Nanomaterials and their Optical Applications

Transcription

1 Nanomaterials and their Optical Applications Winter Semester 2012 Lecture 04

2 Lecture 4: outline 2 Characterization of nanomaterials SEM, TEM Near-field XRD Plasmonics Theoretical background Synthesis methods Applications

3 Electron microscopy 3 Scanning electron microscope (SEM) 0.5 kev to 40 kev Reflected eletron Conductive substrate Surface technique Transmission electron microscopy (TEM) Ultrathin sample On a grid Diffraction is possible Inside structure Transmitted electrons SEM tutorial urces/tutorials/sem

4 How does the SEM works? 4 The electron beam hits the sample, producing secondary electrons from the sample. These electrons are collected by a secondary detector or a backscatter detector, converted to a voltage, and amplified.

5 How does the TEM works? 5 The electron beam travels through the specimen you want to study. Depending on the density of the material present, some of the electrons are scattered and disappear from the beam. At the bottom of the microscope the unscattered electrons hit a fluorescent screen, which gives rise to a "shadow image" of the specimen with its different parts displayed in varied darkness according to their density. copes/tem/index.html The Nobel Prize in Physics, Ernst Ruska

6 Scanning probe microscopy: STM, AFM 6 Scanning tunneling microscope (STM) An extremely fine conducting probe is held close to the sample. Electrons tunnel between the surface and the stylus, producing an electrical signal. The stylus is extremely sharp, the tip being formed by one single atom. It slowly scans across the surface at a distance of only an atom's diameter. The Nobel Prize in Physics, 1986 Gerd Binnig and Heinrich Rohrer

7 Scanning probe microscopy: STM, AFM 7 Atomic force microscopy (AFM) scanning force microscopy (SFM) The AFM consists of a cantilever with a sharp tip (probe) at its end that is used to scan the specimen surface. The cantilever is typically silicon or silicon nitride with a tip radius of curvature on the order of nanometers. When the tip is brought into proximity of a sample surface, forces between the tip and the sample lead to a deflection of the cantilever according to Hooke's law. Depending on the situation, forces that are measured in AFM include mechanical contact force, van der Waals forces, capillary forces, chemical bonding, electrostatic forces, magnetic forces

8 Near field microscopy : SNOM, PSTM 8 SNOM = NSOM= Scanning Near- Field Optical Microscopy, Photon Scanning Tunneling Microscope = PSTM = apertureless probe, evanescent waves created at the sample surface by oblique far-field illumination In the aperture case, light emanates from a small aperture (~ nm), usually a hole drilled in a metal-coated optical fibre, giving a spatial resolution of ~ nm. Low throughput, poor resolution and poor topography limit this technique. In the apertureless or tip-enhanced case, light is scattered from a sharp metal tip (typically nm radius). This typically gives a resolution of nm. Efficient scattering, the ability to combine with Atomic Force Microscopy (AFM), and spectroscopic measurements have enabled this technique to dominate over recent years.

9 Near field microscopy : SNOM, PSTM 9 = mix between an AFM and an optical microscope SNOM = NSOM= Scanning Near- Field Optical Microscopy, Plasmon Near-Field Microscope Photon Scanning Tunneling Microscope = PSTM = apertureless probe, evanescent waves created at the sample surface by oblique far-field illumination

10 X-ray diffraction 10 XRD, powder diffraction To characerize the crystalline form and sizes How? Elastic scattering of x-ray by a periodic lattice : well known Bragg equation Stoichiometry and the lattice constant Energy-dispersive X-ray spectroscopy (EDS or EDX)

11 Outline: Plasmonics Plasmonics vs Electronics and Photonics a) Definitions: plasmon, polariton b) Surface plasmon polariton: Drude Model c) Localized surface plasmon: nanoparticles, nanorods, nanoshells d) Theoretical modelling : light scattering theory (Rayleigh and Mie) 2. Fabrication of Plasmonics nanostructures 3. Applications of plasmonics: Stained glass, Notre Dame de Paris, 1250

12 Why plasmonics? 12 The speed of photonics The size of electronics High transparency of dielectrics like optical fibre Data transport over long distances Very high data rate Nanoscale data storage Limited speed due to interconnect Delay times Brongersma, M.L. & Shalaev, V.M. The case for plasmonics. Science 328, (2010).

