The electronic structure of solids studied using angle resolved photoemission spectroscopy

Prof. $o//d,~t Ot¢,',a.Vol. 21, pp. 49-131, 1991 Pdated in Gtr.at Ikitaia. An r i g ~ rein'red.

0079-6786/91 $0.00 + .50 ~ 1992 Pea~amonPt'eaepic

THE ELECTRONIC STRUCTURE OF SOLIDS STUDIED USING ANGLE RESOLVED PHOTOEMISSION SPECTROSCOPY K e v i n E. Smith* and Stephen D. Kevan'~" *Department of Physics, Boston University, Boston, MA 02215, U.S.A. tDepartment of Physics, University of Oregon, Eugene, OR 97403, U.S.A.

1. INTRODUCTION

In the past two decades, photoelectron spectroscopy has emerged as an indispensable tool for studying the electronic properties of solids and their surfaces. 1'2 This is because it provides the most direct and complete method of measuring all the occupied electronic states in a solid, both core and valence. This review focuses upon angle-resolved photoemission (ARP),3"5 a variant which has proven particularly useful in studying the valence electronic structure of crystalline solids since it provides the only method of directly measuring valence band dispersion relations. For a student of solid state physics ARP is often quite captivating, since it brings to life the simple one-electron models for the electronic structure of crystals. The aficionados stay involved because of the breadth of possible applications and the multitude of interesting physical problems to which ARP can be applied. ARP provides unique information about the occupied electronic states and bonding in solids.

The

application of ARP to understand electronic structure and its impact upon bonding is at the heart of this review. We have endeavored to write a topic-oriented rather than a technique-oriented review. Apart from a brief tutorial in the next few pages which covers enough basics to get started, the phenomenology of ARP is introduced slowly and by way of example as the need arises. In this way, the application of the technique to various problems can be easily understood. Our review is by no means complete; a more exhaustive survey will soon appear.6 Rather, we want to discuss the application of ARP to a few current problems in solid state physics and chemistry which will continue to be important in the future: the interplay between localized and delocalized electronic phenomena, 7'8 the influence of electron correlation on one-electron theory, and the interactions between high energy and low energy phenomena in solids, to name a few. A closely related technique, angle-resolved inverse photoemission, provides complementary information about the unoccupied electronic manifold. Inverse photoemission has been adequately reviewed recently,9'10 and we make no systematic attempt to include discussion of it here. ARP can be applied to a large variety of systems, including adsorbate or thin film covered metals and semiconductors (and even insulators in some cases). It provides information most easily about two-dimensional (2D) or quasi-two-dimensional electronic states localized at surfaces or associated with ultrathin films, but it has also been successfully applied to many bulk, three dimensional (3D) systems. Our own prejudice toward 2D surface states may be apparent from the choice of material to be included, but we have discussed several 3D systems as well. We have minimized the discussion of chemisorption or adsorbate systems except when the phenomena involved are germane to our subject. The review addresses these issues in the following fashion. In the remainder of this section, we review the JPSSC 21:2-A

49

50

K.E. Smithand S.D. Kevan

basic phenomenology of ARP. We discuss briefly what it measures, and how the experiments are undertaken. Section 2 discusses how ARP .can be applied to understand electronic structure in a variety of simple bulk and surface systems. These range from free-electron metals through noble and transition metals to semiconductors and compounds. Section 3 is concerned with how ARP can be applied to help understand the interaction between electronic excitations and other low-energy phenomena such as reconstruction and lattice vibrations. Sections 4 and 5 discuss in more detail the role of electron correlation in electronic structure, first in 3d transition metals and later in narrow band compounds, and how ARP can be applied to these interesting systems. Finally, Section 6 summaxizes out thoughts concerning the current status of the technique and about its future prospects.

A. Angle-Resolved Photoemission Phenomenology. Angle-resolved photoemission spectroscopy is now a well-established technique which has been applied to a variety of systems. The procedures for carrying out an experiment and for analyzing the results have been described in several previous reviews.3"5 For completeness, we outline these briefly in the present section. In a typical ARP experiment, a quasi-monochromatic beam of vacuum ultraviolet or soft x-ray photons is directed at a crystalline sample, and the energy spectrum of photoelectrons emitted in a given direction is measured. It is conceptually viewed as a spectroscopy in which a photon is destroyed, thereby transferring its energy (and momentum) to the photoelectron. In this way, one invokes energy conservation through application of the Einstein relation:

EK = "~c0- E B

(1.1)

where EK is the measured kinetic energy of the photoelectron in vacuum, '~co is the photon energy, and EB is the binding energy of the electron inside the material. In general, the true binding energy relative to the vacuum level is not measured. Instead, the binding energy relative to some more convenient reference level (e.g, the Fermi level, EF, in metallic samples) is directly determined from the experimental spectra. An example is given in Fig. 1.1, which shows ARP spectra collected from atomically clean and oxygencontaminated Cu(111) surfaces at a photon energy of 70 eV. 11 In these spectra only electrons emitted along the surface normal were collected. The horizontal axis plots the binding energy relative to the Fermi level, i.e., the zero of binding energy corresponds to electrons at EF inside the solid. For metals, this a convenient procedure since the Fermi level is physically more important than the vacuum level and is also clearly visible in essentially all ARP spectra from metals. The spectra in Fig. 1.1 exhibit a substantial background which increases at higher binding energy (i.e., lower kinetic energy), a feature commonly observed in all condensed phase photoelectron spectra.

The background arises from relatively strong inelastic scattering of low energy (i.e., 5-1000 eV)

electrons. 12 This same scattering is ultimately the source of the surface sensitivity of photoemission. It results in a sampling depth of only 5-10 A; electrons excited deeper in the solid will have suffered an inelastic scattering event before escaping, thereby losing energy and momentum information. In this sense, ARP is primarily a surface technique, although it can sample the tails of bulk states reflecting from the surface as well, thereby providing useful bulk information. Aside from this extrinsic (and often annoying) background, the spectra in Fig. 1.1 resemble qualitatively the bulk copper density-of-states (DOS). There is a broad region of low photoemission intensity loosely derived from the 4s-4p band, and some more intense features between 2 and 5 eV binding energy associated with the 3d

ARP Studiesof ElectronicStructureof Solids ,

I

51 .,

1

Cu (111) ~ c o . 7 0 eV

s3

a)

e.o*

I I I

clean

'

$3 I 8

1 6 BINDING

ib)

Si i I 4 2 ENERGY (eV)

, Ef,0

Fig. 1.1, Photoemission spectra from clean C u ( l l l ) and from C u ( l l l ) exposed to 1200 L 02 (1 L = 1 Langmuir = 1 x 10-6 Torr Sec). The spectra were collected at normal emission (k I = 0) at a photon energy of 70 eV. The lower curve is the difference between the spectra obtained from the clean and 0 2 exposed surfaces. (Ref. 11). Reprintedwith permission.

bands. Closer examination, however, reveals more structure in the spectra than observed in the calculated bulk density of states. There is a sharp feature on the clean surface near EF which lies within the broad sp-band. Moreover, there are several peaks in the d-band which do not have counterparts in the bulk DOS. Finally, the spectrum of the oxygen-contaminated surface exhibits marked changes from that of the clean. This sensitivity of the ARP spectrum to the adsorption of gases demonstrates the surface sensitivity of the technique and also provides a useful test of surface vs. bulk character of the states being sampled, as explained further below. The deviations from the bulk density of states displayed in these spectra result from the momentum resolution inherent in ARP: essentially only states over a narrow range of momenta are sampled. The simplest view holds that the 3D crystal momentum of the electron is conserved in the photoemission process:

k i = kf + G

(1.2)

where k I and kf are the initial and final momenta of the electron and G is a reciprocal lattice vector. To lowest order, the ARP experimental arrangement measures the final momentum vector, with a length determined roughly by the final kinetic energy and a direction determined roughly by the emission angles relative to the crystalline axes. The initial momenta sampled are then determined by Eq. 1.2. Thus ARP spectra generally contain far more information than just the bulk DOS. The aforementioned surface sensitivity of photoemission implies that this simple view of momentum

52

K.E. Smithand S.D. Kevan

conservation cannot be strictly true. The uncertainty principle requires the finite sampling depth to limit the momentum resolution of the technique normal to the surface. Thus the perpendicular momentum, k±, is only approximately conserved. Eq. 1.2 is only approximately valid, and then only inside the crystal. Upon exiting the crystal, absolute knowledge of k± is lost. However, bulk 3D information can be recovered by making some assumptions about the final state. Such procedures have been worked out and are explained more fully elsewhere and in the next section. 3"5'13"16 The component of crystal momentum parallel to the surface, k I, remains a conserved quantity:

k~,I = kl, f + G a

(1.3)

This explains the statement in the previous section that ARP is most easily applied to 2D states, since in these systems k I is the only good quantum number.

B. Quasiparticle Dispersion Relations An ARP experiment often involves sweeping the two- or three-dimensional final state momentum vector by varying one or more of the experimental parameters at one's disposal. Invoking Eq. 1.1 and either Eq. 1.2 or Eq. 1.3, one thereby systematically determines a valence band dispersion relation along a particular direction or contour in 2- or 3-dimensional momentum space. One can change the kinetic energy and thus the final momentum by varying the photon energy, or alternatively one can sweep the direction of the emitted electron's momentum vector relative to the crystal. An example of the former is given in Fig. 1.2 for the clean Cu(111) surface. 11 This gives ARP spectra, again collected for emission normal to the surface, as a function of photon energy. These spectra exhibit one of the prime benefits of utilizing radiation from a synchrotron to excite the spectra, 17"2° that is, the ability to tune the photon energy so that the length of the final momentum vector may be systematically varied while holding its direction constant. Dispersion in the valence bands is clearly evident, since the binding energies of various features change as the momentum is swept. In this way, an ARP experiment brings to life the simple concepts of well-defined bands in crystalline materials. The bulk features in the spectra in Fig. 1.2 can be analyzed with a good deal of success using the simplest possible ideas. 11'21'22 In particular, we suppose that initial state electrons undergo a direct, 3D momentum conserving transition into a final state band which follows a free-electron dispersion relation. We set the zero of energy for the final state (Eo) at the bottom of the bulk valence bands. This supposition is supported by the observation that the final state electron is typically at high energy relative to the spatial variation of the underlying lattice potential, and thus will behave "freely", as a first approximation.

In the case of emission normal to the

surface plane, the final momentum parallel to the surface is, by default, zero. The final momentum vector lies along the F --->L line of the bulk Brillouin zone, i.e., the [111] crystalline axis. If the energies are expressed in eV, the length of k t (in/~-1) is given by Ikll = 0.512~/hv - Em- Eo

(1.4)

The electronic energies are measured relative to a common reference level, normally EF. We assume that the dominant process involves a reciprocal lattice vector parallel to the surface normal, and Eq. 1.2 implies that the initial state momentum can be reduced to a value in the first Brillouin zone along the [111] axis. If this is the case, then the photoemitted electron is said to be in the primary Mahan cone;23"25 this cone is analogous to the specular

ARP Studies of Electronic Structure of Solids

53

e~J~ 'p*°° ' v F4

{~[4

t I l 1 J 8 6 4 Bind,ng Energy (eV)

Fig. 1.2. Photoemission spectra of clean Cu(111) at normal emission as a function of photon energy. Notice the systematic spectra variations, indicative of the momentum resolution of the technique. (Ref. 11). Reprinted with permission.

beam in low energy electron diffraction (LEED). Umklapp processes (or secondary Mahan cones), for which some other reciprocal lattice vector is invoked are also possible, but are often (though not always) weak. 26 They correspond to non-specular LEED beams. In this way each feature in each spectrum can be assigned a binding energy and an initial momentum, and valence band dispersion relations can be determined. The result, given in Fig. 1.3 for all three low index copper surfaces, has features which are in striking accord with calculated band structures. 28"30 Various improved techniques for determining the momentum normal to the surface have been developed, and even more reliable dispersion relations determined.31'32 It is important to realize that photoemission intrinsically measures the energy of an excited, quasiparticle state. That is, the binding energy plotted on the horizontal axes of Figs. 1.1 and 1.2 refers to the difference in energy between an N-particle ground state and an N-l-particle excited state. Thus, the experimental dispersion relations in Fig. 1.3 are more appropriately called quasiparticle dispersion relations, and they should not be directly compared to a ground state band calculation. This is often viewed as a weakness of the ARP technique. However, essentially all physical measurements, including those pertaining to solids and surfaces, require some excitation to occur. Thus the experimental bands in Fig. 1.3 have a direct relation, for example, to the UV-visible optical properties of copper, while a first-principles calculated band structure does not.

This issue will be further

investigated in the next section where some recent improvements in computational techniques will be discussed. Another manifestation of ARP measuring an excited state is that the resolution of the technique is often

54

K.E. Smithand S.D.Kevan (.v)

,~,

0

~

,o

2o

t

I

I

,o

I

I

6o I

I

8o ~

t

J

. ~A*~A~,~

e2 k

3o ["

* * • a ~IOAO* °

\ "

i

I

S

....... •

Sl°'°°amleeeeeeem~le~l

_,,,.:?x': 41

2 ................ J

' ~

~=

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o

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o

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.~.

-8

.

I;I

,o -I0

2~ I

3~

1:5

1';

'

6'o

'

8o

'

I

2 kj. (2T~/a)

Fig. 1.3. Experimentally determined bulk copper bands along the [I1 I] crystallinedirection,derived from the spectra in Fig. 1.1 and using the analysis technique discussed in the text. Data points marked • are from Ref. 27, all other data are from Ref. 11, and the solid curves give the calculated bands from Ref. 28. (Ref. 11). Reprinted with permission.

limited by intrinsic decay lifetimes for the final state hole and photoelectron. 27'3335 This can be a significant limitation. These lifetimes can be as short as 10"14 - 10"15 seconds, implying energetic lifetime broadening on the order of 1 eV. The individual spectral features in Figs. 1.1 and 1.2 exhibit this intrinsic width. As a general rule, features near the Fermi level are energetically narrower due to the increased lifetime of the photohole state predicted by Fermi liquid theory. 36 The hole state is filled by radiationless Auger-like processes, the density-ofstates for which vanishes at EF. When ARP spectra are reduced to dispersion curves as in Fig. 1.3, the impact of these lifetime effects is lost since the points actually are determined by estimating the centroid of a particular feature.

C. Surface and Bulk Electronic Structure•

Closer examination of the two spectra in Fig. 1.1 indicates that three of the features observed in the cleansurface spectrum, labelled $1, $2, and $3, are significantly reduced in intensity on the oxygen contaminated surface relative to other features. In some sense, the electronic levels giving rise to these features interact more strongly with the oxygen than those associated with the other features.

This so-called "crud test" gives qualitative

information about the degree of surface-localization of the initial state wave function. While by no means proof, the sensitivity of these features to contamination suggests that they arise from intrinsic surface states. These surface states can be viewed as defect states associated with the termination of the bulk crystal.

They are

intrinsically two dimensional in nature, and are located energetically in a projected band gap of the bulk band structure.3-5,37,38 We explain these concepts more fully by describing the state S1 in greater detail. This was one of the f'trst surface states ever detected on a metal surface, and is currently one of the best described by both experiment and

ARP Studies of ElectronicStructureof Solids

55

theory. 39 Consider the result of projecting the bulk band structure along lines parallel to the surface normal, that is, parallel to the [111] axis. The parallel momentum is then equal to the distance in k-space between the [111] axis and a given projected line. Projection of the [111] axis itself corresponds to k| -- 0. This is the F symmetry point of the surface Brillouin zone. In Fig. 1.3 a gap appears at the L-point of the bulk copper band structure along the [111] axis extending from roughly 1 eV below EF to 4 eV above. Thus, while there is no absolute gap in the copper bands as in the case of a semiconductor, there is a "projected gap" atF-. An absolute gap would preclude an electron with an energy in the gap from entering a perfect crystal regardless of its momentum. The existence of this projected gap at F in copper is less stringent: it precludes an electron with an energy in the gap and with zero parallel momentum from propagating inside crystal. Another way to say this is that the crystal momentum normal to the surface in this energy range is complex. Thus, the wave function in an infinite crystal cannot be normalized since the amplitude of its oscillation increases exponentially in one direction. Near a surface, however, it is possible that such an oscillatory exponentially increasing wave function could be matched outside the surface to an appropriate decaying wave function located energetically below the vacuum barrier. In this case, an intrinsic, two-dimensional surface electron state can and often does exist. This is the accepted origin of feature $1 in Fig. 1.1. Such surface states provide a useful probe of surfaces in general, since their spatial localization implies that they are very sensitive to the details of the bulk termination at the surface. 40 In this way they have proven invaluable in checking the accuracy of first-principles calculations of surface electronic structure. Moreover, they are prototypical two-dimensional states and thus should exhibit some of the remarkable phenomena observed in other low-dimensional systems in the past. 4t Over the past 10-15 years, surface states have been observed on most low index elemental metal and semiconductor surfaces. 42 We close this subsection with a discussion of the dispersion relation for the state $1, since this provides a few additional concepts to be used in the remainder of the review. Firstly, note in Fig. 1.2 that the apparent binding energy of $1 does not depend upon the photon energy. This is to be expected, since, given that $1 is a surface state, its energy depends only upon the parallel momentum. All the spectra in this figure were collected at normal emission, so kl is always zero. Indeed, the lack of dispersion with normal momentum provides an additional demonstration that a given spectral features does arise from a 2D surface state. The dispersion relation parallel to the surface for $1 has been determined by several different groups. 43"45 The spectra from the highest energy and momentum resolution ARP study,45 presented in Fig. 1.4, demonstrate in spectacular fashion the parabolic dispersion of a band about a symmetry point, in this case F . These spectra are similar to those in Figs. 1.1 and 1.2, except that photons from a fixed-frequency resonance lamp rather than synchrotron radiation were employed so that the final momentum is varied by changing the polar emission angle ®. The binding energy scale is also much expanded relative to Figs. 1.1 and 1.2, and focuses upon the region near EF where $1 is observed. The feature $1 is seen to be doubled, since the argon resonance lamp actually emits two closely spaced photon energies. The magnitude of the parallel momentum is directly related to O through the simple kinematic relationship which assumes specular transmission through the surface barrier: I k l l . 0.512 ~ x Sin(O)

(1.5)

The kinetic energy is measured relative to the vacuum level. The vector components of k I may be determined if the azimuthal emission angle is known. Symmetrical, parabolic dispersion about k| = 0 is clearly visible in Fig. 1.4. The effective mass of the surface band has been observed to be isotropic in this case, and to have a magnitude 0.42 times the free electron mass. These results sound very much like the simple pseudopotential model for electronic structure. Indeed, the properties of this state can be adequately described using a simple extension

56

K.E. Smithand S.D. Kevan

i

i

l

I

l

i

i

i

cu(lll)

~ . #

e"

h~,lt.8 ev

8.

-

~

÷.5o

-3.5* -5.5"

BINDING ENERGY(ev)

Fig. 1.4. ARP spectra of the Cu(l l 1) surface state located near the Fermi level and centered in the surface Brillouin zone. Note the essentially parabolic dispersion about normal emission. (Ref. 45). Reprinted with permission. of the pseudopotential model for bulk band structure, using as input just one Fourier coefficient for the lattice potential, the work function, and a two plane wave basis set.46"48 Finally, we note that the spectra in Fig. 1.4 imply the existence of a well-defined Fermi surface. The disappearance of the S1 feature at the larger emission angles occurs because the dispersion relation lies above EF so that the initial state is unoccupied. If the dispersion relation is extrapolated to EF, a Fermi wave vector of kF = 0.21 ,~-1 is derived. The azimuthaUy isotropic dispersion relation implies that the 2D Fermi contour is simply a circle of radius kF. The relationship of such a surface Fermi contour to the bulk Fermi surface will be of great interest in the following sections. Recall that the Fermi surfaces of the noble metals are nearly spherical, with the exception that they contact the hexagonal faces of the face-centered cubic Brillouin zone.49 Lines parallel to and in the vicinity of the bulk [111] axis will thus not intersect the bulk Femai surface. Thus there is a projected gap in the Fermi surface. This is shown at the top of Fig. 1.5 which shows graphically how such a projection works for several different low index noble metal surfaces in the FLUX mirror plane of the FCC Brillouin zone.50 The radius of the circular "neck" formed by the intersection of the copper Fermi surface and the Brillouin zone boundary is 0.24 ~-1 as shown on the lower right of Fig. 1.5. The surface Fermi contour exists entirely within the gap in the projected bulk Fermi surface. Fig. 1.5 also shows how this Femai surface neck projects onto other low index surface, and corresponding states have been observed in those cases as well.

D. ARP Spectral Intensities.

While the absolute intensity (or cross section) for a particular ARP spectral feature is normally not of much

AR.P Studies of Electronic Structure of Solids

57

/ p [1/121

3o Bz

/' 11121

I

---

Ly

Bz

.:

i yL-'~

,

~,

I

Y (11U, LU-I~/

0

coo~} (100) 2D BZ

I

7,

8z

2

kN(~_l)

Fig. 1.5. Projection of the "neck" of the noble metal Fermi surface and bulk Brillouin zone onto various low index surface Brillouin zones. Projected gaps at the Fermi level are shaded. (Dimensions shown are for Au). (Ref. 50). Reprinted with permission. interest, the intensity of one feature relative to another or to itself under different experimental conditions can and does provide very useful information. The starting point for discussing ARP intensities is Fermi's Golden Rule,:z4,25~sl which expresses the photocurrent j in terms of initial and final state wave function (Wi and elf) in the dipole approximation:

j(kf) = (e/2mc)(~k/4x 2) Ei I I ~ 5(Ef- E i - %(o)

(1.6)

A is the vector potential of the incident light, and P is the electronic momentum operator. Useful relative intensity variations can arise in three distinct ways: 1) solid state structure factor effects, 2) symmetry or polarization effects, and 3) residual atomic or molecular cross section variations. We now briefly discuss each of these phenomena.

I. Structure Factor Derived Intensity Variations. The dramatic variation in the relative intensity of feature S1 in Fig. 1.2 is an excellent example of the first of these effects. The origin of the variation is conceptually straightforward. The surface state wave function in this case is partially delocalized, having an evanescent decay length of -5,/~. This reflects the imaginary part of the momentum normal to the surface mentioned above. The wave function oscillates as it decays, and the real part of k± is given by the position of the gap in the 3D band structure (the L-point in this case). The emission intensity is approximately given by a coherent superposition of amplitudes emitted by the various lobes of the surface state wave function. When these are in (out of) phase, the intensity is maximized (minimized). The relative phase of these wavelets is given by the product of the final state momentum normal to the surface (determined by the photon energy) and the lattice constant normal to the surface.52 We thus anticipate and observe that the surface state emission intensity will oscillate as a function of photon energy.

Better models for these oscillations,53 the best of which is based upon geometric structure

factors,54 have been developed which provide a numerical estimate of the surface state evanescent decay length.

