Analytics with
Scanning Electron Microscopy
A. Danilewsky
• Energy Dispersive X-Ray Analysis EDX
• Electron Back Scatter Diffraction EBSD
Depth of Signals
Sample surface
Auger - elektrons
Secondary electrons SE
Back scatter electrons BSE
X – rays:
- Characteristic X - rays
- Continuum X- rays
Topographic contrast
Electron beam
Electron beam
Many
secondary
electrons
leave the
sample
Few
secondary
electrons
leave the
sample
Characteristic X - Rays
keV
k α1: LIII → K
k α2: LII → K
k β : MIII→ K
Relative Intensity of Characteristic X - Rays
L shell consists of 3 subshells with quantum numbers n, l, j and spin m:
lI: 2s – orbital n = 2, l = 0, j = ½, m = ± ½ max. 2 electrons
=> forbidden transition
lII: 2p – orbital n =2, l = 1, j = ½, m = ± ½ => max. 2 electrons
=> kα2 – line
lII: 2p – orbitals n = 2, l = 1, j = 3/2, m = ± ½, ± 3/2 max. 4 electrons
=> kα1 - line
Intensity kα1 : kα2 = 2 : 1
Characteristic X - Rays
Characteristic X – rays
k α: L → K
k β: M→ K
Continuum X- rays
X – Ray Detector
sensor
dewar
liq. N2
• Si – crystal drifted by Li with
FET (field effect transistor)
• Be – window
• collimator
• cooling by liquid N2 (77 K)
cold finger
preamplifier
distance
adjustment
collimator
Si - crystal
Be - window
X – Ray Detector: Si – crystal drifted by Li
X-ray photons generate
electron hole pairs
Semiconductor X – Ray Detector
• Valence band of an intrinsic semiconductor is fully occupied
• Conduction band of an intrinsic semiconductor is largely unoccupied
• X-rays raise electrons from valence to conduction band (photo- and
Auger electrons)
• Electron – hole pairs move free in the crystal during their lifetime
• Bias voltage across the detector moves charge carriers to opposite
electrodes
=> signal/pulse
• The number of electron – hole pairs is proportional to the energy of
X-ray photons
• Minimum energy is the energy gap of the semiconductor (Si: 1.1 eV)
+ energy of lattice vibrations + other physical effects => about 3.8 eV
• Multi-channel analyser: 1024 channels set to 10 eV/channel
=> 0.5 – 10 keV
Semiconductor X – Ray Detector:
Silicon drifted by Li
• Low leakage current => high resistivity Si (ultra pure)
Ti – Si = 2.77.keV
• Li as a donor compensates p-type conduction of Si at low temperature
1.74 keV the Si – structure against X- ray radiation damage
•SiLi= stabilises
• p – n - junction from undoped to Li – doped area
• Only one pulse is is processed at a time. To many X-ray photons during the
anlyser is busy:
Ti = 4.51 keV
=> dead time: no other photons are counted ! Timescale: nano seconds
e.g. 30 seconds counting time at 10% dead timekeV
needs
33 seconds real time measurement
• X-rays generated in the Si – detector crystal it-self: escape peak
X – Ray Spectra
M -lines
K –lines at 80.8. keV
L - lines
K α1
K α2
L -lines
keV
Energy of of photons: Characteristic X-ray lines
Number of photons: Concentration of element
X – Rays:
Absorption and Fluorescence
e.g. Fe - Mn
electron beam
Mnkα
ZAF – Correction:
Fekα
SE
SE
Z = atomic number
A = absorption
F = fluorescence
X – Rays: Background Corrections
Continuum spectrum:
• Calculation from elements
• Subtraction
Energy dispersive X-ray analysis (EDX)
BSE
Oxford - Link System ISIS
at Zeiss DSM 960
Acceleration voltage: 20 kV
Magnification:
x200 –x1000
Detector:
Si:Li
Qualitative mapping of elements:
Al, Si, Ti, Ca, Fe, Mn
Energy dispersive X-ray analysis (EDX)
200 µm
200 µm
Si
200 µm
Ti
200 µm
200 µm
Al
Fe
Geometrie EBSD
Bragg: nλ = 2d sin θ
Electron Backscatter Diffraction EBSD
Oxford - Link System
Crystal
Homogenous, anisotropic discontinuum with three-dimensional
periodical arrangement of lattice elements
r r r
Basevectors a, b , c
Angles
α, β , γ
Crystal Lattice
r
c
231
r
a
r
b
[231]
r
τ
r
r
r
r
r
r
r
τ = u ⋅ a + v ⋅ b + w ⋅ c = 2 ⋅ a + 3 ⋅ b + 1⋅ c
straight line through the points 000 and 231: [231]
Atomic Plane
r
c
r
a
r
b
Indices to
Weiß
reciprocal
Miller
plane I
111
111
(111)
plane II
122
1½½
(211)
Zone and Zone Axis
Zone axis
Plain of the
surface normal
Crystal Structure
Gitter
Lattice
Basis
Base
Crystal
structure
Cubic
Crystal Systems
Hexagonal
Rhombohedral
Tetragonal
Orthorhombic
Monoclinic
Triclinic
Cubic
14 Bravais
Lattices
Hexagonal
Tetragonal
Orthorhombic
Monoclinic
Triclinic
Unit Cell
Smallest assembly, which expresses the metric and includes all
symmetry elements
z.B.: F 4 3 m,
Zinkblende structure
Symmetry elements in two-dimensions
Symmetry
Mirror plane m
Symmetry
Transformations:
Deckoperationen
im
Rotation axis
4-fold
2-fold
Continuum
and
Kontinuum
6-fold
3-fold
Translation
Glide reflection
Discontinuum
Diskontinuum
Principle of Symmetry
10 Symmetry elements of the Continuum :
• Rotation axis 1, 2, 3, 4, 6
• Rotary inversion axis
3, 4, 6
• Inversion 1 oder i
• Mirror plane m
=> 32 Crystal classes
10 Symmetry elements of the Continuum +
Translation:
• Glide-reflection plane a, b, c, d
• Rotary inversion axis, z. B.: 41, 42, 43
=> 230 Space groups
Space Groups
Tabulated in:
International Tables
for
Crystallography, Vol A
Asymmetric unit:
Smallest portion of a crystal
structure to which crystallographic symmetry can be
applied to generate one unit cell.
