Studies in Surface Science and Catalysis 74 ANGLE-RESOLVEDPHOTOEMISSION Theory and Current Applications
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Studies in Surface Science and Catalysis Advisory Editors: B. Delmon and J.T. Yates
Vol. 14
ANGLE-RESOLVED PHOTOEMISSION Theory and Current Applications
Editor S. D. Kevan Physics Department, University of Oregon, Eugene, OR 97403, USA
ELSEVIER
Amsterdam -London
-New York -Tokyo
1992
ELSEVIER SCIENCE PUBLISHERSB.V. Sara Burgerhartstraat 25 P.O. Box 21 1, IOOOAEAmsterdam, The Netherlands
ISBN: 0-444-88 183-2
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V
PREFACE
The technique of angle-resolved photoemission (ARP) is at an interesting period in its development. In the past 15 years, a theoretical foundation has been laid upon which most current experiments are interpreted: conservation of parallel momentum, approximate conservation of perpendicular momentum, broadening mechanisms, and prediction, detection, and characterization of intrinsic and extrinsic surface states. It thus appears that ARP can be applied in a relatively straightforward fashion to a wide variety of problems of current and standing interest in solid state and surface physics and chemistry. However, increasingly sophisticated experiments are testing and limiting the application of some of these simple concepts: many body and other final state effects, static and dynamic disorder, theoretical treatment of excitation spectra. In the same period, significant improvements in experimental and theoretical methodology have been attained. The techniques for preparing and characterizing surfaces and interfaces have progressed to the point where reasonably complex yet well-defined systems can be prepared: elemental surfaces of all sorts, metal-metal and metalsemiconductor interfaces, semiconductor heterojunctions, compound and alloy surfaces. The constant improvement in computer technology and in codes for calculating electronic structure have allowed the "routine" introduction of self-consistency, improved treatments of exchange and correlation, and relativistic effects. The first few steps in actually calculating the excitation spectrum of simple systems have recently been reported. Finally, the increased availability and improved quality of synchrotron radiation sources have made the technique more powerful, more generally applicable, and more diverse in the everincreasing array of sub-fields being spawned. The rate at which new storage rings and beam lines dedicated to the production of soft x-rays are being proposed, constructed, and commissioned suggests a very bright and busy future for the technique. This confluence of events is allowing ARP to be applied in many laboratories around the world to a variety of systems. This confluence also makes the present an opportune time to produce a researchlevel monograph on the subject. As yet, no comprehensive treatise exists. Very good reviews of ARP by Plummer and Eberhardt, Himpsel, and Williams, Srivastava, and McGovern have appeared. The several books on photoemission as a whole generally contain but one chapter dealing with ARP. None of these reviews, however, comes close to a comprehensive treatment of this very large and growing field. Indeed, it is unlikely that
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any one small set of authors would endeavor to write a monograph at the level and in the detail the field warrants. What is needed is a reference book that will be of general use both to long-time workers in the field as well as to the uninitiated graduate student just learning how to apply the basics to their particular problem. This is the goal of the current monograph. The first chapter provides an introduction to the motivations, methodologies, and terminologies of the technique, and briefly discusses "the party line" for interpreting ARP data. The next two chapters discuss in detail the physics of the photoemission process and the current understanding of its precise relationship to crystalline electronic structure, primarily €or bulk, three-dimensional states. After a brief review of the one-step, single particle theories, these chapters will focus on the "crucial issues" which all-to-often are not adequately addressed in interpreting experimental results. These would include, for example, the physics of quasiparticle excitation and other many-body effects, the applicability of the local-densityapproximation-calculated electronic structures to photoemission data, and the various contributions to linewidths and shapes. The next eight chapters discuss various wellestablished and currently active experimental applications of the technique. All but chapter 7 are focused upon measurement of intrinsic and extrinsic (i.e., adsorptioninduced) electronic states in two and three dimensions. Chapters 4 and 5 survey the surface electronic structure of metals and semiconductors, respectively, as probed by ARP, and its impact upon surface stability and reconstructive behavior. Chapter 6 discusses more complex metals and metallic compounds and is included as an avenue to test simple data analysis models. Chapters 8-10 center on the application of ARP in studying the electronic and geometric structure of relatively simple atomic and molecular adsorption systems. Chapter 11 discusses the somewhat more complex application to thin film systems. Chapter 7 is the only one specifically directed toward core-level ARP measurements, wherein ARP can provide valuable surface structural information. All of these subjects are quite active in various laboratories around the field. The final chapters examine applications which are still being developed and which hold significant promise for the future. Chapter 12 reviews the application to ferromagnetic systems, an area which has been revolutionized by the ability to distinguish the spin of the excited electron at arbitrary energy and emission angle. Chapter 13 is included to demonstrate the time-reversed application of ARP, inverse photoemission, which, as a complement to ARP, allows the unoccupied levels to be probed. The next chapter reviews recent efforts to apply pumpprobe techniques, using lasers as the pump, to study the dynamical properties of surfaces in real time. Finally, chapter 15 discusses the most recent and perhaps most dramatic application of ARP to highly correlated electronic behavior.
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CONTENTS Preface
..................................................................
v
........................................................
ix
Introduction .............................................................. N.V. Smith and S.D. Kevan
1
The Physics of Photoemission ............................................... J.E. Inglesfield and E.W. Plummer
15
..................................
63
Surface States on Metals ................................................... S.D. Kevan and W. Eberhardt
99
Surface States on Semiconductors ............................................ G.V. Hansson and R.I.G. Uhrberg
145
List of Contributors
Quasiparticle Excitations and Photoemission S.G. Louie
Metallic Compounds and Ordered Alloys: Carbides and Nitrides, Applicability of Simple and Sophisticated Theories to More Complex Systems L.I. Johansson, and C.G. Larsson
.....
213
..................................................
243
.....................................................
291
Molecular Chemisorptian .................................................. H.-J. Freund and M. Neumann
319
........................................
371
Photoelectron Diffraction D.P. Woodruff Atomic Chemisorption A. Goldmann
Metallic Films on Metallic Substrates K. Jacobi
viii
Thin Films on Semiconductors R.D. Bringans
..............................................
Spin- and Angle-Resolved Photoemission from Ferromagnets E. Kisker and C. Carbone
....................
435
469
.....................................................
509
................................................
553
.........................
571
............................
595
.................................................................
601
Inverse Photoemission P.D. Johnson
Multi-Photon Photoemission J. Bokor and R. Haight
New Frontiers: Highly-Correlated Electronic Behavior R.F. Willis and S.D. Kevan
Future Prospects in Angle-Resolved Photoemission S.D. Kevan Index..
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LIST OF CONTRIBUTORS 1) Introduction N.V. Smith, AT&T Bell Laboratories, 600 Mountain Ave., Murray Hill, N.J. USA 07974, and S.D. Kevan, Physics Department, University of Oregon, Eugene, OR. USA 97403.
The Physics of Photoemission J.E. Inglesfield, University of Nijmegen, Faculty of Science, Toernooiveld, NL-6525 ED Nijmegen, The Netherlands, and E.W. Plummer, Department of Physics, David Rittenhouse Laboratory, University of Pennsylvania, Philadelphia, PA. 19104-6396.
2)
3) Quasiparticle Excitations and Photoemission S.G. Louie, Department of Physics, University of California, Berkeley, CA. 94720.
Surface States on Metals S.D. Kevan, Physics Department, University of Oregon, Eugene, OR. USA 97403, and W. Eberhardt, Institut fur Festkorperforschung, Kernforschungsanlage Julich GmbH, Postfach 1913, D-5170 Julich, FRG.
4)
Surface States on Semiconductors G. Hansson and R. Uhrberg, Department of Physics and Measurement Technology, Linkoping Institute of Technology, S-581 83 Linkoping, Sweden.
5)
Metallic Compounds and Ordered Alloys 6) L.I. Johannson, Department of Physics and Measurement Technology, Linkoping University,S-581 83 Linkoping, Sweden; and C.G. Larsson, Department of Physics, Chalmers University f Technology, S-41296 Goteborg, Sweden. 7) Photoelectron Diffraction D.P. Woodruff, Department of Physics, University of Wanvick, Coventry CV47AL UK. 8) Atomic Chemisorption A. Goldmann, Gesamthochschule Kassel, FB 18 Physik, Heinrich-Plett-Strasse 40, 3500 Kassel, FRG
Molecular Chemisorption H.J. Freund, Lehrstuhl fur Physikalische Chemie I, Ruhr-Universitat Bochum, Postfach 10 2148, 4630 Bochum 1, FRG; and M. Neumann, Fachbereich Physik, Universitat Osnabruck, Barbarastrasse 7, 4500 Osnabruck, FRG.
9)
10) Metallic Films on Metallic Substrates K. Jacobi, Fritz-Haber-Institut der Max-Planck Gesellshaft, Faradayweg 4-6, D-1000 Berlin 33 FRG.
X
Thin Films on Semiconductors R.D. Bringans, Xerox Palo Alto Research Center, 3333 Coyote Hill Road, Palo Alto, Ca. 94304 11)
12) Spin- and Angle-Resolved Photoemission from Ferromagnets E. Kisker, Institut fur Angewandte Physik, Universitat Dusseldorf, Universitatstrasse 1,4000 Dusseldorf 1, FRG, and C. Carbone, Institut fur Festkorperforschung der Kernforschungsanlage Julich GmbH, Postfach 1913, D-5170 Julich, FRG. 13) Inverse Photoemission P.D. Johnson, Physics Department, Brookhaven National Laboratory, Upton, N.Y. USA 11973. 14) Multi-Photon Photoemission J. Bokor, AT&T Bell Laboratories, Crawfords Corner Road, Holmdel, N.J. USA 07733, and R. Haight, IBM T.J. Watson Research Center, P.O. Box 218, Yorktown Heights, N.Y. USA 10598.
15) New Frontiers: Highly Correlated Electronic Behavior R.F. Willis, Physics Department, 104 Davey Building, Pennsylvania State University, University Park, PA 16802, and S.D. Kevan, Physics Department, University of Oregon, Eugene, OR. USA 97403. 16) Future Prospects in Angle-ResolvedPhotoemission S.D. Kevan, Physics Department, University of Oregon, Eugene, OR. USA 97403.
1
Chapter 1
INTRODUCTION N.V. SMITH AND S.D. =VAN
From humble beginnings in the early 1970's, angle-resolved photoemission spectroscopy (ARPES) has become established as an indispensable tool for the investigation of solids and their surfaces. This book represents an attempt to assemble in one volume an account of the large variety of work now going on. This opening chapter sets the work against the larger perspectives of the history of the photoelectric effect and of the electronic structure of condensed matter. It offers also a brief treatment of past and present experimental methods, and a brief account of our current understanding.
1. HISTORICALBACKGROUND 1.1 Prehistory Interest in the angular dependence of the photoelectric effect can be traced back to the early decades of this century. Jenkin (1) has written an entertaining and informative history which covers this period, and he documents how a number of Nobel laureates (W. H. Bragg, C. T. R. Wilson, A. H. Compton, W. Bothe, C. D. Anderson and E. 0.Lawrence) contributed to this topic before moving on to other (and evidently more rewarding!) endeavors. The history by Jenkin confines itself to the angular dependence of X-ray photoemission. We attempt here to fill in some of the gaps relating to ultraviolet photoemission and its angular dependence. Our treatment is not exhaustive, but is intended rather to sound a few historical keynotes which resonate strongly with current activity. In the 1920's, the angular dependence of photoemission from alkali metals was investigated by Ives and coworkers at the Bell Telephone Laboratories (2). Their apparatus is shown in Fig 1. These pictures exemplify not just the delightful scientific artwork of an earlier generation but also the two main experimental approaches still in use today: a single movable electron collector, or a sectored collector. The work of Ives and his group was closely linked with their technological interest in the use of alkali-based photocathodes in the emergent industry of television and in the possibilities of videotelephony. One question of physics raised in this work, however, has lost none of its savor in the intervening decades, namely, the vectorial photoeffect, which is concerned with the differences in emission intensity associated with the polarization of the incident radiation. The next landmark occurs in 1945 with the publication by Fan of a theory of the bulk origin of the photoelectric effect (3). This paper, which does not appear to have had
2
F
I
b
Fig. 1 Early angle-resolved photoemission apparatus of Ives and coworkers reproduced from Ref. 2. The method on the right employs a moveable electron collector; that on the left employs a stationary sectored collector. much impact at the time, presented a view of the photoemission process contrary to the prevailing notion that the photoelectric effect was a surface phenomenon (4). The Sommerfeld model of a metal treats electrons confined in a potential well V(r) of rectangular shape. Optical excitation occurs only if VV#O, and this condition, in the Sommerfeld model, occurs only at the surface. If we allow the existence of some atomic structure within the well, we have VV#O in the interior and the existence of a bulk contribution to the photoelectric effect. The Fan paper treats the bulk potential by Fourier synthesis, what in modern parlance we would call a nearly-free-electron (NFE) or pseudopotential model. Figure 2, reproduced from the Fan paper, shows the k-space geometry for optical excitations within a hypothetical NFE metal. We recognize here a number of results which have subsequently been rederived by others (5,6). Surfaces of constant photon energy are planes. Surfaces of constant electron energy are spheres which intersect these planes. Thus the angular distribution of photoelectrons will be about cones (6).
3
1.2 Photoemission as a Soectroscooy The transformation of photoemission into a spectroscopy, as opposed to an interesting and useful physical phenomenon, took place some time in the late 1950s, or early 1960's. The contributions of Spicer (at Radio Corporation of America, and later at Stanford University), Apker, Taft and Phillip (General Electric) and Gobeli and Allen
ll.
V
Fig. 2 Diagram reproduced from Fig. 1 of the 1945 paper by Fan (Ref. 3) showing the kspace geometry for the bulk photoelectric effect. (Bell Labs) are especially important. Parallel efforts were being made in Europe by Mayer and associates (Clausthal). Some future historian of science might wish to note that photoemission research in the United States appears to have been driven not so much by the desire for fundamental knowledge for its own sake but by the imperatives of the burgeoning television industry. The key discovery in this early period was the establishment of the primacy of the bulk photoelectric effect. The personal memoir of W. E. Spicer on his early days at RCA (7) is particularly revealing on this point. He was confronted at the start of his work by a large literature of photoemission experiments performed in ill-defined vacuum using an interpretive approach dominated by the Sommerfeld model. This body of work he found "basically useless". The historical turning point came with the routine attainability of ultrahigh vacuum and the ability to prepare samples which were atomically clean and the availability of bulk band structure calculations for purposes of comparison. A major landmark was the publication in 1964 by Berglund and Spicer (8) of photoemission energy spectra on Cu and Ag. These spectra displayed in a spectacular way the edges of the d bands at respectively 2 eV and 4 eV below the Fermi level. The sight of
4
these spectra convinced one of the authors (NVS), then a graduate student, that he wanted to be a photoemission spectroscopist. He was not alone in this aspiration. There followed an explosive effect to use photoemission in the determination of the densities of states and other electronic properties of a wide variety of materials. The reader is referred to the compendium by Cardona and Ley (9) for a summary of this activity up to about 1977. In the early 1970's, photoemission began to diversify. There was a reawakening in the interest in the angular dependence of photoemission (see Section 1.3 immediately following). The attractive features of synchrotron radiation were also recognized (10, 11). Spin asymmetry in photoemission was detected (12). Surface effects in photoemission, having been in eclipse for a decade, now began to reassert themselves. Band-gap surface states were observed on clean silicon (13, 14). Electronic states associated with adsorbed molecules were observed (15). Even the elusive surface photoelectric effect was unambiguously isolated (16). 1.3 Angle-resolved Dhotoemission sDectroscoDy Photoemission work in the 1960's was almost exclusively angle-integrated. An exception was the work of Gobeli, Allen and Kane in 1964 (17). In a notably prescient paper, Kane argued that the E(k) band structure could in principle be mapped from angular dependent photoemission spectra (IS). This paper recognizes the indeterminacy of kL, the internal perpendicular component of the electron wave vector, and contains within it the energy-coincidence strategy for overcoming this obstacle. Ten years were to elapse however before a band structure was actually mapped (19). Experimental work on the angular possibilities of photoemission spectroscopy started in earnest in the early 1970's. Using a sectored-collector apparatus similar to that in Fig. 1, Gustafsson et al. (20) showed in 1971 that the photoemission from Ag(ll1) was indeed distributed about cones of constant energy, as anticipated in the work of Fan (3) and of Mahan (6). At about this time the following events occurred: Feuerbacher and Fitton showed that normal photoemission from W(100) was dominated by a surface state just below the Fermi level (21); Wooten et al. demonstrated strong angular dependences in photoemission from GaAs (22); Koyama and Hughey, using synchrotron radiation, observed an angular dependence in photoemission from polycrystalline gold (23); and Williams et al. found that the photoemission spectra from MoS2 varied in a spectacular fashion with angle of emission (24). The work of Wooten lends itself to an interesting anecdote. At that time, he was at the Livermore Laboratory, and the underlying motivation for his work was the need to develop better photodetectors to monitor emissions from underground detonation of nuclear devices (25). The first formal demonstration of band mapping using ARPES was published by Smith, Traum and DiSalvo in 1974 (19). In order to circumvent the indeterminacy of k L these workers performed their measurements on the two-dimensional layer-compounds TaS2 and TaSe2 They monitored the variation in energy E of peaks in the photoemission
5
spectrum with polar angle 0 of emission, and then obtained the parallel component of the electron wave vector using
k 11
= ( 2 1 n E / f i ~ )sin ~ / ~8,.
The resulting E(k11) dispersion curves were in good agreement with the first principles band calculations (26). Equation [l] is now the standard algorithm in the reduction of angle-resolved photoemission data. The use of synchrotron radiation to enhance the capabilities of band mapping and to identify wave function symmetry using polarization selection rules was soon established (see below). The work of this era is captured in the compendium by Feuerbacher, Fitton and Willis (27). A number of more mature reviews are also available (28-31). Following this hesitant start, ARPES has burgeoned into a major industry. Activity shows no sign of slackening. Subsequent chapters of this book represent an attempt to organize and to summarize this large body of material. 2. CURRENT UNDERSTANDING AND PRACTICE With some qualifications, there is now a general consensus on the physics of the photoemission process and on how ARPES data should be interpreted. This has been the subject of extensive experimental and theoretical work in the past 20 years. Indeed, these issues were the primary focus of previous monographs and reviews of photoemission which can be found in the literature. The modern extensions pertaining to the theoretical foundations of ARPES can be found in the next two chapters of this book. 2.1 Photoexcitation Drocess (i) Basic Formula. ARPES is intimately tied to investigations of the electronic structure of crystalline systems. Except in the case of very high photon fluences (see Chapter 14), the process is very well described by lowest order time-dependent perturbation theory and thus by Fermi's Golden Rule, derived in Chapter 2: J=(k/4r2)
1 I (Qf I (e/2mc)(A*P +
P.A) I qi) I
6(E-Ei-hw)
i This expresses the observed photocurrent . Iat final energy E in terms of the initial and final state many-body wave functions, respectively q i and qf, and the dipole operator of the incident photon field. Fermi's Golden Rule provides the essence of the so-called singlestep, ultimately quantum mechanical model for photoemission. In general, the many-body wave functions are not known. In order to understand and to interpret a photoemission experiment at a given energy and momentum, various approximations are made. The validity of these, described briefly below, is addressed throughout this book.
6
(ii) IndeDendent Darticle awroximation. A common approximation in applying [2] is to assume that the initial and final state electronic wave functions may be approximated as independent particle states. In this case, qi and qf can be written as product functions of band states. By virtue of Bloch's theorem, these can be labelled by their energy and twoor three-dimensional crystal momentum, depending on the degree of surface localization. Since the energy and momentum of the final-state eiectron is measured, the dispersion relation of the final-state quasiparticle dispersion relations can often be determined. A further approximation is commonly made that these quasiparticle dispersion relations are related to the ground state calculated band structure. The validity of these two major approximations is of central concern in the following two chapters. The validity of the independent particle picture must be examined on a case-by-case basis. For example, "residual" atomic effects (Cooper minima (32), Fano-like resonances (33), shake-up structures (34) etc.) are commonly observed in photoemission spectra from solids. These suggest a higher degree of electron correlation, and thus many-body effects, than the independent particle approximation allows. One of the outstanding problems in solid state physics, understanding the coexistence of, and interplay between, localized electron correlation phenomena and delocalized, band-structure effects is currently also a major focus for ARPES (35). In condensed matter systems the importance of these effects is significant if the on-site correlation energy between two electrons in a band is comparable to the band width. The future of such studies is explored in Chapter 15. One facet of ARPES in which many-body effects can never be entirely neglected is final-state lifetime broadening (36). This damping is of both fundamental and practical interest since it ultimately limits the resolution of the technique. ARPES owes its surface sensitivity to the strong inelastic scattering which the final state electron experiences as it leaves the crystal. The photoelectron is thus endowed with a finite mean-free-path and lifetime. Moreover, photoemission is a final state spectroscopy which measures the energy of the (N-1) particle system relative to that of the N-particle system. The hole states below the Fermi level will also have a finite lifetime due to refilling by radiationless processes. Both of these lifetimes are of order seconds, so that the loss of energy resolution due to uncertainty broadening can be substantial. In the spirit of Fermi liquid theory, these effects are often treated heuristically by allowing the self-energies of the final state quasiparticles to be complex (see Chapters 2 and 3). The imaginary parts are then inversely related to the quasiparticle lifetimes. The use of complex self-energies appended to electron-energy-band calculations is not rigorous, nor is it theoretically satisfying. The above discussion indicates that photoemission spectra cannot be accurately compared to ground state calculations in any case. Recent theoretical advances are allowing quasiparticle spectra to be calculated directly (37). These advances and their impact upon the analysis of ARPES data are examined further in Chapter 3. (iii) Surface Photoeffect. The surface photoelectric effect arises when the dipole operator in the Golden Rule is transformed into a gradient of the electrostatic potential
/
using the commutation relation between the momentum operator and the unperturbed Hamiltonian. The difference between the bulk and surface photoeffects has become blurred since it is now clear that both can exist in the same spectrum. It is generally accepted that the "original" surface photoeffect which is produced by the rapid potential variation near the surface, is most easily measurable in simple metals with very weak bulk pseudopotential. While this was first suggested from total photoyield experiments (16), it has been usefully studied more recently in simple metals using the polarization dependence of the photoemission cross section at photon energies near the plasma frequency (38). 2.2 Phenomenology The manifold of angular parameters in a modern photoemission experiment is illustrated in Fig. 3. Most important are 8, and 4,, the polar and azimuthal angles of electron emission relative to the sample normal and the crystal axes.
++M
CRYSTAL
MAGNET1ZATl ON Fig. 3 All the angles. This diagram is intended to shown all the angular parameters of a fully characterized photoemission experiment. Other angles are oP and $, the polar and azimuthal angles of photon incidence. The degree of polarization of the incident radiation is also significant and is generally expressed as a ratio between amplitudes of electric vector perpendicular (s-polarization) and parallel (p-polarization) to the plane of incidence. Circular or elliptical polarization corresponds to a phase angle A between the s and p components. Finally, we recognize
8
the possibility of a spin asymmetry of the emitted photoelectrons, up or down relative to some appropriately chosen spin-quantizationdirection. No experiment, as far as we are aware, has had variational control over all of these angular and directional parameters. The typical experiment confines itself to some subset of these angles depending on the particular physical phenomenon under investigation. Indeed, the selection of subsets serves as a convenient way to categorize the area of study -band mapping, photoelectron diffraction, symmetry, spin detection and so on. (i) SamDle Orientation. The sample in an ARPES investigation is generally a single crystal of known orientation and of high surface quality. In the case of semiconductors or layered compounds, the surface can be produced by cleavage in vacuum. In the case of most metals and those semiconductor surfaces not achievable by cleavage, a nearly perfect surface may be produced by appropriate cycles of ion bombardments and annealing, or in some cases by vapor deposition film growth. The conditions of surface cleanliness and surface order are established using in situ Auger spectroscopy and low energy electron diffraction (LEED). It is now routine to create ordered overlayers of adsorbed atoms and molecules on these clean surfaces.
(ii) Band MaDDing. The principal angles of concern are 8, and de, the take-off angles of the photoelectrons. The polar angle 8, determines the parallel momentum k in II the crystal azimuth defined by de Herein lies the basis of the bandmapping capability of ARPES. This is a vast topic which will be pursued extensively in the following Chapters. (iii) Photoelectron Diffraction. The emphasis in photoelectron diffraction (PhD) is on the determination of atomic structure rather than electronic structure. The basic notion is to excite electrons out of core levels and to examine the angular distribution. The diffraction patterns observed should, in principle, reveal the environment of the emitting atom. The feasibility of PhD was demonstrated in 1978 (39-41). The topic has now reached considerable maturity, and is treated in Chapter 7. A review by Fadley is also available (42). There are two basic choices of angular variable. One is to hold 8, constant (usually at normal emission, 8, = 0) and to monitor the core photoemission cross section a function of energy E by exploiting the continuum nature of synchrotron radiation. The other approach is to hold ee constant at some off normal Be P 0 position and to measure the azimuthal (4,) dependence of the cross section by rotating the sample. (iv) Svmmetry considerations. The direction of incidence of the photons is specified in Fig. 3 by the angles ePand $y Of more significance is the state of polarization of the incident beam. If the incident beam is linearly polarized, we may distinguish between s and p polarization depending on whether the electric vector is perpendicular or parallel to the plane of incidence.
9
The photon polarization enters into the cross section through the square of the momentum matrix elements as indicated in [ 2 ] . The final state $f is a plane wave at the detector, so we may infer something about the angular dependence of the wave function of the initial state $i by variations of A, the electromagnetic vector. It should be emphasized that a quantitative treatment is quite difficult since A changes from its exterior value to its value inside the solid over a length scale comparable with the sampling depth of the photoemission experiment (43). Many applications of [ 2 ] ,however, are qualitative, and are concerned with identifying odd or even symmetry for the initial state wave function (44). (v) SDin asymmetry. There is a class of experiments which measure the spinpolarization of photoemitted electrons. In such experiments, we must specify a direction of spin quantization. There are two basic physical origins for spin asymmetry. The first is relativistic effects (i.e. spin-orbit interaction) whose detection requires circularly polarized light; the appropriate direction of spin quantization is either the surface normal or the propagation direction of the incident photons. The second is exchange (i.e. magnetic) effects; the appropriate direction of spin quantization direction is the applied magnetic field. These matters are elaborated in Chapter 12. The reader is referred also to the chapters on photoemission in the books by Kirschner (45) and by Feder (46). (vi) Inverse Dhotoemission. The early 1980's witnessed the emergence of angle-resolved inverse photoemission. The inherent cross section for inverse photoemission is lower than that for forward photoemission by the ratio r = (A \A )2, e P where xe and are respectively the wavelengths of the photoelectron and photon. In the P ultraviolet region, we have ra result which explains the relatively late development of inverse photoemission. The angular variables, however, remain unchanged except, of course, that the directions of the electron and photon in Fig. 4 must be reversed. This topic is treated in Chapter 13. Other reviews (e.g. Refs. 47 and 48) are available in the literature.
3. MODERN INSTRUMENTS We offer here a brief general overview of the methods presently in use for angle resolved photoemission spectroscopy. For a more detailed treatment the reader is referred to the review by Leckey (49). Specifics will be treated where appropriate in the individual Chapters. 3.1 Movable Analners The workhorse of the ARPES industry is the spherical deflection analyzer (SDA). Other kinds of electrostatic dispersive instruments which have been used include cylindrical mirror analyzer (CMA), plane mirror analyzers (PMA), elliptical mirror display analyzer (EMDA), 127' cylindrical deflection analyzer (CDA) and others (see Refs. 49 and 50).
10
The 180 SDA is especially well adapted to angle-resolved photoemission for a number of reasons. It can be easily matched to axial input optics composed of cylindrical electron lenses. One such design by one of the authors (SDK) (Ref. 51) is shown in Fig. 4. The four-element input optics permits the angular acceptance and energy resolution to be adjusted by externally applied voltages. Another attractive feature of the SDA is its point-to-point focussing and the fact that the output focal surface is plane, which lends itself well to parallel detection using microchannel plates. The SDA is inherently angle-selective, and a crude angle-resolved experiment can be done simply by tilting a sample in front of a fixed SDA. It is now common practice, however, to mount a modest-sized (typically 50 mm radius) SDA on a one-axis or two-axis goniometer, thereby permitting considerable versatility in the choice of angles of emission. Such instruments are commercially available from a number of manufacturers. These may be regarded as the modern-day version of the movable collector approach of the 1920's illustrated in Fig. 1.
Fig. 4 Layout of a spherical deflection analyzer (SDA), workhorse of the ARPES industry, from Ref. 51.
11
3.2 Multidetection As indicated above, the data-taking capacity of a SDA can be enhanced by using a microchannel plate to perform parallel detection over a range of values of the electron energy E. This practice is now quite commonplace. Other workers have sought to exploit the two-dimensional nature of microchannel plates to perform parallel detection over two variables. The different approaches can be categorized according to the choice of the two variables. In the so-called display analyzers the choice of variables is 8, and de. An early such instrument, built by Rowe and coworkers (SZ), was an adaptation of a multigrid LEED optics permitting a visual display of the photoemission over a large part of the o,, de field. One can think of this as a modern version of the sectored-collector approach of the 1920's illustrated in Fig. 1. Such instruments are really high-pass filters for the electron energy E, and the energy spectrum must be extracted by differentiation of the photocurrent with respect to retarding voltage. This necessity is eliminated in the elliptical mirror display analyzer (EMDA) perfected by Eastman and coworkers (53). It consists of sets of retarding grids (high pass filters) and reflecting grids (low pass filters) permitting the selection of a narrow A E band pass. For the purposes of band mapping, a more appropriate pair of variables would be E and 8,. The aim of such experiments is to determine the E(se), or equivalently E(k 11 ), dispersion relations for one or two high symmetry azimuths. Thus the azimuthal angle be
U
Ba8e Plate
Fig. 5 Layout of the E, ee-multidetecting toroidal analyzer of Riley and Leckey (Ref. 54).
12
is not a particularly useful choice as a continuous variable. An especially noteworthy (E, e,)-multidetecting instrument is the toroidal analyzer of Leckey and Riley (Refs. 49 and 54) a section of which is shown in Fig. 5. Photoelectrons are collected from the sample over a plane containing the surface normal and brought to a focus on a microchannel plate, where contours of constant E and ee are respectively concentric circles and radial lines. This instrument is very well adapted to operation in the synchrotron arena, where beam time is precious and there is a premium on fast data taking. Another very noteworthy (E, ee)-multidetecting instrument is the magnetic deflection instrument perfected by Uveque (Ref. 55). It permits display of the E(k 11 ) band structure on a fluorescent screen in real time. Results obtained on the layer compound GaSe are shown in Fig. 6. This work symbolizes in a rather spectacular way the fulfillment of the dream expressed 25 years ago by Kane (18) that it should be possible to map the energy bands of solids directly from experiment.
m r m
r
r
mk
r
km
Fig. 6 ARPES results on the layer compound GaSe by Uveque Ref. 55). Upper row of panels: (E, 8 ) images taken in real time on a fluorescent screen or four different sample azimuths. d d d l e row: images after processing to enhance band structure effects, and converted to (E,k ) coordinates. Lower row: band structure diagrams corresponding to the experimental kimuths.
6
13
3.3 Time-of-Flipht Methods Time-of-flight (TOF) instruments offer an alternative to deflection instruments in the measurement of electron energy spectra. Indeed, a rather early angle-resolving photoemission instrument built by Bachrach, Skibowski and Brown (56) exploited the pulsed time structure of synchrotron radiation to do TOF energy analysis. The TOF instruments come into their own when the main aim is to do time-resolved photoemission measurements (57). See Chapter 14 for an elaboration of this topic. We are now witnessing the development (58) of photoemission instruments capable of TOF energy analysis combined with two-angle multidetection. REFERENCES: Chapter 1 1.
2. 3. 4.
5.
6. 7. 8. 9. 10. 11.
12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 3 1. 32.
J. G. Jenkin, J. Electron. Spectroscopy 23, 187 (1981). H. E. Ives, A. R. Olpin and A. L. Johnsrud, Phys. Rev. 32,57 (1928). H. Y. Fan, Phys. Rev. 68,43 (1945). A. Hughes and L. DuBridge, Photoelectric Phenomena (McGraw-Hill, New York, 1932). N. V. Smith and W. E. Spicer, Phys. Rev. 188,593 (1969). G. D. Mahan, Phys. Rev. B2,4334 (1970). W. E. Spicer, in Chemistry and Physics of Solid Surfaces IV, edited by R. Vanselow and R. Howe (Springer-Verlag, Berlin, 1982). C. N. Berglund and W. E. Spicer, Phys. Rev. 136, 1030 (1964); ibid., 136,1044 (1964). M. Cardona and L. Ley, Photoemission in Solids (Springer-Verlag, Berlin, VoI I, 1978, Vol II 1979). D. E. Eastman and W. D. Grobman, Phys. Rev. Lett. 28,1327 (1972). G. J. Lapeyre, A. D. Baer, J. Hermanson, J. Anderson, J. A. Knapp and P. L. Gobby, Solid State Commun. 15, 1601 (1974). U. Banninger, G . Busch, M. Campagna, and H. C. Siegmann, Phys. Rev. Lett. 25, 585 (1970). L. F. Wagner and W. E. Spicer, Phys. Rev. Lett. 28, 1381 (1972). D. E. Eastman and W. D. Grobman, Phys. Rev. Lett. 28,1378 (1972). D. E. Eastman and J. Cashion,Phys. Rev. Lett. 27, 1520 (1971). S. A.Flodstrom and J. G. Endriz, Phys. Rev. Lett. 31,893 (1973). G. W. Gobeli, F. G. Allen, and E. 0. Kane, Phys. Rev. Lett. 12,94 (1964). E. 0.Kane, Phys. Rev. Lett. 12,97 (1964). N. V. Smith, M. M. Traum, and F. J. DiSalvo, Solid State Commun. 15,211 (1974). T. Gustafsson, P. 0. Nilsson, and L. Walldkn, Phys. Lett. A37, 121 (1971). B. Feuerbacher and B. Fitton, Phys. Rev. Lett. 29,786 (1972). F. Wooten, T. Huen, and H. V. Winsor, Phys. Lett. A36,351 (1971). R. Y. Koyama and L. R. Hughey, Phys. Rev. Lett. 29,1518 (1972). R. H. Williams, J. M. Thomas, M. Barber, and N. Alford, Chem. Phys. Lett. 17, 142 (1972). F. Wooten, private communication. L. F. Mattheiss, Phys. Rev. B8,3719 (1973). B. Feuerbacher, B. Fitton and R. F. Willis, Photoemission and the Electronic Properties of Surfaces, (Wiley, New York, 1978). B. Feuerbacher and B. Fitton, in Electron Spectroscopy for Surface Analysis, H. Ibach, ed. (Springer, Berlin, 1977). R. H. Williams, G. P. Srivastava and I. T. McGovern, Rep. Prog. Phys. 43, 1357 (1980). E. W. Plummer and W. Eberhardt, in Adv. Chem. Phys. Vol49, edited by I. Priogoine and S. A. Rice (Wiley, New York, 1982). F. J. Himpsel, Adv. Phys. 32, 1, (1983). J.W. Cooper, Phys. Rev. 128,681 (1962).
14
33. for a review, see J. W. Allen, "Resonant Photoemission of Solids with Strongly Correlated Electron", in Synchrotron Radiation Research Advances in Surface Science, R.Z. Bachrach, ed. (Plenum, New York, 1990). 34. C. Guillot, Y. Ballu, J. Paigne, J. Lecante, K.P. Kain, P. Thiry, Y. Petroff, and L. Falicov, Phys. Rev. Lett. 39, 1632 (1978). 35. Narrow Band Phenomena, J.C. Fuggle, G.A. Sawatzky, and J.W. Allen, eds. (Plenum, New York, 1989). 36. J.B. Pendry, in Photoemission and the Electronic Properties of Surfaces, B. Feuerbacher, B. Fitton and R. F. Willis, eds. (Wiley, New York, 1978). 37. M.S. Hybertson and S.G. Louie, Phys. Rev. Lett. 55, 1418 (1985); M.S. Hybertson and S.G. Louie, Phys. Rev. B34, 5390 (1986); J.E. Northrup, M.S. Hybertson, and S.G. Louie, Phys. Rev. Lett. 59,819 (1987). 38. H.J. Levinson, E.W. Plummer, and P.J. Feibelmann, Phys. Rev. Lett. 43,952 (1979). 39. S. D. Kevan, D. H. Rosenblatt, D. Denley, B. -C. Li and D. A. Shirley, Phys. Rev. B20, 4133 (1979). 40. D. P. Woodruff, D. Norman, B. W. Holland, N. V. Smith, H. H. Farrell and M. M. T r a m , Phys. Rev. Lett. 41,1130 (1978). 41. S. Kono, C. S. Fadley, N.F.T. Hall, and Z. Hussain, Phys. Rev. Lett. 41, 117 (1978). 42. C. S. Fadley, Pro Surf. Sci. 16,275 (1984). 43. P. J. Feibelman, bhys. Rev. Bl2, 1319 (1975). 44. J. Hermanson, Solid State Commun. 22, 19 (1977). 45. J. Kirschner, Polarized Electrons at Surfaces, (Springer-Verlag, New York, 1985). 46. R. Feder, Polarized Electrons in Surface Physics, (World Scientific, Singapore, 1985). 47. V. Dose, Surf. Sci. Rep. 5,337 (1985). 48. N. V. Smith, Rep. Prog. Phys. 51, 1227 (1988 . 49. R. C. G. Leckey, J. Electr. Spectr. 43,183 (1 87). 50. N. V. Smith and S. D. Kevan, Nucl. Instr. and Methods 195,309 (1982). 51. S. D. Kevan, Rev. Sci. Instr. 54,1441 (1983). 52. S. P. Weeks, J. E. Rowe, S. B. Christman and E. E. Chaban, Rev. Sci. Instrum. 5Q, 1249 (1979). 53. D. E. Eastman, J. J. Donelon, N. C. Hien and F. J. Himpsel, Nucl. Instr. and Methods 172,327 (1980). 54. R. C. G. Leckey and J. D. Riley, Ap 1. Surf. Sci. 22/23,196 (1985). 55. G. U v e ue, Rev. Sci. Instr. 59, 8!9 (1988); 57 1042 (1986); G. Uveque and J. Robins, $id. 58, 1456 (1987). 56. R. Z. Bachrach, M. Skibowski and F. C. Brown, Phys. Rev. Lett. 37,40 (1976). 57. R. Haight, J. Bokor, J. Stark, R. H. Storz, R. R. Freeman, and P. H. Bucksbaum, Phys. Rev. Lett. 54, 1302 (1984). 58. D. J. Trevor, L. D. Van Woerkom and R. R. Freeman, Rev. Sci. Inst. 60,1051 (1989).
3
15
Chapter 2
THE PHYSICS O F PHOTOEMISSION J.E. INGLESFIELD AND E.W. PLUMMER
1
Introduction
In angle-resolved photoemission the study of the energy and angle dependence of the phot,oemitted electrons provides information about the electronic excitations of the solid. In the simplest picture, these excitat,ions correspond to the one-electron states of band theory, and much of this volume is concerned with the invaluable information about surface and bulk band structure which can be found from the photoemission spectrum. Many features in the spectrum correspond to surface and bulk processes. Surface photoemission comes from electrons in the top few angstroms of the solid, and if the surface is periodic it conserves the component of the electronic wave-vector K parallel to the surface. As the energy of the outgoing electron equals the energy of the initial state plus Rw, the dispersion of surface states, for example, can immediately be mapped out from the photoemission spectrum. In bulk photoemission on the other hand, the component of the Bloch wave-vector perpendicular to the surface kl is also conserved (approximately) in the transition and the bulk band structure can be mapped out. Actually, the surface plays an integral role in photoemission - the electrons have to pass through the surfa.ce on their way to the detector, and the mean free path of these electrons is rather short inside the solid, typically around 10 for photoelectrons with a kinetic energy of 50 - 100 eV. These effects must be included in an accurate description of photoemission. I n this chapter we shall concentrate an the way that one-electron energy bands show up in photoemission, in spite of the complicated electron-electron interactions in solids. These bands really describe the excitations of quasiparticles - screened electrons or holes - and much of the current interest in photoemission (and iiiverse photoemission) is centred on the differences between the quasiparticle states, and the energy bands of conventional density functional theory. The electron-electron interaction can also lead to extra features in the photoemission spectrum - satellites - and we shall see how these can originate. Finally we turn to the electromagnetic field itself, discussing its screening by the electrons.
2 2.1
The photoemission process The final state in the Golden Rule
In angle-resolved photoemission, the energy distribution of electrons travelling in a particular direction is measured. To see how this measurement is related to the electronic structure of the solid we must first understand the wave-function of this final state [l, 2, 3, 41. Switching on the light in the remote past, the wave-function of an electron initially in state q5* is given at t = 0 by the perturbation theory expression [5]:
16
G is the Green function for the system, and the perturbation is:
+
SH = L ( A . p p.A). 2nzc
(2)
with frequency w . We shall study the form of t,he vector potential A in greater detail in section 6. As the electrons reaching the detector are free, let us express G in terms of the free electron Green function Go using Dyson’s equation [5]:
G = Go(1
+ TGo),
(3)
where T is the operator describing the scattering of the emitter. The free electron Green function is given in Hartree atomic units by:
’
where k2/2 is the energy of the emitted electrons, E = E, +FLU. rent a long way from the emitter this can be expanded: GO(r,r’)
-
exp(ikr)
-~
2x7-
exp( -ik.r‘),
As we measure the photocur-
(5)
where k is directed towards the detector: kr
k=-,
By substituting (3) and (5) into (1) we obtain the asymptotic form of the photoelectron
with: q5f(r)= exp(2k.r). This wave-function contains the physics of the famous three-step model [S]: working from the right, the photoelectron is excited by SH, scattered by the crystal, and then propagates to the detector. We can rewrite this as:
where:
+
I4f) = (1 G 3 ’ ) I4f). So the photocurrent per unit solid angle is finally given by:
This expression for the photocurrent corresponds to the Golden Rule [2, 3, 71, with a final state wave-function given by (10). This is the time-reversed LEED state [3]: the final state is obtained by shooting the plane wave e x p ( 4 k . r ) at the sample, letting the sample scatter it via (1 + GOT),and finally taking the complex conjugate. This is not particularly mysterious, because in photoemission the electron which reaches the detector was scattered by the atoms in the emitting sample in the distant past, whereas in most scattering problems this takes place in the future. The energy density of these final states is given by k/8a3 per unit solid ‘e
=h=
n1=
1 au.
17
angle, and when multiplied by the Golden Rule factor of 27r we immediately recover (11). The Golden Rule expression can be generalized to the case where there are many occupied electronic states in the emitter, giving for the photocurrent per unit solid angle and per unit energy:
J ( k )=
.c,k
I ($r I 6 H I
$1)
l2 & ( E- E, - hw).
(12)
1
It can also be generalized to the real case of interacting electrons [l]. The initial state is then the ground state of the N-electron system 1 N , 0); the final state is labelled by the wave-vector k of the electrons reaching the detector, and the state s of the ( N - 1) -electron system left behind, 1 k; N - 1, s ) . This final state can be found by preparing the [ N - 1)-electron system in state s , shooting a free-electron wave with wave-vector -k at the system and letting them interact - finally taking the complex conjugate of the resulting N-electron wave-function.
2.2
Transitions to the final state
As we shall see throughout this book, a great deal can be learnt from photoemission spectra by applying conservation rules [S, 9, lo]. The first of these - energy conservation - is ensured by the &function in the Golden Rule expression (12):
E = E; + hw
(13)
from the measured energy E of the photoelectrons and the photon energy hw we can immediately deduce the energy of the initial state E,. Moreover, in photoemission from a periodic solid surface, the wave-vector component parallel to the surface K of the initial and final states is equal t o within a surface reciprocal lattice vector; this is because the vector potential entering the matrix element in (12) varies comparatively slowly (at least parallel to the surface - see section 6). As surface states have a discrete energy at fixed K , they show up as sha.rp features in the angle-resolved photoemission spectrum [figure I ) , and by applying these two conservation rules their dispersion ca.n be mapped out [S. 101 (section 4). Inside the solid, the LEED state ($;) corresponding to shooting exp(-ik.,r) at the surface consists of the linear superposition of bulk solutions of the Schrodinger equation, with energy E and wave-vector component K , which matches onto the incident wave over the surface. In general these solutions are Bloch waves travelling away from the surface corresponding to the energy bands, together with evanescent waves decaying into the crystal from the surface [11]; in an energy gap of the bulk band structure the wave-function is made up entirely of evanescent waves. These evanescent waves are solutions of the Schrodinger equation which are not allowed in an infinite crystal, but which can occur in the case of a crystal with a surface. We would then expect the matrix element in (12) to be large for bulk initial states with the same total wave-vector ( K , k,) as a travelling wave component of the final state, giving a direct transition. By measuring the energy of direct transitions as a function of photon energy, the initial state bands can then be mapped out - if the perpendicular component of wave-vector inside the solid, k 1 , can be determined [S, 10) (section 4). The presence of the surface means, of course, tha.t kl is not strictly a good quantum number except deep in the solid, and this is why the final state (and initial state) wave-functions contain evanescent wave components near the surface. So the photoemission spectrum also reflects the local density of states at the surface with fixed wave-vector component K - the continua of bulk states reflected by the surface as well as the discrete surface states [ l l ] [figure 1). In fact, even the travelling wave component of the final state wave-fiinction is damped by many-body effects, giving a finite mean free path (section 3.2), and this has the effect of smearing out direct transitions (section 3.4) and enhancing surface sensitivity.
-
18
I
I
I
I
I
I
“
“
I
-20 -18 -16 -14 -12 -10 - 8 -6 -4 - 2
0
INITIAL STATE ENERGY (eV)
Figure 1: Normal emission photoemission from Mg(0001), AI(001) and Be(0001) [9]. Direct bulk transitions are indicated by the arrows, and surface states by the shading.
19
2.3
Calculating photo emission
A calculation of the photoemission spectrum can help with the identification of features as either surface or bulk, and by “tuning” t,he potential felt by the electrons to obtain optimal agreement with experiment, information can be obtained about the energy shifts and broadening effects due to the electron-electron interactions (section 3). The necessary ingredients of such a calculation are an accurate way of finding the electronic states both in the bulk and at the surface, a proper evaluation of the matrix elements, and a way of putting in the many-body effects of lifetime broadening for the initial state and the finite mean free path of the photoelectron (sections 3.2, 3.3). A computer package to do this was developed by Pendry and his co-workers [la]. The starting point is to rewrite the Golden Rule expression for the photocurrent using the following relationship between the sum over states i in (12) and the Green function [5]:
1 $,(r)$;(r’)b(E - E,) = -%nG(r, r’;E) i
7r
- this sum over states is called the spectraEfunction, and we shall meet it again in section 3.1. So we can write (12) as [12]:
J(k) = -%njdrJdr’l/.j(r)sHG(r,r’; k 47r3
E - hw)SH$j(r’).
This expression is very convenient, because it involves the Green function for the initial states, rather than the individual states themselves. In evaluating (15) on the computer, several approximations have to be made. First it is assumed that the vector potential in SH is spatially constant, neglecting the screening effects we shall discuss in section 6. This means that 6 H can be transformed to VV form [12], where V is the potential felt by the electrons. It is assumed that this potential has the muffin tin form inside the solid, that is, a spherically symmetric atomic-like potential at each atomic site, and a flat potential in the interstitial region between the atomic muffin tins. This form of potential gives the electronic states very well for reasonably close-packed systems, but is not satisfactory for open structures like diamond. At the surface, a simplified (one-dimensional) form of the surface barrier is used - usually a step barrier, though recent work uses a barrier taken from self-consistent surface electronic structure calculations [13]. With these simplifications, the way that the program works is as follows. The photoelectron state $r, the time-reversed ( i . e . complex conjugated) LEED state, is calculated using a layer is expanded scattering approach in which the solid is divided up into layers of atoms. in plane waves between the layers, and the reflection and transmission properties of each layer are calculated, giving the probability amplitudes for a plane wave with parallel waveG, where G vector component K to be reflected and transmitted into plane waves K is a two-dimensional layer reciprocal lattice vector. By repeated reflection and transmission operations, the full wave-function for an electron incident on the whole semi-infinite crystal can be determined. Knowing $, J dr’G(r, r’; E - tLw)6H$,(r‘) can be found. In this expression, SH$f acts as a source of electrons for which G describes the propagation in the lower energy (initial) state. An immediate simplification is that 6 H (2.e. VV) is non-zero only inside the muffin tins and at the surface barrier, and then the layer-adapted multiple scattering technique can be used to find the whole wave-field of J dr’GbH$,. As an example of photoemission calculations, figure 2 shows results calculated by Konig et a1 [13] for normal photoemission from Ag(001), at a range of photon energies, compared with experiment [14]. These were obtained using theii extension of the Pendry program to include the more accurate surface barrier. There is fairly good agreement with experiment, and the main features in the spectra are reproduced by the calculation: in particular, this work clearly
+
20
.
.. ..
..._
h u ( PI’) 40
45
55
60
65
70
75
Figure 2: ( a ) Normal emission spectra from Ag(001) at different photon energies, compared with (b) calculated spectra [13].
identifies state B in figure 2(a) as a surface state. The main discrepancy is that the peaks lie about 1 eV closer to the Fermi energy than in experiment, due to shifts in the quasiparticle energy bands compared with the density functional values (section 3.3.1).
3 3.1
Quasiparticles in photoemission Quasiparticle self-energy
Many aspects of photoemission can be described in a single particle picture, as a transition from an occupied one-electron orbital to the state describing the propagation of the photoelectron. In reality the solid is an immensely complicated many-body system of electrons all interacting with one another, but for many purposes this simply results in the screening and decay of the hole left behind and of the photoelectron. These screened, decaying single particle states are the quasiparticles [15, 161, whose wave-functions satisfy a single particle Schrodinger equation:
containing the self-energy (or optical potential) C, which is complex and energy-dependent. The real part of C describes the screening of the quasiparticles, shifting the energy from the Hartree value, and the imaginary part the decay or inelastic scattering processes. The quasiparticle wave-functions (or amplitudes) are given by the matrix elements:
#(r) = ( N
4(r)
-
1,i\&r)lN,O), hole states
= (N,Ol&r)lN
+ l , j ) , electron states.
(17)
Here is the electron annihilation operator, and the hole quasiparticle describes the hole in the ith excited state of the ( N - 1)-electron system, and the electron quasiparticle describes the extra electron in the j t h state of the ( N 1)-electron system. The initial state energy bands measured in photoemission are really the bands of the hole quasiparticles. The imaginary part of the self-energy, which corresponds to the decay of the hole, gives each state a finite energy width (161. The imaginary part of C felt by the photoelectron comes from inelastic scattering processes which cause the spatial decay of the quasiparticle amplitude into the solid, away from the surface [16]. The decay length (+2 to give the decay in intensity) corresponds to the mean free path, one of the factors which determines surface sensitivity in photoemission. To understand the quasiparticle properties of the final state more fully, let us go back to the many-body Golden Rule (section 2.1) [17]. Writing the matrix element between the many-body states as:
+
(k; N - 1,s 16H I N,O) = /dr(k; N - 1,s I G+(r)$(r) [ N,O)SH(r), we can insert a complete set of states of the ( N - 1)-electron system:
(k;N-
1,s
16H 1 N,O) = x / d r ( k ; N - 1,s 1 $+(r) 1 N - l , j ) S H ( N - 1,j 1 &(r) N , 0). j
(19) The matrix element ( N - l,jl$(r)lN, 0) is just the quasiparticle amplitude fof the hole state j . However, the matrix element describing the photoelectron (k;N - l,s]$+(r)lN- 1,j) is not an ordinary quasiparticle amplitude as in (17). An electron quasiparticle amplitude describing the propagation of an electron asymptotically in the would be (k; N, Ol~+(r)lN,O), (time-reversed) plane-wave state k incident on the N-electron system in the ground state; in (k; N - l,sJ$+(r)lN - l , j ) , the electron is incident on the ( N - 1)-electron system in an excited state s, and changes the state from s to j .
22
Fortunately, the matrix element (k; N - l , s J G + ( r ) J N - l , s ) , in which the photoelectron does not change the state of the ( N - 1)-electron system, behaves like the usual quasiparticle amplitude. The term j = s in (19) is the intrinsic contribution to the photoemission matrix element [l],for which the photocurrent can be written as:
k
I d+(r) 1 N - l , s ) G H ( r ) A ( r , r ‘ ; E - b ) x 6H(r’)(N - 1,s I &r’) 1 k; N - l , s ) ,
J(k) = G / d r / d r ’ ( k ; N - l , s
(20)
where A is the interacting spectral function [lS]:
d ( r , r ’ ; E ) = ~ ( N , O ( $ + ( r ’ ) I N - l , s ) ( N - l , sI G ( r ) I N , 0 ) 6 ( E - E o + E , ) .
(21)
3
This has the same form a.,s (la), with the initial state 4, replaced by the hole quasiparticle amplitude ( N - l,s[$(r)[N,O), and the final state by the photoelectron quasiparticle (k; N - 1, sl&+(r)lN - 1, s). The relationship between the interacting spectral function and the interacting single particle Green function (or propagator) is the same as (14). As we shall see later in this chapter and elsewhere in this volume, A describes satellites as well as quasiparticle states associated with single particle energy bands. The intrinsic contribution to photoemission dominates at high enough photon energies, so that the photoelectron escapes before the other ( N - 1) electrons can respond to it [l]. Let us now study the photoelectron quasiparticle in detail. It can easily be shown that the matrix element appearing in (19) satisfies a system of coupled Schrodinger equations [17]:
h is the one-electron part pf the Ilamiltonian, including the Hartree potential, and density fluctuations (N - 1 , j 1 $+$ I N - 1,a) couple the components of the generalized quasiparticle; v is the Coulomb potential, and the s u m excludes the Hartree-like term 1 = j . Ek,+is the energy of the many-body final state I k; N - l,s), that is, E E,. This system of equations can be reduced to a single equation for (k; N - 1 , s I $+(r) 1 N - l,s), assuming that this is the dominant component [17]:
+
x (k; N - 1 , s 1 &+(r”)1 N - 1,s) = ( E k , s - E , ) ( k ; N - 1,s
I &+(r)I N - 1,s).
Here, G is the Green function for the one-electron part of the Hamiltonian, and:
fi,s(r) = /dr’(N
-
1 , s /4+(r‘)d(r’)1 N
-
l,l)v(r’,r).
(24)
(23) is an effective single particle equation for the photoelectron quasiparticle amplitude, containing the self-energy:
This is essentially the same self-energy that appears in (16) [17, 181, evaluated at the energy of the emitted electron.
23
0,
I
,
,
,
,
,
,
,
,
,
1 " " " " ' l
Figure 3: Real and imaginary parts of the self-energy of an electron gas at different densities as a function of wave-vector relative to X.17 [16, 191.
3.2
Mean free path of the photoelectron
When we solve the Schrodinger equation (23) for the (time-reversed) photoelectron, the solution at the energy of measurement E corresponds to a state decaying into the solid [16]. Neglecting band structure effects, the wave-function inside the solid has the form:
+; and when y is small compared with
N
exy i k l z exp - 7 2 ,
(26)
kl:
So the escape depth is given by: kl
d = ___ (28) 21BnC) - the factor of 2 comes from squaring the wave-function to find the intensity. Only the normal component of the electronic motion is involved in the decay, which is why surface sensitivity can be increased by going to large emission angles. The mean free path itself is given by:
where k is the total wave-vector inside the solid (more generally, the group velocity). In a free electron metal, C has a small imaginary part until the electron energy measured relative to the Fermi energy exceeds the plasmon energy (figure 3) 116, 191. A new channel then opens up into which the photoelectron can be scattered by exciting a plasmon. In terms of (as), state 1 consists of the hole state s plus a plasmon, and the imaginary part of the
24
f 0 a m 0 L L
+4
Energy Above Fermi Level (eV)
Energy Above F e r m i Level (eV)
Figure 4: Mean free pat,li as a function of electron energy in A1 and Ag. The lines correspond to different theories, and the points to experiment [22]. potential comes from (25) when E 2 El - E,. Below the plasmon frequency the photoelectron can be scattered out of the elastic cha.nne1 by exciting electron-hole pairs, but we see from figure 3 that they give a small contrihntion to the imaginary part of the self-energy. For a nearly free electron metal like A1 the mean free path should drop sharply at the plasma frequency, and then gra.dually increase with increa.sing energy. This behaviour is found rather generally, in fact, with a minimum in the mean free path of about 5 A at an electron energy of typically 20 eV [20, 211. A theoretical analysis of electron mean free paths in a wide range of elements and compounds has been carried out by Penn [22] and Tanuma e t a2 [23], making use of optical data for the dielectric function to which the electronic self-energy can be related. Results for A1 and Ag are shown in figure 4, together with experimental data from overlayer experiments and photoemission - a.greement, is rather good. I n a,ctual photoemission and LEED calculations, the imaginary part of the self-energy is assumed to be constant spatially, right up to the surface, and this seems a good a.pproxima,tion [24]. The imaginary pa.rt of the self-energy conies from real transitions scattering out of the elastic cha.nnel, hut C also has a real part coming from virtual transitions. These are related by a Kramers-Kronig dispersion relation [lG]. For electrons with energies greater than the plasmon energy, the real part of the self-energy gradually becomes less attractive as the electron energy increases [19] (figure 3). This shift comes from the inability of the electron gas to screen the photoelectron when it is moving fast. There is experimental evidence that this shift is quite important: for example in photoemission calculations for Cu( I l l ) , an upward shift in the inner potential felt by the photoelectron is needed to obtain the right photon energy-dependence of the intensity [ 2 5 ] . Beam threshold measurements for the diffraction of low energy electrons from Cu(ll1) show a 4 eV shift in the real part of the self-energy between 20 and 120 eV kinetic energy 1261, and theoretical a.nalysis of the low energy electron diffraction from Cu(OO1) over an extended energy range ( u p to 700 eV) [27] exhibits an energy-dependence consistent with the beam threshold measurements and the theoretical calculations shown in figure 3. The effect of the energy-dependence of the self-energy can be seen in the inverse photoemission 3xperiments of Speier e t al [as]. In these experiments the quasiparticle amplitude for the 2lectron in its high energy initial state incident on the solid is essentially the same as that for the time-reversed photoelectron. Speier ef a1 [2S] found upward shifts in spectral features in the bremsstra.hlung isochromat spectra for Ni, Cu, Ag and Pd relative to the density of unoccupied states calculated with an energy-independent ground state potential (figure 5). N
25
Figure 5: Bremsstrahlung isochromat spectrum for Ag (top curve), compared with the calculated density of states (bottom curve) and the broadened density of states (middle curve) (281.
3.3
Spectral function of hole states
The core states, energy bands and surface states measured in photoemission correspond to quasipa.rticle states in the hole spectral function A, defined in (21). This enters directly in the intrinsic contribution to the photocurrent (20), which dominates at high photoelectron energies when the outgoing photoelectron does not, change the sta,te of the ( N - 1)-electron system [I]. In (21) we wrote the spectral function in terms of the individual hole excitations of the system, but it is convenient to rewrite this in terms of the interacting Green function or propagator, upon which the diagrammatic and pcrt.urha.tion approach to many-body theory is based. The Green function is given by:
G(r,r';E) = s
(N,O14+(rf)P- I , ~ ) ( N 1,sI4(r)W,O) E - Eo t E, -is
sumsover the excitations of the ( N - 1)-electron system (hole states) and the (N+l)-electron system (electron states) [16]. It is time-ordered, meaning that the denominator for the hole states contains -is, and for the electron states t76. Comparing with (21) we see that for E < 0 (we take the Fermi energy as our zero), A is related to G by:
-
the same as the non-interacting result (14). The Green function satisfies the inhomogeneous version of the Schrodinger equation (16), containing the self-energy [16]:
-
1 2
(--V*+V(r)-
J
E)Q(r,r';E)+ dr"C(r,r";E)O(r",r’,;E) = -6(r-r').
(32)
All the difficulties of the many-body prohlein reside in determining C, but gradually experience is building up in finding the self-energy in simple metals [29, 301 and semiconductors [31], and photoemission provides an invaluable way of testing the theories.
26
Quasiparticle states correspond to peaks in the spectral function A( E ) . For a particular hole state, the Green function varies i n energy like: 1
(33)
4(E)- E-C-(Z(E))'
where c is the energy of the state using the Hartree potential, and (C) is the expectation value of the self-energy. If Z varies slowly with energy, and its imaginary part is small, we then find a quasiparticle peak in A a t energy c A, lifetime broadened to width r', with A = %C, and r = I&CI [is]: n
+
Such a quasiparticle is a solution of the Schrodinger equation (16) at a particular Bloch wavevector, with a complex (analytically continued) eigenvalue (c A X ) [16]. Compare this with the photoelectron quasiparticle which is a scattering solution of (16) at real energy, and consequently complex wave-vector. Not all the structure in A corresponds to quasiparticles, which are usually considered as those states for which there is a one-to-one relationship with energy bands; there are also many-body satellites. However, quasiparticle states are particularly important,, and a constant theme of recent work is that they are often surprisingly well defined.
+ +
3.3.1
Core states and satellites
Photoemission from localized core states shows a shifted and lifetime-broadened quasiparticle peak, and satellite structure. The valence electrons screen the core hole left behind, reducing the energy needed to remove the core electron. This interaction between the core hole and the remaining electrons inevitably leads to the possibility of electronic excitations - plasmons in the case of nearly free electron metals, as well as electron-hole pairs - this gives the satellite structure. To study the core hole spectral function, we shall describe the screening properties of the valence electrons in metals like Na or Al in terms of plasmons, writing the Hamiltonian as [32, 331:
The first term, summed over pla.smon modes, just counts the number of plasmons in each mode the second term gives the unrelaxed energy of and multiplies this by the plasmon energy the core hole e:, or zero when the core st,at,eis occupied - 6+, b are hole creation and annihilation operators; the final t.erm contains the potent,ial energy of interaction between the hole and the plasmons - ( u z a q ) gives the amplitude of the plasmon cha,rge density fluctuation, and A,, is a measure of the potential which t,liis produces at the core. The eigenstates of (35) fall into two classes. Clearly, when the core st;lte is occupied, H just reduces t.o the simple harmonic oscillator for plasmons, with energies: ~
3
~
;
+
E
=T
+
I ~ W ~r i p 2
+ ngw3 + . ..
(36)
where rip is the number of pla.smons in mode q. When the core state is empty the Hamiltonian becomes: 4
This can be diagonalized with new plasmon variables:
27
W*Ec-3Wp
W+€c-2Wp
W’Ec-
Wp
W‘Ec
kinetic energy
Figure 6: Spectral function for a core state i n a free electron gas with the density of Na (rs = 4 ) (displaced by the photon energy hw to give the intrinsic photoemission spectrum) [l]. giving: B
So the energies of the system with a core hole are: E = t: -
+ nlwl + n2w2 +
Xilw,
n3W3
+ .. .
(40)
9
and the spectral function consists of a core peak at energy L , = e: - C , Xi/wq, together with plasmon satellites [33]. The spectral function d ( w ) calculatd for a. core state in a free electron gas with the density of N a (rS = 4 a.u.) is shown in figure 6 [I]. As well as the no-loss peak at t, there are the satellites corresponding to exciting one, two,. . . plasmons, with line-shapes resulting from the plasmon dispersion. When the interaction between the core hole and the remaining electrons is included, the total integrated weight in the spectral function is the same as in the noninteracting case - weight is transferred from the core line to the satellites; moreover, the centre of gravity of the spectral function lies at the unrelaxed core energy c t - the Koopman’s theorem value [33]. This is generally true, for more complicated interactions than we have assumed in (35). Unfortunately these moments results for d do not go over to the photoemission spectrum except in the intrinsic limit of high photon energies, and in the case of plasmon satellites extrinsic plasmon excitation persists even at high photoelectron energies [l, 17, 341. Although the spectral features remain, their weight changes because of extrinsic effects, in which the excitation of plasmons by the photoelectron becomes important (section 5 ) . As well as the plasmons, the core hole can excite electron-hole pairs in the electron gas. Unlike the plasmons, the electron-hole pairs in a metal start with zero energy, so the corresponding satellite begins at the screened core energy. Moreover, the effect of the core hole on the electron gas in its ground state is to modify each one-electron wave-function, resulting in zero overlap between the Sla.ter deterniinant wave-functions of the many-electron system with and without the core hole [35]. This wipes out the 6-function of the core state quasiparticle peak shown in figure 6. It is replared by a power law singularity in the spectral function [l]:
d(E)
-
(t.
1 - E)l-a’
where (Y can be found from the phase shifts of the electrons at the Fermi energy due to the core hole potential: 2
n=--
H2
C(2+ I)&;, 1
(42)
28
il 1-
Ot1078
1076 1074 1072 BINDING ENERGY (OW
1070
Figure 7: Na 1s and 2s photoemission spectra, showing the asymmetric shape of the no-loss peak, fitted by the Doniach-SunjiC lineshape and a Lorentzian at the surface plasmon satellite (solid line) [3S]. to quote the famous Nozitres-de Dominicis result [36). So far we have neglected the lifetime of the hole, due mainly to Auger processes in which an electron drops down from a higher level and a second electron is excited. If these do not interfere with the interactions with plasmons and electron-hole pairs, the full spectral function can be obtained by convoluting the infinite lifetime result, that is (41) close to ccr with a Lorentzian like (34). This gives the Doniach-SunjiC lineshape [37]:
where we write f for the gamma-function, and r is the lifetime broadening. In general this provides an excellent fit to experimental data, and has been applied to a wide range of core states. In a study of photoemission from nearly free electron metals, Citrin et al. [38) obtained the core spectra shown in figure 7 for the N a 1s and 2s levels. Allowing for phonon effects, they found t1ia.t their results could be fitted with (43), with an asymmetry parameter a of 0.20 and lifetime broadening I? of 0.2s eV for these levels. a can also be found from the scattering properties of a static, self-consistently screened core hole via (42), in good agreement with the Na experiments. The lifetimes are harder to calculate, but for the deep 1s hole i t is mainly due to intra-atomic Auger processes and an atomic calculation gives good agreement. The 2s lifetime is dominated by interatomic processes involving valence electrons, but reasonable theoretical estimates can be made for this too. 3.3.2
Valence band quasiparticles
Most electronic structure calculations for the valence states in a solid and at a surface are based on density functional theory, which is designed to give ground state properties correctly, like the total energy and charge density [39]. Although the one-electron wave-functions and energies in
29
density functional theory do not in principle correspond to quasiparticle excitations, the energy bands are often in good agreement with photoemission measurements. The discrepancies will be studied in section 4.3. In density functional theory, the ground state charge density po(r)of the system is written in terms of effective one-electron wave-functions which satisfy a Schrodinger equation containing the exchange-correlation potential Vzc(r) as well as the Hartree potential V.(r) and the potential due to the ions [40]:
V,, corrects VH to describe the effects of exchange - the fact that electrons with the same spin cannot be at the same place at the sa.me time - and the correlated motion of the electrons. Usually Vzc(r) is calculated in the local density approximation, in which it is taken as the exchange-correlation potential of a uniform electron gas with the same charge density as at point r. Density functional theory is remarkably succesful in describing the charge density and energetics of solids and surfxes, but apart from the highest occupied energy level which in (44) have no rigorous meaning as oneequals the ionization energy, the individual t , ’ ~ electron excitation energies. This is unlike the quasiparticle equation (16), for which the c;’s are the excitation energies which enter the hole spectral function. Unlike the self-energy C in (16), the exchange-correlation potential is local, real, and energy-independent. The discrepancies between density functional energy bands and the actual quasiparticle excitations appearing in (16) are due to energy-dependent energy shifts coming from the real part of the self-energy, and lifetime broadenings due to the imaginary part (34). A particularly important energy shift occurs in semiconductors, for which density functional theory generally gives a gap between the valence and conduction bands which is too small [31], but in the following section we will also discuss shifts in met,als. The GW approximation [16] provides a valuable method for calculating C, and this is the way that the free electron results of figure 3 were found. The reason why density functional theory continues t o be the starting point for describing valence band quasiparticles is that it is relatively straightforward to implement; the self-energy is much more difficult to determine even in the GW approximation, and up to now it has been calculated only for semiconductors (311 and s-p bonded metals [29]. The lineshape of surfa,ce states, localized states lying in bulk energy gaps, should in principle be Lorentzian, due to the energy broadening of the imaginary part of the self-energy (section 4.1) [41, 421. Of course the surhce s h t e does not necessarily feel the same self-energy as neighbouring bulk states, but in the ca.se of .4l(OOl) the surface state below E.P extends deep into the solid (431, and we would expect the value of the self-energy to be bulklike. In this case, the apparent lineshape of this state is asymmetric (figure 1) [44], because it lies so close to the bulk band edge that the Lorentzian overlaps with the smeared-out band edge [43]. This does not mean that there is any mixing between the s u r f x e state and bulk quasiparticle amplitudes - the surface state quasiparticle is still spatially localized. In the case of Be(0001) the surface state has the expected Lorentzian lineshape (421 (section 4.1).
3.4
Quasiparticles in direct transitions
The energy broadening of the hole quasiparticle combines with the momentum broadening of the photoelectron, due to the exponential decay of its wave-function away from the surface, to give a width to direct transitions. To obtain this we go back to the Golden Rule, writing
30
the spectral function for the hole state as:
is the initial state band structure, and r h is the energy broadening of this state. The contribution of the final state to the squared matrix element in the Golden Rule (20), in which k L is conserved, is proportional to the spectral function for the photoelectron:
- Eh(k1)
re
kl) c<
[ E - Ee(kl)lz + ra’
(47)
The connection with our discussion of momentum broadening and the mean free path in section 3.2 is that r,/laEe/ak,lis the momentum broadening y appearing in (26) a t fixed E . Summing over initial state wave-vectors, the photocurrent is then given by:
Evaluating this integral we obtain a Lorentzian shape for J ( E ) with a width of [45,461:
In this expression the wave-vector derivatives of the band structure are evaluated at the points at which the unbroadened direct transition would occur. We see that with flat hole bands, the width comes entirely from the hole lifetime, in agreement with our discussion of energy broadening in the initial state and inomeiitum broadening in the final state. All these effects are included automatically in the Green function method for computing the photocurrent (15), by calculating the hole Green function and the electron final state with appropriate self-energies, or complex optical potentials [la].
3.5
Brillouin zone sampling in XPS
X-ray photoemission (XPS) probes the density of states of the valence electrons sampled throughout the Brillouin zone, rather than their band structure which UPS reveals [7,47,481. This is because the number of final sta.te bands folded back into the reduced zone becomes very large at high energies, so that. with angle integra.tion and momentum broadening, direct tmnsitions can take place from initial states through the whole zone. Angle integration is equivalent (in a one-electron picture) to summing over all final states li)f with the measured energy, so the photocurrent from a single initial state $; with energy E, is given by:
J ( E t Aw)
= 2~c($, I6H 1 $,)(+f f
a %ii(.$i I tiHG‘(E,
1 611 [ $i)6(Ej - Ei - hw)
+ h ) 6 H [ 4,).
(50) (51)
As in (3) we write G i n terms of the free electron Green function Go and the T-matrix of the system evalua.tcd at the energy of the photoelectron:
.7
0;
%(4i I ~ H ( G+o GoTGo)hH I
+i).
(52)
With a constant A-field it is also convenient to write 6 H in terms of the potential, using the acceleration form of the matrix element [la]: ($1
1 6H I 4i)= iA (Ictf I VI’ 1 dJi)/[c(Ef- Ei)]. ’
(53)
31
Total Denslty or states
Cu Denslty of Stetes
r---T7
XPS Spectra
Pd Denslty of States
Figure 8: XPS spectrum for disordered Cuo JsPdo.is. The solid and dashed lines in the lower left-hand box show the calculated and measured spectrum, the top left-hand box gives the total density of states, and the right-hand boxes show the local densities of states on the Cu and Pd atoms 1481. Now in many systems, particularly close-packed metals, it is a very good approximation to express T in terms of individual atomic t-matrices using multiple scattering theory, and to write V as a sum of atomic potentials V I . Then the expression for the photocurrent becomes:
J'
%n
C
($i(l IJJ
+
+
+.
(V,VI)(GO G O ~ J G OG O ~ J G O ~ K G. O . ) ( V ~ VI N $ i ))
(54)
- the sums are over atomic sites I , J , . . ., with J # I(
in the t-matrices. At high photoelectron energies the free electron Green function connecting the different sites in (54) oscillates rapidly with energy and position. So averaging over a small energy range we can neglect the coupling between different sites, and the expression for the photocurrent from state i reduces t o sitediagonal form [47]:
J'
%nC($, 1 (VJ)J)(GO+ GotiGo)(V,vr) I +i) I
(55)
a sum of matrix element-weighted charge densities of state i over the different atomic sites. Summing over all states with energy Ei, this becomes a sum over weighted local densities of states. We have finished u p with a local result, i n real space, which is often easier to interpret than the direct transitions in UPS - particuhrly in disordered systems for which the concepts of k-space are not applicable. An example of the application of XI'S to disordered alloys is shown in figure 8, comparing the experimental and theoret,ical spectra with densities of states [48]. Bremsstrahlung isochromat spectroscopy is inverse photoemission with large photon energies, and this probes the unoccupied density of states (figure 5 ) [28].
-
32
,
,
1
I
Be (OOOI I NORMAL EMISSION SPECTRA
3 12 10 8
6
4
2
EF
BINDING ENERGY ( e V I
Figure 9: Normal emission spectra of Be(0001) for differeiit photon energies. The spectra have been rescaled vertically in an arbitrary fashion [52].
4
Band-mapping
Angle-resolved photoemission has become to electronic structure what x-ray scattering is to crystallography and neutron scattering is to phonon structure. In general, the threedimensional bulk or the two-dimensional surface band structure can b e determined for any crystalline solid [49]. In this section the basic physical concepts underlying the use of photoemission to determine the band structure will be described, and the theoretical ideas of the previous sections will be illustrated. Subsequent chapters in this book will describe the utilization of angle-resolved photoemission to determine the band structure of alloys, semiconductors, clean surfaces, adsorbed layers, thin metal films, transition metals and rare-earth compounds. Here we shall concentrate on photoemission from simple metals, so that the fundamental physics can be illustrated more easily. Several review articles have already been published that outline in detail the experimental procedure [S, lo], so this section will not address the “how to measure” question. A good material for the purposes of this section is beryllium. This metal has attracted considerable theoretical attention due to the fact that the atom has a simple closed shell configuration (ls22sz),yet it is strongly bonded as a solid [50]. The Be dimer is weakly bound (- 0.1 eV) [51], while the cohesive energy of the bulk is 3 eV. The crystal structure is hexagonal close-packed and the Debye temperature at 1440I< is very high. In one sense it is a simple metal because it is s-p bonded, but on the other hand it is not a nearly free electron metal. The crystal potential is strong, creating a non-free electron band structure [52], and surface states have been observed in the band gaps [53, 541. Figure 9 shows a set of angleresolved photoemission spectra taken from a Be single crystal, cut and polished so that the hexagonal face is exposed to the vacuum; nearly all the theoretical concepts discussed in the previous sections can be illustrated with these curves. These spectra in figure 9 are recorded with an angle-resolved analyzer positioned to collect the electrons emitted normal to the surface. The intensity is recorded as a funct,ion of the energy of the emitted electrons for a wide range of photon energies 1521, and the curves are then plotted as a function of binding energy measured from the Fermi energy. The binding
-
33
energy is calculated from the measured kinetic energy Ekln(h w ) using the energy conservation equation (13): Ee(t,w) = hw - f$ - E k t n ( h W ) , ( 56) where 4 is the work-function of the surface being investigated. The angle 0 of the analyzer with respect to the crystal normal, together with the measured kinetic energy of any peak uniquely determines the components of the electron momentum hk in the vacuum. The component parallel to the surface, I(, and the component normal to the surface ki are given by:
K is conserved across the surfa.ce to within a surface reciprocal lattice vector G (section 2.2), so the value ol K measured in trhe vacuum is basically identical to its value inside the solid. This is not true, however, for the k 1 component of the momentum, and knowing k l in the vacuum does not determine its value inside the solid. It is necessary to know the relationship between E and k 1 for the photoelectron inside the solid, and the way the wave-function inside the solid matches onto the states in vacuum. There are two distinctly different, types of peaks in the spectra in figure 9. One set of peaks appears at fixed binding energy independent of the incident photon energy, and the other set of peaks disperses as the photon energy is changed. The pea.k with a fixed binding energy of 2.8 eV is a surface state [53, 421, i.e. a two-dimensional state whose energy is only a function of K , the surface wave-vector. Since K = 0 for all of the curves displayed in figure 9, this peak has the same binding energy for all photon energies. In contrast, the deeper peak in each spectrum has a binding energy that depends upon the photon energy and consequently upon the value of 81, indicating that these peaks originate from a transition involving threedimensional states. In principle, this is thc most fundamental difference between a surface and bulk state in a. photoemission spectrum. In practice, there may be bulk and surface states that do not have any dispersion, either as a function of K or ki. In these cases different criteria need to be developed (see chapter 4 ) . All the peaks in t,he spectra shown in figure 9 h m e a finit,e width, which in most cases is not limited by instrumental resolution. This means that there is a short lifetime for this excited state, or in the framework of the theory outlined in section 3, there is an appreciable imaginary part to the self-energy operator. The line-width is obviously dependent upon the binding energy of the peak. For example, the bulk transition seen in the hw = 33eV spectrum has a binding energy of l l e V and a width of 4eV, compared to the 8eV binding energy and 1 eV width of the peak in the hw = 15eV spectrum. In general the width of a peak cannot be associated directly with the lifetime of the initial or final state (see equation 49), but the data in figure 9 clca.rly indicate t1ia.t the imaginary pa.rt of the self-energy is energy-dependent. Since the real a.nd imaginary pa.rts of the sclf-energy are coupled by a Kramers-Kronig-type rehtionship [IG], the energy-dependence of 3 n C will result in an energy-dependent real part. The energy-dependence of %C ca.iises a distortion of the measured bands compared to a ground state (density functional) calculat,ion (section 3.3.2). Section 4.2 will discuss the effect of the energy dependence of the real a,nd iiiiaginary parts of the self-energy on the unoccupied bands of Be (541, and section 4.3 addresses the distortion of the occupied band of Na [55, 561. If an infinite set of spectra were recorded at all collection angles and over a very wide range of photon energies, a plot of the measured peak positions as a function of K would yield figure 10. The data in figure 9 would be used to determine the points for K = 0. The peak at 2.8 eV binding energy is the surfa.ce state and appears at this binding energy for every photon energy. The bulk transition moves from its deepest value of 11.1 eV binding energy at hw = 33eV to its smallest value of 4.5 eV a.t hw = lOOeV [52]. A s the analyzer is moved away from the surface normal, the value of It' increa.ses and the surfa.ce state disperses up towards the Fermi N
-
-
34
Figure 10: Energy us nionientum for the two and three-dimensional states seen on a Be(0001) crystal. The shaded region is the projection of the bulk states onto the 2D SBZ, and the heavy solid lines are the surface states 142, 52, 541.
-
energy, crossing E,c at Zi 0.95,k-I 142). The heavy solid lines indicate where surface states have been observed [53, 421, and the shaded region shows the energy range of allowed bulk states for a given value of K [52]. The syminetry notation at the top of this figure is defined in figure 11, where the relationship of the surface Brillouin zone (SBZ) to the bulk Brillouin zone is displayed; the drawing at the right shows the real-space lattice, and the diagram at the top is the extended SBZ picture. The left-hand side of figure 10 is along the --t &' -+ mirror plane of the SBZ, shown at the top of figure 11, and the right-hand side of figure 10 is along the -+ I( -+A? mirror plane of the SBZ. Since figure 10 is a plot of energy as a function of K it must have the two-dimensional symmetry of the SBZ, and it contains all the information available about the dispersion and symmetry of the states on the Be(0001) surface along the high symmetry directions. Figure 10 was created from experimental data for both the surface states and the bulk states, whereas most figures of this sort are constructed by projecting the calculated band structure onto the SBZ [lo]. This procedure can be illustrated for Be by using the calculated band structure shown in figure 12 [50], and the relationship shown in figure 11 between the surface and bulk Brillouin zones. For example, all of the bulk bands along the A symmetry line (r + A ) project onto K = 0 at I? in the SBZ. This gives bulk states from -11.2 eV up in lthe SBZ, all the bulk states along the U symmetry line ( L -+ M ) are to -4.3 eV '. At & projected out, giving bulk states between -5 eV and -3 eV. These numbers do not correspond exactly to the results shown in figure 10, because there are differences between the measured and calculated band structure of Be [52]. The best example of this difference is the surface to I? in the SBZ, close to the band edge. state shown in the right of figure 10, running from If the calculated band structure is used to construct the shaded area in figure 10, this surface state would lie inside the bulk bands and become a surface resonance.
r
r
r
sf
*Initial state energies in figure 12, measured from E F , are negative, whereas the binding energies shown in figures 9 and 10 have the opposite sign.
35
L,' lz = 2.285
1,: 3.582
r '2.224
d
t
S+ 4’’ RECIPROCAL SFaCE
r-b..0.877
1"
REAL SPACE
Figure 11: Real space (right) and reciprocal space (left) lattices of Be(0001) [42]. The top of the figure shows the extended surface Brillouin zone. 2D indicates the two-dimensional surface Brillouin zone. 3D the three-dimensional hulk Brillouin zone.
36
r
M
K
L
H
A
M
L K
H
Figure 12: Calculated bulk band structure of Be [50]
4.1
Two-dimensional surface states
There are two chapters in this hook devoted to the use of angle-resolved photoemission to study surface states on metals and semiconductors, so this section will be brief. The objective is to use the Be(0001) surface states as a vehicle to formulate a few basic questions. Sections 3.3 and 3.4 presented a discussion of the expected line-shape when lifetime effects are included - this concept is usually applied to core levels or hulk valence states, but of course it should also apply to the two-dimensional surface states. The surface state band in the centre of the Be(0001) SBZ has parabolic dispersion with an effective mass of 1.25. Figure 13 shows a fit to the peak in the hw = 37eV spectrum recorded in noimal emission (K = 0) [42] with a Lorentzian lineshape (equation 34). Tliis is one of the only cases where a surface state peak is clearly fitted by a Lorentzian line-shape. The r (34) obtained by fitting is 0.22 eV, which compares very well with the value of the imaginary part of the self-energy calculated for a bulk electron gas with the density of Be [19]. This is not, so surprising, because h C for a semi-infinite electron gas approaches the bulk value very quickly [24], and in any case the surface state extends into the bulk; on the other hand, Be is not particularly free electron-like. As we learn more about measuring and calculating the energy and dispersion of surface states it will become important to undeistand the variation of the self-energy near the surface in real materials. The surface state at the zone centrp of Re(0001), with its apparent Lorentzian line-shape, would be a prime candidate for detailed temperature-dependent line-shape analysis in order to separate lifetime, phonon and surface roughness contributions to the lineshape. It is easy to measure the two dimensional Feriiii surface of any single crystal. Figure 14 is a plot of the Fermi surface of Be(0001), where as usual the shaded region is the projection of the bulk Fermi surface onto the SBZ. The small pockets at I? are the projection of the “cigar” surface running from €1 to K in the bulk Biillouin zone, and the inner region is the projection of the “coronet” 1571. T h e dark line is the zone centre surface state, while the dashed line is a surface resonance. The intersection of the surface state and EF is a distorted circle, with smaller radius in the to I; direction. The shape of the two-dimensional Fermi surface can
r
37
Be (00011 SURFACE STATE
Figure 13: Lorentzian fit t o the Be surface state a t energy is 37 eV.
r shown in figure 9 [42].
The photon
Figure 14: Two-dimensional Fermi surface of Be(0001). The shaded region is the projection of the bulk Fermi surface.
38
have importaut repercussions for the stability of the surface (chapter 4). In section 4.3 we will describe detailed measurements and calculations of the self-energy for excitations from the bulk bands in simple metals. This is accomplished by comparing the quasiparticle band structure measured by angle-resolved photoemission with the bulk band structure calculations. It would be vcrg interesting to be a.ble to do the same for surface states, in an attempt to understand how the self-energy changes for states near the surface compared with states deep in the bulk. There are two immediate conceptual problems: first, many of the theoretical calculations do not reproduce the experimentally determined bulk gaps; and second, it is not immediately apparent that the local density calculations applied to the bulk will work equally well at the surface, where there is a rapid variation in electron density. Two examples will suffice to illustrate the problem. Two calculations for Be(0001) produce a surface state at the zone centre with a binding energy of 2.6 eV (58, 591, compared to the measured value of 2.8 eV. At face value this looks pretty good, but this theory puts the band edge at 4.3 eV binding energy, compared with the experimental value of 4.8 eV [52]. The correct comparison is the separation from the band edge, 2.0 eV in experiment, and 1.7 eV in theory. The case of AI(001) is even more drarna.tic. See1 calculated a binding energy for the surface state at the centre of the SBZ of 2.92 eV [60), compared with the measured binding energy of 2.75 eV 161, 62, 44). It is ea,sy to understand why Seel's calculation differs from the experimental value, since he calculates a band edge at 2.96 eV, while the experimental value is 2.S3 eV 1441. What is significant here is that both theory and experiment put the surface state very close to the band edge, even though self-energy corrections disphce the calculated ba.nd edge from experiment. The Al surface state is so close to the bulk band edge that the quasipart,iclelineshape due t,o t,he surface state overlaps with that of the bulk, leading theoretically to the asymmetric lineshape [43] observed experimentally [9] (figure 1).
4.2
Three-dimensional unoccupied bands
Normally, the objective of angle-resolved photoemission measurements like those shown in figure 9 is to determine the bulk and surface occupied band structure. For the two-dimensional surface this process is relatively easy since K is conserved in the excitation process. It is more complicated to go from the measured spectra to a plot of E versus k for the three-dimensional bands. For example, the normal emission spectrum taken at fiw = 15eV has a peak at a binding energy of S eV. This data ineaiis that a direct transition occurs from an initial state with a binding energy of S eV to a state 7 eV above the Fermi energy. Both the initial and final states are along the A symmetry line beca.use the detector is normal to the surface, but there is no way of determining the value of k~ from the data. If the dispersion Ef(k) is known, however, the wave-vector of the initial state is given by the value of kl for which E,(O, k l ) = 7eV (measured from the Fermi energy). This section will discuss the effect of electron-electron interactions on t,he calculated unoccupied band structure, and the relevance of this to the determination of initial state band structure. The bulk transitions for normal emission from Be(0001) in the photon energy range tLw < 35eV are intense and seem to disperse with photon energy in a smooth, continuous fashion (figure 9), so this data can be used to a.na1yze the first unoccupied band in the A direction of the bulk Brillonin zone (figure 11). The occupied band structure from r to A is very simple, a,s is indicated by the calculation depicted in figure 12 [50]. There are only two occupied bands, one of A1 and the other of A2 symmetry. These two bands are a result of the two atoms per unit cell in the hcp structure. There can be no ba.nd ga.p at A, and optical transitions between the A, and A2 bands are forbidden, so the band structure can be plotted on an unfolded scale r + A + r, as shown in figure 15a. The experimental data has been used to independentIy determine the top and bottom of the occupied bands at -11.1 eV and -4.8 eV respectively [52, 541. These high symmetry points were then used to scale the calculated band to produce
39
- 0.5 >, v
1
-+
w Q
0
- 0.5
EF -1.0
1.0
r
A,
A
o2 r
ELECTRON MOMENTUM
1.2
1.4
1.6
1.8
2.0
REDUCED MOMENTUM (k/k,)
(b)
(4
Figure 15: (a) Band-structure of Be along the A axis in the energy range of the occupied and first unoccupied bands [54]. The lower curve is the empirically determined occupied band while the upper curve is the calculated final band 150). (b) The difference between theory and experiment shown in (a). The solid line is h e calculated self-energy correction to the free electron bands for an electron gas with the Be average density [50]. k~ is the free electron Fermi momentum for the Be density, 1.94 A-'.