58 It

K.E. Smithand S.D. Kevan

Symmetry and Polarization Effects.

The matrix element in Eq. 1.6 can change in magnitude dramatically by

varying the orientation of the vector potential A relative to the crystalline axes. 3"5'55"57 The most obvious way this can happen is through a symmetry effect. Suppose for simplicity that photoelectrons are detected in a mirror symmetry plane. The initial state and the final state must then be either symmetric or antisymmetrie upon reflection. In an ARP experiment, the final state must always be symmetric, since if it were antisymmetric, there would be a node located in the mirror plane and no photocurrent could be detected. The matrix element will be non-zero if the product of the initial state symmetry and that of the vector potential is non-zero. For example, if the initial state is odd, the feature will be visible if the vector potential has a component perpendicular to the mirror plane. If the vector potential lies within the mirror plane, the feature will vanish. |

I

hc: I

Cu (001)

I

i

1I,cool I

e-

l

--

p- poloriz

IJe

5 4 3 2 I Binding energy (eV)

EF

Fig. 1.6. ARP spectra of a d-like surface state on Cu(001), labeled peak A, located near the M symmetry point of the surface Brillouin zone. The two spectra were collected using odd (upper) and even (lower) polarization. The disappearance of the surface state from the lower spectrum demonstrates that its wave function is of odd mirror plane symmetry. (Ref. 58). Reprinted with permission.

This behavior has proven very useful in determining the symmetry of the state which gives rise to particular spectral features. An example is given in Fig. 1.6, which shows two spectra of Cu(001), collected in the (100) mirror plane, with even and odd polarization. 58 The very sharp feature at a binding energy of 1.6 eV is observed only with odd polarization; the state is thus is of odd symmetry. This state, incidentally, is a surface state which splits to lower binding energy from a particularly fiat bulk copper band. It can thus be understood roughly as a chemically-shifted core level, located energetically in the valence band. It is located near the comer of the square surface Brillouin zone (see Fig. 1.5). Its predicted

3dxy orbital

character was confirmed with the symmetry effect

shown in Fig. 1.6. Such symmetry effects have been most useful in lighter elements where the symmetry breaking impact of

ARP Studiesof ElectronicStructureof Solids

59

the spin-orbit interaction is less pronounced. Listings of the various dipole selection rules in ARP for both the cubic and hexagonal lattices have been published elsewhere. 56"57 These must be applied with some caution in 4dand 5d-derived bands since these often exhibit mixed symmetry due to substantial spin-orbit-induced hybridization.59 We return to this issue in Sec. 2.C in our discussion of platinum (111).

Ill. Residual Atomic or Molecular Effects. It is well known from gas phase photoelectron spectroscopy studies that cross sections can vary rapidly near the threshold for core or valence excitation. For example, in molecular systems a centrifugal barrier can form in the final state potential energy surface due to the contribution from higher spherical harmonics.6°'62 Over some range of energies, the final state electron can be temporarily trapped inside this potential, leading to increased overlap with the initial state wave function and to large cross section variations. This phenomenon, commonly referred to as a shape resonance, is often not entirely quenched by adsorption. Adsorbed molecules thus also exhibit such shape resonances. 61 While these have proven useful in determining molecular orientations of adsorbed molecules, they have not yet found application in determining electronic structures. A different and, for our purposes, more important threshold effect is autoionization,6° which is also called direct recombination within the solid state community. This threshold effect leads to the phenomenon of resonant photoemission.8 Autoionization refers to the excitation of a core electron into an unoccupied, quasidiscrete level located energetically above the first ionization threshold. This state decays through an Auger-like process wherein the excited electron refills the core hole and a lower binding energy (often valence) electron is excited into the ionization continuum.

This conceptually two-step process is degenerate with a process involving direct

photoexcitation of the valence electron.

These two photoionization pathways must add coherently, leading to

interference and resonant behavior in the photoionization cross section of the valence orbital as a function of photon energy. Hence the term resonant photoemission. We will discuss the mechanism of resonant photoemission in much greater detail in Sec. 4. The observation of this residual atomic effect in a solid state or surface environment requires that the quasidiscrete level not be significantly broadened by band structure effects. This is synonymous with the statement that the valence bands must be fairly narrow. For elemental metals, one thus expects resonant photoemission to be most pronounced for 3d and 4f valence bands. 7'8 A particularly dramatic demonstration of both resonant photoemission and the effect of a solid state enviromnent on the phenomenon is presented in Fig. 1.7. This plots the Cr(3d) photoionization cross section as a function of photon energy in the vicinity of the Cr(3p --->3d) threshold for the free Cr atom, for Cr thin films, and for the bulk Cr metal. 62 The very sharp structure in the atomic case, which arises from autoionization, is progressively broadened by increasing hybridization in the film and in the bulk. Resonant photoemission is one dramatic manifestation of a material's narrow valence band. It has been particularly useful in understanding the distribution of orbital character in oxides and other compounds. We will return to some of these applications of resonant photoemission in ARP in Secs. 4 and 5.

E. Spectrometers. Outside the ARP community, it is often forgotten that an ARP experimental apparatus consists of two main components: the source of quasi-monochromatic photons and the spectrometer for detecting the photoelectron's energy and momentum. The first of these, while normally ignored, often consists of a fairly complicated, prototype optical design, while the latter can be purchased "off the shelf". Moreover, the type of science that is possible is

60

K.E. Smith and S.D. Kevan

I

Cr

3p -3d •

~

~

Cr m

75

C

.o I0" 'p~,0

,

~so

L/I ,w

n

E 0

II II

_.~

i

60

J

70

J

90

8o hv (eV}

Fano fit to Cr n 3dt't,s (6D)

~,,~r oss sechon

t-

n

;o s'o 6'o 7o hv (eV Fig. 1.7. Comparison of the intensity of the chromium 3d emission as a function of photon energy near the 3p ---) 3d threshold for bulk Cr metal (top curve, Ref. 63), Cr thin film (middle curve, Ref. 64) and Cr vapor (bottom curve, Ref. 65). (Figure from Ref. 62). Reprinted with permission. determined largely by the former. There exist in the literature several reviews of low-energy electron spectrometers and vacuum ultraviolet and synchrotron radiation sources, 17"20'66"70 and their application to ARP has been adequately explained. We thus make only a few general comments concerning a typical ARP experimental apparatus as it relates to the subject matter in this review. The early photon source of choice for ARP was a hydrogen discharge lamp coupled to a conventional, normal incidence VUV monochromator providing photons with energies up to -11 eV. 67 This was adequate for initial studies but eventually was found to be too limited. The relatively low photon energy limits the final kinetic energy and thus the length of the momentum vector. This was partially remedied by the use of windowless, differentially-pumped, noble gas resonance lamps. 67 These provide several discrete photon energies between roughly 10 and 40 eV. Such systems are still commonly used, and continue to provide useful ARP results in addition to providing a support mechanism for the users of synchrotron radiation. Many ARP practitioners perform at least part of their experimental work with synchrotron radiation sources. Early work centered on low-energy storage rings and used primarily normal incidence photon optics. While limiting the photon energy range to -35 eV, the light was continuously tunable, linearly polarized, and relatively intense.

Much of the ARP

phenomenology discussed above and in the next section was first explored on such beamlines. A rule of thumb is that, with normal incidence optics, one can scan the final momentum vector through one entire Brillouin zone for a typical elemental metal. Through the 1980's, there was a push to use higher photon energies at synchrotron radiation sources. For ARP, this allows a more thorough search of momentum space in addition to providing access to the cross section effects mentioned in the previous section. While many beamline designs exist, the work-horse monochromator has become the toroidal grating monochromator, or TGM. 71'72 Using optics with a

ARP Studiesof ElectronicStrugtur~of Solids

61

typical incidence angle of 75-80 °, these beamlines produce continuously tunable photons up to 150-200 eV, with moderate energy resolution and roughly 90-95% linearly polarized. They have proven very useful in both core and valence level photoemission studies. The spectra in Figs. 1.1 and 1.2 were some of the first produced with a TGM beamline. Interestingly, the field has evolved so that substantial interest in normal incidence beamlines and higher resolution line sources has recently reappeared. This interest has arisen due to the high energy resolution possible (-1 meV) with normal incidence optics. This resolution is on the scale, for example, of typical phonon energies. With such resolution, in principle, subtle many-body phenomena associated with bands near EF can be investigated. For example, several groups claim to have observed the superconducting gap in the high temperature superconductors.73"75 This topic will be further reviewed in detail in Sec. 5. There is significant variability in the electron spectrometer design applied to ARP studies. For example, much early work was undertaken using double-pass cylindrical mirror analyzers (CMA) which had been originally designed to do Auger and X-ray photoelectron spectroscopy. While not intrinsically angle-resolving, the CMA can have its acceptance annulus masked to provide moderate angular resolution. 16 These analyzers made a significant impact upon the development of the ARP field. Most groups have moved to other designs which are better suited to ARP, in terms of energy or angle resolution or detection efficiency. The approaches which have been adopted can be easily categorized in terms of the design of the energy dispersing element. 687° For example, several groups developed spherical deflection analyzer (SDA) designs, coupled to cylindrical element electron lenses to image photoelectrons from the sample onto the entrance plane of the analyzer. An example of a so-called 180°-SDA is given in cross section in Fig. 1.8. 76 In this case, a dual zoom lens allowed independent control of both the energy

Y

Sample

Fig. 1.8. An example of the 180 ° spherical deflection analyzer often employed in ARP studies, Photoelectrons emitted from the sample toward the entrance to the analyzer are focused via an electrostatic lens onto an entrance slit of a hemispherical capacitor. The capacitor disperses the electrons at the exit plane, where several energies can be detected simultaneously using a parallel detection scheme or an individual energy can be detected after passing through an exit slit. (Ref. 76). Reprinted with permission.

62

K.E. Smith and S.D. Kevan

resolution and the angle resolution. Such a design is intrinsically angle-resolving and provides fairly good energy resolution with only moderate overall dimension. In addition, the deflection analyzer allows for straight-forward multidetection in kinetic energy, that is, several energies can be simultaneously detected by replacing the exit slit with some sort of position-sensitive detector. A disadvantage of the SDA design is that only one angle is measured at a time. For example, each of the spectra in Fig. 1.4, were collected individually by positioning the analyzer at a particular angle relative to the sample.

Spectrometers have been designed which allow simultaneous collection and analysis of one or two

emission angles. One obvious way to do this is to change the SDA into a toroidal sector so that the radius of curvature in the energy dispersion plane (i.e., that shown in Fig. 1.8) is different from that in the perpendicular plane.

For example, if the radius of curvature in the perpendicular plane were infinity, one would have a

cylindrical deflection analyzer, or CDA. In this case, there is no focusing in the perpendicular direction and each emission angle maps to a different spatial point at the focal plane in the energy dispersion direction. Designs based upon toroidal sectors have been perfected and are being increasingly used. 78 The ultimate energy and angle resolution of such designs has not yet been clearly determined.

Such design can be easily expanded to include

multidetection in energy, so that, for example, the whole series of spectra in Fig. 1.4 could be simultaneously accumulated. Other approaches for simultaneous collection of several angles have been adopted. One of the earliest employs simple low energy electron diffraction optics as a retarding field, high-pass energy analyzer. 79 An improvement employs ellipsoidal grids to provide both high- and low-pass filters. This is the ellipsoidal mirror display analyzer, or EMDA. 80 These designs provide parallel detection in two angles, but operates at one energy at a time. The EMDA has proven particularly useful in angle-integrated core-level photoemission, but has been used less in valence band ARP studies. The newest variant of this type of design employs a parabolic mirror lowpass filter coupled to a plane grid high-pass filter. 81 The design also integrates time-of-flight detection to allow multidetection in energy when the photon beam in pulsed (as is the case with synchrotron radiation). The newest entrant into the repertoire of ARP spectrometer designs employs a magnetic bottle analyzer. 82 This design allows multidetection in both energy and one angle, and has demonstrated the capability of producing nearly real-time images of valence band dispersion relations.

2. BULK AND SURFACE ELECTRONIC STRUCTURE IN SIMPLE MATERIALS

In this section, we present several examples of ARP studies of simple metal and semiconductor materials which utilize and develop the phenomenology introduced in the previous section. All the systems presented in the present section are well-described by the one-electron model of crystalline electronic structure. By this we mean that for these materials it is a good approximation to treat each electron as independent, except that it interacts with the other electrons in some average way through an effective exchange-correlation potential. Materials for which specific correlation effects are more important are treated in later sections. Our goal now is simply to familiarize the reader with the breadth of materials amenable to study, and some of the analysis techniques commonly used. We start with very simple materials (i.e., the simple "free-electron" metal sodium) and move progressively to somewhat more complicated systems (i.e., the compound semiconductor GaAs). As in the previous section, our goal is not to be exhaustive. Rather, we intend to familiarize the readership sufficiently with ARP that they might be better prepared to evaluate its application in their research areas.

A R P Studies o f Electronic Structure o f Solids

63

A. Simple Metals. Most elementary treatments of the electronic structure of metals start with the alkalis. One finds that approximating these as free electron metals provides a very good description of their ground state properties such as cohesive energy, bulk modulus, and specific heat. 83 Fig. 2.1 provides the quasiparticle dispersion relations for sodium metal along a particular symmetry direction of the bulk Brillouin zone. 15 We will discuss how these data were obtained shortly. Aside from a confusing feature near EF, the experimental points are observed to exhibit approximately parabolic dispersion, in qualitative agreement with what one expects for a quantum free electron gas. Moreover, the Fermi wave vector, the momentum where the band extrapolates to cross EF, is very nearly what one would predict based upon the free electron model. These observations imply that enumerating the states with individual wave numbers and filling each state with two electrons of opposite spin is a valid procedure. This is the essence of the one-electron approximation.

1.0

t

1

Na 0.0

-1.0 V

-2.0

t I

t

s

-3.0

"

oo

I

0.00

'°

s

I

I

0.50

I

I

1.00

£-N Fig. 2.1. Experimentally determined quasiparticle dispersion relations for sodium along the [011] direction. The solid curve is the result of a quasiparticle band calculation (Ref. 90), while the dashed curve is the result from a calculation relying upon the local density approximation. (Ref. 15). Reprinted with permission. A closer examination exhibits a significant deviation from precisely free electron behavior. The occupied band width calculated by the free electron model is -20% larger than the experimental result. This observation also holds for the best calculation based upon the local density approximation (LDA) for exchange and correlation, a result given by the dashed curve. This discrepancy in band width implies that the effective mass (or inverse curvature) of the band at the minimum is calculated to be too small. One might think that the deviations of the band from free electron behavior result from the impact of the underlying lattice potential due to the sodium ion cores. This cannot be the case, however, since the band is far enough removed from the Brillouin zone boundary that the impact of the weak lattice pseudopotential is minimal. One knows this to be the case since the bulk Fermi

64

K.E. Smith and S.D. Kevan

surface for the alkalis is measured to be essentially spherical.84 The band crossing EF in Fig. 2.1 represents the closest approach of the Fermi surface to the Brillouin zone boundary. If there are minimal perturbations from the lattice potential at kF, then clearly these cannot explain the discrepancy between relatively simple theories and experiment near zone center. It is also necessary ascertain that the experimental results in Fig. 2.1 do not include any systematic errors. Indeed, as mentioned in the previous section, ARP has some difficulty determining all three components of momentum. However, the experimental data in Fig. 2.1 were collected in such a way that the indeterminacy of the normal momentum is not a problem, and we now describe this technique. Fig. 2.2 presents the projection of

Br

llouin Zones

Surface

I t

I I

I

H

Bulk

Fig. 2.2. Projection of the BCC bulk Brillouin zone onto the (011) surface Brillouin zone. (Refs 4

and 85). Reprintedwith permission. the body centered cubic Brillouin zone onto the (011) surface BriUouin zone (SBZ).4'$5 Recall that the 2D momentum k I is a conserved quantity. If one fixes k I to lie along the (011) azimuthal direction, and sweeps the photon energy, k± varies in the bulk Brillouin zone along lines parallel to the [011] axis. For a simple metal like sodium, there will be at most one band below EF. This will exhibit a well-defined dispersion relation as a function of k.h (or photon energy here), as shown in Fig. 2.3.15 By symmetry, the maximum binding energy will be given by the quasiparticle dispersion relation along the [011] axis at a momentum given by the chosen value of k I. The experimental points in Fig. 2.1 are the result of this somewhat tedious procedure. 15 This provides a unique way of determining the normal momentum based upon the symmetry of the dispersion relations about a mirror plane. It is actually a special case of the triangulation method described below. While it is general in principle, it is best applied to very simple systems. We are left with an experimental result which cannot be disputed, but which clearly shows the weakness of ground state, LDA-based calculations. As discussed briefly in the previous section, ARP measures an excited quasiparticle state which may not be simply related to the ground electronic structure. The weakness of LDA calculations, which are generally based upon density functional theory,$6 is that these codes were formulated to

ARP Studiesof ElectronicStructureof Solids

I '"OTONJ

I

I

I

!

ERO'

I

'

I

/,,,, -4

-3

-2

65

-I

'

'

'

'

PHOTON ENERGY

,L,_,

_, ,.

EF

E r

INITIAL STATE ENERGY (eV)

Fig. 2.3,

ARP spectra of sodium crystalline films, collected at normal emission as a function of photon energy. The 3s band exhibits a maximum binding energy relative to EF of 2.5 eV. This corresponds by symmetry to the energy at the F point of the bulk Brillouin zone. (Ref. 15). Reprinted with permission. minimize the total energy and thus do not produce dispersion relations for excited states. Recent computational advances (the so-called GW approximation) have allowed quasiparticle dispersions to be calculated directly, at least to lowest order in a diagrammatic perturbation theory. 87"91 These codes include more completely the correlation effects involving the excited photoelectron and photohole with the remainder of the particles in the system. In this sense, the GW approximation still leads to a single-particle-like theory, and still may not adequately treat the stronger correlation effects described in the following sections.

However, calculations based upon the GW

approximation have had spectacular success in treating the excited state properties of several simple materials. In particular, the solid curve in Fig. 2.1 is the quasiparticle dispersion relation for the sodium valence band calculated on first principles.90 Much of the discrepancy between the experiment and the simpler theories has been remedied. As alluded to in the introduction, experimenters in the ARP field see their dispersions as "real" optical properties of materials, and LDA to be a useful approach that is inexact in treating excited state properties. Note that there is no projected gap below EF in the sodium band given in Fig. 2.1. Indeed, the monovalent alkali metals cannot have projected gaps below EF along any direction in momentum space because the lowest band is only half filled and all higher bands must lie entirely above EF. For this reason, none of the alkali metals exhibit occupied intrinsic surface states for any surface orientation. This should be differentiated, for example, from the noble metal copper (Fig. 1.3) where the presence of the d-band allows the lowest sp-like gap to fall below EF, and from essentially all transition metals (see below) where projected gaps in the d-manifold often support surface states. There has been a fair number of ARP investigations of the surface and bulk electronic structure of divalent and trivalent nearly free-electron metals. 92"95 In these cases, the lowest bulk band is either partially or fully occupied.

JPSSC 2 1 : 2 - B

This gives rise to the possibility of projected band gaps and surface states located below EF. For

66

K.E. Smithand S.D. Kevan

example, the best studied is aluminum, where including just the two pseudopotential coefficients corresponding to reciprocal lattice vectors G = (002) 2n/a and G = (111) 2n/a gives a fairly good representation of the bulk bands.92 The lowest band intersects the Brillouin zone boundary at the X and L points below EF, so that gaps exist at these two points. These gaps lead to surface states at the center of the surface Brillouin zone of AI(001) and AI(111), respectively.

B. Noble Metals.

As mentioned in the introduction, the noble metals have provided an excellent proving ground for the ARP technique. Their low index surfaces are generally easy to prepare and maintain using modem vacuum technology, and they give relatively simple spectra which can be interpreted in detail. Some indication of the precision which can be attained is given in Figs. 1.1 - 1.4, where copper was used to indicate our ability to map bulk dispersion relations and also to understand the existence of surface states. One reason that photoemission spectra from noble metals are easy to understand is that correlation effects (at least for single-hole states probed by ARP) are minimized since there are no relatively flat d-bands close to EF. As explained in the next section, this is the primary complicating factor, for example, in nickel ARP spectra. Perhaps the most fundamentally precise technique for determining the normal component of momentum, triangulation using data from two different surfaces, has been developed using noble metals. 14'31'32 The procedure was first outlined in a notably prescient paper by Kane. 13

In general, bulk states should be visible in

photoemission spectra from all surface orientations. If a particular bulk feature is observed at a distinct parallel momentum on two or more surfaces, then projection of the parallel momentum vector from one surface onto the other allows the full 3D momentum vector to be determined.

"Foo2

•

Ix

11121

x

u

.//

Ix

.......

u

\

\

{, ,,'

L Fig. 2.4. Graphical representation of the triangulation technique showing a cut through the extended zone scheme of an FCC crystal. A feature observed in a spectrum collected at normal emission from a [111] crystal will sample point A. The same point can be sampled at some finite value of parallel momentum, kl Ill0] or k I [1121, from a [011] or [112] crystal, respectively. The length of the vector connecting F0o0 to'A can then be determined by simple trigonometry. (Ref. 14). Reprinted with pea~ssion.

