C h a p t e r B
I P O
L A
R
J U
P r o f e s s o r
N
C
T I O
N
H i s h a m
F i t z p a t r i c k
7 T
Z .
R
M
A
N
S I S T
O
R
S
a s s o u d
C e n t e r, R o o m
3 5 2 1
m a s s o u d @ e e . d u k e . e d u
E
C
E
2 1 6
C h a p t e r
7
\u2013 B
i p
o l a r
7 . 1
C h a p t e r
7 \ u 2 0 1 3 B I P O J LU AN R C
T I O
N
T
R
A
N
S I S T
O
R
S
7 . 1 . I n t r o d u c t i o n
E
C
E
2 1 6
7 . 1 0 .
Te m p e r a t u r e
E \ u f b 0 0 e c t s
7 . 1 1 .
F r e q u e n c y
7 . 1 3 .
B J T
B r e a k d o w n
7 . 1 4 .
B J T
S P I C E
7 . 1 5 .
S u m m a r y
E \ u f b 0 0 e c t s
M o d e l
C h a p t e r
7
\u2013 B
i p
o l a r
7 . 2
7 . 1 .
E
C
E
2 1 6
C h a p t e r
7
I n t r o d u c t i o n
\u2013 B
i p
o l a r
7 . 3
7 . 1 .
I n t r o d u c t i o n
¡
¢
E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
7 . 4
7 . 2 .
I n t e g r a t e d - Ci r c u i t
BJ T
S t r u c t u r e s
J u n c t i o n I s o l a t i o n
¡
¦
¢
£¥
§©
$
¡
$
%
¡
&
&
¦
¨
!
#
¡"
¡"
!
!
¡
(
¨
¨
¡
$
¦
!
§
¡
¨
¦
¨
§
E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
7 . 5
7 . 2 .
I n t e g r a t e d - Ci r c u i t
J u n c t i o n - I s o l a t e dB i p o l a r
BJ T
S t r u c t u r e s
J u n c t i o nT r a n s i s t o r
¡
¢
¦
£
£¤
§¨
¢
E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
7 . 6 %
&
¤
7 . 2 .
I n t e g r a t e d - Ci r c u i t
T r e n c h - I s o l a t e d B i p o l a r
BJ T
S t r u c t u r e s
J u n c t i o n T r a n s i s t o r
¦
£¥
¨
§©
¤
¦
§©
¡
¤
E
C
E
2 1 6
C h a p t e r
7
–
B
i p
¤
o l a r
7 . 7
%
&
¨
&
£
7 . 2 .
I n t e g r a t e d - Ci r c u i t
BJ T
S t r u c t u r e s
5
$
"6
¡
¢
¦
£
£¤
§¨
¤
¤
D
$
"C
A
$
"6
@
$
"6
E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
7 . 8
7 . 2 .
N
E
C
E
2 1 6
P
I n t e g r a t e d - Ci r c u i t
N
BJ T
P
C h a p t e r
7
–
B
i p
o l a r
N
S t r u c t u r e s
P
7 . 9
E n e r g y - B a n d
D i a g r a m
@A
£
G
¤
¤B
¢
H
B
I
DF
E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
7 . 1 0
¡
¢
¨
£
¦
£¤
©
¤
¦
§
E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
7 . 1 1
¦
§
E p
B
+
C
n
p
+
d ,B
−
−
a ,C
−
−
a ,E
x
E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
7 . 1 2
7 .4 .
B J T
B a s e / E m i t t e r
J u n c t i o n
R e v e r s e - b i a s e d
B a s e / C o l l e c t o r J u n c t i o n R e v e r s e - b i a s e d
C u t-off
R e v e r s e - b i a s e d
F o r w a r d - A c t i v e
R e v e r s e - b i a s e d
R e v e r s e - A c t i v e
E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
7 . 1 3
7 .4 .
E
C
E
2 1 6
B J T
C h a p t e r
7
–
B
i p
o l a r
7 . 1 4
7 .5 .
P
N
P
B
J T
E
I
B
C
I
E
p
+
n
C
p
R I
E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
L
B
7 . 1 5
7 .5 .
P
N
P
B
J T
E
I
B
C
I
E
p
+
n
p
I
E
C
E
2 1 6
C
B
C h a p t e r
7
–
B
i p
o l a r
7 . 1 6
7 .5 .