By application of all symmetry
operations of the space group,
the whole space is filled.
11 Laue - Groups
Due to the phase problem, all diffraction patterns include an inversion center.
=>
Centro- and noncentrosymmetric groups can not be distinguished
Crystal system
Laue - Group
Acentric subgroups
triclinic
1
1
monoclinic
2/m
2, m
orthorhombic
mmm
222, mm2
tetragonal
4/m
4/mmm
4, 4
4mm, 4m2, 422
trigonal
3
hexagonal
3m
6/m
6/mmm
3
3m, 32
6, 6
6mm, 6m2, 622
m3
m3m
23
43m, 432
cubic
Structure Data
Sample Orientation and Reference System
transverse
direction
Information of EBSD - Pattern
EBSD of Ge
Indexed EBSD of Ge
Demonstration of Sample Orientation
Projection of the
surface normal in a
two-dimensional
plain occurs analogous to the stereographic projection:
=> Pole Figure
Pole Figure Corresponding to ~ [111]
with Slightly Tilt and Rotation
Inverse Pole Figure
Polycrystalline Sample
Few Alignment of Crystallites
Polycrystalline Sample
Alignment of Crystallites Corresponding to [101],
Inverse Pole Figure
Polycrystalline Sample
Alignment of Crystallites, Inverse Pole Figure
Reference System
Demonstration of Orientation –
Euler angle
Orientation:
Rotation of the sample-fixed coordinate system (Cartesian!) into the crystalfixed system of the discrete crystallite.
Convention according to Bunge:
a) Sample orientation
ϕ1 - Rotation on perpendicular direction
Φ - Rotation on longitudinal direction
ϕ2 - Rotation on transversal direction
b) Crystal orientation
ϕ1 - Rotation in (001)
Φ - Rotation on [100]
ϕ2 - Rotation in (001)
Mechanical Sample Preparation
Mechanochemical Sample Preparation
Sample Preparation
Depth of penetration 10 - 100 nm
Good polish
Bad polish
Sample Preparation by Ion Abrasion
(111) - Twinning in polycrystalline Si
back scatter
electrons
quality
pattern (BSE)
rolling
normal
transverse
direction
direction
direction
x 200 pixel size 92,6 µm
Polycrystalline Si
quality electrons
pattern (BSE)
back scatter
transverse
normal
direction
rollingdirection
direction
x 200 pixel size 24 µm
Polycrystalline Si:
Preferential growth direction
5 - 7° deviation from [110]
Literature to Scanning Electron Microscopy
• L. Reimer, G. Pfefferkorn: "Rasterelektronenmikroskopie", Springer 1977
• H. R. Wenk (Ed.): "Electron Microscopy in Mineralogy", Springer Verlag 1976
• L. Reimer: "Scanning Electron Microscopy", Springer 1983
• L. Reimer: "Elektronenmikroskopische Untersuchungs- und Präparationsmethoden",
Springer 1967
• Schmidt, Peter Fritz
Praxis der Rasterelektronenmikroskopie und Mikrobereichsanalyse / Peter
Fritz Schmidt - Renningen-Malmsheim : Expert-Verlag, 1994 (Kontakt &
Studium ; 444 : Meßtechnik)
• Joy et al.: "Electron Channeling Pattern in the Scanning Electron Microscope",
J. Appl. Phys. Vol 53, No 8 (1982) 439 - 461
• U. Holzhäuser: "Charakterisierung von Einkristallen mittels Electron Channeling
Pattern", Diplomarbeit Universit@t Freiburg 1992
• Flegler, Heckmann, Klomparens, Elektronenmikroskopie, Spektrum
Akademischer Verlag Berlin und Heidelberg, 1993
• Humphreys, "Reviw: Grain and subgrain characterisation by electron backscatter
diffraction, J. of Mat. Sci. 36 (2001), 3833 – 3854
Literature to Scanning Electron Microscopy
• and online:
• "Grundlagen der Raster-Elektronenmikroskopie" http://www.reclot.de
by Alexander Fels
•
"SEM Electron Backscattered Diffraction" by Dr Geoff Lloyd
•
"Crash Kurs Textur" http://www.texture.de/Multex-Dateien/crash.htm
by Kurt Helming