ARP Studiesof ElectronicStructureof Solids

67

Figs. 2.4 and 2.5 show how this works for the specific case of a normal emission spectrum from an FCC (111) surface triangulated with off-normal spectra from a (112) surface. 14 A spectrum from the (111) surface necessarily samples states precisely along the F - L line of the bulk Brillouin zone. Spectra from the (112) surface collected in the FLUX mirror plane at some angle Oll 2 from the surface normal will sample exactly the same bulk state. The perpendicular momentum of the transition, measured along the [111] axis, is relat~l to the parallel momentum relative to the [112] axis by simple trigonometry. Spectra for this particular arrangement for Au(111) I

I

I

Au(lll)

I

I

I

I e~'4

f

II

I ~ . i

~' c'

i

[

i

: I

>.-

Z UJ Z

-8

-6

-4 -2 INITIAL ENERGY (eV)

EF

Fig. 2.5. ARP spectra from gold single crystals which demonstrate the triangulation technique. The top spectrum was collected at normal emission from Au(111), while the other spectra were collected from Au(ll2), at emission angles toward the [111] direction. Feature f', observed on A u ( l l l ) , appears at an emission angle o f - 27.5 ° from Au(ll2). (Ref. 14). Reprinted with permission.

and Au(112) are presented in Fig. 2.5.14 Feature f' on the top spectrum collected from Au(111) is exactly matched by one on Au(ll2) at an emission angle of 27.5 ° relative to the [112] axis. These spectra thus determine the energy of each of the occupied bands at one point on the F - L line. The complete dispersion relation along each line can be determined if a range of photon energies (i.e., synchrotron radiation) is available. The low index noble metal surfaces exhibit many intrinsic surface states below EF. These can loosely be placed in three categories. The first category is associated with the sp-gap at L, shown in Fig. 1.3 for copper. This exists for all three metals. It projects onto all of the low Miller index surface Brillouin zones (see Fig. 1.5), and generally supports an sp-like surface state having a fairly long decay length into the bulk.39'43"45"54'55'93"99 The second category of surface state is similar to that shown in Fig. 1.6 for Cu(001). These are highly localized d-like states which split above a very flat band at the top of the bulk d-manifold.5°'58'1°°'1°2 The final type of noble metal surface state is intermediate between these two. They lie in projected gaps in the middle of the d band, but

68

K.E. Smith and S.D. Kevan

generally are not fully localized to the surface plane. The state $3 in Fig. 1.2 provides a good example. The noble metals have also provided very good testing grounds for studying the electronic structure of ultrathin metal films, i.e., epitaxial films having a thickness of less than a few layers. The issues of general interest in such ultrathin films concern band width as a function of both dimensionality and lattice constant, the development of the bulk band structure as the film thickness increases, and the formation of surface alloys.103 Noble metals are particularly attractive substrates since their photoemission properties are well-understood. Also, they exhibit a fairly low background above and below the d-bands which allows states arising from the film to be easily distinguished from those of the bulk. Moreover, the noble metals can be easily and cleanly evaporated. Studies of noble metal films adsorbed onto noble metal substrates have thus become particularly popular. A good example which combines most of these interesting phenomena is a series of experiments performed on the Au/Cu(001) system. This system has been well-characterized by a variety of surface techniques. 104"106 For gold deposition with the Cu(001) substrate held at room temperature, an ordered surface alloy is formed in which half the surface copper atoms are displaced by gold atoms in a "checkerboard" pattern. Further deposition leads to formation of a hexagonal overlayer of gold on top of the fourfold symmetric copper substrate. When the deposition is performed on a cooled substrate (T < -100 ° C), the alloy is not produced: one observes directly the hexagonal layer. These growth modes were determined primarily through a combined valence band and core level photoemission investigation. Some of the ARP results are shown in Fig. 2.6.1°4 This shows spectra of Cu(001)

Au (ML) 2.00 1.50 1.25 1.13 o3 i.-

1.00

0.94 "O.87 0.80 0.73 0.68 0.61 0.54 0,50 0.47 0.4-0

>.cY ,< rr t,-

E

0.34 0.27 0.20 0.13 O.07 I

5

Cu(OOl)

4 3 2 1 E BINDING ENERGY (ev) m

Fig. 2.6. ARP spectra from the initial stages of gold deposition onto Cu(001). The the M point of the Cu(001) surface Brillouin zone is sampled by the spectra. The dramatic changes in the surface state emission at 1.8 eV binding energy were used to understand the growth mode for this system. (Ref. 104). Reprinted with permission.

ARP Studies of Electronic Structure of Solids

69

as a function of gold coverage at room temperature at a parallel momentum which samples the dxy-like surface state described in See. 1.D.II and Fig. 1.6. The sharp surface state above the d-band (bottom spectrum) is observed to move to lower binding energy as gold is deposited up to 0.5 monolayers. At that coverage, the energy of the state is similar (though not identical) to a related state observed on the bimetallic alloy Cu3Au(001 ). The structure of the surface layer in this ordered alloy is similar to the checkerboard structure of the surface alloy produced upon room temperature deposition. Upon further deposition, the surface state is progressively quenched, i.e., it appears to pass the "crud test" as more gold is deposited onto the ordered surface alloy. Deposition at low temperature yields qualitatively different results in which the state associated with the surface alloy in not observed. This study demonstrates the delicate interplay between geometric and electronic structures, and how surfacelocalized states may be used to probe interesting growth phenomena. The field of ultrathin metal t-tim electronic, magnetic, and geometric structures is very active. More complete reviews are available in the literature. 103'1°7"110

C. Sd Transition Metals: Platinum.

We now turn our attention to metals involving the next level of complexity in electronic structure, that is, elemental transition metals. In the present section, we will discuss the electronic structure of the clean (111) surface of platinum. Platinum is a transition metal with a high density of 5d-derived states at EF. We will focus upon the clean surface with a (111) orientation. The chemical, physical, and electronic properties of this surface have been very well-studied. 111 It provides excellent examples of the application of ARP to both surface and bulk P! (111) Normol emission p- polarized

Ef 2 4 6 6 Ef 2 4 6 8 Bindin(] energy (eV)

Fig. 2.7. ARP spectra from Pt(111) collected at normal emission as a function of photon energy. The dramatic spectral variations give information about the bulk quasiparticle band structure along the [ 111] direction. (Ref. 112). Reprinted with permission.

70

K.E. Smithand S.D. Kevan

electronic structure. Unlike 3d transition metals (see Sec. 4), the 5d series has a relatively large band width which renders the impact of electron correlation minimal. Thus the one-electron approximation remains useful, and the simple ideas developed in the previous sections can be directly applied.

I. Pt Bulk Bands. To date, the triangulation method for determining the full 3D wave vector has not been applied in ARP studies of Pt(111). There have been two complementary efforts to determine the bulk bands using a final state which was approximated as a free electron, n2,n3 We can thus expect precision similar to that described in Figs 1.2 and 1.3. The ftrst ARP study 112 of interest here mapped the bands along the A line in this way, using synchrotron radiation between 6 and 33 eV.

A sampling of the spectra, given in Fig. 2.7, indicates similar

sensitivity to photon energy as in Fig. 1.2. All of the features were assigned to bulk, momentum conserving transitions along the [111] crystalline axis. Upon reduction of these data using a parabolic final state fitted to a calculated band structure, the dispersion relations shown in Fig. 2.8 were derived. 112 The use of a calculated final hlJ= 8

I0

12 14 16 18

22

26

30

I

3

e- 5 o~ ~o trn

tinum F (4,4,4)

(8,8,8)

L. 02,12,12)

Fig. 2.8. Bulk band dispersion of Pt along the [111] direction determined from the spectra in Fig. 2.7. The results of a relativistic calculation (Ref. 114) are shown by the solid lines. (Ref. 112). Reprinted with permission. state to determine an experimental initial state at first appears dubious. However, the large difference in band velocities in the initial and final states actually makes the errors produced fairly small. In effect, if the calculated final state is in error by as much as 1 eV at a given momentum, the associated error in determining kf (and thus ki) is fairly small due to the large final band velocity. For a relatively fiat initial state, the error produced in the initial band energy by this uncertainty in momentum is small. A final check on this procedure is that the bands must be symmetric about appropriate symmetry points, e.g., the zone center (1") in Fig. 2.8. The experimental points in Fig. 2.8 are plotted together with the relativistic augmented plane wave bands calculated by Anderson. n4 While the match is not perfect, the deviations are always less than 0.5 eV, and often

ARP Studiesof ElectronicStructureof Solids

71

are negligible. At a minimum, the general trends are well-reproduced. It is surprising that the systematic deviations from the calculated bands as a function of binding energy observed in sodium (Fig. 2.1) arc not apparent in platinum. This is particularly true at zone center, where the splitting between the three highest energy bands arc

very well-reproduced. Further out along the A-line there arc two places where there is uncertainty about the

connectivity of bands. Firstly, it is not clear whether bands 2 and 3 (numbered in the figure from the lowest energy band at zone center) cross about half-way across the Brillouin zone. Also, the apparent "avoided crossing" between bands 3 and 4 about 70% of the way from F to L is not well-reproduced by the calculation. Indeed, an earlier calculation produced a crossing between bands 3 and 4 in this vicinity.115 The sensitivity of this experiment was not adequate to solve these ambiguities. Issues such as this (band connectivity, avoided crossings, and possible band gaps) form the basis for much of solid state physics. It is important that ARP (or any other tool for measuring electronic structure) be calibrated in terms of its abilities to address these features. The ability of bands to cross is determined by their symmetry properties. In the non-relativistic case, these properties are relatively straight-forward and can often be easily addressed using the polarization selection rules described in Sec. 1.2. For a 5d metal such as platinum, the magnitude of the spin-orbit interaction, a relativistic effect which lowers the symmetry of electron states, is comparable to the 5d band width. Thus, more complicated selection rules must be applied using the double-group representations. These rules have been enumerated by Wohlecke and Borstel.59 A particularly interesting and useful application of these rules occurs for circular polarized light at normal incidence upon a (111) surface of a cubic material. In this case, spin-polarized photoelectrons are produced. The polarization of the electrons is either parallel or antiparailel to the propagation direction (and thus angular momentum vector) of the photons. If an apparatus capable of measuring the spin polarization of photoelectrons is available, the double-group symmetries of the bands in Fig. 2.8 can be determined, and the presence or absence of the ambiguous band crossings elucidated. Spin detection of photoelectrons in ultrahigh vacuum (UHV) is difficult, requiring the use of one of several spin detectors all of which have relatively low detection efficiency. However, such experiments are now

10000

.""..

Z

(a)

0

'~,

f~

" %, -_

Z

..

_ j----.-.

Z

I

EF:O Z

+0,~

r l ll

-2

-i

-s

ENER6Y(eV)

*0,2 N

0

<

-0,2

"I I

-0,4

Fig. 2.9• Demonstration of the spectral variations which can arise from coupling spin detection to circular polarization. Spectra arc collected from Pt(ll 1), and allow assignment of the double group symmetries of the bands. See text for details. (Ref. 113). Reprinted with permission.

72

ICE. Smith and S.D. Kevaa

possible, and the application to Pt(111) has been achieved. 107"109 Fig. 2.9 shows a sampling of these experimental results. 113 The upper panel gives the spin-integrated ARP spectrum of Pt(lll) collected at normal emission with 13 eV photons. It is different from the spectra in Fig. 2.7 due to the very different photon polarizations employed. The next panel shows the corresponding spin polarization defined as the difference in counting rates between electrons having spin parallel and antiparallel to the photon momentum, normalized to the total counting rate. The polarization is observed to be large and non-zero over much of the spectrum. It is positive near EF, then turns negative before oscillating around zero. The next panel gives the spin-resolved spectra which clearly show the predicted symmetry effect. For example, the peak near EF was assigned to the A4+5 double group as it was observed most strongly when the angular momentum of the photon and photoelectron were aligned.

The shoulder at slightly higher binding energy was assigned to the A6

representation, since it is observed when these vectors are anti-aligned. In similar fashion, symmetries of all the bands could be deduced. The correct symmetries and band crossings are shown in the bottom panel. Spin-polarized photoemission is a technique which is rapidly growing in popularity. This popularity is driven in large part by its obvious and fruitful applications in the areas of surface, thin film, and bulk magnetism. More complete and technique-oriented reviews of spin-polarized photoemission are available in the literature. 107"109

o) cleon

-10

M T' K

surfoce

7

"F

r

M

E

"F

Fig. 2.10. Projection of the calculated platinum band structure (Ref. 120) onto the (I I I) surface Brillouin zone. Experimental points correspond to surface-relatedfeatures, i.e.,statesand resonances. These often lie in or near projected band gaps. (Ref. 121). Reprintedwith permission.

II. Pt(lll) Surface Bands. The previous section indicates that ARP provides a good and fairly detailed understanding of the bulk platinum bands. Until recently, less was known about the surface-localized bands on Pt(lll).

This is surprising, since the electronic structure of related group VIII metal surfaces [Pd(lll) and

Ni(lll)] have been more thoroughly studied. 116"119 We choose to describe recent results on the Pt(lll) surface

ARP Studies of Electronic Structureof Solids

73

bands here since the larger atomic 5d orbital leads to a larger band width in the 5d metal, making the one-electron approximation better than for the 3d and 4d counterparts. In addition, information about the surface Fermi contours is available, so that the relationship between the simple systems described in this section and those described later will be more distinct. A common first step in understanding the surface electronic structure of a given low index face is to project the bulk band structure onto the surface Brillouin zone (SBZ). In this way, the location of projected band gaps and the possible existence of surface states can be obtained. This was an important step in understanding surface states on Cu(11 I) in Sec. 1.C. In that case, however, we had only to project the experimentally-determined bands along the [111] direction onto the SBZ center. In the present case, we are interested in surface states throughout the SBZ. In order to produce an experimental projection, we would thus need to determine bulk bands similar to those in Fig. 2.8 for many lines in 3D momentum space parallel to the surface normal. As this is a very tedious procedure, calculated bands are often used instead. Given the close match between calculated and experimental bands in Fig. 2.8, this procedure will not introduce serious errors unless one needs to distinguish a surface band very close to a bulk band edge.

Pt(111)

K, II T

h~ = 24 eV

KII(I_,) 8

1.50

P

1.42

{) v

"

~---'~"""~'~-'~"-"~"~

.~

\

1..~3

~.

1.24

'~ 1.15 ~ 1.06 "'-.--10.96

~

o 6

. 4

6

4 2

Ef

BINDING ENERGY (eV)

Fig. 2.11. ARP spectra from Pt(111) indicating the sensitivity to contamination of some of the spectral features. (Ref. 121). Reprinted with permission.

A useful set of interpolation schemes to calculate the bulk band structures of all elements is available 12° which can readily be adapted to produce these projections. The result for Pt(111) is shown in Fig. 2.10.121 This calculation did not include the spin-orbit interaction. ]22 Thus, in the T~ (F - M) mirror plane the states may be classified as either odd or even symmetry. The figure shows only the projection of even states, as these were found to be more relevant in comparing to the experimental data. The T line (F - K - M) does not correspond to a bulk mirror plane so that no separation of even and odd states is possible. The projection of each of the bulk bands is shaded separately so that each continuum may be visually separated from the other, and so that the various upper and lower band edges are readily apparent. The points in Fig. 2.10 are the result of a recent ARP study. 123 They JPSSC 21:2-£

74

K.E. Smithand S.D. Kevan

correspond to energy and parallel momenta of spectral features which pass the tests to be characterized as surfacelocalized states: they exhibit sensitivity to contamination (Fig. 1.I), and they do not disperse with photon energy (Fig. 1.2). A sampling of the spectra along the T line is given in Fig. 2.11. This gives spectra from the clean and hydrogen-covered surfaces. The sensitivity of some of the spectral features is readily apparent. While acknowledging the quantitative problems associated with comparing experimental data with calculated band gaps, it is useful to make qualitative comparisons nonetheless. There are several surface bands, some of which appear to be associated with a particular projected gap while others do not. For example, along Y~ there are two projected gaps of even symmetry below EF, a large one centered in the SBZ and another smaller one roughly halfway from the zone center to the zone boundary. The former of these apparently does not support a surface band. While a band disperses through the latter gap, its relationship to the gap is not obvious since it continues as a resonance throughout the SBZ. Along T, there are several projected gaps in the vicinity of K. These are common features on FCC (111) surfaces and are caused ultimately by the lack of symmetry along the T line which precludes the bulk bands from crossing. The two largest gaps below EF appear to have surface states associated with them. Again, these states disperse out of the gaps to become resonances. In these cases, the resonances are loosely associated with the edges of projected bulk bands, a commonly observed behavior. There axe two surface bands which cross the Femai level and thus are of some importance in the discussion of Fermi surfaces in Sec. 3. One of these is a rapidly dispersing band which crosses EF about half way from F to K, and also about 70-80% of the way from F to M. This band forms a well-defined, closed electron pocket centered at F . The second band is much less dispersive and is localized near K. This also forms a closed electron pocket.

D. Surface and Bulk Electronic Structure of GaAs.

We continue our discussion of increasingly more complex systems with a review of several experimental and theoretical studies of the surface and bulk electronic structure of GaAs(011). This is more complex than the metals discussed above in the sense that it is a compound semiconductor so that its unit cell is larger and also the impact of the different ionicity of the constituent atoms cannot be neglected. The bulk band structure is still relatively simple. However, issues concerning excitation spectra are particularly important in semiconductors since fast-principles ground state calculations yield band gaps which are seriously in error. 90A24 Moreover, GaAs(011) has provided a currently well-understood model for the surface properties of semiconductors, 125"13° as explained in more detail below. There has been more than a decade of work by several different groups with the goal understanding the electronic structure of GaAs(011). 131"136 The primary conclusion of this effort has been that most spectral features may be uniquely associated with direct transitions within the bulk band structure. A fairly good understanding of the bulk quasiparticle dispersion relations has thus been attained. As explained below, intrinsic surface states are swept from the band gap by a surface reconstruction. This reconstruction and the resulting surface band structure are also very well understood. 12513° A comprehensive study of the experimental bulk dispersion relations of several III-V semiconductors along the [011] axis has recently been presented. 135 This investigation employed an approximate but fairly general procedure for overcoming the indeterminacy of the momentum normal to the surface. We discuss this procedure here. Fig. 2.12 presents some spectra of GaAs(011) collected at normal emission as a function of photon energy. As observed earlier for several metal surfaces, the spectra evolve significantly as the photon energy varies. In the case of GaAs, however, the final state is not well-represented by a single plane wave, and a direct inversion of

ARP Studiesof ElectronicStructureof Solids

-8

6

-4

-?

75

0

INITIAL ENERGY(ev)

Fig. 2.12. ARP spectra of GaAs(011), collected at normal emission as a function of photon energy. Note in this case that there are more features than occupied band for this material, implying that more than one final state band is being accessed. The small numbers next to some of the peaks correspond to the initial and final bands involved in the direct transition producing the peak (see Fig. 2.13). (Ref. 135). Reprinted with permission. these data (as was done, for example, for copper in Sec. 1) is not possible. The authors constructed "structure plots" from these spectra. These plot the observed binding energy (relative to the valence band maximum for a semiconductor) of a particular feature as a function of photon energy. Along each such contour, k± varies in some ill-defined way.

Similar structure plots were then constructed using a calculated initial and final states band

structure, 137 where the "photon energy" was equated to the energy difference between two bands at a given value of ki. If the calculated bands were exact, the two structure plots would be identical. In general, this is not the case. However, the calculated bands will have the correct symmetry and their shape and energetic location will be fairly close so that the theoretical structure plots will not be too much in error. The calculated bands were then changed systematically to try to improve the match between the theoretical and experimental structure plots. The occupied bands might be shifted relative to the unoccupied ones (i.e., the band gap might be changed), or one or both manifolds might be linearly stretched. These adjustments are repeated until the best fit is attained. We note that the results from this study are generally supported by those from several others. Using these structure plots, both the occupied and unoccupied manifolds were determined, as shown in Fig. 2.13 for both GaAs(011) and InAs(011). 135 The final bands required to understand all ARP spectral features are clearly not well-represented by a single plane wave. The small numbers next to each spectral feature in Fig. 2.12 correspond to the initial and final bands in Fig. 2.13 associated with the direct transition. We see that several final band numbers appear. The overall precision of this procedure using structure plots to deduce k± in ARP data is indicated by the excellent fit of the resulting "modified theoretical" bands to the experimental points

76

K.E. Smith and S.D. Kevan

in Fig. 2.13. These points may thus be taken to be experimental quasiparticle dispersion relations to be compared

to existing calculations.

4,

O

-4

QA

-5

F

'

× F

×

Wave vector k

Fig. 2.13. Experimental bulk bands of GaAs and InAs along the [011] direction determined using the spectra in Fig. 2.12 with the procedure explained in the text. (Ref. 135). Reprinted with permission. The experimental dispersion relations are qualitatively matched by band structure calculations. 137 However, the so-called "band gap problem ''90'124 appears for first-principles band structure which calculates only ground state properties. This refers to the fact that the semiconducting band gap is not a ground state property, and is generally underestimated by ground state calculations. The quasiparticle calculations discussed above have not been reported for the bulk GaAs bands, but the application to the surface bands (discussed below) has been very successful. A popular, albeit less fundamentally attractive, technique for overcoming this band gap problem has been to undertake semi-empirical band structure calculations in which experimental data concerning, e.g., optical properties and band width are included to constrain the result, t37 These calculations match the experimental dispersions fairly well, although some significant modifications were required to attain the results in Fig. 2.13. The surface electronic structure of GaAs(011) has been of continuing interest through its relation to the reconstruction of the surface atoms. The (011) surface is non-polar since there are equal numbers of gallium and arsenic atoms. A bulk-terminated surface would involved one dangling bond per surface atom. These dangling bonds might be expected to produce a surface band within the fundamental band gap. The fact that no such state was seen in early photoemission studies 131"134 supported existing ideas that the surface reconstructs in such a way that these states are swept from the gap. The reconstruction involves rotation of the surface Ga-As bonds such that the As atom move outward and the Ga move inward. 125 The coordination of the arsenic atoms is nominally trigonal with an accumulation of negative charge. The coordination of the gallium atoms is nominally planar with a deficit of charge.

The doubly-occupied As dangling bond is shifted downward out of the gap by the

ARP Studiesof ElectronicStructureof Solids

77

reconstruction, while the unoccupied orbital on Ga is shifted upward. While somewhat less experimental effort has been applied to understand the surface electronic structure of GaAs(011), these states have now been unambiguously identified by ARP and inverse photoemission. 136'138q~ A summary of the current understanding of this surface is given in Fig. 2.14.141 This shows a projection of the 3.2

2.4

1.6 A

> 0.8 III

VBM

-0.8

-1.6

Fig. 2.14. Summary of the occupied and unoccupied surface bands on GaAs(011), along with the calculated quasiparticle dispersion relations. (Ref. 141). Reprinted with permission. bulk bands onto the surface Brillouin zone, the surface bands calculated using the quasiparticle technique, and the existing and accepted experimental results for surface bands near the top of the valence band and the bottom of the conduction band. The accord between experiment and theory is comparable to the accord between different experiments.

Note also that the calculated result is truly first-principles, that is, it contains no adjustable

parameters, yet it does quantitatively reproduce the observed surface and bulk band gaps.

3. ELECTRONIC STRUCTURE AND ELEMENTARY EXCITATIONS.

In this section we discuss the application of ARP to the study of surface dynamics and structure. As we have seen, ARP provides unique information about the band structure of a surface. We will now show how this knowledge of band structure can reveal the origins of both atomic vibrational and structural phenomena on surfaces. The phenomena we will be particularly concerned with will be electronic damping mechanisms for both intrinsic and adsorbate vibrational modes at surfaces, and electronically driven surface structural instabilities.