P
N
P
B
J T
V a r ia b le
E m i t t e r p
B uilt-in
E
C
E
2 1 6
R e g i o n
+
R e g i o n n
Vo l t a g e s
V
C h a p t e r
B a s e
7
–
B
i p
b i,E /B
o l a r
p
V
b i,C /B
7 . 1 7
7 .5 .
P
N
P
B
J T
V a r ia b le
E m i t t e r
D o p a n t C o n c e n t r a t i o n
N
C
E
2 1 6
C h a p t e r
−
N −
n
a ,E −
◦
a ,E
M i n o r i t y D i ff u s i o n L e n g t h
E
B a s e
a ,E
◦
p n
R e g i o n
7
–
p
R e g i o n
+
N
d ,B +
◦
B
p
d ,B +
◦
B
d ,B
n
−
a ,C −
◦
a ,C −
◦
a ,C
µ
n ,E
µ
p ,B
µ
n ,C
D
n ,E
D
p ,B
D
n ,C
L
n ,E
L
p ,B
L
n ,C
τ
n ,E
τ
p ,B
τ
n ,C
B
i p
o l a r
7 . 1 8
7 .5 .
P
N
P
B
J T
E n e r g y - B a n d
@A
D i a g r a m
£
G
¤
Q
¤B
¢
H
B
C
¡
BR
¤
¡
P
I
DF
D
S
T
UV
h
Y
W
ac
`
Y
S
T
X
h
V
S
T
b
b
Y
W
Y
a
f
e
d
V
g
E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
7 . 1 9
7 .5 .
P
N
P
B
J T
¡
¢
¨
£
¦
£¤
©
¤
¦
§
E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
7 . 2 0
¦
§
7 .5 .
P
N
B
P
J T
E p
B
C
n
p
+
n p n
−
E
C
E
2 1 6
W
E
◦
◦
C
◦
B
E
0
W
C h a p t e r
7
–
B
i p
o l a r
B
7 . 2 1
7 .5 .
P
N
P
B
J T
E
p
B
+
n
C
p
→ →
E
C
E
2 1 6
I
I
C
E
C h a p t e r
7
–
B
i p
o l a r
7 . 2 2
7 .5 .
P
N
P
B
J T
E
p
+
B
C
n
p
I p ,C
I p ,C
I
I r e c ,B I
s c g ,C /B
I n ,C
s c r ,E /B I n ,E
I
E
C
E
2 1 6
C h a p t e r
7
I
–
B
I
i p
o l a r
I
I
7 . 2 3
7 .5 .
P
N
P
B
J T
E
p
+
B
C
n
p
I p ,C
I p ,C I p ,E
I
I r e c ,B I
s c g ,C /B
I n ,C
s c r ,E /B I n ,E
I
E
C
E
2 1 6
C h a p t e r
7
I
–
I
B
i p
o l a r
I
I
7 . 2 4
7 .5 .
P
N
P
B
J T
C u r r e n t I
p ,E
I
n ,E
V o l t a g e e m i t t e r
E l e c t r o n
d i ff u s i o n
c u r r e n t
i n j e c t e d
D e p e n d e n c e
i n t o
f r o bm a s e i n t o
e m i t t e r I
s c r , E /B
I
r e c ,B
I
I
p ,C
s c g ,C /B
I
P o r t i o n
C
p ,E
i n j e c t e d
f r o m
C o l l e c t o r - b a s e s p a c e - c h a r g e g e n e r a t i o n
c u r r e n t
n ,C
o f
E
o f
E
2 1 6
e l e c t r o n s
f r o mc o l l e c t o r
C h a p t e r
7
–
B
t o
i p
o l a r
b a s e
a n d
d u e
t o
t h e
7 . 2 5
7 .5 .
P
N
B
P
J T
I
,
I
,
I
,
B
=
I
p ,E
=
I
p ,C
−
I
,
p ,C
−
I
,
p ,C
.
E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
7 . 2 6
7 .5 .
P
N
P
B
J T
α
≡
γ
α
E
C
E
2 1 6
≡
I
p ,C
I
=
p ,C
I
p ,E
≡
I I
I
I
I
=
I
p ,E
I
p ,E
I
I
=
p ,E
7
–
B
p ,E
.
p ,E
.
p ,E
p ,C
C h a p t e r
I
p ,E
I
=
r e c ,B
i p
o l a r
I I
p ,E
p ,E
·
I
p ,C
I
p ,E
α
.
7 . 2 7
7 .5 .
E
C
E
2 1 6
P
N
P
B
J T
C h a p t e r
7
–
B
i p
o l a r
7 . 2 8
7 .5 .
