Ruud Tromp

IBM T.J. Watson Research Center

Yorktown Heights, NY

Leiden University

Towards 2Towards 2λλλλλλλλ ResolutionResolution((Limits of Aberration Corrected Electron Limits of Aberration Corrected Electron

MicroscopyMicroscopy )

2λλλλ

IBM LEEM/PEEMIBM LEEM/PEEM

gun

condenser

lenses

prism

array

projector

lenses

objective

lens

sample

screen

R.M.Tromp, M. Mankos, M.C. Reuter, A.W. Ellis, M. Copel

Surface Review and Letters 5 , 1189 (1998)

LabLab--based LEEM/PEEM imaging modesbased LEEM/PEEM imaging modes

Selected Area LEED

Local Atomic Structure

200 nm

Dark field LEEM

Structure symmetry

Mirror Microscopy

Topography

Work Function

PEEM imaging

Hg light source / laser

(picosecond) LEED

Atomic Structure

PEEM-ARUPS

Electronic structure

Spectroscopy + Imaging

LEEM-EELS

Local Electronic Structure

Spectroscopy + Imaging

Bright field LEEM

Phase contrast

LEEM-IV Imaging

Local Atomic Structure

2-5 nm

Bright field LEEM

Reflectivity

Structure factor

SynchrotronSynchrotron--based PEEM imaging modesbased PEEM imaging modes

Picosecond

Resolution

Imaging

Linear Magnetic

Dichroism

Antiferromagnetism

PEEM-IV Imaging

20 nm resolution

Local chemistry

Dynamic Imaging

In-situ processing

Elemental/chemical

Cryo-PEEM

Solid State

Bio, soft matter

Localized Spectroscopy

Elemental, chemical

Magnetic, Valence

Circular Magnetic

Dichroism

Ferromagnetism

Valence Band Imaging

Surface, bulk

Topological

Biological Imaging

Organic, Inorganic

Elemental, chemical

Plasmonics

Dynamics, geometry

Recent advances in LEEM/PEEMRecent advances in LEEM/PEEM

MCP+CCD Direct Electron

Improved detector technologyImproved detector technology

(a)

(b) (c)

ARUPS ARUPS HeIHeI / / HeIIHeII

atomic atomic structurestructure

EELSEELS

PRB

IBM J. Res. Development 55 (2011) 1 Ultramicroscopy 110 (2009) 33

Physical Review B79, 121401(R) (2009) ACS Nano 4 (2010) 7073

4x resolution improvement, 10x more data

CRYOLEEM 10K CRYOLEEM 10K ESCHER ESCHER

10-300K 300-2000K

Record Resolution in Aberration Corrected Record Resolution in Aberration Corrected Low Energy Electron MicroscopyLow Energy Electron Microscopy

object uncorrected correctedimage image

70 nm

Highest resolution microscope

in the world: d = 22λ (300 keV)

Goal for LEEM: d < 2λ (5 eV)challenges:

power supplies < 0.1 ppm

vibrations, shielding

image detector

Correct bad objective lens

with equallybad electron

mirror

2009: 4 nm2010: 2 nm2011: 1.4 nm = 2.3λλλλ

2013 goal: 1.0 nm

Graphene on SiC

Ruud Tromp

Jim Hannon

Arthur Ellis

Oliver Schaff -SPECS

Weishi Wan -LBNL

V3 V2 V1

aberration aberration correction ray correction ray

diagramdiagram

electrostatic lens

magnetic lens

axial ray

field ray

sample

contrast

aperture

gun

mirror

screen

Use of double prism array:

US Patent 7348566

filter

aperture

R.M.Tromp, J.B. Hannon, A.W. Ellis, W. Wan, A. Berghaus, O. SchaffUltramicroscopy 110 (2010) 852

Aberrations of the cathode objective lens Aberrations of the cathode objective lens up to 5up to 5thth orderorder

2/7

04

2/5

03

2/5

03

2/3

03

2/3

05

2/1

03

)/(64

5

)/(8

3

)/(8

1

)/(2

1

)/(4

1

)/(

EELC

EELC

EELC

EELC

EELCC

EELCC

c

cc

c

c

cc

c

=

=

−=

−=

==

−=−=

Uniform field:

E.Bauer, Ultramicroscopy 17 (1985) 51

R.M. Tromp, W. Wan, S.M. Schramm, Ultram. 119 (2011) 33

Z=-2L -L 0

E0

V=-E/e 0

Ef = E+E0

How to measure and correct aberrations?How to measure and correct aberrations?

