2/9
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Useful constants (
ε
0, q, ni, etc) are found below.
k = 1.38
*
10
-23
J/K
q = 1.6
*
10
-19
C
ε
0
= 8.85
*
10
-14
F/cm
ε
Si
=
11.7
*
ε
0
ε
SiO2
=
3.97
*
ε
0
n
i
= 1.45
*
10
10
cm
-3
T = 300 K
1-
(25 points) Answer any five of the following six questions: 1.a to 1.f. If you answer all
of the questions, then we will only grade the first five.
(a) (5 points) First, define the VLSI chip manufacturing yield, including functional and
parametric yields. Next, enumerate four causes which are typically responsible for VLSI
chip reliability problems.
Solution:
(3 points) Yield can be calculated as the number of good tested chips divided by the total
number of tested chips (or more strictly, the total number of chip sites available at the
start of the wafer processing.) Functional yield is obtained by testing the functionality of
the chip at a speed usually lower than the required chip speed. It captures shorts/opens,
stuck-at faults, logic and circuit design faults. Parametric yield captures the effect of
uncontrollable process variations as well as dynamic changes in the power/ground
network or substrate temperature on the IC performance. It is performed at the required
speed of the chips.
(2 points) The long-term reliability of a VLSI chip is adversely impacted by:
electromigraion, hot-carrier induced aging, oxide breakdown, latch-up in CMOS I/O and
internal circuits, single event upset, etc. The short term reliability (i.e., integrity) of an IC
is impacted by the power/ground bounce, capacitive crosstalk, non-uniform substrate
temperatures, etc.
(b) (5 points) Define the inverse subthreshold slope, S, and quantify how it impacts the
subthreshold conduction current, e.g., if we reduce the threshold voltage of the nMOS
transistor by 2
*
S volts, then what would be the change in the I
OFF
of an inverter when its
output is low? In comparison, explain what will happen to I
OFF
of the inverter if we reduce
width of the nMOS transistor by a factor of 2?
Solution:
(2 points) The inverse subthreshold slope, S, is equal to the voltage required to increase
subthreshold conduction current, I
D,sub
, by 10X, i.e.,
2.3
nkT
S
q
=×
.
(1 point) Recall that
,
10
GS
T
VV
S
Dsub
IW
−
∝×
.