MOSFET: Subthreshold Operation

1
MOSFET Subthreshold Operation

• Professor Paul Hasler

2
MOSFET Channel Picture
3
MOS Capacitor Picture
4
MOSFET Channel Picture
5
MOSFET Channel Picture
6
Calculation of Drain Current
7
2
n
d
No recombination

Dn Ax B
0
Dn
0
0
2
dx
0
D
2
n
d
dn
-


R
G
D
n
2
dx
dt
0
l
y varies as kVG
(qDn / l) (e-(Y - Vs)/UT - e-(Y - Vd)/UT)
-
dn
n
n



drain
source
qD
J
qD
n
n
dx
l
(
)
(
)
(
)
-
-
k
k
u
V
V
u
V
V
/
/
-

e
e
I
I
T
d
g
T
S
g
0
8
MOSFET Current-Voltage Curves
(
)
-
-
/
/
/
u
V
u
V
u
KV
-

e
e
e
I
I
T
D
T
S
T
G
0
DS
(
)
(
)
(
)
-
k
/
u
V
V
-
-
-

/
u
V
V
1
e
e
I
T
S
g
T
S
d
0
(
)
-
-
/
/
)
(
u
V
u
V
KV
-

1
e
e
I
T
dS
T
S
G
0
-

/
)
(
u
V
KV
e
I
T
S
G
0
9
Channel Current Dependence on Gate Voltage
In linear scale, we have a quadratic dependence
In log-scale, we have an exponential dependence
10
Channel Current Dependence on Gate Voltage
In linear scale, we have a quadratic dependence
In log-scale, we have an exponential dependence
11
Subthreshold MOSFETs
In linear scale, we have a quadratic dependence
In log-scale, we have an exponential dependence
12
Determination of Threshold Voltage
13
Drain Current --- Source Voltage