Atom Probe Tomography (APT)

1. Theory

• Definition: An atom probe tomograph field-evaporates atoms one by one from a needle-shaped specimen and identifies each by time-of-flight mass spectrometry, rebuilding a three-dimensional atom map with sub-nanometre resolution (Wiley; Gault et al.).
• Field evaporation: A field of about $1\times 10^{10}$ V/m at the apex, $F=V/(k_{f}R)$, removes surface atoms as ions when standing voltage plus a voltage or laser pulse exceeds the evaporation threshold (Gault et al.; Wiley).
• Point projection: Ions fly radially to a position-sensitive detector, and back-projection with an image compression factor gives lateral positions (Gault et al.).
• Depth: Each detected ion advances the reconstruction depth by its atomic volume divided by efficiency and analysed area (Gault et al.).

2. Working Principle

• Specimen: A FIB-milled tip with apex radius below 100 $\mathrm{nm}$ at cryogenic temperature (Wiley; background knowledge).
• Pulsing: Voltage pulses for metals, nanosecond or shorter laser pulses for semiconductors and oxides (Wiley).
• Detection: A microchannel-plate delay-line detector records hit position and flight time (Gault et al.).
• Reconstruction: Radius evolution from voltage, compression factor and efficiency set the 3-D scaling (Gault et al.; Henry).

3. Applications

• Dopant distributions in devices: As, B and P in junctions, FinFETs and nanowires (Henry; background knowledge).
• Gate stacks: HfO2, TiN and interface chemistry in 3-D CMOS structures (Henry).
• III-V and SiGe multilayers: Composition fluctuations and interfaces (Henry).
• Metallurgy: Precipitates and segregation in alloys (Gault et al.; Wiley).

Field Evaporation and Mass Analysis

Name	Formula	Related Formulae	Variables/Constants
Field evaporation and tip radius	$F=\frac{V}{k_{f}R}$	$R=\frac{V}{k_f{F}_e}$	$F:surfaceelectricfield$ $V:specimenvoltage$ $k_f:fieldfactor(about3to8)$ $R:apexradius$ $\begin{array}{r}{F}_e:evaporationfield;Gaultetal.:R=\\ V/(k_f{F}_e),fieldabout1\times 10^{10}V/m,radii30to\\ 200\mathrm{nm},shankangles3.6to16.7{}^{\circ },k_{f}and\\ \xi decreasingasthetipblunts;Henry:\\ evaporationfieldsabout27V/nm(Cr)and\\ 35V/nm(Ni);Wiley:apexradiusbelow100\\ \mathrm{nm}froma1to2\mu \mathrm{m}milledcylinder;k_f\\ range(backgroundknowledge,Gaultetal.\\ 2012)\end{array}$ $\begin{array}{r}(assumed:V=5\mathrm{kV},k_f=3.3;computed:Ni\\ at35V/nmgivesR=43\mathrm{nm})\end{array}$
Mass-to-charge from time of flight	$\frac{m}{n}=2eV{\left(\frac{t}{L}\right)}^2$	$MRP=\frac{m}{\Delta m}$	$m/n:mass-to-chargeratio$ $e:elementarycharge$ $t:flighttime$ $L:flightlength$ $\begin{array}{r}MRP:massresolvingpower;energybalance\\ (backgroundknowledge,Gaultetal.2012);\\ Wiley:heavierionsarrivelater,examples\\ 54\mathrm{Da}and206\mathrm{Da};Henry:MRP1500,more\\ than5millionionsperminute\end{array}$ $\begin{array}{r}(assumed:V=5\mathrm{kV},L=100\mathrm{mm};computed:\\ {}^{28}S{i}^{+}arrivesafter0.54\mu \mathrm{s};MRP1500\\ separatespeaks0.019\mathrm{Da}apartat28\mathrm{Da})\end{array}$
Peak overlaps	$\frac{m}{n}\left({}^{28}{\mathrm{Si}}^{2+}\right)=\frac{m}{n}\left({}^{14}{\mathrm{N}}^{+}\right)=14\mathrm{Da}$	$\text{deconvolution by isotope ratios}$	$\begin{array}{r}Henry:peakoverlapscomplicating\\ heterogeneousnanostructures,oxygen\\ detectedinCrlayersmissedbyTEMEDS;\\ overlapexampleandisotope-ratio\\ deconvolution(backgroundknowledge,\\ Larsonetal.)\end{array}$ $\begin{array}{r}(myreading:NinSiisquantifiedfrom\\ {}^{29}S{i}^{2+}and{}^{30}S{i}^{2+}isotopepeaksscaledto\\ subtractthe14\mathrm{Da}Sicontribution)\end{array}$

