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