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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

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    1. Semiconductor Optics Absorption & Gain in Semiconductors: Some Applications Semiconductor Lasers (diode lasers) Low Dimensional Materials: Quantum wells, wires & dots Quantum cascade lasers Semiconductor detectors

    2. More Applications • Light Emitters, (including lasers & LEDs) • Detectors, Sensors, Amplifiers, • Waveguides & Switches, • Absorbers & Filters • Nonlinear Optics

    3. Energy Bands One atom 2 interacting atoms N interacting atoms Eg

    4. Insulator Conductor (metals) Semiconductors

    5. Doped Semiconductors p-type n-type

    6. Interband Transitions   nanoseconds in GaAs

    7. Intraband Transitions   < ps in GaAs n-type

    8. UV “Bandgap Engineering”

    9. InP GaAs ZnSe

    10. Bandgap “Rules” The Bandgap Increases with decreasing Lattice Constant. The Bandgap Decreases with increasing Temperature.

    11. 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

    12. Interband transitions E Conduction band k Valence band

    13. 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

    14. Direct vs. Indirect Band Gap k k GaAs AlxGa1-xAs x<0.3 ZnSe Si AlAs Diamond

    15. Direct vs. Indirect Band Gap Direct bandgap materials: Strong luminescence Light emitters Detectors Direct bandgap materials: Weak or no luminescence Detectors

    16. Fermi-Dirac Distribution Function E 0.5 1 EF f(E)

    17. Fermi-Dirac Distribution Function For electrons kT = 25 meV at 300 K For holes E f(E) 0.5 1 EF kT

    18. E For filling purposes, the smaller the effective mass the better. Conduction band Valence band

    19. Where is the Fermi Level ? E Conduction band n-doped Intrinsic Valence band P-doped

    20. Interband carrier recombination time (lifetime) ~ nanoseconds in III-V compound (GaAs, InGaAsP) ~ microseconds in silicon

    21. Quasi-Fermi levels E E E Ef e Immediately after Absorbing photons Returning to thermal equilibrium Ef h

    22. E fe # of carriers EF e x = EF h

    23. E Condition for net gain >0 EF c Eg EF v

    24. P-n junction unbiased EF

    25. P-n junction Under forward bias EF

    26. Heterojunction Under forward bias

    27. Homojunction hv N p

    28. Heterojunction waveguide n x

    29. Heterojunction 10 – 100 nm EF

    30. Heterojunction A four-level system 10 – 100 nm Phonons

    31. Absorption and gain in semiconductor g Eg E 

    32. Absorption (loss) g Eg   Eg

    33. Gain g Eg   Eg

    34. Gain at 0 K Eg EFc-EFv g EFc-EFv Eg   Density of states

    35. Gain and loss at 0 K g EF=(EFc-EFv) Eg E=hv 

    36. Gain and loss at T=0 K at different pumping rates g EF=(EFc-EFv) Eg E N1 N2 >N1 

    37. Gain and loss at T>0 K laser g Eg N2 >N1 N1 E 

    38. Gain and loss at T>0 K Effect of increasing temperature laser g Eg N2 >N1 N1 E At a higher temperature 

    39. A diode laser Larger bandgap (and lower index ) materials <0.2m p n <0.1 mm Substrate Cleaved facets w/wo coating Smaller bandgap (and higher index ) materials <1 mm

    40. Wavelength of diode lasers • Broad band width (>200 nm) • Wavelength selection by grating • Temperature tuning in a small range

    41. Wavelength selection by grating tuning

    42. A distributed-feedback diode laser with imbedded grating <0.2m p n Grating

    43. 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

    44. 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

    45. Strained layer and bandgap engineering Substrate

    46. Density of states 3-D (bulk) E 

    47. Low dimensional semiconductors When the dimension of potential well is comparable to the deBroglie wavelength of electrons and holes. Lz<10nm

    48. 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 

    49. 2- dimensional semiconductors: quantum well E2c E1c E1v E2v