Ch 11. BJT static characteristics
: to modeling the steady-state response of the BJT.
1. Ideal transistor analysis Basic assumptions
(a) A pnp BJT with nondegenerate uniformly doped emitter, base, and collector regions and E-B and C-B junctions are step-junctions.
(b) Under operation of steady-state conditions.
(c) One-dimensional (d) Low-level injection
(e) Drift, diffusion, thermal recombination-generation. GL=0.
(f) Thermal recombination-generation is negligible throughout the E-B and C-B depletion regions.
(g) The quasineutral widths of the emitter and collector are much greater than the minority diffusion lengths in these regions.
nE0=ni2/NE pB0=ni2/NB nC0=ni2/NC
NE=NAE NB=NDB NC=NAC
DE=DN DB=DP DC=DN
τE=τN τB=τP τC=τN
LE=LN LB=LP LC=LN
n =n n =p n =n
2. BJT parameters
) 1 (
) 0 (
0 ) (
. . 0
region Collector
) (
) 4 . 11 ( ), 1 (
) (
) 4 . 11 ( ), 1 (
) 0 ( . . 0
region Base
) (
) 1 (
) 0 (
0 ) (
. . 0
region Emitter
) (
/ 0
2 2
/ 0
/ 0
2 2
/ 0
2 2
kT qV C C
C
C C C
C
kT qV B B
kT qV B B
B B B
B
kT qV E E
E
E E E
E
CB CB EB
EB
e n x
n x n
C B
n x
d n D d
c
b e
p W p
a e
p p
C B
p dx
p D d
b
e n x
n x n
C B
n x
d n D d
a
C E B
Cn Cp C
En Ep E
dc dc dc
T dc
Ep Cp T
En Ep
Ep
x C C
Cn
W x B B
Cp
x B B
Ep
x E E
En
I I I
I I I
I I I
I I
I I
I
x d
n qAD d
I
dx p qAD d
I
dx p qAD d
I
x x x
d n qAD d
I
1 (6.4) From
0 0
0
(11.22) )
1 1 (
) 1 (
) 1 (
)
(11.20) )
1 1 (
) 1 (
(11.19) )
1 (
)
solution region
llector Emitter/co
) (
/ 0
/ 0
0
/ /
0
/ 0
/ 0
0
/ /
0
kT qV C C
C C
kT qV C C x
C C
Cn
L x kT
qV C C
kT qV E E
E E
kT qV E E x
E E
En
L x kT
qV E E
CB CB
C CB
EB EB
E EB
e L n
qAD e L
n x qAD
d n qAD d
I
e e
n x Δn (
e L n
qAD e L
n x qAD
d n qAD d
I
e e
n x
Δn ( a
3. Ideal transistor
(b) Base region solution
(11.29) )
1 )(
/ sinh(
) cosh(
) 1 )(
/ sinh(
1
(11.28) )
1 )(
/ sinh(
) 1 1 ) (
/ sinh(
) / cosh(
cosh 2 2 ,
sinh (11.26)
) / sinh(
) / sinh(
) ) (
/ sinh(
] / ) sinh[(
) 0 ( )
(
/ / 0
/ /
0 0
kT qV B kT
qV B B
B B W
x B B
Cp
kT qV B kT
qV B
B B
B B x
B B
Ep
x x x
x
B B B
B B B
B
EB CB
CB EB
L e W e W
L p W
L qAD dx
P -qAD d
I
L e e W
L W
L p W
L qAD dx
P -qAD d
I
e x e
e x e
L W
L W x
L Δp W
L x p W
Δp x
(11.31) )
/ cosh(
) / sinh(
1
1
Then r.
transisto pnp
a in 0 V
0, V
biasing, mode
active Under
) 1 )(
/ sinh(
) 1 1 ) (
/ sinh(
) / cosh(
(11.28)
) 1 (
(11.20)
CB EB
/ /
0
/ 0
B B E
B E
B B En E
Ep Ep
kT qV B kT
qV B
B B
B B Ep
kT qV E E
E En
L W
L W N
N L
L D
I D I
I
L e e W
L W
L p W
L qAD I
e L n
qAD I
CB EB
EB
) 33 . 11 ( ) / sinh(
) / cosh(
1
) 32 . 11 )( / cosh(
1 )
/ sinh(
) / cosh(
) / sinh(
1
B E
B E B B E B
T dc
B B
B B Ep
Cp T
L N W
N L L D L D
W
L W L
W L W
L W I
I
) 34 . 11 ( 1 ) / sinh(
) / cosh(
1 1 1
1
1
B E
B E B B E B
dc dc
dc dc
L N W
N L L D L D
W
(11.35) )
1 ) (
/ sinh(
) 1 1 ) (
/ sinh(
) / cosh(
(11.28)
&
(11.20)
/ 0
/ 0
0
kT qV B
B B kT B
qV B
B B
B B E
E E
En Ep E
CB
EB e
L p W
L e D
L W
L p W
L n D
L qA D
I I I
(11.36) )
1 ) (
/ sinh(
) / cosh(
) 1 ) (
/ sinh(
1 /
0 0
/
0
C qV kT
C C B
B B
B kT B
qV B
B B
B Cn
Cp C
CB
EB n e
L D L
W L p W
L e D
L p W
L qA D I
I I
) 0 / sinh(
, 1 ) 1
/ sinh(
) / cosh(
(a) 11.1) Ex
B B
B
B B
L W L
W L W
W/L L
W
) 1 (
) 1 ) (
/ sinh(
) 1 1 ) (
/ sinh(
) / cosh(
(11.35)
/ 0
0
/
0 0
/
1 0
0
kT qV B
B B E
E E
kT qV B
B B kT B
qV B
B B
B B E
E E E
EB
CB EB
e L p
n D L qA D
L e p W
L e D
L W
L p W
L n D
L qA D I
diodes.
back - to - back just two is
r transisto a
, L when W Namely,
equation!
diode Ideal
:
) 1 (
(11.36)
B / 0
0
C qV kT
C C B
B B C
e CB
L n p D
L qA D I
diode!
base - narrow :
) 1 ) (
/ sinh(
) / cosh(
) 1 ) (
/ sinh(
) 1 1 ) (
/ sinh(
) / cosh(
(11.35) 0 V
(b)
/ 0
0
0 / 0
/ 0
0 CB
kT qV B
B B
B B E
E E
kT qV B
B B kT B
qV B
B B
B B E
E E E
EB
CB EB
L e W
L p W
L n D
L qA D
L e p W
L e D
L W
L p W
L n D
L qA D
I
