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APT Data Reconstruction
David J. Larson, Brian P. Geiser & Ty J. Prosa
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Co-Authors / Acknowledgements
■ E. Oltman, D. A. Reinhard, J. H. Bunton, R.M Ulfig, P. H. Clifton, I.
Martin, J. Olson, H. F. Saint Cyr, & T. F. Kelly (CAMECA Madison)
■ F. Vurpillot & N. Rolland (University de Rouen)
■ C. Oberdorfer & D. Beinke (University of Stuttgart)
■ A. Ceguerra, J. Cairney & S. Ringer (University of Sydney)
■ B. Gault (MPIE Dusseldorf)
■ F. DeGeuser (University of Grenoble Alpes)
■ M. Moody & D. Haley (University of Oxford)
■ B. Gorman & D. Diercks (Colorado School of Mines)
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Outline
■ A Bit of History
■ Hemispherical Reconstruction
■ Assumptions
■ Calculation of x, y, and z
■ Field Evaporated Shapes
■ Simulation
■ Experimental Observation
■ Interfaces & Precipitates
■ Limitations & Resulting Inaccuracies
■ Projection
■ Z Increment
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■ Methods of Correction
■ Density Correction
■ Lattice Rectification
■ Radius Evolution
■ Non-Tangential Continuity
■ Variable Image Compression
■ Self-Optimization of Data: A
Priori and A Posteriori to
Reconstruction
■ Dynamic Reconstruction
■ Simulation & Non-Hemispherical
Methods
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From the 1D Atom Probe Era
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Revue Phys. Appl. 17 (1982) 435
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Into the 3D Atom Probe Era
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Varying image compression with (x,y)
The general protocol
Shank reconstruction L=k (revisited)
Density correction
Wide field of view
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The Goal of APT Data Reconstruction
■ The goal of APT data reconstruction is to transform from detector space (X,Y,N) to specimen space (x,y,z) (usually in
nanometers).
■ The standard reconstruction of APT data uses a point-projection algorithm to return the individual atoms to close to
their original location in the x–y plane normal to the tip axis, with the depth location obtained from the sequence of ion
arrivals at the detector. This is based on an algorithm developed over 15 years ago*, which is not entirely accurate for
a wide field of view APT dataset, even in the case where the material is homogeneous.
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Row hitclass x y z tof v pulse TargetEra TargetFlu
0 0 330 367 0 3020.0756 6511.58 90655 0.0049999 0.0049999
1 0 -254 -97 1 4410.3374 6512.08 99413 0.0049999 0.0049999
2 0 60 -73 2 1375.2675 6512.5698 100418 0.0049999 0.0049999
3 0 25 -173 3 1848.0185 6514.0498 116154 0.0049999 0.0049999
4 110 244 -189 4 1378.7691 6529.0698 264404 0.0049999 0.0049999
5 111 206 -194 5 2217.477 6529.0698 264404 0.0049999 0.0049999
6 0 211 423 6 4076.0979 6532.02 298906 0.0049999 0.0049999
7 0 218 117 7 591.83105 6535.2202 326752 0.0049999 0.0049999
8 0 -225 196 8 3138.0258 6537.6899 349007 0.0049999 0.0049999
9 0 55 -68 9 3869.2512 6538.1801 369458 0.0049999 0.0049999
10 0 -52 -239 10 1572.335 6538.1801 371746 0.0049999 0.0049999
11 0 -336 305 11 1353.988 6538.1801 394160 0.0049999 0.0049999
12 0 -415 -436 12 1017.7057 6538.1801 398541 0.0049999 0.0049999
13 0 -224 -287 13 4157.7666 6538.1801 456052 0.0049999 0.0049999
14 0 -209 188 14 3698.7006 6538.1801 482084 0.0049999 0.0049999
15 0 -271 -516 15 3305.3886 6538.1801 495641 0.0049999 0.0049999
16 10 318 -465 16 2874.2915 6538.1801 505987 0.0049999 0.0049999
17 0 -358 -390 17 3967.3359 6538.1801 519973 0.0049999 0.0049999
18 0 -97 402 18 788.37475 6538.1801 529363 0.0049999 0.0049999
19 0 -135 307 19 1444.2463 6538.1801 588556 0.0049999 0.0049999
20 0 -233 -197 20 787.45446 6538.1801 689257 0.0049999 0.0049999
(x,y) Ion Sequence
* P. Bas et al, Appl. Surf. Sci. 87/88 (1995) 298
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Visually: The Goal of APT Data Reconstruction
