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

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Presentation on theme: "9. Semiconductors Optics Absorption and gain in semiconductors Principle of semiconductor lasers (diode lasers) Low dimensional materials: Quantum wells,"— Presentation transcript:

1 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

2 Semiconductors Optics Semiconductors in optics: Light emitters, including lasers and LEDs Detectors Amplifiers Waveguides and switches Absorbers and filters Nonlinear crystals

3 One atomTwo interacting atomsN interacting atoms The energy bands EgEg

4 Insulator Conductor (metals) Semiconductors

5 Doped semiconductor n-type p-type

6 Interband transistion   nanoseconds in GaAs

7 n-type Intraband transitions   < ps in GaAs

8 UV Optical fiber communication

9 GaAs InP ZnSe

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11 Bandgap rules The bandgap increases with decreasing lattice constant. The bandgap decreases with increasing temperature.

12 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

13 E k Conduction band Valence band Interband transitions

14 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

15 Direct vs. indirect band gap k k GaAs Al x Ga 1-x As x<0.3 ZnSe Si AlAs Diamond

16 Direct vs. indirect band gap Direct bandgap materials: Strong luminescence Light emitters Detectors Direct bandgap materials: Weak or no luminescence Detectors

17 Fermi-Dirac distribution function f(E) E 10.5 EFEF

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

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

20 E Conduction band Valence band

21 E Conduction band Valence band For filling purpose, the smaller the effective mass the better.

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

23 Interband carrier recombination time (lifetime) ~ nanoseconds in III-V compound (GaAs, InGaAsP) ~ microseconds in silicon Speed, energy storage,

24 E Quasi-Fermi levels EE Immediately after Absorbing photons Returning to thermal equilibrium E f e E f h

25 E EFeEFe EFhEFh x= fefe # of carriers

26 E E F c E F v EgEg Condition for net gain >0

27 P-n junction unbiased EFEF

28 P-n junction Under forward bias EFEF

29 Heterojunction Under forward bias

30 Homojunction hv Np

31 Heterojunction waveguide n x

32 Heterojunction 10 – 100 nm EFEF

33 Heterojunction A four-level system 10 – 100 nm Phonons

34 E EgEg  g Absorption and gain in semiconductor

35  EgEg EgEg Absorption (loss) g

36 g EgEg Gain  EgEg

37 g EgEg Gain at 0 K  EgEg E Fc -E Fv Density of states E Fc -E Fv

38 E=hv  g EgEg Gain and loss at 0 K E F =(E Fc -E Fv )

39 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 )

40 E  g EgEg N 2 >N 1 N1N1 Gain and loss at T>0 K laser

41 E  g EgEg N 2 >N 1 N1N1 Gain and loss at T>0 K Effect of increasing temperature laser At a higher temperature

42 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

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

44 Wavelength selection by grating tuning

45 <0.2  m p n A distributed-feedback diode laser with imbedded grating Grating

46 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

47 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

48 Strained layer and bandgap engineering Substrate

49 3-D (bulk) E  Density of states

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

51 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

52 2- dimensional semiconductors: quantum well E 1v E 2c E 1c E 2v

53 2- dimensional semiconductors: quantum well E 1v E 2c E 1c E  (E) E 2v

54 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

55 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

56 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

57 3-D vs. 2-D E 2v g  T=300K E=hv 3-D 2-D

58 Multiple quantum well: coupled or uncoupled

59 1-D (Quantum wire) E  EgEg Quantized bandgap

60 0-D (Quantum dot) An artificial atom E  EiEi

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62 Quantum cascade lasers

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