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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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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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Alam ECE-606 S08 22

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