Page 46 - Semiconductor Manufacturing Handbook

Geng(SMH)_CH04.qxd 04/04/2005 19:36 Page 4.9

COPPER, LOW-k DIELECTRICS, AND THEIR RELIABILITY

COPPER, LOW-κ DIELECTRICS, AND THEIR RELIABILITY 4.9

Product lifetime can be estimated from this data. TDDB fails can also be induced by process defects.
Missing liner at the bottom of the trench, CMP residuals between the lines, and chemically or
mechanically damaged copper surface can lead to fails during stress. Thus TDDB helps in assessing
process stability of the manufacturing line.
Electromigration can lead to considerable material transport in metals. It is the migration of metal
atoms in a high current density carrying line, due to momentum transfer from conducting electrons.
A phenomenological description of the electromigration process is Black’s equation
−n
MTF = A J exp[−E/kT]
where MTF = median time to failure
J = current density
n = current exponent
E = activation energy
A = a constant
and E depends on the diffusivity of the metal atom.
Multiple samples are stressed at high current densities and high temperatures. A structure is con-
sidered a fail if its resistance shifts by a predetermined amount. The fail times have been found to be
lognormally distributed. Based on Black’s equation and lognormal statistics, the lifetime of an inter-
connect at typical use conditions can be calculated. Usually a target current density is desired by the
designers. In that case, a failure rate is defined first before calculating the current density.
Figure 4.8 shows the improvement in electromigration lifetime due to copper interconnects. 1
Electromigration leads to increase in line resistance (or even opens) due to void formation during
stress. These voids typically nucleate at regions of flux divergence. Two modes of electromigration—
line depletion and via depletion—are studied for copper interconnects. The via depletion mode looks
at dual-damascene structures. Here the electron flow goes from the via to the line. The bottom of the
via can act as a flux divergence region and thus can cause void nucleation. In the line depletion mode,
the electron flow occurs from the via at a higher level to the line in the adjacent lower level. Again,
flux divergence occurs near the bottom of the via.

99.9
99
+
95
90
75
Percentile 50 t 60 = 1.31 h t 50 = 147.7 h
Cu
AI(Cu)
25
10
5
>110X
1
J = 2.5 E = 6 A/cm 2
0.1
Temp = 295°C
0.01
0.1 1 10 100 1000 10000
Stress time (hours)
FIGURE 4.8 Electromigration lifetime improvement due to copper interconnects. 1

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