·a.
up
---i
Ec
E7P
ge wou
Zam
zen
i
i
Forward Bias
:
t
i
-
↳i
in
-
a
(Vbi-Vf]
. . . . . .
Esp-------
I
due
bias
to
internal
E
opposes
-
Voi-V-Barrier
V
=
V =-
Y
Vr
in FB
+
-
in
R B
.
pot
.
Reverse Bias
Tr
-
Ei
zap
Esp
- - -
I
C
Ezn
Erm
-
w
=
xwa)V)
(Vsi
=
NaNd
%i
- -
T
-+
da
duno
->
-
-x
-
du
e
i-->
↳
&
i
un
-
gNa
gen
,
i
i
+V
am
c
d
=
dD
c
Depletion capacitance
->
gANadUno=
=
=
=
gANadupo
gANd
Ano
dVR
I watral
I
noo-val
c
-
=
=
/is
(Vxi-v)"-
c'<
N]
-
holt
↳ used
.
"
a sanctypepet
cap
Variable
turned
in
cap
ekt
.
c
=
(
EA
(Ubi-V)
#wal)"
In
c
A
=
-
W
Id
plate cap
DOPING
#
fe
Na
Nd
e
x
=
0
Epitaxial junct
we
surface
4
=
0
Linearly graded
junct
doped
show juncti
m
No-Na
m = -
x
=
3
m
=
2
m
2
1
=
Na
pt
i
m
Linearly graded junct
=
1
e
When
m
Higher
Linearly
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=
values
of
depends
profile)
low
denote
depends
Voi
iC
on
Gx
=
Hyper abrupt junct
in
desends
physical
doped junct
on
changes
nature
C
->
C
0
doped junct
Fa
=
=
No
-
ne
0
Nd
x
m
=
V &
Vi
on-
funchon type
changes
Idopuy
of junch
=>
W
&
-
ion
-
(C/mi)
Space charge density
((n)
qGx ;
:
+o
do
~
X
L
-
x
D
=
0
no
=
Ge slope of
dopingnon e
an
-
Poisson
=
n
AE(u) +(m) =
:
jdz(n)
=
=
2 (udn
E(x)
A
n
=
1.
=
No
V(u)
u
At
m
Vo
=
=
=
=
-
Ro
n.
S
-
ni)
(z(u) du
enteragendary
->
v
=
0
-
no=[
2-20 :
C
q(n
=
-
V(x)
A
=
.
E(u)
+
b)"
I
↳rate
-
⑳
-
↑D
C
⑳
nt
Metal
semi
conductor
junctions
Metal
⑪
②
->
conductor
semi
I
unctions
junct
Rectifying/Schotthey
contacts
Non-
-
Junction
-I*
equilibrium
y
↓
"gus
i
- - - - - - - -
.
.
.
.
--Ei
Er
-
Evac
i
:
same
-
peplate region
↳
I
g(Vo-Vf]
I
: can't
This
-
L
barrie
I
In
.
B
:
-
cross this
Evac
const
.
84
=
q(Pm-Us)
- ...
This
z
.
Be
R B
.
+
-
L
2
↓
q(Vo
can
b
&
I
flow of
V)
-
=
=
0
er
->
changed
be
g(0m-Ps)
- - - - - - -
-
x
same
+
barrier
a
qVo
i
--------in
W
-
makes
-
↑
↑
barrier
remains
This
&..... ↓
a
-
↑
eginity
Ess
-
Ps
>
flowd)
(n-type)
Evac
Evac
At
high speed :minosity
Semiconductor
Pm
:
:
Metal
Assume
types
carrer
/ohmic
Schottkey
2
-
Ec
Ess
-
moves
Efm
Zw
Ess not
same
i
Ibarrie reduces
easy
Barrie
in
up
n-type
#
I Atype
Majority
role
No
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Rectifying property
-
of
carrie
minority
-I*
I
-> no
flow
majority flow 4
Schottkey
diodes
Om <@s
,
faster
(p-type)
Semiconductor
Metal
Evac
an
conduct
current
>Ps (n-type)
:
p-type
exa
-
Yards
- - - - - - -
Zem
e
·
Pm
<
Ev
Os
marget
we
harl
I
!
i
-
Ev
e
Pm<5
⑧
tydue
ae
Even
ou
zi
-
Ev
>
Accumulat
i
t
I
nin.
