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Chap.2 VBIC page 4
page 4
VBIC
SPICE Gummel-Poon
(Bipolar Junction Transistor, BJT) 1970
Gummel! Poon"# $ % & ' ( ) * + , - . ' / 0
1 GP2 3 4 5 6 7 8 9 : ; < = , > ? @ A B
BJT C DEFG ; H I (parasitic transistor)JK L M N
C D(avalance mutliplication)J O P Q @ R (self-heating)JS T UC
D(qusai-saturation)V !5 6 Early W X Y Z [ [ @ R > ? 1
\ 4 C DG ] _ ` a GPb A B BJT!c d
(Heter-junction Bipolar TransistorHBT)ef g h i j
k l mn 0 o p 9 q r s t u v w x y z | Vertical
Bipolar Inter-Company (VBIC)VBIC V Gummel-Poon
Chap.2 VBIC page 5
page 5
X . ~ ! Gummel-Poon :
v @ # X 0 GP2 3 0
C n "# 0 C VBIC
2.1 VBIC
¡ Gummel-Poon - ¢ £ ¤ $ VBIC ¥ ¦ / p X | § t ¨
BJT © ª . !P Gummel-Poon« V
¬ ® V ¯ ° # VBIC - ± £ ² ³ . ~ ´ F
1. µ ¶ · ¸ ¹ ' (Base width modulation)@ R m
X b A B º » BJT ¼ HBT½¾ GP 5 6 VA(Early
voltage)X Y Z ¥ : ¿ À a
2. P Á H I (parasitic PNP)
3. ^ a ª Kull"Â S T U(quasi-saturation)C D
Ã Ä Å Æ C D
4. L Ç
5. . ~ È ¸ C D
6. P É Ê (distributed base)!É Ê Ë Æ !Ì Æ
ÍP Æ Î Ï @ R (current crowding effect)
7. . ~ Ð Ñ ÇP 9 epi-layerS T U Ò Ã . ~
Ó Ô Õ
8. P 9 O P Q (self-heating)@ R
9. P Ö × L M N (weak avalanche breakdown) Æ > ?
10. . ~ Ø ¢ £ ½Ù Ú i Û (excess phase shift) « À
a Ü Ý É Þ ß
Chap.2 VBIC page 6
page 6
à NPN VBIC [ C Eá 2-1 â ã n ²
³ 9 à V Gummel-PoonX NPN ! à a ä eå
Gummel-Poonâ v ã PNP H I ½S T UC D
RCIQBCX V !ª å ¤ QBC [ P V ¬ 0 É Ê æ
ç IBEU IBEX ¬ Ö × L M N C D BC è é
ê p ë Ö × L Æ Igc ì b BC í î ï à Y Z ð ñ
Ç CBEOU CBCO a ¬ Double Poly-Silicon BJT [ A B º » ½
ò ó (poly-silicon base)â ê p ¤ H I ÇC Dï à ô
õ RBI! RBIP ç É ö ÷ e Ò (normalized base charge
qbJqbp) P V ª V v ø õ X é W ù Ù Ú i Û
ñ ú X 9 û ü É Þ ý (DCJACJTransient)VBIC^ a
Weil-McNamee þ æ RLC r ¬ P í ð
þ Q r (thermal network) ß È ¸ C D! O P Q C D
¤ > ?
Chap.2 VBIC page 7
page 7
tzfIcxfQ
lxfF
1Ω
1xf 2xf
tzfITHR THC
dt
1t
C
B
E
S
BEOC
BCOCCXR
ER
CIR
BI
b
RqBXR
BP
bp
Rq
BCXQ
BCQ
BEQBEXQ
BEPQ
BCPQ
SR
beIbexI
bc gcI I−txf tzrI I−
tfp trpI I− cx
ci
ei
bibx
bp
si
BEPI
BCPI
Chap.2 VBIC page 8
page 8
2.1.1 (Icc)
!" # $ %&' (
ICC)* +, - . / 0 1 (Transport current) 2 Itzf
3 Itzr 4 5 $ 6 7 8
exp 1 exp 1s bei bcicc tzf tzr
b F th R th
I V VI I I
q N V N V
= − = − − −
(! 2.1a)
th
k TV
q⋅= (! 2.1b)
%&Vth . / 9 , (Thermal voltage):k;< = > ? @ :q;A B
C D T;E F G H (IK)qb;J K L M ( C N
( )2 21 1 2
14
2b S S Sq q q q= + + (! 2.2a)
1 1 je jcS
q qq
VER VEF= + + (! 2.2b)
2 exp 1 exp 1s bei s bciS
F tv R tv
I V I Vq
IKF N V IKR N V
= − + −
(! 2.2c)
%& q1S O $ P E F M ( Q R S R T (Base-width
modulation)Uq2S V W O $ P X Y Z T (High Level injection
effect)qje3 qjc [ \ ;] ^ C _ CJE3 CJC
2.1.2 (Ibe,Ibc)
VBIC ( )
( ! Recombination) "
exp 1 exp 1bei beiBE BE BEI BEN
EI th EN th
V VI W I I
N V N V
= − + −
(# 2.3a)
Chap.2 VBIC page 9
page 9
( )1 exp 1 exp 1bei beiBEX BE BEI BEN
EI th EN th
V VI W I I
N V N V
= − − + −
(# 2.3b)
exp 1 exp 1bci bciBC BCI BCN
CI th CN th
V VI I I
N V N V
= − + −
(# 2.3c)
$ % IBEI&IBCI ' - ( - ) * NEI&
NCI ' - ( - ) + ( , (emission coefficient)-.
