Studies in Surface Science and Catalysis
74
ANGLE-RESOLVED
PHOTOEMISSION
Theory and Current Applications
This Page Intentionally Left Blank
Studies in Surface Science and Catalysis
Advisory
Editors:
B.
Delmon
and
J.T.
Yates
Vol. 14
ANGLE-RESOLVED
PHOTOEMISSION
Theory
and
Current Applications
Editor
S.
D.
Kevan
Physics Department, University
of
Oregon, Eugene,
OR
97403,
USA

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V
PREFACE
The technique
of
angle-resolved photoemission
(ARP)
is at an interesting period in
its development. In the past
15
years,
a
theoretical foundation has been laid upon which
most current experiments are interpreted: conservation of parallel momentum,
approximate conservation of perpendicular momentum, broadening mechanisms, and
prediction, detection, and characterization of intrinsic and extrinsic surface states. It thus

appears that ARP can be applied in a relatively straightforward fashion to a wide variety
of
problems
of
current and standing interest
in
solid
state
and surface physics and chemistry.
However, increasingly sophisticated experiments are testing and limiting the application of
some
of
these simple concepts: many body and other final state effects, static and dynamic
disorder, theoretical treatment
of
excitation spectra.
In the same period, significant improvements in experimental and theoretical
methodology have been attained. The techniques for preparing and characterizing surfaces
and interfaces have progressed to the point where reasonably complex yet well-defined
systems can be prepared: elemental surfaces
of
all sorts, metal-metal and metal-
semiconductor interfaces, semiconductor heterojunctions, compound and alloy surfaces.
The constant improvement in computer technology and in codes for calculating electronic
structure have allowed the "routine" introduction of self-consistency, improved treatments
of exchange and correlation, and relativistic effects. The first few steps in actually
calculating the excitation spectrum of simple systems have recently been reported. Finally,
the increased availability and improved quality of synchrotron radiation sources have made
the technique more powerful, more generally applicable, and more diverse in the ever-
increasing array of sub-fields being spawned. The rate at which new storage rings and

beam lines dedicated to the production of soft x-rays are being proposed, constructed, and
commissioned suggests a very bright and busy future for the technique. This confluence of
events is allowing ARP to be applied in many laboratories around the world to a variety of
systems.
This confluence also makes the present an opportune time to produce
a
research-
level monograph on the subject.
As
yet,
no
comprehensive treatise exists. Very good
reviews of
ARP
by Plummer and Eberhardt, Himpsel, and Williams, Srivastava, and
McGovern have appeared. The several books on photoemission as a whole generally
contain but one chapter dealing with ARP. None
of
these reviews, however, comes close to
a comprehensive treatment
of
this very large and growing field. Indeed, it
is
unlikely that
vi
any one small set of authors would endeavor to write
a
monograph at the level and in the
detail the field warrants. What is needed is
a

reference book that will be of general use
both to long-time workers in the field as well as to the uninitiated graduate student just
learning how to apply the basics to their particular problem.
The first chapter provides an
introduction to the motivations, methodologies, and terminologies of the technique,
and
briefly discusses "the party line" for interpreting ARP data. The next
two
chapters discuss
in detail the physics of the photoemission process and the current understanding
of
its
precise relationship to crystalline electronic structure, primarily €or bulk, three-dimensional
states. After a brief review of the one-step, single particle theories, these chapters will
focus on the "crucial issues" which all-to-often are not adequately addressed in interpreting
experimental results. These would include, for example, the physics of quasiparticle
excitation and other many-body effects, the applicability of the local-density-
approximation-calculated electronic structures to photoemission data, and the various
contributions to linewidths and shapes. The next eight chapters discuss various well-
established and currently active experimental applications
of
the technique.
All
but
chapter
7
are focused upon measurement of intrinsic and extrinsic (i.e., adsorption-
induced) electronic states in
two
and three dimensions. Chapters

4
and
5
survey the
surface electronic structure
of
metals and semiconductors, respectively, as probed by ARP,
and its impact upon surface stability and reconstructive behavior. Chapter
6
discusses
more complex metals and metallic compounds and is included as an avenue to test simple
data analysis models. Chapters
8-10
center on the application of ARP
in
studying the
electronic and geometric structure
of
relatively simple atomic and molecular adsorption
systems. Chapter
11
discusses the somewhat more complex application to thin film
systems. Chapter
7
is the only one specifically directed toward core-level
ARP
measurements, wherein ARP can provide valuable surface structural information. All of
these subjects are quite active in various laboratories around the field. The final chapters
examine applications which are still being developed and which hold significant promise for
the future. Chapter