P
N
P
B
J T
is
g iv e n
b y
I
, , ,
( s o
E
t h a t
C
E
2 1 6
=
0 ) .
C h a p t e r
7
–
B
i p
o l a r
7 . 2 9
7 .5 .
P
N
B
P
J T
¢
©
¤¦
¢¨
¢
£
¢
¤
!
E
p
+
B
C
n
p
£
¡
¢
W
0
E
C
E
2 1 6
W
d ,B /E
W
C h a p t e r
d ,B /C
x
B
7
–
B
i p
o l a r
7 . 3 0
7 .5 .
L
P
N
P
B
J T
p ,B
a t
o r
W
d ,B /E
,
W
d ,B /C
,
W
d ,B /E
b a s e -
t h a t
W
,
B
◦
B
E
t h e
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
k
B
T
,
7 . 3 1
7 .5 .
P
N
B
P
p
J T
◦
◦
B
B
k
B
T
x k x
◦
B
k
B
T
E
C
E
2 1 6
B
B
x k
B
T
7
W
B
x k
B
T
k
T
W
B
form
,
, B
.
W
C h a p t e r
T
the
◦
B
◦
W
◦
B
B
in
B
–
B
i p
o l a r
7 . 3 2
7 .5 .
P
N
P
B
J T
W
B
W
B
0
p
x
◦
B
k
0
W
W
B
2 W
B
2
W
B
k
p
p
C
E
2 1 6
C h a p t e r
T
B
d x
q
A
p
B
k
B
◦
d x
B
,
0
T
◦
◦
B
B
k
B
T
q A k
–
−
B
◦
B
B
7
W
B W
x
2
E
W
◦
0
+
T
B
p
=
B
B
i p
o l a r
B
T
W
B +
d ,B
W
n
B
.
2
k
B
T
.
7 . 3 3
7 .5 .
P
N
P
B
J T
I
=
p ,E
, d , B /E
p
n
= W
I
n ,E
B
N
◦
B
k
B
−
T
1 W
, B
2
+
k
d ,B
B
.
T
=
, d , E
n
n
= W
E
C
E
2 1 6
N
1
◦
E
a ,E
7
B
T
k
B
T
W
,
2
−
C h a p t e r
k
–
B
i p
o l a r
.
7 . 3 4
7 .5 .
P
N
P
B
J T
1
i n
s t e a d y
a n d
t h e
s t a t e .
=
c o n t i n u i t y
e q u a t i o n
b e c o m e s
−
I n t e g r a t i o n o f t h i s
τ
e q u a t i o n y i e l d s B
)
W
q
−
τ J
p , B
p ,B
B
0
( 0 )
w h i c h W
I
r e c ,B
τ J
E
C
E
2 1 6
. p ,B
p , C
J
0
t h e n
g i v e n
b y
B
p p ,B
i s
x
◦
B
k
B
T
W
d x
.
B
p , E
C h a p t e r
7
–
B
i p
o l a r
7 . 3 5
0
7 .5 .
P
N
P
B
J T
I n t e g r a t i o n g i v e s
I
,
r e c ,B
=
=
τ
p
B
q A
E
C
E
2 1 6
Q τ
k
p ,B
W
B
N
=
x
◦
p ,B
B
T
B
2
W
,
0
2
n +
k
d ,B
B
T
,
.
p ,B
C h a p t e r
7
–
B
i p
o l a r
7 . 3 6
7 .5 .
P
N
B
P
I
J T
,
p ,C
n
= W
i s
t h e
r e v e r s e
B
N
s a t u r a t i o n
2
+
k
d ,B
c u r r e n t
I
B
−
T
g i v e n
q A
n
B
N
2
+
k
d ,B
B
W
N
−
.
a ,C
I
b y
,
p ,E
I
n
= W
E
.
2
g iv e n
fo r
T
b y n
n ,C
W
C
E
2 1 6
C h a p t e r
7
–
B
B
N
i p
o l a r
+
d ,B
2
k
B
T
.
7 . 3 7
7 .5 .
o r
P
N
P
B
J T
t h a t I
q A
W
B
n
2
+
k
d ,B
Q
C
E
2 1 6
C h a p t e r
T
W
W
7
–
B
i p
2
,
B
p , B
Q
I
E
B
o l a r
2
p ,B
,
B
7 . 3 8
7 .5 .