IBEN&IBCN&NEN&NCN / ' * 0 + ( , WBE 1 2
3 4 5 (Intrinsic) 6 7 (extrinsic) 8 9
2.1.3 (Weak Avalanche Effect)
` a T W 2 BCbc d +e, fg BC ] h i & j k
eg l m )0 n ] h i - o p q r p s t u W v w f %x y f
g z l m @ a | Nx y L ~ J X D (i)
m @ N)J ? ; E F
m O $ T N l m (m u ) 0 n y
idqEε= f p q r - % D ¡ k D N%¢ £ ¤
exp exp idP
qEε
λ λ = − = −
%&¥;¦ § ¨ 2 © (mean free path)N
` a Igc 2 !ª « 8
maxmax
expn ngc n d
n
bI I x E
b Eα
= −
(# 2.4a)
n cc bcI I I= − (# 2.4b)
Igc; BCbc ¬ £ ` a xd;] h i H Emax; BCb
c &® e j ¯ H In;m (° NPNv w )± 3 ² ;
³ ´ µ ¶ · ¶ ¸ ¹ ¸ º ? @ N» ` a 7 ¼ W Igc<<InN
Chap.2 VBIC page 10
page 10
f® e j ¯ H ½] h i H 2 d +_ z p N
1jc MC
BC
CJCC
VPC
= −
(# 2.5a)
djc
xCε= (# 2.5b)
max 1BC
d
PC Vx E
MC−⋅ =
− (# 2.5c)
%& jcC ; BC_ CJC; BC ¾ +, - A B bc _ PC
; BCbc ¿ À B (Built-in potential)NMC; BCbc Á @ @
(Grading coefficient)
2 j  2 BC ] h i _ z p %. Z (! 2.4a)&
z 8
( )
1
2( ) 1 ( ) exp
( )
11
1
12
gc cc BC bci MCbci
n
n
nMC
AVCi I I AVC PC V
PC V
AVCb MC
b MCAVC
CJC PC
α
ε
−
−= − ⋅ ⋅ − ⋅ −
=−
−=
⋅
(# 2.6)
%&AVC1½ AVC2 Ã ; VBIC Ä @ NÅ z Æ W
) Gummel-Poon &Ç ¿ À » ` a T N
2.1.4 (Quasi-saturation effects)
ÈÉ 3 T ? ¢ £ )Ê Ë ' ( Ì Í s E F &%¢ £ Î Ï 3
Kirk Effect %È« Ð Ñ NÒ Ó Ô Õ Ö * a × ( β )½ Ø Ù
A B Ú (fT) Û Ü Ý N T ¢ £ )eD Y Z Ì Í s
' ( &Þ ;%ß( cρ )Å à e eD á ß
Chap.2 VBIC page 11
page 11
( CIR ), Õ Ö ¿ BC ] h i bc , ( )BCi BC C CX CIV V I R R= − ⋅ + f
â ã ä , BCV UÕ Ö ¿ BC bc  ;å æ +, fç BC +
, è é Ê ê æ +, N% ë 2-2 ì N
Emitter Base Collector Sub collector−
cont
act
cont
act
BC
SCR
BE
SCR
cxci
CXRCIR
cxci
ÈÉ 3 T ½% ì í
á 2 î ï ð ñ [11] z p á Ì Í s ' ( i rciI
ò ó !8
1ln
1
1
bcirci th bci bcx
bcxrci
rci
KV V K K
KI
VRCI
VO
++ − − + = +
(! 2.7)
%&RCI:VO:GAMM Ã ; VBICÄ @ N
2.2 VBIC
)ô õ ö & g O á 2 CIC(÷ ø v ù ú Õ &û )Æ ü ý
þ z GCTC (Global Communication Technology Coporation) £
¬ InGaP/GaAs HBT ; VBIC E F N%E F
Chap.2 VBIC page 12
page 12
2-3
Semi Insulator Substrate−
Subcollector
Collector
n GaAs+
n GaAs
Base p GaAs+
n InGaPLedge Ledge
n GaAs+
n InGaAs+
Emitter
2.2.1
2-1VBIC ! " # $ % & ' ( ) * + , -
. / 0 + 1 2 3 4 5 6 7 8 9 : ; < = > ? @ $ A 5 (RE)
B C 5 " # (RCX)D E % & F G H B 4 5 I J K L $ M N " #
Chap.2 VBIC page 13
page 13
L J L M N O # PQ R 5 S 4T 1 / U 9
: ; 8 V < W 8 V S XY ' Z[ + (RBI)?\ + (RBX)
] * + , 4^ _ ' - ` a 0 * N O bc# d 4
2.2.1.1
e f 6 g h i A RE-flybackj RC-flyback N O # d B N O
kbc> 1 j@ 1 S 2-4ZN O l m n o p q A
r s Z HP 41424
RE t u v w x y z . / \ + > 1 J 3 (E)?[ + > 1 J 3 (ei)H
I 4 g h | T 1 M X~> 1 J l V l N O IC
/ (@ 1 )l VCE ; S U / T 1 M RE
( ; 4 ^ g h Q R VCE IB S Z RE S 45o
p 2-4(a) 4
+
−CEV
0 ~ 10
100BI mA
step uA
= 0CI A=
+
−ECV
0 ~ 20
100BI mA
step uA
= 0EI A=
(a) (b)
RE-flyback(a)j RCX-flyback(b) N O o p
1E
B
CE
RI
V
= ∆∆
(P 2.8)
P 2.8 Q > 1 S Z 4
Chap.2 VBIC page 14
page 14
0 2 4 6 8 10
0.00
0.05
0.10
0.15
0.20
0.25
0.30
VC
E (V
)
IB (mA)
VCE (V) Linear fit of RE
N O ?bc
V w > 1 @ 1 ¡ ¢ g h ^ R £ > 1 2 5
¤ ¥ ¦ H S Z S § Z5N O
Z ¨4
0 5 10 15 20
0.0
0.1
0.2
0.3
0.4
0.5
0.6
VE
C (V
)
IB (mA)
VCE (V) Linear fit of RCX
§© ª N O ?bc
Chap.2 VBIC page 15
page 15
2.2.1.2
VBIC 6 q A « ] * ¬(RBX®RBI)B ! " T 1 ¯
°± ZT 1 ² ³ ] * + , ´(1).T 1 \ + (RBX)´A ^ ! "
T 1 µF G J $ HI J K ¶(2).T 1 [ + (RBI)´A ^ ! "
U 9 : ; < = · 4(P 2.8) Z5¥ ¦ Pi A ¸ ¹ T
1 º B ¢ · [ + T 1 ² ³ » i ¼ ½ (Early Effect) ¾ ¿ T
1 À · ¢ · jÁ M Â Ã l 5 S Ä Å Æ 4 VBIC 6 k
Ç W ² ³ > 1 M È É ¼ ½ (emitter current crowding effect) IRB¬
< z ^ ¬WBE B Ê - T > 1 I [ + ®\ + M Ë4
BIB BX
b
RR R
q= + (P 2.8)
