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

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

62. Quantum cascade lasers