Applied Physics, Cornell Universitymuller.research.engineering.cornell.edu/sites/WEELS/summer06/STEM... · Matt Weyland, Zhiheng Yu, Peter Ercius, Lena Fitting, Earl Kirkland Applied

David Muller

Practical STEM: More than Z Contrast

Applied Physics, Cornell University•Thickness dependence of images

•Common mistakes

•Alignment Tricks

6 months3 weeks 1 yearD. A. Muller, J. Grazul, Journal of Electron Microscopy, 50 (2001) 219.

Matt Weyland, Zhiheng Yu, Peter Ercius, Lena Fitting, Earl Kirkland

Applied Physics, Cornell University

Acknowledgements

Paul VoylesUniversity of Wisconsin, Madison

John Grazul, Mick ThomasCornell Center for Materials Research

Single atom Sensitivity:

Electron Energy Loss Spectrometer

Annular Dark Field (ADF) detector

yx

200 kV IncidentElectron Beam (∆E=1 eV)

Incr

easi

ngen

ergy

loss

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

Elastic Scattering ~ "Z contrast"

Scanning Transmission Electron Microscopy

0 0.5 1 1.

ADF Signal Er M4 Edge

Distance (nm)

3 Å

P. Voyles, D. Muller, J. Grazul, P. Citrin, H. Gossmann, Nature 416 826 (2002)U. Kaiser, D. Muller, J. Grazul, M. Kawasaki, Nature Materials, 1 102 (2002)

ReciprocityReciprocity (or STEM vs. CTEM)(or STEM vs. CTEM)CTEM STEM

Reciprocity (for zero-loss images):A hollow-cone image in CTEM an annular-dark field image in STEM.

Specimen

Illuminationangle α Collector

angle

β

Specimen

Objective Aperture

Objective Aperture

ViewingScreen Gun

Gun Detectors

However: In STEM, energy losses in the sample do not contribute to chromatic aberrations (Strong advantage for STEM in thick specimens)

David Muller 2006 5

Imaging Thick Samples at 200 kVBF-TEM BF-STEM (~2mr θc)

•Less blurring, more contrast in thick samples with STEM•No Signal in W plugs, diffraction in poly

unsuitable for tomography

Phase Contrast for Different Illumination AnglesPhase Contrast for Different Illumination Angles

• For distances larger than 1 nm, there is little phase contrast to start with.

• When the illumination angles exceeds the objective aperture,all phase contrast is suppressed!

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.1 1

Con

tras

t Tra

nsfe

r Fun

ctio

n

Spatial Frequency (1/Å)

0.5 mr

2 mr

5 mr

10, 20, 40 mr

25 Å 5 Å 2 Å10 Å(10.5 mr Objective, E0=200kV, Cs=1 mm, Scherzer Defocus)

Amplitude Contrast for Different Illumination AnglesAmplitude Contrast for Different Illumination Angles

• For distances larger than 1 nm, there is little phase contrast to start with.

• When the illumination angles exceeds the objective aperture,all contrast reversals are removed and the resolution is increased!

(10.5 mr Objective, E0=200kV, Cs=1 mm, Scherzer Defocus)

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.1 1

Am

plitu

de C

TF

0.5 mr

2 mr

5 mr

10, 20, 40 mr

25 Å 5 Å 2 Å10 Å

Spatial Frequency (1/Å)

Why Increased Resolution? Why Increased Resolution? (coherent vs. incoherent imaging)(coherent vs. incoherent imaging)

-1

-0.5

0

0.5

1

0 0.2 0.4 0.6 0.8

ADF STEMCTEMIncoherent BF

Con

tras

t Tra

nsfe

r Fun

ctio

n

k (Inverse Angstroms)

CTEM Scherzer Limit

5% CTFSNRLimit

•E0=200kV•Cs=1.0 mm•Scherzeraperture

•and defocus

( ) ( )22 /exp σϕ rr −≈Eg:

•Coherent imaging PSF is the probe wavefunction,•Incoherent imaging PSF is the square of wavefunction