12
reviews the application to ferromagnetic systems, an area which has
been revolutionized by the ability to distinguish the spin
of
the excited electron at arbitrary
energy and emission angle. Chapter
13
is included to demonstrate the time-reversed
application of
ARP,
inverse photoemission, which, as
a
complement to ARP, allows the
unoccupied levels to be probed. The next chapter reviews recent efforts to apply pump-
probe techniques, using lasers as the pump,
to
study the dynamical properties of surfaces in
real time. Finally, chapter
15
discusses the most recent and perhaps most dramatic
application of ARP
to
highly correlated electronic behavior.
This is the goal
of
the current monograph.
vii
CONTENTS
Preface


v
List of Contributors

ix
Introduction

1
N.V.
Smith and
S.D.
Kevan
The Physics of Photoemission

15
J.E.
Inglesfield and
E.W.
Plummer
Quasiparticle Excitations and Photoemission

63
S.G. Louie
Surface States
on
Metals

99
S.D.
Kevan and
W.

Eberhardt
Surface States on Semiconductors

145
G.V. Hansson and R.I.G. Uhrberg
Metallic Compounds and Ordered Alloys: Carbides and Nitrides,
Applicability
of
Simple and Sophisticated Theories to More Complex Systems

213
L.I. Johansson, and C.G. Larsson
Photoelectron Diffraction

243
D.P. Woodruff
Atomic Chemisorption

291
A.
Goldmann
Molecular
Chemisorptian

319
H J.
Freund and
M.
Neumann
Metallic Films on Metallic Substrates


371
K.
Jacobi
viii
Thin
Films
on Semiconductors

435
R.D.
Bringans
Spin- and Angle-Resolved Photoemission
from
Ferromagnets

469
E. Kisker and C. Carbone
Inverse Photoemission

509
P.D.
Johnson
Multi-Photon Photoemission

553
J.
Bokor and
R.
Haight

New
Frontiers: Highly-Correlated Electronic Behavior

571
R.F.
Willis
and S.D. Kevan
Future Prospects in Angle-Resolved Photoemission

595
S.D.
Kevan
Index

601
ix
LIST
OF
CONTRIBUTORS
1)
Introduction
N.V. Smith, AT&T Bell Laboratories, 600 Mountain Ave., Murray Hill, N.J. USA 07974,
and S.D. Kevan, Physics Department, University
of
Oregon, Eugene, OR. USA 97403.
2)
The Physics
of
Photoemission
J.E.

Inglesfield, University
of
Nijmegen, Faculty
of
Science, Toernooiveld, NL-6525 ED
Nijmegen, The Netherlands, and E.W. Plummer, Department
of
Physics, David Rittenhouse
Laboratory, University
of
Pennsylvania, Philadelphia, PA. 19104-6396.
3)
Quasiparticle Excitations and Photoemission
S.G. Louie, Department
of
Physics, University
of
California, Berkeley, CA. 94720.
4)
Surface States on Metals
S.D. Kevan, Physics Department, University
of
Oregon, Eugene,
OR.
USA 97403, and
W.
Eberhardt, Institut fur Festkorperforschung, Kernforschungsanlage Julich GmbH, Postfach
1913, D-5170 Julich, FRG.
5)
Surface States

on
Semiconductors
G. Hansson and R. Uhrberg, Department
of
Physics and Measurement Technology,
Linkoping Institute
of
Technology, S-581 83 Linkoping, Sweden.
6)
L.I. Johannson, Department
of
Physics and Measurement Technology, Linkoping
University,S-58
1
83
Linkoping, Sweden; and C.G. Larsson, Department
of
Physics, Chalmers
University
f
Technology, S-41296 Goteborg, Sweden.
Metallic Compounds and Ordered Alloys
7)
Photoelectron Diffraction
D.P. Woodruff, Department
of
Physics, University
of
Wanvick, Coventry CV47AL UK.
8)

Atomic Chemisorption
A. Goldmann, Gesamthochschule Kassel, FB
18
Physik, Heinrich-Plett-Strasse 40, 3500
Kassel, FRG
9)
Molecular Chemisorption
H.J.
Freund, Lehrstuhl fur Physikalische Chemie
I,
Ruhr-Universitat Bochum, Postfach
10
2148, 4630 Bochum
1,
FRG; and M. Neumann, Fachbereich Physik, Universitat Osnabruck,
Barbarastrasse 7, 4500 Osnabruck,
FRG.
10)
K.
Jacobi, Fritz-Haber-Institut der Max-Planck Gesellshaft, Faradayweg 4-6,
D-1000
Berlin
33 FRG.
Metallic Films
on
Metallic Substrates
X
11)
Thin Films on Semiconductors
R.D. Bringans, Xerox Palo Alto Research Center, 3333 Coyote Hill Road,

