9. Semiconductors Optics
•Absorption and gain in semiconductors
•Principle of semiconductor lasers (diode lasers)
•Low dimensional materials:
Quantum wells, wires and dots
•Quantum cascade lasers
•Semiconductor detectors
Semiconductors Optics
Semiconductors in optics:
•Light emitters, including lasers and LEDs
•Detectors
•Amplifiers
•Waveguides and switches
•Absorbers and filters
•Nonlinear crystals
The energy bands
One atom
Two interacting atoms
N interacting atoms
Eg
Insulator
Conductor
(metals)
Semiconductors
Doped semiconductor
n-type
p-type
Interband transistion
h  E g
h  E g
  nanoseconds in GaAs
Intraband transitions
  < ps in GaAs
n-type
UV
Optical fiber
communication
GaAs
ZnSe
InP
Bandgap rules
The bandgap increases with decreasing lattice
constant.
The bandgap decreases with increasing
temperature.
Interband vs Intraband
Interband:
C
Most semiconductor devices operated based
on the interband transitions, namely between
the conduction and valence bands.
The devices are usually bipolar involving a pn junction.
V
Intraband:
A new class of devices, such as the quantum
cascade lasers, are based on the transitions
between the sub-bands in the conduction or
valence bands.
The intraband devices are unipolar.
Faster than the intraband devices
C
Interband transitions
Conduction band
E
2
 k
E (k ) 
2mc
k
Valence band
2
E
Conduction band
 2k 2
E (k ) 
2mc
Eg
k
Valence band
Examples:
mc=0.08 me for conduction band in GaAs
mc=0.46 me for valence band in GaAs
Direct vs. indirect band gap
k
GaAs
AlxGa1-xAs x<0.3
ZnSe
k
Si
AlAs
Diamond
Direct vs. indirect band gap
Direct bandgap materials:
Strong luminescence
Light emitters
Detectors
Direct bandgap materials:
Weak or no luminescence
Detectors
Fermi-Dirac distribution function
f (E) 
1
e ( E  EF ) / kT  1
E
EF
0.5
1
f(E)
Fermi-Dirac distribution function
f (E) 
1
e
( E  E F ) / kT
For electrons
1
1  f (E)
For holes
E
kT
EF
0.5
1
f(E)
kT=25 meV at 300 K
Fermi-Dirac distribution function
f (E) 
1
e
( E  E F ) / kT
For electrons
1
1  f (E)
For holes
E
f(E)
kT
EF
kT=25 meV at 300 K
0.5
1
E
Conduction band
Density of States
1 2mc
 (E) 
( 2 ) E
2 
Valence band
E
Conduction band
 (E) 
Valence band
For filling purpose, the smaller the
effective mass the better.
1 2mc
( 2 ) E
2 
E
Where is the Fermi Level ?
 (E) 
Conduction band
n-doped
Intrinsic
Valence band
P-doped
1 2mc
( 2 ) E
2 
Interband carrier recombination time (lifetime)
~ nanoseconds in III-V compound (GaAs, InGaAsP)
~ microseconds in silicon
Speed, energy storage,
E
Quasi-Fermi levels
E
E
Ef e
Immediately after
Absorbing photons
Returning to
thermal equilibrium
Ef h
 (E) 
1 2mc
( 2 ) E
2 
E
fe
# of carriers
EF
e
x
EF
h
 (E) 
1 2mc
( 2 ) E
2 
=
E
Condition for net gain >0
EF c
Rabsorption   v f ( Ev )  c ( Ec )(1  f ( Ec ))
Eg
Remission   v (1  f ( Ev ))  c ( Ec ) f ( Ec )
Rnet  Remission  Rabsorption
Rnet  ( EFc  EFv )  E g
EF v
P-n junction
unbiased
EF
P-n junction
Under forward bias
EF
Heterojunction
Under forward bias
Homojunction
hv
N
p
Heterojunction
waveguide
n
x
Heterojunction
10 – 100 nm
EF
Heterojunction
A four-level system
10 – 100 nm
Phonons
Absorption and gain in semiconductor
E
Conduction band
g
 (E) 
Valence band
Eg
E
 E  Eg

