Biomedical Engineering Reference
In-Depth Information
0.012
Without diagonal testing
With single-diagonal testing
With cross-diagonal testing
0.01
0.008
0.006
0.004
0.002
0
0.89
0.9
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
Defect Occurrence Probability
Figure 4.21
Simulation results highlighting the probability of untestable sites.
If a cross-diagonal diagnosis is carried out as in Figure 4.20b, the probability
P
untest
of an untestable electrode is given by:
P
untest
= (1−(1−
p
)
i−1
)(1−(1−
p
)
N−i
)(1−(1−
p
)
j−1
)
×
(1−(1−
p
)
N−j
)(1−(1−
p
)
m i n{i,j}−1
)(1−(1−
p
)
N−max{i,j}
) × (1−(1−
p
)
min{N−i,j}−1
)(1−(1−
p
)
N+max{N−i, j}
)
Using the preceding formulas, we calculate the probability of false defect
occurrence under when untestable electrode occurs with different probabili-
ties. The results are shown in Figure 4.21. We see that diagonal testing leads to
a significant reduction in the probability that a cell is untestable. Even though
the proposed multiple-defect diagnosis method does not guarantee the test-
ability of all electrodes, it reduces the occurrence probability of untestable
sites to almost zero (less than 0.0001).
4.4 Application to a Fabricated Biochip
In this section, we apply the parallel scan-like test method to a fabricated bio-
chip. The chip under test is a PCB microfluidic platform for DNA sequencing,
as shown in Figure 4.22. The platform consists of a 7 × 7 array, 8 reservoirs,
and routing electrodes that connect reservoirs to the array. A total of 9 cells are
reserved for grounding, and they are not available for droplet transportation.
As a baseline, we first apply Euler-path-based testing to this chip. The
test procedure takes 57 s, assuming a (typical) 1 Hz electrode actuation fre-
quency. Next, we carry out the parallel scan-like test (the column-test stage is