Reconstruction and Resolution

Name	Formula	Related Formulae	Variables/Constants
Point-projection reconstruction	$\theta ={\theta }^{\prime }+\arcsin \left[\left(\xi -1\right)\sin {\theta }^{\prime }\right]$	$M\approx \frac{L}{\xi R}$	$\begin{array}{r}\theta :crystallographiclaunchangle,{\theta }^{\prime }:\\ observedangle\end{array}$ $\xi :imagecompressionfactor$ $\begin{array}{r}M:magnification;Gaultetal.:\\ compressionrelation,Basetal.protocol,\\ simulated\xi =k_f^{1/3}notmatchingexperiment;\\ Henry:magnificationrelationin\xi ,\\ distanceandradius(garbled);\\ magnificationform(backgroundknowledge,\\ Gaultetal.2012)\end{array}$ $\begin{array}{r}(assumed:\xi =1.6,{\theta }^{\prime }=10{}^{\circ },L=100\mathrm{mm},\\ R=50\mathrm{nm};computed:\theta =16.0{}^{\circ }andM=\\ 1.25\times 10^6)\end{array}$
Depth increment per detected ion	$dz=\frac{\Omega }{\eta S_A}$	$S_A=2\pi R^2\left(1-\cos {\theta }_D\right)$	$dz:depthincrement$ $\Omega :atomicvolume$ $\eta :detectionefficiency$ $S_A:analysedcaparea$ $\begin{array}{r}{\theta }_D:detectorhalf-angle;Gaultetal.:\\ relations,efficiencyabout55percent\\ frommicrochannel-plateopenarea;Wiley:\\ 50to80percentinmoderninstruments\\ (seetheQ/A)\end{array}$ $\begin{array}{r}(assumed:Si\Omega =0.020\mathrm{n}{\mathrm{m}}^3,\eta =0.55,R=\\ 50\mathrm{nm},{\theta }_D=20{}^{\circ };computed:S_A=947\mathrm{n}{\mathrm{m}}^2,dz\\ =3.8\times 10^{-5}\mathrm{nm},1\times 10^{6}ionsgive38\mathrm{nm})\end{array}$
Spatial resolution	${\delta }_{lat}\approx 0.2\text{to}0.5\mathrm{nm},{\delta }_z\approx 0.05\text{to}0.3\mathrm{nm}$	$\text{internal check: }{d}_{004}=\frac{a_{Si}}{4}=0.136\mathrm{nm}$	$\begin{array}{r}{\delta }_{lat},{\delta }_z:lateralanddepthresolution;\\ Henry:0.2\mathrm{nm}lateraland0.05\mathrm{nm}depth,\\ fieldofviewabove200\mathrm{nm},Siplanes\\ along<100>resolvedwitha=0.54307\mathrm{nm}\\ inSRM2134;Wiley:0.3to0.5\mathrm{nm}lateral\\ and0.1to0.3\mathrm{nm}depth;Gaultetal.:\\ near-atomicresolution,\\ local-magnificationartefacts(seethe\\ Q/A)\end{array}$ $\begin{array}{r}(computed:Si(004)planesare0.136\mathrm{nm}\\ apart,soresolvingthemrequiresdepth\\ resolutionbetterthanabout0.07\mathrm{nm})\end{array}$

