refers to the gradual displacement of the metal atoms of a conductor as
a result of the current flowing through that conductor. The process
of electromigration is analogous to the movement of small pebbles
in a stream from one point to another as a result of the water gushing
through the pebbles.
the mass transport of metal atoms from one point to another during electromigration,
leads to the formation of voids at some points in
the metal line and hillocks or extrusions at other points. It can
therefore result in either: 1) an
open circuit if the void(s) formed in
the metal line become big enough to sever it; or
circuit if the extrusions become long enough to serve as a bridge
between the affected metal and another one adjacent to it.
is actually not a function of current, but a function of current
density. It is also accelerated by elevated temperature. Thus, electromigration is easily observed
in Al metal lines that are subjected to high current densities at high
temperature over time.
Electromigration is widely
believed to be the effect of momentum transfer from the electrons of the
metal, which move according to the applied electric field, to the ions
that constitute the lattice of the metal.
There are two major driving
factors that make electromigration happen: 1) the direct action of the
on the charged atoms or ions of the metal; and the 2) frictional force
between the flowing electrons and these ions. The total driving force is
the sum of the effects of these two factors.
All metal films have
imperfections or microstructural variations that cause the atomic flow
rates through them to be non-uniformly distributed. This
non-uniform atomic flow rates (or
flux divergence) through different sections of the
conductor result in mass depletion (which causes voids) and mass
accumulation (which causes hillocks) as the mass transport mechanism
occurs during electromigration.
In Al films, the dominant
mechanism of atomic migration is along
and surfaces. Lattice mismatches (such as those between adjacent
large and small grains or when three grain boundaries meet) can create
grain boundary interconnections that provide shorter paths for the
atoms, enabling the latter to move faster through the film.
important thing to note regarding how grain structures affect
electromigration failure rates is the conclusion from various studies that
below a critical value for the metal line width, electromigration is
impeded. Electromigration failure rates predictably decrease with
decreasing line widths, but up to a certain point only.
At the critical
limit, the width of the metal line becomes smaller than the grain size
itself, such that all grain boundaries are now perpendicular to the
current flow. Such a structure is also known as a
This results in
a longer path for mass transport, thereby reducing the atomic flux and
electromigration failure rate.
There is also a critical lower
limit for the length of the metal line that will allow electromigration to
occur. Known as the
any metal line that has a length below this limit will not fail by
electromigration. Thus, the Blech length must be considered when
designing test structures for electromigration. Otherwise, no
failures may be observed, leading to an incorrect conclusion.
acceleration effect of high temperature on electromigration becomes
emphasized only when a void has started to form in the metal line.
Prior to any void formation, the metal can still be under uniform
thermal distribution. Once a void forms, however, the current
density at the section where the void is present increases as a result
of the reduced cross-sectional area of the conductor, leading to
around the void.
The higher current density
around the void results in localized heating that further accelerates
the growth of the void, which again increases the current density.
The cycle continues until the void becomes large enough to cause the
metal line to fuse open.
Electromigration may be modeled by the
following equation, which is known as
t50 = the
median lifetime of the population of metal lines subjected to
a constant based on metal line properties;
J = the current density;
integer constant from 1 to 7; many experts believe that n = 2;
T = temperature in deg K;
k = the Boltzmann constant;
Ea = 0.5 -
0.7 eV for pure Al.
Electromigration failures take time to develop, and are therefore very
difficult to detect until it happens. Thus, the best solution to
electromigration problems is to prevent them from taking place.
can be prevented by: 1) proper design of the device such that the current densities
in all parts of the circuit are practically limited; 2) increasing
of the grain sizes of the metal lines such that these become comparable
to their widths (whereby bamboo structure is achieved); and 3) good selection and
deposition of the passivation or thin films placed over the metal lines
in order to limit extrusions caused by electromigration.
must not be confused with EOS-induced metal reflow, which is a different
occurs gradually whereas EOS-induced metal reflow is gross and abrupt.
Failure Analysis; Reliability Models
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