bcT 1 # $ g h i A N O 8 V : ; _ Ì Í Î >
Ï R T 1 S 4 Ð Ñ Ò 6 Ä Ó l 5 Ô Z
( ) ( )1BX BI b ac ER R i R Rπ β+ + + + < Ì Í Ó ZÕ Ö × l / CπØ Z
Ù ^ Ô S Z ( )BX BI b ER R i R+ + 4< Ú 5[ + ®\ + '
Û q A Ü optimized # PR £ 4
Ý Þ bc u 2-1 4bcl g h ß à
á« _ o p ± Zg h q A InGaP/GaAs HBT ZT 1 â ã
ä(NB>>NE,NC) å 5T 1 ¢ · Å Æ æ ç 8 è é ê X
/ 5¼ ½ 7 Ð å e f 6 RBI o p Z 04
Chap.2 VBIC page 16
page 16
REAL
*j IMAG
( )BX BI b ER R i R+ + ( ) ( )1BX BI b ac ER R i R Rπ β+ + + +
frequency
¨bc RBXj RBI x
u bc
RE() 19.2
RCX() 27
RBX() 31.24
RBI() 0
2.2.2 Gummel plot
/ e f q A InGaP/GaAs HBTZë ì í T î å 5
pnp D í k8 ï ^ ð ñ ò ó ¯ °jô õ Á Ó
ö q A ¶V l ÷ ø Ã l ù ú û ü ¼ ½ 4/ 5
pnp D í 8 ï å g h bc VBIC l 5¼ ½ ù ú 4
Chap.2 VBIC page 17
page 17
g h ^ bcý þ Gummel plotH¬Ã ` a þ Gummel plot
bc# d ÷ V 4Gummel plot z N O 1 í (Diode) °~ VE
/ 0®VB/ VC V l = · VBj VC N O < R 40 ¥ ¬v
° Hv w x y 2-8 56 T 1 M (IB) + , ² ³ « w
(IBEI®NEI)µæ w + , (IBEN®NEN)æ w + , A / ! " VBE
7 Ð l 0 õ (Recombination)¼ ½ (
2kT M 4 VBE 7 × l / M 7 × 5M (RE)
( ; ð ñ T 1 -> 1 J $ ; l q R T 1
j@ 1 M ó P ¶X \ @ 1 M (IC)÷ U £ @ 1 Á
Í ¼ ½ < Ä M Á Í ¼ ½ Z¬ IKF B
H4
IKFNF
NEI
NEN
1RE
IS
IBEI
IBEN
BEV
B
C
I
I
! 0 ¬?5v w x y
Chap.2 VBIC page 18
page 18
IKRNR
NCI
NEN
1RCX
IS
IBCI
IBCN
BCV
B
E
I
I
þ ! ¬?5v w x y
X g h N O ý þµþ Gummel plot " # ¿ B $
2-10 4g h % Å M & W V ' µ M (IS)' - ( z
5Á Í ¼ ½ % l I 8 V å ! " l ( ) * q A # * ' µ
M 4
2-11? 2-12 ' - Z InGaP/GaAs HBT ý þjþGummel
N O j 4/ e f q A Z7 Ð + / N O
r s , - . 8 / ^ N O 2kT M Å 0 1 å æ w ¬g h q
A 7 Ð S ^ t 2 ^ 8 w M ¬Z3 * 4 N 4Xþ
GummelN O l g h % Å HBT Î þ: ; l kÇ W M
4Á M + , ± Z InGaP/GaAs HBT Á Í ¼ ½ 5 6 %
^ g h IKF o Z 14u 2-2Z Gummel plot ¥ ¬bc
4
Chap.2 VBIC page 19
page 19
-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
10-9
10-8
10-7
10-6
1x10-5
1x10-4
10-3
10-2
I C&
I E
VBE
&VCE
IC IE
7 ý þ?þ !
1.0 1.1 1.2 1.3 1.4 1.510-9
10-8
10-7
10-6
1x10-5
1x10-4
10-3
10-2
I C &
I B (A
)
VBE
(V)
Ic Simulation Ib Simulation Ib Measurement Ic Measurement
ý þ ! N O ? 7
Chap.2 VBIC page 20
page 20
0.8 1.0 1.2 1.4 1.610-10
10-9
10-8
10-7
10-6
1x10-5
1x10-4
10-3
10-2
I E &
I B (A
)
VBC
(V)
IB Sim (A) IE Sim (A) IB Mea (A) IE mea (A)
þ ! N O ? 7
uý þ?þ ! ¬bc
2.2.3 (Base Width Modulation Effect)
/ InGaP/GaAs HBT T 1 â ã äq 5T 1 À . : ; = ·
k8 8 ð ^ e f 9 : 6 g h VEF? VER ] * ¬ ; o Z
IS(Amp.) 1.58E-25 IBEI(Amp.) 8.63E-26 IBCI(Amp.) 4.31E-15NF 1.023 NEI 1.11 NCI 1.928NR 1.021 IBEN(Amp.) 1.00E-19 IBCN(Amp.) 1.00E-19IKF 1 NEN 2 NCN 2IKR 1.86E-07
Chap.2 VBIC page 21
page 21
0u T 1 À · ¢ ¼ ½ e 6 kÇ W ( 4
2.2.4 (Quasi-saturation)
VBIC 6 <' µ¼ ½ ¬² ³ W RCI®GAMM®VO®
HRCFµ QCO45 t uHv w x y u 2-3 4< = ü ¬
2-13 2-15 RCI > p ' µÊ ? @
GAMM ! " <' µ¼ ½ Á M ZVO > p ' µA . B S 4
u<' µ¼ ½ ¬?5v w x y
RCI
GAMM (epi)
VO
HRCF
QCO
/ InGaP/GaAs & W æ ç Á C D (mobility)q 5 E
$ S 7 Ä ^ g h F O <' µ¼ ½ k8 U g h W G ×
< H bc B $ I J K 4¬bcS u 2-4 4
Chap.2 VBIC page 22
page 22
CV
CI1500RCI =500RCI =
CV
CI
0GAMM =
100GAMM p=
CV
CI
100VO =
10VO =
RCI 1
GAMM 5.00E-15
VO 100
HRCF 0.1
QCO 1.00E-15
RCI IV GAMM IV
VO IV
Chap.2 VBIC page 23
page 23
0 1 2 3 4 50.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0.040
0.045
0.050
0.055
0.060
Jc (m
A/u
m2 )
Vc (V)
measurement data simulation
! "
0 1 2 3 4 50.0000
0.0625
0.1250
0.1875
0.2500
0.3125
0.3750
0.4375
0.5000
0.5625
Jc (m
A/u
m2 )
Vc (V)
Measurement Data Simulation
# ! "
Chap.2 VBIC page 24
page 24
2.2.5
$ % InGaP/GaAs HBT & ' () * +, - VBIC./
0 .1 23 4 5 6 7 389 : ;
1. $ % GaAs<-= > ? $ @ (ABC +D E pnp F ?
