Chapter 4 PN and Metal-Semiconductor Junctions
4.1 Building Blocks of the PN Junction Theory
– V +
I
Donor ions
N
P
N-type
I
P-type
diode
symbol
V
Reverse bias
Forward bias
PN junction is present in perhaps every semiconductor device.
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-1
4.1.1 Energy Band Diagram of a PN Junction
N-region
P-region
Ef
(a)
Ef is constant at
equilibrium
Ec
(b)
Ec
Ef
Ev
Ec and Ev are known
relative to Ef
Ev
Ec
Ef
Ev
(c)
Neutral
N-region
Depletion
layer
Neutral
P-region
Ec
(d)
Ef
Ev
Ec and Ev are smooth,
the exact shape to be
determined.
A depletion layer
exists at the PN
junction where n  0
and p  0.
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-2
4.1.2 Built-in Potential
(a)
N-type
P-type
NNdd
(b)
q
NNa a
Ec
fbi
Ef
Ev
V
fbi
(c)
xN
0
xP
x
Can the built-in potential be measured with a voltmeter?
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-3
4.1.2 Built-in Potential
N-region
n  Nd  Nce
 q A kT
kT N c
 A
ln
q
Nd
2
ni
kT N c N a
 q B kT
P-region n 
 Nce
B
ln
2
Na
q
ni
Nc
kT  N c N a
 ln
fbi  B  A 

ln
2
q 
Nd
ni
fbi 




kT N d N a
ln
2
q
ni
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-4
4.1.3 Poisson’s Equation
Gauss’s Law:
s: permittivity (~12o for Si)
: charge density (C/cm3)
E (x)
E (x + Dx)

Dx
x
Poisson’s equation
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-5
4.2 Depletion-Layer Model
(a)
N
(b)
4.2.1
Field andN Potential
in the Depletion Layer
P
N
d
a
N eut ra l Re gion
D eple tion L a yer
N e utr al R egi on
N
P
xnN
xpP
0
On the P-side of the
depletion layer,  = –qNa
d E   qN a
s
dx

qNd
xpP
(c)
xnN
x
–qN a
E ( x) 
(d)
xnN
f bi
qN a
s
x + C1 
qN a
s
( x P  x)
On the N-side,  = qNd

(e)
E ( x)  
x pP
0
x
qN d
s
( x - xN )
V
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-6
(a)
(b)
P
N
N d Potential in theNDepletion
4.2.1 Field
and
Layer
a
N eut ra l Re gion
N
D eple tion La yer
–xnN
N e utral R egi on
P
xpP
0

The electric field is continuous at x = 0.
qN
Nda |xP| = Nd|xP|
(c)
xp
Which side –x
of the junction is depleted more? x
n
–qNa
A one-sided junction is called a N+P junction or P+N junction

Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-7
qNd
xp
(c)
4.2.1x Field–qNand Potential in the Depletion Layer
x
n
a
On the P-side,

(d)
xn
N
x pP
0
x
Arbitrarily choose the
voltage at x = xP as V = 0.
V
f bi
(e)
xnN
xpP
x
Ec
fbi ,
qNa
V ( x) 
( xP  x ) 2
2 s
built-in potential
(f)
Ef
Ev
On the N-side,
qNd
V ( x)  D 
( x  xN )2
2 s
qNd
 fbi 
( x  xN )2
2 s
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-8
(a)
N
Nd
P
Na
4.2.2 Depletion-Layer Width
(b)
N eut ra l Re gion
N
D eple tion La yer
–xnN
N e utral R egi on
P
xpP
0

V is continuous at x = 0
xP  xN  Wdep 
d
If Na >> Nd , as in a P+NqN
junction,
(c)
Wdep 
2 sfbi
q
xp
2 sfbi
–xxn N
qN d
–qN a
|x P||xN|N d
 1
1 