40
the initial state band shown in figure 15a [52]. Given this dispersion for the initial band, the data points in figure 9 ca.n now be used to plot out the dispersion of the first unoccupied band. The solid line in figure 15a, taken from the calculation [50], agrees fairly well with the experimental points. It is obvious that even though there is agreement between the theoretical and experimental curves for the first unoccupied A band in Be, there is interesting structure in the data near 15 eV. Figure 15b shows the difference between the experimental and theoretical unoccupied bands as a function of reduced wave-vector [54]. The structure is a many-body distortion of the single particle bands caused by the electron-plasmon interaction. The size of the distortion is shown by the arrows on figure 15b: arrow B indicates the wave-vector of an electron in Be propagating in the A direction at an energy equal to EF plus the Be plasmon energy, and A shows the corresponding wave-vector for a free electron gas. At this energy %nC increases dramatically, and as a consequence there is an oscillation in &E which leads to a distortion of the bands [63]. The solid curve in figure 15b is the theoretical prediction of Hedin and Lundqvist [63] for an electron gas of the density of Be. The comparison between theory and experiment shows that the structure is similar in magnitude, position and width, but there seems to be a phase problem. The disagreement between the theory and experiment in this case is most likely a result of the interaction of the plasmons with interband transitions [54]. This example illustrates the importance of many-body effects on the shape of the unoccupied band structure. In contrast to the data below 33 eV for normal emission from Be(0001), the data in the photon energy range of 33 eV to about 90 eV cannot be explained even qualitatively using the Be band structure calculation. Figure 16a shows a continuation of figure 15a to higher energies. Again, the data points are the circles, and the solid lines are the calculated band structure. It is easy to see that there is no agreement between the experimental points and the theoretical bands in the final state energy range of 22 eV to 70 eV. Unoccupied bands which have a large plane-wave component along A, which will couple strongly to the initial state bands, are iodicated by heavy lines, and we see that if these lines are connected we recover a free electron-like band structure. For Mg [64] and A1 [44] the photoemission spectra can be entirely understood in terms of this nearly free electron final state. But Be is quite different, and if the experimental photon energy range was restricted to the range 30 eV to 90 eV we would be unable to determine the band structure. In this photon range, the experimental and theoretical intensities of the direct transitions are very weak [52] - thus the peak in the spectrum taken at 60 eV is two orders of magnitude weaker than the strong peak at 15 eV. Evidently, when the direct transition is so weak, other secondary effects can become important. One possible explanation for the results shown in figure 16a is that the surface breaks the symmetry and allows the transition from a A, to a A, band [52]. This can be simulated by folding this figure so that the A, and A, bands are on top of each other, and in this way many of the data points in figure 16a can be explained. Figures 15 and 16 illustrated how many-body effects can distort the final state band structure, complicating the interpretation of photoemission spectra in terms of the occupied band dispersion. These many-body effects can also lead to simplifications. The experimental data plotted in figure 16a for a final state energy greater than 60 eV above E,v show that the experimental band structure is much simpler than the calculated bands. The calculated bands have a big band-gap near T’, while the experimental points go through this region almost like a free electron band. Figure 16b shows an expanded drawing of this region and a direct comparison with the free elechon band (dashed line). Pendry [65] ha,s shown that the introduction of a finite mean free path, i e . finite %C (section 3.2), leads to a distortion of the bands, in particular broadening them into the gaps. The final state band structure with finite SmC then looks much more like a free electron band structure than is expected on the basis of band structure calculations. A simple explana.tion of this is tha.t damping is like replacing a large
41
80
-2 >-
I
60
0
W
100 -
a W
z
-
w
a
-2
V
3
0
40
l-
w
I
EXPERIMENT
\
\
-
92-
rF
-1 W
-
-_
'
84 -
20
76 I
-
5
k
-10
r *I
A
A2
r
MOMENTUM ALONG A
(a)
Figure 16: ( a ) Calculated and experimentally determined unoccupied hand structure of Be along the A symmetry direction [52]. The solid data points are from sharp well-defined peaks. ( b ) .4n expanded drawing of the region around 100 eV.
42
0
0
10
20
30 40
50
60
70
80
90
Energy Above EF (eV) Figure 17: Electron inverse lifetimes refor A1 (441, Mg [64], K [6S], Cu [45], NiAl [69], Zn (701, and Li [71] as a function of the electron kinetic energy. diffraction grating with two or three slits, which broadens out all of the diffraction features I661. In section 3.4 the energy broadening of the spectral features in photoemission was described, due to self-energy effects. The line-width, from equation 49, depends on the energy broadening of the electron and hole states re and I?,, - equal to %C for the respective quasiparticles - as well as the dispersion of these states. Now the width of a peak in a photoemission spectrum with an initial state at the Fermi energy tends to be narrow, because r h goes to zero at EF and the dispersion of the hole state is usually less than that of the electron state. This narrow peak has been used to measure re for several metals: if the intensity at E F is measured as a function of the photon energy, the line-width can be directly related to re.The results are shown in figure 17 for a variety of metals, including simple metals like K [SS], A1 [44], Mg (64) and the intermetallic NiAl [69]. The electron mean free path is related to these results through equation 39. It has been the general experience that, an effective mass free electron final state band, adjusted to get the critical points correct, works well for most solids. In section 4.3 we go on to describe a way of determining the occupied band dispersion that does not depend on any knowledge of the final bands [67, 561.
4.3
Initial state quasiparticle band structure
A set of photoemission spectra like those presented in figure 9 for normal emission from Be(0001) can be used to recreate the dispersion of the occupied bulk bands. The conventional
43
procedure for the conversion of this data into dispersion curves requires a knowledge of the dispersion of the final state bands [S, 101, which can be obtained from some ansatz or from a calculation - both of which sound somewhat ad hoc. In practice it is usually possible to determine most of the occupied band st,ructure using the wide photon energy range available with synchrotron radiation, the symmetry selection rules applicable to polarized light, and an educated guess for the final state band dispersion [S,lo]. This procedure works most of the time because the dispersion of the final state bands is much larger than for the initial bands, and damping smears out the structure in the final bands (figure 16b). The energy bands measured in photoemission correspond to quasiparticle bands in the hole spectral function A described i n section 3.3. In the simplest picture, the peak in the photoemission spectrum is shifted with respect to t,he energy in the single particle picture by W C and broadened by %C (equa.tion 34). Thus it is possible to determine the energy or momentum dependence of C by comparing the measured quasiparticle spectrum with the calculated band structure. To make t,his determination of the self-energy quantitative it is important to pick a material where the single particle band dispersion is unambiguous, and to develop a procedure for finding the experimental qiiasiparticle spectrum which does not rely on assumptions about the fitial sta.te disprrsion. Sodium is the ideal material for this type of study because the occupied band is free electron-like. A simple free electron calculation gives an occupied band width of 3.24 eV and a Fermi wave-vector of 0.92 k’, while a sophisticated density functional calculation, within the framework of the local density approximation (LDA), gives the same [72]. Davenport [73] has shown that a Hartree calculation for N a also gives the same band width as LDA, so there is no ambiguity about the choice of exchange-correlation potential in the density functional formalism, or about the method of calculating the single particle band structure: the difference between the measured and calculated ba.nd structure gives %$c. This lack of ambiguity is probably not true for Be [73], so this section will be restricted to Na [55, 561. In 1984 Wohlecke ef nl [G7] proposed a n experimental procedure that would eliminate the need for any a priori knowledge of the final state' bands, by looking for extrema in the initial statc energy which must occur at symniet,ry points in the band structure as a function of the wave-vector component kl perpendicular to t,he surface if the parallel component K is kept fixed. The band structure is always flat a t k l = 0, for example, and at zone boundaries. This extremum searching procedure had actually been used previously to find a few points in the band structure, for example i n measurements on A1 [44]. The physics of the experiments on Na can easily be understood by examining figure 18, which shows the empty lattice band st.ructure of N a in the r N direction [55], the direction normal to the (1 10) surface. The free electron init,ial and final state bands are:
where g is the (110) reciprocal lattice vector, of length 1.11 a.u. in the case of Na. For a given photon energy hw, bulk transit,ions can only occur which conserve energy and crystal momentum, so from equation 13 the allowed transitions occur at an initial state energy given bV:
where E, = fi2g"/2m = 1GS2eV. E, in this equation is measured with respect to the bottom of the occupied band, so E F must be subt,racted to compare with experimental data which is referenced to the Fermi energy. At hw = 26eV the solution of (GO) is E, = 1.25eV, that is, a
44
40
30 Y
> a
c3 W W
20
z
0
a I-
0 W
10
1 W
r
0.5
1 .o
CRYSTAL MOMENTUM k
N
(i-')
Figure 18: Plot of the free electron bands in the direction normal to the (110) face of N a [55]. The shaded region illustrates the energy uncertainty in the final bands due to lifetime effects.
45
'
-4.0 15.0
25.0
35.0
45.0
55.0
65.0
75.0
Photon Energy (eV)
Figure 19: Peak position for normal cinission spectra from N a ( l l 0 ) . The data is from Jensen and Plummer [55] and the theory from Shung ef d. [74]. state with an initial energy of -2.0eV measured from the Fermi energy ( E F = 3.24eV) with a wave-vector k I = 0.30a.u. The heavy arrow in figure 18 shows this direct transition. If the photon energy is reduced, the transition comes from an initial state with a smaller k l and an energy closer to the bottom of the band. A t hw = Eg = 16.8eV the transition comes from the bottom of the band. If the photon energy is increased from the original value of 26eV then the initial state moves to larger kl and closer to the Fermi energy. At hw=32 eV the direct t,ransition comes from the Fermi energy, and in the single particle picture no direct transitions should be seen between 32 and 38 eV, where a transit,ion from the Fermi energy to the next higher final stat,e band will be seen again. As t,he photon energy is increBed beyond this value the direct transition is from initial states moving down in energy, reaching the bottom of the band at hw=67 eV. The experimental results of Jensen a.nd Plummer [55] in this direction are shown by the heavy dots in figure 19, compared with the predictions of the free electron model which are shown by the solid line. Qualitatively the peak positions in the photoemission spectra behave just as predicted from figure 18 and equation 60. It should be noted that N a shows better agreement with free electron theory than almost any other material that has been investigated. Yet there are two notable exceptions to the agreement: firstly, the bottom of the experimental band is not as deep as predicted theoretically; and secondly, a peak appears at the Fermi energy in the photon energy range between 32 aiid 38 eV where no transition should be allowed. The latter issue has attracted considerable attention [6S, 74, 75, 761 but will not be discussed in this chapter. The difference between the measured and calculated values for the bottom of the band is in principle the self-energy correct,ion. Jensen and Plummer [55] reported that the bottom of the measured band is 2.5 eV below the Fermi energy, compared with the theoretical
46
-0.8
4.4
0.0
0.4
0.8
k" (A')
Figure 20: Measured quasiparticle dispersioii for Na [56], compared with the LDA or free electron band structure [72]. The dashed line is the calculated band in the RPA [15]. value of 3.2 eV. In the extremum searching procedure [56, 671, data like those shown in figure 19 are used to determine only one point in the dispersion curve of the initial state - the extreme point. In favourable circumstances the data is fitted by a curve, like the dashed curve in figure 19 which represents a transition from an initial state with an effective mass of 1.28 into a free electron final state band, and from this fit the deepest point is determined. This gives the extremum for K = 0, in other words E, at k = 0. Then, another photon sweep is made with the analyzer fixed at a new value of K from which the extremum energy is determined, and the procedure [56]. is repeated to give the band structure along the line k = (K,O) Figure 20 shows the data for the experiiiiental quasiparticle band structure for Na obtained in this way, compared with theory. The solid curve is the single particle band obtained from the density functional band calculation [72], the same as the non-interacting free electron band, while the dashed curve gives the quasiparticle band calculated in 1965 by Hedin (151 within the random phase approximation (RPA) for an electron gas with the density of Na. It is obvious that the experimental and theoretical quasiparticle bands are appreciably different. The difference between the measured quasiparticle band and the single particle band ( i . e . the )I (figure 3), solid curve) is %E. A slight problem arises since %E # 0 at EF (unlike % whereas the experimental data are referenced to EF. The change in %E with respect to the Fermi energy can be determined, defined by:
ABI=(k) = [E,(k)- E ~ l e x p- [ & ( k ) - EF]theory.
(61)
The experimental data shown in figure 20 are plotted in figure 21 to show the k-dependence of &E [56]. The Hedin calculation for the self-energy [15] is shown as the solid line, marked RPA. The discrepancy between the RPA calculation and the experimental results generated several papers, attempting to improve upon the RPA calculation [29, 30, 77, 78, 79, 801.
47
W F )
Figure 21: Comparison of the experimental and theoretical self-energy correction A%Z(k) [56]. The various theoretical curves are explained i n tlie text. Experimentally the band narrowing seen i i i figure 20 for N a was also reported to have been confirmed by x-ray absorption measurements [Sl]. There seemed to be a straightforward procedure for improving the self-energy calculation that, produced remarkably good agreement with the experimental data [29, 561. Hedin’s GW approximation was used, in which the self-energy is calculated as the first term in an infinite series containing successively higher powers of the dynamically screened Coulomb interaction [15, 161. Hedin employed the free electron Green function and the Lindhard dielectric function (i.e. RPA, without exchange-correlation) for screening the electron-electron interaction [15, 291. An immediate improvement in the a.greement between theory and experiment was achieved by incorporating into the G W scheme a more realistic dielectric function for the electron-electron screening. Northrup ef nl. [29] used a density functional (LDA) dielectric function in a calculation that also included the effect of the ion cores in the Green function. They reproduced the measured quasiparticle Iiands for N a , and their %kX is shown as the dashed line labelled LDA in figure 21. ‘This t,ype of t,heory is now commonly referred to as time-dependent LDA [S2]. Lyo and t’lummer (561 developed a scheme to calculate the selfenergy self-consistently within the G\I! approximation using different, models for the dielectric function. This calculation showed that good agreement with experimental data for a wide range of simple (s-p bonded) metals could be achieved if the long wavelength limit of the dielectric function included the effects of exchange and correlation - a local correction to the RPA . There are many examples in the literature where there are systematic differences between the measured and calculated bands. Probably the most studied discrepancy occurs in Ni, where there is a N 1 eV difference between theory and experiment, 2-3 eV below the Fermi energy [S3]. The difference between theory and experiment has been measured for the intermetallic NiAl [69], and shows a simi1a.r trend to Ni as a function of energy below E F , except that the magnitude is a factor of 2.5 smaller. I n bot,h of these cases the difference has the same sign as in the case of Na, i.e. the occupied quasiparticle Ixmds are narrower than single particle band structure calculations predict. For Ag the reported difference has the opposite sign, as can be seen from figure 2 [13]. Takahashi et el. [S4] have made a comparison of the measured
bands in the high T, superconductor BizSrzCaCuzOS. In the light of the discussion above, it would seem that what is needed for the future is a considerable theoretical effort focused on including the real band structure with an LDA dielectric function in a GW-type calculation of the self-energy, or to develop another equivalent model for treating many-body effects. Wrong! There is in fact no theoretical justification for the LDA procedure outlined above. A calculation which should be better than the GW approximation for the electron gas predicted a broadening instead of a narrowing of the single particle bands [79], and Mahan and Sernelius [30] have shown that if vertex corrections are included properly in a calculation of C, a cancellation occurs which gives back almost the same answer as that obtained by Hedin [15] in the RPA. Vertex corrections describe the correlation between the position of the electron and the positions of the other electrons in the screening charge: the LDA calculation by Northrup et al. [29] includes such corrections in the dielectric function, but Mahan and Sernelius showed that these are largely cancelled by including the vertex correction in the numerator of the selfenergy expression [30]. Their theoretical result for B E is shown in figure 21 by the dashed line labelled G W f . This all presents a theoretical problem which should keep many-body theoreticians occupied for years. But there is a much more serious problem related to the interpretation of angle-resolved photoemission. One of the golden rules of angle-resolved photoemission is that peaks which move with photon energy at fixed K come from bulk transitions, and peaks that are fixed as the photon energy is changed are two-dimensional surface states and surface resonances. In a series of important papers [74, 761, perhaps just a.s seminal as his early work on photoemission theory [3], Mahan and his collaborators have shown that even in transitions identified as bulk-like, surface effects can distort the lineshape. In section 3 it was pointed out that the reduction in symmetry at the surface allows for non-kl-conserving transitions. The amplitude of these surface transitions must be added coherently to the amplitude of the bulk transitions, leading t o the possibility of interference. Shung and Mahan [76] have calculated the photoemission from Na(llO), treating the bulk and surface emission on an equal footing, and they have shown that this interference can lead to measurably large distortions in the position and lineshape of the “bulk” transition. This can lead to discrepancies between the apparent binding energy and the actual energy of the quasiparticle initial state involved in the transition. This suggests that in many applications accurate photoemission calculations, such as those described in section 2.3 [12, 131, may be necessary. In further work, Shung et al. [74] again calculated the photoemission spectra of Na, but this time fully incorporating the self-energy effects as well as the surface effects. They found that both ?%E and %C for the initial and final states contribute to the distortion of the measured photoemission spectra. The crosses in figure 19 are from this calcula.tion, and are in excellent agreement with t,he photoemission data in the low photon energy range. The theory sta.rts off from an RPA quasiparticle band structure (figure 20); the additional band-narrowing shown in figure 19 at low photon energies is a consequence of the smearing-out of the bands - mean free path effects in the final state bands (shown schematically by the shaded regions in figure 18), coupled to the equivalent lifetime effects in the initial state bands. This effect is reduced appreciably at higher photon energies, where the mean free path of the photoelectron is longer and the effect of damping in the final state band is reduced. This calculation indicated that the simple first order expression for the peak shape given by equation 49 is not correct, and that appreciably asymmetric peaks will be observed in the photoemission spectrum. Subtle lineshape asymmetries may be present in the data from the alkali metals that could not be detected due to the low cross-section for excitation [55, 56, 681. In contrast, the signalto -noise and background are adequate for A1 and Be to evaluate the lineshape of a direct transition [9]. Figure 22 shows the fit to the direct transition from the bottom of the Be band seen in normal emission from the (1120) surface of Be at a photon energy of 100 eV. The direct transition is fitted with a Lorentzian lineshape with a FWHM of 3.45 eV (with
-
49
:.,a
16
14
12
10
8
6
Binding Energy (ev)
4
2
*-**a4
0
Figure 22: Normal emission photoemission spectrum [rom Be( 1120) taken at a. photon energy of 10s eV [SS]. The direct transition is fitted by a Loreiitzian line-shape. The insert is the direct transition peak recorded at a photon energy of 30eV normal to the (0001) face [52].
50
a x2 = l.l), in good agreement with the measurements on Be(0001) shown in the insert for a photon energy of 30 eV [52]. The clear theoretical prediction by Shung et al. [74] is that
the lineshape of the peak, and consequently the peak position, in the photoemission spectra for transitions from the bottom of the unoccupied band depends upon the photon energy (see figure 19, for Na). This prediction is not substantiated by the two Be spectra shown in figure 22, or from measurements on Mg [64], Na [55] or K [68]. This is an area where more and better experimental data and theoretical calculations are required. Experimentally the surface interference effect could be completely eliminated by using s-polarized light and measuring at the non-normal r points in the second surface Brillouin zone. In principle, &E and SmIC for the final bands can be obtained experimentally from the real and imaginary parts of the optical potential deduced from a fit to the low energy electron diffraction data [27].
5
Plasmon satellite shake-up and time scales
111 section 3.3.1 we saw that the core hole spectral function in simple metals contains plasmon satellites, and here we shall study their excitation in the photoemission process. The state corresponding to the n’th plasmon satellite is Ik; N - l , c , n ) , in other words a photoelectron in the asymptotically free electron state k, and the ( N - 1)-electron system containing core hole c and excited into the n’th plasmon mode. From (19) we see that there are two ways in which the system can be excited into this state. The first, is the intrinsic contribution:
/dr(k;N-l,c,n
( 5 + ( r ) I N - l , c , n ) s H ( N - l , c , n I $ ( r ) IN,O),
(62)
which we can interpret (reading from the right) as the creation of the core hole and the plasmon excitation occurring together, followed by the propagation of the photoelectron which does not change the state of the system. The other way of exciting the system is the extrinsic contribution:
in which the creation of the core hole leaves the electron gas in its ground state, but the outgoing photoelectron excites the n’th plasmon mode. The intrinsic and extrinsic contributions to the total transition matrix element (19) are coherent, and they interfere with one another in exciting plasmons - the core hole and the outgoing electron have opposite charges 187, 881. The result of this is that the intensity of the plasmon satellites is only significant when the photoelectron has a kinetic energy greater than (typically) 50 eV [89, 90, 911. This has been explained using both semi-classical and quantum mechanical models [92,93, 94, 95, 181. To lowest order i n the coupling with the plasmon, the matrix element describing the creation of the core hole and the corresponding excitation of the plasmon in the intrinsic contribution is [17]:
Here 4c is the core electron wave-function, 6u, is the potential of the plasmon with energy w,, and Y~ is a coupling constant to the plasmons which can be found from dielectric response function theory [96]. The other amplitude entering the intrinsic contribution can be approximated by the plane wave of the photoelectron: (k; N - 1,c,17 I 4 + ( r ) I N - l , c , n ) = e x p ( - i k . r ) .
(65)
51
I
, I
A
/’ / /
3 /
/
I
I I I
,
/
/
/’ ,
-055
I
I
-050
-045 -0.41 iaul %1$2 Figure 23: Surface plasmon satellite fiom a core a t the surface of a free electron gas with the density of A1 1951. J is the photocui I ent noiinal to the surface, as a function of electron kinetic energy measured from the no-losr line at (hw Ec). The broken curve shows the intrinsic contribution; full cuives are tlie total pliotocurrent at (hw E,) = ( A ) 1.2, (B) 2 , (C) 4, (D) 8, (E) 12 a.u.
+
+
In the extrinsic contribution, the core hole amplitude is just:
and from a perturbation treatment of t.he theory presented in section 3.1 [17] it follows that:
where G is the Green function of the photoelectron (the free electron Green function in this model), evaluated at the energy of the photoelectron Ek plus the plasmon energy. This describes the way that the photoelectron is scatateredfrom one free electron state to another by interacting with tlie plasmon. Substituting these amplitudes into (59) and (60) we can find the shape and strength of the plasmon sat,ellit.es. Results for the surface plasinon satellite i l l A1 arc shown in figure 23 for photoemission from a core at the surface [95]. The width of t,he satellite comes from the plasmon dispersion, and we see that the intrinsic and extrinsic contrihutions c,ancel a t the minimum energy-loss end of the satellite, corresponding to the excitation of the long wavelength surface plasmons. This is because the long wavelength plasnions are excited by the average potential which is zero for photoelectron. The shorter wavelcngth plasmons can be excited by the core the core-hole hole photoelectron even at low kinetic energies of the photoelectron. From the figure we see that the interplay between intrinsic arid extrinsic processes leads to more structured satellites as the electron kinetic energy increases, rediiciiig eventually t o the intrinsic contribution alone. Similar behaviour is found for the bulk plasmon satellite, and it has been suggested that the main reason why the satellit,es are not apparent a t low kinetic energies is that they are so featureless that they merge into the background of other inela.stic loss processes [95]. These quantum mechanical results are i l l very good agreement with a semi-classical treatment in which it is assumed that. the photoelectron follows a classical trajectory from the core, and the resulting time-dependent perturlmtion excites the plasmons (figure 24) (951. T h e validity of the semi-classical approach nieaiis that w e can use a time-scale argument to decide
+
+
52
3
iI
i
WOl
f) IOU1
fi
Figure 24: Surface plasmon satellite from a core 10 a.u. in from the surface, at (ftw+E,) = ( A ) 2 and (B) 12 a.u. [95]. The full curve is the quantum mechanical calculation; the broken curve is the semi-classical calculation in which the photoelectron has the energy prior to plasmon loss; the chain curve is the semi-classical calculation in which the photoelectron has the energy after plasmon loss. when plasmons will show up [97]: plasmons with a particular wavelength will only be strongly excited if the electron separates by at least this distance in one plasmon period. For example, the peak in the surface plasmon satellite (figure 23) corresponds to a plasmon wavelength of about 40 a.u., with a period of 14 a.u., so we expect it to show up at an electron kinetic energy of about 4 a.u. - in good agreement with the proper calculation. At lower kinetic energies the perturbation due to exciting the core electron is switched on adiabatically as far as exciting the plasmon is concerned, and at higher kinetic energies it is a sudden perturbation which “shakes up” the plasmon. Many-body satellites can have much more complicated photon energy-dependence than this, with resonance behaviour in cases where there are different transitions which can lead to the sanie final state [l].
6
Screening of the electromagnetic field
Section 2 derived the transition matiix element for photoemission using the Golden Rule, with the induced photocurrent per unit solid angle and per unit energy given by equation 12. The matrix element connecting the initial and final states is M I , = ($,lA . p p . A\&), where p is the momentum operator -zhV and A is the vector potential. It is normally assumed that the spatial variation of A is very small on an atomic scale and that V . A = 0. With these assumptions, which are rigorously true in a vacuum, the matrix element can be written as:
+
hfjf
0: A o .
($,rlVl’l$t),
(68)
where V is the potential felt by the electrons. It is this form of the transition matrix element that is used in almost every calculation of a n angle-resolved photoemission spectrum (section 2.3). The intent of this section is to point out how important the local electromagnetic
53 corrections can be and to illustrate liow the intera.ction of the incident field with the solid can be described theoretically and pictured physically. Photoemission from a simple metal again offers a. good starting point from which the basic principles may be illustrated. If a. metal was really free electron like, the only place where an electroil could be excited by ail incident photon would be a t the surface. Inside the metal it is impossible to simultaneously conserve energy and momentum, or in the framework of (68), V V = 0 inside the material. At the surface, V V # 0 and electrons can be excited (the crystal moves). This is the surface photoelect,ric effect. Mackinson pointed out in 1937 that in the surface region the rapid variations in the electromagnetic field could be as important as the abrupt change in the potential [98]. Remember that in the classical calculation there is a discontinuity a t the surface in the component of the electric field perpendicular to the surface. In a microscopic representation of t h r fields there are rapid oscillations in the surface region which depend in detail upon the incident frequency and the electron density of the solid [99]. The following describes what is known experimentally and theoretically about the importance of the local fields a t the surface. Philosophically there are t,wo approaches to incorpora.ting the induced fields into equation 12 for the pliotocurrent. The first wonld be to consider both the initial and final states as the true many-body stat.es of the system. Then $1 would conta,iii the response of the electrons to the incident field as a true many-hody wave-function. The second approach, which is much more appealing for photoemission calculal ions, is to keep the wave-functions single particle-like and put all of the ma.ny-body screening effects into the effective field. Here we will start with the latter approach and then finish t.liis section by describing the many-body wave-functions in terms of the normal modes of tlie electron gas a t the surface [100]. T h e vector potential inside the solid A(r) can be writ,ten as:
+
A ( r ) = AO AA(z),
(69)
where A0 is the vector potential out,side the solid, and AA the variation in A inside the solid, which is a function of 7 . With this definition the matrix element M I , can be written in the form: Afjz
=&.($jIpl~bt)
+ ($/lAA.p+p.AAI$t).
(70)
The first term is the ordina,ry surface pliotoelcctric effect described by (68) and the last term results from the microscopic variations in the fields at the surface. The last term is zero unless there are longitudinal electromagnetic waves or rapidly varying transverse fields. Such fields may exist only i n the presencca of sources of electric fields, in other words inside ina.tt,er. The matrix element in (70) has been evaluated theoretically for the surface of a jellium metal with the density of A l and compared directly to experiment [101, 1021. Figure 25 shows the comparison of the calculation of the intensity of the Fermi edge emission from an Al( 100) sample i n normal emission as a function of photon energy in the energy range of the surface and bulk plasmons [102]. The bulk plasmon in A1 is at about 15 eV, where there is a minimum in the experimental cross-section. Feibelman’s calculation shown by the solid line is in quantitative a.greement with t.he d a t a if the local field variations are included [loll. The dashed line in this figure is the calculated intensity if only the first term in (70) is included. It is quite obvious that in this photori energy regime the local field variations dominate the cross-section, and analysis of the theory indicates that the p . AA term in (70) is in general the most important. Quite generally the local field corrections i n tlie photoemission matrix element are going to he important whenever there are rapid clia.nges in the dielectric response of the system, either spatially or as a function of frecluency. This is a common occurrence near the threshold for core level excitation and is refrrretl to a.s resonant photoemission. In contrast, the frequency-dependence of the surface dielectric rcsponse is much more difficult to measure and
54
Faml Emldon From Al(lO0) 1.0
0.5
0
I0
(1
12
13
14
16
10
17
10
19
Proton Energy (eV)
Figure 25: Measured and calculated photoemission intensity from the Fermi energy of Al( 100) as a function of photon energy [101, 1021. The solid curve contains local field effects while the dashed line has only the macroscopic field included. The theory and experiment are plotted on the same absolute scale. consequently has mostly been in the province of the theorist [99, 1031. It is now understood that the peak in the cross-section of the emission from A1 shown in figure 25 at about 12 eV is associated with a pole in the surface response function [loo], and as such is really a normal mode of the electrons at the surface. Normal modes of the electron gas are truly many-body effects, therefore in all the theoretical investigations of these modes $, is a many-body wave-function, and consequently the perturbing electromagnetic field in the photo-excitation matrix element should be the applied field Ao. It is an interesting lesson in science to see how these two approaches (single particle us many-body) proceded in parallel without recognizing that they were discussing the same physical effect. The most common normal mode of the electrons at the surface is the surface plasmon, but in fact this mode is determined by the bulk properties, since it occurs when e = -1. In 1970 Bennett suggested that there may be additional surface modes (1041, and in 1975 Eguiluz et al [lo51 described the nature of these modes. They are higher order oscillations of the electron gas, referred to as “multipole modes”, in contrast to the usual surface plasmon which is a monopole mode. Considerablc theoretical interest developed concerning the nature of these modes [106, 107, lOS, 109, 110, 1111, but as there was no evidence that these modes had ever been observed experimentally the field remained a bastion for theorists. The suggestion by Schwartz and Schaich [log] and Kempa and Gerhardts [110] that the multipole mode might be the origin of the enhanced photoyield shown in figure 25 went almost unnoticed. In 1990 measurements of the inelastic loss spectra as a function of momentum transfer from surfaces of the alkali metals revealed the presence of two distinguishable normal modes, the surface plasmon and one multipole mode [112]. Theoretical analysis of the surface response function for jellium showed conclusively that the multipole mode was in fact the origin of the enhancement in the photoyield [loo]. Once it was recognized that there was a new mode at the surface, its presence was identified in the spectra obtained from various surface spectroscopic techniques. Figure 26 compares the spectra from K (curve a ) and Al (curve b) obtained from inelastic electron scattering (ELS), photoemission or photoyield (PY) and inverse photoemission (IPS). The solid line in the top panel is the ELS data for K [loo], where three peaks can be seen: the surface plasmon, the multipole mode and the bulk plasmon. The data points are from photoyield measurements made in 1974. These PY data show only the multipole mode, because light cannot couple to either the surface plasmon or the bulk
55
~~~
~
0.6
0.7
0.8
0.9
o/op
1.0
1.1
1.2
Figure 26: Comparison of the electron loss data (ELS) [loo] with the photoyield (PY) [101, 113) and inverse photoemission (IPS) [114] data for ( a ) I< and ( h ) Al. The observed modes are the surface plasmon (SP), the multipolc mode (Mhl) and the I,ulk plasmon (BP).
56
plasmon unless the surface is rough [113]. The bottom panel shows the data for Al, where in the ELS spectrum the niultipole mode cannot be resolved due to the intensity and width of the surface and bulk plasmon. The photoyield data is reproduced from figure 25, and shows only the multipole mode for a flat surface. The inverse phot,oernission data [I141 should only show the multipole mode if the surface was smooth. Local fields a.t. the surface a.re an import.ant, past, of t,he complet,e picture of aagle-resolved photoemission and appear as coninion features in a variety of surface spectroscopies. More attention needs to be paid to the emission angular dependence at photon energies where the cross-section is dominated by local field efFect,s.
57
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63
Chapter 3 QUASIPARTICLE EXCITATIONS AND PHOTOEMISSION STEVEN G. LOUIE
INTRODUCTION' As discussed throughout this monograph, the photoemission and inverse photoemission spectra of many materials and surface systems may be interpreted in terms of an underlying electronic band structure. The photoelectrons often appear to originate from single-particle states satisfying closely an independent particle picture. This is rather surprising since the electron density in typical condensed matter systems is such that electronelectron interaction is quite strong. The Coulomb interaction energy between electrons is not small compared to the kinetic energy of the electrons. The photoelectron spectrum is then in principle a complex rssponse function of an interacting many-body system. Indeed, very interesting many-body features such as those associated with plasmons, two-hole bound states, and other effects have been observed.1 Nevertheless, experimental evidence shows that, in photo-excitation processes, electron-electroninteraction for the most part leads to only a renormalization of the properties of the electrons with a description in terms of particle-like excitations remains viable. The response of the material can be thought of as due to the creation of particle-like excitations of quasielectrons (or quasiholes) in an interacting many-electron system. In this Chapter, we focus on the theory of quasiparticles and consider photoemission from the point of view of interpreting the essential features in the experimental spectra as being the energies required to photo-excite the system into various quasiparticle states. The relative amplitudes of the structures in the measured spectra, however, depend also on other important factors such as matrix elements in the initial excitation process, final state effects, and transmission of the excited electron to outside of the sample. These issues are covered in other parts of this monograph. 1.
64
Much of the early conceptual development of the quasiparticle picture to electron excitations in solids was made in the late 1950's and early 196Us.2 However, because of the complexity of strong electron-electron interaction in real materials, it has remained a major challenge to calculate the quasiparticle energies from first principles, and hence features of the photoemission spectra. In principle, quasiparticles can have properties quite different from those of band states calculated using standard band structure methods such as the local density functional (LDA) formalism3 or Hartree-Fock (HF) methods. Electron correlations give rise to renormalized energies, effective masses, and finite lifetimes. The use of calculated band structure from oneelectron theories to compare with experimental excitation energies has often led to severe discrepancies. A dramatic example is the band gaps in semiconductors which can be measured by combining direct and inverse photoemission results or, more accurately, by optical spectroscopies. The best calculations using the LDA predicted Ge to be a metal and gave for Si a bandgap of only 0.45 eV instead of the experimental value of 1.2 eV. HartreeFock calculations have given even worse results (see Table I). This is known as the band gap problem. This kind of problem exists not only for the bandgap of semiconductors and insulators, but extends to all excitation spectra of solid-state systems including, for example, the bandwidth of alkali metals.4 The calculated LDA bandwidths are much too broad in comparison with angle-resolved photoemission data. TABLE 1. Comparison of calculated band gaps Eg (in eV) with experiment HF
LDA
Quasiparticle Theoryc
Expt.
13.6 6.4 4.9 16.9
3.9 0.5
5.6 1.29 0.75 9.1
5.48a 1.17a 0.74a 9.4b
~~
diamond Si Ge Lice a Ref. 19
Wef. 10
65
Significant progress has been made, in the past few years, in developing methods for calculating the quasiparticle properties. Predictive calculation$ for the electron excitation energies based on first principles are now possible for many materials. The present Chapter gives an overview of the recent theoretical development in this direction. The theory is shown to be general and has been applied quite successfully to the study of the excitation spectra of semiconductors and metals as well as surfaces, interfaces, and small metal clusters. We present in this Chapter the basic ideas and calculational methods behind the quasiparticle approach together with selected examples from various studies to illustrate the capabilities and predictive power of the approach. QUASIPARTICLE ENERGIES AND PHOTOEMISSION SPECTRA One-electron 7 Traditional interpretation of photoemission spectra has been that of the one-electron picture. In the one-electron (or independent particle) theory, each electron in a solid is assumed to be independent of the other electrons and moving in some effective potential V(r) = Vio"(r) + Vscr(r). Here Via" is the potential due to the ions and Vscr is a screening potential arising from the other electrons. The energy Ei and wavefunction vi of the electron are given by the single-particle Schrodinger equation
2. 2.1.
where i is a quantum number index which, for a crystal, would be a composite of the band index n and wavevector k. In photoemission, the system is perturbed by an external interaction HI, arising from the incident light of wavevector q, of the form (to first order in the vector potential A)
which may be written in second quantized notations as
66
Bnn'(k)cnik+qcnk t
HI =
(3)
nn' k
where c t and c are creation and annihilation operators for electrons in some specified one-particle orbital basis set and B is a matrix element. If one takes the solution to Eq. (1) as the one-particle orbital basis, it is then clear that the action of HI is to promote electrons from an occupied state of wavevector k to an empty state of wavevector k+q. We thus obtain the usual interpretation of photoemission spectra in terms of a one-electron band structure. The major questions are: 1) Under what conditions is this one-electron picture valid? And 2) how does one obtain the appropriate potential Vscr which goes into Eq. (l)? Empirical schemes such as the Empirical Pseudopotential Method6 which fit V = Vion(r) + Vscr(r)to optical and other spectroscopic data have been very useful in interpreting photoemission spectra for bulk crystals. However, since the potential is empirically determined, its physical origin and possible changes arising from alterations in the environment, such as at a surface or in a different compound, are not certain. These schemes hence lack the predictive power to give an accurate account of the spectra of new materials or systems with reduced symmetry. In an attempt to perform ab inifio studies, the most common approach has been to interpret the electron excitation energies as the self-consistent band eigenvalues from either local density functional or Hartree-Fock calculations. Both approaches are, however, ground-state theories which were formulated to give the total energy of the systems and not the electron excitation energies. For example, in the case of the density functional approach,3 the total energy of an interacting electronic system is shown to be a functional of the charge density p(r). The charge density is obtained from the one-electron orbital I$ of an associated noninteracting system of the same charge density via the Kohn-Sham equation
67
where VH is the usual Hartree potential and pxcis an exchange-correlation potential given by the functional derivative of the exchange-correlation energy with respect to p. There is no rigorous justification for interpreting the Kohn-Sham eigenvalues as quasiparticle energies. The same can be said about the Hartree-Fock eigenvalues which are obtained by replacing pxcin Eq. (4) by the exchange operator. Formally, the Hartree-Fock scheme provides the single-particle orbitals which minimize the total energy within the approximation of a single Slater determinant form for the many-electron wavefunction. As we shall see later, one can only view Eq. (4) or the HartreeFock equations as approximation at some crude level to the quasiparticle equation which provides the electron excitation energies. However, until very recently, because of the lack of a better first principles alternative, the LDA has been consistently used to interpret experimental spectra and considered the state-of-the-art approach. b r a c t ina Flectron Svstems The discrepancies between standard band theory and experiment (such as those given in Table I for the band gaps in semiconductors) can be traced to an inadequacy of previous first-principles calculations in treating electron correlation effects for excited-state properties. As seen from the form of the interaction Hamiltonian in Eq. (3),the photo-excitationprocess may be viewed as predominantly that of a single-particle excitation. Thus, a quantitative understanding of the photoemission spectra requires knowing the longlived particle-like excitations (or quasiparticles) of the interacting many-electron systems. Much recent effort has been devoted to developing theoretical methods,s~'-11 either semi-empirically or from first-principles, for calculating the quasiparticle properties going beyond the independent particle picture. The quasiparticles can be thought of as electrons dressed with an electronic polarization cloud giving rise to modified properties. An accurate treatment of the dynamical correlations, arising from the Pauli exclusion principle and Coulomb repulsion, seen by an electron in a solid is then crucial in calculating the excitation energies. A direct and physically transparent approach to determine the quasiparticle properties is that of a Green's function formulation.* The single particle Green's function is defined as 2.2.
68
G(r,r',z) = -i cOIT{W(r,z)yt(r',O)}[O>
(5)
where the y's are the field operators in second quantization notation, )O>is the ground-state wavefunction, and T is the time order operator. An especially useful quantity is the diagonal elements of G in orbital basis representation
where the c t and c are creation and annihilation operators for the single particle states. Physically the single-particle Green's function gives the amplitude of finding a particle in state p at time t = z if one is created into that state at time t = 0. For a noninteracting electron system, this definition leads to a single particle Green function Go given by (for simplicity of notations, we set fi = 1 and the crystal volume v = 1)
where f is the usual Fermi factor. The time Fourier transform of Eq. (7) gives
where 6 is a positive infinitesimaland qp is O+ if the state p is above the Fermi energy Ef and 0- if below. Or equivalently, expressed in a spectral weight function A(p,o),
with A(p,w) for the noninteracting system given by a delta function
69
The contour C runs infinitesimally above the real axis for w < p and below the real axis for w > p where p is the chemical potential. Since in general the spectral function is just proportional to the imaginary part of the Green's function: 1 A(r,r',w) = - Ilm G(r,r',w)l . x
(1 1)
Equation (10) tells us that the single particle Green's function of a noninteract, energy required to add a paring system is characterized by a pole at E ~ the ticle in state p to the system. Thus one expects that in general, if the diagonal matrix element of A with respect to a one-particle state is sharply peaked as a function of energy for an interacting many electron system, then it is meaningful and useful to speak of a particle-like excitation (see Fig. 1). This corresponds to a pole in the Green's function at a complex energy, and a A(p,o) of the form
A(P,m) =
i 27F ZP
- [Ep - PI
k
IJ
+ C.C. + correction terms.
>&
Fig. 1. Qualitative picture of spectral function A(k,E).
The physical content of this picture can be clearly seen by substituting Eq. (12) back to Eq. (9) and obtain for positive z
where rpis the imaginary part of Ep. G, in this particular single-particle orbital basis, describes a propagation amplitude which is oscillatory with characteristic energy given by Re(Ep). This leads to the usual interpretation that the peak position in A is the quzlsiparticle energy (real part of EP) and the width relates to the lifetime of the quasiparticle (imaginary part of Ep). For an interacting many-particle system, finding the quasiparticle properties is then equivalent to solving for the appropriate single-particle orbitals which give rise.to sharp peaks in the diagonal matrix element of A and solving for the position of these peaks in the complex energy plane.
3.
GREEN’S FUNCTION THEORY OF QUASIPARTICLE ENERGIES In this section, we briefly discuss a formulation for solving the singleparticle Green’s function and hence the energies and wavefunctions of quasiparticles in real solids. For simplicity of notation, we suppress the spin indices associated with the electron. 3.1.
Jhe Self FnerFor a many-electron Hamiltonian
H=
2
where h(ri) = pi /2m + Vion(ri) and V,(rij) = e2/lri - r,], the single-particle Green’s function can be shown, via the equation of motion of G, to satisfy
where VH is the usual Hart‘ree potential and Z is called the electron self energy operator which is a functional of G. Equation (15) can be solved formally in the so-called quasiparticle approxirnation by expressing
71
where Erik and Wnk are eigenvalues and eigenfunctions to the homogeneous equation
We may now identify the pole structure of G(r,r',a) with the solution to this equation. Given the self energy operator Z, the problem of solving for the quasiparticle properties is then one of solving Eq. (17), the quasiparticle equation. This equation is similar in form as the Schrodinger equation in one-electron theories. However, owing to electron-electron correlation effects, Z(r,r',m) is now a nonlocal, nonHermitian and energy dependent operator giving rise to a complex Erik. This comes about because the exchange interaction is nonlocal and electron screening is intrinsically energy dependent in a solid. And, as discussed above, the real part of Erik gives the quasiparticle energy and the imaginary part gives the lifetime. The quasiparticle energy is often written 0 as a sum of a single-particle term, En, plus a self-energy znk due to exchange-correlation effects.
This description of excited states of the interacting electron system in terms of quasiparticles depends on the lifetime of the quasiparticle being sufficiently long on the time scale of the relevant experimental probes. For energies near the Fermi level of a metal or the gap region of a semiconductor, the quasiparticles are well defined allowing us to pursue this description. Near the bottom of the occupied bands, for example, lifetime effects are certainly appreciable. Here, in discussion of interpretation of structures in the photoemission spectra, we are primarily concerned with the real part of the selfenergy operator, i.e. the energy of the quasiparlicle.
72
To solve the quasiparticle equation, a useful formulation is to express the self-energy operator in terms of the dynamically screened interaction W: W( r,r’;co) =
E-l(r’,r’’;co)VC( r”,r’)dr’‘
(19)
where E(r,r’,co) is the time-ordered dielectric response function of the system. The dielectric function is related to the irreducible polarization propagator P by E(r,r’;co) = S(r - r’)
-
P(r,r”,o)Vc( r” - r’)dr”
.
(20)
In this formalism, C can be obtained formally by a set of coupled functional derivative equations which are2
j
C(1,2) = i W(1+3)G(1,4)r(423)d(34)
(21a)
P(1,2) = 4
(21c)
G(1,3)G(4,1+)r(342)d(34)
where r as defined is often referred to as the vertex function. The index 1 is a shorthand notation representing the coordinates (r1,tl) and spin. 1+ denotes (rl ,tl + 6) with S a positive infinitesimal. The set of coupled equations given above may be used to generate a series expansion for C in terms of powers of G and W. For example, a starting iterative solution to Eq. (21) is obtained by setting Z = 0 in Eq. (21d) which gives the simple expression
13
and a first order expression for Z as ~ ( 1 , 2= ) i G(1,2)W(1+,2) .
(23)
Successive iteration of Eqs. (21a-d) would lead to correction terms with increasing higher power of W to Eq. (23). This is schematically illustrated in Fig. 2. For a system with large polarizabilify, this series expansion is advantageous over the conventional one in terms of the bare Coulomb interaction and the noninteracting Green's function. W, being the dynamically screened interaction, is much weaker and thus should lead to a significantly more rapid convergence in the expansion for Z. Mathematically, since W and the dressed Green function can be expressed as series expansions in the bare quantities, each term in Fig. 2 is a partial summation over terms in a conventional expansion.
z= 2
+ 2
..... .................
......
__ . ...
...................... . ..... ..
1 + 2 3.
1 + 2
._,.., . ..:.
.
.. 1
..........:-... ........
1 + 2
1
Fig. 2. Diagrammatic expansion of Z in the screened Coulomb interaction
.
.
The GW ADDrOXlmatlon In practical calculations for real materials, the electron self-energy operator has only evaluated to first order in the dynamically screened Coulomb interaction W and the dressed Green function G. This approach is called the GW approximation since C is given by Eq. (23). Or, more explicitly, the selfenergy operator is given by (after Fourier transformation to energy space)
3.2.
74
E(r,r';E) = i
I dw -e-iSw G(r,r';E - w)W(r,r';w) 2x
(24)
where 6 = O+. In this approximation the calculation of the quasiparticle properties reduces to computing Z using Eq. (24) and then solving Eq. (17). As seen from the structure of Eqs. (16), (17), and (24), the quasiparticle energies together with Z and G must be obtained in a self-consistent fashion. Hence, even in this first-order theory, first-principles calculation of the electron excitation properties is a major computational task. The two essential ingredients in the theory are the dynamical dielectric response function and the dressed electron Green's function. Both have to be treated adequately to obtain quantitative results that may be compared with experiment. Note that if W is replaced by the bare Coulomb interaction in Eq. (24), then C becomes the usual exchange operator. The quasiparticle equation, Eq. (17), reduces to the single-particle equation in Hartree-Fock theory. Thus, in this way, one can think of the Hartree-Fock energies as an approximation to the quasiparticle energies. The dielectric function contains the dynamical screening response of the electrons which gives rise to correlation effects going beyond bare exchange. Although, as in any perturbation series, an a priori determination of convergence is difficult, the GW approximation has yielded very good results in comparison with experiment for a wide range of materials. Because of computational difficulties, there have been only limited ~tudies2~12-15 of the effect of higher order terms or vertex corrections on the quasiparticle energies and they were on the uniform electron gas. Even for this simple model case, estimates of the effect of vertex corrections vary considerably. CALCULATION OF THE ELECTRON SELF-ENERGY There is a long history of previous work dating back to the early 1960's on trying to calculate the electron self energy in solids along the approach discussed above.16 The band gap problem of the semiconductors gave impetus to the development of several recent theories. Wang and Pickett7 applied the local density functional approach for the self-energy operator to semiconductors. Horsch, Horsch, and Fulde8 used a linked cluster expansion variational approach to include the effect of electron correlations. Strinati, 4.
75
Mattausch, and Hankeg formulated a tight-binding approach to evaluate Z in the GW approximation. In application, each of these approaches has required empirical input at some stage. First-principlescalculations for real material~5~10~11 are now possible. The work of Hybertsen and Louiesllo and subsequently those of Godby, Schluter, and Sham1 calculated the electron self-energy operator without using empirical input. In particular, the approach developed in Ref. 10 has been applied to compute the quasiparticle properties of a variety of solid-state systems including semiconductors and simple metals as well as surfaces, interfaces, superlattices, and small metal clusters. We describe briefly here the approach and discuss some of the results in the subsequent sections. To calculate the self-energy operator in the GW approximation, the crystalline Green's function and the dynamically screened Coulomb interaction are required input. Both qualities are crucial in determining the final self energy and have to be adequately calculated with all the important physical processes included for the material under consideration. Jhe C r v W e Green's Function In the approach of Ref. 10, a quasiparticle approximation is employed for the Green's function resulting in an expression for G [Eq. (16)] which is similar to the independent particle case. This approximation assumes that all the weight in the spectral function is in a narrow quasiparticle peak which is then approximated by a delta function. The Green's function is constructed initially using the LDA wavefunctions and eigenvalues. For the examples described below, they are obtained with the ab idio pseudopotential method. In principle, the self-consistent Green's function should be obtained by iteration using the successively calculated quasiparticle wavefunctions and energies. It turns out, however, that the LDA eigenvectors are extremely good approximations to the quasiparticle wavefunctions,'O with overlap between the two which is often better than 99.9%. The Green function in practice is then subsequently updated only with the quasiparticle spectrum from Eq. (1 7). There is only very limited experience on the importance of including the detailed structure in the spectral function for the quasiparticle energies.* Comparison of calculated energies with experiment show that Eq. (16) is an 4.1.
76
excellent approximation for semiconductors and insulators and for the s-p metals. However, as in the case of vertex corrections, only a posteriori experience truly justifies the approximation. And, the validity of Eq. (16) and Eq. (24) remains to be assessed for systems with highly correlated electrons. 4.2.
Jhe Screened d -C Io w i e l d Fffea Evaluation of the screened Coulomb interaction requires the full dielectric response function (both the spatial and time dependences) of the system. Because of charge density inhomogeneity, the dielectric response function E(r,r';w) of a solid is a function of r and r' separately. This functional dependence reflects the fact that the response in a solid can be significantly different depending on the location of the perturbation. In Fourier space, for a crystal, the dielectric function is a matrix in the reciprocal lattice vectors G . The off-diagonal elements of EGG(q,w) give the so-called local field effects in screening which describe the variation in the electron polarizability at different positions in the unit cell. For semiconductors and insulators, it is shown10 that the offdiagonal elements must be included in the evaluation of Z,i.e. local field effects are essential in determining the quasiparticle energies. The frequency dependence of E (or the dynarnical screening effects) are also found to be significant for obtaining quantitatively correct results. The dielectric matrix is calculated in two stages in the Hybertsen-Louie approach. The static dielectric matrix <&(q,w = 0), being a ground-state property, is obtainable within the density functional theory.17 It is calculated from first principles using the standard Adler-Wiser formulation with the LDA. To extend the dielectric matrix to finite frequency, a generalized plasmon pole model is introduced.10 in this model, the frequency dependence of each momentum component (G,G',q) of the imaginary part of E-I is represented by a delta function with its strength and position determined by exact sum rules. There are no adjustable parameters, and the theory gives the w and 0-1 moments of the exact response function by construction. This procedure of obtaining the frequency dependence of e-1 has the merits of being numerically simple and, more importantly, avoiding the difficult theoretical problem of how to evaluate the 61 dependence of the polarizability. Also, it allows possible modification of the polarizability going beyond the random phase approximation (RPA).18 Comparison with experiment and with subsequent calculations
77
using alternative methods11 in calculating the frequency dependence of E-' showed that the generalized plasmon pole scheme is highly accurate for the quasiparticle problem in semiconductors. One weakness of the generalized plasmon pole model is that the quasipatticle lifetimes cannot be realistically estimated. This however will have little impact on the comparison to experiment such as photoemission with the possible exception to the deep-lying hole states.
.
.
The Q m i c l e FQ.U&U Once the self-energy operator is given, the quasiparticle energies may be obtained by solving Eq. (1 7) using standard techniques. The only complication is the requirement of self-consistency in the energy argument of Z with the sought-after quasiparticle energy. It has been shown that, in most cases, a petturbative scheme gives very accurate results. Instead of solving Eq. (1 7) directly, Erik is solved to first-order in the difference between the self-energy operator Z and the LDA exchange-correlation potential pxc. The zeroth-order solution is the Kohn-Sham eigenvalue Erik and corresponding eigenfunction Ink>. Making the standard assumption that the energy dependence of the matrix element &k(E) = cnklZ(E)lnk> is linear for E near Erik and that Erik = Erik, the first-order solution is given by 4.3.
Here pf;ck is the matrix element of the LDA exchange-correlation potential and
is the dynamical renormalization constant which may be shown to be the same as the 2 in Eq. (1 2). BULK MATERIALS The quasiparticle approach has been applied to study the excitation spectra of a range of bulk materials. We give several illustrative examples
5.
78
here. 5.1.
Semiconductors and- 1
A first application and major success of the first-principles self-energy approach described in the last section is the quantitative resolution of the band gap problem in semiconductors and insulators. The calculated minimum gaps1* for several selected materials are compared with experimental values19~20in Table 1. Although, in principle, energy gaps deduced from direct and inverse photoemission experiments ought to be different from those measured in optical experiments because of electron-hole interactions. For semiconductors, the differences are usually minor. As seen in Table 1, the calculated quasiparticle gaps are in dramatic better agreement with experimental values than the LDA and HF results. Germanium is no longer predicted as a metal. In general, agreement with experimental values for the gap of semiconductors is at the level of 0.1 eV. We note that the quasiparticle gaps were calculated using input consisting of only the atomic numbers of the constituent elements and the crystal structure. It is found that both local field effects and dynamical screening in the dielectric response are crucial in obtaining quantitatively accurate band gaps for semiconductors. This is because calculation of the gap requires the difference in self energies between the occupied valence band maximum state and the empty conduction band minimum state. These states in general have wavefunctions residing in different regions of the crystalline unit cell (bonding vs. antibonding sites) where the dielectric response can be significantly different owing to local field effects. The frequency-dependence of screening leads to a dynamical renormalization factor Z (Eq. 26) of typically 0.8-0.85 for semiconductors.10 This degree of renormalization is modest, implying that quasiparticles are well-defined in semiconductors. However, this frequency dependence in the self energy of the electrons, which reflects the mixing of the electron degrees of freedom with the elementary excitations (plasmons), is non-negligible in determining quantitatively the quasiparticle energies. In Fig. 3, the calculated quasiparticle band structure for Ge is shown and compared to the energies deduced from angle resolved photoemission21 and inverse photoemi~sion22~23 experiments. The overall agreement between theory and the experimental results of Wachs et d.for the occupied
79
10
1
8
6
4
2
z o v
F
-2
Q)
C
w -4 -6 -8
o Experiment
o I+H
-10
Typical error
-12 -14
L
A
r
A
X
Wave vector i; Fig. 3. Calculated quasiparticle energies of Ge versus direct (0,Ref. 21) and inverse (0,Refs. 22 and 23) photoemission data. states are excellent. Along the A direction the dispersion agrees well with theory for all the bands. The binding energy near the X point seems to be larger in experiment than in theory. The discrepancies are, however, well within the experimental error estimates shown in Fig. 3. Although angle-
80
resolved inverse photoemission studies are less common and typically have poorer energy and angular resolution, the calculated conduction band energies of Ge have been quantitatively verified by the data of Refs. 22 and 23. A similar level of agreement with photoemission experiment has been observed for other insulating materials including a wide rage of gap size (metallicity) as well as ionicity. In Table 2, the calculated bandwidths of the three homopolar materials are compared to photoemission results. The agreement in general is good, but the theory seems to give systematically slightly too small a bandwidth. Some results together with experimental data20t24-26for the ionic insulator LiCl are given in Table 3. A more detailed comparison for the conduction band states at the L point in the Brillouin zone with inverse photoemission data is given in Table 4 for Si and Ge.22 The agreement is again very good, within 0.1 -0.2 eV. Since, as discussed above, photoemission experiments measure the quasiparticle energies whereas optical transitions contain possibly additional electron-hole interactions, comparison of these results to optical data has been made in an effort to extract the influence of excitonic effects.22 Optical TABLE 2. Comparison of calculated bandwidth with photoemission data for the homopolar materials. (Energy in eV.)
diamond Si Ge a Ref. 19
Quasiparticle
Expt.
23.0 12.0 12.8
24.2 f 1a 12.5 0.6a 12.9 f 0.2b
*
b Ref. 21
measurement of the second indirect edge in Si places the Llc state 2.1 eV above the valence band edge.27 This is nominally 0.3 eV different from the inverse photoemission result in Table 4. However, since the experimental error bar is large and the quasiparticle theory result falls almost exactly halfway between the two experimental results, the significance of excitonic effects for this case remains an open question.
81
TABLE 3. Quasiparticle results (in eV) for Lice are compared with experiment for gap E,, Ce 3p bandwidth W3p, and the separation between the Ce 3s and 3p bands E3,, - E3s. J
ice
Theorv
Fxot. 9.4a 4.0 f 0.2b 11.6 & 0.5C 11 .O k 0.6d
9.1
3.8
a Ref. 20
b Ref. 24
CRef. 25
dRef. 26
TABLE 4. Comparison of the calculated conduction band critical point energies at L relative to the valence band edge to the results of angle resolved inverse photoemission experiments for Si and Ge.. ~
Si
r25’v+ Llc r25’v+bc
Theory
Expt.a
2.27
2.4 f 0.15 4.15 k 0.1
4.25
Ge r 8 v --f kic r 8 v + hc r8v +4 . 5 ~ r 8 v + hc
0.75 4.3 4.43 7.61
0.8 4.2 f 0.1 7.8 f 0.1
Comparison of calculated quasiparticle energies with other optical data shows that excitonic effects do not appear significant in bulk semiconductors. The experimental optical transition energies19.28-31 are given in Table 5 together with the calculated transition energies for the crystals diamond, Si, and Ge. The experimental values are from high precision electroreflectance and wavelength modulation spectroscopy measurements. It should be pointed
82
TABLE 5. Comparison between theory and experiment for optical transitions in Ge, Si, and diamond. (Energies in eV.) LDA
Quasiparticle Theory
Expt.
0.30 -0.07 2.34 2.56 3.76
0.30 0.71 3.04 3.26 4.45
0.297a 0.887a 3.006a 3.206a 4.501a
2.57 3.26 2.72 4.58
3.35 4.08 3.54 5.51
3.4b
Ge r7v
+r 8 v
rev +r7c r 8 v + rG, r8v r& x5v xx --j
--j
Si
r2sv+ rlw
r 2 v V -+ rZc
k’v-+ L l C
L3’v -+ L3c
4.2C 3.45b 5.50b
Diamond r25’v-+r15c r25v rTc x4v + X l C
+
a Ref. 28
5.5 13.1 10.8
bRef. 29
7.3d 15.3k5e 12.5C
7.5 14.8 12.9 CRef. 19
dRef. 30
Wef. 31
out that in addition to neglecting electron-hole interactions, the calculated energies correspond to transitions at symmetry points in the quasiparticle band structure. The actual critical points in the experimental optical spectra from which the transition energies are identified may be away from these symmetry points. This introduces an intrinsic but small uncertainty in the comparison of experiment to theory. As seen from the Table, the theoretical results are typically within 0.1-0.2 eV of the experimental values for all transitions except for the very high energy ones in diamond, where the experimental uncertainties are rather large. The accuracy of the present results is a major improvement over previous ab inifio band calculations. It is comparable to what is obtainable from empirical schemes such as the Empirical Pseudopoential Method6 in which the photoemission and optical data are fit to several adjustable parameters.
83
'
-3 -30
3
'
-1 -15
-1
'
-15
I -20
-10
0
10
20
-I0
-5
0
5
Ib
-10
-5
0
5
10
I
-3 -15 -10
-5
0
5
10
15
20
(ev)
Fig. 4. Differencebetween calculated quasiparticle energies and LDA eigenvalues.
Figure 4 displays the difference between the quasiparticle energies and the LDA eigenvalues as a function of the quasiparticle energies for four
a4
insulating materials. Several striking trends may be observed. The manybody corrections to the LDA values, defined by bnk = Erik - &nk, are dominated by a jump at the band gap. This may be understood in terms of a change of the wavefunction character from bonding to antibonding as the gap is crossed. The self energy operator Z is nonlocal with a range which extends over about a bond length.1oll1 It is therefore considerably more sensitive to a change of the nodal structure in the wavefunction than any local potential such as that used in the LDA. In addition to the jump, there is a rather smooth energy dependent part to the correction which is quite large for some of the large gap materials. Also the magnitude of the corrections associated with the valence band states relative to those of the conduction band states are materials dependent. This has important implications on the theory of Schottky barriers and band offsets at semiconductor interfaces since the relative position of the band states are required in determining these junction properties. Also, as we see below, the many-body corrections to LDA surface state energies are not necessarily the same as for the bulk states. Thus, the corrections are not just a simple shift of the LDAconduction bands relative to the valence bands. There appears no simple empirical rules which would allow a determination of the quasiparticle energies quantitatively, especially for surface and defect states, without performing a detailed microscopic calculation.
&mle
MetaIS Comparison of standard band structure energies with photoemission and other spectroscopic data also shows sizable discrepancies for metals4 These again may be attributed to exchange-correlationeffects. Thus far, most of the quasiparticle calculations on metals however have been carried out either for the jellium model or for the simple s-p metals.’6.32-38 A few exceptions are some work on the d-band metals using a simplified version of the GW approximation.39 A case of particular interest is the bandwidth of the alkali metals. Although these are conceptually the simplest of the metals, the measured bandwidth from recent angle-resolved photoemission experiments4140 showed a substantial disagreement of nearly 30% with the corresponding free electron values or results from band calculations using LDA methods. 5.2.
85
1 .o
0.0
-1.0
8
w
-2.0
-3.0 0.00
0.50
1.00
Fig. 5. Comparison of calculated quasiparticle energies (filled circles) with LDA eigenvalues (dashed line) and experimental data from Ref. 4 (crosses) for Na. The experimental data for Na is given in Fig. 5 together with the calculated quasiparticle band structure.36 The surprisingly large observed bandwidth reduction in this case is explained by the self-energy effects. The occupied bandwidth is reduced from the LDA value of 3.16 eV to a value of 2.52 eV when self-energy corrections are included. This value is in excellent agreement with the photoemission values of 2.5 f 0.1 eV (Ref. 4) and 2.65 f 0.05 eV (Ref. 40). However, the origin of the dispersionless feature just below the
86
Fermi energy is still a subject of debate. The calculated quasiparticle energies for Na are also consistent with recent X-ray absorption edge measurements,41 which are sensitive to the position of the empty density of states features deriving from the gap at the Brillouin zone face. The experimental results indicated a 16% contraction in the width of the unoccupied part of the spectrum just above EF. The calculation36 predicted an 18% reduction. Similar narrowing of the occupied states has been calculated for other simple metals37.38 with good agreement with experiment. It is found that the inclusion of exchange-correlation effects in the dielectric screening going beyond RPA is important for the self energy of the alkali metals. But, on the other hand, local field effects do not play a significant role. In general, for a metal, a reduction in bandwidth from the free electron value is expected if the density is such that the electron density parameter r, is greater than one.38 TABLE 6. Quasiparticle energies in eV calculated for Al, relative to EF, compared to experimental angle-resolved photoemission results of Levinson et a/.(Ref. 42).
Theory
Experiment
- 1.51 - 2.89
- 1.15
- 1.00
- 2.39
- 0.95 - 2.4
- 0.87
- 0.90
0.25 0.90 - 4.39 -1 0.01
- 4.55 - 10.6
- 2.83
In Table 6 the calculated quasiparticle energies for Al are compared with experimental values determined from angle resolved photoemission by Levinson et al.42 Overall, the agreement between theory and experiment is
87
again very good. There is however one discrepancy. The calculation gives a value for the X1 state at -1.51 eV below the Fermi level, but the experimental spectra place it at -1.15 eV. On the other hand, the X4, Z1,Z3, and W3 states are all found to be within 0.1 eV of the experimentally determined energies. This difference in the placement of the X1 level results in a calculated gap at X of only 1.38 eV whereas the experimental value is 1.68 eV. The origin of this difference between theory and experiment remains unclear at this time. The quasiparticle bandwidth for Al is 10.01 eV. It is about 6% smaller than experiment. Some of the discrepancy for the bandwidth (also observed in the case of semiconductors) may result from the plasmon pole approximation which tends to overestimate the bandwidth narrowing for systems with rs = 2.
There have been several alternative theorie~32.33~35 proposed for the observed band narrowing in the alkali metals. The work of Ref. 32 and Ref. 33 are both done in the context of the jellium model and include coupling to spin fluctuations in addition to density fluctuations in the electron self-energy, but using rather different models. Results in Ref. 33 gave bandwidths which are too small by approximately 10-20°/0. On the other hand, Ref. 32 obtained bandwidths which are systematically too large. Shung et a1.,35 on the other hand, attribute part of the narrowing of the Na bandwidth to the photoemission process. They found that the measured valence-band width should depend on the range of photon energies. However, no such dependence is seen in A more accurate determination of the effect of the surthe e~periments.4~40 face on the measured photoemission spectrum of Na (including the unexplained flat feature near EF) would require a calculation of the self-consistent surface potential, including atomic relaxation and full response function. SURFACES AND CLUSTERS The self-energy approach has been extended and applied to the excited-state properties of semiconductor surfaces,43-46 heterojunctions,47 superlattices,48 and small metal clusters.49 We briefly discuss here some examples of surface and cluster calculations and the corresponding comparisons with experiment. Since the electronic and geometric structures of these systems are much less intuitive and more difficult to determine unambigu-
6.
88
ously from experiments, the predictive aspect of the self-energy approach here makes it especially valuable in these studies. As a simple illustration of many-body effects on the quasiparticle surface-state energies, we consider the case of the As capped Si(ll1) and Ge(ll1) surfaces. At saturation coverage, these surfaces have a very simple geometry which is a 1x1 structure with the As atoms replacing the outermost layer host atoms.50 The surface is chemically inert and highly stable against reconstruction. There have been very extensive photoemission studies on their surface-state spectra,50 making these surfaces an ideal case for a manybody calculation. Moreover, these are systems of considerable intrinsic importance because of the interest in growth of GaAs on covalent semiconductors. As for bulk materials, the calculations43 involve, first, a determination of the surface geometric structure by total energy minimization and then evaluation of the quasiparticle energies for both the bulk and surface states. A 12layer slab in a repeated supercell geometry was used to simulated the properties of the surface. Figure 6 depicts the calculated quasiparticle energies for the As-capped Si(ll1) with the shaded areas corresponding to the projected bulk quasiparticle band states. The quasiparticle surface-state bands are given together with the LDA surface-state bands for comparison. Very similar results have been obtained for the As/Ge(lll) surface. In Fig. 6, the occupied surface-state band corresponds to the lone-pair states on the chemisorbed As atoms. The calculaton also predicted an empty surface-state band which corresponds to localized states splitting off from the conduction band continuum of Si. The effects of going beyond LDA for the surface state energies can be clearly seen. As compared to the LDA results, the occupied surface-state band has a slightly lower energy and broader dispersion. Both features turn out to be necessary for better agreement with photoemission experiment. The effects of quasiparticle corrections to the energies of the empty surface states are much more dramatic. These states are substantially shifted upward in energy, opening up the energy gap between the occupied and empty surface states by nearly an extra 1 eV at some k-points. Figure 7 compares the calculated lone-pair surface-state energies with results from angle-resolved photoemission experiments50 for As/Si(l 11) and As/Ge(ll 1). For both surfaces, the agreement is excellent in both the place-
89
4
3
-2 2 - 1 h
Y 5a , o -1 -2 -3 M
-
K
Fig. 6. For the As capped Si(111) surface, the calculated quasiparticle surface bands are plotted against the bulk projected bands in the surface Brillouin zone. The LDA surface band energies are also shown (dashed li nes). ment and the dispersion of the surface bands and is well within the estimated uncertainties of +_ 0.1 eV with experiment and theory. Since there is no adjustable parameters in the theory, this lends strong support that the calculated electronic and geometric structures are correct. The empty surface states should be accessible to experimental observation using techniques such as inverse photoemission, surface optical transitions or scanning tunneling spectroscopy. Recent scanning tunneling44 and inverse photoemission experiments51 have indeed given quantitative confirmation to the theoretical predicitons in Fig. 7 for the empty states.
90
0
n
3 -1 a,
W
h M
-3
'
-
M
I
I
-
K
0
-1 A
P a, c
W
-2
-3
M
K
Fig. 7. The calculated occupied surface band is compared to photoemission results (Ref. 50) for As capped G e ( l l 1 ) surface (upper panel) and As capped Si(ll1) surface (lower panel).
91
2.5 2.0
1.5
1.o
s Q)
a
a W
I
0.5 0.0 -0.5 -1 .o
-1.5 -
r
-
J
Fig. 8. Quasiparticle surface-state bands for Si(ll1) 2x1 compared to photoemission (Ref. 53) and inverse photoemission (Ref. 54) experiments. An example of a surface with a more complex structural reconstruction is the Si(ll1) 2x1 surface. This surface has a n-bonded chain reconstruction
92
which extends to 5 layers below the topmost surface layer. Figure 8 compares the calculated quasiparticle surface-state band structure46 with results from photoemission52153and inverse photoemission54 experiments. The plot is for states with k-vector parallel to the K-bonded chain of Si surface atoms. The agreement between theory and experiment is again very good for both the occupied and empty surface states. The calculated surface state band gap of 0.62eV is in agreement with the direcvinverse photoemission gap of 0.75 eV and is substantially larger than the LDA gap of 0.27 eV. However, the optically measured surface-state gap for this surface is found to be only about 0.45 eV at low temperatures.55 This discrepancy between the photoemission results with the optical data may in fact be an indication of the breakdown of the free quasiparticle picture ininterpreting the optical transitions for this case, and other effects such as electron-hole interactions (enhanced by the reduced dimensionality at the surface) need to be included in considering the optical data. Another interesting example of surface calculation is that of the photoemission properties of the clean GaAs(ll0)surface which has a (1x1) relaxed geometry of the buckling type. The geometric structure of this surface is now quite well-determined both theoretically and experimentally. Its excited-state properties are however far from well-determined. In particular, various experiments and theories are giving conflicting results for the position of the empty surface states. Figure 9 depicts the calculated quasiparticle surface-state bands45 for the relaxed GaAs(l10)surface together with four sets of experimental data.56-59 For the occupied surface states, the theory agrees very well with the data from angle-resolved photoemission experiment.56 The controversy is with the empty surface states. The calculation is in good agreement with one set of inverse photoemission data57 (IPE-1) and with results from a laser excited/probe (2-step) photoemission experiment.59 But it is in disagreement with the interpreation of data from a second inverse photoemission measurement (IPE-2).58 First-principles study of the kind we have here is thus useful in helping to unravel the physics of a situation with conflicting experimental results. For the present case of the GaAs(ll0) surface, it seems clear that taking theory and all the experimental results together, a low-lying band of surface states with a band minimum in the bulk gap is favored. The above examples show that quite accurate surface-state energies
93
3.2
2.4
1.6
2
1
z
08
C
w
0
VBM
-0.8
-1.6
-
r
R
M
-
X'
-
r
Fig. 9. Comparison of the GaAs(l10) calculated quasiparticle surface band structure with various experimental data (see text). may be obtained using the self-energy approach. Comparing to the LDA results, the quasiparticle calculations yield the correct surface excitation energies by substantially opening up the gap between empty and occupied surface states. This is quite similar in the behavior of self-energy correction to the bulk-state energies. However, analysis43 of the surface calculations showed that the quasiparticle corrections to the surface states can be quite different from those of the bulk. The differences arise both from change in screening at the surface (hence a change in the self-energy operator) and from change in character of the surface-state wavefunction from those of the bulk states. As a consequence, an accurate determination of the excitation spectra of a surface will generally require a full quasiparticle calculation and
94
- Present
- - - LDA
0
5
15
10
20
NUMBER OF ATOMS P E R CLUSTER
Pre s ent
- - - LDA
2’ 0
5
LO
15
20
NUMBER O F ATOMS P E R CLUSTER
Fig. 10. Absolute values of the highest-occupied quasiparticle energies of alkali-metal clusters and in the LDA with the jellium-sphere-background model. (a) Nan and (b) Kn (n = 2, 8, 18, and 20). Experimental ionization potentials are given by solid circles (Ref. 60). is not expected to be obtainable from a ground-state LDA study and knowledge of the bulk spectra only.
95
The self-energy approach has also been applied to clusters. The calculation49 was carried out using a positive-jellium-backgroundmodel for the alkali metal clusters. This model has been quite successful in explaining a number of ground-state properties of these clusters including the occurrence of the famous "magic" numbers in their mass abundance.60 In calculating the quasiparticle energies, a real space formalism for dielectric screening including local field effects was developed. Figure 10 depicts the absolute values of the highest-occupiedquasiparticle energies for Nan and Kn clusters with n = 2, 8 , 18, and 20. These energies may be compared with available experimental ionization potentials.60 As seen from the figure, the agreement between theory and experiment is satisfactory with both the trend and magnitude of the ionization energies well reproduced. The systematic lowering of the experimental ionization energy as compared with theory may reflect an inadequacy of the jellium-positive-background model for these clusters. Another possible explanation is that the experimental ionization potentials for metal clusters depend on the temperature. Hotter clusters are expected to give smaller ionization potential. The calculations were carried out at T = 0. SUMMARY AND CONCLUSION The interpretation of the photoemission spectra of solids requires the concept of quasiparticles. In this Chapter, a self-energy approach for calculating the quasiparticle energies from first principles is discussed. The approach, which involves a first-order expansion of the electron self-energy operator in the screened Coulomb interaction, is shown to be well-founded as well as applicable in practical computations for real materials. Selected examples of application of the method to bulk crystals, surfaces, and clusters are presented. Results from the calculations have successfully explained the major features in the photoemission and optical spectra of these systems. And, in many cases, the theory has been predictive. The overall agreement between calculated energies and experimental data is generally at the level of a tenth of an eV for semiconductors and simple metals. This ability of theory in computing accurate excitation energies from first principles is a very recent development, and it is a major improvement over using, as quasiparticle energies, eigenvalues from methods based on local density functional formalism or the Hanree-Fock approach. Although application of the
7.
96
present quasiparticle method to transition metals and other more highly correlated electron systems remains to be made, its successes so far have been quite impressive and encouraging. The use of this approach together with total energy methods for structural determination should provide a theoretical framework which enables us to calculate the electron excitation spectra of many materials from first principles. ACKNOWLEDGEMENT This work was supported by NSF Grant No. DMR88-18404 and by the Director, Office of Energy Research, Office of Basic Energy Sciences, Materials Sciences Division of the U.S.Department of Energy under Contract No. DE-AC03-76SF00098. The support of a Guggenheim Foundation Fellowship is also gratefully acknowledged. REFERENCES 1. 2.
3. 4.
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T. K. Ng and K. S. Singwi, Phys. Rev. B 34,7738 (1986); 34,7743
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13456 (1988). R. Haight and J. A. Silberman, Phys. Rev. Lett. 62,815 (1989). W. D. Knight, K. Clemenger, W. A. de Heer, W. A. Saunders, M. Y. Chou, and M. L. Cohen, Phys. Rev. Lett. 32,2141(1984).
99
Chapter 4 SURFACE STATES ON METALS S.D. KEVAN AND W. EBERHARDT
1. INTRODUCTION
Over the past decade angle resolved photoemission spectroscopy (ARP) has matured from a new and exotic technique into a very powerful tool to determine the electronic structure of solids, surfaces, and interfaces. Measuring not only the kinetic energy hut also the direction of the photoexcited electrons and thus the components of the electron momentum vector, allows a determination of all relevant quantum numbers of the electronic states of a solid including the ones located at the surface. ARP is indeed the only existing spectroscopic technique that allows a direct and unambiguous determination of a two o r three dimensional band structure E(k) of a solid or a surface. These band structures have been calculated for many decades, and the basic concepts can be found in any elementary solid state physics textbook. It is therefore very fascinating now to have an experimental technique at hand to verify these calculations. Even more important than this connection with t h e theory of electronic structure in crystalline solids is the technological impact generated by these measurements. The electrctn interactions between the individual atoms forming a solid or a surface, as reflected by the electronic structure, determine all the properties of the material. While the mechanical stability, acoustic properties, electrical and thermal conductivity, or magnetism are generally related to bulk electron interactions, other properties like corrosion or embrittlement as well as the catalytic activity of a material are related to the electronic structure of internal a n d external surfaces. In semiconductor technology, metal semiconductor or semiconductor semiconductor interfaces largely determine the electrical characteristics of a device. Even though the systems in technical applications are very complex and often do not have the perfect two or three dimensional periodicity required for a strict application of ARP, very valuable information can be obtained by studying ideal "model" systems. Two dimensional systems like the interior and exterior surfaces of a solid have their own localized or quasilocalized electronic eigenstates. These states are the two dimensional analogues of the electronic states associated with point defects like shallow and deep band gap levels in semiconductors, or spin polarized resonances associated with transition metal impurities in a free electron host. The defect levels associated with the termination of the perfect crystal structure at the surface are called surface states or resonances. These states have properties which are quite different from the bulk electronic structure of the host. Moreover they are, because of their two dimensional nature, distinct from most other defect levels and therefore easily recognizable.
100
Like other types of defect levels, surface states and resonances have a profound influence on the physical and chemical properties of a surface. Historically this has been more obvious for semiconductor surfaces (see chapter 5). For example the dangling bond states created by forming a surface are often partially satisfied by driving a reconstruction or relaxation of the surface layers. The existence of surface states on semiconductor surfaces has long been postulated to explain surface band bending effects and the Schottky Barrier formation. O n metal surfaces the relationship between the electronic structure and other surface properties is neither so obvious nor intuitive. This is largely due to the more complicated nature of metallic relative to covalent bonding. Thus establishing a linkage between the electronic structure, measured by ARP, and other surface properties such as the geometrical structure, surface dipole layer formation, dynamical properties, and chemical reactivity is one of the most important goals in surface physics. This linkage will be the first step toward an intuitive understanding of these complex phenomena. This goal has been vastly aided by the development of efficient and accurate codes for the calculation of the surface electronic structure from first principle. By coupling ARP data with these calculations in the past decade, the field has progressed to a point where a fairly detailed understanding of simple surfaces has been attained. In this chapter we focus on the surface states and resonances which exist on nominally clean and well ordered metal surfaces, the interactions these support, and the phenomena i n which they participate. W e will exclude metal/semiconductor and metal/metal interfaces, since of this type of research is discussed in later chapters of this volume. W e will start by presenting two simple empirical models, which provide some intuition when and where surface states might occur, what their properties might be, and what they tell us about the surface. We will the describe how a surface state can be identified experimentally and which of its properties can be measured using ARP. We will then review some of the experimental and theoretical results for surface states on various metal surfaces. Finally we will try to assess the overall significance of the work accomplished to date in terms of its relevance to surface properties in general. There are several previous reviews of A R P which provide similar yet less complete information about surface states on metals. These include chapters in books focussing primarily on angle integrated photoemission by Feuerbacher, Fitton , and Willis,' N.V. Smith? and P r ~ t t o n and , ~ articles written by Feuerbacher and W i l l i ~ Plummer ,~ and Eberhardt: and HimpseL6 In addition there exist numerous reviews on surface electronic structure theory, which make extensive reference to surface states on metals and at least recently compare theory with experimental r e s u ts.7-14 ~ Theoretical Concepts for Surface States It is a useful endeavor to try to develop an intuitive understanding of why a surface state exists and what its properties might be. This will lead naturally to a better understanding of the impact that surface states might have on other surface properties. The first step in quantifying the surface electronic structure is a classification of the possible types 1.1
101
o f electronic states that may occur at the surface of a perfect crystal. Obviously tlic' hull;
elcctronic states will extend into the surface region, where they are reflected !>I ilic v:iL'iiiiiii Iurt-ier. True surface states on the other hand, exist only ;it the surface ;ind li:t\c :1ii espoiic'iiti~rllydecaying wave function both i n the direction into the solid i t i i c l ;iI.\ti iiiio i l i c v m i u i i i . I n energy/momenturn space these states are restricted t o regions wticrc IIO Ivilk ii:ites of the same symmetry and qtianttini number are allowed to exist. The \wvc 1'iiiii.iiiiii of the surface state would otherwise mix with the bulk wave function and the st;itc woiild i i o t tic confined to t h e surface region of the crystal. This is the case f o r a surf'Ice rc.sl)11: II)cc. \vhicli may also be viewed as a modification of the wave function of a bulk c l e c i r o i i i c \I:IIC i i w r i l i c surface.
>
w
w>
3 0
A
Auc
BULK STATE b
SURFACE RESONANCE
Fig. I Electronic wave functions in the surt'ace region. Fig. I shows schematically the differen1 types of electron wave functions o l w t - w t l iii lie stirface region. Bulk states (c) exist with periodically varying amplittide tliroughoui [tic
crystal. I f these bulk states are high enough in energy, i.e. above t h e vactitiiii I crystal, then they match to free electron states in the vacuum antl the electrons i i i ~ I i c z c states c ~ leave i the solid (e). Surface states ( a ) are localized strictly to the surfacc i-c'$oii of ilir crystal, l ~ obviously t are periodic i n the two dimensions parallel t o the stii-f;t~~c. S i i i ~ l : ircsonances (b) are equivalent to bulk wave functions with ;in enlarged ariipliiutlc iii tlii, surface region of the crystal. Vacuum electronic states (d), which cannot be iiiiitclic~l ill
~ ~
cncrgy antl momentum to crystalline wave functions in the interior are present i n [ l i e . w i ~ l ~ i ~ i-cgions as evanescent states. These evanescent states contribute a large amoiint ( ( 1 I I l c photoemission process and they are for example responsible for some of the "liackgrriiiiitl" 5igii;iI observed which cannot be explained as direct interband transitions.
102
The goals of several early phenomenological models which will be described Iwieily below1-'-18 were to give an intuitive understanding of why a surface state exists and u h i t its properties might be. These models were based on extensions of simple, empirical iiio(1eIs ol' l i t i l k hand structure: the nearly free electron model and the tight binding model. 111 t l i c w simple models band gaps are located either at the center of the Brillouin zone or iit tlic m i c ' Ix)und;iries, and consequently that is where the early models predict the surface st:iie\ to exist. Later the existence criteria were extended by Gurman and Pendry" t~ includc si:iies existing in gaps located at arbitrary points in the Brillouin zone. The earliest attempts to understand and predict the existence of surface states extended nearly free electron models of bulk band structure to semi infinite crystals.' ’.I2 These non-self-consistent models used empirical pseudopotential parameters, i i i i t l ilie electrostatic potential at the surface was assumed to jump abruptly from the inner pteiiiial to tlie v;~ciiiini level at an arbitrary distance from the plane of the surface ;itom. l'hc Schriicliriger equation was solved for energies both within the bulk band and ;ik;f)fcrr pro.jectetl band gaps. Within the bulk bands all three momentum componeiits :ire r w l . corresponcling to a freely propagating state. For states located in the gaps, however. the iiionieiitum normal to the surface ( lu) must necessarily be complex, assuring ;I finite penetration depth of the state. Thus the surface state decays evanescently into the bilk with :in exponential decay constant related to the imaginary part of k i . Successful matching I)!' this state to a wave function decaying into the vacuum barrier leads to ;I st:itioii;ii-!. noriiializahle eigenstate, located within a band gap. Stirface states Iocaied iii ;I hyliridiz~itional band gap have been labelled Shockley states. The surface state on Al[OO I ). which will be discussed later is well-described as a Shockley state, since i t exists i i i :I zoiie Ix)unclai-y hybridizational band gap which is characterized adequately I)! one pseutlopotential coefficient. The existence criteria for a Shockley state depends upon the choice of the termixitiiig potential at the surface. The step potential used in the original models'7 required m;itcliiiig l o ;I single exponentially decaying wave function outside the surface. There irewll\ ;I coiistr:iint o n the sign of the dominant pseudopotential coefficient VG. I f VG > 0, w i t h the origin of the coordinate system on the lattice planes, the matching condition is nor p)s
le and ;I state will not exist. Conversely, precisely one state will exist when VG < 0. Receiit tre:itiiients used a more realistic image potential outside the The existciicc criterion is relaxed somewhat and two or more surface localized states may exist, reg;irtlles of the sign of VG. Other properties of Shockley states such as their energy and ev;iiiesceiii decay length are also determined by a combination of the characteristics of the hiilk h i i d gap a n d of the assumed crystal Since the properties of b u l k livt~riilizaiiciii~il gilx are generally well understood, these states can provide a very useful prolw ( 1 1 the prol7erties of the potential describing the termination of the crystal. As a testing grountl iolfir-st-principles computations, they have been instrumental in demonstrating tlie riece.ssity I'oi;ich ieviiig self-consistency in surface calculations.
