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APT Data Reconstruction

David J. Larson, Brian P. Geiser & Ty J. Prosa

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SCIENCE & METROLOGY SOLUTIONS

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)

DJ Larson - M&M2016 2

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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


■ 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


Revue Phys. Appl. 17 (1982) 435

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Into the 3D Atom Probe Era


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.


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


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*


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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DJ Larson - M&M2016

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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…

DJ Larson -

M&M2016

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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


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


■ 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


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


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

DJ Larson - M&M2016

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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)

33

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


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


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


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


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”


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.


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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


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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


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


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


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


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


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


■ Methods of Correction

■ Density Correction

■ Lattice Rectification

■ Radius Evolution

■ Non-Tangential Continuity

■ Variable Image Compression

■ Self-Optimization of Data: A


Reconstruction

■ Dynamic Reconstruction

■ Simulation & Non-Hemispherical

Methods

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SCIENCE & METROLOGY SOLUTIONSThank you!


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