->
ev
-
man
ions
.
Eva
-
Es
-
more
ne
-
a
Ec
EEs
-Ev
-
I
↳
-
mic
- -
metal
&
Current
m-type
-
have
of
plentyboth
conduct
direct
e
in
or
s
Pr >4
-
pmcps
Dope
b Schottkey/Rectifigon
Cutty Res
(p-type)
(n-type)
I Now-rectifying/
side
semiconductor
junath
G-21
to
create obnic
m-type
-
:
heavily
Chmic
!
mps
I
ev
er
--
Ec
-
i
I
in
n
M
↳
=
er
0
metal
S
1
If surface of
m-type
Si
created SiOz
-
left
is
as
it is
,
insulator
SiOz
.
The
determine
traps/creates charges
charges
called
These
properties of junct
interface
·
are
.
charges
.
==
--
e-
trafed a
S
-
SiO2
-
I
-
Ev
It
In
may
Homojunct
·
Eg
:
junct
case
a
on
unction
Ec
.
.
.
.
-
-
-
Es
-
- -
. . .
Ea
W
EE
-
-
-
↳
Erac-
letter
capital
global
-
Erac (10c)
->
Ito
Local
for
for highe Eg
level
vacuum
that
convenience)
zar--ggi
zenit
-
Discont
,
I
.
Dza
remains
I
-
-
-
-
-
-
Ev
N
I
-
same
(just
(abrupt jump)
a
-
bending
-
-
-
no
,
level
vaccum
so
material
constant
-
infinity)
Bands
↳
Egi
Ev
-
- - -
P
I=
a
sid
-
-
zv
a
.
--Evac
-
.
of junct
rides
for
materials
used
ferent
Z
.
.
both
for
same
this
in
material
same
Heterojunct
·
If
below
go
Ecz
-
-
~
2
zvz
↓ Egn
&
alligned
Es
=
case
S
conduct
+
Azc
194
=
ben
i
+
,
e
Er
)
Egi)
1Dz1
=
-
~
4
=
.
discontinuity
band
q(x,
=
AEv
Ec
↑
-
DEc
general
already
here
(84-
-
/Azg!
_
i
-
-
zg2)
+
--- er e
I
I
-
Zez
I
-
.
.
.
I
EF1
Evi
-
-
-
e
!
P
-
-
Ecl
E
F
Evi
-
-
-
-
-
-
-
Efz
e
-
-
Li
i
A
zVz
Ev
I
n
I
-
. . .
--
!
Evac
-
in
Ec
.
I
-
-
- - - - - - - -
-
!
DEr
TS
physical phenomenc
same
Ecz
E
Eve
I
as
p-u juncti (homojunct
GaAs-AlmGa ,
As totter
junct
Lattice
matching important for
incr
L-22 :
neterog
Ave
to
Dislocat
charges
change
lattice
mismatch
present- defect
are
thapfed
&
properties
a
changes
changing ste eBandgapheterojunct
,
of
LPE
->
,
Band
layers
LVD)
Ez
Ensure
Earne
-
I
--Ez
Ernie
staggered hellojuncti
Ev2
GaAs
engineering
:
-
straddling heterojmcth
a
.
Epitaxial
/MBE
-
e
400 As
-
.
-
St
-Alo
,
·
blende
Eve
Ea
Ev .
.
Ecz
-
-Evz
Broken
·
Based
gup
material
type of
Aniso +
y
①
on
<P -n
xe
N
Isotype
pN
Eg
p
-
nP
smalle
-n
P
:
-
I
wider
&
used
xN
-
->
PP
N
P
- -
------
↓
Ea
EF
Eve
1Ec
-
qu
↓
,
.
Ec
.
