Transcript “Aspects of the nanomaterials challenge, image-based nanocrystallography by means of transmission electron goniometry & how it might be developed into commercial products” by Peter Moeck PSU, Dep.

“Aspects of the nanomaterials
challenge, image-based
nanocrystallography by means of
transmission electron goniometry &
how it might be developed into
commercial products”
by Peter Moeck
PSU, Dep. Physics & Center
for Emerging Technologies
&
Phil Fraundorf
Dep. Physics and Astronomy & Center
for Molecular Electronics
Seminar at FEI Company, Hillsboro, Oregon, Feb. 7, 2005
Image-based nanocrystallography by means of transmission electron
goniometry in collaboration with Wentao Qin (Freescale
Semiconductors), Eric Mandell (U of Missouri, St. Louis), Chunfei Li
(PSU, Electron Microscopy Center), Bjoern Seipel (PSU, Physics)
Phil
Peter
Chunfei
Wentao
Bjoern
HRTEM and Z-contrast STEM & EELS on semiconductor quantum dots
in collaboration with Teya Topuria, Yuanyuan Lei, Nigel D. Browning (all
U of Illinois at Chicago - UIC - at that time)
Teya
Now NCEM,
TEAM project, and
U of California at
Davis
Yuanyuan
Now IBM Almaden
Now investment
banking
Nigel
Financial support from Research Corporation, National Center for Electron Microscopy
(NCEM) Berkeley, Portland State University, University of Illinois at Chicago
Outline
1. Nanomaterials and need for 3D nanocrystallography
2. The challenge of electron crystallography and how it may be
met
3. Image-based nanocrystallography by means of transmission
electron goniometry
3.1. Basic ideas and literature
3.2. Fringe visibility maps
3.3. Tilt-protocol / Lattice-fringe fingerprinting, …
4. Strain and chemical composition quantification from images
4.1. Strain quantization in Si,Ge by digital dark field techniques
4.2. Epitaxial and endotaxial semiconductor quantum dots
5. Conclusions
Nanomaterials and need for 3D Nanocrystallography
“nanotechnology as a whole is estimated to represent a market of $ 11 trillion by
2010 with nanomaterials growing from $ 490 million today to $ 900 million in
2005 and $ 11 billion in 2010. … impact of nanomaterials will extend way
beyond the immediate value of the materials themselves. … over $ 340 billion
in 2010” M.J. Pitkethly, nanotoday, p. 36-42 (2003) and p. 20-29 (2004).
US government 21st Century Nanotechnology Research and Development Act:
“the market for nanotech products and services in the United States alone could
reach over $ 1 trillion.” http://www.theorator.com/bills108/s189.html
Crystalline nanomaterials
need nanocrystallography of
both individual particles and
ensembles of particles
Phase diagrams and particle morphologies
are size dependent in nm range, but largely
unexplored – so one can produce novel
structures, but needs nanocrystallography
tools to analyze them / optimize their
production process, (nano)materials
engineering
core of (nano)materials science:
structure – property relationships
when nanoparticle structures are know, crystal
physics derives properties a nanocrystal can
have as a matter of principle
Pierre Curie’s PrinCiPle
Gproperty  Gcrystal _ in _ field  G field  Gcrystal
J.P. Mercier, G. Zambelli, W. Kurz, Introduction to Materials Science, Elsevier 2002
Semiconductor quantum dots for nanoelectronics devices
Traps for matter waves, artificial pseudo-atoms, entities with discrete
energy levels
one-dimensional, time independent
Schrödinger’s equation
d 2 ( x )
8  m  2

[ E  U ( x )]  ( x )
dx2
h2
Electron in atom: ΔE ≈ 1-10 eV, L ≈ 0.1 nm
Exciton in semiconductor quantum dot: ΔE ≈ 0.1 eV, L ≈ 10 nm
Why 3D nanocrystallography?
TEM image always 2D projection
1. Nanomaterials and need for 3D nanocrystallography
2. The challenge of electron crystallography and how it may be
met
3. Image-based nanocrystallography by means of transmission
electron goniometry
3.1. Basic ideas and literature
3.2. Fringe visibility maps
3.3. Tilt-protocol / Lattice-fringe fingerprinting, …
4. Strain and chemical composition quantification from images
4.1. Strain quantization in Si,Ge by digital dark field techniques
4.2. Epitaxial and endotaxial semiconductor quantum dots
5. Conclusions
John Spence direct quote April 19th, 2004, Workshop on Electron NanoCrystallography, National Center for Electron Microscopy, Lawrence Berkeley National
Laboratory
“The challenge of electron crystallography
In the age of nanoscience, there is an urgent need for a method of rapidly solving
new, inorganic nanostructured materials. Many are fine-grained, light element,
crystallites with cannot be solved by XRD. The unsolved challenge of 50 years is.
….
To collect three-dimensional diffraction data under kinematical conditions.
Then not restricted to short c axis, Note: centers of each CBED disc in a small
probe pattern provide a point pattern ! Blank disks suggest single-scattering
conditions. …
The difficulties are
Goniometer. Loss of area during tilt
Contamination
Automation of tilt and data collection
Radiation damage”
CDEB is not the answer: Nanocrystals too thin, i.e.
kinematical diffraction conditions which we want for HR-phase
contrast imaging, CBED disk appear featureless, are void of fine
structure, what is too thin?
