the physics of ebsd: an overview
TRANSCRIPT
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The Physics of EBSD:an overview
Aimo Winkelmann
Max-Planck-Institut fürMikrostrukturphysikWeinberg 2D-06120 Halle (Saale)[email protected]
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Towards Quantitative Models
experimentMo bcc 25kV
„Geometry“
„Physics“
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Outline
• Bloch wave model for Kikuchi pattern simulations
• Application to key effects observable in EBSD
• Experimental investigation of energy-resolved Kikuchi band profiles
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Using the reciprocity principle
(e.g. TEM)
diffraction of incoming plane waves
outgoing
waves
A. Winkelmann “Dynamical Simulation of Electron Backscatter Diffraction Patterns”in “Electron Backscatter Diffraction in Materials Science”
Schwartz, A.J.; Kumar, M.; Adams, B.L.; Field, D.P. (Eds.) 2nd ed., 2009 www.springer.com/materials/book/978-0-387-88135-5
Simple model of backscatter diffraction
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Bloch wave model of Electron Diffraction
•excitation of two types of Bloch waves near a Bragg refelction
•changing backscattering probability away from Bragg reflection
• formation of Kikuchi-band
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Bloch wave model of electron diffraction
Fourier expansion ofcrystal potential
Wave function is sum ofBloch waves
Schrödinger Equation
Eigenvalue problem (Matrix) + boundary conditions
Wave function of diffracted electrons
Backscattering proportional to probability density of electrons near atomic cores
])(exp[)exp()( *
, ,
2n
jh
n ji hg
igijnECP rghiMCCtBZI −−∝ ∑ ∑ ∑
CBEDJ.M. Zuo, K. Gjonnes, J.C.H. Spence, J.Electr.Micr.Techn. 12, 29 (1989)
Theory: Rossouw C J, Miller P R, Josefsson T W and Allen L J Phil. Mag. A 70, 985 (1994)
ECP/EBSD Simulation program∑∑=Ψ
)()()( )exp()exp()(
N
g
jg
j
jj rgiCrkicr ∑=
)(
)exp()(N
gg rgiVrV
)()( ,, jjgj kCc
)(2
)()()(2
20
22
2
rmKrrVer
m Ψ=Ψ−Ψ∇−
Simulation
Experiment 6HSiC 15kV
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Electron Channeling Patterns of 3C SiC(111)
A. Winkelmann, B.Schröter, W.Richter Ultramicroscopy 98 (2003) 1-7
4000eV 4200eV 5900eV 7000eV 8000eV
7000
eV
5900
eV
4000
eV
4200
eV
8000
eV
experiment
dynamicalsimulation
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Electron Backscatter Diffraction of GaN{0001}
A. Winkelmann, C. Trager-Cowan, F. Sweeney, A.P. Day, P.Parbrook Ultramicroscopy 107 (2007) 414
a
b c
20kV
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experiment RuO2 20kV dynamical simulation© J.R. Michael,
Sandia
RuO2
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Mo
(pattern by E. Langer)
Mo 25kV
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Excess and Deficiency Lines - Observation
a
b c
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Excess and Deficiency Lines - Explanation
D
A
B
A
E
B
A
B
g
S Fkin
kin
kout(1)
kout(2)
-g
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Excess and Deficiency Lines - Simulation
A.Winkelmann, Ultramicroscopy 108 (2008) 1546GaN 20kV
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Dark Kikuchi Bands
Proc. Roy. Soc. London A 221 (1954) 224http://www.jstor.org/stable/100898
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Incident Beam effects
shallow
incidentbeam
larger effective thickness at grazing emission
different depth of inelastic scattering
steep
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Contrast Reversal of Kikuchi Bands in EBSD
Silicon 20kV52°
72°
A. Winkelmann, G. Nolze Ultramicroscopy 110 (2010) 190
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Bloch-wave dependent absorption in EBSD
A. Winkelmann “Dynamical Simulation of Electron Backscatter Diffraction Patterns”in “Electron Backscatter Diffraction in Materials Science” 2nd ed., 2009
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Contrast Reversal of Kikuchi Bands
backscattering from deeper in sample
backscatteringfrom low thickness
A. Winkelmann, G. Nolze Ultramicroscopy 110 (2010) 190
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HOLZ Ringsin EBSD
experimentand simulation
many-beam dynamical simulation~1000 beams, AW unpublished
Mo(111) 20kVJ. Michael, A. EadesUltramicroscopy 81, 67 (2000)
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HOLZ rings in real and reciprocal space
a
hkl
hkl
real space
reciprocal spacegz
+ghkl
-ghkl
-ghklHOLZRing
lθ
θ
θ
Z
0
+
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Energy dependent HOLZ rings
15kV 20kV 25kV
30kV 35kV 40kV
experimental patterns of E.Langer, phys. stat. solidi (c) 4, 1867 (2007)
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HOLZ ring simulations
15kV 20kV 25kV
30kV 35kV 40kV(~1700beams) same trend: lower visibility at 20kV and 35kV
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Which electrons form the diffraction patterns in EBSD?