2. G% $ HI J K (NB>>NELNC)($ HM NO P Q R S (T VEF(
VER : U 0VW$ H X Y BZ[! \ P V
3. Z GaAs ] ^ _ ` abcd(We f ^ g F h (epi-layer)
A e Bi j Vkl m n o p q rV
s Gt u vw x () * Q 6 y z + " ./ | (VBIC Q 6 ~
z InGaP/GaAs HBT " Vo p 7;
InGaP/GaAs HBT " w x o p
IS(Amp.) 1.58E-25 IBEI(Amp.) 8.63E-26 IBCI(Amp.) 4.31E-15 NF 1.023 NEI 1.11 NCI 1.928 NR 1.021 IBEN(Amp.) 1.00E-19 IBCN(Amp.) 1.00E-19 IKF 1 NEN 2 NCN 2 IKR 1.86E-07 WBE 1
RCI 1 RE() 19.2 VEF 0GAMM 5.00E-15 RCX() 27 VER 0
VO 100 RBX() 31.24 RTH 4.4K HRCF 0.1 RBI() 0 CTH 1.00E-09
QCO 1.00E-15
Chap.2 VBIC page 25
page 25
2.3 VBIC
2.3.1 VBIC
VBIC ./ 3 ^ (-0 F ?
($ H-H$ H- H ^ ( % $
H -H (QBE) (QBEX)$ H - H (QBC)
(QBCX)V (+ VBIC./ $ HD E I (CBEO)$
HD E I (CBCO)(¡G F ? ¢ £ o ¤ ¥ ¦ V
+G§ ¨(space charge)§ © (deplete)ª E « (
VBIC./ <-5 ¬ u ¨./ (¡® SGP ./ ¯t °-
6 ± ² [! 2³ ´ µ FC(° smooth AJ(¶<·
, ( , , , , )BE depQ CJE qj Vbei PE ME FC AJE= ×
( )( )
,
1
( , , , , )
1for Vbei FC PE
1
1 1 for Vbei FC PE1
BE depBE
ME
ME
Q qj Vbei PE ME FC AJEC CJE
Vbei Vbei
CJEVbeiPE
CJE VbeiFC ME ME
PEFC+
∂ ∂= = ×∂ ∂
≈ × < × −
≈ × − × + + × ≥ × −
(¸ 2.9)
(PEU$ H-H ¹ (built-in potential)(MEU$
H-Hº Za(0.5, for uniform doped base)V
$ H-H CBE$ H- H CBC » ;(1).G§
¨§ © ª E (2).G¼a" s ½¾ ¿ 2
À Á V6 7() * Â Ã Ä Å V
(1).$ H-H ¨ QBE
Chap.2 VBIC page 26
page 26
, ,BE BE dep BE duf
tzf
Q Q Q
CJE WBE qje TFF I
= +
= ⋅ ⋅ + ⋅ (¸ 2.10a)
( )2
11 1 exp1.44
tzf bci
tzf
I VTFF TF QTF q XTF
I ITF VTF
= + + +
(¸ 2.10b)
(CJE¡Æ [! 7$ H-H (WBE¡-6
$ H ³ ´ µ VTFF Ç ¡ VBIC-0 À Á
ÈÉ 2(transit time) µ V® Ê +7 ^ Ë Ì Í Î Ï V
(2).$ H-H ¨ QBEX
( ) ( ), 1 1 ( , , , , )BEX BE depQ Q WBE CJE WBE qj Vbex PE ME FC AJE= ⋅ − = ⋅ − ⋅ (¸ 2.11)
(0<WBE<1(VBEX Ç ¡U VBIC./ Vbx-Vei ! Ð V
(3).$ H- H ¨ QBC
, , ,BC BC dep BC duf epi in
tzr bci
Q Q Q Q
CJC qjc TR qb I QCO K
= + +
= ⋅ + ⋅ ⋅ + ⋅ (¸ 2.12)
( 1 exp bcibci
th
VK GAMM
V
= + ⋅
QCOÑKbci¡U5 .1Ò$ H² À Ó H(base pushout Ô Õ
Kirk Effect)2À Á ¨ V
(4).$ H- H ¨ QBCX
BCX bcxQ QCO K= ⋅ (¸ 2.13a)
Chap.2 VBIC page 27
page 27
1 exp bcxbcx
th
VK GAMM
V
= + ⋅
(¸ 2.13b)
2.3.2
Ö × 2() * , - HP 8510 Ø Ù Â Ú +Û Ü 7ÝBÞ[! S
Ö × ß à® Ö × á S s de-embeddingà(â ã Òä å
¶· áÖ ×
G% +` Ü Ö × 2(Pad¥ ¦ D E ® Bâ Q 6 R S (
6 ¿ æ 4 de-embeddingç Ý(6 è é D E ¥ ¦ Ö × 2®
P Ð ê ë V6 ì í ./ m î t BÞ(¶
¥ ¦ .12ï Ð V
) * +× ð t (ñ ¯° dummyò Ù ó ô7
(s GÖ × k open S à(® ä U Y Vâ Ö × × ð
¶· Smea õ ö (ä å U Y à(÷ ø Yopen(T·
Ydeivce õ ö Vù ú kû ü ¡U5 ý ø pad D E × ð
¥ ¦ V
Chap.2 VBIC page 28
page 28
11, 12,
21, 22,
open open
open open
Y Y
Y Y
11, 12,
21, 22,
open open
open open
S S
S S
11, 12,
21, 22,