■ Material is field evaporated from the specimen (direction of evaporation above by the arrow) as shown by the distance
between the blue and green circles above
■ The APT data reconstruction consists of the (x,y,z) positions of some fraction of the ions contained in the region
enclosed by the dashed red lines in the lower TEM image
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Direction of Evaporation
Before Evaporation
Initial radius
Final radius
After Evaporation
Reconstruction of APT Data
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Field Ionization & Evaporation
■ Field ionization (above) is the process of removing one or more
electrons from either an image gas atom (field ion microscopy) or
a specimen atom (atom probe)
■ Increasing the electric field using pulses results in the capability to
remove single atoms in a controllable manner (at right)
DJ Larson - M&M2016 8Figures from M. K. Miller, Atom Probe Tomography (2000)
Evaporation SequenceIonization
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Field Evaporation*
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Fo + In - nwhere is the
sublimation energy,
I is the ionization energy
of the atom
n is the charge state of
the evaporating ion and
is the work function
Evaporation fields may be estimated from
fundamental constants:
Figure from Miller, Atom Probe Tomography (2000)
K e-(Q/kT)
Q f(F0-Fapplied)
* See M. K. Miller et al., “Atom Probe Field
Ion Microscopy” (1996) for further details
T.T. Tsong, Surface Science 70 (1978) 211:
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Projection of a Sphere onto a Plane
Stereographic
Projection
“Ball model” of sample surface
Figure from Miller, Atom Probe Tomography (2000)
“Flat” map
■ In atom probe microscopy the projection of the sample surface onto the detector results in a very high
magnification “map” of the specimen surface
■ Note that there are various ways to project the detector data onto a virtual specimen surface…
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Magnification of the Surface
Projection Microscope
d
~100nm
Mag = d / (ICF*R) = 1 million X
d = constant distance from sample to detector (80mm)
R = sample radius (e.g., 55nm)
ICF = image compression factor (1.4) because sample is not a perfect sphere
R
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Calculation of Sample Radius
F = Voltage / (k*R)
or
R = V/Fk
V = sample voltage
F = material evaporation field (constant)
k = field reduction factor* (constant)
As radius increases (material removed from
sample), voltage must also increase to
maintain constant evaporation rate
V
■ We can use the approximation
above from Gomer relating field
to voltage and radius
■ Thus we know the sample
radius at any point during the
analysis, from this we calculate
XY magnification
* R. Gomer, Field Emission & Field Ionization (1962)
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Magnification Used to Scale the XY Data
Detector Space (40mm) Sample Space (40nm)Magnification
X
Y
1 million X
(x,y) detector (x,y) sample
Specimen Coordinates
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Calculation of Z Dimension
■ We know the XY dimensions from the
magnification and known detector size
■ Using known density (atomic volume) of the
material (atoms/nm3), the distance of the
analysis in the Z direction is now scaled
Example: Density of silicon = 60 atoms/nm3
X(nm) Y(nm) Z(nm) Atoms
40 40 1 100,000
Z
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Calculation of Z Dimension
■ Reconstruction software uses
“element specific” atom volume
or a user-selectable “average
volume” for Z scaling
■ In addition, only about half of the
atoms are detected (MCP open
area plus gain degradation) and
this must be used in scaling the Z
dimension
■ Detection order of the atoms is
used to provide a Z dimension for
each atom collected proportional
to the volume
■ (X,Y) dimension used to correct for the fact that the sample in a curved surface