Less than 1/4 of an extinction distance? for semiconductors = 20 -10
nm? .. to get the most out of a CBED pattern the specimen
should be thicker than one extinction distance …” D.B.
Williams and C.B. Carter
there is also nanoprobe diffraction in TEM (Riecke method) down to a few tens of nm, rocking beam diffraction in STEM down
to about 5 nm, and “tomographic diffractive imaging” J.C.H. Spence et al., J.M. Zuo et al., …
Vcell cos
g 
Fg
John Spence’s comment on
our image-based 3D
nanocrystallography methods:
“… it’s really good ideas …”
Simulated
CBED
pattern for Si
[111],
http://www.hre
mresearch.com
/Eng/download/
documents/CB
EDcatE.html
“for his development of crystallographic
electron microscopy and his structural
elucidation of biologically important nucleic
acid-protein complexes”
which he called himself: “Crystallographic or
Fourier Electron Microscopy”
Basic ideas: weak phase objects, linear imaging theory of TEM, projected
potentials, Fourier transforms, convolutions, Fourier syntheses, …
Quasi-continuous tomography, for every 1 - 2 degrees tilt one image,
applicable to 10 - 100 nm sized biological objects, but also nanocrystals, …
A. Koster et al.,
J. Struct. Biolog. 120, 276 (1997)
Magnetite crystals in bacteria strain MV-1, cell is preserved surrounding the
crystals, tilt series was acquired from +76 degrees to - 76 degrees, each crystal
is ≈ 60nm long
P. R. Buseck et al., Magnetite Morphology and Life
on Mars, Proc. Nat. Acad. Sci., 99 (24), 1349013495, (2001)
http://www-hrem.msm.cam.ac.uk/research/CETP/STEM_Tomo.html
Slightly paraphrased after X. Zuo and
S. Hovmöller, chapter 22 of Industrial
Applications of Electron Microscopy, ed.
Z. R. Li, Marcel Dekker Inc, New York,
Basel, 2003:
“It is the raison d’être of transmission electron microscopy (TEM) that the phase
information is preserved in TEM images, such that they represent a magnified
image of the object. DeRosier and Klug [Reconstruction of three dimensional
structures from electron micrographs, Nature 217 (1968) 130] recognized that the
crystallographic structure factor phase could be extracted directly from the Fourier
transforms of digitized images, under the assumption of weak scattering and
linear imaging (i.e., for very thin crystals). This discovery … can be considered as
the birth of structure determination from high resolution TEM images.”
While image resolution
in that paper is 0.2 nm,
diffraction resolution is
between 0.1 nm and the
size of the atoms, i.e.
some 0.05 nm
When image resolution as good as
diffraction resolution, little need for
diffraction data (since structure factor phases
are preserved in phase contrast images!)
Following Aaron Klug: weak phase objects, linear imaging theory of TEM,
projected potentials, Fourier transforms, convolutions, Fourier syntheses,
are also applicable to nm thin crystals, i.e. nanocrystals, but no need for
quasi-continuous tomography, due to symmetry - discrete atomic resolution
tomography of nanocrystals will do, if there is enough directly interpretable
resolution
0.05 nm
resolution
0.15 nm
resolution
In atom
shape of
particle
Why was this only a simulation of discrete atomic
resolution tomography?
Not yet ready to demonstrate experimentally,
need for better goniometers
need for resolution on the order of magnitude one
Bohr radius, 0.053 nm
1
resScherzer _ Phase  HRTEM  0.67  Cs 4  
resScherzer_ Z STEM  0.4  Cs  
1
either reduce wavelength
4
3
3
4
4
or reduce lens
aberrations, mainly Cs
either reduce wavelength
JEOL JEM ARM 1250, max 1.25
MeV, increasing Scherzer point to
point resolution to about 0.12 nm
Costs about $ 25 million, needs its
own special building, some 10 to
15 m high, problem of beam
damage! Just HRTEM, no added
STEM and analytical TEM
kind of dinosaurs going extinct?
On the other hand, a
contemporary 200-300 kV
TEM/STEM with Cs corrector and
all analytical gadgets may cost less
than about $ 2.5 million (including
special room to house it) for the
same spatial resolution and
significantly reduced beam
damage!
or reduce lens
aberrations, mainly Cs
Directly
interpretable
(point or
Scherzer)
resolution
0.24 nm
Directly
interpretable
resolution
approaching
information
limit = (point
or “Lichte”
resolution)
0.12 nm
Cs corrector
Triebenberg Laboratory Technical University Dresden:
http://www.physik.tu-dresden.de/isp/member/wl/TBG/Equipment/equipment.htm
Cs corrector for TEM/STEM
CEOS GmbH
Englerstr. 28
D-69126 Heidelberg
Increases length of
TEM/STEM column
by 24 cm
Tel.: +49 6221 89467-0
Fax: +49 6221 89467-29
e-mail: [email protected]
[email protected]
http://www.ceos-gmbh.de/
A FEI tecnai F20 ST with Cs corrector and gun monochromator
TEM achieved sub angstrom level point-to point resolution !!!
