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Mextram 504 BJT model
F. Yuan
Advisor : Prof. C. W. LiuGraduate Institute of Electronics Engineering and
Department of Electrical Engineering,
National Taiwan University, Taipei, Taiwan
Outline Charge modeling Collector current Base current series resistance, epilayer resistance Avalanche multiplication Extrinsic region AC small-signal model Noise and temperature effect
Depletion charge (Qte,Qtc)
Set Q=0 at V=0 Change function to
a smooth one to prevent the value become infinite at V=Vd
22
2
1
0
)1(
)1()1(
11
)1()1(
)1(11
)1(
)1(
)1(
)1(
12
12
12
12
12
12
E
E
E
EB
E
E
p
dE
EB
dE
EBp
E
dEjejete
p
dE
EB
E
dEjejetete
p
dE
EB
jeje
Ste
p
dE
EB
jejete
KV
VK
Kp
VCKXCQ
Vp
VCXCdVCQ
V
CXCC
V
CXCC
Base diffusion charge (QBE,QBC)
QBE+QBC=all diffusion charge in base
BB
W
pB WNdxpQB
0
0
Injected , so we caculate injected e- Define base charge at zero bias
pn
01
010'
'
0
2
1
2
1)0(
2
1
2
)0()(
BBBC
BBBB
B
W
BE
QqnQ
QqnWNN
n
Wn
dxxnQB
Assumed linear
Main current (IN)
ef
tC
er
tE
B
tcteB
B
BCBEtcteB
B
W
B
B
VVSN
VVEW
ieBnB
pC
V
V
V
V
Q
QQQq
Q
QQQQQ
Q
dxxp
q
qeeII
eeA
dxnD
p
qI
B
T
CB
T
EB
T
BC
T
BE
B
1
)(
1)(
)(
0
01
0
0
0
0
02
2212
q1=1 means no early effect
Base current (IB1,IB2)
IB1 is ideal forward base current
IB2 is non-ideal forward base current
(2kT current at low bias) S means sidewall
2,)1(
)1(
)1()1(
12
11
1
12
2
1
11
LfVm
BfB
V
f
SB
S
V
f
SBB
meII
eI
XII
eI
XII
TLf
EB
T
EB
B
T
EB
SiGe HBT qB is modified by the bandgap difference of the
base region Only considered the linear graded Ge profile If there are a lot of defects in SiGe base, there is
neutral base recombination current (1kT current)
)1)(2()1)(1()1(
1
1
221212
11
1
1
ef
tCVVrec
Vrec
f
SBB
V
dE
V
dE
V
V
V
dE
V
V
IB
ef
tC
er
tE
V
VeeXeX
IXII
e
eeq
V
V
V
Vq
T
CB
T
EB
T
EB
T
g
T
g
ef
tC
T
g
er
tE
Diffusion charge (QE, Qepi) Emitter diffusion charge QE
Collector epilayer diffusion charge Qepi
11
0
1
00 112
m
ss
EEQ
m
sE
VmEE
Diffusion
I
I
Im
Q
dI
dQ
I
IQeQQ
dI
dQ
E
T
EB
)2(2
)1(
(min),
0
11
12
wepi
i
Cv
Tepiepi
VmS
m
k
SEE
EQk
ppW
x
R
VQ
eII
IQ
LetIIWhen
T
EB
E
Base capacitance Base current is injected from side, the
voltage on B1 and B2 may be different We must compensate the charge
)(5
12121
21
EBEtEBBBB
BB
CCCQ
VV
CVQ
Base resistance DC crowding effect
b
BBV
b
TBB
VB
B
Bvb
bBB
Re
R
VI
eI
q
RR
RRR
T
BB
BE
C
3)1(
3
221
21
21
B1
B2
RBvRBc
B
Collector resistance Buried layer to collector electrode resistance
is constant RCC
Epilayer resistance is a variable
Collector resistance Kull, TED vol.32, no.6, p1103, 1985
2
141
2
1
2
141
2
1
1
1ln22
),(
12
22
1222
21
21
0
00
T
dCCB
T
dCCB
V
V
w
V
V
wwTC
CBCBCv
CCCCC
ep
ep
p
pppVE
fR
EI
.
1
0
0
.