103
A second intuitive model which predicts surface states is based on the tight-binding or Huckel model for band structure.17 This is the natural counterpart to the pseudopoterltial based theories. The model assumes localized orbitals located on a semi-infinite lattice which interact weakly and only with their nearest neighbors. The surface perturlxition is introduced through an empirical parameter A which describes the difference in self-eiiergy o f the orbitals located on the surface plane relative to those of the bulk. Again there exists a hulk band of energies of total width W. Unlike the pseudopotential models, in this model a surface localized state will not split from the bulk band unless x = 4A/W > 1. I f this criterion is satisfied, a surface state splits from the bulk band by an amount
AE, = A(l-I/x)* These are useful and intuitive results. The magnitude of W is directly related to tllc hybridization integrals between neighboring sites or, in three dimensions, between I:itiice planes. It therefore is a measure of how much the layers normal to the surface interact. I f this integral is small, as in the case of core levels, neighboring layers do not interact
:it :ill.
and the surface level splits from the bulk level by an amount equal to A. If A a W, the
perturbation is smaller than the interaction between layers and a surface state will n o t split off. In the limit of small X , the pseudopotential model is probably more applicable. Surface states which are well described using this tight binding model are often called Tamm si:ites. 'The important factors distinguishing Tamm states are a lack of hybridization between Ixiiid\ and fairly localized orbitals, both of which lead to small band widths. This is :tiways appropriate for surface core levels. In addition valence surface states which split off very narrow d-bands on several low index noble metal surfaces are good approximations to Tamm states (see Section 2.1). The empirical parameters in this model clearly coiit;iiii usef~ilinformation about the surface. A, for instance, tells us about the magnitude o f the surface perturbation experienced by an electron. Other wave function parameters ;itso clepend on x in a systematic way.17323 Of course, these paradigmatic models of surface states on metal surfaces c;in iioi IC precisely realized in real systems. Indeed, many states have been observed which do n o t I i I either the Shockley or the Tamm paradigm exactly. The most obvious case, where tliis \\,ill occur is on transition metal surfaces. We can have significant s-d hybridization, for ex:iinple. leading to surface states which are intermediate between Tamm and Shockley states. I n addition, the relatively narrow d-bands undergo significant band hybridization among themselves. Gaps open throughout the bulk Brillouin zone, wherever bands of thc s:tnie symmetry approach, in some cases leading to projected gaps and surface states. Moreovei-. paps can be opened through other symmetry breaking forces such as the spin oihit interaction (Sec. 2.2). Surface states of all types can be observed in such gaps. State-of-the-art self consistent calculations yield not only the energy-momeiitiiiii parameters but also the charge distribution associated with surface state the wave functions. This gives a "visual" confirmation of the degree of surface localization. An example of the calculated charge density for a highly localized d-like surface state on Pd( 111) is shown i n
104
d - LIKE SURFACE STATE
Fig. 2 Top: Charge density contours for a highly-localized d-like surface stilte on Pcl( I I I ) . Bottom: Total charge density in the surface region (from Ref. 24). Fig. 2.24 This state and others, for example, on C U ( O O I ) ~and ~ > ~Ni(O01)29 ~ are welldescribed by the Tamm model. Most of the very successful surface electronic structure calculations approximate the solid by a small number of atomic layers in the appropriate geometry. For computational reasons, this number is so small that these calculations (lo n o t give continuous bands but rather a whole series of discrete states. It can become difficult t o distinguish computationally such surface states if the bulk penetration is too large. l’he computational criterion for a surface state then depends on where the state is locakcl i n energy-momentum space and how much of the charge of the state is located in the oulemiost layer. The first experimental evidence for the existence of a surface state on a metal surfrice was obtained in field emission studies of W(OOl)3O Later the same state was also observed tising ARP?1>32 At about the same time as these early experimental obser\iarions. calculaotions predicting the existence of surface states in hybridizational band gaps in niet:\Is were reported by Pendry and F o r ~ t m a n nand ~ ~ Forstmann and H e i ~ ~ Application e . ~ ~ of these calculations to W(OO1) was not possible however, and the precise origin of this surface state o n W(OO1) was undetermined until recent calculations were able to include relaLivis!ic effects (Sec. 2.2). The prediction and experimental observation of surface states on nietal surfaces has now been accomplished for almost all the low index surfaces of the metallic elements in the periodic system. This was achieved almost exclusively by ARP. We present a few more basic concepts of surface states and their existence criteria before we discuss why ARP is such a powerful tool in identifying surface states and how one
105 SURFACE NORMAL
t I
Fig. 3 Bulk face-centered cubic Brillouin zone, and the projection onto the (001) stir-face Brillouin zone. actually goes about identifying surface states using ARP.
Surface states are truly two-
dimensional states, which decay evanescently into both the bulk and the vacuum. Only two components of crystal momentum, those parallel to the surface (kII ), are well defined f o r these states. Thus by definition surface states exist within a region of three-dimensional energy-momentum space, where no bulk states of the same symmetry are allowed to exist. Most conveniently this is within an absolute energy gap in the bulk band structure. However, as we will see later, surface states are not limited in their existence to ahsolure gaps. To be more precise, the condition for the existence of a surface state is defined such that for a certain parallel momentum k 11, there are no bulk states of the same syrnmeiry ror any momentum normal to the surface (lu). Otherwise the surface state would couple to (his hulk component. We thus say surface states have to exist in symmetry projected bulk I x i r i c l
gaps. Their wave functions are effectively excluded from penetrating into the bulk of tlie material by energy and momentum conservation. We use Al(OO1) as an illustrative example of a surface which has a well defined surface state. Aluminum has the fcc crystal structure. The Brillouin zone for a fcc c y t ; i l a n d the projection onto the (001) surface Brillouin zone (SBZ) are shown in Fig. 3. I n Fig. 7 w e show a calculated band structure of aluminum along the high symmetry directions irsing o n l y the two largest pseudopotential coefficients. This matches very closely the Ixintls calculated using more sophisticated techniques36 A careful look at Fig. 3 reveals that tlie hulk states along r-X of the bulk Brillouin zone are projected onto the center of the SBZ, which is generally labelled r. This point r corresponds to a parallel momentum of li 1 =
106
out in the SBZ along both symmetry azimuths. Thus even though there is no absolute band gap in the occupied bands of aluminum, a well defined surface state may nonetheless exist on the ( 0 0 1 ) ~ ~ 7 and ~ ~ (111)38 7 ~ ~ -surfaces ~ ~ of aluminum. Experimental verification of these states will be discussed below. It is possible for an electronic state with significant surface character to exist outside of one of these projected band gaps, if this state has a well defined symmetry distinguishing it from the underlying continuum of bulk states. Thus this state is still ;I true surface state, since coupling to the bulk states is symmetry forbidden. If on the other hand the surface and bulk states are of the same symmetry, mixing will occur and the state becomes a surface resonance. A surface resonance is a resonance in the classical sense and is analogous, for example, to a Fano resonance in atomic physics. Its wave function penetrates the bulk to infinity, but it has a n enhanced surface amplitude like a surface state as indicated schematically in Fig. lb. The degree of surface localization for a surface resonance depends on the strength of the coupling between the quasi-discrete state and the b u l k continuum. A n electron in a resonant state will thus have a finite probability of tunneling into the bulk continuum and therefore it will be lifetime broadened energetically. Naturally, the upper limit on the inverse lifetime of a surface resonance is the width of the bulk band in which it is embedded. We thus have a very simple picture of three types of levels found near a surface. A true surface state has zero band width in the direction normal to the surface. It therefore does not exhibit any dispersion with change in normal momentum. A surface resonance has a nonzero width which is less than or equal to the width of the bulk band in which it is embedded, and the bulk band has a width given by the solution of the Schrodinger equation deep inside the crystal. In principle any or all of these states might be observed i n ;I photoemission spectrum. The procedures for isolating the contributions from these three different classes of states and the characterization of the surface features is described nest. We will see in section 2.3 that these categories can and will break down when the three types of states are energetically very close to one another at the same parallel momentum.
Exnerimental Characterization of Surface Electronic Levels The application of ARP to study surface localized levels is straight-forward. Energy and k 11 are conserved in the photoemission process and these, together with the symmetry and electron spin on a magnetic surface or when relativistic effects are important, are the only relevant "quantum numbers" characterizing a surface state. The difficulties with the I .2
non-conservation of the normal momentum component, which have to be overcome in determining bulk band structures using ARP, pose no problems in determining the dispersion of surface states. We assume in the following that the one-electron approximation is adequate for the description of the valence state photoemission process. The breakdown of this approximation, which is signalled experimentally by the presence of shake-up satellites in the spectra, is discussed in more detail e l ~ e w h e r e ~and l , ~in~ Chapter2 of this volume. In most cases we are not interested in the absolute intensity of a feature
107
1Z.O.OJ
lZO.Il
lld.O.I.5l
l~,LIl
lO.O.0l
k ($1
Fig. 4 Calculated band structure of aluminum using four plane waves a n d t w o pseudopotential coefficients. Note the nearly-free-electron gaps which open at the X and 1points (from Ref. 35). Aluminum is a nearly free electron metal with a fairly large pseudopotential coefficient V200. This opens a gap at the X point of the bulk band structure such that there are no bulk states between roughly 2.2 eV and 3.0 eV below the Fermi level. From the projection shown in Fig. 3 and from the calculated band structure shown in Fig. 4 we t l l u \ know that at r of the SBZ of tu(0Ol) there exists a band gap for these energies. This is exactly the condition under which we expect a surface state to exist. (0,O).
-%
- 0
G
8 -1 Y
2 - -2
t
r -3
Fig. 5 Aluminum band structure projected onto the mirror planes of the (001) surfacc. Brillouin zone. Data points are the experimentally determined surface state dispersion (Ref. 20). There are several ways to present these projections of bulk states onto t h e SBZ. Most common is to plot the projected bulk bands at any given energy as a function of parallel momentum along the symmetry directions of the SBZ. Such a projection is shown in Fig. 5 for Al(001). In this case the SBZ is a square and the symmetry azimuths are labcllecl A and C. In this figure, the shaded regions indicate projected gaps in the bulk bands o f eveii symmetry under reflection in the mirror planes normal to the surface. The projected gap at t h e zone center described above is observed to pinch off slowly at parallel momenta further
108
observed in the photoemission spectrum, since this is determined by matrix element effects which do not readily give additional information about the surface electronic structure. However, the relative intensity of a photoemission feature measured as a function of photon energy or of the orientation of the photon polarization vector relative to the crystal lattice and the detector does yield important information about the symmetry of the wave functions as we will show below. In a typical ARP experiment the photoelectron emission angles, the incident photon energy, the polarization, and the crystal orientation are held fixed while an energy distribution curve (EDC) of the emitted electrons is recorded. The energy of the photohole can be readily determined relative to the Fermi energy EF. The magnitude of the initial and final state parallel momentum (in A-’) can be calculated for any spectral feature at ;I measured kinetic energy Ek (in eV) via the standard algorithm: k 11 = 0.512 J E k sin
0
(2)
The polar emission angle relative to the surface normal is d. The vector components of k 1 can thus be calculated if the azimuthal emission angle is known. The ARP final state consists of a photohole and a photoelectron. Momentum conservation dictates that the parallel momentum components of these two be identical modulo a surface reciprocal lattice vector. The momentum of the photon is small at VUV energies and can be neglected. I n this way the quasiparticle two-dimensional energy dispersion relation, E(k 11 ), can be determined. This is what we generally use in comparison with a ground state band structure calculation. Many body and self-energy effects introduce some complications in this comparison, since the binding energy determined in photoemission is not the true ground state energy of the system. These effects have been discussed in more detail in chapters 2 and 3. For convenience we exclude these many body effects from the discussion in this chapter even though we are well aware of their presence. The discussion above indicated the importance of the determination of the symmetry of a given state. This can be achieved with a polarized excitation source like synchrotron radiation and has been applied extensively. To show this simple principle, we consider the symmetry properties of the Fermi Golden Rule matrix element, which governs the photoemission process I = 2s/h
I< i I A
.PI f
>I2
6(Ef-E;-
hw)
(3)
where < i I and 1 f > are the initial and final state wave functions, A is the vector potential of the incident light, P is the momentum operator, and the 6-function ensures energy conservation. All these functions are necessarily continuous in space. In order to have nonzero photocurrent at the detector, both the final state and the matrix element as a whole must be totally symmetric with respect to any symmetry operation of the crystal. This means that the product of the initial state wave function and the dipole operator A P must be symmetric. Changing the direction of the polarization of the incoming photon with respect to the crystal lattice and the detector thus allows us to determine the initial state symmetry.
-
109
This js most often done for emission in a mirror symmetry plane, where at least two symmetry representations exist, odd and even upon reflection. If the polarization vector i s located within the mirror plane where the detector is located, then the dipole operator is even and only even initial state wave functions contribute to the photoemission current. If, on the other hand, the polarization vector is normal to the detection plane, then the dipole operator is odd and only odd initial state wave functions contribute. For emission along the normal of the low index planes of the fcc and bcc lattice these symmetry selection rules have been pointed out by HermansonP3 The general symmetry selection rules for optical excitation in the fcc and bcc lattices have been tabulated by Eberhardt and H i m p ~ e and l~~ by B e n b ~ w for~ the ~ hcp lattice. A difficulty often encountered in these studies is distinguishing the spectral features which arise from surface states as opposed to ones caused by bulk interband transitions. While there is no absolute procedure for accomplishing this, several tests have been developed to aid in this process. Historically the first test applied was the so called "crud test". Exposing an atomically clean surface to impurities will preferentially change the surface related features like surface states and resonances in the spectrum, since their existence is dependent on surface perfection and the particular shape of the surface potential. Even though this concept seems to be quite intuitive and has been applied frequently, this test by itself is the least perfect criterion for the proof of existence of a surface state. For example, certain well known surface states do not change when the surface is covered with a particular adsorbate.46 Moreover, the notion that surface states "disappear" when the surface is exposed to an adsorbate does not make sense physically. The charge at the surface does not get completely removed by the adsorbate, but rather on the adsorbate-covered surface it is located in different regions of energy/momentum space than on the clean surface. This means in practice that surface states of the clean surface will be observed to shift and maybe to broaden in energy upon adsorption. Sometimes they \+ill completely disappear out of a particular photoemission spectrum, but then also other interface states will show up at a different place of the energy/momentum space at [lie surface. An example of a successful crud test is shown in Fig. 6 for the state located a t the center of the SBZ of A I ( O O ~ ) . The ~ ~ spectra were accumulated at normal emission (8 = O ) , so that kll = 0 from eq. (2). The upper spectra were collected from the clean surface, while the lowest three were collected from a surface which had been exposed to increasing amounts of oxygen. The feature at a binding energy of 2.75 e V below the Fermi level (EF) i s significantly reduced in intensity following the exposure, indicating its possible origin its 21 surface feature. Comparing the energy at r of this feature with the projected hand structure, Fig. 5. we get further evidence that this feature is caused by a surface state, since its existence falls within a projected band gap. The fact that we compare an experimental result with a projection of calculated bands can lead to some difficulties if many body effects distort the experimental measured energies (see Chapter 2). It is preferable although not always possible to determine the bulk states and projected gaps experimentally.
110 I
I
I
I
I
Al(lO0)
CLEAN
80 L 160 L 200 L
-4
-2
INITIAL ENERGY I
d
Fig. 6 Al(OO1) normal emission spectra indicating the sensitivity of the surface state to contamination by oxygen (Ref. 37). Fig. 7 illustrates the application of polarization selection rules to determine the symmetry of this states Here the spectra are taken with synchrotron radiation and the angle of incidence of the light is varied. A. this angle increases, measured relative to the surface normal, the polarization component in direction of the surface normal increases, whereas the component parallel to the surface decreases. Clearly the surface state emission is stronger, when the light incidence is more grazing to the surface. This indicates that the state is excited by the polarization component of the light normal to the surface. Thus the dipole operator is even with respect to all symmetry operations and the initial state must be even as well. A more definite criterion for the proof of existence of a surface state than the "crud test" is the lack of dispersion as a function of the component of momentum normal to the surface. As explained in chapter 3, the bulk band structure or more exactly the quasiparticle band dispersions for bulk states can be readily obtained using ARP. Since a true surface state has zero band width in a direction normal to the surface we expect to observe experimentally that its energy will not change with change in final normal momentum. Sometimes this test can lead to ambiguous results, since dispersionless features can show u p in the photoemission spectrum which originate from flat or dispersionless bulk bands. Nevertheless, this is a necessary condition for the existence proof of surface states. Surface resonances, due to their intermediate character, might appear to disperse slightly. An
-
111
NORMAL EMISSION AP (100)
-5
-4
-3 -2
-1
E,
INITIAL ENERGY (eV1 Fig. 7 Dependence of Al(O01) surface state intensity on the angle of photon incidence. additional difficulty is caused by bulk "density-of-states" features arising through indirect (momentum non-conserving) transitions from regions of high initial state density. These regions are naturally associated with bulk band edges such that often these features appear to be very close to a band gap. An example of the absence of dispersion of a true surface stare with riornial momentum is given for the Al(OO1) surface state in Fig. 8. This figure shows EDC's collected at normal emission geometry from Al(OO1) as a function of photon energy.35 Since 6 = 0, eq. 2 shows that kll = 0 even though the total final state momentum is roughly proportional to JEk. Thus k~varies significantly for the spectra shown in Fig. 8. However, the binding energy relative to the Fermi level of the surface state feature distinguished earlier is observed not to change. The large intensity variations seen are due to variation in the coupling to the final state wave function, and will be discussed more fully in Sec. 2. I . Successful application of several of these tests provides compelling evidence that a state is indeed a surface state. Distinguishing a surface resonance is still more coniplicated, since it is degenerate with a bulk continuum. Since "normal" bulk states may also be modified at the surface by adsorbates the boundaries become rather vague and the process of distinguishing a surface resonance from a "modified" bulk states is a semantic exercise. After the surface character of a given photoemission feature has been ascertained, it is a simple exercise to determine the dispersion relation by varying the emission angle to vary the final and initial state parallel momentum according to eq. 2. Strictly these tests would have to be repeated for all parallel momenta, but that is usually not done in practice. An example of this is presented in Fig. 9, again for our model case of Al(O01). These
112
.zo
-15 -10 - 5
EF
INIT1AL -STATE ENERGY ( eV I
Fig. 8 Demonstration of the lack of dispersion of the Al(OO1) surface state as a function of l u (from Ref. 35). EDC's were collected as a function of emission angle in the C 1) [loo] azimuth.38 The surface state disperses symmetrically about the normal emission direction. The measured dispersion relation is shown in Fig. 5 along with the projected bulk bands as discussed earlier26,35,37 This surface band exhibits parabolic dispersion centered at r with an effective mass of roughly 1.18 times the free electron mass. This dispersion relation is in reasonable accord with calculations based on the local density approximation using the ~ , date ~ ~ no calculations of the excitation spectrum densi ty functional a p p r ~ a c h . ~To including many body corrections like described in chapter 2 and 3 have been undertaken for this system. Having discussed the basics on both the theoretical and also the experimental side we will now show some examples of how these type of studies have increased our understanding of metal surfaces. Section two of this chapter will deal in more detail with general phenomena of surface states and resonances on simple metals, whereas section three provides a more detailed investigation using ARP of several interesting surface phenomena. The final section projects some of the future possibilities in this field. 2.
SIMPLE SURFACE STATE PHENOMENA After ascertaining the existence of a surface band and perhaps measuring. its dispersion relation, it is often desirable to characterize its properties further in order to
113
Fig. 9 Spectra of Al(OO1) as a function of emission angle indicating the dispersion of the surface state in the c symmetry azimuth (from Ref. 38).
establish correlations with other surface properties. In this section, we give a brief account of additional information that can often be extracted from ARP measurements. Surface Localization of the Wave Function The data presented in Fig. 8 provides useful empirical and sometimes semiquantitative information about the spatial extent of the surface state wave function normal to the surface. The charge density of this state actually is spread out over several lattice planes normal to the surface. If the final state wavelength is matched to the lattice spacing normal to the surface, then optimum coupling is achieved and the contributions from a11 lattice planes add constructively to the total photocurrent. Destructive interference at intermediate final state wavelengths can nearly quench emission from the surface st;ite. Thus surface states extending in charge density over several lattice planes often exhibit characteristic oscillations in cross section, whereas the surface-localized d-like surface states like that shown in Fig. 2 more or less follow the atomic cross section behavior of their tl-like origin and do not exhibit these oscillations. Thus by measuring the variation of the cross section of surface states with photon energy, we can estimate whether the state is located just at the outermost lattice plane or whether it extends into the solid. The first effort47 which documented and utilized this effect was for a well-known surface state existing near EF on C ~ ( I I ~ ) Measurements . ~ ~ ~ ~ of~ the - ~ intensity ~ of this 2.1
114
W IV
1
32
Surface State on Cu (111)
hu = 30 r
70
50 I
1
1
I
110 eV
90 !
I
l
l
'0
12
k l (2da)
00
binding energy. eV
Fig. 10 a) Photon energy dependent normal emission Cu(l1l) spectra. Note the dramatic intensity oscillation of the two surface states S1 and S3. b) Intensity of S1 as a function of !iL.
surface state (Figs. 10a and b) as a function of photon energy at normal emission were found to exhibit a pronounced maximum near hu = 70 eV. This corresponds closely to a final k i near the L-point in the second bulk Brillouin zone (see Chap. 2). The large cross-section for the surface state at this momentum gives experimental verification that the real part of the surface state momentum normal to the surface is given by the zone-boundary L-point momentum. This is in accord with the simple models described in section 1.1, given the existence of a bulk projected gap at L. Moreover, the width of the intensity distribution in Fig. 10b reflects qualitatively the imaginary part of the normal momentum and thus [lie decay length of the surface state wave function into the bulk. A simple model based on the tight-binding algorithm was developed to explain these data. This yielded a measure of the
115
decay length in reasonable accord with calculations. More recently, models based on t h e pseudopotential mode138>50t51 and (equivalently) a geometric structure factor52 have been applied to yield quantitatively similar results for the sp surface state C u ( l l 1 ) and also for similar states on Ag(ll1) and Au(ll1). A useful application of these ideas was reported recently for the zone center state o n The energy of the state was varied within the gap by depositing small amounts of alkali atoms on the surface. As the state approached the band edge, the penetration length was observed to increase, an effect which was quantitatively documented. While the measured decay lengths are in fairly good accord with surface calculations, they differ systematically from what would be predicted from an analytic continuation of the calculated bulk bands into to the complex plane. In some cases, surface state intensity oscillations can be large enough that a state is not visible at some photon energies. A good example exists on Al(111). The pseudopotential coefficient V l l l is about one quarter the magnitude of V200 for this metal, leading to a much smaller bulk band gap at L than at X (see Fig. 4). These coefficients are the same sign, however, and the pseudopotential model thus predicts a surface state t o exist o n both surfaces. A surface state located on Al(111) would be predicted to penetrate much further into the bulk than one on Al(OOl), implying a more sharply peaked intensity distribution. This intuitive result has recently been observed38 The decay length was determined to b e longer than the sampling depth of the photoemission probe and thus could not be experimentally determined. The long penetration length had delayed both experimental and computational characterization of this Al( 111) state. A similar search of copper low-index surfaces at a variety of photon energies indicated the existence of several states which had not previously been d e t e ~ t e d . ~ ' The opposite extreme from these slowly decaying sp-like states is offered by the previously-mentioned d-like Tamm states observed on the noble metals and j 9 The existence of these states arises from a symmetry-related decoupling of layers n o r m a l to the surface. For example, at the M point of the surface Brillouin zone on Cu(OO1). the tixy orbitals are completely nearest-neighbor antibonding within a layer and completely nnnbonding to similar orbitals in nearest neighbor layers. This results in an extremely flat bulk band along the bulk X-W-X line at the top of the copper d-bands. This projects onto M, and ii highly localized Tamm-like state naturally results (Fig. 2). A plot of the intensity of this state as a function of final momentum normal to the surface23 (Fig. 11) is essentially flat, indicative of the predicted extreme surface localization. It is interesting to search for similar localized states on other noble metal low index surfaces. The lower symmetry on Cu(ll1) renders the bulk layers normal to the surface less completely decoupled and thus the bulk band has some width. A Tamm-like state does exist,50*55 but with a splitting from the bulk band 50% smaller than that observed on Cu(OO1). This can b e semiquantitatively explained by Eq. 1 in Sec. 1.1. O n Cu(Oll), where the symmetry is still lower, no related state has been observed. Similar states have been ~ 911 ~l),~ ,Au(001) (lxl), and Au(001) ( 5 ~ 2 0 ) . ~ ~ observed on Ni(OOl),29 ~ g ( 0 0 1 ) , 2 ~ 9 ~Au(
116
Pi i il I
* * 1
1
I I
lk fR
R'.
o Ag (000
cu (001)
Fig. 11 Intensity of the Tamm-like surface states at M on Cu(OO1) and Ag(001) as a function of ILL (from Ref. 23). SDin-Orbit Interaction and Surface Electron States 2.2 One aspect of surface electronic structure which has been increasingly studied in recent years is the impact of the spin-orbit interaction. Dispersion relations will be significantly perturbed by the spin-orbit interaction only when bands approach to within the atomic spin-orbit parameter for the atomic levels included in the band. The symmetry of the electron states is lowered below that of the geometric point group of the surface, and interactions which would otherwise be symmetry-forbidden can occur. The band topologies can be significantly altered as is the case, for example, in semiconductor band structures near the fundamental band gap. New projected band gaps can be produced in which additional surface states and resonances are situated. The existence criteria for such states have not been determined, and are presumably not as intuitive as those for the nearly-free-electron and tight-binding types of surface states. Alternatively, interactions between surface bands or between surface and bulk bands of different nominal symmetry are allowed. The first suggestion that the spin-orbit interaction may lead to the existence of a surface state was for the very first surface state ever observed on a metal surface, that is, the so-called Swanson hump state near the Fermi level on W(O01).6°761 Despite the fact that this is one of the best-studied surfaces from both an experimental and computational point of view, the precise character of this state was uncertain until recently. The difficulty lies in the strongly hybridized relativistically-calculated bands for tungsten along r-X, the line which projects onto the center of the surface Brillouin zone. Early suggestions that the
117
-,I
-I
-6
INITIAL
4 ENERGY
BELOW EF I.VI
I-ig. 12 a ) Norm:il emission spectra of Bi( 1 1 1 ) at two temperatures indicating the existeiicc of :I surface state, labelled A. b) Experimental and calculated energy h a n d s ; i n d stirkicc tlcnaity of slates f o i- Bi( 1 I I ) (from Ref. 73). surface level was a true state located in a spin-orbit gap62 were followed by nearly ek'ery interpretation p o ~ s i b l e . h ~The - ~ ~advance in computational capabilities has been improved to the point where the spin-orbit interaction can be adequately included in a surf:ice slah calculation, hut only in a partially self-consistent way.70-72 These calculations have shown that ttic existence of the Swanson hump feature is not dependent on the spin-orhit iiiter;ictioii. I t i s essentially a tlZ2-like Tanim state ptrshetl o u t of a hulk continutim. \VhiIc [lit' spill-orhit iriter;iction appears to affect the Swanson hump only to 3 m i n o r extent. i t is important to realize that a significant amount of experimental and coniptitationiil development a n d effort has occurred as a result of its existence. A clearer example of a surface state which exists i n a gap opened by the spin-or-l>it interaction was reported for Bi( 11 In this case, the bulk hands are of sp character, and t l i i i s :ire simpler than on W(OO1). The A R P spectra which indicate the existence of thc hiirface state are reproduced in Fig. 1221. The peak at Ep, = 0.5 eV satisfies ;ill the criteria t o r being :I surface state. There is, however, no projected gap in the non-relativistic hiilk Ixintl structure. Rather, 21s shown in Fig. 12b, a gap opens when two bulk bands of differcn\ y i i n e t r y attempt t o cross near this binding energy. This crossing is disallowed by the spinorbit interaction, and a small gap is thereby produced which supports a surface state. Other spin-orbit induced surface levels have recently been observed. Wincott, e!. al.,
have reoorted verv high energv resolution mectra of Cu(OO1) showing a second tl-like
3
2
1
EF
Binding Energy (eV) Fig. 13 a) Photoemission spectra of Mo(Ol1) in the A azimuth as a function of k I The unusually rich spectra result from a spin-orbit induced avoided crossing between krf:rcc hands of differing nominal symmetry. The resulting surface band dispersions and thc projected bulk continutim are shown in b). (from Ref. 76) surface state at M which resides in a narrow spin-orbit gap.s8374 Recent experiments 011 W(O1 I ) , Mo(Oll), and Ta(Ol1) have detected spin-orbit induced surface states and also surface resonances.75-7' The gap shown in Fig. 12b occurs due to the effect of symmetry-breaking spin-orbit interaction on bulk electron states. The same avoided crossing must occur between two .scrt$rce bands whenever they are energetically close. The effect has recently been observed esperiinentally o n Mo(O1 1) and W(O1 l ) , where the bulk band projection esliiliiis overlapping odd and even symmetry gaps, both of which support surface state^.^'^^^ The surface bands are forced to hybridize under the influence of the spin-orbit interaction. The spectra for Mo(O1 1) in t h e vicinity of the spin-orbit induced hybridization ;ilony A are qui!r complex (see Fig. l h ) , and produce the surface band dispersions shown in Fig. 131,. Spinorbit induced avoided crossings roughly 0.3-0.4 eV in width are observed in both syminetry azimuths in the vicinity of small projected bulk gaps which are essentially the intersection of gaps of odd and even symmetry. Theoretical7' and experimental result^^^^^* indicate that this spin-orbit induced interaction between bands of different nominal symmetry plays ;I key role i n the clean-surface reconstrtiction observed on W(OO1) (Sec. 3. I).
119
Another system where the spin-orbit interaction appears to have a pronounced influence on a surface electronic level occurs on the Tamm-like state o n Ag(OOl)23357,5s ;I[ M just above the d-hands, similar to the state observed on Cu(001) described i n the I;~at section. The symmetry decoupling of dxy orbitals in neighboring planes is broken by the spin-orbit interaction, and the associated h u l k hands acquire some width near the X Imints of the bulk Brillouin zone. There is thus expected to be enhanced communication between the layers on Ag(001) relative to Cu(OO1) due primarily to the larger 4tl spin-orlit parameter. From the discussions of Sec. 1.1 and 2.1, one might expect t h a t this communication will manifest itself as a non-zero decay length for the surface state w;we function on Ag(001). The results shown in Fig. 11 indicate that the ideal of ;I surface witc intensity which tracks the relatively smooth atomic cross section is nearly re;ilized for Cu(O0l) but not for Ag(001). This confirms qualitatively the expected result. The situatioii on Ag(001) is more complicated, however, since the observed splitting between the h i i l k and surface bands is less than the calculated hulk band width by about SO meV, placing the w r h c e level in the projected continuum. The hulk band width is dominated by the atomic spin-orbit parameter and thus the calculation should be fairly accurate. The silver st:itc appears to be a resonance due t o the spin-orbit interaction, a conclusion which is difficult t o verify with ARP spectra2' showing two well-separated features (one surface and one 1~111;) ;it :I
II per pe ntli cii I;ir mom en t a. Recent experiment al work preze n ts
11i c ;I different interpret at i o n of t t i e e I e ct I-() are structure near M o n A g ( O O p Fairly similar spectra to those reported interpreted in terms of three peaks rather than just two. There are the same surface and
'
bulk features discussed ahove in addition to ii second surFace state existing in a spin-orbit
induced gap located below the bulk continuum. This interpretation also suggests ; i n anomalously small bulk band width. To date, calculations for this surfacex2 do n o t really solve this enigma, since these are only scalar relativistic. Moreover, they tend to overestimate the splitting o f the surface hand from the hulk by a factor of 2-3, and predict one 01more lower lying surface resonances which are not experimentally observed. Firrtheitheoretical input will be required to solve this discrepancy in the interpretation. 2.3
Surface State Linewidths and LineshaDes The observed peak widths in ARP spectra are normally attributed to lifetimc broadening o f the final hole and electron states.56,83-86 These lifetimes and their relation t o peak widths are of fundamental interest because they determine things such ;is enel-gy resolution of electron and optical spectroscopies, in addition to the momentum resoliltion 0 1 ARP. Simple phenomenological models based on a direct-transition model (see chapter 2 ) relate the final state lifetimes to the observed ARP linewidths. It happens that these broadening phenomena are particularly simple in the case of an intrinsically 2D state such ;IS a surface state.
For example, in the case of emission normal to the surface, the peak witltti i s
predicted t o be83
120
c
A
+65
BINDING ENERGY (eV)
Fig. 14 High resolution photoemission spectra of the zone-center Cu( 1 1 1) s u r f x e state ; I S ;I function of k 11. Note the anomalous increasing linewidth f o r decreasing hindin, enel-?! ( f r o m Ref. 49). I'
\vhei.e rll and re are the final state hole and electron inverse lifetimes, and vll ;tiid vc :trc thc corresponding hand velocities normal to the surface. For a two-cliniensional st;itc, vjl i \ necessarily zero and r = rh.83 The final state hole decays primarily by Iioiii-~i~li~ili\,~~ Auger-like processes, the phase space for which goes to zero for state near EF. We t l i t i h ciii I)reclict that a surface band crossing EF should have zero fiinclamental w i d ~ h . .Jlii\ pi-ediction is qualit;Ltively observed for the Tamrn states observed on Cu(00I) : i n d CII( I I I ) . I n this case, the states lie energetically above the d-band, and only a ~iii;iIl tlc.ii.;iLy 1 1 1 t'lectrons at higher energy in the sp-band are available to fill the pliotohole. Thiis ;I VCI-! narrow photoemission feature is observedz3~s5-s9~74,81 Even though the relationship expressed by Eq. 4 is significantly modified foi- eniisrioii
angles away from the surface normal,87 the conclusion concerning the vanishing lincn4tltli for ;I surface state crossing EF remains valid. In recent years, sufficient esperiiiieiit:il resolution has become available to test the limits of validity of this prediction. T h i s \\':I\ clonc some time ago for the sp-like surface state on Cu( 1 ll).40188 A sampling of rlit'se d ; i r : i i i sho\vn i n Fig. 14. The surface state (observed to be dotibled clue 1 0 the use 01' a i l .+\II
121
resonance lamp) exhibits parabolic dispersion about the zone center. The Iiypot Iic5is concerning vanishing linewidth as the surface state crosses EF is clearly observed n o t to Iic valid. The anomalous broadening was attributed to surface imperfections, a fact whicli n ~ 1 5 later used to study deviations from perfection more s y s t e m a t i ~ a l l y . More ~ ~ ~ ~sigiiific:iiit ~ and more fundamental deviations from the simple lifetime model are observed foi- (1-1 ikc surface states near EF on transition metals. Recent results on surface localized state\ o i i W(O1 1) and Mo(O1 for example, invoked broadening via cre:ition of phonon5 eitlicr during o r after the excitation event.
Sorface Resonant Levels Surface resonances present a particularly interesting problem which impacts dii*crw areas of surface physics and chemistry. There are at present no general models whicli give intuition about when a surface resonance will exist or what its properties might he. I n addition, resonances are not well-described by most first-principles ci)iiil)tit;itioii:il techniques since these utilize slabs having a finite number of layers 10 mimic the I ~ i l kiii ;I tr;ici;ihle way. We note that the simple phase model presented in a I;iter chapter t o IircdicI the energies of image-potential states has been adapted successfully to predict ;in sp-surf:ice rcsonance on C L I ( O O ~ ) This . ~ ~ model is not generally applicable in more complic:itctl situtions. Recently, an embedding technique developed some time ago95 to ;illow ;I s1;iIi IO be appended to a semi-infinite bulk crystal has become both popular and c~)i~ii~tit~ttioii:ill! ~ n a n a g e a b l e . ~The ~ ' ~future ~ promises a more complete theoretical treatment of 511 rl;ic.c resonances. As explained i n Sec. 1.1, a surface resonance should be entliwecl with :I i - c v ) i i : i i i L ' L ' lifetime corresponding t o the tunneling rate out of the quasidiscreet level and i n t o thc h ~ i l l i coiitiiiiium. This resonance width has been the subject of much attention for :icIsorptioii systems a s it forms the physical basis for c h e m i s ~ r p t i o n . ~ ~ - ' ~The ' ' study of intrinhic ~tirl':icc resonances from this point o f view is also of interest since the tunneling is :I tlyn:imic;il phenomenon which determines surface-bulk charge transfer rates and surface dipole 1:iyciformation. As explained in the introduction, experimental studies of surf'ice resonances arc essentially identical to sttidies of intrinsic surface states. One often applies the 5'1llle rc51\ I0 ascertain surface character, albeit with less certainty due t o the mixed 2D-3D chai-;ictcr ill' :I hiirface resonance. I t is likely that many features that have been called states are actually riioi-e prcci\cly I:ihelled resonances. On semiconductor surfaces, for example, surface features are i1orm:illy c;~lIcdsurface states even though these often lie outside the absolute band gap. A siii-f:icc stare lying in a symmetry-projected band gap will often be weakly coupled to the coritiniiiiiii via the spin-orbit interaction (see Sec. 2.2). In these cases, the distinction is norimlly I I O I important since the resonant coupling t o bulk states is small, anti the wave-funelion i t essentially 2D in character. A more interesting case is offered by recent results on the much-stucliecl ('ii(00 I ) A reasonably well-defined feature was observed in the miclclle of the s u r I ' ~ i c c wrface.
2.4
L
122
Ta(Ol1)
4
hv=40eV
2
A
EF
Binding Energy (eV) 1.0
0.4
0.8
Parallel Momentum
1.2
(Ad')
Fig. lS a ) bottom: Surface energy bands and projected bulk bands in the A mirror plane of Ta(0l I). Solid circles indicate the band exhibiting surface characteristics and demoiistr;ite the surface-bulk "avoided crossing". The corresponding surface feature linewiclth ;IS ;I function of kll is shown in the top panel. b) Sampling of the coresponding A R P spectra. 131-illoiiinzone which obeyed all the criteria to be labelled a surface m t e . However. no y:ip exists in the experimentally-measured bulk copper band structure, and t h u s this 5i;itc appears to be a surface resonance which is approximately predicted by calculations.-’I A novel way to study surface resonant coupling using ARP is t o observe ilie S I ; I I C resonance transition, since it can then be isolated from other types of broadeniiiy mechanisms. While this is not possible for most types of resonances, it often occurs i i i ilic' case of a surface resonance since a surface band dispersion relation located in ii pro.jcctctl gap must eventually cross into ;I projected continuum. This is demonstrated by recent rewlt\ on Ta(Oll)." As shown in Fig. 1%. on this surface there is a large projected gap :it i l i c center of the SBZ which pinches off in both symmetry azimuths. The gap supports :I surfacc st:ite o n both t h e clean and hydrogen-covered snrfaces, similar to that described for Ti(000 1 ) in Sec. 3.2. The surface bands milst disperse into the continuum somewhere in the Brillouin zone, thereby becoming resonances. The ARP spectra shown i n Fig. 1Sb exhil3it ;I
123
phenonienon which is approximately described an avoided crossing between S L I r h c e ; i i i O bulk bands at a klI value of 0.3-0.4 A-1.78 The surface band acquires the btilk char;ictcr. while at the same time the bulk band becomes the surface resonance. The resonance is 0.5 eV broader than the state (Fig. 15a, top panel). An important implication of these results is that the terms surface state, bulk state, and surface resonance become ambiguous when the energies of these features are similar at a given momentum. 3.
SELECTED TOPICS IN SURFACE STATES ON METALS
The application of ARP to study surface states o n simple metal surfaces is now wellestablished, and useful information can be attained in a routine fashion. This is howevcr :iii active field with several trends of current and future interest. We review a few of tlicsc iii this section. Surface States and Surface Dvnamical ProDerties Surface states are unusual in the sense that they are truly two-dimensional in iiatiiiw. I t is therefore natural to ask whether the variety of interesting physical phenomena ohscr\,ctl in low-dimensional systems might not also occur at surfaces and be driven hy the two-
3.1
dimensionality of surface bands. For example, the integral and fractional qu:liittiii1 1-l;iIl effects observed in semiconductor inversion layers and heterostructures result front tlic formation of quantized Landau levels in a 2D electron gas. The higher level o f degeneracy and also the increased importance of correlation and many-body effects might l e a d to ;I higher level of complexity and possibly to the observation of new physical phenomena :II metal surfaces. The ongoing interest in thin-film superconductivity also suggests interesting surface analogs. Some of these experiments will ultimately be limited only by o t ~ :tI>ili[y r I(, procluce surfaces with a high degree of perfection. Phenomena in which lowered dimensionality plays a key role often involve electronic screening and the generalized wave vector(q)- and frequency(w)- dependent elect roiiic susceptibility, X(q,w). In the random phase approximation, xo(q,w), the bare susceptiliility takes the formZo3
where f(k) and t(k) are the Fermi factor and band energy at wave vector k. l ' h i > electronic susceptibility must be normalized by the electronic self-energy ~ ( w (zee ) chapter 3) in order to treat shorter-range phenomena, so that x(q,w) = xo(q,w)/[l- C ( W ) x " ( ( I , w ) ] . Eq. 5 suggests that x"(q,w) may be singular, and these singularities translate into instatiilitie5 of some sort. Since ARP measures the energy bands of occupied states, in principle useful information about electronic screening can be extracted. The Fermi factors in the numerator of Eq. 5 require the creation of an electron-holc pairs with wave vector q. At small w , xo(q,w) can exhibit an anomaly when the h i 1 d energies at k and k + q are similar, i.e., they must both be near the Fermi Icvel: - I ' I t t h:ri.tS
124
Fig. 16 Surface Fermi contours for clean and hydrogen-covered W(O11). The s h x l c d regions is the projection of the experimental bulk Fermi surface onto the surface Brilloiiiri zone (from Ref. 90). functional form of the resulting xo(q,w) is strongly dependent on dimensionality. Foiexample, integration of Eq. 5 for a 3 D free electron gas yields a mild logarithmic singtihrity in slope in x"(q,w) at q = 2 k ~ This . becomes a discontinuity in slope in two dimensions aiid ;I singularity in the magnitude of xo(q,w) in one dimension. In bulk systems, this scrce1)ilig often is manifested by unusual anomalies observed in the dispersion relations for low-energy elementary excitations which indicate dynamical coupling with the electron gas. I n sevcrc cases, these anomalies "freeze in" and the lattice reconstructs, as in the Peierls-like ch:irgedensity-wave distortions observed, for example, in quasi-1D and -2D metals,104 or ii spindensity wave is formed, as, for example, in bulk chromium.105 3.1.1
Fermi surface of clean and hydrogen covered W(110)
An important feature of phenomena observed in low-dimensional systems is th:t1 tlicy
occur o n an energy scale which is very small compared to the occupied electronic 1x1110 nklili of the systems under consideration. Thus while the bulk of ARP studies to date have explored all the occupied levels near a surface, generally only those very close to the I-erini level can have a very pronounced impact on the subtle effects associated with Iowet-ed dimensionality. For this reason, there has recently been increasing interest in careful measurements of surface bands in the vicinity of the Fermi level. Bulk three dimensional Fermi surfaces are commonly determined by de Haas van Alphen or related meiisureiiiciits. Unfortunately these bulk-sensitive methods cannot be readily applied t o the deterinii1:ttion of ;I 2D Fermi surface at a surface o r interface. ARP can be used to determine [lie I-crmi
125
Work Function Change (mev)
0
W(0ll)
-
A
+H
bQ,
J 1
11-1 L
Y
a
0.0
0.2
0.4
0.6
Hydrogen Coverage (rnonolayers) Fig. 17 Change in Ferrni wave vector, along the line A in Fig. 16, with hydrogen co\era::c the corresponding work function change. Note the change in slope at recoiistrtictioii (from Ref. 90).
iind
level crossings o f the various bands with reasonable precision and thus to map out the Feriiii surface throughout the SBZ. As an example we show here in Fig. 16 the data of Gaylord et al.oO for the L w t ) dimensional surface Ferrni surface of clean and hydrogen saturated W( 110). The datn poinls show the Fermi level crossings of surface states and resonances throughout the S I C superimposed onto the projections of the bulk Fermi surface.lo6 The clean surface has Iwtli electron and hole orbits. An electron orbit centered around C extends across the first S I X boundary line P-H and surrounds the projection of the bulk electron jack. Three different hole orbits are observed; one is centered around C and the other ones are found at the SI%% boundaries, one along the line P-N-P and the second one along the line P-H. C)iily lllc electron orbit and the last mentioned hole orbit are true surface states, located in ;I gap of the projected bulk bands. The other features are surface resonances embedclecl i n l o tlic projected bulk states. These data suggest unusual behavior of the bare susceptibility. Neglecting rii:ltrix element effects, anomalies appear in integrating Eq. 5 when segments of the Ferrni surt'ace have parallel tangents, and are most severe when the curvatures are similar. For e x a n i l k the sections of the electron orbit along the lines A and R can be strongly coupled t o thc nearby segments of the hole orbit centered at N. This might appear as a Kohn anoinaly i n the surface phonon dispersion relations.'07 Hydrogen chemisorption rapidly attenuates the hole-orbit states. The electroiiorbit state shifts to higher binding energy, resulting in expansion of the Fernii surface. Ultimately the Fermi surfaces in two neighboring SBZs contact each other at the sharp points near H in Fig. 16. This results in the appearance of two hole orbits observed along the P-N-P and P-H lines.
126 I
.
.
.
.
,
.
.
.
.
.
.
.
.
.
.
.
.
.
.
1.1 1 1-01 0.92 0.82
n
W
W
Z
3
1 EF=O Binding Energy (eV)
2
0.76 0.70 0.64 0.54 0.44 0.38 0.31 0.24 0.17 0
Fig. 18 Photoemission spectra of W(00l)jn the E azimuth as a function of k 11. The nondispersive band near EF for k / / - 0.5 A' was suggested to drive the ~ ( 2 x 2 )reconstrucrion (from Ref. 80). Recently this surface has been observed to reconstruct upon adsorbing >0.5 monolayers of hydrogen.lo8 It is observed that the change in magnitude of the stirI';ice Fermi wave vector is approximately linear with hydrogen coverage, with a change in slope near half monolayer coverage, as plotted in Fig. 17. This smooth shift with changing i n coverage is also observed for the surface states observed on Ni(ll1) and P d ( l l 1 ) discussed below. One might speculate that the reconstruction is related to the change of morphology ;issociated with the merging of neighboring Fermi surfaces. However the merging occurs at ;I milch smaller coverage of about 0.2 to 0.3 ML. Thus there seems to be no direct connection between the change in Fermi surface morphology and the geoirierric reconstruction of this surface. This is supported by the observation that Mo(Ol1). which does not reconstruct.109 exhibits similar 2D Fermi surface behavior.92 3.1.2 Clean surface reconstruction of W(OO1)
In 1978, Tossatti suggested that the surface reconstruction of W(001) might be driven hy ii Peierls-like instability o f the electron gas,'" similar to the one operative iii layered quasi-2D transition metal dichalcogenides. lo4 This suggestion, which enjoyed signil'ic:inr popularity for a time, was largely rejected in favor of a tocat driving meclianisrn. 1 - 1 1'.
''
127
-1
.o
0
1 .o
Fig. I0 Surface Fermi contours for clean W(001). The shaded region centered along the L: mirror plane reflects the extent o f the non-dispersive band in Fig. 18 (from Ref. 80). Indeed, an early Fermi surface determination indicated insufficient nesting to support ;I charge-density-wave type of mechanism. A recent calculation for Mo(001). howevei-. suggests that Fermi surface nesting may play an important if not determining role in driving the slightly incommensurate reconstruction observed on that surface.l l 5 An incommensurate structure is difficult to explain within a model based purely upon local bonding considerations. It is unlikely that completely different mechanisms are operative O I I two otherwise so similar surfaces. Indeed, recent atom diffraction results o n W(O0 I ) sugge\t the existence of an incommensurate phase on that surface above room temperature,' " although these results contradict all existing electron and x-ray diffraction data.' 18-120 A more recent 2 D Fermi surface determination on W(001) is at odds with the previous work, and suggestive of the apparently delicate interplay between localized aiid delocalized mechanisms.80 A sampling of the ARP spectra from that study i n the relevant C azimuth is shown in Fig. 18. Near EF, these exhibit a surface band which begins with the intense Swanson hump feature near the zone center (kll = 0.0 A-’), disperses tow;ircI I N I does n o t cross EF, and then disperses away from EF before reversing direction i i i i c l ci-ossiiig near the M symmetry point. The resulting Fermi surface is shown in Fig. 19. The crossiry near M forms a well-defined hole pocket similar to that observed on W(O11). Tlie size of this pocket i s considerably over-estimated by all existing c a l c ~ ~ l a t i o n This s . ~ is~ due ~ ~ ~ ~ ~ ~ ~ i n part to the influence of the spin-orbit interaction along c, where odd and even projected gaps overlap significantly (see Sec. 2.2). The shaded region in Fig. 19 indicates the region of "3’
128
k-space where the surface band is too close to the Fermi level to be measured accurately. A vector connecting shaded regions on opposite sides of the SBZ (i.e., q = 2 k ~ is ) slightly incommensurate with the lattice and is in rough accord with the periodicity seen in the atom diffraction measurements. This delocalized, CDW-like driving force is actually not incompatible with the local mechanism, since the coupling occurs over a large portion of kspace and is thus in some sense localized. These results suggest further first-principles computations are in order to understand these W(OO1) and Mo(001) reconstructions comp I e t ely. 3.1.3 Non-adiabatic surface interactions The adiabatic or Born-Oppenheimer approximation, which implies the separability of
electronic and nuclear wave functions, is always suspect in metallic systems where electronic excitation energies extend to zero energy. Superconductivity is perhaps the most dramatic manifestation of the breakdown of adiabaticity. The interactions described in the previous section provide good examples as well. The general importance of non-adiabaticity cannot he over-stated: breaking or making a chemical bond is in some sense a non-;idi;ilxitic process. We anticipate that non-adiabaticity plays an important role i n a variety of surf:icc. processes including transport, chemistry, ion neutralization, etc.
W(OO1): h v = 4 2 eV, A Ira
n
w
U
z
~~
1
4 3 2 1 EF=O Binding Energy (eV)
Fig. 20 Photoemission spectra of clean (dashed curve) and hydrogen-covered (solid curve) W(OO1) demonstrating the existence of a H-induced feature near EF near X (from Ref. 114).
129
The criterion for the breakdown of adiabaticity is the existence of a significant density of electrons (or pairs of electrons in the case of superconductivity) with a velocity which is comparable to nuclear velocities, at an energy close to EF. The flat band near EF observetl on W(OO1) is a good candidate, and a subtle interaction between electronic and static and dynamic geometrical structures results. Adsorbate vibrations can also be damped non-adiabatically when there is ;i 1;ri-g~ density of surface-localized electrons near EF. The first direct observation of this phenomenon was in a surface infrared reflection-absorption study of W(001)-2H which observed an asymmetric adsorbate vibrational mode, characteristic of a discrete oscillator (the vibration) coupled non-adiabatically to a continuum (the electron-hole pair spectr~rn).A ~ ~narrow ~ ? ~ band ~ ~ of adsorbate-induced surface states was predicted to exist near EF. A recent ARP study has detected such a band, as shown in Fig. 20.124 'I'he symmetry of the band suggested a reassignment of the adsorbate vibration. This sysccni provides an excellent example of how ARP can engage in a useful interplay with otlieilower-energy surface probes. The existence of such adsorbate-induced bands appears n o t 10 be too uncommon; recent results for W(OOl)-tC, Mo(OOl)+H, and W(OIl)+K, W ( O 1 I ) t 0% Mo(Ol1) t 0 indicate similar phenomena occur on those surfaces. The Crud Test Revisited: Hydrogen ChemisorDtion 3.2 An important and growing application of the ARP technique to surface states on inet:il\ amounts to a careful application of the "crud test" (Sec 1.2). Any adsorbate on a surkrcc does not remove all charge from the surface region, as the crud test implies, but rather l l i e surfrice states of the adsorbate-covered surface are located in different areas of energy/momentum space than the electronic states of the clean surface. In principle, using ARP we can study formation of the chemisorption bond, momentum by momentum. While recent efforts studying the interaction between electronegative and electropositive adsorbctl atoms and the underlying surface bands appear promising,543125-127 by far the most w o r k iii this area has been done on hydrogen chemisorption. The results for tungsten and molybdenum surfaces reviewed in the last section are one example of this type of study. Hydrogen atoms, having only one 1s electron, are by definition the simplest chernisorption system. Therefore, various theoretical approaches have been tested on thi. model chemisorption system. These theoretical descriptions range from extensions of (lie Newns-Anderson impurity to quantum chemical methods128 on one hand to solid state band structure calculation^^^^^^^^^^^ and the jellium description of the substratc o i l the other hand.131-135 By their nature each of these models will emphasize a difl'ereiit aspect of the adatom substrate interactions. Some describe the adsorbate substrate bond :is ;Ldirected chemical bond128 or interactions with specific surface states24i129,130 wherca\ other^'^'-'^^ have the interaction delocalized because of the delocalized nature of !lie substrate. The study of hydrogen interaction with metals is not only of interest as a model system for chemisorption but it also has many practical applications. The role o f
130
chemisorbed hydrogen in heterogeneous catalysis is obviously very important h u t nevertheless far from being understood. In materials science, the formation and properties of metal hydrides as well as hydrogen embrittlement of steel and other structural materials are important research areas. This also extends to the application of transition metals ;IS hydrogen storage elements. With the possibilities and well known environmental advantages of a hydrogen based energy economy these technological aspects of the interaction of hydrogen with metals will become even more important in the future. The study of the electronic structure of hydrogen on metal surfaces by ARP largely deals with the changes induced in the surface electronic structure rather than with extrinsic molecular or atomic electronic levels. Hydrogen is dissociated upon chemisorption and exhibits only a very weak Is electron derived band-like state. This is in contrast to other chemisorption systems like CO or NO having quite strong bands derived from the molecular electronic states which often are non-degenerate with substrate electronic states. 3.2.1 Hydrogen saturated surfaces Because of the somewhat elusive character of the hydrogen induced changes i n the surface electronic structure some of the initial attempts to determine the electronic structure
of a hydrogen covered metal surface failed. The first successful studies of this kind we1-r perfommed on H on Ti(OOOl)136 and for H on N i ( l l l ) , P d ( l l l ) , and Pt(ll1) surfaces."" The latter work dealt especially with the phenomenon that the hydrogen induced states on these surfaces could only be clearly detected at low temperatures near 100 K. Room temperature adsorption resulted in no or rather small changes in the surface electronic structure, even though hydrogen was definitely chemisorbed as evident from thermal desorption spectra and a change in work function of the surfaces, Fig. 21 shows the normal emission spectrum for hydrogen on Ti(0001) compared to the emission of the clean surface.136 The peak at EF in the spectrum of the clean surface is quenched by hydrogen adsorption and corresponds to the emission of the surface state of the clean surface. The hydrogen covered surface exhibits a hydrogen 1s derived band at 6.9 eV below EF and another strong emission feature at 1.3 e V below EF. These two features at r correspond in the simplest possible explanation to the bonding-antibonding level combination for the hydrogen chemisorption bond. The bonding state exhibits a Is1 dispersion with a band width of 2.4 eV, whereas the antibonding state is essentially tlat in dispersion but exists only about halfway into the SBZ, not quite to the point where the g;ip iii the projected band structure ceases to exist129 (see Sec. 2.4). The bonding split-off state has hydrogen Is character with a strong admixture of metal 3d-character, whereas the antibonding state originates mostly from the surface state of the clean surface shifted by the interaction with the hydrogen atoms. For hydrogen on Pd( 111) the picture is slightly more complicated because this surface has more intrinsic surface states. These states are shifted by the chemisorption of hydrogen even though they might not be directly involved in the chemisorption bond. Fig. 22 shows ;I plot of the SBZ projected band structure of Pd(ll1) with and without hydrogen. The
131 l
l
i
l
l
~
l7
j
NORMAL EMISSION AREDC f i w = 2 2 eV
-Ti(0001l-H(1x1) ---- Ti (0001l
n
S,p I
I
- POLARIZATION I
I
I
1
I
1
I
-5
1 I'
a
I N I T I A L ENERGY ( e V 1 Fig. 21 Photoemission spectra of clean and hydrogen-covered Ti(0001) exhibiting the bonding and antibonding states in hydrogen chemisorption (from Ref. 129). experimental data points137 are compared to the calculated surface states ( s o l i t l The agreement throughout most of the SBZ between theory and experiment is rather good, except near the M point of the SBZ, where some minor discrepancies are observed. This has been discussed in more detail e 1 ~ e w h e r e . l The ~ ~ hydrogen Is derived band is again split off from the bottom of the bulk sp-band and all the surface states of tlic clean surface are shifted to higher binding energies when hydrogen is chemisorbecl. ' I l i e cross section and the coverage dependent studies discussed below are strong evidence f o r ;I large substrate 4d admixture in the H 1s derived band. The surface state on Pd( 11 1). which i\ equivalent to the antibonding state found for the Ti(OOO1) surface, is unoccupiecl on Pd( I I I ) arid thus is located above EF. The existence of this state, at least on the clean sirrf;.ice, has been verified by inverse p h o t o e m i ~ s i o n . ~ ~The ~ , ' comparison ~~ between experiment a n d theory points toward the threefold hollow position as the hydrogen adsorption site o n this surface, but no definite distinction can be made as to whether the hydrogen atoms are located in the fcc o r hcp hollow sites. This whole research area of hydrogen chemisorption on metals is a very nice example demonstrating how a positive interaction between theory and experiment can stimulate research in both directions. In the first round, comparing the ARP1367137 results shown i n Fig. 21 and Fig. 22 with state of the art electronic structure calculation^'^^^^^^ it became obvious that, even though most of the possible adsorbate structures could be ruled out. based upon the spectroscopic information alone the adsorbate geometry coiild not bc uniquely determined. This was somewhat disappointing because these were quite extensive data sets, where a lot of work had been put into both theory and experiment. The principal
132
(a)
CLEAN P d ( l l t ) SURFACE STATES
(b)
H, ADSORPTION 0 - I -2 - 3
E,
- 4
- 5
I
I
n i i
I
r
1
w
P
Fig. 22 Surface band dispersion curves and projected bulk continuum in the mirrorsymmetry planes for clean and hydrogen-covered Pd(1ll) (from Refs. 128 and 129).
question, which still remains to b e answered even as of today, is how well theory and experiment should be expected to agree with each other. Assuming that the experiment really tells us what nature is about (see Chapters 2 and 31, we have to be concerned niostly about the theory. These calculations are of the highest quality, but nevertheless conlain certain approximations, mainly with respect to the treatment of exchange and correlation. Also both calculation^^^^^^^^ use special but different sets of Gaussian wave functions to describe the charge distribution in the surface region. This is done fully self-consistently l l u t nevertheless the degree of localization of the surface states seems to depend on t h e Ixisk sets used in these theoretical schemes. three to f o u r For H on Ti(OOO1) there were, according to Feibelman et "sl.'ectroscopicaIly acceptable" adsorption geometries which all produced about the sanw electronic structure, characterized by the split off hydrogen 1s derived band ant1 the antibonding state at -1.3 e V derived from interaction of the intrinsic surface state with the
133
hydrogen atoms. Possibly this choice could be narrowed down somewhat by requiring niore stringent agreement between theory and experiment, as discussed in Ref. 5 but there is still n o unique solution for the adsorbate structure based upon the spectroscopy alone. Including into the calculations a scheme to evaluate the total energy of the system and thus to further determine the heat of adsorption for the hydrogen atom let Feibelman e t narrow down the choice for the adsorption sites of H on Ti(OOO1) to propose the "long bond length fcc" surface site as the most likely adsorbate geometry. As already mentioned atlove in the equivalent studies of hydrogen chemisorption on Pd(l1 1)138 the results point toward hydrogen chemisorption in the three fold hollow site on the surface, where the question remains open, whether the hcp or fcc surface site should be favored. Recent total energy calculations for hydrogen chemisorption on R u ( O O O ~ find ) ~ ~ that ~ the fcc site is abotit 0. I eV lower in energy per hydrogen atom and thus should be favored on that surface. 3.2.2 Coverage-dependent studies The most puzzling result of the early studies was the existence of an "invisihle" hydrogen adsorption phase corresponding to saturation coverage at room temperature.137s138 Hydrogen is clearly present on these surfaces under these conditions, with a coverage equivalent to approximately 0.5 saturation coverage at 90 K for Ni(l1 I ) and 0.3 for Pd( 111), as evident by thermal desorption and nuclear m i c r ~ a n a l y s i s . ~ ~ ~ ~ ~ Absolute coverage studies using the latter143 found that for D on Pt(ll1) at 300K and 5 . 5 ~ 1 0 'Pa ~ the coverage is o = 0.15 monolayer, substantially less than previously estimated. Nevertheless, apart from a work function change this room temperature adsorption state is spectroscopically almost "invisible". This applies not only to photoemission studies, but to low energy electron energy loss vibrational spectroscopy as well.144
I
I
- 10
I
I
I
I
I
-5 E - E,(eV)
I
I
I
I
I
0
Fig. 23 Normal emission ARP spectra of Pd( 111) as a function of hydrogen coverage ( f r o m
Ref. 46).
134 Pd(l11) + Ht
K Surface Stales
- 6.0
1
H 1s s p on ~ State at
r
50
100%
50%
OW
H, Coverage
Fig. 24 Summary of results for coverage-dependent hydrogen adsorption on Pd(ll1). Upper panels show the energies of surface bands, while the bottom panel shows the work function change. The angle resolved photoemission data on Ni, Pd, and Pt(ll1) discussed abow were taken for saturation coverage at low temperatures (90K). This coverage corresponds 10 the adsorption of one monolayer of hydrogen atoms. Therefore it is not surprising, that t h e H induced split off band exhibits a (1x1) dispersion. For a coverage less than oiic monolayer, down to about 0.5 on Ni(ll1) or 0.3 on Pd(ll1) the hydrogen induced changes i n the surface electronic structure are still visible. At the lower coverages the total band width of the H 1s split-off state is reduced, but somewhat unexpectedly this band still exhibits ;I (1x1) periodicity with the substrate in its d i ~ p e r s i o n .At ~ ~the same time a continuous shift of the intrinsic surface states back toward the position of the clean surface has been observed. This is illustrated in Fig. 23 and Fig. 24. Fig. 23 shows normal emission AREDC'\ of hydrogen on Pd( 111) as a function of hydrogen coverage. The results for all the surfx.t. features of this surface are summarized in Fig. 24 as a function of hydrogen coverage. The reduced width of the split-off state together with the continuous shift of the intrinsic surface states cause us to rule out the formation of adsorbate islands as explanation for the (1s I ) dispersion of the split-off band. This is also consistent with the large H-H repulsion fourid for the adsorbed Thus the (1x1) periodicity can only be explained I)!
135
the large admixture of substrate d-character as suggested by the theoretical analysis of the orbital content in this state.130,137 Both at the zone center and at the zone boundary this state is largely characterized by substrate d-states "pulled down" by the presence of the Hatoms on the surface. This also causes the relatively large cross section of this state compared to the emission of the substrate sp-band, which is barely visible in the spectra. This substrate d admixture to the H Is split-off band also causes the difference in the band width between the P d ( l l 1 ) and Ni(ll1) surfaces. The band width of the H induced band on Ni is about twice as large (4.2 eV) as on Pd ( 2 eV), which cannot be solely explained by the 10% decrease in lattice constant between Pd and Ni. Moreover, an isolated monolayer of H-atoms in the correct spacing to match the P d ( l l 1 ) surface has a calculated band width of 4 eV,145 or twice the actually measured band width for H on Pd(ll1). Thus the width of the hydrogen Is induced band on Ni(ll1) corresponds roughly to the estimate for the monolayer, whereas the band width on Pd(ll1) is way too small. Additionally, the shape of the H induced split-off band on Pd deviates strongly from the "normal" parabolic band shape and exhibits an almost flat dispersion from the halfway point to the zone boundary. The explanation for both, the unusual dispersion and small band width of H on Pd( 111) lies in the interaction with the Pd d electrons. At the zone boundary the location of the split off state is largely determined by the energy of the bulk substrate d-bands and the surface component split off the bottom of these bands. The exact nature of the H adsorbate layer for sub-monolayer coverage is still a mystery. We have reconciled the observation of a (1x1) periodicity in the H induced band by the strong admixture of substrate d-states and ruled out island formation because of the continuous, almost linear shift of the intrinsic surface states with coverage and t h e strong repulsion between adsorbed hydrogen atoms. Whether the H-atoms actually form a kind of delocalized lattice gas,147 where the average distance varies with concentration, or whether the atoms are adsorbed in fixed threefold hollow positions with a random distribution of vacancies is as yet unresolved. Also, because of the strong repulsion between the H-atoms they could move into a subsurface p ~ s i t i o n , ' ~which ~ , ~ ~for ~ both Ni(111)138 and R u ( O O ~ ) ~is~ calculated ' to have a lower binding energy. Thus these sites would not be occupied without some further stimulation. Moreover, the subsurface hydrogen is supposed to change the symmetry of the surface state near EF at the center of the SBZ.I4' We have experimentally checked the symmetry of this state and did not observe a change in symmetry at low hydrogen coverages46 The latest turn in the mutual stimulation between theory and experiment are the calculations by M.Y. Chou and J.R. Chelikowski for hydrogen chernisorption on R U ( O O ~ ) . ~ ~ ' These total energy calculations demonstrate that for hydrogen monolayer adsorption on Ru(001) the fcc three fold hollow surface site is definitely the energetically favored adsorption site. It takes substantial energy (0.7 eV/atom) to push a hydrogen atom from this position into the subsurface site. This is illustrated by the potential energy curve shown i n the top panel of Fig. 25. However if the coverage is doubled, the hydrogen repulsion for the surface sites becomes so strong that now the energetically favored chemisorption geometry
136 -1.8
-
f
-2.2
-I r I
g
yf
s
C)
-
I
-
-2.4 -2.8
-2.8
HIRu (0001)
-I
-3.2’.
I
I
I
I
-1
0
I
I
I
I
-0.8
I: -1.4 -1.6 -1.1)
-3
-2
1
2
3
Poaitlon of Hydrogen Atom (0.u.)
Fig. 25 Potential energy curve for hydrogen motion perpendicular to the surface layers of Ru(0001), at one (a) and two (b) monolayer coverages (from Ref. 141). has half the adsorbed hydrogen atoms occupy the octahedral subsurface sites just below the fcc surface sites, where the other half of the adsorbed hydrogen atoms are located. Thus for the complete monolayer the chemisorbed surface atoms provide an attractive force for adsorption in the subsurface positions, as indicated by the potential energy curve in the bottom panel of Fig. 25. This model does not contradict the general observations about the sequential filling and depletion of these sites. Since the subsurface site becomes favorable for adsorption only after completion of the first surface layer of hydrogen atoms, in adsorption the surface sites still are occupied first. On the other hand in thermal desorption the surface hydrogen atoms are expected to be removed first, but as soon as the surface site is unoccupied, the chemisorption in the connected subsurface site is energetically less favorable such that this hydrogen atom will move into the vacated surface site. Thus de fact0 in desorption the subsurface layer gets depleted first. 3.2.3 The hydrogen dissociation mechanism All hydrogen chemisorption studies described above implicitly assume that the hydrogen molecule is dissociated upon contact with the metal surface and then chemisorbed as two independent hydrogen atoms. This assumption is verified experimentally by the complete isotope sdrambling of an H2/D2 mixture upon desorption. In this context, it is of special interest that the bond strength of hydrogen atoms and the desorption temperature on Cu and Ni surfaces are quite but Cu does not dissociate the H7, molecules.
137 I
~
NI / C u 11111
I
~
I
~
hv = 9.5 eV
INiIlll) hv:95eV
/II
k,,=O
il I .J I
E,=O
2
I
I
L
Energy above E,
I
I
,
6 lev1
1
E,=O
1
1
,
1
1
1
1
2
L 6 Energy above E, lev1
Fig. 26 Inverse photoemission spectra at normal electron incidence for clean and nickelcovered copper (left), and clean and copper-covered nickel (right). The difference between these two surfaces is in the existence of a dissociation harrier oil Cu(ll1). The height of this dissociation barrier has been experimentally determined i n H 2 scattering experimentslS1 to be 3-5 kcal/mole. Hydrogen permeation studies give an even higher value for this barrier152 from the analysis of the desorption velocity and angular profile, which might be due to direct desorption from a subsurface bound state. While there were different theoretical models proposed explaining the nature of this dissociation barrier1s3-156 experimentally the possible electronic origin of this barrier was only recently explored by studies of the modification of electronic structure of Cu( 11 1) a n d N i ( l l 1 ) surfaces by adsorption of epitaxial monolayers of Ni or Cu, respe~tively.'~' The
model presented by Harris and Andersson,lS6 was essentially confirmed by these experiments. I n this model the main interaction between the H2 molecule and the surface is through the sp-electrons. On both surfaces these s electrons must orthogonalize to the ug orbital of the approaching H2 molecule. On Cu this can only be accomplished by shifting the s electrons up in energy and therefore this leads to a considerable activation barrier. On the Ni surface on the other hand, the d-holes at the Fermi surface may serve as sink for the metal s electrons through a change in s-d hybridization, which costs much less energy. This model is very similar in its nature but not its language to the quantum chemical approach taken bv t ~ p t 0 n . l ~ In ' this description a large density of states near EF allows the substrate
138
orbitals to adjust to the approaching H2 molecule and maximize bonding interaction, while minimizing Pauli repulsion between the states. The presence of d-holes in the electronic structure of a monolayer of Ni o n Cu(ll1) is demonstrated by the left panel of Fig. 26. The bottom curve shows the inverse photoemission spectrum of the C u ( l l 1 ) surface under normal incidence of the electrons. This curve shows a step like rise at the Fermi level EF and a peak at 4.25 eV assigned to an image potential state. Upon deposition of a pseudomorphic monolayer of Ni onto this surface, the top curve is obtained, which is dominated by a large peak at EF. The persistence of the image potential state near 4.2 eV is evidence for a well ordered surface. Measurements of the dispersion of the hole states near EF show that the hole states extend only over a small region of momentum space near the center of the SBZ. The well known surface state on C u ( l l 1 ) still exists on this composite surface without any noticeable change in dispersion. This modified surface is able to dissociate hydrogen, whereas the bare Cu(ll1) surface does not. Upon hydrogen chemisorption the hole state emission is strongly attenuated. Combining these inverse photoemission studies with angle resolved photoemission experiments on the same surface systems Frank et al.157 find that the total density of states at EF for the composite surface is not much larger than for the clean Cu surface, since these holes are only present within a small fraction of the two dimensional SBZ. On the other hand, deposition of a monolayer of Cu, which also grows pseudomorphically on Ni( 11l), causes hardly any change in the inverse photoemission spectrum. This system displays the equivalent d-holes, but now for a semi-infinite Ni crystal. as shown in right side of Fig. 26. However this surface does not dissociate hydrogen anymore. This indicates that the dissociation mechanism is directly related to the immediate states at the surface. The localized d-holes of the substrate do not extend far enough to have any effect on the dissociation, even though they are clearly visible in the inverse photoemission spectrum. These experiments confirm the theoretical model of the hydrogen dissociation mechanism of Harris and A n d e r ~ s o nto~ the ~ ~ extent that they show the importance of surface localized d-holes for this step. We have to add here that the attenuation of the dhole derived peak in the inverse photoemission spectrum upon hydrogen exposure of the composite Ni on Cu(ll1) surface is related to the bonding of the hydrogen atoms and not necessarily to the dissociation. Obviously the photoemission and inverse photoemission do not monitor the actual dynamic dissociation process, but only cause and effect. Nevertheless this result is another important step forward in gaining a better understanding of the interaction of hydrogen with transition metal surfaces. CONCLUSIONS AND FUTURE POSSIBILITIES I n this chapter, we have reviewed physical phenomena of interest in the area of surface electron states which exist on nominally clean metal surfaces. We began with a historical perspective of why surface states exist and what their properties might be. We 4.
139
followed with several examples of increasing sophistication, ultimately to indicate the fairly good fundamental understanding we have in this area. While the review cannot be comprehensive for such a large and active field, we have tried to capture a few of the interesting and important current trends. We now use this as a basis for speculation about what might be important research areas in the future. Obvious extensions of the current work exist in preparing and measuring novel surfaces of unusual materials and films. This is the subject of several of the following chapters, and we leave a description of the future in these areas to those chapters. Instead, we mention a few subjects of general interest in the surface chemical physics communities. Much of the unexplored frontier in this area lies in very high resolution studies. The ultimate goal is to make contact with the subtle electronic phenomena studied in other areas of surface and solid state physics. For example, the self-energy of an electron is modified by the electron-phonon interaction so as to modulate energy bands as they cross the Fermi level. This effect is also reflected in the low temperature specific heat of metals, and is ultimately related to the formation of the superconducting gap. It has not been measured t o date by ARP, primarily due to the lack of adequate energy and angle resolution and possibly of an adequately narrow photoemission feature. To do so would provide a very useful, momentum-resolved probe of the dynamical coupling between electrons and phonons. The best chance of measuring this fundamentally important phenomenon is with ARP studies of 2D metallic states, as these are intrinsically narrow. These wiggles in dispersion relations near EF can turn into gaps if the electron-phonon interaction is strong enough so that the lattice reconstructs or the system becomes superconducting. Related phenomena may he observable on magnetic systems which undergo a spin-density-wave transition. C a p anisotropy, a phenomenon of significant current interest in the high temperature superconductivity field, should b e a fairly general phenomenon which ARP is just beginning to address. The idea of the breakdown of the Born-Oppenheimer approximation also clearly linked to these high resolution experiments. With better resolution and sensitivity than currently available, we may be able to provide very concise and useful information in systems which exhibit nonadiabatic adsorbate vibrational damping. An important theme will continue to be to understand interactions between adsorbates and electrons in the vicinity of the surface. This will be increasingly important as the sophistication of surface phonon measurements improves. We have in mind extensions of the experiments reviewed i n Sec. 3.1 and 3.2 to other adsorbates which are more strongly interacting than hydrogen. The field from these adsorbates is screened by Fermi surface electrons, which in turn are scattered by the adsorbate potential. This interaction is fundamentally the source of lateral adsorbate interactions. A complete understanding of such energetically weak interactions will be important in achieving a general knowledge of surface phenomena.
140
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Chapter 5
SURFACE STATES ON SEMICONDUCTORS GORAN V . HANSSON AND ROGER I . G .
1
UHRBERG
INTRODUCTION
The atomic and e l e c t r o n i c s t r u c t u r e of semiconductor s u r f a c e s and i n t e r f a c e s a r e of widespread s c i e n t i f i c and t e c h n o l o g i c a l i n t e r e s t , and s t u d i e s of semiconductor s u r f a c e s have become a v e r y a c t i v e a r e a
i n t h e f i e l d of s u r f a c e s c i e n c e /l-lO/. P h o t o e l e c t r o n spectroscopy
i s t h e main t o o l f o r i n v e s t i g a t i o n s of t h e e l e c t r o n i c s t r u c t u r e of semiconductor s u r f a c e s . By t h e use of a n g l e - r e s o l v e d photoemission t h e complete s u r f a c e s t a t e band s t r u c t u r e h a s been determined f o r s e v e r a l s u r f a c e s . Due t o t h e i n t i m a t e r e l a t i o n s h i p between t h e atomic and e l e c t r o n i c s t r u c t u r e of a semiconductor s u r f a c e , it has f u r t h e r m o r e been p o s s i b l e t o use i n f o r m a t i o n about t h e s u r f a c e e l e c t r o n i c s t r u c t u r e t o draw important c o n c l u s i o n s concerning t h e atomic geometry of semiconductor s u r f a c e s /11-13/. A r i s i n g from t h e c o v a l e n t c h a r a c t e r of most semiconductors t h e r e i s a v e r y l a r g e change i n t h e e l e c t r o n i c s t r u c t u r e a s s o c i a t e d w i t h t h e b r e a k i n g of bonds i n t h e formation of a s u r f a c e . I t i s well known t h a t semiconductor s u r f a c e s i n g e n e r a l r e l a x o r r e c o n s t r u c t by rebonding and moving t h e s u r f a c e atoms t o reduce t h e s u r f a c e f r e e e n e r g y . A wide v a r i e t y of e x p e r i m e n t a l t e c h n i q u e s has been a p p l i e d t o t h e s t u d y of semiconductor s u r f a c e r e c o n s t r u c t i o n s and d u r i n g t h e l a s t few y e a r s t h e r e has been a remarkable p r o g r e s s i n t h e unders t a n d i n g of s e v e r a l of t h e s e r e c o n s t r u c t i o n s . More t h a n twenty y e a r s have now p a s s e d s i n c e t h e f i r s t evidence of photoemission from semiconductor s u r f a c e s t a t e s was r e p o r t e d i n
experiments on c l e a v e d S i ( l l 1 ) s u r f a c e s /14/. During t h e e a r l y p e r i o d t h e main o b j e c t of photoemission s t u d i e s was r e l a t e d t o t h e q u e s t i o n s of whether t h e r e a r e any s u r f a c e s t a t e s i n t h e bulk band gap and whether t h e s u r f a c e e l e c t r o n i c s t r u c t u r e i s m e t a l l i c o r semiconducting. From a n g l e - i n t e g r a t e d photoemission s t u d i e s it became e v i d e n t t h a t t h e s u r f a c e band s t r u c t u r e s of many semicond u c t o r s have band gaps t h a t a r e r e l a t e d t o r e l a x a t i o n a n d / o r r e c o n s t r u c t i o n of t h e s u r f a c e s . I n t h e l a s t few y e a r s t h e r e has been
146
a l a r g e number of a n g l e - r e s o l v e d p h o t o e l e c t r o n s p e c t r o s c o p y (ARPES) s t u d i e s , which have g i v e n v e r y d e t a i l e d i n f o r m a t i o n a b o u t t h e s u r f a c e e l e c t r o n i c s t a t e s . I n s e v e r a l cases, a s f o r t h e S i ( l l l ) 2 x l and 7x7 s u r f a c e s , t h e i n f o r m a t i o n a b o u t t h e s u r f a c e e l e c t r o n i c s t r u c t u r e from ARPES s t u d i e s and t h e o r e t i c a l c a l c u l a t i o n s g i v e s s t r o n g s u p p o r t f o r t h e r e c o n s t r u c t i o n models t h a t a r e a l s o p r e f e r r e d from a m u l t i p l i c i t y of o t h e r e x p e r i m e n t s s u c h a s s c a n n i n g tunneling-microscopy
(STM), t r a n s m i s s i o n - e l e c t r o n - d i f f r a c t i o n
(TED)
and H e a t o m - s c a t t e r i n g . I n t h i s c h a p t e r w e w i l l g i v e a s u r v e y o f t h e ARPES s t u d i e s of semiconductor s u r f a c e s t a t e s by d i s c u s s i n g s e v e r a l o f t h e most w e l l - s t u d i e d s u r f a c e s . E x p e r i m e n t a l s t u d i e s on o t h e r semiconductor s u r f a c e s are summarized i n a compendium and f o r a d i s c u s s i o n of t h e s e r e s u l t s , w e r e f e r t o a r e c e n t , e x t e n s i v e review paper /15/. 2
CHARACTERISTICS OF SEMICONDUCTOR SURFACE STATES A s u r f a c e of a c r y s t a l b r e a k s t h e t h r e e - d i m e n s i o n a l
bulk period-
i c i t y and t h e r e i s an a s s o c i a t e d change i n t h e e l e c t r o n i c s t r u c t u r e . The Bloch states of t h e i n t e r i o r of t h e c r y s t a l have t o b e matched t o s t a t e s d e c a y i n g e x p o n e n t i a l l y from t h e s u r f a c e i f t h e energy i s below t h e vacuum l e v e l . The matching c o n d i t i o n s c a n g i v e rise t o an increase o r decrease i n t h e surface l o c a l density of s t a t e s f o r a c e r t a i n e l e c t r o n e n e r g y . S t a t e s w i t h s i g n i f i c a n t l y i n c r e a s e d amplitude a t t h e s u r f a c e , r e l a t i v e t o t h e p e r i o d i c bulk values, a r e c a l l e d s u r f a c e r e s o n a n c e s . There can a l s o e x i s t new s t a t e s , c a l l e d s u r f a c e s t a t e s , t h a t a r e completely l o c a l i z e d t o t h e s u r f a c e r e g i o n . These a r e e l e c t r o n i c s t a t e s w i t h e n e r g y , E i , and wavevector p a r a l l e l t o t h e s u r f a c e , k,,
,
such t h a t E i (k//)i s w i t h i n a f o r b i d d e n gap o f
t h e b u l k band s t r u c t u r e p r o j e c t e d o n t o t h e s u r f a c e B r i l l o u i n zone. A b a s i c u n d e r s t a n d i n g of s u r f a c e s t a t e s was a l r e a d y o b t a i n e d by
t h e 1 9 3 0 ' s /16,17/ and, d u r i n g t h e l a s t decade i n p a r t i c u l a r ,
there
h a s been a s t r o n g development i n c a l c u l a t i o n a l methods f o r t h e o r e t i c a l s t u d i e s of s u r f a c e e l e c t r o n i c s t r u c t u r e . For a number of semiconductor s u r f a c e s , s e l f - c o n s i s t e n t l y c a l c u l a t e d s u r f a c e e l e c t r o n i c s t r u c t u r e s have now been r e p o r t e d and i n combination w i t h energy-minimization
schemes i t h a s been p o s s i b l e t o c a l c u l a t e t h e
l o w e s t e n e r g y c o n f i g u r a t i o n f o r d i f f e r e n t t y p e s of r e c o n s t r u c t i o n s . T h e band d i s p e r s i o n s Ei (k//)of s u r f a c e s t a t e s and s u r f a c e r e s o n a n c e s from s u c h c a l c u l a t i o n s can b e d i r e c t l y compared w i t h e n e r g y d i s p e r s i o n s o b t a i n e d from ARPES measurements.
147
T h e o r e t i c a l s t u d i e s show t h a t s u r f a c e s t a t e s on semiconductors can o f t e n be d e s c r i b e d a s v e r y l o c a l i z e d bonds a t t h e s u r f a c e s , e . g . d a n g l i n g bond o r back bond s t a t e s . S u r f a c e resonances,
which by
d e f i n i t i o n a r e d e g e n e r a t e w i t h bulk s t a t e s , can on t h e o t h e r hand have a v a r y i n g degree of l o c a l i z a t i o n i n t h e s u r f a c e r e g i o n . There
i s no a b s o l u t e d e f i n i t i o n f o r how s t r o n g s u r f a c e l o c a l i z a t i o n a s t a t e s h o u l d have t o be d e f i n e d a s a s u r f a c e r e s o n a n c e . From t h e e x p e r i m e n t a l p o i n t of view, it i s g e n e r a l l y d i f f i c u l t t o conclude whether a s u r f a c e r e l a t e d photoemission f e a t u r e i s due t o a s u r f a c e s t a t e o r a s t r o n g s u r f a c e resonance, u n l e s s it i s c l e a r where t h e edges of t h e p r o j e c t e d bulk bands a r e . T h i s has i n p r a c t i c e l e d t o t h e f a c t t h a t a c t u a l s u r f a c e resonances i n e x p e r i m e n t a l s t u d i e s a r e o f t e n denoted a s s u r f a c e s t a t e s .
I n t h e p r e v i o u s d e s c r i p t i o n of s u r f a c e s t a t e s / r e s o n a n c e s it was i m p l i c i t l y assumed t h a t t h e s u r f a c e s t a t e band s t r u c t u r e i s charact e r i s t i c of a s u r f a c e w i t h p e r f e c t two-dimensional
periodicity,
i.e.
t h e i n t r i n s i c s u r f a c e s t a t e band s t r u c t u r e . Another important c l a s s of s u r f a c e s t a t e s on semiconductor s u r f a c e s i s t h e d e f e c t - r e l a t e d s u r f a c e s t a t e s . I n t h e c a s e of a low-doped semiconductor w i t h n o
i n t r i n s i c s u r f a c e s t a t e s i n t h e bulk band gap, a small number of d e f e c t s t a t e s i n t h e band gap can have a major e f f e c t on t h e s u r f a c e band bending,
s e e below. During t h e 1 9 7 0 ' s t h e r e were some contro-
v e r s i e s concerning t h e e x i s t e n c e of s u r f a c e s t a t e s i n t h e bulk band gaps of c l e a v e d 1 1 1 - V compound semiconductors. I t was e v e n t u a l l y shown by c a r e f u l s t u d i e s of t h e s u r f a c e F e r m i l e v e l p o s i t i o n on nand p-doped c r y s t a l s t h a t t h e occurrence of s u r f a c e s t a t e s i n t h e gap was r e l a t e d t o d e f e c t s on t h e c l e a v e d s u r f a c e s f o r s e v e r a l of t h e s e semiconductors. Although t h e s e s t u d i e s /18,19/ were made using c o n t a c t p o t e n t i a l d i f f e r e n c e measurements,
it i s possible t o get the
same i n f o r m a t i o n from energy s h i f t s of photoemission s p e c t r a . A d i r e c t o b s e r v a t i o n of photoemission from d e f e c t s t a t e s i s however, i n most c a s e s , n o t p o s s i b l e because t h e d e f e c t d e n s i t y i s t o o low and t h e emission from l o c a l i z e d d e f e c t s w i l l be d i s t r i b u t e d over a l l emission a n g l e s . S u r f a c e s t a t e s i n t h e band gap of semiconductors w i l l a f f e c t t h e p o s i t i o n of t h e Fermi-level
(chemical p o t e n t i a l ) a t t h e s u r f a c e . For
s u r f a c e s w i t h a very high d e n s i t y of s u r f a c e s t a t e s i n t h e gap, t h e Fermi l e v e l can appear pinned a t a c e r t a i n p o s i t i o n i n t h e gap i r r e s p e c t i v e of t h e doping. Concurrent w i t h t h e F e r m i - l e v e l p i n n i n g t h e r e i s a band bending i n t h e n e a r s u r f a c e r e g i o n which depends s t r o n g l y on t h e doping.
148
I n Fig. l ( a ) i s shown a h y p o t h e t i c a l band diagram o f a n n+-doped semiconductor c l o s e t o a s u r f a c e w i t h s u r f a c e s t a t e s i n t h e gap. I f both b u l k and s u r f a c e c o u l d be e l e c t r i c a l l y n e u t r a l t h e energy bands would b e f l a t u p t o t h e s u r f a c e and t h e F e r m i l e v e l of t h e s u r f a c e would be a t t h e s o - c a l l e d n e u t r a l l e v e l Eo. T h i s i s o b v i o u s l y a none q u i l i b r i u m s i t u a t i o n , s i n c e t h e Fermi-level
i s not c o n s t a n t
throughout t h e c r y s t a l . E l e c t r o n s w i l l flow from t h e bulk of t h e c r y s t a l t o t h e s u r f a c e , making t h e s u r f a c e n e g a t i v e l y charged and t h e b u l k c l o s e t o t h e s u r f a c e p o s i t i v e l y charged, r e s u l t i n g i n t h e s i t u a t i o n shown i n F i g . l ( b )
.
I t i s q u i t e s t r a i g h t f o r w a r d t o deduce t h e r e l a t i o n s h i p between
t h e s u r f a c e d e n s i t y of e x c e s s e l e c t r o n s , n s , t h e band bending, VB, and t h e doping c o n c e n t r a t i o n N, / 2 0 / :
n,
=
( 2 c e0
vB N,
(1)
/e)1/2
where K i s t h e s t a t i c d i e l e c t r i c c o n s t a n t of t h e semiconductor. There a r e two o p p o s i t e cases t h a t a r e of p a r t i c u l a r importance f o r ARPES s t u d i e s on semiconductor s u r f a c e s .