A. Non-Adiabatic Adsorbate Vibrational Damping.

Figure 3.1 shows the grazing incidence infra-red (IR) spectrum obtained by Chabal of the adsorbate vibrational modes of a hydrogen saturated W(001) surface. 142 Absorption by two vibrational modes is clearly

78

K.E. Smithand S.D. Kevan

visible in this spectrum, one at 130 meV (1069 cm"1) and another at 157.5 meV (1270 cm'l). The absorption at 157.5 meV displays a very sharp asymmetric lineshape, a so-called Fano lineshape. 143 The shape of a peak in an IR absorption spectrum is determined in part by the damping mechanism of the vibration excited by the IR radiation. 144 However, a Fano lineshape is the clear signature of the interaction of a discrete state with a 700

900

I

'

I

t 100 '

I

'1500 i

I

IZ~R/R = 5 x 10-4

t I

1000

I

I

1200 t400 FREQUENCY (cm -I)

1600

1

Fig.3.1. Grazing incidence infra-red reflection absorption spectra from both H-saturated and D-saturated W(001). A linear background has been subtracted from the spectra to remove non-vibrational absorption. The dashed lines are fits. See Ref. 142 for details. Reprinted with permission. continuum, implying that such an interaction is the dominant damping mechanism for the mode observed at 157.5 meV. Langreth considered theoretically the possibility of a discrete vibrational mode of an atom adsorbed on a metal surface being damped by the excitation of electron-hole pairs at EF.145 Since these electron-hole pairs form a continuum of states near EF, Langreth predicted a distinct Fano lineshape for any vibrational mode where this is the primary damping mechanism. Chabal thus ascribed the origin of the asymmetric lineshape of the mode at 157.5 meV to non-adiabatic electronic dampingJ 42 This was the first unambiguous observation of non-adiabatic electronic damping of an adsorbate vibrational mode. A very similar observation was made shortly thereafter for H-saturated Mo(001) surfaces, where one of the vibrational modes seen in IR spectra (at 161.2 meV) was found to also display a Fano lineshape)44 This model to explain the origin of the asymmetric lineshapes observed in IR spectra of adsorbate vibrational modes of H-saturated W(001) and Mo(001) surfaces places very severe constraints on the electronic structure of these surfaces. If a vibration with less than 200 meV of energy is to excite electron-hole pairs, then clearly the H-saturated W(001) and Mo(001) surfaces must have H-induced electronic surface states within 200 meV of EF. (These states must be H-induced since even small amounts of H will completely destroy intrinsic surface states near EF on these surfaces. 146'147) If there is to be a strong coupling of the motion of the adsorbed H atoms to electrons in the substrate, i.e. a strong breakdown of the adiabatic approximation, then the velocity of electrons in these surface states must be comparable with the velocity of the atom cores. 83 The need for slow electrons in a solid translates in the one-electron band picture as a need for flat, non-dispersive bands. Thus in addition to requiring that there be a H-induced surface state within 200 meV of EF, the model of non-adiabatic electronic damping also requires that these surface states show little dispersion across the SBZ. Of course, the

ARP Studiesof ElectronicStructureof Solids

79

existence of a non-dispersive two dimensional band very close to EF implies that the two dimensional density of states is very high, which is a further requirement for a strong breakdown of adiabaticity. 148 The model of electron-hole pair damping explains the observed asymmetric lineshapes for selected vibrational modes of H-saturated W(001) and Mo(001) only if the two dimensional electronic structure of these surfaces has the characteristics just described. Clearly, then, ARP can be used to test the validity of this model. Figure 3.2 presents a series of ARP spectra from H-saturated Mo(001) taken with 40 eV photons along the A line in the SBZ. 149 Along a large part of the~- line (from 0.11 /~-1 to 0.68/~4) a small peak close to EF is visible '

'

' ' 1

. . . .

I

. . . .

I

. . . .

H/Mo(O01)

_

1.04 0.94 0.85 0.73 0.63 0.53 0,42 0.,52 0.21 0.11 0

N(E)

i

L

,

I

. . . .

I

,

.

i

i

J

i

i

~

i

Z 2 1 EF=O Binding Energy (eV) Fig. 3.2. ARP spectra taken from H-saturated Mo(001). The light was incident at 65 ° to the surface normal in the (001) plane and the detector was rotated perpendicular to this plane. The photon energy was 40 eV. The (001) surface Brillouin zone is shown as an inset. (Ref. 149). Reprinted with permission.

in these spectra. Using the tests discussed in previous sections, we can assign this peak as emission from a two dimensional H-induced surface resonance. The binding energy of this peak is never more than 0.2 eV, and it shows virtually no dispersion while below EF. Thus the associated resonance satisfies the criteria listed above for effective coupling to an adsorbate vibrational mode at 161.2 meV. ARP studies of H-saturated W(001) reveal an almost identical H-induced surface resonance on that surface. 15° Thus by directly measuring the two dimensional electronic structure of these surfaces, ARP could be used to show the validity of the model used to explain the anomalous vibrational lineshapes. In a novel application, ARP could also be used in this case to help assign the peak in the IR spectra that displayed the asymmetric lineshape to a particular vibrational mode. There exists a basic ambiguity in the IR spectra about the identification of this mode. There are three zone center acoustic vibrational modes for the H/W(001) and H/Mo(001) systems: the symmetric stretch, the asymmetric stretch and the wag mode; the first is a H vibration perpendicular to the surface, the latter two are parallel to the surface. All these modes have been measured using electron energy loss spectroscopy (EELS); for H/W(001) the symmetric stretch is observed at

80

K.E. Smithand S.D. Kevan

130 meV, the asymmetric stretch at 160 meV and the wag at 80 meV. 151A52 The 157.5 meV absorption in the grazing incidence IR spectra was not assigned to the asymmetric stretch since, being parallel to the surface, this mode is not dipole allowed and should not be visible in this geometry.

Instead, it was assigned to the ftrst

overtone of the wag mode, 142 which has a component perpendicular to the surface. 153 This assignment leads to a paradox since it implies that the overtone of the wag should also be visible in quasi-specular (dipole) EELS, where, in fact, only the symmetric stretch at 130 meV is seen. 151'152 A resolution was offered by Reutt et al, who proposed that the overtone of the wag mode couples strongly to the small parallel component of the electric field in the grazing incidence 1R experiment.144 Since the parallel component of the electric field is strictly zero in the dipole EELS experiment, the mode would thus remain unobserved in EELS. However, Zhang and Langreth have pointed out that this coupling to the parallel field is only allowed if the surface has no reflection symmetry (i.e. is disordered), t48 Furthermore, if the parallel electric field is a significant factor, then the asymmetric stretch should also be visible in the IR spectra, with no surface disorder required. Thus the possibility exists that the mode at 157.5 meV for H/W(001) and 161.2 meV for H/Mo(001) are asymmetric stretch modes and indeed the large intensity of the asymmetric modes relative to that of the symmetric stretch modes favors the identification of the former as fundamental modes rather than as overtones. 148 One significant difference between the wag and asymmetric stretch modes is that the former is of odd symmetry and the latter even with respect to the (100) mirror plane of the surface. It can be easily shown that for non-adiabatic coupling to occur, the final electronic state is required to be of the same symmetry as the initial state for an even vibration, and to be of opposite symmetry if the vibration is odd. As has been discussed previously, ARP can often be used to directly measure the symmetry of an electronic state with respect to a mirror plane of the surface. The H-induced resonance observed close to EF in the ARP spectra of H/W(001) was found to be primarily of even symmetry with respect to the (100) mirror plane. 15° Thus if this resonance is the initial state in the damping transition, then the final bulk state must be odd if the vibration is odd (wag), and even if the vibration even (asymmetric stretch). From a projection of calculated bulk states for W(001) onto the (001) plane, it can be shown that there are no bulk W states of odd symmetry close to EF alongA- .120 Thus the vibration is constrained to be even with respect to (001) if it is to couple to the H-induced resonance. Consequently, the Hinduced resonance can be responsible for the electronic damping of the 157.5 meV mode of H/W(001) only if that mode be identified as the asymmetric stretch. Therefore ARP data leads to an assignment of the non-adiabatically damped mode on H/W(001) to the asymmetric stretch. For H/Mo(001) the situation is less clear since the ARP data indicated that the H-induced resonance on that surface (Fig. 3.2) was of mixed symmetry with respect to the (001) mirror plane.149 Hence this resonance could couple to either the asymmetric stretch or the wag mode, and indeed probably couples to both. Although not a common application of ARP, its ability in this case to address the issue of mode assignments in IR spectra is indicative of the widespread utility of the spectroscopy. Of more general significance is the use of ARP illustrated above in the study of how the detailed electronic structure of a surface can influence dynamic processes. In this regard, we now consider how ARP can be used to probe to origins of two dimensional surface structural instabilities and reconstructions.

B. Surface Reconstruction in Metals.

The surfaces of some metals are inherently unstable. When they are heated or cooled, or have foreign atoms adsorbed on them, their surface crystal structure changes in a phenomenon called surface reconstruction.

ARP Studiesof Elec~'onicStructureof Solids

81

Understanding why certain metal surfaces reconstruct and others do not is a complex problem of enduring importance.

Prototypical surfaces in the study of this problem are W(001) and Mo(001).

Both these surfaces

reconstruct when cooled below room temperature. 154"156 To first order, the room temperature structures of both surfaces give simple (lxl) LEED patterns, while at 230 K W(001) gives a c(2x2) pattern and at 200 K Mo(001)

gives

a c(2.2 x 2.2) pattern. 154 It is noteworthy that even though W(001) and Mo(001) reconstruct, W(011) and

Mo(011) do not. The structural stability of many metal surfaces has been investigated, and in this section we wish to discuss the role ARP can play in revealing the origin of the inherent instability of some metal surfaces. We will initially concentrate our discussion on W(001) and Mo(001) since these are the most exhaustively studied surfaces. Using these surfaces as examples, basic concepts will be introduced and the importance of ARP studies in understanding this subject will be described. Subsequently, ARP data for other surfaces will be presented, and we will discuss the stability or instability of many surfaces in the context of their electronic structure.

I. The Reconstruction of W(O01) and Mo(O01). The origins of the Mo(001) and W(001) reconstructions have been the subject of great controversy since their first unambiguous observation in 1977,154'155 with much of the debate resulting from the existence of numerous theoretical models that propose to explain them. Broadly defined, these models can be split into two classes, which differ according to the role collective electronic phenomena play in the surface atomic motion. The f'trst class are known as local bonding models, which view the reconstruction as the result of the formation of local molecular orbital-type bonds between neighboring atoms in the Mo(001) and W(001) surface layer; collective electronic effects play only a minor role. 157A58 The explanation for the reconstruction of both surfaces yielded by local bonding models was widely accepted until quite recently. The second class of model is known as the charge density wave (CDW) model, and it provided the original explanation for these reconstructions.154'159'160 In this model collective phenomena dominate and the reconstructions are viewed as periodic lattice distortions resulting from potential screening anomalies produced by the spanning of heavily nested portions of the two dimensional Fermi surface by a surface phonon wavevector.

Thus the

reconstructed surface is produced by the freezing in of a particular surface phonon mode [the M 5 mode in the case of W(001) and Mo(001)]. As we shall see, identical concepts are used to explain structural instabilities in layered compounds such as the transition metal dichalcogenides. The CDW model is very attractive from an experimental point of view since it includes an accessible test of its own validity. Without a heavily nested Fermi surface (i.e. a Fermi surface that contains large fiat parallel segments) a periodic lattice distortion cannot occur. (The converse is not true, however; the observation of a nested Fermi surface does not alone guarantee the occurrence of a periodic lattice distortion.) Thus if the two dimensional Fermi surface can be measured for a surface that undergoes reconstruction, then the validity of the CDW model can be immediately revealed. The experimental techniques that can be used to measure bulk three dimensional Fenni surfaces (such as magnetic resonance techniques or positron annihilation) cannot be used to measure the two dimensional Fermi surface of a surface. The only routine method for measuring two dimensional surface Fermi surfaces is by using ARP. The reasons for the demise of the CDW model as the explanation for these reconstructions will be presented in a moment, as will be the reasons for its rebirth. We will begin our discussion of the stability of these surfaces in the context of the classic CDW model, then progress to a more sophisticated version of this model which displays some of the characteristics associated with local bonding models.

a) Two Dimensional Fermi Surfaces of W(O01) and Mo(O01). We have seen how ARP easily measures both two and three dimensional band dispersions.

The Fermi surface is simply defined as the contour in k-space that

82

K.E. Smith and S.D. Kevan

encloses all the occupied or unoccupied electronic states in a system.83 In a one-electron band model, a single point on the Fermi surface is thus defined by the location in k-space that a band disperses through EF. If we use ARP to measure the dispersion of a two dimensional state, and if we observe that state to cross EF (i.e. the associated peak in the spectra approaches EF and then disappears), then we have experimentally determined one point on the two dimensional Fermi surface of that state. Clearly then, the entire Fermi surface can be measured by taking ARP spectra along every direction in the two dimensional SBZ. An early ARP measurement of the two dimensional Fermi surface of W(001) revealed no significant nesting along the appropriate directions in the SBZ that might have caused the M5 phonon mode to freeze out. 158 Consequently, the charge density wave model for the reconstruction of both W(001) and Mo(001) was generally discarded in favor of local bonding models. This occurred despite a contemporaneous photoemission study of W(001) 161 which, while not providing an independent measurement of the Fermi surface, called into doubt the accuracy of the surface state dispersion reported in Ref. 158. Recent theoretical and experimental results have revived the debate concerning the driving mechanism for the W(001) and Mo(001) reconstructions.

Surface phonon dispersion curves generated from tight binding

calculations of the electronic structure of both surfaces indicate that Fermi surface nesting should play a significant role in driving the reconstructions. 162'163 Helium atom scattering experiments indicate that very significant softening of surface phonon modes occurs for both W(001) 164 and Mo(001). 165 (These experiments also indicate that the room temperature W(001) surface may be slightly incommensurate. 164) The results of these scattering experiments are interpreted as strong evidence for a collective electronic origin to the reconstruction. Given these theoretical and experimental results, there existed a clear need for a re-examination of the experimentally determined two dimensional Fermi surface for W(001). 166 Note that, although of almost equal importance, an ARP determination of the two dimensional Fermi surface of Mo(001) has only recently been published. 167

"To

kI

bJ Z

3

2

1

EF=O

(A-')

1.11 1.01 0.92 0.82 0.76 0.70 0.64 0.54 0.44 0.38 0.31 0.24 0.17 0

Binding Energy (eV) Fig. 3.3. ARP spectra taken with 20 eV photons from W(001) for different values of k~. The light was incident at 60 ° to the sample normal in the (110) plane; the detector was rotated in this plane. The surface Brillouin zone is shown as an inset. (Ref. 166). Reprinted withpermission.

ARP Studiesof ElectronicStructureof Solids

83

Figure 3.3 presents a series of ARP spectra from clean W(001). 166 The detector was moved in the (110) direction and thus states with k I along the Y~ line in the SBZ are detected.

The normal emission (k I = 0 A "1)

spectrum in Fig. 3.3 is dominated by an intense, narrow peak approximately 0.35 eV below EF. This is emission from a two dimensional surface state (the so-called Swanson hump state). 160'161'168 As states with non-zero k I along Y~ are detected, significant changes in the spectra are observed. Focussing only on emission close to EF, it is clear that the peak 0.35 eV below E F at k I = 0 disperses slowly towards E F and looses intensity as k! increases to 0.31/~-1. At k a = 0.31 ~-1 the apparent binding energy of this peak is approximately 0.25 eV. As k I is varied from 0.31/~-1 to 0.64/~-1, it remains clearly visible (though of low intensity) close to EF and shows no dispersion. For k! > 0.64 ,~-1, the peak disperses away from E F, reaching a maximum binding energy of 0.67 eV at k I = 0.79/~4. Finally, it is seen to disperse back towards E F for kll > 0.79/~-1 and to cross above E F at approximately 1.19/~,-1. This behavior is shown in detail in Fig. 3.4, where the dispersion of all two dimensional states within 1 eV of EF along E is plotted.

F

T

M EF

>,, L_

r-Ld t"(:3 0.8, c a3 1.0

~T

"~'~

°_

0.00

~~'~ i

,

0.50

1.00

1.50

klI (~,-I) Fig. 3.4. Dispersion curve (E vs. kll) for surface localized states within 1 eV of E F along Z in W(001). See text for discussion of the asymmetric error bars. (Ref. 166). Reprinted with permission. Once a photoemission peak approaches EF to within the intrinsic energy width of the peak, it becomes difficult to determine the precise location of the peak centroid. Thus there is some uncertainty in the binding energy assigned to the non-dispersive feature seen close to EF in Fig. 3.3 for 0.31 /~-l < kH < 0.64/~-t. It is not clear whether the state crosses EF at one or more points along Y~; hence the large asymmetric error bars for some points in Fig. 3.4. Despite this uncertainty, it is clear that a non-dispersive band is observed close to, or at, EF over a wide range of k u along Y.. As will be discussed, this state will have a pronounced impact on the generalized susceptibility (and hence the screening) of the surface.

A similar two dimensional state was observed for

Mo(001). 167 As explained above, by moving the detector out of the mirror plane and following in k-space where particular peaks cross E F, the two dimensional Fermi surface can be measured. Figure 3.5 presents the result of just such an experiment for W(001) 166 while Figure 3.6 presents the results of the equivalent experiment on Mo(001). 167 We consider W(001) first. The measured two dimensional Fermi surface for W(001) (Fig. 3.5)

84

K.E. Smith and S.D. Kevan

i i

I l l ' l I T ' I l l

i i i

×

g

0 i

oi i0 0--o--0

I

V

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r

i

0 I I

/

I

I

,,,

I

t

I

-1.0

I

I

i

I

I

i

I

0

I

1.0

kt,(i-') Fig. 3.5. Experimentally determined two dimensional Fermi surface for W(001). Measurements were made for one quarter of the zone and mapped into the full zone by symmetry. (Ref. 166). Reprinted with permission.

o

~%.

r--

. . . . .

,- - - $-

- •

'

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o<:

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/

x_l/. . . . . . . ,/IN, /

I

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:

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t _j

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t

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-I .0

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k__J I

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kl ] (/~-1) Fig. 3.6. Experimentally determined two dimensional Fermi surface for Mo(001). (Ref. 167). Reprinted with permission. consists of three major structures. Well defined hole pockets (i.e. Femai surface contours that enclose unoccupied states) were measured around the X and M points in the SBZ. These structures mimic closely the projection of the measured bulk Fermi surface on to a (001) plane, 169 as shown in Fig. 3.7. The M hole pocket in Fig. 3.5 is formed when the peak closest to EF in Fig. 3.3 crosses Er: at approximately 1.19 A "l along'-~'. However, these structures are not significant in driving the reconstruction since they are poorly nested along Y~. Of much greater significance is the shaded region in Fig. 3.5. This is the region in the surface zone where a two dimensional surface state is observed to be very close to, or at, EF; i.e. this is the two dimensional extent of the fiat plateau between 0.31 A "1 and 0.64 A,"1 along"~- in Fig. 3.4. Given the limitations of the photoemission measurement explained above, we should not rigorously include this region as part of the Fermi surface. Nevertheless, since

ARP Studiesof ElectronicStructureof Solids

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Fig. 3.7. Projection of the measured bulk Fermi surface from Ref. 169 onto the (001) plane. (Ref. 166). Reprinted with permission. an electronic state this close to EF will significantly impact low energy surface excitations such as phonons, its inclusion is warranted. For Mo(001), the measured two dimensional Fermi surface (Fig. 3.6) consists of two structures. Around the M points in the surface Brillouin zone there exist hole pockets, similar to those on W(001). However, no hole pockets were observed around X. In fact for Mo(001) a well defined surface resonance was observed at X that extended along both the A and Y axes. The shaded area in Fig. 3.6 indicates the extent of the region where the observed two dimensional surface state comes to within 0.2 eV of EF. The magnitude of this structure is significantly smaller than the corresponding structure in the Fermi surface of W(001). It must be stressed that the choice of 0.2 eV as the binding energy at which the ambiguity in the state energy (as revealed by photoemission) becomes significant is arbitrary.

Given the resolution of the spectrometer used (<100 meV; < 1° full angular

acceptance), there is little error for example in assigning a state energy of 1 eV to a spectral feature at 1 eV. However, deciding at what smaller binding energy the ambiguity becomes significant is subjective. It would not be unreasonable to set the cut-off at 0.3 eV, in which case almost half the area of the zone would be included in the shaded structures. LEED studies indicate that the wavevector of the displacements on W(001) when the surface reconstructs is 1.41 /~-l, assuming the room temperature surface to be a simple (lxl) termination of the bulk lattice. 154'155 Thus the classic CDW model for the W(001) reconstruction requires that the two dimensional Fermi surface display large flat nested regions along the E line, separated by 1.41 /~-l. Similarly, since LEED indicates that the wavevector of the displacements on Mo(001) is 0.91 (n/a,n/a),154 i.e 1.29/~-I along--E-,the CDW model requires a Fermi surface for Mo(001) that displays a nesting vector of this magnitude along Y.. The W(001) Fermi surface shown in Fig. 3.5 clearly displays large scale nesting along E. In fact, there exists a continuum of nesting vectors in this direction connecting different points in the shaded region across the zone center. This continuum of nesting vectors is not a usual occurrence, and is a consequence of the non-standard Fermi surface. The minimum nesting vector is 0.62 ,/~", 1 while the maximum vector is 1.28/~-1. Thus even though there exists large scale nesting along E, the measured Fermi surface does not support the classic CDW model for the reconstruction.

Likewise for

86

K.E. Smith and S.D. Kevan g

Mo(001), there are nesting vectors along Y.. These are the vectors associated with the shaded triangular structures in Fig. 3.6. If the obvious lack of large segments perpendicular to Y~ is neglected momentarily, then the vector connecting the centers of these structures across the zone center (2kF) is 1.15 A "t long. If k F is taken as the vector extending to the flat segment furthest from'F-- (the base of the triangle), then 2k F becomes 1.22 A "1. These vectors are close in magnitude to the displacement vectors observed in the LEED experiment. However, the magnitude of the nesting is much smaller than in the case of W(001). In neither case, then, do the measured two dimensional Fermi surfaces support the classic CDW model in its entirety.

b) Non-Adiabaticity and the CDW Model. The W(001) and Mo(001) Fermi surfaces strongly support a modified version of the CDW model, where electron-phonon (or non-adiabatic) effects are explicitly considered. 162,163 Indeed, these Fermi surfaces give experimental justification for the inclusion of such effects in the model, as will be explained. The inclusion of non-adiabatic effects in the CDW model was prompted by He atom scattering experiments on the structure and dynamics of the W(001) and Mo(001) surfaces. 164,165 These experiments revealed a collective electronic origin to the reconstructions, since large scale softening of the M 5 phonon mode was observed for both surfaces. However, for W(001) the wavevector at which the M 5 mode was observed to go to zero is not that expected from a simple commensurate ( l x l ) to commensurate c(2x2) reconstruction. Rather, the He data indicates that for temperatures above 280K, the W(001) surface is slightly incommensurate with respect to the bulk lattice.164 fit should be noted that an x-ray diffraction study of the W(001) surface has not observed this slight incommensurability and in fact indicates a disordered surface at high temperatures. 170 Reconciling this observation with the He scattering data and the Fermi surface measurements is difficult.:Tt) The wavevector of the W(001) reconstruction observed by He diffraction varied from < 1.1 /~-1 at T > 400K to the commensurate value of 1.41 ,~-1 for T < 280K. 164 For Mo(001), the M5 phonon mode was observed to go to zero at approximately 1.1/~-1, not 1.29 A "1 as expected from the original LEED analysis. 165 While these results contradict the classic CDW model, 159 it was found that if electron-phonon coupling effects on the generalized susceptibility were included in the model, 162'163 then the He scattering data could be explained. For Mo(001) the maximum phonon instability was predicted to occur at a phonon wavevector of 1.17/~-I along--~-,163while for W(001), theory predicted an incommensurate structure. 162 The two dimensional Fermi surfaces presented in Figs. 3.5 and 3.6 support the theory of a collective electronic origin for the reconstruction of Mo(001) and W(001). If we consider W(001), the centers of the shaded regions in the W(001) Fermi surface (Fig. 3.5) are separated by approximately 1.0 A "1, in agreement with the largest incommensurability observed in He diffraction,164 while the existence of a continuum of nesting vectors is consistent with the existence of a continuum of incommensurate structures above the transition. The measured Fermi surface could also explain the existence of an intermediate incommensurate phase for the W(001) reconstruction. Since there exists a continuum of nesting vectors for states very close to EF, there also exists a continuum of possible structural instabilities driven by a continuum of phonon wavevectors. Considering Mo(001), the centers of the small triangular regions are separated by 1.15 A':, which is consistent with the value of 1.1 A"1 where the M5 mode is observed to go to zero, 165 and the nesting vector of 1.17 A "1 predicted by the modified CDW model. :63 Note that CDW model is delocalized, and any reconstruction need not be commensurate with the lattice. In contrast, the local bonding model generally favors a commensurate structure. The interplay between localized and de-localized electronic effects results in a competition between commensurate and incommensurate structures.