Palo
Alto, Ca.
94304
12)
E.
Kisker, Institut fur Angewandte Physik, Universitat Dusseldorf, Universitatstrasse
1,4000
Dusseldorf
1,
FRG, and C. Carbone, Institut fur Festkorperforschung der
Kernforschungsanlage Julich GmbH, Postfach 1913, D-5170 Julich, FRG.
Spin- and Angle-Resolved Photoemission from Ferromagnets
13)
Inverse Photoemission
P.D. Johnson, Physics Department, Brookhaven National Laboratory, Upton, N.Y. USA
11973.
14)
Multi-Photon Photoemission
J. Bokor,
AT&T
Bell Laboratories, Crawfords Corner Road, Holmdel, N.J. USA 07733, and
R.
Haight, IBM
T.J.
Watson Research Center, P.O. Box
218,
Yorktown Heights, N.Y. USA
10598.
15)
R.F. Willis, Physics Department,

104
Davey Building, Pennsylvania State University,
University Park,
PA
16802, and
S.D.
Kevan, Physics Department, University of Oregon,
Eugene, OR. USA 97403.
New Frontiers: Highly Correlated Electronic Behavior
16)
S.D. Kevan, Physics Department, University
of
Oregon, Eugene, OR. USA 97403.
Future Prospects in Angle-Resolved Photoemission
1
Chapter
1
INTRODUCTION
N.V.
SMITH
AND S.D.
=VAN
From humble beginnings in the early
1970's,
angle-resolved photoemission
spectroscopy
(ARPES)
has become established as an indispensable tool for the
investigation of solids and their surfaces. This book represents an attempt to assemble
in

one volume an account of the large variety of work now going
on.
This opening chapter
sets the work against the larger perspectives
of
the history
of
the photoelectric effect and of
the electronic structure of condensed matter. It offers also a brief treatment
of
past and
present experimental methods, and a brief account of our current understanding.
1.
HISTORICAL
BACKGROUND
1.1
Prehistory
Interest in the angular dependence of the photoelectric effect can be traced back to
the early decades of this century. Jenkin
(1)
has written an entertaining and informative
history which covers this period, and he documents
how
a number of Nobel laureates
(W.
H.
Bragg,
C.
T.
R.

Wilson,
A.
H.
Compton,
W.
Bothe, C.
D.
Anderson and
E.
0.
Lawrence)
contributed to this topic before moving
on
to
other (and evidently more rewarding!)
endeavors. The history by Jenkin confines itself to the angular dependence
of
X-ray
photoemission. We attempt here to fill in some
of
the gaps relating to ultraviolet
photoemission and its angular dependence. Our treatment is not exhaustive, but is
intended rather to sound a few historical keynotes which resonate strongly with current
activity.
In the
1920's,
the angular dependence
of
photoemission from alkali metals was
investigated by Ives and coworkers at the Bell Telephone Laboratories

(2).
Their
apparatus
is
shown in Fig
1.
These pictures exemplify not just the delightful scientific
artwork of an earlier generation but also the two main experimental approaches still in use
today:
a
single movable electron collector, or a sectored collector. The work of Ives and
his
group was closely linked with their technological interest
in
the use of alkali-based
photocathodes in the emergent industry of television and in the possibilities
of
videotelephony. One question of physics raised in this work, however, has lost none
of
its
savor in the intervening decades, namely, the vectorial photoeffect, which
is
concerned with
the differences in emission intensity associated with the polarization of the incident
radiation.
The next landmark occurs in
1945
with the publication by Fan of a theory
of
the

bulk origin
of
the photoelectric effect (3). This paper, which does not appear
to
have had
2
F
I
b
Fig.
1
Early angle-resolved photoemission apparatus of Ives and coworkers reproduced
from Ref.
2.
The method
on
the right employs a moveable electron collector; that
on
the
left employs
a
stationary sectored collector.
much impact at the time, presented a view
of
the photoemission process contrary to the
prevailing notion that the photoelectric effect was a surface phenomenon
(4).
The
Sommerfeld model of
a