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■ Atom probe data reconstruction consists of:
■ A magnification transformation (to calculate x and y)
■ A depth transformation (to calculate z)
■ The 1995 assumptions* are:
■ The specimen is comprised of a hemisphere on a cone with
some shank angle (usually using a tangential constraint)
■ The depth transformation is a constant with respect to x and y
■ In ~2008, Geiser et al. expanded the method to remove limitations
due to small angle approximations
Summary: Two Primary Assumptions
* Bas et al, Appl. Surf. Sci. 87/88 (1995) 298 ** B. P. Geiser et al., Microscopy and Microanalysis 15(S2) (2009) 292
**
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■ Magnification is the key calculation for the xy
transformation from detector space to specimen
space
■ d is distance between specimen and
detector
■ is the image compression
■ R is the average radius of the specimen
Reconstruction: Two Transformations
■ A z increment must be calculated in
order to transform from ion arrival
number to z in specimen space
■ is the atomic volume
■ A is the detector area
■ is the efficiency
Magnification Depth
R
dM
22
2
RA
dz
z
DJ Larson - M&M2016 17The RADIUS is a large driver in both of these equations…
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Why are Specimens Non-spherical?
■ Crystallographic dependence of work function and/or surface energy (different for every sample)
■ Varying field distribution above specimen (above right) due to shank angle (predicted by various
electrostatic models*)
■ Different phases/features with different evaporation fields are present at the surface – practically, this
is the most important factor?
■ Let us now examine some examples …
100
110
Higher Fapplied
Lower Fapplied
Field Strength:
*G. S. Gipson, J. Appl. Phys. 5 (1980) 3884DJ Larson - M&M2016 18
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Experimental & Simulated Specimen Shapes…
B. P. Geiser et al., Micro.
Microanalysis 15(S2) (2009) 302
F. Vurpillot, Ph.D. Thesis (2001)
Université de Rouen
■ Field evaporated specimen shapes often deviate substantially from hemispherical
■ This conclusion is based on observations from both electron microscopy and simulation
B. Loberg and H. Norden, Arkiv
for Fysik 39 (1968) 383
T. Wilkes et al., Metallography 7
(1974) 403
Image courtesy J. Lee (Samsung) D. J. Larson et al., J.
Microscopy 243 (2011) 15
D. J. Larson et al., Mat. Sci. Eng.
A270 (1999) 1D. J. Larson et al., Ultramicroscopy
111 (2011) 506
D. J. Larson et al., Micro.
Microanalysis 18 (2012) 953
C. Oberdorfer and G. Schmitz,
Ultramicroscopy 128 (2013) 55
D. Haley et al., J. Micro
Microanalysis 19(6) (2013) 1709
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A Closer Look: Precipitates & Layers
■ For even simple cases such as those shown above we
have significant difficulties in obtaining the correct
reconstruction
■ A single 10nm precipitate of high or low field
A single interface separating high/low field materials
■ Disclaimer: I don’t have the answer for you…
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Fevap(top) < Fevap(bottom) by 20%
Fevap(top) > Fevap(bottom) by 20%
D. J. Larson et al., J. Microscopy 243 (2011) 15
D. J. Larson et al., Current Opinion in Solid State and Materials Science 17 (2013) 236
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Limitations of the Primary Assumptions
■ The assumed reconstruction radius is contained in both equations: Magnification & Depth
■ Anisotropic (in evaporation field) regions in x and y (above left) may result in expansion or compression
in the reconstruction
■ Differing evaporation fields also produce hit density variations which are not the result of xy projection
errors (above right), but are simply uneven field evaporation from certain regions on the specimen
surface
Magnification (XY Projection) Depth (Z Increment)
R
dM
A
Mz
2
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Limitations of the Primary Assumptions
