3D Imaging of Nanostructures Using Electron Tomography

Peter Ercius, Cornell University

3D Imaging of Nanostructures Using Electron Tomography, and the Impact

of Aberration Correctors

3D Imaging of Nanostructures Using Electron Tomography, and the Impact

of Aberration Correctors

Peter ErciusHuolin XinVarat IntaraprasonkDavid Muller

Applied and Engineering Physics, Cornell University

Lynne GignacIBM T.J. Watson Research Center, SRC


Tomographic ReconstructionTomographic ReconstructionGoal: 3D information from thick, crystalline, high atomic number materials

- Measure structure thicknesses, x-sections, CDsChallenges:

• Image intensities for electron tomography must be monotonic with thickness

Not Conventional TEM• Contrast reversal in HAADF Scanning TEM (Z-contrast)

High mass-thickness materials appear dark at high tilts

• Samples must be tilted to ±70° to recover 3D informationTilting causes translations and rotations between images that must be corrected (post-processing)

Impact of aberration correctors:• Lateral and depth resolution significantly improved

Depth resolution < sample thickness


For the best results:

• Acquire many images over as large a tilt range as possible

→ One every 1-2° from ±70°

→ Filling Fourier Space

Tomography ExperimentTomography Experiment

Acquisition

e-

Requires

Reconstruction:

• Accurate spatial alignment

• Determination of tilt axis

• Accurately spaced angular increments


V2 Via Liner Layer by HAADF STEMV2 Via Liner Layer by HAADF STEMEtch Roughness

LithographyRoughness

90nm Cu line width


Contrast Reversal in HAADF STEMContrast Reversal in HAADF STEM

Annular Dark Field detector

y

x

200 keV IncidentElectron Beam

(∆E≈0.6 eV)

1 atom wide (0.2 nm) beam is rasteredacross the sample to form a 2-D image

ADF image


Contrast Reversal with ThicknessContrast Reversal with Thickness

Cu via

• HAADF STEM• 0° tilt

Cu line

300nm

Cu via

Cu line



Why the Contrast Reversal in HAADF?Why the Contrast Reversal in HAADF?

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2 2.5 3 3.5

Ta Cu Si

Nor

mal

ized

Inte

nsity

(a.u

.)

Target thickness (µm)

Signal drops when electrons scatter outsideouter angle of detector(e.g. backscattering)

But no electrons stop in the sample: Backscatter

DF

BF

200keVfor Cu in 500 mEKR µρ

γ ≅=


Maximum Material Thickness: HAADF vs IBFMaximum Material Thickness: HAADF vs IBFApparent thickness is increased ~threefold by tilting

t

tmax

70°

HAADF IBFTantalum 47 73±7

220±201160±30

Copper 143Silicon 855

Maximum material thickness, tmax (in nm), for ±70° tilt


IBF vs. HAADF for Cu: SNRIBF vs. HAADF for Cu: SNR

0

10

20

30

40

50

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Contrast for 5nm thickness changesnormalized by Poisson noise

ADF (100-250R)IBF (0-100R)

SNR

Cu Thickness (µm)

ADF contrast reversal

• Question: when does IBF become advantageous over HAADF?– Compare for ∆t=5nm at relevant thicknesses

• IBF is better even before contrast reversal thicknesses are reached


Stress Void ReconstructionsStress Void ReconstructionsHAADF IBF

~500nm


Stress Void and Via ReconstructionStress Void and Via Reconstruction


Copper Line ResistivityCopper Line Resistivity

• By preparing one sample for tomography we can gain information about ~2nm slices of each line.

• Getting the same information by CTEM requires preparation and measurement of many samples.

