Chapter 10 BJT Fundamentals - Erwin Sitompul
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Transcript Chapter 10 BJT Fundamentals - Erwin Sitompul
Semiconductor Device Physics
Lecture 9
Dr.-Ing. Erwin Sitompul
President University
http://zitompul.wordpress.com
President University
Erwin Sitompul
SDP 9/1
Chapter 9
Optoelectronic Diodes
Photodiodes
Reverse current due to
carriers swept by the E-field
Electron-hole pair
generation due to light
I I dark I L
I L qA ( L N W L P ) G L
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Erwin Sitompul
SDP 9/2
Chapter 9
Optoelectronic Diodes
I–V Characteristics and Spectral Response
Open circuit
voltage voc
Upper limit
~ highest wavelength
~ lowest frequency
~ lowest energy
I L GL
Short circuit
current isc
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Erwin Sitompul
SDP 9/3
Chapter 9
Optoelectronic Diodes
p-i-n Photodiodes
p-i-n : positive–intrinsic– negative
W ≈ Wi-region
most carriers are
generated in the depletion
faster response time
(~10 GHz operation)
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Reverse biased
• current arises mostly in the totally
•
•
depleted i-region, not in quasineutral
region as in pn diode
generated carriers do not need to
diffuse into the depletion region
before they are swept by the E-field
enhanced frequency response
Erwin Sitompul
SDP 9/4
Chapter 9
Optoelectronic Diodes
Forward bias
Increasing EG
Light Emitting Diodes (LEDs)
LEDs are typically made of
compound semiconductors
(direct semiconductors with
band-to-band recombination)
It releases energy by
dissipating light / emitting
photon
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Erwin Sitompul
SDP 9/5
Chapter 10
BJT Fundamentals
Bipolar Junction Transistors (BJTs)
Over the past decades, the higher layout density and lowpower 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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Erwin Sitompul
SDP 9/6
Chapter 10
BJT Fundamentals
Introduction
There are two types of BJT: pnp and npn.
VEB VE VB
VCB VC VB
VEC VE VC
VEB VCB
VBE VB VE
VBC VB VC
VCE VC VE
VCB VEB
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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Erwin Sitompul
SDP 9/7
Chapter 10
BJT Fundamentals
Circuit Configurations
Common-Emitter
I–V Characteristics
Most popular
configuration
Active Mode
dc
Saturation Mode
IC < IB
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IC
100
IB
In active mode,
dc is the common
emitter dc current gain
Erwin Sitompul
SDP 9/8
Chapter 10
BJT Fundamentals
Modes of Operation
Common-Emitter Output Characteristics
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
President University
Erwin Sitompul
SDP 9/9
Chapter 10
BJT Fundamentals
BJT Electrostatics
Under equilibrium and normal operating conditions, the BJT
may be viewed electrostatically as two independent pn
junctions.
N AE N D B N AC
W C B W EB
W W B x nEB x nC B
W : quasineutral
base width
President University
Erwin Sitompul
SDP 9/10
Chapter 10
BJT Fundamentals
BJT Electrostatics
Electrostatic potential, V(x)
Electric field, E(x)
Charge density, ρ(x)
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Erwin Sitompul
SDP 9/11
Chapter 10
BJT Fundamentals
BJT Design
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
pnp BJT, active mode
President University
Erwin Sitompul
SDP 9/12
Chapter 10
BJT Fundamentals
