The physics of electron backscatter diffraction

Maarten VosAMPL, RSPHYSSE, Australian National University,Acton 0200, Canberra

Aimo WinkelmannMax Planck Institute for Microstructure Physics,Halle, Germany

We are here(John Curtin Medical School)

Our Laboratory

If you want to have a look, just ask!

“standard EBSD set up”

schematic view

sample

phosphor screen

e-

Perfect for practical applications!

Limited use for understanding questions like:-Is the level of contrast of the pattern in agreement with theory?-What is the energy of the electrons that contribute to the contrast?-What is the depth of the sample that contributes to the contrast?-For compounds, do atoms at different sites generate the same contrast?

Our focus: Electron spectroscopy using high-energy (up to 40 keV)electrons.

slit lens

Hemisphericalanalyser 0.5 eV resolution

Measure simultaneously quantitatively intensity along a line with good energy resolution.

We use single crystals and a 0.3mm diameter beam

case 1: contrastSilicon

Greyscale image:calculated using the dynamical theory of diffraction(Winkelmann).We measure in between the yellow arrows.

(022) plane

spectrum of Si for two different outgoing directions(incoming beam along surface normal)

nocontrast

contrast

(on average) increasing depth

Contrast always maximum for zero energy loss? No!

Energy loss is determined bylength of incoming and outgoing path

Outgoing path has to be long enough to build up diffraction pattern.

Energy loss along incoming path does not affect contrast, energy loss along outgoing path does!

Glancing in: incoming trajectorymuch longer than outgoing trajectory. For zero energy loss outgoing trajectory too short to build up contrast.

Momentum p0

Energy p02/2m

After collision (for scattering over 180° momentum transfer q 2p0)

small ball (e.g. electron mass m) hits very large ball (e.g. nucleus mass M) (m << M)

Momentum -p0

Energy p02/2m- q2/2M

Momentum 0

Momentum = q

Energy q2/2M

•What is the recoil effect?:

This can be used to detect (large amounts of) hydrogen

polymer filmscattering angle 45 degree

Difference in elastic peak widthis due to momentum of the scattering atoms (Doppler broadening)

elastic peaks

C

H

H

H

C

C

For larger scattering angles we can separate even heavier elements

spectra of sapphire with some Au impurities at the surface.Cross section proportional to Z2 .Changing the crystal orientation appears to change the relative intensity.Here the Al intensity is enhanced in orientation “b”

A comparison of the Al and O Kikuchiband for different orientations

Why the difference?

Al2O3 total Al2O3 Al only Al2O3 O only

calculated patterns

similar behaviourtotally differentbehaviour

Easiest understood using the reciprocity principle (due to time reversal symmetry): diffraction along an outgoing direction affects the experiment in the same way as diffraction of an incoming beam along that direction would.

Near diffraction conditions standing waves forms in the crystal.For some diffracting plane, the standing waves cause preferentialinteraction with either O or Al,in other cases no such preferential interaction occurs.

-Is the level of contrast of the pattern in agreement with theory?quite good: Ultramicroscopy Vol. 109 , pp. 1211   2009

-What is the energy of the electrons that contribute to the contrast?-What is the depth of the sample that contributes to the contrast?These are 2 related questions. Answer depends on geometry.New Journal of Physics Vol. 12 , pp. 053001   2010

-For compounds, do atoms at different sites generate the same contrast?Yes, when the crystal structure is favourable.(Physical Review Letters, in press)

Answers to our question

Thanks for your attention!