(N)TEAM stands for
(National) Transmission
Electron Achromatic
Microscope or (National)
Transmission Electron
Aberration-corrected
Microscope
http://www.zyvex.com/nanotech/feynman.html
“Materials research in an aberrationfree environment” electron microscopists’
contribution to National Nanoscience &
Nanotechnology initiative
Feynman: “…. I know
that there are theorems
which prove that it is
impossible, with axial
symmetric stationary
field lenses, …, and
therefore the resolving
power at the present
time is at its theoretical
maximum. But in every
theorem there are
assumptions. Why
must the field be
symmetrical?”
National Center for Electron Microscopy, Lawrence Berkeley National Laboratory
(California)
Oak Ridge National Laboratory (Tennessee)
Argonne National Laboratory (Chicago, Illinois)
Brookhaven National Laboratory (New York)
Frederick Seitz Materials Research Laboratory (Urbana-Champaign, Illinois)
point-to-point
resolution ≤ 0.06 nm
modified
after H.
Rose
19th century
20th century
21st century
1
Aberration corrected TEM
0.15 nm
Tecnai F20 ST &
Cs corrector
resScherzer _ Phase  HRTEM  0.67  Cs 4  
Bohr
radius
Point-to-point resolution [Å-1]
0.2 nm Tecnai F20 ST
Transmission
Electron Microscope
Scherzer
■ (theory)
1
nm
10
nm
100
nm
Light Microscope
(theory)
far field
resolution limit
≈ 250 nm
1
μm
3
4
resScherzer_ Z STEM  0.4  Cs   4
1
4
3
electron phase or Zcontrast imaging for
optimal Cs, large-tilt range
goniometer (preferentially with
an extra degree of freedom to tilt)
and on-line power spectra
of images will lead to
(discrete) atomic
resolution tomography of
nanocrystals
just one application of
image-based
nanocrystallography by
means of transmission
electron goniometry
All atoms are roughly of the same size, all
bond length in chemical compounds are in
the range 0.12 to 0.25 nm !!! (except H-bonds)
So with enough image resolution
we basically see the equivalents
of ball (and stick) models - we
may as well analyze them by
transmission goniometry
0.053 nm, Bohr
radius
directly interpretable crystal zone axes orientations (crossed lattice
fringes in electron phase-contrast) as function of point-to-point (Scherzer)
resolution, accessible with a common ± 18.4° ≤ double-tilt holder ≥ ± 26°
0.24
nm
CdTe (0.648 nm)
Si
(0.543 nm)
Al
(0.405 nm)
W (0.3165 nm)
2
1
0
0
0.2 0.15 0.12 ≤ 0.06 structural
nm nm nm nm
prototype
4
1
2
1
8
4
2
3
PSU
tecnai F20 ST
Scherzer resolution
0.24 nm
 20
8
8
5
 60
 20
 30
 15
sphalerite
diamond
Cu-type
W-type
TU-Dresden/Triebenberg
tecnai F20 ST + Cs corrector
0.12 nm
space
group
F43m
Fd3m
Fm3m
Im3m
NCEM
TEAM (2008)
≤ 0.06 nm
last 3 crystals above have highest symmetric Laue group (m3m), one
really needs Scherzer resolution well below 0.2 nm, one extra degree
of freedom to adjust nanocrystal orientations will make goniometry
method much more feasible and easily employable to noncubic
nanocrystals
(N)TEAM stands for (National) Transmission Electron Achromatic Microscope or (National) Transmission Electron Aberration-corrected Microscope
1. Nanomaterials and need for 3D Nanocrystallography
2. The challenge of electron crystallography and how it may be
met
3. Image-based nanocrystallography by means of transmission
electron goniometry
3.1. Basic ideas and literature
3.2. Fringe visibility maps
3.3. Tilt-protocol / Lattice-fringe fingerprinting, …
4. Strain and chemical composition quantification from images
4.1. Strain quantization in Si,Ge by digital dark field techniques
4.2. Epitaxial and endotaxial semiconductor quantum dots
5. Conclusions
Basic ideas and literature
As crystallography is a general approach, large field comprising:
- structural and tomographic analysis of a single nanoparticle will require more accurate and precise quasi-eucentric
goniometers
- structural and tomographic analysis of a whole ensemble of
nanoparticles – can be done with current generation of side
entry goniometers
- also structural (and if required tomographic) analysis of any
sufficiently thin crystalline film or details within such film, (e.g.
cross-section of layered semiconductor device structure, …)
- both ideal crystal structure for known and unknown specimens
on basis of crystal matrix as determined by goniometry, and
structural defects for known specimens on basis of amendment
of crystal matrix by space group information
Just as tomography, whole general field “invented” by D.J. DeRosier and A.
Klug, Reconstruction of Three Dimensional Structures from Electron
Micrographs, Nature 217 (1968) 130-134.
For crystals and using electron goniometry: only about 50 papers in this field
worldwide
Transmission electron goniometry can be done either on the basis of the
reciprocal lattice Philip Fraundorf, Ultramicroscopy 22 (1987) 225
Or complementary on the basis of the direct lattice P. Moeck, Cryst. Res.
