B B Bt ¿ G $.° Á C B1 n Ä $ H
35
2-1 ᖱႎ䊂䊋䉟䉴Ꮏቇ․⺰ ╙䋲࿁ 䌃䌍䌏䌓䌆䌅䌔䈱ၮᧄ․ᕈ
Transcript of B B Bt ¿ G $.° Á C B1 n Ä $ H
2-1
2-2
Si
2-3
2 4 6 8
-0.2
-0.1
0.1
0.2
0.3
0.4
2-4
2-5
I II III IV V VI VII VIIIH He
Li Be B C N O F NeNa Mg Al Si P S Cl ArK Ca Ga Ge As Se Br KrRb Sr In Sn Sb Te I XeCs Ba Tl Pb Bi Po At Rn
+e +2e +3e +4e +5e +6e +7e +8e
2-6
+4e
+4e
+4e
+4e
+4e
+4e +4e
+4e +4e +4e
+4e +4e +4e
+4e
+4e
+4e +4e +4e
2-7
+4e
+4e
+4e
+4e
+4e
+4e
+4e
+4e
+4e
+4e
+4e
+4e
2-8
k
ET = 0
E
f(E)
ET > 0
f(E)
CCE
n D E f E dE
1VE
Vp D E f E dE
3 2*
2 3
2
2e
C C
mD E E E
3 2*
2 3
2
2h
V V
mD E E E
1
1F
B
E Ek T
f Ee
EF
Fermi –Dirac
E : EF : kB : Boltzmann T : (conduction band)
EC
EV
(valence band)
me* :
mh* :
2-9
3 2 3 2* *
2 3 20
22 exp
2 21
C F
B
e e B C FE E E
Bk T
m m k T E EEn dEk T
e
3 2 3 2* *
2 3 20
22 exp
2 21
V F
B
h h B V FE E E
Bk T
m m k T E EEp dEk T
e
0
12
axe xdxa a
C F BE E k T
F V BE E k T
exp C FC
B
E En Nk T
exp V FV
B
E Ep Nk T
3 2*
222
e BC
m k TN
3 2*
222
h BV
m k TN
EF
EC
EV
kBT ~ 0.026eV
EG =1.1eV(Si)
EG = EC EV
2-10
2inp n
exp2
Gi C V
B
En N Nk T
in p n
ln2 2
C V VBFi
C
E E Nk TEN
1.45 x 1010 cm-3
T [K]
Si
n i[c
m-3
]
exp C FC
B
E En Nk T
exp V FV
B
E Ep Nk T
Si 300K
NC = 2.8 x 1019 cm-3
NV = 1.04 x 1019 cm-3
ni = 1.45 x 1010 cm-3
EG = 1.08 eV
2-11
TlInGaAlB
III
PbSnGeSiC
IV
BiSbAsPN
V
PoTeSeSO
VI
RnAtBaCsXeISrRbKrBrCaKArClMgNaNeFBeLi
HeHVIIIVIIIII
TlInGaAlB
III
PbSnGeSiC
IV
BiSbAsPN
V
PoTeSeSO
VI
RnAtBaCsXeISrRbKrBrCaKArClMgNaNeFBeLi
HeHVIIIVIIIII
+e +2e +3e +4e +5e +6e +7e +8e
+4e
+4e
+4e
+3e
+4e
+4e
+4e +4e +4e
+4e
+4e
+4e
+5e
+4e
+4e
+4e +4e +4e
p n
III V
2-12
p n
1.1eV
~0.05eV
~0.05eV
f (E)0 1
E
f (E)0 1
E
f (E)0 1
E
EF
EF
EF
2-13
n
~0.05eV +q
-q
+q
4
2 28mqE
h
Rydberg =13.6 eVSi = 11.9 0
2
13.6 0.1 eV11.9
2-14
EC
EFEV
C F
B
E Ek T
Cn N e
F V
B
E Ek T
Vp N e
F Fi
B
E Ek T
in n e
F Fi
B
E Ek T
ip n e
EFi
D AN N n p
1sinh2
B D AF
i
k T N Nq n
F
B
qk T
in n e
F
B
qk T
ip n e
F :
ND : NA :
ND , NA [cm-3]
1 2sinh ( ) ln 1x x x
ln(2 )xln( 2 )x
1x
1x
F[V
]
ND
NA
1016 1017 1018 1019 1020 1021 1022 1023
