Course Outline (EN (EN 5305 5305) Semiconductor ) Semiconductor Devices & Technology Devices & Technology Course Outline By Dr. Yaseer A. Durrani Dept. of Electronics Engineering University of Engineering & Technology, Taxila Course Outline Technology: – Introduction & Historical Perspective – Modern CMOS Technology – Crystal Growth, Wafer Fabrication & Basic Properties of Si Wafers – Semiconductor Manufacturing – Lithography – Thermal Oxidation, Dopant Diffusion, Ion Implantation, Thin film deposition, Etching – Back-End Technology 2 – Back-End Technology Device: – Semiconductor Devices – Dielectric Materials & Insulations – Magnetic Properties & Superconductivity – Optical properties of Materials
Introduction 1
Dec 03, 2015
semiconductor devices 1
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Cours
e O
utlin
e
(EN
(E
N 5
305
5305) S
em
icond
ucto
r ) S
em
icond
ucto
r D
evic
es &
Technolo
gy
Devic
es &
Technolo
gy
Cours
e O
utlin
e
By D
r. Yaseer
A. D
urra
ni
De
pt. o
f Ele
ctro
nic
s E
ng
ine
erin
gU
niv
ers
ity o
f En
gin
ee
ring
& T
ech
no
log
y, Ta
xila
Cours
e O
utlin
e�
Technolo
gy:
–In
troductio
n &
His
toric
al P
ers
pectiv
e–
Modern
CM
OS
Technolo
gy
–C
rysta
l Gro
wth
, Wafe
r Fabric
atio
n &
Basic
Pro
pertie
s o
f S
i Wafe
rs–
Sem
iconducto
r Manufa
ctu
ring
–Lith
ogra
phy
–T
herm
al O
xid
atio
n, D
opant
Diffu
sio
n, Io
n Im
pla
nta
tion,
Thin
film d
epositio
n, E
tchin
g–
Back-E
nd T
echnolo
gy
2
–B
ack-E
nd T
echnolo
gy
�D
evic
e:
–S
em
iconducto
r Devic
es
–D
iele
ctric
Mate
rials
& In
sula
tions
–M
agnetic
Pro
pertie
s &
Superc
onductiv
ity–
Optic
al p
ropertie
s o
f Mate
rials
Refe
rence B
ooks
�S
ilico
nV
LS
IT
echno
logy,
Fund
am
enta
ls,
Pra
ctic
e&
Mode
ling,
Jam
es
D.
Plu
mm
er,
M.D
.Deal,
P.
B.
Griffin
,P
ears
on
Publis
her,
ISD
N:978-8
1-3
17-2
60
4-4
�S
em
icon
du
cto
rD
evic
es,
Kanna
an
Kan
o,
Pre
ntic
eH
all
Publis
her,
ISB
N:81-2
03-2
877-9
�D
evic
eE
lectro
nic
sfo
rIn
tegra
ted
Circ
uits
,R
.S
.M
ulle
r,T
.I.
Kam
ins,IS
BN
:978-8
1-2
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09
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3
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id2
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ou
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ject/C
ase
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die
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ina
l 4
0%
4
Intro
ductio
n to
Devic
e &
(EN
5305) S
em
icond
ucto
r (E
N 5
305) S
em
icond
ucto
r D
evic
es &
Technolo
gy
Devic
es &
Technolo
gy
Intro
ductio
n to
Devic
e &
Technolo
gy
By D
r. Yaseer
A. D
urra
ni
De
pt. o
f Ele
ctro
nic
s E
ng
ine
erin
gU
niv
ers
ity o
f En
gin
ee
ring
& T
ech
no
log
y, Ta
xila
5
Outlin
e
�C
MO
S T
ech
on
log
yS
ca
ling
�H
isto
rica
l Tre
nd
s &
Fu
ture
Pre
dic
tion
s
�M
ate
rials
& D
evic
es
�S
em
ico
nd
ucto
r Te
ch
no
log
y F
am
ilies
6
CM
OS
Technolo
gy
�In
tegra
ted
Circ
uit
(IC)
isan
ele
ctro
nic
netw
ork
fabric
ate
din
asin
gle
pie
ce
of
sem
iconducto
rm
ate
rial
�S
em
icon
ducto
rsurfa
ce
issubje
cte
dto
vario
us
pro
cessin
gste
ps
inw
hic
him
puritie
sand
oth
er
mate
rials
are
added
with
specific
geom
etric
alpatte
rns
�F
abric
atio
nste
ps
are
se
que
nced
tofo
rmth
ree
dim
ensio
na
lre
gio
ns
that
act
as
transis
tors
&in
terc
onnects
that
form
the
sw
itchin
gor
am
plific
atio
nnetw
ork
19
60
s1
99
0s
Technolo
gy S
calin
g�
Evolu
tion
of
Silic
on
Inte
gra
ted
Circ
uits
sin
ce
1960s
–In
cre
asin
g:
circ
uit
com
ple
xity
,packin
gdensity
,chip
siz
e,
speed
&re
liability
–D
ecre
asin
g:
featu
resiz
e,
pric
eper
bit,
pow
er
(dela
y)
pro
duct
�C
urre
ntly
,te
chnolo
gy
scalin
ghas
ath
reefo
ldobje
ctiv
e:
–R
educe
the
gate
dela
yby
30%
(43%
incre
ase
infre
quency)
–D
ouble
the
transis
tor
density
–S
avin
g50%
ofpow
er
(at
43%
incre
ase
infre
quency)
�H
ow
isscalin
gachie
ved?
�H
ow
isscalin
gachie
ved?