metal treats electrons confined
in
a
potential well
V(r)
of
rectangular shape. Optical excitation occurs only if
VV#O,
and this condition, in the
Sommerfeld model, occurs only at the surface.
If
we allow the existence of some atomic
structure within the well, we have
VV#O
in the interior and the existence
of a bulk
contribution to the photoelectric effect. The Fan paper treats the bulk potential
by
Fourier
synthesis, what in modern parlance we would call
a
nearly-free-electron (NFE) or
pseudopotential model. Figure
2,
reproduced from the Fan paper, shows the k-space
geometry for optical excitations within
a
hypothetical
NFE
metal. We recognize here

a
number
of
results which have subsequently been rederived by others
(5,6).
Surfaces
of
constant photon energy are planes. Surfaces of constant electron energy are spheres which
intersect these planes.
Thus
the angular distribution of photoelectrons will be about cones
(6).
3
1.2
Photoemission
as
a
Soectroscooy
The transformation of photoemission into a spectroscopy, as opposed to
an
interesting and useful physical phenomenon, took place some time in the late 1950s, or
early 1960's. The contributions of Spicer (at Radio Corporation of America, and later at
Stanford University), Apker, Taft and Phillip (General Electric) and Gobeli and Allen
ll.
V
Fig.
2
Diagram reproduced from Fig.
1
of

the 1945 paper by Fan (Ref.
3)
showing the
k-
space geometry for the bulk photoelectric effect.
(Bell Labs) are especially important. Parallel efforts were being made in Europe by Mayer
and associates (Clausthal). Some future historian
of
science might wish to note that
photoemission research in the United States appears to have been driven not
so
much by
the desire for fundamental knowledge for its
own
sake but by the imperatives
of
the
burgeoning television industry.
The key discovery in this early period was the establishment
of
the primacy of the
bulk photoelectric effect. The personal memoir of
W.
E.
Spicer on his early days at
RCA
(7)
is particularly revealing
on
this point. He was confronted at the start of his work by

a
large literature of photoemission experiments performed in ill-defined vacuum using an
interpretive approach dominated by the Sommerfeld model.
This
body
of
work he found
"basically useless". The historical turning point came with the routine attainability of
ultrahigh vacuum and the ability to prepare samples which were atomically clean and the
availability
of
bulk band structure calculations for purposes of comparison.
A
major landmark was the publication
in
1964 by Berglund and Spicer
(8)
of
photoemission energy spectra on
Cu
and Ag. These spectra displayed in a spectacular way
the edges
of
the d bands at respectively
2
eV and
4
eV below the Fermi level. The sight of
4
these spectra convinced one

of
the authors
(NVS),
then a graduate student, that he wanted
to be a photoemission spectroscopist. He was not alone in this aspiration. There followed
an
explosive effect to use photoemission in the determination of the densities of states and
other electronic properties
of
a wide variety
of
materials. The reader is referred to the
compendium by Cardona and Ley (9) for a summary of this activity up to about 1977.
In the early 1970's, photoemission began to diversify. There was
a
reawakening
in
the interest in the angular dependence of photoemission (see Section 1.3 immediately
following). The attractive features
of
synchrotron radiation were also recognized (10, 11).
Spin
asymmetry in photoemission was detected
(12).
Surface effects in photoemission,
having been in eclipse for a decade, now began to reassert themselves. Band-gap surface
states were observed on clean silicon (13, 14). Electronic states associated with adsorbed
molecules were observed (15). Even the elusive surface photoelectric effect was
unambiguously isolated (16).
1.3

Angle-resolved Dhotoemission sDectroscoDy
Photoemission work in the 1960's was almost exclusively angle-integrated.
An
exception was the work of Gobeli, Allen and Kane in 1964 (17).
In
a notably prescient
paper, Kane argued that the E(k) band structure could in principle be mapped from
angular dependent photoemission spectra (IS). This paper recognizes the indeterminacy
of
kL,
the internal perpendicular component of the electron wave vector, and contains within
it the energy-coincidence strategy for overcoming this obstacle. Ten years were to elapse
however before a band structure was actually mapped (19).
Experimental work on the angular possibilities of photoemission spectroscopy
started in earnest in the early 1970's. Using
a
sectored-collector apparatus similar to that
in Fig. 1, Gustafsson et al. (20) showed in 1971 that the photoemission from Ag(ll1) was
indeed distributed about cones of constant energy, as anticipated in the work
of
Fan (3)
and of Mahan (6). At about this time the following events occurred:
Feuerbacher and
Fitton showed that normal photoemission from W(100) was dominated by
a
surface state
just below the Fermi level
(21);
Wooten et al. demonstrated strong angular dependences in
photoemission from GaAs