.
i
-
g(x-
=
& Ev
=
DEg
↓
I
T ----.
.
-------
-
x
.
)
-IEc
· Ev
.
↓ qUz
.
.
-
I
-
Ecz
212
-
Evz
N
P
-
-
-
-
-
-
T
.
-
in
i
i
EF
-
Eve
-
-
-
I
I
-
-
-
I
-
-
I
-
P
Evz
-
N
n
-
EC ,
EF
-
-
-
-
Ecz
-
-
↑
-
-
i
I
Ec
-
-
Ecz
EF2
-
Eine
ily
doped
slightly doped
GaAs
Zes
Al
-
~1A~
-
Evz
GaAs
Jee
-
-
Zz
Evi
in
-
-
-
-
-
-
-
-
-↳
zez
-
-
I
A
Ev
-
tele
no
depleth layer
.
Accumulate
layer
is
present
.
Eve
N
I
i=
-
- -
AlGaAs
GaAs
,
-
VI2]
1
~
levels
Energy
quantized
here
fatial well created
at
junct energy levels
quantized
Triangular potential
V(z)
=
qz
well
>
2
;
z
=
>z
there
D
O
;
2 DEG
- -
- -
2
-
~
electrow quanle
D
gas
direct
AlGaAs
GaAs
-
-
mobility
well
all
.
There
eron
Gats
scattering is
low
temp lattice
M
hig h
We
,
is
highly
to
y
in
junct
direct
a
but not
direct (quantized
levels)
energy
Emquinity
At
not
-=>
dopede
of
in
in
.
direct
current y conduct
in
Livel
->
cont
levels
energy
and
doped
side
very high
low baoz
seattering
created
&
?
N
etcross
is
potential
low
.
lightly doped
?
streetman
A
Donald
L
-
23
MOS
Banerjee
Neamen
ictr
for mostet
for
.
-
:
④
-
Metal
E
z1TF--foxide
A
. . .
Eox
I
kamud adenee
d
V
e
-
bir
when-we
semiconductor
appried
interface
#
accumulate
holes
of
-
④
Metal
z4+e oxide
+
⑳
p-type
f
- -
W
-
-
pation
I
oxide
.
+
at
T
↑
-
when
regin
E7
BIAS
p-type
--te
-Ent
at
a
instant
-
--
- -
-
i
3
p-type
(Depleth region width)
====
!
---
=
-
Sina
/
Harge)
Esi
e-
Band
is
bending
functi
becomes
m-type
bias
from
come
material
=>
Ep
mosses
at
of
bias
Mos
interface
semiconductor
oxide
voltage
.
oxide
↳tagamit-I
-
el
I
p-type
Ec
--<epsp
I=
I
S
↳
be
considered
as
one
sided
i
↓
-
-
zI
un
-
->
Ei
--
-
cam
e
! ud
pro
e
Moderate
I
junct
-
Ev
the
applied
bias
Exi
Es
=
epp
=
w
=
Je
merei
I
In()
=
potential
/ (a "wa)]"
potential ept
face
ps
ind=
V
=
contact
-
p-n junct
larger
Ppp
:
e
Yogio
mos
width
p-type
e
zc
--
--
E
-
-
-
2qs
=
247p
L
24
↓
I p
- - -
-
fr ePAp
↑
I
-
.
.
.
.
.
.
.
7
- -
-Ev
S
I
Ei
- - - - - -
2
pyp
Ezi
=
-
ZE
↳-
ad
I come
at
,
oxide-semiconductor
interface-hole
bulk
come
.
In
p-type
sein conductor
This
gate
holt.
If Temp
ad
at
occurs
not
,
4
.
certain
.
much
more
,
e
Further
gate voltage Ec
change created
in
.
be
can
Ud
inc
.
in
maximizes
(invlayer - 4)
inc
-S
247p
=
corresponding
ma
=
->
gate
(p)
Threshold
inversion
holt
threshold
.
is
"
max.
value
pt
.
voltage
fold
.
at inversion
pt
.