mea mea
mea mea
S S
S S
11, 12,
21, 22,
mea mea
mea mea
Y Y
Y Y
11, 12,11, 12, 11, 12,
21, 22,21, 22, 21, 22,
open opendevice device mea mea
open opendevice device mea mea
Y YY Y Y YY YY Y Y Y
= −
k2+Û [! 7D E Q þ U 2-18V
Port 1 Port 2
aC bCcC
Û [! 7D E
( )11, 12,Imag
2device device
a
Y YC
fπ+
= (¸ 2.14a)
( )22, 12,Imag
2device device
b
Y YC
fπ+
= (¸ 2.14b)
( )12,-Imag
2device
c
YC
fπ= (¸ 2.14c)
s GBÞ[! Ö × ) * Q 6 z CV (Ò ú
CBE Ö × 2() * ® Vc : U 0(VbG [á ± ² [! (â G
(¸ 2.14)w x z VÖ × : Û 2-19VÖ × $ H- H
(Ö × : Û 2-20V
Chap.2 VBIC page 29
page 29
Port 1
Port 2
0cV V=5 ~ 1
0.2bV V
step V
= −
CBE Ö × : Û
Port 1
Port 2
0bV V=
1 ~ 7.5
0.425cV V
step V
= −
CBC Ö × : Û
2-21 2-22U InGaP/GaAs HBT$ H-H$ H- H
Ö × .1o p V 2-6U w x o p V
Chap.2 VBIC page 30
page 30
-5 -4 -3 -2 -1 0 1
22
24
26
28
30
32
CB
E (f
F)
VBE (V)
CBE Measurement CBE Simulation
CBE Ö × .1o p
-8 -6 -4 -2 0 2
5
10
15
20
25
30
35
40
45
CB
C (f
F)
VBC (V)
Measurement Data Simulation
CBC Ö × .1o p
Chap.2 VBIC page 31
page 31
2.3.3
G% e B 6 ~ F ? N (6 ¿ æ ¯
F ? ÈÉ 2./ -6 À Á V F ? ÈÉ 2
Q 6 6 , -Ö × ft(unit current gain frequency)¶· á(¶ VBIC-
0 ú U(¸ 2.15);
12 T
TFFfπ
=
( )2
11 1 exp1.44
tzf bci
tzf
I VTFF TF QTF q XTF
I ITF VTF
= + + +
(¸ 2.15)
(TFU ± ² ÈÉ 2(XTFU TF[! (
QTFU TF$ HM NO N (ITF¡ TF` "
(VTF¡ TF VBC[! Vk°| v¸0 % Gummel-
Poon./ (VBIC¯ 5 VTF Q 6 + v(ÈÉ 2
VBC[! V
Ö × 2(¡+Û Ü 7Ö × BÞ[! S (s u
de-embbeding u v(â ® ä U H (e Ö × H21 (
CJE(fF) 27.5 CJC(fF) 10.22
PE 1.35 PC 1.09
ME 75.01m MC 481.2m
AJE 1m AJC 1m
FC 0.9
w x o p
Chap.2 VBIC page 32
page 32
· á ft VG% ¡<- | · áÖ × (+Ö × Ü d t
! ÒI æ (°Û æ + H21 " # ê -20dB/decade½¾ (kÖ ×
$ ] ^ %VÖ × 2(¿ 4 n & (T Ö × °[! 7 ' DC~20GHz
S (e ä U H (y y Ü d¡( ) Òà( $ Q ú
Ö × V¢ * m n Ö × Ü dU 2GHzVÖ × 2: Û 2-23
V
Port 1
Port 2
1.2 ~ 1.5
0.01bV V
step V
=
1 ~ 3
0.5cV V
step V
=
ÈÉ 2Ö × : Û
$ % InGaP/GaAs HBTI J K $ H(6 f ^ $ HM NO P
(6 ) * Q 6 9 : QTFU 0Vâ , - IC-CAP + , - . 4 w x
/ 0 1 ç ÝVÖ × .1o p 2-24(w x o p 2-7
V
Chap.2 VBIC page 33
page 33
1x10-5 1x10-4 10-3 10-2 10-1
0
5
10
15
20
25
30
35
40
Ft (G
Hz)
Ic (A)
Measurement Simulation
0 2 4 6 8 10
0
5
10
15
20
25
30
35
Ft (G
Hz)
Ic (mA)
Measurement Simulation
ÈÉ 2Ö × 2 VBIC.1³ _
Chap.2 VBIC page 34
page 34
#VBICÈÉ 2 w x o p
TF(psec) 3.012 ITF 20.61m
QTF 0 VTF 20XTF 14.48 TR 0
G6 t o p Q 3 (VBIC./ + ÈÉ 2t ^ Q 6 ¯6
4 5 6 7 V+8 " 9N « (G% f ^ ¯ VBC[! (
6 : ; < F ? +8 " 9N2ú U(T VBIC./ e f
^ = G$ H- H(BC) § © ½ª E ÈÉ 2 V
G% ê + v(ÈÉ 2> ?¡G$ HÈÉ 2U/ @ 8(
A ZU$ HM NBB P C (6 D ÈÉ 2;$ H- H§ ©
½ÈÉ 2(Kirk Effect¥ ¦ ÈÉ 2» Ë ¯I æ VVBIC.