–A
llth
edevic
edim
ensio
ns
(late
ral&
vertic
al)
are
reduced
by
1/α
–C
oncentra
tion
densitie
sare
incre
ased
by
α
–D
evic
evolta
ges
reduced
by
1/α
(not
inall
scalin
gm
eth
ods)
–T
ypic
ally
1/α
=0.7
(30%
reductio
nin
the
dim
ensio
ns)
�S
calin
gvaria
ble
sare
:–
Supply
volta
ge:
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d →V
dd/α
–G
ate
length
:L
→L/α
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ate
wid
th:
W→
W/α
–G
ate
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eth
ickness:
tox →
tox/α
–Junctio
ndepth
:X
j →X
j /α–
Substra
tedopin
g:
NA →
NA ×
α
Technolo
gy S
calin
g�
Ele
ctric
field
acro
ss
gate
-oxid
edoes
not
chang
ew
hen
techno
log
yis
scale
dcalle
dconsta
nt
field
scalin
g�
Ifpo
wer
sup
ply
volta
ge
ism
ain
tain
ed
consta
nt
the
scalin
gis
calle
dco
nsta
nt
volta
ge.
Inth
iscase,
ele
ctric
field
acro
ss
ga
te-o
xid
ein
cre
ases
as
technolo
gy
isscale
ddow
n�
Due
togate
-oxid
ebre
akdo
wn,
belo
w0.8
µm
only
“consta
nt
field
”scalin
gis
used
�S
om
econsequences
30%
scalin
gin
consta
nt
field
regim
e(α
=1.4
3,
1/α
=0.7
):–
Devic
e/d
ieare
a:
W×
L→
(1/α
)2
=0.4
9–
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ctic
e,
uP
sdie
siz
egro
ws
about
25%
per
technolo
gy
genera
tion
�T
ransis
tor
density
:(u
nit
are
a)
/(W×
L)
→α
2=
2.0
4�
Tra
nsis
tor
density
:(u
nit
are
a)
/(W×
L)
→α
2=
2.0
4–
Inpra
ctic
e,
mem
ory
density
has
been
sca
ling
as
exp
ecte
d.
(nottru
efo
ruP
s…
)�
Gate
capacita
nce:
W×
L/
tox
→1/α
=0.7
�D
rain
curre
nt:
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)×
(V2/to
x )→
1/α
=0.7
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ate
dela
y:
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V)
/I
→1/α
=0.7
,F
requency
→α
=1.4
3–
Inpra
ctic
e,
uP
sfre
quency
ha
sdouble
devery
techn
olo
gy
genera
tion
(2to
3years
)!T
his
faste
rin
cre
ase
rate
isdue
totw
ofa
cto
rs:
•N
um
ber
of
ga
tedela
ys
inclo
ck
cycle
decre
ases
with
time
(desig
ns
becom
ehig
hly
pip
elin
ed)
•A
dvanced
techniq
ues
reduce
avera
ge
gate
dela
y30%
per
genera
tion
Technolo
gy S
calin
g�
Pow
er:
C×
V2
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→(1
/α)2
=0.4
9�
Pow
er
density
:1/to
x×
V2
×f
→1
�A
ctiv
ecapacita
nce/u
nit-a
rea:
Po
we
rdis
sip
atio
nis
afu
nctio
nof
op
era
tion
frequency,
pow
er
supply
volta
ge
and
of
circ
uit
siz
e(n
um
ber
ofdevic
es)
�If
we
norm
aliz
eth
epo
we
rde
nsity
toV
2×
fw
eobta
inth
eactiv
ecapacita
nce
per
unit
are
afo
ra
giv
en
circ
uit.
This
para
me
ter
can
be
co
mpare
dw
ithoxid
ecapacita
nce
per
unit
are
a:
1/to
x→
α=
1.4
3–
Inp
ractic
e,
for
uP
s,
activ
eca
pa
cita
nce
/unit-a
rea
on
lyin
cre
ase
sb
/w3
0%
-3
5%
.
Tw
ofo
ldim
pro
ve
me
nt
inlo
gic
de
nsity
b/w
tech
no
log
ies
isn
ot
ach
ieve
d
�In
terc
onnects
scalin
g:
�In
terc
onnects
scalin
g:
–H
igher
densitie
sare
only
possib
leif
the
inte
rconnects
als
oscale
.–
Reduced
wid
th→
incre
ased
resis
tance
–D
enser
inte
rconnects
→hig
her
capacita
nce
–T
oaccount
for
incre
ase
dpara
sitic
s&
inte
gra
tion
com
ple
xity
more
inte
rconnectio
nla
yers
are
added:
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hin
ne
r&
tigh
ter
laye
rs→
loca
lin
terc
on
ne
ctio
ns
–T
hic
ke
r&
sp
ars
er
laye
rs→
glo
ba
lin
terc
on
ne
ctio
ns
&p
ow
er
Inte
rco
nn
ects
are
sca
ling
as
exp
ecte
d
Technolo
gy S
calin
gP
ara
me
ter
Co
nsta
nt F
ield
Co
nsta
nt V
olta
ge
Su
pp
ly v
olta
ge
(Vdd )
1/α
1
Le
ng
th (L
)1
/α1
/α
Wid
th (W
)1
/α1
/α
Ga
te-o
xid
e th
ickn
ess (to
x )1
/α1
/α
Ju
nctio
n d
ep
th (X
j )1
/α1
/α
Su
bstra
te d
op
ing
(NA )
αα
Ele
ctric
field
acro
ss g
ate
oxid
e (E
)1
α
De
ple
tion
laye
r thic
kn
ess
1/α
1/α
Sca
ling
Va
riab
les
Ga
te a
rea
(Die
are
a)
1/α
21
/α2
Ga
te c
ap
acita
nce
(loa
d) (C
)1
/α1
/α
Dra
in-c
urre
nt (Id
ss )
1/α
α
Tra
nsco
nd
ucta
nce
(gm
)1
α
Ga
te d
ela
y1
/α1
/α2
Cu
rren
t de
nsity
αα
3
DC
& D
yn
am
ic p
ow
er d
issip
atio
n1
/α2
α
Po
we
r de
nsity
1α
3
Po
we
r-De
lay p
rod
uct
1/α
31
/α
De
vic
e
Re
pe
rcu
ssio
n
Circ
uit
Re
pe
rcu
ssio
n
Technolo
gy S
calin
g�
Ele
ctro
n B
eam
Lith
ogra
phy (E
BL)
–P
atte
rns a
re d
eriv
ed d
irectly
from
dig
ital d
ata
–P
rocess c
an b
e d
irect: n
o m
asks
–P
atte
rn c
hanges c
an b
e im
ple
mente
d q
uic
kly
–H
ow
ever:
•E
quip
ment c
ost is
hig
h•
Larg
e a
mount o
f time re
quire
d to
access a
ll the p
oin
ts o
n w
afe
r
Optic
s te
chnolo
gy
Technolo
gy
node
248nm
merc
ury
-xen
on la
mp
180 -
250nm
248nm
kry
pto
n-flu
orid
e la
ser
130 -
180nm
248nm
kry
pto
n-flu
orid
e la
ser
130 -
180nm
193nm
arg
on-flu
orid
e la
ser
100 -
130nm
157nm
fluorin
e la
ser
70 -
100nm
13.4
nm
extre
me U
V50 -
70nm
�W
e a
re n
ow
in a
perio
d w
here
technolo
gy &
devic
e in
novatio
ns a
re re
quire
d.