+
 Na Nd 
x
Na @ 0
What about a N+P junction?
Wdep  2 s fbi qN where
1
1
1
1

+

N N d N a lighter dopantdensity
(d)
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
–xn
0
xp
Slide 4-9
x
EXAMPLE: A P+N junction has Na=1020 cm-3 and Nd
=1017cm-3. What is a) its built in potential, b)Wdep , c)xN ,
and d) xP ?
Solution:
a)
kT N d N a
1020 1017 cm6
fbi 
ln
 0.026V ln
1V
2
20
6
q
ni
10 cm
1/ 2
b) W  2 sfbi   2 12 8.8510 1 
dep
 1.6 1019 1017 
qNd


14
 0.12 μm
c) xN  Wdep  0.12 μm
d) xP  xN Nd Na  1.2 104 μm  1.2 Å  0
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-10
4.3 Reverse-Biased PN Junction
+
V
–
N
P
Ec
qfbi
Ec
Ef
Ev
Ef
Ev
(a) V = 0
Ec
qfbi + qV
Ec
Efn
qV
Efp
Ev
Wdep 
2 s (fbi + | Vr |)
2 s  potentialbarrier

qN
qN
1
1
1
1

+

N N d N a lighter dopant density
• Does the depletion layer
widen or shrink with
increasing reverse bias?
Ev
(b) reverse-biased
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-11
4.4 Capacitance-Voltage Characteristics
N
Nd
Conductor
P
Na
Insulator
Conductor
Wde p
Reverse biased PN junction is
a capacitor.
s
Cdep  A
Wdep
• Is Cdep a good thing?
• How to minimize junction capacitance?
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-12
4.4 Capacitance-Voltage Characteristics
1/C dep 2
1
Cdep
2

Wdep
2
A 2 s
2
Capacitance data
2(fbi + V )

qN S A2
Slope = 2/qN s A2
– fbi
Vr
Increasing reverse bias
• From this C-V data can Na and Nd be determined?
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-13
EXAMPLE: If the slope of the line in the previous slide is
2x1023 F-2 V-1, the intercept is 0.84V, and A is 1 mm2, find the
lighter and heavier doping concentrations Nl and Nh .
Solution:
N l  2 /( slope q s A2 )
 2 /(2 1023 1.6 1019 12 8.851014 108 cm2 )
 6 1015 cm3
2 qf
0.84
kT N h N l
ni kTbi
1020 0.026
18
3
fbi 
ln 2  N h 
e 
e

1
.
8

10
cm
q
ni
Nl
6 1015
• Is this an accurate way to determine Nl ? Nh ?
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-14
4.5 Junction Breakdown
I
Forward Current
V B, breakdown
voltage
V
R
Small leakage
Current
A
P N
R
A
C
3.7 V
Zener diode
B
IC
D
A Zener diode is designed to operate in the breakdown mode.
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-15
4.5.1 Peak Electric Field
N+
Na
0
Neutral Region
increasing
reverse bias
P
xp
 2qN

(fbi + | Vr |) 
Ep  E (0)  
 s

(a)
E
Ep
1/ 2
increasing reverse bias
xp
x
VB 
 s Ecrit 2
2qN
 fbi
(b)
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-16
4.5.2 Tunneling Breakdown
Dominant if both sides of
a junction are very heavily
doped.
Filled States -
Empty States
Ec
Ev
J Ge
H /
εp
I
V
Ep  Ecrit  106 V/cm
Breakdown
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-17
4.5.3 Avalanche Breakdown
Ec
original
electron
Efp
Ev
• impact ionization: an energetic
electron generating electron and
hole, which can also cause
impact ionization.
• Impact ionization + positive
feedbackavalanche breakdown
VB 
electron-hole
pair generation
Ec
Efn
 s Ecrit 2
2qN
1
1
1
VB  
+
N Na Nd
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-18
4.6 Forward Bias – Carrier Injection
Forward
biased
Forward biased
VV=0
=0
V
I=0
– +
Ec
N
 qfbi
P
-
Ef
Ev
Ec
qfbi –qV
Ef n
qV
Efp
Ev
+
Drift and diffusion cancel out
Minority carrier injection
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-19
4.6 Forward Bias –
Quasi-equilibrium Boundary Condition
n( xP )  Nce
( Ec  E fn ) / kT
 Nce
( Ec E fp ) / kT ( E fn E fp ) / kT
e
( E fn E fp ) / kT
EEcc
 nP0e
 nP0e
qV / kT
• The minority carrier
EEfnfnfn
fp
EEfp
EEv v
xx
densities are raised
by eqV/kT
• Which side gets more
carrier injection?
xN0 x0 P
N
P
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-20
4.6 Carrier Injection Under Forward Bias–
Quasi-equilibrium Boundary Condition
qV
n(xP )  nP 0 e
p (xP)  p N 0 e
kT