The f i r s t c a s e concerns t h e p o s s i b i l i t y of u s i n g h i g h l y doped c r y s t a l s t o s t u d y normally empty s u r f a c e s t a t e s . For c l e a v e d G e ( l l l ) 2 x l s u r f a c e s t h e s i t u a t i o n i s very f a v o r a b l e f o r making ARPES s t u d i e s of s t a t e s above t h e n e u t r a l l e v e l , s i n c e t h e Fermi l e v e l i s known t o be pinned c l o s e t o t h e v a l e n c e band edge. For an n-doping c o n c e n t r a t i o n of lxlO1* cm-3 t h e e x c e s s s u r f a c e charge i s e s t i m a t e d t o be = 3x1Ol2 e l e c t r o n s p e r cm2, which corresponds t o = 0 . 0 0 5 e l e c t r o n s p e r s u r f a c e atom. I n s t u d i e s by N i c h o l l s e t a l . /21/ on
-Ev
F i g . 1. ( a ) H y p o t h e t i c a l band diagram of an n+-doped semiconductor with s u r f a c e s t a t e s i n t h e gap, assuming t h a t both b u l k and s u r f a c e could be n e u t r a l . S h o r t and long l i n e s denote empty and f i l l e d surface s t a t e s , respectively. (b) Band diagram a f t e r e l e c t r o n s have been t r a n s f e r r e d t o t h e s u r f a c e and e q u i l i b r i u m has been e s t a b lished.
149
emission from t h e minimum of t h e a n t i b o n d i n g (almost empty) s u r f a c e
s t a t e band on G e ( l l l ) Z x l , t h i s c o n c e n t r a t i o n of e x c e s s e l e c t r o n s was e a s i l y d e t e c t a b l e . I t can be e s t i m a t e d , t h a t t h e s e n s i t i v i t y of t h e ARPES experiment i s a t l e a s t enough t o d e t e c t = 5 ~ 1 0 -e l~e c t r o n s per s u r f a c e atom f o r e l e c t r o n s i n t h i s almost empty band. The high s e n s i t i v i t y i s p a r t l y due t o t h e s t r o n g a n i s o t r o p y i n emission from t h e m i n i m u m of a s u r f a c e s t a t e band.
i s exemplif i e d by t h e e r r a t i c s h i f t s of ARPES s p e c t r a of moderately doped The second c a s e , f o r which band bending i s important,
semiconductors w i t h no i n t r i n s i c s u r f a c e s t a t e s i n t h e band gap. Small changes i n t h e number of d e f e c t s t a t e s i n t h e gap, a s a r e s u l t of c o n t a m i n a t i o n o r v a r y i n g s u r f a c e t r e a t m e n t s , can sometimes be a problem. Consider f o r example t h e c l e a v e d ( 1 1 0 ) s u r f a c e of a 111-V compound semiconductor l i k e GaAs. For a c r y s t a l with a doping of lXlOl7
~ m a- s~ h i f t of t h e Fermi l e v e l by 0 . 2 eV can be accomplished i . e . of t h e o r d e r of l ~ l O - ~
by 5x1Ol1 s u r f a c e s t a t e s p e r c m 2 ,
e l e c t r o n s p e r s u r f a c e atom. This number i s l a r g e r t h a n t h a t e s t i m a t e d a s t h e s e n s i t i v i t y of ARPES f o r o b s e r v i n g t h e normally empty s u r f a c e band on G e ( l l 1 ) Z x l . However, because of t h e more i s o t r o p i c emission from d e f e c t induced s u r f a c e s t a t e s , t h e s e a r e more d i f f i c u l t t o observe i n a n a n g l e - r e s o l v e d photoemission experiment. S i n c e t h e e x p e r i m e n t a l t e c h n i q u e and t h e p h y s i c s of photoemission a r e d e s c r i b e d i n c h a p t e r s 1 and 2 , we w i l l h e r e o n l y v e r y b r i e f l y i n t r o d u c e t h e b a s i c i d e a s n e c e s s a r y f o r d i s c u s s i n g ARPES s t u d i e s of semiconductor s u r f a c e s t a t e s . I n an AWES experiment, with photons of energy hv, t h e k i n e t i c energy E k i n i s measured f o r e l e c t r o n s e m i t t e d a t an a n g l e Be from t h e s u r f a c e normal. I n t h e absence of i n e l a s t i c s c a t t e r i n g , t h e energy and p a r a l l e l wavevector conserva t i o n f o r p h o t o e l e c t r o n s , e x c i t e d from a s t a t e with i n i t i a l energy E i and p a r a l l e l wavevector ki,/, can be w r i t t e n : Ekin = E i
+
hv - Q
(2)
E; i s d e f i n e d r e l a t i v e t o t h e Fermi l e v e l EF and Q i s t h e semicond u c t o r work f u n c t i o n . S i n c e t h e wavevector of t h e photon u s u a l l y can be n e g l e c t e d i n ARPES experiments, t h e p a r a l l e l wavevector compon e n t , k,,,
i s conserved t o w i t h i n a s u r f a c e r e c i p r o c a l l a t t i c e
v e c t o r G s . The r e l a t i o n s h i p between e m i s s i o n a n g l e and p a r a l l e l wavevector i s given by e q . ( 4 ) .
By m e a s u r i n g t h e k i n e t i c e n e r g y , E k i n , of e l e c t r o n s g i v i n g r i s e t o a c h a r a c t e r i s t i c photoemission f e a t u r e , as f u n c t i o n o f emission a n g l e , Oe, one c a n o b t a i n a d i s p e r s i o n c u r v e E i ( k / / ) . For e m i s s i o n f e a t u r e s which a r e due t o d i r e c t t r a n s i t i o n s i n t h e b u l k , s u c h d i s p e r s i o n c u r v e s w i l l i n g e n e r a l b e photon energy dependent, s i n c e f o r a given k/,-value
t h e r e i s a r a n g e o f i n i t i a l e n e r g i e s from
which d i r e c t t r a n s i t i o n s c a n o c c u r . I n c o n t r a s t , f o r e m i s s i o n f r o m a s u r f a c e s t a t e band t h e d i s p e r s i o n c u r v e o b t a i n e d i s p h o t o n e n e r g y i n d e p e n d e n t a n d t h e ARPES e x p e r i m e n t g i v e s t h e two-dimensional s u r f a c e band s t r u c t u r e , i . e . E i ( k / / ) . I n t h e s t r i n g e n t o n e - s t e p d e s c r i p t i o n o f t h e p h o t o e m i s s i o n pro-
cess it i s n o t p o s s i b l e t o s e p a r a t e t h e e x c i t a t i o n o f t h e e l e c t r o n from t h e t r a n s p o r t t o and t h r o u g h t h e s u r f a c e . I t i s a l s o n e c e s s a r y t o t a k e i n t o a c c o u n t t h e e f f e c t s of e l e c t r o n a n d h o l e l i f e t i m e s when t h e p h o t o e m i s s i o n p r o c e s s i s d e s c r i b e d i n more d e t a i l . A m a j o r consequence of e x t e n d i n g t h e t h e o r y beyond t h e s i m p l e s t t h r e e - s t e p model i s t h e i n t r o d u c t i o n o f mechanisms f o r b r o a d e n i n g i n t h e p h o t o e m i s s i o n s p e c t r a . O f p a r t i c u l a r i m p o r t a n c e i s t h e r e l a x a t i o n of t h e c o n d i t i o n of k l - c o n s e r v a t i o n i n t r a n s i t i o n s c o r r e s p o n d i n g t o e m i s s i o n from b u l k s t a t e s n e a r t h e s u r f a c e . I t i s c l e a r f r o m p h o t o e m i s s i o n s p e c t r a t h a t t h e r e a r e s u c h b r o a d e n i n g mechanisms, which g i v e r i s e t o k , / - r e s o l v e d i n t h e surface region /22/.
e m i s s i o n from t h e d e n s i t y of s t a t e s
T h i s p r e s e n t s a problem when t r y i n g t o
i d e n t i f y e m i s s i o n from s u r f a c e s t a t e s / r e s o n a n c e s i n p h o t o e m i s s i o n s p e c t r a , s i n c e s u c h k / / - r e s o l v e d e m i s s i o n from band e d g e s i n t h e bulk e l e c t r o n i c s t r u c t u r e w i l l a l s o g i v e rise t o photon energy independent d i s p e r s i o n s E i ( k / / ). I t c a n sometimes be d i f f i c u l t t o p r o v e t h a t a c e r t a i n f e a t u r e i n
a p h o t o e m i s s i o n s p e c t r u m i s due t o a s u r f a c e s t a t e / r e s o n a n c e . There
are t h r e e c r i t e r i a o f t e n u s e d t o s u p p o r t t h e i d e n t i f i c a t i o n of e m i s s i o n from s u r f a c e s t a t e s / r e s o n a n c e s : 1) t h e e n e r g y o f t h e o b s e r v e d f e a t u r e l i e s w i t h i n a g a p o f t h e
p r o j e c t i o n o f t h e b u l k band s t r u c t u r e o n t o t h e s u r f a c e B r i l l o u i n zone. 2 ) t h e measured d i s p e r s i o n E i (k//)i s i n d e p e n d e n t o f p h o t o n e n e r g y
3) t h e f e a t u r e i s s e n s i t i v e t o c h e m i s o r p t i o n o f a t o m s o r molecu-
les on t h e s u r f a c e . The f i r s t c r i t e r i o n i s n o r m a l l y ( i n t h e a b s e n c e o f s t r o n g d i f f u s e
151
s c a t t e r i n g ) s u f f i c i e n t f o r i d e n t i f y i n g a s u r f a c e s t a t e , however i n many cases t h e u n c e r t a i n t y i n t h e p o s i t i o n s of t h e bulk band edges
are l a r g e enough t o make i t d i f f i c u l t t o u s e . Furthermore, when emission from band edges can be c o n s i d e r e d a s a p o s s i b i l i t y t o e x p l a i n a f e a t u r e , n e i t h e r of c r i t e r i a 1 and 2 a r e c o n c l u s i v e . We f i n d t h a t t h e u s e of well-ordered
c h e m i s o r p t i o n s y s t e m s t o modify
t h e s u r f a c e e l e c t r o n i c s t r u c t u r e of semiconductor s u r f a c e s i s very v a l u a b l e f o r t h e i d e n t i f i c a t i o n of s u r f a c e s t a t e s and s u r f a c e r e s o n a n c e s . T h e t h i r d c r i t e r i o n must however be used w i t h g r e a t c a r e s i n c e a l s o bulk f e a t u r e s a r e a f f e c t e d by a d s o r p t i o n of atoms o r molecules due t o i n c r e a s e d s c a t t e r i n g of t h e e m i t t e d e l e c t r o n s .
3
CLEAVED S i (111)2x1 AND Ge (111)2x1 SURFACES The c l e a v e d S i ( l l 1 ) and G e ( l l 1 ) s u r f a c e s have been s t u d i e d exten-
s i v e l y w i t h a n g l e - r e s o l v e d photoemission /23-57/
and t h e e l e c t r o n i c
s t r u c t u r e s of t h e s e two s u r f a c e s a r e p r e s e n t l y w e l l u n d e r s t o o d . Both s u r f a c e s a r e b e l i e v e d t o r e c o n s t r u c t a c c o r d i n g t o t h e x-bonded chain model o r i g i n a l l y s u g g e s t e d f o r t h e S i ( l l l ) 2 x l s u r f a c e by Pandey / l l / . F i g . 2 ( a ) shows a schematic view of t h e x-bondei model f o r t h e
G e ( l l l ) 2 x l s u r f a c e a s o b t a i n e d i n c a l c u l a t i o n s g i v i n g t h e geometry w i t h minimum energy / 5 8 / . For both s i l i c o n and germanium t h e recons t r u c t i o n g i v e s rise t o a f i l l e d bonding d a n g l i n g bond band, t h a t is found below t h e v a l e n c e band edge i n ARPES s t u d i e s , and an a n t i bonding dangling-bond band t h a t d i s p e r s e s from t h e conduction band
I
Ge (11112.1
F i g . 2 . ( a ) B a l l and s t i c k model of t h e energy-minimized x-bonded c h a i n geometry f o r G e ( l l l ) 2 x l / 5 8 / . ( b ) S u r f a c e B r i l l o u i n zones f o r t h e diamond-structure ( 1 l l ) l x l and ( 1 1 1 ) Z x l s u r f a c e s .
152
r e g i o n down i n t o t h e a b s o l u t e band gap. I n e a r l y low-energy e l e c t r o n d i f f r a c t i o n (LEED) s t u d i e s by Lander
e t a l . /59/ it was f i r s t found t h a t c l e a v e d S i ( l l 1 ) s u r f a c e s a r e r e c o n s t r u c t e d and e x h i b i t 2x1 LEED p a t t e r n s , b e c a u s e of a d o u b l i n g of t h e u n i t c e l l a l o n g a < Z l l > - d i r e c t i o n . F i g . 2 ( b ) shows t h e shape of t h e s u r f a c e B r i l l o u i n zone f o r b o t h t h e u n r e c o n s t r u c t e d 1x1 and t h e r e c o n s t r u c t e d 2x1 s u r f a c e . There a r e t h r e e e q u i v a l e n t <311>-type d i r e c t i o n s and t h e LEED-pattern i s o f t e n a s u p e r p o s i t i o n of p a t t e r n s from domains o r i e n t e d a l o n g e a c h of t h e s e e q u i v a l e n t d i r e c t i o n s . I n o r d e r t o d e t e r m i n e t h e s u r f a c e s t a t e band s t r u c t u r e w i t h a n g l e r e s o l v e d p h o t o e m i s s i o n it i s e s s e n t i a l t o s t u d y a single-domain s u r f a c e , which can be o b t a i n e d w i t h h i g h p r o b a b i l i t y f o r b o t h S i (111)2x1 and G e (111)2x1 s u r f a c e s by s p e c i a l c l e a v a g e t e c h n i q u e s .
3 . 1 S t u dies o f t h e b o n d i n a d a n a l i n s bond band on S i ( l l l ) 2 x l E a r l y e v i d e n c e f o r s u r f a c e e l e c t r o n i c s t a t e s on t h e c l e a v e d S i ( l l 1 ) - s u r f a c e was o b t a i n e d i n p h o t o e l e c t r i c y i e l d measurements i n t h e p i o n e e r i n g work of A l l e n and Gobeli / 6 0 / .
The f i r s t photo-
e l e c t r o n e n e r g y d i s t r i b u t i o n c u r v e s showing e m i s s i o n from s u r f a c e s t a t e s on t h e c l e a v e d S i ( l l 1 ) s u r f a c e w e r e o b t a i n e d from a n g l e i n t e g r a t e d measurements by Eastman and Grobman / 6 1 / ,
and by Wagner
and S p i c e r / 6 2 / . The same c l e a r e v i d e n c e f o r s u r f a c e s t a t e s n e a r t h e t o p of t h e v a l e n c e band was a l s o o b t a i n e d i n l a t e r a n g l e - i n t e g r a t e d measurements by I b a c h and Rowe / 6 3 , 6 4 / . S i n c e t h e more powerful t e c h n i q u e of a n g l e - r e s o l v e d photoemission was f i r s t a p p l i e d t o t h e c l e a v e d S i ( l l 1 ) s u r f a c e by Rowe e t a l . /23, 2 4 / t h e r e h a s been a l a r g e number o f s t u d i e s o f t h e e l e c t r o n i c
s t r u c t u r e of t h e S i ( l l l ) 2 x l s u r f a c e /25-52/.
Up t o 1981 it seemed
t h a t a l l g r o u p s r e p o r t e d d i f f e r e n t r e s u l t s f o r t h e d i s p e r s i o n of t h e dangling-bond band. I n a review p a p e r by Plummer and E b e r h a r d t / 6 5 / a comparison was made between t h e r e s u l t s of Rowe e t a l . / 2 3 / ,
Parke
e t a l . / 2 5 / , Hansson e t a l . / 3 0 / , Houzay e t a l . /34/, and Himpsel e t a l . /36/.
Since a l l s t u d i e s r e p o r t e d d i f f e r e n t r e s u l t s , t h e s i t u -
a t i o n seemed v e r y c o n f u s e d . One r e a s o n f o r t h e s m a l l o v e r l a p between t h e r e s u l t s of t h e d i f f e r e n t groups is t h a t t h e S i ( l l l ) 2 x l s u r f a c e h a s low symmetry and t h e d i s p e r s i o n was r e p o r t e d f o r i n e q u i v a l e n t directions i n different studies. An u p d a t e d review o f t h e c o n s i s t e n c y of ARPES measurements on
S i ( l l l ) 2 x l s u r f a c e s was g i v e n i n 1983 i n r e f . 43. I t was p o s s i b l e t o b r i n g t o g e t h e r e x p e r i m e n t a l d a t a from Uhrberg e t a l . / 3 1 , 3 8 / ,
153
Himpsel e t a l . /36/,
Houzay e t a l . /34/
,
and Rowe e t a l . /23/ and
form a c o n s i s t e n t p i c t u r e of t h e d a n g l i n g bond band d i s p e r s i o n . F u r t h e r s u p p o r t f o r t h i s d i s p e r s i o n was l a t e r o b t a i n e d i n t h e s t u d i e s by Mirtensson e t a l . / 4 8 /
and Bokor e t a l . / 5 1 / .
Early
d i s p a r a t e r e s u l t s from Parke e t a l . /25/ and Rowe e t a l . /23/ could be e x p l a i n e d a s multidomain e f f e c t s and b u l k c o n t r i b u t i o n s ,
respec-
t i v e l y . The most r e c e n t , d e t a i l e d h i s t o r i c a l review and d i s c u s s i o n
of t h e c o n s i s t e n c y of d i f f e r e n t ARPES s t u d i e s on S i ( l l l ) 2 x l has been given i n r e f . 1 5 . I t w a s concluded t h a t t h e r e i s indeed a l a r g e degree of c o n s i s t e n c y between t h e v a r i o u s ARPES experiments and a p l a u s i b l e e x p l a n a t i o n was a l s o g i v e n f o r a recent d i s p a r a t e r e s u l t /42/.
What h a s been d e s c r i b e d above a s c o n s i s t e n t r e s u l t s on t h e dangl i n g bond d i s p e r s i o n of c o u r s e c o n t a i n some v a r i a t i o n i n t h e d e t a i l s of t h e r e p o r t e d d i s p e r s i o n s . The bandwidth of t h e d a n g l i n g bond band v a r i e s between 0 . 6 and 0 . 8 eV, which, a t l e a s t p a r t i a l l y ,
is a
r e s u l t of d i f f e r e n t a n g u l a r r e s o l u t i o n s . The a b s o l u t e p o s i t i o n of t h e band v a r i e s by 0 . 2 5 eV between extreme c a s e s , which can be r e l a t e d t o u n c e r t a i n t i e s i n t h e e x p e r i m e n t a l l y determined Fermi l e v e l (EF) p o s i t i o n combined w i t h v a r i a t i o n s of t h e p i n n i n g p o s i t i o n of EF a t t h e s u r f a c e . An example of t h e agreement between d i f f e r e n t experiments, t h a t o r i g i n a l l y were i n t e r p r e t e d q u i t e d i f f e r e n t l y , i s shown i n F i g . 3 . Angle-resolved p h o t o e l e c t r o n s p e c t r a p r o b i n g t h e e l e c t r o n i c s t r u c -
t u r e a l o n g t h e long a x i s ,
r-j,
of t h e s u r f a c e B r i l l o u i n zone (SBZ)
a r e shown i n F i g . 3a (from r e f . 3 8 ) . The dominating s t r u c t u r e A has a s t r o n g energy d i s p e r s i o n w i t h maximum energy a t a p o l a r a n g l e of approximately 45O,
which corresponds t o emission from s t a t e s a t t h e
SBZ boundary f o r t h e photon energy used ( 1 0 . 2 e V ) . f o r emission from s t a t e s a l o n g t h e r - j - l i n e
Similar r e s u l t s
have a l s o been o b t a i n e d
i n t h e s t u d i e s by Houzay e t a l . / 4 2 / and MBrtensson e t a l . / 4 8 / . I n F i g . 3b some e a r l i e r photoemission r e s u l t s from t h e work by
Himpsel e t a l . / 3 6 / a r e shown. The s u r f a c e s t a t e emission was i n t h i s c a s e o b t a i n e d a s t h e d i f f e r e n c e between s p e c t r a from t h e c l e a n 2x1 r e c o n s t r u c t e d s u r f a c e and s p e c t r a from t h e hydrogen exposed
1x1-H s u r f a c e . Besides t h e s t r o n g upwards d i s p e r s i o n found along t h e r-j-line
t h e r e i s a weak downwards d i s p e r s i o n a l o n g t h e i=’-J’-line.
I n t h e o r i g i n a l p a p e r by Himpsel e t a l . / 3 6 / it w a s proposed t h a t t h e s u r f a c e s t a t e peak was a s u p e r p o s i t i o n of emission c o n t r i b u t i o n s from two f l a t bands and t h a t i n t e n s i t y v a r i a t i o n s l e d t o an apparent
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Fig. 3. ( a ) ARPES s p e c t r a probing t h e s u r f a c e e l e c t r o n i c s t r u c t u r e along t h e f-3 symmetry l i n e i n t h e 2 x 1 S B Z . Peak A and shoulder A ' are surface s t a t e contributions / 3 8 / . ( b ) ARPES d i f f e r e n c e s p e c t r a between c l e a n and hydrogen expose_d S i ( l l l ) 2 x l s u r f a c e s / 3 6 / . S u r f a c e s t a t e s a r e probed along t h e T-J and symmetry l i n e s . From r e f . 5 0 . ( c ) Comparison between experimental and t h e o r e t i c a l / l o / r e s u l t s f o r t h e s u r f a c e s t a t e d i s p e r s i o n on S i ( l l 1 ) Z x l . Data p o i n t s 0 , 0 from Uhrberg e t a l . / 3 8 / and m , D from Himpsel et a l . / 3 6 / have been From r e f . 5 0 . s h i f t e d -- 0 . 1 5 e V upwards r e l a t i v e t o E,.
r-3'
band d i s p e r s i o n . This s u g g e s t i o n s t i m u l a t e d a l o t of d i s c u s s i o n concerning c o r r e l a t i o n e f f e c t s and t h e v a l i d i t y of t h e s i n g l e p a r t i c l e i n t e r p r e t a t i o n of photoemission from s u r f a c e s t a t e bands /66-68/.
Regardless of t h e ambiguity i n t h e e v a l u a t i o n of t h e d a t a ,
155
it was c l e a r t h a t any c a l c u l a t e d s u r f a c e s t a t e bands f o r t h e , a t t h a t t i m e , w e l l e s t a b l i s h e d b u c k l i n g model /69/ could not e x p l a i n t h e photoemission r e s u l t s . The i d e n t i f i c a t i o n of s t r u c t u r e A a s a s u r f a c e s t a t e i s c l e a r s i n c e it d i s p e r s e s f a r i n t o t h e gap of t h e p r o j e c t i o n of t h e bulk bands. I n F i g . 3c t h e d i s p e r s i o n of t h e s u r f a c e s t a t e band i s shown r e l a t i v e t o t h e edge of t h e p r o j e c t e d bulk v a l e n c e bands. The d a t a p o i n t s a r e from Uhrberg e t a l . /38/ and Himpsel e t a l . / 3 6 / , and t h e i n c l u d e d t h e o r e t i c a l s u r f a c e s t a t e band d i s p e r s i o n i s from a c a l c u l a t i o n by Pandey u s i n g an energy-minimized v e r s i o n of h i s a-bonded c h a i n model /11,70/. There was a b r e a k t h r o u g h i n t h e u n d e r s t a n d i n g of t h e S i (111)2x1 s u r f a c e , when Pandey, a f t e r i n v e s t i g a t i n g many different possible surface reconstructions,
proposed t h e new 71-
bonded c h a i n model. The e l e c t r o n i c s t r u c t u r e of t h i s model was found t o be c o n s i s t e n t with t h e e x p e r i m e n t a l r e s u l t s of Himpsel e t a l .
/36/, i f t h e main photoemission peak was a s s o c i a t e d w i t h a s t r o n g l y d i s p e r s i n g band i n s t e a d of two almost f l a t bands w i t h i n t e n s i t y v a r i a t i o n s . The e x i s t e n c e of a h i g h l y d i s p e r s i v e s u r f a c e s t a t e band
was f i n a l l y proven by Uhrberg e t a l . /38/ through an a n a l y s i s of t h e s u r f a c e s t a t e peak width and d i s p e r s i o n i n h i g h - r e s o l u t i o n ARPES s p e c t r a l i k e t h e ones i n F i g . 3 a . A s seen i n F i g . 3c, t h e r e i s very good agreement between t h e o r y and experiment concerning t h e shape of t h e d i s p e r s i o n of t h e s u r f a c e s t a t e band. The s t r o n g p o s i t i v e d i s p e r s i o n found i n t h e o u t e r h a l f of t h e ?->-line f o r t h e u n d e r s t a n d i n g of t h e 2 x l - r e c o n s t r u c t i o n ,
i s very s i g n i f i c a n t s i n c e o u t of t h e
many models i n v e s t i g a t e d , o n l y t h e x-bonded c h a i n model has r e s u l t e d i n t h i s k i n d of d i s p e r s i o n .
Besides t h e main s u r f a c e s t a t e band, t h e r e i s a s m a l l f e a t u r e A '
i n F i g . 3a, t h a t has been a s s i g n e d t o a s u r f a c e s t a t e . The energy of t h i s f e a t u r e i s w i t h i n t h e p r o j e c t e d bulk band gap n e a r t h e j - p o i n t a s shown i n F i g . 3 c . The weak s h o u l d e r h a s v e r y c o n s i s t e n t l y been reported near t h e %point i n
d i f f e r e n t studies /36,38,42,48/.
The
o r i g i n of t h i s emission was a p o i n t of c o n t r o v e r s y f o r some t i m e . Himpsel e t a l . /36/ s u g g e s t e d t h a t t h e emission was from t h e same s u r f a c e s t a t e band a s i s seen i n t h e normal d i r e c t i o n . This w a s r u l e d o u t by Uhrberg e t a l . / 3 8 / who proposed t h a t emission from secondary domains, t h a t were r o t a t e d by f 120
r e l a t i v e t o t h e main
domain, was s t r o n g enough t o be s e e n . I t had been found t h a t m u l t i domain c l e a v e s gave a peak a t t h e same energy and a n g l e s a s t h e c o n t r o v e r s i a l s h o u l d e r . Although it i s d i f f i c u l t t o r u l e o u t t h i s
156
e x p l a n a t i o n , t h e above mentioned c o n s i s t e n c y of t h e i n t e n s i t y of t h e s h o u l d e r i n d i c a t e s t h a t it i s a f e a t u r e c h a r a c t e r i s t i c of a s i n g l e domain c l e a v e . An e x p l a n a t i o n of t h i s second s u r f a c e s t a t e w i t h i n t h e K-bonded c h a i n model h a s been s u g g e s t e d through t h e o r e t i c a l c a l c u l a t i o n s by S e l l o n i and B e r t o n i /71/,
who found a second s u r f a c e
s t a t e / r e s o n a n c e l o c a t e d below t h e d a n g l i n g bond band a t k / / - p o i n t s close t o
3.
Through t h e y e a r s t h e r e have been s e v e r a l f u r t h e r s u g g e s t i o n s t h a t backbond s u r f a c e s t a t e s / r e s o n a n c e s have been d e t e c t e d i n ARPES experiments on S i ( l l l ) 2 x l s u r f a c e s /24,25,30,36,37/.
The main
s u p p o r t f o r t h e s e s u g g e s t i o n s have been e i t h e r an e x p e r i m e n t a l l y determined l a r g e contamination s e n s i t i v i t y o r agreement w i t h some c a l c u l a t e d backbond s t a t e d i s p e r s i o n s . However no c o n c l u s i v e evidence f o r t h e s e backbond resonances have been p r e s e n t e d . Since emission from bulk d i r e c t t r a n s i t i o n s h a s been shown t o be both i n t e n s e and contamination s e n s i t i v e /45/,
we f i n d it q u e s t i o n a b l e
whether any t r u e backbond s u r f a c e resonance was i d e n t i f i e d i n t h e s e s t u d i e s on t h e c l e a v e d S i ( l l l ) 2 x l s u r f a c e . I t c e r t a i n l y would be very h e l p f u l t o have a d e t a i l e d c a l c u l a t i o n of where t o e x p e c t backbond s u r f a c e s t a t e s w i t h i n t h e x-bonded
c h a i n model.
3 . 2 S t u di e s of t h e bo n d i n s d a n a l i n a bond ba nd on G e ( l l l ) 2 x l Evidence f o r s u r f a c e e l e c t r o n i c s t a t e s on t h e c l e a v e d G e ( l l 1 ) s u r f a c e was f i r s t found i n p h o t o e l e c t r i c y i e l d measurements on d i f f e r e n t l y doped germanium c r y s t a l s / 7 2 / .
Independent of doping,
t h e Fermi l e v e l was pinned c l o s e t o t h e v a l e n c e band edge and two groups of s u r f a c e s t a t e s j u s t below and above t h e v a l e n c e band maximum were c o n s i d e r e d t o be r e s p o n s i b l e f o r t h e observed p i n n i n g of t h e Fermi l e v e l . P h o t o e l e c t r o n s p e c t r a c l e a v e d germanium,
(angle-integrated)
from
showing emission from s u r f a c e s t a t e s , were f i r s t
r e p o r t e d by Eastman and Grobman / 6 1 / .
They found a 0 . 7 eV wide
s u r f a c e s t a t e band c e n t e r e d a t about 0 . 7 5 eV below t h e valence band edge. A s i m i l a r s u r f a c e s t a t e d i s t r i b u t i o n was l a t e r observed by Murotani e t a l . /73/ and Rowe / 1 4 / .
Rowe a l s o i d e n t i f i e d f o u r more
s t r u c t u r e s a s i n t r i n s i c s u r f a c e s t a t e f e a t u r e s . However, no f i r m support f o r t h i s i d e n t i f i c a t i o n w a s presented. The f i r s t ARPES s t u d y of t h e c l e a v e d G e ( l l l ) 2 x l s u r f a c e w a s r e p o r t e d by N i c h o l l s e t a l . / 5 3 / . They used photons i n t h e range 7.4-11.6
eV,
and i n accordance w i t h t h e S i ( l l l ) 2 x l s u r f a c e t h e
dominating s t r u c t u r e i n t h e s p e c t r a corresponds t o a h i g h l y d i s p e r s i v e d a n g l i n g bond s t a t e . The d i s p e r s i o n , E i ( k / / ) , was s t u d i e d along
157
- - -
the r-J-K-r-lines
i n t h e s u r f a c e BZ a n d c o n s i s t e n t r e s u l t s w e r e
o b t a i n e d for t h e t h r e e d i f f e r e n t photon e n e r g i e s used ( 8 . 6 , 10.2, and 11.0 eV)
.
I n a s t u d y o f t h e A-bonded c h a i n model o f t h e G e ( l l 1 ) Z x l s u r f a c e by N o r t h r u p a n d Cohen / 5 8 / ,
t h e y compared t h e c a l c u l a t e d d i s p e r s i o n
of t h e d a n g l i n g bond band w i t h t h e e x p e r i m e n t a l r e s u l t s from r e f . 53 a n d f o u n d good a g r e e m e n t c o n c e r n i n g t h e s h a p e o f t h e d i s p e r s i o n , w h i l e the a b s o l u t e energy w a s about 0 . 8 e V t o o high.
S i n c e t h e y used
t h e l o c a l - d e n s i t y a p p r o x i m a t i o n , which does n o t c a l c u l a t e removal
e n e r g i e s , such a d i s c r e p a n c y i n t h e a b s o l u t e energy is r e a s o n a b l e . The s i m i l a r i t y i n t h e s h a p e o f t h e d i s p e r s i o n s was c o n s i d e r e d a s
s t r o n g s u p p o r t f o r t h e x-bonded
c h a i n model.
The a p p l i c a b i l i t y o f t h e A-bonded c h a i n model w a s l a t e r q u e s t i o n -
ed when c o n f l i c t i n g ARPES r e s u l t s were o b t a i n e d by S o l a l e t a l . /55/ u s i n g p h o t o n e n e r g i e s i n t h e r a n g e 35-50 e V . A s i g n i f i c a n t l y d i f f e r e n t d i s p e r s i o n was p r e s e n t e d a l o n g t h e f - j - l i n e
w i t h a measured
b a n d w i d t h o f o n l y 0 . 2 5 e V compared t o 0 . 7 5 e V i n r e f . 5 3 . Although
it h a d b e e n r e p o r t e d i n r e f . 53 t h a t 2 0 . 5 e V of t h i s d i s p e r s i o n w a s o b s e r v e d w i t h i n t h e p r o j e c t e d b u l k band g a p , it was c l a i m e d by S o l a l
e t a l . t h a t b u l k c o n t r i b u t i o n s i n t h e s p e c t r a c o u l d have i n f l u e n c e d t h e m e a s u r e d v a l u e f o r t h e d a n g l i n g bond d i s p e r s i o n . S i n c e t h e d i s p e r s i o n o f s u r f a c e s t a t e s s h o u l d be independent o f t h e photon e n e r g y , it was i m p o r t a n t t o d e t e r m i n e w h e t h e r t h e o b s e r v e d d i f f e r e n c e s were s t i l l d u e t o t h e d i f f e r e n t p h o t o n e n e r g i e s u s e d . F u r t h e r ARPES s t u d i e s on t h e G e ( l l l ) 2 x l s u r f a c e were t h u s c a r r i e d o u t w i t h r e s o n a n c e r a d i a t i o n o f 1 6 . 8 a n d 2 1 . 2 eV-photon s y n c h r o t r o n r a d i a t i o n of 2 1 . 2 ,
e n e r g y and w i t h
3 2 . 0 , a n d 3 5 . 0 eV-photon
e n e r g y by
Nicholls et a l . /56/. A summary o f t h e d i f f e r e n t e x p e r i m e n t a l r e s u l t s f o r t h e d a n g l i n g
bond b a n d d i s p e r s i o n a l o n g t h e f - 3 - l i n e
i s given i n F i g . 4 (from
r e f . 5 6 ) . The s o l i d c u r v e shows t h e ARPES peak p o s i t i o n i n t h e
e a r l i e s t 10.2-eV d a t a , w h i l e t h e crosses w e r e o b t a i n e d by a n a l y z i n g t h e p e a k p o s i t i o n i n d i f f e r e n c e s p e c t r a o b t a i n e d by s u b t r a c t i n g
spectra f o r a h y d r o g e n e x p o s e d s u r f a c e f r o m s p e c t r a f o r t h e c l e a n s u r f a c e . The o p e n c i r c l e s show t h e d i s p e r s i o n m e a s u r e d b y S o l a l e t
a l . /55/,
w h i l e t h e s q u a r e s a n d f i l l e d c i r c l e s are f r o m r e f . 5 6 . A s
s e e n i n F i g . 4 t h e d i s p e r s i o n o b t a i n e d by S o l a l e t a l . i s much
smaller t h a n t h a t o b t a i n e d i n t h e o t h e r s t u d i e s , i n p a r t i c u l a r o n e c a n n o t e t h a t t h e a g r e e m e n t b e t w e e n t h e t w o s t u d i e s u s i n g 35-eV p h o t o n e n e r g y i s v e r y p o o r . One d i f f e r e n c e b e t w e e n t h e two 35-eV s t u d i e s , which m i g h t be s i g n i f i c a n t ,
is t h a t the dispersion was
158
-
2
+
10.2 Diff. spectra
0
35 Sclal e t a1
I
Y
W
g L w
O
m
u > W CL
Z, -0.5
-t L
a
z
-1 .o
5
F
F i g . 4 . Comparison between e x p e r i m e n t a l r e s u l t s /_53,55,56/ f o r t h e d a n g l i n g bond d i s p e r s i o n on G e ( l l l ) 2 x l a l o n g t h e T-J symmetry l i n e . From r e f . 5 6 . measured a t room t e m p e r a t u r e d i r e c t l y a f t e r c l e a v a g e i n r e f . 56, w h i l e i n t h e s t u d y by S o l a l e t a l . t h e sample w a s c o o l e d t o 20 K a f t e r c l e a v a g e . T h i s c o u l d , a t l e a s t i n p r i n c i p l e , lead t o temperat u r e dependent changes i n t h e e l e c t r o n i c s t r u c t u r e o r t o a higher l e v e l of c o n t a m i n a t i o n t h a t would e f f e c t t h e d a n g l i n g bond dispersion. I n t h e room t e m p e r a t u r e s t u d i e s r e p o r t e d i n r e f s . 5 3 and 56 t h e r e
i s a s m a l l d e c r e a s e i n t h e measured d i s p e r s i o n w i t h i n c r e a s i n g photon energy. This r e f l e c t s a d e c r e a s e i n t h e k,,-resolution,
as
t h e k i n e t i c e n e r g y o f t h e e m i t t e d e l e c t r o n s i n c r e a s e , which w a s d i s c u s s e d i n some d e t a i l i n r e f . 5 6 . To summarize, t h e d i s p e r s i o n o f t h e f i l l e d d a n g l i n g bond band on t h e G e ( l l l ) 2 x l s u r f a c e h a s been s t u d i e d f o r a wide r a n g e of p h o t o n e n e r g i e s . F o r room t e m p e r a t u r e s t u d i e s t h e r e s u l t s are v e r y c o n s i s t e n t , g i v i n g a s t r o n g l y d i s p e r s i n g d a n g l i n g bond band i n good a g r e e m e n t w i t h c a l c u l a t i o n s u s i n g t h e x-bonded
c h a i n model /50/.
3 . 3 2 an-na
d-nu
b
m band on G e a n d SifU.l)-&l
A c c o r d i n g t o t h e c a l c u l a t i o n s of t h e e l e c t r o n i c s t r u c t u r e of t h e x-bonded c h a i n model t h e d a n g l i n g bond s t a t e s s h o u l d form o n e f i l l e d ( b o n d i n g ) a n d one empty ( a n t i b o n d i n g ) d a n g l i n g bond b a n d on t h e
159
n e u t r a l G e and S i ( l l l ) 2 x l s u r f a c e s .
As w a s d i s c u s s e d i n S e c t i o n 2 ,
it i s p o s s i b l e t o occupy p a r t s of s u c h a n empty band by u s i n g h i g h l y n-doped c r y s t a l s . The f i r s t ARPES s t u d y o f t h i s t y p e w a s m a d e by N i c h o l l s e t a l . / 5 7 / u s i n g h i g h l y n-doped G e ( l l l ) 2 x l s a m p l e s . F o r t h e d o p i n g l e v e l u s e d ( = 1 ~ 1 0 ~~ r8 n - ~ S, b ) t h e e s t i m a t e d o c c u p a t i o n l e v e l of t h e almost empty b a n d i s 0 . 0 0 5 e l e c t r o n s p e r s u r f a c e atom,
i . e . 0 . 5 % o f t h e almost empty band f o r t h e 2x1 r e c o n s t r u c t e d s u r f a c e w i l l be o c c u p i e d a t t h e band minimum. High r e s o l u t i o n ARPES s p e c t r a , p r o b i n g t h e e l e c t r o n i c s t r u c t u r e o f a h i g h l y n-doped G e ( l l l ) 2 x l s a m p l e a l o n g t h e T - z - l i n e t h e 3-point,
a r e shown i n F i g . 5a (hv
=
close t o 10.2 e V ) / 5 7 / . I n a very
limited a n g u l a r range around t h e j - p o i n t
a s h a r p f e a t u r e , B,
s p o n d i n g t o e m i s s i o n from t h e a n t i b o n d i n g band, level.
corre-
i s s e e n a t t h e Fermi
I n t h e s a m e a n g u l a r r a n g e t h e f i l l e d d a n g l i n g bond band, A,
i s a t i t s maximum e n e r g y . A t = 0 . 9 e V below EF, t h e r e i s a s m a l l shoulder,
similar t o t h e shoulder seen a t t h e 3-point
s p e c t r a f r o m S i ( l l l ) 2 x l . The s t r o n g p e a k ,
-1.6
eV,
i n ARPES
seen i n a l l s p e c t r a near
i s due t o t r a n s i t i o n s i n t h e b u l k .
The i n t e n s i t y o f e m i s s i o n from t h e two s u r f a c e s t a t e b a n d s h a s a v e r y s t r o n g p o l a r i z a t i o n dependence. t w o 3-points,
I n F i g . 5b, s p e c t r a a and d,
on o p p o s i t e s i d e s of t h e s u r f a c e normal
(see i n s e t i n
F i g . S a ) , a r e p r o b e d w i t h l i g h t i n c i d e n t a t 60° f r o m t h e s u r f a c e n o r m a l . I n s p e c t r u m c, e m i s s i o n f r o m t h e 3 - p o i n t
w a s obtained with
8 i = Oo a n d t h e e m i s s i o n from b o t h t h e f i l l e d a n d t h e a l m o s t empty b a n d i s v e r y much r e d u c e d , which i s c o n s i s t e n t w i t h t h e e x p e c t e d p o l a r i z a t i o n d e p e n d e n c e o f b o n d i n g and a n t i b o n d i n g n - s t a t e s
w i t h pz-
c h a r a c t e r . S p e c t r a b and e i n F i g . 5b show t h e e f f e c t on t h e s u r f a c e
s t a t e e m i s s i o n o f moderate e x p o s u r e s t o e x c i t e d hydrogen, a f t e r which t h e s u r f a c e s t i l l e x h i b i t e d a 2x1 LEED p a t t e r n . T h e r e a r e p r a c t i c a l l y no e l e c t r o n s r e m a i n i n g i n t h e a n t i b o n d i n g band a n d t h e bonding state emission i s s i g n i f i c a n t l y reduced, while t h e bulk emission i s l a r g e l y unaffected.
I n F i g . 5c t h e experimentally o b t a i n e d d i s p e r s i o n s / 5 1 / f o r t h e f i l l e d a n d a l m o s t empty s u r f a c e s t a t e b a n d s a r e shown t o g e t h e r w i t h t h e b a n d s c a l c u l a t e d f o r t h e n-bonded c h a i n model / 5 0 / .
The measured
d i s p e r s i o n o f t h e f i l l e d d a n g l i n g - b o n d b a n d ( A ) i s t h e same as found i n e a r l i e r s t u d i e s on undoped a n d l i g h t l y n-doped c r y s t a l s / 5 3 , 5 6 / . The o b s e r v e d s u r f a c e s t a t e band g a p ( 0 . 5 e V ) i s i n v e r y good a g r e e m e n t w i t h t h e band g a p f o u n d i n a b s o r p t i o n e x p e r i m e n t s w i t h p h o t o t h e r m a l d i s p l a c e m e n t s p e c t r o s c o p y ( 0 . 5 e V ) / 7 5 / and o p t i c a l
160
......
.................. ......
-2 -1 0 ENERGY BELOW E,
(eV)
P
3
r-j
F i g 5. ( a ) Photoemissi.on s p e c t r a probing t h e symmetry l i n e f o r t h e ( 1 1 1 ) 2 x 1 s u r f a c e of a h i g h l y n-doped Ge-crystal / 5 1 / . Peaks A and €3 correspond t o t h e bonding and anti-bonding d a n g l i n g bond band, r e s p e c t i v e l y . hv = 1 0 . 2 eV. b ) S e l e c t e d ARPES s p e c t r a showing t h e p o l a r i z a t i o n dependence and contamination s e n s i t i v i t y of photoemission from t h e bonding and anti-bonding s u r f a c e s t a t e s on G e ( l l l ) 2 x l / 5 7 / . c ) Comparison between t h e measured s u r f a c e s t a t e d i s p e r s i o n s / S 7 / and t h o s e c a l c u l a t e d f o r t h e n-bonded c h a i n model of t h e G e ( l l l ) 2 x l s u r f a c e / 5 8 / . From Ref. 5 7 . II
r e f l e c t i v i t y ( 0 . 5 eV) / 1 6 / and t h e agreement between t h e observed band gap v a l u e s i m p l i e s t h a t p o s s i b l e e x c i t o n i c e f f e c t s a r e q u i t e small i n t h e a b s o r p t i o n experiments. There a r e s t r o n g s i m i l a r i t i e s between t h e measured d i s p e r s i o n s and t h o s e c a l c u l a t e d f o r t h e
x-
bonded chain model concerning t h e shape of t h e f i l l e d (bonding) band and t h e p o s i t i o n i n k l l - s p a c e of t h e minimum of t h e antibonding band. The agreement between experiment and t h e o r y i s q u i t e s a t i s f a c t o r y s i n c e t h e underestimation of t h e band gap and t h e e r r o r i n a b s o l u t e p o s i t i o n of t h e f i l l e d band can be expected /ll/ a s t h e l o c a l - d e n s i t y approximation was used i n t h e c a l c u l a t i o n . The p r e s e n t photoemission experiments a r e a l s o c o n s i s t e n t with a number of p r e v i o u s s t u d i e s using s u r f a c e c o n d u c t i v i t y , Kelvin probe, and photoemission y i e l d measurements on d i f f e r e n t l y doped G e c r y s t a l s , which have shown t h a t t h e Fermi l e v e l i s pinned c l o s e t o
161
t h e valence-band
edge a t t h e s u r f a c e independent o f t h e doping. For
h e a v i l y p-doped
s a m p l e s , t h e b a n d s are f l a t up t o t h e s u r f a c e , w h i l e
f o r h e a v i l y n-doped
samples t h e bands are b e n t upwards. S i n c e t h e
g a p b e t w e e n t h e b u l k v a l e n c e band a n d t h e a n t i b o n d i n g s u r f a c e s t a t e band i s 5 0 . 1 e V , d e f e c t induced v a r i a t i o n s i n t h e Fermi level p o s i t i o n a c r o s s t h e s u r f a c e are l i m i t e d t o t h i s narrow energy r a n g e . T h i s c o u l d b e t h e r e a s o n why ARPES s p e c t r a f r o m t h e G e ( l l l ) 2 x l s u r f a c e h a v e b e e n f o u n d t o be s i g n i f i c a n t l y b e t t e r r e s o l v e d t h a n f r o m t h e S i ( l l l ) 2 x l s u r f a c e . I n s t u d i e s o f t h e a n t i b o n d i n g band on t h e S i ( l l l ) 2 x l s u r f a c e by M a r t e n s s o n e t a1 / 4 8 / ,
t h e minimum o f t h e
empty s u r f a c e s t a t e band was f o u n d t o be = 0 . 4 e V a b o v e t h e v a l e n c e b a n d e d g e , p e r m i t t i n g a l a r g e r d e f e c t i n d u c e d v a r i a t i o n of t h e Fermi l e v e l p o s i t i o n over t h e cleaved s u r f a c e . I n summary, ARPES s t u d i e s o n t h e S i a n d G e ( l l l ) 2 x l s u r f a c e s have p r o v e n t h e e x i s t e n c e o f a f i l l e d d a n g l i n g bond band w i t h a s t r o n g d i s p e r s i o n s e p a r a t e d by a = 0 . 5 e V band g a p from a n a n t i b o n d i n g d a n g l i n g bond b a n d . T h e r e i s a l s o s t r o n g s u p p o r t f o r t h e i d e n t i f i c a t i o n of a weak s t r u c t u r e n e a r
5
(A')
as an i n t r i n s i c s u r f a c e
s t a t e . T h e s e f e a t u r e s a r e a l l c o n s i s t e n t w i t h r e s u l t s from c a l c u l a t i o n s o f t h e e l e c t r o n i c s t r u c t u r e s f o r t h e n-bonded
chain
model f o r b o t h s u r f a c e s . 4
ANNEALED (111) SURFACES OF S i AND G e I t i s p o s s i b l e t o p r e p a r e c l e a n Si a n d G e ( l l 1 ) s u r f a c e s by therm-
a l o r laser a n n e a l i n g such t h a t s m a l l areas of t h e s u r f a c e s e x h i b i t v a r i o u s r e c o n s t r u c t i o n s . I n scanning-tunneling-microscopy
studies,
e x t e n d e d a r e a s w i t h 7x7, 2x1, and 2x2 symmetry h a v e b e e n r e p o r t e d f o r t h e S i ( l l 1 ) s u r f a c e , as w e l l a s s i n g l e u n i t c e l l s e x h i b i t i n g 5x5,
9x9, 2x2, ~ ( 4 x 2 )a n d 43x43 symmetry /78-80/.
The G e ( l l 1 ) s u r -
f a c e h a s b e e n o b s e r v e d h a v i n g r e g i o n s w i t h 7x7, c ( 4 x 2 ) , c ( 2 ~ 8 and ) ~ 2x2 symmetry / 8 0 / .
F o r p r e p a r a t i o n of macroscopic s u r f a c e s needed
f o r e . g . p h o t o e m i s s i o n a n d LEED s t u d i e s , i t i s r e l a t i v e l y e a s y t o o b t a i n S i ( l l 1 ) s u r f a c e s w i t h 7x7 a n d q u a s i - 1 x 1 symmetry a n d G e ( l l 1 ) s u r f a c e s w i t h ~ ( 2 x 8 )symmetry. I n t h e f o l l o w i n g s e c t i o n s w e summar i z e t h e e x p e r i m e n t a l r e s u l t s f o r ARPES s t u d i e s on t h e S i ( 1 1 1 ) 7 x 7 a n d G e ( l l l ) - c ( 2 x 8 ) s u r f a c e s . F o r a more e x t e n s i v e r e v i e w i n c l u d i n g a d i s c u s s i o n o f t h e r e s u l t s on q u a s i - 1 x 1 s u r f a c e s w e r e f e r t o r e f . 1 5 .
162
4 . 1 %far.!
s t a t e s on t h e S i ( l l 1 ) 7x1 s u r m
The most s t a b l e r e c o n s t r u c t i o n o f t h e S i ( l l 1 ) s u r f a c e h a s a 1x7 s u r f a c e u n i t c e l l , i . e . t h e u n i t c e l l i s 4 9 t i m e s l a r g e r t h a n on a h y p o t h e t i c a l i d e a l , u n r e c o n s t r u c t e d , 1x1 s u r f a c e . The 1x7 recons t r u c t i o n i s o b t a i n e d by a n n e a l i n g a c l e a n S i ( l l 1 ) s u r f a c e , where t h e d e t a i l s o f t h e a n n e a l i n g p r o c e d u r e t h a t i s needed, depend on whether t h e c l e a n s u r f a c e h a s been o b t a i n e d by c l e a v i n g , s p u t t e r i n g o r heat c l e a n i n g . Ever s i n c e t h e 7x7 r e c o n s t r u c t i o n w a s f i r s t o b s e r v e d i n LEED-experiments by S c h l i e r and Farnsworth i n 1 9 5 9 /81/ it h a s been a c h a l l e n g e f o r s u r f a c e s c i e n t i s t s t r y i n g t o u n d e r s t a n d semiconductor s u r f a c e r e c o n s t r u c t i o n s , and it i s c e r t a i n l y one of t h e most e x t e n s i v e l y s t u d i e d s u r f a c e s b o t h e x p e r i m e n t a l l y and theoretically. A l a r g e number of models h a s been proposed t o e x p l a i n t h e a v a i l able e x p e r i m e n t a l d a t a , b u t none o f t h e s u g g e s t e d models c o u l d be c o n s i d e r e d a s r e l i a b l e , u n t i l Takayanagi e t a l . / 8 2 / proposed a model f o r t h e 1x7 r e c o n s t r u c t i o n based on r e s u l t s from t r a n s m i s s i o n e l e c t r o n d i f f r a c t i o n experiments. This model, r e f e r r e d t o a s t h e DAS (dimer, adatom, s t a c k i n g - f a u l t ) model, a l s o a c c o u n t s f o r STM, ions c a t t e r i n g and X-ray d i f f r a c t i o n d a t a / 8 3 - 8 8 / . I n t h e model t h e r e are 1 2 adatoms, 6 r e s t atoms, 9 dimers and one c o r n e r h o l e per s u r f a c e u n i t c e l l , and i n one h a l f o f t h e u n i t c e l l t h e r e is a s t a c k i n g fault. S i n c e t h e 1x7 s u r f a c e i s s o complex one might imagine t h a t t h e r e would be many d i f f e r e n t s u r f a c e s t a t e s c o r r e s p o n d i n g t o t h e h i g h number o f i n e q u i v a l e n t atoms i n t h e s u r f a c e u n i t c e l l . Furthermore, t h e l a r g e s i z e of t h e u n i t c e l l w i l l l e a d t o a l a r g e number of bands even f o r e q u i v a l e n t s u r f a c e atoms. E . g . , i f an i d e a l 1x1 s u r f a c e w a s t r e a t e d a s a s u r f a c e w i t h 1x7 p e r i o d i c i t y , t h e r e would be 4 9 dangl i n g bond bands i n t h e s m a l l 7x1 s u r f a c e B r i l l o u i n zone and t h e s e bands would form a c o n t i n u o u s d e n s i t y o f s u r f a c e s t a t e s t h a t i s h a l f - f i l l e d . For a r e c o n s t r u c t e d 7x1 s u r f a c e t h e l o w e r i n g o f t h e symmetry w i l l l e a d t o energy gaps a t t h e B r i l l o u i n zone e d g e s . There w i l l b e a s e p a r a t i o n of t h e s u r f a c e s t a t e s i n t o d i f f e r e n t manifolds of bands which correspond t o t h e d i f f e r e n t t y p e s o f s u r f a c e s t a t e s on t h e r e c o n s t r u c t e d s u r f a c e . The energy s e p a r a t i o n between t h e bands w i t h i n a manifold m u s t be s m a l l and one can h a r d l y expect t o r e s o l v e i n d i v i d u a l bands i n ARPES s t u d i e s , u n l e s s t h e m a t r i x elements f o r t r a n s i t i o n s make one band i n a manifold dominate i n each spectrum. I t s h o u l d be n o t e d t h a t , i n t h e f o l l o w i n g s e c t i o n s , t h e d e n o t a t i o n of t h r e e d i f f e r e n t s u r f a c e s t a t e s / b a n d s (Sl, S2 and
163
S3)
on t h e 1x7 s u r f a c e , i s u s e d f o r t h r e e s e p a r a t e m a n i f o l d s w i t h a n
unknown number o f b a n d s from t h e 7x1 band s t r u c t u r e . T h r o u g h o u t t h e l a s t t w e n t y y e a r s a l a r g e number of p h o t o e m i s s i o n s t u d i e s o f t h e s u r f a c e e l e c t r o n i c s t r u c t u r e on t h e S i ( 1 1 1 ) 7 x 7 s u r f a c e h a s b e e n p u b l i s h e d /29,31-35,44,46,64,89-105/. A l r e a d y by
1964 A l l e n a n d G o b e l i /14/ h a d p u b l i s h e d t h e f i r s t p h o t o e l e c t r o n e n e r g y d i s t r i b u t i o n c u r v e s showing d i f f e r e n c e s between t h e c l e a v e d
2x1 s u r f a c e a n d t h e c l e a v e d a n d a n n e a l e d ( s u p p o s e d l y 7x7) s u r f a c e . F o r t h e a n n e a l e d s u r f a c e t h e y f o u n d a c h a r a c t e r i s t i c e m i s s i o n from j u s t b e l o w t h e Fermi l e v e l , which t e n t a t i v e l y was a s s i g n e d t o s u r f a c e s t a t e s t h a t h a d moved up i n t o t h e g a p . T h i s i n t e r p r e t a t i o n
i s i n good a c c o r d w i t h t h e p r e s e n t u n d e r s t a n d i n g o f t h e S1 s u r f a c e
s t a t e , see below. I n t h e s e e a r l y s t u d i e s t h e p h o t o n e n e r g y was v e r y low, 5 6.2 e V , which made i t p o s s i b l e t o s t u d y e m i s s i o n from t h e S1 s u r f a c e s t a t e o n l y . R o w e e t a l . /64,89/ d i d s e v e r a l a n g l e - i n t e g r a t e d s t u d i e s w i t h h i g h e r p h o t o n e n e r g i e s and e m i s s i o n from a l l t h r e e s u r f a c e s t a t e s Sl, S2 a n d S 3 c o u l d be o b s e r v e d f o r t h e f i r s t t i m e . The f i r s t a n g l e - r e s o l v e d p h o t o e m i s s i o n s t u d y on t h e S i ( 1 1 1 ) 7 x 7 s u r f a c e was made by Eastman e t a l . /go/. The a n g l e - r e s o l v e d s p e c t r a showed s i g n i f i c a n t i n t e n s i t y v a r i a t i o n s i n t h e s u r f a c e s t a t e e m i s s i o n w i t h a n g l e , w h i l e v e r y s m a l l e n e r g y d i s p e r s i o n s were r e p o r t e d . With t h e mixed s , p - p o l a r i z a t i o n
employed, t h e S3 s u r f a c e
s t a t e w a s s t r o n g a t h i g h a n g l e s o f e m i s s i o n , w h i l e t h e r e was o n l y a weak f e a t u r e a t t h e same e n e r g y i n n o r m a l e m i s s i o n . I n a low p h o t o n e n e r g y (hv
=
10.2 e V ) ARPES s t u d y on t h e S i ( 1 1 1 ) 7 x 7 s u r f a c e b y
Hansson e t a l . /91/, t h e e m i s s i o n from Sl and S2 was c h a r a c t e r i z e d w i t h r e s p e c t t o e n e r g y d i s p e r s i o n , p o l a r i z a t i o n d e p e n d e n c e and c o n t a m i n a t i o n s e n s i t i v i t y . The a g r e e m e n t w i t h t h e r e s u l t s o f Eastman
e t a l . /90/ w a s good, e . g . a s t r o n g m e t a l l i c e d g e (S1) was r e p o r t e d a n d t h e e m i s s i o n from b o t h S1 and S 2 was f o u n d t o b e s u p p r e s s e d f o r normal i n c i d e n c e o f t h e l i g h t . High p h o t o n - e n e r g y
ARPES s t u d i e s
(hv = 20-90 e V ) were r e p o r t e d by
Houzay a n d c o w o r k e r s /31-34/. The S 2 s u r f a c e s t a t e s e e n i n normal e m i s s i o n was shown t o h a v e s t r o n g v a r i a t i o n s i n i n t e n s i t y w i t h phot o n e n e r g y . I n c o n t r a s t t o t h e p r e v i o u s s t u d i e s o n l y a s m a l l metal-
l i c e d g e (S1) w a s r e p o r t e d and i t w a s p r o p o s e d /34/ t h a t t h e m e t a l -
l i c edge i s a r e s u l t o f e x t r i n s i c e f f e c t s . S i m i l a r l y , a s m a l l m e t a l l i c e d g e w a s a l s o r e p o r t e d by Hansson e t a l . /30/ on 7x7 s u r f a c e s o b t a i n e d by a n n e a l i n g o f 2 x i s u r f a c e s . A s d i s c u s s e d by Eastman e t a l . /92/, a n u n d e r s i z e d m e t a l l i c e d g e c a n be d u e t o
164
e x p e r i m e n t a l parameters l i k e e m i s s i o n a n g l e , p o l a r i z a t i o n and photon e n e r g y o r due t o improper a n n e a l i n g of t h e 7x1 s u r f a c e . The d i s p e r s i o n s o f t h e s u r f a c e s t a t e s on t h e S i ( 1 1 1 ) 7 x 7 s u r f a c e a l o n g t h e h i g h symmetry d i r e c t i o n s , Neddermeyer e t a l . / 9 8 / ,
ri?
and FM, h a v e been s t u d i e d by
Uhrberg e t a l . /102/ a n d Mgrtensson e t a l .
/105/ and t h e r e s u l t s of t h e l a s t s t u d y a r e d e s c r i b e d below. The
e a r l i e r s t u d i e s gave q u i t e s i m i l a r r e s u l t s , a l t h o u g h s l i g h t l y small e r d i s p e r s i o n s were r e p o r t e d . T h i s can p r o b a b l y be a t t r i b u t e d t o t h e somewhat p o o r e r r e s o l u t i o n i n t h e s p e c t r a i n r e f s . 98 and 1 0 2 .
F i g . 6a shows A W E S s p e c t r a from t h e s t u d y by Mdrtensson e t a l . /105/
f o r v a r i o u s a n g l e s of e m i s s i o n a l o n g t h e [lo?] a z i m u t h a l
d i r e c t i o n . The i n c i d e n t r a d i a t i o n was p - p o l a r i z e d w i t h 2 1 . 2 e V photon e n e r g y . There a r e t h r e e s t r u c t u r e s S l , S2 and S3,
in the
r a n g e 0-2 e V below t h e F e r m i l e v e l , which a r e due t o e m i s s i o n from t h e p r e v i o u s l y e s t a b l i s h e d s u r f a c e s t a t e s . T h e r e i s a l s o a number of o t h e r s t r o n g f e a t u r e s i n t h e s p e c t r a , t h a t a r e i n t e r p r e t e d as e m i s s i o n from b u l k b a n d s . I n r e f . 102 Uhrberg e t a l . a n a l y z e d b u l k contributions t o 21.2-eV
s p e c t r a l i k e t h e o n e s i n F i g . 6a, and e . g .
t h e s t r o n g b r o a d peak r a p i d l y d i s p e r s i n g from -3 t o -4
e V around 15’
e m i s s i o n a n g l e can be i d e n t i f i e d a s due t o d i r e c t t r a n s i t i o n s from t h e s e c o n d topmost v a l e n c e band. A s t r o n g s u p p o r t f o r t h e s u r f a c e
s t a t e i n t e r p r e t a t i o n of S,
S2
and S3 i s g i v e n by t h e c o n s i s t e n c y of
t h e i r d i s p e r s i o n s f o r d i f f e r e n t phot,on e n e r g i e s , which i s n o t found
for the other structures i n the spectra. The S1 s u r f a c e s t a t e h a s a peak p o s i t i o n t h a t i s 2 0 . 2 e V from t h e Fermi l e v e l and t h e h i g h e n e r g y c u t o f f i s s i m i l a r t o t h e Fermiedge o f a metal s u r f a c e . T h i s m e t a l l i c c h a r a c t e r of t h e 1 x 7 s u r f a c e h a s a l s o b e e n found i n e l e c t r o n - e n e r g y - l o s s
measurements, where it
r e s u l t s i n a v e r y s t r o n g b r o a d e n i n g of t h e e l a s t i c p e a k /106/. The i n t e n s i t y of e m i s s i o n from t h e S 1 s u r f a c e s t a t e has a c h a r a c t e r i s t i c v a r i a t i o n w i t h t h e p a r a l l e l wavevector, k,,, i . e . maximum e m i s s i o n i n t e n s i t y i s o b t a i n e d a p p r o x i m a t e l y h a l f w a y between t h e f - p o i n t
and
t h e 1 x 1 s u r f a c e BZ boundary / 9 3 / . A s mentioned above, it has been s u g g e s t e d t h a t t h e S,
s t r u c t u r e r e s u l t s from e x t r i n s i c e f f e c t s / 3 4 / ,
s i n c e i t was s e e n w i t h v e r y low i n t e n s i t y i n some s t u d i e s . I t i s i n t e r e s t i n g t o n o t e t h a t i n t h o s e s t u d i e s /30,34/
the reported
s p e c t r a were a l l o b t a i n e d a t e m i s s i o n a n g l e s f o r which t h e i n t e n s i t y of S,
i s low anyway, i . e . i n normal e m i s s i o n o r a t h i g h a n g l e s . I t
now seems t o be g e n e r a l l y a c c e p t e d t h a t S1 i s a n i n t r i n s i c s u r f a c e s t a t e o f t h e 7x7 s u r f a c e .
165
I
I
I
I
I
I
I
I
I
I
I
I
I
I
LI I
-6 -4 -2 O ENERGY BELOW E, (eV)
ENERGY BELOW E,
(eV)
F i g . 6 . ( a ) Photoemission s p e c t r a r e c o r d e d from S i ( 1 1 1 ) 7 x 7 f o r e m i s s i o n a l o n g t h e [ l o l l a z i m u t h a l d i r e c t i o n . E x c i t a t i o n w i t h pp o l a r i z e d 21.2-eV r a d i a t i o n i n c i d e n t a t 45' /105/. (b) Normal-emission s p e c t r a from S i ( 1 1 1 ) 7 x 7 f o r v a r i o u s photon e n e r g i e s . The a n g l e of i n c i d e n c e of t h e photons i s O i = 15' and t h e p o l a r i z a t i o n v e c t o r i s i n t h e (Oil) p l a n e , 15’ from t h e [Zllld i r e c t i o n . From r e f . 5 2 . The second s u r f a c e s t a t e S2 i s seen c l e a r l y i n a l l s p e c t r a i n F i g . 6 a . I t has o f t e n been d e s c r i b e d a s a d i s p e r s i o n l e s s f e a t u r e , however, t h e r e i s a small = 0 . 1 eV p o s i t i v e d i s p e r s i o n from
r
to
0.5(r-K). The d i s p e r s i o n s of t h e s u r f a c e s t a t e s a l o n g t h e main symmetry l i n e s
r-k
and
T-fi a r e shown i n F i g . I t o g e t h e r with t h e
v a l e n c e band edge a s p r o j e c t e d o n t o t h e 1x1 s u r f a c e B Z . A v a l u e of 0.63 eV f o r E,-E,
was used, which has been r e p o r t e d as an average
v a l u e f o r many 1x7 s u r f a c e s w i t h a maximum d e v i a t i o n of = 0 . 0 7 eV /107/.
The energy of S 2 i s 0 . 8 - 0 . 9 e V b e l o w t h e F e r m i l e v e l i n t h e
whole s u r f a c e BZ which means t h a t it i s l o c a t e d i n t h e p r o j e c t e d bulk band gap, except f o r k / / - p o i n t s c l o s e t o
f.
F i n a l l y , t h e S3 s u r f a c e s t a t e i s c l e a r l y seen a t h i g h a n g l e s i n F i g . 6 a . I n t h e [lOi] azimuthal d i r e c t i o n , S j has a n e g a t i v e d i s p e r s i o n of = 0 . 3 eV f o r i n c r e a s i n g emission a n g l e s a n d it f a l l s
166
It-
M
-
-
K -rloiI
r
WAVEVECTOR
F i g . 7 . The e x p e r i m e n t a l l y measured d i s p e r s i o n s o f s u r f a c e s t a t e s on t h e S i ( 1 1 1 ) 7 x 7 s u r f a c e . D a t a from r e f . 1 0 5 . w i t h i n t h e p r o j e c t e d bulk band gap i n a l a r g e r e g i o n around t h e
E-
p o i n t as s e e n i n F i g . 7 . I n t h e [ 2 i i ] a z i m u t h , S3 d i s p e r s e s down t o
i t s a b s o l u t e minimum e n e r g y , = 2 . 0 e V below EF, a t t h e M-point r e s u l t i n g i n a t o t a l bandwidth o f
= 0.4 eV.
F o r t h e f u r t h e r d i s c u s s i o n o f S 3 , it i s i m p o r t a n t t o n o t e t h a t it
i s n o t p o s s i b l e t o f o l l o w t h i s s t r u c t u r e from h i g h e m i s s i o n a n g l e s a l l t h e way t o normal e m i s s i o n . I n s t e a d w e a s s o c i a t e t h e e m i s s i o n s e e n i n t h e normal d i r e c t i o n ,
a t -2.0
eV,
t o e m i s s i o n from b u l k
s t a t e s . I t h a s been p r o p o s e d i n two s t u d i e s u s i n g 21.2-eV /90,97/
radiation
t h a t e m i s s i o n from S3 c a n be s e e n i n t h e normal d i r e c t i o n
a n d t h a t it i s t h e n e x c i t e d by l i g h t p o l a r i z e d p a r a l l e l t o t h e surface. Since p-polarized
l i g h t at a high angle of incidence w a s
u s e d t o o b t a i n t h e 21.2-eV
s p e c t r a i n F i g . 6a, t h i s t y p e of e m i s s i o n
should be suppressed. F i g . 6b shows normal e m i s s i o n s p e c t r a , o b t a i n e d w i t h a n a n g l e o f l i g h t i n c i d e n c e Oi=15' and t h e p o l a r i z a t i o n v e c t o r i n t h e (Oil) plane /52/.
A s s e e n when comparing t h e 21.2-eV
spectrum i n F i g . 6b
w i t h t h e normal e m i s s i o n s p e c t r u m i n F i g . 6a, t h e r e are v e r y s t r o n g p o l a r i z a t i o n e f f e c t s . When t h e p o l a r i z a t i o n v e c t o r i s c l o s e t o p a r a l l e l t o t h e [ 2 1 1 1 d i r e c t i o n a l o n g t h e s u r f a c e , t h e e m i s s i o n from t h e S 1 and S2 s u r f a c e s t a t e s i s v e r y much r e d u c e d w h i l e a s t r o n g f e a t u r e a p p e a r s a t 2 . 0 e V below EF i n normal e m i s s i o n . From t h e p h o t o n e n e r g y dependence o f t h e p e a k p o s i t i o n it m u s t , however, be c o n c l u d e d t h a t t h i s s t r u c t u r e i s due t o e m i s s i o n from t h e b u l k . F u r t h e r c o n f i r m a t i o n of t h i s a s s i g n m e n t i s o b t a i n e d from s i m i l a r s t u d i e s on t h e S i ( l l l ) 2 x l s u r f a c e , where t h e same b u l k c o n t r i b u t i o n
167
h a s b e e n i d e n t i f i e d a s b e i n g due t o d i r e c t t r a n s i t i o n s from t h e two t o p m o s t v a l e n c e b a n d s , which a r e d e g e n e r a t e a l o n g t h e a p p r o p r i a t e l-L l i n e i n t h e b u l k BZ /45/.
I n some earlier s t u d i e s /90,97/, normal e m i s s i o n u s i n g 2 1 . 2 - e V
t h e p o l a r i z a t i o n dependence of
p h o t o n e n e r g y had b e e n u s e d t o con-
c l u d e t h a t t h e S1 and S2 s u r f a c e s t a t e s h a v e S3
s t a t e w a s a s s i g n e d t o have
A3
A l symmetry, w h i l e t h e
symmetry. From t h e p h o t o n e n e r g y
d e p e n d e n t d a t a i n F i g . 6b it c a n i n s t e a d b e i n f e r r e d t h a t t h e p o l a r i z a t i o n d e p e n d e n c e o f t h e s t r u c t u r e a t 2 . 0 e V below EFI s e e n i n n o r m a l e m i s s i o n , r e f l e c t s t h e A 3 symmetry o f t h e t o p m o s t t w o b u l k b a n d s . We f i n d t h a t , f o r a l l t h r e e s u r f a c e s t a t e s S l , S2 and S 3 i n F i g . 6 a , t h e p o l a r i z a t i o n d e p e n d e n c e i s q u a l i t a t i v e l y t h e same. J u s t
as f o r S 1 and S p . t h e
S3 s u r f a c e
s t a t e e m i s s i o n i s s u p p r e s s e d when
t h e p o l a r i z a t i o n v e c t o r of t h e photons i s p a r a l l e l t o t h e s u r f a c e /102/.
T h i s i s c h a r a c t e r i s t i c f o r s-p,
t y p e o r b i t a l s and t h e p o l a r i -
z a t i o n d e p e n d e n c e t h u s i m p l i e s a l a r g e s-p,
( d a n g l i n g bond) c o n t e n t
i n a l l three s u r f a c e s t a t e s . T e s t s o f t h e c o n t a m i n a t i o n s e n s i t i v i t y have been u s e d t o s u p p o r t
t h e i d e n t i f i c a t i o n o f s u r f a c e s t a t e s . I n r e f . 102 b o t h 0 2 and C12 e x p o s u r e s w e r e u s e d t o modify t h e s u r f a c e i n o r d e r t o r e d u c e t h e i n t e n s i t y o f e m i s s i o n from s u r f a c e s t a t e s . I t w a s f o u n d t h a t low e x p o s u r e s of oxygen h a d a l a r g e r e f f e c t on t h e S1 s u r f a c e s t a t e t h a n on S2,
w h i l s t c h l o r i n e had t h e o p p o s i t e e f f e c t . A c o m p a r i s o n between
ARPES s p e c t r a from t h e S i ( l l l ) 2 x l a n d 7x7 s u r f a c e s i s a l s o u s e f u l
f o r i d e n t i f i c a t i o n of b u l k a n d s u r f a c e c o n t r i b u t i o n s . I t i s c l e a r t h a t t h e r e a r e no f e a t u r e s i n t h e 2x1 s p e c t r a t h a t c o r r e s p o n d t o t h e S l , Sz and S 3 s t r u c t u r e s ,
while t h e r e a r e bulk t r a n s i t i o n s t h a t a r e
f o u n d i n s p e c t r a from b o t h s u r f a c e s . The o r i g i n o f t h e s u r f a c e s t a t e s on t h e S i ( 1 1 1 ) 7 x 7 s u r f a c e h a s r e c e n t l y b e e n d i s c u s s e d by N o r t h r u p /108/. H e p e r f o r m e d model c a l c u l a t i o n s f o r (111) s u r f a c e s w i t h o n e S i adatom per u n i t c e l l i n
4 3 x 4 3 o r 2x2 s u r f a c e p e r i o d i c i t i e s . These adatom u n i t s a r e e s s e n t i a l components i n t h e DAS model of t h e 7x7 s u r f a c e . I n p a r t i c u l a r t h e 2x2 s u r f a c e g e o m e t r y w i t h o n e 3 - f o l d c o o r d i n a t e d adatom a n d one rest
a t o m p e r u n i t c e l l can s i m u l a t e t h e l a r g e t r i a n g u l a r u n i t s cont a i n i n g 1 2 adatoms a n d 6 r e s t atoms p e r 7x7 u n i t c e l l i n t h e DAS-
model. F o r t h e 2x2 adatom geometry t h r e e s u r f a c e s t a t e s a r e f o u n d , a l l w i t h a p p r e c i a b l e s-p, ( d a n g l i n g bond) c h a r a c t e r . The s t a t e labelled
i s composed o f s u b s t r a t e d a n g l i n g bond s t a t e s c o u p l e d t o
adatom p z o r b i t a l s , which a r e p r e d i c t e d t o form a p a r t l y f i l l e d m a n i f o l d o f b a n d s on t h e 1x7 s u r f a c e . X2 i s a d o u b l y o c c u p i e d
168
d a n g l i n g bond s t a t e l o c a l i z e d on t h e rest atoms, a n d f i n a l l y C3 i s composed o f s u b s t r a t e d a n g l i n g bond o r b i t a l s c o u p l e d t o adatom px
,&
and py o r b i t a l s . The e n e r g y p o s i t i o n s a n d d i s p e r s i o n s o f t h e
and C3 s u r f a c e s t a t e b a n d s f o r t h e 2x2 a n d 43x43 model g e o m e t r i e s g i v e v e r y s t r o n g s u p p o r t f o r i d e n t i f y i n g C1 , C p and C3 w i t h t h e S1, Sg and S 3 s u r f a c e
s t a t e s s e e n i n ARPES m e a s u r e m e n t s .
H a m e r s e t a l . /log/ v e r y r e c e n t l y d e v e l o p e d a new method, current-imaging-tunneling o b t a i n energy-resolved
s p e c t r o s c o p y (CITS) which w a s u s e d t o
real-space
images o f t h e f i l l e d and empty
s u r f a c e s t a t e s o f t h e S i ( 1 1 1 ) 7 x 7 s u r f a c e . I t was shown, v e r y conv i n c i n g l y , t h a t t h e S1 s u r f a c e s t a t e i s l o c a l i z e d on t h e p o s i t i o n s i n t h e 1x7 u n i t c e l l which c o r r e s p o n d t o t h e adatoms i n t h e DASmodel a n d t h e S2 s u r f a c e s t a t e i s l o c a l i z e d on t h e rest atom p o s i t i o n s . H a m e r s e t a l . a l s o f o u n d some e v i d e n c e f o r t u n n e l i n g from a lower l y i n g s u r f a c e s t a t e , a s s i g n e d t o adatom backbonds,
which
would c o r r e s p o n d t o t h e s t a t e S 3 . Thus, b a s e d on t h e o r e t i c a l c a l c u l a t i o n s a n d CITS s t u d i e s , t h e r e i s p r e s e n t l y a good u n d e r s t a n d i n g o f t h e o r i g i n o f t h e d i f f e r e n t s u r f a c e s t a t e s o b s e r v e d i n ARPES e x p e r i m e n t s on t h e S i ( 1 1 1 ) 7 x 7 s u r f a c e .
4.2.
G e ( l l 1 ) -c ( 2 &
The c l e a v e d G e ( l l l ) 2 x l s u r f a c e i s m e t a s t a b l e a n d upon h e a t i n g t o
= 3OO0C it t r a n s f o r m s t o a more s t a b l e s u r f a c e which e x h i b i t s a complex LEED p a t t e r n w i t h 1 / 2 a n d 1 / 8 o r d e r s p o t s . I n s e v e r a l r e c e n t s t u d i e s t h e LEED p a t t e r n h a s b e e n a s s i g n e d t o a t h r e e - d o m a i n
~(2x8)
r e c o n s t r u c t i o n . S i n c e t h e r e a r e some e x p e c t e d 1/4 o r d e r s p o t s m i s s i n g i n t h e ~ ( 2 x 8 )LEED p a t t e r n , t h e i n t e r n a l s t r u c t u r e of t h e ~ ( 2 x 8 )u n i t c e l l h a s t o a c c o u n t f o r t h e c o r r e s p o n d i n g s t r u c t u r e f a c t o r c a n c e l l a t i o n s , as h a s b e e n d i s c u s s e d b y Chadi and Chiang
/llO/ and Yang and Jona / l l l / . I n t h e f i r s t a n g l e - i n t e g r a t e d p h o t o e m i s s i o n s t u d y on a n n e a l e d G e ( l l 1 ) s u r f a c e s by Murotani e t a l . / 7 3 /
t h e e x i s t e n c e of s u r f a c e
s t a t e s c l o s e t o t h e v a l e n c e band e d g e was s u g g e s t e d . F u r t h e r s u p p o r t f o r t h i s i d e n t i f i c a t i o n was o b t a i n e d i n p h o t o e m i s s i o n y i e l d measurements by G u i c h a r e t a l . / 1 1 2 / ,
i n which a s u r f a c e s t a t e band
0 . 6 e V below t h e v a l e n c e band e d g e was f o u n d . H i m p s e l e t al. /93/ s t u d i e d t h e a n g u l a r d i s t r i b u t i o n s o f p h o t o e l e c t r o n s from t h e t h e r m a l l y a n n e a l e d G e (111)-c ( 2 x 8 ) a n d t h e l a s e r a n n e a l e d G e (111)1 x 1 s u r f a c e s . On b o t h s u r f a c e s t h e y f o u n d two s u r f a c e s t a t e s a t - 0 . 1 eV a n d -1.3 e V r e l a t i v e t o t h e v a l e n c e band e d g e , which e x h i b i t e d
169
c h a r a c t e r i s t i c e m i s s i o n p a t t e r n s w i t h i n t h e 1 x 1 s u r f a c e B Z . The
f i r s t s t u d i e s of t h e d i s p e r s i o n s o f t h e s u r f a c e s t a t e band s t r u c t u r e
w e r e p r e s e n t e d by B r i n g a n s a n d Hochst / 1 1 3 ,
114/, who r e p o r t e d two
a l m o s t f l a t b a n d s c o n s i s t e n t w i t h t h e r e s u l t s o f Himpsel e t a l . /93/.
Yokotsuka e t a l . /115/ r e p e a t e d t h e s e measurements w i t h b e t t e r e n e r g y r e s o l u t i o n and more d e t a i l s f o r t h e d i s p e r s i o n s o f t h e s u r f a c e s t a t e b a n d s were f o u n d . F o r c e r t a i n e m i s s i o n a n g l e s t h e r e were t r i p l e t s t r u c t u r e s i n t h e s p e c t r a i n d i c a t i n g t h a t t h e r e are a t l e a s t t h r e e d i f f e r e n t s u r f a c e s t a t e b a n d s . Yokotsuka a n d c o w o r k e r s a l s o s t u d i e d t h e e m i s s i o n from t h e G e ( l l l ) - c ( 2 x 8 ) s u r f a c e a s t h e temper a t u r e w a s r a i s e d and t h e s u r f a c e f i n a l l y t r a n s f o r m e d i n t o a 1x1 r e c o n s t r u c t e d s u r f a c e /116/. A t h i g h e r t e m p e r a t u r e s a weak s t r u c t u r e c o r r e s p o n d i n g t o a n o t h e r w i s e empty s u r f a c e s t a t e a p p e a r e d j u s t a b o v e t h e Fermi l e v e l . The a n g u l a r dependence o f t h e e m i s s i o n from t h i s s t a t e w a s f o u n d t o be t h e same a s t h a t of t h e m e t a l l i c s t a t e on t h e S i ( 1 1 1 ) 7 x 7 s u r f a c e . S t r o n g s i m i l a r i t i e s between t h e a n g u l a r d i s t r i b u t i o n s o f t h e two l o w e r l y i n g s u r f a c e s t a t e s on S i ( 1 1 1 ) 7 x 7 a n d G e ( l l l ) - c ( 2 x 8 ) had a l s o p r e v i o u s l y b e e n r e p o r t e d by Himpsel e t
a l . Both Himpsel e t a l . / 9 3 /
and Yokotsuka e t a l . /116/ s u g g e s t e d
t h a t s i m i l a r b u i l d i n g b l o c k s a r e p r e s e n t on t h e S i ( 1 1 1 ) 7 x 7 a n d G e ( l l l ) - c ( 2 x 8 ) s u r f a c e s and t h a t t h e l o n g r a n g e o r d e r i n g of t h e s e b u i l d i n g b l o c k s a f f e c t s t h e o c c u p a t i o n of t h e s u r f a c e s t a t e n e a r t h e Fermi l e v e l . T h e r e h a v e r e c e n t l y been p u b l i s h e d s e v e r a l d e t a i l e d s t u d i e s of t h e s u r f a c e s t a t e / r e s o n a n c e b a n d s t r u c t u r e on t h e G e ( l l l ) - c ( 2 x 8 ) s u r f a c e . The e n e r g y d i s p e r s i o n s of t h e s u r f a c e s t a t e c o n t r i b u t i o n s , measured a l o n g t h e
F-l?
l i n e i n t h e s u r f a c e BZ i n t h e d i f f e r e n t
e x p e r i m e n t s , a r e shown i n Fig. 8 ( f r o m r e f . 1 1 7 ) . Data p o i n t s from Yokotsuka e t a l . /115/ and N i c h o l l s e t a l . / l l E /
are p l o t t e d assu-
ming a d i f f e r e n c e o f 0 . 1 5 e V between t h e v a l e n c e band maximum and t h e F e r m i l e v e l . The d a t a p o i n t s from B r i n g a n s e t a l . /119/ a r e s h i f t e d by 0 . 2 5 e V t o o b t a i n b e t t e r o v e r a l l a g r e e m e n t . F i n a l l y , t h e r e s u l t s from A a r t s e t a l . / 1 1 7 / a r e summarized a s f u l l drawn d i s p e r s i o n c u r v e s f o r f o u r s e g m e n t s of t h e s u r f a c e s t a t e band s t r u c t u r e . A p a r t from a weak, r a p i d l y d i s p e r s i n g s h o u l d e r r e p o r t e d by A a r t s e t a l . n e a r normal e m i s s i o n , t h e r e i s good a g r e e m e n t between t h e f o u r s t u d i e s u s i n g d i f f e r e n t photon e n e r g i e s and t h i s i s s t r o n g s u p p o r t f o r t h e i d e n t i f i c a t i o n of t h e f e a t u r e s as s u r f a c e states/resonances. A c e r t a i n spread i n t h e data points i s t o be e x p e c t e d , s i n c e t h e f e a t u r e s are n o t e a s y t o r e s o l v e and, f u r t h e r -
170
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II I I
I I I I I I
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Fig, 8 . Summary o f t h e [ O l l l - d i r e c t i o n on t h e p o i n t s from r e f s . 115, while t h e r e s u l t s from
-
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measured s u r f a c e s t a t e d i s p e r s i o n s a l o n g t h e G e ( l l l ) - c ( Z x 8 ) s u r f a c e , from r e f . 117. Data 118 and 1 1 9 a r e shown w i t h d i f f e r e n t symbols, r e f . 1 1 7 are shown a s c u r v e s .
more, b u l k c o n t r i b u t i o n s c a n i n t e r f e r e , as most o f t h e measured s u r f a c e s t a t e band s t r u c t u r e i s n o t i n t h e p r o j e c t e d 1x1 b u l k band gap
-
I t i s c l e a r from F i g . 8 t h a t t h e s u r f a c e s t a t e band s t r u c t u r e
along t h e
f‘-E l i n e i s more c o m p l i c a t e d t h a n j u s t t h e two a l m o s t
flat
bands t h a t w e r e p r o p o s e d i n t h e f i r s t ARPES s t u d i e s . I n t h e l a t e r high r e s o l u t i o n s t u d i e s , t h e r e a r e resolved f e a t u r e s a t intermediate e n e r g i e s found a t two p o s i t i o n s a l o n g t h e T-k-line, v a l u e s of 0 . 3 and 0 . 6 A-1
i . e . f o r k,,-
r e s p e c t i v e l y . The s u r f a c e s t a t e band
s t r u c t u r e h a s a l s o been s t u d i e d a l o n g t h e [1211 and [Zii] a z i m u t h a l d i r e c t i o n s /115,117-119/ and s m a l l e r d i s p e r s i o n s o f t h e bands have c o n s i s t e n t l y been found i n t h e s e d i r e c t i o n s i n t h e d i f f e r e n t experiments. In p a r t i c u l a r ,
u n l i k e f o r s p e c t r a i n t h e [Oli] azimuth,
no d i s p e r s i n g f e a t u r e s a r e s e e n i n between t h e two r e g i o n s , t h a t have s o m e t i m e s been d e s c r i b e d a s c o n t a i n i n g f l a t b a n d s . I n summary, w e f i n d t h a t q u i t e c o n s i s t e n t r e s u l t s have been reported f o r t h e e l e c t r o n i c s t r u c t u r e of t h e G e ( l l l ) - c ( 2 x 8 ) surface. With m o d e r a t e r e s o l u t i o n i t a p p e a r s t o c o n s i s t of t w o r a t h e r f l a t bands, w i t h t h e topmost band dominant n e a r normal e m i s s i o n w h i l e t h e
l o w e r band h a s h i g h e r i n t e n s i t y a t h i g h e r e m i s s i o n a n g l e s . With h i g h e r r e s o l u t i o n it h a s been p o s s i b l e t o f i n d s i g n i f i c a n t f i n e
171
s t r u c t u r e i n t h e d i s p e r s i o n l e a d i n g t o t h e i d e n t i f i c a t i o n of f o u r s u r f a c e s t a t e bands. Since t h e G e ( l l l ) - c ( 2 x 8 ) s u r f a c e has, so f a r , a l w a y s c o n t a i n e d t h r e e d i f f e r e n t l y r o t a t e d domains i t i s c l e a r t h a t t h e p h o t o e m i s s i o n s p e c t r a s h o u l d be i n f l u e n c e d b y m u l t i - d o m a i n
e f f e c t s a s w e l l as p o s s i b l e d i s o r d e r b e t w e e n t h e d o m a i n s . I t c e r t a i n l y would b e v e r y h e l p f u l f o r t h e e v a l u a t i o n o f t h e p h o t o e m i s s i o n d a t a and t h e u n d e r s t a n d i n g o f t h e e l e c t r o n i c s t r u c t u r e , i f it c o u l d b e p o s s i b l e t o p r e p a r e s i n g l e - d o m a i n s o f t h e ~ ( 2 x 8 )r e c o n s t r u c t i o n by some s p e c i a l method.
