SPICE Gummel-Poon (SGP) BJT Model
• SPICE Gummel-Poon (SGP) model improves dc characterization
of EM3 model by a unified theory.
• The SGP unified model was developed to improve:
– base-width modulation
– high-injection effects
– base-widening effect resulting in τF vs. IC.
• The starting point of SGP model is:
– EM2-model
– two additional diodes in EM2 representing the extra component of
IB for β roll-off at low IC.
5-Feb-04
HO #10: ELEN 251 - SGP BJT Model
Saha #1
SGP BJT Model: Starting Point
C
qV B′C ′

C 4 I S (0) e nC kT − 1


Csub
r'c
C'
CDC
B
r'b
CjC
IEC/βR
B'
CDE
ICT = ICC - ICE
CjE
ICC/βF
qV B′E ′

E'
I CC = I S  e kT − 1
r'e


qV B′E′
qV B′C ′
C 2 I S (0) e nEkT − 1

I EC = I S  e kT − 1


E


The starting point of SGP model is EM2-model with two extra diodes
to account for β roll-off at low current level.
5-Feb-04
HO #10: ELEN 251 - SGP BJT Model
Saha #2
SGP BJT Model: Model Parameters
• EM2-parameter set:
dc (EM1) bulk-ohmic resistors charge storage effects • Extra model parameters:
transistor sat. current low-current β roll-off forward Early voltage inverse Early voltage knee current in ln(IC) vs. VBE inverse knee current τF vs. IC model 5-Feb-04
βF, βR, Tref, Eg (re-define IS in SGP)
r'c, r'e, r'b,
CjE0, φE, mE,CjC0 , φC, mC, τF,τR Csub
ISS (replacement of IS)
C2, nE, C4, nC
VA
VB
IK
IKR
B
HO #10: ELEN 251 - SGP BJT Model
Saha #3
Derivation of ISS
Emitter
Base
Spacecharge
layer
Collector
p (x )
← ε (x )
Spacecharge
layer
n(x )
xjE xE
xC
xjC
x
• Assumptions:
– one-dimensional current equations hold
– npn-BJT with EB junction forward biased and BC reverse biased
– depletion approximation, that is, no mobile charge inside the
depletion region
– BJT gain is high, that is IB ≅ 0.
5-Feb-04
HO #10: ELEN 251 - SGP BJT Model
Saha #4
Derivation of ISS
One-dimensional current equations (HO #2, slide #66) are:
Jn = qµnn(x)ε(x) + qDn(dn(x)/dx)
(1)
Jp = qµpp(x)ε(x) − qDp(dp(x)/dx)
(2)
Since, we assume IB ≅ 0,
∴ Jp = hole current in base ≅ 0 and from (2) we get,
or, qµpp(x)ε(x) − qDp(dp(x)/dx) = 0
D p 1 dp( x) kT 1 dp( x )
∴ε (x ) =
=
q p ( x) dx
µ p p ( x) dx
(3)
(4)
here we used, Dn/µn = Dp/µp = kT/q
The direction of the ε-field in (4) aids e- flow from E → C and
retards e- flow from C → E.
5-Feb-04
HO #10: ELEN 251 - SGP BJT Model
Saha #5
Derivation of ISS
The e- flow between E and C is given by (1):
Jn = qµnn(x)ε(x) + qDn(dn(x)/dx)
(1)
Using (4) in (1) we get:
J n = kT µ n
n (x ) dp(x )
dn(x )
+ q Dn
p (x ) dx
dx
(5)
qDn 
dp( x)
dn( x) 
+ p( x )
∴ J n = p ( x )  n( x )
dx
dx 

q Dn d
=
or, J n p ( x) [n( x) p( x)]
dx
(6)
We integrate (6) over the neutral base width WB from xE to xC .
5-Feb-04
HO #10: ELEN 251 - SGP BJT Model
Saha #6
Derivation of ISS
Emitter
Base
Spacecharge
layer
Collector
p (x )
← ε (x )
Spacecharge
layer
n(x )
xjE xE
∴Jn
xC
XC
∫ p( x )dx = qDn
XE
∴Jn =
XC
∫
XE
xjC
d [n( x) p ( x) ]dx
dx
qDn [n( xC ) p( x C ) − n( x E ) p ( x E )]
XC
x
(7)
(8)
∫ p ( x)dx
XE
5-Feb-04
HO #10: ELEN 251 - SGP BJT Model
Saha #7
Derivation of ISS
From PN-junction analysis, we know that the pn-product at the
edge of the depletion regions are:
p( xC ) n( xC ) = n e
qV B ′C ′
kT
(9)
p ( x E )n ( x E ) = n e
qV B ′E ′
kT
(10)
2
i
2
i
Substituting (9) and (10) in (8) we get:
q V B′C ′
qV B′E ′

q Dn n e kT − e kT 


∴Jn =
xC
∫ p( x)dx
2
i
(11)
xE
5-Feb-04
HO #10: ELEN 251 - SGP BJT Model
Saha #8
Derivation of ISS
If A = cross-sectional area of the emitter, then from (11) we can
show that:
qV B′E ′
qV B′C ′