■ The assumed reconstruction radius is contained in both equations: Magnification & Depth
■ Anisotropic (in evaporation field) regions in x and y (above left) may result in expansion or compression
in the reconstruction
■ Differing evaporation fields also produce hit density variations which are not the result of xy projection
errors (above right), but are simply uneven field evaporation from certain regions on the specimen
surface
Magnification (XY Projection) Depth (Z Increment)
R
dM
A
Mz
2
A
A
B
Low Field
High Field
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General Radius Considerations*
■ While it may be clear that in complicated microstructures it is difficult (or impossible) currently to find a
radius that reconstructs everything perfectly, there are some general things to keep in mind with respect
to a single interface
■ One of these is that if the curvature is concave toward lower z values, then your radius is likely too small
■ Likewise if the curvature is concave toward higher z values, then your radius is too large
DJ Larson - M&M2016 23* B. P. Geiser et al., Microscopy and Microanalysis 19(S2) (2013) 936
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Methods of Improvement/CorrectionMethod References
Density Correction X Sauvage et al., Acta Materialia 49 (2001) 389
F. Vurpillot, D.J. Larson and A. Cerezo, Surface and Interface Analysis 36 (2004) 552
F. DeGeuser et al., Surface and Interface Analysis 39 (2007) 268
Lattice Rectification M. Moody et al., Microscopy and Microanalysis 17 (2011) 226
Radius Evolution F. DeGeuser et al., Surface and Interface Analysis 39 (2007) 268
D. J. Larson et al., Ultramicroscopy 111 (2011) 506
Non-Tangential Continuity D. J. Larson et al., Microscopy and Microanalysis 17(S2) (2011) 740
Variable Image Compression J. M. Hyde et al., Applied Surface Science 76/77 (1994) 382
D. J. Larson et al., Journal of Microscopy 243 (2011) 15
S. T. Loi et al., Ultramicroscopy 132 (2013) 107
Projections and Transforms D. J. Larson et al., Current Opinion in Solid State and Materials Science 17 (2013) 236
N. Wallace, S. Ringer et al. University of Sydney (2016)
F. DeGeuser and B. Gault, Microscopy and Microanalysis (2016) Submitted
P. Felfer and J. Cairney, Ultramicroscopy (2016) Submitted
Self-Optimization of Data: A
Priori and A Posteriori to
Reconstruction
D.J. Larson et al., Microscopy and Microanalysis 17(S2) (2011) 724
F. Vurpillot et al., Ultramicroscopy 111(8) (2011) 1286
B. P. Geiser et al., Microscopy and Microanalysis 19(S2) (2013) 936
B. P. Geiser et al., Unpublished (2016)
Dynamic Reconstruction B. Gault et al., Ultramicroscopy 111(11) (2011) 1619
F. Vurpillot et al., Ultramicroscopy 111(8) (2011) 1286
D. J. Larson et al., Current Opinions in Solid State and Materials Science 17(5) (2013) 236
S. T. Loi et al., Ultramicroscopy 132 (2013) 107
F. Vurpillot et al., Ultramicroscopy 132 (2013) 19
Tip Shape Modeling / Non-
Hemispherical Methods
D. Haley et al., Journal of Microscopy 244 (2011) 170, Microscopy and Microanalysis 19(6) (2013) 1709
D. J. Larson et al., Microscopy and Microanalysis 18(5) (2012) 953
Z. Xu et al., Computer Physics Communications 189 (2015) 106
N. Rolland et al., Ultramicroscopy 159 (2015) 195
N. Rolland et al. Eur. Phys. J. Appl. Phys..72 (2015) 21001
N. Rolland et al., Microscopy and Microanalysis (2016) Submitted.
D. Beinke, C. Oberdofer and G. Schmitz, Ultramicroscopy 165 (2016) 34DJ Larson - M&M2016 24
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Density Correction Methods
■ Differential evaporation causes a variety of effects that combine together to produce density irregularities on the detector map and in therefore in the reconstructed volume.
■ One suggested approach*:1. Pick a small “Tube” of data and uniformly redistribute reconstructed z values within a small tube.
2. I.e., process it like it is Small Field of View.
■ The larger the tube diameter, the less effective the correction.
