Post on 04-Sep-2018
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Lecture 9
Semiconductor Device Physics
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Chapter 10BJT Fundamentals
Semiconductor Device Physics
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Bipolar Junction Transistors (BJTs)
Chapter 10 BJT Fundamentals
Over the past decades, the higher layout density and low-power advantage of CMOS (Complementary Metal–Oxide–Semiconductor) has eroded away the BJT’s dominance in integrated-circuit products.
Higher circuit density better system performance
BJTs are still preferred in some digital-circuit and analog-circuit applications because of their high speed and superior gain
Faster circuit speed (+)
Larger power dissipation (–)
• Transistor: current flowing between two terminals is controlled by a third terminal
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Introduction
EB E B
CB C B
EC E C
EB CB
V V V
V V V
V V V
V V
BE B E
BC B C
CE C E
CB EB
V V V
V V V
V V V
V V
Chapter 10 BJT Fundamentals
There are two types of BJT: pnp and npn.
The convention used in the textbook does not follow IEEE convention, where currents flowing into a terminal is defined as positive.
We will follow the normal convention: . . . . . .
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Common-Emitter
I–V Characteristics
Circuit Configurations
Most popular configuration
Saturation Mode
IC < bIB
Active Mode
In active mode, bdc is the common
emitter dc current gain
Chapter 10 BJT Fundamentals
Cdc
B
100I
Ib
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Mode E-B Junction C-B Junction
Saturation forward bias forward bias
Active/Forward forward bias reverse bias
Inverted reverse bias forward bias
Cutoff reverse bias reverse bias
Modes of Operation
Chapter 10 BJT Fundamentals
Common-Emitter Output Characteristics
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BJT Electrostatics
AE DB ACN N N
CB EBW W
B nEB nCBW W x x
W : quasineutral base width
Chapter 10 BJT Fundamentals
Under equilibrium and normal operating conditions, the BJT may be viewed electrostatically as two independent pnjunctions.
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BJT Electrostatics
Chapter 10 BJT Fundamentals
Electrostatic potential, V(x)
Electric field, E(x)
Charge density, ρ(x)
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pnp BJT, active mode
BJT Design
Chapter 10 BJT Fundamentals
Important features of a good transistor:
Injected minority carriers do not recombine in the neutral base region short base, W << Lp for pnp transistor
Emitter current is comprised almost entirely of carriers injected into the base rather than carriers injected into the emitter the emitter must be doped heavier than the base
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EMITTER BASE COLLECTOR
p-type n-type p-type3
1
4
2
Base Current (Active Bias)
CB0i
Chapter 10 BJT Fundamentals
The base current consists of majority carriers (electrons) supplied for:
1. Recombination of injected minority carriers in the base
2. Injection of carriers into the emitter
3. Reverse saturation current in collector junction
4. Recombination in the base-emitter depletion region
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Decrease relative to
to increase transport factor
Decrease relative to
and to increase efficiency
Cp
T
Ep
I
I
dc T Common base dc current gain:
BJT Performance Parameters (pnp)
Ep Ep
E Ep En
I I
I I I
IEn
IEp
ICn
ICp
Negligible compared to holes injected
from emitter
1
5
2
1 2
Chapter 10 BJT Fundamentals
Emitter Efficiency Base Transport Factor
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C dc C B CB0α ( )I I I I
C dc E CB0αI I I
Common emitter dc current gain:
dc Cdc
dc B1
I
I
b
ICB0 :collector current when IE = 0
2
3
dc CB0C B
dc dc
α
1 α 1 α
II I
Collector Current (Active Bias)
CB0I
Chapter 10 BJT Fundamentals
The collector current is composed of:
Holes injected from emitter, which do not recombine in the base
Reverse saturation current of collector junction
C dc B CE0I β I I
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Chapter 11BJT Static Characteristics
Semiconductor Device Physics
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Notation (pnp BJT)
E AE
E N
E n
E N
E0 p0
2
i E
N N
D D
L L
n n
n N
B DB
B P
B p
B P
B0 n02
i B
N N
D D
L L
p p
n N
C AC
C N
C n
C N
C0 p0
2
i C
N N
D D
L L
n n
n N
Minority carrier
constants
Chapter 11 BJT Static Characteristics
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2
E EE 2
E
0d n n
Ddx
EB
E
E E0
( ) 0
( 0) ( 1)qV kT
n x
n x n e
Emitter Region
Chapter 11 BJT Static Characteristics
Diffusion equation:
Boundary conditions:
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2