F
i s
p ,B
P
B
J T
w r i tt e n
a s
N
P
x
◦
B
I
I
E
C
E
2 1 6
k
B
T
W
x
◦
p ,B
B
k
=
p ,B
C h a p t e r
7
–
B
i p
o l a r
B
T
W
p W
B
. B
, B
◦
B
k
B
T
.
7 . 3 9
7 .5 .
P
N
e x p r e s s e d
P
B
J T
a s D W
W
B
W
W
B
= 0
C
E
2 1 6
0
C h a p t e r
7
=
x
=
E
p ,B
–
B
i p
o l a r
D
p ,B
.
B
B
W D
2
B
.
p ,B
7 . 4 0
7 .5 .
G
u m
P
m
N
P
e l
N
B
u m
J T
b e r
W
G
B
≡
N
+
0
+
d ,B
n
I W
B
N
2
n
+
k
d ,B
B
T
G
2
k
B
T
.
i nh i g h - p e r f o r m a n c e
E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
7 . 4 1
7 .5 .
P
N
P
B
γ
≡
=
J T
I I
p ,E
1 I
n ,E
I
p ,E
+
D D
n ,E
p ,B
N N
D D
E
2 1 6
, s c r , E /B
I
p ,E
+
d ,B −
a ,E
W
N
B
+
W
+
W
d ,B
, B
W
,E B
τ
p ,B
1
=
C
I
1
=
E
,
p ,E
n ,E
p ,B
N N
+
d ,B −
a ,E
W
N
B
+
W
C h a p t e r
+
d ,B
, W
B
W 2
,E B
−
p ,B
7
–
B
i p
o l a r
7 . 4 2
7 .5 .
P
N
P
B
−
a ,E
s o
J T
N
+
t h a t γ i n c r e a s e s , t h e
is
I
α
g iv e n
r e c ,B
I
b y
,
p ,E
q A
W
B
N
n
2
+
d ,B
N
+
d ,B
W
B
n
2
,
2
W
B
.
L
E
C
E
2 1 6
C h a p t e r
7
–
e ff e c t
B
i p
o l a r
p ,B
7 . 4 3
o f
7 .5 .
¡
P
N
P
B
J T
¢
¦
£
¥
£¤
§¨
¤
¤
£
©
=
0 .
¥
"
#%
&
0
)
E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
7 . 4 4
7 .5 .
¡
P
N
P
B
J T
¢
¦
£
¥
£¤
§¨
¤
¤
£
©
a n d
&
E
C
E
2 1 6
r e v e r s e - b i a s e d
c o l l e c t o r - b a s e
ju n c t io n .
¥
"
a
#%
)
C h a p t e r
7
–
B
i p
o l a r
7 . 4 5
7 .5 .
¡
P
N
P
¢
B
J T
¦
£
£¤
¥
§¨
¤
¤
£
©
i s
k e p t
c o n s t a n t .
)
&
¢0
¥
¤
"
E
C
E
2 1 6
§¨
¤
¨
#
C h a p t e r
7
–
B
i p
o l a r
7 . 4 6
7 .5 .
¡
P
N
P
B
J T
¢
¦
£
¥
£¤
§¨
¤
¤
£
©
=
0 .
¥
"
&
E
C
E
2 1 6
#%
)
C h a p t e r
7
–
B
i p
o l a r
&
7 . 4 7
)
1
3
7 .5 .
¡
P
N
P
B
J T
¢
¦
£
¥
£¤
§¨
¤
¤
£
©
r e g io n w i t h
b o t h
j u n c t i o n s
¥
"
#%
&
0
')
¥
"
#%
&
0
'2
E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
7 . 4 8
7 .5 .
¡
P
N
P
¢
B
J T
¦
£
£¤
¥
§¨
¤
¤
£
©
E
C
E
2 1 6
C h a p t e r
¥
7
–
B
i p
o l a r
7 . 4 9
7 .5 .
P
N
P
B
J T
in
a
P
N
P
a n d
E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
t h e
7 . 5 0
7 .5 .
P
N
P
B
J T
in
I
I
a
P
N
P
B
.
B
o u t p u t c u r r e n t w r i t t e n
a s I
E
C
E
2 1 6
.
C h a p t e r
7
–
B
i p
o l a r
7 . 5 1
7 .5 .
P
N
P
B
J T
in
I
a
N
P
.
I o r
P
,
t h a t ,
I
I
α
=
I
I
≡
=
I
2 1 6
C h a p t e r
7
–
α
.