/ E ¸B 6 ~ +BÞ VCE(VBC) V
2.3.4 S
, - 6 F Ý./ (â G r H BÞ[! S TD
, - ADSÝ / 0 1 à() * Q 6 ª E G VBIC I ./ ª E S
(6 , ` Ü Ù : J VK " w x o p 2-8V
2-25á 2-28U S 6 .12 Ö × o p V
Chap.2 VBIC page 35
page 35
InGaP/GaAs HBT VBIC./ K " w x o p
CJE(fF) 27.5 CJC(fF) 10.22
PE 1.35 PC 1.09
ME 75.01m MC 481.2m
AJE 1m AJC 1m
FC 0.9
TF(psec) 3.012 ITF 20.61m QTF 0 VTF 20 XTF 14.48 TR 0
0 5 10 15 20-7
-6
-5
-4
-3
-2
-1
0
-30
-28
-26
-24
-22
-20
-18
-16
-14
-12-10
-8
-6
-4
-2
0
2
S11
Pha
se(d
egre
e)
S11
Mag
. (dB
)
Freq. (GHz)
VBIC Model Measurement Data(Mag.)
Q2x4 Ib=15µµµµA V
c=2V
VBIC Model Measurement Data (Phase)
InGaP/GaAs HBT Ö × S 2 VBIC./ .1o p (S11)
Chap.2 VBIC page 36
page 36
0 5 10 15 20
-70
-60
-50
-40
-30
-20
5456586062646668707274767880828486889092
Q2x4 Ib=15µµµµA V
c=2V
S12
Pha
se (d
egre
e)
S12
Mag
. (dB
)
Freq. (GHz)
VBIC Model Measurement Data (Mag.)
VBIC Model Measurement Data (Phase)
InGaP/GaAs HBT Ö × S 2 VBIC./ .1o p (S12)
0 5 10 15 20
-2
0
2
4
6
8
80
100
120
140
160
180Q2x4 I
b=15µµµµA V
c=2V
S21
Pha
se(d
egre
e)
S21
Mag
. (dB
)
Freq. (GHz)
VBIC Model Measurement Data (Mag.)
VBIC Model Measurement Data (Phase)
# InGaP/GaAs HBT Ö × S 2 VBIC./ .1o p (S21)
Chap.2 VBIC page 37
page 37
0 5 10 15 20-1.4
-1.2
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
-8
-6
-4
-2
0Q2x4 I
b=15µµµµA V
c=2V
S22
Pha
se (d
egre
e)
S22
Mag
. (dB
)
Freq. (GHz)
VBIC Model Measurement Data (Mag.)
VBIC Model Measurement Data (Phase)
InGaP/GaAs HBT Ö × S 2 VBIC./ .1o p (S22)
2.4 InGaP/GaAs HBT
G 2.3.3 L o p (GP./ VBIC./ ÈÉ 2| v
¸( 6 7 M N O ; BiCMOS HBT v(µ µ + ft ICÝ
2P " 9N Q | VCER VCB ^ i j P 1 (e f ^ =
- S ° TF 0 6 VXTFLVTF ITF e B] ^ T
%V/ à(GP VBICÈÉ 2Û %U f
C
Q
I(G S Ö × ¶
· f
C
dQ
dIe B°Û ÞV$ % 6 t G(Ì Í Â HBTÈÉ
2 ./ ¹ U ¡ ÒI æ V
+k L () * ® Î Ï ½¾ H- HÈÉ 2
V+ HBT() * ® U ½¾ 0 Î Ï +Î Ï 6 F () * æ
Chap.2 VBIC page 38
page 38
Û %°7Ã V 8 " ½¾ ( " ½¾ ` " ½¾ Û %½
¾ 2-29V
1x10-5 1x10-4 10-3 10-2
0
5
10
15
20
25
30
35
40
High current region
Middle current region
Low current region
Vce
Ft (G
Hz)
Ic (A) Ö × Ft IcÝ
BEwBw
BCw
Emitter Base Collector Sub collector−
cont
act
cont
act
BC
SCR
BE
SCR
high currentdensity
CwEw
InGaP/GaAs HBT½¾ ./
Chap.2 VBIC page 39
page 39
2.4.1 (Neutral Base Region)
+8 " 9N2(C +$ HM N Bw $ H ½ W ¼a
X Q 6 Y ¦ 7/ ¸;
( )2
2
1 1 1B BnB T
nB T c
ew w eQ i
V e v e
ζ ζ
ζ ζ
ζµ ζ ζ
− + −= +
(¸ 2.16)
( nBµ U$ H Z [ abcd(W\ cZa(drift factor)Û %U;
n B
th
E wV
ζ = − (¸ 2.17)
ζ ³ % Bw G$ HJ K ]N( BN ) ^ _ ` (intrinsic)¼a]
N( in ) \ c a nE U
2 iT B Tn
B i
dnV dN VE
n N dx n dx= −
+ (¸ 2.18)
^ _ ` ¼a]N( in ) Q 6 G0 I J K bGJ K B
Þ c d? e f ;ghe f (SiGe)¥ ¦ band-gap grading ¯
a V
(¸ 2.16) i °8 j 0 % $ ¢ À Á Ï (j ¡G \ c/
À Á « 8Vi k 8 +ê l v m ¿ ¯G¯ a ¥ ¦
+$ H n o aN( cv )8XV
Ò " 9N p 82(Kirk Effect q n r E )( Bw cv s $ H- H
! Ð BCiv ^ t(6 $ HÈÉ 2Q 6 u v w U;
( )2
2
1 1 1nB B BBf Bfd Bfv
T nB T c
edQ w w edI V e v e
ζ ζ
ζ ζ
ζτ τ τ
µ ζ ζ− + −= = + = + (¸ 2.19)
Chap.2 VBIC page 40
page 40
Ò " 9N x ¯( Bw cv B y ! ^ t(Þ2l Ic ^
t(¶t Ò z K (e Bã r¯ Ù .1VZk4
« | 1 ¡ m æ V 9 : ζ 2 bias : t( Bfdτ Bfvτ [! t
Q U° _ ! t8° _ " t8V
( _ ! t8Q 6 G6 7t
( )0 1 1B B bw w k c= − − (¸ 2.20)
( ( )0 0B B BCiw w V= = (kbU°µ (6 1 $ H- H
~ 0jCi jCic C C= VQ ·
( )( )
2
0
2
0 2
1 1
1 1
Bfd Bfd b
BBfd
nB T
k c
ewV e
ζ
ζ
τ τ
ζτ
µ ζ
= − −
− +=
(¸ 2.21)
