1 . Lecture #16
OUTLINE
The Bipolar Junction Transistor
– Narrow-emitter and/or narrow-collector
– Ebers-Moll model
– Base-width modulation, Early voltage
Reading: Chapter 11.2
Spring 2003 EE130 Lecture 16, Slide 1
Narrow-Emitter and Narrow-Collector
cosh(WE ' / LE ) qVEB / kT
I En = qA DLEE nE 0 (e − 1)
sinh(WE ' / LE )
cosh(WC ' / LC ) qVCB / kT
I Cn = − qA DLCC nC 0 (e − 1)
sinh(WC ' / LC )
I E = qA [( DE
WE′ nE 0 + DB
LB pB 0
cosh(W / LB )
sinh(W / LB ) )(e qVEB / kT
− 1) − ( DB
LB )(
pB 0 sinh(W1 / LB ) e qVCB / kT − 1 )]
= qA[( ) ( )(e )]
cosh(W / LB )
IC DB
LB pB 0 sinh(W1 / LB ) (e qVEB / kT − 1) − DC
WC′ nC 0 + DB
LB pB 0 sinh(W / LB )
qVCB / kT
−1
Spring 2003 EE130 Lecture 16, Slide 2
1
2 . Performance Parameters (revisited)
1
γ = n iE 2
1 + n DD NN LW 2
E
B
B
Replace with W ’ if short emitter
E E E
iB
1
αT =
1 + 12 ( ) W 2
LB
1
α dc =
1+
ni E 2 D N W
E B
ni B 2 DB N E LE
+ 12 ( )
W 2
LB
1
β dc = ni E 2 D N W
E B
ni B 2 DB N E LE
+ 12 ( )
W 2
LB
Spring 2003 EE130 Lecture 16, Slide 3
Ebers-Moll Model
IC IB
saturation active region
region
V CE
0
The Ebers-Moll model is a large-signal equivalent circuit which
describes both the active and saturation regions of BJT operation.
Spring 2003 EE130 Lecture 16, Slide 4
2
3 .IC is driven by two forces, VEB and VCB .
V EB V CB
If only VEB is applied (VCB = 0):
IB
I E = I F 0 ( e qVEB / kT − 1)
I C = α F I F 0 ( e qVEB / kT − 1) E B C
I B = (1 − α F )I F 0 ( e
IC
qVEB / kT
− 1)
If only VCB is applied (VEB = 0): : αR : reverse common base gain
αF : forward common base gain
I C = − I R 0 (e qVCB / kT − 1)
I E = −α R I R 0 (e qVCB / kT − 1)
I B = I R 0 (1 − α R )(e qVCB / kT − 1)
Spring 2003 EE130 Lecture 16, Slide 5
In the general case, both VEB and VCB are non-zero:
I C = α F I F 0 ( e qVEB / kT − 1) − I R 0 ( e qVCB / kT − 1)
IC: C-B diode current + fraction of E-B diode current that makes it to the C-B junction
I E = I F 0 ( e qVEB / kT − 1) − α R I R 0 ( e qVCB / kT − 1)
IE: E-B diode current + fraction of C-B diode current that makes it to the E-B junction
Spring 2003 EE130 Lecture 16, Slide 6 VCE (V)
3
4 . Reciprocity Relationship
DB pB 0
α F I F 0 = α R I R 0 ≡ qA
LB sinh(W / LB )
Spring 2003 EE130 Lecture 16, Slide 7
Base-Width Modulation
VBE B
E + N C
N P V CE
emitter base collector
}
WB 3
reduction of base width
WB 2 VCE 1 < VC E2 <VC E3
WB 1
∆nn'
B
1
β dc = niE 2
DE N B W
niB 2 DB N E LE
+ 12 ( )
W 2
LB
x
How can we reduce the base-width modulation effect?
Spring 2003 EE130 Lecture 16, Slide 8
4
5 . V BE B
E + N C
The base-width modulation N P VCE
emitter base
effect is reduced if we collector
}
WB 3
reduction of base width
(A) Increase the base width, WB 2 VCE 1 < VC E2 <VC E3
(B) Increase the base doping WB 1
n'
concentration, NB , or
(C) Decrease the collector doping
concentration, NC .
x
Which of the above is the most acceptable action?
Spring 2003 EE130 Lecture 16, Slide 9
Early Voltage
Output resistance :
−1
∂I V
r0 ≡ C = A
∂VCE IC
IC IB3
(b) IB2 A large VA (i.e. a
VA : Early Voltage IB1
larger ro ) is desirable
VA 0 VCE
Spring 2003 EE130 Lecture 16, Slide 10
5
6 . Punchthrough
Spring 2003 EE130 Lecture 16, Slide 11
Summary: BJT Performance Requirements
• High gain (βdc >> 1)
→ One-sided emitter junction, so emitter efficiency γ ≈ 1
• Emitter doped much more heavily than base (NE >> NB)
→ Narrow base, so base transport factor αT ≈ 1
• Quasi-neutral base width << minority-carrier diffusion length
(W << LB)
• IC determined only by IB (IC ≠ function of VCE,VCB)
→ One-sided collector junction, so quasi-neutral base width W
does not change drastically with changes in VCE (VCB)
• Based doped more heavily than collector (NB > NC)
(W = WB – xnEB – xnCB for PNP BJT)
Spring 2003 EE130 Lecture 16, Slide 12
6
7 . Review: Modes of Operation
Common-emitter output characteristics
(IC vs. VCE)
IC
Note that βdc = is lower for inverted mode operation. Why?
IB
Spring 2003 EE130 Lecture 16, Slide 13
7
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