2
ni qV
e
Na
kT
2
qV kT
ni qV

e
Nd
n( xP )  n( xP )  nP0  nP0 (eqV
kT
kT
p( xN )  p( xN )  pN 0  pN 0 (eqV
1)
kT
1)
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-21
EXAMPLE: Carrier Injection
A PN junction has Na=1019cm-3 and Nd=1016cm-3. The applied
voltage is 0.6 V.
Question: What are the minority carrier concentrations at the
depletion-region edges?
Solution: n( xP )  nP0eqV kT  10 e0.6 0.026  1011 cm-3
p( xN )  pN 0eqV kT  104  e0.6 0.026  1014 cm-3
Question: What are the excess minority carrier concentrations?
Solution: n( xP )  n( xP )  nP0  1011 10  1011 cm-3
p( xN )  p( xN )  pN 0  1014 104  1014 cm-3
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-22
4.7 Current Continuity Equation
A
a
a re
J p ( x)
q
 A
J p ( x + Dx)
+ A  Dx 
q
p

A
Jp (x)
Jp (x + Dx)
p
Volume = A·Dx
Dx

J p ( x + Dx)  J p ( x)
Dx

dJ p
dx
q
q
p

p

x
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-23
4.7 Current Continuity Equation

dJ p
dx
q
p

Minority drift current is negligible;
 Jp= –qDpdp/dx
d2p
p
qDp 2  q
dx
p
d p
p
p

 2
2
dx
Dp p Lp
2
d 2 n n
 2
2
dx
Ln
Lp and Ln are the diffusion lengths
L p  D p p
Ln  Dn n
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-24
4.8 Forward Biased Junction-- Excess Carriers
P
+
N
d 2 p
p
 2
2
dx
Lp
xP
-x N
0
x
p()  0
p( xN )  pN 0 (eqV / kT 1)
x / Lp
 x / Lp

p ( x)  Ae + Be
 x  xN  / L p
qV / kT

p ( x)  pN 0 (e
1)e
, x  xN
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-25
4.8 Excess Carrier Distributions
1.0
P-side
N-side
Na = 1017 cm -3
nP ' ex /L n
Nd = 21017 cm-3
– 3L n
–2L n
0.5
–Ln
pN ' e–x /L p
0 L p 2L p 3L p 4Lp
 x  xN  / L p
qV / kT

p ( x)  pN 0 (e
1)e
, x  xN
n( x)  nP0 (eqV / kT 1)e x xP / Ln , x  xP
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-26
EXAMPLE: Carrier Distribution in Forward-biased PN Diode
N-type
Nd = 5  cm-3
Dp =12 cm2/s
p = 1 ms
P-type
Na = 101 7 cm-3
Dn=36.4 cm2 /s
n = 2 ms
• Sketch n'(x) on the P-side.
n( xP )  nP 0 (eqV
2
ni
1020 0.6 0.026
kT
qV / kT
 1) 
(e
 1)  17 e
 1013 cm3
Na
10
N-side
1013cm-3
P-side
n’ ( = p’ )
2
p´ ( = n’ ) 2´
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
x
Slide 4-27
EXAMPLE: Carrier Distribution in Forward-biased PN Diode
• How does Ln compare with a typical device size?
Ln  Dn n  36  2 10 6  85 μm
• What is p'(x) on the P- side?
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-28
4.9 PN Diode I-V Characteristics
Jtotal
Jtotal
Jn = Jtotal – Jp
Jp = Jtotal – Jn
JnP
JnP
JpN
JpN
x
P-side
0
J pN
N-side
P-side
Dp
dp( x)
 qDp
q
pN 0 (eqV
dx
Lp
J nP  qDn
D
dn( x)
 q n nP 0 (e qV
dx
Ln
kT
kT
0
 1)e
N-side
 x  x N  L p
 1)e x  xP  Ln
 Dp
 qV
Dn

