Transcript 072_16_2009

MOS capacitor before joining
metal
 ox
oxide tox
p type
semiconductor
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
Evacuum
Positive
ei electron affinity
em
Ec
Eg big
EFm
e
Ec
EFi
EFs
Ev
metal
electron
energy
oxide
p typeEv
semiconductor
MOS capacitor after joining
Assume that there is no charge in
the oxide layer
metal
oxide
tox
p type
 ox
semiconductor
MOS capacitor energy levels
ei electron affinity Evacuum
em
Ec
Eg big
e
Ec
EFi
E
Fm bands bend,
If the energy
EFs
then there is a localized
E
v charges.
p typeEv
electric field and electric
metal
oxide
semiconductor
2 capacitor energy levels
MOS
d V ( x)
 ( x)
dE ( x)
dx
em
2




electron
affinity E
e i 
vacuum
dx
s
Ec
Eg big
e
Ec
EFi
E
Fm bands bend,
If the energy
EFs
then there is a localized
E
v charges.
p typeEv
electric field and electric
metal
oxide
semiconductor
MOS capacitor p type semiconductor
voltage bias effects
VG
tox
 ox
E
E
VG
toxide
C
 oxide A
toxide
d V ( x)
 ( x)
dE ( x)




2

dx
dx
2
MOS capacitor p type semiconductor
voltage bias effects –battery switched
VG
tox
 ox
E
E
VG
toxide
C
 oxide A
toxide
d V ( x)
 ( x)
dE ( x)




2

dx
dx
2
MOS capacitor n type semiconductor
voltage bias effects
VG
tox
 ox
E
E
VG
toxide
C
 oxide A
toxide
d V ( x)
 ( x)
dE ( x)




2

dx
dx
2
MOS capacitor n type semiconductor
voltage bias effects –battery switched
VG
tox
 ox
E
E
VG
toxide
C
 oxide A
toxide
d V ( x)
 ( x)
dE ( x)




2

dx
dx
2
MOS capacitor after joining
Assume that there is charge in the
oxide layer
metal
oxide
+++
p type
semiconductor
oxygen and silicon
diffuse across
the interface
and form SiO 2
1 d  Energy 
Electric field 
e
dx
MOS capacitor p type semiconductor
gate voltage VG = VFlatband
EF
VG
tox
 ox
eVFB
Ec
EFi
EF
Ev
metal
p semiconductor
oxide
MOS capacitor p type semiconductor
gate voltage VG = VT “threshold”
VG
tox
 ox
VGFB VT
eV
EFm
Ec
EFi
EFx
Ev

electrons
MOS capacitor –charge distribution
.
.
"accumulation" voltage
"flatband" voltage
"threshold" voltage
"inversion" voltage
metal oxide
p type semiconductor
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
M
O
S
O
S
Electric field due to charges
dV
E
dx
dE v

dx  s
s ( x )
E( x )  
dx  c
s
 s Es   oxide Eoxide  surface charge density
E
s ( x ) is a constant
s ( x ) is inhomogeneous
oxide p type semiconductor
MOS capacitor – changing charge
distribution with changing voltage
accumulation mode
 oxide A
.
Coxide 
toxide
.
Q
C 
V
1
1
1


C Coxide C
p type
metal oxide
semiconductor
MOS capacitor – changing charge
distribution with changing voltage
depletion mode
 oxide A
Coxide 
.
.
xD x
toxide
Q
C 
V
1
1
1


C Coxide C
p type
metal oxide
semiconductor
MOS capacitor – changing charge
distribution with changing voltage
 oxide A

A
1
1
1 C
s

C

Coxide

C
Coxide C
C

Coxide  C
oxide
Coxide
Coxide
1
C
Coxide
C
  oxide  xD 
1 


  s  toxide 
toxide
C 
xD
  oxide A 
 t

oxide 


  oxide A 
 t

oxide 

1
 s A 
 x 
 D 
MOS capacitor – changing charge
distribution with changing voltage
C
high frequency
Coxide
C
  oxide  xD 
low
frequency
1 
 t


 s  oxide 
VFB
VT
VG
inversion
depletion
accumulation
VFB
Qoxide

Coxide
definition
Approximate proportion of charge located at x
x


Qoxide  x    ( x ) 
x

 toxide 
VFB
1  x 

 ( x )x


Coxide  toxide 
Problem 6.22 Using superposition, find the dependence of
the “flat bad voltage” as the charge density changes.
Nonuniform charge density @ x
( x )x C
cm
2
Change of flat band voltage
VFB
1  x 


(
x
)

x
Coxide  toxide 
Superimposition applies
VFB  
1
Coxide
toxide 
t
0

x 
  ( x )dx
 oxide 
Problem 6.23 Using superposition, find the dependence of the
“flat bad voltage” for a particular charge density profiles..
Charges located just at the interface
Q
( x ) 
toxide
VFB 
VFB
VFB
toxide
 toxide


t

t


oxide
oxide
Coxide
 toxide
1

Qoxide

Coxide
 Q 
 t
 dx
 oxide 
1  Q 
toxide   toxide  toxide  



Coxide  toxide 
Problem 6.23 Using superposition, find the dependence of the
“flat bad voltage” for a particular charge density profiles..
Charge density is nonuniform
( x ) 
Q
toxide
VFB  
VFB
x
1
Coxide
toxide 
t
0


Q
oxide

x  dx

1  Q   toxide 

Coxide  toxide  2
2
Problem 6.28 Consider the high-frequency capacitancevoltage relationship. Locate the inversion; threshold;
depletion; flat band, and accumulation points.
C
flat band
accumulation
depletion
inversion
threshold
VG