Beyond 2
020, n
ew
curre
ntly
unkno
wn in
ventio
ns w
ill be re
quire
dCell d
imensio
ns
Devic
e S
calin
g O
ver T
ime
1µ
m
10µ
m
10
0µ
m
Fea
ture
Siz
e
0.1
µm
130
nm
in 2
00
2 Era
of S
imple
Scalin
g
Scalin
g +
Innovatio
n(IT
RS
)
Inventio
n
~16%
incre
ase in
com
ple
xity
each y
ear (n
ow
:6.3
% fo
r µP,
12%
for D
RA
M)
~13%
decre
ase in
featu
re s
ize e
ach y
ear (n
ow
: ~10%
)
0.2
5µ
m in
1997
His
toric
al T
rends &
Futu
re P
redic
tions
Ato
mic
dim
ensio
ns
0.1
nm
1n
m
10n
m
19
60
1980
2000
202
02040
Tran
sitio
n R
eg
ion
Qu
an
tum
Effects
Do
min
ate
Ato
mic
Dim
en
sio
ns
Ye
ar
18 n
m in
2018
Inventio
n
Year o
f Pro
ductio
n
1998
2000
2002
2004
2007
2010
2013
2016
2018
Tech
nolo
gy N
ode (h
alf p
itch)
250 n
m
180 n
m
130 n
m
90 n
m
65 n
m
45 n
m
32 n
m
22 n
m
18 n
m
MPU
Prin
ted G
ate
Length
100 n
m
70 n
m
53 n
m
35 n
m
25 n
m
18 n
m
13 n
m
10 n
m
DR
AM
Bits/C
hip
(Sam
plin
g)
256M
512M
1G
4G
16G
32G
64G
128G
128G
MPU
Tra
nsisto
rs/Chip
(x10
6)
550
1100
2200
4400
8800
14,0
00
Min
Supply
Volta
ge (v
olts)
1.8
-2.5
1.5
-1.8
1.2
-1.5
0.9
-1.2
0.8
-1.1
0.7
-1-0
06-0
.9
0.5
-0.8
0.5
-0.7
His
toric
al T
rends &
Futu
re P
redic
tions
14
�In
ventio
n o
f BJT
transis
tor -
1947, B
ell L
abs
�E
xposed ju
nctio
ns h
ad d
egra
ded s
urfa
ce p
ropertie
s a
nd n
o p
ossib
ility o
f connectin
g m
ultip
le d
evic
es
�B
ell
Lab,
1957:
Double
Diffu
sed
Pro
cess
�A
dvanta
ge:
Connectio
nof
multip
ledevic
es
but
no
ICs
�D
isadvanta
ge:
Degra
datio
nby
exposed
junctio
ns
at
the
surfa
ce
�In
1950s,
Allo
yju
nctio
nte
chn
olo
gy
used.
Ge
used
as
cry
sta
l,III
&V
gro
up
ato
ms
used
as
dopants
Inte
gra
ted C
ircuits
Gro
wn ju
nctio
n te
chnolo
gy in
1950s
Al w
ires
NN
P
N
P
N
N
PN
NN
P
Do
ub
le d
iffused
Me
sa
tech
no
logy
So
lid S
tate
B d
iffusio
n
So
lid S
tate
P d
iffusio
n
Co
nta
cts
Allo
ye
d
Me
sa
Etc
he
d
NN PN PN
N PN
N
NP
P
NNN
P
N
SiO
2
N
PN
�P
lanar p
rocess (H
oern
i-Fairc
hild
, late
1950s). F
irst “passiv
ate
d”
junctio
ns
Pla
nar D
esig
n o
f BT
Js
Boro
n d
iffusio
n
N
�B
egin
nin
g o
f Silic
on te
chnolo
gy &
end o
f Ge d
evic
es
�Im
ple
menta
tion o
f maskin
g o
xid
e to
pro
tect ju
nctio
ns a
t Si s
urfa
ce
SiO
2
Mask
Oxid
atio
n p
ossib
le fo
r S
i not g
ood fo
r Ge
Oxid
atio
n &
out d
iffusio
n
Lith
ogra
phy to
open
win
dow
in S
iO2
Phosphoru
s d
iffusio
n
thro
ugh th
e o
xid
e m
ask
P
NNN
P
N
SiO
2
N
PN
Boro
n d
iffusio
n
Dep
osited F
ilm
Ph
otoresist Mask
Ligh
t
�B
egin
nin
gof
ICs
in1959
�B
asic
ph
oto
lithogra
ph
ypro
ce
ss.
