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Semiconductor Optics. Absorption & Gain in Semiconductors: Some Applications Semiconductor Lasers (diode lasers) Low Dimensional Materials: Quantum wells, wires & dots Quantum cascade lasers Semiconductor detectors. More Applications Light Emitters, (including lasers & LEDs)
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Semiconductor Optics Absorption & Gain in Semiconductors: Some Applications Semiconductor Lasers (diode lasers) Low Dimensional Materials: Quantum wells, wires & dots Quantum cascade lasers Semiconductor detectors
More Applications • Light Emitters, (including lasers & LEDs) • Detectors, Sensors, Amplifiers, • Waveguides & Switches, • Absorbers & Filters • Nonlinear Optics
Energy Bands One atom 2 interacting atoms N interacting atoms Eg
Insulator Conductor (metals) Semiconductors
Doped Semiconductors p-type n-type
Interband Transitions nanoseconds in GaAs
Intraband Transitions < ps in GaAs n-type
UV “Bandgap Engineering”
InP GaAs ZnSe
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. C 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 E Conduction band k Valence band
E Conduction band 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 k GaAs AlxGa1-xAs x<0.3 ZnSe 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 E 0.5 1 EF f(E)
Fermi-Dirac Distribution Function For electrons kT = 25 meV at 300 K For holes E f(E) 0.5 1 EF kT
E For filling purposes, the smaller the effective mass the better. Conduction band Valence band
Where is the Fermi Level ? E Conduction band n-doped Intrinsic Valence band P-doped
Interband carrier recombination time (lifetime) ~ nanoseconds in III-V compound (GaAs, InGaAsP) ~ microseconds in silicon
Quasi-Fermi levels E E E Ef e Immediately after Absorbing photons Returning to thermal equilibrium Ef h
E fe # of carriers EF e x = EF h
E Condition for net gain >0 EF c Eg 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 g Eg E
Absorption (loss) g Eg Eg
Gain g Eg Eg
Gain at 0 K Eg EFc-EFv g EFc-EFv Eg Density of states
Gain and loss at 0 K g EF=(EFc-EFv) Eg E=hv
Gain and loss at T=0 K at different pumping rates g EF=(EFc-EFv) Eg E N1 N2 >N1
Gain and loss at T>0 K laser g Eg N2 >N1 N1 E
Gain and loss at T>0 K Effect of increasing temperature laser g Eg N2 >N1 N1 E At a higher temperature
A diode laser Larger bandgap (and lower index ) materials <0.2m p n <0.1 mm Substrate Cleaved facets w/wo coating Smaller bandgap (and higher index ) materials <1 mm
Wavelength of diode lasers • Broad band width (>200 nm) • Wavelength selection by grating • Temperature tuning in a small range
A distributed-feedback diode laser with imbedded grating <0.2m 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
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 constant For wells of infinite depth E2 E1
2- dimensional semiconductors: quantum well E2c E1c E1v E2v