2.4

2.6

2.8

3

3.2

9000 10000 11000

Conductor area vs. resistivity

Tomo slicesTomo meanTEM mean

Res

istiv

ity (µΩ

cm)

Cu area (nm2)

- TEM data from L. Gignac


Electron Lens AberrationsElectron Lens Aberrations

∆s = path difference due to wave aberration

C3=0C3>0

• Use circular aperture to cutoff electrons with a large phase shift ∆s across the lens


Balance Aberration and DiffractionBalance Aberration and Diffraction

α00d

• The image of a point transferred through a lens with a circular aperture of semiangle α0 is an Airy disk of diameter:• Balance spherical aberration against the aperture’s diffraction limit

• Less diffraction with a larger aperture• Design correctors to eliminate phase shift across the lens

• Lens aberrations are a non-convergent power series• Correct C3 C5 ; Correct C5 C7 ; ETC…

00 1 α∝d


Depth Point Spread Function (PSF)Depth Point Spread Function (PSF)C5 limited:C3 limited:

200nm z

x

nmz 33≈∆ nmz 6.3≈∆200keV, α=29.1mRadC3=-0.0842mm, C5=100mm, ∆f=-132Å

200keV, α=9.6mRad, C3=1.2mm, ∆f=550Å


Depth Sectioning by Focal SeriesDepth Sectioning by Focal Series

∆f0

∆f1

∆f2

∆f3


Prospects for Depth SectioningProspects for Depth Sectioning

1

10

100

0 20 40 60 80 100

100 kV200 kV300 kV

Dep

th o

f Foc

us (Å

)

Probe Forming Semi-Angle (mrad)

C3>0

C3~0

C5~0

Current STEM correctors: ∆z ~ 3-8 nm Super STEM: ∆z ~ 1 nm?


Tomography or Depth SectioningTomography or Depth Sectioning

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10

Focal SeriesTilt Series

Nor

mal

ized

inte

nsity

(a.u

.)

Depth (nm)

Focal Series: Change defocus to sample at different depthsTilt Series: Tilt sample to fill Fourier-Space with projections


Information Limit for Depth SectioningInformation Limit for Depth Sectioning

0 0.5 1 1.5 2 2.5 3 3.5 4−0.05

−0.04

−0.03

−0.02

−0.01

0

0.01

0.02

0.03

0.04

0.05

kr (1/angstrom)

k z (1/

angs

trom

)

C3−limited, α

max = 10 mrad

C5−limited, α

max = 29 mrad

C7−limited, α

max = 49 mrad

Information limit: 0.05-1 = 20ÅHalf-angle:

kr cutoff:λαα

max

max

22

°°=

1.1 :covers55.mrad6.9

C3 limited:

°°=

32.3 :covers66.1mrad29

C5 limited:


Fourier Reconstruction with Depth Sectioning at Different Tilts

Fourier Reconstruction with Depth Sectioning at Different Tilts

0° -45°, 0°

kz

ky

-45°, 0°, 45°

±70° @ 7° inc.


Fourier Reconstruction MethodsFourier Reconstruction Methods

Focal & Tilt SeriesTilt Series


Convolution Simulation: PSFConvolution Simulation: PSFFocalSeries

Focal &Tilt SeriesTilt Series

z

y

200keV, C3=-0.0842mm, C5=100mm, f0=-132, α=29.1mRad±70° @ 7° increments


Spread of PSF IntensitySpread of PSF Intensity

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5

Focal&TiltTilt

Nor

mal

ized

Inte

grat

ed In

tens

ity (a

.u.)

Distance from center (nm)

• Intensity is decentralized for both methods


Convolution Simulation: CTFConvolution Simulation: CTFTilt SeriesFocal & Tilt Series

Fourier Transform of the PSF0

0.2

0.4

0.6

0.8

1

-0.3 -0.2 -0.1 0 0.1 0.2 0.3

Focal&TiltTilt

Mag

nitu

de o

f Fou

rier

Com

pone

nt (a

.u.)

Ky (1/nm)

kz

ky


Depth ResolutionDepth Resolution

0

0.2

0.4

0.6

0.8

1

-1 -0.5 0 0.5 1

Focal&TiltTiltTF20 Tilt

Nor

mal

ized

Inte

nsity

(a.u

.)

