Hardware Reference
In-Depth Information
4.
Connecting routing rings to input pads.
In the contact region, P contact pads
are fabricated using the first metal layer, and each routing ring is connected to its
corresponding contact pad. The connection wires are fabricated using the second
metal layer.
Among the above steps, we note that the routability of a pin-limited biochip is
determined in Step 3, i.e., if there is enough space underneath each electrode to
place the parallel routing wires, the pin-limited biochip is routable. As shown in
Fig.
7.2
c, at the edge of the sub-array that is perpendicular to the routing wires, the
electrodes have the maximum number of routing wires underneath them (i.e., the
four electrodes at the first row of the 4
4 sub-array each has four routing wires
underneath it). Similarly, for a W
s
H
s
(W
s
¤
H
s
) rectangular sub-array, if the
routing wires are aligned parallel to the longer edge of the rectangle, the maximum
number of routing wires fabricated underneath the electrodes is max
f
W
s
;H
s
g
;ifthe
routing wires are aligned parallel to the shorter edge of the rectangle, the maximum
number of routing wires fabricated underneath the electrodes is min
f
W
s
;H
s
g
.Asthe
orientation of routing wires can be parallel to either the longer or shorter edge of
the sub-array, we will always align routing wires parallel to the shorter edge of the
rectangle when designing the wire-routing solution for the W
s
H
s
rectangular
sub-array. Hence, the maximum number of routing wires fabricated underneath
electrodes in the sub-array is min
f
W
s
;H
s
g
.
Therefore, based on the size of the electrode array, as well as the geometric
sizes of electrodes, routing wires, and vias, we can determine whether a pin-limited
biochip has a feasible wire routing solution. For a W
H pin-limited biochip, the
sufficient condition for the existence of its wire routing solution can be derived as
follows.
The top view of an electrode and the underneath routing wires are shown in
Fig.
7.2
d. Here we assume that the diameter of the via is D
via
, the width and length
of each electrode are both D, and the width of a routing wire is T
w
.Inorderto
prevent electrical shorting of the two wires, the gap between them is T
bw
. Therefore,
the average “occupied” width of each routing wire can be estimated as .T
w
C
T
bw
/.
As shown in Fig.
7.1
b and Fig.
7.2
d, there is a via at the center of each electrode.
Since the routing wire cannot overlap with the via, the “effective width” under each
electrode that can be used for aligning routing wires is estimated as .D
D
via
/.
Therefore, the maximum number of routing wires that can be fabricated underneath
an electrode can be estimated as
b
D
D
via
T
w
C
T
bw
c
,where
bc
represents the largest integer
not greater than “
”.
As discussed above, a W
H electrode array can be “equally” partitioned into
four sub-arrays, and the size of the maximum sub-array is
d
2
ed
2
e
,where
de
represents the smallest integer not less than “
”. Therefore, a W
H two-metal-
layer biochip is routable when: min.
d
2
e
;
d
2
e
/
j
DD
via
T
w
CT
bw
k
:
The typical values for D, D
via
, T
w
, T
bw
are 1,000 m, 200 m, 20 m, and
20 m, respectively [
6
,
7
]. Therefore, if W
40 or H
40, the pin-limited biochip
fabricated by two-metal-layer technique is routable. For most of the benchmark
