ECE-305: Fall 2017
Bipolar Junction Transistors
Instructor: Professor Peter BermelElectrical and Computer Engineering
Purdue University, West Lafayette, IN [email protected]
Pierret, Semiconductor Device Fundamentals (SDF)Chapters 10 and 11 (pp. 371-385, 389-403)
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Outline
Bermel ECE 305 F17 2
1) Introduction to Bipolar Junction Transistors
2) Definitions and conventions
3) Band diagram with and without biases
4) Forward active band-diagram
5) Currents in bipolar junction transistors
6) Conclusions
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Background
3
Point contact Germanium transistor (Bell Labs)
E C
Base!
E B C
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Shockley’s Bipolar Transistors
Bermel ECE 305 F17 4
n+emitter
pbase
ncollector
n+
Double
Diffused BJT
p basen-collector
n+
n+
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Modern Bipolar Junction Transistors (BJTs)
Bermel ECE 305 F17 5
SiGe Layer
Transistor speed increases
as the electron's travel
distance is reduced
SiGe intrinsic base Dielectric trench
N+P+
N
P-
N-
CollectorEmitterBase
N+
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Symbols and Conventions
Bermel ECE 305 F17 6
Poly emitter
Low-doped base
Collector dopingoptimization
N+
P
N
Symbols
NPN PNP
Collector
Emitter
Base
Collector
Emitter
Base
E
B
C
IC+IB+IE=0
VEB+VBC+VCE=0
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Polarities
Bermel ECE 305 F17 7
NPN Transistors
Collector
Emitter
Base
IC
IE
IB
PNP Transistors
Collector
Emitter
Base
IC
IE
IB
VEB
VCB
+
+
VBE
VBC
++
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Configurations: Common Emitter/Common Base
Bermel ECE 305 F17 8
P+
N
P
C
E E
B
VEB (in)
ICIB P+
N PE
IE IC
C
BB
VEB(in) VCB (out)
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Current Gain
Bermel ECE 305 F17 9
P+N
P
C
E E
B
VEB (in)
ICIB
Common Emitter current gain ..
CDC
B
I
I =
Common Base current gain ..
P+
N PE
IE IC
C
BB
VEB(in) VCB(out)
CDC
E
I
Ia =
C CDC
B E C
I I
I I I = =
- 1DC
DC
a
a=
-
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Current Gain
Bermel ECE 305 F17 1011/28/2017
Topic Map
Bermel ECE 305 F17 11
Equilibrium DC Small signal
Large Signal
Circuits
Diode
Schottky
BJT/HBT
MOS
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Band Diagram at Equilibrium
Bermel ECE 305 F17 12
BaseEmitter Collector
Vacuum level
EC
EV
EF
c2c1 c3
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Electrostatics in Equilibrium
Bermel ECE 305 F17 17
( )0
,
2 s Bn E bi
E B E
k Nx V
q N N N=
+
( )0
,
2 s Ep BE bi
B E B
k Nx V
q N N N=
+
( )0
,
2 s Bn C bi
C C B
k Nx V
q N N N=
+
( )0
,
2 s Cp BC bi
B C B
k Nx V
q N N N=
+
BaseEmitter Collector
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Electrostatics in Equilibrium
18
( )( )0
,
2 s Bn E bi EB
E B E
k Nx V V
q N N N
= -
+
( )( )0
,
2 s Ep BE bi EB
B E B
k Nx V V
q N N N
= -
+
( )( )0
,
2 s Bn C bi CB
C C B
k Nx V V
q N N N
= -
+
( )( )0
,
2 s Cp BC bi CB
B C B
k Nx V V
q N N N
= -
+
BaseEmitter Collector
VEB VCB
Bermel ECE 305 F1711/28/2017
Topic Map
Bermel ECE 305 F17 19