(22);
Koyama and Hughey, using synchrotron radiation,
observed an angular dependence in photoemission from polycrystalline gold (23); and
Williams et al. found that the photoemission spectra from
MoS2
varied in
a
spectacular
fashion with angle of emission (24). The work of Wooten lends itself to an interesting
anecdote. At that time, he was at the Livermore Laboratory, and the underlying
motivation for his work was the need to develop better photodetectors to monitor
emissions from underground detonation of nuclear devices
(25).
The first formal demonstration of band mapping using
ARPES
was published by
Smith, Traum and DiSalvo in 1974 (19).
In
order
to
circumvent the indeterminacy of
kL
these workers performed their measurements on the two-dimensional layer-compounds
TaS2 and TaSe2 They monitored the variation in energy
E
of peaks in the photoemission
5
spectrum with polar angle
0
of

emission, and then obtained the parallel component
of
the
electron wave vector using
k
11
=
(21nE/fi~)~/~
sin
8,.
The resulting
E(k11)
dispersion curves were in good agreement with the first principles
band calculations
(26).
Equation
[l]
is now the standard algorithm in the reduction
of
angle-resolved photoemission data.
The use of synchrotron radiation to enhance the
capabilities
of
band mapping and to identify wave function symmetry using polarization
selection rules was soon established (see below). The work of this era is captured in the
compendium by Feuerbacher, Fitton and Willis
(27).
A
number
of

more mature reviews
are also available
(28-31).
Following this hesitant start, ARPES has burgeoned into
a
major industry. Activity
shows no sign of slackening. Subsequent chapters of this book represent an attempt to
organize and to summarize this large body
of
material.
2.
CURRENT
UNDERSTANDING
AND
PRACTICE
With some qualifications, there is now a general consensus on the physics of the
photoemission process and on how ARPES data should be interpreted. This has been the
subject of extensive experimental and theoretical work in the past
20
years. Indeed, these
issues were the primary focus of previous monographs and reviews of photoemission which
can be found in the literature. The modern extensions pertaining to the theoretical
foundations
of
ARPES can be found in the next
two
chapters of this book.
2.1
Photoexcitation
Drocess

(i)
Basic
Formula.
ARPES is intimately tied to investigations of the electronic
structure
of
crystalline systems. Except in the case
of
very
high photon fluences (see
Chapter
14),
the process is very well described by lowest order time-dependent
perturbation theory and thus by Fermi's Golden Rule, derived
in
Chapter
2:
J=(k/4r2)
1
I
(Qf
I
(e/2mc)(A*P
+
P.A)
I
qi)
I
6(E-Ei-hw)
i

This expresses the observed photocurrent
.I
at final energy
E
in terms of the initial and final
state many-body wave functions, respectively qi and qf, and the dipole operator of the
incident photon field. Fermi's Golden Rule provides the essence of the so-called single-
step, ultimately quantum mechanical model for photoemission. In general, the many-body
wave functions are not
known.
In order
to
understand and
to
interpret a photoemission
experiment at
a
given energy and momentum, various approximations are made. The
validity of these, described briefly below, is addressed throughout this book.
6
(ii)
IndeDendent
Darticle
awroximation.
A
common approximation in applying
[2]
is to assume that the initial and final state electronic wave functions may be approximated
as independent particle states. In this case, qi and
qf

can be written as product functions
of band states. By virtue of Bloch's theorem, these can be labelled by their energy and two-
or three-dimensional crystal momentum, depending
on
the degree of surface localization.
Since the energy and momentum
of
the final-state eiectron
is
measured, the dispersion
relation of the final-state quasiparticle dispersion relations can often be determined.
A
further approximation is commonly made that these quasiparticle dispersion relations are
related to the ground state calculated band structure. The validity of these two major
approximations is
of
central concern in the following two chapters.
The validity
of
the independent particle picture must be examined
on
a case-by-case
basis. For example, "residual" atomic effects (Cooper minima (32), Fano-like resonances
(33), shake-up structures (34) etc.) are commonly observed in photoemission spectra from
solids. These suggest
a
higher degree of electron correlation, and thus many-body effects,
than the independent particle approximation allows. One of the outstanding problems in
solid state physics, understanding the coexistence of, and interplay between, localized
electron correlation phenomena and delocalized, band-structure effects is currently also

