principles of semiconductor devices-lecture36
TRANSCRIPT
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Alam ECE-606 S08 1
EE-606:
Lecture 36MOSFET Current-Voltage (II)
Muhammad Ashraful AlamElectrical and Computer Engineering
Purdue University
West Lafayette, IN USAFall 2007
www.nanohub.org
NCN
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Alam ECE-606 S08 2
topic map
MOS-FET
BJT/HBT
Schottky
Diode
CircuitsLargeSignalSmallsignalDCEquilibrium
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Alam ECE-606 S08 3
outline
1) Square law/ simplified bulk charge theory
2) Velocity saturation in simplified theory
3) Few comments about bulk charge theory, small transistors
2) Conclusion
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Alam ECE-606 S08 4
square law theory
1, 1,
1, 0
( )D
ii
i N i N
V
Dox G th
i N
J dyQ dV
Jdy C V V mV dV
= =
=
=
=
VG VD>001 1 1 11
2 2 2 2
2
3 3 3 3
3
4 4 4 4
4
dV J Q Q
dy
dV J Q Qdy
dV J Q Q
dy
dV J Q Qdy
= =
= =
= =
= =
E
E
E
E
( )2
2
ox D D G th D
ch
C V J V V V m
L
=
VD
Q
V
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Alam ECE-606 S08 5
square law or simplified bulk charge theory
( )2
2
o D G T
ch
W C I V V
mL=
ID
VDS
VGS
( ) D o G T DW
I C V V V L
=
VDSAT = VGS VT( )/m
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Alam ECE-606 S08 6
outline
1) Square law/ simplified bulk charge theory
2) Velocity saturation in simplified theory
3) Few comments about bulk charge theory, small transistors
2) Conclusion
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Alam ECE-606 S08 7
velocity vs. field characteristic (electrons)
electric field V/cm --->
velocityc
m/s--->
107
104
= sat
d = E1 + (E Ec )
2 1/ 2
d = E
1 + ( E Ec )
EC = sat = E
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Alam ECE-606 S08 8
velocity saturation
VG VD>00
1 1 1 1 1 1
1
2 2 2 2 2 2
2
3 3 3 3 3 3
3
4 4 4 4 4 4
4
dV J Q Q
dy
dV J Q Q
dy
dV J Q Q
dy
dV
J Q Q dy
= =
= =
= =
= =
E
E
E
E
1, 1,( )
ii
i N i N
J dyQ dV
x= = =
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Alam ECE-606 S08 9
velocity saturation
1,00
( )
1
DV
D ox G th
i N
c
dy J C V V mV dV
=
=
+
E
E
VG VD>00
( )2
0
2
ox D D G th D
Dch
c
C mV J V V V
VL
=
+E
VD
Q
V
( )2
0 0
11
2
chL
D Dox G th D
c
J dV mV dy C V V V
dy
+ =
E
vsat( )
2
0 02
ch DSL V
D D D ox G th D
c
I mV I dy dV C V V V
E
+ =
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VDSAT
dID
dVDS= 0
ID = FveffCOXW
LVGS VT( )VDS m
VDS2
2
VDSAT =2 VGS VT( )/m
1 + 1 + 2eff VGS VT( ) msatL inf
VDSAT =2 VGS VT( )/m
1 + 1 + 2eff VGS VT( ) msatL
IDSAT = W CGsat VGS VT( )1 + 2eff VGS VT( ) msatL 1
1 + 2eff VGS VT( ) msatL + 1
VDSAT
VGS VT( )m
IDSAT effCGW
2L
VGS VT( )2
m
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IDSAT
IDSAT = W CGsat VGS VT( )1 + 2eff VGS VT( ) msatL 11 + 2eff VGS VT( ) msatL + 1
eqn. (3.78) of Taur and Ning
Examine two limits:
i) L
ii) L 0
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L --> 0
VDSAT =2 VGS VT( )/m
1 + 1 + 2eff VGS VT( ) msatL
IDSAT = W CGsat VGS VT( )
VDSAT
2sat
L VGS
VT( )
meff
IDSAT = W CGsat VGS VT( )1 + 2eff VGS VT( ) msatL 1
1 + 2eff VGS VT( ) msatL + 1
complete velocity saturation
current independent of L
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near threshold
VDSAT =2 VGS VT( )/m
1 + 1 + 2eff VGS VT( ) msatL
VDSAT
VGS
VT( )
m
IDSAT = W CGsat VGS VT( )1 + 2eff VGS VT( ) msatL 1
1 + 2eff VGS VT( ) msatL + 1
2eff VGS VT( )msatL