Lecture 18
The Bipolar Junction Transistor (II)
Regimes of Operation
Outline
• Regimes of operation
• Large-signal equivalent circuit model
• Output characteristics
Reading Assignment:
Howe and Sodini; Chapter 7, Sections 7.3, 7.4 & 7.5
Announcement:
Quiz #2: April 25, 7:30-9:30 PM at Walker. Calculator
Required. Open book.
6.012 Spring 2007
Lecture 18
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1. BJT: Regions of Operation
VBE
-
C
+
VBC
+
B
forward
active
saturation
VCE
+
VBC
VBE
-
-
cut-off
reverse
E
•
•
•
•
Forward active: device has high voltage gain and
high β;
Reverse active: poor β; not useful;
Cut-off: negligible current: nearly an open circuit;
Saturation: device is flooded with minority
carriers;
– ⇒ takes time to get out of saturation
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Forward-Active Regime: VBE > 0, VBC <0
n-Emitter
p-Base
n-Collector
IC>0
IE<0
IB>0
VBE > 0
VBC < 0
Minority Carrier profiles (not to scale):
emitter
base
pnE
npB
collector
pnC
pnCo
npBo
pnEo
x
-WE-XBE
6.012 Spring 2007
-XBE 0
WB WB+XBC
Lecture 18
WB+XBC+WC
3
Forward-Active Regime: VBE > 0, VBC < 0
• Emitter injects electrons into base, collector extracts
(collects) electrons from base:
[ ];
I C = I Se
VBE
Vth
IS =
qAE npBo Dn
WB
• Base injects holes into emitter, holes recombine at
emitter contact:
[ ]
⎡
IS ⎢
IB =
e
⎢
βF ⎣
VBE
Vth
⎤
− 1⎥;
⎥
⎦
IS
βF
=
• Emitter current:
[ ]
I E = −IC − I B = −I Se
VBE
Vth
qAE pnEo D p
WE
[ ]−1⎟⎞
⎛
IS ⎜
−
e
⎜
βF ⎝
VBE
Vth
⎟
⎠
• State-of-the-art IC BJT’s today: IS ≈ 0.1 - 1 fA
• βF ≈ 50 - 300.
• βF hard to control tightly: ⇒ circuit design techniques
required to be insensitive to variations in βF.
Dn
WB NdE Dn WE
I
βF = C =
=
IB p • Dp
NaB Dp WB
nEo
WE
npBo •
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Reverse-Active Regime: VBE < 0, VBC > 0
n-Emitter
p-Base
n-Collector
IE>0
IC<0
IB>0
VBE < 0
VBC > 0
Minority Carrier Profiles (not to scale):
emitter
base
pnE
npB
collector
pnC
pnCo
npBo
pnEo
x
-WE-XBE
6.012 Spring 2007
-XBE 0
WB WB+XBC WB+XBC+WC
Lecture 18
5
Reverse-Active Regime: VBE < 0, VBC > 0
• Collector injects electrons into base, emitter extracts
(collects) electrons from base:
VBC
qAC n pBo Dn
Vth
IE = IS e
;
IS =
WB
[ ]
• Base injects holes into collector, holes recombine at
collector contact and buried layer:
⎡
IS ⎢
IB =
e
⎢
βR ⎣
( )−1⎥⎤;
VBC
Vth
IS
⎥
⎦
=
βR
qAC pnCo D p
• Collector current:
[ ]
I C = −I E − I B = −I Se
VBC
Vth
WC
[ ]−1⎟⎞
⎛
IS ⎜
−
e
⎜
βR ⎝
VBC
Vth
⎟
⎠
• Typically, βR ≈ 0.1 - 5 << βF .
Dn
npBo •
I
WB NdCDn WC
βR = E =
=
D
IB p
p
NaB Dp WB
•
nCo
WC
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Cut-Off Regime: VBE < 0, VBC < 0
n-Emitter
p-Base
n-Collector
IE>0
IC>0
IB<0
VBE < 0
VBC < 0
Minority Carrier Profiles (not to scale):
emitter
base
pnE
npB
collector
pnC
pnCo
npBo
pnEo
x
-WE-XBE
6.012 Spring 2007
-XBE 0
WB WB+XBC WB+XBC+WC
Lecture 18
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Cut-Off Regime: VBE < 0, VBC < 0
• Base extracts holes from emitter:
I B1 = −
IS
βF
= −I E
• Base extracts holes from collector:
I B2 = −
IS
βR
= −I C
• These are tiny leakage currents (≈10-15 A).