a
major focus for ARPES (35). In condensed matter systems the importance of these effects
is significant
if
the on-site correlation energy between two electrons in
a
band is
comparable to the band width. The future of such studies is explored in Chapter
15.
One facet of ARPES in which many-body effects can never be entirely neglected is
final-state lifetime broadening (36). This damping is
of
both fundamental and practical
interest since it ultimately limits the resolution of the technique. ARPES owes its surface
sensitivity
to
the strong inelastic scattering which the final state electron experiences as it
leaves the crystal. The photoelectron is thus endowed with a finite mean-free-path and
lifetime. Moreover, photoemission is
a
final state spectroscopy which measures the energy
of the
(N-1)
particle system relative to that
of
the N-particle system. The hole states below
the Fermi level will also have a finite lifetime due to refilling
by
radiationless processes.
Both of these lifetimes are of order seconds,

so
that the loss of energy resolution due
to uncertainty broadening can be substantial.
In the spirit of Fermi liquid theory, these
effects are often treated heuristically by allowing the self-energies
of
the final state
quasiparticles to be complex (see Chapters
2
and
3).
The imaginary parts are then
inversely related to the quasiparticle lifetimes. The use of complex self-energies appended
to electron-energy-band calculations
is
not rigorous, nor is it theoretically satisfying. The
above discussion indicates that photoemission spectra cannot be accurately compared to
ground state calculations in
any
case. Recent theoretical advances are allowing
quasiparticle spectra to be calculated directly (37). These advances and their impact upon
the analysis of
ARPES
data are examined further in Chapter
3.
(iii)
Surface
Photoeffect.
The surface photoelectric effect arises when the dipole
operator in the Golden Rule is transformed into a gradient of the electrostatic potential

/
using the commutation relation between the momentum operator and the unperturbed
Hamiltonian. The difference between the bulk and surface photoeffects has become
blurred since
it
is now clear that both can exist in the same spectrum.
It
is generally
accepted that the "original" surface photoeffect which is produced by the rapid potential
variation near the surface, is most easily measurable in simple metals with very weak bulk
pseudopotential. While this was first suggested from total photoyield experiments
(16),
it
has been usefully studied more recently in simple metals using the polarization dependence
of
the photoemission cross section at photon energies near the plasma frequency
(38).
2.2
Phenomenology
The
manifold of angular parameters in
a
modern photoemission experiment is
illustrated in Fig. 3. Most important are
8,
and 4,, the polar and azimuthal angles of
electron emission relative to the sample normal and the crystal axes.
++
M
CRYSTAL

MAGNET1
ZATl
ON
Fig.
3
All
the angles. This diagram is intended to shown all the angular parameters of a
fully characterized photoemission experiment.
Other angles are
oP
and
$,,
the polar and azimuthal angles
of
photon incidence. The
degree of polarization
of
the incident radiation is also significant and is generally expressed
as a ratio between amplitudes of electric vector perpendicular (s-polarization) and
parallel (p-polarization)
to
the plane
of
incidence.
Circular or elliptical polarization
corresponds to a phase angle
A
between the
s
and p components. Finally, we recognize

8
the possibility of a spin asymmetry of the emitted photoelectrons, up or down relative to
some appropriately chosen spin-quantization direction.
No
experiment, as far
as
we are aware, has had variational control over all of these
angular and directional parameters. The typical experiment confines itself to some subset
of these angles depending
on
the particular physical phenomenon under investigation.
Indeed, the selection of subsets serves as a convenient way to categorize the area of study

band mapping, photoelectron diffraction, symmetry, spin detection and
so
on.
(i)
SamDle Orientation.
The sample in an ARPES investigation is generally a
single crystal of
known
orientation and of high surface quality. In the case of
semiconductors or layered compounds, the surface can be produced by cleavage in vacuum.
In
the case of most metals and those semiconductor surfaces not achievable by cleavage, a
nearly perfect surface may be produced by appropriate cycles of ion bombardments and
annealing, or in some cases by vapor deposition film growth. The conditions of surface
cleanliness and surface order are established using in situ Auger spectroscopy and low
energy electron diffraction (LEED). It is now routine to create ordered overlayers of
adsorbed atoms and molecules