Technol. 26, 653 and 797 (1991)
It can be done with either electrons or X-rays: P. Moeck, X-ray goniometry of
reciprocal lattice vectors, PhD thesis (1992)
PhD thesis “Direct Space (Nano)Crystallography via High-Resolution
Transmission Electron Microscopy” by Wentao Qin (2001), experimental
demonstration and conceptual extension of Phil’s 1987 paper; W. Qin and P.
Fraundorf, Ultramicroscopy 94 (2003) 245
P. Fraundorf at al., arXiv:cond-mat/0212281 v2 31 Jan 2005
Image based nanocrystallography by means of
transmission electron goniometry from images so
far demonstrated experimentally in high resolution
microscopes:
with double tilt-holders ± 15° around eucentric axis, ± 10°
perpendicular
both in Philips EM430 ST, 0.19 nm Scherzer resolution (W.
Qin and P. Fraundorf, Ultramicroscopy 94 (2003) 245 )
and in JEOL JEM 3010, 0.17 nm Scherzer resolution (P.
Moeck et al., Mat. Res. Soc. Symp. Proc. 829 (2005) B9.4.1)
Direct crystallographic analyses on basis of transmission
electron goniometry in TEM (and SEM)
using two degree’s of freedom to tilt a TEM specimen
P. Fraundorf, Determining the 3D Lattice Parameters of Nanometer-sized Single Crystals from Images, Ultramicroscopy 22, 225-230 (1987).
P. Möck, A Direct Method for Orientation Determination Using TEM (I), Description of the Method, Cryst. Res. Technol. 26, 653-658 (1991).
P. Möck, A Direct Method for Orientation Determination Using TEM (II), Experimental Example, Cryst. Res. Technol. 26, 797-801 (1991).
P. Möck, A Direct Method for the Determination of Orientation Relationships Using TEM, Cryst. Res. Technol. 26, 975-962 (1991).
P. Möck and W. Hoppe, Direkte kristallographische Analysen mit SEM, Beitr. Elekronenmikroskop. Direktabb. Oberfl. 23, 275-278 (1990).
P. Möck and W. Hoppe, Direkte Kristallographische Analysen mit Elektronenmikroskopen, Beitr. Elektronenmikroskop. Direktabb. Oberfl. 24, 99-104 (1991).
P. Möck, In-situ indexing of Two-Beam Electron Diffraction Vectors, Cryst. Res. Technol. 26, K157-K159 (1991).
P. Möck, P. Möck, W. Hoppe, Direct crystallographic analyses using electron microscopy, Vide-Couches Minces-Suppl. 259, 123-125 (1991)
P. Möck and W. Hoppe, ELCRYSAN – A program for direct crystallographic analyses, Proc. 10th European Conference on Electron Microscopy Vol. 1 193-194
(1992).
P. Möck, Estimation of Crystal Textures using Electron Microscopy, Beitr. Elektronenmikroskop. Direktabb. Oberfl. 28, 31-36 (1995).
W. Qin, Direct space (nano)crystallography via high-resolution transmission electron microscopy, PhD thesis, University of Missouri-Rolla, 2000.
W. Qin and P. Fraundorf, Lattice parameters from direct-space images at two tilts, Ultramicroscopy 94, 245-262 (2003).
P. Moeck, W. Qin, and P. Fraundorf, Image-based Nanocrystallography by means of Transmission Electron Goniometry, Proc. 4th World Congress of
Nonlinear Analysts, Symposium on Nanoscience and Nanotechnologies in Engineering Problems & Systems, June 30 - July 7, 2004, Orlando, FL
P. Moeck, W. Qin, P.B. Fraundorf, Image-based nanocrystallography in future aberration-corrected transmission electron microscopes, Mat. Res. Soc. Symp.
Proc. Vol. 818, M11.3.1-M11.3.6 (2004)
P. Moeck, B. Seipel, W. Qin, and P.B. Fraundorf, Image-based nanocrystallography by means of transmission electron goniometry, Microscopy and
Microanalysis, Vol. 10, Suppl. 3, 50-51 (2004)
P. Moeck, M. Kapilashrami, A. Rao, K. Aldushin, J. Lee, J. Morris, N. D. Browning, and P. J. McCann, Nominal PbSe nano-islands on PbTe: grown by MBE,
analyzed by AFM and TEM, Mat. Res. Soc. Symp. Proc. 829, B9.4.1-B9.4.6 (2005)
P. Moeck, W. Qin, and P.B. Fraundorf, Towards 3D image-based nanocrystallography by means of transmission electron goniometry, Mat. Res. Soc.
Symp. Proc. Vol. 839, P4.3.1-P4.3.6 (2005)
P. Fraundorf, W. Qin, P. Moeck, E. Mandell, Making sense of nanocrystal lattice fringes; Los Alamos Archives: http://arXiv.org, document
http://xxx.lanl.gov/abs/cond-mat/0212281 v2 (31 Jan 2005)
P. Moeck, W. Qin, and P. Fraundorf, Image-based Nanocrystallography by means of Transmission Electron Goniometry, Nonlinear Analysis (2005),
accepted
Peter Moeck et al., Image-based 3D Nanocrystallography by Means of Tilt Protocol/Lattice-Fringe Fingerprinting with Contemporary Side-entry Specimen
Goniometers, submitted to Microscopy & Microanalysis 2005, July 31-August 4, 2005, Hawaii Convention Center, Honolulu, Hawaii
Bjoern Seipel et al., Image-Based Nanocrystallography by Means of Tilt Protocol / Lattice Fringe-Fingerprinting: Proof of Principle on TiO2 Nanoparticles,
submitted to Microscopy & Microanalysis 2005, July 31-August 4, 2005, Hawaii Convention Center, Honolulu, Hawaii
using a double-tilt rotation TEM specimen goniometer (3 degrees of freedom to tilt)
S. Turner and D.S. Bright, Characterization of the Morphology of Facetted Particles by Transmission Electron Microscopy, Mat. Res. Soc.