.
small
very
M
Evan
S
n
e
If y
-Jedio
zojen: Frnt-
I
- . . .
modified
work
com
~------
functio
Devac
Ew)
-
=m
-
Ec
---------Ei
.
.
.
.
.
EF
-
-Ev
11
Eco
very close
freeL-24
e
trac
to
.
Ev
the
needssmallever
I
late
:
-
↓
-----
eV OXO
-
-
-
......
i
-
-
-
pin
Ec
Ey/z
-
epso
x
Ev
>
equilibrium
-
I
-
-
-
In
zvan
t
-
-
Modified
f
te
moth
~metal
affinity
e
defined
-
m
to
reference
conduct
band e)
Voxo
potential
->
surface
pso-
drop
softential
/
of
energiesto from
of side
metal
fermi
the
-
conductor
epin
e
+
Voxo
side
+
semiconductor
formi
sum
at zelobias
oxide
across
-
level
level
at
o
on
on
bias
the
semi-
.
Voxo
ex'+
=
+
pso=-[Pi-IX'+
ePIp-epso
+
22
Pep(I
-
=
Pms
-
(x
S
Pn
-
+
+
2
Pep) /metalconducte
funct
difference
und
work
metal
degenerately
->
doped poly
entI
-
si
-
↑
epeei
~
Er Earne
I
-
W
--
1
-10
(n+ poly si)
I
m
Melting
pt
.
of
Al
$700
S
(p-type)
Ev
done
Dofing
temp
high
-
by
substrate
p-type
I
+1
n
->
gate
self aligned
For
Si
poly
For
p-type
pas=
(2'
-
avoid
4ns
)
+
x
=
.
poly
-
=
metting problem
(x' z 45p)
+
(2 4-r)
&
poly si
p
(v
-
EF
-
4
+
-
=
p)
Pep
+
E
-
P
(n)
S
Ec
Hat
+
+
=
p'n-(4
Mo
El
used to
si
substrate
m-type
- - - - -
Band
condit
done
is
2
substrate
-
Gas
which
process
E
=
For
implantat"
Al
melts
down
iou
i
zv
which
nott for
Gate
is
there
is
no
band
bed
a
fe a t
scasion
F
additional
Broken/ Dangling bond-contributeinterface
charges at oxide semiconductor interface
in
minimize
is
on
volt
If gate
applied
-
Vi
,
X-25 :
=
done
Vox
charges
appears
which
It
.
depends
Als
-Noxo)+(0s-Pso)
Vox
Vox
argon)
Pms
+
Nox
=
(like
.
static
why
-
=
A Vox
=
Va
temp-
+450
=
bonds
dangling
rise
to
the
oxidat
atmosphere
inert
gives reason
voxo
Si-SiOz
.
Annealing
to
This
at
atoms
floating
Ps
+
4s
+
+
Pms
Gms
+
gate
Flatbandvoltage
molt
-I
I I
↑
-
& VER
-
-
which
For
Ea
EI :
-
-
=== -
s
-Er
mo
Va VIB
=
S
bad e
band
No
Oss
-
sen
bending
trapped
charge
conductor
-
0
M
Ps
=
=
0
(surface potential)
unit
pur
ale
interface
at
oxide
S(p-type)
A
On
induced
-charge
Ndeplet
Om
Voxo
+
450
+
↳
Va
V
=
Dss
=
=
here
-
0
=
per
I no
unit
area
deplet at
neutrality
charge
condit
-Gms
serface potential
AVox
=
=
Vox
charge
laych
metal
on
A
+
ps
Nox-Voxo)
Vox
+
at
(Ps
obias
-
Pso)
4s+ Oms
+
;
Cox
-oxide
cap per
unit
area
Nox
-
=
Ver =Va
-
=
(Ps
ums
+
0
=
at
F
.
condit)
pusthreshold
At
Patr
->
↳
max
.
S
O
M
I-
*
-
MAT
-
-
I
19
=
Rit+Rss
19's
Va
DVox
=
=
Va
=
Vox
Viw
V
=
e
(max
.