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87

Thus far we have shown that the two dimensional Fermi surfaces measured using ARP for Mo(001) and W(001) are in good agreement with what would be expected from both the results of He atom scattering experiments, and the predictions of a non-adiabatic CDW-type model. We now turn our attention to the question of why non-adiabatic effects should be important for these surfaces.

c) Non-Adiabaticity and the Inherent Instability of Mo(O01) and W(O01). Electron-phonon coupling can be viewed as a direct manifestation of the breakdown of the adiabatic approximation in a solid. 83 In this approximation, the motion of atoms and electrons in a solid are considered to be completely independent. This is often a valid approximation because electron velocities are far larger than atom velocities in most solids. As we discussed in the context of adsorbate vibrational damping, the adiabatic approximation will breakdown if the velocity of electrons (or summed velocity of pairs of electrons) is reduced. 83 In a one electron band picture the requirement of slow electrons translates as a need for flat, non-dispersive bands. Additionally, since phonon vibrational energies are typically much smaller than electron binding energies, a strong breakdown of adiabaticity will only occur if flat electron bands reside close to EF. In this section we wish to discuss in general terms how the electronic structure measured by ARP for both Mo(001) and W(001) leads to strong non-adiabatic effects, and is ultimately responsible for the inherent instability of both surfaces towards reconstruction. Using ARP it is found that both Mo(001) and W(001) have two dimensional bands that are non-dispersive very close to EF over significant regions of the surface Brillouin zone. 166't67 Consequently, there is a very high two dimensional DOS close to EF in these regions. Thus, with both a high density of states and slow electrons in flat bands at EF, strong non-adiabatic effects are inevitable. Consequently, non-adiabatic damping of intrinsic surface vibrations (i.e. strong electron-phonon coupling) must occur at both Mo(001) and W(001) surfaces. This would imply that these surfaces are inherently unstable to reconstruction, since with strong electron-phonon coupling it is logical to assume that the energy of electrons at EF can be reduced by many lattice distortions, and thus many lattice distortions (reconstructions) are energetically favorable. The argument that non-adiabatic effects lead to surfaces that are unstable to arbitrary displacements has been considered in a number of theories. 172'173 These theories have usually viewed this as pointing towards a localized mechanism for the reconstructions. However, it is clear from the ARP data discussed above that the reconstruction of both Mo(001) and W(001) is a result of a strong interplay between non-adiabatic and Fermi surface phenomena. This conclusion is reached by the observation on both surfaces of an electronic structure that contains appropriately nested two dimensional Fermi surfaces and a high density of electrons in non-dispersive bands close to EF. This idea is in essence the same as that underlying the theory of Wang et a! for the Mo(001) and W(001) reconstructions. 162'163 That theory was shown above to be compatible with the measured Fermi surfaces. However, strong electron-phonon coupling plays a major role in this theory, and the ARP measurements predict that such a strong breakdown of adiabaticity should occur.

d) Non-Adiabaticity and Local Bonding. The two dimensional electronic structure of both Mo(001) and W(001) leads to a strong breakdown of adiabaticity at these surfaces. This in turn allows subtle details of the interaction between two dimensional vibrational modes and the electronic structure to determine the stability of these surfaces. However, the same experimental evidence that leads to the identification of non-adiabatic electrons also leads us to reconsider the degree of spatial localization of the electrons themselves. To this point we have concentrated exclusively on the CDW model for the reconstruction.

From an experimental approach, this model is the most

easily tested using ARP. The result of the ARP experiments showed that there were indeed two dimensional

88

K.E. Smithand S.D. Kevan

dispersive bands at the Mo(001) and W(001) surfaces; i.e. there are electrons that are confined to the surface layer, but delocaiized within it. These delocalized electrons have a Fermi surface, and this Fermi surface displays nesting in the appropriate regions of the SBZ to support a periodic lattice distortion. This, together with all the other reasons discussed above, leads us to approach the origins of the reconstructions from a collective electron standpoint. The observation of a relatively fiat, non-dispersive band over large regions of the SBZ reveals that nonadiabatic effects are important for these surfaces. However, it also indicates that the electrons in these bands are somewhat spatially localized. An ideal atomic orbital should show little dispersion across the Brillouin zone since it is localized in real space. Thus the two dimensional surface states that drive the reconstruction in the nonadiabatic CDW model are actually rather spatially localized. Consequently, while probably not the primary origin of the reconstruction of these surfaces, local bonding effects may play a role. In the local bonding model, the reconstruction is viewed in terms of cooperative Jahn-Teller distortions, where the surface lattice adjusts to lower the symmetry of degenerate localized electronic d-states. Some degree of de-localization of the electronic states at the surface must occur, if for no other reason than the observation of incommensurate structures. (Localized bonding would tend to keep the surface lattice in registry with the bulk.) If we do allow some de-localization into the local bonding model, then it soon becomes clear that the physics underlying a cooperative Jahn-Teller distortion involving partially collective electronic states and a non-adiabatic periodic lattice distortion driven by the "Fermi surface" resulting from partially localized surface band states is identical. At this stage the controversy between the CDW and local bonding models reduces to semantics.

II. Electronic Effects in Reconstruction. Trivially, a surface will reconstruct if the energy gained by deforming the surface lattice is greater than the energy associated with the restoring force provided by the underlying bulk lattice. For many surfaces, bonding between the surface layer of atoms and the bulk atoms is considerably stronger than bonding within the surface layer, and reconstruction does not occur. If, however, the bonding is roughly equivalent, then electronic effects such as those we have been discussing can be the determining factor in the stability of the surface. We have discussed in great detail the origins of the Mo(001) and W(001) reconstructions. From this discussion of our prototypical surfaces we can pose a number of questions regarding the characteristics of the two dimensional electronic structure that are necessary and sufficient to de-stabilize metal surfaces. First, will a clean metal surface reconstruct in the absence of both strong non-adiabatic effects and a nested Fermi surface? Second, would the surface reconstruct if there were just a nested Fermi surface? (i.e. do two dimensional periodic lattice distortions occur at metal surfaces?) Finally, if a metal surface displays both a nested two dimensional Fermi surface and an electronic structure that allows a strong breakdown of adiabaticity, will it inevitably reconstruct? We will attempt to answer these questions from an experimental viewpoint by discussing ARP data from a number of different metals and surfaces.

a) Pt(lll), Pd(O01), Mo(Oll) and W(OI1) Fermi Surfaces. We mentioned earlier that while the clean (001) surfaces of W and Mo are unstable to reconstruction, their (011) surfaces are not. We now consider the measured two dimensional Fermi surfaces for these faces of W and Mo.

The W(011) Fermi surface is presented in

Fig. 3.8,174 while that for Mo(011) is presented in Fig. 3.9. 85 The shaded areas in these figures are projections of the either measured or calculated bulk Fermi surfaces on to the (011) plane. The first thing to note about both these Fermi surfaces is that all the structures result from conventional Fermi surface crossings. Two dimensional surface states or resonances are observed to cross EF at a single point, and not to hug close to E F over large regions

ARP Studiesof ElectronicStructureof Solids

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Fig. 3.8. Measured two dimensional Fermi surface for W(011). The shaded areas are the projection of the measured bulk Fermi surface from Ref. 169 onto the (011) plane. (Scale: F - N = 1.407 ,/C1). (Ref. 174). Reprinted with permission.

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Fig. 3.9. Measured two dimensional Fermi surface for Mo(011). Panel a) shows hole structures, while b) shows electron structures. The shaded regions are projections of the calculated bulk Fermi surface onto the (011) plane. (Ref. 85). Reprinted with permission.

of the SBZ as was the case for the (001) Fermi surfaces. The two dimensional Fermi surfaces of both W(011) and Mo(011) clearly display a variety of different nesting vectors, coupling to both electron and hole structures. For example, on W(011) there is a nesting vector of magnitude 0.3/~-t that couples the electron structure around zone center (the distorted cross shaped structure) to the hole pocket around N, along the A (F - N ) line. Similarly, on Mo(011) there is a vector of magnitude 1.26/~-1 along&" coupling the hole pocket about'F'- to the hole pocket about N. Significantly, many of these nesting vectors could be expected to produce anomalies in the generalized susceptibility. From the structure of the Fermi surface alone, we are of course unable to predict the magnitude of the anomalies, but we can predict their existence.

However, since these surfaces are stable against intrinsic

reconstructions, we can say that none of the possible screening anomalies is large enough to induce a periodic

JPSSC 21-2-0

90

K.E. Smithand S.D.Kevan

lattice distortion. A prelude to a phonon mode freezing into the lattice is the occurrence of a Kohn anomaly. Here, the screening anomaly is not large enough to lower the phonon frequency completely to zero at a non-zero wavevector.

It is large enough, however, to cause an anomalous dip in the phonon dispersion curve at a

wavevector equal to the nesting vector of the Fermi surface. Thus while the W(011) and Mo(011) surfaces are stable against reconstruction, we predict that Kohn anomalies should be visible in two dimensional phonon dispersion curves. Unfortunately, such measurements have not yet been made. A surface whose two dimensional vibrational structure has been measured is Pt(111). A number of He atom scattering experiments have been performed on this surface. 175"177 Two anomalies in the phonon dispersion curve taken along the (1T0) direction, at 0.8 A "1 and 1.2 A "1 have been reported in some of these experiments, 175'176 although this observation is disputed by other experiments 177 and theory. 178 One point of agreement is that while

G) 6TH BAND PROJECTION

b) 5TH BAND PROJECTION

Fig. 3.10. Measured two dimensional Fermi surface for Pt(111). Filled circles are measured points while open circles have been produced by symmetry. Data points in a) and b) are identical. The shaded region in a) is the projection of one of the two calculated bulk bands (band 6) that cross EF (Ref. 120), while that in b) is the projection of the other bulk band (band 5). (Ref. 121). Reprinted with permission. Kohn anomalies may occur, the Pt(111) surface is stable towards reconstruction. Fig. 3.10 shows the measured two dimensional Fermi surface for Pt(ll 1). 121 The same data points are shown in both parts a) and b) of this figure; the shaded area in part a) is the projection of one of the two calculated bulk bands that cross EF (band 6) onto the (111) plane, while the shaded area in part b) is the projection of the second calculated bulk band (band 5). 121 The bulk and surface band structure of Pt(111) was described in Sec. 3. The measured Fermi surface consists of two structures, a slightly distorted hexagon around zone center and distorted triangular structures around the six comers of the zone (K points); both structures are electron pockets. The zone center hexagonal structure in the Pt(111) Fermi surface (Fig. 3.10) is a conventional Fermi surface structure, i.e. it is produced by the unambiguous crossing of EF by a band. The triangular structures, however, are produced by a relatively non-

ARP Studiesof ElectronicStructureof Solids

91

dispersive band. A noteworthy feature of this Fermi surface is the large scale nesting displayed by the zone center hexagon. The flat sides of this structure are nested far more heavily than any other Fermi surface that we have yet discussed, and this nesting allows the possibility of an associated large screening anomaly. This structure allows for two nesting vectors, one of length 1.7 A -l spanning the zone center, and the other of length 2.83 A "t linking the face of the hexagon in the first zone to that in the third zone. Despite the existence of this heavily nested two dimensional Fermi surface, clean Pt(111) is stable. Thus neither of the nesting vectors induces a large enough anomaly in the generalized susceptibility to support a periodic lattice distortion. They may, however, predict the existence of two Kohn anomalies, at 1.7.3, -1 and 2.83 A -1. None of the previously mentioned He scattering experiments measured phonon dispersions beyond 1.5 A -t, so the existence of these anomalies is unknown. With regard to the two phonon anomalies that were reported at 0.8 A "1 and 1.2 A "t, it is clear that the measured two dimensional Fermi surface does not display significant nesting at these vectors. Consequently, the measured Fermi surface adds credence to a non-electronic model for observed phonon anomalies. 178 Figure 3.11 presents the measured two dimensional Fermi surface for Pd(001); t79 the shaded region is a projection of the bulk Fermi surface on to the (100) plane. The Fermi surface for this state proved difficult to

Fig. 3.11. Measured two dimensional Fenui surface for Pd(001). Shaded region indicates the projection of calculated bands (Ref. 120) at EF onto the (001) plane. (Ref. 179). Reprinted with permission.

measure, and only segments of the surface could be determined. These segments, however, are heavily nested along'A--. The nesting vectors are 1.7/~-I long for nesting across the zone center, and 0.6 A-t long for nesting in to the second zone. As before, this nesting allows the possibility of a screening discontinuity. Pd(001) is found not to reconstruct, and so this discontinuity must not be extraordinarily large. Electron correlation, which will be discussed in Sec. 4, is not insignificant in the electronic structure of Pd, and the effect of this correlation on the anomalies in the generalized susceptibility are unclear. The existence of Kohn anomalies is unknown as no He scattering experiments have been perfon~ned on this surface.

b) The Stability o(Clean Metal Surfaces. From the measured two dimensional Fermi surfaces presented in the previous sections, we can begin to answer some of the questions posed earlier. Perhaps the easiest to answer

92

ICE. Smithand S.D. Kevan

concerns the possibility of a classic periodic lattice distortion at a clean metal surface. If a lattice distortion driven purely by Fermi surface nesting were to occur, then P t ( l l l ) should be the surface to display this. Clearly the P t ( l l l ) Fermi surface is heavily nested, and yet the surface does not reconstruct. Thus the existence of a heavily nested Fermi surface is not sufficient to destabilize a surface. It is, however, necessary. By comparison to the P t ( l l l ) Fermi surface, the Mo(011) and W(011) Fermi surfaces are not particularly heavily nested, and they do not reconstruct. The surfaces that do reconstruct, W(001) and Mo(001), display nested Fermi surfaces, although not on the same scale as P t ( l l l ) . The major difference in the two dimensional Fermi surfaces of W(001) and

Mo(001) is that the bands forming the nested regions are very fiat close to EF across large parts of the SBZ. Consequently, it is the existence of a strong breakdown of adiabaticity that proves to be of importance in determining the stability of these surfaces. Flat non-dispersive bands close to EF were not observed on any of the other surfaces described above (with the exception of the small triangular structures in Pt(111), 121 Fig. 3.10). We will see when discussing the stability of adsorbate covered surfaces, that even the existence of non-dispersive bands and nested Fermi surfaces does not guarantee that a surface reconstruct. However for the clean surfaces studied here, it seems to be a necessary combination. It was mentioned earlier that a surface will not reconstruct if the bonding o f the atoms in the surface layer to the bulk atoms is significantly stronger than that between atoms at the surface. If the bonding is similar, then electronic or non-adiabatic effects can be significant. There is a competition between the lowering of the surface energy achieved by the opening up of band gaps at the zone boundaries formed by a periodic lattice distortion and the raising of energy associated with the lattice strain resulting from the distortion. (At finite temperatures, this competition is complicated by non-adiabatic effects, which couple the atomic and electronic effects.) Independent of electronic effects, it is worth noting that of the surfaces we have been discussing, the ones that do reconstruct are open packed bee (001) faces, while the more close packed bee (011) and fcc (111) surfaces do not reconstruct. An argument based on the increased strain energy required to distort a close packed surface can be made, but this linkage of packing fraction with instability will prove to be unsuitable when discussing the stability of adsorbate covered surfaces.

C. Adsorbate Induced Reconstructions on Metal Surfaces.

Extrinsic, or adsorbate induced, reconstructions on metal surfaces have been extensively studied using ARP. Many different adsorbates on many different metal surfaces have been investigated. The motivation for these studies ranges from interest in two dimensional critical phenomena to a desire to understand adsorption dynamics. When foreign atoms are adsorbed on a metal surface a number of structural changes can occur. Aside from any relaxation or contraction of the surface layer relative to the bulk layers, the adsorbate layer can form a variety of two dimensional structures as a function of coverage, and these structures can change as the temperature of the crystal is altered. This can lead to complex phase diagrams for adsorbate systems. As an example, Fig. 3.12 shows the phase diagram for the H/Mo(001) system, which reveals that H can form a number of different structures on Mo(001) depending on the temperature and the coverage. 18° In this section we will consider two applications of ARP to the study of adsorbed layers on metal surfaces. We will begin by considering ARP studies of two dimensional Fermi surfaces for adsorbate systems, and relate these structures to the reconstructions using the same reasoning as was used in our discussion of clean metal surfaces. Then we consider more conventional ARP studies of bonding in other adsorbate systems.

ARP Studies of Electronic Structure of Solids

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I. Fermi Surfaces and Extrinsic Reconstructions. The models discussed earlier that attempt to explain the reconstruction of clean metal surfaces are equally applicable when considering adsorbate covered metal surfaces. Defining the role of delocalized electrons in destabilizing adsorbate covered surfaces is thus a problem of some significance that ARP can address. We discussed at the start of this section the electronic structure of the ( l x l ) H-saturated Mo(001) surface. That discussion centered on the importance of a flat non-dispersive H-induced surface resonance in non-adiabatically damping H-vibrations. The two dimensional Fermi surface associated with that H-induced resonance is shown in Fig. 3.13.149 The Fermi surface consists of two structures, a small hole pocket about the zone center, and a large, almost square electron structure, also about the zone center. This Fermi surface is heavily nested along theA- line, with nesting vectors of 1.36 A-I and 0.64 A "1. As before, this allows

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94

K.E. Smithand S.D. Kevan

the possibility of anomalies in the generalized susceptibility at these phonon wavevectors. Additionally, as is clear in Fig. 3.2, the resonance defining this Fermi surface never disperses more than 0.2 eV away from EF. Thus the entire electron density in this resonance is concentrated essentially at EF. Indeed, we could easily shade in the interior of the entire annular electron structure in the Fermi surface and allow a continuum of nesting vectors. We have already seen one consequence of this unusual electron density, namely the non-adiabatic H-vibrational damping.144 But given our experience with clean metal surfaces, this combination of a very heavily nested Fermi surface and a very high density of electrons close to EF, we would expect that this surface would reconstruct. In fact, the (lxl) H-saturated Mo(001) surface can be cooled to 10K without showing any reconstruction, lSl Furthermore, preliminary He atom scattering measurements of the phonon dispersion curve do not observe any Kohn anomalies.182 The ftrst of these results succinctly illustrates that adsorbate systems do not necessarily behave like clean surfaces. The bonding between the H overlayer and the Mo(001) substrate is not similar to that between the surface layer of clean Mo and the second bulk Mo layer. The second result, the absence of Kohn anomalies, 182 must wait further experimental verification. It would be a genuinely surprising result given the behavior of the H-modes observed in IR spectroscopy, t44 if this surface were not to display significant H vibrational mode anomalies.

II. Band Structure and Extrinsic Reconstructions. An adsorbate induced reconstruction that has received significant experimental and theoretical attention occurs when C is adsorbed on the Ni(001) surface.

LEED

indicates that at a 0.5 monolayer coverage of C atoms, a (2x2) structure is formed on the Ni(001) surface. 183 The Ni atoms in the top layer move slightly as the C atoms adsorb into the four-fold hollow sites on the surface. Figure 3.14 shows the proposed structure of (2x2) C/Ni(001), and the SBZ of the reconstructed and unreconstructed surfaces, is4 By contrast to the behavior of C, O on this surface forms a similar overlayer structure, but does not induce any reconstruction of the Ni substrate, t85 In this section we wish to briefly describe an ARP study of this

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ARP Studiesof ElectronicStructureof Solids

95

system, and discuss the information an ARP experiment can provide about the origins of a reconstruction other than by measuring the two dimensional Fermi surface. Ni is a transition metal with a partially filled 3d-band. Electron correlation effects complicate the photoemission process in 3d transition metals, and the application of ARP to the study of bonding in correlated materials is the subject of a significant fraction of the remainder of this paper. We will discuss the band structure of Ni(001) as revealed by ARP in Sec. 4, and will describe there the complications that electron correlation introduce into the interpretation of ARP spectra from Ni. Here we note that once these complications have been addressed, ARP allows accurate determination of the two and three dimensional band structure of Ni. In this section we discuss ARP studies of C and O covered Ni(001) surfaces, and for the purposes of this discussion we can neglect any correlation effects on the ARP spectra; the justification for this will become clear later. Figure 3.15 presents a comparison of the experimentally determined surface state dispersions from (2x2) C/Ni(001) and the predictions of a self-consistent density functional calculation of these surface states. 184 Three

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Of more importance in

this regard is the C-induced surface state that exists over much of the SBZ with a binding energy of approximately 1 eV. We shall see in our discussion of the band structure of clean Ni(001) that a surface state exists almost at EF on the clean surface where a surface state is seen 1 eV below EF on (2x2) C/Ni(001). This state on the clean surface is suppressed by adsorption of C, but not by O. 184 (Note that O adsorption does not induce the surface to reconstruct.) The behavior of this state is shown in Fig. 3.16.184 Another significant aspect of this state is that it was not theoretically predicted, as is clear in Fig. 3.15. Given that this state observed in ARP is not theoretically predicted, nor does it appear when O is adsorbed

96

K.E. Smithand S.D. Kevan

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Fig. 3.16. Comparison of ARP spectra at two takeoff angles in the F M azimuth at a photon energy of 37 eV for clean Ni(001), the (2x2)C overlayer and a c(2x2)O overlayer. (Ref. 184). Reprinted with permission. on the surface, it is possible that this state is related to the reconstruction. The behavior of the surface state on Ni(001) with C adsorption can be qualitatively explained by a shift to higher binding energy of the Ni d-states. This lowering of the d-state energy is to be expected if the surface reconstruction is to be stable, and this C-induced state close to, but not at, EF may be a direct result of the reconstruction. 184'186

D. Structural Instabilities in Layered Compounds. Many transition metal compounds have a layered structure, with strong covalent bonding in the layers, and only weak van der Waals bonding between the layers; 187 TiSe 2 is typical of this structure. However TiSe2 displays a (2x2) superlattice when cooled below 200 K. 188 This observation has prompted numerous studies of this material in an attempt to understand its instability. As we shall see shortly, the models proposed to explain this superlattice are almost identical to those proposed to explain the surface reconstructions we have focused on above. Consequently, ARP can have just as significant an impact on our understanding of these compounds. Serendipitously, ARP has been widely applied to the transition metal dichalcogenides for many years. As discussed earlier, a major complication in ARP studies of band structure is the fact that k± is no longer a good quantum number. However, in the layered compounds, bonding perpendicular to the plane is supposedly insignificant with respect to that in the plane, and so many of the early ARP experiments were performed on the transition metal dichalcogenides for reasons of simplicity of interpretation. 189 Here, as an example, we will focus on ARP studies of bonding in TiSe 2, and describe what i,npact these measurements have had on the understanding of the superlattice structure.