1 2mc
(
) E
2  2
Absorption (loss)
g
Eg


Eg
Gain
g
Eg


Eg
Gain at 0 K
g
EFc-EFv
Eg
EFc-EFv
Eg


Density of states
Gain and loss at 0 K
g
Eg
EF=(EFc-EFv)
E=hv

 E  Eg
Gain and loss at T=0 K
at different pumping rates
g
EF=(EFc-EFv)
Eg
E
N1
N2 >N1
 E  Eg

Gain and loss at T>0 K
laser
g
Eg
N1
N2 >N1
E

 E  Eg
Gain and loss at T>0 K
Effect of increasing temperature
laser
g
Eg
N1
N2 >N1
E
At a higher temperature

 E  Eg
A diode laser
Larger bandgap (and lower index ) materials
<0.2m
p
n
<0.1 mm
Substrate
Cleaved facets
Smaller bandgap (and higher index ) materials
<1 mm
w/wo coating
Wavelength of diode lasers
• Broad band width (>200 nm)
• Wavelength selection by grating
• Temperature tuning in a small range
Wavelength selection by grating tuning

A distributed-feedback diode laser
with imbedded grating
<0.2m
p
n
Grating
Typical numbers for optical gain:
Gain coefficient at threshold: 20 cm-1
Carrier density: 10 18 cm-3
Electrical to optical conversion efficiency: >30%
Internal quantum efficiency >90%
Power of optical damage 106W/cm2
Modulation bandwidth
>10 GHz
Semiconductor vs solid-state
Semiconductors:
• Fast: due to short excited state lifetime ( ns)
• Direct electrical pumping
• Broad bandwidth
• Lack of energy storage
• Low damage threshold
Solid-state lasers, such as rare-earth ion based:
• Need optical pumping
• Long storage time for high peak power
• High damage threshold
Strained layer and bandgap engineering
Substrate
Density of states
3-D (bulk)
 (E)  E
E

Low dimensional semiconductors
When the dimension of potential well is comparable to the
deBroglie wavelength of electrons and holes.
Lz<10nm
2- dimensional semiconductors: quantum well
Example: GaAs/AlGaAs, ZnSe/ZnMgSe
Al0.3Ga0.7As
GaAs
Al0.3Ga0.7As
E
For wells of infinite depth
En  n 2

2mc L2z
2
2
 (E ) 
constant
n  1,2,....
E2
E1

2- dimensional semiconductors: quantum well
E2c
 2 2
Enc  n
2me L2z
2
n  1,2,....
E1c
E1v
E2v
 2 2
Env  n
2mh L2z
2
n  1,2,....
2- dimensional semiconductors: quantum well
E
E2c
E1c
E2v
E1v
(E)
2- dimensional semiconductors: quantum well
T=0 K
g
E2c
E1c
E2v
E1v
N0=0
N1>N0
 N2>N1
2- dimensional semiconductors: quantum well
T=300K
g
E2c
E1c
E=hv
E2v
E1v
N0=0
N1>N0
 N2>N1
2- dimensional semiconductors: quantum well
Wavelength : Determined by the composition
and thickness of the well and the barrier heights
g
E2c
E1c
E=hv
E2v
E1v
N0=0
N1>N0
 N2>N1
3-D vs. 2-D
T=300K
g
2-D
3-D
E2v

E=hv
Multiple quantum well:
coupled or uncoupled
1-D (Quantum wire)
 (E) 
1
E  Eg
E
Quantized
bandgap
Eg

0-D (Quantum dot)
An artificial atom
 ( E )   ( E  Ei )
E
Ei

Quantum cascade lasers