ICpatte
rnis
transfe
rred
from
mask
tosilic
on
by
prin
ting
iton
wafe
rusin
glig
ht
sensitiv
ere
sis
tm
ate
rial
Photo
lithogra
phy u
sed fo
r Patte
rn F
orm
atio
n
Su
bstrate
Film
dep
ositionP
hotoresist ap
plication
Dep
osited F
ilm
Exp
osure
Develop
men
tE
tchin
g R
esist removal
Etch
mask
�IC
sused
pho
tolith
ogra
ph
y&
maskin
gto
fabric
ate
that
allo
ws
inte
gra
tion
of
multip
ledevic
es
sid
eby
sid
eon
aw
afe
r�
Bip
ola
rT
ransis
tor
&re
sis
tors
made
inbase
regio
n�
Accura
cy
of
pla
cem
ent
~1/4
to1/3
oflin
ew
idth
bein
gprin
ted
�IC
islo
cate
datsurfa
ce
ofS
iw
afe
r(~
500µ
mth
ick)
Vcc
C
B BJT
0V
Alig
nm
ent o
f Layers
Via
Inte
rconnect
M1
M2O
XID
E
Em
itter
Colle
cto
r
PN
N
PN
PB
Resis
tor C
E
Conta
ct to
colle
cto
r
R=
L/W
•Rs
P
P W
ell
N W
ell
PN
P+
P+
N+
N+
PM
OS
NM
OS
Via
Silic
ide
Oxid
e
Isola
tion
M1O
XID
E
TiN
Sch
em
atic
of IC
s w
ith T
wo
Me
tal L
eve
ls
Resis
tor
E
�M
eta
l Pla
nariz
atio
n re
quire
s m
ultip
le m
eta
l layers
�M
eta
l Depositio
n�
Patte
rnin
g�
Fill D
iele
ctric
�P
lanariz
atio
n�
Conta
ct V
ias
�C
onta
ct D
epositio
n
IC w
ith 5
-Level M
eta
llizatio
n S
chem
e
�M
ost o
f the b
asic
technolo
gie
s in
silic
on c
hip
manufa
ctu
ring c
an b
e s
imula
ted
�S
imula
tion is
now
used fo
r:�
Desig
nin
g n
ew
pro
cesses a
nd d
evic
es
�E
xplo
ring th
e lim
its o
f sem
iconducto
r devic
es a
nd te
chnolo
gy (R
&D
)�
“C
ente
ring”
manufa
ctu
ring p
rocesses
�S
olv
ing m
anufa
ctu
ring p
roble
ms
Com
pute
r Sim
ula
tion T
ools
(TC
AD
)
Sim
ula
tion o
f advanced
local o
xid
atio
n p
rocess
Sim
ula
tion o
f photo
resis
t exposure
�N
PN
& P
NP
Bip
ola
r Junctio
n T
ransis
tors
�F
ield
Effe
ct T
ransis
tors
(FE
T)
�M
eta
l-Oxid
e-S
em
iconducto
r FE
T (M
OS
FE
T)
�Junctio
n F
ET
(JF
ET
)�
Oth
ers
:�
PN
Junctio
n, R
esis
tor, C
apacito
r, Photo
-Dio
de a
nd P
hoto
-Tra
nsis
tor
Physic
al D
evic
es
21
�S
em
iconducto
rs:
Si,
Ge,C
om
pound
(III-V,II-V
I)�
Siato
mhas:
�E
lectro
norb
its2-8
-4oute
rhalf
filled
�C
ovale
nt
boun
deach
(share
ele
ctro
n)
with
4oth
er
Siato
ms
�S
table
,hig
him
pedance
(poor
conducto
r)�
Conductio
nin
Pure
Silic
on
Cry
sta
l�
Energ
yadded
tofre
eshare
dele
ctro
nin
lattic
e�
Ele
ctro
nis
free
but
leaves
anet
+ve
charg
eor
hole
trapped
at
mis
sin
gele
ctro
nsite
Mate
rials
& D
evic
es
hole
trapped
at
mis
sin
gele
ctro
nsite
�H
ole
sw
illattra
ct&
recaptu
reele
ctro
ns
�E
lectro
ns
will
flow
thro
ugh
lattic
eu
ntil
recom
bin
ing
with
hole
�S
ponta
neous
therm
al
ge
nera
tion
of
hole
-ele
ctro
npairs
alw
ays
occurrin
g;
there
fore
,S
ican
conduct
poorly
Intrin
sic
Carrie
r Concentra
tion
�In
trinsic
concentra
tion o
f carrie
rs fo
r thre
e c
om
mon s
em
iconducto
r mate
rials
�S
i, at ro
om
tem
pera
ture
: ni~
1.4
x 1
010/ c
ubic
cm
�S
i lattic
e h
as ~
5x10
22
ato
ms/c
ubic
cm
. There
fore
tem
pera
ture
, only
1 in
3.5
x10
12
ato
ms in
volv
ed
•Ele
ctro
n &
hole
genera
tion o
ccur a
t ele
vate
d
tem
pera
ture
(above 0
K). n
=p
•Energ
y B
and G
ap d
ete
rmin
es th
e in
trinsic
carrie
r concentra
tion. n
iE
gG
e < E
gS
i < E
gG
aA
s
•For d
evic
es w
e n
eed c
oncentra
tions: n
& p
>>
ni
Sem
iconducto
r Mate
rials
& D
opants
�In
trinsic
Sem
iconducto
rs�
Colu
mn 4
ato
ms in
a la
ttice (S
i, Ge)
�C
om
pound S
em
iconducto
rs�
Colu
mn 3
-5 a
tom
s (G
aA
s, In
P)
�C
olu
mn 2
-6 a
tom
s (C
dS
, CdS
e, C
dTe, Z
nO
)�
Dopants
�R
epla
ce a
n in
trinsic
ato
m w
ith o
ne th
at a
s a
dditio
nal o
r few
er e
lectro
ns in
oute
r orb
it�
For S
ilicon:
�F
ew
er e
lectro
ns: B
24
�F
ew
er e
lectro
ns: B
�M
ore
ele
ctro
ns: P
or A
s
Doped S
i Lattic
en≈N
Dp≈N
A�
Re
pla
ce
an
ato
m�
B–
mobile
hole
�P
or
As–
mobile
ele
ctro
n
�N
-typ
eD
op
an
t�
Donate
an
ele
ctro
n�
Colu
mn
5m
ate
rials
(P,
As)
�P
-typ
eD
op
an
t�
Acceptele
ctro
ns
(additio
nalhole
s)
�C
olu
mn
3m
ate
rials
(B)
�L
igh
tlyd
op
ed
or
he
avily
do
pe
d�
Lig
htly
do
pe
do
rh
ea
vily
do
pe
d�
Lig
htly
doped
N-,
N--,
P-,
P—
�H
eavily
doped
N+
,N
++
,P
+,P
++
Resis
tivity
Change w
ith D
opin
g
µn >
µp
�R
esis
tivity
(ρ):
Inohm
-mete
rs�
R=ρ
.Length
/Are
a=ρ
.L/A
�D
opant
Perc
enta
ges
�N
--or
P--
:<
10
14
cm
-3
�1
in5
x10
8cm
-3
�N
-or
P-
:10
14
to10
16
cm
-3
�N
or
P:10
16
to10
18
cm
-3
�N
+or
P+
:10
18to
10
20
cm
-3
�N
++
or
P+
+:>
10
20
cm
-3
�1
in5
x10
2cm
-3(0
.2%
)�
1in
5x
10
2cm
-3(0
.2%
)�
r=1/(q
µn n
+qµ
p p)
�µ
carrie
rm
ob
ilitydep
ends
on
scatte
ring
i.e.
dopa
nts
,la
ttice
imperfe
ctio
ns
(defe
cts
)&
vib
ratio
n(te
mpera
ture
)
Donor &
Accepto
r Bands
�B
and
Model&
Bond
Modelof
Intrin
sic
(Undoped)
Silic
on
�B
and
Model&
Bond
Modelof
n-ty
pe
Silic
on
doped
with
As
�V
ale
nce
Band
–ele
ctro
ns
bound
inla
ttice
�C
onductio
nB
and
–fre
eele
ctro
ns
�E
nerg
yG
ap
(EG)
–am
ount
of
energ
yre
quire
dto
move
an
ele
ctro
nfro
mE
Cto
EV
�D
onors
�E
Dclo
se
toE
C
�Little
energ
yre
quire
dto
rele
ase
ele
ctro
n�
Accepto
r�
EA
clo
se
toE
V
n=
p
n=
p=
ni
Energ
y
Gap
T>
0K
�E
Aclo
se
toE
V
�Little
energ
yre
quire
dto
rele
ase
hole
tovale
nce
band
Very
sm
all io
niz
atio
n
energ
ies E
D a
nd E
A
n=
NA
s
ni =
1.4
5x10
10c
m-3
at R
T (3
00K
)
Intrin
sic
Carrie
r Concentra
tion�
N=
ND
�R
ela
tively
consta
nt o
ver
opera
ting ra
nge
�F
rom
freezeout
regio
n�
To p
rocessin
g te
mpera
ture
�A
t pro
cessin
g te
mpera
ture
s�
Intrin
sic
carrie
r levels
dom
inate
nn >
>p
nn
i ≈p
i
n-ty
pe s
em
iconducto
r
intrin
sic
sem
iconducto
r
Fre
e c
arrie
r concentra
tion V
s. T
em
p
Ferm
i-Dira
c P
robability
F(E
)=
1F
erm
i level is
the e
nerg
y a
t whic
h p
robability
of
Ferm
i Dira
c p
robability
functio
n:
�P
robability
ofan
ele
ctro
noccupy
an
energ
ysta
te�
Pauli
Exclu
sio
nP
rincip
le(n
otw
oele
ctro
ns
can
occupy
sam
equantu
msta
te)
�E
fF
erm
ile
vel
defin
ed
as
the
energ
yw
here
the
pro
bability
of
findin
ga
nele
ctro
nis
50%
�E
fF
erm
iLevel
�C
ente
red
for
intrin
sic
:E
F=
Ei(S
om
eele
ctro
ns,
som
ehole
s)
�N
-doped
causes
the
levelto
rise:
EF
>E
i(More
ele
ctro
ns,
few
hole
s)
�P
-doped
causes
the
levelto
fall:
EF
<E
i(Few
ele
ctro
ns,
more
hole
s)
F(E
)=
1
1+
exp(
E−
EF
kT
)
Intrin
sic
Sem
iconducto
rn-ty
pe S
em
iconducto
rp=
type S
em
iconducto
r
Conductio
n B
and
Vale
nce B
and
Ferm
i level is
the e
nerg
y a
t whic
h p
robability
of
findin
g a
n e
lectro
n F
(Ef)=
1/(1
+1)=
0.5
belo
w E
i
above E
i
p=
Na
n=
Nd
Majo
rity
carrie
rs
EF
≈E
g /2
Majo
rity c
arrie
rs
Undoped
N-d
oped S
i
P-d
oped S
i
Dis
tributio
n o
f Fre
e C
arrie
rs�
EF
isa
gre
ate
st
use
insem
iconducto
rsis
invis
ualiz
ing
the
ele
ctro
nic
pro
pertie
s(c
arrie
rconcentra
tions
&ty
pe)
thro
ugh
the
band
dia
gra
mconcept
�To
calc
ula
ten
&p
ina
giv
en
situ
atio
n,
we
need
tokno
wth
epro
ba
bility
of
findin
gth
em
at
energ
yle
velE
,num
ber
&positio
nof
allo
wed
energ
yle
vels
�A
llow
able
energ
yle
vels
:�
Energ
yle
vels
exis
tsabove
Ec
&belo
wE
v
�A
ppro
xim
atio
ns
for
num
ber
ofallo
we
dele
ctro
nenerg
yle
vels
are
:
n=
F(E
)N(E
)dE
≅E
C
∞∫N
C
1
1+
exp(
E−
EF
kT)
NV
=2( 2
πm
h ∗
h2
)3
/2N
C=
2( 2
πm
e ∗
h2
)3
/2
p=
[1−F
(E)]N
(E)dE
≅−∞ E
V∫N
Vexp(−
EF
−E
V
kT)
Carrie
rs in
Bands
EG=
ECE
V
EC-E
VB
an
d g
ap
EF
Heavy d
opin
g m
oves E
Fto
EC
2/
3
2)
2(
2h
kTm
Nh
V
∗π
=
2/
3
2)
2(
2h
kTm
Ne
C
∗π
=
p=
[1−
F(E
)]N(E
)dE
≅−
∞
EV
∫N
Vex
p(−
EF
−E
V
kT)
�E
lectro
ns in
Conductio
n B
and
�H
ole
s in
Vale
nce B
and
n=
F(E
)N(E
)dE
≅E
C
∞∫N
C
1
1+
exp(
E−
EF
kT
)
Carrie
r Concentra
tion
Charg
e N
eutra
lity
Energ
y B
and D
ependence o
n T
em
pera
ture
�
La
rge
rte
mp
era
ture
we
ake
ns
the
bo
nd
ing
b/w
ato
ms
ca
usin
gb
an
dg
ap
en
erg
yE
G(e
ne
rgy
ne
ed
ed
tofre
ee
-hp
airs
)to
de
cre
ase
�E
Gis
tem
pe
ratu
red
ep
en
de
nt
•Co
nd
uctio
n&
va
len
ce
ba
nd
be
nd
•Fe
rmile
ve
lb
ase
do
nd
op
an
tco
nce
ntra
tion
•Co
nve
rge
on
Eia
ste
mp
era
ture
incre
ase
s
•EG(e
V)=
1.1
7-4
-4.