5
S i ( 1 0 0 ) AND G e ( 1 0 0 ) SURFACES The e q u i l i b r i u m s u r f a c e p e r i o d i c i t i e s o f t h e S i and G e ( 1 0 0 ) s u r -
f a c e s r e m a i n a m a t t e r o f d i s c u s s i o n i n t h e l i t e r a t u r e . F o r reviews o f t h e p r e s e n t u n d e r s t a n d i n g we r e f e r t o r e c e n t p u b l i c a t i o n s by
H a m e r s e t a l . /120/,
Lambert e t a l . / 1 2 1 / ,
Kubby e t a l . / 1 2 2 /
and
r e f e r e n c e s t h e r e i n . The b a s i c 2x1 r e c o n s t r u c t i o n i s g e n e r a l l y accepted t o e n t a i l t h e formation of dimers, c r e a t e d through p a i r i n g o f t h e n e a r e s t n e i g h b o r s u r f a c e a t o m s . I n t h e room t e m p e r a t u r e STM s t u d i e s of S i ( 1 0 0 ) by Hamers e t a l . / 1 2 0 /
a l . /122/
and G e ( 1 0 0 ) b y Kubby e t
i t w a s found t h a t t h e s e d i m e r s are o r d e r e d i n domains o f
rows o r i e n t e d a l o n g t h e p e r p e n d i c u l a r
[ O l l ] and
[ O l i l d i r e c t i o n s and
t h e two t y p e s o f domains a r e s e p a r a t e d by monatomic s t e p s . The d i s t a n c e b e t w e e n t h e rows i s t w i c e t h e l a t t i c e c o n s t a n t o f t h e u n r e c o n s t r u c t e d s u r f a c e , r e s u l t i n g i n a n a p p a r e n t 2x1 r e c o n s t r u c t i o n . I n h i g h r e s o l u t i o n images o f t h e G e ( 1 0 0 ) s u r f a c e , a n asymmetry of
most o f t h e d i m e r s i s f o u n d , which i s a t t r i b u t e d t o a b u c k l i n g o f t h e d i m e r s . I n g e n e r a l , t h e rows o f d i m e r s h a v e a n a p p a r e n t z i g - z a g s t r u c t u r e i n STM-images,
i n d i c a t i n g t h a t t h e d i r e c t i o n of buckling
a l t e r n a t e s from d i m e r t o d i m e r a l o n g a row. C o n c e r n i n g t h e o r d e r b e t w e e n n e i g h b o r i n g rows, a l o c a l ~ ( 2 x 2 )symmetry o c c u r s when t h e b u c k l i n g i n two rows a r e i n p h a s e , w h i l e a ~ ( 4 x 2 )symmetry o c c u r s when t h e b u c k l i n g i s 180’ o u t o f p h a s e . I n t h e STM-images p r e s e n t e d , t h e m a j o r p a r t c o n s i s t s of z i g - z a g r o w s b u t t h e i n d i v i d u a l ~ ( 2 x 2 ) a n d ~ ( 4 x 2 )domains a r e s m a l l , i n d i c a t i n g a weak c o r r e l a t i o n between t h e p h a s e o f t h e b u c k l i n g i n n e i g h b o r i n g r o w s . Although o n l y v e r y
s m a l l r e g i o n s were f o u n d t o h a v e t r u e 2x1 symmetry, t h e s u r f a c e a s p r e p a r e d b y Kubby e t a l . e x h i b i t e d a s h a r p 2x1 LEED-pattern. T h e r e
was no e v i d e n c e o f q u a r t e r o r d e r s p o t s o r s t r e a k s t h a t would b e i n d i c a t i v e o f ~ ( 4 x 2 )o r ~ ( 2 x 2 domains ) extending over l a r g e r regions.
172
Top view
Top view
IOlil
Side view
Side view
............................. domain b
( a ) IDEAL
(b) ASYMMETRIC DIMERS
i
(c) TWO-DOMAIN 2x1 SBZs
F i g . 9. ( a ) S c h e m a t i c views of t h e u n r e c o n s t r u c t e d S i ( 1 0 0 ) s u r f a c e . ( b ) The asymmetric dimer-model o f t h e S i ( 1 0 0 ) 2x1 s u r f a c e . (c) Superimposed s u r f a c e B r i l l o u i n zones of t h e two d i f f e r e n t S i ( 1 0 0 ) 2x1 domains, i n t h e r e p e a t e d zone scheme. I n o t h e r LEED /123-125/
and H e d i f f r a c t i o n /121/ s t u d i e s of t h e
G e ( 1 0 0 ) s u r f a c e a t room t e m p e r a t u r e , b e s i d e s s t r o n g 2x1 s p o t s , a d d i t i o n a l s t r e a k s passing through t h e q u a r t e r o r d e r p o s i t i o n s of t h e ~ ( 4 x 2 )and t h e c e n t e r p o s i t i o n of t h e ~ ( 2 x 2 )d i f f r a c t i o n p a t t e r n s have been r e p o r t e d . These d i f f r a c t i o n s t u d i e s and t h e STMs t u d y /122/ t h u s i n d i c a t e t h a t t h e G e ( 1 0 0 ) s u r f a c e a t room temperat u r e h a s a m i x t u r e of r e g i o n s w i t h ~ ( 4 x 2 )and ~ ( 2 x 2 )symmetry and t h a t d e p e n d i n g on t h e sample p r e p a r a t i o n t h e y can b e l a r g e enough t o b e e v i d e n c e d i n LEED and H e d i f f r a c t i o n .
I n s t u d i e s of t h e tempera-
t u r e dependence, b o t h Kevan / 1 2 3 , 1 2 4 / and Lambert e t a l . /121/ have r e p o r t e d i n c r e a s e d i n t e n s i t y of t h e ~ ( 4 x 2 )f e a t u r e s w i t h d e c r e a s i n g t e m p e r a t u r e i n d i c a t i v e of a g r a d u a l s u r f a c e o r d e r i n g of t h e ~ ( 4 x 2 ) phase. I n STM-images of t h e S i ( 1 0 0 ) s u r f a c e , most of t h e d i m e r s a p p e a r t o b e symmetric / 1 2 0 / . The s u r f a c e a l s o c o n t a i n s a h i g h d e n s i t y of vacancy-type d e f e c t s , which c o u l d l o c a l l y s t a b i l i z e an a l t e r n a t i n g ( z i g - z a g ) b u c k l i n g of t h e d i m e r s a t room t e m p e r a t u r e .
I t was a r g u e d
t h a t t h e o b s e r v a t i o n of symmetric d i m e r s i n d e f e c t - f r e e r e g i o n s c o u l d r e f l e c t t h e time-averaged c o n f i g u r a t i o n o f d i m e r s t h a t a r e d y n a m i c a l l y b u c k l i n g , on a t i m e s c a l e s h o r t compared t o t h e STM measurement t i m e . Schematic views of t h e i d e a l (100) s u r f a c e and t h e asymmetric dimer model o f t h e ( 1 0 0 ) 2 x 1 r e c o n s t r u c t i o n a r e shown i n F i g . 9 ( a , b ) .
173
N o t e t h a t t h e a s y m m e t r i c d i m e r s o b s e r v e d i n STM a r e a l t e r n a t i n g
a l o n g t h e dimer r o w s a n d f o r m r e g i o n s w i t h 2x2 or ~ ( 4 x 2 )s y m m e t r y . Fig.
9 ( c ) shows t h e s u r f a c e B r i l l o u i n z o n e s c o r r e s p o n d i n g t o t h e
dominating
two-domain
(100)2x1 reconstruction t h a t normally has
b e e n o b s e r v e d i n LEED i n c o n j u n c t i o n w i t h r e p o r t e d ARPES s t u d i e s on both S i a n d G e ( 1 0 0 ) 2 x l . 5.1
Si ( 1 0 0 ) 2 x 1
T h e f i r s t e v i d e n c e of p h o t o e m i s s i o n from s u r f a c e s t a t e s o n t h e S i ( 1 0 0 ) 2 x l s u r f a c e was p r e s e n t e d i n t h e a n g l e - i n t e g r a t e d
s t u d i e s by
A s u r f a c e s t a t e s t r u c t u r e w a s o b s e r v e d a t -1.1
Rowe and Ibach /89/.
eV b e l o w E F . A more d e t a i l e d p i c t u r e o f t h e s u r f a c e e l e c t r o n i c s t r u c t u r e w a s presented i n t h e f i r s t angle-resolved photoemission This study w a s performed along
s t u d y b y Himpsel a n d Eastman / 1 2 6 / .
t o avoid ambiguities due t o the superposition
the [010]-direction,
of e m i s s i o n f r o m t h e t w o t y p e s o f 2 x 1 d o m a i n s , r o t a t e d by 90' r e l a t i v e t o each o t h e r . E q u i v a l e n t k / / - p o i n t s a r e p r o b e d f o r t h e t w o d o m a i n s a l o n g t h e [OlO] - d i r e c t i o n ,
which s h o u l d r e s u l t i n i d e n t i c a l
s u r f a c e s t a t e c o n t r i b u t i o n s from t h e t w o domains. A dominant s u r f a c e
s t a t e s t r u c t u r e l o c a t e d 0 . 7 eV below EF a t
J’,
t o 1 . 2 e V b e l o w EF a t
f,
d i s p e r s i n g downwards
was o b s e r v e d i n t h e s t u d y .
dominant s u r f a c e state s t r u c t u r e , a peak a t -0.7
'
I ,
..
'
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'
'
'
Besides t h i s
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s5
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.
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15.0 eV a21.2 eV A
. -
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WAVE VECTOR (A*')
- [OlO]
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F i g . l c . - ( a ) E x p e r i m e n t a l s u r f a c e band s t r u c t u r e for S i ( 1 0 0 ) 2 x 1 a l o n g T-J’ i n t h e [OlO] a z i m u t h a l d i r e c t i o n ( f r o m r e f . 1 4 0 ) . Data p o i n t s f o r s t r u c t u r e S,, f r o m r e f . 1 2 8 , h a v e a l s o b e e n i n c l u d e d i n t h e f i g u r e . The s o l i d l i n e shows t h e u p p e r e d g e o f t h e p r o j e c t e d b u l k v a l e n c e - b a n d s i n t h e - 1 x 1 SBZ. (b) Experimental s u r f a c e state b a n d s t r u c t u r e a l o n g t h e T-J’ a n d r-3 s y m m e t r y l i n e s / 1 3 8 / .
174
a s h o u l d e r a t -1.3 e V a t ?I were a l s o i d e n t i f i e d as s u r f a c e s t a t e emission. S i n c e t h e s e e a r l y s t u d i e s , a l a r g e number of a n g l e - r e s o l v e d s t u d i e s has been performed on t h e S i ( 1 0 0 ) 2 x l s u r f a c e / 1 2 7 - 1 4 0 / ,
and
t h e y have r e s u l t e d i n a v e r y d e t a i l e d and c o n s i s t e n t p i c t u r e of t h e s u r f a c e e l e c t r o n i c s t r u c t u r e . The s u r f a c e band s t r u c t u r e a s obtained i n some r e c e n t a n g l e - r e s o l v e d photoemission s t u d i e s of t h e S i ( 1 0 0 ) 2x1 s u r f a c e /128,138,139/ s u r f a c e s t a t e s , S1-S5,
i s summarized i n F i g . 1 0 . A l t o g e t h e r f i v e
have been observed i n t h e [ O l O ] azimuth,
while only S1 and S5 have been i d e n t i f i e d i n t h e [Oli] and [Oll] symmetry d i r e c t i o n s . Below i s given a b r i e f d e s c r i p t i o n of t h e various surface s t a t e s , but f o r a d e t a i l e d discussion o f , e.g. the degree of c o n s i s t e n c y between t h e d i f f e r e n t a n g l e - r e s o l v e d photoemission s t u d i e s r e p o r t e d i n t h e l i t e r a t u r e , we r e f e r t o r e f . 1 5 . F i g . l l ( a ) shows some photoemission s p e c t r a , from a s t u d y by Goldmann e t a l . /131/, probing t h e s u r f a c e e l e c t r o n i c s t r u c t u r e along t h e [OlO] azimuthal d i r e c t i o n . Besides t h e S 1 and S2 s u r f a c e s t a t e s , t h a t f i r s t were i d e n t i f i e d by Himpsel and Eastman /126/, Goldmann e t a l . a l s o r e p o r t e d a s t a t e , S4, around t h e j ' - p o i n t .
symmetrically d i s p e r s i n g
All t h e s e t h r e e s u r f a c e s t a t e s a r e , a t t h e 3 ' -
p o i n t , w i t h i n t h e band gap of t h e bulk band s t r u c t u r e p r o j e c t e d onto t h e 1x1 s u r f a c e B Z . The e x i s t e n c e of t h e dominant d i s p e r s i n g s u r f a c e s t a t e s t r u c t u r e
(Sl), o r i g i n a l l y r e p o r t e d i n r e f . 1 2 6 , was f i r s t confirmed i n s t u d i e s by van Hoof and van d e r W i e l / 1 2 7 / /128/.
and by Uhrberg e t a l .
I n t h e s e two s t u d i e s , photoemission s p e c t r a were a l s o
o b t a i n e d a l o n g t h e [Oll] and [ O l i l d i r e c t i o n s
(see Fig. 9 ( c ) ) i n
o r d e r t o determine t h e d i s p e r s i o n a l o n g both t h e
r-3
and
r-3'
symmetry l i n e s . Due t o t h e presence of two t y p e s of domains, s u r f a c e s t a t e emission from t h e
r-3
and
F-3' l i n e s
w i l l be superimposed i n
t h e s p e c t r a f o r such d i r e c t i o n s . An i d e n t i f i c a t i o n of t h e d i s p e r s i o n s along t h e two symmetry l i n e s was proposed based on symmetry arguments /128/.
Both groups r e p o r t e d a very small
d i s p e r s i o n (< 0 . 1 e V ) a l o n g t h e 0 . 1 e V ) along t h e
r-3'
line.
I=-3 l i n e and a l a r g e d i s p e r s i o n
A l l t h r e e experiments,
d i f f e r e n t photon e n e r g i e s 13 eV /126/, 2 1 . 2 e V / 1 2 1 / ,
(=
performed a t and 1 0 . 2 eV
/128/, gave a c o n s i s t e n t p i c t u r e e x c e p t f o r s m a l l d i f f e r e n c e s i n t h e
bandwidth and a b s o l u t e energy. L a t e r ARPES s t u d i e s /129-140/ have a l s o been v e r y c o n s i s t e n t and t h e d i s p e r s i o n of S 1 shown i n F i g . 1 0
i s t y p i c a l f o r a high r e s o l u t i o n study.
175
-
Si ( 1 0 0 ) 2 x l towards [ O l O l
' 2 5 '
-2 - 1
0
'
10'
L -2 - 1 0
INITIAL-ENERGY BELOW E,
F=O
-2
-L
-6
-8
-2 -1 lev)
0
-lC
Initial state energy Ei(eV]
F i g . 11. ( a ) A n g l e - r e s o l v e d p h o t o e m i s s i o n s p e c t r a (hv = 2 1 . 2 e V ) o b t a i n e d a l o n g t h e [OlO] a z i m u t h a l d i r e c t i o n f o r v a r i o u s a n g l e s of e m i s s i o n (8,) ( f r o m r e f . 1 3 1 ) . The s u r f a c e s t a t e s S,, S, and S , a s w e l l a s s e v e r a l b u l k s t r u c t u r e s a r e i n d i c a _ t e d i n t h e s p e c t r a . The maximum i n t h e d i s p e r s i o n of S , o c c u r s a t J ' (8, = 3 6 ' ) . ( b ) P h o t o e m i s s i o n s p e c t r a from a h i g h l y n-doped S i ( 1 0 0 ) s a m p l e , o b t a i n e d a t 2 1 . 2 e V p h o t o n e n e r g y , f o r v a r i o u s a n g l e s of e m i s s i o n ( 8 , ) a l o n g t h e [OlO] a z i m u t h a l d i r e c t i o n . The s u r f a c e s t a t e S, and a t t h e 3 ' shows n a r r o w i n t e n s i t y maxima a t t h e ? - p o i n t (8,=0") p o i n t (8,=34') /139/. ( c ) Dependence o f t h e s u r f a c e s t a t e e m i s s i o n i n t e n s i t i e s on t h e a n g l e of i n c i d e n c e ( 8 , ) /139/. S t r u c t u r e S 2 , which l i e s w e l l w i t h i n t h e p r o j e c t e d b u l k band gap, has been observed around
3 ' i n p r a c t i c a l l y a l l ARPES e x p e r i m e n t s i n
which t h e [ O l O ] d i r e c t i o n was p r o b e d /126,128,130-132,134-140/.
It
h a s b e e n s u g g e s t e d t h a t t h e e x i s t e n c e o f ~ ( 4 x 2 )a n d 2x2 r e c o n s t r u c t i o n s c o u l d e x p l a i n t h e p r e s e n c e of s t r u c t u r e S2 / 2 9 / . reconstruction the
For a 2x2
3' p o i n t would c o r r e s p o n d t o a r - p o i n t i n t h e
s e c o n d 2x2-SBZ and t h u s t h e S 2 s t r u c t u r e would c o r r e s p o n d t o t h e d a n g l i n g bond s t a t e a t a f - p o i n t .
However, a s w a s p o i n t e d o u t i n
r e f . 1 3 2 , i n p h o t o e m i s s i o n s t u d i e s where s t r u c t u r e S2 i s w e l l r e s o l -
176
ved /128,132/ t h e e n e r g y i s f o u n d t o be s i g n i f i c a n t l y l o w e r ( 0 . 1 5 eV) t h a n the energy a t
r,
which r u l e s o u t t h i s e x p l a n a t i o n .
r e s o l u t i o n s t u d i e s /132,136/,
In high
t h e s t r u c t u r e S2 f u r t h e r m o r e w a s found
t o h a v e a d i s p e r s i o n minimum a t
3 ' . This i s incompatible with an
e x p l a n a t i o n i n t e r m s of s c a t t e r i n g from t h e r e g i o n w i t h a h i g h dens i t y of states c l o s e t o
?.
One way t o o b t a i n f u r t h e r i n f o r m a t i o n a b o u t S 2 i s t o p e r f o r m s t u d i e s on s i n g l e - d o m a i n
2x1 s u r f a c e s . Single-domain S i ( 1 0 0 ) 2 x l
s u r f a c e s h a v e b e e n o b t a i n e d on S i ( 1 0 0 ) s a m p l e s which a r e c u t o f f a x i s b y t y p i c a l l y 4O. I n t h e s t u d y by B r i n g a n s e t a l . /133/, t h e d i s p e r s i o n o f t h e d a n g l i n g - b o n d s t a t e S1 a l o n g t h e
r-3 and I;-3'
l i n e s w a s unambiguously d e t e r m i n e d , a n d f o u n d t o c o n f i r m t h e e a r l i e r r e s u l t s on two-domain s u r f a c e s / 1 2 8 / . s u r f a c e s /133/, >'-point
I n t h e s t u d y o n s i n g l e domain
it a l s o was c o n c l u d e d t h a t S2 i s n o t o b s e r v e d a t t h e
a l o n g a [Oll] symmetry d i r e c t i o n . I n a l a t e r s t u d y by
U h r b e r g e t a l . /15,138/, i n which a l s o t h e [ 0 1 0 ] - d i r e c t i o n was probed,
s t r u c t u r e S2 w a s o b s e r v e d j u s t as c l e a r l y a s f o r t h e t w o -
domain S i ( 1 0 0 ) 2 x l s u r f a c e s . C o n s i d e r i n g a l l t h e i n f o r m a t i o n a b o u t s t r u c t u r e Sg w e f i n d t h a t it i s a c h a r a c t e r i s t i c s u r f a c e s t a t e band on s i n g l e - d o m a i n
a s w e l l as two-domain
Si(100) surfaces exhibiting
2x1 LEED p a t t e r n s . The s u r f a c e s t a t e s t r u c t u r e S4 was f i r s t o b s e r v e d i n t h e s t u d i e s by Koke e t a l . /130/ a n d Goldmann e t a l . /131/ ( s e e F i g . l l ( a ) ) and t h e d i s p e r s i o n w a s f o u n d t o be t h e same f o r b o t h 1 6 . 8 5 a n d 21.2 e V p h o t o n s . The S 4 s u r f a c e s t a t e h a s a l s o b e e n s t u d i e d by J o h a n s s o n and coworkers w i t h photon e n e r g i e s of 2 1 . 2 e V , eV /140/.
T h e obtained d i s p e r s i o n around
1 6 . 8 5 e V / 1 3 1 / and 1 5 . 0
3' i s v e r y s i m i l a r t o t h a t
o b s e r v e d by K o k e e t a l . /130/, a n d it i s shown i n F i g . 1 0 . There i s some e x p e r i m e n t a l e v i d e n c e t h a t S4 i s d u e t o e m i s s i o n from t h e dimer b o n d s . F i r s t l y , t h e S 4 s u r f a c e s t a t e i s n o t r e d u c e d t o t h e same e x t e n t as t h e s t a t e s S 1 and S 2 , when n o r m a l l i g h t i n c i d e n c e is u s e d , which i n d i c a t e s a h i g h e r d e g r e e o f p x r p y c h a r a c t e r f o r t h e S4 s t a t e
/137,140/. S e c o n d l y , hydrogen c h e m i s o r p t i o n s t u d i e s / 1 3 1 / h a v e shown t h a t f o r t h e ( d i m e r i z e d ) monohydride p h a s e , S i ( 1 0 0 ) 2xl:H, t h e s t a t e s S1 a n d S 2 w i t h d a n g l i n g bond c h a r a c t e r a r e removed a n d S4 r e m a i n s , w h i l e a l l t h r e e s u r f a c e s t a t e s a r e removed on t h e d i h y d r i d e p h a s e , Si(100)1x1:2H. A weak s u r f a c e r e l a t e d s t r u c t u r e
(S3) w a s o b s e r v e d i n t h e e a r l y
s t u d y by Uhrberg e t a l . /128/. The s t r u c t u r e w a s a s s i g n e d to e m i s s i o n from a s u r f a c e resonance ( o v e r l a p p i n g i n e n e r g y w i t h t h e b u l k b a n d s ) s i n c e it showed t h e same s e n s i t i v i t y t o c o n t a m i n a t i o n a s
177
t h e dangling-bond s t a t e . A contamination s e n s i t i v e s t r u c t u r e w a s a l s o o b s e r v e d a t t h e same i n i t i a l e n e r g i e s a n d i n t h e same p a r t o f t h e SBZ i n t h e s t u d y by Koke e t a l . / 1 3 0 / . photon e n e r g y /139/
I n a d d i t i o n , a t 21.2 e V
a contamination s e n s i t i v e s t r u c t u r e i s observed
with a d i s p e r s i o n overlapping with t h o s e r e p o r t e d f o r 1 0 . 2 e V /128/ and 16.85 e V /130/.
The p r e s e n c e of a n e m i s s i o n s t r u c t u r e f o r a l l
t h r e e photon e n e r g i e s with a similar behaviour supports t h e o r i g i n a l s u r f a c e r e s o n a n c e i n t e r p r e t a t i o n . However, t h i s a s s i g n m e n t i s n o t unambiguous a n d more s t u d i e s a r e n e e d e d b e f o r e a p o s i t i v e a s s i g n m e n t c a n b e made. The a n g l e - r e s o l v e d p h o t o e m i s s i o n t e c h n i q u e h a s a l s o b e e n employed i n s t u d i e s o f t h e n o r m a l l y empty s u r f a c e b a n d s . I t w a s shown i n t h e s t u d y by M s r t e n s s o n e t a l . /132/
t h a t by u s i n g h i g h l y n-doped
s a m p l e s ( p = 6 d c m ) a l a r g e enough p o p u l a t i o n o f t h e "empty" s u r f a c e states could be achieved t o f a c i l i t a t e a direct observation of t h e s e s t a t e s i n photoemission.
A new s u r f a c e s t a t e s t r u c t u r e
see F i g s . 1 0 a n d l l ( b , c ) , was o b s e r v e d a t t h e F e r m i l e v e l a n d t h e e m i s s i o n was l o c a t e d i n a v e r y s m a l l k / / - r e g i o n a r o u n d and a r o u n d t h e J ' - p o i n t i n b o t h t h e [ O l l ] , [Oli] a n d [ 0 1 0 ] - d i r e c t i o n s . I n t h e f i r s t s t u d y of t h i s s t a t e /132/ 1 0 . 2 e V p h o t o n s were u s e d , (S5),
r
a n d q u i t e l o w i n t e n s i t y of t h e Fermi s t r u c t u r e w a s o b t a i n e d . I n
l a t e r s t u d i e s u s i n g h i g h e r photon e n e r g i e s c o n s i d e r a b l y h i g h e r i n t e n s i t y of e m i s s i o n h a s been o b t a i n e d / 1 3 6 , 1 3 9 / .
E.g., i n t h e
s p e c t r a i n F i g . l l ( b , c ) , obtained with 2 1 . 2 e V photon energy, t h e e m i s s i o n i n t e n s i t y from t h e F e r m i s t r u c t u r e i s s i m i l a r t o t h e i n t e n s i t y f r o m t h e f i l l e d s u r f a c e s t a t e b a n d (S1)
/139/. I n s t u d i e s
u s i n g s y n c h r o t r o n r a d i a t i o n i n t h e r a n g e 8-27 e V t h e r e l a t i v e e m i s s i o n i n t e n s i t y from t h e Fermi s t r u c t u r e w a s f o u n d t o i n c r e a s e m o n o t o n i c a l l y w i t h photon energy /139/.
From t h e n a r r o w k , , - l o c a l i -
z a t i o n of t h i s s t a t e t h e r e a l - s p a c e e x t e n s i o n o f t h e wave f u n c t i o n w a s c a l c u l a t e d t o be 2 30 A /132/. Due t o t h i s l a r g e v a l u e it was
concluded t h a t t h e s t r u c t u r e s a t t h e Fermi-level
c o u l d n o t b e due t o
l o c a l i z e d d e f e c t s t a t e s , b u t were i n s t e a d due t o e m i s s i o n f r o m minima of a n a l m o s t empty d i s p e r s i n g s u r f a c e b a n d . A s p o i n t e d o u t i n t h e s t u d y by M h r t e n s s o n e t a l . / 1 3 2 / t h e s e s t a t e s , c o r r e s p o n d i n g t o
t h e bottom of t h e empty band, a r e r e s p o n s i b l e f o r t h e F e r m i - l e v e l p i n n i n g o f t h e S i ( 1 0 0 ) s u r f a c e on n-doped
samples.
A small s t r u c t u r e c l o s e t o t h e Fermi level
i n t h e s t u d y by Goldmann e t a l . / 1 3 1 /
at
r
w a s a l s o observed samples.
on l i g h t l y p-doped
T h i s s t r u c t u r e w a s f o u n d t o be h i g h l y l o c a l i z e d a r o u n d t h e l= p o i n t
178
s i m i l a r l y t o t h e s t r u c t u r e o b s e r v e d f o r t h e h i g h l y n-doped samples
/132/, b u t i n c o n t r a s t t o t h e r e s u l t s f o r t h e h i g h l y n-doped s u r f a c e t h e F e r m i - s t r u c t u r e was n o t o b s e r v e d a t 3 ' . The Fermi s t r u c t u r e w a s i n t e r p r e t e d b y Goldmann e t a l . /131/ a s due t o e x t e n d e d defect s t a t e s on t h e s u r f a c e , i n a c c o r d a n c e w i t h t h e i n t e r p r e t a t i o n o f a s i m i l a r s t r u c t u r e on Ge(100)Zxl (see s e c t i o n 5 . 2 ) . It i s worth n o t i n g t h a t f o r t h e h i g h l y n-doped samples /132/ t h e i n t e n s i t y of t h e Fermi-structure a t
5'
was found t o b e h i g h l y reduced when normal
l i g h t i n c i d e n c e was u s e d . The geometry i n t h e e x p e r i m e n t by Goldmann
e t a l . /131/ was s u c h t h a t l i g h t i n c i d e n t c l o s e t o t h e normal w a s u s e d ( e i = 6 " ) , when p r o b i n g s t a t e s c l o s e t o t h e 3' p o i n t , which must have s u b s t a n t i a l l y reduced t h e p o s s i b i l i t y of o b s e r v i n g t h e Fermis t r u c t u r e . An a l t e r n a t i v e e x p l a n a t i o n t o t h a t p u t f o r w a r d by Goldmann e t a l . i s t h a t t h e p r e s e n c e of donor-type d e f e c t s on t h e S i ( 1 0 0 ) s u r f a c e l e a d s t o a s m a l l b u t f i n i t e o c c u p a t i o n a t t h e minima of t h e a n t i b o n d i n g dangling-bond band. I t i s o u r e x p e r i e n c e , t h a t
r e p e a t e d h e a t t r e a t m e n t s and hydrogen e x p o s u r e s of S i ( 1 0 0 ) s u r f a c e s can r a i s e t h e s u r f a c e F e r m i l e v e l p o s i t i o n on l i g h t l y doped c r y s t a l s /139/. T h e s t r u c t u r e a t t h e F e r m i - l e v e l would t h e n n o t be due t o
e m i s s i o n from d e f e c t s t a t e s b u t i n s t e a d due t o e m i s s i o n from s u r f a c e band s t a t e s .
F u r t h e r s t u d i e s a r e needed t o f u l l y c h a r a c t e r i z e t h e
F e r m i s t r u c t u r e on t h e p-doped samples t o f a c i l i t a t e a comparison
with t h e r e s u l t s f o r t h e h i g h l y n-doped s a m p l e s . A d e t a i l e d and c o n s i s t e n t p i c t u r e o f t h e s u r f a c e band s t r u c t u r e
h a s emerged from t h e a n g l e - r e s o l v e d p h o t o e m i s s i o n s t u d i e s , a s was i l l u s t r a t e d i n F i g . 1 0 . I t was e a r l y e s t a b l i s h e d t h a t t h e S i ( 1 0 0 ) 2 x l s u r f a c e i s semiconducting / 8 8 , 1 2 6 / .
The s u r f a c e s t a t e band gap
between t h e S 1 and S5 s u r f a c e bands has been d e t e r m i n e d t o be 0 . 1 e V /132/. The e a r l i e s t s u g g e s t e d models f o r t h e s u r f a c e geometry,
i n c l u d i n g vacancy, c h a i n , and symmetric dimer models, a l l gave metallic s u r f a c e s t a t e b a n d s . T o a c c o u n t f o r t h e s e m i c o n d u c t i n g s u r f a c e e l e c t r o n i c s t r u c t u r e , a m o d i f i c a t i o n of t h e dimer model was p u t f o r w a r d by Chadi /141,142/ w i t h s u p p o r t from e n e r g y m i n i m i z a t i o n c a l c u l a t i o n s . T h i s model c o n s i s t s of asymmetric d i m e r s i n a 2x1 arrangement on t h e s u r f a c e and i s shown i n F i g . 9 ( b ) . The c a l c u l a t e d e l e c t r o n i c s t r u c t u r e f o r t h e asymmetric dimer model /141,143/ showed a s e m i c o n d u c t i n g s u r f a c e w i t h a dangling-bond
dispersion i n quali-
t a t i v e agreement w i t h t h e ARPES r e s u l t s f o r t h e d i s p e r s i o n of S1 /126/. However, some d i s c r e p a n c i e s a l r e a d y e x i s t e d a t t h i s s t a g e ,
e . g . t h e t i g h t - b i n d i n g c a l c u l a t i o n gave a dangling-bond band t h a t was more t h a n twice a s wide a s t h e e x p e r i m e n t a l s u r f a c e s t a t e band
179
( 1 . 2 e V compared t o 0 . 5 e V ) . A s e l f - c o n s i s t e n t
pseudopotential
c a l c u l a t i o n for t h e same s t r u c t u r e /143/ g a v e a b a n d w i d t h of t h e r i g h t magnitude b u t t h e dangling-bond band w a s l o c a t e d = 0.8 e V t o o high i n energy. Improvements i n t h e a b s o l u t e e n e r g y a n d e s p e c i a l l y i n t h e band w i d t h o f t h e d a n g l i n g - b o n d b a n d were o b t a i n e d i n l a t e r c a l c u l a t i o n s by Bowen e t a l . /144/ a n d by Mazur a n d Pollmann /145,146/.
The
c o m p a r i s o n s b e t w e e n t h e o r y a n d t h e e x p e r i m e n t a l r e s u l t s /144,145/ f o r t h e S 1 b a n d from r e f s . 1 2 6 , 1 2 7 a n d 1 2 8 w e r e v e r y f a v o u r a b l e for t h e a s y m m e t r i c d i m e r m o d e l . However, t h e s u p p o r t i s e s s e n t i a l l y based on o n l y o n e s u r f a c e s t a t e band,
t h e dangling-bond
band ( S l ) ,
w i t h some a d d i t i o n a l s u p p o r t b a s e d on t h e a g r e e m e n t b e t w e e n t h e c a l c u l a t e d d i m e r bond b a n d and s t r u c t u r e S, f o u n d i n e x p e r i m e n t s . The s u r f a c e s t a t e s which c a n n o t be e a s i l y a c c o u n t e d f o r by t h e a s y m m e t r i c 2 x 1 dimer-model a r e S 2 , S4 and S g ( a t
r ) . Around
Sg s t r u c t u r e c a n be e x p l a i n e d b y t h e empty d a n g l i n g - b o n d
j’ t h e
b a n d which
shows a minimum a t t h i s symmetry p o i n t i n most c a l c u l a t i o n s . The s u r f a c e band c a l c u l a t i o n s u s u a l l y show s e v e r a l s u r f a c e s t a t e s / r e s o n a n c e s i d e n t i f i e d a s d i m e r bond and back-bond s t a t e s . I n t h e c a l c u l a t i o n s by Pollmann e t a l . /13,141/ t h e s e s u r f a c e r e s o n a n c e s
were f o u n d c l o s e t o
and 3' i n t h e e n e r g y r a n g e 1-4 e V below t h e
v a l e n c e b a n d maximum. A m a t c h i n g o f t h e e x p e r i m e n t a l b a n d s w i t h c a l c u l a t e d b a n d s i s d i f f i c u l t however, s i n c e o n l y t h r e e k , , - p o i n t s o v e r l a p b e t w e e n t h e e x p e r i m e n t a l l y p r o b e d [OlO]- d i r e c t i o n
(F-3' )
and
t h e symmetry l i n e s s t u d i e d i n t h e c a l c u l a t i o n . For S 2 t h e r e does n o t
s e e m t o be a n y r e a s o n a b l e e x p l a n a t i o n i n a n y o f t h e t h e o r e t i c a l band s t r u c t u r e s p r e s e n t e d for t h e 2x1 d i m e r model of t h e S i ( 1 0 0 ) s u r f a c e . I t h a s been s u g g e s t e d t h a t S p c o u l d be a n a r t i f a c t due t o t h e
p r e s e n c e of t h e two 2x1 domains on t h e s u r f a c e .
A s d i s c u s s e d above,
s t u d i e s on s i n g l e - d o m a i n S i ( 1 0 0 ) Z x l s u r f a c e s h a v e shown, however, t h a t S2 i s a l s o p r e s e n t on t h e s e s u r f a c e s w i t h t h e same r e l a t i v e i n t e n s i t y compared t o t h e d a n g l i n g bond s t a t e S 1 . D e s p i t e t h e f a c t t h a t t h e s u r f a c e band s t r u c t u r e c a l c u l a t i o n s f o r t h e d i m e r model g i v e good a g r e e m e n t w i t h e x p e r i m e n t a l d a t a f o r t h e d a n g l i n g - b o n d b a n d S1, w e f i n d t h a t more d e t a i l e d c o m p a r i s o n s have t o b e done,
s i n c e o n l y a s m a l l number o f t h e e x p e r i m e n t a l s u r f a c e
s t a t e s h a v e so f a r b e e n a c c o u n t e d f o r . F u r t h e r t h e o r e t i c a l a n a l y s i s of t h e e l e c t r o n i c s t r u c t u r e o f a l t e r n a t i n g asymmetric dimers w i t h 2x2 or ~ ( 4 x 2 )symmetry i s l i k e l y t o improve t h e u n d e r s t a n d i n g of t h e S i ( 1 0 0 ) 2 x 1 s u r f a c e with a seemingly i n h e r e n t d i s o r d e r e d d i s t r i b u t i o n o f symmetric and asymmetric d i m e r s .
180
5.2
G e ( 100)2x1 and c (4x2) s u r f a c e s
ARPES s t u d i e s of t h e photon energy dependence o f e m i s s i o n i n t h e
normal d i r e c t i o n from Ge(100)2x1 s u r f a c e s have been r e p o r t e d by Nelson e t a l . / 1 4 8 / ,
Neave e t a l . / 1 4 9 /
and H s i e h e t a l . /150/.
Although t h e sample s u r f a c e s w e r e p r e p a r e d q u i t e d i f f e r e n t l y , t h e e x p e r i m e n t a l r e s u l t s a r e v e r y c o n s i s t e n t . Nelson e t a l . p r e p a r e d t h e s u r f a c e by a r g o n i o n bombardment and a n n e a l i n g , w h i l e Hsieh e t a l . a l s o u s e d h o m o e p i t a x i a l l y MBE-grown G e ( 1 0 0 ) 2 x 1 s u r f a c e s . F i n a l l y , Neave e t a l . s t u d i e d Ge(100) s u r f a c e s grown by MBE on GaAs(100) s u b s t r a t e s . I n a l l t h r e e s t u d i e s /148-150/,
s t r o n g , dispersive
f e a t u r e s c o u l d be i d e n t i f i e d a s d i r e c t t r a n s i t i o n s from t h e b u l k v a l e n c e bands and t h e r e w e r e a l s o two n o n - d i s p e r s i v e
features a t
=0.6 e V and ~ 1 . 3e V below t h e v a l e n c e band e d g e . I n t h e work by Nelson e t a l . and Neave e t a l . t h e s e n o n - d i s p e r s i v e f e a t u r e s were a t t r i b u t e d t o s u r f a c e s t a t e s . In a l a t e r study t h e s u r f a c e s t a t e i n t e r p r e t a t i o n f o r low p h o t o n e n e r g i e s was c h a l l e n g e d by Hsieh e t a l . , who concluded t h a t t h e s e s t r u c t u r e s were o v e r l a p p i n g w i t h b u l k t r a n s i t i o n s . Although t h e y , a l s o for t h e h i g h e r p h o t o n e n e r g i e s , o f f e r e d a l t e r n a t i v e e x p l a n a t i o n s of t h e s t r u c t u r e s i n terms of b u l k e m i s s i o n , t h e y concluded t h a t most l i k e l y t h e r e a r e two s u r f a c e s t a t e s g i v i n g e m i s s i o n a t -0.5
and -1.3 e V i n t h e normal e m i s s i o n
s p e c t r a f o r h i g h photon e n e r g i e s . I n an a t t e m p t t o r e s o l v e t h e c o n t r o v e r s y , Kruger e t a l . /151/ t h e o r e t i c a l l y s t u d i e d t h e e l e c t r o n i c s t r u c t u r e o f t h e asymmetric dimer model f o r t h e ( 1 0 0 ) 2 x 1 s u r f a c e s o f G e and S i . Using t h e s e l f c o n s i s t e n t s c a t t e r i n g t h e o r e t i c a l method t h e y c a l c u l a t e d wave-vector r e s o l v e d l a y e r d e n s i t y of s t a t e s a t d i f f e r e n t p o i n t s i n t h e s u r f a c e BZ.
Two s u r f a c e s t a t e s , c o r r e s p o n d i n g t o a d a n g l i n g bond s t a t e on
t h e r a i s e d dimer atom and a back-bond s t a t e , were found n e a r t h e e x p e r i m e n t a l l y found e n e r g y p o s i t i o n s . I t was shown t h a t t h e topmost s t a t e ( t h e d a n g l i n g bond s t a t e ) i s a w e l l d e f i n e d s t a t e o n l y i n t h e o u t e r p a r t s of t h e s u r f a c e BZ, w h i l e it becomes a v e r y b r o a d and weak r e s o n a n c e a t
r,
decaying slowly i n t o t h e b u l k . D i f f i c u l t i e s i n
i d e n t i f y i n g t h i s s u r f a c e r e s o n a n c e i n measurements of t h e e m i s s i o n i n t h e normal d i r e c t i o n can t h u s be e x p e c t e d f o r Ge(100) 2x1, w h i l e f o r S i ( 1 0 0 ) 2 x l t h e d a n g l i n g bond s u r f a c e s t a t e remains a pronounced r e s o n a n c e a l l t h e way up t o t h e F - p o i n t . I n t h e p a p e r by Nelson e t a l . /148/ t h e s u r f a c e s t a t e d i s p e r s i o n s were r e p o r t e d f o r t h e LO111 a z i m u t h a l d i r e c t i o n , which c o r r e s p o n d s t o t h e i=s d i r e c t i o n f o r one 2x1 domain-type and t h e
Fj’
direction
181 S i ( 1 0 0 ) 2 x l t h e r e w a s a l s o e m i s s i o n i n a narrow a n g u l a r r a n g e around t h e 3'-point
o f t h e 2x1 s u r f a c e BZ. F i n a l l y , t h e t e m p e r a t u r e
d e p e n d e n c e o f e m i s s i o n i s o p p o s i t e f o r S i a n d G e . For S i ( 1 0 0 ) 2 x l t h e peak h e i g h t i n c r e a s e s w i t h d e c r e a s i n g t e m p e r a t u r e ,
which p r o b a b l y
j u s t r e f l e c t s t h e change i n t h e F e r m i - D i r a c d i s t r i b u t i o n ,
i.e. the
e l e c t r o n s p i l e up a t t h e minimum o f t h e a l m o s t empty b a n d . The t o t a l number o f e l e c t r o n s i n t h i s band i s e x p e c t e d t o be c o n s t a n t f o r S i r s i n c e t h e minimum of t h e s u r f a c e s t a t e b a n d i s 0 . 4 e V a b o v e t h e v a l e n c e b a n d e d g e which e x c l u d e s t h e r m a l e x c i t a t i o n from t h e v a l e n c e band. What c o u l d be t h e r e a s o n f o r t h e i n c r e a s e o f t h e m e t a l l i c p e a k with i n c r e a s i n g temperature f o r Ge(100)? F i r s t l y , t h e increase i n t h e number o f s u r f a c e s t a t e e l e c t r o n s n e a r t h e l=-point
(seen i n
normal e m i s s i o n ) , can r e f l e c t a s i g n i f i c a n t change i n t h e e l e c t r o n i c s t r u c t u r e a s t h e s u r f a c e d i s o r d e r s , a s w a s s u g g e s t e d by Kevan /124/. Secondly,
s i n c e t h e e n e r g y o f t h e m e t a l l i c peak i s v e r y c l o s e t o t h e
v a l e n c e b a n d e d g e on G e ( 1 0 0 ) , i t i s p o s s i b l e t h a t t h e o c c u p a t i o n of t h e s u r f a c e s t a t e b a n d i s due t o t h e r m a l e x c i t a t i o n from t h e b u l k e n e r g y b a n d s , i n which case t h e s i m u l t a n e o u s o c c u r r e n c e o f t h e change i n o r d e r o f t h e s u r f a c e would be a c c i d e n t a l . I n c o n c l u s i o n , t h e i n f o r m a t i o n o b t a i n e d i n ARPES e x p e r i m e n t s on G e ( 1 0 0 ) s u r f a c e s i s somewhat f r a g m e n t a r y . T o d e s c r i b e and u n d e r s t a n d t h e s u r f a c e e l e c t r o n i c s t r u c t u r e s o f t h e G e ( 1 0 0 ) 2 x l and ~ ( 4 x 2 ) s u r f a c e s t h e r e i s a g r e a t n e e d f o r e x t e n s i v e b a n d mapping s t u d i e s . The o r i g i n o f t h e m e t a l l i c s u r f a c e s t a t e i s s t i l l a n open q u e s t i o n ,
a n d it would p r o b a b l y be v e r y h e l p f u l t o s t u d y t h i s s t a t e on h i g h l y n-doped
c r y s t a l s , where t h e r e s h o u l d b e more e l e c t r o n s i n t h i s
state.
6
CLEAVED (110) SURFACES OF 1 1 1 - V
SEMICONDUCTORS
F o r 1 1 1 - V compound s e m i c o n d u c t o r s , t h e ( 1 1 0 ) s u r f a c e s e x h i b i t simple 1x1 r e l a x a t i o n s , while t h e p o l a r
(111) a n d ( 1 0 0 ) s u r f a c e s a r e
c o n s i d e r a b l y more complex, o f t e n e x h i b i t i n g a l a r g e number of rec o n s t r u c t i o n s . I n b o t h t h e o r e t i c a l and e x p e r i m e n t a l s t u d i e s of t h e s u r f a c e e l e c t r o n i c s t r u c t u r e o f 1 1 1 - V compound s e m i c o n d u c t o r s u r faces,
t h e emphasis h a s t h e r e f o r e been on t h e ( 1 1 0 ) s u r f a c e . I t i s
t h e o n l y non-polar
s u r f a c e a n d it c a n b e e a s i l y p r e p a r e d i n a c l e a n
and s t o i c h i o m e t r i c s t a t e i n s i t u , a s i t i s t h e n a t u r a l c l e a v a g e plane. S i n c e GaAs i s t h e t e c h n o l o g i c a l l y most i m p o r t a n t 1 1 1 - V compound
182
f o r t h e o t h e r 2x1 domain-type.
These d i s p e r s i o n s a r e q u i t e s i m i l a r
t o t h e r e s u l t s of Uhrberg e t a l . /128/ f o r t h e same a z i m u t h a l d i r e c t i o n on S i ( 1 0 0 ) 2 x l . Although t h i s l i m i t e d s e t of r e s u l t s i s c o n s i s t e n t w i t h t h e c a l c u l a t e d d i s p e r s i o n s f o r t h e asymmetric dimer model,
it seems v e r y l i k e l y t h a t f u r t h e r d e t a i l e d s t u d i e s of t h e
e l e c t r o n i c s t r u c t u r e of t h e Ge(100)2x1 s u r f a c e w i l l i d e n t i f y s u r f a c e s t a t e s t h a t cannot be e x p l a i n e d by t h e asymmetric dimer model,
just
l i k e t h e case f o r t h e Si(100)2xl surface. High-resolution
ARPES s t u d i e s on t h e Ge(100) s u r f a c e by Kevan and
S t o f f e l /123,124/
c o n c e n t r a t e d on t h e emission from a p r e v i o u s l y not
observed m e t a l l i c s u r f a c e s t a t e , which was observed o n l y o v e r a very narrow range of p a r a l l e l momenta n e a r t h e c e n t e r of t h e s u r f a c e BZ. The emission was found t o slowly d i s a p p e a r a s t h e t e m p e r a t u r e was lowered from room t e m p e r a t u r e t o 7 1 K . T h i s behaviour was d e s c r i b e d a s a m e t a l - i n s u l a t o r t r a n s i t i o n , which was found t o be c o i n c i d e n t with t h e g r a d u a l t r a n s i t i o n of t h e LEED p a t t e r n from 2x1 t o ~ ( 4 x 2 ) . The emission from t h e s u r f a c e s t a t e a t t h e Fermi l e v e l and some LEED p r o f i l e s a r e shown i n F i g . 1 2 f o r d i f f e r e n t s u b s t r a t e t e m p e r a t u r e s (from r e f . 1 2 3 ) . The p h y s i c a l o r i g i n of t h e m e t a l l i c s u r f a c e s t a t e i s not p r e s e n t l y c l e a r . I n r e f . 1 2 4 Kevan s u g g e s t e d t h a t d e f e c t dangling bond s t a t e s appeared i n t h e b u l k band-gap
due t o d i s o r d e r of t h e
c (4x2) r e c o n s t r u c t i o n , induced by f l i p p i n g s i n g l e dimers. From t h e narrow k/,-range FWHM),
f o r which t h i s s t a t e was observed
(
Ak = 0 . 0 9 A - l ,
it was concluded t h a t t h e m e t a l l i c s t a t e was r e l a t e d t o
d e f e c t s with an e s t i m a t e d r e a l space e x t e n t of 10-12
A, i . e .
approximately t h r e e d i m e r s . T h i s e s t i m a t e was l a t e r q u e s t i o n e d by Mdrtensson e t a l . /132/,
who d e r i v e d a lower l i m i t of 30
A for the
r e a l space e x t e n t of t h e s u r f a c e s t a t e s . Since t h e s u r f a c e s t a t e t h u s e x t e n d s over a t l e a s t 50 atoms, i t was s u g g e s t e d t h a t t h e m e t a l l i c peak i s n o t due t o emission from l o c a l i z e d d e f e c t s , but t o emission from t h e bottom of an almost empty d i s p e r s i n g s u r f a c e s t a t e band p i n n i n g t h e Fermi l e v e l . T h i s e x p l a n a t i o n could account f o r t h e f a c t t h a t t h e k/,-range,
f o r which t h e emission was observed,
i n c r e a s e d w i t h t e m p e r a t u r e /123/,
s i n c e a temperature increase w i l l
l e a d t o an i n c r e a s e d o c c u p a t i o n i n s t a t e s away from t h e m i n i m u m of t h e almost empty band. I n t h e experiments by Kevan e t a l . on G e ( 1 0 0 ) , l i g h t l y n-doped
c r y s t a l s w e r e used,
so a f i n i t e occupation
of e l e c t r o n s i n such a band i s e x p e c t e d . We want t o p o i n t o u t h e r e t h a t , whether a semiconductor s u r f a c e a p p e a r s a s m e t a l l i c o r n o t ,
183
ARP
LEED
0 5 BINDING
EF
ENERGY ( e v )
0
2
4
MOMENTUM TRANSFER
F i g . 1 2 . L e f t h a l f : The t e m p e r a t u r e d e p e n d e n t p h o t o e m i s s i o n n e a r t h e F e r m i - l e v e l , s e e n i n normal e m i s s i o n s p e c t r a from t h e Ge(100) s u r f a c e u s i n g 2 0 eV p h o t o n e n e r g y . R i g h t h a l f : LEED i n t e n s i t y p r o f i l e s e x t e n d i n g from t h e ( 0 , O ) beam t o t h e (1,1/2) beam a t t h e s a m e t e m p e r a t u r e s . T h e g r a d u a l a p p e a r a n c e of a p e a k a t 2 . 2 A-1 i s i n d i c a t i v e o f t h e t r a n s i t i o n t o a n o r d e r e d ~ ( 4 x 2 )s t r u c t u r e . From r e f . 123. d e p e n d s on t h e d o p i n g o f t h e b u l k s e m i c o n d u c t o r . E . g . ,
t h e (111)2x1
and ( 1 0 0 ) 2 x 1 s u r f a c e s o f h i g h l y n-doped S i - c r y s t a l s a p p e a r to b e
m e t a l l i c , s i n c e t h e r e c a n be a n a p p r e c i a b l e o c c u p a t i o n of e l e c t r o n s i n s u r f a c e s t a t e b a n d s i n t h e b u l k band-gap,
which would be empty
f o r u n c h a r g e d s u r f a c e s o f undoped s i l i c o n . T h e r e a r e some s t r o n g s i m i l a r i t i e s between t h e m e t a l l i c s t a t e s on Ge(100)Zxl and S i ( 1 0 0 ) 2 x l s u r f a c e s , suggesting similar o r i g i n s . F i r s t l y , the emission f r o m both s t a t e s i s s t r o n g l y l o c a l i z e d around t h e normal d i r e c t i o n . S e c o n d l y , t h e y have t h e same p h o t o n e n e r g y dependence, i . e . t h e i n t e n s i t y of t h e metallic s t a t e s relative t o t h e o t h e r s t r u c t u r e s i n c r e a s e monotonically w i t h photon energy i n t h e range 1 4 t o 2 1 e V /123,139/. There are a l s o s i g n i f i c a n t d i f f e r e n c e s i n t h a t t h e metallic s t a t e on G e ( 1 0 0 ) was o n l y s e e n n e a r t h e s u r f a c e n o r m a l , w h i l e on
184
s e m i c o n d u c t o r it h a s become a p r o t o t y p e f o r basic s u r f a c e s t u d i e s on t h i s t y p e o f s e m i c o n d u c t o r . Both t h e cleaved and t h e s p u t t e r e d and a n n e a l e d G a A s ( l l 0 ) s u r f a c e s g i v e a 1x1 p a t t e r n i n LEED e x p e r i m e n t s , and t h e r e i s s t r o n g e v i d e n c e i n t h e e l e c t r o n e n e r g y dependence o f t h e s p o t i n t e n s i t i e s t h a t t h e s u r f a c e has a large r e l a x a t i o n / 1 5 2 / . A schematic v i e w o f t h e s u r f a c e atom c o n f i g u r a t i o n i s g i v e n i n F i g .
1 3 ( a , b ) . The r e l a x a t i o n i s c h a r a c t e r i z e d by a d i s p l a c e m e n t o f t h e A s atoms o u t o f t h e s u r f a c e p l a n e and o f t h e G a atoms i n t o t h e c r y s t a l , g i v i n g r i s e t o a bond r o t a t i o n a n g l e a. The Ga-As
bonds on t h e f i r s t
s u b s u r f a c e p l a n e c o u n t e r r o t a t e b y a s m a l l a n g l e . The g r o s s f e a t u r e s o f t h e G a A s ( l l 0 ) r e l a x a t i o n h a s been a c c e p t e d f o r a l o n g t i m e , b u t d u r i n g t h e mid-80's
some c o n t r o v e r s i e s a r o s e c o n c e r n i n g t h e magni-
t u d e o f t h e bond-angle
r o t a t i o n a n d t h e changes i n bond l e n g t h s . A
r e c e n t r e v i e w of t h e h i s t o r i c a l development of t h e d e t e r m i n a t i o n of t h e G a A s ( l l 0 ) r e l a x a t i o n h a s been g i v e n by Duke and P a t t o n / 1 5 2 / .
The e l e c t r o n i c s t r u c t u r e of t h e G a A s ( l l 0 ) s u r f a c e h a s been s t u d i e d e x p e r i m e n t a l l y and t h e o r e t i c a l l y by a l a r g e number of g r o u p s
/153-182/. One m a j o r q u e s t i o n h a s been w h e t h e r t h e r e a r e a n y s u r f a c e
states i n t h e a b s o l u t e , fundamental gap. For a n unrelaxed s u r f a c e geometry t h e d a n g l i n g bond s t a t e s on t h e A s and Ga atoms a r e c a l c u l a t e d t o b e w i t h i n o r v e r y n e a r t h e band gap, while t h e y a r e pushed o u t o f t h e g a p by c e r t a i n r e l a x a t i o n s . E a r l y e x p e r i m e n t a l d a t a on Fermi l e v e l p i n n i n g i n p h o t o e m i s s i o n measurements /183/ and c o n t a c t p o t e n t i a l d i f f e r e n c e measurements /184/ s u g g e s t e d t h a t t h e r e w e r e empty s u r f a c e s t a t e s i n t h e g a p . However, it w a s c o n v i n c i n g l y shown b y s e v e r a l g r o u p s /185-187/ t h a t t h e s e s t a t e s a r e d e f e c t s t a t e s a b s e n t on h i g h q u a l i t y c l e a v e s . P a r t i a l y i e l d measurements
/188/ a l s o g a v e some e v i d e n c e f o r empty s u r f a c e s t a t e s i n t h e gap, s i n c e e x c i t a t i o n s of G a 3d e l e c t r o n s i n t o empty s u r f a c e s t a t e s below
(a) Side view
(b) Top view
a (c) SBZ
x
i=
X'
F i g . 1 3 . S c h e m a t i c view of t h e bond a n g l e r e l a x a t i o n model f o r t h e ( b ) t o p view, (c) surface G a A s ( l l 0 ) s u r f a c e . ( a ) s i d e view, B r i l l o u i n zone.
185
t h e c o n d u c t i o n b a n d e d g e seemed t o b e p o s s i b l e
.
The low v a l u e o f
t h e e x c i t a t i o n t h r e s h o l d was l a t e r e x p l a i n e d by s t r o n g e x c i t o n i c i n t e r a c t i o n s between t h e e l e c t r o n e x c i t e d t o t h e empty s u r f a c e s t a t e a n d t h e G a 3d c o r e h o l e / 1 8 9 / .
I t i s now w e l l e s t a b l i s h e d t h a t t . h e r e
a r e n o i n t r i n s i c s u r f a c e s t a t e s i n t h e a b s o l u t e b a n d g a p of GaAs ( 1 1 0 )
.
From c o n t a c t p o t e n t i a l d i f f e r e n c e measurements on c l e a v e d 1 1 1 - V ( 1 1 0 ) s u r f a c e s by H u i j s e r and c o w o r k e r s / 1 8 , 1 9 /
t h a t besides GaAs n e i t h e r o f GaSb,
it w a s c o n c l u d e d
InAs o r I n P have i n t r i n s i c
s u r f a c e s t a t e s i n t h e a b s o l u t e band g a p . F o r Gap, however, l e v e l on n-doped
the Fermi
( 1 1 0 ) s u r f a c e s was p i n n e d a t = 0 . 5 e V below t h e
c o n d u c t i o n b a n d e d g e , i n d i c a t i n g t h e e x i s t e n c e of a n empty s u r f a c e s t a t e band i n t h e band g a p . O c c a s i o n a l l y , on t h e o t h e r s u r f a c e s , d e f e c t s t a t e s i n t h e gap were o b s e r v e d t o a f f e c t t h e Fermi l e v e l p o s i t i o n . T h i s c o u l d e x p l a i n why i n some e a r l i e r s t u d i e s , on f o r example InP,
t h e r e had b e e n r e p o r t s o f i n t r i n s i c s u r f a c e s t a t e s i n
t h e gap.
6.1
ARPES s t u d i e s o f G a A s ( l l 0 )
P h o t o e m i s s i o n s t u d i e s on G a A s ( l l 0 ) s u r f a c e s h a v e b e e n p e r f o r m e d by many d i f f e r e n t g r o u p s / 9 0 , 1 5 3 - 1 6 8 / ,
c o v e r i n g a wide r a n g e o f
p h o t o n e n e r g i e s f r o m 9 t o 1 0 0 e V . S e v e r a l o f t h e s e s t u d i e s have been concerned w i t h t h e photon energy dependence o f t h e e m i s s i o n i n t h e normal d i r e c t i o n /90,153,161-165/.
I t can be concluded t h a t emission
a r i s i n g f r o m b u l k t r a n s i t i o n s h a s b e e n i d e n t i f i e d o v e r t h e whole photon energy range, while t h e only suggested s u r f a c e s t a t e i n t h e s e n o r m a l e m i s s i o n s t u d i e s i s a v e r y weak s h o u l d e r a t = 0 . 1 e V below t h e v a l e n c e band e d g e , t h a t was r e p o r t e d by M i l l s e t a l . / 1 6 1 / . ARPES s t u d i e s on G a A s ( l l 0 ) i n v e s t i g a t i n g e m i s s i o n from s u r f a c e
s t a t e s / r e s o n a n c e s h a v e b e e n p u b l i s h e d by Knapp a n d c o w o r k e r s /1541 5 6 / , W i l l i a m s e t a l . /157/, H u i j s e r e t a l . / 1 5 8 / , /166/
and M g r t e n s s o n e t a l . / 1 6 8 /
Solal et a l .
a n d t h e r e s u l t s a r e summarized i n
t h e e n e r g y b a n d d i a g r a m i n F i g . 1 4 . The most e x t e n s i v e e x p e r i m e n t a l s u r f a c e s t a t e d i s p e r s i o n s a r e from t h e s t u d y by H u i j s e r e t a l . . To o b t a i n t h e measured d i s p e r s i o n s t h e y used b o t h H e I ( 2 1 . 2 I (16.8 eV)
s e v e r a l d i f f e r e n t c o l l e c t i o n geometries. E . g . , t h e ??.-line
ev) a n d
Ne
r a d i a t i o n and t h e y s t u d i e d t h e photoemission using t h e d i s p e r s i o n s along
w e r e m e a s u r e d w i t h f o u r d i f f e r e n t g e o m e t r i e s , by u s i n g
p o s i t i v e o r negative angles of l i g h t incidence,
f o r emission angles
e i t h e r on t h e Ga, o r t h e A s d a n g l i n g bond s i d e o f t h e n o r m a l . The
186
h
2
........
HUlJSer et al
Y
Knspp, Eastrnan e t a1
>
-. -, -.-
(3
Knapp and Lapeyre
K
w Z w
0
W i l l i a m s e t a1
-. ._..-
-..
Solal e t al
1
5 t
r i b t e n s s o n e t al
z
SURFACE WAVEVECTOR Fia. 14. Summary of the experimental surface state bands reported fo; the GaAs(ll0) surface orientation of the surface BZ relative to the surface unit cell is shown in Fig. 13(c). To identify the emission from surface states, they used contamination tests (lo5 - lo6 L of hydrogen) and studied the dispersions with two different photon energies. Unfortunately, very little primary data, i.e. spectra or measured peak energy positions, were published in the paper by Huijser et al. /158/, so it is difficult to assess the credibility of the measured band dispersions and their interpretation as surface state bands. It is somewhat surprising that it seems that practically all structures seen by Huijser et al. could apparently be interpreted as due to surface states/resonances, especially since bulk transitions dominate the normal emission spectra in the same photon energy range /161,164,165/. In the summary of reported surface state dispersions in Fig. 14, there is rather good agreement between different experiments concerning some major features in the photoemission spectra, like the energy positions of the uppermost surface state bands at the X and 2' points. A l s o in unpublished ARPES studies by Aust / 1 6 1 / using 21.2 eV radiation, good agreement was obtained with the results of Huijser et al. /158/ concerning the dispersion of the topmost surface state band and the peak positions at the f and 2 ' points.
187
However, e x c e p t f o r t h e topmost band, t h e d i s p e r s i o n s away from t h e high s y m m e t r y p o i n t s were s i g n i f i c a n t l y d i f f e r e n t from t h e r e s u l t s of H u i j s e r e t a l . . Considering t h e l a c k of r e p r o d u c i b l e r e s u l t s concerning most of t h e f e a t u r e s r e p o r t e d , w e f i n d t h a t t h e r e i s a need f o r a new e x t e n s i v e band mapping s t u d y b e f o r e t h e s u r f a c e s t a t e band s t r u c t u r e can be e s t a b l i s h e d . I t would a l s o be very h e l p f u l i f t h e c o n t r i b u t i o n s from bulk emission i n t h e off-normal d i r e c t i o n s could be a n a l y z e d i n d e t a i l . T h e o r e t i c a l s t u d i e s of t h e e l e c t r o n i c s t r u c t u r e of G a A s ( l l 0 ) have been performed by many groups u s i n g d i f f e r e n t computational t e c h n i q u e s i n o r d e r t o i n v e s t i g a t e s e v e r a l d i f f e r e n t model geometries f o r t h e r e l a x a t i o n of t h e s u r f a c e /156,171-181/. The c a l c u l a t e d s u r f a c e s t a t e band s t r u c t u r e s have a l o t i n common, b u t t h e r e a r e a l s o s i g n i f i c a n t d i f f e r e n c e s , r e l a t e d t o t h e model used o r t o t h e t y p e o f c a l c u l a t i o n u s e d . For d e t a i l e d comparisons between t h e c a l c u l a t e d s u r f a c e s t a t e band s t r u c t u r e s and t h e r e s u l t s from ARPES s t u d i e s , we r e f e r t o t h e o r i g i n a l t h e o r e t i c a l p a p e r s . I n g e n e r a l , t h e r e i s good agreement between t h e c a l c u l a t e d ,
occupied d a n g l i n g
bond band on t h e A s s u r f a c e atoms and t h e topmost e x p e r i m e n t a l l y observed band. Although t h e agreement i s not s o good f o r t h e o t h e r e x p e r i m e n t a l l y observed bands,
i t has been p o s s i b l e t o a s s o c i a t e a
c a l c u l a t e d s u r f a c e s t a t e / r e s o n a n c e /176/ t o each of t h e s t r o n g f e a t u r e s s e e n i n t h e ARPES s p e c t r a from H u i j s e r e t a l . /158/. I n c o n c l u s i o n , ARPES s t u d i e s o n t h e G a A s ( l l 0 ) s u r f a c e have i n d i c a t e d a l a r g e number of s u r f a c e s t a t e s o r r e s o n a n c e s , some of which have been r e p o r t e d o n l y i n a s i n g l e and b r i e f l y r e p o r t e d s t u d y . From LEED,
medium-energy
i o n - s c a t t e r i n g and t h e o r e t i c a l c a l c u l a t i o n s
s t r o n g s u p p o r t f o r t h e bond a n g l e r e l a x a t i o n model h a s been o b t a i n e d
/152/. C a l c u l a t i o n s of t h e s u r f a c e e l e c t r o n i c s t r u c t u r e u s i n g t h i s model can a t l e a s t q u a l i t a t i v e l y e x p l a i n most of t h e r e p o r t e d s u r f a c e s t a t e f e a t u r e s . For t h e topmost s u r f a c e s t a t e band, d i f f e r e n t e x p e r i m e n t s have given a c o n s i s t e n t d i s p e r s i o n , which i s i n good agreement with c a l c u l a t i o n s f o r t h e A s d a n g l i n g bond band. I n particular,
t h i s s u r f a c e s t a t e band i s found o u t s i d e t h e a b s o l u t e
band gap i n b o t h experiments and c a l c u l a t i o n s . 6.2
GaSbf 110)
GaSb i s a 1 1 1 - V compound semiconductor with a band s t r u c t u r e s i m i l a r t o e . g . t h a t of GaAs. However, due t o t h e l a r g e atomic number of Sb, r e l a t i v i s t i c e f f e c t s , l i k e s p i n - o r b i t
splitting, are
more i m p o r t a n t f o r GaSb. The e l e c t r o n i c s t r u c t u r e of GaSb has been
s t u d i e d q u i t e e x t e n s i v e l y by C h i a n q a n d Eastman /190/. They d e t e r mined t h e b u l k b a n d e n e r g y d i s p e r s i o n s , E ( k ) , a n d c r i t i c a l p o i n t s , u s i n g ARPES s t u d i e s o f t h e c l e a v e d G a S b ( l l 0 ) s u r f a c e . C o n c e r n i n g t h e s u r f a c e e l e c t r o n i c s t r u c t u r e o f G a S b ( l l O ) , C h i a n g a n d Eastman p r o b e d e m i s s i o n from t h e
r
a n d M p o i n t s o f t h e s u r f a c e BZ, b u t t h e y d i d n o t
r e p o r t a n y e m i s s i o n from s u r f a c e s t a t e s a t t h e s e symmetry p o i n t s .
A d e t a i l e d ARPES s t u d y o f t h e e m i s s i o n n e a r t h e v a l e n c e band edge
w a s r e c e n t l y p r e s e n t e d by Manzke e t a l . /191/. They u s e d v e r y h i g h energy and angular r e s o l u t i o n i n t h e i r s t u d i e s of t h e cleaved G a S b ( l l 0 ) s u r f a c e . I n t h e normal e m i s s i o n s p e c t r a i n F i g . 1 5 ( a ) , e m i s s i o n f r o m t h e t o p m o s t t h r e e v a l e n c e b a n d s a r e i n d i c a t e d by A, B, a n d C , w h i l e a weak c o n t r i b u t i o n i n t e r p r e t e d a s s u r f a c e s t a t e e m i s s i o n i s d e n o t e d S S . C o n s i s t e n t w i t h s t u d i e s on o t h e r 1 1 1 - V
(110)
s u r f a c e s , t h e s u g g e s t e d s u r f a c e s t a t e e m i s s i o n i n t h e normal d i r e c t i o n h a s v e r y low i n t e n s i t y a n d it i s d i f f i c u l t t o s e p a r a t e it from e m i s s i o n f r o m t h e t o p of t h e v a l e n c e b a n d . F i g . 1 5 ( b ) shows t h e ARPES s p e c t r a f o r o f f - n o r m a l e m i s s i o n a l o n g t h e r % ' - l i n e i n t h e s u r f a c e B Z . F o r b o t h 1 7 e V a n d 2 1 . 2 eV p h o t o n e n e r g y a n a r r o w f e a t u r e , SS, i s o b s e r v e d on t h e h i g h k i n e t i c e n e r g y s i d e o f t h e s p e c t r a . As shown i n t h e l o w e r r i g h t p a r t o f F i g . 1 5 ( b ) , t h e m e a s u r e d d i s p e r s i o n o f t h i s s t r u c t u r e i s t h e same f o r b o t h photon e n e r g i e s , s u p p o r t i n g a s u r f a c e s t a t e i n t e r p r e t a t i o n o f t h e f e a t u r e . I n t h e l o w e r l e f t p a r t o f F i g . 1 5 ( b ) it c a n be s e e n t h a t t h e s t r u c t u r e v e r y r a p i d l y d i s p e r s e s down i n e n e r g y a s t h e d e t e c t i o n a n g l e i s c h a n g e d away f r o m t h e n o r m a l d i r e c t i o n . T h i s e x c l u d e s t h e p o s s i b i l i t y t h a t t h e e m i s s i o n i n t h e normal d i r e c t i o n i s r e l a t e d t o d e f e c t s , i n which case t h e e m i s s i o n would be more i s o t r o p i c and non-dispersive.
The t o t a l d i s p e r s i o n o f t h e f e a t u r e SS i s 1.1 e V
along t h e ??'-direction,
which i s t h e same v a l u e a s t h e d i s p e r s i o n
o f t h e p r o j e c t e d v a l e n c e band e d g e , i . e . t h e b u l k r L - d i s p e r s i o n
as
r e p o r t e d by Chiang a n d Eastman /190/. I t i s r e a s o n a b l e t o d i s c u s s a l s o a n a l t e r n a t i v e i n t e r p r e t a t i o n of SS. I . e . ,
it c o u l d b e d u e t o i n d i r e c t
( a n d i n some s p e c t r a d i r e c t )
t r a n s i t i o n s from t h e p r o j e c t e d b u l k b a n d e d g e . I n f a c t , some m a j o r f e a t u r e s i n ARPES s p e c t r a from 1 1 1 - V s e m i c o n d u c t o r s , peak = 4 e V below E,
l i k e the strong
s e e n f o r p h o t o n e n e r g i e s i n t h e r a n g e 21-24
eV
i n F i g . 1 5 ( a ) , h a v e c o n s i s t e n t l y b e e n a s s i g n e d t o t r a n s i t i o n s from c r i t i c a l p o i n t s i n t h e o n e - d i m e n s i o n a l d e n s i t y o f s t a t e s /163,190, 192/.
One m a j o r c o n c l u s i o n drawn by Manzke e t a l . /191/ w a s t h a t t h e
p r o p o s e d s u r f a c e s t a t e b a n d l i e s w e l l w i t h i n t h e f u n d a m e n t a l gap,
189 hv = 17eV
hr = 112eV
kinetic energy
F i g . 1 5 . ( a ) Normal emission s p e c t r a from G a S b ( l l 0 ) f o r d i f f e r e n t photon e n e r g i e s /191/. A i s due t o d i r e c t t r a n s i t i o n s from t h e uppermost b u l k band, while SS has been a s s i g n e d t o a s u r f a c e s t a t e . T h e i n s e t shows t h e e x p e r i m e n t a l band s t r u c t u r e c l o s e t o t h e valence band maximum i n t h e rKX d i r e c t i o n of t h e bulk BZ. ( b ) ARPES s_p_ectra showing t h e p o l a r a n g l e dependence of emission a l o n g t h e r X ' - d i r e c t i o n f o r 1 7 and 2 1 . 2 eV photon e n e r g y . Right i n s e t : The d i s p e r s i o n of t h e SS f e a t u r e a t 1 7 e V ( s o l i d c i r c l e s ) and 2 1 . 2 e V (open c i r c l e s ) . L e f t i n s e t : S e l e c t i o n of h i g h e s t r e s o l u t i o n s p e c t r a (AE = 5 0 m e V ) f o r 17-eV photon e n e r g y . From r e f . 1 9 1 . s i n c e t h e s u r f a c e s t a t e maximum was r e p o r t e d t o be ( 0 . 1 9 f 0 . 0 3 ) eV above t h e t o p of t h e bulk valence bands. I n t h e h i g h r e s o l u t i o n s p e c t r a i n F i g . 1 6 ( a ) t h e y were a b l e t o r e s o l v e two c o n t r i b u t i o n s s e p a r a t e d by 0 . 1 9 e V i n t h e h i g h energy peak i n t h e normal emission s p e c t r a o b t a i n e d w i t h 23 e V photon e n e r g y . NOW, c o n s i s t e n t w i t h t h e p r e v i o u s s u g g e s t i o n t h a t SS could be due t o emission from t h e topmost (heavy h o l e ) valence band, one may a t t r i b u t e t h e second c o n t r i b u t i o n t o bulk emission from t h e l i g h t h o l e band. A schematic
190
(a)
-
0
1 I 23eV
*17eV
Y)
f 13
n
1I I
0 I
-
) .
t c W c .-c
-0.1 0 0.1 WAVEVECTOR 1
(6’
kinetic energy F i g . 1 6 . ( a ) High r e s o l u t i o n normal e m i s s i o n spectra a t 1 7 a n d 23 e V p h o t o n e n e r g y . I n t h e l o w e r p a r t a r e shown t h e G a u s s i a n p e a k s res u l t i n g from a f i t o f t h e 23-ev s p e c t r u m i n t o two components /191/. ( b ) S c h e m a t i c e n e r g y d i a g r a m o f t h e b u l k bands o f GaSb n e a r t h e v a l e n c e band e d g e a t t h e r - p o i n t , showing t h e e f f e c t s o f s p i n - o r b i t splitting. d i a g r a m o f t h e b u l k b a n d s n e a r T, u s i n g e x p e r i m e n t a l l y o b s e r v e d band
masses f o r GaSb /193/ a n d assuming a s i m i l a r s h a p e f o r t h e bands a s o b t a i n e d i n d e t a i l e d r e l a t i v i s t i c c a l c u l a t i o n s on G e /194/, i s shown i n F i g . 1 6 ( b ) . T o p r o b e t h e maximum e n e r g y p o s i t i o n o f t h e l i g h t h o l e band w i t h direct t r a n s i t i o n s it i s n e c e s s a r y t o have the c o r r e c t p h o t o n e n e r g y . One c a n estimate, a s s u m i n g e . g . f r e e e l e c t r o n f i n a l b a n d s , t h a t t h e d i r e c t t r a n s i t i o n from t h e l i g h t h o l e band w i l l d i s p e r s e down by 0 . 1 9 e V f o r a change i n t h e p h o t o n e n e r g y by = 1 eV.
I n fact, one can n o t e t h a t t h e r e i s a s t r o n g photon energy
dependence o f t h e s h a p e o f t h e combined A, SS p e a k i n F i g . 1 5 ( a ) and t h e p e a k seems t o b e most n a r r o w i n t h e 24-eV s p e c t r u m . The s t r o n g e s t e v i d e n c e a g a i n s t a s u r f a c e s t a t e l y i n g 0 . 1 9 e V w i t h i n t h e b u l k b a n d gap,
i s t h a t p r e v i o u s measurements of t h e
c o n t a c t p o t e n t i a l d i f f e r e n c e s between n- and p-type surfaces /19/
GaSb(ll0)
have shown t h a t t h e r e i s no Fermi l e v e l p i n n i n g by
s u r f a c e s t a t e s i n t h e g a p . T o summarize, a n i n t e r e s t i n g n a r r o w f e a t u r e s e e n n e a r t h e p r o j e c t e d v a l e n c e band e d g e i n ARPES s t u d i e s on t h e G a S b ( l l 0 ) s u r f a c e i s , s o f a r , t h e o n l y s u g g e s t e d s u r f a c e
s t a t e on t h i s s u r f a c e . D e s p i t e t h e v e r y h i g h r e s o l u t i o n i n t h e r e p o r t e d ARPES s t u d i e s , w e c a n n o t y e t c o n s i d e r t h e i d e n t i f i c a t i o n o f t h i s s u r f a c e s t a t e as e s t a b l i s h e d .
191
7
MBE-GROWN
111-V SEMICONDUCTOR SURFACES
The d e v e l o p m e n t of t h e MBE
( m o l e c u l a r beam e p i t a x y ) - t e c h n i q u e h a s
made it p o s s i b l e t o p r e p a r e p o l a r s u r f a c e s o f 1 1 1 - V compound s e m i c o n d u c t o r s w i t h a wide r a n g e o f a n i o n ( o r c a t i o n ) c o n c e n t r a t i o n s i n t h e s u r f a c e l a y e r . F o r a d e s c r i p t i o n o f t h e u s e of MBE f o r sample p r e p a r a t i o n w e r e f e r t o c h a p t e r 1 3 . Below t h e r e i s a r e v i e w o f t h e ARPES s t u d i e s o f MBE-grown p o l a r GaAs s u r f a c e s . The GaAs(100) s u r f a c e i s c e r t a i n l y one o f t h e t e c h n o l o g i c a l l y most i m p o r t a n t s e m i c o n d u c t o r s u r f a c e s , s i n c e it i s t h e n o r m a l l y u s e d s u r f a c e i n e p i t a x i a l g r o w t h o f GaAs/GaAlAs s t r u c t u r e s f o r d e v i c e a p p l i c a t i o n s . The b u l k GaAs c r y s t a l i s b u i l t up by e q u i d i s t a n t , a l t e r n a t i n g G a and A s monolayers i n t h e [ l O O I - d i r e c t i o n .
Depending
on t h e r e l a t i v e c o n c e n t r a t i o n o f Ga a n d A s i n t h e m o d i f i e d s u r f a c e l a y e r s o f a GaAs(100) c r y s t a l and t h e method o f p r e p a r a t i o n , it i s p o s s i b l e t o c r e a t e a l a r g e number o f r e c o n s t r u c t i o n s . Commonly o b s e r v e d r e c o n s t r u c t i o n s a r e , i n o r d e r of i n c r e a s i n g A s t o G a s u r f a c e atomic r a t i o s , t h e c ( 8 ~ 2 4x6, ) ~ c ( 6 ~ 4 1x6, ) ~ Zx4/c ( 2 ~ 8 ) ~ ~ ( 4 x 4 1 ,a n d As-covered 1 x 1 s u r f a c e s / 1 9 5 / .
F o r t h e ~ ( 8 x 2 )s u r f a c e
t h e r e i s some u n c e r t a i n t y i n t h e o r d e r i n g b e c a u s e o f t h e wide r a n g e of G a / A s c o n c e n t r a t i o n s r e p o r t e d f o r t h i s r e c o n s t r u c t i o n /195,196/. The m i x i n g o f 2x4 and ~ ( 2 x 8 )r e c o n s t r u c t i o n s i s c a u s e d by v a r i a t i o n s i n t h e l o n g r a n g e o r d e r a n d t h e mixed p h a s e h a s o f t e n b e e n d e s c r i b e d a s a 2x4 r e c o n s t r u c t i o n , due t o d i f f i c u l t i e s i n o b s e r v i n g t h e u n i q u e ~ ( 2 x 8 )f e a t u r e s i n t h e RHEED p a t t e r n s . The c r y s t a l s t r u c t u r e o f GaAs c a n a l s o b e d e s c r i b e d a s a s t a c k i n g of d o u b l e - l a y e r s i n t h e [ I l l ] - d i r e c t i o n , e a c h d o u b l e - l a y e r i n g o f one G a - l a y e r and o n e A s - l a y e r .
I f the crystal i s separated
i n t o two h a l v e s i n between two d o u b l e - l a y e r s , t e r m i n a t e d and t h e o t h e r As-terminated. a r e d e n o t e d as t h e (111) and
(777)
consist-
o n e h a l f w i l l b e Ga-
The c o r r e s p o n d i n g s u r f a c e s
s u r f a c e s , r e s p e c t i v e l y . By
c h a n g i n g t h e d e t a i l s o f s u r f a c e p r e p a r a t i o n it i s p o s s i b l e t o v a r y t h e r e l a t i v e s u r f a c e c o n c e n t r a t i o n s of Ga a n d A s , which c a n r e s u l t i n d i f f e r e n t s t a b l e s u r f a c e r e c o n s t r u c t i o n s . F o r t h e (111) ( i d e a l l y Ga-terminated)
s u r f a c e a 2x2 p e r i o d i c i t y h a s b e e n r e p o r t e d i n
e l e c t r o n d i f f r a c t i o n e x p e r i m e n t s on b o t h MBE-grown and s p u t t e r e d and a n n e a l e d s u r f a c e s . The ( i i i ) - s u r f a c e c a n , however, e x h i b i t s e v e r a l d i f f e r e n t reconstruction p a t t e r n s . In order of decreasing A s content 2x2, 43x43-
R30°, 419x419-
R23.4'
and mixed 3x3 a n d 1 x 1
r e c o n s t r u c t i o n s have been obtained /191/.
192
7.1
GaAs (100) s u r f a c e s
The e l e c t r o n i c s t r u c t u r e of MBE-grown GaAs(100) s u r f a c e s h a s been s t u d i e d by Larsen and coworkers /198-204/,
Bachrach e t a l . /205/ and
Chiang e t a l . /206/. Both Bachrach e t a l . and Chiang e t a l . r e p o r t e d angle-integrated
s p e c t r a from f i v e r e c o n s t r u c t i o n s , and d i f f e r e n c e s
i n t h e i r r e s p e c t i v e s p e c t r a were a s s i g n e d t o d i f f e r e n c e s i n e i t h e r t h e s u r f a c e e l e c t r o n i c s t r u c t u r e o r t h e s u r f a c e d i f f r a c t i o n of e l e c t r o n s e m i t t e d from t h e s u r f a c e and t h e b u l k . I n t h e s t u d y by Chiang et a l . a n g l e - r e s o l v e d photoemission i n t h e normal d i r e c t i o n was s t u d i e d over a wide range of photon e n e r g i e s and s t r o n g bulk c o n t r i b u t i o n s w e r e found t o dominate t h e emission f o r a l l s u r f a c e s s t u d i e d , i . e . t h e ~ ( 2 x 8,) 1x1, ~ ( 6 x 4,) and ~ ( 4 x 4 )s u r f a c e s . N o s u r f a c e s t a t e emission c o u l d be i d e n t i f i e d i n t h e normal emission spectra. E x t e n s i v e s t u d i e s of t h e s u r f a c e e l e c t r o n i c s t r u c t u r e of t h e 2x4/c(2x8)
(denoted 2x4) and ~ ( 4 x 4 )phases have been performed by
Larsen e t a l . /198-203/.
They combined s t u d i e s of a n g l e - r e s o l v e d
photoemission from t h e v a l e n c e bands and c o r e l e v e l s with RHEED s t u d i e s and t h e o r e t i c a l c a l c u l a t i o n s of t h e s u r f a c e e l e c t r o n i c s t r u c t u r e , t o develop models f o r t h e s e A s r i c h s u r f a c e s . By u s i n g t h e t u n a b i l i t y of s y n c h r o t r o n r a d i a t i o n and by comparing t h e s p e c t r a from s u r f a c e s with d i f f e r e n t r e c o n s t r u c t i o n s t h e y were a b l e t o i d e n t i f y bulk and s u r f a c e c o n t r i b u t i o n s t o t h e photoemission s p e c t r a . The s u r f a c e s t a t e band s t r u c t u r e o b t a i n e d f o r t h e G a A s ( 1 0 0 ) - 2 ~ 4 / ~ ( 2 ~s 8 u r) f a c e i s shown i n F i g . 1 7 ( a ) d i s p l a y e d i n a 2x1 s u r f a c e B r i l l o u i n zone / 2 0 1 / .
The s u r f a c e BZ:s f o r t h e 1x1, 2x1,
and 2x4 r e c o n s t r u c t i o n s a r e shown i n F i g . 1 7 ( b ) . The a u t h o r s argued /201,203/ t h a t t h e main c o n t r i b u t i o n t o t h e r e c o n s t r u c t i o n of t h e GaAs(001)2x4 s u r f a c e ( u s i n g t h e i r n o t a t i o n ) i s t h e two-fold p e r i o d i c i t y a l o n g t h e [ ? l o ] - d i r e c t i o n ,
i . e . i n the s a m e
azimuthal d i r e c t i o n a s t h e A s d a n g l i n g bonds on t h e i d e a l s u r f a c e , and t h a t it i s t h e r e f o r e r e l e v a n t t o compare t h e e x p e r i m e n t a l l y o b t a i n e d bands w i t h c a l c u l a t i o n s f o r a 2x1 r e c o n s t r u c t e d s u r f a c e . Larsen e t a l . c a l c u l a t e d t h e s u r f a c e s t a t e bands f o r a 2x1 model corresponding t o a f u l l monolayer of asymmetric As-dimers. assumption of a f u l l As-layer
The
was s u p p o r t e d by t h e measured c o r e
l e v e l i n t e n s i t i e s . The main c o n c l u s i o n s from t h e comparison between t h e o r y and experiment were, f i r s t l y , t h a t a l t h o u g h t h e r e i s no oneto-one
correspondence between t h e e x p e r i m e n t a l and c a l c u l a t e d bands,
one should e x p e c t a number of s u r f a c e s t a t e bands i n t h e range 0 . 5 -
193
( a ) GaAs(001I-ZxL Surface bands 0
I
111 .1
SBZ
12.11
SBZ 01
( 2 4 SBZ
J
I
r
J2,i
1
Jzri
F i g . 1 7 . ( a ) The e x p e r i m e n t a l l y o b t a i n e d s u r f a c e s t a t e bands f o r t h e ( 2 x 8 ) s u r f a c e . Open and f i l l e d symbols i n d i c a t e t h e GaAs ( 0 0 1 ) - 2 ~ 4 / c energy p o s i t i o n s of s h o u l d e r s and peaks i n ARPES s p e c t r a , r e s p e c t i v e l y . hv = 2 9 e V ( s q u a r e s ) , hv = 21.2 e V ( t r i a n g l e s ) o r 2 0 < hv < 32 eV ( c i r c l e s ) . From r e f . 2 0 1 . ( b ) The s u r f a c e B r i l l o u i n zones f o r 1x1, 2x1, and 2 x 4 r e c o n s t r u c t i o n s of t h e GaAs(001) s u r f a c e . 1 . 6 eV below t h e v a l e n c e band edge. Secondly, t h e o b s e r v a t i o n of a
s u r f a c e s t a t e band ( S q ) a t = -3 eV along t h e &xl-K2xl s t r o n g s u p p o r t f o r a d i m e r i z a t i o n of As-atoms
l i n e provides
on t h e 2x4/c(2x8)
s u r f a c e , s i n c e t h i s band i s i n good agreement with t h e c h a r a c t e r i s t i c c a l c u l a t e d dimer bond band. I t was a l s o emphasized t h a t emission from t h i s band was not found on o t h e r s t u d i e d GaAs(100) s u r f a c e s .
