• Large-signal equivalent circuit model
Lecture 18The 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- +
forward� saturation VBC active
+ B VCE
+ VBC
VBE reverse - cut-off -
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 2
Minority Carrier profiles (not to scale):
ForwardActive Region: VBE > 0, VBC <0
n-Emitter p-Base n-Collector
IE<0
IB>0
IC>0
VBE > 0 VBC < 0
Minority Carrier profiles (not to scale):
npB pnE pnC
npBo pnEo
pnCo
0 WB-XBE WB+XBC -WE-XBE WB+XBC+WC
x
emitter base collector
6.012 Spring 2009 Lecture 18 3
• Emitter current:
ForwardActive Region: VBE > 0, VBC < 0
• Emitter injects electrons into base, collector extracts
(collects) electrons from base:
IC = ISe VBE Vth[ ]
; IS = qAEnpBo Dn
WB
• Base injects holes into emitter, holes recombine at
emitter contact:
IB = IS ββββF
e VBE Vth[ ]− 1
;
IS ββββF
= qAE pnEoDp
WE
• Emitter current:
IE = −IC − IB = −ISe VBE Vth[ ]−
IS ββββF
e VBE Vth[ ]−1
• 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.
βF = IC
IB
= npBo •
D n WB
pnEo • D p WE
= NdE D n WE
NaB D p WB
6.012 Spring 2009 Lecture 18 4
ReverseActive Region: VBE < 0, VBC > 0
n-Emitter p-Base n-Collector
IE>0
IB>0
IC<0
VBE < 0 VBC > 0
Minority Carrier Profiles (not to scale):
npB pnE pnC
npBo pnEo
pnCo
0 WB-XBE WB+XBC -WE-XBE WB+XBC+WC
x
emitter base collector
6.012 Spring 2009 Lecture 18 5
• Collector current:
ReverseActive Region: VBE < 0, VBC > 0
• Collector injects electrons into base, emitter extracts
(collects) electrons from base:
IE = ISe VBC Vth[ ]
; IS = qACnpBoDn
WB
• Base injects holes into collector, holes recombine at
collector contact and buried layer:
IB = IS ββββR
e VBC Vth
( )−1
;
IS ββββR
= qAC pnCoDp
WC
• Collector current:
IC = −IE − IB = −ISe VBC Vth[ ]−
IS ββββR
e VBC Vth[ ]−1
• Typically, βR ≈ 0.1 - 5 << βF .
βR = IE
IB
= npBo •
D n WB
pnCo • D p WC
= NdC D n WC
NaB D p WB
6.012 Spring 2009 Lecture 18 6
CutOff Region: VBE < 0, VBC < 0
n-Emitter p-Base n-Collector
IE>0
IB<0
IC>0
VBE < 0 VBC < 0
Electrons flow only if
Generation occurs
Minority Carrier Profiles (not to scale):
npB pnE pnC
npBo pnEo
pnCo
0 WB-XBE WB+XBC -WE-XBE WB+XBC+WC
x
emitter base collector
6.012 Spring 2009 Lecture 18 7
• These are tiny leakage currents (≈10 A).-
CutOff Region: VBE < 0, VBC < 0
• Base extracts holes from emitter:
IB1 = − IS = −IEββββF
• Base extracts holes from collector:
IB2 = − IS = −ICββββR
-15 • These are tiny leakage currents (≈10 15 A).
6.012 Spring 2009 Lecture 18 8
Saturation Region: VBE > 0, VBC > 0
n-Emitter p-Base n-Collector
IE
IB<0
IC
VBE > 0 VBC > 0
IB>0
Minority Carrier profiles (not to scale):
npB pnE pnC
npBo pnEo
pnCo
0 WB-XBE WB+XBC -WE-XBE WB+XBC+WC
x
emitter base collector
6.012 Spring 2009 Lecture 18 9
E S = th th S th
Saturation Region: VBE > 0, VBC > 0
Saturation is superposition of forward active + reverse
active: [VBE ] [VBC ] IS
[VBC ] IC = IS
e
Vth − e Vth − ββββR
e
Vth − 1
IS [VBE ]
IS [VBC ]
IB = e Vth − 1 + e Vth − 1 ββββF
ββββR
[VBE ] [VBC ] IS
[VBE ] VthI = −I e Vth − e Vth − e −1IE −IS e
[ ]− e[ ]
−
ββββF e[ ]−1
• IC and IE can have either sign, depending on relative
magnitudes of VBE and VBC and βF and βR.
6.012 Spring 2009 Lecture 18 10
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
Equivalent-circuit model representation (nonlinear
2. Largesignal equivalent circuit model
System of equations that describes BJT operation:
IC = IS e VBE Vth[ ]
− e VBC Vth[ ]
−
IS ββββR
e VBC Vth[ ]
− 1
IB = IS ββββF
e VBE Vth[ ]− 1
+
IS ββββR
e VBC Vth[ ]− 1
IE = −IS e VBE Vth[ ]− e
VBC Vth[ ]
−
IS ββββF
e VBE Vth[ ]−1
Equivalent-circuit model representation (nonlinear hybridπ model) [particular rendition of Ebers-Moll
model in text]:
Three parameters in this model: IS, βF, and βR.
B
C
E
IB
IR
IF
IS/βR
IS/βF
IE
IC
βFIF - βRIR
=IS[exp(qVBE/kT) - exp(qVBC/kT)]+
-
+
-
VBE
VBC
6.012 Spring 2009 Lecture 18 12
Simplification of equivalent circuit model: • Forwardactive region: VBE > 0, VBC < 0
For today’s technology: VBE,on ≈ 0.7 V. IB depends on
outside circuit.
B
C
E
B
C
E
VBE,on
ISe VBE Vth
[ ]
• Reverseactive region: VBE < 0, VBC > 0
For today’s technology: VBC,on ≈ 0.6 V
B
C
E E
B
C
VBC,on
ISe VBC Vth
[ ]
6.012 Spring 2009 Lecture 18 13
Simplification of equivalent circuit model: • Saturation region: VBE > 0, VBC > 0
For today’s technology: VCE,sat ≈ 0.1 V. IC and IB depend
on outside circuit.
B
C
E
B
C
E
VBE,on VBE,on
VCE,sat
VBC,on VBC,on
B
C
E
+
-
6.012 Spring 2009 Lecture 18 14
• Cutoff region: VBE < 0, VBC < 0
on outside circuit.
Only negligible leakage currents.
B
C
E
I =0
3. Output Characteristics
Commonemitter output characteristics:
IC
IB
IB=0
6.012 Spring 2009 Lecture 18 15
VCE=VCB+VBE
VCE,sat
B
0 0
CommonEmitter Output Characteristics
6.012 Spring 2009 Lecture 18 16
What did we learn today? Summary of Key Concepts
• Forwardactive region: For bias calculations:
• Saturation Region: For bias calculations:
B C
E
VBE,on
C
+
ISe VBE Vth[ ]
6.012 Spring 2009 Lecture 18 17
• Cutoff Region: For bias calculations:
VBE,on
VCE,sat
VBC,on
B
E
-
B
C
E
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6.012 Microelectronic Devices and Circuits Spring 2009
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