Physics-based Simulation Models for EBSD: Advances and Challenges 14th EMAS Workshop on MODERN DEVELOPMENTS AND APPLICATIONS IN MICROBEAM ANALYSIS 2015, May 3 – 7, Portoroz, Slovenia
Aimo Winkelmann Bruker Nano, Berlin
[email protected]
Maarten Vos
Gert Nolze
Research School of Physics and Engineering Australian National University Canberra, Australia
Federal Institute for Materials Research and Testing Berlin, Germany
Francesc Salvat-Pujol Wolfgang Werner Vienna University of Technology Vienna, Austria
Outline
• Introduction • Simulation of EBSD patterns • Application: Orientation Mapping using Pattern Matching • Electron Scattering Experiments: Electron Spectroscopic Diffraction
EBSD
EBSD
Kikuchi Pattern intensity on Diffraction Sphere fixed to crystal
EBSD as a cartographic problem
Towards Quantitative Models
dynamical electron diffraction chemical resolution Al
contrast reversal
excess-deficiency band profile
O
background formation
6
Using the reciprocity principle
EBSD
ECP
outgoing waves diffraction of incoming plane waves (→ TEM)
D
Simple model of backscatter diffraction A. Winkelmann “Dynamical Simulation of Electron Backscatter Diffraction Patterns” in “Electron Backscatter Diffraction in Materials Science” 2nd ed., 2009 7 www.springer.com/materials/book/978-0-387-88135-5
Bloch wave model of electron diffraction Wave function is sum of Bloch waves ( j) (N ) ( j) (r ) c j exp(ik r ) C g exp(igr ) j
g
Fourier expansion of crystal potential (N ) V ( r ) Vg exp(igr ) g
ECP/EBSD Simulation program Experiment 6HSiC 15kV
K 2 (r ) e V (r ) (r ) (r ) 2m 2m 2
Schrödinger Equation
2
2 0
Eigenvalue problem (Matrix) + boundary conditions Wave function of diffracted electrons
( j) cj,C ,k ( j) g
See: M. De Graef „Introduction to Conventional Transmission Electron Microscopy“ github.com/marcdegraef/CTEMsoft
Backscattering proportional to probability density of electrons near atomic cores
I ECP
Z Bij (t ) C C exp( M ) exp[i(h g )rn ] 2 n
n
i g
i, j
j* h
g ,h
Simulation Theory:
Rossouw C J, Miller P R, Josefsson T W and Allen L J Phil. Mag. A 70, 985 (1994)
Bloch Wave Visualization: bit.ly/1IgmEuk
8
RuO2
experiment © J.R. Michael, Sandia
RuO2 20kV
dynamical simulation 9
EBSD + Electron Channeling Patterns
www.bruker.com 10
Gallium Phosphide: Zincblende Structure
11
Applications film growth of non-centrosymmetric semiconductors: - antiphase domains
- polarity inversion
12
Point-group sensitivity of Kikuchi patterns ●
conventional EBSD is limited to Laue group-resolved analysis, kinematical intensities: Ihkl = I-h-k-l
●
(„Friedel's rule“)
Kikuchi patterns are sensitive to the point group of a crystal K. Marthinsen and R. Høier, Acta Cryst. A 44, 700 (1988) K. Z. Baba-Kishi and D. J. Dingley, Scanning 11, 305 (1989)
●
Space group discrimination (chirality of quartz): A. Winkelmann and G. Nolze, Ultramicroscopy 149, 58 (2015)
13
Gallium Phosphide: Kinematic EBSD
90°
14
Gallium Phosphide: Kinematic EBSD
90°
15
Gallium Phosphide: Dynamical Theory
90°
16
Gallium Phosphide: Dynamical Theory
90°
17
Gallium Phosphide: Sample
18
Quantitative Kikuchi Pattern Matching
experiment: 20kV, 5nA, 160x120px, 15ms
cross-correlation coefficient
normalized difference
19
GaP Orientation Mapping: Point Group Resolved
30°
!
120°
20
Orientation Mapping of Polar Materials
●
Kikuchi patterns are sensitive to the point group of a crystal
●
conventional, kinematic EBSD is limited to Laue group-resolved analysis
●
Dynamical diffraction: Friedel's rule is not valid for Kikuchi patterns
●
Point-group resolved EBSD orientation mapping possible via matching of experimental to simulated Kikuchi patterns: A. Winkelmann, G. Nolze, Appl. Phys. Lett. 106, 072101 (2015)
●
Orientation determination by EBSD Pattern Library: Y. Chen, S.U. Park, D. Wei, G. Newstadt, M. Jackson, J.P. Simmons, M. De Graef, A.O. Hero, arxiv.org/abs/1502.07436 21
electron scattering
Recoil effects: Photoemission, Electron Scattering, Neutron Scattering M. Vos, M. R. Went, Y. Kayanuma, S. Tanaka, Y. Takata, and J. Mayers Phys.Rev. B 78, 024301 (2008)
Energy dependent measurements of Kikuchi band profiles High energy electrostatic electron energy analyzer, Australian National University, Canberra DE
