固体物理基础学：讲座：光子晶体

1、学术讲座之,光子晶体 Photonic crystal,光子晶体(photonic crystal,周期性结构调制，波的运动产生色散，形成带结构，带隙之间的波禁止通过，称为禁带。 电子的运动 光子的运动？ 光子晶体:在高折射率材料的某些位置周期性出现低折射率的材料. 这种光的折射率指数的周期性变化产生了光带隙结构，控制着光在晶体中的运动。 1987年提出概念: E. Yablonovitch (PRL 58, 2059) S. John (PRL 58, 2486) 1990年理论预言第一个有完整光子带隙的三维光子晶体 (PRL 65, 3152) 1991年实验制备第一个有完整光子带隙的三维

2、光子晶体 (PRL 67, 2295,光子晶体多为人工设计, 自然界也有: 蛋白石、蝴蝶翅膀,Opal,Butterfly,Traditional multi-layer film,三维光子晶体,二维光子晶体,Photonic Crystals:Periodic Surprises in Electromagnetism,Steven G. Johnson MIT,Photonic Crystals,periodic electromagnetic media,with photonic band gaps: “optical insulators,Photonic Crystals,peri

3、odic electromagnetic media,with photonic band gaps: “optical insulators,and waveguides (“wires”,Photonic Crystals,periodic electromagnetic media,with photonic band gaps: “optical insulators,and waveguides (“wires”,Photonic Crystals,periodic electromagnetic media,Image: /lat

4、tice/struk/a4.html,The Mother of (almost) All Bandgaps,The diamond lattice: fcc (face-centered-cubic) with two “atoms” per unit cell,a,The First 3d Bandgap Structure,K. M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990,11% gap,overlapping Si spheres,MPB tutorial, http:/ab-initi

5、/mpb,光子晶体制备,dissolve latex spheres,6-layer 001 silica diamond lattice,F. Garcia-Santamaria et al., Adv. Mater. 14 (16), 1144 (2002).,Layer-by-Layer Lithography,Fabrication of 2d patterns in Si or GaAs is very advanced (think: Pentium IV, 50 million transistors,So, make 3d structure one laye

6、r at a time,inter-layer alignment techniques are only slightly more exotic,A Layered Structure,diamond-like: rods “bonds”,A,B,C,S. G. Johnson et al., Appl. Phys. Lett. 77, 3490 (2000),Up to 27% gap for Si/air,hole layer,Making Rods & Holes Simultaneously,s,u,b,s,t,r,a,t,e,top view,side view,Si,Makin

7、g Rods & Holes Simultaneously,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,A,A,A,A,expose/etch holes,Making Rods & Holes Simultaneously,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,A,A,A,A,backfill with silica (SiO2) & polish,Making Rods & Holes Simultaneously,s,u,b,s,t

8、,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,A,A,A,A,deposit another Si layer,l,a,y,e,r,1,Making Rods & Holes Simultaneously,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,s,u,b,s,t,r,a,t,e,l,a,y,e,r,1,A,A,A,A,B,B,B,B,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,dig more holes offset & overlapping,Mak

9、ing Rods & Holes Simultaneously,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,s,u,b,s,t,r,a,t,e,l,a,y,e,r,1,A,A,A,A,B,B,B,B,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,backfill,Making Rods & Holes Simultaneously,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,s,u,

10、b,s,t,r,a,t,e,l,a,y,e,r,1,l,a,y,e,r,2,l,a,y,e,r,3,A,A,A,A,B,B,B,B,C,C,C,C,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,etcetera (dissolve silica when done,one period,Making Rods & Holes Simultaneously,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,s,u,

11、b,s,t,r,a,t,e,l,a,y,e,r,1,l,a,y,e,r,2,l,a,y,e,r,3,A,A,A,A,B,B,B,B,C,C,C,C,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,etcetera,one period,hole layers,Making Rods & Holes Simultaneously,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,s,u,b,s,t,r,a,t,e,l

12、,a,y,e,r,1,l,a,y,e,r,2,l,a,y,e,r,3,A,A,A,A,B,B,B,B,C,C,C,C,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,A,etcetera,one period,rod layers,A More Realistic Schematic,M. Qi, H. Smith, MIT,e-beam Fabrication: Top View,M. Qi, H. Smith, MIT,e-beam Fabrication: Side Views(cleaving worst sample,M. Qi, H.

13、 Smith, MIT,X-ray Interference Lithography,The Good,Large area: up to 10 x10cm,Cheap ($50k vs. $500k for e-beam,M. Qi, H. Smith, MIT,The Ugly,Layer alignment still tricky,From Rectangular to Hexagonal,M. Qi, H. Smith, MIT,The Woodpile Crystal,an earlier design, currently more popular,K. Ho et al., S

14、olid State Comm. 89, 413 (1994),H. S. Szer et al., J. Mod. Opt. 41, 231 (1994),Up to 17% gap for Si/air,Figures from S. Y. Lin et al., Nature 394, 251 (1998),1.25 Periods of Woodpile,S. Y. Lin et al., Nature 394, 251 (1998),4 “log” layers = 1 period,/media/photonic.htm,Si,1.25 Pe

15、riods of Woodpile 1.55m,S. Y. Lin et al., Nature 394, 251 (1998),gap,4 “log” layers = 1 period,1.3m,180nm,Si,Its only wafer-thin.,S. Noda et al., Science 289, 604 (2000),M. Python,Woodpile Gap from 1.31.55m,S. Noda et al., Science 289, 604 (2000),A Metal Photonic Crystal,J. G. Fleming et al., Nature

16、 417, 52 (2002),Start with Si woodpile in SiO2,dissolve Si with KOH,fill with Tungsten via chemical vapor deposition (CVD) (on thin TiN layer,dissolve SiO2 with HF,enough layer-by-layer already,A Two-Photon Woodpile Crystal,B. H. Cumpston et al., Nature 398, 51 (1999),much work on materials with low

17、er power 2-photon process,Difficult topologies,Arbitrary lattice No “mask” Fast/cheap prototyping,fig. courtesy J. W. Perry, U. Arizona,One-PhotonHolographic Lithography,D. N. Sharp et al., Opt. Quant. Elec. 34, 3 (2002),absorptive material,Four beams make 3d-periodic interference pattern,1.4m,k-vec

18、tor differences give reciprocal lattice vectors (i.e. periodicity,beam polarizations + amplitudes (8 parameters) give unit cell,One-PhotonHolographic Lithography,D. N. Sharp et al., Opt. Quant. Elec. 34, 3 (2002),huge volumes, long-range periodic, fcc latticebackfill for high contrast,10m,One-Photon

19、Holographic Lithography,D. N. Sharp et al., Opt. Quant. Elec. 34, 3 (2002),5m,1m,1m,111 cleavages,111 closeup,simulated structure,titania inverse structure,Mass-production II: Colloids,microspheres (diameter 1m,silica (SiO2,sediment by gravity into close-packed fcc lattice,evaporate,Mass-production

20、II: Colloids,http:/www.icmm.csic.es/cefe,Inverse Opals,fcc solid spheres do not have a gap,but fcc spherical holes in Si do have a gap,Inverse-Opal Photonic Crystal,Y. A. Vlasov et al., Nature 414, 289 (2001).,Inverse-Opal Band Gap,good agreement between theory (black) & experiment (red/blue,Y. A. Vlasov et al., Nature 414, 289 (2001).,Original butterfly,The cylindrical main ribs are L