Not so easy…

R M Tromp. Ultramicroscopy 111 (2011) 273-81

• Aberrations of the cathode lens are energy dependent; measurement/correction at one energy is not good enough…

• Cc and C3 have different energy dependence• Aberrations contain contributions from the uniform field and from the magnetic part of the objective lens; how do we measure?

• Cc scales with M2, C3 with M4: must control magnification• Would like to automatically track the energy dependence with theelectron mirror

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●V3-V2=7000

V3-V2=0

V1=-1200

V1=-1800

-4E3

0

2E3

-2E3

Cs

(m)

-Cc (m)

◘●

V1=-1200

V1=-1800

0 10 20 30

Correlation of first and higher order propertiesCorrelation of first and higher order propertiesfocus aberrations

R.M. Tromp, J.B. Hannon, A.W. Ellis, W. Wan, A. Berghaus, O. Schaff, Ultram. 110 (2010) 852

d=

175

mm

object/image

1% error 50-100% error

Aberration map (right) directly correlated to focus map (left)Small error in focus setting gives large error in aberration constants

Mirror focusing: theory Mirror focusing: theory vsvs experimentexperiment

V1=-1800

V1=-1200

V3 V2 V1

Adjustable parameter:

V1 offset of 10 V(out of 16500, i.e. 0.06% )

Electron Mirror:Electron Mirror:

C3 = 0.3943+0.0001472C3m

C3 = C3o + C3

m/M4

1/M4 = (0.0001472)1/4

M = 9.07 (8.5, +7%)

Objective lens:Objective lens:

C3o = a + b/√E0

Track sphericalaberration:

a + b/√E0 + C3m/M4 = 0

Measurement and Correction of CMeasurement and Correction of C3 3 : : δ δ δ δ δ δ δ δ = c= c11α α α α α α α α + c+ c33αααααααα33

R.M. Tromp, J.B. Hannon, W. Wan,

Berghaus, O. Schaff, Ultramicroscopy

http://dx.doi.org/10.1016/j.ultramic.2012.07.016

Measurement and Correction of CMeasurement and Correction of Cc c :: EEff = E= E0 0 + E+ E

LEEM:change E0Ef fixed

measurement

raytracing

Uniform field (LEEM):Uniform field (LEEM):

I=I0+a√E0dI/dE0 = a/(2√E0)

Magnetic field + mirrorMagnetic field + mirror(Hg PEEM):(Hg PEEM):

dI/dE = c – s.Ccm

Correction:Correction:

dI/dE0 + dI/dE = 0

◊ Ccm = 0

+ Ccm = 5.8

□ Ccm = 10

Track chromaticaberration:

Ccm=(c+a/(2√E0))/s

+ C3m = 0

◊ C3m = -1000

□ C3m = -2000

Hg PEEME0 fixedchange E Cc

m

R.M. Tromp, J.B. Hannon, W. Wan,

Berghaus, O. Schaff, Ultramicroscopyhttp://dx.doi.org/10.1016/j.ultramic.2012.07.016

Experiments conform very closely to theoryExperiments conform very closely to theory

• Excellent agreement focusing properties <0.1%

• Cc and C3 of the electron mirror can be set quantitatively, independent of each other, and at fixed mirror focal length

• Cc and C3 of the objective lens are in good agreement with theory, and can be measured routinely with simple experimental procedures

• Electron mirror can seamlessly track Cc and C3 aberrations of objective lens as E0 is changed:

Automatic Tracking Aberration Correction (ATrAC)

ButBut…… every ointment has its flyevery ointment has its fly……

How does the resolution depend on the degree to which we correct? Does it make a big difference if we are a few percent off?How stable is the corrected state?

R. Hooke, R. Hooke, MicrographiaMicrographia, 1665, 1665

TEM Stability ITEM Stability I

J. Barthel, A. Thust, Ultramicroscopy 11 (2010) 27

Lifetime of the corrected state is just a few minutes.Enough for a focus series, but problematic for longer experiments.

