Transcript Slide 1
EM Course – Inelastic Scattering Professor Rodney Herring Inelastic Scattering - Introduction Quasiparticle Property Measurements Two reasons why we can generate and detect: 1) Since the fast electrons passing through a material can create plasmons, phonons, magnons, etc., i.e, signal generating, their resulting energy-loss electrons (used for signal detecting) carry the information of their properties. 2) Every electron that scatters off the same quasiparticle mode picks up the same scattering phase. - if an electron scatters off the quasiparticle, this electron carries information about the quasiparticle. e.g., the phonon gluing Cooper pair electrons together to make the superconducting fluxon. Inelastic Scattering - Introduction Electron Scattering Inelastic Scattering - Introduction We will focus on the collective interactions produced by inelastic scattering since no new information concerning x-rays and secondary electrons is available in Williams and Carter. Electron Energy Loss Spectrum (EELS) Elastically scattered electrons – Bragg diffracted and diffuse elastically scattered electrons Zero-loss + phonon loss ,I (Bulk Plasmons) Low-energy, diffuse inelastically scattered electrons (Surface Plasmons) (excitons, bandgap, dopants, defects) ,E g hkl 000 beam g hkl E Diffracted beam EELS spectrum of elastically & inelastically scattered electrons Zero-loss & Phonon-loss Intensities for GaAs 10 total 8 Intensity Aplanatic STEHM required 6 Zero-loss 4 2 444 222 666 atomic planes Phonon-loss 0.2 0.4 0.6 0.8 1.0 s (1/Å) 0 10 f (mrad) Doyle and Turner Acta Cryst. (1968). A24, 390 20 Similar intensity loss for plasma loss electrons Inelastic Scattering - Introduction Plasmons and Phonons Plasmons and Phonons (next slide) * Longitudinal Waves * for bulk plasmons, which exist inside the material. There is also a surface plasmon, which can be delocalized on the surface and exist for microseconds Recall: the electron emitted from the source is a transverse wave. Bulk Plasmons If the specimen is >100 nm, then another bulk plasmon can be created. The diffracted beams can also produce bulk plasmons. Surface Plasmons The surface plasmon energy is equal to the bulk plasmon energy (10s of eV) divided by square root 2. For some specimen and certain conditions, surface plasmons can have a high intensity, e.g., gold nanoparticles, carbon nanotubes, etc., anything where the surface dominates over the volume of the specimen. Their creation by the electron beam creates a high intensity of surface plasmon loss electrons. Plasmons 1. Localized Surface Plasmons Surface Plasmon 2. Propagating Surface Plasmons Localized Surface Plasmons Simple semi-classical model: electron wave Surface plasmon densities around differently shaped nanoparticles A.J. Haes, C.L. Haynes, et al, MRS BULLETIN, 30 368 (2005) Surface Plasmon Polariton The smaller the wavelength of surface plasmon, the shorter length it travels or propagates over the surface! H.A. Atwater, S. Maier, et al, MRS BULLETIN, 30 385 (2005) Plasmons Loss Electrons Phonon Loss Electrons Interband and Intraband Loss Electrons plus the presence of dopants and defects (electronic and photonic defects) in the band gap Elastically & Inelastically Scattered Electrons Elastically scattered electrons – Bragg diffracted and diffusely scattered Zero-loss + phonon loss ,I (Bulk Plasmons) (Surface Plasmons) (excitons, bandgap, dopants, defects) ,E g hkl 000 beam g hkl E Diffracted beam What is the better electron source that represents elastically and inelastically scattered electron coming from material specimens? Lorentzian: Represents electrons from specimen that have lost energy such as inelastically scattered electrons including plasmon loss electrons and phonon loss electrons. Lorentzian Gaussian: Represents electrons from electron emitter plus Bragg diffracted beams, which have no energy loss. Gaussian The mean is and the half-width is . The Lorentzian distribution has very extended wings and is not defined as the integral is unbounded! Lateral coherence enables continued interfere of beams as they are separated by changing voltage on electron biprism. New position on source, RS’1 and RS’2 enable the source size, shape and coherence to be determined. Perhaps, first time to aB measure properties of electron source coming from specimen. Primary Beam Condenser Aperture ac RS’1 Crystal Specimen 2qB RS’2 Apparent Sources, Rs’ (virtual sources) Electron Biprism ( ) Main Beam Diffracted Beam Region 1 Region 2 Fringe Contrast versus Beam Separation 86V 82V a) b) 79V 74V The Lateral spatial coherence, do, is given as a function of electron source size, Rs, to be: d 2 Rs The reduced fringe contrast as the beams separate gives a measure of the shape of the electron sources. 2 1 2 c) d) Beam Damage Beam Damage Beam Damage Beam Damage - Heating Beam Damage - Heating Beam Damage – Polymers Beam Damage - Polymers Beam Damage – Covalent & Ionic Materials * * cathodoluminescence Beam Damage in Metals Beam Damage Beam Damage Beam Damage Inelastic Scattering - Sputtering Inelastic Scattering - Summary Surface Plasmon Polariton Propagating Surface Plasmons: Surface Plasmon Polaritons (SPPs) SPP are electromagnetic modes bound to metal/dielectric interface which propagates as a longitudinal wave along the surface. Localized Surface Plasmons Surface Plasmon Polaritons Nanoparticles size: 10-200 nm Metal thickness : 10-200 nm Field enhancement 100-10,000 times 10-100 times Field spatial range 10-50 nm ~1000 nm A.J. Haes, C.L. Haynes, et al, MRS BULLETIN, 30 368 (2005) Plasmon Polariton Propagation in Gold Rod Plasmon Polariton Propagation in stripe with d < λ Surface Plasmon Bio Sensors (SPR-like experiment ) Sensor chip with gold film Advantages: Evanescent field interacts with adsorbed molecules only Coupling angle strongly depends on εd Bandgap Engineering 0.95 eV 0.78 eV Figure 9: Energy band diagram versus lattice constant.