Transmission electron microscopy in materials science A. Mogilatenko, H. Kirmse Humboldt-Universität zu Berlin, Institut für Physik, AG Kristallographie Newtonstrasse 15, D-12489 Berlin
Telefon 030 2093 7868, Fax 030 20937760 E-mail:
[email protected] [email protected] Web: http://crysta.physik.hu-berlin.de/ag_tem/ Raum 2‘403
pdf-Dateien der Vorlesungen unter: http://crysta.physik.huberlin.de/~kirmse/ Teaching „Inorganic Materials" Vorlesungen zur Elektronenmikroskopie: Teil 1, Teil 2
Introduction and short history
First transmission electron microscope First TEM built in 1931 by Max Knoll and Ernst Ruska in Berlin
1931: magnification 17
resolution > light microscope
Nobel Prize in Physics 1986
1933: magnification 12.000 resolution < light microscope
Ray diagram in light microscopy and TEM lamp
illumination
glass lens
condensor lens
glass lens
specimen objective lens
electrons
electromagnetic lens
electromagnetic lens
first image
glass lens
electromagnetic lens
projective lens final image
ocular eye
eye fluorescent screen
Theory of image formation and resolution limit 1866 - starts working with Carl Zeiss 1873 - theoretical description of resolution limit
d Ernst Abbe: 1840-1905
: n: :
2n sin
wavelength refractive index of medium between object and objective opening angle of rays originating from object and collected by objective
„… it is poor comfort to hope that human ingenuity will find ways and means of overcoming this limit.“
Resolution: Light Microscopy no lens imperfections => resolution is limited by diffraction at edges of lens system
d
2n sin
!
To get a better resolution – decrease the wave length!
Light optics:
: n: :
wavelength 400 .. 800 nm refractive index of medium 1 .. 1.5 (air .. immersion system) between object and objective 70° opening angle of rays originating from object and collected by objective
=> d ~ 250 nm
Monument in Jena (Germany)
Wave-Particle Duality Louis de Broglie, 1924
h p
h 2m0eV
h 2m0eV 1
eV 2m0c 2
!
with 100 keV electrons travell at about 1/2c! V: acceleration voltage, m0: electron mass e: electron charge, c: velocity of light
Wave-Particle Duality
wave
coherent ↔ incoherent
imaging, high resolution imaging, diffraction
particle elastic ↔ inelastic
spectrometry
/ pm
Electron wavelength
V / kV V = 300kV =>
= 1.97 pm => resolution only ~ 0.1 nm ?
„magnetic lenses of TEMs have similar quality as bottom of bottle of champagne would have for light microscope“
TEM – multi lens system
How can I focus electron beam? electric field E electron charge e => force F
E
F = -e*E force in opposite direction of electric field magnetic induction B
electron velocity v => Lorentz force F = -e(v x B) force perpendicular to magnetic field and electron velocity direction B
Magnetic electron round lens
~ 1 - 2 Tesla
Williams & Carter
Magnetic electron round lens
Wine glass with water = optical lens with huge aberrations
Electron lenses are bad lenses too!!! “if the lens in your own eyes would be as bad as electromagnetic lenses, then you would be legally blind“ Williams & Carter
Ray diagram (Strahlengang) lens object optic axis
Ray diagram
lens
back focal plane
image plane
Brennebene
Bildebene
object optic axis optische Achse
d1 d2
Ray diagram
lens
back focal plane
image plane
Brennebene
Bildebene
object optic axis
d1 d2
lens
back focal plane
image plane
object optic axis
diffraction pattern
Perfect imaging by a round lens the same focus for all rays Object marginal ray paraxial ray
Objective lens
Image plane
Spherical aberration (Öffnungsfehler) - off-axis rays are focused stronger! disk of least confusion marginal ray paraxial ray
marginal focus Objective lens
paraxial focus Image plane
A point object is imaged as a disk of finite size – limits the resolution!
