mextram 504 bjt model
DESCRIPTION
Mextram 504 BJT model. F. Yuan Advisor : Prof. C. W. Liu Graduate 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 - PowerPoint PPT PresentationTRANSCRIPT
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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
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Outline Charge modeling Collector current Base current series resistance, epilayer resistance Avalanche multiplication Extrinsic region AC small-signal model Noise and temperature effect
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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
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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
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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
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Total base charge (qB) Early effect (base width modulation)
Qte,Qtc
High level injection
QBE,QBC
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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
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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
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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
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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
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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
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Collector resistance Buried layer to collector electrode resistance
is constant RCC
Epilayer resistance is a variable
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Collector resistance When IC large, RC : small to high to small
emsatepihc AvqNI
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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
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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
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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
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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
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Extrinsic region Base-SIC : intrinsic Base-epilayer-buried layer : extrinsic Base-(p-poly)-buried layer : external
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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
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Extrinsic region
External reverse base current, XIex
Extrinsic depletion charge, Qtex
External depletion charge, XQtex
Extrinsic diffusion charge, Qex
External diffusion charge, XQex
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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
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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
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Small-signal equivalent circuit
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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
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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
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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
)(
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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
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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,,,,
,,,,
,,
,,,,,,
)(
)(
)(
)(
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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
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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
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Cutoff frequency fT
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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
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Temperature
Temperature rules are applied to various parameter
Self-Heating is considered
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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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Still unconsidered B-E junction breakdown High injection current breakdown