T otalcurrent  J pN ( x N ) + J nP ( xP )  q
p +q
n P 0 ( e
 L N0

Ln
p


 J at all x
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
kT
 1)
Slide 4-29
The PN Junction as a Temperature Sensor
I  I 0 (eqV kT 1)
 Dp
Dn 

I 0  Aqni
+
L N

 p d Ln N a 
2
What causes the IV curves to shift to lower V at higher T ?
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-30
4.9.1 Contributions from the Depletion Region
n  p  ni eqV / 2kT
Net recombination (generation) rate:
ni qV / 2 kT
(e
 1)
 dep
I  I 0 (e
qV / kT
 1) + A
qniWdep
τ dep
(eqV / 2kT  1)
Space-Charge Region (SCR) current
I leakage  I 0 + A
qniWdep
τ dep
Under forward bias, SCR current is an extra
current with a slope 120mV/decade
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-31
4.10 Charge Storage
1013 cm -3
N-side
QI
P-side
I  Q s
Q  I s
n'
p’
22
x
What is the relationship between s (charge-storage time)
and  (carrier lifetime)?
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-32
4.11 Small-signal Model of the Diode
I
V
1 dI
d
d
qV / kT
G 

I 0 (e
 1) 
I 0 e qV / kT
R dV dV
dV
R
C

q
kT
I 0 (e qV / kT )  I DC /
kT
q
What is G at 300K and IDC = 1 mA?
Diffusion Capacitance:
dQ
dI
kT
C
s
  sG   s I DC /
dV
dV
q
Which is larger, diffusion or depletion capacitance?
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-33
Part II: Application to Optoelectronic Devices
4.12 Solar Cells
•Solar Cells is also known
as photovoltaic cells.
•Converts sunlight to
electricity with 10-30%
conversion efficiency.
•1 m2 solar cell generate
about 150 W peak or 25 W
continuous power.
•Low cost and high
efficiency are needed for
wide deployment.
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-34
4.12.1 Solar Cell Basics
I
Short Circuit
light
N
P
Dark IV
Eq.(4.9.4)
I
sc
0
-
V
Solar Cell
IV
Eq.(4.12.1)
Ec
Ev
0.7 V
–I
+
sc
(a)
Maximum
power-output
I  I 0 (eqV kT 1)  I sc
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-35
Direct-Gap and Indirect-Gap Semiconductors
•Electrons have both particle and wave properties.
•An electron has energy E and wave vector k.
direct-gap semiconductor
indirect-gap semiconductor
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-36
4.12.2 Light Absorption
Light intensity(x) e-x
α(1/cm): absorption
coefficient
1/α : light penetration
depth
P hot onEnergy(eV) 
hc

1.24

( mm)