Improvement in resolution
sub-Å resolution
H. Rose, Journal of Electron Microscopy: 1-9 (2009)
Problems / disadvantages in TEM • time consuming specimen preparation is required • only small sample regions can be investigated (~ 1 nm…some µm) • electron beam damage damage dose: living objects: bio molecules: anorganic substances:
10-4 – 1 e/nm² 103 – 105 e/nm² 106 – 1011 e/nm²
Rose equation: links resolution d and contrast c c * d > 5/n0.5 n: number of electrons per unit area example: c = 5 %; d = 0.3 nm => n > 105 e/nm²
Electron beam induced segregation effects Electron beam damage in InGaN QWs - In-clustering
Smeeton et al., Appl. Phys. Lett. 83 (2003) 5419
Interaction of electrons and matter
100…400 keV
primary electrons
Energy-Dispersive X-ray Spectrometer
backscattered electrons
X-rays secondary electrons
10…200 nm
thin crystalline specimen
Electron Diffraction, Conventional imaging, High resolution imaging
diffracted beam
direct beam
elastically and inelastically scattered electrons Electron Energy Loss Spectrometer
High-Angle Annular Dark-Field Detector
Electron forward scattering from thin specimen coherent • single scattering incident beam • plural scattering (>1) • multiple scattering (>20)
thin specimen incoherent elastic coherent scattered incoherent elastic scattered electrons inelastic scattered electrons (> ~10°) electrons (1…10°) (< 1°) direct beam
Scattering of electrons Bulk material
TEM specimen
50 nm 1 nm 200 nm
50 µm
Monte-Carlo Simulation of the paths of electrons (acceleration voltage: 100 kV) trough Silicon of different thicknesses
Full width at half maximum 12 nm
TEM/STEM IMAGING
Amplitude contrast (diffraction contrast)
Electron holography
Phase contrast (highresolution imaging)
Z-contrast imaging
Lorenz microscopy
DIFFRACTION
Selected area diffraction
Convergent beam diffraction
SPECTROSCOPY
Energy dispersive X-ray spectroscopy
Micro-/ nanodiffraction
Tomography
X-ray mapping
Electron energy loss spectroscopy
Energy-filtered TEM (EFTEM)
TEM specimen preparation
Why sample preparation for Transmission Electron Microscopy
• Electrons with properties of particles and waves • Strong interaction between electrons of the beam and atoms of the samples scattering
• Sufficient intensity/number of transmitted electrons only for small thickness (about 100 nm) • Essential thickness depends on, e.g., materials properties, acceleration voltage, and requirements of individual investigation method
Demands on sample preparation • No change of materials properties including: – Structure (amorphous, polycrystalline, crystalline) – Chemistry (composition of the bulk material, of surfaces, and of interfaces) • But: Artifacts inherent in every preparation method! • Criterion of appropriate preparation technique: Influence on structural and chemical properties as small as possible!
Shape of the sample • TEM sample holders
• Limits of sample size: – Diameter: 3 mm due to the furnace of the TEM sample holder – Maximum thickness of sample edge: ca. 100 µm
Aim of investigation
Type of sample
• Structural properties – size distribution of entities – area density – structural defects • Chemical properties – composition – modification – interface sharpness • Electronic properties • Magnetic properties
• Particles • Bulk material • Epitaxial structures Materials properties • Hardness • Sensitivity for chemical solutions
Preparation strategy
TEM preparation of small particles • Dispersion in a non dissolving liquid (e.g.: methanol, water, etc.) in an ultrasonic bath • Transfer to a carbon film supported by a copper grid
Evaporation of a droplet
Dipping
TEM grids
and many more
holey carbon film
lacey carbon film
CaF2 with Pd particles (after reaction) transmission electron microscopy bright-field image Pd-CaF_HF25_slotB2; hrtem01_particel01_ovw_3kx
Humboldt-Universität zu Berlin, Institut für Physik (AG Kristallographie), Institut für Chemie (AG Festkörperchemie)
0.16 nm 0.16 nm Lattice plane distances d (nm) CaF2
Pd
PdF2
PdO
0.31541
0.22458
0.30756
0.30431
0.27315
0.19451
0.26868
0.26680
0.19314
0.13754
0.23832
0.26430
0.16472
0.11730
0.21748
0.21521
0.15770
0.11230
0.18834
0.20060
0.13657
0.09725
0.17757
0.16751
0.12533
0.08925
0.16061
0.15358
0.12216
0.08699
0.15378
0.15215
0.24 nm 0.27 nm 0.27 nm
Matrix (after reaction) high-resolution transmission electron microscopy imaging Pd-CaF_HF25_slotB2; hrtem01_particle03_25kx
Humboldt-Universität zu Berlin, Institut für Physik (AG Kristallographie), Institut für Chemie (AG Festkörperchemie)
TEM preparation of epitaxial structures
Plan-view and cross-sectional TEM preparation Plan view (PVTEM)
Cross section (XTEM)
Initial sample
Formatting
Thinning of substrate
face-to-face gluing
Gluing in a cylinder and sawing
Mechanical thinning Cutting of a disc
Gluing of dummies Dimpling
Dimpling
Ultrasonic disc cutting Ion-beam milling
Ion-beam milling
Mechanical thinning
damage
Region 1
Beilby layer: change of chemical composition, strong deformation, amorphisation
Region 2
macro-deformed layer: tilt of grains, increased dislocation density
Region 3
micro-deformed layer: weak tilt of grains, dislocation density as grown
~ 100 nm
Situation after sawing Next preparation step has to remove the damage!