Symp. Proc. 703, V6.6.1-V6.6.6 (2001).
S. Turner, Systematic Characterization of Reciprocal Space by SAED: Advantages of a Double-Tilt, Rotate Holder, Microscopy and
Microanalysis Proceedings 2002, 668CD.
U. Kolb, Electron Crystallography on polymorphs, Nato Summer School Erice, June 2004
general approach tested on basis of goniometry of reciprocal lattice vectors
P. Möck, Darstellung und Analyse der Orientierungsbeziehungen von Epitaxiesystemen unter Benutzung des Matrizenkalküls am Beispiel von CdTe auf
GaAs, PhD thesis, Humboldt University Berlin,1992
P. Möck, Complete characterization of epitaxial systems from the lattice geometrical point of view, Fundamentals, J. Cryst. Growth 128, 122-126 (1993).
P. Möck, Complete characterization of epitaxial CdTe on GaAs from the lattice geometrical point of view, Mater. Sci. Eng. B16, 165-167 (1993).
P. Möck, Description of the real orientation relationships of epitaxial samples using transformation matrices, Inst. Phys. Conf. Ser. No. 134, 593-596
(1993).
H. Berger, P. Möck, and B. Rosner, Description and Interpretation of systematic Deviations from Epitaxial Laws of Overgrowth, Acta Phys. Polon. A84,
279-286 (1993).
Image-based transmission electron goniometry
The “cubic minimalistic” tilt
protocol
1st step: tilting crystals into at
least two different orientations
that can be easily recognized
by, e.g. crossing of lattice
fringes in high-resolution
images or symmetric spots in
their associated Fourier
transforms
2nd step: at each of adjusted
zone axes, goniometer
readings which are by
themselves coordinates of the
direct lattice vectors in the
curvilinear coordinate system
of the specimen goniometer
are recorded
tilt from 9.74º, 15º
to -9.74º, -15º, =
combined 35.3º
WC0.7
a  0.425 nm
only (larger) W atoms are shown, make up an fcc sublattice
3rd step: coordinates of these
goniometer readings are
transformed into a cartesian
coordinate system (Eem) that is
fixed to electron microscope.
-------------------------------------------------Crystallographic background: (direct space)
lattice vectors of any crystal (denominated by letters
A, B, ... which refer to direct lattice base) can always
be expressed in a cartesian coordinates system (E)
as a 3 by 3 matrix that is called crystal matrix of the
direct lattice (ETA) = (ASE)-1, which lends itself
perfectly to all sorts of crystallographic analyses - that
can be performed directly while working at the
microscope (rather than later on while being back to
the office)
4th step: full blown
crystallographic analysis, e.g.
phase identification, … on basis of
direct space matrices (ETA),
cartesian coordinate system E (that makes the matrix (ASE), metric tensor G = (AS*E)
notation of the direct lattice possible in the first place)
can be chosen freely, i.e. can be set to be identical to
(ETA); or in reciprocal space on
Eem – that’s why the procedure works for any kind of
basis of matrices (ET*A) and
crystal
(AS*E)
http://www.physics.pdx.edu/~pmoeck/goniometry.htm
Spherical
aberration
coefficient, Cs,
of objective
lens [cm],
(prototypes,
kV)
Directly
interpretable
(electron
phase
contrast,
Scherzer)
point to point
resolution (x)
[nm]
1.2
(Tecnai G2 F20
SuperTwin, 200
kV)
0.24
≈0
(Cs -corrected
Tecnai G2 F20
SuperTwin, 200
kV)
0.12
(approaching the
information limit)
≈0
(Cs and possibly
also chromatic
aberrationcorrected
TEAM*** project
microscopes,
200-300 kV)
≤ 0.06
Relative
resolution
improvement
RRI (x) = (1 –
x/
0.24 nm) 100 %
(i.e. with
respect to
Tecnai G2 F20
SuperTwin)
Visible zone
axes, i.e.
lattice fringe
crosses
within one
stereographic
triangle [001][011]-[111]
0%
[011]
50 %
[001], [011],
[013], [111],
[112], [114],
[233], [125]
i.e.