I n t h e i r s t u d i e s of t h e ~ ( 4 x 4 )r e c o n s t r u c t e d s u r f a c e , Larsen e t a l . /202/
r e p o r t e d emission from one s u r f a c e s t a t e band (S1)
d i s p e r s i n g from - 0 . 3
eV a t
f' t o - 1 . 0 eV a t Jlxl. From core l e v e l
s t u d i e s it was concluded t h a t t h e occurrence of a 0 . 6 eV s h i f t e d A s 3d component was evidence f o r A s atoms bonding e x c l u s i v e l y t o o t h e r As atoms. The i n t e n s i t y of t h e A s 3d emission a l s o i n d i c a t e d more than a complete A s l a y e r on t h e s u r f a c e . A ~ ( 4 x 4 )model of As-dimers on t o p of a f u l l A s l a y e r was suggested t o e x p l a i n t h e c o r e l e v e l r e s u l t s , while no e x p l a n a t i o n f o r t h e S1 s u r f a c e s t a t e band was given.
I n summary, except f o r t h e G a A s ( 1 0 0 ) - 2 x 4 / c (2x8) s u r f a c e , t h e e l e c t r o n i c s t r u c t u r e s of GaAs(100) s u r f a c e s a r e not well known. To improve t h e understanding it seems n e c e s s a r y t o have a wide range of experimental t e c h n i q u e s t o reduce t h e u n c e r t a i n t i e s i n s t o i c h i o m e t r i e s . Furthermore,
i n c o n j u n c t i o n with t h e o r e t i c a l c a l c u l a t i o n s ,
one must l i m i t t h e number of p o s s i b l e r e c o n s t r u c t i o n models. Isola-
194
t e d s t u d i e s o f t h e s u r f a c e e l e c t r o n i c s t r u c t u r e on t h e d i f f e r e n t
s u r f a c e s w i l l p r o b a b l y b e o f l i m i t e d v a l u e , s i n c e f o r a w e l l founded d i s c u s s i o n of s u c h r e s u l t s , it i s n e c e s s a r y t o have a n a c c u r a t e e s t i m a t e of t h e s u r f a c e s t o i c h i o m e t r y .
7.2
__-
G a A s ( l l 1 ) m d (111) s u r f a c e s
The e l e c t r o n i c s t r u c t u r e s o f GaAs (111) and b e e n s t u d i e d w i t h ARPES /207-211/
(iii) s u r f a c e s
a n d a l a r g e number o f s u r f a c e
s t a t e b a n d s have b e e n p r o p o s e d . J a c o b i e t a l . /208/ a n g l e - r e s o l v e d p h o t o e m i s s i o n from t h e 2x2, on t h e
(777)
have
43x43,
studied the
a n d 419x419 p h a s e s
s u r f a c e u s i n g 2 1 . 2 a n d 1 6 . 8 e V r a d i a t i o n . They
e v a l u a t e d t h e d i f f e r e n c e s i n t h e s p e c t r a f o r t h e 2x2 a n d 419x419 p h a s e s a n d a t t r i b u t e d t h e s e t o c h a n g e s i n t h e s u r f a c e s t a t e s . From t h e i r e x t e n s i v e s t u d i e s of e m i s s i o n a l o n g t h e [iOl],
[ i i 2 1 , and
[211] a z i m u t h s , t h e y s u g g e s t e d a n i d e n t i f i c a t i o n of f i v e d i f f e r e n t s u r f a c e s t a t e bands on t h e G a A s ( i i i ) 2 x 2 s u r f a c e . T h r e e o f t h e s e , observed a t = 1.8, = 4 . 0 ,
a n d = 6 . 6 e V below t h e v a l e n c e band edge,
r e s p e c t i v e l y , were r e p o r t e d t o e x h i b i t t h e e x p e c t e d 2x2 symmetry i n t h e surface BZ:s.
F o r t h e 419x419 s u r f a c e o n e s u r f a c e s t a t e band
d i s p e r s i n g from 0 . 4 e V a t
r
t o 1.0 eV a t
glxl was i d e n t i f i e d .
From t h e p o l a r i z a t i o n dependence o f t h e two topmost b a n d s on t h e ( i i i ) 2 x 2 s u r f a c e , t h e s e were a t t r i b u t e d t o t h e l o n e p a i r o r b i t a l s on As-atoms
i n t h e s u r f a c e l a y e r . However, a b u c k l i n g r e c o n s t r u c t i o n of
t h e 2x2 s u r f a c e , t h a t was c o n s i d e r e d as b e i n g c o n s i s t e n t w i t h t h e d a t a , was l a t e r r u l e d o u t u s i n g t h e r e s u l t s o f e n e r g y m i n i m i z a t i o n c a l c u l a t i o n s / 2 1 2 / . When e x a m i n i n g t h e p r o c e d u r e t o e v a l u a t e s u r f a c e s t a t e c o n t r i b u t i o n s from d i f f e r e n c e s p e c t r a u s e d by J a c o b i e t a l . /208/,
some words of c a u t i o n a r e n e e d e d . F i r s t l y ,
c h a n g e s i n band-bending,
i f t h e r e a r e any
even i d e n t i c a l b u l k c o n t r i b u t i o n s from t h e
two s u r f a c e s w i l l g i v e rise t o s t r u c t u r e i n t h e d i f f e r e n c e s p e c t r a . Secondly, c h a n g e s i n t h e s u r f a c e geometry w i l l a l s o a f f e c t e m i s s i o n from t h e b u l k . ARPES s t u d i e s o f t h e ( 1 1 1 ) 2 x 2 a n d ( i i i ) 2 x 2 s u r f a c e s have been r e p o r t e d by B r i n g a n s and Bachrach / 2 0 9 , 2 1 0 / .
F i g . 1 8 ( a ) shows t h e
measured d i s p e r s i o n s of s u r f a c e r e l a t e d s t r u c t u r e s o b s e r v e d i n t h e
[Oli] a z i m u t h . It i s g r a t i f y i n g t h a t t h e f i v e s u r f a c e r e l a t e d f e a t u r e s r e p o r t e d a t l= by J a c o b i e t a l . /208/
for the (iii)2x2
s u r f a c e were a l s o found i n t h e s t u d y by B r i n g a n s and Bachrach / 2 0 9 / . There a r e , however, d i f f e r e n c e s i n t h e i n t e r p r e t a t i o n o f t h e s e features, i . e . i n t h e later study t h e features a t 0.3,
1 . 7 5 , and 3 . 1
195
.[lii]
[ o i i]
[i2i]
(iii)
Fig. 18. ( a ) Measured d i s p e r s i o n s o f s u r f a c e r e l a t e d f e a t u r e s i n ARPES s t u d i e s on GaAs(111)2x2 a n d ( i i i ) 2 x 2 s u r f a c e s . Data t a k e n a t 1 7 , 2 0 , 22, 25 a n d 2 7 e V are shown by , x , a n d + symbols r e s p e c t i v e l y . Open symbols c o r r e s p o n d t o w e a k e r f e a t u r e s . L i n e s t h r o u g h t h e G a A s ( i i i ) 2 x 2 d a t a a r e r e p e a t e d t o show 2x2 symmetry. From r e f . 2 0 9 . ( b ) The s u r f a c e B r i l l o u i n zone f o r G a A s ( 1 1 1 ) 2 x 2 i s shown by t h e f u l l l i n e a n d t h e 1 x 1 z o n e i s shown b y t h e b r o k e n l i n e .
+,
e V b e l o w Em
were i n t e r p r e t e d a s s u r f a c e s t a t e s , w h i l e t h e f e a t u r e s
a t 2 . 7 a n d 1.0 e V w e r e a t t r i b u t e d t o b u l k t r a n s i t i o n s , t h a t were o b s e r v e d i n t h e normal d i r e c t i o n b e c a u s e o f s u r f a c e s c a t t e r i n g i n t h e 2x2 r e c o n s t r u c t e d s u r f a c e l a y e r . A s shown i n F i g . 1 8 ( a ) , B r i n g a n s and Bachrach a l s o found s t r o n g s u r f a c e r e l a t e d e m i s s i o n i n b e t w e e n t h e two u p p e r m o s t f u l l - d r a w n b a n d s , s u g g e s t i n g o n e more s u r f a c e s t a t e band i n t h i s e n e r g y r e g i o n . I n t h e comparison between t h e
( 1 1 1 ) 2 x 2 and
( i i i ) 2 x 2 surfaces it
was c o n c l u d e d , t h a t t h e e l e c t r o n i c s t r u c t u r e of t h e two s u r f a c e s a r e r e m a r k a b l y d i f f e r e n t . The d i s p e r s i o n s o b t a i n e d o n t h e ( 1 1 1 ) 2 x 2 s u r f a c e showed a n a p p a r e n t 1 x 1 symmetry, i n s t e a d o f t h e 2x2 symmetry o b s e r v e d f o r s e v e r a l f e a t u r e s on t h e ( T i I ) 2 x 2 s u r f a c e . F u r t h e r m o r e , t h e p o l a r i z a t i o n d e p e n d e n c e o f t h e t o p m o s t s u r f a c e f e a t u r e showed
196 o p p o s i t e b e h a v i o u r f o r t h e two s u r f a c e s . T h i s i s c o n s i s t e n t w i t h c a l c u l a t i o n s f o r relaxed geometries /213/,
where t h e p , - l i k e
dang-
l i n g bond band was f o u n d t o b e t h e t o p m o s t o c c u p i e d band on t h e
(Ti?)
s u r f a c e , w h i l e i t w a s a p,-band
on t h e (111) s u r f a c e .
I n c o n c l u s i o n , l a r g e d i f f e r e n c e s h a v e been o b s e r v e d i n t h e e l e c t r o n i c s t r u c t u r e o f GaAs(111)2x2 a n d ( i i i ) 2 x 2 s u r f a c e s , a n d a l s o between t h e ( i i i ) 2 x 2 and ( i i i ) q 1 9 x d 1 9 s u r f a c e s . So f a r , i t h a s n o t b e e n p o s s i b l e t o compare t h e measured s u r f a c e s t a t e d i s p e r s i o n s w i t h a n y band c a l c u l a t i o n s f o r t h e r e c o n s t r u c t e d s u r f a c e s . C o n c e r n i n g t h e experimentally obtained surface state dispersions, t h e correct i d e n t i f i c a t i o n of s e v e r a l o f t h e o b s e r v e d s u r f a c e r e l a t e d f e a t u r e s r e m a i n s t o be e s t a b l i s h e d .
8
11-VI
AND I V - V I
The 1 1 - V I
SEMICONDUCTOR SURFACES compound s e m i c o n d u c t o r s a r e c o n s i d e r a b l y more
and IV-VI
i o n i c than t h e 111-V
semiconductors / 2 1 4 / ,
and t h e y c a n be s e p a r a t e d
i n t o t h r e e c a t e g o r i e s a c c o r d i n g t o t h e i r c r y s t a l l i n e s t r u c t u r e . They c a n form i n t h e c u b i c z i n c b l e n d e s t r u c t u r e ( e . g . C d T e ) , i n t h e hexagonal w u r t z i t e s t r u c t u r e t u r e ( t h e IV-VI
( e . g . ZnO), o r i n t h e r o c k s a l t s t r u c -
s e m i c o n d u c t o r s , e . g . P b S e ) . Some of them,
l i k e ZnS
o r CdS, can a p p e a r i n e i t h e r z i n c b l e n d e o r w u r t z i t e s t r u c t u r e . Reviews o f t h e e x p e r i m e n t a l l y o b t a i n e d LEED-patterns s t o i c h i o m e t r i e s o f d i f f e r e n t Zn- a n d C d - c h a l c o g e n i d e b e e n g i v e n by T a k a h a s h i a n d E b i n a / 2 1 5 , 2 1 6 / . polar cleave surfaces,
and s u r f a c e
s u r f a c e s have
I n g e n e r a l , t h e non-
i . e . t h e (110) s u r f a c e o f t h e z i n c b l e n d e
s t r u c t u r e a n d t h e (lOi0) a n d (1170) s u r f a c e s o f t h e w u r t z i t e s t r u c t u r e e x h i b i t 1 x 1 LEED-patterns and a n n e a l e d p o l a r or non-polar
a f t e r cleavage,
while t h e s p u t t e r e d
s u r f a c e s e x h i b i t LEED-patterns
i n d i c a t i n g s u p e r s t r u c t u r e s o r even f a c e t t i n g . Concerning t h e atomic geometry o f t h e n o n - p o l a r /215,216/
( 1 1 0 ) and (1070) s u r f a c e s it was c o n c l u d e d
t h a t r e s u l t s from LEED I - V
a n a l y s i s i n d i c a t e t h a t probably
a l l t h e s e s u r f a c e s have r e l a x e d g e o m e t r i e s a l t h o u g h t h e LEED symmetry i s 1x1. A r e l a x a t i o n of t h e Z n T e ( l l 0 ) and Z n S e ( l l 0 ) s u r f a c e s h a s b e e n p r e d i c t e d from e n e r g y - m i n i m i z a t i o n c a l c u l a t i o n s by Chadi /211/.
An o u t w a r d r e l a x a t i o n o f t h e a n i o n s i m i l a r t o t h e r e l a x a t i o n
o f t h e G a A s ( l l 0 ) s u r f a c e w a s f o u n d t o lower t h e e n e r g y o f t h e s e s u r f a c e s . A f a i r l y good a g r e e m e n t c o n c e r n i n g t h e d i s p l a c e m e n t of s u r f a c e atoms i s o b t a i n e d between L E E D - r e s u l t s total-energy
minimization c a l c u l a t i o n s / 2 1 1 / .
/218,219/ a n d t h e
197
8.1
The c l e a V ed C d T e i l 10) s u r f a c e
T h e C d T e ( l l 0 ) s u r f a c e i s p r o b a b l y t h e most w e l l - s t u d i e d
11-VI
semiconductor s u r f a c e a s f a r as e x p e r i m e n t a l s t u d i e s of t h e elect r o n i c s t r u c t u r e a r e c o n c e r n e d . S e v e r a l d i f f e r e n t g r o u p s /216,2202 2 6 / h a v e p e r f o r m e d ARPES s t u d i e s a n d some of them have d i s c u s s e d
p o s s i b l e c o n t r i b u t i o n s from s u r f a c e s t a t e s i n t h e s p e c t r a . I n o t h e r s t u d i e s t h e focus has been on comparisons w i t h t h e t e c h n o l o g i c a l l y and s c i e n t i f i c a l l y i m p o r t a n t Cdl-xHg,Te
/225/
and Cdl_,MnxTe
/221/
alloys. S i l b e r m a n e t a l . / 2 2 5 / a n d Magnusson e t a l . / 2 2 6 / h a v e measured t h e n o r m a l e m i s s i o n s p e c t r a from C d T e ( l l 0 ) f o r p h o t o n e n e r g i e s i n t h e r a n g e 13-26 e V . The s p e c t r a shown i n F i g . 1 9 ( a ) were o b t a i n e d w i t h t h e p o l a r i z e d r a d i a t i o n i n c i d e n t a t 15O from t h e s u r f a c e normal and t h e E-vector w i t h i n t h e ( i l O ) - p l a n e / 2 2 6 / .
Magnusson e t a l .
r e p o r t e d t h a t d i r e c t t r a n s i t i o n s i n t h e b u l k d o m i n a t e i n t h e normal d i r e c t i o n s i n c e f e a t u r e s A-D
a l l a r e d i s p e r s i n g w i t h photon energy,
f u r t h e r m o r e t h e s t a t i o n a r y s t r u c t u r e a t - 6 . 2 e V below t h e F e r m i
.-
e n e r g y w a s i n t e r p r e t e d a s b e i n g due t o b u l k e m i s s i o n a s i t h a s maximum i n t e n s i t y when d i r e G t t r a n s i t i o n s a r e e x p e c t e d from a f l a t p o r t i o n o f t h e b u l k band s t r u c t u r e . The s p e c t r a shown i n F i g . 19(a) a r e c o n s i s t e n t w i t h t h e s p e c t r a of Silberman e t a l . ,
although t h e r e
a r e l a r g e d i f f e r e n c e s between t h e two s e t s o f d a t a b e c a u s e v e r y d i f f e r e n t p o l a r i z a t i o n s o f t h e l i g h t w e r e u s e d . Examples o f t h e s e s t r o n g p o l a r i z a t i o n e f f e c t s were a l s o g i v e n i n t h e s t u d y by Silberman e t a l . . I n t h e c a s e of l i g h t p o l a r i z e d mainly a l o n g t h e s u r f a c e n o r m a l , t h e e m i s s i o n i s d o m i n a t e d by e x c i t a t i o n s t o t h e s i m p l e [ k + (110)4Wa] f r e e e l e c t r o n p a r a b o l a /225/.
Excitations t o other free-electron
( p r i m a r y cone e m i s s i o n )
l i k e b a n d s and i n d i r e c t
t r a n s i t i o n s h a v e t o be i n v o k e d t o e x p l a i n some o f t h e f e a t u r e s s e e n , i n p a r t i c u l a r , with s-polarized
light /226/.
An i m p o r t a n t c o n c l u s i o n
i n t h e p r e s e n t c o n t e x t i s t h a t no e v i d e n c e f o r s u r f a c e s t a t e s h a s been found i n t h e normal e m i s s i o n s p e c t r a . Magnusson e t a l . / 2 2 6 /
a l s o d i d q u i t e e x t e n s i v e o f f - n o r m a l ARPES
s t u d i e s on C d T e ( l l 0 ) s u r f a c e s , i n v e s t i g a t i n g t h e s u r f a c e e l e c t r o n i c s t r u c t u r e along t h e
r%I%'F symmetry l i n e s i n t h e s u r f a c e
BZ.
In F i g .
1 9 ( b ) ARPES s p e c t r a , o b t a i n e d w i t h 18-eV p h o t o n e n e r g y , a r e shown,
which p r o b e t h e e l e c t r o n i c s t r u c t u r e a l o n g t h e r % ' - l i n e . A l l f e a t u r e s s e e n a t s m a l l e m i s s i o n a n g l e s , 8,<15°,
a r e i d e n t i f i e d t o be
o f b u l k o r i g i n , s i n c e t h e i r i n i t i a l e n e r g y d i s p e r s i o n s a r e dependent on t h e p h o t o n e n e r g y . However, f o r l a r g e r e m i s s i o n a n g l e s two s t r u c t u r e s S1 and S2 a p p e a r a t t h e % ' - p o i n t a n d d i s p e r s e upwards
198
CdTe(ll0)
hv-18 eV
rl[ooll
r-F-
..!.
....
e
I
,. ...
47.5
.'., ~ .. . .. .
.-.. ... '..' .I .... .. . . . .. . .. . ....... . . .
>
<-'. ..,,,, .-.42.5
..
h
m " ._ c
.......... ...... .I.. ........
4
..
J- ..... 1.
,. .-._-...Ls '.
v
...
.-cx
-*:
-1..
. . ., ". . .1.
.
I
.
22.5
-----
2u
.
v1
W
Y
t -
............
...
~
2s
I
....
..... .
. . . . .
' -7
-6
-5
-4
-3
1
-2
Initial state energy (ev rel.
*.-
............
.
J2.5
_.
.
I
. . . I
....
.!o-
13
-I
C)
Initial state energy (ev rel. E,)
F i g . 1 9 . (a) Photoemission s p e c t r a f o r emission a l o n g t h e s u r f a c e normal on t h e C d T e ( l l 0 ) s u r f a c e m e a s u r e d w i t h d i f f e r e n t p h o t o n e n e r g i e s . From r e f . 2 2 6 . ( b ) P o g a r a n g l e v a r i a t i o n of p h o t o e l e c t r o n s p e c t r a f r o m C d T e ( l l 0 ) i n t h e ( 1 1 0 ) m i r r o r p l a n e o f t h e s u r f a c e . The l i g h t was i n c i d e n t a t 0i = 44O. / 2 2 6 / . g o i n g t h r o u g h a maximum a t 2r. These t w o s t r u c t u r e s show t h e p e r i o d i c i t y o f t h e s u r f a c e BZ,
f u r t h e r m o r e t h e y have, w i t h i n t h e
e x p e r i m e n t a l u n c e r t a i n t y , t h e same E i ( k , , ) d i s p e r s i o n s i n d e p e n d e n t
of p h o t o n e n e r g y i n t h e r a n g e 13-18 e V . Two m o r e s t r u c r u r e s , Sq s e e n n e a r t h e Xl-point
i n F i g . 1 9 ( b ) , a n d Sg o b s e r v e d a l o n g t h e e - l i n e
were a l s o i n t e r p r e t e d by Magnusson e t a l . t o b e o f s u r f a c e o r i g i n .
199
F i g . 2 0 . T h e e x p e r i m e n t a l s u r f a c e e l e c t r o n i c band s t r u c t u r e a r o u n d the b o u n d a r y o f t h e s u r f a c e BZ o f C d T e ( l l 0 ) . The h a t c h e d area i n d i c a t e s t h e p r o j e c t e d RAPW v a l e n c e b a n d s / 2 2 6 / .
r-%’-%g-r
The e x p e r i m e n t a l s u r f a c e band s t r u c t u r e i s shown i n F i g . 2 0 t o g e t h e r w i t h t h e p r o j e c t i o n of t h e b u l k v a l e n c e b a n d s from a r e l a t i v i s t i c APW-calculation
using t h e local-density self-consistent
field
approximation. A g e n e r a l problem f o r t h e i d e n t i f i c a t i o n o f s u r f a c e s t a t e s / r e s o -
n a n c e s on 1 1 - V I a n d I V - V I
semiconductor s u r f a c e s i s t h e d i f f i c u l t y
t o e x p e r i m e n t a l l y s e p a r a t e them from i n d i r e c t t r a n s i t i o n s from band e d g e s . It c a n b e n o t e d t h a t t h e d i s p e r s i o n s o f a l l f o u r p r o p o s e d s u r f a c e f e a t u r e s , S I - S ~ , h a v e s h a p e s t h a t a r e s i m i l a r t o n e a r b y band e d g e s . For s t r u c t u r e S 2 t h i s i s n o t e v i d e n t from F i g . 20, b u t t h e s e p a r a t i o n o f S 1 and S2 i s c l o s e t o t h e s e p a r a t i o n between t h e band e d g e s of t h e t o p m o s t s p i n - o r b i t s p l i t v a l e n c e b a n d s . T o h e l p e s t a b l i s h t h e i d e n t i f i c a t i o n of t h e s u r f a c e s t a t e s w e f i n d t h a t i t would
be v a l u a b l e t o i n v e s t i g a t e o r d e r e d c h e m i s o r p t i o n s y s t e m s on t h e
C d T e ( l l 0 ) s u r f a c e and t h e r e b y s t u d y m o d i f i c a t i o n s t o t h e s u r f a c e electronic structure. The e x i s t e n c e o f t h e s u r f a c e s t a t e S1 was f i r s t s u g g e s t e d i n ARPES s t u d i e s r e p o r t e d b y E b i n a and T a k a h a s h i / 2 1 6 / .
They u s e d 2 1 . 2
e V r a d i a t i o n t o map t h e d i s p e r s i o n o f ARPES f e a t u r e s a l o n g t h e
-_
TX , a n d
rG
FA?,
symmetry l i n e s a n d p r o p o s e d t h a t f e a t u r e s e x h i b i t i n g t h e
1x1 symmetry o f t h e s u r f a c e BZ c o u l d be a t t r i b u t e d t o s u r f a c e
s t a t e s / r e s o n a n c e s . By comparing w i t h t h e r e s u l t s o f Magnusson e t a l . /226/
it seems c l e a r t h a t f o r 2 1 . 2 e V r a d i a t i o n t h e S 1 c o n t r i b u t i o n
i s o v e r l a p p i n g w i t h b u l k e m i s s i o n i n t h e f i r s t s u r f a c e BZ, w h i l e i n
t h e second s u r f a c e BZ t h e peak can be i d e n t i f i e d a s t h e p r e v i o u s l y d i s c u s s e d photon energy independent s t r u c t u r e t h a t i s due t o s u r f a c e s t a t e o r band edge e m i s s i o n . Grandke e t a l . have performed ARPES s t u d i e s on cleaved l e a d chalcogenide c r y s t a l s / 2 2 7 - 2 2 9 / . PbS(100) s u r f a c e / 2 2 7 /
I n t h e f i r s t s t u d i e s on t h e
t h e s p e c t r a were i n t e r p r e t e d i n terms of
one-dimensional d e n s i t y - o f - s t a t e s
f e a t u r e s i n t h e bulk, i . e . , the
emission was c o n s i d e r e d t o be due t o n o n d i r e c t but k,/-conserving t r a n s i t i o n s i n t h e b u l k . I n a more e x t e n s i v e s t u d y i n c l u d i n g a l s o ARPES measurements on PbSe ( 1 0 0 ) and PbTe ( 1 0 0 ) s u r f a c e s , Grandke e t
a l . /228/
concluded t h a t both n o n d i r e c t and d i r e c t t r a n s i t i o n s
c o n t r i b u t e t o t h e ARPES s p e c t r a . A model, which c o n s i d e r s how t h e f i n i t e e l e c t r o n l i f e t i m e r e l a x e s t h e momentum c o n s e r v a t i o n i n t h e d i r e c t i o n normal t o t h e s u r f a c e , was found t o e x p l a i n a l l e s s e n t i a l f e a t u r e s i n t h e ARPES s p e c t r a from t h e l e a d c h a l c o g e n i d e s . I n t h e s t u d i e s by Grandke e t a l . no evidence was r e p o r t e d f o r emission from s u r f a c e s t a t e s o r s u r f a c e resonances on t h e cleaved I V - V I semiconductor s u r f a c e s . We want t o p o i n t o u t , a g a i n , t h e d i f f i c u l t y t o e x p e r i m e n t a l l y s e p a r a t e emission from s u r f a c e resonances and emission from f e a t u r e s
i n t h e one-dimensional d e n s i t y - o f - s t a t e s .
Both p r o c e s s e s a r e
c h a r a c t e r i z e d by t h e i n v a r i a n c e of t h e E ( k , / ) - d i s p e r s i o n with photon energy. Furthermore, f o r t h e i o n i c semiconductors d i s c u s s e d i n t h e p r e s e n t s e c t i o n , c a l c u l a t e d s u r f a c e s t a t e resonances o f t e n d i s p e r s e c l o s e t o and p a r a l l e l with t h e p r o j e c t e d valence band edges and t h e i d e n t i f i c a t i o n of s u r f a c e resonances i n such a case t h u s becomes very d i f f i c u l t
.
I n summary, t h e r e have been s e v e r a l ARPES i n v e s t i g a t i o n s of t h e
e l e c t r o n i c s t r u c t u r e of d i f f e r e n t 1 1 - V I and I V - V I
semiconductor
s u r f a c e s . Despite t h i s e f f o r t , r e l a t i v e l y l i t t l e i s known about s u r f a c e s t a t e s o r resonances on t h e s e s u r f a c e s . For e . g . t h e C d T e ( l l 0 ) s u r f a c e t h e r e a r e undoubtedly emission f e a t u r e s with d i s p e r s i o n s , E i ( k / / ) , t h a t a r e i n s e n s i t i v e t o t h e photon energy and these a r e t h u s strong candidates f o r surface states/resonances. I n ARPES s t u d i e s on l e a d chalcogenides s i m i l a r f e a t u r e s have been
i n t e r p r e t e d i n terms of emission from band edges i n t h e bulk bands. We f i n d t h a t f u r t h e r s t u d i e s concerning t h e r e l a t i v e importance of emission from band edges v e r s u s s u r f a c e resonances a r e necessary t o uniquely e s t a b l i s h t h e i d e n t i f i c a t i o n of t h e s u r f a c e e l e c t r o n i c s t r u c t u r e of 1 1 - V I
and I V - V I
semiconductor s u r f a c e s .
201
9
COMPENDIUM Below a r e t a b l e s showing t h e approximate sequence of p u b l i s h e d
p a p e r s concerned with photoemission s t u d i e s of v a r i o u s semiconductor i n d i c a t e s t h a t t h e s t u d y w a s n o t made w i t h a n g l e -
surfaces.
r e s o l v e d photoemission.
' i n d i c a t e s t h a t emission from s u r f a c e
s t a t e s o r resonances was r e p o r t e d and f i n a l l y
"
indicates that also
d i s p e r s i o n s of t h e s u r f a c e s t a t e bands were r e p o r t e d . TABLE 1
Silicon surfaces
Surface
Reference numbers f o r p u b l i s h e d p a p e r s
Si(ll1)Zxi
14’ 24" 30" 234 46’ '
230 233" 32’ 39 47"
61O’ 64O’ 33’ 40’ ' 48’ '
62O’ 25" 34" 41’ ' 49
231O’ 26’ ' 36’ ' 42" 50’ '
232’’ 27 65’ ' 43" 51’ '
63"’ 28" 37" 44" 52"
23’ 29" 38" 45’’ 15"
Si(111)7x7
14’’ 30’ 95’ 100 52"
89"
63’’ 33’ 98" 46’ 105"
64''
34’ 235 102" 267’
90’ 35’ 99’ 47"
91'
96’ 101" 103’
232O’ 32’ 97’ 44’ 104’
92’ 40’ 50’
29’ 93’ 41’ 236’
S i ( 1 l l ) " l x l " 92’
35’
93’
94’
95’
96’
97’
98’
127" 132" 269’
29" 133" 139’
128’ ' 134"
40’ 135"
and 5x5
31'
99’ Si(100)2xl
89" 50’ 136"
232" 129’ 137"
63"’ 130" 140"
126" 131" 268’
S i (110)
236"
237O
238"
52"
TABLE 2
Germanium s u r f a c e s
Surface
Reference numbers f o r p u b l i s h e d p a p e r s
Ge(l1l)Zxl
61" 240’
239"’ 54’ '
73’’
74"
53"
55’ '
56’ '
57"
Ge (111)c (2x8)
13" 241"
93’ 118"
113" 242"
114’’ 119"
40’ 117"
115"
236’
54"
Ge(100)2x1
148’’ 243
149’
150’
123’
124’
270"
202
TABLE 3
111-V compound s e m i c o n d u c t o r s u r f a c e s
R e f e r e n c e numbers f o r p u b l i s h e d papers
Surface
GaAs ( 1 1 0 )
61’’ 159’ 161’’
153 154" 160"’ 161’ 168’ 271’
155" 162
156" 163
157’ ' 164
90 165
158’ ' 166"
GaAs (100)
198’ ' 204
199" 210’ '
205’
200"
201"
206’
202"
203"
GaAs (111)
207’
159"
208"
209"
210"
211O
GaP (110) GaP (111)
192’ ' 245’’
244"
GaSb (110)
190
191’ '
InP (110) InP (100) I n P (111)
246’ ' 241" 252"’ 253’ 212’ 254"
248’ 212’
249’
250’
251"
InSb (110) I n S b (111)
255’ ' 251"
InAs (110)
256’ '
TABLE 4
11-VI
Surface
256’
a n d IV-VI
compound s e m i c o n d u c t o r s u r f a c e s
R e f e r e n c e numbers f o r p u b l i s h e d papers
ZnSe(ll0)
258’’ 215"
216"
CdS(1010) CdS (1120)
259" 261
260
261
262’’
CdTe(ll0)
220" 213’
216"
221
222’
CdSe(1010)
263
262’ '
ZnO(1010)
197
264’
265’
266
PbS (100)
227
228
229
PbSe (100)
228
PbTe (100)
228
223’
224
225
226"
203
10
SUMMARY I n t h i s c h a p t e r we have c r i t i c a l l y reviewed t h e e x t e n s i v e photo-
emission s t u d i e s o f t h e e l e c t r o n i c s t r u c t u r e of d i f f e r e n t semicond u c t o r s u r f a c e s . With t h e development of a n g l e - r e s o l v e d photoemission it has become p o s s i b l e t o perform d e t a i l e d s t u d i e s of t h e band d i s p e r s i o n s o v e r t h e s u r f a c e B r i l l o u i n zone f o r s u r f a c e s t a t e s ( l o c a t e d w i t h i n gaps of t h e p r o j e c t e d b u l k band s t r u c t u r e ) and s u r f a c e r e s o n a n c e s ( d e g e n e r a t e w i t h b u l k s t a t e s ) . Recently t h e r e have a l s o been photoemission s t u d i e s of normally empty s u r f a c e s t a t e s t h a t have been f i l l e d e i t h e r by donor e l e c t r o n s i n h i g h l y ndoped s u b s t r a t e s o r by t h e u s e of o p t i c a l pumping i n two-photon photoemission e x p e r i m e n t s . With t h e s e t y p e s of experiments t h e value f o r s u r f a c e s t a t e band gaps can be a c c u r a t e l y determined. For many semiconductor s u r f a c e s t h e r e have a l s o been t h e o r e t i c a l s t u d i e s of t h e s u r f a c e e l e c t r o n i c s t r u c t u r e f o r d i f f e r e n t model g e o m e t r i e s and d e t a i l e d comparisons w i t h e x p e r i m e n t a l l y determined s u r f a c e s t a t e band s t r u c t u r e s have been made. However, s o f a r most t h e o r e t i c a l c a l c u l a t i o n s have been done w i t h i n t h e l o c a l - d e n s i t y approximation and t h e c a l c u l a t e d band gaps a r e t h e r e f o r e undere s t i m a t e d , f u r t h e r m o r e t h e a b s o l u t e b i n d i n g e n e r g i e s and band widths a l s o t e n d t o be u n d e r e s t i m a t e d . Through t h e r e c e n t development of many-body c a l c u l a t i o n s o f q u a s i - p a r t i c l e
surface s t a t e energies
t h e r e i s hope t h a t such d e t a i l e d comparisons between e x p e r i m e n t a l and t h e o r e t i c a l s u r f a c e e l e c t r o n i c s t r u c t u r e s w i l l be even more v a l u a b l e f o r t h e u n d e r s t a n d i n g of semiconductor s u r f a c e s . I t i s e v i d e n t from t h i s review t h a t a n g l e - r e s o l v e d photoemission
i s a v e r y powerful t e c h n i q u e f o r s t u d i e s of s u r f a c e e l e c t r o n i c s t r u c t u r e s . Through t h e i n t i m a t e r e l a t i o n s h i p between atomic and e l e c t r o n i c s t r u c t u r e of a s u r f a c e , it has been p o s s i b l e t o use i n f o r m a t i o n about t h e s u r f a c e s t a t e band s t r u c t u r e t o draw conclus i o n s about t h e s u r f a c e atomic geometry f o r s e v e r a l semiconductor s u r f a c e s . There a r e , however, many q u e s t i o n s concerning semicond u c t o r s u r f a c e s t a t e s t h a t remain unsolved and a n g l e - r e s o l v e d photoemission should c o n t i n u e t o be a powerful t o o l for f u r t h e r i n v e s t i g a t i o n s . For t h o s e semiconductor s u r f a c e s , where i t has been d i f f i c u l t t o s e p a r a t e s u r f a c e s t a t e c o n t r i b u t i o n s from b u l k photoemission, we t h i n k t h a t p a r a l l e l s t u d i e s of t h e c l e a n semiconductor s u r f a c e and well-ordered
o v e r l a y e r systems o n t h i s
s u r f a c e should, i n many c a s e s , be a way t o p o s i t i v e l y i d e n t i f y p o s s i b l e s u r f a c e s t a t e s on t h e semiconductor s u r f a c e .
204
ACKNOWLEDGEMENTS I t i s a p l e a s u r e t o e x p r e s s o u r g r a t i t u d e t o P . M a r t e n s s o n , M.
N i c h o l l s and L. J o h a n s s o n f o r t h e i r v a r i o u s c o n t r i b u t i o n s t o t h i s
review a r t i c l e , m a i n l y i n c o n n e c t i o n t o t h e i r p u b l i s h e d a n d u n p u b l i s h e d p h o t o e m i s s i o n s t u d i e s a t L i n k o p i n g I n s t i t u t e of T e c h n o l o g y . F i n a l l y , w e want t o t h a n k t h e v a r i o u s a u t h o r s a n d p u b l i s h e r s o f e a r l i e r p h o t o e m i s s i o n s t u d i e s , who have given u s p e r m i s s i o n t o u s e f i g u r e s from p r e v i o u s l y p u b l i s h e d papers, as i n d i c a t e d i n the f i g u r e c a p t i o n s . REFERENCES
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a,
u,
m,
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a, m,
a,
a,
212 2 6 6 . K . J a c o b i , G . Z w i c k e r , a n d A . Gutmann, S u r f . S c i . M, 109 (1984) 2 6 7 . R . I . G . U h r b e r g , E . L a n d e m a r k , a n d L . S . O . J o h a n s s o n , P h y s . Rev B 3.9, 1 3 5 2 5 ( 1 9 8 9 ) 2 6 8 . Y . X u , X.-H. Chen, a n d H . - Y . L i , C h i n . P h y s . 8, 250 (1988) 2 6 9 . Y . E n t a , T . K i n o s h i t a , S . S u z u k i , and S . Kono, P h y s . Rev B 2, 1125 (1989) 2 7 0 . E . Landemark, L . S . O . J o h a n s s o n , C . J . Karlsson, a n d R . I . G . Uhrberg, Vacuum, i n press ( 1 9 8 9 ) 2 7 1 . R . Haight a n d J . A . S i l b e r m a n , P h y s . R e v . L e t t . 62, 8 1 5 ( 1 9 8 9 ) 2 7 2 . X . Wang, A p p l . Surf. S c i . 33/34, 8 8 ( 1 9 8 8 ) 2 7 3 . H . Qu, P . O . N i l s s o n , J . K a n s k i , a n d L . I l v e r , P h y s . R e v . B 2, 5276 (1989)
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Chapter 6 METALLIC COMPOUNDS AND ORDERED ALLOYS: CARBIDES AND NITRIDES, APPLICABILITY OF SIMPLE AND SOPHISTICATED THEORIES TO MORE COMPLEX SYSTEMS.
L.I. JOHANSSON AND C . G . LARSSON
1. INTRODUCTION
The d i s t r i b u t i o n of charge between t h e atoms i n a s o l i d determine t h e n a t u r e o f t h e chemical bond and t h e r e f o r e t h e c o r r e s p o n d i n g e l e c t r o n i c s t a t e s are of fundamental importance f o r most of t h e p h y s i c a l and chemical p r o p e r t i e s of a s o l i d . I n an o r d e r e d s o l i d band t h e o r y i s u s e d t o d e s c r i b e t h e d i s t r i b u t i o n o f t h e s e e l e c t r o n s i n energy and momentum, t h e band s t r u c t u r e E ( k ) , and p r o v i d e s a means f o r u n d e r s t a n d i n g t h e e l e c t r o n i c p r o p e r t i e s on a microscopic l e v e l . Angle r e s o l v e d photoemission (ARP) is a powerful e x p e r i m e n t a l method f o r i n v e s t i g a t i n g t h e e l e c t r o n i c s t a t e s i n s o l i d s and t h i s a r t i c l e a i m s a t e l u c i d a t i n g t h e a p p l i c a b i l i t y of ARP t o some m e t a l l i c compounds. The p r e s e n t a t i o n w i l l be focused on r e f r a c t o r y t r a n s i t i o n metal c a r b i d e s and n i t r i d e s . These compounds a r e c h a r a c t e r i z e d by high m e l t i n g p o i n t s , u l t r a h a r d n e s s , good e l e c t r i c a l and t h e r m a l conduct i v i t y and good c o r r o s i o n r e s i s t a n c e and a r e commonly r e f e r r e d t o a s r e f r a c t o r y h a r d m e t a l s ( r e f . 1). This unusual combination of p r o p e r t i e s h a s c h a l l e n g e d t h e o r i s t s t o s t u d y t h e chemical bonding i n t h e s e compounds which a r e b u i l t up from two d i f f e r e n t atoms MX, where M l a b e l s t h e t r a n s i t i o n metal and X d e n o t e s carbon o r n i t r o g e n . Band t h e o r e t i c a l methods a p p l i e d t o s t o i c h i o m e t r i c phases of t h e s e compounds, MX,,,, have shown t h a t t h e bonding i n v o l v e s s i m u l t a n e o u s c o n t r i b u t i o n s from m e t a l l i c , c o v a l e n t a n d i o n i c bonding ( r e f s . 2 - 4 ) . The t h e o r i e s have a t t e m p t e d t o d e t e r m i n e t h e r e l a t i v e importance of each t y p e o f c o n t r i b u t i o n and t h e r e l a t i v e importance of metal-metal v e r s u s metal-nonmetal bonding and have a l s o been concerned w i t h t h e d i r e c t i o n of charge t r a n s f e r between m e t a l and nonmetal atoms. Because o f t h e s e bonding c h a r a c t e r i s t i c s and t h e f a c t t h a t t h e s e compounds can a c t u a l l y e x i s t o v e r a f a i r l y l a r g e
214
composition range, t h e s e m a t e r i a l s a r e regarded a s r a t h e r complex systems. ARP i n v e s t i g a t i o n s of t h e s e metallic compounds aims a t e l u c i d a t i n g t h e i r bonding c h a r a c t e r i s t i c s v i a a c r i t i c a l assessment of t h e t h e o r e t i c a l p r e d i c t i o n s . D e t a i l e d i n f o r m a t i o n about e l e c t r o n s t a t e s i n s o l i d s can be e x t r a c t e d i n d i f f e r e n t ways from ARP experiments on s i n g l e c r y s t a l s ( r e f s . 5 - 8 ) . L o c a t i o n s and d i s p e r s i o n s of two dimensional energy bands a r e u s u a l l y mapped o u t by d e t e r m i n i n g t h e energy p o s i t i o n s of f e a t u r e s i n photoemission s p e c t r a . Given a r e l i a b l e band s t r u c t u r e c a l c u l a t i o n , even t h e t h r e e dimensional band s t r u c t u r e can be r e a l i s e d u s i n g t h e so c a l l e d t h r e e s t e p model ( r e f . 5 ) . This c o n s t i t u t e s t h e most common and s i m p l e s t l e v e l of i n t e r p r e t i n g ARP d a t a . Examples of band mappings made f o r t r a n s i t i o n m e t a l c a r b i d e s and n i t r i d e s a r e p r e s e n t e d and d i s c u s s e d i n s e c t i o n 2 . For a more complete i n v e s t i g a t i o n , i n c l u d i n g an a n a l y s i s of t h e r e l a t i v e i n t e n s i t i e s of t h e s t r u c t u r e s observed i n photoemission s p e c t r a , a f u l l c a l c u l a t i o n of t h e p h o t o c u r r e n t i s needed and t h i s r e p r e s e n t s t h e n e x t l e v e l of i n t e r p r e t a t i o n . I n a more r i g o r o u s t h e o r e t i c a l t r e a t m e n t t h e photoemission p r o c e s s i s d e s c r i b e d a s a one s t e p e v e n t ( r e f s . 9-11).
A
scheme f o r c a l c u l a t i n g t h e p h o t o c u r r e n t w i t h i n t h e
one s t e p model, u s i n g t h e t i m e r e v e r s e d LEED t h e o r y , was devoloped by Hopkinson, Pendry and T i t t e r i n g t o n
(ref. 1 2 ) . T h i s original
scheme a l l o w s c a l c u l a t i o n s t o be made on pure o r d e r e d m e t a l s ( w i t h o v e r l a y e r s ) c o n t a i n i n g one atom p e r two dimensional u n i t c e l l . The scheme h a s been extended t o i n c l u d e s u b s t i t u t i o n a l l y d i s o r d e r e d systems ( r e f . 1 3 ) and a l s o t o i n c l u d e o r d e r e d b i n a r y compounds ( r e f . 1 4 ) . The l a t e s t developments a r e b r i e f l y d e s c r i b e d i n s e c t i o n 3 and
t h e a p p l i c a b i l i t y of t h e t h e o r y t o some m e t a l l i c compounds i s exemplified i n s e c t i o n 4 . P e r f e c t s t o i c h i o m e t r i c composition i s assumed i n t h e above c a l c u l a t i o n s . T h i s h a s a l s o been assumed i n t h e m a j o r i t y of band s t r u c t u r e c a l c u l a t i o n s r e p o r t e d f o r t r a n s i t i o n metal c a r b i d e s and n i t r i d e s , a s summarized and d i s c u s s e d i n r e c e n t review a r t i c l e s (refs. 2-4).
The l a t e s t of t h e s e ( r e f . 4 ) c o n c e n t r a t e s on t h e m e r i t s
and accuracy o f c a l c u l a t i o n s based on t h e APW (Augmented P l a n e Wave) o r LAPW ( L i n e a r i z e d - A P W ) methods f o r t h e l a r g e group o f c a r b i d e s and n i t r i d e s t h a t c r y s t a l l i z e i n t h e sodium c h l o r i d e s t r u c t u r e . The examples s e l e c t e d below belong t o t h i s group and t h e i n t e r p r e t a t i o n made of ARP r e s u l t s i s based on p o t e n t i a l s g e n e r a t e d i n s e l f c o n s i s t e n t A P W c a l c u l a t i o n s made for s t o i c h i o m e t r i c composition. The
215
e x p e r i m e n t a l r e s u l t s a r e , however, c o l l e c t e d on s i n g l e c r y s t a l s o f s u b s t o i c h i o m e t r i c b u l k c o m p o s i t i o n , MX,
w h e r e z<1.0, s i n c e r e a l
c r y s t a l s a l m o s t a l w a y s c o n t a i n v a c a n c i e s , randomly d i s t r i b u t e d i n m o s t cases, m a i n l y on t h e n o n m e t a l l a t t i c e s i t e s ( r e f s . 1/15). T h e e x i s t e n c e o f v a c a n c i e s i s bound t o i n t r o d u c e some d i s o r d e r t h a t a f f e c t s t h e e l e c t r o n i c s t r u c t u r e , b u t by how much? W i l l ,
for
example, 1 0 % o r 2 0 % v a c a n c i e s on t h e n o n m e t a l l a t t i c e s i t e s a f f e c t t h e e l e c t r o n i c s t r u c t u r e t o t h e e x t e n t t h a t a n a n a l y s i s assuming a
p e r f e c t l y o r d e r e d compound i s n o t m e a n i n g f u l ? The c o r n p a r i s i o n s made i n s e c t i o n 2 a n d 4 of s t o i c h i o m e t r i c t h e o r e t i c a l a n d s u b s t o i c h i o m e t r i c e x p e r i m e n t a l r e s u l t s e l u c i d a t e s t h i s q u e s t i o n . How w e l l do t h e o r e t i c a l r e s u l t s f o r t h e p e r f e c t l y ordered phase using t h e simple a n d more s o p h i s t i c a t e d t h e o r i e s o f p h o t o e m i s s i o n d e s c r i b e ARP d a t a c o l l e c t e d on r e a l c r y s t a l s ? A l o g i c a l r e f i n e m e n t o f t h e i n t e r p r e t a t i o n would be d i r e c t
c o m p a r i s i o n s o f t h e o r e t i c a l a n d e x p e r i m e n t a l r e s u l t s f o r subs t o i c h i o m e t r i c compounds. T h i s h a s however n o t been p o s s i b l e t o p e r f o r m u n t i l v e r y r e c e n t l y when a method was d e v e l o p e d ( r e f . 16) t h a t a l l o w s t h e p h o t o c u r r e n t f o r d i s o r d e r e d complex l a t t i c e s t o be c a l c u l a t e d . The method, a l s o b a s e d on t h e t h e o r e t i c a l c o n c e p t s g i v e n by P e n d r y ( r e f s . 10-12), i s a n e x t e n s i o n of t h e t h e o r y o f photoe m i s s i o n f o r d i s o r d e r e d b i n a r y a l l o y s ( r e f . 13), a s b r i e f l y d e s c r i b e d i n s e c t i o n 3 . T h i s new method a l l o w s v a c a n c y i n d u c e d e f f e c t s i n t h e e l e c t r o n i c s t r u c t u r e o f t r a n s i t i o n m e t a l c a r b i d e s and n i t r i d e s t o be modelled ( r e f s . 17-19),
which i s e x e m p l i f i e d i n
s e c t i o n 4. 2 . BULK BAND STRUCTURE MAPPING How i n f o r m a t i o n a b o u t t h e t h r e e d i m e n s i o n a l e n e r g y b a n d s i n a
s o l i d i s e x t r a c t e d from ARP s p e c t r a h a s b e e n d e s c r i b e d i n d e t a i l e a r l i e r ( r e f s . 5 - 8 ) . The b a s i c a s s u m p t i o n s made i n a n i n t e r p r e t a t i o n a r e t h a t e n e r g y a n d momenta a r e c o n s e r v e d i n t h e p h o t o e x c i t a t i o n s t e p a n d t h a t t h e momentum component p a r a l l e l l t o t h e s u r f a c e i s conserved f o r t h e photoelectron i n t h e escape s t e p a c r o s s t h e s u r f a c e . F o r ARP s p e c t r a r e c o r d e d a t normal e l e c t r o n e m i s s i o n from a low i n d e x c r y s t a l s u r f a c e t h e i n t e r p r e t a t i o n o f e x p e r i m e n t a l d a t a c o n s i s t s o f d e t e r m i n i n g t h e p o s s i b l e d i r e c t t r a n s i t i o n s between b u l k e n e r g y b a n d s a l o n g t h e h i g h symmetry d i r e c t i o n s p e c i f i e d by t h e s u r f a c e n o r m a l . Symmetry s e l e c t i o n r u l e s ( r e f . 2 0 ) f u r t h e r s i m p l i f y t h e interpretation since they specify that only a f e w of t h e
216
a v a i l a b l e f i n a l states can c o n t r i b u t e t o t h e photocurrent f o r t h i s e x p e r i m e n t a l geometry. F o r a f c c o r sodium c h l o r i d e s t r u c t u r e , f o r example, t h e o n l y a l l o w e d f i n a l s t a t e s a t normal e l e c t r o n e m i s s i o n from t h e ( 1 0 0 ) s u r f a c e are t h o s e of Alsymmetry. S e v e r a l band s t r u c t u r e c a l c u l a t i o n s f o r t r a n s i t i o n m e t a l n i t r i d e s a n d c a r b i d e s c r y s t a l l i z i n g i n t h e sodium c h l o r i d e s t r u c t u r e have been p u b l i s h e d a n d have r e c e n t l y been r e v i e w e d ( r e f . 4 ) . Most c a l c u l a t i o n s have been made f o r s t o i c h i o m e t r i c c r y s t a l c o m p o s i t i o n u s i n g t h e APW and LAPW methods a n d i t i s t h e r e f o r e o f i n t e r e s t t o compare t h e s e t h e o r e t i c a l p r e d i c t i o n s w i t h e x p e r i m e n t a l f i n d i n g s , a l t h o u g h s i n g l e c r y s t a l s o f t h e s e compounds r a r e l y e x i s t i n s t o i c h i o m e t r i c c o m p o s i t i o n . ARP i n v e s t i g a t i o n s of s e v e r a l n i t r i d e and c a r b i d e c r y s t a l s have been p u b l i s h e d and, below, a s t y p i c a l examples of s u c h band mappings w e d e s c r i b e i n some d e t a i l r e s u l t s o b t a i n e d f o r VN,,,,
a n d T i N o . 8 3 . The p r e s e n t a t i o n w i l l be f o c u s e d on
r e s u l t s c o l l e c t e d on (100) s u r f a c e s , s i n c e f o r c r y s t a l s h a v i n g t h e sodium c h l o r i d e s t r u c t u r e t h i s i s t h e d e n s e l y p a c k e d and n o n p o l a r s u r f a c e which h a s been s t u d i e d most e x t e n s i v e l y .
2.1 The b u l k b a n d s t r u c t u r e of VNl.o c a l c u l a t e d ( r e f . 2 1 ) a l o n g t h e r-X
d i r e c t i o n i s shown by t h e s o l i d l i n e s i n F i g . l a . A t t h e lower
Tli p o i n t a t h r e e f o l d d e g e n e r a t e s t a t e h a v i n g N-2p o r i g i n g i v e s r i s e t o t h r e e b a n d s i n t h e T-X d i r e c t i o n , t h e A5 band b e i n g d o u b l y d e g e n e r a t e . T h e s e t of bands o r i g i n a t i n g from
rZ5,a n d
t h e upper Tis
p o i n t a r e p r e d o m i n a n t l y d e r i v e d from V-3d s t a t e s . Along t h e T-X d i r e c t i o n t h e r e i s , however, a s t r o n g m i x i n g o f t h e V-3d a n d N-2p s t a t e s . The l o w e s t l y i n g A1 band a r i s i n g from N - 2 s
s t a t e s , and
i s n o t i n c l u d e d i n t h e f i g u r e and i s of l e s s i m p o r t a n c e i n t h e i n v e s t i g a t i o n of t h e bonding of t h e two
l o c a t e d a r o u n d -15 e V ,
c o n s t i t u e n t s . I t i s t h e s t r o n g h y b r i d i z a t i o n between metal-d
states
and nonmetal 2p s t a t e s t h a t g i v e s r i s e t o t h e complex bonding c h a r a c t e r i s t i c s i n t h e t r a n s i t i o n metal c a r b i d e s and n i t r i d e s . T h e band s t r u c t u r e of T i N i s f a i r l y s i m i l a r t o t h a t of VN,
s e e n i n F i g . I b , t h e main d i f f e r e n c e b e e i n g t h a t t h e upper i s l o c a t e d above t h e F e r m i l e v e l i n T i N . a r e t h e c a l c u l a t e d h i g h e n e r g y A1 bands
as
r15p o i n t
Also shown i n t h i s f i g u r e ( t h i n s o l i d l i n e s ) t h a t can
c o n t r i b u t e t o t h e p h o t o c u r r e n t a t normal e l e c t r o n e m i s s i o n . These bands a r e shown d i s p l a c e d dowcwards i n e n e r g y by t h e amounts i n d i c a t e d . The i n t e r s e c t i o n s between t h e d i s p l a c e d h i g h e n e r g y band
217
F i g . 1 C a l c u l a t e d and e x p e r i m e n t a l e n e r g y band d i s p e r s i o n s a l o n g t h e < l o o > d i r e c t i o n f o r ( a ) VN and ( b ) T i N . The l i g h t s o l i d l i n e s i n ( b ) r e p r e s e n t t h e A, f i n a l s t a t e b a n d s d i s p l a c e d downwards by t h e amounts i n d i c a t e d . and t h e low e n e r g y b a n d s show t h e t h e o r e t i c a l e n e r g y l o c a t i o n s o f p e a k s t h a t may be o b s e r v e d i n a n AFQ
spectrum recorded a t t h a t
photon e n e r g y . Symmetry s e l e c t i o n r u l e s may however e x c l u d e some o f t h e t r a n s i t i o n s . Symmetry a r g u m e n t s ( r e f . 2 0 ) c a n a l s o b e e x p l o i t e d i n p o l a r i z a t i o n dependent s t u d i e s f o r e x p e r i m e n t a l i d e n t i f i c a t i o n o f t h e symmetry o f t h e i n i t i a l s t a t e i n v o l v e d . When a n a l y s i n g normal e m i s s i o n ARP spectra t h e determined p e a k l o c a t i o n s are s i m p l y p l o t t e d a l o n g t h e p r o p e r l y d i s p l a c e d bands, F i g . lb f o r p h o t o n e n e r g i e s o f 15, 2 0 , The s o l i d d o t s i n F i g .
as i l l u s t r a t e d i n
25 a n d 30 e V .
1 represent experimental d a t a t h a t could
b e unambiguously i d e n t i f i e d a s o r i g i n a t i n g from b u l k band t r a n s i t i o n s ( r e f s . 22-23).
Before d i s c u s s i n g t h e r e s u l t s f o r T i N w e t u r n
t o t h e band mapping made f o r VN,
shown i n F i g . l a , which was c a r r i e d
o u t i n a s l i g h l y d i f f e r e n t manner. I n s t e a d of u s i n g t h e c a l c u l a t e d h i g h e n e r g y A1 b a n d s , which showed f a i r l y l a r g e band g a p s , a f i t t e d f r e e e l e c t r o n band w a s u t i l i z e d . F o r VN, c o n t r i b u t i o n s from t h r e e bands c o u l d be i d e n t i f i e d e x p e r i m e n t a l l y and t h e i r d i s p e r s i o n and symmetry c o u l d be d e t e r m i n e d . The p o l a r i z a t i o n dependence o f t h e p e a k s i n t h e r e c o r d e d ARP s p e c t r a showed t h e symmetry b e h a v i o u r p r e d i c t e d by t h e c a l c u l a t e d r e s u l t s .
One s t r u c t u r e l o c a t e d a r o u n d
218
-7 eV o r i g i n a t i n g from a A, i n i t i a l s t a t e band and two s t r u c t u r e s
l o c a t e d c l o s e r t o t h e Fermi energy o r i g i n a t i n g from i n i t i a l s t a t e bands of
A5 symmetry. The l o c a t i o n of t h e minimum of t h e A, band and
t h e l o c a t i o n of t h e upper A5 band a g r e e r e a s o n a b l y w e l l w i t h t h e t h e o r e t i c a l p r e d i c t i o n s . The main A5 band on t h e o t h e r hand i s found t o be l o c a t e d c o n s i d e r a b l y deeper below t h e F e r m i l e v e l t h a n calcul a t e d and t h e d i s p e r s i o n of t h e band i s s m a l l e r t h a n t h e t h e o r e t i c a l d i s p e r s i o n . The s t e e p p a r t of t h e A, band c o u l d not be mapped out and t h e p r o b a b l e reason f o r t h i s i s d i s c u s s e d i n s e c t i o n 4 . Most of t h e s t r u c t u r e s observed i n t h e normal emission s p e c t r a from
VNo,89(100)c o u l d be e x p l a i n e d a s o r i g i n a t i n g from bulk band t r a n s i t i o n s . The e x c e p t i o n b e i n g a weak s t r u c t u r e l o c a t e d around - 3 eV, i n s p e c t r a r e c o r d e d a t photon e n e r g i e s l a r g e r t h a n 3 0 eV, which i s i n d i c a t e d by c i r c l e s i n F i g . l a and i n t e r p r e t e d a s a r i s i n g from vacancy induced s t a t e s . The band mapping made f o r T i N shows s e v e r a l s i m i l a r i t i e s b u t a l s o c e r t a i n d i f f e r e n c e s compared t o VN,
a s seen i n F i g . l b . The f l a t
p a r t of t h e A1 band i s found t o be i n f a i r l y good agreement with t h e c a l c u l a t e d r e s u l t s . The d i s p e r s i o n of t h e along t h e r - X
A5 band is mapped o u t
l i n e and i t s l o c a t i o n i s , a s f o r VN,
found t o be
c o n s i d e r a b l y d e e p e r below t h e Fermi l e v e l t h a n t h e c a l c u l a t e d band. The d i s p e r s i o n of t h e A,, band has i n t h i s c a s e a l s o been mapped o u t d e s p i t e symmetry s e l e c t i o n r u l e s which f o r b i d o a s e r v a t i o n of t h e A * , band a t normal e l e c t r o n e m i s s i o n . However, t h e r u l e s apply s t r i c t l y only f o r a system w i t h a v a n i s h i n g l y s m a l l a c c e p t a n c e s o l i d a n g l e , a requirement t h a t cannot be f u l l f i l l e d f o r an e x p e r i m e n t a l ARP spectrum. The d o t t e d l i n e s and open d o t s i n F i g . l b r e p r e s e n t t h e p o s i t i o n of s h o u l d e r s and peaks i n t h e ARP s p e c t r a t h a t could not be unambigouosly i d e n t i f i e d with bulk band t r a n s i t i o n s . The s t r u c t u r e s t h a t appeared between about -5 e V and - 6 eV may o r i g i n a t e from band edge emission and from c o n t r i b u t i o n s from t h e s t e e p p a r t of t h e
A, band. Of more i n t e r e s t though i s t h e s t r u c t u r e observed around -3 eV which e x h i b i t e d no o b s e r v a b l e d i s p e r s i o n and a p o l a r i z a t i o n dependence t y p i c a l f o r As s t a t e s . I t has been i n t e r p r e t e d 24-25)
(ref.
a s a r i s i n g from a T a m s u r f a c e s t a t e s p l i t off t h e A5 bulk
band. Thus f o r T i N o , , , ( l O O )
cannot o n l y c o n t r i b u t i o n s from d i r e c t
bulk band t r a n s i t i o n s and band edge emission e x p l a i n t h e f e a t u r e s observed i n t h e r e c o r d e d s p e c t r a b u t t h e occurence of a s u r f a c e s t a t e was a l s o r e v e a l e d . How d i f f e r e n t t y p e s of s u r f a c e s t a t e s may a r i s e i s d i s c u s s e d i n s e c t i o n 3 and e x e m p l i f i e d i n s e c t i o n 4 .
219
The above described band mappings were derived from normal e m i s s i o n spectra r e c o r d e d u s i n g s y n c h r o t r o n r a d i a t i o n a n d p h o t o n e n e r g i e s from a b o u t 15 t o 30 eV. So f a r o n l y a few more n i t r i d e and carbide c r y s t a l s h a v e b e e n i n v e s t i g a t e d u s i n g s y n c h r o t r o n r a d i a t i o n . An i n v e s t i g a t i o n of ZrNo,,,(lOO)
shows ( r e f . 2 6 ) s t r o n g s i m i l a r i t i e s
w i t h t h e r e s u l t s p r e s e n t e d f o r T i N , , 8 3 ( 1 0 0 ) r e g a r d i n g l o c a t i o n s and
d i s p e r s i o n s of t h e A5 and A1 b u l k b a n d s . A s u r f a c e s t a t e i n t e r p r e t e d a s a Tamm s t a t e s p l i t o f f t h e A5 b u l k w a s a l s o o b s e r v e d f o r Z r N ( r e f s . 26-27), TiC,,,,(100)
which w i l l b e i l l u s t r a t e d i n s e c t i o n 4 . For
t h e e x p e r i m e n t a l l y d e t e r m i n e d b i n d i n g e n e r g i e s were
a g a i n f o u n d ( r e f . 2 8 ) t o be c o n s i s t e n t l y l a r g e r t h a n t h e c a l c u l a t e d v a l u e s . For NbC,.,,(100)
,
however, a b e t t e r agreement between
e x p e r i m e n t a l and t h e o r e t i c a l b u l k band l o c a t i o n s and d i s p e r s i o n s was found ( r e f . 2 9 ) . The A5 band and t h e A1 band minimum a g r e e d w i t h i n a few t e n t h s o f a n e V b u t l a r g e r d i s c r e p a n c i e s o c c u r e d f o r t h e s t e e p e r p o r t i o n of t h e A1 band. A s t r u c t u r e t e n t a t i v e l y i n t e r p r e t e d a s a r i s i n g from a S h o c k l e y s u r f a c e s t a t e was o b s e r v e d on NbC a s w e l l a s s t r o n g c o n t r i b u t i o n from band edge e m i s s i o n . I n d i v i d u a l b u l k bands and t h e i r symmetry and d i s p e r s i o n c o u l d t h u s be i d e n t i f i e d a n d mapped o u t i n t h e s e e x p e r i m e n t a l i n v e s t i g a t i o n s on ( 1 0 0 ) s u r f a c e s by a p p l y i n g
t h e d i r e c t t r a n s i t i o n model.
S i m i l a r r e s u l t s were o b t a i n e d i n an i n v e s t i g a t i o n of t h e p o l a r (111) s u r f a c e of T i c ( r e f . 2 8 ) ,
(ref. 30).
where a s u r f a c e s t a t e was a l s o i d e n t i f i e d
F o r TaC(100) ( r e f . 31) a n d t h e ( 0 0 0 1 ) s u r f a c e of
h e x a g o n a l WC ( r e f . 3 2 ) , however, p r o m i n e n t f e a t u r e s were o b s e r v e d i n
recorded ARP s p e c t r a t h a t c o u l d n o t be a c c o u n t e d f o r by d i r e c t b u l k band t r a n s i t i o n s . 2.2
mnd w
a
s
off no-sion
. .
ARP SD-
When u s i n g a c o n v e n t i o n a l l i g h t s o u r c e p r o d u c i n g p h o t o n s of o n l y a few f i x e d e n e r g i e s a s l i g h t l y d i f f e r e n t p r o c e d u r e t o map t h e d i s p e r s i o n o f t h e i n i t i a l s t a t e bands h a s t o b e employed. The common method i s t o r e c o r d ARP s p e c t r a a t d i f f e r e n t e l e c t r o n e m i s s i o n a n g l e s , e e , a n d t o map t h e i n i t i a l s t a t e e n e r g i e s v e r s u s t h e e m i s s i o n a n g l e o r v e r s u s t h e p a r a l l e l l component o f t h e e l e c t r o n wave v e c t o r ,
k,,. An e m i t t e d p h o t o e l e c t r o n i s assumed t o obey a f r e e e l e c t r o n d i s p e r s i o n a n d s i n c e i t s p a r a l l e l l momentum component i s c o n s e r v e d d u r i n g p r o p a g a t i o n t h r o u g h t h e s u r f a c e t h e p a r a l l e l l wave v e c t o r component c a n b e e x p r e s s e d a s ;
220
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hv
21.2 eV
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Y
Y I
+ Y
a UI c J
-5
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I k,,
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20'
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40'
POCAR ANGLE
I
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(b)
Fig. 2 Comparision between e x p e r i m e n t a l and c a l c u l a t e d peak p o s i t i o n s a s f u n c t i o n s o f ; ( a ) k// a l o n g t h e <011> azimuth f o r V"(100) and ( b ) e l e c t r o n emission a n g l e a l o n g t h e <011> azimuth f o r T i N (100) .
whereg,,
t h e d e t e c t i o n a n g l e , and Ekin, t h e measured e l e c t r o n k i n e t i c
energy, a r e determined e x p e r i m e n t a l l y . The peak p o s i t i o n s observed i n t h e r e c o r d e d s p e c t r a and p l o t t e d v e r s u s e i t h e r k,, o r
ee can
then
be compared w i t h t h e o r e t i c a l l y p r e d i c t e d d i s p e r s i o n s . However, i n t h i s c a s e i n i t i a l s t a t e energy s u r f a c e s on which d i r e c t t r a n s i t i o n s between bulk bands a r e p o s s i b l e have t o b e c a l c u l a t e d i n t h e r e p e a t e d zone scheme. A d e n s e r mesh i n k-space t h a n t h a t i s normally used i n ApW c a l c u l a t i o n s is o f t e n needed and r e a l i z e d u s i n g i n t e r p o l a t i o n schemes. Examples of band mappings ( r e f s . 3 3 , 2 3 ) c a r r i e d out a l o n g t h e <011> a z i m u t h a l d i r e c t i o n on (100) c r y s t a l s of V N o , 8 9 and T i N , . , 3
u s i n g He1 r a d i a t i o n a r e shown i n F i g . 2 .
The
e x p e r i m e n t a l l y determined peak p o s i t i o n s a r e shown by s o l i d d o t s . The c a l c u l a t e d energy p o s i t i o n s u s i n g t h e f u l l c a l c u l a t e d band s t r u c t u r e a r e shown a s d o t t e d l i n e s i n F i g . 2a f o r VN and by dashed c u r v e s i n F i g . 2b f o r T i N . The d o t t e d c u r v e s i n F i g . 2b were o b t a i n e d u s i n g a f i t t e d f r e e e l e c t r o n band a s t h e f i n a l s t a t e . These r e s u l t s i l l u s t r a t e what i s t y p i c a l l y observed:
A f a i r l y good
agreement concerning t h e l o c a t i o n and d i s p e r s i o n of t h e lowest l a y i n g band, t h e A, band a t normal e m i s s i o n . A r e l a t i v e l y l a r g e energy d i f f e r e n c e a t normal emission f o r t h e A5 band t h a t d e c r e a s e s
221
w i t h i n c r e a s i n g 8, o r k,,
s i n c e t h e e x p e r i m e n t a l d i s p e r s i o n i s found t o be s m a l l e r t h a n t h e c a l c u l a t e d o n e . T h e d i s p e r s i o n c u r v e s c a l c u l a t e d u s i n g a l l a v a i l a b l e f i n a l s t a t e bands do c o n t a i n some b r a n c h e s f o r which no c o r r e s p o n d i n g e m i s s i o n f e a t u r e c o u l d be i d e n t i f i e d i n t h e r e c o r d e d A R P s p e c t r a . T h i s i s e x p e c t e d however s i n c e f o r some of t h e bands t h e t r a n s i t i o n p r o b a b i l i t y ( m a t r i x element) should be very s m a l l . D i r e c t b u l k band t r a n s i t i o n s do e x p l a i n
most of t h e s t r u c t u r e s
o b s e r v e d i n r e c o r d e d ARP s p e c t r a . Thus i n t h e c a s e s shown, t h e o r e t i c a l r e s u l t s f o r t h e s t o i c h i o m e t r i c compund account f a i r l y w e l l f o r e x p e r i m e n t a l r e s u l t s from s u b s t o i c h i o m e t r i c c r y s t a l s . ARP s t u d i e s u s i n g c o n v e n t i o n a l l i g h t s o u r c e s have been r e p o r t e d f o r TiN ( r e f . 2 3 ) , T i C ( r e f . 3 4 ) , VN ( r e f . 331, VC ( r e f . 3 5 ) , Z r N ( r e f . 3 6 ) , ZrC (ref. 3 7 ) , NbN
( r e f . 33) and N b C ( r e f . 38) and i n a l l cases
e x c e p t NbN t h e t r e n d i s t h e same. The experiment l o c a t e s t h e bands d e e p e r below t h e F e r m i l e v e l t h a n c a l c u l a t e d , w i t h t h e l a r g e s t d i s c r e p a n c y o c c u r i n g f o r t h e lower A5 band, a n d t h e band d i s p e r s i o n i s , i n g e n e r a l , found t o be s m a l l e r t h a n t h e o r e t i c a l l y c a l c u l a t e d . 3. THEORETICAL PHOTOEMISSION SPECTRA, THE ONE STEP MODEL 3.1 The most s u c c e s s f u l , and t h e computanionally most u s e f u l ,
t h e o r e t i c a l one s t e p model o f AFiP i s t h e one f o r m u l a t e d by Pendry i n 1 9 7 6 ( r e f . 10). I t was t h e f i r s t model t o b e u s e d i n r e a l i s t i c n u m e r i c a l c a l c u l a t i o n s , and it h a s s i n c e t h e n found i t s u s e i n several different applications. The s t r e n g t h o f P e n d r y ' s t h e o r y i s t h e completeness o f t h e model. I t includes t h e f u l l multiple s c a t t e r i n g e f f e c t s f o r t h e electrons,
t h e e l e c t r o n - p h o t o n i n t e r a c t i o n i n t h e e x c i t a t i o n p r o c e s s and t h e many body e f f e c t s d e s c r i b e d a s a damping o f t h e e l e c t r o n s (and h o l e s ) which can b e s e e n as peak b r o a d e n i n g s i n t h e c a l c u l a t e d and. r e c o r d e d s p e c t r a . The c r y s t a l i s d e s c r i b e d a s a s e m i i n f i n i t e s t a c k of l a y e r s , e a c h l a y e r c o n s i s t i n g of a c o p l a n a r a r r a y of atoms. On t o p o f t h e s e m i i n f i n i t e c r y s t a l , d i f f e r e n t o v e r l a y e r s can be added i n o r d e r t o model c o a t i n g s of v a r i o u s k i n d s (CO, 0, e t c ) . The t r a n s i t i o n from t h e c r y s t a l t o vacuum i s d e s c r i b e d a s a p o t e n t i a l s t e p f u n c t i o n , whose h e i g h t c o r r e s p o n d s t o t h e work f u n c t i o n of t h e actual material. Inside the crystal t h e electronic potential is approximated a c c o r d i n g t o t h e m u f f i n - t i n model, i . e . s p h e r i c a l symmetric p o t e n t i a l s around e a c h atom and a c o n s t a n t p o t e n t i a l i n
222
between. The original computer code based on Pendry’s model was PEOVER, a program presented in Computer Physics Communications (ref. 12). A drawback with PEOVER was the limited possibilities for describing complicated crystal structures. In fact only cubic structures with one atom per two dimensional unit cell could be processed. To be able to calculate photoemission spectra from substitutionally disordered alloys, Durham developed a computer program based on Pendry’s theory. He used the Coherent Potential Approximation to develop a KKR-CPA version of PEOVER (ref. 13). For ordered alloys and for crystal structures other than cubic, Larsson (ref. 14) has developed a model for photoemission based on Pendry’s theory. This model will be described in some detail in the next .section. Recently Readinger et a1 (ref. 16) has further extended the original model by making it possible to study substitutionally disordered alloys with more than two constituents. They have applied their model to study vacancies in metallic carbides and nitrides (refs. 17-19). 3.2 The limitations in the original photoemission model were set by
repeating one layer, containing only one atom per unit cell, to form the bulk crystal. This restricts our choice of bulk material, not only from an elemental point of view, but also from the crystal structure. Magnesium, for example, forms the hexagonal closed packed structure, and can therefore, in the (0001) direction, only be represented by repeating a unit of two layers. For metallic compounds (carbides and nitrides) the situation is similar. These materials are formed out of two different atomic constituents, and in some crystallographic directions more than one atomic layer is needed to model the bulk crystal. The first step towards a more generalized treatment is to include more atoms in the layer unit cell. To do this we have to consider the model we use to describe the electrons in the crystal. To calculate the electron and hole Green functions we use essentially two sets of basis functions (ref. 10). Within the layers, in the vincinity of the atoms, we use an expansion in spherical waves and between the planar layers a plane wave expression is utilized. The plane wave expression is unaffected by the number of atoms in the layer and therefore, we have to consider only the effects on the spherical wave expansion. Since we are using the muffin-tin
223
a p p r o x i m a t i o n w e do n o t have t o c o n s i d e r t h e problem o f o v e r l a p p i n g p o t e n t i a l s , which s i m p l i f i e s o u r problem. To i n c r e a s e t h e number of atoms i n t h e l a y e r u n i t c e l l w e have t o i n c l u d e t h e wave f i e l d s from a l l o t h e r atoms when d o i n g t h e summation o v e r s p h e r i c a l waves around
e must however i n c l u d e t h e p r o p e r p h a s e one p a r t i c u l a r atom. W f a c t o r , d e p e n d i n g on a t o m i c p o s i t i o n . The s p h e r i c a l wave c o e f f i c i e n t s a t atom t i n l a y e r j , c o r r e c t e d f o r m u l t i p l e s c a t t e r i n g , can b e w r i t t e n ;
r t , i s t h e p o s i t i o n of atom t ' i n t h e u n i t c e l l . These e x p r e s s i o n s
a r e t o be compared w i t h e q u a t i o n s ( 4 7 ) and ( 5 0 ) i n r e f . 1 0 . When a l l t h e d e t a i l s of t h e s p h e r i c a l waves w i t h i n t h e l a y e r a r e found, i t i s p o s s i b l e t o c a l c u l a t e t h e r e f l e c t i o n and t r a n s m i s s i o n m a t r i c e s f o r that layer
(
f o r p r o p e r e x p r e s s i o n s of t h e s e m a t r i c e s see r e f . 3 9 ) .
When a l l d e t a i l s of e v e r y s i n g l e l a y e r t o be u s e d i s known, t h i s i n f o r m a t i o n i s u s e d t o b u i l d a complete c r y s t a l . I f a l l l a y e r s a r e e q u a l w e u s e t h e l a y e r d o u b l i n g method ( r e f . 4 0 ) u n t i l w e have r e a c h e d a c r y s t a l t h i c k n e s s l a r g e enough. T h e l i m i t b e i n g d e t e r m i n e d by t h e decay of t h e w a v e f u n c t i o n f o r t h e damping p a r a m e t e r u s e d . F o r s t r u c t u r e s c r e a t e d o u t o f two o r more d i f f e r e n t l a y e r s a somewhat e x t e n d e d l a y e r d o u b l i n g method i s t o be employed ( r e f . 1 4 ) . What w e
Fig. 3 Two d i m e n s i o n a l model of a l a y e r r e p e a t u n i t c o n s i s t i n g of t h r e e l a y e r s ; l a y e r s one and two h a v e g o t two d i f f e r e n t atoms p e r u n i t c e l l a n d l a y e r t h r e e h a s one; d, i s t h e d i s t a n c e between l a y e r i and l a y e r i t l ; r / / i s t h e c o o r d i n a t e p a r a l l e l t o t h e s u r f a c e and z i s t h e o r t h o g o n a l component.
224
want t o do i s t o create a b u l k r e p e a t u n i t c e l l c o n s i s t i n g o f t h e l e a s t number of l a y e r s needed t o describe t h e c o m p l e t e c r y s t a l . The r e p e a t u n i t is t h e n t o be u s e d i n a l a y e r ( o r r a t h e r r e p e a t u n i t ) d o u b l i n g p r o c e d u r e . T h i s i s done i n t h e f o l l o w i n g way: h a v e c a l c u l a t e d t h e r e f l e c t i o n , Ri,
Assume w e
and t h e t r a n s m i s s i o n , Ti,
m a t r i c e s f o r a l l l a y e r s i . W e t h e n , by u s i n g m u l t i p l e s c a t t e r i n g , c a l c u l a t e t h e new r e f l e c t i o n , R,, and t r a n s m i s s i o n , T,,
matrices f o r
two l a y e r s i and i+l p u t t o g e t h e r .
T,
=
Ti+lPt(l
R,
=
Ri
+
-
RiP-RitlPt)-l
Ti
TiP-Ri+lPt (1 - RiP-Ri+lP+)-l Ti
(3.4) (3.5)
Where P + and P- a r e t h e p r o p a g a t o r s which add t h e c o r r e c t p h a s e f a c t o r when t h e wave p r o p a g a t e s from l a y e r i t o l a y e r i+l and v i c e v e r s a . I f t h e r e a r e more t h a n two l a y e r s i n t h e b u l k r e p e a t u n i t t h e p r o c e d u r e i s r e p e a t e d w i t h t h e m a t r i c e s , Ti+2, Ri+2, T, and R, t o compute t h e new T, a n d R,.
This i s repeated u n t i l a l l d i f f e r e n t
l a y e r s i n t h e b u l k a r e i n c l u d e d . The b u l k r e f l e c t i o n m a t r i x can t h e n b e found u s i n g s t a n d a r d LEED t e c h n i q u e s on t h e m a t r i c e s T, and R , a n d a l l c a l c u l a t i o n s f o l l o w i n g can be done i n a s i m i l a r manner a s
d e s c r i b e d by Pendry ( r e f . 10). F i n a l l y when t h e p h o t o c u r r e n t i s t o b e c a l c u l a t e d a l l d i f f e r e n t l a y e r s and a l l d i f f e r e n t atoms w i t h i n e a c h l a y e r have t o be i n c l u d e d . A t t h i s s t a g e it i s important t o i n c l u d e a l l d i f f e r e n t
terms i n t h e c a l c u l a t i o n s of t h e m a t r i x e l e m e n t s .
3.3
SYtface s t a t =
T r a d i t i o n a l l y , i n t h e l i t e r a t u r e , t h e r e h a s been a d i s t i n c t i o n between two d i f f e r e n t t y p e s o f s u r f a c e s t a t e s , Shockley s t a t e s ( r e f . 4 1 ) and Tamm s t a t e s ( r e f . 4 2 ) . The main d i f f e r e n c e i s t h a t t h e
former e x i s t s c l o s e t o t h e s u r f a c e a s soon a s t h e i n f i n i t e p e r i o d i c i t y is b r o k e n and t h e matching c o n d i t i o n s of t h e o t h e r w i s e d e c a y i n g wave f u n c t i o n s a t t h e s u r f a c e a r e f u l l f i l l e d . Tamm s t a t e s on t h e o t h e r hand, need a p e r t u r b a t i o n t o t h e o u t e r m o s t a t o m i c l a y e r or layers t o exist. I n t h e c o n t e x t o f o u r c o m p u t a t i o n a l model, t h i s means t h a t when u s i n g t h e a t o m i c p o t e n t i a l from a t r a d i t i o n a l b u l k band c a l c u l a t i o n i n a l l t h e l a y e r s , o n l y Shockley s t a t e s c a n b e m o d e l l e d . I n terms of m u l t i p l e s c a t t e r i n g t h e o r y Echenique and Pendry ( r e f . 4 3 ) and McRae
225
( r e f . 4 4 ) developed a simple c o n d i t i o n f o r t h e e x i s t e n c e of such a s t a t e . I f w e assume t h e c r y s t a l bulk r e f l e c t i v i t y ,
neglecting the
and t h e b a r r i e r r e f l e c t i v i t y t o be rbqg,, this b a r r i e r , t o be rcqq,, condition can be w r i t t e n :
I n o u r model t h i s can be f u r t h e r s i m p l i f i e d . S i n c e we have no k//-dependence i n o u r s u r f a c e p o t e n t i a l model, t h e rbqq, - matrix becomes d i a g o n a l . For low e n e r g i e s a l l components i n our p l a n e wave expansion where t h e g-vector # 0 decay v e r y r a p i d l y and m u l t i p l e = 0 for g s c a t t e r i n g of t h e s e waves may be n e g l e c t e d (Pqg
#
0 ) . This
combines t o a s i m p l i f i e d e x p r e s s i o n :
1
-
rcO0rbo0 = 1 - rc e x p ( i 0 , ) r, e x p ( i 0 , )
I n a band gap rc
=
=
O
(3.7)
1 and s i m i l a r l y below t h e vacuum l e v e l r,
1.
=
T h e r e f o r e , t h e c o n d i t i o n f o r e x i s t e n c e of a s u r f a c e s t a t e of Shockley t y p e b o i l s down t o : 0, + 0,
=
2x11 ,
where n i s a p o s i t i v e
integer.
CRYSTAL
VACUUM V(Z) I
I
I
L
t
CRYSTAL
VACUUM
t
V(Z)
Fig. 4 Schematic i l l u s t r a t i o n o f : ( a ) t h e c o n d i t i o n s , d e s c r i b e d i n t h e t e x t , f o r t h e e x i s t e n c e of a Shockley s u r f a c e s t a t e where d i s t h e d i s t a n c e between t h e outermost l a y e r of atoms and t h e s u r f a c e b a r r i e r . That d o f t e n i s chosen t o be z e r o does n o t i n v a l i d a t e t h e d i s c u s s i o n . ( b ) t h e way t o model Tamm s u r f a c e s t a t e s .
226
Tamm states, on the other hand, will only appear if we use a different atomic potential in the outermost layer (or layers) compared to the bulk. To model these states we need to introduce some sort of perturbation to the surface layer atomic potential. This has been done quite successfully, by just adding a constant part to the potential used in the bulk (refs. 45-46), making the potential slightly less attractive and thereby creating suitable conditions for the existence of Tamm surface states. For metallic carbides and nitrides such a method can be justified by the argument presented in ref. 24: For the ionic component of the bonding the change in number of nearest neighbours at the surface will affect the electrostatic potential in the surface layer in such a way that it can be described simply by a shift in the atomic potential. -v instatThe above described method of photoemission calculations is in principle only valid for the perfect stoichiometric compound. Single crystals of metallic nitrides and carbides are rarely available in stoichiometric compositions, and therefore, all experiments to date have been performed on non stoichiometric samples. The vacancies which appear in all real samples can be included in a theoretical treatment only by adopting a somewhat different approach to the theory. In the literature there has been a discussion on the importance of the vacancies in the interpretation of the 3.4
experimental results. In order to clarify the influence of the vacancies, the need for a computational method to describe more realistically the composition of the specimens is obvious. The vacancies in the crystal are assumed to be distributed randomly on the nonmetal sites (refs. 1,15). One way of addressing this problem is, therefore, to regard the crystal as a substitutionally disordered alloy with o n e ordered constituent, the metal atom, and two disordered constituents, the nonmetal atom and the empty site. A successful theoretical method to address the problem of substitutionally disordered systems is the Coherent Potential Approximation (CPA) (ref. 48). The adoption of this method onto "band-theory’’ is done using the Korringa-Kohn-Rostoker method to create the KKRCPA technique (ref. 49) for electron structure calculations on disordered alloys. Based on KKRCPA ideas, Durham (ref. 1 3 ) formulated a theory of photoemission from surfaces of substitutionally disordered alloys.
227
H e a l s o d e v e l o p e d a computer code t o c a l c u l a t e p h o t o e m i s s i o n s p e c t r a
from b i n a r y random a l l o y s . T h i s code h a s been s u c c e s s f u l l y used t o i n t e r p r e t d a t a from a l l o y s s u c h a s Cu,-xNi,(ref.
50).
By combining t h e t h e o r i e s f o r o r d e r e d and d i s o r d e r e d a l l o y s ,
Redinger e t a 1 have d e v e l o p e d a computer program which can be u s e d t o s t u d y v a c a n c i e s i n m e t a l l i c c a r b i d e and n i t r i d e s ( r e f . 1 6 ) . Using t h i s code t h e y have p r e d i c t e d f e a t u r e s o r i g i n a t i n g from vacancy i n d u c e d s t a t e s t o a p p e a r i n e x p e r i m e n t a l ARP-spectra
(refs. 17-19).
They have a l s o v e r i f i e d t h e i n t e r p r e t a t i o n of c e r t a i n p e a k s a s b e i n g s u r f a c e s t a t e s . F u r t h e r m o r e t h e y have c a l c u l a t e d t h e KKRCPA s c a t t e r i n g a m p l i t u d e s f o r s e v e r a l d i f f e r e n t c o n c e n t r a t i o n s of v a c a n c i e s a n d t h e r e b y have been a b l e t o model t h e e f f e c t s of vacancy c o n c e n t r a t i o n g r a d i e n t s away from t h e s u r f a c e . I n t h e p h o t o e m i s s i o n program t h i s i s done by r e g a r d i n g t h e l a y e r s w i t h d i f f e r e n t c o n c e n t r a t i o n s of v a c a n c i e s a s o v e r l a y e r s on t o p of a b u l k w i t h homogeneous s t r u c t u r e .
4.
THEORETICAL PHOTOEMISSION SPECTRA, APPLICATION EXAMPLES T h e o r e t i c a l p h o t o e m i s s i o n s p e c t r a c a l c u l a t e d u s i n g t h e methods
d e s c r i b e d i n paragraph 3 provide information n o t only about t h e e n e r g y l o c a t i o n o f s p e c t r a l f e a t u r e s i n ARP s p e c t r a b u t a l s o on t h e i r r e l a t i v e i n t e n s i t y and w i d t h . They t h u s p r o v i d e i m p o r t a n t a d d i t i o n a l i n f o r m a t i o n a b o u t t h e e l e c t r o n s t a t e s from which t h e s p e c t r a l f e a t u r e s o r i g i n a t e . I n t h i s s e c t i o n a p p l i c a t i o n s of t h e above d e s c r i b e d t h e o r e t i c a l models which were d e v e l o p e d t o c a l c u l a t e t h e p h o t o c u r r e n t from more complex s y s t e m s , i . e . m a t e r i a l s l i k e t h e t r a n s i t i o n m e t a l c a r b i d e s and n i t r i d e s among o t h e r s , a r e p r e s e n t e d . R e s u l t s c a l c u l a t e d f o r o r d e r e d compounds u s i n g t h e model d e v e l o p e d by L a r s s o n ( r e f . 1 4 ) a r e p r e s e n t e d i n s e c t i o n 4 . 1 and 4 . 2 and r e s u l t s c a l c u l a t e d f o r d i s o r d e r e d s y s t e m s , by Readinger e t . a l . ( r e f s . 1 6 - 1 9 ) , a r e p r e s e n t e d i n s e c t i o n 4.3.