( ) ( )222 /2exp σϕ rr −≈ 2σσ =′

David Muller 2006 9

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

David Muller 2006 10

WiSi40 - 40Å HfO2 on O3 Underlayer + 850C/Spike/NO (6/12/2)

8±1 Å

Si

Poly-Si

HfO2

SiO2

40±1 Å

Bright-field STEM with small collector- like conventional TEM

20 Å


Imaging Thick Samples at 200kVADF-STEM (θc>45 mr) ADF-STEM (θc>75 mr)

•No more diffraction contrast•Signal in W plug not monotonic, could be mistaken for voids•Effect reduced by increasing the collector angle


Annular Dark Field STEM at 200 kV

•Interpretable (monotonic, single valued) signal in Silicon to ~1 um depth•There is a geometric limit to the detector angles (~200-400 mr)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 1 2 3 4 5

30-120 mr50-200 mr100-400 mr

I/I0

Thickness (um)

Electrons fall outside the detector


Effect of Camera Length

1.65

1.60

1.55

1.50

Z ex

pone

nt

50403020camera length (cm)

2.5

2.0

1.5

1.0

I sb /

I Si

50403020camera length (cm)

Sb atom invisible

DP2 on-column Sb2V DP2 off-column

Channeling enhances on-column Sb intensity.

Strain Contrast at Si/SiO2 Interfaces

David Muller 2001

50 mrad 25 mrad

c-Si

SiO2

a-Si

(JEOL 2010F, 200 kV, Cs=1mm)

Strain Fields cause dechanneling (and scattering to small angles)

ADF Inner angle:

Z. Yu, D. A. Muller, and J. Silcox, J. Appl. Phys. 95, 3362 (2004).

Strain Contrast vs. Sample ThicknessStrain Contrast vs. Sample ThicknessContrast at a c-Si/-aSi is strongly depends on sample thickness

130 Åthick

340 Åthick

Strain Contrast effects at the interface:for 130 Å thick sample, ~0%; for 340 Å thick sample, 15%.

100 kV, 45 mrad ADF inner angle



Contrast from Random Strain FieldsContrast from Random Strain Fields(treated as a static Debye-Waller Factor)

No channeling No thickness dependence



Contrast from Random Strain FieldsContrast from Random Strain Fields(using frozen phonons in multislice)

Channeling Thickness dependence

LAADF HAADF



Contrast from Random Strain FieldsContrast from Random Strain Fields(using frozen phonons in multislice)

Channeling Thickness dependence


Contrast from Random Strain FieldsContrast from Random Strain Fields(treated as a static Debye-Waller Factor)



Imaging Light AtomsDechanneling contrast from the Strain Field around impurities

Si substrate

4 nm Gate Oxide

Polysilicongate

Implanted BB segregated

to the interface?

Single atom contrast is expected at 77K (Hillyard and Silcox)


1

1.5

2

-5 0 5 10LA

AD

F C

ontr

ast

Distance (nm)

La Markersubstrate

0

0.5

1

-5 0 5 10

Ti3+

La

Frac

tion

Distance (nm)

Imaging Vacancies?( grow 25 layers of SrTiO3-δ on SrTiO3)

HAADF “Z” map

LAADF “Strain” map

Thin x/s

0 5 10 15 20 25 30

Inte

nsity

(arb

. uni

ts)

Number of monolayers

RHEED

LAADF

EELS

4 nm

4 nm

5 nm

LAADF “Strain” map

Thick x/s

Detection sensitivity: 1-4 Oxygen vacancies

D. A. Muller et al Nature 430, 657-661 (2004).


Ronchigrams

• Most accurate manual method of alignment

• Easy to find the optic axis

• Easy to correct serious astigmatism

• Easy to bring the sample into focus

• Works best on an amorphous layer

• Start with the largest aperture

E. M. James, N. D. Browning, Ultramicroscopy, 78 (1999) 125-139 J. M. Cowley, Ultramicroscopy 4, 413-418.(1979)


Ronchigrams – no Cs

Lens

sampleViewing screen

(beam is at cross-over before sample)

Sample is magnified, erect



Lens

sampleViewing screen

(beam is at cross-over after sample)

Sample is magnified, inverted


Lens

Cs=0

Cs>0sample


(beam is at almost cross-over on the sample)

Almost infinite magnification


Ronchigrams with Spherical Aberration, Cs

Lens

Cs=0

Cs>0sample

For Cs>0, rays far from the axis are bent too strongly and come to a crossover before the gaussian image plane.