Base Current (Active Bias)
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
EMITTER
COLLECTOR
BASE
1
iC B 0
4
p-type
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2
n-type
Erwin Sitompul
3
p-type
SDP 9/13
Chapter 10
BJT Fundamentals
BJT Performance Parameters (pnp)
IEn
ICn
ICp
IEp
Emitter Efficiency
I Ep
Negligible compared
to holes injected
from emitter
Base Transport Factor
I Ep
IE
I Ep I En
Decrease 5 relative to
1 and 2 to increase efficiency
T
Decrease
I Cp
I Ep
1 relative to 2
to increase transport factor
Common base dc current gain:
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Erwin Sitompul
dc T
SDP 9/14
Chapter 10
BJT Fundamentals
Collector Current (Active Bias)
The collector current is comprised of:
Holes injected from emitter, which do not recombine in the
base 2
Reverse saturation current of collector junction 3
I C α dc I E I C B0
ICB0 :collector current when IE = 0
I C α dc ( I C I B ) I CB0
IC
α dc
1 α dc
IB
I C β dc I B I C E0
I CB0
I CB0
1 α dc
Common emitter dc current gain:
dc
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dc
1 dc
IC
IB
SDP 9/15
Chapter 11
BJT Static Characteristics
Notation (pnp BJT)
Minority
carrier
constants
N B N DB
DB DP
B p
N E N AE
DE DN
E n
LE LN
n E0 np0
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2
ni
LB LP
p B0 p n0
NE
ni
2
Erwin Sitompul
NB
N C N AC
DC D N
C n
LC L N
nC 0 np0
ni
2
NC
SDP 9/16
Chapter 11
BJT Static Characteristics
Emitter Region
Diffusion equation:
d nE
2
0 DE
dx
2
nE
E
Boundary conditions:
n E ( x ) 0
n E ( x 0) n E 0 ( e
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qV E B kT
1)
Erwin Sitompul
SDP 9/17
Chapter 11
BJT Static Characteristics
Base Region
Diffusion equation:
d pB
2
0 DB
dx
2
pB
B
Boundary conditions:
p B (0) p B0 ( e
qV EB kT
p B (W ) p B0 ( e
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1)
qV C B kT
1)
Erwin Sitompul
SDP 9/18
Chapter 11
BJT Static Characteristics
Collector Region
Diffusion equation:
d nC
2
0 DC
dx
2
nC
C
Boundary conditions:
nC ( x ' ) 0
n C ( x ' 0) n C 0 ( e
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qV C B kT
1)
Erwin Sitompul
SDP 9/19
Chapter 11
BJT Static Characteristics
Ideal Transistor Analysis
Solve the minority-carrier diffusion equation in each quasineutral region to obtain excess minority-carrier profiles
n ( x ),
Each region has different set of boundary conditions E
p B ( x ),
Evaluate minority-carrier diffusion currents at edges of
n C ( x )
depletion regions
I E n qA D E
I C n qA D C
d nE
dx
I E p qA D B
x 0
d nC
dx
I C p qA D B
x 0
d pB
dx
x0
d pB
dx
x W
Add hole and electron components together terminal
currents is obtained
I E I Ep I En
IC
IE
IB
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Erwin Sitompul
I C I Cp I Cn
IB IE IC
SDP 9/20
Chapter 11
BJT Static Characteristics
Emitter Region Solution
d nE
2
Diffusion equation:
0 DE
dx
2
x
n E ( x ) A1 e
General solution:
Boundary conditions:
L E
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d nE
dx
x L E
n E ( x ) 0
n E ( x ) n E 0 ( e
I E n qA D E
E
A2 e
n E ( x 0) n E 0 ( e
Solution
nE
qA
x 0
qV E B kT
qV E B kT
DE
LE
Erwin Sitompul
1) e
nE0 (e
1)
x L E
qV E B kT
1)
SDP 9/21
Chapter 11
BJT Static Characteristics
Collector Region Solution
2
Diffusion equation:
General solution:
d nC
0 DC
dx
n C ( x ) A1 e
Boundary conditions:
2
x LC
I C n qA D C