73
x1
0-4T
2/(T+
63
6)≈
1.1
6-
(3x1
0-4)T
EG
sh
rinks w
ith T
Exam
ple
En
erg
y le
ve
ls fo
r
sh
allo
w d
op
an
ts a
re
clo
se
to th
e m
ajo
rity
ca
rrier b
an
ds
RT
1000°
C
�D
opin
g b
y A
s &
B re
sults
in p
-type S
i at R
T
In in
trinsic
Si a
t 1000°
C
n≈p≈n
i at 1
000°
C
p>
>n
Ele
ctro
n-H
ole
Pair G
enera
tion
�W
he
nio
niz
ing
rad
iatio
nstrik
es
ase
mic
on
du
cto
r,it
ma
ye
xcite
an
ele
ctro
no
ut
of
itse
ne
rgy
leve
la
nd
co
nse
qu
en
tlyle
ave
ah
ole
.T
his
pro
ce
ss
isca
lled
EP
H
�E
PH
are
co
nsta
ntly
ge
ne
rate
dfro
mth
erm
al
en
erg
ya
sw
ell,
inth
ea
bse
nce
of
an
ye
xte
rna
l
en
erg
yso
urc
e
�E
PH
are
als
oa
pt
tore
co
mb
ine
.C
on
se
rva
tion
of
en
erg
yd
em
an
ds
tha
tth
ese
reco
mb
ina
tion
eve
nts
,in
wh
ich
an
ele
ctro
nlo
se
sa
na
mo
un
to
fe
ne
rgy
larg
er
tha
nth
eb
an
dg
ap
,b
e
acco
mp
an
ied
by
the
em
issio
no
fth
erm
al
en
erg
y(in
the
form
of
ph
on
on
s)
or
rad
iatio
n(in
the
form
of
ph
oto
ns)
34
Tra
ppin
g P
henom
ena
�N
on
-eq
uilib
rium
free
ca
rriers
ca
nb
eg
en
era
ted
inb
ulk
se
mic
on
du
cto
rm
ate
rials
by
va
riou
s
pro
ce
sse
s,
su
ch
as
ligh
ta
bso
rptio
n,
hig
he
lectric
field
,ca
rrier
inje
ctio
nth
rou
gh
ab
arrie
r,
irrad
iatio
nw
ithh
igh
-en
erg
yp
artic
les
�A
fter
the
pro
ce
ss
wh
ich
ha
sg
en
era
ted
the
no
n-e
qu
ilibriu
mca
rriers
ha
sce
ase
d,
the
syste
m
retu
rns
toe
qu
ilibriu
md
ue
toth
ea
nn
ihila
tion
of
EP
Hb
yre
co
mb
ina
tion
.If
the
ca
rriers
tha
t
reco
mb
ine
are
bo
thfre
e(e
lectro
nin
co
nd
uctio
nba
nd
&h
ole
invale
nce
ba
nd
),th
eir
an
nih
ilatio
n
pro
ce
ss
isca
lled
ba
nd
-to-b
an
dre
co
mb
ina
tion
�If
on
eo
fth
eca
rriers
isca
ptu
red
on
alo
ca
lize
dsta
te(i.e
.,it
ha
sa
fixe
dp
ositio
nin
se
mic
on
du
cto
r)&
oth
er
on
eis
free
ca
lled
reco
mb
ina
tion
on
loca
lize
dsta
tes
�In
reco
mb
ina
tion
pro
ce
ss,
an
am
ou
nt
of
en
erg
yis
rele
ase
db
ye
mis
sio
no
fe
ithe
ra
ph
oto
n
(rad
iativ
ere
co
mb
ina
tion
),o
ra
ph
on
on
(no
n-ra
dia
tive
reco
mb
ina
tion
),o
rse
co
nd
ary
ele
ctro
n35
(rad
iativ
ere
co
mb
ina
tion
),o
ra
ph
on
on
(no
n-ra
dia
tive
reco
mb
ina
tion
),o
rse
co
nd
ary
ele
ctro
n
(Au
ge
rre
co
mb
ina
tion
),e
tc.
�C
arrie
rca
ptu
red
on
alo
ca
lize
dsta
teca
nre
co
mb
ine
with
an
op
po
site
sig
nca
rrier,
ifth
is
op
po
site
sig
nca
rrier
issu
bse
qu
en
tlyca
ptu
red
on
sa
me
localiz
ed
sta
te,
or
itca
nb
ere
lea
se
din
the
co
rresp
on
din
gb
an
d.