4.1 grdered CornWhen c a l c u l a t i n g ARP s p e c t r a f o r o r d e r e d compounds t h e m u f f i n t i n p o t e n t i a l s g e n e r a t e d i n APW b u l k band s t r u c t u r e c a l c u l a t i o n s f o r c r y s t a l s of s t o i c h i o m e t r i c c o m p o s i t i o n were u s e d . The s u r f a c e b a r r i e r was r e p r e s e n t e d b y a p o t e n t i a l s t e p f u n c t i o n l o c a t e d just o u t s i d e t h e m u f f i n t i n s i n t h e s u r f a c e l a y e r . Although it i s w e l l known t h a t t h e p o t e n t i a l i n t h e topmost s u r f a c e l a y e r might be d i f f e r e n t from t h e b u l k p o t e n t i a l , t h e l a t t e r h a s o f t e n been u s e d i n
228
a l l l a y e r s when t h e e x p e r i m e n t a l s p e c t r a t o b e modelled showed no s t r u c t u r e t h a t c o u l d unambigously be i d e n t i f i e d w i t h s u r f a c e s t a t e emission. S p e c t r a c a l c u l a t e d t h i s way s h o u l d , when t h e e f f e c t i v e p o t e n t i a l i n t h e ion core regions is strong, a s it generally is f o r d-band m e t a l s , be dominated by b u l k photoemission p r o c e s s e s b u t c o n t r i b u t i o n from t h e s u r f a c e p o t e n t i a l b a r r i e r w i l l a l s o be present. I n c a s e s where s u r f a c e s t a t e s have been r e v e a l e d e x p e r i m e n t a l l y and found n o t t o be w e l l modelled when u s i n g b u l k p o t e n t i a l s i n a l l l a y e r s t h e p o t e n t i a l i n t h e s u r f a c e l a y e r h a s been s h i f t e d i n e f f o r t s t o m i m i c t h e experimental f i n d i n g s . For t h e ordered compounds w e t h e r e f o r e f i r s t i l l u s t r a t e b u l k photoemission a p p l i c a t i o n s , i . e . c a s e s where t h e bulk p o t e n t i a l and bulk l a t t i c e p a r a m e t e r a r e used i n a l l l a y e r s , and t h e r e a f t e r c a s e s where a s h i f t e d s u r f a c e l a y e r p o t e n t i a l h a s been u t i l i z e d t o model c o n t r i b u t i o n s from s u r f a c e s t a t e s . Most of t h e selected examples d e s c r i b e t h e o r e t i c a l r e s u l t s c a l c u l a t e d f o r t h e n o n p o l a r ( 1 0 0 ) s u r f a c e of a c r y s t a l having t h e sodium c h l o r i d e s t r u c t u r e . I n t h i s c a s e t h e c r y s t a l is c o n s t r u c t e d by s t a c k i n g t o g e t h e r i d e n t i c a l l a y e r s , e a c h l a y e r c o n s i s t i n g o f a two dimensional s q u a r e l a t t i c e and a b a s i s c o n s i s t i n g o f two atoms, a metal and a nonmetal atom. I n t h e c a l c u l a t i o n s t h e e l e c t r o n and h o l e l i f e t i m e broadening p a r a m e t e r s were chosen t o b e 2 . 0 e V and 0 . 1 4 e V f o r t h e h i g h and low energy s t a t e s r e s p e c t i v e l y . These a r e n o t o p t i m i z e d b u t m e r e l y r e a s o n a b l e v a l u e s based on e x p e r i e n c e from c a l c u l a t i o n s made on o t h e r m a t e r i a l s . The e l e c t r o m a g n e t i c f i e l d i n s i d e t h e s o l i d was t r e a t e d a s i n vacuum and i s r e p r e s e n t e d by a r e a l v e c t o r p o t e n t i a l . I n g e n e r a l no c o r r e c t i o n s f o r t h e r e f r a c t i o n of l i g h t a t t h e s u r f a c e have been t a k e n i n t o a c c o u n t . 4.2
. .
PhQtQenlDirect b u l k band t r a n s i t i o n s seemed t o a c c o u n t f o r t h e s t r u c t u r e s
o b s e r v e d i n normal e m i s s i o n ARP s p e c t r a r e c o r d e d from t h e ( 1 0 0 ) s u r f a c e o f VN, a s d i s c u s s e d i n s e c t i o n 2 . T h e r e f o r e c a l c u l a t e d ARP s p e c t r a f o r VN a r e s e l e c t e d a s a f i r s t example t o i l l u s t r a t e t h e a p p l i c a b i l i t y o f t h e t h e o r e t i c a l model when u s i n g t h e b u l k p o t e n t i a l i n a l l l a y e r s ( r e f . 2 2 ) . The t h e o r e t i c a l s p e c t r a , shown i n F i g s . 5 and 6, were c a l c u l a t e d assuming l i n e a r l y p o l a r i z e d r a d i a t i o n with t h e e l e c t r i c f i e l d v e c t o r i n t h e i n c i d e n c e p l a n e . Also shown i n
229
VN (100)
Exp .
’ lev1
31 29
27 25
23
22
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Fig. 5 Normal emission ARP-spectra for VN(100) at different photon energies using p-polarized radiation incident along the <010> azimuth at an angle of 8i=1Eo. (a) Experimental and (b) calculated spectra. these figures are experimental ARP spectra collected at normal electron emission using synchrotron radiation for excitation. Several prominant structures appear in the spectra and are labelled from A to D in the figure. The strong polarization dependence exhibited by these structures when changing the incidence angle of the radiation, ei, most clearly observed in the calculated spectra, allows an identification of their origin utilizing symmetry selection rules (ref 2 0 ) . At 8,=18 two dominant structures appear ~
in the theoretical spectra, B and C, that originate from initial states of A5 symmetry. When increasing the incidence angle to 0 1 = 4 5 ” the two other structures, A and D, become more prominent indicating an origin from A1 initial state bands. The main characteristics of the structures in the calculated spectra agree fairly well with experimental observations. The polarization dependence of the peaks and the dispersion of peaks B and C are bell reproduced by the calculated results. The actual peak positions however deviate considerably, as expected, since in these computations the same potential a s used in the band structure calculation, shown in Fig. la, was utilized s o the discrepancies observed in the band mapping should remain. At photon energies above 25 eV the relative intensity
230
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Fig. 6 Normal emission ARP-spectra f o r VN(lO0) a t d i f f e r e n t photon e n e r g i e s u s i n g p - p o l a r i z e d r a d i a t i o n i n c i d e n t a l o n g t h e <010> azimuth a t an a n g l e of ei=4So. ( a ) Experimental and ( b ) c a l c u l a t e d spectra
.
o f peak D i n t h e e x p e r i m e n t a l s p e c t r a i s n o t w e l l r e f l e c t e d by t h e c a l c u l a t e d r e s u l t s . While t h e t h e o r e t i c a l s p e c t r a i n d i c a t e a s t r o n g d i s p e r s i o n of t h e lowest l y i n g A, band a t e n e r g i e s between 2 3 eV and 2 9 eV, t h e e x p e r i m e n t a l s p e c t r a show a s t r o n g and e s s e n t i a l l y
n o n d i s p e r s i n g s t r u c t u r e having A, symmetry which a p p e a r s t o a r i s e from s t r o n g band edge emission a t t h e h i g h e r photon e n e r g i e s . The reason why t h e s t e e p p a r t of t h i s A, band i s d i f f i c u l t t o map o u t i s c l e a r l y i l l u s t r a t e d b y t h e c a l c u l a t e d s p e c t r a . The i n i t i a l and f i n a l s t a t e bands i n v o l v e d become almost p a r a l l e l r e s u l t i n g i n a l a r g e peak width and an a p p e a r a n t loss i n i n t e n s i t y which i s c l e a r l y seen i n t h e t h e o r e t i c a l s p e c t r a a t photon e n e r g i e s around 2 1 e V . For t h e s t r u c t u r e l o c a t e d c l o s e t o t h e Fermi energy t h e c a l c u l a t e d s p e c t r a p r e d i c t a h i g h e r r e l a t i v e i n t e n s i t y than t h a t observed i n t h e recorded s p e c t r a , e s p e c i a l l y a t photon e n e r g i e s below 2 5 eV. T h e main reason f o r t h i s i s , however, t h a t no Fermi f u n c t i o n t o model t h e e l e c t r o n occupation has been i n c l u d e d i n t h i s c a l c u l a t i o n . Both A, and A, i n i t i a l s t a t e bands e x i s t s c l o s e t o t h e Fermi energy, a s shown i n F i g . l a , and t h e i r r e l a t i v e c o n t r i b u t i o n s can be d i s t i n g u i s h e d i n t h e s p e c t r a c a l c u l a t e d a t photon e n e r g i e s
231
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Fig. 7 Off normal e m i s s i o n ARP-spectra f o r VN(100) a t d i f f e r e n t e l e c t r o n e m i s s i o n a n g l e s a l o n g t h e <010> a z i m u t h , e x c i t e d by u n p o l a r i z e d 2 1 . 2 e V r a d i a t i o n i n c i d e n t a t a n a n g l e of ei= 45'. ( a ) E x p e r i m e n t a l a n d (b) c a l c u l a t e d s p e c t r a . l a r g e r t h a n 2 3 e V . The o v e r a l l agreement between these c a l c u l a t e d and e x p e r i m e n t a l normal e m i s s i o n ARP s p e c t r a i s v e r y s a t i s f a c t o r y .
Off normal e m i s s i o n ARP s p e c t r a from VN(lOO), r e c o r d e d a t e,, a l o n g t h e <010> azimuth, a r e shown i n F i g . 1. U n p o l a r i z e d H e 1 r a d i a t i o n , i n c i d e n t a t an a n g l e of 8,=45O, was u s e d f o r e x c i t a t i o n of t h e s e s p e c t r a . The c a l c u l a t i o n s i n d i f f e r e n t e l e c t r o n emission angles,
t h i s c a s e w e r e made assuming l i n e a r l y p o l a r i z e d r a d i a t i o n i n c i d e n t along t h e s p e c i f i e d azimuthal d i r e c t i o n but with t h e e l e c t r i c f i e l d v e c t o r a t a n a n g l e of 4 5 ' r e l a t i v e
t o t h e p l a n e of i n c i d e n c e ( r e f .
5 1 ) . W e have t o r e s o r t t o t h i s simple d i s t r i b u t i o n s i n c e a c o r r e c t t r e a t m e n t o f t h e f i e l d d i s t r i b u t i o n i n s i d e t h e s o l i d a t t h e s e photon e n e r g i e s i s p r e s e n t l y n o t p o s s i b l e . F o r t h e same r e a s o n t h e s p e c i f i e d f o r t h e recorded s p e c t r a are a l s o used i n t h e c a l c u l a t i o n s . The t w o pronounced s t r u c t u r e s d i s t i n g u i s h e d i n t h e s p e c t r u m r e c o r d e d a t 8,=Oo
c o r r e s p o n d t o e m i s s i o n from A1 a n d A5 s t a t e s
r e s p e c t i v e l y . The A, c o n t r i b u t i o n ,
l o c a t e d a r o u n d -7
eV,
is rela-
t i v e l y weaker, as e x p e c t e d , s i n c e u n p o l a r i z e d r a d i a t i o n w a s u t i l i z e d i n t h i s c a s e . For c o m p a r i s i o n o b s e r v e t h e r a t i o between p e a k s D and C i n Figs.
5 and 6 . Upon i n c r e a s i n g t h e e m i s s i o n a n g l e t h e s t r u c t u r e
a r o u n d -4 e V i s f i r s t s e e n t o s h i f t towards l a r g e r b i n d i n g e n e r g y and t h e n t o s t a r t t o s h i f t back t o w a r d s smaller b i n d i n g e n e r g y a t
232
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Fig. 8 Off normal emission ARP-spectra f o r Z r C ( 1 0 0 ) a t d i f f e r e n t e l e c t r o n emission a n g l e s a l o n g t h e <010> azimuth, e x c i t e d by u n p o l a r i z e d 1 6 . 8 eV r a d i a t i o n i n c i d e n t a t an a n g l e of 6,= 17'. ( a ) Experimental and ( b ) c a l c u l a t e d s p e c t r a . emission a n g l e s l a r g e r t h a n 24'.
The lower l y i n g s t r u c t u r e e x h i b i t s
almost no energy s h i f t but an a p p r e c i a b l e v a r i a t i o n i n i n t e n s i t y with emission a n g l e . These s p e c t r a l c h a r a c t e r i s t i c s a r e f a i r l y w e l l modelled by t h e t h e o r e t i c a l r e s u l t s but t h e r e a r e a l s o some differences. I n general the t h e o r e t i c a l s p e c t r a l features a r e s h a r p e r , r e s u l t i n g i n b e t t e r r e s o l v e d s t r u c t u r e s . T h i s i s most obvious a t t h e l a r g e s t emission a n g l e s where t h e e x p e r i m e n t a l s p e c t r a show f a i r l y broad f e a t u r e s b u t a l s o s u f f e r from p o o r e r s t a t i s t i c s . That t h e t h e o r e t i c a l s p e c t r a p r e d i c t a much s t r o n g e r i n t e n s i t y c l o s e t o t h e Fermi energy a t t h e s m a l l e s t emission a n g l e s , and a l s o around 2 4 O . t h a n t h a t observed e x p e r i m e n t a l l y i s again p a r t l y due t o t h a t a Fermi f u n c t i o n has n o t been i n c l u d e d i n t h e c a l c u l a t i o n s . The r e c o r d e d s p e c t r a show, however, an i n c r e a s e i n t h e emission c l o s e t o t h e Fermi energy a t a n g l e s around 24'. So f a r o n l y examples of t h e o r e t i c a l ARP s p e c t r a from VN have been
used t o show how c a l c u l a t e d r e s u l t s model recorded ARP s p e c t r a . In o r d e r t o i l l u s t r a t e t h a t j u s t a s good agreement between c a l c u l a t e d and e x p e r i m e n t a l r e s u l t s i s a l s o o b t a i n e d f o r o t h e r m a t e r i a l s , some r e s u l t s ( r e f . 5 2 ) from Z r C ( 1 0 0 ) a r e shown i n F i g . 8 . I n t h i s case u n p o l a r i z e d N e I r a d i a t i o n , i n c i d e n t a t a n a n g l e of 8,= 1 7 O , was u s e d f o r e x c i t a t i o n , and t h e s p e c t r a were c o l l e c t e d a t d i f f e r e n t emission
233
a n g l e s a l o n g t h e <010> a z i m u t h . Most o f t h e s p e c t r a l f e a t u r e s i n t h e r e c o r d e d c u r v e s a r e s e e n t o b e f a i r l y w e l l r e p r o d u c e d by t h e c a l c u l a t e d r e s u l t s . Two p e a k s a p p e a r i n t h e normal e m i s s i o n s p e c t r u m . The u p p e r s t r u c t u r e , l o c a t e d a r o u n d -1 e V a t normal e m i s s i o n , s h i f t s r a p i d l y t o w a r d s l a r g e r b i n d i n g e n e r g y upon i n c r e a s i n g t h e e m i s s i o n a n g l e . The l o w e r l y i n g s t r u c t u r e e x h i b i t s n o n d i s p e r s i v e c h a r a c t e r , a n d a n e x t r a s t r u c t u r e a p p e a r s a r o u n d -1 eV a t e m i s s i o n a n g l e s l a r g e r t h a n a b o u t 24'. These examples, t o g e t h e r w i t h r e c e n t p u b l i s h e d comRarisions of e x p e r i m e n t a l a n d t h e o r e t i c a l ARP s p e c t r a u s i n g t h e b u l k p o t e n t i a l i n a l l l a y e r s ( r e f s . 22,35,38,51-53),
show t h e a p p l i c a b i l i t y o f t h i s
model t o o r d e r e d compounds. 4.3
S t r u c t u r e s o b s e r v e d i n r e c o r d e d ARP s p e c t r a are u s u a l l y i d e n t i f i e d a s o r i g i n a t i n g from s u r f a c e s t a t e s i f t h e y :
-
e x h i b i t no
d i s p e r s i o n w i t h t h e normal component o f t h e wave v e c t o r , - show l a r g e r s e n s i t i v i t y t o surface contamination than bulk derived s t r u c t u r e s , - appear i n gaps of t h e b u l k band s t r u c t u r e . A s t r u c t u r e f u l l f i l l i n g t h e s e c o n d i t i o n s was o b s e r v e d on T i N ( 1 0 0 ) a n d was i n t e r p r e t e d as a Tam s u r f a c e s t a t e ( r e f s . 2 3 - 2 5 ) ,
as mentioned i n
s e c t i o n 2 . A similar s t r u c t u r e o b s e r v e d on ZrN(100) ( r e f . 27) i s shown i n t h e b o t t o m c u r v e s i n F i g . 9 . These normal e m i s s i o n s p e c t r a , r e c o r d e d a t two d i f f e r e n t i n c i d e n c e a n g l e s u s i n g H e 1 and N e I r a d i a t i o n , show t h a t t h e s t r u c t u r e o r i g i n a t i n g from i n i t i a l s t a t e s
o f A5 symmetry c o n s i s t s o f two p e a k s . The u p p e r one o f t h e s e , t h e i s i n t e r p r e t e d a s a r i s i n g from a s u r f a c e s t a t e . S i m i l a r t o t h e b e h a v i o u r f o u n d on T i N ( 1 0 0 ) , t h i s p e a k
peak l o c a t e d a r o u n d - 3 . 5 e V ,
d o e s n o t e x h i b i t a n y d i s p e r s i o n w i t h p h o t o n e n e r g y a n d i t i s found t o s h i f t a n d become a t t e n u a t e d upon g a s a d s o r p t i o n w h i l e b u l k d e r i v e d f e a t u r e s a r e e s s e n t i a l l y u n a f f e c t e d . T h e o r e t i c a l ARP s p e c t r a c a l c u l a t e d u s i n g t h e b u l k p o t e n t i a l i n a l l l a y e r s a r e shown by c u r v e s b i n F i g . 9 . The s t r o n g p o l a r i z a t i o n e f f e c t s p r e d i c t e d i n t h e c a l c u l a t e d s p e c t r a f o r t h e A5 a n d Al d e r i v e d f e a t u r e s r e f l e c t f a i r l y w e l l t h e e x p e r i m e n t a l f i n d i n g s b u t t h e s t r u c t u r e r e f l e c t i n g A5
e m i s s i o n c l e a r l y c o n s i s t s o f a s i n g l e peak, as e x p e c t e d , a n d n o t a doublet. T h e o r i g i n of t h e s u r f a c e s t a t e h a s been e x p l a i n e d ( r e f . 25) a s
c a u s e d by a change i n t h e e l e c t r o s t a t i c p o t e n t i a l a t t h e s u r f a c e , l a r g e enough t o p u l l a T a m s u r f a c e s t a t e o f f t h e A5 b u l k b a n d . The
234
Normal emission ARP-spectra f o r ZrN(100) u s i n q 2 1 . 2 eV r a d i a t i o n a t an i n c i d e n c e a n g i e of ei= 15O ( l e f t p a n e l ) - and u s i n g 1 6 . 8 eV r a d i a t i o n a t an i n c i d e n c e a n g l e of ei= 45' ( r i g h t p a n e l ) . The lower c u r v e s show e x p e r i m e n t a l s p e c t r a and t h e s t r u c t u r e around - 3 . 5 eV r e p r e s e n t s s u r f a c e s t a t e e m i s s i o n . T h e o r e t i c a l s p e c t r a c a l c u l a t e d u s i n g t h e bulk p o t e n t i a l i n a l l l a y e r s a r e shown i n c u r v e s b and when u s i n g a s u r f a c e l a y e r p o t e n t i a l s h i f t e d by + 0 . 2 eV and + 0 . 4 eV i n c u r v e s c and d r e s p e c t i v e l y .
Fiq. 9
width o f t h i s band i n T i N i n d i c a t e t h a t a s h i f t g r e a t e r t h a n + 0 . 2 e V
i s needed i n o r d e r t o p u l l a s u r f a c e s t a t e o f f t h e t o p of t h e A, band. When u s i n g an i o n i c model, a p p l i c a b l e t o t h e i o n i c component of t h e bonding, t h i s w a s p r e c i s e l y t h e c a l c u l a t e d upward s h i f t a t t h e N atoms i n t h e s u r f a c e l a y e r assuming a charge t r a n s f e r of + 0 . 5 e i n t h e b u l k and a t t h e s u r f a c e . A p o t e n t i a l s h i f t of comparable magnitude i s e x p e c t e d t o be r e q u i r e d f o r Z r N s i n c e i t has a A5 band of s i m i l a r w i d t h . S i n c e t h e A, b u l k band i s predominantly l o c a l i z e d on t h e n i t r o g e n atoms t h e p o t e n t i a l a t t h e N atoms i n t h e s u r f a c e l a y e r h a s been s h i f t e d r e l a t i v e t o t h e bulk p o t e n t i a l i n o r d e r t o model t h i s s u r f a c e s t a t e . T h e o r e t i c a l ARP s p e c t r a f o r Z r N c a l c u l a t e d when s h i f t i n g t h e p o t e n t i a l of t h e N atoms i n t h e s u r f a c e l a y e r by + 0 . 2 eV and + 0 . 4 eV a r e shown by c u r v e s c and d r e s p e c t i v e l y i n F i g . 9 . For t h e s m a l l e r s h i f t t h e A5 s t r u c t u r e becomes a s s y m e t r i c with a s h o u l d e r on t h e l o w b i n d i n g energy s i d e b u t f o r t h e l a r g e r s h i f t a d o u b l e t s t r u c t u r e i s c l e a r l y o b s e r v e d . A p o t e n t i a l s h i f t of about + 0 . 3 eV was found t o g i v e t h e b e s t o v e r a l l agreement w i t h normal emission s p e c t r a recorded a t photon e n e r g i e s of 2 1 . 2 eV and 1 6 . 8 eV. A s i m i l a r modelling of t h e T a m s u r f a c e s t a t e observed on T i N ( 1 0 0 ) has been reported e a r l i e r ( r e f s . 45-46).
These c a l c u l a t e d s p e c t r a support t h e
235
i n t e r p r e t a t i o n of t h e s u r f a c e s t a t e a s a r i s i n g from a Tamm s t a t e p u l l e d o f f t h e t o p of t h e A, bulk band. These d a t a cannot d i s t i n g u i s h between an o v e r a l l s h i f t i n t h e e l e c t r o s t a t i c p o t e n t i a l i n t h e s u r f a c e l a y e r and t h e nonmetal 2s and 2p v a l e n c e s t a t e s sampling a l e s s a t t r a c t i v e p o t e n t i a l i n t h e surface-vacuum r e g i o n . A t h e o r e t i c a l s t u d y , u s i n g t h e p r e c i s e f u l l - p o t e n t i a l LAPW method, of t h e T i C ( 1 0 0 ) s u r f a c e ( r e f . 54) i n d i c a t e t h e l a t t e r , g i v i n g a s u r f a c e induced s h i f t by about 0 . 5 eV t o s m a l l e r b i n d i n g energy of t h e C 2 s and C2p d e n s i t i e s of s t a t e s while t h e c o r e l e v e l b i n d i n g e n e r g i e s showed no c o r r e s p o n d i n g s h i f t s . T h e o r e t i c a l ARP s p e c t r a f o r T i c (100) c a l c u l a t e d u s i n g t h e s u r f a c e p o t e n t i a l g e n e r a t e d i n t h a t s t u d y ( r e f . 55) show prominent s u r f a c e induced s t r u c t u r e s a t o f f normal e m i s s i o n . . A s u r f a c e s t a t e on V C ( 1 0 0 ) was r e p o r t e d i n a r e c e n t ARP
investigation
( r e f . 5 6 ) . I t s i d e n t i t y as a Tamm o r Shockley s t a t e
could however n o t be determined s i n c e f o r t r a n s i t i o n metal c a r b i d e s Shockley s t a t e s may a r i s e due t o t h e e x i s t e n c e of h y b r i d i z a t i o n band g a p s . T h i s p o s s i b i l i t y could be excluded f o r t h e n i t r i d e s because of absence of t h e n e c e s s a r y band c r o s s i n g s . For NbC, which has a s i m i l a r band s t r u c t u r e t o VC,
a band gap o c c u r s i n t h e p r o j e c t e d
energy band s t r u c t u r e c l o s e t o t h e G p o i n t of t h e s u r f a c e B r i l l o u i n zone ( r e f . 5 7 ) . A s t r u c t u r e which may o r i g i n a t e from a s u r f a c e s t a t e l o c a t e d i n t h a t gap was observed on NbC(100) ( r e f s . 2 9 , 5 3 ) , but i n t h i s c a s e o t h e r p o s s i b l e e x p l a n a t i o n s c o u l d n o t be e x c l u d e d .
The (111) s u r f a c e of t h e s e compounds i s q u i t e d i f f e r e n t from t h e ( 1 0 0 ) s u r f a c e s i n c e it i s a p o l a r s u r f a c e and e x p e r i m e n t a l evidence
i n d i c a t e i t t o be metal t e r m i n a t e d ( r e f s . 2 8 , 5 8 ) . T h i s s u r f a c e has been found t o be much more r e a c t i v e and t h u s more d i f f i c u l t t o p r e p a r e t h a n t h e ( 1 0 0 ) s u r f a c e and f a r fewer e x p e r i m e n t a l s t u d i e s have been r e p o r t e d f o r t h i s s u r f a c e . For T i C ( 1 1 1 ) however a s u r f a c e s t a t e has been r e v e a l e d c l o s e t o t h e Fermi energy, i n ARP experiments
( r e f s . 2 8 , 3 0 ) , which has been s u g g e s t e d t o o r i g i n a t e
from Tamm s t a t e s . C a l c u l a t e d ARP s p e c t r a u s i n g a s h i f t e d T i p o t e n t i a l f o r t h e s u r f a c e l a y e r showed good agreement w i t h experiment and produced a s u r f a c e s t a t e c l o s e t o t h e Fermi energy ( r e f . 5 9 ) . This c a l c u l a t e d surface s t a t e did not e x h i b i t t h e symmetry observed e x p e r i m e n t a l l y however. By a l t e r i n g t h e p o s i t i o n 'of t h e s u r f a c e b a r r i e r a Shockley s u r f a c e s t a t e was found t o appear
i n t h e same p o s i t i o n a s t h e Tamm s t a t e i n t h e c a l c u l a t e d s p e c t r a . Moreover i t e x h i b i t e d t h e same symmetry a s t h e s t r u c t u r e seen i n
236
Tic11111
10 12 14
14 0 13.0
F i g . 10 C a l c u l a t e d normal emission s p e c t r a from t h e (111) s u r f a c e of Tic f o r d i f f e r e n t photon e n e r g i e s . The prominent peak c l o s e t o t h e Fermi l e v e l i s t h e Shockley s t a t e and t h e f e a t u r e a t - 2 . 5 e V i s emission from a A, bulk band. T h e amplitude v a r i a t i o n of t h i s l a t t e r peak a s a f u n c t i o n of photon energy i s shown i n t h e i n s e r t .
120 11.5 11.0
10.5
10.0 9.5
9.0
t h e r e c o r d e d ARP s p e c t r a . The c a l c u l a t e d r e s u l t s a r e shown i n Fig. 10. 4.4
The f i r s t o b s e r v a t i o n o f a s t r u c t u r e a t t r i b u t e d t o vacancy induced s t a t e s was made i n XPS v a l e n c e band s p e c t r a ( r e f . 6 0 ) o f p o l y c r y s t a l l i n e NbC,,,,
.
A t h e o r e t i c a l e f f o r t t o describe the
i n f l u e n c e of v a c a n c i e s on t h e e l e c t r o n i c s t r u c t u r e i n c l u s t e r c a l c u l a t i o n s had been i n i t i a t e d e a r l i e r
( r e f . 6 1 ) and have been
followed b y o t h e r t h e o r e t i c a l approaches
( s e e r e f . 6 2 and r e f e r e n c e s
given t h e r e i n ) . S t a t e of t h e a r t KKR-CPA
c a l c u l a t i o n s were needed
( r e f . 6 3 ) t o confirm t h e e x p e r i m e n t a l r e s u l t s ,
and t h e y r e v e a l e d a
v i r t u a l bound s t a t e a t t h e vacancy s i t e . A computanional method t o c a l c u l a t e t h e p h o t o c u r r e n t from d i s o r d e r e d complex l a t t i c e s based on t h e KKR-CPA
t h e o r y was developed, a s d e s c r i b e d i n s e c t i o n 3 . 4 , and
w a s a p p l i e d t o ARP s p e c t r a from s u b s t o i c h i o m e t r i c c r y s t a l s
(refs.
17-19).
A s t r u c t u r e a r i s i n g from vacancy induced s t a t e s e x h i b i t i n g
A,-like
symmetry and no d i s p e r s i o n was found t o appear around -2 e V
i n c a l c u l a t e d normal emission ARP s p e c t r a from t h e ( 1 0 0 ) s u r f a c e of
s u b s t o i c h i o m e t r i c T i N and Z r N a t photon e n e r g i e s above 30 eV. The c a l c u l a t e d r e s u l t s f o r ZrN,.,,
(100) and T i N , , , 3 ( 1 0 0 ) a r e shown i n
237 I
ZrN,,,
I
I
(1001
I
Exp.
I
-6
-4
-2
0
INITIAL ENERGY (eV)
F i g . 11 Normal emission s p e c t r a f o r Z r N x ( l O O ) a t d i f f e r e n t photon e n e r g i e s u s i n g p - p o l a r i z e d r a d i a t i o n i n c i d e n t along t h e <010> azimuth a t an a n g l e of 30 : ( a ) c a l c u l a t e d s p e c t r a f o r x=O.85 showing a vacancy induced peak, l a b e l l e d C, l o c a t e d a t -2 e V : ( b ) e x p e r i m e n t a l s p e c t r a f o r x=O.93, showing a prominent s t r u c t u r e around -2 eV. F i g s . l l a and 12a r e s p e c t i v e l y . The vacancy induced s t r u c t u r e l a b e l l e d C i n F i g . l l a i s , i n both c a s e s , s e e n t o appear most pronounced a t photon e n e r g i e s around 4 2 eV. Experimental normal emission ARP s p e c t r a recorded from t h e ( 1 0 0 ) s u r f a c e of Z r N , , , , ( r e f . 2 6 ) and TiN,,,,
( r e f . 6 4 ) a r e shown i n F i g s . l l b and 12b
r e s p e c t i v e l y and a s t r u c t u r e i s observed around -2 e V i n both c a s e s . The r e l a t i v e i n t e n s i t y of t h e recorded s t r u c t u r e i s f o r Z r N seen t o be h i g h e r and f o r T i N t o be lower t h a n t h e c a l c u l a t e d i n t e n s i t y . The v a r i a t i o n i n r e l a t i v e i n t e n s i t y p r e d i c t e d with photon energy i s f a i r l y w e l l reproduced f o r Z r N b u t f o r T i N t h e experimental s p e c t r a i n d i c a t e t h e maximum t o appear around 35 e V i n s t e a d of around 4 2 eV. The experiments confirmed a A,-like
symmetry behaviour of t h i s
s t r u c t u r e . Thus t h e energy p o s i t i o n , t h e n o n d i s p e r s i v e n a t u r e , t h e s y m m e t r y c h a r a c t e r and, f o r Z r N ,
t h e p r e d i c t e d i n t e n s i t y modulations
w i t h photon energy of t h e vacancy induced s t r u c t u r e a r e c o r r e c t l y
reproduced by t h e e x p e r i m e n t a l r e s u l t s . A t t h e s e photon e n e r g i e s t h e i n t e r p r e t a t i o n of e x p e r i m e n t a l
238
(a)
4
6
-1
-2
0
F i g . 1 2 Normal emission s p e c t r a f o r TiN,,.,,(100) a t d i f f e r e n t photon e n e r g i e s using p-polarized r a d i a t i o n i n c i d e n t along t h e <010> azimuth a t a n a n g l e of 4 5 O : ( a ) c a l c u l a t e d s p e c t r a , showing a prominent vacancy induced s t r u c t u r e a t -2 e V f o r photon e n e r g i e s above 3 6 e V : ( b ) e x p e r i m e n t a l s p e c t r a , showing a s t r u c t u r e around - 2 eV most pronounced a t t h e lower photon e n e r g i e s u s e d . r e s u l t s i s o t h e r w i s e complicated by resonance e f f e c t s above t h e Zr4p and t h e Ti3p a b s o r p t i o n t h r e s h o l d r e s p e c t i v e l y
( r e f s . 26,64) which
i s c l e a r l y evidenced by t h e r e s o n a n t l y enhanced emission c l o s e t o
t h e F e r m i l e v e l a t e n e r g i e s around 40 eV. A t lower photon e n e r g i e s , however, t h e vacancy induced s t r u c t u r e i s not seen a t normal e l e c t r o n emission i n e i t h e r c a l c u l a t e d o r e x p e r i m e n t a l ARP s p e c t r a ( r e f s . 1 7 , 1 9 ) . A t o f f normal emission it should a l s o be p o s s i b l e t o observe t h i s f e a t u r e a t lower photon e n e r g i e s ( r e f . 1 7 ) and such a s t r u c t u r e was r e c e n t l y observed on t h e ( 1 0 0 ) and ( 1 1 0 ) s u r f a c e s o f VC ( r e f s . 6 5 - 6 6 ) .
The c a l c u l a t e d r e s u l t s f o r Z r N and T i N showed t h a t upon t h e i n t r o d u c t i o n of v a c a n c i e s
t h e A5 d e r i v e d f e a t u r e , peak B i n F i g .
l l a , i s more a f f e c t e d t h a n t h e o t h e r bulk d e r i v e d s p e c t r a l f e a t u r e s . The i n t e n s i t y of t h i s N-p d e r i v e d peak w a s found t o be reduced w i t h r e s p e c t t o t h e metal-d
d e r i v e d f e a t u r e s i n d i c a t i n g n o t only a g l o b a l
l o s s of N-p s t a t e s b u t a l s o a p r e f e r r e d i n t e r a c t i o n of t h e v a c a n c i e s w i t h A,-like
N-p s t a t e s . T h i s s t r o n g e r i n t e r a c t i o n was a l s o mani-
239
f e s t e d i n a lower e n e r g e t i c p o s i t i o n and a reduced d i s p e r s i o n of t h e A,-like
s t a t e s . These f i n d i n g s may e x p l a i n p a r t of t h e d i s c r e p a n c i e s
concerning t h e l o c a t i o n and d i s p e r s i o n of t h e
A5 band d i c u s s e d i n
section 2 .
ARP s p e c t r a from a s u b s t o i c h i o m e t r i c c r y s t a l having a vacancy c o n c e n t r a t i o n g r a d i e n t i n t h e s u r f a c e r e g i o n h a s been modelled i n a t h e o r e t i c a l s t u d y ( r e f . 1 8 ) . Such g r a d i e n t s can be c r e a t e d d e l i b e r a t e l y by ion s p u t t e r i n g ( r e f . 6 7 ) b u t most s t u d i e s , s o f a r , have used sample p r e p a r a t i o n methods t h a t a r e b e l i e v e d ( r e f . 6 8 ) not t o c r e a t e such e f f e c t s .
5
SUMMARY AND OUTLOOK The a p p l i c a b i l i t y of simple and more s o p h i s t i c a t e d t h e o r i e s of
photoemission t o some m e t a l l i c compounds have been demonstrated i n t h e p r e c e e d i n g s e c t i o n s u s i n g a few s e l e c t e d examples. The band mappings i n s e c t i o n 2 showed t h a t c a l c u l a t e d r e s u l t s f o r a p e r f e c t l y o r d e r e d compound do, when assuming d i r e c t t r a n s i t i o n s , account f a i r l y w e l l f o r t h e bulk r e l a t e d f e a t u r e s observed in ARP s p e c t r a from s u b s t o i c h i o m e t r i c compounds. D i s c r e p a n c i e s i n band l o c a t i o n s and d i s p e r s i o n s w e r e observed, however, most pronounced f o r t h e main
A, band. This i s not b e l i e v e d t o be due o n l y t o t h e w e l l known problem of i d e n t i f y i n g l o c a l - d e n s i t y e i g e n v a l u e s w i t h q u a s i p a r t i c l e e x c i t a t i o n s ( r e f . 6 9 ) . I n s t e a d it i s b e l i e v e d t o r e f l e c t a p r e f e r r e d vacancy i n t e r a c t i o n with t h e A5 nonmetal p - s t a t e s ,
a s discussed i n
section 4 . The i n t e n s i t i e s of bulk d e r i v e d f e a t u r e s were shown t o be modelled f a i r l y a c c u r a t e l y when u s i n g t h e r e c e n t developments of t h e one s t e p model. A l s o f e a t u r e s i n recorded ARP s p e c t r a t h a t could not be e x p l a i n e d by d i r e c t bulk band t r a n s i t i o n s b u t i n t e r p r e t e d a s s u r f a c e s t a t e s and vacancy induced s t a t e s could be modelled q u i t e w e l l , which a l s o was e x e m p l i f i e d i n s e c t i o n 4 . These developments have t h u s proved very important i n t h e i n t e r p e t a t i o n of e x p e r i m e n t a l d a t a and a l s o provided new o p p o r t u n i t i e s f o r a c r i t i c a l assessment of t h e o r e t i c a l p r e d i c t i o n s . The importance of photoemission a s an
e x p e r i m e n t a l t e c h n i q u e has been enhanced by t h e use of a c c u r a t e t h e o r e t i c a l t o o l s . The r e a l i s t i c models and powerful computer codes have proven t o be v a l u a b l e a i d s i n t h e s c i e n t i f i c work towards a g r e a t e r u n d e r s t a n d i n g of more complex systems. The t h e o r e t i c a l models do have a wider a p p l i c a t i o n range among o r d e r e d compounds and a l l o y s than t h e r e s u l t s on t r a n s i t i o n m e t a l c a r b i d e s and n i t r i d e s
240
presented here. A c r y s t a l composed of c o p l a n a r l a y e r s h a s s o f a r always been assumed i n t h e t h e o r e t i c a l t r e a t m e n t b u t t h e p o s s i b i l i t y t o i n l u d e r e c o n s t r u c t e d o v e r l a y e r s h a s become o f c u r r e n t i n t e r e s t . F o r most c a r b i d e s and n i t r i d e s no r e c o n s t r u c t i o n s have been a n t i c i p a t e d t o occur s i n c e s h a r p 1x1 d i f f r a c t i o n p a t t e r n s have been r e p o r t e d i n LEED s t u d i e s . A r e c e n t a n a l y s i s of LEED I - V s p e c t r a from TaC(100) however i n d i c a t e t h a t a r i p p l e d r e c o n s t r u c t i o n occur on t h i s s u r f a c e a l t h o u g h a s h a r p 1x1 d i f f r a c t i o n p a t t e r n was o b s e r v e d ( r e f . 7 0 ) . To i n c l u d e such r e c o n s t r u c t i o n s i n t h e one s t e p model i s a c h a l l e n g e for the future. Vacancy induced e f f e c t s i n t h e e l e c t r o n i c s t r u c t u r e i s a t o p i c t h a t need t o be f u r t h e r e x p l o r e d e x p e r i m e n t a l l y . D i f f e r e n t sample t r e a t m e n t s , o r i n s i t u c r y s t a l growth ( r e f . 7 1 ) , t o c r e a t e vacancy c o n c e n t r a t i o n s and g r a d i e n t s i n a c o n t r o l l e d manner o r t o c r e a t e vacancy o r d e r i n g , s u p e r s t r u c t u r e s , are t o p i c s t h a t p r o b a b l y w i l l a t t r a c t a t t e n t i o n i n t h e f u t u r e . Vacancy o r d e r i n g does occur f o r some c a r b i d e s and n i t r i d e s and t o s t u d y and model how t h e o r d e r i n g a f f e c t s t h e e l e c t r o n i c s t r u c t u r e may p r o v e f r u i t f u l . S t u d i e s u t i l i z i n g h i g h e r photon e n e r g i e s and h i g h e r energy r e s o l u t i o n t h a n p r e s e n t l y a c h i e v a b l e w i l l p r o b a b l y a l s o be p e r s u e d i n t h e f u t u r e . To i n v e s t i g a t e t h e c o r e l e v e l s w i t h h i g h enough a n g l e and energy r e s o l u t i o n t o a l l o w i d e n t i f i c a t i o n of p o s s i b l e s u r f a c e s h i f t e d l e v e l s and o f s u r f a c e d i f f r a c t i o n e f f e c t s would open up new p o s s i b i l i t e s t o e x t r a c t i n f o r m a t i o n about b o t h t h e s u r f a c e e l e c t r o n i c and g e o m e t r i c s t r u c t u r e . To t r y t o a p p l y t h e powerful computer codes d i s c u s s e d above t o model such e x p e r i m e n t a l r e s u l t s i s also a challenge f o r t h e future.
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(1976) 169. Smith, Photoemission i n S o l i d s I , e d . by M. Cardona and L . Ley, S p r i n g e r V e r l a g , N e w York, 1978, pp. 237. E.W. Plummer and W. E b e r h a r d t , Adv. Chem. Phys., ed. by I . P r i g o g i n e and S.A. R i c e , Wiley, N e w York, 1982, pp. 533. P . J . Feibelman and D.E. Eastman, Phys. Rev. B 1 0 ( 1 9 7 4 ) 4932.
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10 J . B . P e n d r y , S u r f . S c i . 5 7 ( 1 9 7 6 ) 6 7 9 . 11 J . B . P e n d r y a n d J . F . L . H o p k i n s o n , J . P h y s . F: Metal P h y s . 8 12 13 14 15
16 17 18 19 20 21 22 23 24 25 26 27 28
29 30 31 32 33 34 35 36 37 38 39 40 41 42
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242
43 P.M. E c h e n i q u e a n d J . B . P e n d r y , J . P h y s . C : S o l i d S t a t e P h y s i c s 11 44
(1978) 2065. M c R a e , R e v . Mod. P h y s . 51 ( 1 9 7 9 ) 5 4 1 . L a r s s o n , L . I . J o h a n s s o n a n d A . C a l l e n i s , S o l i d S t a t e Commun. 49 .‘1984) 7 2 7 . L . & . J o h a n s s o n , C . G . L a r s s o n a n d A . C a l l e n i s , J . P h y s . F : Metal Phys.14 (19 84) 1761. S.G. Davison a n d J . D . Levin, S o l i d S t a t e Phys. 25 (1970) 1. P . Soven, P h y s . Rev. 1 5 6 ( 1 9 6 7 ) 8 0 9 . W.M. Temmerman a n d Z . S z o t e k , Computer P h y s . R e p . 5 ( 1 9 8 7 ) 1 7 3 . P . J . Durham, R . G . J o r d a n , G . S . S o h a l a n d L.T. W i l l i e , P h y s . Rev. L e t t . 53 ( 1 9 8 4 ) 2 0 3 8 . P . A . P . L i n d b e r g a n d L . I . J o h a n s s o n , P h y s i c a S c r i p t a 37 ( 1 9 8 8 ) 8 0 3 . P.A.P. L i n d b e r g , P.L. Wincott, L . I . J o h a n s s o n a n d A.N. C h r i s t e n s e n , P h y s . Rev. B 3 6 , ( 1 9 8 7 ) 4 6 8 1 . P . A . P . L i n d b e r g , L . I . J o h a n s s o n , J . B . L i n d s t r o m a n d D . S . L . Law, S u r f . S c i . 189/190 (1987) 751. E . W i m m e r , A . N e c k e l a n d A . J . Freeman, P h y s . Rev. B 31 ( 1 9 8 5 ) 2370. J . R e d i n g e r , P . W e i n b e r g e r , E . Wimmer, A . N e c k e l a n d A . J . Freeman, P h y s Rev. B 3 2 , ( 1 9 8 5 ) 6 9 9 3 . P . A . P . L i n d b e r g a n d L . 1 J o h a n s s o n , Surf. S c i . 1 9 2 ( 1 9 8 7 ) 3 6 6 . M . Tomasek, S. P i c k a n d K . S c h w a r z , C z e c h . Chem. Commun. 45 ( 1 9 8 0 ) 1317. S . Z a i m a . Y. S h i b a t a , H . A d a c h i , C . Oshima, S . O t a n i , M . Aono a n d Y . I s h i z a w a , S u r f . S c i . 157 ( 1 9 8 5 ) 1 5 7 . C . G . L a r s s o n , J . B . P e n d r y a n d L . I . J o h a n s s o n , S u r f . S c i . 162 (1985) 1 9 . H . H o c h s t , R . D . B r i n g a n s , P . S t e i n e r a n d T h . Wolf, P h y s . Rev. B 25 (1982) 7183. K . Schwarz and N . Rosch, J. P hys. C : S o l i d S t a t e P h y s i c s 9 (1976) 1433. J . R e d i n g e r , P . M a r k s t e i n e r a n d P . W e i n b e r g e r , Z. P h y s . 63 ( 1 9 8 6 ) 321. J . K l i m a , G. S c h a d l e r , P . W e i n b e r g e r a n d A . N e c k e l , J . P h y s . P : Met. P h y s . 1 5 ( 1 9 8 5 ) 1 3 0 7 . P.A.P. Lindberg, L . I . Johansson, J . B . Lindstrom and D.S.L. Law, P h y s . Rev. B 3 6 ( 1 9 8 7 ) 939. P . A . P . L i n d b e r g a n d L . I . J o h a n s s o n , Z. P h y s . B 68 ( 1 9 8 7 ) 8 3 . P . A . P . L i n d b e r g a n d L . I . J o h a n s s o n , Z. P h y s . B 69 ( 1 9 8 8 ) 5 2 1 . M . Aono, Y. H O U , R . S o u d a , C . Oshima, S . O t a n i a n d Y . I s h i z a w a , P h y s . R e v . L e t t . 50 ( 1 9 8 3 ) 1 2 9 3 . C . Oshima, M . Aono, T . T a n a k a , S . K a w a i , S . Z a i m a a n d Y . S h i b a t a , S u r f . S c i . 102 ( 1 9 8 1 ) 3 1 2 . J . P . P e r d e w , D e n s i t y F u n c t i o n a l Methods i n Physis,NATO Advanced S t u d y I n s t i t u t e S e r i e s B123, E d . b y R . M . D r e i z l e r a n d J . d a P r o v i d e n c i a , Plenum, N e w York ,1 9 8 5 , pp. 265. J.R. Noonan, H.L. Davies, a n d G . R . G r u z a l s k i , J . V a c . S c i . T e c h n o l . 5 (1987) 787. L . H u l t m a n , S.A. B a r n e t t , J . - E . S u n d g r e n a n d J . E . G r e e n e , J . C r y s t . Growth 92 ( 1 9 8 8 ) 6 3 9 .
E.G. 45 C . G .
46 47 48 49 50 51 52 53 54 55 56 57
58 59 60 61 62 63 64 65 66 67 68 69 70 71
243 Chapter 7
PHOTOELECTRON DIPFRACTION
D. P. WOODRUFF
1.
INTRODUCTION Photoemission is intrinsically a probe of electronic structure and in
angle-resolved studies in particular the primary objective of the measurements is usually to try to understand the initial state electronic structure, although final state effects, and particularly the fact that photoemission is an excited state spectroscopy, are commonly very important in interpreting the results.
In photoemission from core levels (particularly from s and p initial
states), the initial state is, by contrast, often regarded as well- understood. An
exception is the study of "chemical shifts"; the exact value of the
photoemission binding energy can be influenced by the valence electronic structure at the emitter through both initial and final state effects, and changes i n this binding energy can provide information on the electronic, o r ’chemical’ state of
the emitter on the surface.
Insofar as such measurements
do not usually make use of angular resolution in their measurement (except, perhaps, to enhance surface sensitivity at grazing emission angles), they do not concern us here, although angle-resolved measurements of core level shifts will be mentioned briefly later in this chapter.
More generally, however, the
use of angle-resolved photoemission to study core level photoemission from solid surfaces is concerned with exploiting final state elastic scattering effects (photoelectron diffraction) to investigate the local geometrical structure, and particularly adsorbate-substrate registry, at the surface. The essential physical processes involved in photoelectron diffraction (PhD) are shown schematically in fig. la.
Components of the photoelectron
wavefield emitted from a surface atom can be elastically scattered by the surrounding atoms and these scattered waves can interfere coherently with the directly emitted wave.
These interferences depend on the relative phase of the
directly emitted and scattered waves which depends in turn on the photoelectron wavelength (energy), on the position of the emitter (relative to the scatterers) and on the angle of collection, the latter two influencing the scattering path lengths.
The influence of these scattering interferences on
the angle-resolved photoemitted intensity may be monitored by measuring the variations which occur when one of the non-structural parameters which influence the phase differences (energy or angle) is varied.
form a basis for deducing the surface structure.
These data then
In fact three different
244
a
b
C Fig. 1
Schematic diagram of the main
(single scattering) electron
interference phenomena contributing to photoelectron diffraction (a), surface EXAFS (b) and LEED (c).
methods of measurements have been used.
In the scanned energy mode, the
incident and collection geometries are kept fixed and the photon energy is scanned, the energy selected by the electron spectrometer being scanned synchronously in order to detect the yield from the constant initial (core) state.
Two types of angular scan have been used, one in azimuthal angle at
fixed polar angle, the other in polar angle at fixed azimuthal angle.
In both
of these angular modes it is usual to achieve the scan by rotating the sample, keeping the incident and collection directions fixed in space.
This has the
virtue that the relative geometry of the incident photon and collected electron is fixed so that the intrinsic angular dependence of the atomic core state emission (i.e. that seen from a free atom in the absence of the surrounding solid) is not observed directly.
Each type of measurement has its virtues and
disadvantages for specific structural problems, and these will be discussed in more detail in section 3 .
In this introduction, however, it is of most
interest to compare photoelectron diffraction with other, closely related techniques used for the study of surface structure which also rely on the coherent interference of electrons scattered from the surface atoms. For this
245
purpose, it is most helpful to concentrate on the scanned energy mode of data collection. The other two principal techniques which are closely related are shown schematically
in figs. lb and lc.
Surface EXAFS(l# )
(extended X-ray
adsorption fine structure) is particularly similar in that this process is also based on elastic scattering of the photoelectron wavefield emitted from a core state, but in this case the interference monitored is between the outgoing wavefield and the 180 site itself.
backscattered components which interfere at the emitter
This interference modulates the final state wavefield at the
emitter which in turn causes a modulation of the photoionisation cross-section. These EXAFS interference modulations are monitored by scanning the photon energy and thus the photoelectron energy (and wave length), exactly as in the scanned energy mode of PhD.
The essential difference between PhD and SEXAFS is
therefore that in SEXAFS one monitors the total (angle-integrated) photoionisation cross-section for a particular core ionisation, while in PhD one measures the derivative (angle-resolved) photoionisation cross-section for the same core ionisation.
In effect SEXAFS uses the emitter itself as a
detector to ensure full angular averaging of all scattering effects apart from those scattered back to the emitter.
Of course the angle resolved partial
cross-section monitored in PhD must itself be modulated by the EXAFS variation in the total (angle-integrated) photoionisation cross-section.
However, the
amplitude of the modulations seen in EXAFS ( - 1-5%) are typically a factor of 10 smaller than those produced in PhD, so they are of little consequence in
interpretting PhD data. Perhaps the most familiar technique for investigating surface structure using
electron scattering
interferences is low energy electron diffrac-
t i ~ n ( ~ #(LEED) ~) shown schematically in figure lc.
In this case an external
source of electrons is used providing an incident plane wave, the scattering interferences causing most of the scattered intensity to be concentrated in outgoing plane waves which define the diffracted beams.
One interesting
feature of LEED as opposed to SEXAFS and PhD is that the information on the (adsorbate) surface layer relative to the substrate arises only from that component of the incident flux scattered by the surface layer, and its interference with all the components scattered by deeper layers.
By contrast,
the fact that the other techniques rely on emission from the sites of interest means that
all
scattering path lengths depend on the sites occupied by the
emitter species.
As
a result, we might expect SEXAFS and PhD to be more
sensitive to adsorption site than LEED in their primary information content. The difference between local and extended sources of electrons also leads
to two other distinctions.
Firstly, SEXAFS and PhD are techniques in which the
interferences depend on the local structure around the emitter and are thus
246
rather insensitive to the state of long-range order of the overlayer (although some scattering off other overlayer atoms can occur).
By contrast LEED is, as
a true ’diffraction’ technique, intrinsically dependent on long range order. Only by studying subtle changes in the diffusely scattered background of a diffraction pattern can
local
structural information be extracted in the
absence of long-range order. ( 5 * 6 ) The second distinction concerns the relative importance of multiple scattering
in the three processes.
Although the
schematic diagrams in fig. 1 show only single elastic scattering events and their subsequent interference, it is well known that LEED is very strongly influenced by multiple scattering of the electrons, particularly at low energies
((
200 eV) for which the scattering is strong over a wide range of
angles.(3r4)
By contrast in EXAFS a large amount of data interpretation is
achieved successfully using only a single scattering description;( 3 t 4 r 7 ) multiple scattering effects do occur,(8) but in a much less generally pervasive fashion. The reason for this can also be largely traced to the localisation of both the electron source and, in the case of EXAFS, the wavefield detection. Both introduce 1/r terms in the amplitude (where r is the radial distance to a scatterer) which enhance the localisation of the process and suppress the effects of those multiple scattering trajectories which involve much longer path lengths.
In so far as photoelectron diffraction shares the local source
(but not the local detector) with EXAFS. it is also less influenced by multiple scattering than is LEED; we shall return to this point
in the following
sect ion. Before going into further detail over the theory of photoelectron diffraction, and giving examples of its application in different forms to investigate a variety of surface structural problems, we should complete a review of the basic physics of closely related techniques.
In all the examples
shown in fig. 1 the main elastic electron scattering events of interest involve backscattering (by angles of between 90° and 180O). be very strong at the low energies
((
Backscattering is known to
200eV) used in LEED but attenuates quite
strongly as the electron energy increases.
Both PhD and SEXAFS can detect
significant interference modulations in back- scattering to about 500eV photoelectron energy, but even with this relatively large energy range such experiments are only possible for a wide range of materials by using a continuously tunable form of radiation source (synchro- tron radiation). Conventional soft X-ray sources using Mg and A%
radiation (photon energies
of 1254 and 1 4 8 7 e V ) lead to substantially higher photoelec- tron energies from atomic species which do not have a convenient core level binding energy in the 800-1400eV energy range.
At high electron energies, however, elastic scattering is still strong in the forward direction as illustrated in fig.
2,
and variants of the back-
247
0
Fig. 2 Normalised modulus of the elastic scattering factor as a function of scattering angle from a Ni atom at various energies (adapted from ref. 9).
scattering geometry of fig. la still allow photoelectron diffraction to be used
to elucidate surface structures.
A
rather simple modification illustrated in
fig. 3a shows that if the photoelectrons are detected at grazing emission angles, scattering can occur from the top substrate layer with quite small scattering angles.
Using the fixed photon energy of a laboratory X-ray source,
substrate scattering photoelectron diffraction can therefore be monitored by varying the azimuthal angle at fixed grazing emission angle.
Note that this
technique is likely to be particularly sensitive to scattering within the top adsorbate layer and will show the strongest scattering effects from the substrate if the adsorbate emitter layer lies at a small spacing above the top substrate layer.
Fig. 3b shows yet another variation of the photoelectron
diffraction experiment utilising the forward scattering geometry.
In this case
emission is excited from one atomic species within a molecule adsorbed on the surface and the forward scattering within the molecule is utilised.
The
interpretation of data from such an experiment can be particularly simple
/
0 0
0
0
.
0
0
a Fig. 3
.
b
Schem tic diagram
f alternative conditions for performing
photoelectron diffraction to use forward scattering effects.
(a)
shows grazing emission angle geometry utilizing substrate scattering while (b) shows a forward intramolecular scattering event in an adsorbed molecule.
because the scattering produces an enhancement of the photoelectron signal along the intramolecular axis.
The molecular orientation on the surface can
therefore be obtained from a polar angle scan of the collection geometry, again at fixed photon energy.
The same forward scattering effect has also been used
recently with Auger electron emission to study intralayer scattering and registry in epitaxial multilayers In the remainder of this chapter the main points of this introduction are developed in greater depth.
First we review the theoretical description of
photoelectron diffraction and describe the main features of the computa- tional methods used to interpret the data.
In section 3 there follows a more detailed
discussion of the main variants of the method and examples of their application including, in section 3 . 4 ,
their application to the study of clean surface
structure or to more complex adsorption structures through the use of ’chemically shifted’ photoelectron peaks.
Finally, in section 4 the present
state of PhD is summarised and some assessment of its future potential and impact is made.
2.
TBEORETICAL MGPHODS
The essential physics to be incorporated in a theory of photoelectron diffraction is that the observed photoemission intensity in a given collection
249
direction is given by the modulus squared of the sum of the directly emitted amplitude and of all the amplitudes of the scattered components from the surrounding atoms.
Essential ingredients in the formulation include the
influence of inelastic electron scattering (which attenuates the propagation of the coherent electron wavefield through the crystal and so enhances the localisation of the structural information) and of thermal vibrations (which introduce path length and thus phase ’smearing’ into the interference).
The
simplest (most restrictive and approximate) theory incorporating these effects and that of the essential coherent interference is one which assumes only single scattering is important, and that the scattering can be treated in the plane wave approximation.
In this form(lO) the expression for the intensity of
photoemission measured in a given direction and energy specified by the electron wavevector
5
is given by
X exp ~ - L j / A ( k ) l e x p ~ i k r j ( l - ~ o s 0 j ) l ~ ~ (1) Some of the key parameters in this equation are specified in fig. 4 .
Assuming
the initial state is s-character (angular momentum quantum number equal to zero), the directly emitted amplitude is given by the first term COSOk, where
Ok is the angle between the polarisation vector and the collection direction. The second term sums over scatterers located relative to the emitter at fj, 0, being
the
angle
between
the
polarisation vector
and 5,.
while 0, is the
4-k I
c
Fig.
4
I
I
I I
I I
4 I
A
Diagram showing a definition of several of the terms in equation 1.
i\ denotes the incident light polarisation vector.
250
scattering angle (the angle between r j and
k).
f(Qj,k)
is the complex
scattering factor at the electron energy determined by k and through a scattering angle 8j while W(@j,If)
is a Debye-Waller factor.
Finally the two
exponential terms account for the inelastic damping due to an additional path length of the scattered trajectory, Lj with an inelastic scattering mean-freepath h(k)
and for the interference phenomenon itself with a path length
difference of rj(l-cos8j).
Note that the mean-free-path h(k) is an amplitude
attenuation parameter and is expected to be a factor of 2 larger than the intensity attenuation parameter usually discussed in electron spectroscopies. Moreover the Debye-Waller factor is given by W(9j.k)
= exp(-Ak*uj2) where
is
the change in the electron wavevector on scattering (Akz = 2k2(l-cos@j)) but uj2 is the relative mean square vibrational amplitude of the scatterer relative
to the emitter.
For uncorrelated isotropic vibrations of mean-square
vibrational amplitude uz we have ujz = 2u2, but near neighbours do, of course, have correlated vibrations and some account needs to be taken of this.
EXAFS
studies, (7) also influenced by relative vibrational amplitudes, have shown that for the nearest neighbour scatterers uj2 is typically a factor of 2-3 smaller than the uncorrelated value so this correction may be applied only to these nearest neighbours, although more sophisticated formulations have also been proposed.
Finally we should remark that a further term which represents
the thermal diffuse background (proportional to l-W(@j,k)’
has been omitted
from equation 1 as this contributes only a background to the emitted signal which is smoothly varying in If. Before discussing improvements in this formulation it is instructive to compare the theory in this form with that of the closely related technique of (SIEXAFS.
Taking the modulus square as in equation (1) leads to three groups
of terms; a directly emitted component cos2&
(the signal Io(k) in the absence
of scattering), a set of terms composed of cosek multiplied by the interference terms, arranged in pairs with one term being the complex conjugate of the other, and a double summation of cross interference terms.
Computations
show, as might be anticipated, that these cross terms cancel on average so that if a "fine structure function", X(k) is defined as
(as in EXAFS). then the form of this function becomes
X cos [krj(l-cos Oj) + cb(Ojtk)l where @(ej,k) is the phase factor from the complex scattering factor
25 1
f(Oj,k) = If(Qj,k)I exp (i $(8j,k)).
This may be compared with the well-
known EXAFS fine structure function, ~ ’ ( k )which may be written (using similar approximations and restrictions as
x sin [Zkrj + ~$j’(ll,k)l
(3)
The similarity of these expressions has led to the acronym ARPEFS (angle resolved photoemission extended fine structure) which is sometimes applied to the scanned energy mode of photoelectron diffraction.
Comparison of these
expressions also highlights the particularly strong localisation of the EXAFS structural data (l/rj2 dependence rather l / r j
in PhD) and the fact that the
fine structure of PhD is governed by the scattering pathlengths (rj(l-cosQj)) which in EXAFS are directly assigned to bondlengths ( Z r j ) .
This similarity
briefly encouraged the use of Fourier Transform(16r17) methods in the analysis of ’ARPEFS’ data similar to those used in EXAFS, although it is clear that the fact that the phase factors depend on the geometry in ARPEFS ($(@j,k)) in EXAFS (@’(ll,k))
and not
reduces the simplicity of interpretation even if this
theoretical description is adequate. (I1)
In addition to the rather different degree of localisation of the scattering contributions in EXAFS and PhD mentioned above, the relative importance of different scatterers at the same distance is also different.
In
EXAFS, the various atoms in a given scattering "shell" (i.e. having the same value of rj) differ in their contributions only through the polarisation term as cos%,
which is rather slowly varying.
factor f(@j,k)
In PhD, however, the backscattering
depends on the scattering angle: i.e.
the scatterer location,
fj, relative to the collection direction specified by
k.
Fig. 2 shows the
modulus of these scattering factors is quite strongly structured, peaking at most energies in the forward (Oj = O o ) and backward (0, = 180’)
directions.
This means that the dominant contributions to the PhD modulation given in equations (1) and ( 2 ) are governed by the real space collection direction relative to the surface crystallography.
This is a key feature of PhD which
helps to simplify the data interpretation in favourable geometries: specific examples of this will be given in the following section which concentrates on the different modes of performing the experiment. The two main limitations of the formulation given in equation 1, as a basis for computing PhD intensities, are the assumption of a plane wave description of the wave incident on each scatterer, and the neglect of multiple scattering.
Both of these simplifications may lead to substantial errors under
certain circumstances and while there is some debate as to the level of importance of a proper treatment of these effects, some underlying trends can
252
be identified.
No attempt is made here to present the detailed formalism Of
the ’curved wave’ and multiple scattering theories which have been discussed extensively elsewhere.
Rather we concentrate on the underlying physical ideas
and the results of a few simple calculations to illustrate their importance (or otherwise). As
is well known, photoemission is governed by the usual optical
selection rules which dictate that the orbital angular momentum quantum number of the final state should differ from that of the initial state by unity.
Thus
in emission from a core state of orbital angular momentum state 1, the final state consists of a sum of 8 + 1 and $
-
1 outgoing spherical harmonics.
the special case of an initial s-state (9, = 0) considered so far, only the
For +
1 (p-state) is possible leading to a particularly simple situation in which it
is not necessary to try to calculate the relative amplitudes of these two components (although at high energies the
(f,
+ 1) state dominates).
Thus more
generally the outgoing electron wavefield from the emitter has the form(18)
+(r) a
1
Yam (g) h;i(kr)
f,,m with 9, and m denoting the allowed quantum numbers: for an initial s-state only a single term with 8 = 1, m = 0 is needed.
The spherical Iiankel functions,
hf,+(kr) have the form of a phase factor, exp(ikr) multiplied by a polynomial in (l/kr).
The plane wave approximation assumes that the wave is sampled
sufficiently far from the emitter for the ’curvature of the wave’ not to be noticed: it is thus a large r approximation which allows all but the first term of the polynomial to be neglected.
Evidently this assumption is particularly
inappropriate for a near neighbour scatterer (small r) if k is also small (small kr) corresponding. to low energies.
The calculation of the scattering
with a full spherical wave treatment is, however, rather consuming of computational time (particularly as the kinetic energies used in PhD are often higher than those of LEED in which this proper treatment is usually included) and a number of approximate methods have recently been introduced for both EXAFS and PhD.(19-23)
f(Q,,k)
These allow one to substitute an effective value of
into the plane wave formula which can be computed rapidly but largely
removes the deficiencies of the plane wave approximation. Figs. 5 and 6 give some indication of the type of correction introduced by incorporating spherical wave effects.
In fig. 5 the angular dependence of
the modulus of the scattering factor from a Ni atom 2.23A from a p-wave emitter is shown in both approximations at energies of 95eV (k = 5 A - l ) lCd-l).
and 38leV (k =
Note that while there are significant differences between the plane
wave and spherical wave treatments at most angles at the lower energy, the main discrepancies at the higher energy occur only near forward scattering. provides a second example, also f o r Ni scattering (now at 2.49A
Fig. 6
from the
253
I
I
1.8.-
I
k = 5A’
I
I
-- II
I
I
1
1
7
k = 10$
\
I \ I
Scattering angle €3(degrees) Fig. 5
Modulus of the scattering factor of Ni at 5A-l and 10A-l for different scattering angles for a scatterer 2 . 2 3 A from the electron source in the plane wave (dashed) and spherical wave (full line) formulations (from Barton and Shicley( )).
emitter) but in this case the interference between the scattered and directly emitted waves is included so the plot is of the photoelectron diffraction fine structure function ( i . e . the variations relative to the angular dependence expected with no scattering).
The main modulations in the curves of fig. 6
therefore result from interference (photoelectron diffraction).
Small shifts
in peak positions in the results of the two calculations therefore reflect changes in the phase of the scattering due to the inclusion of spherical wave effects.
Fig. 6 also shows that at higher energies, backscattering is
represented quite well by a plane wave approximation, but forward scattering is poorly represented.
For even smaller emitter-scatterer ( r j ) separation, the
effect becomes particularly acute.
Both examples therefore stress the
importance of spherical wave events when forward scattering events are important in a photoelecton diffraction experiment. This conclusion also bears on the second limitation of the simple formulation presented in equation 1 which is the neglect of multiple scattering effects.
In LEED, the need for proper inclusion of these contributions is well
known and no serious calculation of diffracted intensities omits their role. In PhD and EXAFS the role of multiple scattering is far less dominant, due mainly to the local nature of the electron source (and in the case of EXAFS, of a local
detector
-
the emitter itself).
In addition LEED is usually
254
Fig. 6
Photoelectron diffraction modulations as a factor of angle for different kinetic energies from an emitter positioned 2 . 4 9 A from a Ni atom. axis. as
The angles are measured relative to the emitter-scatterer
Spherical wave and plane wave scattering results are shown
labelled (after Sagurton et a1(21)).
conducted at energies below
-
200eV while most EXAFS analysis (and recent PhD
work) concentrates on scattering effects in the 100-500eV energy range or higher.
At these higher energies (c.f. fig. 3 ) the scattering is only very
strong in the forward direction so that in EXAFS, for example, multiple scattering is of primary importance only when several scatterers are approximately co-linear relative to the emitter:
in this case forward
scattering can ’focus’ the electron wavefield on to the subsequent atoms in the chain and thus modify their scattering amplitude and phase.
Indeed, even in
the case of LEED many perturbation methods for treating the multiple scattering recognise the dominance of forward scattering events in contributing to multiple scattering (see, for example, ref. 3 ) .
Recent calculations in PhD
have indicated that the important multiple scattering processes in this technique are also those largely involving forward scattering.
In view of our
earlier remarks that the spherical wave treatment of the scattering modifies the forward scattering most strongly, it is clear that multiple scattering
255 calculations must also incorporate a spherical wave scattering treatment if significant improvement in the quality of the calculation is to emerge.
A
simple illustration of this effect is shown in fig. 7 in which the photoelectron diffraction in the scanned energy mode, plotted as a fine structure function, is shown for p-wave emission from a S atom positioned 2 . 2 3 A from a Ni atom which is almost directly behind the emitter relative to the collection direction (actually ’7
off this direction).
The model relates to
the simulation of scattering in the [110] direction from
S
adsorbed on Ni(100).
Three components can interfere in this two-atom model: the directly emitted wave, a component backscattered from the Ni atom and on to the detector, and a double scattering component involving 180’ scattering off the S emitter.
scattering at the Ni and 7'
forward
Note that this double scattering event causes an
enhancement of the PhD modulation amplitude and a shift in the phase of the modulations (which might be interpreted as a slightly different bondlength if
0.4
0-2 h
Y
3
0.0
-0.2
v v
-0.4
Double scat.,pC Single scat..SW
II I
6
8
10
12
Wavenumber (A") Fig. 7
Comparison of calculated energy ( k ) dependent photoelectron diffraction for S Is emission scattering off a Ni atom 2 . 2 3 A behind (and ’7
to the side) of the collection angle.
The role of multiple
scattering in spherical wave and plane wave models is compared with the result for spherical wave single scattering only. refs 15 and
22.
Adapted from
256
analysed in single scattering) but including the double scattering in a plane wave formulation overestimates the effect while retaining some phase error. This overestimate appears to result not from the forward scattering amplitude (which is underestimated), but from the forward scattering phase, which is too small, leading to stronger constructive interference. Before moving on to discuss specific experimental approaches and results
it is appropriate to summarise the situation regarding PhD computations and computational methods.
Historically, much of the early experimental work
around 1978-82 concentrated on studies in which electron kinetic energies in the LEED range
(<
200eV) were used because it was known that strong back-
scattering occurred, so it could safely be predicted that an effect would be observed.
Also
following this analogy, LEED computational methods, including
their full complexity, were carried over to interpret the results.
Some
parallel work at much higher energies, concentrating on forward scattering geometries, was conducted during this period by Fadley and his co-workers who found single scattering methods rather effective in the interpretation of their results. More recently a move to intermediate energies, and an appreciation of the comparison with EXAFS, have highlighted the fact that the full rigour (and expense) of LEED methods may not be necessary, and that simple calculations can reproduce most of the main features of the data.
What is still not entirely
clear is the extent to which multiple scattering effects do need to be included, and the level of precision, or loss of precision, incurred by different levels of approximation.
Some specific examples in the following
sections will provide an impression of the importance of these refinements and approximations in the interpretation of different types of data.
3.
SDRVEP OF EXPERIMENTAL APPROACHES AND RESULTS
3.1
Grazing emission studies at high kinetic energies In the theoretical discussion of the previous section the comparison with
LEED and
EXAFS
has tended to stress the scanned energy mode of the PhD
experiment, and thus by implication to focus on synchrotron radiation studies
for which wide continuous energy ranges are available.
However, considerable
PhD work has been performed at fixed energies using conventional soft X-ray sources (A11 Q, hV = 1487eV; Mg Kg,
hv = 1254eV) normally used for
XPS.
Variations in the photoemitted signal associated with photoelectron diffraction must in this case be monitored by variations in the direction of
5,
either
by varying the polar emission angle 8 or the azimuthal emission angle 4.
In
XPS the best signal-to-background ratio is achieved from relatively small
binding energy states (EB 5 700eV) so the kinetic energies associated with such photoemission peaks are typically quite high
(-
IkeV).
For these conditions
257
forward scattering is strong so photoelectron diffraction modulations from adsorbed species on a surface are typically only pronounced at grazing emission angles when forward scattering events from the substrate are possible (see fig. 3(a)).
In order to retain this optimum grazing emission condition, it is then
appropriate to scan the azimuthal angle to observe PhD modulations. achieved
Fig. 8
by
keeping
A z imuthz
the
This is
detector (and X-ray source) fixed, and rotating the
angle plots of the intensity o 0 Is photoemission --om 0
chemisorbed on Cu(100) at various emission angles.
The polar
diagrams show the raw data as dashed lines while the full curves correspond to data which has been 4-fold averaged and amplified after removal of the minimum value.
The amplitude of modulations
are quoted in percentage of the maximum intensity.
After ref.
24.
258 The exact angle of photon incidence is not
crystal about its surface normal.
normally regarded as too important although it does, of course, influence the polarisation angles 8k and Qj in equation 1.
Note also that a conventional
X-ray source is not linearly polarised (unlike synchrotron radiation) and the influence of the two polarisation components needs to be incorporated into the theoretical analysis through modification of equation 1.
of this kind are shown in f i g . 8.
Data from the first
Radial plots of the intensity of the 0 Is photoemission signal from oxygen chemisorbed on Cu(100) are shown as a function of azimuthal angle at several where 8 is the usual
different grazing emission angles (i.e. values of 90’-8 polar emission angle referred to the surface normal). raw data.
The dashed lines are the
One special virtue of this mode of data collection is that the point
group symmetry of the crystal surface provides a check o n the data
For
reproducibility.
the special case here the azimuthal patterns should
t
~
0
Pig. 9
0
A
"
'
!
"
'
!
"
'
;
"
'
~
'
20 40 60 80 Azimuth angle 0 (degrees)
'
'
~
100
Is photoemission intensities as a function of azimuthal angle
from Cu(100) after 4-fold averaging.
These are the same data as in
fig. 8 but replotted on Cartesian coordinates (from ref
25).
259
display 4mm (C4v) symmetry which in general they do, particularly in the fine structure which represents the photoelectron diffraction effect.
Adding
symmetrically equivalent data points provides a method of improving the data quality.
The data, symmetrised in this way (using the 4-fold rotational
symmetry only) are shown, following amplification and subtraction of their smallest values, as full lines in fig. 8 .
Most of the earliest data taken
using azimuthal angle as the variable were shown in this rather visually appealing form of radial "flower" plots, but proper qualitative assessment is more easily achieved with Cartesian plots, and the symmetrised data are replotted in this form, over a single quadrant, in fig. 9 .
Clearly the
strongest PhD modulations are seen at the most grazing emission angles, consistent with our expectations from the relative importance of forward scattering events.
Fig. 10 shows a comparison of one of these experimental
plots with the results of a plane wave single oxygen atoms in $-fold hollow sites at several
scattering calculation f o r different layer spacings
l ~ " : " ' : " ' : " ' ; " ' I 20 40 60 80 100 Azimuth angle 4 (degrees)
0
Fig.10
Comparison of one of the experimental 0 Is azimuthal plots from fig. 9 with the results of plane wave single scattering calculations for
0
in the 4-fold hollow site of Cu(100) at
different 0-Cu top layer spacings (from ref. 25).
260
relative to the top copper atom plane.
The theoretical modulation amplitudes
have been divided by a factor of 2.0 to improve agreement with experiment: one reason why this is necessary could be the tendency of the plane wave approximation to overestimate the strength of forward scattering interferences (fig. 6).
The comparison indicates that the oxygen atoms occupy a site close
to coplanar with the top copper atom layer (z = 0.0A) assignment of around 5 0.lA.
with a precision in this
In fact this particular adsorption system has
proved rather contentious with significant support being given to a z value of around 0.EA by some other methods,(26n27) but more recent w o r k lends further support(28) to the original analysis of Kono et a1 presented here. In view of the underlying need to optimise the forward scattering
geometry at these high energies it is clear that 0 on Cu(lOO),
if it does
indeed occupy a coplanar site within the top Cu layer, is a particularly favourable case.
If the adsorbed species occupies a site much higher above the
surface, the scattering will be weaker, and potentially dominated by scattering within the adsorbate layer, rather than from the substrate: this would give poor sensitivity to adsorption site position.
This seems to be supported by
the results(29) of a study of S on Ni(100) (fig. 11) in which the S atoms are believed to lie around 1 . 3 A above the top Ni atom layer.
Comparison of theory
and experiment in fig. 11 shows that the agreement at this spacing is quite good, but the sensitivity to the exact value of this parameter is poor
(z
2
It is possible that improvements in analyser acceptance angle or the
0.2A).
use of p-polarised X-radiation could improve the sensitivity,(29t30) but it is clear that this version of the photoelectron diffraction experiment is best suited to problems in which deeper penetration of the substrate is suspected. For this reason the technique has proved less incisive in studies of S and Se(31) on Ni(100) than of 0 on Cu(100) and stepped surfaces(32) (Cu (410) and (211)).
A recent study of the initial stages of oxidation of Ni(100) has also
proved rather successful(33) while studies of metal (e.g. Ga(34) and Ag(35) on Si(ll1))
-
semiconductor systems
are of particular interest due to the
possibility of incorporation in the top substrate layers.
3.2
Backscattering geometries The forward scattering grazing angle studies of the previous section
might reasonably be regarded as a PhD analogue of medium or reflection high energy electron diffraction (MEED or RHEED) while a more natural analogue of LEED would concentrate on somewhat lower energies and a backscattering geometry.
Two versions of the experiment in this form have been used,
azimuthal angle plots of the kind discussed above, and scanned energy mode at fixed geometry.
The need to select
the
energy of the photoelectron has meant
26 1
: 13'
L
A I/I max.= 4 6 'lo
l
46 'lo
-51'lo 60%
h 66% 0 Fig.11
45 90 Azimuth angle (d (degrees)
Comparison of azimuthal PhD Scan from S Zp state of a Ni(100) ~(2x2)sstructure at a grazing emission angle of 13’
compared with
calculations for S atoms in the 4-fold hollow s-ites at various S-Ni top layer spacings (from ref. 29).
that both versions of this experiment have been developed using synchrotron radiation.
O n e advantage of
the azimuthal angle variation measurements
mentioned above is that the symmetry of the data provides a valuable test of
its integrity. This symmetry can also, however, be informative in itself. Fig. 12 shows azimuthal angle
taken at several photon
energies but a fixed polar angle 0 = 2 5 O for I 4d photoemission ( E p 5 0 eV) from I chemisorbed on Ag(ll1) in an ordered (/Sx/5)R30 monolayer), and at low coverage.
structure (coverage 1/3
The fcc(ll1) surface has 3-fold rotational
symmetry, clearly shown by both data sets, although each Ag atomic layer
(including the top one) has 6-fold rotational symmetry (fig. 13).
I is
expected to occupy a 3-fold coordinated hollow site on this surface (and is,
262
1.0
0.8
0
120
.3i Azimuth angle, 0 (degrees)
240
Azimuthal plots(36) of I 4d photoemission
Fig.12
adsorbed in a
(/3x/31R30
ordered phase
disordered phase (b) on Ag(ll1).
signal from iodine
(a) and a low coverage
The open circles represent the
raw data, the full lines are drawn through symmetrised data.
The
dashed lines o n (b) are theoretical calculations(37) based on the mixed site model described in the text.
indeed,
found to do so) but o n such a surface there are two different such
sites.
One of these, the "fcc" site, lies directly above a substrate atom in
the 3rd layer, while the other, the "hcp" site, lies directly above a substrate atom
in the 2nd layer.
As fig.
13 shows, the distinction in these sites
relative to the top layer is simply that the nearest neighbours are rotated in azimuth by 60’
in one site relative to those in the other.
We might expect,
therefore, that the anticipated PhD plots for the two different sites would simply be displaced by 60
in azimuth and this is supported by full multiple
scattering calculations(37)
(see fig 14), although the contributions of lower
layer scatterers
introduce some other minor
changes.
Because the role of
intra-adsorbate scattering is relatively small in the backscattering geometry (the other adsorbates being well away from the favoured 180
or Oo scattering
geometries) we would expect the observed P h D to be largely independent of adsorbate coverage a s long as the same local sites are occupied.
The
263
Fig.13
Plan view of the top layer of Ag(ll1). (J3x/3)R30
In the upper diagram a
ordered overlayer occupying one type (fcc) of 3-fold
hollow sites is shown.
In the lower diagram mixed occupation of
the two sites is shown at lower coverage.
pronounced difference between the low coverage and ordered I phase therefore suggests different sites are occupied in the two coverage regimes.
One
possibility is that while the ordered phase adopts a single optimum 3-fold hollow site, the low coverage regime involves occupation of both sites due to the relatively high mobility of I on Ag(ll1) expected at room temperature and the rather small binding energy difference expected between the two sites.
If
these two sites are equally occupied it is clear that the PhD patterns should approach 6-fold rotational symmetry, a n effect seen in the data. suggestion is supported by the calculation which shows the (/5;(fi)R30
The phase
involves occupation of the fcc site alone (c.f. figs 12 and 14), while at low coverages a model based on equal occupation of the two sites gives generally satisfactory agreement (fig. 12). This example provides a clear illustration of one of the potential virtues of azimuthal plots.
Although conclusions of the kind arrived at above
could be made by scanned energy plots collected off normal emission (see
264
240
180
Azimuth angle 0 (degrees) Fig.14
Theoretical azimuthal plots(37)
(based on a full multiple
scattering calculation) for I 4d emission from Ag(lll)(J3x/3)R3Oo-I at 2 5 '
polar emission angle for occupation of fcc hollows (full
lines) and hcp hollows (dashed lines).
below), the symmetry arguments provide a simple and strong clue to the solution even before numerical model calculations are made.
Moreover, this particular
case of I 4d photoemission is an example of an experiment which could not easily be performed in the scanned energy mode because the intrinsic atomic energy dependence of the 4d photoemission cross-section is very strongly structured.
This results Erom two effects: delayed onset due to the
’centrifugal barrier’ of the d-state, and a Cooper minimum when the cross-section matrix element for excitation to the %+l(f-state) wave field changes sign and thus passes through zero.
final state
The atomic cross section
is therefore low at onset ( h V ~ 6 0eV) and at the Cooper minimum (hV"l70eV) with a strong enhancement in between.
Clearly, the scanned energy mode measurement
of PhD modulation is most satisfactory when the atomic photoionisation
265
cross-section is unstructured.
Ideally it should also not decay too rapidly
with energy above threshold so that a large energy range of data can be This requirement is similar to that in
collected.
SEXAFS
and means that
scanned energy mode studies are not ideal if the binding energy of the core level to be studied is small, because the rate of decay of the atomic photoionisation cross-section above threshold scales with the binding energy. Typically the energy range available for measurement is of the order of 1-2 times the binding energy of the core level studied. Se 3d and
S
Thus early measurement of
2p photoemission ( 3 8 r 3 9 ) (binding energies -57eV and -160eV) were
somewhat restricted in energy range relative to more recent studies of deeper core levels, although in these early studies most measurements deliberately concentrated
on the energy range optimal for LEED-type calculations (below
CUCl
I
2.0
4.0
6-0
8.0
1( 0
Wavevector k (A')
Fig.15
SEXAFS fine structure f ~ n c t i o n ( ~ ~above 1 ~ ~ )the C!?. K-edge from Cu(lll)(~3xr/3)R30 -C~ at two different incident polarisation directions relative to the surface normal, and from the model compound CuCJ?..
266
-200eV).
In summary, therefore, we see that the azimuthal plots retain a value
in the backscattering geometry in cases where symmetry considerations may prove valuable, when the photelectron energy range is restricted, or in cases in which the atomic cross-section is strongly dependent on photon energy. The scanned energy mode, however, is the most natural analogue of LEED. Moreover, in view of the comments in Section 2 regarding the similarity of PhD
to EXAFS, but with PhD probing scattering path lengths rather than bond lengths, this mode of data collection may provide a more natural route to effective adsorption site determination.
A simple example in which direct
comparison with SEXAFS is possible illustrates some of the main features of the capability.
The example(40n41) concerns the study of the (fixfi)R30 -C%
structure on Cu(lll), a system rather similar to the I/Ag(111) case described above, although C& is a more reactive and more tightly bound adsorbate than I. The key structural problem, however, once again concerns the distinction between the fcc and hcp adsorption site.
SEXAFS measurements above the C%
K-edge reveal oscillations dominated by a single nearest neighbour scatterer as seen in fig. 15.
Here the raw fine structure function for two angles of
incidence (and for a CuCa model compound) are shown together with the smooth lines corresponding to the contribution from this nearest neighbour scattering shell.
Any contributions from more distant scatterers are clearly too weak to
provide additional information on the adsorption site.
The SEXAFS analysis
proceeds by a determination of the exact value of the Ca-Cu nearest neighbour distance (by comparison of the modulation frequency with that from CuC&) and a determination of the angle of these Cu-C& bonds, relative to the surface normal, from the EXAFS amplitudes(lS2).
This reveals that the data are
consistent with adsorption at 3-fold coordinated hollows.
SEXAFS does not
allow the azimuthal direction of the neighbours to be determined, however, for surfaces having greater than 2-fold rotational symmetry, so in the absence of more distance shell information, the fcc and hcp sites cannot be distinguished. A parallel scanned energy PhD study on the Ck Is photoemission peak (ie. over the same photon energy range) resolves this question.
Fig. 16 shows such scans
for normal emission (along [ill]) and off-normal emission along [110] (the latter data having a gap around 200eV due to the disturbing influence of an X-ray Bragg reflection set up in the crystal in this energy range).
Also shown
are the results of plane wave single scattering calculations from a large (convergent) cluster, and from a cluster comprising o n l y the nearest neighbour atom(s) behind the emitter.
In the normal emission data it is clear that
although the main modulations in the data are reproduced by the theoretical curves, a clear distinction between the two sites is not possible.
These data
also show that the main modulations arise from the scattering by the three nearest neighbours;
because these are symmetrically equivalent for the fcc and
267
t1111
Photoelectron kinetic energy (eV)
Fig.16
Cg Is
PhD curves taken in the [111] and [110] directions from
Cu(ll1) (r/3x/3)R3O0-CJ?., compared with plane wave single scattering
calculations for the fcc and hcp hollow sites.
The dashed curves
are based on scattering calculations incorporating nearest neighbour effects only(40).
hcp site for emission along the surface normal (ie. along the symmetry axis), this lack of distinction is not surprising.
It is possible that more
sophisticated calculations would allow the site to be distinguished, but the problem is more readily resolved by going to the off-normal data.
As fig. 17
shows, the different azimuthal directions of the nearest neighbours in the two sites now leads to quite different scattering conditions, and it is clear, even from the calculations based on the backscattering from these neighbours alone, that the fcc sites is the one occupied by the Cg atoms.
This example shows the
utility of the real space directional probing capability of photoelectron diffraction.
These results also highlight the possibility that the main
periodicity seen in a scanned energy PhD spectrum may arise from scattering by a single near neighbour which is close to an optimum backscattering geometry. Of course the rather simple calculations used in this analysis are not satisfactory for high precision in the structural analysis (cf. fig 7) and the
268
4
Plan
’4
-+yy0
0
2
4
0
3
2'
.
0
1
.