Dimple grinding
Detail of a dimple grinder
Principles of dimpling technique sample Dimpler grinder of Gatan
thickness in the center ~ 20 µm
Ion-beam milling
sample
Ion gun arrangement for milling of both sides of the sample; possible ions: Ar+, Xe+, I+, ... acceleration voltage: 1...5 kV usual angle : < 10°
Layout of a vacuum chamber with two ion guns
GaAs
Ga(Sb,As) (In,Ga)As GaAs
GaAs TEM Philips CM200 FEG cS, GaAs spacer thickness: 4.5 nm HRTEM of Ga(Sb,As) QD on (In,Ga)As seed QD TU#5294cs/2, links: qdot4_012c.jpg, rechts: qdot5_012c.jpg
Humboldt-Universität zu Berlin, Institut für Physik, AG Kristallographie Forschungszentrum Jülich GmbH, Institut für Festkörperforschung
Contrast in TEM
most important for amorphous samples
most important for crystalline samples
most important in HRTEM
Amplitude contrast: mass-thickness contrast total cross section Qtot for scattering from sample (thickness t): Avogadro number total scattering cross section of an isolated atom
Q tot t
N0
tot
A
t)
! product
density atomic weight of atoms
t is called „mass thickness“
Thicker and /or higher mass (Z) areas will scatter more electrons and appear darker in the image
Amplitude contrast: diffraction contrast primary beam
Bragg’s law: n·λ = 2·d·sinθ
sample
objective lens
objective aperture
intermediate lenses projective lenses
imaging plane
Two beam conditions: Tilting the specimen unitl direct beam and one diffracted beam are strong!
Phase contrast: high resolution TEM primary beam
2-beam condition
sample
objective lens
objective aperture
intermediate lenses projective lenses
imaging plane
multiple-beam condition
Phase shift due to the inner potential of specimen Electron beam
Path through the vacuum:
2 m e E
m e E
– – – –
Plancks constant electron mass electron charge electron energy
Path through the specimen:
' d
2me E V x, y, z V x, y , z – inner potential energy
Phase shift due to the inner potential of specimen Plane wave 0
r, t
local charge energy
V x, y , z
mean inner potential
x atomic nucleus object exit wave Object
r,t
t
projected potential: Vt (thin sample)
x, y
V x, y, z dz 0
Phase shift due to the inner potential of specimen Electron beam
Phase shift:
d
2
dz
dz 2 '
with
E
V x, y , z (interaction constant)
Total phase shift: z
d
d
V x, y, z dz
Vt x, y
! phase change depends on potential V which electrons see, as they pass through sample
HRTEM – Imaging Process y
Object
x
Diffraction pattern
gy
gx
Image
y
x
Role of optical system transfer of each point in specimen into region in final image f(x,y): specimen (transmission) function describes specimen g(x,y): extended region of point x,y in image h(r-r`): weighting term: point spread function
gr
f r' h r r' dr'
f(x,y)
point
f r
t r r' 2 points
optical system
disc
image g(x,y)=g(r)
each point in final image has contributions from many points in specimen
HRTEM: contrast transfer function T(u)
! opposite sign of T(u) -
information limit
oposite contribution to contrast u < point resolution: -1 u, [nm ] images are directly interpretable u > point resolution: no direct interpretation is possible
point resolution
E u sin χ(u)
Eu
No simple correspondence between the image intensity and the atom column positions! Additional calculations are necessary!
u
f
u
2
1 2
Cs
3
u4
f - defocus - wave length Cs - spherical aberration u - spatial frequency
Contrast transfer
sin
Optimum for f : Scherzer
u
sin
f
u
2
1 2
Cs
Minimization of Cs
3
u4
Example: HRTEM simulation for GaAs projected potential
same thickness, only defocus change
by courtesy of Prof. Kerstin Volz
HRTEM of an isolated ZnTe nanowire
- visualization of crystal structure - analysis of defects
HRTEM of an isolated ZnTe nanowire {211}
{111}
{110}
HRTEM of an isolated ZnTe nanowire {211}
{111}
{110}
Twin formation