F Fi FE E q
2-15
EC
EV
EF
E
f(E)
E E
0 1 D(E)0.5 0
EF EC , EV
2-16
+
q
=
2-17
FiECE
VE
E
qEE 0
qEE CC0
qEE VV0
qEE FiFi0
FFiF qEE 0
FFiF qEE
F Fi
B
E Ek T
in n eF Fi
B
E Ek T
ip n e
FB
qk T
in n e
FB
qk T
ip n e
FE
2-18
VA X
V
X = VA VB
VB
X > 0
X < 0
VA VB VAB
2-19p n
p
n
1
pn
2
F nB
qk T
D iN n eF p
B
qk T
A iN n e 2lnB A Dbi n p
i
k T N NVq n
qVbi
= p = n
2-20
q M
q
qV1 qV2
p n
(V1 = V2)
qV1qV2
(V1 V2)
2-21
0
FB
qk T
in n e
FB
qk T
ip n e
FnB
qk T
in n e
FpB
qk T
ip n e
F : Fn : Fp :
n nnj q nE qD n
p ppj q pE qD p
n Fnnj q n
p Fppj q p
= 0
V
Fn = Fp = V
imrefimref Fermi
2-22
p Si
VG
0V)
0
x
EC
EV
EF-qVG
-q S
x0
EFi
0FiE
-q F
2-23Flat-band
EC
EF
EVEFM
-qVFB
-q-q M
EM FB F Cq qV E E q
C FiFB M F
E EVq
EC
EF
EV
EFM
Qi+0 0
( )1oxt
iFB FB
ox ox ox
x xdxQV VC C t
oxox
ox
Ct
Al 4.1 eV
n+-polySi 4.0 eVM
p+-polySi 5.2 eV
4.05 eV
(EC-EFi)/q 0.55 eV
(300K)
2-24x > 0
Poisson
2
2S
ddx
( )D Aq N N n p
x = 0, = 0
F FB B
q qk T k T
D A i iN N n e n e
2
2 1 1F F
B B B B
q q q qk T k T k T k Ti
S
qnd e e e edx
EC
EV
EF-qVG
-q S
x0
EFi
0FiE
-q F
FB
qk T
in n e
FB
qk T
ip n e
2-25
-0.5 0 0.5 1 1.5
1. 10 8
1. 10 6
0.0001
0.01
xdEdx
22 ,F
B
qk TB
xD B
k T qE F eqL k T
, 1 1x xF x y sign x e x y e x
2B S
DA
k TLq N
: extrinsic Debye length
2
0
20 ,F
B
qk TS B S
S S xD B
k T qQ dx E x F eqL k T
|QS
| [C
/cm
2 ]
S [V]
EV Ei EC
accumulation depletion weakinversion
stronginversion
EFF F
QS < 0QS > 0
NA = 2x1017 cm-3
2-26
-0.5 0 0.5 1 1.5
1. 10 8
1. 10 6
0.0001
0.01
|QS
| [C
/cm
2 ]
S [V]
EV Ei EC
accumulation depletion weakinversion
stronginversion
EFF F
QS < 0QS > 0
1 10-7 2 10-7 3 10-7 4 10-7 5 10-7
-1.5
-1
-0.5
0.5
1
1.5
5 10-6 0.00001 0.000015 0.00002
-1.5
-1
-0.5
0.5
1
1.5
5 10-6 0.00001 0.000015 0.00002
-1.5
-1
-0.5
0.5
1
1.5
1 10-7 2 10-7 3 10-7 4 10-7 5 10-7
-1.5
-1
-0.5
0.5
1
1.5
5 10-6 0.00001 0.000015 0.00002
-1.5
-1
-0.5
0.5
1
1.5
x = 0
Ec
EV
EF
s = 1.4V
s = 0.5V
s = 0.5V
LD
LD ~ 9.2nm
~1nm
LD 5~10LD
x
2-27
-15 -10 -5 5 10 15
-0.25
0.25
0.5
0.75
1
-qVox
VG VFB
tox = 10 nmNA = 2x1017 cm-3
S
F
G FB ox SV V V
Sox
ox
QVC
oxox
ox