on
these clean surfaces.
(ii) Band MaDDing.
The principal angles of concern are
8,
and de, the take-off
angles of the photoelectrons. The polar angle
8,
determines the parallel momentum
k
in
the crystal azimuth defined by
de
Herein lies the basis of the bandmapping capability of
ARPES.
This is a vast topic which
will
be pursued extensively in the following Chapters.
II
(iii) Photoelectron Diffraction.
The emphasis in photoelectron diffraction (PhD) is
on the determination of atomic structure rather than electronic structure. The basic notion
is to excite electrons out of core levels and to examine the angular distribution. The
diffraction patterns observed should, in principle, reveal the environment of the emitting
atom. The feasibility of PhD was demonstrated in
1978
(39-41).
The topic has now
reached considerable maturity, and
is

treated in Chapter
7.
A
review by Fadley is also
available
(42).
There are two basic choices of angular variable. One is to hold
8,
constant
(usually at normal emission,
8,
=
0)
and to monitor the core photoemission cross section a
function of energy
E
by exploiting the continuum nature of synchrotron radiation. The
other approach is to hold
ee
constant at some off normal
Be
P
0
position and to measure
the azimuthal (4,) dependence of the
cross
section by rotating the sample.
(iv)
Svmmetry considerations.
The direction of incidence of the photons is

specified in Fig.
3
by the angles
eP
and
$y
Of more significance is the state of polarization
of the incident beam.
If
the incident beam is linearly polarized, we may distinguish
between
s
and p polarization depending on whether the electric vector is perpendicular or
parallel to the plane of incidence.
9
The photon polarization enters into the cross section through the square of the
momentum matrix elements as indicated in
[2].
The final state $f is a plane wave at the
detector,
so
we may infer something about the angular dependence of the wave function of
the initial state
$i
by variations
of
A,
the electromagnetic vector. It should be emphasized
that a quantitative treatment is quite difficult since
A

changes from its exterior value to its
value inside the solid over
a
length scale comparable with the sampling depth of the
photoemission experiment
(43).
Many applications of
[2],
however, are qualitative, and are
concerned with identifying odd or even symmetry for the initial state wave function
(44).
(v)
SDin asymmetry.
There is a class of experiments which measure the spin-
polarization of photoemitted electrons. In such experiments, we must specify a direction of
spin quantization.
There are two basic physical origins for spin asymmetry. The first is
relativistic effects (i.e. spin-orbit interaction) whose detection requires circularly polarized
light; the appropriate direction of spin quantization is either the surface normal or the
propagation direction of the incident photons. The second is exchange (i.e. magnetic)
effects; the appropriate direction of spin quantization direction is the applied magnetic
field.
These matters are elaborated in Chapter
12.
The reader is referred also
to
the
chapters on photoemission in the books by Kirschner
(45)
and by Feder

(46).
(vi) Inverse Dhotoemission.
The early
1980's
witnessed the emergence of
angle-resolved inverse photoemission. The inherent cross section for inverse
photoemission is lower than that for forward photoemission by the ratio r
=
(A
\A
)2,
where
xe
and are respectively the wavelengths of the photoelectron and photon. In the
P
ultraviolet region, we have r- a result which explains the relatively late development
of inverse photoemission. The angular variables, however, remain unchanged except, of
course, that the directions of the electron and photon in Fig.
4
must be reversed. This topic
is treated in Chapter
13.
Other reviews (e.g. Refs.
47
and
48)
are available in the
literature.
eP
3.

MODERN
INSTRUMENTS
We offer here
a
brief general overview
of
the methods presently in use for angle
resolved photoemission spectroscopy. For a more detailed treatment the reader is referred
to the review by Leckey
(49).
Specifics will be treated where appropriate in the individual
Chapters.
3.1
Movable Analners
The workhorse of the
ARPES
industry
is
the spherical deflection analyzer
(SDA).
Other kinds of electrostatic dispersive instruments which have been used include cylindrical
mirror analyzer
(CMA),
plane mirror analyzers
(PMA),
elliptical mirror display analyzer
(EMDA),
127'
cylindrical deflection analyzer
(CDA)

and others
(see
Refs.
49
and
50).
10
The
180
SDA
is especially well adapted to angle-resolved photoemission for
a
number of
reasons. It can be easily matched
to
axial
input optics composed of cylindrical electron
lenses.
One such design by one of the authors
(SDK)
(Ref.
51)
is shown in Fig.
4.
The
four-element input optics permits the angular acceptance and energy resolution to be
adjusted by externally applied voltages.
Another attractive feature
of
the

