Quantum Dots in Photonic Structures

1. Lecture 4: Photoniccrystals Quantum Dots in PhotonicStructures Wednesdays, 17.00, SDT Jan Suffczyński Projekt Fizyka Plus nr POKL.04.01.02-00-034/11 współfinansowany przez Unię Europejską ze środków Europejskiego Funduszu Społecznego w ramach Programu Operacyjnego Kapitał Ludzki

2. Plan for today 2. Two-dimensionalphotoniccrystals – band structure DBR mirrors 3. Two-dimensionalphotoniccrystal – fabricationmethods

3. Reminder • Refractiveindex: Polarization by EM wave Complexdielectricfunction

4. Reminder • Refractiveindex: Polarization by EM wave Complexdielectricfunction Simultaneousdescription of refraction and absorption Speedlight in a medium: Dispersion • After: AndrásSzilágyi

5. Reminder • Photoniccrystal: periodicarrangement of dielectric (ormetallic…) objects • periodicrefractiveindexcontrast • the periodcomparable to the wavelength of light in the material. • 1D photoniccrystal: • Distributed BraggReflector (DBR) • Examplecalculation: Transfer Matrix Method

6. Bragg mirror from the University of Warsaw Low n: 20 x Superlattice 1:1 1 mm SEM: T. Jakubczyk J.-G. Rousset 20 stack DBR MgTe High n: Cd0.86Zn0.14Te Cd0.86Zn0.14Te buffer Cd0.86Zn0.14Te GaAssubstrate

7. Refractiveindexengineering • For a good DBR we need a pair of materials thathave: • largerefractiveindexcontrastΔn= nhigh-nlow • latticeparamters as close as possible

8. Bragg mirror latticematched to CdTe The structure 15 par ZnTe 53nm superlattice 18 periods ZnTe 53 nm ZnTe 0.7 nm MgTe 0.9 nm superlattice ZnTe 0.7 nm ZnTe buffer 1000 nm MgSe 1.3 nm ZnSe 62 nm GaAs 1 μm W. Pacuski, UW

9. Bragg mirror latticematched to CdTe The structure 15 par ZnTe 53nm supersieć 18 powtórzeń ZnTe 53 nm ZnTe 0.7 nm MgTe 0.9 nm supersieć ZnTe 0.7 nm ZnTe buffer 1000 nm MgSe 1.3 nm ZnSe 62 nm GaAs W. Pacuski, UW

10. ZnTe 0.7 nm MgTe 0.9 nm ZnTe 0.7 nm MgSe 1.3 nm ZnTe 0.7 nm MgTe 0.9 nm ZnTe 0.7 nm MgSe 1.3 nm 1 nm Bragg mirror latticematched to CdTe The structure 15 par ZnTe 53nm supersieć 18 powtórzeń ZnTe 53 nm ZnTe 0.7 nm MgTe 0.9 nm supersieć ZnTe 0.7 nm ZnTe buffer 1000 nm MgSe 1.3 nm ZnSe 62 nm GaAs W. Pacuski, UW

11. DBR mirror and DBR cavityreflectivity DBR Microcavity W. Pacuski, UW

12. DBR mirror and DBR cavityreflectivity DBR Q = λ/Δλ = 3600 Microcavity

13. CdTebasedmicrocavity – 60 pairs But sometimestechnologymakesjokes…

14. Planarcavity with DBR mirrors Stop band Δλ=(n1-n2)/π(n1+n2) Δθ ~ 20otypically in the caseogGaAs/AlAs DBR Reflectivity Antinode of the field in the center of the cavity lBr λ-cavity Electric field distribution Cavitymode Exponentialdecay of the stationary field from the center of the cavity

15. Low index of refraction High index of refraction 3D photonic crystal Towards 2D and 3D photoniccrystals

16. a Photoniccrystals– howitworks? a>>l incoherent scattering a a~l coherent scattering a<<l averaging a Photonic crystals

17. 2D, 3Dphotonic bandgap? J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light

18. Dispersion relation and origin of the band gap in 1D Considermedium of refractiveindex n1 and light of wavelenght of l = 2a Lightline: freespace n1 Lightline: medium frequency ω standing wave in n1 0 π/a wave vector k

19. Dispersion relation and origin of the band gap in 1D Consider the stack of layers of refractiveindeces n1and n2 and light of wavelenght of l = 2a n1 n2 n1 n2 n1 n2 n1 frequency ω a 0 π/a n1: high index material n2: low index material wave vector k

20. Dispersion relation and origin of the band gap in 1D Consider the stack of layers of refractiveindeces n1and n2 and light of wavelenghtl = 2a standing wave in n2 n1 n2 n1 n2 n1 n2 n1 frequency ω standing wave in n1 0 π/a n1: high index material n2: low index material wave vector k

21. Dispersion relation and origin of the band gap in 1D Consider the stack of layers of refractiveindeces n1and n2 and light of wavelenghtl = 2a standing wave in n2 n1 n2 n1 n2 n1 n2 n1 frequency ω bandgap standing wave in n1 0 π/a n1: high index material n2: low index material wave vector k

22. frequency ω -π/a 0 π/a wave vector k Bloch wave with wave vector k is equal to Bloch wave with wave vector k+m2p/a: modified slide from Rob Engelen