Visible lattice
fringe types*
within one
stereographic
triangle [001][011]-[111]
Average angle
between
visible zone
axes
Minimum
double-tilt
range
requirement to
achieve
average angle
between
visible zone
axes
{111}
60°
± 22.5°
± 30° eucentric tilt, ± 18° noneucentric tilt / one [011]-[110] tilt
protocol
{111}, {200},
{220}, {311}
18.2° (out of the
28 pairs in one
stereographic
triangle)
± 6.5°
± 30° eucentric tilt, ± 18° noneucentric tilt = combined
maximum range 66.1 °
/ twenty eight different tilt
protocols when including large
tilts of up to 54.7°
≥ 12, i.e. {111},
{200}, {220},
{311}, {331},
{420}, {422},
{511}, {531},
{442}, {620},
{622}, …
≤ 9.3° (out of
only those 21
pairs of zone
axes with [u + v
+ w] ≤ 8 in one
stereographic
triangle that are
along {111},
{200}, and {220}
bands)
≤ ± 3.3° (when
aiming only for
those zone axes
with [u + v + w] ≤
8 that are along
{111}, {200}, and
{220} bands)
no specification by Gatan Inc, but
could possibly be as large as ±
90° about two axes in addition to
360° rotation = covering all of
projected orientation space ! / for
WC1-x already more than
twenty different tilt protocols
when only aiming for those lowtilt zone-axis pairs mentioned in
rows 6 and 7 !!
20
i.e. 23
≥ 75 %
[001], [011],
[111], [012],
[112], [013],
[122], [113],
[114], [123],
[015], [133],
[125], [233],
[116], [134], …
i.e. ≥ 25
Tilt range of a Gatan Model
925 double-tilt rotation
goniometer** / type and
number of tilt protocols
Parameters of current state-of-the-art and future aberration-corrected TEMs for image-based 3D
nanocrystallography by means of tilt protocol/lattice-fringe fingerprinting.
The visible zone axes and lattice fringe types of WC 1-x nanocrystals for these parameters are also given. The number of possible tilt protocols - as given in the last column may be considered as a measure of the viability of our novel discrete atomic resolution electron tomography technique for an ensemble of nanocrystals. * Different types of
lattice fringes have different crystallographic multiplicities; ** as communicated to us by Gatan Inc. in January 2005; *** TEAM stands for Transmission Electron Aberrationcorrected Microscope, http://ncem.lbl.gov/team3.htm.
Why TEM specimen goniometers with three degrees of
freedom?
side entry double-tilt rotation holder – a goniometer with an extra degree of
freedom, allowing eucentric tilts around chosen crystallographic axes,
similarly to crystallometry, e.g. ± 24 ° around eucentric axis after up to
360 ° rotations and up to ± 24 ° tilts to orient a low indexed, crystal zone
axis parallel to eucentric axis, different modes of operation: two of them yield 23.7 % of
orientation space (22 out of 32 crystal classes)
for FEI/Philips TEMs, two goniometer axes can be run by
compustage in addition to x,y,z translation,
software compucentricity compensates for x, y, z shifts
Goniometry of reciprocal lattice vectors in TEM
spherical fringe visibility-band maps visualizing lattice fringe visibility for
spherical 8 nm diameter nanocrystals left: Al (fcc structure, resScherzer = 0.2
nm), middle: Si (diamond structure, resScherzer = 0.19 nm), right: W (bcc
structure, resScherzer = 0.15 nm), for small unit cell and closest 74 % space filling packing,
i.e. aAl = 0.405 nm, and current HRTEM only very few zone axes “separated” by fairly large tilt
angles
2 bands, 2 zones
[001]
Al
Si
2 bands, 4 zones
[001]
(220) 35.3º
45º
(020)
60º
[112]
[011]
(-1-11)
(-1-11)
45º
[011]
19.5º
[111]
W
2 bands, 3 zones
[001]
60º
(020) 54.7º
[011]
35.3º
[111]
35.3º
(1-10)
no [111] pole visible for Al as crossing
{220} bands are only 0.143 nm wide
more spheres and maps at: http://www.umsl.edu/~fraundor/
note dominance of crossed {110} fringes at the three-fold <111> zone in the body-centered
case, dominant crossed {111} fringes at the two-fold <110> zone in the face-centered case,
and the wider disparity between largest and next-to-largest spacings in the diamond structure,
different structures have different combinations of visible bands and zone axes,
i.e. directly interpretable characteristic for goniometry
Let’s use fringe visibility maps to demonstrate what lens
aberration correction will by us for nanocrystallography
[001]
[001]
[-112]
[1-12]
[011]
[101]
[010]
[100]
[110]
at 0.2 nm Scherzer
resolution; as crossing
{220} bands are only
0.143 nm wide, only
<100> and <110>
poles available
two different
projections
[1-11]
[112] [011]
[101]
[111]
[1-12]
[121]
[211]
[010]
[100]
[110]
with 0.14 nm
Scherzer resolution;
{220} bands and
<111>, <112> poles
become available !
