Hardware Reference
In-Depth Information
/
"
0
V
2
2
"
rd
"
rh
t
h
"
rd
C
t
d
"
rh
dA
p
dx
F
D
.
;
(3.1)
where "
rd
is the dielectric constant of dielectric layer, "
rh
is the dielectric constant
of the hydrophobic layer, t
d
is the thickness of the insulator layer, t
h
is the thickness
of the hydrophobic layer, "
0
is the permittivity of vacuum, x is the position of the
droplet, V is the voltage applied to the actuated electrode, and A
p
is the area of the
overlapping region between the droplet and the actuated electrode [
32
].
In an ideal situation, at the beginning of the splitting operation, the droplet in
Fig.
3.6
stays at the center of Electrode 2. The overlap region between the droplet
and Electrode 1 (A
p
1
) are the same with the overlap region between the droplet and
Electrode 3 (A
p
3
), therefore we have:
dA
p
1
dx
dA
p
3
dx
. For Electrodes 1 and 3, their
parameters t
d
and t
h
are also the same. Thus the forces generated on the surfaces of
Electrodes 1 and 3 are symmetric, i.e.,
k
F
1
k
k
D
D
1. The droplet will be split over the
F
3
k
two electrodes into droplets of equal size.
However, due to the randomness inherent in the fabrication process, the param-
eters t
h
and t
d
may vary from electrode to electrode, and the electrowetting forces
generated on the surfaces of Electrodes 1 and 3 may not be exactly the same. The
droplet will be split under asymmetric forces in this case.
The droplet on Electrode 2 may be split into two droplets that have unequal
volumes if asymmetric forces are applied [
32
]. For example, when we split a droplet
whose volume is 2 units, if
k
F
1
k
kF
3
k
D
1:10, the volumes of the droplets derived will be
1.13 and 0.87 units, respectively [
32
]. If the “standard” volume of a droplet is 1 unit,
and the error limit for the volume of droplets is 10 %, then both of these droplets
will be abnormal. In this case, errors are generated on the biochip.
The simulator can mimic the behavior of splitting operations in the bioassay
by considering the distributions of parameters t
d
and t
h
for the biochip. For any
electrode E
i
, the thickness of the insulator layer is written as t
d
.E
i
/, the thickness
of the hydrophobic layer is written as t
h
.E
i
/. For given distributions of parameters
t
d
and t
h
for the biochip, and the given synthesis result of the bioassay, the simulator
can calculate the ratio of the two electrowetting forces generated in each splitting
operation.
We assume that the splitting operation O
S
is performed by electrodes E
L
and E
R
.
According to (
3.1
), the ratio of the electrowetting forces generated on E
L
and E
R
(written as F
E
L
and F
E
R
) can be expressed as:
k
F
E
R
k
k
F
E
L
k
.t
h
.E
L
/"
rd
C
t
d
.E
L
/"
rh
/
.t
h
.E
R
/"
rd
C
t
d
.E
R
/"
rh
/
:
D
(3.2)
If the ratio of
k
F
E
R
k
to
k
F
E
L
k
is out of acceptable range, the splitting operation
O
S
will generate two droplets that have abnormal volumes. In this way, an error
is generated during fault simulation, i.e., we mimic the occurrences of errors by
running the fault simulation under parameter variations.
