Transcript Document
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
Avalanche multiplication
Extrinsic region
AC small-signal model
Noise and temperature effect
Depletion charge (Qte,Qtc)
C je
Cte (1 XC je )
(1
2 1
VdE
) pE
C je
CteS XC je
(1
B2E1
B E
B E
2 1
VdE
) pE
B2 E1 1 pE
C jeVdE
Qte CtedV (1 XC je )
1
(
1
)
1 pE
VdE
0
pE
(1 K ) 2 (1 B2 E1 )
(1 K )C jeVdE
VdE
Qte (1 XC je )
1
pE
1 pE K
B2 E1 2
2
(1
) K
V
dE
Set Q=0 at V=0
Change function to
a smooth one to
prevent the value
become infinite at
V=Vd
Base diffusion charge (QBE,QBC)
Injected n p , so we caculate injected eDefine base charge at zero bias Q p dx N W
WB
B0
p
0
WB
QBE n( x)dx
0
QBC
n(0) '
WB
2
Assumed linear
1 n(0)
1
N BWB' n0 q1QB 0
2 NB
2
1
nB q1QB 0
2
QBE+QBC=all diffusion charge in base
B
B
Main current (IN)
I C WB
D
0
BE
q
pp
AE (e VT e VT )
2
nB ieB
n
dx
B2E1
I N I S (e
VT
BC
B2C2
e
VT
)
1
qB
WB
qB
q1
p( x)dx
0
QB 0
QB 0 Qte Qtc QBE QBC
QB 0
QB 0 Qte Qtc
V
V
1 tE tC
QB 0
Ver Vef
q1=1 means no early effect
Total base charge (qB)
Early effect (base width modulation)
Qte,Qtc
High level injection
QBE,QBC
Base current (IB1,IB2)
I B1 (1 XI B1 )
I B1 XI B1
S
IS
f
IS
f
B2E1
(e
VT
1)
B1E1
(e
VT
1)
B2E1
I B 2 I Bf (e
mLf VT
1) , mLf 2
IB1 is ideal forward base
current
IB2 is non-ideal forward
base current
(2kT current at low bias)
S means sidewall
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)
q1 1
qBI
e
VtE VtC
Ver Vef
VtE dE g
V 1 V
er T
dE g
VT
e
VtC dE g
Vef VT
1
B2E1
B2E1
B2C2
IS
VtC
VT
VT
VT
(1 X rec )(e
I B1 (1 XI B1 )
1) X rec (e
e
2)(1
)
f
Vef
e
Diffusion charge (QE, Qepi)
Emitter diffusion charge QE
Collector epilayer diffusion charge Qepi
dQDiffusion
When I I k , Let QE (min) E
dI
B2E1
I
m VT
QE QE 0 e
1 QE 0
Is
Q
E
dQE QE 0
dI
m I s
I
Is
1
1
m
1
m
1
1
m
B
2 1
IS
QE E
I S (e m VT 1)
Ik
2VT xi
Qepi epi
( p 0 p w 2)
RCv Wepi
E
Base capacitance
Base current is injected from side, the
voltage on B1 and B2 may be different
We must compensate the charge
Q CV
VB1 VB2
1
QB1B2 B1B2 (CtE C BE C E )
5
Base resistance
DC crowding effect
B2
B
Rb
B1
RBc
R B RBC Rb
RBv
RBv
qB
I B eVBE
I B1B2
2V
T (e
3Rb
B1B2
VT
1)
B B
1 2
3Rb
Collector resistance
Buried layer to collector electrode resistance
is constant RCC
Epilayer resistance is a variable
Collector resistance
When IC large, RC :small to high to small
I hc qNepivsat Aem
Collector resistance
Kull, TED vol.32, no.6, p1103, 1985
N epi const.
EC C1C2
f ( B2C2 , B2C1 )
n p N epi
I C1C2
Jp 0
p0 1
EC VT 2 p0 2 pw ln
pw 1
d p
dx
n
0
1
n0
n 0 n
vsat x
J n const.
