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Lecture 18
The Bipolar Junction Transistor (II)
Regions of Operation
Outline
• Regions of operation
• Large-signal equivalent circuit model
• Output characteristics
Reading Assignment:
Howe and Sodini; Chapter 7, Sections 7.3, 7.4 & 7.5
6.012 Spring 2009
Lecture 18
1
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;
• Cut­off: negligible current: nearly an open circuit;
• Saturation: device is flooded with minority
carriers;
– ⇒ takes time to get out of saturation
6.012 Spring 2009
Lecture 18
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Forward­Active Region: 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 2009
-XBE 0
WB WB+XBC
Lecture 18
WB+XBC+WC
3
Forward­Active Region: 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:
[ ]− 1;
I S 
IB =
e

βF 
VBE
Vth
IS


βF
=
qAE pnEo D p
WE
• Emitter current:


IS  [ ] 
[
]
I E = −IC − I B = −I Se
−
e
−1
VBE
Vth
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
I
WB N dE DnWE
βF = C =
=
D
IB
N aB D pWB
pnEo • p
WE
n pBo •
6.012 Spring 2009
Lecture 18
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Reverse­Active Region: 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 2009
-XBE 0
WB WB+XBC WB+XBC+WC
Lecture 18
5
Reverse­Active Region: 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:
I S 
IB =
e

βR 
( )−1;
VBC
Vth
IS


βR
=
qAC pnCo D p
WC
• Collector current:


IS  [ ] 
[
]
I C = −I E − I B = −I Se
−
e
−1
VBC
Vth
βR 
VBC
Vth


• Typically, βR ≈ 0.1 - 5 << βF .
Dn
IE
WB N dC DnWC
βR = =
=
D p N aB D pWB
IB
pnCo •
WC
n pBo •
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Lecture 18
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Cut­Off Region: VBE < 0, VBC < 0
n-Emitter
p-Base
n-Collector
IE>0
IC>0
Electrons flow only if
Generation occurs
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 2009
-XBE 0
WB WB+XBC WB+XBC+WC
Lecture 18
7
Cut­Off Region: 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
-15
• These are tiny leakage currents (≈10-15
A).
6.012 Spring 2009
Lecture 18
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Saturation Region: VBE > 0, VBC > 0
n-Emitter
p-Base
n-Collector
IC
IE
<0
IBIB>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 2009
-XBE 0
WB WB+XBC WB+XBC+WC
Lecture 18
9
Saturation Region: VBE > 0, VBC > 0
Saturation is superposition of forward active + reverse
active:
[ ]− e[ ]

IC = IS  e


VBE
Vth
VBC
Vth
[ ]
I S 
IB =
e

βF 
VBE
Vth
 I 
 − S e
 βR 


[ ]− 1
V BC
Vth


[ ]
 I 
− 1 + S  e
 βR 


VBC
Vth

− 1


[ ]− e[ ] − IS e[ ]−1

I E = −I S  e


VBE
Vth
VBC
Vth
 βF 


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
6.012Spring 2009
Lecture 18
2. Large­signal equivalent circuit model
System of equations that describes BJT operation:
[ ] [ ]
[ ]
VBC 
 VBE
 V BC

I
V
V
V
I C = I S  e th − e th  − S  e th − 1

 βR 





V
 I  VBC

I S  VBE
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 (non­linear
hybrid­π 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:
• Forward­active region: 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.
• Reverse­active region: 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
6.012 Spring 2009
Lecture 18
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Simplification of equivalent circuit model:
• Saturation region: 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.
• Cut­off region: VBE < 0, VBC < 0
C
B
E
Only negligible leakage currents.
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Lecture 18
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3. Output Characteristics
Common­emitter output characteristics:
IC
IB
IB=0
0
0
VCE=VCB+VBE
VCE,sat
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Lecture 18
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Common­Emitter Output Characteristics
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Lecture 18
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What did we learn today?
Summary of Key Concepts
• Forward­active region: For bias calculations:
C
B
VBE,on
[ ]
I Se
VBE
Vth
E
• Saturation Region: For bias calculations:
C
+
VBC,on
B
VCE,sat
VBE,on
E
• Cut­off Region: For bias calculations:
C
B
E
6.012 Spring 2009
Lecture 18
17
MIT OpenCourseWare
http://ocw.mit.edu
6.012 Microelectronic Devices and Circuits
Spring 2009
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