Th
eca
ptu
reo
fse
co
nd
ca
rrier
with
an
op
po
site
sig
no
nsa
me
localiz
ed
sta
tele
ad
sto
an
nih
ilatio
no
fp
air
an
dit
isca
lled
reco
mb
ina
tion
on
alo
ca
lize
dsta
te.
Ifth
e
ca
ptu
red
ca
rrier
isre
lea
se
din
the
ba
nd
,th
eca
ptu
rece
nte
ris
ca
lled
atra
p.
Th
en
the
ca
ptu
re
pro
ce
ss
isca
lled
trap
pin
ga
nd
the
rele
ase
pro
ce
ss
isca
lled
de
trap
pin
g
a.
Intrin
sic
absorp
tion &
band-to
-band re
com
bin
atio
nb.
Recom
bin
atio
n le
vels
c.
Tra
ppin
g le
vels
Shockle
y, R
ead , H
all R
ecom
bin
atio
n (S
RH
)�
SR
Hre
co
mb
ina
tion
isin
dire
ct
tran
sitio
no
fca
rriers
b/w
co
nd
uctio
n&
va
len
ce
ba
nd
s
•Tra
ps
du
eto
imp
uritie
sre
su
ltin
inte
rme
dia
tetra
psta
tes
•Ca
rriers
tran
sitio
nto
trap
&th
en
ca
ptu
reth
eo
pp
osite
ca
rrier
at
trap
sa
te
�M
ino
rityca
rrier
co
nce
ntra
tion
isa
limitin
ge
lem
en
tin
ca
ptu
rep
roce
ss
(lots
of
ma
jority
ca
rrier
alre
ad
ytra
pp
ed
)
�R
eco
mb
ina
tion
of
Ca
rriers
�S
iis
an
ind
irect
se
mic
on
ducto
rso
ind
irect
reco
mb
ina
tion
(Sh
ockle
y-R
ea
d-H
all)
occu
rs
thro
ug
htra
ps
loca
ted
inth
em
id-g
ap
�C
arrie
rR
eco
mb
ina
tion
&G
en
era
tion
�T
rap
s(d
efe
cts
,m
eta
lim
pu
rities)
pre
se
nt
insilic
on
act
eith
er
toa
nn
ihila
teca
rriers
(reco
mb
ina
tion
)o
rp
rod
uce
(ge
ne
ratio
n)
the
m
36
(reco
mb
ina
tion
)o
rp
rod
uce
(ge
ne
ratio
n)
the
m
�S
urfa
ce
of
Siw
ithtra
ps
lea
dto
su
rface
reco
mb
ina
tion
ve
locity,
wh
ich
affe
cts
ca
rrier
lifetim
e
intrin
sic
Si
n-ty
pe S
i; a tra
p (b
elo
w E
F ) is a
lways
filled w
ith e
lectro
n=
majo
rity c
arrie
r and w
aits
for a
min
ority
hole
tR =1/s
vth N
t
Life
time, c
aptu
re c
ross s
ectio
nth
erm
al v
elo
city, &
traps
SR
H re
com
bin
atio
n/g
enera
tion ra
te
U=
np−
ni 2
τ(p+
n+
2ni cosh( E
T−
Ei
kT))
np>
ni 2
U>
0 re
com
bin
atio
nnp<
ni 2
U<
0 g
enera
tion
lifetim
e tr ≠
tgU
max
for E
T =E
i
s=
sv
th Nit
U=
s(np
−n
i 2)
p+
n+
2n
i cosh
(E
T−
Ei
kT)
Sem
iconducto
r Devic
es
Re
ve
rse
bia
se
d d
iod
eF
orw
ard
bia
se
d d
iod
e
n+
for lo
w re
sis
tance
p-n
Dio
des a
t Therm
al E
quilib
rium
Dopants
positio
ns
are
fixed
Carrie
rs m
ove &
cre
ate
deple
tion la
yers
Majo
rity
hole
sM
inority
hole
s
Majo
rity
ele
ctro
ns
Min
ority
ele
ctro
ns
Uncom
pensate
d a
ccepto
rs &
donors
At th
erm
al e
quilib
rium
charg
e n
eutra
lity
qN
+d x
n =qN
-A xp
leads to
asym
metric
al d
eple
tion la
yers
Ele
ctric
field
only
in
deple
tion la
yer
p-n
Dio
des a
t Therm
al E
quilib
rium
Bu
ild-in
vo
ltag
e d
ete
rmin
ed
by d
op
ing
on
bo
th s
ide
s o
f the
p-n
jun
ctio
n
No
cu
rren
t flow
s a
t the
rma
l
eq
uilib
rium
n0n ≈
ND
p0n ≈
ni 2/N
D
p-n
Dio
des U
nder B
ias
Revers
e b
iased d
iode
(-+
)Min
ority
ele
ctro
ns &
ho
les d
rift
(sm
all c
urre
nt)
I
V
Forw
ard
bia
sed d
iode
Ma
jority
ele
ctro
ns (a
nd
ho
les) d
iffuse
,
be
co
me
min
ority
ca
rriers
an
d p
rod
uce
larg
e c
urre
nt
hole
s
(+ -)
I~exp(q
V/k
T)
I
V
p-n
Dio
des U
nder F
orw
ard
Bia
s
De
ple
tion
laye
r sh
rinks
Ele
ctric
field
de
cre
ase
s
Ju
nctio
n p
ote
ntia
l de
cre
ase
s b
y V
a
En
erg
y b
arrie
r de
cre
ase
s b
y q
Va
J ⇑
J~
exp(q
Va /k
T)
p-n
Dio
des U
nder R
evers
e B
ias
De
ple
tion
laye
r sp
rea
ds m
ain
ly to
the
low
do
pe
d s
ide
Ele
ctric
field
incre
ase
s
Ju
nctio
n p
ote
ntia
l incre
ase
s b
y V
a
En
erg
y b
arrie
r incre
ase
s b
y q
Va
J0A
Boltz
man
appro
xim
atio
n
Built-in
volta
ge
Junctio