Quantification, Artefacts and Preparation

Name	Formula	Related Formulae	Variables/Constants
Composition and counting statistics	$C_i=\frac{N_i}{{\sum }_j{N}_j},{\sigma }_C=\sqrt{\frac{C\left(1-C\right)}{N_{tot}}}$	$N_{det}=\eta c{V}_{box}$	$C_i:atomicfraction$ $N_i:detectedionsofi$ ${\sigma }_C:statisticaluncertainty$ $c:concentration$ $\begin{array}{r}{V}_{box}:analysedvolume;binomialstatistics\\ (backgroundknowledge,Gaultetal.2012);\\ Henry:accuratedosemeasurementwithbest\\ practices,SIMSasindustrystandardover\\ severalhundredsquaremicrometres;Wiley:\\ efficiency50to80percent\end{array}$ $\begin{array}{r}(assumed:20by20by100\mathrm{nm}box,\eta =\\ 0.55;computed:1\times 10^{19}\mathrm{c}{\mathrm{m}}^{-3}gives220\\ detectedatoms(6.7percentuncertainty),\\ 1\times 10^{18}gives22(21percent))\end{array}$
Evaporation-field mismatch artefacts	$F_{e,A}\ne F_{e,B}\Rightarrow \text{non-hemispherical apex}$	$\text{local magnification at interfaces and precipitates}$	$\begin{array}{r}Henry:dissimilarevaporationfields\\ givinganon-uniform,non-sphericaltipat\\ interfaces,ledgesfromdifferentsputter\\ yieldsatNi/Crinterfaces;Gaultetal.:\\ localmagnificationfromlocalcurvature,\\ k_{f}and\xi varyingduringtherun,dynamic\\ reconstruction;HfO,TiNandIII-V\\ multilayerexamples(Henry)\end{array}$ $\begin{array}{r}(computed:NiandCrfieldsdifferby30\\ percent,sotheCr-richsideevaporates\\ firstandflattens)\end{array}$
Specimen preparation and laser pulsing	$\text{FIB lift-out and annular milling to}R<100\mathrm{nm}$	$\text{laser pulses (ns or shorter) for semiconductors and oxides}$	$\begin{array}{r}Wiley:milledcylinder1to2\mu \mathrm{m}thinnedto\\ below100\mathrm{nm}apexradius,nanosecondor\\ shorterlaserpulses,pulse-energytrends;\\ Henry:3-DCMOSstructureswithSi,O,HfO\\ andTiN;site-specificFIBpreparation\\ (backgroundknowledge,Larsonetal.)\end{array}$ $\begin{array}{r}(computed:froma1.5\mu \mathrm{m}cylindertoa100\\ \mathrm{nm}apexisa15-foldreductioninradius)\end{array}$

Important Questions

Ques: How does an atom probe turn field evaporation into a 3-D map?

By timing each ion’s flight and back-projecting its hit position. A field of about $1\times 10^{10}$ V/m (Gault et al.) evaporates surface atoms; mass-to-charge follows from $m/n=2eV(t/L{)}^2$ (background knowledge, Gault et al. 2012), so at 5 $\mathrm{kV}$ over an assumed 100 $\mathrm{mm}$ path ${}^{28}$Si${}^{+}$ arrives after 0.54 $\mu \mathrm{s}$ (computed). Lateral positions come from point projection with an image compression factor, $\theta ={\theta }^{\prime }+\arcsin [(\xi -1)\sin {\theta }^{\prime }]$ (Gault et al.); with $\xi$ = 1.6, a 10 ${}^{\circ }$ observed angle maps to 16.0 ${}^{\circ }$ (computed). Depth advances by $dz=\Omega /(\eta S_A)$ per ion: for silicon on a 50 $\mathrm{nm}$ tip and 20 ${}^{\circ }$ detector, $3.8\times 10^{-5}$ $\mathrm{nm}$, so a million ions add 38 $\mathrm{nm}$ (computed). Reference: B. Gault, S. T. Loi, V. J. Araullo-Peters, L. T. Stephenson, M. P. Moody, S. L. Shrestha, R. K. W. Marceau, L. Yao, J. M. Cairney and S. P. Ringer, ‘Dynamic reconstruction for atom probe tomography’, arXiv:1510.02849 (fetch-tool summary); B. Gault, M. P. Moody, J. M. Cairney and S. P. Ringer, Atom Probe Microscopy, Springer 2012, and D. J. Larson et al., Local Electrode Atom Probe Tomography, Springer 2013 (background knowledge; not opened).

Ques: Is APT detection efficiency 55 per cent or up to 80 per cent?

Gault et al. state that detection efficiency is limited to about 55 per cent on most microscopes by the open area of the microchannel plates, whereas the Wiley briefing gives 50 to 80 per cent for modern instruments. The higher value reflects newer detectors with larger open area, while 55 per cent applies to the instruments of the period Gault et al. studied (my reading); both are therefore right for their generation, and 80 per cent is the more likely best case today (background knowledge, Larson et al.). Efficiency matters twice: it enters the depth scale $dz=\Omega /(\eta S_A)$, so a wrong value stretches or compresses depth by the same factor, and it sets counting statistics for dilute dopants. Raising efficiency from 0.55 to 0.80 improves dopant counting uncertainty by 17 per cent (computed). Reference: B. Gault, S. T. Loi, V. J. Araullo-Peters, L. T. Stephenson, M. P. Moody, S. L. Shrestha, R. K. W. Marceau, L. Yao, J. M. Cairney and S. P. Ringer, ‘Dynamic reconstruction for atom probe tomography’, arXiv:1510.02849 (fetch-tool summary); Wiley, ‘Atom Probe Tomography’, Essential Knowledge Briefings, 1st ed. (2017) (fetch-tool summary); B. Gault, M. P. Moody, J. M. Cairney and S. P. Ringer, Atom Probe Microscopy, Springer 2012, and D. J. Larson et al., Local Electrode Atom Probe Tomography, Springer 2013 (background knowledge; not opened).