0
0
constJ
xv
dx
d
J
Npn
constN
n
n
sat
n
nn
p
p
epi
epi
Collector resistance
hcCvCBdC
epi
ihcCvCBdC
epi
iCv
CBdCCC
w
ww
CvCC
T
epi
i
IRV
Wx
ISCRV
Wx
SCR
VI
pp
pppp
RI
V
W
x
12
12
12
21
21
)1(
)1(
2
12
2
0
00
Jeroen, SSC vol.36, no.9, p1390, 2001
Also considered the high current base push-out (Kirk effect)
Velocity saturation Final equation is
RF performance fT roll-off at high IC, IC1C2 is the key
When IC get large enough, base push-out occurs, increase and makes fT roll-off
Mextram model based on more physical parameters
ceBCBCBEC
FT
rrCCCqI
kT
f
21
F
Avalanche multiplication Weak avalanche effect Valid only for IC1C2 < Ihc Kloosterman, p172, BCTM 2000
)1(
0
)(
21
21
1)1()(
d
M
n
M
n
tC n
x
E
B
E
B
Mn
nCCavl
MM
WxE
B
nCCavl
eeEB
AII
xEx
ExE
dxeAII
Extrinsic region Base-SIC : intrinsic Base-epilayer-buried layer : extrinsic Base-(p-poly)-buried layer : external
Reverse base current (Iex,IB3)
Iex is ideal reverse base current
IB3 is non-ideal reverse base current
(2kT current at low bias) Xext is partitioning factor
r
T
CB
r
T
CB
r
T
rL
T
CB
T
CB
T
EB
LCBV
Br
LCBV
Br
B
L
V
V
V
V
BrB
SCBBexkri
extex
VS
fBB
VeI
VeII
V
ee
eII
InIXI
eIXII
11
11
11
11
11
11
11
12
,
,
2,1
))(2
1(
1)1(
)1(1
)1(
2
3
22
3
11
Extrinsic region
External reverse base current, XIex
Extrinsic depletion charge, Qtex
External depletion charge, XQtex
Extrinsic diffusion charge, Qex
External diffusion charge, XQex
Parasitic PNP Base-Collector-Substrate : parasitic PNP Only for it’s main current
smalliseI
bigise
I
I
I
I
eI
I
eII
CBV
ss
CBV
kS
S
ss
sub
V
kS
S
Vss
sub
T
CB
T
CB
T
CB
T
CB
11
11
11
11
11
11
,)1(
,
411
)1(2
2
Others Collector-Substrate depletion capacitance Reverse substrate current Constant B-E, B-C overlap capacitance
00
)1(1
BCBE
ts
VSSsf
CC
C
eII T
SC
Small-signal equivalent circuit x : VB2E1
y : VB2C2
z : VB2C1
z
Ig
y
Ig
x
Ig
z
Ig
y
Ig
x
Ig
z
Ig
y
Ig
x
Ig
z
Ig
y
Ig
x
Ig
BCz
BCy
BCx
BEz
BEy
BEx
CCzR
CCyR
CCxR
Nz
Ny
Nx
CvCvCv
,,,
,,,
,,,212121
dzggdyggdxggdzgdygdxg
III
III
II
zzRyyRxxRzyx
CCBCN
CCBCN
avlBC
CvCvCv ,,,,,,
21
21
Small-signal equivalent circuit x : VB2E1
y : VB2C2
z : VB2C1 yyyR
zzRz
x
yyyR
xxRx
z
ggg
ggg
z
y
dz
dy
ggg
ggg
x
y
dx
dy
Cv
Cv
Cv
Cv
,,
,,
,,
,,
dz
dygg
dx
dygg
z
I
x
I
x
z
z
I
x
x
x
I
x
Ig
yRzRyRxR
x
CC
z
CC
vx
CC
vz
CC
v
CCm
CvCvCvCv
ECECEC
,,,,
2121
11
21
11
21
11
21
Small-signal equivalent circuit x : VB2E1
y : VB2C2
z : VB2C1
dz
dygg
z
I
zx
I
v
Ig
dz
dy
dx
dygggggg
z
II
x
II
x
IIg
yRzR
x
CC
x
CC
xEC
CCout
yyzzxx
x
BCBE
z
BCBE
v
BCBE
CvCv
EC
,,
,,,,,,
2121
11
21
11
)(
Small-signal equivalent circuit x : VB2E1
y : VB2C2
z : VB2C1
dz
dyCCCC
dx
dyCCCCC
dz
dygggg
z
II
v
IIg
yBCyBEzBCBC
yBCyBExBCxBEBE
yyzz
x
BCBE
xEC
BCBE
)(
)(
,,,
,,,,
,,,,
11
Small-signal equivalent circuit x : VB2E1
y : VB2C2
z : VB2C1
Can get more precise parameters
Extrinsic added
BCexBCexBCyBCyBEzBCBC
BEyBCyBExBCSBExBEBE
bvBcTB
exexyyzz
m
yRzRm
yyzxzxS
XCCCdz
dyCCCC
Cdx
dyCCCCCC
rRr
Xggdz
dyggggg
g
g
dz
dy
dx
dyggg
dz
dy
dx
dygggggggg
CvCv
0,,,
0,,,,
,,,,
,,
,,,,,,
)(
)(
)(
)(
Hybrid-π model Let the equivalent circuit has only One
current source
'
''
'
'
'
'
g
g
gg
ggg
ggg
ggg
m
outout
mm
B2-E1-(C1-E1)=B2-C1
Cutoff frequency fT
CcexBCOBEOexBCexexBCex
zzBCzBEyyBCyBExxBCSBExBE
CC
i
ii
CC
i
i i
totT
CEVCC
T
TT
RXrCCXrXCrC
rCCrCCrCCC
I
vC
I
v
v
Q
constisVI
Q
f
CE
,,,,,,
0
2121
21
.
2
1
Noise (for AC) Thermal noise
-- consider variable resistance Shot noise
Flicker noise (1/f noise)
-- non-ideal base current use KfN
kTRf
v4
2
DqIf
i2
2
1,2
bf
IK
f
ib
A
f
f
Comparison to GP fT-IC is more accurate
Mextram parameters are base on more physical way
Noise is considered more accurate because the variable resistance
Linear graded SiGe HBT model in Mextram 504
Weak avalanche breakdown
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