Depth (nm)• Depth information from focal series does not add to depth resolution• Tomography resolution: experiment is 1-2nm (Why!?)

- Tomography yields 10x worse resolution in practiceAlignment, stage movement (low mag)

FWHM-Corrected

F&T: 1.4ÅTilt: 1.4Å

UncorrectedTilt: 2.5Å


Conclusions: Tomography & CorrectorsConclusions: Tomography & Correctors

• Electron Tomography• Quantitative measurements of 3D objects• Incoherent Bright Field (IBF) STEM

• high ρ*Z and t• Impact of Correctors

• Improved lateral and depth resolution • Focal and Tilt series

• necessary for corrected instruments• 3x fewer tilts needed Faster!

• Resolution limits• No considerable increase in resolution predicted• Tilt stage quality, alignment, blurring



Contrast Reversal with ThicknessContrast Reversal with Thickness

Cu via


Cu line

300nm

Cu via

Cu line



Cu lines: PlanviewCu lines: Planview


Increasing the Collector Angle (θc)Increasing the Collector Angle (θc)

1 2

3 430 nm

3 mr 10 mr

80 mr ADF

θc>>θobj

•No Phasecontrast

•No Diffractioncontrast

θc<<θobj•Phasecontrast

•Diffractioncontrast

θc≈θobj

•No Phasecontrast

•Diffractioncontrast

The incoherent BF image is the complement of the ADF image


Fourier ReconstructionFourier Reconstruction“A 2D projection of a object is equivalent to a 2D slice through the Fourier transform of that object at the angle of projection.”

High frequencies under sampled

Missing wedge of information

Object 1 projection:the ‘ray-integral’

2 projections

3 projections 10 projections 32 projections

Weighted backprojection: Backprojection can be made more accurate by restoring the correct distribution of the spatial frequencies using a weighting filter.


Tomographic ReconstructionTomographic Reconstruction

Under sampling Missing wedge

Features perpendicular with the tilt axis are distorted

Yields a blurred reconstruction


Z-contrast Simulation MethodZ-contrast Simulation Method

⊗ =

PSF39 depth slicesDepth: 5.1 Å/sliceLateral: .2 Å/pixel

( )zyx ,,δ

( )3Å100

z

x

y

Focal Series

20 depth slices∆f: 5 Å

3D incoherent Z-contrast STEM imaging simulation


Fourier Slice TheoryFourier Slice Theory

t

projection

θ

θ

F[f(x,y)]

Real space

ky

kx

Frequency space


Aberration CorrectorsAberration Correctors• Lens aberrations create phase shifts for e-’s

incident at different angles

• For given C-values…maximize α to maximize resolution– Including depth resolution ∆z

( )

281

61

41

212

max

87

65

43

2

πχ

ααααλπαχ

=

⎟⎠⎞

⎜⎝⎛ ++++∆−= LCCCf

2

22.1α

λ∝∆z


Balance Spherical Aberration Against Diffraction

Balance Spherical Aberration Against Diffraction

1

10

100

1 10

Prob

e Si

ze (A

ngst

rom

s)

α (mrad)

ds

d0

220

2stot ddd +≈

Optimal apertureAnd minimum

Spot size

• Balance sperical aberration against the aperture’s diffraction limit• Less diffraction with a large aperture – must be balanced against C3

• For a rough estimate of the optimum aperture size, convolve blurring terms• Add in quadrature:


Electron Lens Aberration CorrectorsElectron Lens Aberration Correctors

Design corrector to give no phase shift across the lensThere are other higher order aberrations that limit resolution

Lens aberrations are a power series that does not convergeYou can correct C3 but C5 limits you, correct C5 but C7 limits you, etc…

Documents

3D Imaging of Nanostructures Using Electron Tomography