principles of semiconductor devices-l35

8/8/2019 Principles of Semiconductor Devices-L35

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Alam ECE-606 S09 1

www.nanohub.org

NCN

ECE606: Solid State DevicesLecture 35: MOSFET I-V Characteristics (I)

Muhammad Ashraful [email protected]


2/22

Topic Map

Alam ECE-606 S09 2

Equilibrium DC Small

signal

Large

Signal

Circuits

Diode

Schottky

BJT/HBT

MOSCAP

MOSFET


3/22

Outline

Alam ECE-606 S09 3

1. Introduction

2. Sub-threshold (depletion) current

3. Super-threshold, inversion current

4. Conclusion


4/22

Subthreshold Region (VG < Vth)

4

n+ n+p

GS D

n

y

EC

EV


5/22

Subthreshold Region (VG < Vth)

5

n

y

EC

EV y

( )

1

2

2

1sqi

D nc

A

v

h

c

in

h

W

Q

ne

Q I qD

L

Dq W

L N

=

=

ln ID

s

or VG/m

Subthreshold

slope

( )

2/

1GqV

iinv

c A

m

h

D nqWW eL N

Q1

Q2


6/22

Recall the definition of body coefficient (m)

Alam ECE-606 S09 6

( )1 S Om C C= +VG

OC

CSS

O GS G

O S

C VV

C C m =

+

Body Effect Coefficient

( )01 S O Tm x W = +

1.1 m 1.4

in practice:


7/22

Outline

Alam ECE-606 S09 7

1. Introduction

2. Sub-threshold (depletion) current

3. Super-threshold, inversion current

4. Conclusion


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Post-Threshold MOS Current (VG>Vth)

Alam ECE-606 S09 8

( )0

= DSV

D eff

ch

iQI VV

Wd

L

1) Square Law

2) Bulk Charge

3) Simplified Bulk Charge

4) Exact (Pao-Sah or Pierret-Shields)

[ ]) )( = i G G TC V VQ mVV

[ ]) )( = G Ti GC V VV VQ

( )2 22( )

+ =

Si A B

G Gi FB B

O

Qq N V

C V V V VC


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Effect of Gate Bias

9

P

S G D

B

VGS

n+ n+

Gated doped or p-MOS with adjacent n+ region

a) gate biased at flat-band

b) gate biased in inversion

A. Grove, Physics of Semiconductor Devices, 1967.

WDM

VGS >VT

WD

2BVBI

y


10/22

The Effect of Drain Bias

Alam ECE-606 S09 10

2D band diagram for an n-MOSFET

a) device

b) equilibrium (flat band)

c) equilibrium (S > 0)

d) non-equilibrium with VG and VD>0 applied

SM. Sze, Physics of Semiconductor

Devices, 1981 and Pao and Sah.

FN


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Effect of a Reverse Bias at Drain

Alam ECE-606 S09 11

S = 2B +VRVBI+VR

WDM

VGS >VT VR( )

WD

VR VR VR

Gated doped or p-MOS with adjacent, reverse-biased n+ region

a) gate biased at flat-band

b) gate biased in depletion

b) gate biased in inversion

A. Grove, Physics of Semiconductor Devices, 1967.


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Inversion Charge in the Channel

Alam ECE-606 S09 12

P

S G

B

n+ n+ ( )

( ( 0)( ) )

i ox G th

TA T

Q C V V V

q VVN W W

=

+ =

VG=0

VD

=0

VVB

VG=0

VD>0

VD

VB

VG>0

VD>0

D


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Inversion Charge at one point in Channel

Alam ECE-606 S09 13

VGVD

VBVG

( )* 2( )A

th F

ox

Tq W VNV VC

= + 2( 0)

A Tth F

ox

Wq

C

VNV =

=

( )* ( ( 0))T TAth th

ox

qNV V

W WVV

V

C

== +

*( )

i ox G th

Q C V V =

V


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Approximations for Inversion Charge

Alam ECE-606 S09 14

( )( ) ( ) ( 0)i O G th A T T Q C V V V q N W V W V = + =

( ) ( )2 2( ) 22 = + +O G th S o A S oB A BC V V V q N q N V

( )i ox G thQ C V V V

( )i ox G th

Q C V V mV

Approximations:

Square law approximation

Simplified bulk charge approximation


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The MOSFET

Alam ECE-606 S09 15

P

S G D

B

n+ n+

VS = 0 VD > 0

Fn = Fp = EF Fn = Fp qVD

Fn increasingly negative from source to drain

(reverse bias increases from source to drain)


16/22

Elements of Square-law Theory

Alam ECE-606 S09 16

VG VD>0

0

y

GCA : Ey


17/22

Another view of Channel Potential

Alam ECE-606 S09 17

FP

FNFN

FPFP

FN

ECE

FEV

N+ N+

P-doped

Source Drain

x

x


18/22

Square Law Theory

18

VG VD>00

VD

Q

V

1, 1,

1, 0

( )D

ii

i N i N

VD

ox G th

i N

J dyQ dV

Jdy C V V mV dV

= =

=

=

=

1 1 1 1

1

2 2 2 22

3 3 3 3

3

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

( )2

2

ox D D G th D

ch

C V J V V V m

L

=

Q1 Q2 Q3 Q4


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Square Law or Simplified Bulk Charge Theory

Alam ECE-606 S09 19

( )22

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

( )2

2

ox D D G th D

ch

C V I W V V V m

L

=

( )2

2

ox D D G th D

ch

C V J V V V m

L

=

( ) ( )*,0= = = D G th D D sat G thdI

V V mV V V V mdV


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Why does the curve roll over?

Alam ECE-606 S09 20

( )2

2

o D G T

ch

W C I V V

mL

=

ID

VDS

VGS

VDSAT = VGS VT( )/m

( )i ox G thQ C V V mV

VG VD>00

Q

loss of inversion


21/22

Linear Region (Low VDS)

Alam ECE-606 S09 21

ID

VDS small

VGS

( ) D o G T Dch

DS

CH

W I C V V V

L

V

R

=

=

Actual

Subthreshold

Conduction

VT

Mobility degradation

at high VGSSlope gives mobility

Intercept gives VT


22/22

Summary

Alam ECE-606 S09 22

1) MOSFET differs from MOSCAP in that the field from theS/D contacts now causes a current to flow.

2) Two regimes, diffusion-dominated Subthreshold and

drift-dominated super-threshold characteristics, define

the ID-VD-VG characteristics of a MOSFET.

3) The simple bulk charge theory allows calculation of drain

currents and provide many insights, but there are

important limitations of the theory as well.

principles of semiconductor devices-l35

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