Ques: What spatial resolution does APT really have?

Henry lists 0.2 $\mathrm{nm}$ lateral and 0.05 $\mathrm{nm}$ depth resolution, while the Wiley briefing gives 0.3 to 0.5 $\mathrm{nm}$ lateral and 0.1 to 0.3 $\mathrm{nm}$ depth, and Gault et al. say near-atomic. Henry’s values are best cases along crystallographic poles, where atomic planes are resolved: she uses Si planes along <100> with a = 0.54307 $\mathrm{nm}$ as an internal check, and (004) planes 0.136 $\mathrm{nm}$ apart need depth resolution near 0.07 $\mathrm{nm}$ (computed). The Wiley ranges are more likely for typical semiconductor data away from poles, where trajectory aberrations and local magnification dominate (my reading). Lateral resolution is always worse than depth because ions are deflected by the surface curvature near launch (background knowledge, Gault et al. 2012). Reference: K. T. Henry, ‘Frontiers of Atom Probe Microscopy’, slides (2013), hosted by NIST (fetch-tool summary; equations garbled); Wiley, ‘Atom Probe Tomography’, Essential Knowledge Briefings, 1st ed. (2017) (fetch-tool summary); B. Gault, S. T. Loi, V. J. Araullo-Peters, L. T. Stephenson, M. P. Moody, S. L. Shrestha, R. K. W. Marceau, L. Yao, J. M. Cairney and S. P. Ringer, ‘Dynamic reconstruction for atom probe tomography’, arXiv:1510.02849 (fetch-tool summary); B. Gault, M. P. Moody, J. M. Cairney and S. P. Ringer, Atom Probe Microscopy, Springer 2012, and D. J. Larson et al., Local Electrode Atom Probe Tomography, Springer 2013 (background knowledge; not opened).

Ques: Can APT measure dopant concentrations in a transistor?

Yes, but counting statistics limit small volumes. In a 20 by 20 by 100 $\mathrm{nm}$ box with 55 per cent efficiency, $1\times 10^{19}$ $\mathrm{c}{\mathrm{m}}^{-3}$ gives about 220 detected dopant atoms, a 6.7 per cent uncertainty, while $1\times 10^{18}$ $\mathrm{c}{\mathrm{m}}^{-3}$ gives only 22, a 21 per cent uncertainty (computed from binomial statistics; background knowledge, Gault et al. 2012). Henry notes that SIMS remains the industry standard over areas of several hundred square micrometres, while APT suits device-level volumes and can give accurate doses with best practices. Peak overlaps complicate some species: ${}^{28}$Si${}^{2+}$ and ${}^{14}$N${}^{+}$ both appear at 14 $\mathrm{Da}$, so nitrogen must be found from isotope ratios (background knowledge, Larson et al.). A mass resolving power of 1500 (Henry) separates peaks only 0.019 $\mathrm{Da}$ apart at 28 $\mathrm{Da}$ (computed). Reference: K. T. Henry, ‘Frontiers of Atom Probe Microscopy’, slides (2013), hosted by NIST (fetch-tool summary; equations garbled); B. Gault, M. P. Moody, J. M. Cairney and S. P. Ringer, Atom Probe Microscopy, Springer 2012, and D. J. Larson et al., Local Electrode Atom Probe Tomography, Springer 2013 (background knowledge; not opened).

Ques: Why do interfaces distort APT reconstructions?