B
≡
E
,
a s
β
C
+
B
d e fi n e d
E
B
B
i p
.
o l a r
7 . 5 2
7 .5 .
P
N
P
B
J T
in
a
P
N
P
c a n
b e
m u c h =
o r
t h e
c o l l e c t o r
c u r r e n t
i n d i c a t e s
t h a t
a t
s m a l l
β
E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
7 . 5 3
v a l u e s
7 .5 .
E
C
E
2 1 6
P
N
P
B
J T
C h a p t e r
7
–
B
i p
o l a r
7 . 5 4
7 .6 .
B J T
S t a t i c
T h e
=
E
C
E
2 1 6
c u r r e n t s
0 .
C h a p t e r
7
–
B
i p
o l a r
7 . 5 5
7 .6 .
B J T
S t a t i c
I
k
B
T
,
i s
t h e
b a s e - t o -
i s
t h e
b a s e - t o -
e m i t t e r v o l t a g e .
i s g i v e n
f o r t h e b a s e - c o l l e c t o r j u n c t i o n
I
k
B
T
a s
,
c o l l e c t o r v o l t a g e .
E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
7 . 5 6
7 .6 .
B J T
S t a t i c
th e
I
e x p r e s s e d
i n
t e r m s
I
t h a t d u e t t o
T h e
b a s e
t h e b a s e - c o l l e c t o r j u n c t i o n .
c u r r e n t
i s
g i v e n
I
E
C
E
2 1 6
b y
B
C h a p t e r
7
–
B
i p
o l a r
7 . 5 7
7 .6 .
B J T
S t a t i c
¡
©
§
E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
7 . 5 8
¡
©
7 .6 .
C o n s i d e r
B J T
S t a t i c
a n
w h e r e D
≡ W
W
E
C
E
2 1 6
C h a p t e r
7
–
N
B
D
≡
B
i p
o l a r
n ,B
2
,
−
a ,B
p ,E
N
n
+
n
2
.
d ,E
7 . 5 9
7 .6 .
B J T
S t a t i c
w h e r e D
≡ W
W
E
C
E
2 1 6
C h a p t e r
7
–
N
B
D
≡
B
i p
o l a r
n ,B
2
,
−
a ,B
p ,C
N
n
+
n
2
.
d ,C
7 . 6 0
7 .6 .
B J T
S t a t i c
α
=
α
α
=
W
α
h e n
α
E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
7 . 6 1
7 .6 .
S P I C E
B J T
E b e r s - M
S t a t i c
o l l
M
o d e l
I
,
k
k
B
E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
B
T
,
T
,
T
k
k
B
B
,
T
.
7 . 6 2
7 .6 .
B J T
S t a t i c
I
−
=
I
I
B
=
=
E
C
E
2 1 6
,
α
,
α
+
α 1
+
α
C h a p t e r
β
≡
β
≡
7
–
B
i p
α
α
o l a r
α 1 α
,
.
,
.
7 . 6 3
7 .6 .
B J T
S t a t i c
¡
¤
¢
¥
¦
E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
7 . 6 4
¡
©
7 .6 .
B J T
S t a t i c
I
−
,
α
−
α
,
,
α ,
β
I
=
,
α
+
α
,
α
β E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
,
,
7 . 6 5
7 .6 .
B J T
S t a t i c
k
T h e
t w o
d i o d e
c u r r e n t s
β
C
E
2 1 6
T
−
k
B
T
.
b e c o m e
β
E
B
=
=
C h a p t e r
I
S
β
I
k
B
T
k
B
T
S
β
7
–
B
i p
o l a r
,
,
7 . 6 6
7 .6 .
B J T
S t a t i c
¡
¢
¡
¤
¢
¢
¦
¡
©
¡
¢
E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
7 . 6 7
¡
¢
¢
7 .6 .
E
C
E
B J T
S t a t i c
2 .
P u n c h t h r o u g h
7 .
S e r i e s
2 1 6
R e s i s t a n c e
C h a p t e r
7
–
B
i p
o l a r
7 . 6 8
7 .7 .
B J T
D y n a m
ic
i n
+
E
C
E
2 1 6
t h e
τ
d e p l e t i o n
+
+
p ,N
C h a p t e r
7
–
B
i p
r e g i o n .
o l a r
T h e
τ
r e l a t i o n s h i p
+
b e t w e e n
t h e
.
n ,P
7 . 6 9
t o t a l
7 .7 .