Ò 0nE = ( ( )2 2
0 2
1 12
B BBfd
nB T nB T
ew wV e V
ζ
ζ
ζτ
µ ζ µ− +
= = S _ À Á F ? ^
ÞÈÉ 2V
+ Bfvτ aNQ 6 , - N E ¸ 6 V
limlim2
0
,1
sc s
c nC
vVuv v E
wu µ= = =
+ (¸ 2.22)
( ( ) lim, /jc BCi Tu E v i E= ¡ 1 6 BC a ( limE U°=
a 5 N(j Ò a 5 NI % k 2 aNÊ ^ ê ë ( 0nCµ
¡ H8 a 5 N abcdV
( )2
0 11 1
1B
Bfv bs
w u ek c
v u e
ζ
ζζτ += − − −
(¸ 2.23)
Chap.2 VBIC page 41
page 41
( 11
ee
ζ
ζζ ≥−
V° ² [! BC 21
1u
u+ ≈ W
( )1 1 1bk c− − > Gk8 k[! ú UV¶± ² [! BC (
211
uu+ > ( ( )1 1 1bk c− − ≈ Gk8 k[! ú UVG% + BC
G ² [! Ó ± ² [! 2($ HÈÉ 2?G Bfdτ U / I 8VA
) * Q 6 R S ( )1 1bk c− − 8(W®21 u
u+| 1 U
11
u +
¶· ;
00 00
0
00
0
11 1
1 1
11
1
BfvBBfv Bfv
s
BBfv
s
w uev e u u u
w ev e u
ζ
ζ
ζ
ζ
τζτ τ
ζτ
= + = + − − +
= + −
(¸ 2.24)
0Bfvτ U 0BCiV = ÈÉ 2(W 0 1u u c≈ V
2.4.2 - (BC Space Charge Region)
8 " 9N2(G$ H- H§ ¨½ + , 6 ÈÉ 2U
2BC
BCc
wv
τ = (¸ 2.25)
( BCw U ! t§ © ½M N( cv U a+$ H- H§
¨½ NVÛ %Ò BC § © 2(punch-through)
U jCiPC (G$ ¢ E ¸A
Cw
ε= (Q ·
0
jCiP jCiPBC BCP BCP
jCi jCi
C Cc
C Cτ τ τ= = (¸ 2.26)
Chap.2 VBIC page 42
page 42
punch-throughÈÉ 2U2
CBCP
c
wv
τ = V
Ò` " 9N r E 2(k½¾ ¥ ¦ z K (e Bã r-+
./ t V
2.4.3 (Neutral Emitter Region)
9 : +M N Ew H ½(ÈÉ 2 0pEτ Q 6 u Y ¦ 7
¸;
2 2
0 2pE E E
pEB kE pE T
dQ w wdI v V
τµ
= = + (¸ 2.27)
( kEv ¡°^ I ^ â o rd (contact
recombination velotcity)( pEµ U bcdVZU+ Ý F ? ./
2( ¡ . p , - IC ÝU ( $ ã r0 4 w x V6 Û %8 Ü
" x 0 C BdI dIβ = V6 t Q u ä å U a C 2;
0
0
pEEf
ττ
β= (¸ 2.28)
U5 dË ã rÝ w x ^ t¸a(Û % ( )0 ,C LowIβ U 0BCiV =
2 " x (â ¯t +8 " 9N2 0β [! " : t() * Q 6
Y z [! " t ¸
( )( )
0 ,0
0 ,C Low
Ef EfC BCi
I
I V
βτ τ
β= (¸ 2.29)
, - ¨ t (Integral Charge-Control Relation)(Q 6 ®
Chap.2 VBIC page 43
page 43
[! ^ t " x ³ Y ¦ ;
( )( )
0 ,
0
1,
EgC Low T
C BCi CK
I II V I
τββ
≈ +
(¸ 2.30)
( Egτ U°./ ( CKI U° H ` "
" (t % Û %(Q 2.4.5 L V / à( Efτ C
¨ EfQ Q u Y ¦ 7¸;
0
0
1
1
E
E
g
TEf Ef
CK
g
TEf Ef T
CK
II
IQ i
I
τ
τ
τ τ
τ
= +
= +
(¸ 2.31)
2.4.4 - (BE Space Charge Region)
C +$ H-H§ ¨½ W ¼a(Q 6 Y ¦ 7 ¸;
2 exp 1BEiTBE E BE i
T
vVQ qA w n
PE V
= −
(¸ 2.32)
( BEw U$ H-H§ ¨½M N( in U$ H-H§
¨½ Z [ _ ` ¼a]N(PEU BE ¹ V
6 ÈÉ 2U;
exp1
BEiE BE i
TBE
m C
vqA w n
Vg PE I
τ
= ∝
⋅ (¸ 2.33)
( mg U ² [! ä dVZU m Cg I∝ (Ò` " 9N2 BEτ Ê
Chap.2 VBIC page 44
page 44
" x ¯¶ 8V
2.4.5 (Neutral Collector Region)
+ " 9NR " 9N½¾ ( H ½¼aX
0 ñ (<· 0 +$ H- H§ ¨½t a 8(
/ àcÓ H* H(Sub-Collector)6 (¥ + ¢ HP ¦
½( ! < ¡$ H u @ ° Vk Õ U Kir-effectVG%
Krik-effect (Ê ¥ ¦ " x 8(6 fT 8V
U5 k r E (Û %° " CKI ;
( )2 3
20
lim
1 101
21
ceffCK
Ciceff
v x xI
r v V
− + += + +
(¸ 2.34a)
limceff
PT
v Vx
V
−= (¸ 2.34b)
(xU° Za(X¡ ¡ ¢ | v¸+8 a a
£ ( PTV U H punchthrough ! ( limV U° ! j 8
a (8; limceffv V< )( " CKI v ( limV L PTV )8 a
2 H X 0Cir t(6 ^ H ! ceffv
00
CCi
E nC C
wr
qA Nµ= (¸ 2.35a)
ln 1 exp 1 1CEi CEsceff T
T
v vv V
V
−= ≤ + − +
(¸ 2.35b)
¸( CEsv U CE ! Vs GÄ Å | v¸(< CKI ¦ U°
Chap.2 VBIC page 45
page 45
CEiv £ ¤ WQ ¥ V
Ò T CKI I= 2( W ¼a( )ò ¦ H( C + M
N ¨ pCQ C 2 pCsτ ;
( )2
04
pC pCs T i C
CpCs
nC T
Q i w w
wV
τ
τµ
= =
(¸ 2.36)
½M N ( )1i C CK Tw w I i= − Ê pCQ ñ § V
Ò T CKI I< 2(t ¸Ê ¥ ¦ °f ^ T % pCQ (Ä ¡æ ì í +
I ./ z ê ¨ © VÄ ª ¨ © Q 6 , -7¸ 6 « ¬ V
2
21 1
1
hci
C hc
CK T
i i aww
w a
i I i
+ + = = + +
= −
(¸ 2.37)
( 0hca > V6 (+ HÈÉ 2 pCτ U;
2
2
21pC CK
pC pCsC T hc
dQ Iw
di i i aτ τ
= = + +
(¸ 2.38)
2.4.6
F M L 6 ½¾ ./ (> H] T %W: J F ?