SDA
is its
point-to-point focussing and the fact that the output focal surface is plane, which lends
itself well to parallel detection using microchannel plates.
The
SDA
is inherently angle-selective, and
a
crude angle-resolved experiment can
be done simply by tilting
a
sample
in
front
of
a
fixed
SDA.
It
is now common practice,
however,
to
mount
a
modest-sized (typically
50
mm
radius)
SDA
on

a
one-axis or two-axis
goniometer, thereby permitting considerable versatility
in
the choice
of
angles
of
emission.
Such instruments are commercially available from a number of manufacturers. These may
be regarded
as
the modern-day version of the movable collector approach of the
1920's
illustrated
in
Fig.
1.
Fig.
4
Layout
of
a spherical deflection analyzer
(SDA),
workhorse
of
the
ARPES
industry,
from

Ref.
51.
11
3.2
Multidetection
As
indicated above, the data-taking capacity
of
a SDA can be enhanced by using
a
microchannel plate
to
perform parallel detection over
a
range
of
values of the electron
energy
E.
This practice is now quite commonplace. Other workers have sought
to
exploit
the two-dimensional nature
of
microchannel plates to perform parallel detection over
two
variables. The different approaches can be categorized according to the choice of the
two
variables.
In

the so-called display analyzers the choice of variables is
8,
and
de.
An
early
such instrument, built by Rowe and coworkers
(SZ),
was an adaptation
of
a multigrid
LEED optics permitting a visual display
of
the photoemission over
a
large part of the
o,,
de
field. One can think of this as
a
modern version of the sectored-collector approach
of
the
1920's
illustrated in Fig.
1.
Such instruments are really high-pass filters for the electron
energy
E,
and the energy spectrum must be extracted by differentiation

of
the photocurrent
with respect to retarding voltage. This necessity
is
eliminated in the elliptical mirror
display analyzer
(EMDA)
perfected by Eastman and coworkers
(53).
It
consists of sets of
retarding grids (high pass filters) and reflecting grids (low pass filters) permitting the
selection of
a
narrow
AE
band pass.
For the purposes of band mapping, a more appropriate pair of variables would be
E
and
8,.
The aim of such experiments is to determine the E(se), or equivalently
E(k
11
),
dispersion relations for one or
two
high symmetry azimuths.
Thus
the azimuthal angle

be
Ba8e
Plate
U
Fig.
5
Layout of the
E,
ee-multidetecting toroidal analyzer of Riley and Leckey (Ref.
54).
12
is not
a
particularly useful choice as
a
continuous variable.
An
especially noteworthy
(E,
e,)-multidetecting instrument is the toroidal analyzer of Leckey and Riley (Refs.
49
and
54)
a section of which is shown
in
Fig.
5.
Photoelectrons are collected from the sample
over a plane containing the surface normal and brought
to

a
focus
on
a microchannel plate,
where contours of constant
E
and
ee
are respectively concentric circles and radial lines.
This
instrument is very well adapted to operation
in
the synchrotron arena, where beam
time
is
precious and there is
a
premium
on
fast data taking.
Another very noteworthy
(E,
ee)-multidetecting instrument is the magnetic
deflection instrument perfected by Uveque (Ref.
55).
It permits display
of
the E(k
11
)

band
structure
on
a
fluorescent screen in real time. Results obtained
on
the layer compound
GaSe are shown in Fig.
6.
This work symbolizes in
a
rather spectacular way the fulfillment
of
the dream expressed
25
years ago by Kane
(18)
that it should be possible to map the
energy bands of solids directly from experiment.
mrm
r
r
mk
r
km
Fig.
6
ARPES
results
on

the layer compound GaSe by Uveque Ref.
55).
Upper row
of
azimuths. dddle row: images after processing to enhance band structure effects, and
converted to (E,k
)
coordinates. Lower row: band structure diagrams corresponding to
the experimental
kimuths.
panels:
(E,
8
)
images taken in real time
on
a
fluorescent screen
6
or four different sample
13
3.3
Time-of-Flipht Methods
Time-of-flight (TOF) instruments offer an alternative to deflection instruments in
the measurement of electron energy spectra. Indeed,
a
rather early angle-resolving
photoemission instrument
built
by Bachrach, Skibowski and Brown (56) exploited the

pulsed time structure
of
synchrotron radiation to do TOF energy analysis. The TOF
instruments come into their
own
when the main aim is
to
do
time-resolved
photoemission
measurements (57).
We are now
witnessing the development (58) of photoemission instruments capable
of
TOF energy
analysis combined with two-angle multidetection.
See Chapter 14 for an elaboration of this topic.
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