− q ADn n  e kT − 1 −  e kT − 1

 


In =
xC
2
i
(12)
∫ p( x)dx
xE
Where In = total dc minority injection current from E → B in the
positive x-direction. We have shown in EM1-model:
I CT ( EM1− model) ≡ I CC − I EC
qV B ′C ′
qV B ′E ′




= I S  e kT − 1 −  e kT − 1
 


5-Feb-04
HO #10: ELEN 251 - SGP BJT Model
(13)
Saha #9
Derivation of ISS
At low level injection, p(x) ≅ NA(x) in the neutral base region
where xE ≤ x ≤ xc. Then we can write (12) as:
q AD n ni2  qV B′E′   qV B′C′  
I CT ( low − level) = xC
 e kT − 1 −  e kT − 1 
∫ N A ( x)dx
(14)
xE
Since xE and xC depend on applied voltages, we define the
fundamental constant, ISS @ VBE = 0 = VBC.
I SS ≡
q AD n n2i
xC 0
∫ N A ( x) dx
(15)
xE0
Where xE0 and xC0 are the values of xE and xC with applied zero
voltages.
5-Feb-04
HO #10: ELEN 251 - SGP BJT Model
Saha #10
Derivation of ISS - Base Charge, QB
Again, (14) can be expressed as:
I CT
 xC 0

 qA N A ( x)dx 
∫
2 
  qV B′E ′   qV B′C′ 
q AD n ni
xE 0
= xC
 xC 0
  e kT − 1 −  e kT − 1
 




∫x p ( x)dx  qAx∫ N A ( x)dx 
E

E0

xC 0
=
q AD n n
2
i
qA ∫ N A ( x) dx
xC 0
xE 0
xC
xE 0
xE
qA ∫ N A ( x )dx
∫ p( x)dx
 qV B′E′ − 1 −  qV B′C′ − 1
  e kT

 e kT
 

(16)
5-Feb-04
HO #10: ELEN 251 - SGP BJT Model
Saha #11
Derivation of ISS - Normalized Base Charge, qb
Defining:
Q B ≡ qA
xC (V B′C′ )
∫ p ( x)dx
(17)
x E (VB′E ′ )
xC 0
Q B 0 ≡ qA ∫ N A ( x )dx
(18)
xE 0
We get:
I CT = I SS
I SS
=
qb
QB 0
QB
 qV B′E ′ − 1 −  qV B ′C′ − 1
  e kT