Parenthetically, we should note the TiSe 2 is a correlated material, and the problems

associated with photoemission from a correlated material will be discussed in See. 4. These problems have little impact on what we will discuss in this section. The group IV transition metal dichalcogenides have a 1-T layer structure in which the transition metal is octahedraUy coordinated by six ehalcogen atoms. Figure 3.17 shows the reciprocal lattice for 1T - TiSe,2 and the

ARP Studies of Electronic Structure of Solids

(o)

R

~ L' ~

L

H (b)

97

L' A

.

i

(c)

I Fig. 3.17. Reciprocal lattices of TiSe2: a) surface and b) bulk lattices for the normal phase, and c) the bulk reciprocal lattice for the reconstructed CDW phase. (Ref. 190). Reprinted with permission.

reconstructed phase below 200 K. 190 There is a long-running controversy about whether TiSe 2 is a narrow gap semiconductor or a semimetal. Band structure calculations indicate that if any band overlap occurs, it is primarily between Ti 3d and Se 4p states. 191 These are also the states involved in a supposed CDW origin to the TiSe2 superlattice. 188 Figure 3.18 presents a schematic of a possible bulk Fermi surface of TiSe2)92 The hole structure at zone center is Se 4p derived, while the electron pockets at the zone boundaries (zone centers in the superlattice)

qlc i I i

i i i

t

I 1 Fig. 3.18. Schematic Fermi surface for TiSe2, with rod-like electron pockets along LML and hole pockets along AI"A. Electron-electron couphng may occur with spanning vector (tee = % / 2 from M to M between electron pockets, and electron-hole couphng with spanning vector qen = (%/2,c0/2) from M to A or F to L. Incommensurate dlffracUon spots (q = 0.2%/2) may arise from spanning vectors across mdw~dual electron pockets, as for qlc. (Ref. 192)• Reprintedwith permission.

are Ti 3d derived.

As illustrated in this figure, there are a number of possible nesting vectors for this Fermi

surface. Clearly then an ARP measurement of the band structure of this material can determine the validity of the CDW model. Just as in the case of the metal surfaces discussed above, a local bonding model is also proposed

98

K.E. Smith and S.D. Kevan

to explain the superlattice. This model views the structural distortion as a band Jahn-Teller effect, where the electronic energy of the lattice is reduced by the local distortion of the TiSe 2 unit cell from octahedral to trigonal. 192 Some incommensurate structures are observed in this system, 188 which again as discussed above, local bonding models have difficulty explaining. While ARP has been applied frequently to this material the full Fermi surface has not been experimentally determined. However, band dispersions along various directions both parallel and perpendicular to the layers have been measured. 190'193'194 A series of ARP spectra from room temperature TiSe 2 for states along the'~ line in the SBZ is shown in Fig. 3.19.19° These spectra are taken over a wide angle range that corresponds to detecting states from to zone center to well into the second zone. The strong peak close to E F at around 30 ° is emission from the Ti 3d states. These make up the electron pocket at the first zone boundary as illustrated in Fig. 3.19. The Se 4p contribution to these spectra, expected around 0% is not very intense at 18 eV photon energy. Spectra taken at other photon energies by the authors of Ref 190 indicated that TiSe 2 is a narrow band semiconductor at all

T.'3OOK e.5o°

i

-

~

20*

,oo

~

~

.10o

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I

I

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Fig. 3.19. Series of AR_._Pspectra from room temperature TiSe 2. The photon energy was 18 eV and the detector rotated in the E azimuth (See Fig. 3.17). Ti 3d and Se 4p bands are both visible, but dispersion in the latter is difficult to determine at high photon energies. (Ref. 190). Reprinted with permission. temperatures, with little overlap between the Se 4p and Ti 3d states. A second high resolution ARP study of this material observed spin-orbit splitting of the Se 4p band near EF, and verified the existence of a hole pocket around F caused by the dispersion of one of the spin-orbit split bands above EF.193 This study also revealed that TiSe2 is semimetallic, but with only a very small indirect band overlap. Figure 3.20 shows ARP spectra taken from TiSe2 at the F and L points of the bulk Brillouin zone. 193 The spectrum from the L point shows a sharp peak essenfi~l~ at EF. The spectrum from the F point in Fig. 3.20 shows a smooth Fermi edge, and a peak at less than 200 meV below EF. The spin orbit splitting for the Se 4p states was found to be typically 200 meV, and thus the upper Se

4p band lies slightly above EF.193 (This is the hole pocket around 1-J. However, for the very same reasons we discussed above in the context of photoemission from W(001) and Mo(001), there is an inescapable uncertainty in determining the exact binding energy of a state very close to EF using photoemission. This problem is

ARP Studiesof ElectronicStructureof Solids

99

ad .,-4 t-

£3

L

rD >, a.-I

/.

t~

c" QJ ~J c" t--4

t Energy

(ev)

0 b e l o w EF

Fig. 3.20. ARP spectra taken at L and F in the Brillouin zone showing the overlap of the Ti 3d band at L and the Se 4p band at F. (Ref. 193). Reprintedwith permission.

exacerbated in correlated materials, where hole lifetimes can be much larger than in metals. Thus there is a finite overlap between the Ti 3d states and the Se 4p states, estimated at about 120 meV. Interestingly, this partial determination of the Fermi surface of this material would seem to cast doubt on the classic CDW mechanism as an explanation for the supedattice. The nesting in the plane of the layers is quite small, and the Se 4p band forming the crucial hole pocket about F is estimated to never disperse more than 50 meV above EF. (The Fermi surface may look more like that illustrated in Ref. 194 than in Fig. 3.18) It is likely, then, that a more local JahnTeller type mechanism may be the origin of the structural instability of this material.

E. Summary.

To briefly summarize this section, we have reviewed the application of ARP to the study of vibrational and structural phenomena at surfaces and in the bulk of both metals and compounds. The ability of ARP to determine the electronic structure of a material close to EF has allowed a far greater understanding of the role electrons play in determining the stability of two and three dimensional structures. This area of application of ARP is one that is particularly fruitful, although it requires high energy and angular resolution, and a great deal of caution in interpreting the spectra. While the electronic structure close to EF is the area of primary interest in these problems, it lies in the energy range where photoemission spectroscopy has some fundamental limitations, even when applied to metals. We now turn our attention for the remainder of this article to materials where the photoemission process can be quite complex, and where the spectroscopy can have fundamental limitations, even far from EF.

4. CORRELATED MATERIALS: 3d TRANSITION METALS.

The previous sections described the application of angle resolved photoemission to simple metals, semiconductors and compounds, and emphasized the success of the spectroscopy in revealing the detailed electronic structure of these solids. One of the key assumptions made in the interpretation of ARP valence band spectra is

100

K.E. Smithand $.D. Koran

that many-body effects can be ignored. While this assumption is quite good for most of the solids discussed above, we now turn our attention to materials where this assumption is less valid.

ARP can still provide unique

information on the electronic structure of solids in the presence of many-body effects; however, the interpretation of the spectra becomes difficult and, in many caseg, controversial. In this section we discuss the application of ARP in the study of the electronic structure of 3d transition metals, where many-body effects are relatively weak, and only minor changes to the photoemission formalism we have been using up to now are required. In See. 5 we discuss narrow band materials where correlation effects are much greater, the very existence of delocalized bands is questionable, and where many-body effects can dominate the photoemission spectra. However, it is in these very materials that some of the more fascinating solid state electronic phenomena occur, not least of these being high temperature superconductivity.

A. 3d Transition Metals.

A breakdown of the free electron theory in metallic elements occurs in the first row (3d) transition metals.83 The 3d orbitals are more localized than s and p orbitals, and their overlap is small, resulting in a narrow d-band (typically a few eV). However, since up to ten electrons have to be accommodated by the d-states, the density of states of the narrow d-band is quite large. Although in these metals the Fermi level intersects both the sp bands and the d-bands, the large density of states of the d-bands means that their structure and occupation determine many of the physical properties of the transition metals.83 A major consequence of the partial occupation of semilocalized d-states is the occurrence of magnetic phenomena. Thus electron-spin interactions have to be taken into account explicitly, a sharp departure from the free electron metals. As discussed by Harrison, the d-bands are mathematically very complicated and cannot be easily determined theoretically.195

This places a large

responsibility upon ARP to provide meaningful experimental data against which self-consistent theories can be tested.

B. ARP in Correlated Systems: Satellites.

It is worth stressing from the outset that the topic of photoemission from transition metals is fraught with controversy. We do not intend to resolve any of these controversies here. We merely aim to discuss some of the pertinent issues involved in trying to get information on valence band electronic structure of transition metals from photoemission spectroscopy. Our discussion of these issues will be illustrated throughout by reference to Ni, which is a transition metal that displays significant correlation effects, but whose electronic structure can be accurately determined by careful application of ARP. Numerous many body effects can appear in photoemission spectra from narrow band metals. One of the most important of these is the occurrence of satellites. Satellite emission is a term used to describe secondary peaks that can be observed both in core level and valence band photoemission spectra from materials due to many-body effects. They can have a variety of origins and even free electron metals can exhibit satellites. For example in core level photoemission from simple metals, extra peaks can appear close in energy to particular core level features that can be associated with the excitation of plasmons by the outgoing photoemitted electron. 196'197 Since our focus here is on valence band structure, we limit our discussion of satellites to consideration only of those observed in valence band emission. Such satellites have been reported in 3d transition metals such as Ni, 198"200 Cr, 201 Fe,201 Co, 201 and Mn, 202 and the post-transition metal element Cu. 203 (A detailed review of resonant photoemission and satellite structures in transition metals and

ARP Studies of Electronic Structure of Solids

101

compounds has been published by Davis. 2°4) However, the observations for the wansition metals other than Ni have been disputed, 204 with the satellite emission being ascribed to emission from small amounts of oxygen contamination on the surfaces. 205 Valence band satellites in transition metals are a direct consequence of the narrow d-bands. 2°4 If we consider a localized picture we can write the d-electron ground state configuration as 3d n. The conventional photoemission process results in the formation of a 3d n'l state with a hole in the d-band, and the emission of a d-electron into the vacuum with a kinetic energy E d. We can write this process as:

3p63dn4s + hv --~ 3p63dn'14s + e-(Eo)

(4.1)

However, there is no reason from a quantum mechanical viewpoint, that the incident photon cannot create two or more d-holes. In this case we could, for example, simultaneously excite one d-electron into the continuum, and a second to an empty state just above E F. Since energy has to be conserved in this process, the photoemitted delectron will have a kinetic energy E s less than E d. This process can be written as:

3p63dn4s + hv --~ 3p63dn'24snl + e-(Es)

(4.2)

Here, the electron excited above E F is in a state designated nl. In metals with unfilled d-bands, nl is primarily 3d. In general, hole lifetimes in metals are so short that e~rfission associated with a two-hole final state is not observed. In transition metals however, the d-band width W is smaller than the intra-atomic coulomb potential U between two holes (or electrons) on the same atom.

In this situation, the two hole state has a significant lifetime and

satellite emission can be observed. The energy difference between the main line (Eq. 4.1) and the satellite line (Eq. 4.2) is Ueff = E d - E s and is a measure of the effective interaction energy between two 3d holes that are screened by the nl electron. 201 Some quite fundamental information about hole lifetimes, correlation and dbandwidth effects can be obtained from simple photoemission spectra. The measurement of Ueff reveals significant differences in the screening behavior of 3d transition metals. 2°1 We shall see that in Ni metal, with an unfilled d-band, Ueff is of the order of 6 eV, while in Cu, with a filled band, Ueff = 11.5 eV. The difference originates in the nature of the local screening electron nl, which is in a localized 3d state in Ni, but has to be in a 4s state in Cu. 201 The phenomenon of resonant photoemission was discussed earlier in much the same terms as we have used here to describe valence band satellites. Just as conventional photoemission features derived from one-electron states can show strong resonances as the photon energy is swept through a shallow core level absorption edge, so satellite peaks derived from two-hole states also resonate. 2°4 For the valence band structures we are considering here, the absorption edge in question is the 3p ~ 3d transition. Conventional resonant photoemission from a oneelectron state is written as:

3p63dn4s + hv ---) 3p53dn4snl --* 3p63dn'14s + e-(Ed)

(4.3)

where, as discussed above, nl is primarily 3d for these transition metals. In this process a 3p electron is excited to an empty 3d state above E F. This excited state de-excites through an autoionization process where one 3d electron falls back to fill the 3p hole, transferring all its energy to a second 3d electron which is emitted from the atom. Since the final state in Eq. 4.3 is the same as that arrived at by conventional photoemission in Eq. 4.1, it

102

K.E. SmithalldS.D. Kevan

is clear that when the photon energy reaches the 3p ~ 3d threshold, the number of electrons emitted with kinetic energy Ed increases. However, the intensity of the satellite also resonates at the 3p --->3d threshold. To see this we allow the final state to contain the nl excited electron, which requires that there be two holes in the previously filled 3d states. This is written as:

3p63dn4s + hv --->3p53dn4snl --->3p63dn'24snl + e-(Es)

(4.4)

Here the final state is just that of conventional satellite emission, and thus the satellite intensity increases at the

3p --> 3d threshold. Photon induced Auger transitions can often be mistaken for resonances in emission from both one-electron states and satellites, and this has led to significant confusion in the literature. 2°4'2°6 The discussion above has shown that correlation and narrow bands lead to peaks in photoemission spectra from transition metals that are not directly related to their one-electron band structure per se.204 Rather, these peaks are a manifestation of, and indeed can be used as a measure of, the partial breakdown of the independentelectron approximation in these solids. We stress that these satellite peaks appear in the spectra in addition to the usual peaks associated with one-electron transitions in the solid. So long as we are aware of the possible existence of these peaks, ARP spectra can still in principle be used to measure a meaningful valence band electronic structure. We now illustrate these concepts by discussing the electronic structure of Ni, and we shall see that even when satellites are taken into account, correlation effects still complicate interpretation of the ARP results.

D. Electronic Structure of Ni.

Figure 4.1 shows a series of ARP spectra from Ni(001) taken by Eberhardt and Plummer.199 The detector geometry was varied so that even and odd states could be separated (in the manner described in Sec. 1). The peak in these spectra at approximately 6 eV below EF that is marked with an arrow is a satellite. A complication in making this assignment is that emission from the Ni sp-band can occur at the same energy as the satellite. The peaks closest to EF in Fig. 4.1 are primarily Ni 3d related, while the broad dispersive structure between 3 and 7 eV below EF indicated by the dashed line is primarily Ni sp-derived. The satellite emission can be distinguished from the sp-emission in a number of ways. Figure 4.1 shows how by selecting a geometry in which sp-emission is forbidden, the satellite peak can be clearly identified)99 Supporting the identification of the 6 eV peak as a satellite is the behavior of the intensity of this peak as the incident photon energy is varied. Figure 4.1 reveals that as the photon energy approaches the 3p ~ 3d edge in Ni at approximately 65 eV, the intensity of the satellite increases. Since resonant photoemission at this edge is restricted to states with d character, emission from the Ni sp-band cannot contribute significantly to this increase in intensity)99 However, as was discussed in Sec. 1, the intensity of photoemission features varies with incident photon energy for many reasons other than resonant photoemission, an important one being final state effects.

Clauberg et al have shown that there is a strongly

allowed interband transition from the sp(A1)-band to an empty final state that occurs for photon energies around 65 eV, and thus coincides with the 3p --->3d transition. 2°7 This would complicate the definitive assignment of the 6 eV peak to a satellite were it not for the different angular anisotropies of the satellite and the interband transition. The final conclusion of Clauberg et al is that there is indeed a satellite in Ni.2°7 Further evidence (not considered here) comes from spin-polarized experiments. 2°° The existence of a satellite in these ARP spectra reveals that correlation effects are strong in Ni. Further proof of this comes from an analysis of the quasi-particle band dispersions.

Figure 4.2 shows the bulk band

ARP Studies of ElectronicStructureof Solids i , , ~ j , , s , I

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Fig. 4.1. ARP spectra from Ni(001) for various photon energies. In the odd geometry, no bulk sp states can be excited and the emission at approximately 6 eV can be identified as a satellite. In the even geomelry, the sp band can be excited. (Ref. 199). Reprinted with permission.

dispersion for Ni as measured by Himpsel et al. 2°8 Comparison of these data with a succession of sophisticated fLrstprinciple (though not correlated) theories leads to the conclusion that the d-bands measured by ARP are almost 30% narrower than theoretically predicted. 199'209 (Empirically adjusted calculations can be made to fit the ARP data reasonably well. 210) Similarly, the measured exchange splitting of the d-bands is significantly smaller than theoretically expected. 209 These effects are a direct consequence of strong correlation in Ni. A question to be ENERGY(ABOVE EF)

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Fig. 4.2. Experimental band dispersions for Ni. (Ref. 208). Reprinted with permission. answered is whether these differences between theory and experiment are due to correlation effects in the ground state or in the excited state measured by photoemission. Satellite emission is an artifact of the photoemission process whereby holes are created in the Ni d-band. The satellite peak is unrelated to the ground state electronic

104

K.E. Smith and S.D. Kevan

structure of Ni. When the band dispersions of Fig. 4.2 are measured, correlation in the d-band between the existing and photo-excited d-holes causes the measured d-band to appear narrower than it actually is On the ground state). A calculation of the quasiparticle band dispersion in Ni (with U as an adjustable parameter) where this correlation is explicitly considered leads to quite good agreement with the ARP measurements for the band widths, but less so for the exchange splitting.211 Thus many of the discrepancies are excited state effects. However, even in the ground state, it is unlikely that correlation effects are negligible. There is another reason that narrower than expected band dispersions are observed by ARP from correlated systems (i.e. when satellites are present). There exists a sum rule that relates the intensity and ionization energy of spectral function peaks in correlated systems.212'213 We write the spectral function as A(k,¢o), and the expression for the single particle Hartree-Fock eigenenergies as

E k - f?coA(k,~)dco.

(4.5)

As discussed by Freund et al, in the absence of correlations A(k,~) is simply a delta function, 8(ek - co), and a conventionally dispersive (k dependen0 structure is obtained.213 However, in a correlated system with satellite peaks in the spectrum, emission features from the one hole and two hole states are coupled via the sum rule. Thus the intensity and frequency distribution of the spectral function changes with k. Consequently, both emission features can show little dispersion, but have significant k-dependent intensities.213

This mechanism was

demonstrated to exist in a definitive experiment on the CO/Cu(lll) overlayer system, where the predicted dispersion of the CO 4o state is obtained only if the intensity variation of the emission from both the 4o and satellite states is taken into account. 213 Thus the very presence of a satellite in a photoemission spectrum can result automatically in smaller than expected band dispersions. We have seen that ARP does not provide an exact determination of the ground state electronic structure of Ni. This a departure from all solids discussed previously. However, Ni is a relatively simple correlated system, since its electronic structure, even in the presence of correlation, is well described in terms of band electrons. We now consider far more complicated correlated materials, and discuss how ARP can probe their electronic structure.

5. CORRELATED MATERIALS: NARROW BAND COMPOUNDS.

"Narrow band material" is a loosely defined phrase used to describe solids whose valence electrons display both localized and collective electronic characteristics.7 In uncorrelated metals the valence electrons are completely delocalized and, as we have seen above, one-electron band theory works well. By contrast, in molecular solids (such as Xe or C6H6) or ionic solids (such as MgO or CaF2), the valence electrons are completely localized on the individual atoms or molecules, and tight-binding calculations for electronic structure are appropriate.214 Finding a suitable theoretical model for the valence electronic structure in narrow band materials is a significant challenge. Examples of the narrow bands we are discussing are the 3d bands in transition metal compounds, the 4f bands in the lanthanides and the 5f bands in the actinides.7 Narrow bands can occur for a variety of reasons, the most obvious being due to the small spatial extent of thef-orbitals with respect to interatomic spacing in 4f and 5f solids. This small extent leads to very small orbital overlap, which in turn leads to narrow bands. 7 In 3d transition metal compounds, the size of the orbitals is larger, but narrow bands can still occur due large metal-metal distances in the solid.215 The unusual phenomena displayed by narrow band materials are quite numerous. We list Mott insulators, metal-insulator transitions, mixed valence

ARP Studiesof ElectronicStructureof Solids

systems and heavy Fermion effects as examples.

105

As pointed out by Fuggle, Sawatzky and Allen, almost all

ferromagnetic and antiferromagnetic materials can be considered as narrow band materials, 7 and high temperature superconductivity occurs in exactly the systems we are describing.

A. ARP in Highly Correlated Materials: Screening.

When considering the photoemission process in a narrow band material, the most important difference from an uncorrelated metal is how the system responds to the hole left behind by the photoemitted electron. If we consider a simple metal with wide valence bands then the hole created in the valence band by photoemission is

screened by electrons at EF, and this screening only perturbs slightly the quasiparticle energy distributions. In a narrow band material, screening processes are much slower than in simple metals, and this is reflected in photoemission spectra. The topic of core and valence photo-hole screening in correlated materials is a subject of much complexity and has been reviewed elsewhere. 2°4 More than one mechanism exists to screen these holes: charge transfer mechanisms where the screening charge comes from ligand orbitals seem to explain many observations, 216 although an exciton model based on ligand orbital polarization is required to explain screening in the light (Z < 25) insulating transition metal oxides. 217 In general a valence band photoemission spectrum from a narrow band compound will contain emission corresponding to both well-screened and poorly-screened states. Since screening will reduce the net attractive potential of the valence band hole with respect to the photoemitted electron, this electron is emitted with progressively higher kinetic energy as the screening increases.