A thinner layer of direct-gap semiconductor can absorb most
of solar radiation than indirect-gap semiconductor. But Si…
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-37
4.12.3 Short-Circuit Current and Open-Circuit Voltage
ea
ar
A
Jp (x + Dx)
Jp (x)
p
Volume = A·Dx
Dx
If light shines on the N-type
semiconductor and generates
holes (and electrons) at the
rate of G s-1cm-3 ,
d 2 p p G
 2 
2
dx
Lp Dp
x
If the sample is uniform (no PN junction),
d2p’/dx2 = 0  p’ = GLp2/Dp= Gp
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-38
Solar Cell Short-Circuit Current, Isc
Assume very thin P+ layer and carrier generation in N region only.
Isc
P+
G
p()  L
  pG
Dp
2
p
p(0)  0
N
0
x
p( x)   pG(1  e
P'
Lp
)
Dp
dp( x)
 x / Lp
J p  qDp
q
 pGe
dx
Lp
 pG
0
 x / Lp
x
I sc  AJ p (0)  AqLpG
G is really not uniform. Lp needs be larger than the light
penetration depth to collect most of the generated carriers.
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-39
Open-Circuit Voltage
•Total current is ISC plus the PV diode (dark) current:
ni2 Dp qV / kT
I  Aq
(e
 1)  AqLpG
N d Lp
•Solve for the open-circuit voltage (Voc) by setting I=0
(assuming eqVoc / kT  1)
2
ni D p qVoc / kT
0
e
 LpG
N d Lp
kT
2
Voc 
ln( p GNd / ni )
q
How to raise Voc ?
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-40
4.12.4 Output Power
A particular operating point on the
solar cell I-V curve maximizes the
output power (I V).
Output Pow
er  I sc Voc  FF
•Si solar cell with 15-20% efficiency
dominates the market now
•Theoretically, the highest efficiency (~24%) can be obtained with
1.9eV >Eg>1.2eV. Larger Eg lead to too low Isc (low light
absorption); smaller Eg leads to too low Voc.
•Tandem solar cells gets 35% efficiency using large and small Eg
materials tailored to the short and long wavelength solar light.
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-41
4.13 Light Emitting Diodes and Solid-State Lighting
Light emitting diodes (LEDs)
• LEDs are made of compound semiconductors such as InP
and GaN.
• Light is emitted when electron and hole undergo radiative
recombination.
Ec
Radiative
recombination
Non-radiative
recombination
through traps
Ev
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-42
Direct and Indirect Band Gap
Trap
Direct band gap
Example: GaAs
Indirect band gap
Example: Si
Direct recombination is efficient
as k conservation is satisfied.
Direct recombination is rare as k
conservation is not satisfied
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
4.13.1 LED Materials and Structure
1.24
1.24
LED wavelength ( m m) 