 e kT
 

 qV B ′E ′ − 1 −  qV B′C′ − 1 
  e kT

 e kT
 

where qb ≡ QB/QB0
5-Feb-04
(19)
(20)
HO #10: ELEN 251 - SGP BJT Model
Saha #12
Saturation Current ISS - Summary
I CT
I
= SS
qb
 qV B′E′   qV B′C ′ 
 e kT − 1 −  e kT − 1
(19)
• Eq. (19) is the generalized expression for current source at all
injection levels.
•
I SS ≡
q ADn ni2
xC 0
∫N
A
is a fundamental constant @ VBE = 0 = VBC.
( x) dx
xE 0
• qb ≡ QB/QB0 is the normalized majority charge in the neutral base
region and accurately models base width modulation:
– QB0 = majority carrier concentration @ V BE = 0 = VBC
– QB = majority carrier concentration under applied voltages.
• qb is expressed as bias-dependent measurable parameters in SGP.
5-Feb-04
HO #10: ELEN 251 - SGP BJT Model
Saha #13
Derivation of Base Charge, QB
• In order to evaluate qb, we first determine the components of QB.
• For the simplicity of QB analysis, we assume:
– npn-BJT is in saturation, that is, VB'E' > 0 and VB'C' > 0, then
♦
minority carriers are injected into the Base both from Emitter and
Collector
♦
from the charge neutrality, total increase in majority carriers in
Base = total increase in minority concentration
– superposition of carriers in different regions hold
♦
total excess majority carrier density = sum of the excess majority
carrier density due to each junction separately
∴
excess majority carrier concentration in base = excess carriers
due to forward voltage [VB'E' + VB'C']
− depletion approximation holds.
5-Feb-04
HO #10: ELEN 251 - SGP BJT Model
Saha #14
Components of Base Charge, QB
If
pF(x) = majority carrier concentration in base @ VB'C' = 0
pR(x) = majority carrier concentration in base @ VB'E' = 0
NA(x) = base doping concentration
QF
pF (x)
↓
↓
↑
N A (x )
QE
xjE xC(VB'E') xE0
5-Feb-04
p (x )
pR (x)
↓
QR
QB0
Base
Collector
Emitter
Then the excess majority carrier concentration in the base is given
by: p'(x) = [pF(x) − NA(x)] + [pR(x) − NA(x)]
(21)
QC
xC0 xC(VB'C' ) xjC
HO #10: ELEN 251 - SGP BJT Model
x
Saha #15
Components of Base Charge, QB
From (17), the total majority charge in the base is given by:
QB ≡
xC (VB′C′ )
∫ qAp( x)dx
xE (VB′E′ )
=
xC (VB′C′ )
∫ qAN
A
( x )dx +
xE (VB′E′ )
xC (V B′C′ )
∫ qAp′( x)dx
(22)
x E (VB′E′ )
equilibrium component excess component
The equilibrium component of QB can be split into three-components:
xC (VB′C ′ )
∫ qAN
x E (VB′E′ )
A
xE0
( x) dx =
∫ qAN
A
( x ) dx +
x E (VB′E′ )
∫ qAN
A
( x ) dx +
xE 0
QE
5-Feb-04
xC 0
xC ( VB′C ′ )
∫ qAN
A
( x ) dx
xC 0
QB0
HO #10: ELEN 251 - SGP BJT Model
QC
Saha #16
Components of Base Charge, QB
So that:
∫ qAN
A
( x) dx +
x E (VB′E′ )
xC 0
∫ qAN
A
( x ) dx +
xC (VB′C ′ )
∫ qAN
xE0
QE
∴ Q B = QE + QB 0 + QC +
xC (VB′C ′ )
A
( x ) dx +
xC 0
QB0
xC ( VB′C ′ )
∫ qAp′( x)dx
xE (VB′E′ )
QC
∫ qAp′( x)dx
(23)
Emitter
x E (VB′E′ )
QF
pF (x)
↓
↓
↑
N A (x )