■ This is inherently a small field of view correction.
■ The problem becomes worse with wide FOV analysis.
■ Can also do with a ‘lateral relaxation’ technique**
* F.Vurpillot, D.J. Larson and A. Cerezo, Surface and Interface Analysis 36 (2004) 552
** F. DeGeuser et al., Surface and Interface Analysis 39 (2007) 268
Before Correction After Correction
Surface and Interface Analysis 36 (2004) 552.
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Lattice Rectification
■ Moody et al. have developed a method to extract the lattice from the data and place the atoms back on the lattice, expanding further along the lines of the method suggested earlier by Camus et al.*
Original Data
Lattice Rectified Data
The Method
* P. P. Camus et al., Applied Surface Science 87/88 (1995) 305DJ Larson - M&M2016 26
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Evolving the Radius (Field)
■ Simulation can suggest the specimen radius when evaporating across interfaces for a more accurate
reconstruction** – simply using evaporation field to scale the radius is not sufficient*
■ For off axis improvement, separate radius evolution for each element (or a non-hemispherical shape) is required
0
50
100
150
0.E+00 1.E+06 2.E+06 3.E+06 4.E+06 5.E+06 6.E+06
Sp
ec
ime
n R
ad
ius
(n
m)
Depth (ion number)
Cr-to-Co
Transition
Co-to-Cr
Transition
* F. DeGeuser et al., Surf. Int. Anal. 39 (2007) 268
** D. J. Larson et al., Ultramicroscopy 111 (2011) 506
Cr
Cr
Co
Co
Cu
Si
10nm
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Removing Tangential Continuity in the Reconstruction
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■ For tangential continuity, there is a simple relationship between Rtip and Rcone (fs/c ≡ Rtip/Rcone = sec )
■ Blavette et al.* has described the formula for evolving the tip radius with analysis depth as dRtip/dZtip =
sin / (1- sin ) ≡ K
■ As observed experimentally however (above right**), field evaporated specimens do not necessarily
assume a shape with tangential continuity (above right shows a specimen with fs/c=1.5 although values
with vary from specimen to specimen)
* D. Blavette et al., Revue Phys. Appl. 17 (1982) 435, and also P. Bas et al., Appl. Surf. Sci. 87/88 (1995) 298
** A. Shariq et al., Ultramicroscopy 109 (2009) 472, and also S.S.A. Gerstl et al., Micro. Microanal. 15(S2) (2009) 248
Image from **
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Larger Effect at Smaller Shank Angles
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If tangential continuity constraint is removed (as shown above left) we can generalize the
dRtip/dZ term as:
Above right shows the behavior of the dRtip/dZ term (normalized to the case of fs/c = sec )
as a function of shank angle over a range of fs/c values
Note that a hemispherical surface is still used in the reconstruction
1)tan()tan(1
)tan(
2
//
/,
cscs
csf
ff
fK
fs/c:
* D. J. Larson et al., Microscopy and Microanalysis 17(S2) (2011) 740
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No Tangential Continuity Allows More Accurate Microscopy Input
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The dependence of the variation in interplanar spacing with analysis depth is shown above left (for these
results we have used R0 = 20 nm assuming the original evaporation shape occurred with fs/c = 1.5)
Above right illustrates the change in shank angle that is required (for a variety of fs/c values) if data
reconstruction constrained to tangential continuity is imposed
Summary: Assumptions of tangential continuity bias reconstructions toward parameters with unphysically
large shank angles -- the new developments* enable APT reconstructions to take advantage of electron
microscopy-based information about the real physical size of specimens as well as shank angle and the
level of discontinuity between the apex and the shank to provide real constraint on the selection of
reconstruction parameters
fs/c:
fs/c:
* D. J. Larson et al., Microscopy and Microanalysis 17(S2) (2011) 740
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Image Compression is NOT Constant
31
Image Compression Definition Real Specimen Shape FCC <100> Function*