By

convention, the well screened emission is described as the main line and the poorly-screened emission as satellite emission.216'217 This is essentially the same argument that we used to explain satellite emission in transition metals, where the two hole final state can only be significant for the photoemission experiment if the screening process is slow. A major difference when considering these narrow band compounds is the origin of the screening charge. In many cases this screening occurs via the formation of a localized hole in a ligand orbital. 216 For the purposes of this review the details of the screening mechanism that apply in each of the experiments we shall discuss is not relevant and the reader is referred to Refs. 216 and 217 for further details of screening processes. ARP has not been widely applied in the past to measure electronic structure in highly correlated materials, although given the intense interest in the electronic origins of oxide superconductivity, there have been many more studies recently. There are numerous reasons why there have been relatively few ARP studies of narrow band compounds. One of the most important was the assumption that there would be minimal or insignificant band dispersion in these compounds. If this were the case, there was no particular use in doing an angle resolved experiment, as the simple density of states could be measured using angle integrated photoemission. As we shall see, the determination of even minimal band dispersions can be of great significance. Another reason for the dearth of ARP studies of these materials is the difficulty in preparing a clean well ordered surface.

As discussed in

Sec. 1, accurate information about the bulk electronic structure of a solid can only be obtained using ARP if the surface is clean and well ordered. The methods of surface preparation suitable for a metal are often unsuitable for compounds. Usually the only way to obtain stoichiometric surfaces of these compounds is to cleave single crystals in UHV, 218 although in some special cases other techniques can succeed. 219 The difficulty in obtaining large stoichiometric single crystals that cleave well has limited the study of many interesting multi-element solids with ARP. Finally, as we shall see, some of the most interesting compounds are insulators. This leads to special problems in the photoemission experiment, since as electrons are photoemitted, the sample charges up, often leading to irreproducible spectra. The charging problem can be approached in many ways. Some workers flood JPSSC 21:2-E

106

K.E. Smithand S.D.Kevan

the material with low energy electrons from an extcmal source in order to minimize the charging. 220 Unfortunately this is not feasible for valence band photoemission where low energy electrons are themselves being detected. More successful solutions have been to heat the sample to induce thermally enough conductivity to overcome the charging,221 or to make the extremities of the sample (the sides of a cleavage rod) conducting by either coating with a metal film,222 or by sputtering with inert gas ions,223 to cause the sample to charge uniformly. In some instances, low energy (UV) photoemission experiments are reported not to cause significant charging.224 There are problems with any method designed to overcome charging, and the reader is advised that ARP work from insulating samples should be treated with caution, since changes in charging can lead to the relative motion of spectral peaks, which could be mistaken for band dispersion. In this section we will discuss some examples of the application of ARP to narrow band compounds. In many cases we consider first the localized electronic structurc (i.e. the molecular orbital and crystal field structure) of the solid, then see what information ARP provides on the degree of delocalization of this structure. We will begin with discussion of a very simple 3d transition metal oxide, Ti20 3, that has relatively narrow d-bands by virtue of its crystal structure. 215 Then we will consider the application of ARP to the insulating transition metal oxides, NiO, CoO and MnO: the so-called Mott insulators. Next we examine the application of ARP to heavy fcrmion materials, where the valence f-levels are so narrow as to constitute core levels. Finally we shall consider ARP studies of oxide superconductors, and discuss some recent very high resolution ARP work on single crystals of these superconductors.

B. Simple 3d Transition Metal Oxides: Ti203. Ti20 3 is a particularly simple transition metal oxide with which to begin consideration of ARP studies of narrow band compounds. There is significant interest in the electronic structure of Ti20 3 and the related compound V20 3 due to the metal-insulator transitions these materials undergo with temperature, pressure and doping, some of which are believed to be Mott transitions.215 (ARP studies of so-called Mort insulators will be discussed below). Ti20 3 has a corundum structure with a trigonal Bravais lattice and a ten atom unit cell made up of two Ti20 3 units. The crystal field splits the atomic d-states into a pair of e~ orbitals, a pair of egn orbitals and a lone alg orbital.

The alg orbital is directed along the hexagonal c axis, and forms a covalent bond between pairs of metal cations, the ~ orbitals are involved in bonding between cations in the basal plane, and the eg orbitals are directed towards nearest neighbor oxygen anions. 215 Ti20 3 is a 3d I system, with one d-electron per Ti atom, and the Ti cations are in a 3+ state. In the absence of crystal field effects the material would be metallic. However, at room temperature Ti20 3 is a narrow gap semiconductor, with the filled alg band separated from the empty ~ band by less than 0.1 eV. 215 The empirical band structure is shown in Refs. 215 and 225. From optical measurements 226 and angle integrated photoemission spectroscopy227 the width of the occupied d-band (alg) is estimated at approximately 1.5 eV. The d-electrons in Ti20 3 are expected to be partially localized from consideration of the size of the unit cell alone.215 However, the electron transport properties are described well by a semiconductor band model. 228 ARP should be able to verify the existence of delocalized bands. Figure 5.1 presents a series of normal emission ARP spectra from Ti203(1012). 225 As mentioned earlier, these materials must be cleaved to obtain stoichiomelric surfaces. Unfortunately, the only cleavage plane in the Ti20 3 corundum lattice is the (1012) plane, which is not of particularly high symmetry.219,225 Consequently the normal emission spectra of Fig. 5.1 do not probe a line of high symmetry in the bulk Brillouin zone. A furtber problem with this data is that the detector used had poor

ARP Studiesof ElectronicStructureof Solids

Ti203 (10t"2)

h~c~,e-

Normal Emission hv

8= 3

107

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n ( E ) 39-

72

36" 33~ 30 ~ 57~ 54"

69 66 63 60 57

¢81

54 51

42

Binding Energy (eV) Fig. 5.1. Series of normal emission ARP spectra from cleaved Ti203(1012 ). (Ref. 225). Reprinted with permission. energy and angular resolution.225 Nevertheless, as we shall see, these spectra provide important information regarding the degree of localization of the d-electrons in Ti20 3. There are two primary emission features in the spectra of Fig. 5.1. Between 4 and 10 eV below EF there is a broad manifold of peaks associated with the filled O 2p band. Emission from the Ti 3d band (alg) is visible just below EF. This assignment is consistent with the empirical band structure. Satellites have been observed in core level emission features in Ti20 3 indicating that correlation effects exist in this oxide. 229 However, valence band satellites have not been observed. 225'227'229 A valence band satellite has been reported for the related compound V203 ,225 but V20 3 has twice as rnany d-electrons per cation as does Ti203; that no valence band satellite is observed in Ti20 3 is then ascribed to the probable weak intensity of this structure. 225'229 Given that correlation effects exist, the Ti 3d peak seen close to Err should be considered as well-screened emission. As the photon energy is varied it is clear in Fig. 5.1 that components of the O 2p emission show significant dispersion. More importantly, the Ti 3d band also shows some dispersion along this low symmetry line in the bulk zone. This dispersion is very slight ( < 0.3 eV), but suggests the existence of delocalized d-bands. Also visible in the spectra of Fig. 5.1 is a strong resonance in the emission from the Ti 3d states as the photon energy is swept through the Ti 3p ~ 3d absorption edge (at approximately 47 eV photon energy). This resonance changes the intensity of the Ti 3d emission in the region where the dispersion is observed. The resonance is due to emission from d-states, and should show the dispersion of these states, although the interference between localized resonance effects and delocalized states is not fully understood. 225 Analysis of the spatial characteristics of this resonance provides further insight on the electronic structure of Ti203 .230 Figure 5.2 shows the photon energy dependence of the Ti 3d emission (area of the Ti 3d emission above background) as measured in three different modes: using an angle integrated detector, using an angle resolved detector set normal to the surface, and using the same detector set at 55 ° from the surface normal, parallel to the bulk c-axis.230 A very curious result is that the Ti 3d resonance profile as measured in a normal emission experiment peaks at approximately 9 eV higher photon energy than the profile measured in an angle integrated

108

ICE. Smith and S.D. Kevan

Ti 3d Emission

~

u)

• AngleIntegrated a NormalEmission

o c-axisEmission

:i

410

510 6~0 7'0 Photon Energy (eV)

Fig. 5.2. Photon energy dependence of the Ti 3d emission from Ti203(1012 ) as measured in an angle integrated mode, in an angle resolved normal emission mode, and in an angle resolved mode where the detector is set 55 ° off normal, along the bulk c-axis direction. The emission intensity measured is the area above background of the Ti 3d peak in the appropriate photoemission spectra. (Ref. 230), Reprinted with permission. experiment.

(The profiles in Fig. 5.2 have been scaled in relative intensity so that the slopes at higher photon

energies are roughly equivalent; see Ref 230 for details.) Clearly the ARP measurement is not delaying the onset of the 3p --* 3d resonance by 9 eV with respect to the angle integrated measurement. This anomalous result can be explained if we consider the molecular orbital structure of Ti2Oy The only occupied d-orbital is the alg orbital which is essentially a dz ~ orbital directed along the c-axis of the crystal. The third resonance profile in Fig. 5.2 shows the photon energy dependance of the Ti 3d emission for a series of ARP spectra taken with the detector aligned along the bulk c-axis, i.e. at 55 ° to the normal of the (10~2) surface. As is clear, the maximum emission intensity as measured in this ARP experiment now occurs at almost the identical photon energy to the angle integrated experiment.

Thus if we postulate that electrons are preferentially photoemitted along the axis of the

occupied molecular orbital, then the results of Fig. 5.2 can be partially explained, since in the normal emission experiment, the detector is set far from this axis. This system warrants further study, in particular a very high resolution ARP study along the high symmetry lines in the bulk Brillouin zone, but the work discussed here illustrates a theme that runs through much of the remainder of this paper, namely the coexistence of localized and collective phenomena in correlated materials.

D. Insulating Transition Metal Monoxides.

We now consider materials that have been the subject of intense theoretical and experimemal study for many decades, the insulating 3d transition metal monoxides. The reason for the enduring interest in these oxides is that they embody a dramatic breakdown of the one-electron band picture for the electronic structure of solids. At its most fundamental level, band theory predicts that solids with partially filled bands should be conductors. However, NiO which has a partially filled d-band is an excellent (antifcrromagnedc) insulator, with a band gap on the order of 4 eV. 7'231 Likewise, CoO, MnO and FeO are also insulators with large band gaps despite partially filled d-bands.

Significant debate continues about the origin of the insulating ground state in these materials.

ARP Studiesof ElectronicSa'uctureof Solids

109

Much of this debate concerns an issue we have encountered many times in this paper, namely the degree of localization of the cation d-electrons. A popular explanation for the insulating nature of these monoxides is that they are Mott-Hubbard insulators, with the intra-atomic Coulomb potential U much larger than the bandwidth W.7'231 The easiest way to see how U >> W leads to an insulating state is by considering a simple array of atoms, each with one s-electron.214 Simple band theory predicts a metallic ground state for this system. If, however, the orbital overlap is very small (i.e, the bandwidth W is small), then an insulating ground state will exist, consisting of electrons localized on each atom. U is then defined as the energy required to move an electron from one site to another, and is given as the difference between the ionization energy (I) which is the energy required to remove an electron from one site, and the electron affinity (A) which is the energy gained by adding the electron to another site; thus U -- I - A. As the bandwidth is increased, the orbital overlap increases and U decreases, with a metallic state occurring for U < W. 214 That these materials are highly correlated is not in doubt. Spectroscopic evidence for the strength of the correlation is provided by the frequent observation of satellite emission in both core and valence photoemission. However, an issue of some controversy is the degree to which this correlation is so strong as to invalidate completely the one-electron band description of electronic structure in these solids. ARP should in principle be able to address this problem: if the ARP experiment reveals significant dispersion of the cation states, then those states are delocalized.

Figure 5.3 presents a series of normal emission ARP spectra taken from COO(001) by

Shen et al. 224 The sample was cleaved in UHV at room temperature and no experimental precautions were made

CoO (I 00) D

hv(eV).

~'-

-10

-8

-6

-4

-2

2a

~--

31

\

33 i

I

o

2

ENERGY RELATIVETO E F (eV)

Fig. 5.3. Series of normal emission ARP spectra taken from COO(001). (Ref. 224). Reprinted with permission. to avoid charging. The authors claim that no spurious effects were observed due to charging. 2~ The spectra presented in Fig. 5.3 are similar to those obtained in another recent study of CoO by Brookes et al.221 In this latter study the sample was heated to 393 K to avoid charging and the agreement between the data in the energy range where the data sets overlap is good enough to believe that charging is absent from the data of Shen et al, although they do not attempt to explain why it does not appear. 224 In both studies the spectra are referenced to the Fermi level of a metal (the Cu sample holder in the work of Brookes et al, 221 an evaporated Au film in the case of

110

K.E. Smithand S.D. Kevan

Shen et a~ 24) in contact with the sample; given the insulating nature of CoO it is unclear that this is a valid procedure. However, so long as all the spectra are referenced on the same kinetic energy scale, then relative motion of peaks can be determined. If we examine the normal emission spectra in Fig. 5.3 it is clear that the structure of these spectra changes as the photon energy is changed. These broad valence band spectra are typical of spectra obtained from metallic oxides. We have seen from Fig. 5.1 for Ti20 3 that O 2p emission usually lies 4 - 10 eV below EF, and that the cation emission lies closer to EF. Similarly, emission at the bottom of the broad band in Fig. 5.3 can be assigned to the O 2p states, while that at the top of the band is cation derived.221'224 These assignments can be verified using resonant photoemission.224 If the various features in the valence band spectra of Fig. 5.3 are associated with emission from discrete band states, then the changes with photon energy displayed by the spectra can be associated with changes of the states with k.L, i.e. band dispersion. The extraction of a meaningful band dispersion from spectra such as these is far from trivial, although attempts have been made to do this. Figure 5.4 shows quasiparticle dispersion curves generated from these spectra (inner potential = 8 eV, effective mass = 0.98 me);224 the solid lines in the figure are a result of a non-magnetic one-electron band calculation for CoO. 224'232 The emission at higher binding energy (below 4 eV) can be associated with the O 2p i

I

i

I

CoO (C01)

'

I

1

i

I

'

.

2

5vv

,~

P

~

~

o

o 0.2

04 06 Crystal Momentum

08

Fig. $.4. Comparison of the experimental band dispersion with the results of a nonmagnetic band calculation (Refs. 224,232). The absolute position of the calculated bands is arbitrary. (See Ref. 224 for a discussion of the points enclosed in an ellipse.) Reprinted with permission. related bands in the calculation. Thus the O 2p states in CoO are delocalized and form bands that can be described in terms of a one-electron picture. 221'224 Similar results have been found for NiO224 and MnO. 222 However, the issue of interest is the extent to which the cation d-states are delocalized. The features that lie closest to EF in the spectra of Fig. 5.4 do seem to show some very slight dispersion, but it is difficult to obtain any unambiguous measure of this dispersion from these broad spectra. The dispersion claimed to be measured by Shen et al is only about 25% of that predicted by the one-electron theory.224 (Brookes et al report a larger dispersion for the 3d states in CoO, 221 but their result is disputed by Shen eta/. 224 The origin of the differences between these two groups probably lies in the difficulty of extracting unambiguous peak positions from these type of spectra.) Similar weakly dispersing cation 3d states were observed in NiO224 although in MnO virtually no dispersion was reported.222 Thus the cation 3d bands in the insulating transition metal monoxides appear to be rather flat. Once

ARP Studiesof ElectronicStructureof Solids

111

again then we face the conundrum of describing in real space the behavior of a state that shows a small, but nonzero, dispersion in k-space. It should be noted that these materials have not been studied using very high energy resolution. When we discuss the oxide superconductors we shall see that vital information about their structure would have been lost if high resolution were not employed. Thus as in the case of Ti203, a very high resolution study of these transition metal monoxides is desirable. A complicating feature that we have ignored thus far is the degree to which the highly correlated nature of these materials modifies the photoemission process. The description of the satellites observed in these materials in terms of poorly screened emission, leaves the main line emission, i.e. the features that are observed to be dispersive, to be described as well screened emission. We discussed similar issues earlier in the case of Ti203, but a significant difference between these systems is that for the insulating monoxides, the screening charge must come from the ligand. The degree to which the details of the screening mechanism will modify the observation of dispersive peaks, assuming dispersive bands exist, is unclear. The observation of even small dispersion is used as evidence for the existence of delocalized cation band states in these insulators,224 and thus ARP has proven an invaluable tool in understanding their electronic structure. However the ARP experiments have also revealed a clear need for more sophisticated theories of the electronic structure of these solids.

E. Heavy Fermion Materials.

Next we consider materials where there are states in the valence band that are so narrow as to constitute weakly bound core level states. The narrow band states are f-levels, either the 4f states in the rare earths and their compounds, or the 5f states in the lanthanides and their compounds. 7 These materials are called heavy Fermion materials as a consequence of the extraordinarily large effective masses that result from the existence of these flat narrow bands. 7 The large effective mass manifests itself as an anomalously large coefficient of the linear temperature term in the expression for the electronic specific heat of these materials. Heavy Fermion materials display a host of other unusual phenomena, many thought to be related to the structure of the f-states close to EF.7 There have been numerous photoemission studies undertaken on a variety of heavy Fermion materials in an effort to understand their detailed electronic structure. 7'233 The majority of these studies involved x-ray photons and angle integrated detection. There have been fewer ARP studies of heavy Fermion solids, and in this section we will briefly describe two of these experiments. We will first consider ARP studies of Ce metal, 234'235 then a recent study of the heavy Fermion superconductor UPt3.236 (Although Ce is not a compound, this section is the appropriate context for discussion of the Ce data). Of the many unusual properties of Ce, the isostructural 7 --* cc phase transition that occurs with a 15% reduction in volume when the sample is cooled or pressurized stands out. 237 The relationship between this phase transition and the electronic structure of Ce, in particular the degree of delocalization of the lone 4f electron in the

4ft(5d6s) 3 y-Ce atomic configuration, has been the subject of intensive investigation.234'235'238 Figure 5.5 shows a series of ARP spectra taken from Ce(001). 235 The photon energy was fixed at 21.2 eV, and the detector moved in the (110) mirror plane (FXW azimuth). The spectra in Fig. 5.5 show that there are dispersive valence bands between 0.5 eV and 2 eV below EF. More significantly, they reveal two non-dispersive features, at approximately 2.2 (+ 0.1) eV and at 0.25 (+ 0.05) eV below Er:. These features have also been seen in angle integrated photoemission spectra, 239 and can both be identified as emission from states with predominantlyf-like character since their intensity is observed to resonate as the photon energy is swept through the 4d --~ 4f threshold above 100 eV. 240 The observation of two 4f-derived features in the photoemission spectra sparked much debate about

112

K.E. Smithand S.D. Kevan

i

i

o~. i

Fig. 5.5. ARP spectra taken from Ce(001) with 21.2 eV photons. The detector was moved in the FXW azimuth. The tick marks indicate the theoretical transition energies. (Ref. 235). Reprinted with permission.

their origin.238 Strong correlation effects exist in the heavy Fermion systems, and the ultimate origin of these two peaks has to be related to this correlation. Just as we have seen in many other systems, these peaks can be ascribed to either highly correlated ground state effects, or to an artifact of the photoemission process from a highly correlated material, i.e. screening effects. From our discussion of transition metal compounds we are familiar with how correlation can result in emission features related to both well-screened and poorly-screened hole-states, and this seems to be the most reasonable explanation of the bimodal spectra. 234'235'238 Thus the peak closest to EF in Fig. 5.5 can be associated with well-screened emission, while that at 2.1 eV below EF can be associated with poorly-screened emission.

In neither case do the peaks show any dispersion within the resolution of the

spectrometer used. 235 This result has been reported independently by Jensen and Wieliczka, who also show that the 4frelated peaks do not obey simple one-electron selection rules for the photoemission process. 234 Thus it is clear that the 4f states in Ce are highly localized and cannot be described in a one-electron band picture. Of all the rare earth elements, Ce could be expected to experience the largest hybridization with the (5d6s) valence band.

ARP indicates that this hybridization must be small, since the 4f state shows no dispersion.

However, if we consider heavy Fermion compounds, then the degree of hybridization is again an important question. Figure 5.6 shows a series of photoemission spectra taken from the heavy Fermion superconductor UPt3 .236 The spectra are taken with a fixed photon energy of 40 eV and the detector moved in the (10T0) mirror plane of the (1010) surface. All the peaks below about 0.5 eV show significant dispersion and can thus be related to one-electron bands. The features below 1 eV can be related to Pt 5d bands, while the dispersive feature at approximately 1 eV can be associated with U 6d states; these assignments can be verified using resonant photoemission. The peak at 0.25 eV below EF is related to the U 5]' states, again as revealed by its resonance profile. The analyzer used in this experiment did not have sufficient resolution to unambiguously measure a dispersion of this state. However, it is clear from the spectra in Fig. 5.6 that the peak disappears for angles between 17.5 ° and 20 ° off normal. These angles correspond to the Brillouin zone boundary. It is unlikely that the disappearance of this peak is due to matrix element effects, and so a logical explanation for this observation is that the 5f peak has dispersed above EF at the zone edge. 236 A conclusive determination of the dispersion in

ARP Studiesof ElectronicStructureof Solids

113

UPt 3 (IOTO) hv = 40 eV

37~5' L_~_o 27.5*

15°

i~ 0

10.5

°

10 °

j~_s° JL 2.._s

i

-8

L

i

-6

i

*4

i

r

°

i

-2

Energy (eV)

Fig. 5.6. ARP spectra taken from UPt3(1010) with 40 eV photons. The detector was moved in the (10T0) direction. (Ref. 236). Reprinted with permission. this system will have to await a study that utilizes much higher energy resolution.

Similar results have been

reported for UIr3.24t

F. High T c Superconducting Oxides.

As our f'mal example of the use of ARP to study bonding and electronic structure in solids we consider recent work on high T¢ superconducting oxide materials.

Since their initial discovery, 242 the nature of the

electronic structure of these extraordinary materials has been controversial.

In particular, the relevance of even

a correlated one electron band picture in describing the normal state properties of these oxides is questionable. Given the ability of ARP to determine both densities of states and band dispersions, there have been a vast number of photoemission studies of all varieties of superconducting oxides. (A comprehensive review of all but very recent core and valence level photoemission studies of all classes of oxide superconductors has been published). 243 The goal of many of these valence band studies was to determine if there was any appreciable density of states at EF for these oxides. Unfortunately, the majority of these studies provided little or no relevant information.243 The simple reason for this is that photoemission is a surface sensitive spectroscopy.