Because phases with different evaporation fields reshape the tip. Henry notes evaporation fields of about 27 $V/nm$ for Cr and 35 $V/nm$ for Ni, a 30 per cent difference (computed), so the lower-field phase evaporates faster and the apex becomes non-hemispherical at interfaces; differing sputter yields also leave ledges after FIB preparation. Gault et al. describe the resulting local magnification and show that the field factor and image compression factor change as the tip blunts, motivating dynamic reconstruction. The tip radius itself follows $R=V/(k_f{F}_e)$: 5 $\mathrm{kV}$ with $k_f$ = 3.3 on Ni gives 43 $\mathrm{nm}$ (assumed values; computed). In gate stacks with HfO2, TiN and Si, Henry’s example, such field contrasts distort layer thickness and interface widths unless corrected. Reference: K. T. Henry, ‘Frontiers of Atom Probe Microscopy’, slides (2013), hosted by NIST (fetch-tool summary; equations garbled); B. Gault, S. T. Loi, V. J. Araullo-Peters, L. T. Stephenson, M. P. Moody, S. L. Shrestha, R. K. W. Marceau, L. Yao, J. M. Cairney and S. P. Ringer, ‘Dynamic reconstruction for atom probe tomography’, arXiv:1510.02849 (fetch-tool summary).

Ques: How are APT specimens of semiconductor devices prepared?

By focused-ion-beam lift-out and annular milling. The Wiley briefing describes milling a 1 to 2 $\mu \mathrm{m}$ cylinder and sharpening it to an apex radius below 100 $\mathrm{nm}$, a reduction of about 15 times in radius (computed). Gault et al. report radii of 30 to 200 $\mathrm{nm}$ and shank angles of 3.6 to 16.7 ${}^{\circ }$ in their specimens, both of which change the reconstruction scaling. Semiconductors and oxides are poorly conducting, so field evaporation is triggered with nanosecond or shorter laser pulses rather than voltage pulses (Wiley). Site-specific preparation lets a single transistor or a FinFET fin be placed at the apex, as in Henry’s 3-D CMOS examples (background knowledge, Larson et al.). Gallium implantation from the FIB is minimized with low-voltage final milling (background knowledge). Reference: Wiley, ‘Atom Probe Tomography’, Essential Knowledge Briefings, 1st ed. (2017) (fetch-tool summary); B. Gault, S. T. Loi, V. J. Araullo-Peters, L. T. Stephenson, M. P. Moody, S. L. Shrestha, R. K. W. Marceau, L. Yao, J. M. Cairney and S. P. Ringer, ‘Dynamic reconstruction for atom probe tomography’, arXiv:1510.02849 (fetch-tool summary); K. T. Henry, ‘Frontiers of Atom Probe Microscopy’, slides (2013), hosted by NIST (fetch-tool summary; equations garbled); B. Gault, M. P. Moody, J. M. Cairney and S. P. Ringer, Atom Probe Microscopy, Springer 2012, and D. J. Larson et al., Local Electrode Atom Probe Tomography, Springer 2013 (background knowledge; not opened).

References

1. B. Gault, S. T. Loi, V. J. Araullo-Peters, L. T. Stephenson, M. P. Moody, S. L. Shrestha, R. K. W. Marceau, L. Yao, J. M. Cairney and S. P. Ringer, “Dynamic reconstruction for atom probe tomography,” preprint arXiv:1510.02849. Available: https://arxiv.org/pdf/1510.02849
2. B. Gault, M. P. Moody, J. M. Cairney and S. P. Ringer, Atom Probe Microscopy, Springer, 2012; D. J. Larson, T. J. Prosa, R. M. Ulfig, B. P. Geiser and T. F. Kelly, Local Electrode Atom Probe Tomography, Springer, 2013 (cited from background knowledge).
3. John Wiley and Sons, Atom Probe Tomography, Essential Knowledge Briefings, 1st ed., 2017. Available: https://content.knowledgehub.wiley.com/wp-content/uploads/2023/08/Atom-Probe-Tomography-First-Edition-pdf-1.pdf
4. K. T. Henry, “Frontiers of Atom Probe Microscopy,” slides, 2013. Available: https://www.nist.gov/document/henrypdf

Related pages in this vault: Secondary Ion Mass Spectrometer (SIMS and ToF-SIMS), Focused Ion Beam (FIB), Transmission Electron Microscope (TEM and STEM), Rutherford Backscattering Spectrometer (RBS), Auger Electron Spectrometer (AES), X-Ray Photoelectron Spectrometer (XPS), X-Ray Fluorescence Spectrometer (XRF and TXRF), Fin Field Effect Transistor (FinFET), Scanning Spreading Resistance Microscope (SSRM), Residual Gas Analyzer (RGA).