oxide

metal

oxt ox

p type

semiconductor

MOS capacitor before joining

The metallic gate may be replaced with a heavily doped p+ polysilicon gate. The Fermi energy levels are approximately at the same level.

MOS capacitor before joining

cE

vE

FsE

FiEFmE

metal oxide

p type

semiconductor

vE

cE

vacuumE

me biggE

ie electron affinity

e

Positive electron energy

oxide

metal

oxt oxp type

semiconductor

MOS capacitor after joiningAssume that there is no charge in

the oxide layer

MOS capacitor energy levels

cE

vE

FsE

FiEFmE

metal oxide

p type

semiconductor

vE

cE

vacuumE

me

biggE

ie electron affinity

e

If the energy bands bend,

then there is a localized

electric field and electric charges.

MOS capacitor energy levels

cE

vE

FsE

FiEFmE

metal oxide

p type

semiconductor

vE

cE

vacuumE

me

biggE

ie electron affinity

e

If the energy bands bend,

then there is a localized

electric field and electric charges.

2

2

( ) ( ) ( )

s

d V x x dE x

dxdx

MOS capacitor p type semiconductorvoltage bias effects

oxide

oxide

AC

t

G

oxide

VE

toxt oxEGV

2

2

( ) ( ) ( )

s

d V x x dE x

dxdx

MOS capacitor p type semiconductorvoltage bias effects –battery switched

oxide

oxide

AC

t

G

oxide

VE

toxt oxGV E

2

2

( ) ( ) ( )

s

d V x x dE x

dxdx

MOS capacitor n type semiconductorvoltage bias effects

oxide

oxide

AC

t

G

oxide

VE

toxt oxGV E

2

2

( ) ( ) ( )

s

d V x x dE x

dxdx

MOS capacitor n type semiconductorvoltage bias effects –battery switched

oxide

oxide

AC

t

G

oxide

VE

toxt oxEGV

2

2

( ) ( ) ( )

s

d V x x dE x

dxdx

oxide

metal

p type

semiconductor

MOS capacitor after joiningAssume that there is charge in the

oxide layer

+ + +

2

oxygen and silicon

diffuse across

the interface

and form SiO

Electric field

d Energy1

e dx

cE

vE

FE

FiE

metaloxide

p semiconductor

oxt oxGV

MOS capacitor p type semiconductor gate voltage VG = VFlatband

FBeV

FE

MOS capacitor p type semiconductor gate voltage VG = VT “threshold”

cE

vE

FxE

FiE

FmE

G TV Voxt oxGV

electrons

FBeV

MOS capacitor –charge distribution

metal oxide p type semiconductor

."accumulation" voltage

"threshold" voltage

. "flatband" voltage

"inversion" voltage

Problem 6.1 Charge distributions are depicted in an MOS capacitor. 1) Is the semiconductor n or p type?

2) Does the bias make it an accumulation mode, depletion mode or an inversion mode?

M O S M O S

Problem 6.1 Charge distributions are depicted in an MOS capacitor. 1) Is the semiconductor n or p type?

2) Does the bias make it an accumulation mode, depletion mode or an inversion mode?

M O SM O S

Electric field due to charges

dVE

dx v

s

dE

dx

surface charge densitys s oxide oxideE E

oxide

E

p type semiconductor

s

s

( x )E( x ) dx c

is a constants( x )

is inhomogeneouss( x )

.

MOS capacitor – changing charge distribution with changing voltage

accumulation mode

metal oxide

p type

semiconductor

.

QC

V

oxide

1 1 1

C C C

oxideoxide

oxide

AC

t

.

MOS capacitor – changing charge distribution with changing voltage

depletion mode

metal oxide

p type

semiconductor

.

QC

V

oxide

1 1 1

C C C

oxideoxide

oxide

AC

t

Dx x

MOS capacitor – changing charge distribution with changing voltage

oxide

1 1 1

C C C

oxide

oxideoxide

AC

t

s

D

AC

x

oxide

oxide

C CC

C C

oxide

oxide

CC

1C

oxide

oxide

oxide

oxide

s

D

A

t

A

t1

A

x

oxide

oxide D

s oxide

CC

x1

t

MOS capacitor – changing charge distribution with changing voltage

accumulation depletion inversionTVFBV GV

C

low frequency

high frequency

oxide

oxide D

s oxide

CC

x1

t

FBoxide oxide

1 xV ( x ) x

C t

oxideFB

oxide

QV

C

oxide

oxide

xQ x ( x ) x

t

definition

Approximate proportion of charge located at x

Problem 6.22 Using superposition, find the dependence of the “flat bad voltage” as the charge density changes.

toxideFB 0

oxide oxide

1 xV ( x )dx

C t

2C

cm( x ) x

FBoxide oxide

1 xV ( x ) x

C t

Nonuniform charge density @ x

Change of flat band voltage

Superimposition applies

Problem 6.23 Using superposition, find the dependence of the “flat bad voltage” for a particular charge density profiles..

toxide oxide

FB t toxide oxideoxide oxide oxide

t1 QV dx

C t t

oxide

Q( x )

t

Charges located just at the interface

FB oxide oxide oxideoxide oxide

1 QV t t t

C t

oxideFB

oxide

QV

C

Problem 6.23 Using superposition, find the dependence of the “flat bad voltage” for a particular charge density profiles..

toxideFB 0

oxide oxide

1 QV x dx

C t

oxide

Q( x ) x

t

Charge density is nonuniform

2oxideFB

oxide oxide

t1 QV

C t 2

Problem 6.28 Consider the high-frequency capacitance-voltage relationship. Locate the inversion; threshold; depletion; flat band, and accumulation points.

inversion

GV

C

accumulation

depletion

flat band

threshold