B J T
D y n a m
τ
ic
1
−
1
+
τ
+
Q τ
+
−
+
1 τ
+
1
+
+
+
−
,
,
,
w h e r e
E
C
E
2 1 6
k
B
T
k
B
T
C h a p t e r
,
,
7
–
B
i p
o l a r
7 . 7 0
7 .8 .
i
B J T
M
o d e l
B
W e
r e c o g n i z e
Q
Q
Q
Q
t h a t , ,
i
B
i E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
7 . 7 1
7 .8 .
a n d
r e w r i t e
t h e
a b o v e
i
i
b
c
B J T
M
e q u a t i o n s
o d e l
a s
= Q
Q
Q
Q
=
w h e r e g
i n p u t c o n d u c t a n c e
≡ Q
g
≡
r e v e r s e
t r a n s c o n d u c t a n c e
f o r w a r d
t r a n s c o n d u c t a n c e
Q
g
m
≡ Q
g
o
o u t p u tt r a n s c o n d u c t a n c e
≡ Q
E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
7 . 7 2
7 .8 .
B J T
M
I
g
m
k
k
Q
g
T
B
k
T h e o u t p u t c o n d u c t a n c e
Q
i s g i v e n
C
E
2 1 6
I
=
≡
C h a p t e r
g
m
1
≡
β
r
.
.
b y
Q
E
I
=
T
=
Q
o
B
=
≡
g
.
T
q
=
≡
B
o d e l
7
–
B
i p
o l a r
=
≡
1 r
.
o
7 . 7 3
7 .8 .
B J T
+
N
d ,E
C
M
−
+
−
d ,E
t h e
j u n c t i o n
i s
V
a ,B
r e v e r s e - b a i s e d .
a ,B
I t
V
)
i s
b i , B
g i v e n
−
a ,B
C
N
−
a ,B
c h a n g e
i n t h e
b a s e
w i d t h . T h e v a r i a t i o n
b i , B
o d e l
/ E
k
/ E
B
T
k
B
T
.
b y
+
V
d ,C +
d ,C
)
i n b a s e
V
b i , B
b i , B
/ C
.
/ C
w i d t h r e s u l t s
i n a
c h a n g e
i nth e
r
r
E
C
E
2 1 6
=
C h a p t e r
=
7
–
B
r
i p
o l a r
o
.
7 . 7 4
7 .8 .
B J T
M
N
o d e l
P
N
¡
£
¤
¤
¦
¡¢
¥
¡¢
©
§
¥
E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
7 . 7 5
7 .8 .
B J T
M
o d e l
N
P
N
B ip o la r
¡
¥
£
£
£
¦
¤
¥
§
£
£
¡
¨
¨
¡
¦
¨
§
¨
©
E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
7 . 7 6
7 .8 .
C u t o ff
B J T
M
F r e q u e n c y
a n d
E
C
E
2 1 6
o d e l
C h a p t e r
7
–
B
i p
o l a r
c o n n e c t s
µ
7 . 7 7
7 .8 .
C u t o ff
a n d
B J T
M
o d e l
F r e q u e n c y
t h e o u t p u t c u r r e n t i s
π
g
=
m
.
π
E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
7 . 7 8
7 .8 .
C u t o ff
is
B J T
M
o d e l
F r e q u e n c y
g iv e n
b y f
g
=
m
.
C
1
f
.
2
D
f
n ,B 2
.
B
E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
7 . 7 9
7 .8 .
M
B J T
M
o d e l
a x im u m
R w h ich
f
m
a
=
g
m
=
f
.
B o t h
E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
7 . 8 0
E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
7 . 8 1
T h e
E
C
E
2 1 6
a r e a
C h a p t e r
7
p a r a m e t e r
–
B
i p
o l a r
s p e c i fi e s
h o w
7 . 8 2
7 . 1 0 .
E
C
E
2 1 6
T e m
C h a p t e r
7
–
p e r a t u r e
B
i p
o l a r
E ff e c t s
7 . 8 5
7 . 1 1 .
E
C
E
2 1 6
C h a p t e r
F r e q u e n c y
7
–
B
i p
o l a r
E ff e c t s
7 . 8 6
E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
7 . 8 7
7 .1 3 .
E
C
E
2 1 6
C h a p t e r
B J T
7
–
B
i p
B
o l a r
r e a k d o w
n
7 . 8 8
E
C
E
2 1 6
C h a p t e r
7
–
B
i p
o l a r
7 . 8 9
