9. Semiconductors Optics Absorption and gain in semiconductors Principle of semiconductor lasers (diode lasers) Low dimensional materials: Quantum wells,

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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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  • One atomTwo interacting atomsN interacting atoms The energy bands EgEg
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  • Insulator Conductor (metals) Semiconductors
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  • Doped semiconductor n-type p-type
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  • Interband transistion nanoseconds in GaAs
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  • n-type Intraband transitions < ps in GaAs
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  • UV Optical fiber communication
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  • GaAs InP 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 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
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  • E k Conduction band Valence band Interband transitions
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  • E k Conduction band Valence band Examples: m c =0.08 m e for conduction band in GaAs m c =0.46 m e for valence band in GaAs EgEg
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  • Direct vs. indirect band gap k k GaAs Al x Ga 1-x As x
  • E E F c E F v EgEg Condition for net gain >0
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  • P-n junction unbiased EFEF
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  • P-n junction Under forward bias EFEF
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  • Heterojunction Under forward bias
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  • Homojunction hv Np
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  • Heterojunction waveguide n x
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  • Heterojunction 10 100 nm EFEF
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  • Heterojunction A four-level system 10 100 nm Phonons
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  • E EgEg g Absorption and gain in semiconductor
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  • EgEg EgEg Absorption (loss) g
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  • g EgEg Gain EgEg
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  • g EgEg Gain at 0 K EgEg E Fc -E Fv Density of states E Fc -E Fv
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  • E=hv g EgEg Gain and loss at 0 K E F =(E Fc -E Fv )
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  • E g EgEg N 2 >N 1 N1N1 Gain and loss at T=0 K at different pumping rates E F =(E Fc -E Fv )
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  • E g EgEg N 2 >N 1 N1N1 Gain and loss at T>0 K laser
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  • E g EgEg N 2 >N 1 N1N1 Gain and loss at T>0 K Effect of increasing temperature laser At a higher temperature
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  • Larger bandgap (and lower index ) materials Substrate Smaller bandgap (and higher index ) materials Cleaved facets w/wo coating
  • Wavelength of diode lasers Broad band width (>200 nm) Wavelength selection by grating Temperature tuning in a small range
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  • Wavelength selection by grating tuning
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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: >30% Internal quantum efficiency >90% Power of optical damage 10 6 W/cm 2 Modulation bandwidth >10 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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  • 3-D (bulk) E Density of states
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  • Low dimensional semiconductors When the dimension of potential well is comparable to the deBroglie wavelength of electrons and holes. L z
  • 2- dimensional semiconductors: quantum well E 1v E 2c E 1c E 2v g N 0 =0 N 1 >N 0 N2>N1N2>N1 T=0 K
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  • 2- dimensional semiconductors: quantum well E 1v E 2c E 1c E 2v g N 0 =0 N 1 >N 0 N2>N1N2>N1 T=300K E=hv
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  • 2- dimensional semiconductors: quantum well E 1v E 2c E 1c E 2v g N 0 =0 N 1 >N 0 N2>N1N2>N1 E=hv Wavelength : Determined by the composition and thickness of the well and the barrier heights
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  • 3-D vs. 2-D E 2v g T=300K E=hv 3-D 2-D
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  • Multiple quantum well: coupled or uncoupled
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  • 1-D (Quantum wire) E EgEg Quantized bandgap
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  • 0-D (Quantum dot) An artificial atom E EiEi
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  • Quantum cascade lasers
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