Semiconductor Device Physics
Lecture 9
Dr.-Ing. Erwin Sitompul
President University
http://zitompul.wordpress.com
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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
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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
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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
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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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Erwin Sitompul
 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
x0
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
Erwin Sitompul
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
x0
 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
1W 
 

LE 2  LB 
2
,
 dc 
1
1W 
1 

2  LB 
1
1W 
 

LE 2  LB 
DE N B W
DE N B W
DB N E
DB N E
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Erwin Sitompul
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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Erwin Sitompul
SDP 9/29
(10.14)