Page 1 Phys Baski Diffraction Techniques Topic #7: Diffraction Techniques Introductory Material –Wave-like nature of electrons, diffraction/interference of waves –Reciprocal space LEED = Low Energy Electron Diffraction –Incoming electron beam (< 100 eV) is perpendicular to sample. –Undistorted reciprocal unit cell, but no real-time data collection. RHEED = Reflection High Energy Electron Diffraction –Incoming electron beam (~keV) has glancing angle to sample. –Real-time data collection, but observe distorted unit cell. XRD = X-ray Diffraction (3D)

Page 2 Phys Baski Diffraction Techniques Electron Scattering: Elastic (Diffraction) & Inelastic LEED RHEED TED Auger, SEM

Page 3 Phys Baski Diffraction Techniques Intro: Wave-like Behavior of Electrons De Broglie wavelength for an electron is given by: For accelerating voltage V o = 100 V, = 0.12 nm (atomic spacing).

Page 4 Phys Baski Diffraction Techniques Intro: Wave Interference d = slit spacing  Incoming Wave Intensity on Screen

Page 5 Phys Baski Diffraction Techniques Intro: Real vs. (Reciprocal, Diffraction, or k) Space k-Space (i.e. spacing of diffraction spots in nm –1 ) Real Space (i.e. spacing of surface atoms in nm) larger real-spacesmaller k-space

Page 6 Phys Baski Diffraction Techniques LEED: History Low Energy Electron Diffraction (LEED) = e – in, e – out (elastic) 1924: Discovered accidentally by Davisson and Kunsman during study of electron emission from a Ni crystal. 1927: Davisson and Germer found diffraction maxima for: –n = D sin  where D = surface spacing, = electron wavelength 1934: Fluorescent screen developed by Ehrenburg for data imaging. 1960: UHV technology enabled LEED of clean surfaces.

Page 7 Phys Baski Diffraction Techniques LEED: Front-view Apparatus Sample Grid 1: retarding voltage (selects only elastic electrons) Grid 2: accelerating voltage (creates fluorescence on screen) Fluorescent Screen

Page 8 Phys Baski Diffraction Techniques k-Space: Bragg Scattering vs. LEED Equation X-ray Diffraction Derive LEED equation using Bragg’s Law for X-ray diffraction, where appropriate angles are substituted and is for the electron wavelength. kiki kfkf D Angle  kiki kfkf   d d Electron Diffraction

Page 9 Phys Baski Diffraction Techniques k-Space: Ewald Sphere for LEED sample LEED spots Diffracted e-beams Ewald Sphere Reciprocal Lattice Rods Incoming e-beam

Page 10 Phys Baski Diffraction Techniques k-Space: Square Lattice Reconstructions Real space LEED

Page 11 Phys Baski Diffraction Techniques LEED: Si(111)7x7 35 eV65 eV Larger D spacings give closer LEED spots (smaller  ). Higher energy electrons give closer spots. Bulk 1x spacing Surface 7x spacing Real Space: Si surface atoms 7× bulk spacing

Page 12 Phys Baski Diffraction Techniques LEED: Data Analysis Sample Electron Gun  R LEED spot x Spacing D

Page 13 Phys Baski Diffraction Techniques RHEED: Schematic of Technique RHEED has higher energy (keV) and lower angle (2°) vs. LEED. Real-time data acquisition possible, but diffraction pattern is distorted. k-Space Real Space LEED

Page 14 Phys Baski Diffraction Techniques k-Space: Ewald Sphere for RHEED Incoming e-beam Diffracted e-beams sample Reciprocal Lattice Rods Ewald Sphere RHEED spots

Page 15 Phys Baski Diffraction Techniques RHEED: Si(111)7x7 k-Space: Larger period  e-beam k-Space: Smaller period  e-beam E-beam Real Space: Smaller period  e-beam Real Space: Larger period  e-beam

Page 16 Phys Baski Diffraction Techniques RHEED: AlN Surface periodicity given by spacing between peaks. Surface quality given by full-width at half-max of peaks. Intensity RHEED image of AlN Line profile of AlN FWHM Slide courtesy of Lei He

Page 17 Phys Baski Diffraction Techniques X-ray Diffraction (XRD) Bragg’s Law and Ewald Construction Types of Scans: –Theta/2Theta (  /2  ) –Rocking Curve –Diffraction-Space Map Philips Materials Research Diffractometer

Page 18 Phys Baski Diffraction Techniques XRD: Diffraction Condition Ewald Construction d Bragg’s Law

Page 19 Phys Baski Diffraction Techniques XRD: (  /2  ) Scan or “Gonio” on MRD Vary MAGNITUDE of  k while maintaining its orientation relative to sample normal. HOW? Usually rotate sample and detector with respect to x-ray beam. Resulting data of Intensity vs. 2  shows peaks at the detector (k f ) for  k values satisfying the diffraction condition. Detects periodicity of planes parallel to surface.

Page 20 Phys Baski Diffraction Techniques XRD:  /2  Example Polycrystalline sample has a number of peaks due to mixture of crystal orientations Polycrystalline Silicon Powder Intensity (counts/sec) 

Page 21 Phys Baski Diffraction Techniques XRD: “Rocking” Curve Scan Vary ORIENTATION of  k relative to sample normal while maintaining its magnitude. How? “Rock” sample over a very small angular range. Resulting data of Intensity vs. Omega (  sample angle) shows detailed structure of diffraction peak being investigated. “Rock” Sample Sample normal

Page 22 Phys Baski Diffraction Techniques XRD: Rocking Curve Example Rocking curve of single crystal GaN around (002) diffraction peak showing its detailed structure GaN Thin Film (002) Reflection Intensity (Counts/s) Omega (deg)

Page 23 Phys Baski Diffraction Techniques XRD: Diffraction-Space Map Vary Orientation and Magnitude of  k. Diffraction-Space map of GaN film on AlN buffer shows peaks of each film.  /2   GaN(002) AlN

Page 24 Phys Baski Diffraction Techniques XRD: X-ray Tube (non-monochromatic) min Bremsstrahlung Characteristic Spectrum (target dependent) Max. X-ray energy = Max. electron energy Characteristic Spectrum K-series radiation created via incoming electron beam. Bremsstrahlung Broad spectrum of “braking” radiation due to decelerating electrons. KK KK ELECTRON IN  PHOTON OUT