View
228
Download
3
Tags:
Embed Size (px)
Citation preview
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
One atom Two interacting atoms N interacting atoms
The energy bands
Eg
Insulator Conductor(metals)
Semiconductors
Doped semiconductor
n-type p-type
Interband transistion
gEh gEh
nanoseconds in GaAs
n-type
Intraband transitions
< ps in GaAs
UV
Optical fiber communication
GaAs InPZnSe
Bandgap rules
The bandgap increases with decreasing lattice constant.
The bandgap decreases with increasing temperature.
Interband vs Intraband
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.
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
V
C
E
k
cm
kkE
2)(
22
Conduction band
Valence band
Interband transitions
E
k
cm
kkE
2)(
22
Conduction band
Valence band
Examples:
mc=0.08 me for conduction band in GaAs
mc=0.46 me for valence band in GaAs
Eg
Direct vs. indirect band gap
k k
GaAsAlxGa1-xAs x<0.3ZnSe
SiAlAsDiamond
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
1
1)(
/)( kTEE Fe
Ef
f(E)
E
10.5EF
Fermi-Dirac distribution function
1
1)(
/)( kTEE Fe
Ef
f(E)
E
10.5EF
For electrons
)(1 Ef For holes
kT
kT=25 meV at 300 K
Fermi-Dirac distribution function
1
1)(
/)( kTEE Fe
Ef
f(E)
E
10.5EF
For electrons
)(1 Ef For holes
kT
kT=25 meV at 300 K
E
Conduction band
Valence band
Em
E
StatesofDensity
c )2
(2
1)(
2
E
Conduction band
Valence band
Em
E c )2
(2
1)(
2
For filling purpose, the smaller the effective mass the better.
E
Conduction band
Valence band
Em
E c )2
(2
1)(
2
Where is the Fermi Level ?
Intrinsic
P-doped
n-doped
Interband carrier recombination time (lifetime)
~ nanoseconds in III-V compound (GaAs, InGaAsP)
~ microseconds in silicon
Speed, energy storage,
E
Em
E c )2
(2
1)(
2
Quasi-Fermi levels E E
Immediately after Absorbing photons
Returning to thermal equilibrium
Ef e
Ef h
Em
E c )2
(2
1)(
2
E
EF e
EF h
x =
fe # of carriers
gFvFcnet
absorptionemissionnet
cccvvemission
cccvvabsorption
EEER
RRR
EfEEfR
EfEEfR
)(
)()())(1(
))(1)(()(
E
EF c
EF v
Eg
Condition for net gain >0
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
E
Eg
gEE
g
Absorption and gain in semiconductorE
Conduction band
Valence band
Em
E c )2
(2
1)(
2
Eg
Eg
Absorption (loss)
g
g
Eg
Gain
Eg
g
Eg
Gain at 0 K
Eg
EFc-EFv
Density of states
EFc-EFv
E=hv
gEE
g
Eg
Gain and loss at 0 K
EF=(EFc-EFv)
E
gEE
g
Eg
N2 >N1N1
Gain and loss at T=0 K
at different pumping rates
EF=(EFc-EFv)
E
gEE
g
Eg N2 >N1N1
Gain and loss at T>0 K
laser
E
gEE
g
Eg N2 >N1N1
Gain and loss at T>0 K
Effect of increasing temperature
laser
At a higher temperature
Larger bandgap (and lower index ) materials
Substrate
Smaller bandgap (and higher index ) materialsCleaved facets
w/wo coating
<0.2mp
n
A diode laser
<1 mm
<0.1 mm
Wavelength of diode lasers
• Broad band width (>200 nm)
• Wavelength selection by grating
• Temperature tuning in a small range
Wavelength selection by grating tuning
<0.2mp
n
A distributed-feedback diode laser
with imbedded grating
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
3-D (bulk) EE )(
E
Density of states
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
)(EE
constant
Example: GaAs/AlGaAs, ZnSe/ZnMgSe
Al0.3Ga0.7As
Al0.3Ga0.7As
GaAs
,....2,12 2
222 n
LmnE
zcn
E1
E2
For wells of infinite depth
2- dimensional semiconductors: quantum well
,....2,12 2
222 n
LmnE
zenc
E1v
E2c
,....2,12 2
222 n
LmnE
zhnv
E1c
E2v
2- dimensional semiconductors: quantum well
E1v
E2c
E1c
E
(E)
E2v
2- dimensional semiconductors: quantum well
E1v
E2c
E1c
E2v
g
N0=0
N1>N0N2>N1
T=0 K
2- dimensional semiconductors: quantum well
E1v
E2c
E1c
E2v
g
N0=0
N1>N0N2>N1
T=300K
E=hv
2- dimensional semiconductors: quantum well
E1v
E2c
E1c
E2v
g
N0=0
N1>N0N2>N1
E=hv
Wavelength : Determined by the composition and thickness of the well and the barrier heights
3-D vs. 2-D
E2v
g
T=300K
E=hv3-D
2-D
Multiple quantum well:coupled or uncoupled
1-D (Quantum wire)
gEEE
1)(
E
Eg
Quantized bandgap
0-D (Quantum dot)
An artificial atom
)()( iEEE
E
Ei
Quantum cascade lasers