B BB 2
B
0d p p
Ddx
EB
CB
B B0
B B0
(0) ( 1)
( ) ( 1)
qV kT
qV kT
p p e
p W p e
Base Region
Chapter 11 BJT Static Characteristics
Diffusion equation:
Boundary conditions:
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2
C CC 2
C
0d n n
Ddx
CB
C
C C0
( ' ) 0
( ' 0) ( 1)qV kT
n x
n x n e
Collector Region
Chapter 11 BJT Static Characteristics
Diffusion equation:
Boundary conditions:
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EEn E
0x
d nI qAD
dx
BEp B
0x
d pI qAD
dx
BCp B
x W
d pI qAD
dx
Cn C
0
C
x
d nI qAD
dx
E
B
C
( ),
( ),
( )
n x
p x
n x
IC
IB
IE
E Ep En
C Cp Cn
B E C
I I I
I I I
I I I
Ideal Transistor Analysis
Chapter 11 BJT Static Characteristics
Solve the minority-carrier diffusion equation in each quasi-neutral region to obtain excess minority-carrier profilesEach region has different set of boundary conditions
Evaluate minority-carrier diffusion currents at edges of depletion regions
Add hole and electron components together terminal currents is obtained
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2
E EE 2
E
0d n n
Ddx
E E
E 1 2( ) x L x Ln x Ae A e
EB
E
E E0
( ) 0
( 0) ( 1)qV kT
n x
n x n e
EB E
E E0( ) ( 1)qV kT x Ln x n e e
EEn E
0x
d nI qAD
dx
Emitter Region Solution
Chapter 11 BJT Static Characteristics
Diffusion equation:
General solution:
Boundary conditions:
Solution
EBEE0
E
( 1)qV kTDqA n e
L
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C C
C 1 2( )x L x L
n x Ae A e
CB C
C C0( ) ( 1)qV kT x L
n x n e e
2
C CC 2
C
0d n n
Ddx
CB
C
C C0
( ) 0
( 0) ( 1)qV kT
n x
n x n e
CCn C
0x
d nI qAD
dx
Collector Region Solution
Chapter 11 BJT Static Characteristics
Diffusion equation:
General solution:
Boundary conditions:
Solution
CBCC0
C
( 1)qV kTD
qA n eL
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B B
B 1 2( ) x L x Lp x Ae A e
2
B BB 2
B
0d n p
Ddx
EB
CB
B B0
B B0
(0) ( 1)
( ) ( 1)
qV kT
qV kT
p p e
p W p e
B B
EB
B B
B B
CB
B B
( ) ( )
B B0
B0
( ) ( 1)
( 1)
W x L W x LqV kT
W L W L
x L x LqV kT
W L W L
e ep x p e
e e
e ep e
e e
Base Region Solution
Chapter 11 BJT Static Characteristics
Diffusion equation:
General solution:
Boundary conditions:
Solution
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sinh( )2
e e
EB
CB
B
B B0
B
BB0
B
sinh ( )( ) ( 1)
sinh( )
sinh( ) ( 1)
sinh( )
qV kT
qV kT
W x Lp x p e
W L
x Lp e
W L
as
B B
EB
B B
B B
CB
B B
( ) ( )
B B0
B0
( ) ( 1)
( 1)
W x L W x LqV kT
W L W L
x L x LqV kT
W L W L
e ep x p e
e e
e ep e
e e
Base Region Solution
Chapter 11 BJT Static Characteristics
Since
We can write
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CBEB
BEp B
0
B BB0
B B B
cosh( ) 1( 1) ( 1)
sinh( ) sinh( )
x
qV kTqV kT
d pI qAD
dx
D W LqA p e e
L W L W L
CBEB
BCp B
B BB0
B B B
cosh( )1( 1) ( 1)
sinh( ) sinh( )
x W
qV kTqV kT
d pI qAD
dx
D W LqA p e e
L W L W L
sinh( ) cosh( )2 2
d d e e e e
d d
Base Region Solution
Chapter 11 BJT Static Characteristics
Since
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EB
CB
E B BE E0 B0
E B B
BB0
B B
cosh( )( 1)
sinh( )
1 ( 1)
sinh( )
qV kT
qV kT
D D W LI qA n p e
L L W L
Dp e
L W L
EB
CB
BC B0
B B
C B BC0 B0
C B B
1( 1)
sinh
cosh( ) ( 1)
sinh( )
qV kT
qV kT
DI qA p e
L W L
D D W Ln p e
L L W L
E En Ep ,I I I C Cn CpI I I
B E CI I I
Terminal Currents
Chapter 11 BJT Static Characteristics
Since
Then
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EB
CB
/
B B0
/
B0
( ) ( 1) 1
( 1)
qV kT
qV kT
xp x p e
W
xp e
W
Due to VEB
Due to VCB
Simplified Relationships
02
0
limsinh( )
limcosh( ) 12
B B B B( ) (0) ( ) (0)x
p x p p W pW
Chapter 11 BJT Static Characteristics
To achieve high current gain, a typical BJT will be constructed so that W << LB.
Using the limit value
We will have
ΔpB(0)
ΔpB(W)
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E B
B E E
1
1D N W
D N L
dc 2
E B
B E E B
1
1
2
D N W W
D N L L
b
T 2
B
1
11
2
W
L
dc 2
E B
B E E B
1,
11
2
D N W W
D N L L
Performance Parameters
Chapter 11 BJT Static Characteristics
For specific condition of
“Active Mode”: emitter junction is forward biased and collector junction is reverse biased
W << LB, nE0/pB0 NB/NE
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Ebers-Moll BJT Equations
EB
CB
E B BE E0 B0
E B B
BB0
B B
cosh( )( 1)
sinh( )
1 ( 1)
sinh( )
qV kT
qV kT
D D W LI qA n p e
L L W L
Dp e
L W L
EB
CB
BC B0
B B
C B BC0 B0
C B B
1( 1)
sinh
cosh( ) ( 1)
sinh( )
qV kT
qV kT
DI qA p e
L W L
D D W Ln p e
L L W L
IF0
IR0
αFIF0=
αRIR0
IF0, IR0: Emitter and Collector
Diode Saturation CurrentsαF and αR: Forward
and Reverse Gains
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Ebers-Moll BJT Model
• Rewriting IE and IC equations yields:
• Those equations can be represented by the
Ebers-Moll BJT model shown below: