Photoelectron holography = holography + photoelectron diffraction

Journalof Electron Spectrosco~ and RelatedPhemnenu, 51 (1990) 37-53 Elsevier Science Publishers B.V., Amsterdam -

Photoelectron

Holography

37

Printed in The Netherlands

= Holography

+ Photoelectron

Diffraction John

J. Barton

IBM T. J. Watson

Research

Yorktown

NY 10498

Heights,

Center

Abstract. Photoelectron holography produces three dimensional images of surface sites with atomic scale (0.5A) resolution. While experimentally identical to two angle photoelectron diffraction, photoelectron holography is a true holographic technique. The atomic resolution images can be obtained by Fourier transformation. I will review the principles of holography, focusing on the orginal work of the inventor of holography, D. Gabor, and the principles of photoelectron diffraction, discussing my own view of the important steps which brought us to our present understanding. Finally I will show how photoelectron holography partially fulfills the orginal goals of Gabor and provides the long sought direct-analysis of photoelectron diffraction for surface structure determination.

1.

HOLOGRAPHY.

Holography

commonly

uses a laser.

The laser, a coherent

illuminates

an object, but rather than recording

holography

records the interference

the reflected waves directly,

between the object waves and a reference

wave(l).

When the record - called a hologram

reference

wave, an image of the original object appears.

A hologram reference

contains

wave source,

- is re-illuminated

with the

a “whole” record of the object wave. Without

the

wave, the film will record the absolute square of the object (scat-

036%2048/90/$03.50

1990 Elsevier Science Publishera B.V.

38

tered) wave:

Whatever

the phase, d,, of the scattered

wave, it is lost in the photograph:

Biasing the recorded image with featureless $0, prevents

destruction

Reillumination

but coherent

reference

wave,

of the phase:

with the reference

wave produces

a flat background,

a real

image, a virtual image, and a small residual: Ih’& = A~[&'~0

+

A,@# + A,e-+l +

Under suitable conditions, dimensional

Ao

the second term can be isolated:

it is a fully three

image of the original object.

While lasers are often associated In fact Gabor(2) aid to electron and reconstruct character

A2

d.,i9o]

devised holography

them optically.

ratio of the optical to electron the electron microscope Unfortunately,

to create

In this application

Instead,

of lasers as an

electron

holograms

the three dimensional

the 105 magnification

wavelengths

aberrations

they are not essential.

prior to the invention

He proposed(3)

microscopy.

was not essential.

with holography,

and the potential

during the reconstruction

obtained

for correcting step were vital.

Gabor’s orginal aims were largely not met. Coherent

tron sources were difficult to obtain and few samples were adequately parent to electrons.

Furthermore

some and inflexible.

Despite these problems,

prize for holography. application

the optical reconstruction

by the

electrans-

proved cumber-

Gabor received the 1971 Nobel

The basic physical principle

he revealed has had wide

in fields where coherent sources are easier to obtain and the waves

are easier to transport,

39

Recent reviews by Lichte(4) raphy in electron

and by Tonomura(5)

microscopes.

update the use of holog-

Many books discuss holography,

Ref. 1. We shall return to examine how photoelectrons several of the problems

Gabor faced in electron

I will trace the development

of photoelectron

goal was also high resolution

structure

seemed to have no other connection

2.

PHOTOELECTRON Photoelectron

single crystal sch proposed(6) energy(7),

from

to vary with emission

scattering

complex surface structure

structure

angle(9,lO)

diffraction

groups using

dependencies

was understood

effect with great potential

problem(l1).

of individual

confirmed

to be a pho-

for aiding in the

Key among the advantages

of pho-

species using their elemental or even chemically shifted.

However, it was albo considered

LEED and no direct interpretation connection

shared by LEED, techniques

and numerical difficulties

of the measurements

photoelectron

is strong electron

treatments

to be closely related

of multiple

diffraction,

multiple

was expected.

The

and other electron

scattering.

scattering

to

The theoretical

are quite complex.

These

had been overcome for LEED and quite successful simulations

experimental

measurements

had been made.

Thus, despite

cal discussion linking photoelectron

diffraction

order technique

it was natural

scattering

A. Lieb-

is the ability to dissect a complex surface system by isolating the

core level energies.

scattering

angle and energy.

from

in 1978.

the outset photoelectron

toemission

but which

intensity

in 1974 and three experimental

experimentally

final-state

with electrons,

to holography.

polar angle(8), OI azimuthal

toelectron

a field whose main

causes core level photoemission

its existence

the phenomenon

diffraction,

First however,

DIFFRACTION.

diffraction

s&faces

can be used to solve

holography.

studies

for example

of EXAFS(lZ,ll),

theory to be adapted

Empirical

evidence

to photoelectron

also connected

of

some theoreti-

with the simpler short-range for the LEED

multiple

diffraction.

photoelectron

diffraction

to LEED.

The peaks in normal emission electron strongly

correlated

resembled

energy-dependent

with surface interplanar

the Bragg peak correlation

No EXAFS like short-range

diffraction

spacing(l3).

already explained

curves

This correlation in LEED IV curves.

order theory seemed likely to explain this layer

correlation. Progress

towards

direct analysis of photoelectron

pirically in two experimental

groups.

applied Fourier transforms work demonstrated measurement At about

Fourier

theory to simulate

numerical

allow considerable

qualitative

that

the correlation

Hussain Fourier scattering

interlayer

the same time, C. Fadley’s

work had limited

diffraction

group developed experimental

sucess, the calculations analysis.

In particular,

was a consequence

a simple plane-

data(l5).

While this

were simple enough to they were able to show spacing evident

experiemental

cross section, not a complex multiple scattering

cross-sections

in the

geometry

phenomenon.

and The

for Ni atoms used by Hussain et al peaked for backscattering,

making normal emission data respond

to atoms directly

below the emitter,

atoms whose distance from the emitter are multiples of the interlayer Thus, rather

This

spacing, G?J_.

of NPD peaks and interplanar

transforms

curves(l4).

a.na.lysis could - almost - lead to direct

of adsorbate-substrate

wave single scattering

began em-

Z. Hussain et al. in D. Shirley’s group

to energy dependent

that

diffraction

than dl, the diffraction

length difference

between

phenomenon

the direct photoemission

spacing.

was sensitive to the path path and the scattering

path. At this point the potential clear.

Developed

of the cluster

from the work of Lee(l2),

simple form analogous

scattering

approach

became

the cluster theories predicted

to EXAFS for photoelectron

diffraction,

a

at least for

single scattering:

Here I is the measured the scattering

intensity,

Fj exp(i4j)

the scattering

angle, and rj the vector from the emitter

amplitude,

to the scattering

8

41

atom. Using this form, the Shirley group was able to extract differences, dependent

Tj - Tj cos 8j by Fourier transforming experimental

diffraction

(ARPEFS)

wide energy range energy

curves at a variety of emission angles(16).

These curves came to be called Angle-Resolved Structure

the path length

to distinguish

Photoemission

Extended

Fine

them from NPD and to connect

them

with EXAFS rather than LEED. While the single scattering merical predictions scattering

were poor.

treatments

transformation.

formula,

The more sophisticated

Thus we began

tion theory( 19,20,21). are written

to extend

related

and multiple

its numultiple

the idea for Fourier

the cluster

In these formulations,

scattering

scattering

the multiple

method,

by perturba-

scattering

contri-

in the same cosine form as Eq. 1, with only a different

path length and scattering accurate

LEED-like

did not yield formulas supporting

adding curved wave corrections(l7,lS)

butions

Eq. 1, worked empirically,

factor.

This gave a theory which was numerically

and which showed that peaks in the Fourier

transform

are always

to path length differences.

The improved of the multiple

understanding

scattering

ward scattering(22,23).

of the scattering

events for electron

energies

most

above 1OOeV are for-

These forward events add no path length - Fourier

peaks for single and multiple

scattering

plitude

must be included

- multiple

also showed that

scattering

coincide - but they have large amin any electron

scattering

simulatibn( 24). The development total scattering

multiple

scattering

theory

where the

phase shift for each event can be isolated is vital to under-

standing photoelectron scattering

of an accurate

holography.

can be written

The fact that all medium energy electron

in this form (25) links photoelectron

diffraction

back to LEED as we shall see. I have omitted toelectron part$ularly

many important

diffraction,

to the development

both in theory and experiment,

germane to holography.

reviews(26,27)

contributions

to concentrate

of phoon those

Some of the other work can be found in

or the recent work of those active in the field.

42

In favorable isolated

cases, the scattering

by Fourier

transforming

path lengths for a surfaces site can be

ARPEFS

tures will fit any small set of path lengths. experiment diffraction

data,

tool of analyzing

These data are difficult to measure.

of structure

curves were required Certainly

assignments.

be made with an apparatus simultaneously(28) the experiment electron

capable

or even multiple or theory

diffraction

fits between photoelectron

Recording

points on angle or energy scans was far too slow for routine Several experimental

many struc-

Thus trial-and-error

and theory remain the primary data.

but typically

individual

structure

work.

for success in the detective

the experimental of measuring

measurement

multiple

would not justify its routine

should

emission angles

angles and energies(29,30,31).

becomes much simpler,

work

Unless

the advantages

use for structure

of photodetermina-

tion.

3.

PHOTOELECTRON Photoelectron

raphy.

HOLOGRAPHY.

holography

was conceived from an understanding

A. Ssoke proposed(32)

might be accomplished

that

Gabor’s

with photoelectrons

original

electron

Nearby

graphic reference toemitted

scattering

atoms would be the objects

wave would be the unscattered

Photoex-

coherent point

studied.

The holo-

direct propagation

of pho-

wave amplitude.

Szoke was unaware of the work on photoelectron that

holography

acting as the source.

cited electrons from atomic cores would be the monochromatic source.

of holog-

the interference

and was measurable.

effect reqnired Moreover,

veloped for photoelectron of photoelectron

holography.

electron

It proved

holography scattering

existed

theory de-

could be taken over to create a theory

From the other

gested that two angle photoelectron sure, might be reconstructed

for photoelectron

the complete

diffraction

diffraction.

diffraction

view, Szoke’s proposal patterns,

if feasible to mea-

to provide direct surface structure

is in fact the case as I will now discuss.

sug-

images. This

43

4.

PRINCIPLES

OF PHOTOELECTRON

Two steps lead to three dimensional first step is holography

HOLOGRAPHY

images from photoelectrons.

with an interal, self-referencing

second step is image synthesis,

most practically

The

electron source. The

done by computer

Fourier

transform. The holographic trons, a suitable

step requires

sample, and a electron

gram. These requirements measurements

an x-ray source to create

are identical

except that

spectrometer

the photoelec-

to measure

to those of photoelectron

the holodiffraction

a full range of angles must be measured;

I will

describe each of them in turn. Laboratory principle,

x-ray sources are adequate

but the higher intensity

sources is much prefered.

Tunability

for photoelectron

and tunability

holography

of synchrotron

in

radiation

allows control over the electron’s wave-

length via excess energy from the photoabsorption.

That is, we can control

the kinetic energy Ek by the photon energy hu in Ek = hv - Eb for the constant

core level energy, Eg, and the wavelength

the kinetic energy in electron

can be related to

volts by:

X,=J15o/EI, For example, if Ek varies from 75eVto 75OeV, X, varies from 2Ato 0.3A. The x-ray source should not be coherent. wave is coherent, and laterally

both longitudinally

(limited

by the extent

The created

core level photoelectron

(limited by the lifetime of the core hole) of the initial state orbital)(33).

any radius

from the core, the photowave

dependence

is given by the dipole selection

is a spherical

Along

wave; its angular

rules of photoabsorption.

The

coherent electron wave radiates from the emitter until the core hole is refilled. Part of the wave propagates wave for holography. can scatter

away from the surface, becoming

The remainer

off the ion core potentials

propagates

the reference

into the sample.

of the surrounding

atoms,

There it creating

44

waves. These secondary

secondary interfere

with the primary

waves can travel out of the crystal

reference wave. The resulting interference

and

pattern

is a hologram. The secondary

waves can scatter

tering adds complexity in the theoretical the emitter

both in the total number

description

are of interest,

when they scatter for any electron and spherical

as well. This repeated

of each wavelet.

electron

the great bulk of other

scattering

is not difficult to understand

intensity. and nearby

scattering

the hologram

atoms.

Holography

order, but the orientation the photoemitter

If all emitters

substrate

periodicity

position

between

scattering

samples pro-

the emitter

positions,

of emitters

to the hologram.

then

lie in differ-

An image from such

images of both sites in proportion periodicity

to

or any long range

of atoms surrounding

if a single surface site image is to result.

sample will give a completely periodicity

washed out image.

has no role in photoelectron

order is needed; few systems

without

at least

will qualify.

Note that various similar photoemitters chemical

of

record the hologram

with respect to the detector

Thus long range two-dimensional but orientational

multiple

lie in identical

does not require

must be identical

disoriented

as a product

Thus the scattering

will record that site. If some fraction

their number.

Furthermore,

Each photoelectron

function.

encodes the relative

will show superimposed

A completely

on its path.

samples.

amplitude

ent sites, both sites will contribute a hologram

Thus only a small

to the hologram(l9).

several million times to accurately

The hologram

dominates

< ZA, E > 75eV),

event) can be written

suitable

wave probability

cess must be repeated

us only

or compute.

Now we turn to describe

holgraphy,

work (&

factors for each atom encountered

the electron

atoms concern

waves rapidly decay with distance.

each wavelet (or multiple

wavelets and

Forward scattering

useful for structure

number of atoms and wavelets contribute

scattering

of scattered

Since only the few atoms near

back into the main cluster. energy

or multiple scat-

shifts can be energy resolved.

can be isolated if their core level Adsorbates

on single crystal

sub-

45

skates,

core level shifted surface species on clean crystals,

at shallow buried interfaces, atoms or molecules, for photoelectron In addition

incommensurate

and subsurface

Simultaneous

measurement

measurements.

must be at least angle and energy resolving.

of multiple

Fortunately

angles is a practical

between

The angular intensity

multipler

fitted

thresholds

mirror

projects

screen.

more than 4000 angle

and the high pass filter

onto a large channel electron

A SIT camera

to video voltage;

noise for low count rates. with a resolution

approach

of approximately

should allow holograms

preserves

The analyzer

converts

a video digitizer

each video frame and adds the binary pattern

This full pulse counting

a

U8 at NSLS. Energy selection

the ellipsoidal pattern

requirement:

already exist. I am using IBM’s

on beamline

with a phosphor

pulses for each electron

contains

such analyzers

display analyzer(28)

occurs by bandpass

buffer.

atoms in crystals are all suitable samples

of 64x64 pixels in each direction

ellipsoidal

of large

to an x-ray source and a sample, we also require an electron The spectrometer

grids.

but ordered overlayers

sites

holography.

spectrometer.

hologram

core-shifted

accepts

the light

board in a PC

in to a stored frame

the maximum

signal to

a cone of angles 80” wide

2’. Count rates around 30000 per second

to be accumulated

in fifteen minutes to an hour.

IMAGE RECONSTRUCTION

5.

Up to this point we have done n thing but rename

two angle photo-

by calling it photo lectron holography. The new physics P comes in the second stage of the holg aphic imaging, the image reconstrucelectron

tion.

diffraction

From the photoelectron

directly

analyzes

To reconstruct a reference proposed

wave.

the diffraction

diffrac : ion viewpoint, pattern

image reconstruction

for atom positions.

the stored image in a hologram

we re-illuminate

it with

The wave need not be identical

to the original.

Gabor

using light waves to reconstruct

nifing the image by 105. Such an approach

electron

holograms,

thereby

requires constructing

mag-

an optical

46

apparatus

to complete the magnification

avoid this entirely by synthesizing is cheaper, The

hologram

of image

opaque (Fig.

converging

the image numerically.

more flexible, and allows arbitrary

equations

ical surface

and to render the resulting image. I

1).

spherical

are derived

except

over

range

The

hologram

wavefield incident

chaff approximation(34),

acts

imagery

magnifications.

synthesis the

Synthetic

by imagining

of angles

contained

as a transmission

upon the sphere.

we ignore the discontinuity

a spherin the

filter

Applying

for a

the Kir-

along the boundary

of

synthetic Image Reconatnacdon

Converging Spherical Wave

/-y$$$

r:

: : : ; .

Hologrim

FIG. 1. Model for image reconstruction. Green’s theorem is applied to an enclosed sphere, opaque except over the region where the hologram can be measured. The hologram acts as a transmission filter for a converging spherical wave.

the hologram.

For a sphere fo radius R then:

,-ikR

U(R)= xX@)

V&E hologram

= 0

otherwise

Knowing the wavefield on the surface allows the wavefield in the interior be derived from Green’s theorem. U(r)

=

The result(35)

is a Fourier-like

to

integral:

--& J J x(k)e-ir’kda s

For numerical

purposes,

sums replace the integrals.

bles, k, and k,, are conjugate

to two lateral

space varibles,

third dimension

in space, z comes from a phase factor.

use, the integral

becomes

up,q(z)

=

N-l C

$e-irrirrl

N-l C

The two angle variz and y. The

When digitized

for

xm,neikrJ1-k=(n)-ky(m)ei2*qm/Nei~~pn/N

[2]

m=O n=O

where p and Q are lateral z and y indices in the image. The summation be computed

by inserting

Transform.

the N x N points of X,,,

Thus image reconstruction,

diffraction,

comes down to repeated

transforms.

into the Fast Fourier

or direct analysis of photoelectron

application

Note that the coordinates

can

of two dimensional

are refered to the holograms

Fourier optical

axis, not the sample. The

theory

of photoelectron

calculated(35) c(2x2)S/Ni( inelastic,

the hologram

diffraction one expects

being well understood(l9), for S(ls)

photoelectrons

100). The theory includes full multiple scattering, and thermal

used corresponds

effects for room temperature.

to the analyzer described

I from

curved wave,

The range of angles

above. The images, generated

by

applying Eq. 2, shown in Ref. 35, contain ellipsiodal shaped blobs, elongated along the z axis three or four times their extent for the S, each Ni nearest-neighbor nearest-neighbor demonstrates

directly

in the z and y directions,

in the first Ni layer, and the one Ni next

below the S in the second Ni layer.

that atomic resolution

be derived directly from holograms

images of surface adsorption if they can be measured.

This result sites can

6.

DISCUSSION

6.1

Resolution

The atom images in Ref. 35 are well seperated the axis through

the center of the hologram

axis (z). Roughly

the lateral resolution

in the direction

lateral to

(z and y) but extend along this

is given by

1.22a

’Ax’= Icsin (e/2) for a hologram

subtending

an angle 8 at the origin( 1). For the above example,

this works out to O.SA, certainly crystal

of apertured

for positions hologram) IAzI =

The vertical

structures.

property

respect direction

to resolve the atoms in all known

z axis resolution

optical systems.

along the optical

Integration

is poorer,

a well known

of the Debye integral(34)

axis (from the image to the center

gives a curve whose first zero is empirically

of the

given by

4 sin(0/2)

4a ksin’(8/2)

-

For the above example, common

adequate

crystal

k

this is 2.3& just adequate

structures

to the optical

’

Note that the crystal

axis so that

to distinguish

atoms in

axis can be tipped

the poor resolution

with

falls in a different

in the crystal.

It is interesting

that the theoretical

only the experimentally into the crystal

accessible

limit (at 8 = 7r) on resolution

angles outside

carries no new information,

ment of the real part of the wavefunction. wavelength

of the electron:

ment of the evanescent

resolution

the sample; the emission

a consequence

of the measure-

The limit on resolution beyond

requires

is just the

this would require measure-

waves which decay within a few wavelengths

of the

surface( 1). Of course the precision ther analysis of holographic atom images.

of the atomic

coordinates

images will greatly

obtainable

from fur-

exceed the resolution

of the

This precision will meet or exceed that available from present

49

angle dependent electron

photoelectron

holography

separation

diffraction

techniques,

has many more angle measurements.

of atom images implies that

analysis should be feasible to further any surface structure toelectron

simply because photo-

technique

holography

more extensive

Furthermore, multiple

reduce uncertainty.

scattering

The accuracy

is difficult to assess; properly

should preform

the

analyzed,

similar to other photoelectron

of

phobased

techniques.

6.2

Fourier Transformation

The lateral

resolution

the hologram. inate

Omitting

any z resolution

Astronomers a parabolic

depends

while retaining

reflection

telescopy.

The extreme

structure

scattering

has no mysterious

Diffraction

(APD)(iG).

of the We

to give projections

of the

There is no t information

in the

or fundamental

holography.

form peaks at positions in r space conjugate

to k. The multiple scattering

impact

upon the

The imaging Fourier trans-

to k. In other words, search the

formula for terms like exp(ik-r,):

terms in the photoelectron

the peaks will occur at r,. All

multiple scattering

expression

have rj conjugate

terms are imaged at the last atom in the event

chain, the atom just preceeding

the waves exit from the crystal.

atom image will be built up flom numerous contributes

at the center

Scattering

images derived from photoelectron

theoretical

in z and y.

case of one pixel around

Photoelectron

onto a plane.

elim-

phase terms of APD.

Multiple

Multiple

much of the resolution

APD can be Fourier Transformed

three dimensional

6.3

will completely

use this fact when they place their detector

that

geometrical

to first order only on the outer ring of

the central region altogether

edge is the same as Azimuthal conclude

of APD.

scattering

Thus each

events and every event

to one and only one atom.

Slight shifts between the positions for the events contributing

to an atom

50

image lead to a blurring the range of scattering

of the image. This shift is caused by differences in angles measured

for each event. This blurring can be

eliminated

by filtering out the multiple scattering.

holograms

for a range of wavenumbers

The phase of each scattering

To do this, a collection of

must be measured

event oscillates through

and reconstructed.

this series according to

the length of its path in the solid. The series of images are themselves Fourier transformed

with respect to electron wavenumber

analysis(l6).

The resulting four dimensional

only the single scattering resolution, additional

6.4

space can be rearranged

events remain.

both from the elimination

There

of multiple

Photoelectron damental

holography

origin of complexity

is for x-ray diffraction.

also be improved

scattering

and from the

of LEED.

can also provide insight into LEED. The funin LEED is loss of phase information,

&arching

the theoretical

ten in the same fashion as for photoelectron that the imaging Fourier transform tron hologram-like difference

transform

features,

single-scattering

yielding

photoelectron

nets. Applying the wavenum-

above for photoelectron from triple

a Patterson-like‘ holography

holography

will

and higher multiple

map superimposed

upon the

like image from each atom in the

angle might allow another

single and double scattering.

information

see Ref. 25, shows

scattering,

two dimensional

as proposed

unit cell. Varying the incident

ple scattering,

for LEED writ-

of LEED will show the sum of photoelec-

the single and double scattering

scattering

expression

just as it

images from all atoms in the unit cell and peaks for every

between individual

ber Fourier

seperate

should

so that

Fourier summation.

Fourier Transforms

seperate

in the manner of ARPEFS

transformation

to

While this will eliminate

the multi-

no direct images will result from this processing:

the phase

is missing from LEED.

51

Gabor’s Goal.

6.5

Photoelectron

holography

solves several

of Gabor’s

original

problems.

The electron source is highly coherent.

The sample is semitransparent

electrons,

are so widely used in surface studies.

the precise reason electrons

And the computer-aided physical optics.

image reconstruction

Only the conjugate

to the

is a vast improvement

image problem

remains,

and it too may

yield to numerical

treatments

the reconstruction.

Our samples are not those that Gabor envisioned,

photoelectron 8.6

holography

if atom scattering

over

physics is considered

in but

comes close to his original aims.

Experimental Progress. Many practical

issues must be resolved

holography.

I have re-built

tranmission,

judged

started

our two-dimensional

by the spectrum

no serious mid-frequency

structure

to test the video/computer

ble of manipulating

before

display

of background

system.

photoelectron

analyzer

and the

photoemission,

now. Exploratory

the large amount

z) and four (add Ic) dimensional

applying

experiments

New computer

shows

have been

equipment

capa-

of two (Ic, and k,), three (CC,y, and

data are being installed.

Software for this

complex data analysis is under development. ‘7.

CONCLUSION. The deep theoretical

phy provides

fertile

based upon

electron

measurements dimensional

base of both photoelectron

ground

to develop

scattering.

requires

diffraction

new ideas for structure

The new emphasis

some additional

and hologra-

experimental

images of surface adsorption

techniques

on multidimensional development.

Three

sites is within reach.

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