photonenergy Eg (eV )
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-44
4.13.1 LED Materials and Structure
compound semiconductors
E
Eg(eV)
(eV )
Wavelength
(μm)
Color
Lattice
constant
(Å)
binary semiconductors:
- Ex: GaAs, efficient emitter
InAs
0.36
3.44
InN
0.65
1.91
InP
1.36
0.92
GaAs
1.42
0.87
6.05
infrared
red
Red
yellow
Yellow
blue
Green
violet
Blue
3.45
ternary semiconductor :
5.87
- Ex: GaAs1-xPx , tunable Eg (to
vary the color)
5.66
5.46
GaP
2.26
0.55
AlP
3.39
0.51
5.45
GaN
2.45
0.37
3.19
AlN
6.20
0.20
UV
quaternary semiconductors:
- Ex: AlInGaP , tunable Eg and
lattice constant (for growing high
quality epitaxial films on
inexpensive substrates)
3.11
Light-emitting diode materials
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-45
Common LEDs
Spectral
range
Material
System
Substrate
Infrared
InGaAsP
InP
Optical communication
Infrared
-Red
GaAsP
GaAs
Indicator lamps. Remote
control
AlInGaP
GaA or
GaP
Optical communication.
High-brightness traffic
signal lights
GreenBlue
InGaN
GaN or
sapphire
High brightness signal
lights.
Video billboards
Blue-UV
AlInGaN
GaN or
sapphire
Solid-state lighting
RedBlue
Organic
semiconductors
glass
RedYellow
Example Applications
AlInGaP
Quantun Well
Displays
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-46
4.13.2 Solid-State Lighting
luminosity (lumen, lm): a measure of visible light energy
normalized to the sensitivity of the human eye at
different wavelengths
Incandescent
lamp
Compact
fluorescent
lamp
Tube
fluorescent
lamp
17
60
50-100
White
LED
Theoretical limit at
peak of eye sensitivity
( λ=555nm)
Theoretical limit
(white light)
683
~340
90-?
Luminous efficacy of lamps in lumen/watt
Organic Light Emitting Diodes (OLED) :
has lower efficacy than nitride or aluminide based compound semiconductor LEDs.
Terms: luminosity measured in lumens. luminous efficacy,
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-47
4.14 Diode Lasers
4.14.1 Light Amplification
(a) Absorption
(d) Net Light
Absorption
(b) Spontaneous
Emission
(e) Net Light
Amplification
(c) Stimulated
Emission
Light amplification requires
population inversion: electron
occupation probability is
larger for higher E states than
lower E states.
Stimulated emission: emitted photon has identical frequency and
directionality as the stimulating photon; light wave is amplified.
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-48
4.14.1 Light Amplification in PN Diode
Population inversion
is achieved when
qV  E fn  E fp  Eg
Equilibrium, V=0
Population inversion, qV > Eg
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-49
4.14.2 Optical Feedback and Laser
P+
light
out
Cleaved
crystal
plane
N+
Laser threshold is reached (light
intensity grows by feedback)
when
R1  R2  G  1
•R1, R2: reflectivities of the two ends
•G : light amplification factor (gain)
for a round-trip travel of the light
through the diode
Light intensity grows until R1  R2  G  1 , when the light intensity
is just large enough to stimulate carrier recombinations at the same
rate the carriers are injected by the diode current.
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-50
4.14.2 Optical Feedback and Laser Diode
• Distributed Bragg
reflector (DBR) reflects
light with multi-layers of
semiconductors.
•Vertical-cavity surfaceemitting laser (VCSEL) is
shown on the left.
•Quantum-well laser has
smaller threshold current
because fewer carriers
are needed to achieve
population inversion in
the small volume of the
thin small-Eg well.
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-51
4.14.3 Laser Applications
Red diode lasers: CD, DVD reader/writer
Blue diode lasers: Blu-ray DVD (higher storage density)
1.55 mm infrared diode lasers: Fiber-optic communication
4.15 Photodiodes
Photodiodes: Reverse biased PN diode. Detects photogenerated current (similar to Isc of solar cell) for optical
communication, DVD reader, etc.
Avalanche photodiodes: Photodiodes operating near
avalanche breakdown amplifies photocurrent by impact
ionization.
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-52
Part III: Metal-Semiconductor Junction
Two kinds of metal-semiconductor contacts:
• Rectifying Schottky diodes: metal on lightly
doped silicon
•Low-resistance ohmic contacts: metal on
heavily doped silicon
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-53
fBn Increases with Increasing Metal Work Function
Vacuum level, E0
y M : Work Function
cSi = 4.05 eV
qyM
of metal
qfBn
Ec
c Si : Electron Affinity of Si
Ef
Theoretically,
Ev
fBn= yM – cSi
Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-54
4.16 Schottky Barriers
Energy Band Diagram of Schottky Contact
Metal
Depletion
layer
Neutral region
qfBn
Ec
Ef
• Schottky barrier height, fB ,
N-Si
Ev
Ec
P-Si
qfBp
Ef
Ev
is a function of the metal
material.
• fB is the most important
parameter. The sum of qfBn
and qfBp is equal to Eg .
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-55
Schottky barrier heights for electrons and holes
Metal
f Bn (V)
f Bp (V)
Work
Function
y m (V)
Mg
0.4
3.7
Ti
0.5
Cr
0.61
0.61
0.5
4.3
4.5
W
0.67
Mo
0.68
Pd
0.77
0.42
4.6
4.6
Au
0.8
Pt
0.9
0.3
5.1
5.1
5.7
fBn + fBp  Eg
fBn increases with increasing metal work function
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-56
Fermi Level Pinning
Vacuum level, E0
cSi = 4.05 eV
qyM
qfBn
+ 
Ec
Ef
Ev
• A high density of
energy states in the
bandgap at the metalsemiconductor interface
pins Ef to a narrow
range and fBn is
typically 0.4 to 0.9 V
• Question: What is the
typical range of fBp?
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-57
Schottky Contacts of Metal Silicide on Si
Silicide: A silicon and metal compound. It is conductive
similar to a metal.
Silicide-Si interfaces are more stable than metal-silicon
interfaces. After metal is deposited on Si, an annealing step is
applied to form a silicide-Si contact. The term metal-silicon
contact includes and almost always means silicide-Si contacts.
Silicide ErSi1.7 HfSi MoSi2 ZrSi2 TiSi2 CoSi2 WSi2 NiSi2 Pd2Si PtSi
ffBnBn (V) 0.28 0.45 0.55 0.55 0.61 0.65 0.67 0.67 0.75 0.87
0.55 0.49 0.45 0.45 0.43 0.43 0.35 0.23
ffBpBp (V)
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-58
Using C-V Data to Determine fB
qfbi  qf Bn  ( Ec  E f )
qfbi
qfBn
Ec
Ef
Ev
qfBn
q(fbi + V)
qV
Nc
 qf Bn  kT ln
Nd
Wdep 
C
Ec
Ef
Ev
2 s (fbi + V )
qNd
s
Wdep
A
Question:
How should we plot the CV
data to extract fbi?
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-59
Using CV Data to Determine fB
1/C2
1
2(fbi + V )

