# ELECTRONICS II VLSI DESIGN SPRING 2005 - Rowan

Electronics - Devices

Nov 26, 2013 (4 years and 7 months ago)

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ELECTRONICS II

VLSI DESIGN

FALL 2013

LECTURE 5

ELECTRICAL & COMPUTER ENGINEERING

ROWAN UNIVERSITY

Deriving the I/V Equation

)
(
0
y
V
V
and
V
V
DS
THN
GS
)
(
y
V
V
GS

Voltage along the

channel.

Is the potential difference
between the gate electrode
and the channel. Includes
both the voltage needed to
turn on the MOSFET and the
voltage to build the inversion
layer.

)
(
)
(
'
'
'
'
y
V
V
C
Q
C
Q
y
V
V
GS
ox
ch
ox
ch
GS

Charge/unit area in the

inversion layer.

THN
ox
b
ox
b
THN
V
C
Q
C
Q
V
'
'
'
'

Charge/unit area required

to create a conducting
channel from source to drain.

THN
GS
ox
b
ch
I
I
V
y
V
V
C
Q
Q
y
Q
Q

)
(
)
(
'
'
'
'
'
Charge in inverted channel = difference between
charge in the inversion layer and charge required to
create the conducting channel.

Differential resistance in
the channel:

W
dy
Q
W
dL
Q
dR
W
L
Q
W
L
t
W
L
t
R
t
Q
qn
A
L
R
I
I
I
I
'
'
'
'
1
1
1
1
1

Deriving the I/V Equation

dy
y
Q
W
I
dR
I
y
dV
IdR
dV
IR
V
I
n
D
D
)
(
)
(
'

)
(
)
(
)
(
)
(
'
'
y
dV
V
y
V
V
C
W
dy
I
y
dV
y
Q
W
dy
I
THN
GS
ox
n
D
I
n
D

2
2
)
(
)
(
2
2
0
0
DS
DS
THN
GS
D
DS
DS
THN
GS
n
D
V
THN
GS
n
L
D
V
V
V
V
I
V
V
V
V
L
W
KP
I
y
dV
V
y
V
V
WKP
dy
I
DS

ox
ox
p
ox
p
p
ox
ox
n
ox
n
n
t
C
KP
t
C
KP
let

'
'

2
2
)
(
)
(
2
2
0
0
DS
DS
THN
GS
D
DS
DS
THN
GS
n
D
V
THN
GS
n
L
D
V
V
V
V
I
V
V
V
V
L
W
KP
I
y
dV
V
y
V
V
WKP
dy
I
DS

This is the linear or triode region
equation and is valid for:

V
GS
≥ V
THN

and

V
DS
≤ V
GS

V
THN

β

is
the gain.

Saturation

When
V
DS
=V
GS

-

V
THN

2
2
2
2
2
2
THN
GS
D
THN
GS
THN
GS
THN
GS
D
THN
GS
DS
DS
DS
THN
GS
D
V
V
I
V
V
V
V
V
V
I
V
V
V
when
V
V
V
V
I

Valid for
V
DS

≥ V
GS

V
THN

and
V
GS

>

V
THN

Channel Length Modification

dl
drawn
elec
X
L
L

DS
elec
elec
D
DS
elec
THN
GS
elec
n
DS
D
THN
GS
elec
n
D
dV
dL
L
I
dV
dL
V
V
L
W
KP
V
I
V
V
L
W
KP
I
1
2
2
2
2
2
Channel resistance changes because
the dimensions are changing.

The change in output current with increasing
V
DS

Channel Length Modulation

THN
GS
THN
GS
sat
DS
DS
sat
DS
DS
THN
GS
n
D
sat
DS
DS
D
D
D
V
V
and
V
V
V
V
for
V
V
V
V
L
W
KP
I
V
V
when
I
I
I

,
,
2
,
1
2

DS
elec
elec
dV
dL
L
1

I
-
V Characteristics