■ Real specimen shapes are complicated (not a new observation!) – See T. J. Wilkes et al.,
Metallography 7 (1974) 403, for example – in reality this results in:
■ Effective image compression (or angular magnification) functions that vary in (R,,Z)
■ Implementing methods to use this knowledge can result in improved atom probe data
reconstruction* D. J. Larson et al., J. Microscopy 243 (2011) 15 DJ Larson - M&M2016
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Constant ICF
■ Using individual ICF functions* for each layer
separate allows a reconstruction without the density
variations and planar curvature seen above left
■ A Z coordinate rescaling** was also applied to
reconstruct the interface at above right
ICF Function Applied to Low/High Field Interface
32
10nm
With ICF Functions
10nm
ICF (yellow) ICF (blue)
* D. J. Larson et al., J. Microscopy 243 (2011) 15
** F. Vurpillot et al., Surf. Int. Anal.36 (2004) 552
Low Field
High Field
Rdet (mm) Rdet (mm)
Ima
ge
Co
mp
ressio
n
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Evolving Image Compression with Z
■ Simulation allows us to create an evolving function
■ Impression compression also should be a function of depth, not just of (X,Y)
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5n
m
Low Field
High Field
Specimen Shape Evolution*
* D. J. Larson et al., Microscopy & Microanalysis 18(5) (2012) 953DJ Larson - M&M2016
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Optimizing the Projection / Transformations
■ The equidistant projection varies from the
more standard pseudo-stereographic
projection after angles of 35 to 40
■ Evolutionary improvement - especially for
features comprising larger angles
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Azimuthal Equidistant Projection
L=k
■ The barycentric coordinate system is a coordinate
system in which the location of a point of a simplex (a
triangle, tetrahedron, etc.) is specified as the center
of mass, or barycenter, of usually unequal masses
placed at its vertices
■ This transform can assist in using known shape
criteria to improve APT reconstructions
DeGeuser & Gault (2016)
Barycentric TransformFelfer & Cairney (2016)
Using 41 poles in
pure Al
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Automated Parameter Optimization
■ Use the data itself in
order to improve the
reconstruction by
optimizing■ Global parameters
■ Radius (Fevap) vs. Z
■ Image compression (angular
magnification)
■ Metrics to be
optimized include:■ Known (x,y,z) positions
(simulated data only)
■ Density
■ Interface planarityDJ Larson - M&M2016 35
Global Reconstruction Parameters:
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Automated Parameter Optimization* – Known Positions
Using known (x,y,z) positions, global reconstruction parameters may be optimized and the results used
for comparison to optimization obtained using parameters present in experimental data
DJ Larson - M&M2016 36
1a 1c
5nm
5nm
5nm
Normalized Density
0
3nm
Distance (nm)
Co
un
tsC
ou
nts
Co
un
ts
0
0.25nm
0
0.25nm
1b
2a 2c2b
3a 3c3b
■ Fig. 1. (a) atom map, (b) density
metric and (c) planarity for initial
reconstruction parameters R0=20nm,
shank=5, and ICF=1.4.
■ Fig. 2. . (a) atom map, (b) density
metric and (c) planarity for optimized
global parameters of R0=27nm,
shank 6.5, and ICF=1.25.
■ Fig. 3. Same as Fig. 2 using
optimized image compression
functions (seven points in detector
radius space automatically
determined from the data).
* D.J. Larson et al., Microscopy and Microanalysis 17(S2) (2011) 724
Atom Map Density Planarity
A
B
FA=FB
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Automated Parameter Optimization* – Planarity
The reconstruction shown in Figure 2a was obtained without using the
known (x,y,z) values:■ Define the interface in space
■ Assume image compression function determined on previous slide
■ Optimize interface planarity using global reconstruction parameters
DJ Larson - M&M2016 37
1a 1c
5nm
5nmNormalized Density
0
3nm
Distance (nm)
Co
un
tsC
ou
nts
0
0.25nm
1b
2a 2c2b
■ Fig. 1. (a) atom map, (b)
density metric and (c) planarity
for initial reconstruction
parameters R0=20nm,
shank=5, and ICF=1.4.