: J ^ H I < 7 (A <-+ I ./ 6 : J Ù m Ýt (?
¡ u z K WB w x VA?¿ 6 ÷ 1 (6 , I .
/ m ÝV
Chap.2 VBIC page 46
page 46
(1).
G 6 F t ¸() * 3 ® 8 " 9NÈÉ 2( $ HÀ
Á drift 2(H ½ Efτ ($ H- H§ © ½ BCτ ($ H-
H§ © ½ BEτ (+k4 5 Å | 1 9 : 1T CI I= << (6 R S
( )220 1Bfd bk cτ −
8V
( ) [ ]( ) [ ]( ) [ ]
0
0 0 0 0 0
0 0 0 0
0 0 0
2 1 1 / ( )
1 1 / ( )
1 1 1 / ( )
f Bfd Bfv BC Ef BE
BCP jciP jci Bfd b Bfvl BE T
h Bfvl BE T
h Bfvl BE T
C C k c u u sqrt i
c u u sqrt i
c c sqrt i
τ τ τ τ τ τ
τ τ τ τ τ
τ τ τ τ
τ τ τ τ
= + + + +
= + − − + − +
= + ∆ − + − +
+ ∆ − + − +
(¸ 2.39)
( ( )0 0 0 0 0Ef Bfd Bfv BCP jCiP jCiC Cτ τ τ τ τ= + + + UÒ 0BCiV = 2ÈÉ 2
(U./ ° V °./ 0hτ∆ -6 ¯ G$ H- H
§ © ½M NP 1 Early Effect¥ ¦ ÈÉ 2P 1 V¼aN
^ t8Ç ¡- Bfvlτ 0 .1V
(2).
+L " 9N2(Ê <ÈÉ 2x ¯8 Efτ L Bfτ pCτ (
G Efτ ª E 8U;
( )( )
0
1
EgEf Ef T CK
Ef Ef T E
i I
Q i g
τ
τ
τ ττ
∆ =
∆ = ∆ + (¸ 2.40)
G% Bfτ pCτ ^ x ¯ p [11](6 ® r ° +° ± (t
¸U;
Chap.2 VBIC page 47
page 47
2
2
2
2
0 0
21
2 1 4
CKfh hcs
T hc
fh hcs T
Bm C Chcs Bfvs pCs
nC T nC T
Iw
i i a
Q w i
w w weV e V
ζ
ζ
τ τ
τ
ζτ τ τµ µ
∆ = + +
∆ =
= + = +−
(¸ 2.41)
( 0Efτ L Egτ L hcsτ L hca U./ V
w x 2(G) * e f ^ Ö × 0BCiV = 2WÞ2 BEV (6
¡ , -/ ° ( 1.5CEV V= ) ® ÈÉ 2ý ø § © ½
t8V ® 8 " 9N « x z V
( ) 1' ,
2je jc
f CE CT m
C CV I
f gτ
π+
= − (¸ 2.42)
· áÈÉ 24 U² ¦ Vâ D 6 t · á
0hτ∆ ^ t8Vâ , - matlab Y z J ³ t ¸(4 ´ ç / 0 1 (
Bfvlτ 0BEτ « V
â , - " 3 « v µ z
00
75CCi
E nC C
wr
qA Nµ= ≈ Ω (¸ 2.43a)
2PTV V≈ (¸ 2.43b)
limlim
0
s
c nC
vVE
w µ= = ¶ lim
0
0.2sc
nC
vV w V
µ= ≈ (¸ 2.43c)
( Cw L CN L PTV Q 6 , - CV | · z Vâ , - matlabv
¸Ý / 0 1 7 V/ à(w x ~ 2-9V.1Ö × o
p ³ _ 2-31 2-32V
Chap.2 VBIC page 48
page 48
¸nGaP/GaAs HBTÈÉ 2 w x o p
0fτ (psec) 2.6 0Efτ 0.4 0Cir 77
0hτ∆ (psec) 1.3 Egτ 2.7 PTV 2.5
Bfvlτ (psec) 0.01 hcsτ (psec) 5 limV 0.34
0BEτ 5.5e-14 hca 0.65 CEsV 0.2
1x10-5 1x10-4 10-3 10-2
0
5
10
15
20
25
30
35
40
Ft (G
Hz)
Ic (A)
Measurement Simulation
, -° ¹ ./ w x º » ¼ ½ ¾ » ¼ ¿ À ÈÉ 2(log)
Chap.2 VBIC page 49
page 49
0 2 4 6 8 10
0
5
10
15
20
25
30
35
Ft (G
Hz)
Ic (mA)
Measurement Simulation
, -° ¹ ./ w x º » ¼ ½ ¾ » ¼ ¿ À ÈÉ 2(lin)
