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All distances are in lambda (
l
) design rules. The following assumptions also
apply to the mathematical model:
The process allows stacked contacts (stacked vias).
Placement issues are not taken into account; every window is used by one
connection to/from the core under study.
Metal layer n is the highest metal layer in the process.
The metal layers below m are used for local interconnections inside the core.
The metal layers from m+1 to n are used to connect outside the core.
These dimensions are shown in Figure 17.9.
The number of connections possible to a core C with area H
H,canbe
computed with Equations 17.6 to 17.8 [80]. Equation 17.6 computes the maximum
number of possible connections on metal layer j.
4
5
H
2 E
þ
P
j
1
i
¼
1
ð
D
i
þ
L
i
Þ
D
j
C
j
¼
4
ð
17
:
6
Þ
D
j
þ
S
j
The inequality shown in Expression 17.7 ensures that there is enough space in
the center of the core to continue adding rings of windows.
"
#
4
0
H
2 E
þ
X
j
1
i
¼
1
ð
D
i
þ
L
i
Þ
ð
17
:
7
Þ
S1
W1
W1
W1
W1
W1
W1
W1
W1
W1
D1
L1
S2
W2
W2
W2
W2
W2
W1
W1
E
D2
L2
W1
W1
S3
W2
W3
W2
W3
W1
W1
D3
Figure
17.9.
The model parameters.
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