Equilibrium DC Small signal
Large Signal
Circuits
Diode
Schottky
BJT/HBT
MOS
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Current flow with Bias
Bermel ECE 305 F17 20
EC-Fn,C
Fp,B-EV
EC-Fn,EV
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Coordinates and Convention
Bermel ECE 305 F17 21
, , ,
0 0 0 0 0 0
= = =
= = =
= = =
E D E B A B C D C
E P B N C P
E p B n C n
N N N N N N
D D D D D D
n n p p n n
BaseEmitter Collector
N+ P N
0 WX’’ X’X
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Carrier Distribution in Base
VEB
VCB
( )
( ) ( )
2
2
0
0
" 0
" 0 1
=
= =
= = -BE B
EE
E E
qV k TE E
d pD
dx
p x W
p x p e
x”
( ) ( )( ) ( )
2
2
0
0
0
0 1
1
BE B
BC B
BB
qV k TB B
qV k TB B
d nD
dx
n x n e
n x W n e
=
= = -
= = -
( )
( ) ( )
2
2
0
0
' 0
' 0 1
=
= =
= = -BC B
CC
C C
qV k TC C
d pD
dx
p x W
p x p e22
Carrier Distribution in Base
Bermel ECE 305 F17 23
( )2,(0 ) 1BEi B qV
B
B
nn e
N+ = - ( )
2,( ) 1BCi B qV
B B
B
nn x W e
N = = -
( ) ( ), ,2 2
( ) 11 1BE BCi B qV
B B
i B qV
B
B
B
x xn x
W W
ne
ne
N N æ ö æ ö
= - +ç ÷ ç ÷è ø è
-ø
-
VEB
VCB
( ) 1B
B B
x xn x Ax B
WDCW
æ ö æ ö = + = - +ç ÷ ç ÷
è ø è ø DC
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Collector Electron Current
Bermel ECE 305 F17 24
( ) ( )2,
2,( ) 11 1BE B BC Bi B qV i B qV k T
B
kB
B
T
B B
x ne
N
xn x
W W
ne
N
æ ö æ ö = - +ç ÷ ç ÷
è ø è-
ø-
( ) ( )2
,
,
2,1 1B CE B B B
B
i B qV k Tn
B B
n C n
i B qV k Tn
B BW
nqDe
W N
d nqDe
WJ D
N
nq
dx= = - - -+
( )
,
2
1BE
p E p
p qVi
n D
dpJ qD
dx
D ne
W N
= -
= - -
VBE
VBE
Emitter Current
25
( ) ( )2 2,
,
0
,1 1=
= = - + -- BC BBE Bi B i B qV k TqV k Tnn E n
B B B Bx
nn nqdn
J qDd
D qDe e
W W Nx N
( ),
0 '
2
1
=
= - = - -BEp qVi
n D
p E p
x
D ndpJ
d W ND eq
x
VBE
VBE
, ,= +p E nE EJ J J
Bermel ECE 305 F17
26
essence of current gain
( )2, 1BEp i E q
E
BV
E
qD ne
NI
W» -
N+
N
P
( )2, 1BEi B
B
VE
qn
B
nqDe
NI
W» -
Input Response Input
Response
VBE VBC
Bermel ECE 305 F1711/28/2017
Outline
Bermel ECE 305 F17 34
1) Equilibrium and forward band-diagram
2) Currents in bipolar junction transistors
3) Ebers Moll model
4) Conclusions
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emitter current crowding
35
p base
n-collector
n+
n+
IBIB
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emitter current crowding
36
p base
n-collector
n+
n+
IBIB
Vbase+
-
Bermel ECE 305 F1711/28/2017
emitter current crowding
37
n-collector
n+
n+
IBIB
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emitter and collector areas
38
p base
n-collector
n+
n+
IBIB
AE
AC
AC >> AE
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forward active region
39
n+emitter
pbase
ncollector
n+
FB RB
IE ICIEn
IEpIE = IEn + IEp
ICn » IEn
IC » IEn
IB = IEp
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emitter current: forward active region
40
n+emitter
pbase
ncollector
n+
FB RB
IE ICIEn
IEpIE = IEn + IEp
IEn
IC » IEn
IB = IEp
IEn = qAEni2
NAB
æ
èçö
ø÷DnWB
eqVBE /kBT
IEp = qAEni2
NDE
æ
èçö
ø÷Dp
WE
eqVBE /kBT
IE = IEn + IEp
IE = IF0 eqVBE kBT -1( )
IF0 = qAEni2
NAB
æ
èçö
ø÷DnWB
+ qAEni2
NDE
æ
èçö
ø÷Dp
WE
collector current: forward active region
41
n+emitter
pbase