Almost infinite magnification,Only at small angles

Spherical Aberration

Apparent deflection at the object is proportional tothe cube of the distance off-axis within the imaging lens. Deflection towards axis is always too strong.

Phil Batson, IBM

Screen

Specimen

Shadow Map: “Ronchigram”

Objective

20 nm

Source

Ronchi, V. (1964) Forty years of history of a grating interferometer. Applied Optics 3, 437 – 450. Phil Batson, IBM

Screen

Specimen


Objective

20 nm

Source


Screen

Specimen


Objective

20 nm

Source


Screen

Specimen


Objective

20 nm

Source


Screen

Specimen


Objective

50 nm

Source


viewing screen or CCD camera

specimen

electron source

probe-forming lens

defocus

The Electron Ronchigram

Cowley, J. Elec Microsc Tech 3, 25 (1986)

u

v

uvM =

Nigel Browning, UC Davis


Effect of Cs on Ronchigram

James and Browning, Ultramicroscopy 78, 125 (1999)


Ronchigrams from Si <110>overfocused

underfocused

∆f=0 nm Scherzer focus ∆f=-100 nm ∆f=-150 nm

∆f=-200 nm ∆f=-300 nm ∆f=-350 nm

∆f=100 nm ∆f=50 nm∆f=150 nm


Two fold astigmatism Three fold astigmatism

Correcting for Astigmatism


Forming the Smallest Probe

Put aperture over area of constant phase in Ronchigram to give CBED pattern



Ronchigram focus series on a-C

This apertureIs too big


Correcting Severe Astigmatism in Ronchigrams

+y

-y

+x-x

(don’t image probe)


Ronchigrams on Crystals

Tilted On Axis (not in focus)

Ronchigrams on Crystals

TiltedIn focus overunder

More over way over


Measuring the Aperture Size(Using [110] Silicon as a reference)

Scan the beam over a small area to remove ronchigram structure

AB

Distance ABIs 4 x Bragg Angle


Measuring the Aperture Size


Reality Check(Can I see a lattice spacing)

Disks must overlap to form a lattice fringe

(more overlap, more contrast)*

000

No lattice fringes thisdirection


Balancing Spherical Aberration against the Diffraction Limit(Less diffraction with a large aperture – must be balanced against Cs)

4/34/1min 43.0 λsCd =

A more accurate wave-optical treatment, allowing less than λ/4 of phase shift across the lens gives

Minimum Spot size:

4/14

⎟⎟⎠

⎞⎜⎜⎝

⎛=

sopt C

λαOptimal aperture:

At 200 kV, λ=0.0257 Ǻ, Cs = 1.0 mm, dmin = 1.55Ǻ and αopt = 10 mradCs = 1.2 mm, dmin = 1.59Ǻ and αopt = 9.6 mrad

Cs = 0.5 mm, dmin = 1.28Ǻ and αopt = 12 mradCs = 0.6 mm, dmin = 1.34Ǻ and αopt = 11 mrad

David Muller 2006 46D. Muller, Bell Labs, 1998

Multislice simulated Annular-Dark-Field Images of Silicon [110] in a 200 kV STEM

c dba

(a) The projected potential along [110](b) The ADF image for a 2.7 Å thick crystal(c) The ADF image for a 81 Å thick crystal(d) The ADF image for a 2.7 Å thick crystal (1.6 Å information limit)