13 Definition of Plasmonics 13 Metallic nanostructures = the field of plasmonics Not the confinment of electrons or holes as in semiconductors dots but Electrodynamics effect Modification of the dielectric environment How does plasmonic material look like? Metallic thin film Metallic nanoparticle Metallic nanorod Metallic nanoshell Different point of view of SURFACE PLASMON: Lycurgus cup (British Museum, London, UK). Electrodynamic: surface wave like in radiowave propagation along the earth Optics: modes of an interface Solid-state physics: collective oscillations of electrons

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18 Plasmon = collective oscillations of electrons 18 n free electron per unit volume Gauss theorem: Newton equation: ON: Displacement of electrons which cancel the field inside the metal OFF: electrons inside the metal accelerated by the surface charges Plasma frequency for a film infinite surface oscillations For a nanosphere Oscillations due to an electric field caused by all the electrons

19 Concept of polariton 19 When an em propagate in a material medium, the field polarizes the medium and therefore excite a mechanical movement of the charges Field and charges are coupled -> polariton In metal: field coupled to a longitudinal charge density wave = plasmon polariton In ionic crystal : field coupled to ion motion = phonon polariton In semiconductor: field couple to an electron-hole pair = exciton polariton Bulk plasmon polariton: propagation in a 3D medium Surface plasmon polariton: propagation along an interface Transverse magnetic wave solution of Maxwell equation that propagates along the interface and decay exponentially perpendicular to this interface General model: metal or crystal in any wavelength range Particular case: interface between a dielectric and a metal

20 Drude model (1900) 20 The model, which is an application of kinetic theory, assumes that the microscopic behavior of electrons in a solid may be treated classically and looks much like a pinball machine, with a sea of constantly jittering electrons bouncing and re-bouncing off heavier, relatively immobile positive ions Dielectric constant: Strong frequency dependence meaning dispersion 1/γ is the relaxation time of 10 fs for noble metals For a non-lossy model γ = 0! Frequency dependent!

21 Non lossy Drude model (1900) 21 Dispersion relation = solution of Maxwell equation with boundary conditions o Negative permittivity o SPP wavevector always larger than photon ->coupling of light is then tricky in planar structure to match the wave vector : Subwavelength scatterer Periodic grating Evanescent field o Large tunability of the dispersion but propagation losses Dispersion of photon Surface plasmon polariton

22 Localized surface plasmon in nanoparticles 22 No wavevector or special geometry, but absorption of light with the right plasmon band 1. Spheres Absorption within a narrow wavelength range The maximum of absorption depends on the size, the shape of the nanoparticles and the surrounding medium Small shift for particle smaller than 25 nm, red shift for bigger nanoparticles

23 Localized surface plasmon in nanoparticles Spheres From classical electrodynamic: resonance condition Polarizability of a sphere: εr = -2, true in the visible range for noble metal Microscopic view: 1 atom Take the simplest atom: hydrogen Macroscopic view: N atoms You end up with a dipole moment Put it into an electric field p = α E where α is the answer of the atom to electric field the macroscopic dipole moment (per unit volume) is called the POLARIZATION : P = χε E 1 0 Electric susceptibility is a measure of how easily a dielectric material can be polarized = εr -1

24 Localized surface plasmon in nanoparticles Wires, rods or rices Prolate spheroid a, b as axis εr = -2 (wavelength of 400 nm) to =-21.5 (wavelength of 700 nm) Two plasmon bands for nanorods: long and short axis Transverse mode is close to nanoparticles and longitudinal mode is red shifted

25 Non lossy Drude model (1900) 25 Semi-infinite geometry: Energy and momentum must be conserved : light cannot be coupled directly. Finite geometry: Momentum conservation is possible when light is coupled to the localized plasmon excitations of a small metal particle = optical antennas resonances

26 Localized surface plasmon in nanoparticles 26 No wavevector or special geometry, but absorption of light with the right plasmon band 2. Wires, rods or rices Two plasmon bands for nanorods: long and short axis Transverse mode is close to nanoparticles and longitudinal mode is red shifted

27 Localized surface plasmon in nanoparticles Nanoshell 60 nm core radius 20 to 5 nm shell thickness For a constant core, a thinner shell shift the plasmon resonance to the red For a constant core/shell ratio, small particles predominantly aborbs light and big particles scattered light. Over the dipole limit, multiple plasmon resonance occurs A broad spectral region is covered

28 Type of nanoantennas 28

29 Theoretical models to calculate the radiated field 29 Dipole approximation (or quasi-static) Mie scattering

30 Light Scattering and Absorption Theory 30 Extinction cross-section (cm 2 ) = absorption cs + sctattering cs 1. Dipole approximation (or quasi-static) particle much smaller than the wavelength σ scat σ abs total scattered or removed energy rate

31 Light Scattering and Absorption Theory Mie scattering Maxwell's equations are solved in spherical co-ordinates through separation of variables The incident plane wave is expanded in Legendre polynomials so the solutions inside and outside the sphere can be matched at the boundary Bessel and Haenkle functions are solution are also used in the complex expression for simplification Legendre polynomials Bessel and Hankel functions

32 Outlook 32 Plasmonics beyond the diffraction limit, Nature Photonics, 4, 83, 2010 H. Atwater, The promise of Plasmonics, Scientific Amercian, 2007 Brongersma, M.L. & Shalaev, V.M. The case for plasmonics. Science 328, (2010). D. W. Hahn, Light scattering theory, Notes, July 2009