2
C
qNd  s A2
V
fbi
qfBn
qfbi
Ec
Ef
Once fbi is known, fB can
be determined using
E
v
Nc
qfbi  qfBn  ( Ec  E f )  qfBn  kT ln
Nd
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-60
4.17 Thermionic Emission Theory
vthx
-
V
Metal
N-type
Silicon
q(f B  V)
qfB
qV
Efm
Ec
Efn
Ev
x
 2mn kT 
n  N c e  q (f B V ) / kT  2
2

 h

vth  3kT / mn
J S M
3/ 2
e  q (f B V ) / kT
vthx   2kT / mn
4qmn k 2 2 qf B / kT qV / kT
1
  qnvthx 
T e
e
3
2
h
 J 0 e qV / kT , where J o  100e  qf B / kT A/cm2
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-61
4.18 Schottky Diodes
Forward
biased
V=0
I
Reverse
biased
Reverse bias
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
V
Forward bias
Slide 4-62
4.18 Schottky Diodes
I 0  AKT 2 e  qf B / kT
4qmn k 2
2
2
K

100
A/(cm

K
)
3
h
I  I S  M + I M  S  I 0 e qV / kT  I 0  I 0 (e qV / kT  1)
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-63
4.19 Applications of Schottly Diodes
I I
I  I 0 (e qV / kT  1)
Schottky diode
I 0  AKT 2 e  qf B / kT
ffBB
PN junction
junction
PN
diode
V
V
• I0 of a Schottky diode is 103 to 108 times larger than a PN
junction diode, depending on fB . A larger I0 means a smaller
forward drop V.
• A Schottky diode is the preferred rectifier in low voltage,
high current applications.
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-64
Switching Power Supply
PN Junction
rectifier
110V/220V
AC
utility
power
Schottky
rectifier
Transformer
100kHz
Hi-voltage
Hi-voltage
DC
MOSFET
AC
Lo-voltage
AC
50A
1V
DC
inverter
feedback to modulate the pulse width to keep Vout = 1V
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-65
4.19 Applications of Schottky diodes
Question: What sets the lower limit in a Schottky diode’s
forward drop?
• Synchronous Rectifier: For an even lower forward drop,
replace the diode with a wide-W MOSFET which is not
bound by the tradeoff between diode V and leakage current.
• There is no minority carrier injection at the Schottky
junction. Therefore, Schottky diodes can operate at higher
frequencies than PN junction diodes.
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-66
4.20 Quantum Mechanical Tunneling
Tunneling probability:
P  exp(2T
8 2m
(VH  E ) )
2
h
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-67
4.21 Ohmic Contacts
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-68
4.21 Ohmic Contacts
Wdep 
2 sf Bn
qN d
Silicide
N+ Si
fBn – V
fBn
-
-
Ec , Ef
-
Efm
V
Ec , Ef
Tunneling
probability:
Pe
 HfBn
Nd
T  Wdep / 2 
4
H 
h
J S M 
x
Ev
Ev
x
 sfBn / 2 qNd
 s mn / q
1
qNd vthx P  qNd
2
kT / 2mn e
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
 H ( fBn V ) /
Nd
Slide 4-69
4.21 Ohmic Contacts
1
Hf Bn / N d
2e
 dJS M 
Hf Bn /
Rc  
e
 