■ Fig. 2. . (a) atom map, (b)
density metric and (c) planarity
for planarity-optimized global
parameters.
Atom Map Density Planarity
A
B
FA=FB
* D.J. Larson et al., Microscopy and Microanalysis 17(S2) (2011) 724
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Pragmatic Interface Flattening*
■ Atoms present on interfaces are chosen by an isoconcentration surface after a preliminary
reconstruction (left) and then corrected in detector space (X,Y,N) by modifying the detection order
■ Atoms situational between two successive interfaces are linearly interpolated
DJ Larson - M&M2016 38
Detector Space Pos Space
Pre-Correction Post-Correction
* F. Vurpillot et al., Ultramicroscopy 111(8) (2011) 1286
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Landmark Registration
■ Based on the algorithms of the previous slide
(Vurpillot et al.) Geiser et al. have
implemented this formulation in pos space
rather than in detector space
■ Adjustments are made to the POS data based
on geometric offsets between the interface
geometry mesh and best-fit-planes■ Flattening isosurfaces to planes
■ Rotating the resulting isosurfaces to a specified
direction
■ Displacing the resulting isosurfaces to specified
distances from a selected key interface
■ It can be difficult to obtain complete isolated
interfaces (critical to successful registration)
■ Since it is POS-based, it is generic with
respect to direction, works with plan-view,
cross-section, or arbitrary orientations
■ Future capabilities: flattening subsets of
interfaces, specifying distances between
selected interfaces, interfaces “healing”
DJ Larson - M&M2016 39
Geiser et al. (2016)
Pre-Correction Post-Correction
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Dynamic Reconstruction
■ Because the shape of the specimen is not a constant with evaporation depth, it is reasonable to
assume that the input parameters to the reconstruction are not constant with depth
■ Gault et al. have proposed a dynamic reconstruction which evolves the image compression and the
field factor with depth – however Vurpillot et al. have proposed that the ratio of these terms is a
constant…
Gault et al. Loi et al. Vurpillot et al.
DJ Larson - M&M2016 40
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Reconstruction Transformations Based on Simulation*
■ Knowledge of original atom positions allows us to create
a series (in N) of R and Z transforms as a function of
detector hit position
■ The vertical distance between the points and the solid
line at right show the error that results from the current
standard reconstruction method
■ After fitting these curves, the transforms may be applied
to simulated or experimental data by using an initial
scaling factor
Tz TR
TR
Tz
Evaporation of 10k ions Transformations for N=280k ions
* D. J. Larson et al., Microscopy & Microanalysis 18(5) (2012) 953
DJ Larson - M&M2016 41
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Transformations for N=280k ions
TR
Tz
Reconstruction Transformations Based on Simulation*
Tracer Plane Analysis** of Radial Variation
■ By introducing “tracer planes”** of different mass atoms we
can qualitative view the errors in the reconstruction that are
introduced by using a hemisphere to reconstruct the high-
field on low-field case
■ The lines of white atoms shown above should be
reconstructed as vertical
■ Deviation is quantitatively shown by the vertical distance
between the black line and the blue/yellow data points
shown above right (arrowed)* D. J. Larson et al., Microscopy & Microanalysis 18(5) (2012) 953
** B. Gault, B. P. Geiser et al., Ultramicroscopy 111 (2011) 448 ,D. J. Larson et al., Current Opinion in Solid State and Materials Science 17 (2013) 236DJ Larson - M&M2016 42
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Quantification of Improvement: Sim-Informed Reconstruction*
■ Knowledge of original atom positions allows us to create a
series (in N) of R and Z transforms as a function of detector hit
position
■ After fitting these curves, the transforms may be applied to
simulated or experimental data by using an initial scaling factor
■ For the high-on-low field case, use of the simulation
transformation improves xyz errors by about a factor of two