QE
xjE xC(VB'E') xE0
5-Feb-04
p (x )
pR (x)
↓
QR
QB0
Base
Collector
QB =
xE 0
QC
xC0 xC(VB'C' ) xjC
HO #10: ELEN 251 - SGP BJT Model
x
Saha #17
Components of Base Charge, QB
From (21) and (23),
QB = QE + QB 0 + QC +
QF
xC (VB′C′ )
∫ qA[ p
F
( x) − N A ( x)]dx
xE (VB′E′ )
∫ qA[ p
R
( x) − N A ( x)]dx
xE (VB′E′ )
QR
Emitter
∴ Q B = QE + QB 0 + QC + QF + QR
QF
pF (x)
↓
↓
↑
N A (x )
QE
xjE xC(VB'E') xE0
5-Feb-04
p (x )
pR (x)
↓
QR
QB0
Base
(24)
Collector
+
xC (VB′C ′ )
QC
xC0 xC(VB'C' ) xjC
HO #10: ELEN 251 - SGP BJT Model
x
Saha #18
QF
pF (x)
↓
p (x )
pR (x)
↓
↓
↑
N A (x )
QE
xjE xC(VB'E') xE0
QR
QB0
Base
Collector
Emitter
Components of Base Charge, QB
QC
xC0 xC(VB'C' ) xjC
x
QB0 = charge in the neutral base under VB'E' = 0 = VB'C' .
QE = increase in QB under V B'E' and is only a mathematical entity.
QC = increase in Q B under V B'C' and is only a mathematical entity.
QF = excess majority charge in the biased-device with VB'C' = 0. It is
only a mathematical entity and important under high level injection.
QR = excess majority charge in the biased-device with VB'E' = 0. It is
only a mathematical entity and important under high level injection.
5-Feb-04
HO #10: ELEN 251 - SGP BJT Model
Saha #19
Components of Normalized Base Charge, qb
From Eq. (24), we get the normalized components of base charge:
QB
Q
Q
Q
Q
Q
= E + B0 + C + F + R
QB 0 QB 0 QB 0 QB 0 QB 0 QB 0
qb = qe + 1 + qc + q f + qr
∴ qb = 1 + qe + qc + q f + qr
Where, qe ≡
QE
QB 0
qc ≡
QC
QB 0
qf ≡
QF
QB 0
qr ≡
QR
QB 0
5-Feb-04
HO #10: ELEN 251 - SGP BJT Model
(25)
Saha #20
Evaluation of qb: Component qe
We defined, QE = increase in the majority charge due to VB'E'.
∴ QE =
VB′E ′
∫C
jE
(V )dV
(26)
0
1
and, qe =
QB 0
VB′E′
∫C
jE
(V )dV
(27)
0
Assume, C jE = constant ≡ C jE = average value of C jE
then, qe =
C jE VB′E ′
QB 0
≡
VB′E ′
VB
where VB = inverse Early voltage defined as :
QB 0
QB 0
VB ≡
=
VB′E′
C jE
1
C
(
V
)
dV
jE
VB′E′ ∫0
5-Feb-04
HO #10: ELEN 251 - SGP BJT Model
(28)
(29)
Saha #21
Evaluation of qe
• VB in Eq. (29) models base-width modulation due to the variation
of E-B junction depletion layer under VB'E'.
• VB due to VB'E' is the inverse of Early voltage due to VB'C'.
• In Eq (29), VB = constant ⇒ CjE = constant independent of VB'E'.
• Constant CjE is justified as:
since Q E << QB0
∴ qe << 1 and is not a dominant components of qb.
• VB = constant may cause large error in qe, especially, @ VB'E' > 0.
• The error in (29) due to qe for VB'E' > 0 can be eliminated by:
– integrating CjE over the bias range
– extracting VB from the slope of ln(IC) vs. qVB'E'/kT plot.
5-Feb-04
HO #10: ELEN 251 - SGP BJT Model
Saha #22
Evaluation of qe
• In order to determine the effect of qe accurately, we set:
qc = qr = qf = 0 ⇒ qb = 1 + qe,
• Then from (19) in the normal active region, we have:
I SS  qV B ′E ′ 
IC =
 e kT − 1