RCv
1
p0
1 4e
2
pw
B2C2 VdC
1
1 4e
2
VT
1
2
B2C1 VdC
VT
1
2
Collector resistance
Jeroen, SSC vol.36, no.9, p1390, 2001
Also considered the high current base
push-out (Kirk effect)
Velocity saturation
Final equation is
xi
2VT
p 0 p w p0 p w 1
Wepi I C1C2 RCv
p0 p w 2
I C1C2
VdC B2C1
xi 2
SCRCv (1
)
Wepi
VdC B2C1 SCRCv I hc (1
VdC B2C1 RCv I hc
xi
)
Wepi
RF performance
fT roll-off at high IC, IC1C2 is the key
When IC get large enough, base push-out
occurs, F increase and makes fT roll-off
Mextram model based on more physical
parameters
1
kT
CBE CBC CBC re rc
F
2fT
qIC
Avalanche multiplication
Weak avalanche effect
Valid only for IC1C2 < Ihc
Kloosterman, p172, BCTM 2000
I avl I C1C2
WtC
An e
Bn
E ( x)
dx
0
x
E
E ( x) EM (1 ) M
1 x
I avl I C1C2
B
x
n (1 d )
EBn
An
EM e M e EM
Bn
Extrinsic region
Base-SIC:intrinsic
Base-epilayer-buried layer:extrinsic
Base-(p-poly)-buried layer:external
Reverse base current (Iex,IB3)
I B1 (1 XI B1 )
B2E1
1
f
I S (e
VT
1)
1 1
I ex (1 X ext )
( I k nBex ( B1C1 ) I S )
ri 2
B1C1
I B 3 I Br
e
VT
B1C1
1
VLr
, VLr 2
e 2VT e 2VT
I B3
B1C1
I Br e 2VT , B1C1 VLr
B1C1
V
I Br e T , B1C1 VLr
Iex is ideal reverse base
current
IB3 is non-ideal reverse
base current
(2kT current at low bias)
Xext is partitioning factor
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
B1C1
I sub
2 I ss (e
VT
1 1 4
I sub
1)
IS
e
I kS
B1C1
VT
B1C1
I
ss e 2VT , B1C1 is big
I S
I kS
B1C1
V
I ss (e T 1) , B1C1 is sm all
Others
Collector-Substrate depletion capacitance
Reverse substrate current
Constant B-E, B-C overlap capacitance
SC 1
I sf I SS (e VT 1)
Cts
C BE 0
C BC 0
Small-signal equivalent circuit
Small-signal equivalent circuit
I N
I
I
g y N gz N
x
y
z
I C1C2
I C1C2
I C1C2
g RCv , x
g RCv , y
g RCv , z
x
y
z
I
I
I
g , x BE g , y BE g , z BE
x
y
z
I
I
I
g , x BC g , y BC g , z BC
x
y
z
gx
x:VB2E1
y:VB2C2
z:VB2C1
I BC I avl
I N I BC I C1C2
I N I BC I C1C2
g x dx g y dy g z dz g RCv , x g , x dx g RCv , y g , y dy g RCv , z g , z dz
Small-signal equivalent circuit
g x g RCv , x g , x
dy y
dx x z g RCv , y g , y g y
g z g RCv , z g , z
dy y
dz z x g RCv , y g , y g y
I C1C2
g m
x
I C1C2
x
I C1C2
vC1E1 x
x
I
C1C2
z x vC1E1 z
I C1C2
z z x
dy
dy
g RCv , x g RCv , y
g RCv , z g RCv , y
dx
dz
x:VB2E1
y:VB2C2
z:VB2C1
z
x x vC1E1
Small-signal equivalent circuit
I I
g BE BC
x
vC1E1
I I I I
BE BC BE BC
x
z
z
x
dy dy
g , x g , x g , z g , z g , y g , y
dx dz
I C1C2 I C1C2
I C1C2
g out
vC E ( x z )
z x
x
1 1 x
g RCv , z g RCv , y
dy
dz
x:VB2E1
y:VB2C2
z:VB2C1
Small-signal equivalent circuit
I BE I BC I BE I BC
g
vC E
z
x
1 1
x
dy
g , z g , z g , y g , y
dz
dy
C BE C BE , x C BC , x (C BE , y C BC , y )
dx
dy
C BC C BC , z (C BE , y C BC , y )
dz
x:VB2E1
y:VB2C2
z:VB2C1
Small-signal equivalent circuit
dy dy
g g S g , x g , z g , x g , z ( g , y g , y )
dx dz
dy dy
g m g RCv , z g RCv , y
dx dz
g
m
g
g g , z g , z ( g , y g , y )
dy
g ex Xgex
dz
rB RBcT rbv
S
C BE C BE , x C BE
C BC , x (C BE , y C BC , y )
C BC C BC , z (C BE , y C BC , y )
x:VB2E1
y:VB2C2
z:VB2C1
dy
C BE 0
dx
dy
C BC 0 C BCex XCBCex
dz
Can get more
precise
parameters
Extrinsic added
Hybrid-π model
Let the equivalent circuit has only One
current source
g m' g m g
g' g g
'
g out
g out g
g ' g
'
g
' m'
g
B2-E1-(C1-E1)=B2-C1
Cutoff frequency fT
T
1
2fT
Q
T
I C1C2
VCE 0
VCE is const.
Qtot vi
vi
T
Ci
vi I C1C2
I C1C2
i
i
S
C BE , x C BE
C BC , x rx C BE , y C BC , y ry C BE , z C BC , z rz
C BCex rex XCBCex Xrex C BEO C BCO Xrex RCc
Cutoff frequency fT
Noise (for AC)
v2
4kTR
f
Thermal noise
-- consider variable resistance
Shot noise
i
2
f
2qID
Flicker noise (1/f noise)
-- non-ideal base current use KfN
A
i2
I f
K f b , b 1
f
f
Temperature
Temperature rules are applied to various
parameter
Self-Heating is considered
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
Still unconsidered
B-E junction breakdown
High injection current breakdown