Thus to extract meaningful

information about the bulk electronic structure of a solid, great care has to be taken in preparing and characterizing the surface of that solid. The point has been made at the start of this section that in the study of oxide materials, it is essential to use single crystal material, cleaved under ultra-high vacuum conditions. This principle has only recently been applied to studies of the superconducting oxides. A further complication in the case of many of the superconducting oxides is that, at room temperature, oxygen diffuses from the bulk to the surface of the solid when under vacuum.243 This produces surfaces that are not representative of the bulk. The results of room temperature valence band photoemission experiments where the samples are either polycrystalline, or single crystals that are "scraped" clean should be treated with a great deal of caution. For example, many of these early studies indicated that there were essentially no states at EF in YBa2Cu306.9-type superconductors in their normal state. 2A3 Only

114

K.E. Smithand S.D. Kovan

when single crystal samples were used, and the surfaces produced by cleaving these crystals while held at approximately 8 K, did ARP reveal that there was a significant density of states at EF, and that indeed the dispersion of spectral features across EF could be observed. 244 Although the first observation of dispersing bands in an oxide superconductor were made for YBa2Cu3Ot.9 ,244 we will discuss in this section an ARP study of the electronic structure near E F of single crystal Bi2Sr2CaCu208. 245 This material becomes superconducting at 82 K, and is much more stable in vacuum than YBa2Cu3Ot.9-type compounds. 243

The ARP spectra obtained from Bi2Sr2CaCu20 8 are considerably less

ambiguous than those from YBa2Cu3Ot. 9. Bi2Sr2CaCu208 has a quasi-tetragonal structure with Cu-O planes separated vertically by Ca, Sr-O and Bi-O layers, and weak bonding between the layers.243'246 Figure 5.7 shows a series of ARP spectra from Bi2Sr2CaCu20 8 at 90 K (slightly above Tc). 245 The crystal was cleaved at 20 K in a vacuum better than 5 x 10"tl Torr, and could be cycled between 20 K and 90 K without appreciable changes in the ARP spectra; holding the crystal at room temperature for prolonged periods in vacuum resulted in degradation of the spectra.245 The spectra in Fig. 5.7 are taken at a fixed photon energy of 22 eV and the detector is moved

_g c

-05 -OA -0.3 -0.2 -O.t 0.0 binding energy(eV)

Fig. 5.7. ARP spectra from Bi2Sr2CaCu208(001 ) taken with 22 eV photons. The detector was rotated in the (100) plane. (The inset shows the measured band dispersion [dots] and the calculated bands from Ref. 248.). fRef. 245). Reprintedwith permission. in the (100) mirror plane of the surface. [Bi2Sr2CaCu20 8 cleaves along a (001) Bi-O plane]. Since the photon energy is fLxed, any dispersion observed is related to changes in the momentum of the state parallel to the surface, i.e. parallel to the cleavage plane. Indeed, by sweeping the photon energy and moving the detector to keep k I constant, it was shown that the features near EF in Fig. 5.7 show little dispersion perpendicular to the surface. 247 A remarkable result illustrated by the data in Fig. 5.7 is that there exists a dispersive band close to EF, that this band disperses above EF, and that thus Bi2Sr2CaCu208 in its normal state possesses a well-defined Fermi surface.245 This implies that a one electron band picture is as valid a description of the electronic structure in this material as it is in any of the simple metallic oxides (such as Ti203 or V203). The full Fermi surface of the state is yet to be accurately determined,245 although a partial measurement seems to indicate encouraging agreement with

ARP Studiesof ElectronicStructureof Solids

115

band calculations.246 The peak in Fig. 5.7 is due to emission from a hybridized Cu-O band, and emission from what is believed to be a hybridized Bi-O band has also been observed at EF. While the observation of a Fermi surface in these oxide superconductors alone has profound implications for the theoretical models that attempt to explain the phenomenon of high T c superconductivity, the spectra in Fig. 5.7 a reveal further significant feature of the electronic structure near EF for Bi2Sr2CaCu2Os. 245 A close look at the energy scale on Fig. 5.7 shows that this peak shows dispersion only over a very narrow energy range. (The dispersion is much less than expected from a simple one-electron band calculation, as shown in the inset to Fig. 5.7). Indeed, it is probable that no dispersion would have been observed at all were it not that the sample is at 90 K and that thermal broadening of the peak is reduced. This situation is yet again an example of a flat band close to EF, and shows that correlation effects are large in the normal state of this material, consistent with the reported observation of satellites. We can only speculate at this stage on the significance of any non-adiabatic phenomena (such as electron-phonon coupling) that would be associated with these flat bands. A similar flat band has recently been observed in ARP spectra from a different type of oxide superconductor, Nd2.xCexCuO4. 249 This material differs from other oxide superconductors in that the charge

Nd2.x CexC u Oz. (009 h~=5OeV ~ , - - - ~

~

. F~

M

'

JX

- ~ - -I ~'~".

. 6.5")

.

t \'-,.,-(~) I c ,.st ,.¢)

i 1.0 0,5

I ~''v'(a) F' ( O" ' O"

0

Cr

Bindi,~cJ Energy (eV)

Fig. 5.8. ARP spectra from Nd2.xCexCuO4(001) taken with 50 eV photons. The detector was rotated along the (110) direction. (Ref. 249). Reprinted with permission. carriers are electrons (n-type) rather than holes (p-type). The tetragonal crystal structure, however, is similar to most other oxide superconductors, with Cu-O layers separated by Nd and Ce. 243'250 Figure 5.8 presents a series of high resolution ARP spectra from Nd2.xCexCuO4(001) single crystal films grown epitaxially on SrTiO3(001). 249 The spectra were taken with the sample held at 80 K, and the photon energy fixed at 50 eV. Clearly, as the detector is swept along the (I 10) direction, a sharp intense feature appears close to EF which disperse with km. This peak is due to emission from primarily Cu d-states, as determined by resonant photoemission.249 As in other oxides, a valence band satellite is observed, immediately revealing that correlation effects are strong.

Not

surprisingly, the dispersion of the state near EF is almost an order of magnitude smaller than that predicted by

116

K.E. Smith and S.D. Kevan

simple one-electron band calculations. Beyond determining the relevance of one-electron band structure for describing the normal state of these oxides, a further goal of high resolution ARP studies is the direct observation of the superconducting gap A when T < Tc. According to BCS theory, in the superconducting state the occupied and unoccupied quasiparticle states should be separated by an energy gap of magnitude 2A.83 The open!ng up of this gap should in theory be visible in ARP spectra.73"75 Figure 5.9 shows a series of ARP spectra from Bi2Sr2CaCu20 8 where only the temperature of the sample is varied between spectra.75 The photon energy and detector angle are chosen so that a region in

\

I

_ ,

L

a,~ Sr~ C ~

i

,

300

i

Cu~O 6 I • , , ~ - .~ ' ~ "

• ""

-'--~"""

O~

I

300

\ i~-. ' ~2 ~

E-EFIeV)

0

Fig. 5.9. Temperature dependant ARP spectra near EF from Bi2Sr2CaCu208 taken with 18 eV photons. The detector was set at 9 ° off the sample normal along the FX direction. The full line is a guide to the eye. Also shown is a spectrum of clean Au under all the same experimental conditions other than the photon energy is 21.2 eV. (Ref. 75). Reprinted with permission. k-space that has a well defined Fermi function cut off of the density of states at EF at room temperature is sampled. This is illustrated by comparing the 300 K spectrum from Bi2Sr2CaCu20 8 and that from an evaporated gold film also taken at 300 K shown in Fig. 5.9. As the temperature is reduced and the sample becomes superconducting, the emission is seen to move away from EF, indicative of a gap opening up. Additionally, a new peak appears (marked S in Fig. 5.9) close to EF when the material becomes superconducting. The finite energy and angular resolution of the spectrometer, and inevitable peak broadening mechanisms associated with photoemission result in the persistence of a small emission intensity at EF even at 63 K. 75 However, by monitoring the shift of the onset of emission through the superconducting transition, an estimate of 30 (+4) meV for A can be made. The magnitude of A measured here is almost twice that expected from simple BCS theory, and indicates (if accurate) that Bi2Sr2CaCu208 is a strong-coupling superconductor.75 The results of a further high resolution ARP study of the superconducting gap and electronic structure near EF in Bi2Sr2CaCu20 8 are presented in Fig. 5.10. 251 As in Fig 5.9, a gap is clearly seen to appear at EF as the material becomes superconducting. However, in addition to the appearance of a well defined peak close to EF in the superconducting state, a small dip (loss of intensity) appears in the F ---)M spectrum at a higher binding energy. Additionally, the authors report that the magnitude of the gap is not isotropic within the a-b (Bi-O, Cu-O) planes.

ARP Studies of ElectronicStature of Sofids

~.

Hs reduced Bi2Sr2CaCu2Os,s (Tc=91K)

:

- -

^ ~ ,~'~1/l"

80K

....... 100K

1~

117

,

-0.4

"0.4

-0.3

-0.3

-0~2

-0.2

-0.1

0

0.1

-0.1

0.0

0.1

ENERGY RELATIVE TO EF (eV)

Fig. 5.10. ARP spectra for Bi2Sr2CaCu208 from two points in the surface Brillouin zone, with the sample held at three different temperatures. Spectra were normalized to have equal intensities below 0.2 eV. The inset shows the expected behavior of the spectra based on simple BCS theory with A = 27 meV; an instrument resolution function was included. (Ref. 251). Reprinted with permission. The results of ARP studies of the electronic structure of high T c superconductors continue to be hotly debated in the literature. 252 Each new investigation (on high quality samples) reveals more anomalous phenomena that are difficult to explain using conventional models of superconductivity (and sometimes photoemission). We anticipate a continued high degree of interest in the results of these ARP studies. This intense focus on ARP should ultimately enhance our understanding of the normal and superconducting states of these oxides, and also further our understanding of the photoemission process itself in novel correlated materials.

6. FUTURE PROSPECTS IN ANGLE-RESOLVED PHOTOEMISSION.

The preceding sections have provided an introduction to current applications

of angle-resolved

photoemission. We have tried to emphasize the power of the technique to address various issues in solid state physics and chemistry. The technique will continue to be employed with increasing sophistication in these areas. For example, although the underlying technology is largely in place, the variant spin-polarized photoemission has barely started to address a wealth of issues concerning bulk and thin film magnetism. It is clear, however, that ARP has not yet been systematically applied in several active research areas which might stand to benefit significantly. In this concluding section, we explore a few of these. There is an obvious symbiosis between new scientific disciplines and new experimental capabilities. This has been, and continues to be, true of ARP. For example, while conventional light sources still play an important role, the capabilities of ARP have been vastly improved by the accessibility of Synchrotron radiation. 17"20 Improvements in instrumentation associated with synchrotron radiation in turn have continually fine-tuned ARP experiments.

Synchrotron radiation technologies currently being implemented around the word, particularly

high-brightness insertion devices (undulators) 253'254 and high resolving power monochromators,255'256 have not been significantly applied in ARP experiments. We anticipate that they will be in the very near future. Many of the new applications envisaged here are based upon these emerging technologies.

118

K.E. Smithand S.D.Kcvan

A. Spatial Resolution. A source of continuing aggravation to ARP practitioners is that its application to many new and interesting materials depends upon the availability of fairly large (>1-2 mm. dimension) single crystals. As discussed earlier, this limitation was particularly apparent immediately following the discovery of the copper oxide superconductors. The polycrystalline, multiphase nature of the early materials severely limited the first photoemission experiments. This sample-size limitation arises in a wide variety of different materials systems and synthetic microstructures. In many instances, these materials exhibit unusual electronic, structural, and magnetic properties that arise from finite size effects associated with limited dimension in one or more directions. An obvious, though experimentally non-trivial, enhancement of ARP experiments would thus be the study of microcrystals and mesoscopic structures. This will be enabled through use of undulator radiation which is of intrinsically high optical brightness and may in principle be imaged into a spot only a few hundred Angstroms in diameter. 257,258 The ability to apply ARP routinely to polycrystalline or microcrystalline materials, and possibly to the regions between microcrystals, will thus be possible. Similar advances can be envisaged in the study of thin film growth processes and of various quantum nanostructures, where the important length scales often are as small as a few hundred Angstroms as well. One might, for example, hope to measure spectroscopically the quantized energy levels in a 2D heterostructures or in a 1D quantum dot. Finally, when coupled to spin detection, spatial resolution will allow study of a single magnetic domain, thereby alleviating the problematic requirement that microscopically magnetic samples be macroscopically magnetized.

B. Cross-Section Variations.

There are several mechanisms which dramatically modulate photoemission cross-sections. While some of these have been crucial in applications of angle-integrated photoemission, to a large extent they have been treated as a nuisance in ARP. We envisage that these variations will be increasingly employed in the future. This is particularly true in applications which combine studies of solid state valence band electronic structure with more localized atomic or molecular cross-section variations. One of the simpler mechanisms whereby cross-sections can be significantly modified in the so-called Cooper minimum. 259 This occurs when the atomic radial wave function has at least one node. In this case, the Fermi Golden Rule matrix element must pass through zero at some energy and in principle the atomic cross-section into the dominant final state partial wave can vanish. The effect is diluted by solid state hybridization, but its remnant is readily observed. A very nice example of the application of the Copper minimum in ARP is provided by the work of E1-Batanouny et al on monolayer coverages of Pd on Nb(011). 260 The Nb(4d) Cooper minimum is located near hv = 90 eV, while that of Pd is located near 130 eV. Thus spectra accumulated near 90 eV should exhibit enhanced sensitivity to the Pd(4d) levels. This hypothesis is demonstrated by Fig. 6.1, which shows spectra accumulated at normal emission at three photon energies. The enhanced relative intensity of the Pd(4d) levels between 1 and 5 eV binding energy at a photon energy of 90 eV is readily apparent. This work used the Cooper minimum to enable mapping of the adsorbate bands without interference from the underlying substrate bands, and to demonstrate unambiguously that the first palladiurn monolayer exhibits an electronic structure with an essentially filled d-shell, much like a noble metal. Practical limitations have resulted in the Cooper minimum not being widely used in ARP. The difficulty lies in the relatively high photon energy often required. The need for fairly good energy resolution (~4).1 eV) and

ARP Studiesof ElectronicStructureof Solids

119

.o.v

Z

~

9 0 eV

5

4

3

2

I

EF

Fig. 6.1. Normal emission spectra of one monolayer of Pd adsorbed onto Nb(011), collected at three different photon energies. Comparison of the bottom spectrum, collected from clean Nb(011), with the second from the bottom spectrum, indicates the large sensitivity to adsorbate states at photon energies near the substrate Cooper minimum. (Ref. 260). Reprinted with permission.

flux places special demands upon the monochromator and beamline. In addition, the need for good momentum resolution requires increasingly higher angular resolution at higher kinetic energies. Finally, while the cross-section of the interfering substrate 4d and 5d levels is drastically reduced at the Cooper minimum, those of an adsorbate level are often not particularly large. These matters have conspired to leave these experiments with very limited signal in the past. Another atomic mechanism whereby photoemission cross-sections can be significantly modulated is resonant photoemission, described in more detail in Sections 4 and 5. This has also not been widely exploited by ARP practitioners, although an example was given in Sec. 5 for Ti203. In principle, such experiments provide the ability to map a given band while also distinguishing its atomic character, a very useful procedure in complex materials. Most other narrow band systems would benefit from similar studies. These experiments suffer from some of the same limitations as those involving use of the Cooper minimum and will thus benefit from the new technologies described above. A substantial amount of computational and experimental effort has been invested in understanding the unusual and often dramatic photoabsorption and photoemission cross-section variations observed near photothreshold in molecular systems.261 To a large extent these phenomena can be directly extended to the case of adsorbed molecules,61 and perhaps to more complex solids as well.

Classic examples are the ~ and c

resonances observed at threshold and 15-20 eV above threshold, respectively, in the o-symmetry molecular levels of chemisorbed CO. Related effects have been observed in a variety of chemisorbed molecules and have been widely used to determine molecular orientation on the surface. Similar phenomena will be observed in bulk compounds as well, where the final state scattering occurs within a cluster of neighboring atoms. There may be an interesting way to use this phenomenon to derive new and useful electronic structural information. In a fashion analogous to resonant photoemission discussed above, resonance with a core-to-bound or core-to-quasi-bound molecular transition can be manifested by an enhanced valence level cross-section. This has been observed in the gas phase, and has been called de-excitation spectroscopy.262 An example is shown in Fig. 6.2 for the case of N20. In this molecule, the nitrogens are inequivalent, and two well-separated core-to-bound

120

ICE. Snfithand S.D. Keve~

NTNcO DES & PES

hU=401 2ev

~

h c[

~,v.1OOeV

V

] I I/

;l~,',,

'

,

ilv ~,-:I i

L 411

~

211

IB

BINDING ENERGY (eV)

Fig. 6.2. De-excitation spectra of gas phase N20 compared to a photoemission spectrum on a common binding energy scale. The valence band intensities are substantially modified at photon energies near the core-to-bound transition. Moreover, the spectra collected at resonance with the terminal and central nitrogen atoms are quite different, indicating the differential information available with this technique. (Ref. 262). Reprinted with permission. resonances are observed near the N(ls) threshold. The valence photoelectron spectra shown in the figure were collected at photon energies resonant with these transitions and well off-resonance.

The molecular orbital

intensities are seen to be dramatically different among these three spectra, a result which was interpreted in terms of an atomic projection of the valence levels onto the core hole state. The added information arises from the fact that the matrix element for the core-to-bound transition picks out a certain angular momentum component of the unoccupied density of states in the proximity of the absorbing nucleus. An ARP experiment carried out in the deexcitation spectroscopy mode will, in the same way, give infonnation about the atomic constitution of the band being observed. This is another experiment which will be starved for signal due to the need for high energy resolving power and for very good angular resolution.

C. Ultrahigh Energy and Momentum Resolution ARP. The last frontier we wish to mention, studies utilizing much higher energy and momentum resolution than the current norm, is actually being actively pursued at present. The motivation for doing this arises from another source of aggravation to ARP spectroscopists, that is, the limited ability to make contact with a variety of phenomena in solid state physics and chemistry. The studies of the high temperature superconductors described See. 5 provide just one example of how vasdy improved resolution might provide the sensitivity to enable the technique to have a major impact upon our understanding of complex electronic phenomena. The current limitations of ARP easy to understand. Many interesting phenomena occur on the energy scale of phonons, magnons, or other low energy quasiparticle excitations (0.1-10 meV). This is why these phenomena are generally manifested by some ordered, macroscopic state only at low temperature. In order to provide precise information about these phenomena, ARP needs to measure electron states within this energy of F_~. Unfortunately, ARP experiments typically utilize an energy resolution not much better than 50 - 100 meV (the aforementioned experiments on high T e materials being a notable exception). Moreover, the momentum resolution is typically

ARP Studiesof ElectronicStructureof Solids

121

> 0.05 ,~,'], so that b~nds with significant velocity ( > 0.5 eV//~-:) are further broadened. While these experimental resolutions are adequate to address relatively high energy issues such as bulk cohesion, lattice structure, and ehemisorption, sensitivity to low energy phenomena is normally not available. Thus the signal/resolution trade-off provides a practical limit to the sensitivity and applicability of the technique. An example of the sort of experiment which might be possible by employing new technologies to achieve very high resolution is provided by materials containing lanthanide elements. At low temperature these exhibit a variety of unusual phenomena, including the Kondo effect, heavy Fermion conduction, and mixed valency. These are all the result of the substantial electron correlation which occurs in the highly localized 4f-shell.263 A large number of angle-integrated photoemission and inverse photoemission (or Bremsstrahlung isochromat) spectroscopy experiments have been reported on these systems. Such studies have been very successful in understanding the "high-energy" phenomena related to electron correlation. For example, combined photoemission and inverse photoemission studies can measure the correlation and ligand field energies associated with atomic multiplet splittings. While these high energy parameters impact the low temperature phenomena in crucial ways, one really would like to measure the electrons directly involved, for example, in fomaing the Kondo resonance. A beautiful series of angle-integrated photoemission experiments on several related 4fcompounds and elements have indicated that this is indeed possible.264 We show in Fig. 6.3 the results for CeSi 2, a heavy fermion conductor which develops a Kondo resonance just above EF for temperatures below about 50K. This figure shows photoemission

t

I

I

I

I

I I I I I I

hv : Z,08 eV

15K (a)

It)

T=ISK 80 K

hv : 21.2 eV

[

..~(d )

"'-~.....

I

I

I

I

3

2

I

E~

200K

"

300 K

~,',.If]

I

I

OA.

I

I

0.2

I

lel

I

EF

ENERGY leVi

Fig.

6.3. Angle-integrated photoemission spectra of the lanthanide compound CeSi2. Panel a shows spectra accumulated at T = 15K; these are compared to a many-body simulation of the 4fcontribution in panel b. Panels c-f show the region near EF expanded, as a function of sample temperature, and demonstrate clearly the collapse of the Kondo resonance at higher temperature. (Ref. 264). Reprinted with permission. spectra near EF as a function of temperature at two photon energies. The development of a very narrow feature at EF at low temperatures is interpreted to be essentially the tail o f the Kondo resonance.

Note also the

characteristic delayed onset as manifested by the larger intensity of the 4f-derived Kondo feature at the higher photon energy. Spectra such as those in Fig. 6.3 have normally been interpreted using variants of the Anderson

JPSSC 21:2-F

122

K.E. Smith and S.D. Kevan

singie-impurity Hamiltonian. 265 This model treats the f-levels as largely localized and thus independent of one another, but weakly hybridized with other band states. A significant accomplishment of this treatment is that states very close to El: are essentially delocalized and metallic, while those far from EF acquire increasing atomic multiplet character. It thus very nicely unifies the high resolution results like those in Fig. 6.3 with the high energy results mentioned earlier. However, the low temperature phenomena of interest are often concerned with transport, and thus with the degree of coherence between neighboring f-levels in the lattice. The single-site Anderson Hamiltonian specifically excludes these interactions. It will be important to measure and to model the momentum dependence of the resonances near EF to understand these coherence properties.

D. Concluding Remarks.

The purpose of this review has been to explain the fundamental issues involved in using ARP to study electronic phenomena in a host of different materials, and we have tried throughout to indicate the technique's enormous breadth of application. The spectroscopy can now be considered to be "mature", in the sense that the fundamental details of interpretation have been (or are being) worked out, and we have indicated how it might be applied in emerging fields and technologies. An evaluation of this sort is useful and timely. A technique like ARP needs to be applied in a variety of contexts lest experiments become purely technique-oriented, with little relation to solid state physics and chemistry in general. The most striking current example of how ARP is being applied to unusual materials is undoubtedly in the area of high Tc materials. Never before has so much attention been focused upon the technique. We envision a bright future with similar high-profile applications for some time to come.

ACKNOWLEDGEMENTS.

The authors wish to express their gratitude to the many people they have worked with in the study of solids with ARP. Especially important among these people are S. Dhar, G.S. Elliott, R.H. Gaylord, V.E. Henrich, K. Jeong, R. Kneedler, R.J. Lad, N.V. Smith, N.G. Stoffel and D. Wei. We also thank R. Georgiadis for reviewing the manuscript. Part of the work reported here was supported by the U.S. Department of Energy (DOE) under grant No. DE-FG06-86ER45275, and some of this work was undertaken at the National Synchrotron Light Source, Brookhaven National Laboratory, which is supported by the U.S. DoE, Divisions of Materials Sciences and Chemical Sciences.

S.D.K. acknowledges the financial support of the National Science Foundation and the

A.P. Sloan Foundation.

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