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Reliability
Models for Failure Mechanisms
Electromigration
Electromigration is the movement
of metal atoms of a metal line in the direction of the current flow
through that metal line. This mechanism is similar to pebbles in a stream,
which are picked up and transported by the water in the direction of the
water currents. As such, during electromigration, metal atoms are
removed from the starting end of the metal line and accumulates at the
other end, forming voids at the entrance and hillocks at the exit of the
metal line. Thus, electromigration can result in open circuits (due
to the voids) or line-to-line short circuits (due to the hillocks).
See also:
Electromigration is accelerated by
temperature and current density, and is modeled as follows:
tf =
CJ-ne(Ea/kT)
AF = (Jtest/Juse)n
e(Ea/k)
(1/Tuse-1/Ttest)
where:
C =
a constant based on metal line properties
n =
integer constant from 1 to 7
Tuse,
Ttest = temperature during use and under test, respectively
Juse,
Jtest = current density during use and under test, respectively
Ea = 0.5 -
0.7 eV for pure Al
Corrosion
Corrosion is
metal degradation due to chemical or electrolytic reactions in the
presence of moisture, contaminants, and bias.
Corrosion rate
is a function of temperature (T), relative humidity (RH), and bias (V).
and
tf
= C(RH)-3e(0.9/kT).
With no applied
voltage:
AF = (RHtest/RHuse)3
e(0.9/k)
(1/Tuse-1/Ttest)
With voltage V
applied:
AF =
(V) (RHtest/RHuse)3
e(0.9/k)
(1/Tuse-1/Ttest)
where:
C =
a constant
RHuse, RHtest = relative humidity during use
and under test, respectively
Tuse,
Ttest = temperature during use and under test, respectively
Time-dependent Dielectric Breakdown (TDDB)
Time-dependent Dielectric Breakdown, or TDDB, is the destruction of
dielectric layers occurring over time.
R = A1e(-Ea/kT+CV)
AF
= e([-Ea/k]
[1/Ttest-1/Tuse] + C [Vtest-Vuse])
where:
A1,
C
= constants
Ea = 0.8 - 0.9 eV
Vuse,
Vtest = voltage applied during use and under test, respectively
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