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The
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
current crowding
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
Black's Equation:
t50 =
CJ-ne(Ea/kT)
where:
t50 = the
median lifetime of the population of metal lines subjected to
electromigration;
C =
a constant based on metal line properties;
J = the current density;
n =
integer constant from 1 to 7; many experts believe that n = 2;
T = temperature in deg K;
k = the Boltzmann constant;
and
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.
Electromigration
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.
Electromigration
must not be confused with EOS-induced metal reflow, which is a different
phenomenon. Electromigration occurs gradually whereas EOS-induced
metal reflow is gross and abrupt.
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See
Also:
Die Failures;
Failure Analysis; Reliability Models
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