Nano-optics Topics: How do we image things on the nanoscale? How do we use nanofabrication for new optical devices?
Wave Optics 1. Electromagnetic wave x Ex λ Direction of Propagation y z z plane wave r 2π E( x, y, z, t) = Acos( z ωt) λ light spectrum: E
Wave Optics 2. Interference cos(x) cos(x) + = + = cos(x) -cos(x) 2cos(x) 0 phase matters! (constant phase surfaces) k=k z z
Wave Optics Huygens principle Every unobstructed point of a wavefront serves as a source of spherical secondary waves. aperture The total field at a point P is the superposition of all secondary wavelets. P interference between all secondary waves
Wave Optics λ<<a λ a max. path difference a>λ all phases appear across aperture waves remain confined to center little diffraction effect λ>a max. path difference a<λ waves interfere constructively extend in all directions and angles
r i R Wave Optics 3. Fraunhofer Diffraction light distribution at z=d given aperture at z=0 one-dimension: single slit y P θ a Fourier transform y -a/2 a/2 aperture diffraction pattern ka/2 sinθ
Wave Optics rectangular aperture a b circular aperture δ Airy rings Bessel function Rλ first minimum δ =1. 22 a
Wave Optics 4. Resolution smallest separation between two features to appear separate in far-field Can we see this? 10nm 10nm quantum dots
Wave Optics y S 1 A 2 S 1 θ s θ S 2 A 1 S 2 L (after Kasap) I Screen Airy disks need to be separated diffraction limited resolution δ = 0. 61 λ NA Example: λ=0.5µm, NA=1 (after Kasap) δ = 0.3µ m = 300nm Now what??
Wave particle duality 5. Electron as wave double-slit experiment with electrons DeBroglie wavelength λ = h p wavelength 1/momentum Example: tennis ball, m=50g, v=20m/s λ=h/(mv)=6.6x10-34 m electron, m=m e =9x10-31 kg, V=100V W=100eV=m e v 2 /2 λ=h/(mv)=0.12 nm
Wave-particle duality diffraction: θ d path length difference: L = 2d sinθ constructive interference: L = mλ (Bragg condition) key: d λ for diffraction
Lattice types simple cubic (e.g. NaCl) face-centered cubic (fcc) (e.g. Au, Ag) a a a body-centered cubic (bcc) (e.g. Na) diamond (fcc with basis) (e.g. Si) C zinc blende (fcc with basis) (e.g. GaAs, InP) a S a a Zn a a a a
Nanostructure imaging
SEM 1. Scanning Electron Microscope (SEM) most useful imaging technique focus beam on surface generates secondary electrons (SE) collect SE
SEM focused spot E~5-25keV best resolution: 0.3-0.5 nm Depth of focus SEM advantage: large depth of focus
SEM Versatility: many things can be imaged semiconductor devices (dead) animals individual nanoparticles biological material processed cheese human teeth
SEM gallery spider hair honey bee aphid head louse http://www.pbrc.hawaii.edu/bemf/microangela/ neuron pollen mitochondria (TEM) termite??
Scanning optical microscopy NSOM NSOM = SNOM = Near-field Scanning Optical Microscope scanning probe microscope derivative sub-λ aperture within sub-λ distance to surface feedback for monitoring aperture-sample distance
Scanning optical microscopy Imaging modes: collection illumination collection/ illumination oblique collection oblique illumination dark field (after Paesler)
Near-field probes: Fiber tips: Scanning optical microscopy sharp fiber tip, etched or pulled usually metal-coated (Al) on sides low coupling: ~10-6 -> problem for collection/illumination mode polarization purity/conservation pulse broadening limited reproducibility
Scanning optical microscopy Hollow tips: Si cantilever 100nm Al tip (Witec GmbH) Al tip Si cantilevers with hollow Al tips batch (!!!) microfabrication -> better reproducibility
Scanning optical microscopy rat neuron cells human blood cell VCSEL emission chromosome DRAM test structure Polysterene particles
5. Infinite potential well confine electron wave in small space One-dimensional potentials V(x) I II III? 0 L x particle in a box What happens to the electron???
Infinite quantum well BC at x=l: ψ ΙΙ (L) = A sin(kl)=0 k n π = n L L k n = nπ ; n =1,2,3,... wave vector quantized π h 2mL 2 2 2 E n n 2 = particle energy quantized nπ ψ II, n( x) = An sin( x) L 0 L
Infinite quantum well V(x) E 3 E 2 E 1 0 L x ψ symm./antisymm. w.r.t. center of well number of nodes: n-1
Nano-optics Confinement of electrons on the nanoscale bulk material D(E) ~ E 1/2 quantum well D(E) staircase quantum wire D(E) ~ E -1/2 quantum dot/box D(E) ~ δ(e-e i ) atom-like
Optical processes 1. Absorption hυ E 2 3 2 3 2 n=1 n=1 E 1 L 1 L 2 absorbed energy depends on size (L) different energy corresponds to different wavelength/color
Optical processes 2. Emission hυ E 2 E 3 hυ E2 E 1 (b) Spontaneous emission E 1 (d) Fluorescence (molecules) photoluminescence (semiconductors) energy released = light emitted at discrete wavelengths single particle detection -> suitable for nanoparticles can design emission wavelength with size ( E~1/L 2 in infinite well) E n = 2 π h 2mL 2 2 n 2 fluorescence from CdSe/ZnS quantum dots (Bawendi et al)
Optical processes 2.1 Organic molecules molecules can vibrate vibration energies are quantized -> levels vibronic transitions in infrared band-like structure above electronic states
Optical processes Application: Fluorescence labeling in biology fluorescent molecule = fluorophore selectively tag cell parts with fluorophore locate and identify
Optical processes Epitaxial nanoparticles (quantum dots) a) Top-down z mask for 70nm GaAs/AlGaAs dots b) Bottom-up wetting layer lattice constants differ (stress) layer breaks -> islands (dots) form self-organization pyramids rather than spheres overgrowth possible -> devices (after Grundmann)
Optical processes Chemically synthesized nanoparticles (dots) based on group II (Zn,Cd) and group VI (S,Se,Te) elements synthesized from solution core-shell (ZnSe/ZnS) or organic cap layer spherical, relatively narrow size distribution size tunable emission wavelength dots mark tumor location (Seydel, Science, 300, 80, (2003))