(1 + qe ) 
(30)
• Thus, the slope of IC vs. VB'E' plot is given by:
dI C
qI  kT C jE (VB′E ′ ) 

= C 1 −
dV B′E′ kT 
q (1 + qe )QB 0 
 kT C jE (VB′E ′ ) 
kT 1 dI C
d

(ln (I C )) = 1 −
=
q I C dVB′E′
q (1 + qe )QB 0 
 qV 

d  B′E ′ 
 kT 
(31)
5-Feb-04
HO #10: ELEN 251 - SGP BJT Model
Saha #23
Evaluation of qe
• From (31), the slope of ln(IC) vs. qVB'E'/kT plot is given by:
1 kT 1 dI C
≡
nE
q I C dVB′E ′
∴ nE =
VB′C′=0
 kT C jE (VB′E′ ) 

= 1 −
q (1 + qe )QB 0 

1
 kT C jE (VB′E ′ ) 
1 −

q (1 + qe )QB 0 

(32)
• When CjE = constant ≡ <CjE>, then
from (28), qe = VB'E'/B; and from (29), <CjE> = QB0/VB
therefore, from (32):
1
nE ≅
 kT

1
(33)
1 −

q (VB + VB′E′ ) 

5-Feb-04
HO #10: ELEN 251 - SGP BJT Model
Saha #24
Evaluation of qe: Summary
• For most transistors:
– qe = VB'E'/VB
– VB = QB0/<CjE> is the inverse of Early voltage = constant.
• VB = constant ⇒ CjE = constant independent of VB'E'.
• Constant CjE is justified:
since Q E << QB0
∴ qe << 1 and is not a dominant component of qb
• VB = constant may cause large error in qe, especially, @ VB'E' > 0.
• The error due to qe for VB'E' > 0 can be eliminated by:
– integrating CjE over the bias range
– extracting VB from the slope of ln(IC) vs. qVB'E'/kT plot.
5-Feb-04
HO #10: ELEN 251 - SGP BJT Model
Saha #25
Evaluation of qb: Component qc
• qc models base-width modulation and therefore, Early voltage by
changing depletion layer-width due to VB'C' at low current level.
• Using the procedure used for qe, we can show:
1
qc =
QB 0
V B′C′
∫C
jC
(V ) dV
(34)
0
Assume, C jC = constant ≡ C jC = average value of C jC
then, qc =
C jC VB′C ′
QB 0
≡
VB′C ′
VA
where VA = Early voltage defined by
QB 0
QB 0
VA ≡
=
V
C jC
1 B′C′
C
(
V
)
dV
jE
VB′C′ ∫0
5-Feb-04
HO #10: ELEN 251 - SGP BJT Model
(35)
(36)
Saha #26
Evaluation of qc
• VA in Eq. (36) models base-width modulation due to the variation
of C-B junction depletion layer under VB'C'.
• In Eq (36), VA = constant ⇒ CjC = constant independent of VB'C'.
• Constant CjC is justified in the normal active region when B-E
junction is reversed biased, that is, VC'B' < 1.
• VA = constant may cause large error in qc, when B-C junction is
forward biased, that is, the device is in:
– inverse region
– saturation region.
• A more accurate expression for qc is required for accurate
modeling of Early voltage in the:
– inverse region
– saturation region.
5-Feb-04
HO #10: ELEN 251 - SGP BJT Model
Saha #27
Effect of qc on Ic
• The effect of qc on BJT device characteristics in the normal active
region is finite output conductance g0.
• In order to determine g0, we set: qe = qr = qf = 0 ⇒ qb = 1 + qc,
• Then neglecting bulk-ohmic resistors, we get:
I SS  qV BE 
IC =
 e kT − 1

(1 + qc ) 
qV BE
I SS


=
 e kT − 1

 VBC  
1 +

VA 

• From (37), we can show:
g0 =
dI C
I (0)
≅ C
dVCE V = constant
VA
BE
5-Feb-04
HO #10: ELEN 251 - SGP BJT Model
(37)
(38)
Saha #28
Evaluation of qb: Component qf
• qf can be considered as the normalized excess carrier density in the
base with E-B bias VB'E' and models high level injection.
• From charge neutrality:
total excess majority carriers = total excess minority carriers.
Therefore, for an npn transistor with |VB'E' | > 0; VB'C' = 0

ni2 
QF = ∫ qA[ pF ( x) − N A ( x) ]dx = ∫ qA  nF ( x ) −
dx

N A ( x) 

xE
xE
xC
xC
(39)
• QF in (39) is shown as QB in EM2 model (HO #7) and is given by:
QF = QBEM2 = τBICC
(40)
τ B I CC
τ B I SS
∴q f =
=
QB 0
QB 0 qb
5-Feb-04
 qVkTB′E ′ − 1
e


HO #10: ELEN 251 - SGP BJT Model
(41)
Saha #29
Evaluation of qb: Component qr
• qr can be considered as the normalized excess carrier density in the
base with C-B bias VB'C' and models high level injection.
• From charge neutrality:
total excess majority carriers = total excess minority carriers.
Therefore, for an npn transistor with |VB'C'| > 0; VB'E' = 0

ni2 
QR = ∫ qA[ pR ( x ) − N A ( x )]dx = ∫ qAnR ( x ) −
dx
N A ( x) 

xE
xE
xC
xC
(42)
• QR in (42) is shown as QBR in EM2 model and is given by:
QR = QBREM2 = τBRIEC
(43)
τ BR I EC τ BR I SS
∴ qr =
=
QB 0
QB 0 q b
5-Feb-04
 qVkTB ′C ′ − 1
e


HO #10: ELEN 251 - SGP BJT Model
(44)
Saha #30
Solution for qb
• We know: qb = 1 + qe + qc + q f + qr
(25)
• Then substituting (28), (35), (41), (44) in (25) we get:
VB′E′ VB′C ′ τ Bdc
qb = 1 +
+
+
VB
V A QB 0
q1
τ BRdc
+
QB 0
I SS  qV B′E′ 
 e kT − 1

qb 
I SS  qV B′C′ 
 e kT − 1

qb 
(45)
q2/qb
Where
τBdc ≡ modified forward base transit time due to mobile charge in
the depletion region (i.e., without depletion approximation).
τBRdc ≡ modified reverse base transit time due to mobile charge in
the depletion region (i.e., without depletion approximation).
5-Feb-04
HO #10: ELEN 251 - SGP BJT Model
Saha #31
Solution for qb
We can simplify (45) to get:
q2
qb = q1 +
qb
(46)
Here
VB′E ′ VB′C′
q1 ≡ 1 +
+
VB
VA
(47)
qV B′C ′
qV B ′E ′



τ Bdc I SS  e kT − 1 + τ BRdc I SS  e kT − 1




q2 ≡
QB 0
(48)
Where
q1 in (47) models the base width modulation
q2 in (48) models the effect of high level injection.
5-Feb-04
HO #10: ELEN 251 - SGP BJT Model
Saha #32
Solution for qb
• From (45) we get,
qb2 − qbq1 − q2 = 0
(49)
2
q
q 
∴ qb = 1 +  1  + q2
2
2
(50)
since qb > 0, (50) is obtained talking the positive solution only.
• Equation (50):
– offers solution for IC
– defines injection level
♦
if q 2 << q12/4, q b = q1, then q f = qr = 0 ⇒ low level injection
♦
if q 2 >> q12/4
qb = (q1)1/2
∴
5-Feb-04
⇒ high level injection
HO #10: ELEN 251 - SGP BJT Model
(51)
(52)
Saha #33
Solution for qb: High Level Injection
For simplicity, we assume VB'C' = 0 (i.e., qr = 0). Then from (48)
and (52), for high level injection in the forward active region:
qb = q2 ≅
=
τ Bdc I SS
QB 0
τ Bdc I SS
QB 0
e
qVB′E′
kT
e
qVB′E′
2kT
(53)
∴ Substituting for qb in (19), we get for high level injection @ VB'C'
= 0 and V B'E' >> kT/q:
qV B′E ′

I SS  e kT − 1
B′E′
QB 0 I SS qV2kT


(54)
I C ≅ I CT =
≅
e
qVB′E ′
τ Bdc
τ Bdc I SS 2 kT
e
QB 0
5-Feb-04
HO #10: ELEN 251 - SGP BJT Model
Saha #34
High Level Injection: Knee Current, IK
• For low level injection, if we assume, qe = qc = 0, then qb = 0:
• From (19), we get for low level injection @ V B'C' = 0 and VB'E' >>
kT/q:
qV B′E′
(55)
I C ( low−level ) ≅ I SS e kT
• The intersection of high current and low current asymptote is
given by (IK,VK) where IC(high-level) = IC(low-level).
• Therefore, from (54) and (55):
QB 0 I SS
IK =
τ Bdc
I K = I SS e
K
 qV
 e 2 kT






qVK
kT
5-Feb-04
(56)
(57)
HO #10: ELEN 251 - SGP BJT Model
Saha #35
High Level Injection: Knee Current, IK
• From (56) and (57), we get:
QB 0
IK =
τ Bdc
ln (I K )
• Similarly, for inverse
region:
I KR
QB 0
=
τ BRdc
slope = 1/2
ln(IC)
(58)
(59)
• Model parameters: (VA, VB,
ISS, IK, IKR) are extracted
from
– ln(IC) vs. V B'E' plot
– ln(IE) vs. VB'C' plot.
5-Feb-04
slope = 1
VBC = 0
qVK/kT
HO #10: ELEN 251 - SGP BJT Model
qVB'E'/kT
Saha #36
SGP Model: Summary
I CT
I
= SS
qb
 qV B′E′   qV B′C′ 
 e kT − 1 −  e kT − 1
where
(19)
2
q1
 q1 
∴ qb = +   + q2
2
2
V
V
q1 ≡1 + B′E′ + B′C ′
VB
VA
(50)
(47)
From (58) and (59)
q2 ≡
τ Bdc
qV B′E′
τ BRdc
qV B ′C ′



I SS  e kT − 1 +
I SS  e kT − 1

 QB 0


QB 0
I SS  qV B′E′  I SS  qV B′C ′ 
=
 e kT − 1 +
 e kT − 1
 I KR 

IK 
5-Feb-04
HO #10: ELEN 251 - SGP BJT Model
(60)
Saha #37
SGP Model: Summary
• q1 models base-width modulation
• q2 models high level injection
– the condition for high level injection:
2
q1
q2 ≥
4
• The model parameters: (VA, VB, ISS, IK, IKR) are extracted from
– ln(IC) vs. V B'E' plot in the normal mode of BJT operation
– ln(IE) vs. VB'C' plot in the inverse mode of BJT operation
– IC vs. VCE characteristics in the normal mode of BJT operation
– IE vs. V EC characteristics in the inverse mode of BJT operation.
• A parameter, B is used to model base widening (base push-out)
effect at high currents.
5-Feb-04
HO #10: ELEN 251 - SGP BJT Model
Saha #38