ncollector
n+
FB RB
IE ICIEn
IEpIE = IEn + IEp
aT IEn
IC » IEn
IB = IEp
IEn = qAEni2
NAB
æ
èçö
ø÷DnWB
eqVBE /kBT
IEp = qAEni2
NDE
æ
èçö
ø÷Dp
WE
eqVBE /kBT
IC = aT IEn
IC =aFIF0 eqVBE kBT -1( )
IC =aTg F IE
aF = aTg F
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base current: forward active region
42
n+emitter
pbase
ncollector
n+
FB RB
IE ICIEn
IEpIE = IEn + IEp
IEn
IC » IEn
IB = IEp
IC =aFIF0 eqVBE kBT -1( )
aF =aTg F
IE = IF0 eqVBE kBT -1( )
IB = IE - IC
IB = 1-aF( ) IF0 eqVBE kBT -1( )
Bermel ECE 305 F1711/28/2017
summary: forward active region
43
n+emitter
pbase
ncollector
n+
FB RB
IE ICIEn
IEpIE = IEn + IEp
IEn
IC » IEn
IB = IEp
IC =aFIF0 eqVBE kBT -1( )
IE = IF0 eqVBE kBT -1( )
IB = 1-aF( ) IF0 eqVBE kBT -1( )IF0 = qAE
ni2
NAB
æ
èçö
ø÷DnWB
+ qAEni2
NDE
æ
èçö
ø÷Dp
WE
aF = aTg F
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Ebers-Moll model
44Bermel ECE 305 F17
Question:
How do we describe the BJT in any region of operation?
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emitter-base junction (the forward diode)
45
n+emitter
pbase
ncollector
n+
IE IC
IB
IEn ICn
IEp
Bermel ECE 305 F17
ICp
IEn = -qADnWB
ni2
NABeqVBE kBT -1( )
IEp = -qADp
WE
ni2
NDEeqVBE kBT -1( )
IE VBE( ) = -IEn VBE( ) - IEp VBE( )
IE VBE( ) = IF0 eqVBE kBT -1( )
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Base-collector junction (the reverse diode)
46
n+emitter
pbase
ncollector
n+
IE IC
IB
IEn ICn
IEp
Bermel ECE 305 F17
ICp
ICn VBC( ) = qADnWB
ni2
NABeqVBC kBT -1( )
ICp VBC( ) = qADp
WC
ni2
NDCeqVBC kBT -1( )
IC VBC( ) = - ICn VBC( ) + ICp VBC( )éë ùû
IC VBC( ) = -IR0 eqVBC kBT -1( )
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Both junctions….
47
n+emitter
pbase
ncollector
n+
IE IC
IB
IEn ICn
IEp
Bermel ECE 305 F17
ICp
IC VBC( ) = -IR0 eqVBC kBT -1( )
IE VBE( ) = IF0 eqVBE kBT -1( )
But….The two junctions are coupled!
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Ebers-Moll model
48
n+emitter
pbase
ncollector
n+
IE IC
IB
IEn ICn
IEp
Bermel ECE 305 F17
ICp
IC VBE ,VBC( ) = aF IF0 eqVBE kBT -1( ) - IR0 eqVBC kBT -1( )
IE VBE ,VBC( ) = IF0 eqVBE kBT -1( ) -a RIR0 eqVBC kBT -1( )
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Ebers-Moll model
Bermel ECE 305 F17
IC VBE ,VBC( ) = aF IF0 eqVBE kBT -1( ) - IR0 eqVBC kBT -1( )
IE VBE ,VBC( ) = IF0 eqVBE kBT -1( ) -a RIR0 eqVBC kBT -1( )
IB VBE ,VBC( ) = IE VBE ,VBC( ) - IC VBE ,VBC( )
See Pierret SDF, Chapter 11, sec. 11.1.4
aF IF0 = a RIR0
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Conclusion
51
• Bipolar junction transistor (BJT) physics is most easily understood as an extension of junction diode behavior
• The equations can be encapsulated in a simple equivalent circuit, appropriate for dc applications
• It is important to remember the definitions and conventions, so that we can recall them in various situations.
• Being able to draw the band-diagram for arbitrary bias conditions in a key skill, which will be on the final exam
• For a terrific and interesting history of invention of bipolar transistor, read the book, Crystal Fire
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