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n C ( x ) n C 0 ( e
d nC
dx
C
A2 e
x LC
nC ( x ) 0
n C ( x 0) n C 0 ( e
Solution
nC
qA
x 0
qV C B kT
qV C B kT
DC
LC
Erwin Sitompul
1) e
nC0 (e
1)
x LC
qV C B kT
1)
SDP 9/22
Chapter 11
BJT Static Characteristics
Base Region Solution
d nB
2
Diffusion equation:
General solution:
0 DB
dx
p B ( x ) A1 e
2
x LB
Solution
p B ( x ) p B0 (e
p B0 (e
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qV C B kT
qV E B kT
ex
1) W
e
B
A2 e
Boundary conditions: p (0) p ( e qV
B
B0
p B (W ) p B0 ( e
pB
x LB
kT
1)
qV C B kT
1)
EB
e (W x )
1)
W
e
LB
e
x LB
LB
e
W LB
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LB
e
(W x ) LB
LB
e
W LB
SDP 9/23
Chapter 11
BJT Static Characteristics
Base Region Solution
Since sinh( )
e e
2
We can write
p B ( x ) p B0 (e
p B0 (e
as
qV C B kT
qV E B kT
ex
1) W
e
p B ( x ) p B0 (e
LB
e
x LB
LB
e
W LB
qV E B kT
p B0 (e
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e (W x )
1)
W
e
Erwin Sitompul
1)
qV C B kT
LB
e
(W x ) LB
LB
e
W LB
sinh (W x ) L B
1)
sinh(W L B )
sinh( x L B )
sinh(W L B )
SDP 9/24
Chapter 11
BJT Static Characteristics
Base Region Solution
Since
d e e e e
sinh( )
cosh( )
d
d
2
2
d
I E p qA D B
qA
DB
LB
I C p qA D B
qA
DB
LB
d pB
dx
x0
cosh(W L B ) qV E B
(e
sinh(W L B )
p B0
kT
1)
1
(e
qV C B kT
(e
qV C B kT
sinh(W L B )
1)
d pB
dx
p B0
x W
1
qV E B
(
e
sinh(W L B )
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kT
1)
Erwin Sitompul
cosh(W L B )
sinh(W L B )
SDP 9/25
1)
Chapter 11
BJT Static Characteristics
Terminal Currents
Since I E I E n I E p , I C I C n I C p
Then
DE
DB
cosh(W L B ) qV E B
I E qA
nE0
p B0
(e
LB
sinh(W L B )
LE
DB
qV C B kT
1
p B0
1)
(e
sinh(W L B )
LB
D
qV
1
B
I C qA
p B0
( e EB
sinh W L B
L B
kT
kT
1)
1)
DC
DB
cosh(W L B ) qV C B
nC0
p B0
(e
LB
sinh(W L B )
LC
kT
1)
IB IE IC
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Erwin Sitompul
SDP 9/26
Chapter 11
BJT Static Characteristics
Simplified Relationships
To achieve high current gain, a typical BJT will be constructed
so that W << LB.
Using the limit value lim sin h ( )
0
lim co sh ( ) 1
0
2
2
Due to VEB
We will have
x
p B ( x ) p B0 (e
1) 1
W
x
qV C B / kT
p B0 (e
1)
W
qV E B / kT
p B ( x ) p B (0) p B 0 (W ) p B (0)
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Erwin Sitompul
x
W
Due to VCB
SDP 9/27
Chapter 11
BJT Static Characteristics
Performance Parameters
For specific condition of
“Active Mode”: emitter junction is forward biased and
collector junction is reverse biased
W << LB, nE0/pB0 NB/NE
1
1
T
DE N B W
D B N E LE
1
dc
1
1W
LE 2 LB
2
,
dc
1
1W
1
2 LB
1
1W
LE 2 LB
DE N B W
DE N B W
DB N E
DB N E
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2
SDP 9/28
2
Chapter 6
pn Junction Diodes: I-V Characteristics
Homework 7
1.
(10.17)
Consider a silicon pnp bipolar transistor at T = 300 K with uniform dopings
of NE = 5×1018 cm–3, NB = 1017 cm–3, and NC = 5×1015 cm–3 . Let DB = 10
cm2/s, xB = 0.7 μm, and assume xB << LB. The transistor is operating in
saturation with JP = 165 A/cm2 and VEB = 0.75 V. Determine:
(a) VCB, (b) VEC(sat), (c) the number/cm2 of excess minority carrier holes in
the base, and (d) the number/cm2 of excess minority carrier electrons in the
long collector, take LC = 35 μm.
2.
Problem 10.4, Pierret’s “Semiconductor Device Fundamentals”.
Deadline: 07.04.2011, at 07:30 am.
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SDP 9/29
(10.14)