401
Bipolar Junction Transistor Compact Models
where:
X E0 and X C0 are the locations inside the neutral base region at the edge of
the EB- and CB-junction depletion regions, respectively without the
applied bias
Thus, I SS defined in Equation 11.66 is a bias-independent fundamental constant. Since negative sign indicates the direction of collector current flowing
out of the device terminal, we have omitted the negative sign in the above
Equation 11.65. Now, Equation 11.63 can be expressed as
I
qA D n
p x dx
qA
N x dx
qA
N x dx
CT
E n i
x
x
E
a
x
x
E
a
x
x
E
C
E
C
E
C
= ∫
∫
∫
2
0
0
0
0
( )
.
( )
( )
×
−
−
−
exp
e xp
V
v
V
v
BE
kT
BC
kT
1
1
= ∫
∫
qA D n
N x dx
qA
N x dx
qA
E n i
a
x
x
E
a
x
x
E
E
C
E
C
2
0
0
0
0
( )
.
( )
p p x dx
V
v
V
v
x
x
BE
kT
BC
kT
E
C ( )
exp
e xp
∫
×
−
−
1
−
1
(11.67)
If we define Q B and Q B0 as the neutral base charges with and without the
applied biases, respectively, then we can show
Q
qA
N x dx
Q qA
N x dx
B
E
a
x
x
B
E
a
x
x V
E
C
E VBE
C BC
0
0
0
=
=
∫
∫
( )
( )
(
)
(
)
(11.68)
Now, using Equation 11.68 in Equation 11.67, we can show that the expression
for current source for an npn-BJT is given by
I
I
Q
Q
V
v
V
v
CT
SS
B
B
BE
kT
BC
kT
=
−
−
−
0
1
1
exp
e xp
=
−
−
−
I
q
V
v
V
v
SS
b
BE
kT
BC
kT
exp
e xp
1
1
1
(11.69)
Bipolar Junction Transistor Compact Models
where:
X E0 and X C0 are the locations inside the neutral base region at the edge of
the EB- and CB-junction depletion regions, respectively without the
applied bias
Thus, I SS defined in Equation 11.66 is a bias-independent fundamental constant. Since negative sign indicates the direction of collector current flowing
out of the device terminal, we have omitted the negative sign in the above
Equation 11.65. Now, Equation 11.63 can be expressed as
I
qA D n
p x dx
qA
N x dx
qA
N x dx
CT
E n i
x
x
E
a
x
x
E
a
x
x
E
C
E
C
E
C
= ∫
∫
∫
2
0
0
0
0
( )
.
( )
( )
×
−
−
−
exp
e xp
V
v
V
v
BE
kT
BC
kT
1
1
= ∫
∫
qA D n
N x dx
qA
N x dx
qA
E n i
a
x
x
E
a
x
x
E
E
C
E
C
2
0
0
0
0
( )
.
( )
p p x dx
V
v
V
v
x
x
BE
kT
BC
kT
E
C ( )
exp
e xp
∫
×
−
−
1
−
1
(11.67)
If we define Q B and Q B0 as the neutral base charges with and without the
applied biases, respectively, then we can show
Q
qA
N x dx
Q qA
N x dx
B
E
a
x
x
B
E
a
x
x V
E
C
E VBE
C BC
0
0
0
=
=
∫
∫
( )
( )
(
)
(
)
(11.68)
Now, using Equation 11.68 in Equation 11.67, we can show that the expression
for current source for an npn-BJT is given by
I
I
Q
Q
V
v
V
v
CT
SS
B
B
BE
kT
BC
kT
=
−
−
−
0
1
1
exp
e xp
=
−
−
−
I
q
V
v
V
v
SS
b
BE
kT
BC
kT
exp
e xp
1
1
1
(11.69)