Ct
SG FB S
ox
QV VC
tox
p Si
VG
0V)
EC
EV
EF-qVG
-q S
x0
EFi
0FiE
-q F
2-28
-3 -2 -1 1 2 3 4 5
0.2
0.4
0.6
0.8
1
MOS
Cs :
Cox :
SS
S
dQCd
VG VFB
C/Cox
CFB
S F
( 0) ss s
D
CL
1 1 1
ox SC C C
attox = 10nmNA = 2x1017cm-3 1
FBox D
ox S
C t L
p Si
VG
0V)
2-29
-3 -2 -1 1 2 3 4 5
0.2
0.4
0.6
0.8
1
MOS
2 ,S B SS
D B
k T qQ F yqL k T
SS
S
dQCd
VG VFB
C/Cox
SG fb S
ox
QV VC
p Si
VG
0V)
y = 0
y = 0
y = 02 F
B
qk Ty e
2 F
B
qk Ty e
2 F
B
qk Ty e
2-30
s = 1V
5 10-6 0.00001 0.000015 0.00002
5 1016
1 1017
1.5 1017
2 1017hole concentration
5 10-6 0.00001 0.000015 0.00002
1 1015
2 1015
3 1015
4 1015
5 1015
6 1015
7 1015
electron concentration
5 10-6 0.00001 0.000015 0.00002
-1.5
-1
-0.5
0.5
1
1.5
EC
EFEV
NA
p [cm-3]
n [cm-3]
QB
x
Qn
0S n BQ dx Q Q
0B A DQ q N N p dx
0nQ q ndx
0
2-31
0.5 1 1.5 2 2.5 3 3.5
2 10-6
4 10-6
6 10-6
8 10-6
QB
5 10-6 0.00001 0.000015 0.00002
5 1016
1 1017
1.5 1017
2 1017hole concentration
NA
p [cm-3]
x
NA
p
00 W
2
2A
S
qNddx ( 0 < x < W )
2
2 0ddx
( W < x )
2( )2
A
S
qN W x
2
2A
SS
qN W0ddx
( x = W )
B AQ qN W
W [cm]
VG VFB
( S = 2 F )max 2 S F
A
WqN
2B A S SQ qN
(p = NA/2
2-32
15 16 17 18
0.5
1
1.5
2
2.5
3
S n BQ Q Q
2S F
10 10 1010
[V]
NA [cm-3]
SG FB S
ox
QV VC
2 20 A S F
T T F Fox
qNV V
C
0T T FV V
Bn ox G FB S
ox
QQ C V VC
ox G TC V V
2 22 A S FB
T FB S FB Fox ox
qNQV V VC C
2-33MOSFET
MOSFET
gradual channel
y x
2 2B A S F BQ qN V V
2 Bn ox GB FB F B
ox
QQ C V V V VC
2 22 A S F BS
T FB Fox
qN VV V
C
n n
p
0 L
x
VDy
VS
VG
VB
n ox G TQ C V V V y
(0) SV V
( ) DV L V
qVBqV
q(V VB+2 F)q F
q F
x0
EFi
EFi q F
2-34
(0) SV V
( ) DV L V
n ox G TQ C V V V y
ydVEdy
n n n yI W Q E
n n ox G TdVI W C V V Vdy
0
1 D
S
L Vn oxD n G TV
W CI I dy V V V dVL L
212
n oxD GS T DS DS
W CI V V V VL
0GS T DSV V V
n n
p
0 L
x
VDy
VS
VG
VB
VC (y)
2-350DS GS TV V V
n ox G TQ C V V V y
Qn < 0 Qn > 0
pinch-off
pinch-off (Qn = 0)
0 Lp L
VDS
pinch-off
2 12
n oxD GS T DS
W CI V V VL
VDsat
VDS VDsat
Dsat GS TV V V
L1 1 1 11 1 DS
p
L VL L L L L L
n n
p
0 L
x
VDy
VS
VG
VB
VC (y)
Lp
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