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Saturation Regime: VBE > 0, VBC > 0
n-Emitter
p-Base
n-Collector
IC
IE
IB<0
VBE > 0
VBC > 0
Minority Carrier profiles (not to scale):
emitter
base
pnE
npB
collector
pnC
pnCo
npBo
pnEo
x
-WE-XBE
6.012 Spring 2007
-XBE 0
WB WB+XBC WB+XBC+WC
Lecture 18
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Saturation Regime: VBE > 0, VBC > 0
Saturation is superposition of forward active + reverse
active:
[ ]− e[ ]
⎛
I C = I S ⎜⎜ e
⎝
VBE
Vth
VBC
Vth
⎞ I ⎛
⎟ − S ⎜e
⎟ β ⎜
R⎝
⎠
[ ]
⎡
IS ⎢
IB =
e
⎢
βF ⎣
VBE
Vth
VBE
Vth
⎞
− 1⎟⎟
⎠
[ ]− 1⎥⎤
⎤
⎡
I
− 1⎥ + S ⎢ e
⎥ βR ⎢
⎦
⎣
VBC
Vth
[ ]− e[ ]
⎡
I E = −I S ⎢ e
⎢
⎣
[ ]
V BC
Vth
VBC
Vth
⎤ I
⎥− S
⎥ βF
⎦
⎥
⎦
[ ]−1⎥⎤
⎡
⎢e
⎢
⎣
VBE
Vth
⎥
⎦
• IC and IE can have either sign, depending on relative
magnitudes of VBE and VBC and βF and βR.
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Saturation - The Flux Picture
•
•
•
•
•
Both junctions are injecting and collecting.
Electrons injected from emitter into base are
collected by the collector as in Forward Active case.
Electrons injected from collector into the base are
collected by the emitter as in Reverse Active case.
Holes injected into emitter recombine at ohmic
contact as in Forward Active case.
Holes injected into collector recombine with
electrons in the n+ buried layer
;;;
;;;;;;;;;;;;;
;;;;;;;;;;;;;;
;;;;;;;;;;;;;;
;;;;;;;;;;;;;;
;;;;;;;;;;;;;;
;;;;;;;;;;;;;;
;
;
;
n+ polysilicon
hole diffusion flux
majority hole flux from base contact
n+emitter
majority
electrons
electron
diffusion
p-type base
n-type collector
minority hole diffusion flux
n+ buried layer
majority electron flux from collector
contact supplying injection into base
majority electron flux
to collector contact
majority electron flux from collector contact
to recombine with hole diffusion flux
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2. Large-signal equivalent circuit model
System of equations that describes BJT operation:
[ ] [ ]
[ ]
VBC ⎞
⎛ VBE
⎛ V BC
⎞
I
I C = I S ⎜⎜ e Vth − e Vth ⎟⎟ − S ⎜⎜ e Vth − 1⎟⎟
⎝
⎠ βR ⎝
⎠
⎡ V
⎤
⎡ VBC
⎤
I S ⎢ VBE
I
IB =
e th − 1⎥ + S ⎢ e Vth − 1⎥
⎥ βR ⎢
⎥
βF ⎢⎣
⎦
⎣
⎦
VBC ⎤
⎡ VBE
⎡ VBE
⎤
I
V
V
V
I E = −I S ⎢ e th − e th ⎥ − S ⎢e th −1⎥
⎢
⎥ βF ⎢
⎥
⎣
⎦
⎣
⎦
[ ]
[ ]
[ ] [ ]
[ ]
Equivalent-circuit model representation (non-linear
hybrid-π model) [particular rendition of Ebers-Moll
C
model in text]:
IC
VBC
IS/βR
B
+
IR
+ IB
IF
βFIF - βRIR
=IS[exp(qVBE/kT) - exp(qVBC/kT)]
IS/βF
VBE
IE
E
Three parameters in this model: IS, βF, and βR.
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Simplification of equivalent circuit model:
• Forward-active regime: VBE > 0, VBC < 0
C
C
[ ]
Ie
VBE
Vth
B
B
S
VBE,on
E
E
For today’s technology: VBE,on ≈ 0.7 V. IB depends on
outside circuit.
• Reverse-active regime: VBE < 0, VBC > 0
C
C
VBC,on
B
[ ]
Ie
VBC
Vth
B
S
E
E
For today’s technology: VBC,on ≈ 0.6 V
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Simplification of equivalent circuit model:
• Saturation regime: VBE > 0, VBC > 0
C
C
C
+
VBC,on
B
VBC,on
B
B
VBE,on
VCE,sat
VBE,on
E
E
E
For today’s technology: VCE,sat ≈ 0.1 V. IC and IB depend
on outside circuit.
• Cut-off regime: VBE < 0, VBC < 0
C
B
E
Only negligible leakage currents.
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3. Output Characteristics
Common-emitter output characteristics:
IC
IB
IB=0
0
0
VCE=VCB+VBE
VCE,sat
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Common-Emitter Output Characteristics
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What did we learn today?
Summary of Key Concepts
•
Forward-active regime: For bias calculations:
C
B
VBE,on
[ ]
I Se
VBE
Vth
E
•
Saturation Regime: For bias calculations:
C
+
VBC,on
B
VCE,sat
VBE,on
E
•
Cut-off Regime: For bias calculations:
C
B
E
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