23. Band diagram k is periodic: k + 2π/aisequivalent to k

24. frequency ω frequency ω -π/a -π/a 0 0 π/a π/a wave vector k wave vector k Band diagram -2π/a 2π/a 2π/a -2π/a This isthe first Brillouin zone modified slide from Rob Engelen

25. Band diagram – one moreview Anticrossing of modesleading to formation of the band gap

26. Anotherlook- Braggscatteringconditions When a wave impinges on a crystal it will be reflected at a particular set of lattice planes characterized by its reciprocal lattice vector gonlyif the so-called Braggconditionis met If the Bragg condition is not met, the incoming wave just moves through the lattice and emerges on the other side of the crystal (whenneglecting absorption)

27. Photoniccrystals - introductoryexample from the prevouslecture 1. Braggscattering Regardless of how small the reflectivity r is from an individual scatterer, thetotalreflection R from a semiinfinitestructure: Complete reflectionwhen: • Propagation of the light in crystalinhibitedwhenBraggconditionsatisfied • Origin of the photonicbang gap

28. Reciprocal lattice

29. Dispersion relation for 2D photoniccrystal 2D squarelattice

30. Dispersion relation for 2D photoniccrystal 2D hexagonallattice Band gap: no propagation possible at that frequency densityof optical states (DOS) is 0

31. Dispersion relation for 2D photoniccrystal vs transmission

32. Photoniccrystals in Nature Sea mouse Opal McPhedran et al.

33. Need a 3d crystal with constant cross-section layers Artificial PC production:Layer-by-Layer Lithography • Fabrication of 2d patterns in Si or GaAs is very advanced (think: Pentium IV, 50 million transistors) …inter-layer alignment techniques are only slightly more exotic So, make 3d structure one layer at a time

34. A Schematic [ M. Qi, H. Smith, MIT ]

35. Making Rods & Holes Simultaneously Steven G. Johnson, MIT side view Si s u b s t r a t e top view Steven G. Johnson, MIT

36. Making Rods & Holes Simultaneously expose/etch holes A A A A s u b s t r a t e A A A A A A A A A A A A A A A A A A A A A Steven G. Johnson, MIT

37. Making Rods & Holes Simultaneously backfill with silica (SiO2) & polish A A A A s u b s t r a t e A A A A A A A A A A A A A A A A A A A A A Steven G. Johnson, MIT

38. Making Rods & Holes Simultaneously deposit another Si layer l a y e r 1 A A A A s u b s t r a t e A A A A A A A A A A A A A A A A A A A A A Steven G. Johnson, MIT

39. Making Rods & Holes Simultaneously dig more holes offset & overlapping l a y e r 1 B B B B A A A A s u b s t r a t e B B B B A A A A B B B A A A B B B B A A A A B B B A A A B B B B A A A A B B B A A A Steven G. Johnson, MIT

40. Making Rods & Holes Simultaneously backfill l a y e r 1 B B B B A A A A s u b s t r a t e B B B B A A A A B B B A A A B B B B A A A A B B B A A A B B B B A A A A B B B A A A Steven G. Johnson, MIT

41. Making Rods & Holes Simultaneously etcetera (dissolve silica when done) l a y e r 3 one period A A A A l a y e r 2 C C C C l a y e r 1 B B B B A A A A s u b s t r a t e C B C B C B C B A A A A C B C B C B C A A A C B C B C B C B A A A A C B C B C B C A A A C C C C B B B B A A A A C B C B C B C A A A Steven G. Johnson, MIT

42. Making Rods & Holes Simultaneously etcetera l a y e r 3 one period A A A A l a y e r 2 C C C C l a y e r 1 B B B B hole layers A A A A s u b s t r a t e C B C B C B C B A A A A C B C B C B C A A A C B C B C B C B A A A A C B C B C B C A A A C C C C B B B B A A A A C B C B C B C A A A Steven G. Johnson, MIT

43. Making Rods & Holes Simultaneously etcetera l a y e r 3 one period A A A A l a y e r 2 C C C C l a y e r 1 B B B B rod layers A A A A s u b s t r a t e C B C B C B C B A A A A C B C B C B C A A A C B C B C B C B A A A A C B C B C B C A A A C C C C B B B B A A A A C B C B C B C A A A Steven G. Johnson, MIT

44. 7-layer E-Beam Fabrication [ M. Qi, et al., Nature429, 538 (2004) ]

45. Three-dimensional Si photonic crystal Y. A. Vlasov et al., Nature 414, 289 (2001) S.-Y. Lin et al., Nature 394, 251 (1998)

46. 3d Lithography lens …dissolve unchanged stuff (or vice versa) some chemistry (polymerization) Two-Photon Lithography 2-photon probability ~ (light intensity)2

47. Lithography – the bestfriend of a man λ = 780nm resolution = 150nm 7µm (3 hours to make) 2µm S. Kawataet al., Nature(2001)

48. Holographic Lithography Four beams make 3d-periodic interference pattern k-vector differences give reciprocal lattice vectors (i.e. periodicity) absorbing material (1.4µm) beam polarizations + amplitudes (8 parameters) give unit cell [ D. N. Sharp et al., Opt. Quant. Elec.34, 3 (2002) ]

49. Holographic Lithography [ D. N. Sharp et al., Opt. Quant. Elec.34, 3 (2002) ] 10µm huge volumes, long-range periodic, fcc lattice…backfill for high contrast

50. Colloidal photonic crystals Colvin, MRS Bulletin 26, (2001)