four different
projections
Increase in resolution (x) [%]
= 100 % (1 – x/0.2 nm)
(defining Scherzer resolution of
0.2 nm as that of a current
standard high-resolution TEM)
increasing
resolution by 30 %
leads to doubling
of visible zone
axes
http://www.umsl.edu/~fraundor/help/imagnxtl.htm,
http://newton.umsl.edu/~run/nano/jmoltesu.html
http://www.umsl.edu/~fraundor/hilights.html#visifringe
Fringe visibility maps: looking at 1/48 of orientation space for a
8 nm diameter spherical Al crystal for 0.12 nm Scherzer resolution,
left, we have 8 zone axes accessible for goniometry, as d{111} = 0.234
nm, d{200} = 0.202 nm, d{220} = 0.143 nm, d{311} = 0.122 nm bands are all visible
Increase in resolution (x) [%] = 100 % (1 – x/0.2 nm)
40 % increase in resolution
70 % increase in resolution
[011]
[011]
3 more
types of
fringes
visible
[001]
(200)
(31-1)
[013]
(-220)
(0-22)
(-1-11)
[125]
[233]
(1-31)
(-311)
[114]
[112]
[111]
13 more
types of
fringes
visible
(13-1)
[001]
[111]
but for 0.06 nm Scherzer resolution, we have for 1/48 of orientation
space for the same 8 nm diameter spherical Al crystal more than 16
for u + v + w ≤ 8 (or more than 32 with larger indices) accessible
zone axes for goniometry !!! after P. B. Fraundorf, http://www.umsl.edu/~fraundor/
If the image resolution gets down to 0.06 nm, we have the same amount of
information on the structure factor amplitude as from diffraction patterns
But we can also get the
phases of the structure
factors from digitized images!
[001]
[011]
[111]
Widths of diffraction bands = 2 θ, ~ 1 /d, higher
indexed bands are wider – just reciprocal to fringe
visibility maps
analogous to stereographic
projection of Kikuchi-maps
in TEM and Coates-maps
(electron channeling in
SEM)
Problem of TEM: derive 3D (structure) information
from 2D (structure) projection (tomography)
[001] direction
(002)
band
Al nanocrystal at Scherzer
resolution 0.14 nm
stereographic projection of
fringe visibility sphere
(project from 3D to down
to 2D) to foster direct
comparison with highresolution TEM image
(which is 2D) while one is
tilting the nanocrystal
Simulation parameters:
tilt procedure, structure,
nanocrystal thickness,
directly interpretable
resolution, acceleration
voltage
Spherical nanoparticle, Al,
fcc, Fm3m, 3 nm diameter,
1 nm Scherzer resolution,
300 kV
Spherical nanoparticle, Si, Fd3m,
8 nm diameter, 0.06 nm
Scherzer resolution, 300 kV
Tilt protocols charts for fcc and bcc cubic crystals, in
principle for all crystals
Utility
35.3 tilt & rSch= 0.19 nm,
applicable to all cubic lattices
with a  0.38 nm,
including: > 85 % fcc and
nearly 40 % of elemental bcc
crystals
in Wyckoff’s, Crystal Structures,
1982, reference text.
http://www.umsl.edu/~fraundor/help/imagnxtl.htm
http://www.umsl.edu/~fraundor/covariances.html
Calculated and experimental nanocrystal fingerprint maps
Much more experimental patches for
less symmetric nanocrystals, unique
fingerprints for nanomaterials at
chosen microscope resolution !
Bjoern Seipel et al., Image-Based
Nanocrystallography by Means of Tilt Protocol
/ Lattice Fringe-Fingerprinting: Proof of
Principle on TiO2 Nanoparticles, submitted to
Microscopy & Microanalysis 2005, July 31August 4, 2005, Hawaii Convention Center,
Honolulu, Hawaii
P. Fraundorf at al., arXiv:cond-mat/0212281 v2 31 Jan 2005
1. Nanomaterials and need for 3D nanocrystallography
2. The challenge of electron crystallography and how it may be
met
3. Image-based nanocrystallography by means of transmission
electron goniometry
3.1. Basic ideas and literature
3.2. Fringe visibility maps
3.3. Tilt-protocol / Lattice-fringe fingerprinting, …
4. Strain and chemical composition quantification from images
4.1. Strain quantization in Si,Ge by digital dark field techniques
4.2. Epitaxial and endotaxial semiconductor quantum dots
5. Conclusions
http://www.umsl.edu/~fraundor/modelstrains.html
Component and Complex Color Map
The brightness/saturation and hue of a single pixel can be used to represent respectively
the log[magnitude] and direction of a vector, or the log[amplitude] and phase of a complex
number. Applications include for example strain mapping, wave & reciprocal space
visualization, and vector geometry.
A cyclic array of hues based on the three types of color sensors in the human eye looks like...
red, orange, yellow, chartreuse, green, seagreen, cyan, turquoise, blue, indigo, magenta, pink, red, etc.
More examples: http://www.umsl.edu/~fraundor/expstrain.html
What happens if we select different g-vectors (in the TEM: "operating
reflections") in Fourier space for the calculation... Example an elastically
strained crystalline inclusion in a crystalline matrix, following the well known
Ashby-Brown theory A.F. Ashby and L.M. Brown, Phil. Mag. 8 (1963) 1083, 1649
… it appears from above that regions of the specimen with strain directions parallel to
the g-vector (e.g. the yellow inclusion in the 4th panel of the top image above) are
showing tensional strains relative to the reference periodicity, while regions with strain
directions antiparallel to the g-vector (e.g. blue in that image) are compressed relative to
the reference. Thus as the operating reflection changes direction (in the 2nd panel), so
do the strain colors of regions interior and exterior to the inclusion.