TEM Stability II TEM Stability II –– TEAM ITEAM I

P. Ercius, M. Boese, Th. Duden and U. Dahmen (2012).

Operation of TEAM I in a User Environment at NCEM.

Microscopy and Microanalysis,18 (2012) pp 676-683

Intrinsic Instability of Corrected Electron OpticsIntrinsic Instability of Corrected Electron Optics

intrinsically unstable….

Image = FT-1 ( FT(object) x Contrast Transfer Function x MTF )

Object Objective lens aberrations Detector

∂δδδδ/∂C = 1/Cn/(n+1) diverges to ∞ as C 0

)2ln16

)(exp()( 2

22

ελπ qC

qE cc −= 2/1

2

/1

)2ln(24

ci

ic

Cq

qC

∝=

=

δ

πλε

65

5

43

3

2

2

6

1

4

1

2

1

)2sin()2cos(

qCqCzq

ieWi

λλλχ

πχπχπχ

++∆−=

+== 4/1

3/1 Cqr ∝=δ

6/1

5/1 Cqr ∝=δ

S.M. Schramm, S.J. van der Molen, R.M. Tromp Phys. Rev. Lett.109 (2012) 163901

Aberration correction in LEEMAberration correction in LEEM

S.M. Schramm, S.J. van der Molen, R.M. Tromp Phys. Rev. Lett. 109 (2012) 163901

∂δδδδ/∂Cc,3 diverges near corrected state

3D contrast transfer function3D contrast transfer function

positive defocus Scherzer defocus

Contrast transfer function is given by ei2πχwhere χ is the aberration function.

χ(q)=C1λq2/2+ C3λ3q4/4+C5λ5q6/6+…

Re(C

TF

)

Im(CTF)

q(nm-1)

http://dlippman.imathas.com/

Optimization ofOptimization of χ χ χ χ χ χ χ χ

0<φ<π/20<φ<π/20<φ<π/20<φ<π/2

Scherzer C3=0 Optimized C3<0

NCSI

φφφφ

S.M. Schramm, S.J. van der Molen, R.M. Tromp Phys. Rev. Lett. 109 (2012) 163901; R.M. Tromp, S.M. Schramm, Ultramicroscopy 125 (2013) 72-80

Working parameters ACWorking parameters AC--TEM, ACTEM, AC--LEEMLEEM

δδδδ/2

Further 2x resolutionimprovement is probablyimpossible.Situation for LEEM will bethe same below 1 nm.

Operating margins are razor-thin.φ φ φ φ = ππππ/4:Range of defocus < 0.3 nm∆∆∆∆C3 < 0.25 µµµµm

S.M. Schramm, S.J. van der Molen, R.M. Tromp Phys. Rev. Lett. 109 (2012) 163901; R.M. Tromp, S.M. Schramm, Ultramicroscopy 125 (2013) 72-80

π/4 ± 0.5 nm ππππ/4, ∆∆∆∆E=100 meV60 mV ripple60 mV shift

What does this mean in practice?What does this mean in practice?

instability budget

C1 and C3

Highly sensitive to: DefocusZ-driftAstigmatism Voltage fluctuationsT-variationsetc

Trade resolution Trade resolution vsvs stabilitystability……

At 0.1 nm resolution system is very stable

At < 0.05 nm resolution life becomes difficult,

and lifetime of the corrected state becomes very short.

Pick where you want to be.

The hunt for 1 nm in ACThe hunt for 1 nm in AC--LEEMLEEM

• Improve power supplies ( < 0.1 ppm)• reduction of AC ripple

• New sample stage • improved stability and shielding

• Improve acoustic/vibration isolation• improvements to pump isolation

• active damping installed

• Improve electromagnetic shielding• integrated shielding in new stage

• more µµµµ-metal

• Improve MTF of detector• Medipix detector tested (2x)

• Direct Electron detector (4x)

• Don’t lose patience

Jim HannonJim Hannon

Art EllisArt Ellis

Oliver Oliver SchaffSchaff

Andreas Andreas BerghausBerghaus

WeishiWeishi WanWan

Sebastian SchrammSebastian Schramm

Sense Jan van Sense Jan van derder MolenMolen

Robert Robert BilhornBilhorn

Liang JinLiang Jin