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Energy dependent measurements of Kikuchi band profiles
Energy-resolved EBSD with grid.based filter: A. Deal, T. Hooghan, A. Eades, Ultramicroscopy 108 (2008) 116
High energy Electrostatic electron energy analyzer, Australian National University, Canberra ∆E<0.5eV @10..40kV
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Measurement of energy-dependent Kikuchi band profiles
Si(001) angle-resolved energy loss spectra of backscattered electrons E0=30kV
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Data treatment and incidence angle dependent contrast
Mo sample holder
Si 30kV
Si 30kV
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Energy dependent contrast for different geometries
A. Winkelmann, K.Aizel, M. Vos, New Journal of Physics, in press
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Depth dependent backscattering
A. Winkelmann, K.Aizel, M. Vos, New Journal of Physics, in press
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Incident beam energy: E0
What is the energy of the elastically scattered electrons?
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Electron Rutherford Backscattering Spectroscopy
AuAl O
AuAl O
element-selectiverecoil energy of elastically scatteredelectrons
Au atoms on Al2O
3
M. Vos, K. Aizel, A. WinkelmannSurface Science 604 (2010) 893–897
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Element-resolved Kikuchi bands in Saphire
Al O
Experiment
-4 -2 0 2 40
2
4
6
8
10
12
14
16
18
20
22
24 O x5 Al
Al2O
3 35kV
inte
nsity
(arb
. uni
ts)
angle φ (degrees)
SimulationAl
2O
3
35kV
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Thanks
UK:UK:C. Trager-CowanC. Trager-CowanA. DayA. DayA. WilkinsonA. Wilkinson
USA:USA:A. EadesA. EadesJ. MichaelJ. MichaelL. BrewerL. BrewerA. DealA. Deal
AUSTRALIA:AUSTRALIA:M. VosM. VosM. WentM. WentK. AizelK. Aizel
GERMANY:GERMANY:G. NolzeG. NolzeE. LangerE. Langer
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Loss of coherence
∆x=0λ ∆x=0.1λ ∆x=0.5λ
∆φ=0.2*π ∆φ=π
diso
rder
∆φ=0
phas
e ra
ndom
izat
ion
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Incoherent backscattering of electrons
Sources of phase randomization•recoil in elastic scattering•thermal movements•lattice defects•inelastic scattering
loss of coherence between lattice points via elastic and inelastic scattering
Low energies High energies
25kV
1kV
170eV
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3C SiC(111) Si2p ring-like structures
ZOLZ000
FOLZg
|K|= 1/λ|K’|=
K
H-1
K’
2θ
H 2θ
A B
A. Winkelmann et al., Phys. Rev. B 69, 245417 (2004)
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Ultrathin magnetic films: Tetragonally distorted FeCo alloys on Pd(001)
8ML
38ML
A
B
Change
-+
decreasing c/a ratiowith thickness
Definition of c/a ratio
fcc c/a=√2
bcc c/a=1
15 ML Fe0.4Co0.6/Pd(001)c/a=1.13
Pd(001)cluster simulationexperiment
A. Winkelmann et al.,Phys. Rev. Lett. 96, 257205 (2006)
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Beam Selection and Bethe Perturbation
neglect
strong (exact treatment)
weak (perturbative treatment)
Beam Selection
Bethe perturbation: reduce matrix dimensions ----> effective structure factors
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Previous Studies
L. J. Allen, C. J. Rossouw„Effects of thermal diffuse scattering and surface tilt on diffraction and channeling of fast electrons in CdTe“Phys. Rev. B 39, 8313 - 8321 (1989)
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Geometry of Diffraction
lattice planes
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Geometry of Diffraction
incident beamdiffracted beam
lattice planes
θL
θL
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Geometry of Diffraction
lattice planes
diffracted beamincident beam
transmitted beamdiffracted beam
θL
θL
θL
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Geometry of Diffraction
lattice planes
diffracted beamincident beam
transmitted beamdiffracted beam
Bragg reflectionθL
θL
θL
θB
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Geometry of Diffraction
lattice planes
diffracted beamincident beam
transmitted beamdiffracted beam
Bragg reflection
interference cones tied to lattice planes
projection
θL
θL
θL
θL
θB
θB
θB
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Mo(100)Changing visibility of Mo (100) HOLZ rings with energyexperimental patterns of E.Langer, phys. stat. solidi (c) 4, 1867 (2007)
15kV 20kV 25kV
30kV 35kV 40kV
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Kikuchi-Patterns of backscattered electrons
Proc. Roy. Soc. London A 221 (1954) 224http://www.jstor.org/stable/100898
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Diffraction of backscattered and back-reflected electrons
Scanning electron microscopy:Electron Backscatter Diffraction (EBSD)
Low Energy Electron Diffraction(LEED)
p h o s p h o r s c r e e n
e le c tr o n g u n
s a m p leg r id s
s u p p r e s s o r
~ +5 kV
-V + VE ∆
-V E
Mo bcc 25kV 6H SiC 1kV 6H SiC 170eV