instability wavelength on vicinal surfaces, too [19], but like we have mentioned the principle of instability on low energy surfaces is still lacking. Now we investigate the different BCC W (tungsten) surface evolution under electrical current using the in situ TEM method, in the aim of answering the above questions.
Section snippets
Experimental
The fresh W surfaces are prepared by an electrochemical technique [20] using 1 M NaOH solution and 3–4 V bias from 0.3 mm diameter W wires; the as prepared W tips are immediately mounted together with the electric circuits on the Nanofactory™ in situ TEM-STM single tilt holder and inserted into the JEOL 2010 F TEM. Two W tips are positioned head-to-head. One of the W tips has very large aspect ratio at the top (smaller than 100 nm in diameter and longer than 1000 nm in length); therefore, the top
Results and discussion
After applied with the static electric bias (0.1–0.5 V) and direct current (DC) (1–5 mA) for a short while (5–100 s), some of the surfaces of the W nws obviously buckle and form periodic facets (Fig. 1(a)). For comparison, the inset (white dashed rectangle area) of Fig. 1(a) shows the original flat surface. With different initial current density on different W nws, the wavelength of the initial surface instability period is also different, in the range 1 nm–20 nm (Fig. 1(b–e)). Statistics on a
Conclusions
Now the main principles for rebuilding surfaces with electrical current can be established. Firstly, the surface atom diffusivities of the closest low energy surface and the original surface in the direction of the electrical current are crucial; if the original diffusivity is larger, then it's stable, otherwise it's unstable. This criterion may be named “maximum diffusivity tendency in electrical current direction”. This is also relevant to the slip systems in crystallography, because the slip
Acknowledgments
This work is financially supported by the National 973 Project of China and the National Natural Science Foundation of China. This work made use of the resources of the Beijing National Center for Electron Microscopy and Shanghai Supercomputer Center.
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