Na
IQ'ss (max)
=
(max) 1
eNaxdT
=
Als
+
Ps
+
Pms
GS= 20yp
,
Voxe
+
2
+
↳ nolt
.
45p
across
+
Pms
oxide
at
B
threshold
)
!
UdY
Voxe
=
[10s(wex) 1-D's]
=
I
=
Threshold
Ver
-
Ex (l@ss
=
nott
when
p-type
VEB
substrate used
Vir
(max)1
+
Pas
+
24
P
Pas -x
=
&max)
=
& ss)
-
VFB
+
2 PEP
+
20x
Form-ty/
substrate
s
-
Vip
-2max))
=
Oss=
!
↑iOss=
+
......
in
........
w()
↑
/
--
/
~
& ss
-
->
=
0
5
->
Oss
=
x
24
+
10"
.........
1
&
V
VEB
+
-2
am
10" am
101 -2
#why
trend
-
-
...
1
1613
jo'n
~i
&n
In
inte
:
I
1991
Pan
.
-3)
(n
strong
Accumn-
-
-
lation
=
L
-
Io
ou
-
inversion
-
Deplete
-
>
wick
Is
4
P
#
de
this
?
L
-
26
·
consider
& is
V
+
10" um2
=
w
substrate
p-type
tox=
,
>
=
pop
r's
&'
(max)
,
(max)
Na
e
=
/max.)
Vin
3
=
=-0
.
.
89
.
layer
So
charge
inversion
.
is
-
d
,
83V
.
(capacitance
i jus
-
-
.
43
Pep
&
2200
of deplet region
um
Clam2
the
dol
it induces
->
layer
red
&Oms
at
Fou
.
age
is
induce
even
volt)
mad
.
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-> why-ve ?
layer
ve
2
+10-9
In
&
oxide
cr
Na= 10
Pms=-0
,
max-width
=
341V
is
0
=
W
Trapped charges (9ss)
inversion
chargeit
Also
lightly
is
it
enough
CV
SiO2
essy
-
(p("
:
R'ss
-
300K
=
,
#
en()
v=
=
was
VEN
500
T
Y
=
Ver
get
at
in
low
-
version
doping
characteristics
Assumpth
-ve
nort
he
No
ve
-
We
.
conc
-
fixed
charges
(D's
=
0)
,
vn-ve
3
regions
c
=
e
Accumulation
-
14die
V
DC
->
+
depletion
,
Differential change
Differential
small
charge
in
change
inversion
in
holt
.
AC
m
S
0
M
i
-Ze
---------
Eri
. . . . . . . . . .
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-Er
Accumulat (
-
Now
effect
ideal
charges
,
M
can
frequency
&
S
0
I
from fixed
come
interface changes
veva)
oxide
.
Fildal
+
I
charge
e
distribut
#
-
!..
X
190'
Capacitance
C
acc=
here
cox
=
only
due
->
to
oxide
in
charges
-
accumulation
region
S
M
j
prtype
Ec
-
.
.
.
.
.
un
Depletion
Id
-
S
0
M
Er
I
+
Q
nd-
*
ar
top"
C'ap
+
:
+
Cox
s
mage
we
acitance
cap
I
pation
acrol
I
-
cox/cion
Lox
=
i
x
C
dep
cisp
= I
-(ad
->
min
:
und is
When
max
-
At theshold
inversion
Ma=
:
not
->
max
.
pleti
layer
ci=
width
*) was
O
M
=*
M
re
Ec
EI
-
I
Inversion
1
M
=
#
i
+
S
0
I
( veva)
-S
I
-
=
-
da
dete
FT
↳
Einv
=
Cox
Inversion
-
de
2no
=
x
cap
ar
Cim=
x,
Cix
=
charge
B
e
Ex
change
-lett
by
charge
is
in
differential change
-
~
en
charge
2
/
I
Cox
Accumulation
Strong inversion
------->
YseplW
et"
ion j
I
W
c'dep
I
weak
. . .
·
↓
inversion
Cin
-
w
Vo