qvthx H N d
 dV 
Nd
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Ω  cm2
Slide 4-70
4.22 Chapter Summary
Part I: PN Junction
kT N d N a
fbi 
ln
2
q
ni
depletion width
junction capacitance
Wdep
The potential barrier
increases by 1 V if a 1 V
reverse bias is applied
2 s  potentialbarrier

qN
Cdep  A
s
Wdep
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-71
4.22 Chapter Summary
• Under forward bias, minority carriers are injected
across the jucntion.
• The quasi-equilibrium boundary condition of
minority carrier densities is:
n( x p )  nP0eqV kT
p( xN )  pN 0eqV kT
• Most of the minority carriers are injected into the
more lightly doped side.
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-72
4.22 Chapter Summary
• Steady-state
continuity equation:
d 2 p
p
p

 2
2
dx
Dp p Lp
L p  D p p
• Minority carriers
diffuse outward  e–|x|/Lp
and e–|x|/Ln
• Lp and Ln are the
diffusion lengths
I  I 0 (eqV kT 1)
 Dp
Dn 

I 0  Aqni
+
L N

L
N
p
d
n
a


2
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-73
4.22 Chapter Summary
Charge storage:
Q  I s
Diffusion capacitance:
C   sG
Diode conductance:
G  I DC
kT
/
q
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-74
4.22 Chapter Summary
Part II: Optoelectronic Applications
Solar cell power  I sc Voc  FF
•~100um Si or <1um direct–gap semiconductor can absorb most of solar
photons with energy larger than Eg.
•Carriers generated within diffusion length from the junction can be
collected and contribute to the Short Circuit Current Isc.
•Theoretically, the highest efficiency (~24%) can be obtained with 1.9eV
>Eg>1.2eV. Larger Eg lead to too low Isc (low light absorption); smaller Eg
leads to too low Open Circuit VoltageVoc.
•Si cells with ~15% efficiency dominate the market. >2x cost reduction
(including package and installation) is required to achieve cost parity with
base-load non-renewable electricity.
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-75
4.22 Chapter Summary
LED and Solid-State Lighting
•Electron-hole recombination in direct-gap semiconductors such as GaAs
produce light.
•Tenary semiconductors such as GaAsP provide tunable Eg and LED color.
•Quatenary semiconductors such as AlInGaP provide tunable Eg and lattice
constants for high quality epitaxial growth on inexpensive substrates.
•Beyond displays, communication, and traffic lights, a new application is
space lighting with luminous efficacy >5x higher than incandescent lamps.
White light can be obtained with UV LED and phosphors. Cost still an issue.
•Organic semiconductor is an important low-cost LED material class.
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-76
4.22 Chapter Summary
Laser Diodes
•Light is amplified under the condition of population inversion – states at
higher E have higher probability of occupation than states at lower E.
•Population inversion occurs when diode forward bias qV > Eg.
•Optical feedback is provided with cleaved surfaces or distributed Bragg
reflectors.
•When the round-trip gain (including loss at reflector) exceeds unity, laser
threshold is reached.
•Quantum-well structures significantly reduce the threshold currents.
•Purity of laser light frequency enables long-distance fiber-optic
communication. Purity of light direction allows focusing to tiny spots and
enables DVD writer/reader and other application.
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-77
4.22 Chapter Summary
Part III: Metal-Semiconductor Junction
I 0  AKT 2eqfB / kT
•Schottky diodes have large reverse saturation current, determined by the
Schottky barrier height fB, and therefore lower forward voltage at a given
current density.
•Ohmic contacts relies on tunneling. Low resistance contact requires
low fB and higher doping concentration.
Rc  e
(
4
fB  s mn / qN d )
h
Ω cm2
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-78
fBn Increases with Increasing Metal Work Function
Vacuum level, E0
cSi = 4.05 eV
qyM
q fBn
Ideally,
fBn= yM – cSi
Ec
Ef
Ev
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 4-79