Spring 2007EE130 Lecture 30, Slide 1 Lecture #30 OUTLINE The MOS Capacitor Electrostatics Reading:...

EE130 Lecture 30, Slide 1Spring 2007

Lecture #30

OUTLINE The MOS Capacitor• Electrostatics

Reading: Chapter 16.3


Bulk Semiconductor Potential, F

• p-type Si:

• n-type Si:

FiF EbulkEq )(

0)/ln( iAF nNq

kT

0)/ln( iDF nNq

kT

Ec

EF Ev

EiqF

EcEF

Ev

Ei

|qF|


Voltage Drops in the MOS System

• In general,

where

qVFB = MS = M – S

Vox is the voltage dropped across the oxide(Vox = total amount of band bending in the oxide)

sis the voltage dropped in the silicon (total amount of band bending in the silicon)

For example: When VG = VFB, Vox = s = 0 i.e. there is no band bending

soxFBG VVV

)()( surfaceEbulkEq iiS


MOS Band Diagrams (n-type Si)

• Inversion

– VG < VT

– Surface becomes p-type

• Accumulation

– VG > VFB

– Electrons accumulate at

surface

• Depletion

– VG < VFB

– Electrons repelled from surface

Decrease VG (toward more negative values)

-> move the gate energy-bands up, relative to the Si

decrease VG decrease VG


Biasing Conditions for p-type Si

VG = VFB VG < VFB VT > VG > VFB

increase VG increase VG


FBGox VVV

0)( FBGoxacc VVCQ

Accumulation Layer Charge Density

p-type Si

+_VG

VG < VFB

++ + + + +

- - - - - -GATE

Qacc (C/cm2)

From Gauss’ Law:

oSiOox

oxaccooxox

SiOaccox

xC

CQxV

Q

/ε where

/

ε/

2

2

(units: F/cm2)

xo


Depletion (n+ poly-Si gate, p-type Si)

Ec

EFSEv

Ec= EFM

Ev

3.1 eV

4.8 eV

p-type Si+_VG

VT > VG > VFB

-- - - --

+ + + + + +GATE

qVG

qVox

qS

M O S

W

Si surface is depleted of mobile carriers (holes)=> Surface charge is due to ionized dopants (acceptors)


Depletion Width W (p-type Si)• Depletion Approximation:

The surface of the Si is depleted of mobile carriers to a depth W.

• The charge density within the depletion region is

• Poisson’s equation:

• Integrate twice, to obtain S:

)0( WxqN A

)0( εε

WxqNρ

dx

d

Si

A

Si

2

2W

qN

Si

AS

A

SSi

qNW

2

To find s for a given VG, we need to consider the voltage drops in the MOS system…


Voltage Drops in Depletion (p-type Si)

ox

SsiASFBoxSFBG C

qNVVVV

2

p-type Si

+_VG

-- - - --

+ + + + + +GATE

Qdep (C/cm2)

From Gauss’ Law:

oxdepooxox

SiOdepox

CQxV

Q

/

ε/2

Qdep is the integrated charge density in the Si:

SSiAAdep qNWqNQ 2


Surface Potential in Depletion (p-type Si)

• Solving for S, we have

ox

SsiASFBG C

qNVV

2

1

)(21

2

2

siA

FBGox

ox

siAS qN

VVC

C

qN

22

2 1)(2

12

siA

FBGox

ox

siAS qN

VVC

C

qN


Asurface

FiFi

Fiii

FS

Nn

EbulkEEsurfaceE

EbulkEsurfaceEbulkE

)()(

)(2)()(

2

Threshold Condition (VG = VT)

• When VG is increased to the point where s reaches 2F, the surface is said to be strongly inverted.

(The surface is n-type to the same degree as the bulk is p-type.)

This is the threshold condition.

VG = VT


A

FSiT

i

AFS

qNWW

n

N

q

kT

)2(2

ln22

MOS Band Diagram at Threshold (p-type Si)

Ec

EFSEv

Ec= EFM

Ev

qVG

qVox

qs

M O S

WT qF

qF


ox

FSiAFFBT C

qNVV

)2(22

Threshold Voltage

• For p-type Si:

• For n-type Si:

ox

SsiASFBoxSFBG C

qNVVVV

2

ox

FSiD

FFBT C

qNVV

222


A

FsiT

FS

qNWW

)2(2

2

Strong Inversion (p-type Si)

p-type Si+_VG

-- - - --

+ + + + + +GATE

Significant density of mobile electrons at surface(surface is n-type)

As VG is increased above VT, the negative charge in the Si is increased by adding mobile electrons (rather than by depleting the Si more deeply), so the depletion width remains ~constant at W= WT

xM O S

x

WT


ox

invT

ox

inv

ox

FsAFFB

ox

invdepFFB

oxSFBG

C

QV

C

Q

C

qNV

C

QQV

VVV

)2(22

)(2

)( TGoxinv VVCQ

Inversion Layer Charge Density (p-type Si)

Spring 2007EE130 Lecture 30, Slide 1 Lecture #30 OUTLINE The MOS Capacitor Electrostatics Reading:...

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