(Cs=0.5 mm, Probe forming aperture=11.9 mr, ADF inner angle=30 mr)

Note: (i) The dumbbells are visible even when the (400) spot is excluded(ii) Except the dumbbell spacing is not 1.36A, but closer to 1.6A

David Muller 2006 47S. Hillyard, PhD Thesis,Cornell University


Beam Spreading

E0=200 keV E0=20 keV

1 µm of Carbon

Electron Range (in µm):

5.10

064.0 ERρ

≈

(density ρ in g/cm3, E0 in keV)

R~ 100 µm at 200 keV


Beam Spreading

Beam Spreading ( )

0

5.1

EZt

∝

At 100 kV0.16 nm for 10 nm thick C1.8 nm for 50 nm thick C

At 300 kV

N. Zaluzec, Microscopy Today (2004)


0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50

Bea

m D

iam

eter

(A)

Thickness (A)

Beam Broadening in a-Si at 100kV

Loss of resolution, loss of apparent brightnessIncreased Apparent Source size

•Ignore for probes larger than 0.4Ǻ

How does an amorphous layer on the entrance surface degrade resolution?

•No FIB’ed samples!

Phase vs. ADF Contrast

David Muller, 2000

ADF Signal is much weaker than HR-TEM

E. J. Kirkland et al, Acta Cryst, 1987

0-200 mr20-200 mr50-200 mr

100-200 mr


Imaging a Single Antimony Atom in 4.5 nm of Silicon(the atom is 2.1 nm from the top surface)

ADF-STEMExit Wave Reconstruction

Cs = 0 mm0.75 Å information limit

Cs=0.5 mm(JEOL 2010F URP)

Multislice simulations assume a 200 kV electron beam

Sb contrast: HRTEM 0%, EWR: 10% (5% at 1.2Å) , ADF-STEM:65%

HRTEM

Cs=0.5 mm(JEOL 2010F URP)

Why do we get more signal in ADF? Channeling!


ADF in Thicker Samples

• Simple specimen transmission function model: 22~ thI ADF ⊗

• Suggests that wave amplitude is important, not phase as in conventional HRTEM

• Interaction of the fast electrons with the periodic lattice including phonons is difficult

• Numerical simulations


Probe Channelingz=0 nm

z=10 nm

z=33.0 nm

z=23.5 nm

ADF Signal tracks Probe Amplitude1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

J(z)

8006004002000z (Å)

column under beam adjacent column

5

4

3

2

1

dI /

dz

8006004002000z (Å)

dI / dz J(z) on both columns × 0.25 Å-1

simulation error

Si [110] at 300K(200 kV, Cs=1 mm)

( ) ( ) zzrtzrhIz

rADF d,,~0

0

22∫ ⊗ rr


Channeling down

1.6x10-4

1.2

0.8

0.4

0.0

dI/d

z (1

/ Å

)

8006004002000z (Å)

[110] Si multislice fit to Bloch wave fit uncertainty band amorphous Si


Signal vs Collection Angle

-0.05

0

0.05

0.1

0 50 100 150 200 250 300

θc/θ

0=4.5

θc/θ

0=2.4

θc/θ

0=1.3

dI/d

t (%

of i

ncid

ent b

eam

)

Thickness (A)

x 0.14

x .25

[011]Si, 300 kV, 9 mr probe angle

Isolated Atomsignal

Imaging Thick Cross-Sections

Gate Oxide Thickness: 20 Å

• ADF Images decay gracefully with increasing thickness

•Apparent Oxide Thickness is unchanged with thickness

•Apparent Interface Roughness increases from 1.6 to 2.7 Å rms

•“white band” develops (depends on thickness and ADF angles)

3000 Å

5500 Å

6000 Å

1 nm

Poly-Si c-SiSiO2


One Sb Atom vs. Depth

Scattering from one Sb atom ∝ Si scattering at the same depth.