n a
t Therm
al E
quilib
rium
Min
ority
& m
ajo
rity c
arrie
rs
Ferm
i pote
ntia
ls in
n a
nd p
-regio
ns
Epeak
=2V
b
xd
Pois
son’s
equatio
n:
divE
=ρ
ε0 ε
Si
E=
1q
dE
i
dx
E-fie
ld is
wh
ere
Ei =
f(x)
E=
−d
φdx
;φ=
−E
i
q
Ele
ctro
sta
tic p
ote
ntia
l
p-n
Dio
des U
nder B
iasCarrie
r In
jectio
n a
nd E
xtra
ctio
n
Curre
ntdis
tributio
n in
a p
-n d
iode
For th
e fo
rward
bia
sin
g c
onditio
n
No re
com
bin
atio
n
assum
ed in
the
SC
R
Bre
akdow
n o
f a p
-n D
iode
Ze
ne
r effe
ct
Ava
lan
ch
e e
ffect
Bre
akdow
n V
olta
ge o
f a p
-n D
iode
Eg ⇑
5-7
V5-7
V
•E
brfie
ld in
cre
ases w
ith N
Dbut n
ot v
ery
much
•W
depl ~
1/√
ND
Vbr =
Ebr •W
depl
so V
brdecre
ases w
ith N
D
Bip
ola
r Tra
nsis
tors
�E
-Bju
nctio
nis
forw
ard
bia
sed=
inje
cts
min
ority
carrie
rsto
base
�B
ase
(ele
ctric
ally
neutra
l)is
responsib
lefo
rele
ctro
ntra
nsp
ort
via
diffu
sio
n(o
rdrift
als
oif
the
build
inele
ctric
field
exis
ts)
tocolle
cto
r�
C-B
dio
de
isre
vers
ebia
sed
&colle
cts
transporte
dcarrie
s
VB
E >0
VB
C <0
p-n
-p
IE =IE
n +IE
pIC
=a
IEa<
1
IB =IE
p +Ire
c
IEIC
IB
n-p
-nIC
p-n
-p
Ind
ivid
ua
l
de
vic
e
Bip
ola
r Junctio
n T
ransis
tors
Forw
ard
s b
ias
Revers
e b
ias
Cu
rren
tC
om
po
ne
nts
sm
allF
orw
ard
Opera
tion M
ode
Early
Effe
ct
min
ority
carrie
rs
Inje
cte
dele
ctro
ns
Extra
cte
d
ele
ctro
ns
hole
s
Forw
ard
Opera
tion M
ode
Early
V
olta
ge
Bip
ola
r Junctio
n T
ransis
tors
Bre
akd
ow
n V
olta
ge
s
Co
mm
on
Ba
se
Co
mm
on
Em
itter
Colle
cto
r-Base ju
nctio
n
Cu
rren
t Ga
in β
=α
/1-α
Kirk
Effe
ct
Recom
bin
atio
n in
the E
-B S
pace C
harg
e R
egio
n
β =
IC/IB
MO
SF
ET
, NM
OS
& P
MO
SV
G>
VT
to c
reate
s
stro
ng in
vers
ion
deple
tion
Lin
ea
r Re
gio
n, L
ow
VD
Op
era
tion
of N
MO
S-F
ET
Sa
tura
tion
Re
gio
n, C
ha
nn
el S
tarts
to P
inch
-Off
Sa
tura
tion
Re
gio
n,
ch
an
ne
l sh
orte
ns b
eyo
nd
pin
ch
-off, L
’<
L
Modern
MO
S T
ransis
tors
Gate
LD
D
Lig
htly
Do
pe
dD
rain
(LD
D)
use
d
tore
du
ce
the
ele
ctric
field
in
dra
ind
ep
letio
nre
gio
n&
ho
t
ca
rrier
effe
cts
isola
tion
Dra
inS
ourc
e
Self a
ligned c
onta
cts
decre
ase re
sis
tance
Sem
iconducto
r Technolo
gy F
am
ilies
�F
irst
circ
uits
were
based
on
BJT
as
asw
itch
beca
use
MO
Scirc
uits
limita
tions
rela
ted
tola
rge
oxid
echarg
es
19
60
s
19
70
s
19
80
s &
be
yo
nd
Sm
alle
r pow
er
consum
ptio
n
Futu
re C
halle
nges
�3
sta
ge
sfo
rfu
ture
de
ve
lop
me
nt:
Ma
teria
ls/p
roce
ss in
no
va
tion
sB
eyo
nd
Si C
MO
S
“Technolo
gy P
erfo
rmance B
ooste
rs”
Inventio
nS
ilicid
e
Po
lyG
ate
Su
bstr
ate
Silic
ide
Sid
ew
all
Sp
acer
Rch
an
Sou
rce
Drain
S/D
Ext
S/D
Ext
Gate
Die
lectr
ic
??
?
Gate
Sourc
eD
rain
• Spin
-based d
evic
es
• Mole
cula
r devic
es
• Rapid
sin
gle
flux q
uantu
m• Q
uantu
m c
ellu
lar a
uto
mata
• Resonant tu
nnelin
g d
evic
es
• Sin
gle
ele
ctro
n d
evic
es
Ma
teria
ls/p
roce
ss in
no
va
tion
s
NO
WD
evic
e in
no
va
tion
s
IN 5
-15
YE
AR
S
IN 1
5 Y
EA
RS
??
�T
rad
ition
al fin
FE
T (u
pp
er le
ft), a trig
ate
on
SO
I (up
pe
r righ
t), triga
te o
n b
ulk
silic
on
(low
er le
ft)
an
d a
pse
ud
o-trig
ate
on
SO
I (low
er rig
ht)
�M
an
y o
the
r ap
plic
atio
ns e
.g. M
EM
s &
ma
ny n
ew
de
vic
e s
tructu
res e
.g. c
arb
on
na
no
tub
e
de
vic
es, a
ll use
ba
sic
silic
on
tech
no
log
y fo
r fab
rica
tion
So
urc
e
Ga
te
Dra
in
SiO
2
Futu
re C
halle
nges
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