Surface Electromigration and Current Crowding - Nanophenomena at Surfaces - page 113

of tens of percent to a factor of 2. The perpendicular component of the current flow
around defects forms a dipole pattern with length scale determined by the length
of the defect along the direction of the current flow. The shape and localization of
the dipole pattern vary with the sharpness and symmetry of the defect. The current
crowding affect alone is not sufficient to explain the greatly enhanced electromigra-
tion force observed for scattering at kink sites at steps.
5.1 Introduction
Electromigration is the mass transport of atoms in or on an electrically conduct-
ing material, where the transport is driven by applied electric fields and the result-
ing current flow. Study of the mechanisms of electromigration has yielded deep
physical insights about the mechanisms of electron scattering, and in particular the
special characteristics (e.g., surface resistivity) of surfaces and interfaces [ 1 - 3 ]. As
the size scale of electrical interconnects shrinks, and as interest in nanoelectronic
grows, the role of electron scattering at surfaces, and thus at surface defects and
non-uniformities, becomes more important [ 4 - 6 ]. Electromigration failure can arise
from a surface diffusion flux that is driven by competition between the electromigra-
tion and healing capillary forces. These surface processes may couple constructively
along a void surface [ 7 , 8 ], with increased effect due to anisotropic surface diffusion
to drive catastrophic void formation [ 9 , 10 ]. In addition, current crowding [ 9 - 12 ]in
the vicinity of a defect may also have a great role in its evolution by increasing the
local magnitude of the electromigration force.
The tools of surface science opened the study of electromigration to atomic
scale characterization [ 13 ], and the surprising and complex behavior in the
electromigration-induced evolution of Si surface structure [ 14 - 18 ] led to deep the-
oretical investigations [ 19 ] of the development of kinetic instabilities in the pres-
ence of an electromigration force. In the same time frame, fundamental scattering
calculations [ 20 , 21 ] have made it possible to quantify the electromigration forces
acting on surface atoms including different defect sites. More recently, there has
been renewed interest, focused on nanoscale structures, in fundamental issues of
current flow at constrictions and interfaces [ 22 , 23 ]. The combination of theoreti-
cal and experimental advances in the understanding of electromigration opens the
possibility for using nanoscale structures to tailor surface resistivity [ 21 , 24 - 26 ]
and to control structure as in nanogap formation [ 27 - 29 ], for driving dopants into
nanowires [ 30 ], for coupling electrical signals to atomic fluctuations [ 25 , 31 ] and
even the possibility of driving nanoscale rotational motion [ 32 ].
In the following, we will review an example of the use of direct imaging (STM)
to follow the evolution of structure during electromigration. Analysis of the obser-
vations using the continuum step model approach [ 33 ] reveals an unexpectedly
large electromigration force, which we will argue indicates a substantial effect
of nanoscale current crowding. We will then present a parallel set of investiga-
tions, carried out on micron-scale structures, which demonstrate the direct obser-
vation of non-uniform current flow around defects. Because the classical laws of