24.2 Bipolar Transistors
697
Fig. 24.6 Collector
current I C and base current
I B as a function of the
emitter–base voltage V EB
(Gummel plot). Adapted
from [2049]
10
-2
10
10
10
10
10
10
10
10
10
10
10
10
10
10
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12
-13
-14
-15
-16
0
V (V)
EB
0.2
0.4
0.6
0.8
1.0
1.2
n=1
n=1
n=2
n=2
I B
I C
nonideal
region
ideal
region
high
injection
r b
24.2.3 Ebers-Moll Model
The Ebers-Moll model (Fig. 24.7) was developed in 1954 and is a relatively simple transistor model that
needs, at its simplest level (Fig. 24.7a) just three parameters. It can (and must) be refined (Figs. 24.7b,c).
The model considers two ideal diodes (‘F’ (forward) and ‘R’ (reverse)) back to back, each feeding a
current source. The F diode represents the emitter–base diode and and the R diode the collector–base
diode. The currents are
I F = I F0
exp (βV EB ) − 1
(24.21a)
I R = I R0
exp (βV CB ) − 1
.
(24.21b)
Using (24.8a,b)–(24.11), the emitter and collector currents are
I E = ˆ
a 11
exp (βV EB ) − 1
+ ˆ
a 12
exp (βV CB ) − 1
(24.22a)
I C = ˆ
a 21
exp (βV EB ) − 1
+ ˆ
a 22
exp (βV CB ) − 1
,
(24.22b)
with
ˆ
a 11 = e A
p B
D B
L B
coth
w
L B
+ n E
D E
L E
(24.23a)
ˆ
a 12 = −e Ap B
D B
L B
csch
w
L B
(24.23b)
ˆ
a 21 = e Ap B
D B
L B
csch
w
L B
= −ˆ a 12
(24.23c)
ˆ
a 22 = −e A
p B
D B
L B
coth
w
L B
+ n C
D C
L C
.
(24.23d)
The currents at the three contacts are
I E = I F − α I I R
(24.24a)