Just as observed for semiconductor quantum dots in twobeam diffraction contrast bright- and dark field images
Semiconductor quantum dots (QDs) should be self-assembled
(for economic gains, not quite in reach of nano-lithography)
1) semiconductor with smaller bandgap embedded into matrix with large bandgap
2) just right size, large enough to accommodate an exciton, small enough in all directions
for quantum confinement
3) no structural defects such as dislocations, stacking faults or voids
KEY ISSUE: uniformities of size, shape, chemical composition, strain distribution,
crystallographic phase, mutual alignment, …
optoelectronics (no contacting problem, only problem QD array homogeneity)
- active medium in lasers, (In,Ga,Al)As based 1.3
μm!
- far infrared detectors
- novel device concepts such as quantum cellular
automata
Novel crystalline nanostructured phases result from
atomic ordering inside epitaxial quantum dots, need
image-based nanocrystallography by means of
transmission electron goniometry for the full
determination of the atomic arrangements
Endotaxial Sn quantum dots in Si
bulk α-Sn (grey tin) direct, 0.08 eV,
band gap, bulk substitutional SnxSi1-x
solution direct band gap for 0.9 < x < 1
Problems: 41.8 % bulk unit cell volume
mismatch, solid solubility 0.12 %, conventional
molecular beam epitaxy restricted to ≤ 10 %
Sn, ≤ 10 nm
Our discovery: void filling
mechanisms that may be
employed generally for all kinds
of endotaxial (direct band gap)
semiconductor quantum dots in
Si !
100 nm Si 550 ºC, 0.05 nm s-1
4-6 nm Si ≈ 140 – 170 ºC, 0.01 –
0.03 nm s-1
1-2 nm SnxSi1-x x = 0.02 - 0.1
≈ 140 – 170 ºC, 0.02 nm s-1
100 nm Si 550 ºC, 0.05 nm s-1
4-6 nm Si, ≈ 140 – 170 ºC, 0.01 –
0.03 nm s-1
1-2 nm SnxSi1-x x = 0.02 - 0.1
≈ 140 – 170 ºC, 0.02 nm s-1
Si buffer layer 550 ºC
(001) Si substrate, 550 ºC
K.S. Min and H.A. Atwater, Appl. Phys. Lett. 72 (1998)
1884
Directly interpretable resolution in these images: 0.2 nm,
simply because 0.2 nm electron probe selected - since
EELS was done with same probe, but could have been as
small as 0.134 nm at the UIC STEM/TEM (JEOL JEM 2010F)
Main conclusion:
this mechanism may
work for other
materials as well,
if so, one could grow
other direct bandgap semiconductor
quantum dots in Si
matrix for effective
optoelectronics on
the basis of the
mature Si IC
technology !
Z-contrast STEM tomography on these samples in
progress
Neumann’s symmetry
principle and energy
minimization both predict
shape of the void to be a
tetrakaidecahedron
tetrakaidecahedron shape is seen in these
experiments
4 2 4 2 4 2
3  3  3
m m m m m m
More Z-contrast STEM tomography on semiconductor
quantum dots and their predecessor nano-islands
1. Nanomaterials and need for 3D nanocrystallography
2. The challenge of electron crystallography and how it may be
met
3. Image-based nanocrystallography by means of transmission
electron goniometry
3.1. Basic ideas and literature
3.2. Fringe visibility maps
3.3. Tilt-protocol / Lattice-fringe fingerprinting, …
4. Strain and chemical composition quantification from images
4.1. Strain quantization in Si,Ge by digital dark field techniques
4.2. Epitaxial and endotaxial semiconductor quantum dots
5. Conclusions
Conclusions
To address the nanomaterials challenge:
collect three-dimensional data under kinematical phase
contrast or incoherent imaging conditions, (HRTEM or ZSTEM images)
Instrument parameters that need to be improved:
Goniometer accuracy/precision/3rd degree of freedom and
Directly Interpretable Image Resolution (for extracting
information on the atomic and nanometer scale in 3D)
Automation of tilt and data collection: when novel
goniometers exist - novel methods can be automated / such
software can be developed simultaneously to novel hardware
developments (to serve FEI’s customers with the information
they need)
Software that could be developed and sold right now
Generator for fringe visibility maps
Simulator for different tilt protocols employing different types of
goniometers
Generator for lattice fringe fingerprint maps
Digital dark field image analysis software to derive quantitative values
of strains
Chemical composition analysis software for high resolution images
Demonstration/application software for image-based
nanocrystallography / discrete atomic resolution tomography on
individual nanocrystals
Demonstration/application software for image-based
nanocrystallography / discrete atomic resolution tomography on an
ensemble of nanocrystals
…
A few ideas on the drawing board employing
compustage/double tilt rotation specimen holder for developing
1) a method that follows a cubic and a hexagonal tilt procedure for
randomly oriented nanocrystalline (colloidal quantum dots)
powders at a series of preset rotation axis settings in order to get
directly interpretable phase contrast images of most of the
nanocrystals on a TEM grid (when looking at powders, noneucentricity is a small concern)
2) a method that “guesses” the crystal phase of epitaxial quantum
dots from possible strain minimizing orientation relationships with
the matrix, using Kikuchi diffraction in order to orient the matrix
suitable for the quantum dot phase to be identified (when looking
at large matrices, non-eucentricity is a smaller concern)
3) a method for deriving all of the strain tensor components from a
combination of digital dark field imaging and transmission
electron goniometry
….