9. Semiconductors Optics

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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

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Semiconductors Optics

• Semiconductors in optics
• Light emitters, including lasers and LEDs
• Detectors
• Amplifiers
• Waveguides and switches
• Absorbers and filters
• Nonlinear crystals

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The energy bands
One atom
Two interacting atoms
N interacting atoms
Eg
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Insulator
Conductor (metals)
Semiconductors
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Doped semiconductor
p-type
n-type
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Interband transistion
? ? nanoseconds in GaAs
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Intraband transitions
? ? lt ps in GaAs
n-type
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UV
Optical fiber communication
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InP
GaAs
ZnSe
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Bandgap rules The bandgap increases with
decreasing lattice constant. The bandgap
decreases with increasing temperature.
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Interband vs Intraband
C
Interband Most semiconductor devices operated
based on the interband transitions, namely
between the conduction and valence bands. The
devices are usually bipolar involving a p-n
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
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Interband transitions
E
Conduction band
k
Valence band
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E
Conduction band
Eg
k
Valence band
Examples mc0.08 me for conduction band in
GaAs mc0.46 me for valence band in GaAs
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Direct vs. indirect band gap
k
k
GaAs AlxGa1-xAs xlt0.3 ZnSe
Si AlAs Diamond
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Direct vs. indirect band gap
Direct bandgap materials Strong
luminescence Light emitters Detectors
Direct bandgap materials Weak or no
luminescence Detectors
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Fermi-Dirac distribution function
E
1
0.5
EF
f(E)
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Fermi-Dirac distribution function
For electrons
For holes
E
1
0.5
EF
f(E)
kT
kT25 meV at 300 K
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Fermi-Dirac distribution function
For electrons
For holes
E
f(E)
1
0.5
EF
kT
kT25 meV at 300 K
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E
Conduction band
Valence band
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E
Conduction band
Valence band
For filling purpose, the smaller the effective
mass the better.
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Where is the Fermi Level ?
E
Conduction band
n-doped
Intrinsic
Valence band
P-doped
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Interband carrier recombination time (lifetime)
nanoseconds in III-V compound (GaAs, InGaAsP)

microseconds in silicon
Speed, energy storage,
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Quasi-Fermi levels
E
E
E
Ef e
Immediately after Absorbing photons
Returning to thermal equilibrium
Ef h
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E
fe
of carriers
EF e
x

EF h
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E
Condition for net gain gt0
EF c
Eg
EF v
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P-n junction unbiased
EF
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P-n junction Under forward bias
EF
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Heterojunction Under forward bias
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Homojunction
hv
N
p
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Heterojunction waveguide
n
x
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Heterojunction
10 100 nm
EF
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Heterojunction A four-level system
10 100 nm
Phonons
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Absorption and gain in semiconductor
g
Eg
E
?
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Absorption (loss)
g
Eg
?
?
Eg
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Gain
g
Eg
?
?
Eg
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Gain at 0 K
Eg
EFc-EFv
g
EFc-EFv
Eg
?
?
Density of states
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Gain and loss at 0 K
g
EF(EFc-EFv)
Eg
Ehv
?
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Gain and loss at T0 K at different pumping rates
g
EF(EFc-EFv)
Eg
E
N2 gtN1
N1
?
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Gain and loss at Tgt0 K
?laser
g
Eg
N2 gtN1
N1
E
?
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Gain and loss at Tgt0 K Effect of increasing
temperature
?laser
g
Eg
N2 gtN1
N1
E
At a higher temperature
?
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A diode laser
Larger bandgap (and lower index ) materials
lt0.2?m
p
n
lt0.1 mm
Substrate
Cleaved facets w/wo coating
Smaller bandgap (and higher index ) materials
lt1 mm
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Wavelength of diode lasers

• Broad band width (gt200 nm)
• Wavelength selection by grating
• Temperature tuning in a small range

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Wavelength selection by grating tuning
?
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A distributed-feedback diode laser with imbedded
grating
lt0.2?m
p
n
Grating
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Typical numbers for optical gain Gain
coefficient at threshold 20 cm-1 Carrier
density 10 18 cm-3 Electrical to optical
conversion efficiency gt30 Internal quantum
efficiency gt90 Power of optical damage
106W/cm2 Modulation bandwidth gt10 GHz
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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

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Strained layer and bandgap engineering
Substrate
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Density of states
3-D (bulk)
E
?
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Low dimensional semiconductors
When the dimension of potential well is
comparable to the deBroglie wavelength of
electrons and holes.
Lzlt10nm
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2- dimensional semiconductors quantum well
Example GaAs/AlGaAs, ZnSe/ZnMgSe
Al0.3Ga0.7As
GaAs
Al0.3Ga0.7As

E
constant
For wells of infinite depth
E2
E1
?
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2- dimensional semiconductors quantum well
E2c
E1c
E1v
E2v
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2- dimensional semiconductors quantum well
E
E2c
E1c
E1v
E2v
?(E)
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2- dimensional semiconductors quantum well
T0 K
g
E2c
E1c
E1v
E2v
N00
N1gtN0
?
N2gtN1
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2- dimensional semiconductors quantum well
T300K
g
E2c
E1c
Ehv
E1v
E2v
N00
N1gtN0
?
N2gtN1
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2- dimensional semiconductors quantum well
Wavelength Determined by the composition and
thickness of the well and the barrier heights
g
E2c
E1c
Ehv
E1v
E2v
N00
N1gtN0
?
N2gtN1
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3-D vs. 2-D
T300K
g
2-D
3-D
Ehv
E2v
?
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Multiple quantum wellcoupled or uncoupled
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1-D (Quantum wire)
E
Quantized bandgap
Eg
?
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0-D (Quantum dot) An artificial atom
E
Ei
?
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Quantum cascade lasers
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