compared to the standard reconstruction
43
Standard Recon Sim-Informed Recon
Interface Type
Reconstruction
Type
Initial Radius
(nm) ICF
Shank
(deg)
NTC
Ratio
XYZ Error
(nm)
Sigma
(nm)
Standard 28 1.2 5 1.5 1.049 0.553
Simulation
Transformation 0.472 0.224
High-on-low
interface N/A
* D. J. Larson et al., Microscopy & Microanalysis 18(5) (2012) 953DJ Larson - M&M2016
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A Faster Field Evaporation Simulation
■ Delaunay surfaces are used in the creation of an analytical model of field evaporation of multilayers that
is much faster that conventional electrostatic atomistic models
■ This results in a series of specimen shapes just as you would have expected in a more standard
electrostatic model
DJ Larson - M&M2016 44
Fast Analytical Simulation* Evolution of Specimen Shape Through an ABC Structure
* N. Rolland et al. Eur. Phys. J. Appl. Phys..72 (2015) 21001,
N. Rolland et al., Ultramicroscopy 159 (2015) 195
Fred=2Fblue
Fblue=0.45Fgreen
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Use of Simulated Shapes to Reconstruct
■ A sequence of (non-hemispherical) specimen shapes spanning the entire evaporated volume is
used to produce surface normals that result in projection transforms – still within a voltage or
shank angle evolution model
■ Application of this to both simulated and experimental data is shown above and suggests good
feasibility
DJ Larson - M&M2016 45
Simulated Data
(Low-on-High Field Material)
Experimental Data
(GaN/InAlN/GaN)
N. Rolland et al., Microscopy and Microanalysis (2016) Submitted
Expected New Method Standard Bas
InAlN layer expected to measure ~35nm
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Best Trajectory Reconstruction
■ Method is evolutionary in that the order of reconstruction is inverted - it is last in first out (LIFO)
■ A final surface must be assumed, either based on simulation or electron microscopy
■ A detector hit position is first projected on this surface and then its hit position is compared to the
simulated hit positions from a number of possible original positions near the initial projected position
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Final Surface is Assumed Variety of Initial Positions Evaluated
D. Beinke, C. Oberdofer and G. Schmitz, Ultramicroscopy 165 (2016) 34
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Best Trajectory-based Reconstruction - Feasibility
■ Results above are for a precipitate with a lower evaporation field than the matrix
■ Currently is a factor of ~200X too slow to do realistic size data sets of 10-20M ions
■ Good feasibility has been shown
DJ Larson - M&M2016 47
Standard Bas Reconstruction Method of Beinke et al.
D. Beinke, C. Oberdofer and G. Schmitz, Ultramicroscopy 165 (2016) 34
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General Iterative Method
■ All of these recent
examples fall into a
category using simulated
data in order to improve
reconstruction
■ The chart at right shows
a general overview of
how both microscopy and
simulation may be used
in adding accurate
reconstruction of APT
data
DJ Larson - M&M2016 48
D. J. Larson et al., “Atom Probe Tomography for Microelectronics”; in Handbook of Instrumentation
and Techniques for Semiconductor Nanostructure Characterization, eds. R. Haight, F. Ross and J.
Hannon, (World Scientific Publishing/Imperial College Press, 2011) p. 407.
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Summary
■ A Bit of History
■ Hemispherical Reconstruction
■ Assumptions
■ Calculation of x, y, and z
■ Estimation of Field Evaporated
Shapes
■ Simulation
■ Experimental Observation
■ Interfaces & Precipitates
■ Limitations & Resulting Inaccuracies
■ Projection
■ Z Increment
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■ Methods of Correction
■ Density Correction
■ Lattice Rectification
■ Radius Evolution
■ Non-Tangential Continuity
■ Variable Image Compression
■ Self-Optimization of Data: A
Priori and A Posteriori to
Reconstruction
■ Dynamic Reconstruction
■ Simulation & Non-Hemispherical
Methods
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SCIENCE & METROLOGY SOLUTIONSThank you!
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