The Physics of EBSD:an overview

Aimo Winkelmann

Max-Planck-Institut fürMikrostrukturphysikWeinberg 2D-06120 Halle (Saale)winkelm@mpi-halle.mpg.de

2

Towards Quantitative Models

experimentMo bcc 25kV

„Geometry“

„Physics“

3

Outline

• Bloch wave model for Kikuchi pattern simulations

• Application to key effects observable in EBSD

• Experimental investigation of energy-resolved Kikuchi band profiles

4

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

5

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

6

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

7

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

8

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

9

experiment RuO2 20kV dynamical simulation© J.R. Michael,

Sandia

RuO2

10

Mo

(pattern by E. Langer)

Mo 25kV

11

Excess and Deficiency Lines - Observation

a

b c

12

Excess and Deficiency Lines - Explanation

D

A

B

A

E

B

A

B

g

S Fkin

kin

kout(1)

kout(2)

-g

13

Excess and Deficiency Lines - Simulation

A.Winkelmann, Ultramicroscopy 108 (2008) 1546GaN 20kV

14

Dark Kikuchi Bands

Proc. Roy. Soc. London A 221 (1954) 224http://www.jstor.org/stable/100898

15

Incident Beam effects

shallow

incidentbeam

larger effective thickness at grazing emission

different depth of inelastic scattering

steep

16

Contrast Reversal of Kikuchi Bands in EBSD

Silicon 20kV52°

72°

A. Winkelmann, G. Nolze Ultramicroscopy 110 (2010) 190

17

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

18

Contrast Reversal of Kikuchi Bands

backscattering from deeper in sample

backscatteringfrom low thickness

A. Winkelmann, G. Nolze Ultramicroscopy 110 (2010) 190

19

HOLZ Ringsin EBSD

experimentand simulation

many-beam dynamical simulation~1000 beams, AW unpublished

Mo(111) 20kVJ. Michael, A. EadesUltramicroscopy 81, 67 (2000)

20

HOLZ rings in real and reciprocal space

a

hkl

hkl

real space

reciprocal spacegz

+ghkl

-ghkl

-ghklHOLZRing

lθ

θ

θ

Z

0

+

21

Energy dependent HOLZ rings

15kV 20kV 25kV

30kV 35kV 40kV

experimental patterns of E.Langer, phys. stat. solidi (c) 4, 1867 (2007)

22

HOLZ ring simulations

15kV 20kV 25kV

30kV 35kV 40kV(~1700beams) same trend: lower visibility at 20kV and 35kV

23

Which electrons form the diffraction patterns in EBSD?

24

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

25

Measurement of energy-dependent Kikuchi band profiles

Si(001) angle-resolved energy loss spectra of backscattered electrons E0=30kV

26

Data treatment and incidence angle dependent contrast

Mo sample holder

Si 30kV

Si 30kV

27

Energy dependent contrast for different geometries

A. Winkelmann, K.Aizel, M. Vos, New Journal of Physics, in press

28

Depth dependent backscattering

A. Winkelmann, K.Aizel, M. Vos, New Journal of Physics, in press

29

Incident beam energy: E0

What is the energy of the elastically scattered electrons?

30

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

31

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

32

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

33

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

34

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

35

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)

36

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)

37

Beam Selection and Bethe Perturbation

neglect

strong (exact treatment)

weak (perturbative treatment)

Beam Selection

Bethe perturbation: reduce matrix dimensions ----> effective structure factors

38

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)

39

Geometry of Diffraction

lattice planes

40

Geometry of Diffraction

incident beamdiffracted beam

lattice planes

θL

θL

41

Geometry of Diffraction

lattice planes

diffracted beamincident beam

transmitted beamdiffracted beam

θL

θL

θL

42

Geometry of Diffraction

lattice planes

diffracted beamincident beam

transmitted beamdiffracted beam

Bragg reflectionθL

θL

θL

θB

43

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

44

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

45

Kikuchi-Patterns of backscattered electrons

Proc. Roy. Soc. London A 221 (1954) 224http://www.jstor.org/stable/100898

46

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