Download President University Erwin Sitompul SDP 9/23 Base Region Solution

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( LN  W  LP )GL
President University
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
President University
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
President University
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
President University
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: . . . . . .
President University
Erwin Sitompul
SDP 9/7
Chapter 10
BJT Fundamentals
Circuit Configurations
Common-Emitter
I–V Characteristics
Most popular
configuration
Active Mode
Saturation Mode
IC <  IB
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IC
 dc 
IB
100
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 DB  N AC
WCB  WEB
W  WB  xnEB  xnCB
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)
President University
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
iCB0
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
Negligible compared
to holes injected
from emitter
ICp
IEp
 Emitter Efficiency
I Ep
I Ep
 

IE
I Ep  I En
 Decrease 5 relative to
 Base Transport Factor
T 
 Decrease
1 and 2 to increase efficiency
I Cp
I Ep
1 relative to 2
to increase transport factor
Common base dc current gain:
President University
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  αdc I E  I CB0
ICB0 :collector current when IE = 0
I C  αdc ( I C  I B )  I CB0
I CB0
α dc
I CB0
IC 
IB 
1  α dc
1  α dc
I C  βdc I B  I CE0
Common emitter dc current gain:
 dc
IC
 dc 

1   dc I B
President University
Erwin Sitompul
SDP 9/15
Chapter 11
BJT Static Characteristics
Notation (pnp BJT)
Minority
carrier
constants
N E  N AE
DE  DN
E  n
LE  LN
nE0  np0
 ni2 N E
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N B  N DB
DB  DP
B  p
LB  LP
pB0  pn0
 ni2 N B
Erwin Sitompul
N C  N AC
DC  DN
C  n
LC  LN
nC0  np0
 ni2 N C
SDP 9/16
Chapter 11
BJT Static Characteristics
Emitter Region
 Diffusion equation:
d 2 nE nE
0  DE

2
dx
E
 Boundary conditions:
nE ( x  )  0
nE ( x  0)  nE0 (e qVEB
President University
kT
 1)
Erwin Sitompul
SDP 9/17
Chapter 11
BJT Static Characteristics
Base Region
 Diffusion equation:
d 2 pB pB
0  DB

2
dx
B
 Boundary conditions:
pB (0)  pB0 (eqVEB kT  1)
qVCB kT
pB (W )  pB0 (e
 1)
President University
Erwin Sitompul
SDP 9/18
Chapter 11
BJT Static Characteristics
Collector Region
 Diffusion equation:
d 2 nC nC
0  DC

2
dx
C
 Boundary conditions:
nC ( x '  )  0
nC ( x '  0)  nC0 (e qVCB
President University
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
pB ( x),
 Evaluate minority-carrier diffusion currents at edges of
nC ( x)
depletion regions
d pB
d nE
I Ep  qADB
I En  qADE
dx x 0
dx x0
d pB
d nC
I Cp  qADB
I Cn  qADC
dx x W
dx x0
 Add hole and electron components together  terminal
currents is obtained
IC
IE
IB
President University
Erwin Sitompul
I E  I Ep  I En
I C  I Cp  I Cn
IB  I E  IC
SDP 9/20
Chapter 11
BJT Static Characteristics
Emitter Region Solution
d 2 nE nE
0  DE

2
dx
E
 Diffusion equation:
 General solution:
 x LE
x LE

nE ( x )  A1e
 A2e
nE ( x  )  0
nE ( x  0)  nE0 (e qVEB kT  1)
 Boundary conditions:
nE ( x)  nE0 (e qVEB
 Solution
I En
d nE
 qADE
dx
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kT
 1)e  x LE
DE
 qA
nE0 (e qVEB
LE
x0
Erwin Sitompul
kT
 1)
SDP 9/21
Chapter 11
BJT Static Characteristics
Collector Region Solution
d 2 nC nC
0  DC