30

20

10

0

dIA

DF/

dt

8642depth into sample (nm)

Sb at z=3.3 nm Si

1086420depth (nm)

5

4

3

2

dI/d

t (ar

b un

its)

Sb Si matrix

0.25

0.20

0.15

0.10

0.05

sim

ulat

ed I A

DF

0.25

0.20

0.15

0.10

0.05

sim

ulat

ed I A

DF

3210-1

position (Å)

3210-1

position (Å)

Bi Bi

Bi

(a) no Bi (b) zBi = 20 Å

(c) zBi = 342 Å (d) zBi = 750 Å Wrong columnAppears bright!

Dopants as probes of Beam Spreading

(Multislice for 75.8 nm Si in 100 kV Cs-corrected STEM)

P. M. Voyles, D. A. Muller, E. J. Kirkland, Microscopy and Microanalysis 10, 291-300 (2004).

Channeling Down Si [110]

Si Siprobe

1.00.80.60.40.20.0

ψ(z)

1000

800

600

400

200

0

z (n

m)

midpoint left column right column

• Probe doesn’t stay between atom columns -oscillates

•Almost entirely on atom columns at 100, 400Ǻ

•When on-column, scattering is large

Will reduce dumbbell contrast


Si Dumbell Contrast vs.Probe Angle

0

0.2

0.4

0.6

0.8

1

0

0.01

0.02

0.03

0.04

0.05

0 50 100 150 200 250 300 350 400

Con

tras

t

Depth (A)

10 mr

100 mr20 mr

50 mr

On-column vs Off

1.6

1.4

1.2

1.0

I Sb /

I Si

40302010

Sb depth (Å)

On-column Sb Off-column Sb


Effect of Camera Length

yx

simultaneous acquisition in

exact registration

P. M. Voyles, D. A. Muller et al, Phys. Rev. Lett. 91, 125505 (2003).


Clipping an Image is BadClipping an Image is Bad(and easy to do)(and easy to do)

x

τ

d

=Black level set too high

*

Equivalent to multiplying by square wave


Fourier Transform of a Square WaveFourier Transform of a Square Wave

x

τ

d k1/d 5/d3/d

sinc(πnτ/T)

f = 1/nτ

FT

f(t) = )tnfcos(T/n

)T/nsin(TA

TA

,,n0

53122 π

πτπτττ

∑∞

=+

FT

d1/d


Fourier Transform of a Square WaveFourier Transform of a Square Wave

x

τ

d k1/d 5/d3/d

sinc(πnτ/T)

f = 1/nτ

FT

FT

d1/d

multiplication convolution

Clipping adds extra spots To diffractogram

k1/d 5/d3/d


Original image

clipped image

Original histogram Power SpectrumCut-off at 0.3 nm

clipped histogram


Summary

• BF STEM – fake TEM

• LAADF STEM – strain contrast, single vacancy

• HAADF – depth dependent imaging of single dopants

• Check histograms to avoid clipping (extra spots)

• Ronchigrams – easier than imaging probe for align


Comparison of Brightness MeasurementsFor Cold and Thermal Field Emitters

David MullerApplied and Engineering Physics

Cornell University

• Few good measurements of Brightness.

• Need to measure or extract the source size (easy to overestimate)

• No reliable studies of Brightness vs. Field, Temperature or monochromation

Current State of the Art:


Sample Tilt in ADF-STEM

0 10 20 300

1

2

3

4

5

Tilt [mrad]

(Imax

-Imin

)/(Im

ax+I

min

)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 1 2 3 4 5 6

300 A LAADF300 A HAADF

Rel

ativ

e In

tens

ityTilt angle (degree)

300Ǻ of [011] Si200Ǻ of [001] SrTiO3

1º2º

Up to~ 5 mrad of mistilt is OK before fringe contrast is reduced

(200kV, 10 mrad)

Documents

Applied Physics, Cornell Universitymuller.research.engineering.cornell.edu/sites/WEELS/summer06/STEM... · Matt Weyland, Zhiheng Yu, Peter Ercius, Lena Fitting, Earl Kirkland Applied