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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<0.3 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 f(E) E 10.5 EFEF

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Fermi-Dirac distribution function f(E) E 10.5 EFEF For electrons For holes kT kT=25 meV at 300 K

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Fermi-Dirac distribution function f(E) E 10.5 EFEF For electrons For holes kT kT=25 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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E Conduction band Valence band Where is the Fermi Level ? Intrinsic P-doped n-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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E Quasi-Fermi levels EE Immediately after Absorbing photons Returning to thermal equilibrium E f e E f h

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E EFeEFe EFhEFh x= fefe # of carriers

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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 <0.2 m p n A diode laser <1 mm <0.1 mm

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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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<0.2 m p n A distributed-feedback diode laser with imbedded grating 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: >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 <10nm

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2- dimensional semiconductors: quantum well E constant Example: GaAs/AlGaAs, ZnSe/ZnMgSe Al 0.3 Ga 0.7 As GaAs E1E1 E2E2 For wells of infinite depth

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2- dimensional semiconductors: quantum well E 1v E 2c E 1c E 2v

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2- dimensional semiconductors: quantum well E 1v E 2c E 1c E (E) E 2v

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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=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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