2
dx
C
 Diffusion equation:
 General solution:
nC ( x)  A1e  x LC  A2e x LC
nC ( x  )  0
nC ( x  0)  nC0 (e qVCB kT  1)
 Boundary conditions:
nC ( x)  nC0 (eqVCB
 Solution
I Cn
kT
 1)e x LC
DC
d nC
qVCB


qA
n
(
e
 qADC
C0

L
dx x0
C
President University
Erwin Sitompul
kT
 1)
SDP 9/22
Chapter 11
BJT Static Characteristics
Base Region Solution
 Diffusion equation:
 General solution:
d 2 nB pB
0  DB

2
dx
B
pB ( x)  A1e x LB  A2e x LB
 Boundary conditions: p (0)  p (eqVEB
B
B0
pB (W )  pB0 (eqVCB
 Solution
kT
kT
 1)
 1)
(W  x ) LB
 (W  x ) LB


e

e
qVEB kT
pB ( x)  pB0 (e
 1) 

W LB
W LB
e
 e

x LB
 x LB


e

e
qVCB kT
 pB0 (e
 1)  W LB
W LB 
e
e

President University
Erwin Sitompul
SDP 9/23
Chapter 11
BJT Static Characteristics
Base Region Solution
e  e
 Since sinh( ) 
2
(W  x ) LB
 (W  x ) LB


e

e
qVEB kT
 We can write pB ( x)  pB0 (e
 1) 

W LB
W LB
e
 e

x LB
 x LB


e

e
qVCB kT
 pB0 (e
 1)  W LB
W LB 
e

e


as
pB ( x)  pB0 (e
qVEB kT
 pB0 (eqVCB
President University
Erwin Sitompul
 1)
kT
sinh  (W  x) LB 
sinh(W LB )
sinh( x LB )
 1)
sinh(W LB )
SDP 9/24
Chapter 11
BJT Static Characteristics
Base Region Solution
d
d  e  e
sinh( ) 
 Since

d
d  2
I Ep
I Cp
 e  e
 cosh( )

2

d pB
 qADB
dx x 0
 cosh(W LB ) qVEB
DB
 qA
pB0 
(e
LB
 sinh(W LB )
d pB
 qADB
dx x W

DB
1
 qA
pB0 
(e qVEB
LB
 sinh(W LB )
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kT
kT
1
 1) 
(e qVCB
sinh(W LB )
cosh(W LB ) qVCB
 1) 
(e
sinh(W LB )
Erwin Sitompul
kT
kT
SDP 9/25

 1) 


 1) 

Chapter 11
BJT Static Characteristics
Terminal Currents
 Since I E  I En  I Ep , I C  I Cn  I Cp
 Then
 DE
DB
cosh(W LB )  qVEB
 I E  qA 
nE0 
pB0
 (e
LB
sinh(W LB ) 
 LE

 DB
 qVCB kT
1

pB0
 1) 
 (e
sinh(W LB ) 
 LB

 D
 qVEB kT
1
B
 I C  qA 
p
(e
 1)
 L B0 sinh W L  
 B
B 
 DC
DB
cosh(W LB )  qVCB

nC0 
pB0
 (e
LB
sinh(W LB ) 
 LC
kT
kT
 1)

 1) 

 IB  IE  IC
President University
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 sinh( )  
 0
lim cosh( )  1 
 0
2
2
Due to VEB
 We will have
x

pB ( x)  pB0 (e
 1) 1  
 W
 x
qVCB / kT
 pB0 (e
 1)  
W 
qVEB / kT
x
pB ( x)  pB (0)   pB0 (W )  pB (0)
W
President University
Erwin Sitompul
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

DE N B W
1
DB N E LE
 dc 
T 
1
DE N B W 1  W 
1
  
DB N E LE 2  LB 
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2
,  dc 
Erwin Sitompul
1
1W 
1  
2  LB 
2
1
DE N B W 1  W 
  
DB N E LE 2  LB 
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.
President University
Erwin Sitompul
SDP 9/29
(10.14)