8'
1'
0
A -a0
0
4 0
0
L
2
FCC
HCP (110) SITE NORMAL I
Side
,/
NORMAL A
1J
7
-
B
2&2'
Sectional and plan views of the Cu(ll1) surface with adsorbed C!?,
Fig.17
atoms in the fcc and hcp hollows, showing the geometries of the PhD experiments of fig. 16.
fact that the optimum layer spacing found in this study differs slightly by (-0.06A)
from that found by SEXAFS is probably attributable to the
oversimplified computational approach. In fact the use of medium photoelectron energies
(in the range
-100-500eV), of good energy range, and in the backscattering mode, is an method
pioneered by Shirley and his c ~ l l a b o r a t o r s ( ~ ~ ~By ~ ~ using ~ ~ ~ ) deeper . Is states fie. with binding energies in excess of tkeV), there is a large energy range over which the atomic cross-section is not strongly decaying, and the synchrotron radiation monochromator design (using crystal rather than grating optics) is much more straightforward than at softer X-ray
energies.
So
far
this group have mainly worked on S adsorption systems (on Ni(100)(15r42), C U ( ~ O O ) ( ~ ~ G) ,e ( ~ l ) ( ~ ~monitoring ) )
the S Is emission.
They have also
contributed significantly to the work on approximate computational methods which allow refinements beyond the plane wave scattering
method^(^^^*^)
without
the full expense of LEED-type calculations (which with proper inclusion of the large number of scattering partial wave phase shifts and large scattering
269
clusters become prohibitive in the medium to high energy range).
An example of
the quality of data and associated theoretical fits is shown in fig 18 for the system S/Ni(100), also taken along the surface normal and in a [Olll direction. This o f f normal condition is the one which places a nickel nearest neighbour atom almost directly behind the emitter (c.f. fig 7 ) leading to a short dominant path length difference and a long periodicity in k.
Along the surface
normal, by comparison, the main modulations (higher periodicity in k ) arise from scattering by the second layer Ni atom directly behind the S atom in the 4-fold
coordinated hollow site.
Interestingly, the combination of these two
-experiment
0.5
0.0
-
-0.5
h
.x
%
0.5
0.0
-0-5 6 8 Wavevector, k (,&-'I Fig.18
10
Scanned energy S Is PhD, plotted as a fine structure function, collected from Ni(lOO)c[2x2)-S
in two specified directions.
The
theoretical curves are based on spherical wave multiple scattering calculations as described in the text.
From ref. 15.
270
measurements (which predominantly probe first and second layer Ni atom locations) allowed a deduction to be made about the top Ni layer atom spacing which is found to be expanded relative to the underlying bulk by 0.08A. The data set of fig 18 were the first, wide range, medium energy data of their kind and have therefore been subjected to analysis by several different methods (eg. refs llr45): they have therefore become something of a proving ground for more, or less, sophisticated computational methods.
Most of these
alternative calculations were based on a structure in which the top substrate layer was not expanded and so are not ideal for direct comparison, but recently Sagurton
et al(14)
have presented the results of a spherical wave single
0.5
0.25
0.0
0.00
4.0 I
100
Fig.19
200 300 400 Electron energy (eV1
The same S Is data as in fig. 18 but compared with a single scattering calculation (based on the same structural model as that used in ref 18) by Sagurton et ~l(~ ).
27 1
scattering calculation using the optimum structure of Barton et al(15) described above. data.
These are shown in fig 19 compared with the same experimental
Although there is a slight deterioration in the quality of the fit there
is remarkably little difference between the two theoretical curves, particularly in view of the significant effects which can occur in double scattering in just one pair of atoms relevant to the calculation (fig 7 ) and it is clear that some of the more serious modifications introduced by multiple scattering must average out over many scatterings.
One interesting feature of
both of these calculations is they are conducted with rather small scattering clusters (ie. the number of r j included in the summation of equation 1 or modifications of it).
The cluster used in the multiple scattering (to 4th
order) calculation comprises approximately 40 atoms, while the one used for the single scattering calculation contained
6 4 atoms.
Clearly in general it is
important that the cluster size used is sufficiently large that adding further atoms on the periphery does not modify the calculated results.
One computation
on this system based on plane wave single scattering(45) indicated up to 1500 atoms were needed in the cluster to ensure this type of convergence.
On the
other hand, the discussion of the experi- mental data we have made so far has tended to stress the very strong role of just the nearest neighbour scatterers (eg. fig 16).
Correlated vibrations of nearest neighbours help to reinforce
these nearest scatterers but it is also notable that most calculations seem to use a damping length somewhat shorter (by -30% or more) than that commonly used in LEED calculations or in electron spectroscopic studies of surface composition.
One further effect which attenuates the role of more distant
scatterers is that of the finite angular acceptance (typically a few degrees) of the electron energy analyser which leads to some angular averaging. Different collection angles introduce different path lengths but for more distant scatterers this change in path length is largest, so that the phase smearing of the contributions from these scatterers makes them less important. This effect can be taken into account by numerically averaging (eg. ref 11,14) although this method is obviously time consuming.
An
alternative approach,
using an approximate analytic expression to treat the problem, has been used by Barton et al(15).
Of course the use of small scattering clusters is
computationally attractive, particularly for multiple scattering calculations, but if proper convergence is not achieved, any fit to experiment is unsound without an identifiable physical origin to the reduced importance of more distant scatterers.
This issue of the proper cluster size for convergence is
still a matter of some debate. Before leaving this area of medium energy, scanned energy PhD some mention should be made of experiments on C, N and 0 1s photoemission because these comprise the important ingredients of many molecular adsorbates.
Most
272
other structural methods have proved troublesome for molecular adsorbates (although there have been some notable successes) but
recent work,
in
particular, has demonstrated the considerable potential for PhD as a particularly successful means of determining adsorbate-substrate site registry. This potential is demonstrated in a rather direct qualitative way by the data presented in fig 20 which shows 0 Is normal emission PhD spectra from formate (HC00-1, methoxy (CH30-) and chemisorbed oxygen on Cu(100).
In each case the
oxygen atom is known to bond directly to the surface with Cu-0 nearest neighbour bondlengths which appear to differ by less than 0.lA.
The local site
of the oxygen atom is, however, likely to differ in each case.
The very great
difference between the three spectra of fig 20 demonstrates clearly that this is, indeed, the case and that PhD is sensitive to these differences. A second, essentially qualitative example, is given in fig 21 which shows
cu(iooi e=oo 0 1 s ............ ....... 0 . -....
.... -.....
...... ...... -._.. f
.-.
....
......-. .. .....- .... ....
I
50
Fig.20
100
.:'.... ............-:,. :'-..-
. . . . *..
..
.*.
HCOO
.......,.'....
200 250 300 350 Photoelectron kinetic energy 150
4 3
Scanned energy mode PhD measurements of 0 Is emission along the surface normal of a Cu(100) surface with, respectively, adsorbed formate (HCOO-), methoxy (CH3O-) and chemisorbed oxygen. ref. 46.
Data from
273
Cu/HCOO
.. -
..*. .. "- ..
.
.
.:...
*
..
.-.
. .... ...:. .**'. .: ... *
*
200 300 400 Photoelectron kinetic energy (eV)
100
Fig.21
Scanned energy mode PhD measurements of 0 1s and C 1s emission along the surface normal of Cu(100) and Cu(100) surfaces with adsorbed formate species(47).
both 0 1s and C 1s PhD spectra collected along the surface normal for formate adsorbed on Cu(100) and Cu(ll0).
These two adsorption systems are of especial
interest because of the conflicts in earlier SEXAFS studies which indicated different local adsorption sites for the two surfaces, although the exact adsorption site was also not entirely ~lear[~’-~’).
Bearing in mind the large
differences seen in the 0 1s spectra from different species on Cu(100) in fig 20, it is difficult to see how the remarkable similarity of the spectra from
formate on these two surfaces can be reconciled with different local adsorption sites.
The clear conclusion, even without quantitative evaluation, is that
formate adopts the same local site on these two surfaces.
In view of the
different local substrate symmetries, this conclusion greatly narrows down the number of possible adsorption sites. In fact quantitative evaluation(47) shows that the adsorbed formate occupies a site bridging two nearest neighbour copper
274
atoms with the 0-0 axis aligned along this near neighbour (<110>) direction, so the oxygen atoms are just off atop sites.
These calculations also show that
the 0-Cu layer spacing is essentially identical on the two surfaces, the small differences between the 0 Is PhD from the two surfaces, for example, being attributable to scattering from more distant (lower layer) cu atoms which have different locations on the two surfaces.
Interestingly the C 1s data, although
inferior in quality, can also be matched by theory with the conclusion that the 0-C-0 bond angle in the adsorbed formate is probably slightly larger (by about 10’)
than in the free formate ion. One further interesting phenomenon in PhD emerges from analysis of the Fig 2 2 shows the C Is and 0 1s PhD
adsorption of methoxy (CH3O-) on Cu(100).
spectra collected along the surface normal for this system in which it is known that the moeity bonds through the 0 atom with the methyl group above, although the
0-C
axis may be tilted away from the surface normal.
One striking feature
of these data is that the dominant periodicity in the C Is data is clearly longer in k (energy) than for the 0 Is PhD, indicating that the most important scattering path length for C is shorter than for 0, despite the fact that the C
cu ClOO~/CyO
..-. .. .. ..
. '.
. . .. .. .... . ... +..
.
.*/.- c 1s
: :
,.*
..-..A.. . ,: ...... .*...... . . +. . -. r;
..5...-m":r
- . ,*+*..0 Is .-A
f
f *:
**.
*, 2#
./
100 200 300 Photoelectron kinetic energy [eV) Fig.22
400
Scanned energy mode PhD measurements of 0 Is and
C
1s emission
measured along the surface normal from methoxy (CH30-) adsorbed on ~ ~ ( 1 0( 05 3)) .
275
atom must be further from the surface.
The interpretation of this result
appears to be that although the 0 Is is dominated by Cu substrate scattering, the C Is signal is primarily influenced by intra-molecular backscattering from the 0 atom(53).
Fig 23 shows a calculation of this latter effect (the dash-dot
curve is a single scattering spherical wave calculation, while the full curve Notice that if the 0-C axis is tilted away from
includes double scattering).
the surface normal the scattering path length is reduced and the periodicity of the photoelectron diffraction modulation decreases. illustrate
These calculations
not only that this intramolecular scattering can be important for
~
c Is
~-
Intramolecular scattering only
*
*.
'
.. ' . . ....:--
*
.,.:.' .:
.,-..
..p*:.
1.
expt.
160 200 360 460 Photoelectron kinetic energy (eV) Fig.23
Comparison of the
C
Is PhD spectra of Fig. 2 2 with spherical wave
single (dash-dot) and double (full line) calculations for a free oriented methoxy species tilted at various angles relative to the collection
2 76
emission close to the intramolecular axis, but also that it provides a basis for determining the molecular orientation;
clearly a fit with experiment is
only achieved if the molecule is essentially untilted (although earlier NEXAFS results(49) had indicated a tilt of some 30 ).
More complete calculations of
both the 0 and C PhD signals, including substrate scattering effects, confirm the conclusion and identify the adsorption site as a low symmetry (off-hollow) site which would appear to have interesting molecular bonding implications. These results illustrate that medium energy scanned energy mode PhD has developed considerably in the last few years and many systems have now been studied: in addition to those mentioned already, other systems studied in the backscattering regime include Na, Te(54r55), 0 ( ~ 6 g ~ ~ 1N(57v58) ~ ~ ) , and C(57R58)
on Ni(l@@), 0(26,2*,57) on Cu(lOO), 0(59),~(60) on Cu (110). CO on Ni(100)(62),
Ni(111)(62)
on NifllO),
and C U ( ~ O O ) ( ~ rnetho~y(~*) ~) on Cu(ll1) and
acetate (CH~COO-)(65) on CU(UOI. 3.3
Intramolecular and interlayer forward scattering
So
far the discussion has centred on substrate scattering effects as a
means of determining adsorbate-substrate registry, utilizing the interference
of scattering events from a cluster of scatterers.
A
particularly simple form
of photoelectron diffraction arises from exploitation of the very sharply peaked forward scattering behaviour of atoms, particularly at relatively high photoelectron energies (eg. >500eV)(66).
Until recently it had been applied
mainly to the determination of the orientation of adsorbed diatomic (or "pseudo-diatomic") molecules, particularly CO. schematically in fig 2 4 .
The basic idea is illustrated
If we consider the photoelectron diffraction suffered
by the C Is photoemission wavefield as it is scattered by the 0 atom lying further outside the surface, there will be a series of diffracted orders as the collection angle is scanned away from the C-0 bond axis.
Evidently, however,
if the electron energy is reasonably high the zero order forward scattering will be dominant and will produce an emission lobe centred on the molecular axis.
The width of this central lobe is dictated largely by its separation
from the first order diffraction peak, which in turn is influenced by the intramolecular bond length and the electron wavelength (energy).
It will be
narrowest for long bond lengths and high energies although for short bond lengths particularly, some additional narrowing will derive from the intrinsically narrow forward scattering peak.
This version of PhD therefore is
potentially particularly simple to interpret; an observation of a directed lobe of emission is a direct measure of the intramolecular bond orientation. Note, incidentally, that this effect is illustrated quite clearly for a Ni atom (rather than 0) as the forward scatteror by the results in fig 6 which show, at
277
/
’ I ’ Fig.24
\
-
C
Schematic illustration of the forward scattering of
C
Is emission
by the oxygen atom in a CO molecule (cf fig. 3b).
all but the lowest energy, an enhanced signal along the forward direction followed by oscillations due to higher order diffraction features. Notice that although the forward ( O o ) scattering involves zero path length difference between the direct and scattered waves, there is a phase difference involved in the scattering (represented by the complex scattering factor).
Thus the fact
that the zero order feature does appear as a peak along the axis is due to the small value of this phase shift at high energies.
For example, at only 50eV
for a Ni scatterer, the large low energy phase shift introduced leads to a minimum close to the anticipated zero order condition (fig 6 ) .
Despite these
remarkably simple qualitative arguments, quantification is required to assess the sensitivity of the effect and the ability to extract further details such as "wagging" vibrational amplitudes.
Most calculations so far have used a
plane wave scattering description although, as we have already discussed and has been shown in some of the earliest work, this does tend to overestimate the strength of this zero order feature ( s e e also ref 66).
A
simple attenuation
factor has tended to be used to correct for this in a pragmatic fashion, but the recent work on simple spherical wave approxima- tions will doubtless lead
to much more use of this more accurate theory in the future.
Double
scattering, on the other hand, is unlikely to be very important in describing this effect because i t must involve a relatively weak backscattering event.
By
contrast in a backscattering experiment, forward scattering can contribute much more to multiple scattering as we have already shown.
POLAR ANGLE ,8 (degrees) Fig.25
(a)Theoretical (plane wave single scattering) calculations of the forward scattering diffraction effect the C Is emission in a CO molecule with various tilt angles and values of the vibrational amplitude. (b)
Shows experimental data and a further group of calculations,
all with a root-mean-square vibrational amplitude of loo.
From ref
67.
Fig. 25 shows the results of an experiment on CO adsorbed on Ni(100) and of some simple plane wave scattering calculations(67).
The calculations in
fig. 25(a) show the effect of the forward scattering of the 0 atoms on the C Is signal (using hV=1487eV) for different angles of tilt, 8t, of the CO molecule away from the surface normal (G4=9O0) and for different wagging vibrational amplitudes specified by a root-mean-square amplitude
ern,.
is assumed to be random in its azimuthal orientation.
The tilted species
For this reason, small
angles of tilt simply broaden the emission lobe along the surface normal, but only when the tilt angle exceeds about L5O (dependent on peaks emerge on either side of the surface normal.
ermS)do
two resolved
Similarly the intrinsic
width of the emission lobe, even for a molecule aligned along the surface normal, is sufficiently broad that substantial additional broadening only results for
arms
greater than about 10’.
Nevertheless, it is clear from a
279
comparison of the experimental data in fig. 25(b) system (Ni(lOO)c(2x2)-CO)
that in this adsorption
the CO molecules are untilted to within about 10’.
Note that although the calculations presented are for the C 1s emission, it is usual, in the experimental data, to plot the
ratio of the
C
1s to 0 1s signal.
This procedure simply allows a number of experimental effects (associated with changing incident and collection directions) t o be normalised out; the 0 Is signal contains only these instrumental factors and no significant scattering features.
We should perhaps also remark that although there is some
imprecision in the method, due to the finite width of the zero order scattering lobe, the angular variation is much sharper than the cos28 type of dependence commonly used in NEXAFS and valence level photoemission to determine bond orientations.
I
c 1s
Ni (110) + CO T=120K
too11
I -80
Fig.26
-40
0 40 Polar angle 8(degl
eo
Polar angle scan of the C 1s photoemission signal in the [ O O l ] azimuth for CO adsorbed onto Ni(100) at various exposures.
ref 68.
After
280
Another recent study(68) of CO adsorption illustrates some of the extended potential of this method.
In the case of CO adsorption on Ni(ll0) it
is known that at saturation coverage and low temperature a monolayer coverage structure develops having a space group which suggests the CO molecules tilt out of the ill01 close packed azimuth.
Fig. 26 shows polar angle plots of the
C 1s signal (normalised, in this case, by a simple instrumental function) taken
in the [OOlI azimuth perpendicular to the [110] close packed rows at various coverages.
The highest coverage clearly shows a double peaked structure
characteristic of tilt (both positive and negative) in this azimuth of approximately 21 , but the results indicate there is no tilt at low coverage.
In this low coverage range, however, measurements at 120K and 300K in the two perpendicular azimuths show that the wagging vibrational amplitudes are azimuthally anisotropic on this low symmetry substrate (fig 27).
In the more
open [OOll azimuth the zero order lobe shows a slight broadening relative to that in the close packed [110] azimuth even at 120K, but the effect is much more pronounced at 300K. surface dynamics.
These results therefore provide valuable data on
Note, incidentally, that the data of figs 26 and 27 also
clearly show the first order, as well as the zero order, diffraction lobes, at least at low temperature.
Apart from one study of adsorbed m e t h o ~ y ( ~ ~ ~ ~ ~ ) ,
this technique has so far only been applied fully to adsorbed CO, although the results of
fig 26 and 2 7 , and of
some companion
work on
the influence of
(Ni llO+CO) Cls T= 300K
-
3-9mPas
'
.-
39'
27'
I
-80
Fig.27
-40
0
-80 -40 Polar angle, 8 (degrees) . .
40
0
40
Polar angle scans of the C Is photoemission signal from a low coverage of CO on Ni(ll0) at two temperatures of 120K and 300K and in the two principle azimuths of the surface.
From ref 68.
281
coadsorbed potassium(71) on the CO tilt angle, already demonstrate a valuable
role for such studies.
There is little reason to suppose that these
measurements should not be easily extended to many other species in the future. In addition to these studies of adsorbed molecules, recent work has
utilised exactly the same physical process to investigate the growth of epitaxial films.
Fig. 28 shows an example of this work(72) in which Cu is
grown epitaxially on Ni(100); as is shown schematically in the lower panel, the growth is believed to occur in a ’layer-by-layer’ form.
Fig. 28(a) shows the
results of measuring the Cu 2 ~ 3 1 2photoemission signal (at a kinetic energy of 317eV) as a function of polar angle for several different average coverages of
Cu
on the Ni(100).
Up to the first monolayer (1ML) the polar plot is largely
POLAR ANGLE ,9 (degrees)
.-
I } Fig.28
2MLCu
Lorn
Ni(l00)
Polar angle dependence of Cu Zp3/2 photoemission (a) and Cu L W Auger electron emission ( b ) from copper layers of various thickness (labelled in monolayers) grown on Ni(100).
Panel (c) shows a
schematic of the epitaxial overlayer at ZML thickness. 72.
From ref
282
featureless (the weak modulations may result from backscattering at this intermediate electron energy) but as further layers are added structure appears, the most conspicuous being a peak at 45’ direction in the epitaxial film.
corresponding to a <110>
This peak can be assigned to forward
scattering by the second (and subsequent) copper atom layers and this provides a clear monitor of the onset of the second layer of growth.
Fig. 28(b) shows
similar measurements on the Cu L W Auger electron peak at a kinetic energy of
In this case the higher energy emission will be expected to lead to
917eV.
narrower forward scattering lobes so it is now possible to resolve additional forward scattering peaks corresponding to <310> and directions in the film.
This latter observation highlights a result which has emerged from
several studies (eg 31,73) of Auger electron diffraction in conditions in which forward scattering effects are dominant.
In fact studies of Auger electron
diffraction (eg ref 12) predate those of photoelectron diffraction, but early studies concentrated on low energy (-100eV) emission peaks typically dominated by backscattering. Under these conditions a proper description of the outgoing electron wavefield from the emitter prior to scattering is potentially rather important, but the complexities of the two-electron process, coupled with the fact that most strong Auger electron emission is associated with valence band transitions, appeared to present a problem of enormous theoretical complexity. At high electron energies, on the other hand, the forward scattering only picks out a narrow range of the initial incident wavefield for enhancement; providing the initial wavefield is not strongly structured in angle, therefore, a detailed description is no longer important.
A range of measurements of
grazing angle emission, and of forward scattering through epitaxial films, have indicated that the observed angular scans are insensitive to whether this source is a photoelectron or an Auger electron. The extension of the
oriented molecule
forward scattering technique to
the study of film growth is an interesting one which derives from an increasing interest in fundamental studies of interfaces and ultrathin films.
We
should
note, however, that the very simple interpretation we have discussed so far needs to be treated with caution if the forward scattering is through several layers.
In this case multiple forward scattering will be important and while
this is unlikely to change the qualitative pictures of emission lobes along real space atom string directions, it will certainly influence the quantitative description of these photo-(or Auger) electron scattering lobes.
3.4
Photoelectron diffraction of split peaks All of the discussion so far has centred on the idea that the core level
binding energy is used only to identify the element from which emission is
283
studied so that in the case of adsorbed layers, for example, photoelectron diffraction can be studied by emission from an adsorbate site.
In the case of
molecules, elementally distinct sites within the molecule (e.g. C and also be probed. limitations.
0)
can
In this form of the experiment there are two important
Firstly if an adsorbed molecule contains more than one atom
Of
the same species which is in a different structural environment, photoelectron diffraction from a core level of this species will yield an (incoherent) sum of the diffraction effects from these two ( o r more) sites.
Similarly, a study of
photoelectron diffraction of emission from a substrate core level will yield structural information averaged over many layers which will be of little value in elucidating the structure of the surface of the substrate ( o r , indeed, of a clean surface). It is, however, well known that atoms in different local electronic (or ’chemical’) environments yield slightly different photoemission core level binding energies due to a mixture of initial and final state effects.
In different states of adsorbed species, or within molecules, these
effects are normally known as ’chemical shifts’.
Similar effects can occur on
a clean surface: the electronic environment of the surface atoms differ from those of the bulk, but these ’surface shifts’ are typically small compared with the intrinsic broadening effects and have largely been observed in the narrow 4f e m i s s i ~ n ( ~ peaks ~ @ ~ ~from ) materials around the 5d transition metals. The application of chemical shift or surface shift PhD is as yet in its infancy, but some early experiments do indicate a real potential.
Obviously
the need to separate out different components of a core level photoemission peak, which may be weakly resolved, places greater demands o n the signal-to-noise quality of the data (exacerbated by the need to work at high resolution in order to optimise the peak separation).
One study which has been
performed using chemical shifts is of dinitrogen on Ni(100)(76).
The nitrogen
molecule is believed to bond end-on to the surface rather like CO, but of course both ends of the molecules now comprise nitrogen atoms.
Photoemission
from the N Is does show a splitting, however, which has been proposed to arise from the different chemical environment of the N atoms at the two ends of the molecule.
Polar angle scans of the two components appear to support this view,
a marked enhancement of one component (thought to be associated with the nitrogen atom close to the surface) being seen along the surface normal.
A
recent scanned energy mode study(65) of the acetate species on Cu(ll0) also indicates the large C Is splitting, believed to be associated with the two chemicallly distinct carbon atoms (in the CH3 and COO groups), may be used to explore the structural environment of each atom. Surface shift studies have been conducted on the W 4f emission from W ( 1 0 0 ) ( 7 7 f 7 8 ) and w(110)(79) by
emission
two groups.
On these surfaces the W 4f
is split into several components due to the slightly different
284
W(100) 4f,fl
31.5
Fig.29
hV=7OeV
31.0 Binding energy (eV)
W 4f7/2 emission spectrum from W(100) showing the surface (S1) first underlayer (Sz) and bulk (B) contributions(* ).
electronic environment of successive surface layers.
Fig. 29 shows the form of
the W 4f712 emission seen from W(lO0) resolved into three components, the surface layer (Sl), the first underlayer
(Sz),
and the bulk emission (B).
One
difficulty with measurements of these effects in the 4f emission is the need to work in quite a narrow energy range, relatively close to threshold, in order to retain a strong photoemission cross-section, a good surface specificity (i.e. a large amplitude of the surface shifted component) and good resolution. Measurements have therefore concentrated on angular scans (particularly azimuthal angle scans) at kinetic energies well below 10OeV.
An example of
such data is shown in fig 30, spectra being recorded at a photon energy of 65eV (binding energy =31eV) and a polar angle of 30 .
The symmetrised experimental
data on the left shows the total (a), bulk (b) and surface (c) contributions to the azimuthal scans.
In view of the rather low kinetic energies it is rather
surprising that theoretical calculations in one of these studies have concentrated on single scattering methods, although the results do appear to
285
Fig.30
Symmetrised experimental azimuthal scans, at 30
polar angle and
65eV photon energy, of the total (a), bulk contribution (b) and
surface contribution (c) to the W 4f7/2 emission from W(100). The inset shows the raw experimental data for the total emission.
The
panels a’, b’, c’ show a matching set of single scattering theoretical results(77).
give quite good agreement with experiment ( s e e fig 30).
Further work is
required on these systems, but structural studies by this method may well prove rather incisive in those favourable cases in which substantial surface shifts are observed.
One final version of photoelectron diffraction which utilises split components of core level photoemission peaks, but in a very different way, is spin-polarised PhD(80v81).
The atomic multiplet splitting of s-levels in
magnetic ions leads to two distinct emission peaks which are substantially spin polarised.
Photoemission from these states therefore provides an internal
source of spin polarised electrons which can be used to probe local magnetic ordering through the different scattering cross sections due to magnetic (exchange interaction) effects.
So far one such experiment has been performed
286
using Mn 3s emission (which shows a multiple splitting of 6.7eV) antiferromagnetic KMnF3.
Simple model calculations(80)
in
indicate that the
exchange-induced assymetries should be greatest at relatively low kinetic energies
(<
100eV) and experiments were conducted at kinetic energies around
lOOeV using a laboratory X-ray source (MOMS, hV=192.6eV).
The experiments(’l)
involved the measurement of the relative intensities of the two spin split components at different take-off angles and different temperatures. One set Of data, with the spectra normalised to a constant amplitude of the 7S peak, are shown for a fixed take-off angle in fig. 3 1 .
One interesting feature of these
data is that substantial changes are seen at temperatures well above the Nee1 temperature (88K) indicating that short range magnetic order persists Well above this point.
Although a quantitative understanding of these phenomena
will not be simple to achieve, these data clearly demonstrate a potential utility f o r this approach to the study of local spin ordering.
Fig.31
Mn3s photoemission spectra, normalized to a constant intensity of the 7S component, recorded at several temperatures from KMnF3. After ref. 81.
4.
Summary and Prognosis
Photoelectron diffraction was first ’discovered’ in 1978(24r38t54) and has developed quite slowly over most of its first 10 years.
This slow
development was due at least in part to a perceived difficulty in performing structural analysis using this method.
The low kinetic energy backscattering
studies appeared to suffer the disadvantages of complex LEED calculations for analysis, coupled with the difficulty in gaining access to suitable sources of synchrotron radiation.
The laboratory source measurements utilising mainly
forward scattering were also seen as difficult (the emitted photoemission flux at grazing emission angle is low, and the requirements on sample goniometers are quite stringent) although simple single scattering methods appeared to be adequate for analysis. The range of methods has slowly expanded, however.
Oriented
molecule
and overlayer forward scattering techniques have been more widely appreciated, along with their extension to Auger electron diffraction, while the expansion of synchrotron radiation sources and good monochromators and beam lines to explore the soft X-ray energy range (-300-3000eV) have greatly extended the scope of the technique to study a wider range of materials and to work at intermediate kinetic energies with a good energy range.
Many of these
facilities were originally developed for SEXAFS but are proving ideal for PhD, creating the possibility of parallel studies by these complementary methods. In addition the analogy with SEXAFS has highlighted the potential utility of single scattering methods over a much wider energy range than was supposed.
originally
Currently the whole question of the extent to which multiple
scatteing is important, and the general level of computational complexity needed, is under review, but it is clear that much can be learnt with very simple methods. All of these effects have aided a marked
increase in the rate of
application of photoelectron diffraction to a range of problems of increasing complexity and variety in the last three or four years.
At the moment there
seems every reason to believe that this trend will continue into the forseeable future.
ACKNOWL~MENTS
It is a pleasure to acknowledge the contributions of many collaborators
on photoelectron diffraction over the last 10-15 years.
Many of these are
cited in the references but I would particularly like to mention Neville Smith (A.T. and T.Bell Laboratories) and their collegues.
Alex
Bradshaw (Fritz Haber Institute) and
Continued support in the form of research grants from the
Science and Engineering Research Council is also gratefully acknowledged.
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11.
12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26.
27. 28. 29. 30. 31. 32. 33.
34.
J. Stohr in X-ray Absorption: Principles, Techniques, Applications of EXAFS, SEXAFS and XANES, eds. R. Prins and D.C. Konigsberger (Wiley, New York, 1988) p443. D.P. Woodruff, Rep. Prog. Phys. 49 (1986) 683. J.B. Pendry, Low Energy Electron Diffraction , Academic Press, New York, 1974. M.A. Van Hove and S.Y. Tong, Surface Crystallography by LEED , Springer Series in Chemical Physics, Vol. 2, Springer-Verlag, Berlin, 1979. J.B. Pendry and D.K. Saldin, Surface Sci. 145 (1984) 33 P.A. Lee, P.H. Citrin, P. Eisen erger and B.M. Rincaid, Rev. Mod. Phys. 53 (1981) 769. eg. P.A. Lee and J.B. Pendry. C.S. Fadley, Physica Scripta T17 1987) 39. The formulation presented here is essentially that developed and used by Fadley and coworkers in many papers (eg. ref. 11). Other, more complete expressions have been given by many authors (eg. refs 12-15). P.J. Orders and C.S. Fadley, Phys. Rev. B27 (1983) 781. L. McDonnell, D.P. Woodruff and B.W. Holland, Surface Sci, 51 (1975) 249. T. Fujikawa, J. Elect. Spect. Rel. Phenom. 26 (1982) 79. M. Sagurton, E.L. Bullock and C.S. Fadley, Surface Sci. 182 (1987) 287. J.J. Barton, S.W. Robey and D.A. Shirley, Phys. Rev. B 34 (1986) 778. J.J. Barton, C.C. Bahr, Z. Hussain, S.W. Robey, J.G. Tobin, L.E. Klebanoff and D.A. Shirley, Phys. Rev. Lett 51 (1983) 272. J.J. Barton, C.C. Bahr, Z. Hussain, S.W. Robey, L.E. Klebanoff and D.A. Shirley, J. Vac. Sci. Technol. A2 (1984) 847. see, eg. B.W. Holland, Surface Sci. 68 (1977) 490 for an explicit expansion of this expression. S . J . Gurman, N. Binsted and I. Ross, J. Phys. C. 17 (1984) 143. J.J. Rehr, R.C. Albers, C . R . Natoli and E.A. Stern, Phys. Rev. B . M. Sagurton, E.L. Bullock, R. Saiki, A. Kaduwela, C.R. Brundle, C.S. Fadley and J.J. Rehr, Phys. Rev. B. J.J. Barton and D.A. Shirley, Phys. Rev. B . 32 (1985) 1982;1906. V. Fritzsche and P. Remnert, Phys. Stat. Sol. b135 (1986) 49; 142 (1987) 15. S . Kono, S.M. Goldberg, N.F.T. Hall and C.S. Fadley, Phys. Rev. Lett. 41 (1978) 1831. S . Kono, S.M. Goldberg, N.F.T. Hall and C.S. Fadley, Phys. Rev. B 22 (1980) 6065. J.G. Tobin, L.E. Klebanoff, D.H. Rosenblatt, R.F. Davis, E. Umbach, A.G. Baca, D.A. Shirley, Y. Huang, W.M. Kang and S.Y. Tong, Phys. Rev. B26 (1982) 7076. U. Dobler, K. Baberschke, J. Stohr and D.A. Outka, Phys. Rev. B 31 (1985) 2532. M.C. Asenso, M.J. Ashwin, A.L.D. Kilcoyne, D.P. Woodruff, A.W. Robinson, Th. Lindner, J. Somers and A.M. Bradshaw, Surface Sci.to be published. R.E. Connelly, C.S. Fadley and P.J. Orders, J. Vac. Sci. Technol. A2 (1984) 1333. C.S. Fadley, Prog. Surface Sci. 16 (1984) 275. P.J. Orders, R.E. Connelly, N.F.T. Hall and C . S . Fadley, Phys. Rev. B 24 (1981) 6163. K.A. Thompson and C.S. Fadley, Surface Sci. 146 (1984) 231. R . Saiki, A. Kaduwela, J. Osterwalder, M . Sagurton, C.S. Fadley and C.R. Brundle, J. Vac. Sci. Technol. A (1987). K. Higashiyama, S. Kono and T. Sagawa, Surface Sci. 175 (1986) L794.
289
35. 36. 37. 38. 39. 40. 41. 42. 43. 44.
45. 46. 47.
48.
49 50.
51.
52. 53. 54. 55.
56. 57. 58. 59. 60. 61.
62. 63. 64.
65. 66.
S . Kono, K. Higashiyama and T. Sagawa, Surface Sci 165 (1986) 21. H.H. Farrell, M.M. Traum, N.V. Smith, W.A. Royer, D.P. Woodruff and P.D. Johnson, Surface Sci 102 (1981) 527. W.M. Kang, C.H. Li and S.Y. Tong, Solid State Commun. 36 (1980) 149. S.D. Kevan, D.H. Rosenblatt, D. Denley, B.-C. Lu and D.A. Shirley, Phys. Rev. Lett. 41 (1978) 1565. S.D. Kevan, D.H. Rosenblatt, D.R. Denley, B.-C. Lu and D.A. Shirley, Phys. Rev. B 20 (1979) 4133. M.D. Crapper, C.E. Riley, P.J.J. Sweeney, C.F. McConville, D.P. Woodruff and R.G. Jones, Europhys. Lett. 2 (1986) 857. M.D. Crapper, C.E. Riley, P.J.J. Sweeney, C.F. McConville, D.P. Woodruff and R.G. Jones, Surface Sci 182 (1987) 213. J.J. Barton, C.C. Bahr, S.W. Robey. Z. Hussain, E. Umbach and D.A. Shirley, Phys. Rev. B 34 (1986) 3802. C.C. Bahr, J.J. Barton, 2 . Hussain, S.W. Robey, J.G. Tobin and D.A. Shirley, Phys. Rev. B 35 (1987) 3773. S.W. Robey, C.C. Bahr, Z. Hussain, J.J. Barton, K.T. Leung, J.-R. Lou, A.E. Schach von Wittenau and D.A. Shirley, Phys. Rev. B35 (1987) 5657. D.P. Woodruff, Surface Sci 166 (1987) 377. D.P. Woodruff, Vacuum, 39 (1989) 621 D.P. Woodruff, C.F. McConville, A.L.D. Kilcoyne, Th. Lindner, J. Somers, M. Surman, G . Paolucci and A.M. Bradshaw, Surface Sci, 201 (1988) 228. J. Stohr, D. Outka, R.J. Madix and U. Dobler, Phys. Rev. Lett. 54 (1985) 1256. D. Outka, R.J. Madix and J . Stohr, Surface Sci. 164 (1985) 235. A. Puschmann, J. Haase, M.D. Crapper, C.E. Riley and D.P. Woodruff, Phys. Rev. Lett. 54 (1985) 2250. M.D. Crapper, C.E. Riley, D.P. Woodruff, A. Puschmann and J. Haase, Surface Sci 171 (1986) 1. M.D. Crapper, C.E. Riley and D.P. Woodruff, Surface Sci 184 (1987) 121. Th. Lindner, J. Somers, A.M. Bradshaw, A.L.D. Kilcoyne and D.P. Woodruff, Surface Sci, 203 (1988) 333 D.P. Woodruff, D. Norman, B.W. Holland, N.V. Smith, H. H. Farrell and M.M. Traum, Phys. Rev. Lett. 41 (1978) 1130. N.V. Smith, H.H. Farrell, M.M. Traum, D.P. Woodruff, D. Norman, M . S . Woolfson and B.W. Holland, Phys. Rev. 821 (1980) 3119. S.Y. Tong, W.M. Kang, D.H. Rosenblatt, J.G. Tobin and D.A. Shirley, Phys. Rev. B27 (1983) 4632. A.L.D. Kilcoyne, D.P. Woodruff, Th. Lindner, J . Somers and A.M. Bradshaw, J. Vac. Sci. Technol. A 7 (1989) 1926. A.L.D. Kilcoyne, D.P. Woodruff, A.W. Robinson, Th. Lindner, J. Somers, D. Ricken and A.M. Bradshaw Far. Disc. Chem. SOC. 89 (1990). A.W. Robinson, J. S. Somers, A.M. Bradshaw, A.L.D. Kilcoyne and D.P. Woodruff, Surface Sci., in press. A.W. Robinson, D.P. Woodruff, J . S . Somers, A.L.D. Kilcoyne, D.E. Ricken and A.M. Bradshaw, Surface Sci., to be published. A. Robinson, Th. Lindner, J. Somers, A.M. Bradshaw, A.L.D. Kilcoyne and D.P. Woodruff, to be published. S.D. Kevan, R.F. Davis, D.H. Rosenblatt, J . G . Tobin, M.G. Mason, D.A. Shirley, C.H. Li and S.Y. Tong, Phys. Rev. Lett. 46 (1987) 1629. C.F. McConville, D.P. Woodruff, K.C. Prince, G. Paolucci, V. Chab, M. Surman and A.M. Bradshaw, Surface Sci. 166 (1986) 221. D.E. Ricken, A.W. Robinson, J . S . Somers, A.M. Bradshaw, A.L.D. Kilcoyne and D.P. Woodruff, to be published. A.L.D. Kilcoyne, D.P. Woodruff, A.W. Robinson, J . S . Somers and A.M. Bradshaw, to be published L.-G. Petersson, S . Kono, N.F.T. Hall, C.S. Fadley and J.B. Pendry, Phys. Rev. Lett 42 (1979) 1545.
290
67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78.
79. 80. 81. 82 *
P.J. Orders, S. Kono, C.S. Fadley, R. Trehan and J.T. Lloyd, Surface Sci 119 (1982) 371. D.A. Wesner, F.P. Coenen and H.P. Bonzel, Surface Sci. 199 (1988) L419. K.C. Prince, E. Rolub-Krappe, K. Horn and D.P. Woodruff, Phys. Rev. B32 (1985) 4249. E. Holub-Krappe, K.C. Prince, K. Horn and D.P. Woodruff, Surface Sci 173 (1986) 176. D.A. Wesner, F.P. Coenen and H.P. Bonzel, Phys. Rev. Lett. 60(1988) 1045. W.F. Egelhoff, Jr, Phys. Rev. 830 (1984) 1052. S.A. Chambers, S.B. Anderson and J.H. Weaver, Phys. Rev. 8. 32 (1985) 581. Tran Minh Duc, C. Guillot, Y. Lassailly, J. Lecante, Y. Jugnet and J.C. Vedrine. Phys. Rev. Lett. 43 (1979) 789. J.F. Van der Veen, F.J. Himpsel and D.E. Eastman, Phys. Rev. Lett, 44 (1980) 189. W.F. Egelhoff, Jr., Surface Sci 141 (1984) L324. D. Sebilleau, M.C. Desjonqueres, D. Chauveau, C. Guillot and J. Lecante, G. Treglia and D.Spanjaard. Surface Sci, 185(1987) L527. D. Sebilleau, G. Treglia, M.C. Desjonqueres, D. Spanjaard, C. Guillot. D. Chauveau and J. Lecante, J. Physique, (Paris), 49(1988) 227. Y. Jugnet, N.S. Prakash, L. Porte, Tran Minh Duc. T.T.A. Nguyen, R. Cinti, H.C. Poon and G. Grenet, Phys. Rev. B 37(1988) 8066. B. Sinkovic and C.S. Fadley, Phys. Rev. B 31 (1985) 4665. B. Sinkovic, B. Hermsmeier and C.S. Fadley, Phys. Rev. Lett. 55 (1985) 1227. D.E. Eastman, F.J. Himpsel and J.F. Van der Veen, J.Vac.Sci.Techno1. 20 (1982) 609
29 1
Chapter 8
ATOMIC CHEMISORPTION A. GOLDMANN
1 INTRODUCTION
Considerable
experimental
and t h e o r e t i c a l work w i t h i n t h e l a s t
years
been d e v o t e d t o t h e s t u d y o f a t o m i c a d s o r p t i o n on low-index s u r f a c e s . due
t o the fact,
t h a t " s i n g l e " f o r e i g n atoms physisorbed
has
This
is
( d u e t o t h e Van d e r
Waals d i s p e r s i o n f o r c e ) o r c h e m i s o r b e d ( v i a a n a t t r a c t i v e exchange i n t e r a c t i o n ) on
a f o r m e l y c l e a n and w e l l - c h a r a c t e r i z e d
ther
simple
questions:
problem. On
which
s u r f a c e r e p r e s e n t an a p p a r e n t l y
S u r f a c e s c i e n c e f o c u s e s its i n t e r e s t t o site
d o e s t h e f o r e i g n atom a d s o r b ?
the
What a r e
ra-
fallowing the
bond
l e n g t h s t o t h e ( s u b s t r a t e ) n e i g h b o u r s , what a r e t h e bond a n g l e s ? \dhich e l e c t r o n
of
orbitals functions? gies?
Does
t h e a d s o r b a t e o v e r l a p a n d / o r i n t e r a c t w i t h which
substrate
How a r e t h e s e o r b i t a l s s p a t i a l l y o r i e n t e d and what a r e t h e i r t h e geometry o f t h e s u b s t r a t e change by a d s o r p t i o n ?
wave ener-
What a r e
the
thermodynamic p r o p e r t i e s of a d s o r b e d a t o m s ? A n g l e - r e s o l v e d p h o t o e m i s s i o n ( A R P ) s h o u l d be a b l e t o s u p p l y a n s w e r s t o sever a l of t h e f o r e m e n t i o n e d q u e s t i o n s , p r o p e r t i e s a r e intimately connected.
s i n c e a l l t h e s e e l e c t r o n i c and g e o m e t r i c a l It t u r n s o u t ,
experimental problems prevent d e f i n i t e answers: p r e s e n t v e r y low c o v e r a g e s . rent
however,
First,
that i n
" i s o l a t e d " adatoms re-
Hence t h e i r c o n t r i b u t i o n t o t h e o b s e r v e d p h o t o c u r -
w i l l o f t e n b e i n v i s i b l e a s compared t o p h o t o e m i s s i o n f r o m t h e
Second,
no
general
substrate.
It
r e a l s u r f a c e i s p e r f e c t l y smooth on an a t o m i c s c a l e .
exhibits
s t e p s , k i n k s , d i s l o c a t i o n s and o t h e r d e f e c t s of low s u r f a c e c o n c e n t r a t i o n which d i f f i c u l t t o d e t e c t and e v e n more d i f f i c u l t t o q u a n t i f y .
are
may t h e n b e t r a p p e d by s u c h d e f e c t s , would
not
yield
" S i n g l e " adatoms
and t h e i r i n v e s t i g a t i o n by
any i n f o r m a t i o n r e l a t e d t o t h e o r d e r e d
photoemission
low-index
plane
of
interest. T h e r e f o r e most ARP-studies c o n c e n t r a t e on h i g h e r a d s o r b a t e c o v e r a g e s , c a l l y between one t e n t h o f a monolayer and w e l l - o r d e r e d o v e r l a y e r s , adsorbates
contribute clearly detectable intensity,
g o v e r n e d by t e r r a c e - s i t e s ,
where
t h e a d s o r p t i o n p r o c e s s is
and t h e i n f l u e n c e o f d e f e c t s i s n e g l i g i b l e . I n p a r -
t i c u l a r t h e 2D o r d e r e d o v e r l a y e r s have a t t r a c t e d e x p e r i m e n t a l a s w e l l a s retical interest. face
typithe
theo-
B e c a u s e of t h e i r p e r i o d i c i t y , t h e wave v e c t o r k,, i n t h e sur-
B r i l l o u i n zone (SBZ) i s a good quantum number,
l e v e l s a r e b a n d s i n a 20 band structure E ( k , , ) ,
and t h e e l e c t r o n i c e n e r g y
which i s i m m e d i a t e l y a c c e s s i b l e
292
to
ARP.
Moreover,
t h e long-range o r d e r e n a b l e s t h e use of d i f f r a c t i o n
n i q u e s l i k e LEE0 o r He-atom s c a t t e r i n g f o r d e t a i l e d s t r u c t u r a l and
makes d e t a i l e d c a l c u l a t i o n s o f t h e i n t e r p l a y between t h e e l e c t r o n i c energy
bands and g e o m e t r i c a l parameters p o s s i b l e . a
tech-
investigations,
variety
strongly
of
a d s o r p t i o n systems,
chemisorbed
Such 20 bands have been s t u d i e d f o r
ranging
from
physisorbed
atoms on f r e e - e l e c t r o n - l i k e m e t a l s ,
rare-gases
d-band
to
metals
and
semiconductors. We w i l l i n s p e c t s e v e r a l t y p i c a l examples f u r t h e r below. The
l a t e r a l i n t e r a c t i o n s observed among adsorbed atoms a t h i g h e r
coverages
may be e i t h e r by d i r e c t o r b i t a l o v e r l a p ( " t h r o u g h space") o r i n d i r e c t l y t h r o u g h e l e c t r o n i c l e v e l s of t h e s u b s t r a t e .
the
substrate
has
dispersion
I n cases o f weak
physisorption,
o f t e n o n l y l i t t l e e f f e c t on t h e 20 e l e c t r o n i c bands
is
almost
e x c l u s i v e l y determined by d i r e c t
lateral
and
the their
interaction.
Physisorbed
l a y e r s a r e t h u s model systems t o s t u d y ( n e a r l y ) " i s o l a t e d "
monolayers.
We w i l l t h e r e f o r e r e v i e w such d a t a , d e s p i t e some c o n f l i c t w i t h t h e
c h a p t e r heading, i n s e c t i o n 2.1. gen
atomic
I n s e c t i o n 2.2 we f o c u s o u r i n t e r e s t t o hydro-
as t h e " s i m p l e s t " atomic adsorbate on t r a n s i t i o n
metal
surfaces.
Oxygen
c h e m i s o r p t i o n w i l l be d i s c u s s e d i n s e c t i o n 2.3, w i t h t h e n o b l e m e t a l s Cu and Ag as s u b s t r a t e s . layers
substrate,
On t h e same s u r f a c e s ,
s t r o n g i n t e r a c t i o n s w i t h i n halogen-over-
been observed which a r e p r e s e n t e d i n s e c t i o n 2.4.
have
To change
the
s e c t i o n 2.5 r e p o r t s about halogens on semiconductors. F i n a l l y , sec-
t i o n 3 p r e s e n t s an o u t l o o k t o some f u t u r e p o s s i b i l i t i e s o f ARP.
2
SELECTED EXPERIMENTAL RESULTS
2.1 I n t e r a c t i o n s i n rare-gas l a y e r s As
already
systems. near
physisorbed rare-gas l a y e r s are prototypes
B a n d - s t r u c t u r e c a l c u l a t i o n s by Hermann e t a l .
rigorous
strongly
mentioned, cellular
(LRC)
method show t h a t t h e
c o r r e l a t i o n was f i r s t v e r i f i e d by M a r i a n i e t a l . system shows a commensurate -incommensurate
rage
of
ordered
about 0.9 monolayers:
(ref.
widths
2) f o r Xe on
quite this
Cu(ll0).
phase t r a n s i t i o n a t a
cove-
a ~ ( 2 x 2 )o r d e r e d o v e r l a y e r t r a n s f o r m s i n t o
pseudohexagonal compressed l a y e r as more Xenon i s adsorbed.
[1?0] azimuth.
are
Experimentally,
p r e s s i o n occurs o n l y a l o n g t h e t r o u g h s o f t h e C u ( l l 0 ) s u r f a c e , in
2D
( r e f . 1) u s i n g t h e liband
dependent on t h e adsorbate-adsorbate d i s t a n c e .
This
for
i.e.
The
an com-
along t h e
The d i s t a n c e between Xe atoms l o n g t h e [1?0] t r o u g h s i s 5.10
t h e ~ ( 2 x 2 )l a y e r and 4.58
8
i n t h e incommensurate l a y e r .
1
The c o r r e s p o n d i n g
geometries o f r e a l and r e c i p r o c a l space a r e summarized i n F i g . 1. A s e t o f ARP s p e c t r a t a k e n w i t h He Ir a d i a t i o n f r o m t h e incommensurate phase a t maximum Xe coverage i s reproduced f r o m t h e work o f M a r i a n i e t a l .
(ref.
2)
293
(c)
R
R.
&$O 0
0
(d 1
incommensurate
Oo 0
0
Q k
0
OR. 0
F i g . 1. S t r u c t u r e models f o r t h e c(2x2)-Xe l a y e r ( a , b) and t h e maximum cover a g e xenon l a y e r ( c , d) on C u ( l l 0 ) . I n F i g u r e s (b) and ( d ) t h e d i r e c t l a t t i c e i s r e p r e s e n t e d by f i l l e d c i r c l e s , w h i l e empty c i r c l e s i n d i c a t e t h e r e c i p r o c a l l a t t i c e . Note t h a t o n l y t h e T K d i s t a n c e i s changed upon t h e phase t r a n s i t i o n , w h i l e TM i s u n a l t e r e d . Data f r o m r e f . 2 .
LO0 30°
zoo .. .. . ..-.- ::..t Z' 9
I
I
8
7
I
I
-I
1oo , ?
..
O0
c
I
I
I
6 5 L 3 2 1 Energy below EF lev)
EF
F i g . 2. Angle-dependent s p e c t r a t a k e n f r o m an incommensurgte o r d e r e d xenon l a y e r on C u ( l l 0 ) as a f u n c t i o n o f p o l a r a n g l e 3 a l o n g t h e [110] azimuth. Sample t e m p e r a t u r e T = 45 K , photon energy 21.2 eV (ref. 2 ) .
i n Fig.
2.
The p r o m i n e n t Xe 5p bands (5-8 eV below EF) a r e e n e r g e t i c a l l y w e l l
s e p a r a t e d f r o m t h e s u b s t r a t e Cu 3d s t a t e s (2-4 eV below EF). dispersion
with
They show a c l e a r
e l e c t r o n e m i s s i o n a n g l e 0 , w i t h maximum s h i f t
about 0 . 8 eV. I t i s now s t r a i g h t f o r w a r d t o determine
k,, = s i n 0-[ (2m/?i2) .E
11" kin
amounting
to
294
a l o n g t h e e x p e r i m e n t a l azimuth,
= ho
where E nki
-
is t h e obser-
- @ , Ei
\Eil
ved peak p o s i t i o n below EF, and 0 i s t h e work f u n c t i o n o f t h e adsorbate-covered sample. strate
R e s u l t s s i m i l a r t o F i g . 2 have a l s o been o b t a i n e d a l o n g t h e "3011 subazimuth
azimuths i.e.
f r o m t h e maximum coverage incommensurate l a y e r ,
f r o m t h e commensurate ~ ( 2 x 2 )l a y e r .
peak
position
The e x p e r i m e n t a l
a r e summarized i n F i g . 3.
v e r s u s k,,,
and f o r energy
It
is
both bands,
immediately
e v i d e n t f r o m these r e s u l t s , t h a t t h e shape o f t h e bands i s s i m i l a r and r e f l e c t s t h e dimensions o f t h e SBZ, same
within
reach and
o r along
along a
compare F i g . 1. We n o t e t h a t t h e energy a t
t h e e x p e r i m e n t a l error o f
rough
m. I n f a c t ,
0 . 1 eV,
irrespective o f
t o the
line,
difference
between
t h e two
we
f r o m t h e shape o f t h e d i s p e r s i o n curves
knowledge o f t h e SBZ dimensions we can
corresponds
i s the
whether
assess
which
s i n c e E(k,,) must be symmetric around data sets i n Fig. 3 i s t h a t
the
8.
direction The main
bandwidths
are
i n c r e a s e d c o n s i d e r a b l y for t h e compressed l a y e r .
!
I
.
0.5
I
R
I
1.0
I ,
1.5
,
P
I
P
I
0.5
I
I
Rl.0
I
1
fi 1.5
k,,tA"I
F i g . 3 . E x p e r i m e n t a l 20 band s t r u c t u r e s o f Xe on C u ( l l 0 ) i n t h e ~ ( 2 x 2 )mer, t h e maximum coverage incommensurate l a y e r , bottom, along t h e TM and TKM d i r e c t i o n s of t h e s u r f a c e B r i l l o u i n zone. S u b s t r a t e t e m p e r a t u r e s were 75 K ( t o p ) and 45 K ( b o t t o m ) . All d a t a f r o m r e f . 2.
9, and
295
Before we d i s c u s s t h e d i s p e r s i o n curves f u r t h e r , of
t h e t h r e e bands a t k,, = 0
only
t w o peaks.
i n t o 5p
origin
s p e c t r a f r o m gaseous Xe
These a r e due t o e m i s s i o n f r o m t h e 5p o r b i t a l ,
which
show splits
and 5p components by t h e s p i n - o r b i t i n t e r a c t i o n . The onset o f t h e 312 i n t e r a c t i o n w i t h i n t h e Xe l a y e r l o w e r s t h e symmetry f u r t h e r and l i f t s
1/2
lateral the
(TI. P h o t o e l e c t r o n
l e t us e x p l a i n t h e
degeneracy ( a t f i x e d a n g u l a r momentum j ) o f s t a t e s w i t h d i f f e r e n t magnetic
quantum
numbers m . .
subbands with m . = ref.
J
T h i s l e a d s t o a f u r t h e r s p l i t t i n g o f t h e p312
1 / 2 and m . =
J
J
4 ) . I n f a c t , t h r e e peaks a r e observed f r o m t h e ~ ( 2 x 2 ) l a y e r a t
shown i n F i g . linear
band
r. T h i s
lines).
8). However, t h e
(ref.
data
additional
f r o m t h e compressed l a y e r ( F i g .
i.These
layers (ref.
peaks
The assignment o f quantum numbers has been c o n f i r m e d r e c e n t l y
by s p i n - p o l a r i z e d ARP experiments o f Schonhense e t a l .
label
i s
4a which reproduces t h e e x p e r i m e n t a l r e s u l t ( s o l i d l i n e ) a f t e r a
background s u b t r a c t i o n and i t s decomposition i n t o t h r e e Gaussian
(dashed
into
312 (Horn e t a l . , r e f . 3, S c h e f f l e r e t a l . ,
have
2-7).
4b) e x h i b i t t w o
been observed f r e q u e n t l y i n ARP s p e c t r a
structures,
from
rare-gas
They do n o t d i s p e r s e w i t h 0 and a r e t h e r e f o r e assigned
to
i n d i r e c t t r a n s i t i o n s . Obviously t h e y do n o t conserve k,, and g i v e r i s e t o angleaveraging density
m a i n l y f r o m t h e v i c i n i - t y of c r i t i c a l p o i n t s w i t h h i g h
emission, of
states.
The
physical
mechanism
leading
t o
these
20
indirect
> c m
c
01
4-
c
H
I
I
I
7
I
5
Energy below E,(eV)
F i g . 4 . Comparison o f Xe 5p p h o t o e m i s s i o n peaks observed ( a f t e r background subt r a c t i o n ) i n normal e m i s s i o n f r o m ( a ) t h e ~ ( 2 x 2 )l a y e r and (b) t h e compressed l a y e r a t maximum coverage on C u ( l l 0 ) . Note t h e i n d i r e c t t r a n s i t i o n s (arrows) i n t h e spectrum o f t h e incommensurate l a y e r . The t h r e e main peaks (dashed l i n e s ) a r e l a b e l e d by quantum numbers a p p r o p r i a t e a t k,, = 0 . Data f r o m r e f . 2.
296 Cassuto e t a l . ( r e f . 6) and Mandel e t a l .
c o n t r i b u t i o n s has l o n g been detabed.
7)
(ref.
discuss
e x p e r i m e n t a l evidence t h a t (even weak) d i s o r d e r w i t h i n
xenon l a y e r produces s t r o n g enhancement of t h e i n d i r e c t t r a n s i t i o n s .
LEE0
good
patterns
were observed i n t h e cases
reported
above.
the
Note t h a t This
again
demonstrates t h e h i g h . s e n s i t i v i t y o f ARP t o t h e s u r f a c e p e r f e c t i o n ( r e f . 6 ) . Returning t o Fig.
3 we see t h a t t h e moderate compression o f t h e xenon l a y e r
(about 11 % o f t h e d i s t a n c e between atoms a l o n g an
i n c r e a s e i n bandwidth e . g .
-
TM.
o f the p
I n addition, the s p l i t t i n g o f the p
interaction,
is
[ 1701,
band f r o m 0.20 eV t o 0.40 eV
112
has
rized
3/2
a l s o c l e a r l y i n c r e a s e d e.g.
at
w.
Thus a s t r o n g
For
i n Fig.
comparison
supported
5.
This
exists.
summa-
The f i l l e d symbols i n d i c a t e t h e observed band w i d t h o f
monolayer ( r e f .
1) are included.
the
substrates.
t h e r e s u l t s o f t h e LRC b a n d - s t r u c t u r e c a l c u l a t i o n f o r
experiment i s q u i t e good. (open
dependence
been v e r i f i e d f o r s e v e r a l o t h e r systems and some r e s u l t s a r e
band f o r hexagonal monolayers o f Xe p h y s i s o r b e d on d i f f e r e n t
5p1,2
along
band which i s caused by t h e l a t e r a l
between t h e energy band d i s p e r s i o n and t h e s t r u c t u r a l parameters fact
1) causes
compare F i g .
an
The agreement between t h e o r y
unand
We have a l s o p l o t t e d i n F i g . 5 t h e r e s u l t s o f r e f . 2
c i r c l e s ) f o r pseudohexagonal arrangements of Xe.
Although t h e
calcula-
t i o n s were performed f o r a hexagonal l a y e r , t h e c o r r e l a t i o n i s e v i d e n t .
Graphite 10011,Ref 7
0 Al l1111, Ref 5
Pdl0011,Ref3
06
A
Pt 11111. Ref 6
n. n. Xe -Xe distance
(A)
F i g . 5 . Band w i d t h o f 5p subband f o r a hexagonal monolayer o f Xe p h y s i s o r b e d on v a r i o u s s u b s t r a t e s a s 1 i 2 f u n c t i o n o f t h e Xe-Xe d i s t a n c e ( f u l l symbols). Open squares c a l c u l a t e d f o r an unsupported monolayer, dashed l i n e o n l y serves t o g u i d e t h e eyes. A f t e r r e f . 7. Open c i r c l e s : e x p e r i m e n t a l r e s u l t s f o r pseudohexagonal arrangements o f Xe on C u ( l l 0 ) f r o m r e f . 2 .
Physisorbed
rare-gas m u l t i - l a y e r s o f f e r t h e unique experimental p o s s i b i l i t y
t o study l a y e r - b y - l a y e r
band d i s p e r s i o n s .
e m i s s i o n f r o m t h e work o f Mandel e t a l . spectrum. of a Xe monolayer,
Corresponding ARP s p e c t r a a t
normal
( r e f . 5) a r e reproduced i n F i g . 6. The
w e l l a l i g n e d b u t incommensurate w i t h t h e
Al(111)
297 r
I
I
I
XelAl (111)
I
Normal Emission d) Trilayer a
.
i el Monoloyer
h v = 21 2eV
. 'a
:-
1st Layer
o2nd Layer A
00
..
*.
l"d,, I r o n s
a) Monolayer
I
r
Indirect
110
-
00
110
I
M
-13 -12 -11 -10 -9 Binding Energy re1 l o EvAcleV1
F i g . 6 . Normal-emission ARP s p e c t r a o f (a) a monolayer, (b) a b i l a y e r , (c) about 2.5 l a y e r s and (d) a t r i l a y e r o f Xe adsorbed on A l ( 1 1 1 ) . D i r e c t and i n d i r e c t t r a n s i t i o n s f r o m t h e f i r s t (second) l a y e r a r e i n d i c a t e d by s o l i d (dashed) l i n e s . F e a t u r e s A and A' a r e due t o d i r e c t t r a n s i t i o n s f r o m Xe b u l k bands ( r e f . 5 ) . E x p e r i m e n t a l 20 energy bands a r e d e r i v e d f r o m angle-dependent s p e c t r a o f t h e monolayer (e) and f o r t h e two l a y e r s o f t h e b i l a y e r ( f ) . From r e f . 5.Curves t h r o u g h t h e d a t a p o i n t s r e p r e s e n t c a l c u l a t i o n s f o r an unsupported monolayer ( r e f . l), d i s p l a c e d by layer-dependent b i n d i n g - e n e r g y s h i f t s .
s u b s t r a t e , i s shown i n F i g . 6a. A s expected i t i s v e r y s i m i l a r t o t h e r e s u l t o f Fig.
4b. The spectrum o f t h e b i l a y e r , F i g . 6b, i s composed o f almost i d e n t i c a l
s i n g l e - l a y e r c o n t r i b u t i o n s f r o m t h e f i r s t and t h e second Xe l a y e r , s e p a r a t e d by a
b i n d i n g energy s h i f t o f 0.50 eV.
differences
in
T h i s layer-dependent s h i f t i s e x p l a i n e d by
t h e image-charge s c r e e n i n g o f t h e p h o t o h o l e l e f t
in
the
two
l a y e r s ( f o r d e t a i l s , see a l s o r e f . 9 and 1 0 ) . W i t h i n c r e a s i n g Xe coverage ( F i g . 6c,
from
d) new s t r u c t u r e s A and A' bulk-Xe.
energy:
the
The
become dominant, which a r e a s c r i b e d t o emission
l a t t e r assignment i s c o n f i r m e d by v a r i a t i o n o f t h e
b u l k peaks e x h i b i t a s h i f t w i t h ho a t n o r m a l e m i s s i o n (k,,
i n d i c a t i n g a dependence on kl
as expected f o r t h r e e - d i m e n s i o n a l bands.
photon =
O),
I n con-
298
t r a s t , no
with
such s h i f t s a r e observed i n t h e b i l a y e r spectrum, i n agreement
t h e i n t e r p r e t a t i o n o f e m i s s i o n o u t o f t w o 20 energy bands. From
angle-dependent
ARP s p e c t r a t a k e n a l o n g t h e
direction o f
SBZ
the
( i n s e r t i n F i g . 6e) t h e e x p e r i m e n t a l band d i s p e r s i o n s f o r t h e monolayer and t h e see F i g u r e s 6e and 6f. We see t h a t
b i l a y e r c o n f i g u r a t i o n s c o u l d be determined, the
o f t h e second l a y e r o f t h e b i l a y e r (dashed l i n e s i n
bands
Fig.
6f)
are
almost i d e n t i c a l t o t h o s e i n t h e f i r s t l a y e r , e x c e p t f o r t h e r i g i d s h i f t by 0.5 eV.
Also, t h e f i r s t l a y e r bands r e m a i n unchanged upon a d s o r p t i o n o f t h e second
layer.
The
s o l i d c u r v e s drawn t h r o u g h t h e d a t a p o i n t s a r e f r o m t h e LRC c a l c u -
l a t i o n s o f Hermann e t a l .
(ref.
1 ) f o r an unsupported monolayer, w i t h a Xe-Xe
d i s t a n c e a c c o r d i n g t o t h e experiment.
The dashed c u r v e s i n F i g . 6 f a r e i d e n t i -
e x c e p t f o r a r i g i d s h i f t by 0.50 eV.
cal both
cases.
The d a t a o f F i g .
f i r s t t w o Xe l a y e r s .
Moreover,
obtained
such s t u d i e s a l l o w t o i d e n t i f y t h e
20 t o 30 b u l k band f o r m a t i o n and,
from
E x c e l l e n t agreement i s
in
6 n i c e l y c o n f i r m t h e almost 20 c h a r a c t e r o f t h e
i n particular,
transition
t o obtain quantitative
r e s u l t s w i t h r e s p e c t t o f i n a l - s t a t e h o l e - s c r e e n i n g e f f e c t s . F i n a l l y , we mention a r e c e n t study ( r e f .
t h e band w i d t h s of
7) o f a Xe b i l a y e r on g r a p h i t e ( 0 0 1 ) :
second l a y e r a r e observed t o be much s m a l l e r t h a n t h o s e o f t h e
the
monolayer.
According t o F i g . 5 t h i s i n d i c a t e s i n c r e a s e d Xe-Xe d i s t a n c e . I n f a c t , t h e monol a y e r and t h e f i r s t l a y e r o f t h e b i l a y e r a r e compressed, w h i l e t h e second l a y e r approaches spacings t y p i c a l f o r b u l k Xe.
I n conclusion,
t h e study o f rare-gas
l a y e r s allows t o i n v e s t i g a t e l a t e r a l i n t e r a c t i o n s i n considerable d e t a i l .
Even
s t r u c t u r a l i n f o r m a t i o n may be o b t a i n e d from t h e a n a l y s i s o f ARP r e s u l t s .
2 . 2 Hydrogen on t r a n s i t i o n m e t a l s Hydrogen on
(H2) i s a c h e m i c a l l y r e a c t i v e gas which chemisorbs
most t r a n s i - t i o n m e t a l s .
electron,
and
the
p r o t o t y p e system.
The i n t e r a c t i o n between t h e H atom,
introduces
It t u r n e d o u t ,
altered
a
simple
however, t h a t t h i n g s a r e r a t h e r c o m p l i c a t e d : surface.
Therefore
a strong p e r t u r b a t i o n t o several neighbouring substrate
t h e a d s o r p t i o n s i t e has a h i g h c o o r d i n a t i o n ,
is
w i t h o n l y one
m e t a l s u r f a c e has been viewed f o r many y e a r s as
due t o i t s s m a l l s i z e t h e H atom can g e t v e r y c l o s e t o t h e it
dissociatively
and o f t e n t h e s u b s t r a t e
by r e l a x a t i o n o r even r e c o n s t r u c t i o n ,
atoms, geometry
see f o r example t h e
recent
review
by Christmann ( r e f .
distinction
between
mutual
i n t e r a c t i o n s w i t h i n an o v e r l a y e r and i n t e r a c t i o n s n o r m a l t o o r
through
the
surface g e t s l o s t .
11). I n consequence a c l e a r
N e v e r t h e l e s s one may s t a t e t h a t t h e H / m e t a l system
dominated by adatom-substrate f o r c e s , generally
is
w h i l e t h e adatom-adatom i n t e r a c t i o n s a r e
much weaker ( t y p i c a l l y 1 / 1 0 of t h e h e a t o f c h e m i s o r p t i o n ,
see
ref.
11).
ARP
monitors
H induced changes of t h e surface e l e c t r o n i c
structure
often
299
quite sensitively. a r e observed, is
shown
I n most c a s e s f a i r l y b r o a d r e s o n a n c e s a t 5
10 eV below EF which are sometimes v e r y weak and e a s i l y o v e r l o o k e d . An example
i n Fig.
-
7 where we r e p r o d u c e r e s u l t s o b t a i n e d by E b e r h a r d t
et
al.
( r e f . 1 2 ) f o r H on P d ( l l 1 ) . F i g . 7a shows t h e e f f e c t of s a t u r a t e d H2 a d s o r p t i o n
a t T = 100 K ,
which c o r r e s p o n d s t o 1 monolayer of a t o m i c H, on normal e m i s s i o n
s p e c t r a . S e v e r a l o b s e r v a t i o n s a r e o b v i o u s : ( 1 ) t h e d-band e m i s s i o n s t r u c t u r e i n the
f i r s t 4 eV below EF c h a n g e s d r a s t i c a l l y w i t h H a d s o r p t i o n ;
( 2 ) t h e new H-
i n d u c e d l e v e l ( a r r o w ) below t h e d-bands o f Pd d o e s n o t s h i f t when h v i s changed from 40 eV t o 50 eV,
a n e c e s s a r y c o n d i t i o n f o r 20 c h a r a c t e r ; (3) t h e H peak i s
accidentally
below a s e c o n d a r y e l e c t r o n e m i s s i o n peak a t hv =
This
hidden
s t r u c t u r e r e m a i n s a t a c o n s t a n t k i n e t i c e n e r g y a s t h e photon t h e use o f s e v e r a l photon e n e r g i e s a t
changed.
Hence,
Fig.
reproduces s i m i l a r data taken a t t h e
7b
K point
r was q u i t e
eV.
is
important.
o f t h e SBZ:
i n d u c e d l e v e l h a s d i s p e r s e d from - 7 . 9 eV a t r t o -5.9 eV a t
30
energy now t h e
K. However,
H-
indica-
t i n g 20 c h a r a c t e r , i t s p o s i t i o n i s i n d e p e n d e n t o f hv
- clean
30 e I
-5 O=EF Initial state energy (eV1 - 10
I
f
1
1
,
1
1
1
I
-10 -5 O=EF Initial state energy (eV)
F f g . 7 ( a ) Normal-emission s p e c t r a from P d ( l l 1 ) and P d ( l l l ) ( l x l ) - H a t 100 K f o r d i f f e r e n t p h o t o n e n e r g i e s hv. ( b ) S p e c t r a t a k e n a t K f o r t h e same system. The c o l l e c t i o n a n g l e was a d j u s t e d a t e a c h h v t o keep k,, f i x e d f o r an i n i t i a l s t a t e e n e r g y E. = - 3 eV. A l l d a t a from r e f . 1 2 .
300
( a ) Pd(111) (1x1) - H
( b ) Ru(001) (1x1)-H E= , 0 -1
-2 -3 -1.
-5
-6 -7
-a
-
r
-
r
k
k
K
-
r
F i g . 8 ( a ) C a l c u l a t e d and measured s u r f a c e e l e c t r o n i c bands f o r P d ( l l l ) ( l x l ) - H . Shaded r e g i o n s : B u l k band s t r u c t u r e p r o j e c t e d o n t o t h e (111) s u r f a c e . S o l i d l i n e s : c a l c u l a t e d s u r f a c e s t a t e s o r resonances. S o l i d c i r c l e s : e x p e r i m e n t a l d a t a . A l l d a t a f r o m r e f . 12. ( b ) Analogous r e s u l t s f o r ( 1 x l ) H on Ru(001). Data f r o m r e f . 13.
It
is now easy t o use t h e d i s p e r s i o n of t h e H peak w i t h e m i s s i o n
and/or
with h u ( a t 0
d 0)
angle
t o determine t h e s i z e and symmetry o f t h e H
0
overlay
u n i t c e l l . The r e s u l t s o f E b e r h a r d t e t a l . ( r e f . 12) a r e summarized i n F i g . 8a. As
e v i d e n t t h e d i s p e r s i o n between -6 eV and -8 eV f o l l o w s t h e SBZ
is
s u b s t r a t e a l o n g b o t h azimuths. lation to
t h a t H forms an ordered (1x1) s t r u c t u r e .
the
T h i s f a c t enabled t h e a u t h o r s
analyze t h e H-induced changes o f t h e 0-4 eV e m i s s i o n r a n g e :
cannot
of
We may t h u s conclude w i t h o u t any f u r t h e r c a l c u a (1x1)
i n d u c e s u r f a c e umklapp processes by which b u l k e m i s s i o n f r o m
layer
other
k-
space d i r e c t i o n s may be s c a t t e r e d i n t o t h e d e t e c t o r ( r e f . 1 4 , 1 5 ) . T h e r e f o r e a l l observed
modifications
a r e i n t r o d u c e d by t h e H-metal i n t e r a c t i o n .
A
careful
comparison w i t h t h e s p e c t r a o f t h e c l e a n s u r f a c e t h e n r e v e a l s 2D bands quenched by
H
the
o v e r l a y e r ( t h e s e a r e i n t e r p r e t e d as " i n t r i n s i c "
surface
bands
of
f o r f u r t h e r d e t a i l s see r e f . 12) and new " e x t r i n s i c " 20 bands induced
Pd(lll),
by t h e a d s o r b a t e - s u b s t r a t e c o u p l i n g .
The l a t t e r ones a r e i n c l u d e d i n F i g .
8a.
Also shown is a comparison o f t h e e x p e r i m e n t a l d a t a w i t h t h e o r e t i c a l c a l c u l a tions
by L o u i e ( r e f .
method.
16) u s i n g a s e l f - c o n s i s t e n t p s e u d o p o t e n t i a l
l a r around
7 and K.
ment was performed,
I n the calculation,
which was done b e f o r e t h e ARP e x p e r i -
t h r e e d i f f e r e n t hydrogen s i t e s ( f c c , t h r e e f o l d hcp and on-
t o p ) were t r i e d w i t h a H-Pd bond l e n g t h o f 1.69 metallic equally
mixed-basis
The agreement between t h e o r y and experiment i s r e m a r k a b l e , i n p a r t i c u -
radius
and t h e H c o v a l e n t r a d i u s .
8,
Both
good agreement w i t h t h e e x p e r i m e n t a l bands,
which i s t h e sum o f t h e threefold
geometries
Pd give
w h i l e t h e on-top s i t e can
be excluded. The c a l c u l a t i o n shows t h a t t h e c h e m i c a l bonding a t t h i s s u r f a c e i s
301
mainly between t h e H 1s o r b i t a l and t h e Pd 4d o r b i t a l s .
r.
of t h e H-Pd s p l i t - o f f band below -6 eV i s A1 a t Greuter e t a l .
by
demonstrates
very
17).
Moreover,
comparison of ARP data t o theory may not only
b u t a l s o s u p p l y b a s i c s t r u c t u r a l information.
-
i n the calculation ( r e f .
recently
t h e example of P d ( l l l ) ( l x l ) - H again explain
the
after
ad-
d e t a i l s of t h e e l e c t r o n i c s u r f a c e s t r u c t u r e - both before and
sorption that
that
(ref.
The p r e d i c t e d symmetry
T h i s was v e r i f i e d
We mention,
however,
16) t h e energy p o s i t i o n s of t h e H-induced bands
were found t o be r a t h e r i n s e n s i t i v e t o reasonable v a r i a t i o n s (15 %) of t h e H-Pd d i s t a n c e . This i n d i c a t e s t h e l i m i t a t i o n s of ARP from valence s t a t e s f o r q u a n t i t a t i v e structural analysis. Fig.
8b
shows experimental r e s u l t s of Hofmann and Menzel ( r e f .
13) f o r
a
Ru(001) s u r f a c e exposed t o hydrogen s a t u r a t i o n a t 200 K . Ru(001) i s q u i t e simil a r t o Pd(ll1):
both a r e close-packed s u r f a c e s ,
w i t h almost i d e n t i c a l l a t t i c e
c o n s t a n t s , and a l s o t h e b u l k band s t r u c t u r e s a r e very s i m i l a r . We a r e t h e r e f o r e not
too
t h a t a l s o t h e H-induced energy bands on Ru(001)
surprised
s i m i l a r t o t h e r e s u l t s of Fig.
are
very
8a. I n f a c t , t h e "theory" reproduced i n Fig. 8b
i s t h e r e s u l t of Louie-s c a l c u l a t i o n s f o r Pd ( r e f . 1 6 ) , s h i f t e d r i g i d l y down by eV w i t h r e s p e c t t o EF i n order t o account f o r t h e s l i g h t l y
0.5
w i d t h of Ru.
allows
larger
d-band
The good o v e r a l l agreement of t h e Ru d a t a w i t h t h e s e c a l c u l a t i o n s
two immediate conclusions:
t h e H atoms a r e adsorbed i n t h r e e f o l d s i t e s
and they form an ordered (1x1) overlayer. A very s u c c e s s f u l i n t e r p l a y of theory and
sur-
experiment was a l s o reported f o r a ( 1 x 1 ) - H overlayer on t h e Ti(0001)
f a c e . For d e t a i l s we r e f e r t o t h e work of Feibelman e t a l . ( r e f . 1 8 ) . Another i n t e r e s t i n g example f o r t h e combined geometric and e l e c t r o n i c i n f o r mation of ARP s p e c t r a is given by t h e work of Christmann e t a l . ( r e f . 1 9 ) . They studied This
the
Ni(llO)(lx2)-H s u r f a c e which i s r e c o n s t r u c t e d by
the
system i s prepared a t T = 120 K and corresponds t o a s a t u r a t i o n
( a t 4 L H2) of 1 . 5 monolayers. references buckling
therein)
coverage
Several s t r u c t u r a l i n v e s t i g a t i o n s ( r e f . 1 1 , and
determine a pairing-row c o n f i g u r a t i o n with
f o r t h e N i atoms.
adsorbate.
However,
second
t h e p o s i t i o n s of t h e H atoms
layer
are
still
unknown. Hence t h e e l e c t r o n i c s t r u c t u r e i s not understood, and c a l c u l a t i o n s a r e not a v a i l a b l e . Nevertheless i n t e r e s t i n g conclusions follow from ARP d a t a . T y p i c a l s p e c t r a a r e reproduced i n Fig. 5-10
eV
t i o n s of t h e SBZ. to Y
[lTOl
9.
The resonant H l s - N i band i s observed a t
below E F and e x h i b i t s l a r g e d i s p e r s i o n along t h e h i g h symmetry d i r e c T h i s i s evident from t h e E(k,,)-plot along
of t h e s u b s t r a t e ) and
([OOl])
r e f l e c t t h e dimensions of t h e c l e a n ,
(1x2) reconstruction, t u r a l model of F i g .
a s shown i n F i g .
TX
(corresponding
1 0 . Note t h a t
unreconstructed N i ( l l 0 )
x and
surface.
The
a s observed f o r t h e N i atoms and i n d i c a t e d i n t h e s t r u c 11 l e a d s one t o expect symmetry of t h e H band around
observed indeed, and around
YlX2
which b i s e c t s
5.However,
x, a s
we f i n d an obvious
302
x
c
C
.+.
C
P h o t o e l e c t r o n s p e c t r a (hu = ! . I s V ) of a c l e a n and a (lx2)H-covered s u r f a c e siiowinq a b r o a d H-induced resonance l e v e l ( a r r o w ) . From r e f .
Fig. 9 Ni(ll0)
I
,
I
w--L -9
-lo
15
F i g . 10 Two-dimensional band s t r u c t u r e o f t h e H-induced l e v e l o f t h e ( 1 x l ) H covered N i ( l l 0 ) surface. For d e f i n i t i o n o f symmetry l a b e l s see F i g . 11. Y4xa i n d i c a t e s - t h e boundary o f t h e f i r s t B r i l l o u i n zone o f t h e 1 x 2 r e c o n s t r u c e s u r f a c e , YH shows t h e observed p e r i o d i c i t y of t h e H-band d i s p e r s i o n ( r e f . 1 1 ) . -
symmetry around YH,
i.e.
a t t h r e e t i m e s t h e expected
-
rYlX2 d i s t a n c e .
This i s
o n l y c o n s i s t e n - t w i t h arrangements o f t h e H atoms as i n F i g . 11: a l o n g [lTO] t h e periodicity contains
i s equal t o t h e substrate,
w h i l e a l o n g [ O O l ] t h e (1x2) u n i t
cell
t h r e e e l e c t r o n i c a l l y e q u i v a l e n t H atoms i n an almost c h a i n l i k e a r r a n -
gement ( r e f . 1 9 ) . Finally
we mention an i n t e r e s t i n g f a c t which had induced c o n s i d e r a b l e
con-
f u s i o n f o r some years. As G r e u t e r e t a l . ( r e f . 17) demonstrate f o r H on P d ( l l 1 )
303
F i g . 11 Proposed r e a l space r e p r e s e n t a t i o n ( r e f . 19) o f N i ( l l O ) ( l x 2 ) H . All H atoms ( s m a l l c i r c l e s ) s i t on t e t r a h e d r a l s i t e s , shaded c i r c l e s a r e l o c a t e d below surface atoms. Black and shaded atoms c o n s t i t u t e an almost l i n e a r c h a i n of "subsurface" hydrogen a l o n g [OOl]. The shaded a r e a o f t h e s u r f a c e B r i l l o u i n zone corresponds t o t h e (1x2) s u b s t r a t e u n i t mesh.
w i t h d e c r e a s i n g H c o n c e n t r a t i o n t h e H-induced band below t h e sub-
and N i ( l l l ) ,
s t r a t e b u l k bands moves upwards.
Finally,
a t a H c o n c e n t r a t i o n o f 0.3 ( - 0 . 5 )
o f t h e s a t u r a t i o n coverage f o r Pd ( N i ) , i t merges i n t o t h e b u l k bands and l o s e s i t s identity.
T h i s " i n v i s i b i l i t y " o f H - o r b i t a l s on s u r f a c e s ,
was c l e a r l y d e t e c t e d by o t h e r t e c h n i q u e s as e . g .
t h e r m a l d e s o r p t i o n , had o f t e n
been i n t e r p r e t e d e a r l i e r by s u b s u r f a c e hydrogen s i t e s . interest:
as shown by Himpsel e t a l .
on N i ( l l l ) , invisibly check
where adsorbed H
Another p o i n t may be o f
( r e f . 20) f o r room t e m p e r a t u r e a d s o r p t i o n
hydrogen may i n d u c e c o n s i d e r a b l e i n t e n s i t y enhancement o f ( f o r m e r l y weak) sp-band b u l k t r a n s i t i o n s .
Therefore i t i s q u i t e important
t h e 2D c h a r a c t e r o f H-induced s p e c t r a l changes and t o p r o v e t h e
to
absence
o f d i s p e r s i o n w i t h p h o t o n energy a t f i x e d k,,.
2.3 Oxygen on copper and s i l v e r
Oxygen
reacts
adsorption (ref.
almost a l l elements and a l a r g e b u l k o f
with
exists.
data
on
atomic
F o r e a r l i e r work we r e f e r t o t h e r e v i e w a r t i c l e o f Wandelt
2 1 ) . A p r o t o t y p e system i s t h a t o f a t o m i c oxygen on C u ( l l 0 ) . I n p a r t i c u -
l a r t h e p(2xl)O structure,
c o r r e s p o n d i n g t o one h a l f o f a monolayer o f
0,
is
easy t o p r e p a r e and has a t t r a c t e d much a t t e n t i o n i n s t r u c t u r a l ( r e f . 22-25) and electronic special
(ref.
26-29) s t u d i e s .
Furthermore,
t h e copper-oxygen bond i s
i n t e r e s t w i t h r e s p e c t t o some r e c e n t h i g h T
C
superconductors.
of
We w i l l
t h e r e f o r e d i s c u s s t h i s system i n some d e t a i l .
There in
i s g e n e r a l agreement now t h a t i n C u ( l l O ) p ( 2 x l ) O t h e oxygen atoms
long-bridge s i t e s .
geometrical
structure.
However, In
a debate s t i l l e x i s t s on t h e d e t a i l s
our context it i s o f p a r t i c u l a r i n t e r e s t
reside of that
the an
e x t e n s i v e ARP s t u d y o f t h e oxygen-derived bonding bands (below t h e s u b s t r a t e d-
304
performed by DiDio e t a l .
bands)
(ref.
c l a i m s i n c o n s i s t e n c y w i t h a "missing-row''
27) f a v o r s a "buckled-row''
and
However, a n o t h e r d e t a i l e d ARP
model.
28) l e a d s t h e
authors t o
c o n c l u d e t h a t a l l t h e a v a i l a b l e d a t a do n o t a t a l l c o n t r a d i c t t h e
missing-row
study
t h e same system by C o u r t h s e t a l .
model
of
model.
Obviously
structures.
ARP
However,
(ref.
i s n o t a b l e t o d i s t i n g u i s h between t h e s e two the
photoemission
data
give
clear
different
evidence
that
C u ( l l O ) p ( 2 x l ) O c a n very w e l l be d e s c r i b e d by Cu-0 rows a l o n g t h e [OOl] d i r e c tion. 1
2 Ep a, C
a,
ul .-C U
.c
m
__ p ( 2 x l I OICu(11OI
5-
-
1
62 -
7-
-
x
s - polarized p-polarized
8-
-
-
-
-
-
F i g . 1 2 . L e f t : Top and s i d e view o f t h e missing-row model f o r C u ( l l O ) p ( 2 x l ) O . The oxygen atoms a r e shown by t h e f i l l e d c i r c l e s . 1 , 2 and 3 d e n o t e t h e f i r s t , s e c o n d and t h i r d Cu p l a n e . R i g h t : D i s p e r s i o n o f oxygen 2 p - d e r i v e d bonding b a n d s f o r s e v e r a l B r i l l o u i n z o n e d i r e c t i o n s of t h e r e c o n s t r u c t e d s u r f a c e . Data-from r e f . 2 7 . TY is o r i e n t e d a l o n g [$O>], i.e,along t h e oxygen c h a i n s , w h i l e T X is o r i e n t e d a l o n g [ 1 1 0 ] . S b i s e c t s X-X and Y-Y, r e s p e c t i v e l y , i n t h e e x t e n d e d zone scheme. The
missing-row model i s r e p r o d u c e d i n F i g .
symmetric
long-bridge
will
be
chains.
'A
Oxygen
occupies
above t h e topmost Cu l a y e r and e v e r y
the
second
I n t h e buckled-row model a l t e r n a t i n g [001]-rows a r e
displaced
outwards.
It i s o b v i o u s t h a t i n b o t h c a s e s t h e e l e c t r o n i c
structure
described
to
row i s m i s s i n g . slightly
s i t e 0.3
12 (left):
first o r d e r by
almost
one-dimensional
oxygen-copper
T h i s r e s u l t i s c l e a r l y e v i d e n t from t h e e x p e r i m e n t a l d i s p e r s i o n of t h e
bonding bands ( r e f . 27) a s r e p r o d u c e d i n F i g . 1 2 ( r i g h t ) : t h e r e i s an u n u s u a l l y l a r g e (1,85 eV) d i s p e r s i o n measured a l o n g
n and %,
i . e . i n directions paral-
l e l t o t h e oxygen-copper c h a i n s . T h i s d i s p e r s i o n is much t o o l a r g e ( r e f . 27) t o b e e x p l a i n e d by 0-0 o v e r l a p i n a t i g h t - b i n d i n g a p p r o a c h . It must t h e r e f o r e b e due t o a s t r o n g Cu-0 c o u p l i n g . I n c o n t r a s t t o and t h e r e is a l m o s t n o and 3.These o b s e r v a t i o n s t h u s p r o v e a h i g h l y d i s p e r s i o n (< 0 . 3 eV) a l o n g d i r e c t i o n a l bond a l o n g [ 0011. B e s i d e s t h e t h r e e bonding bands shown i n F i g . 1 2
n
Courths e t a l .
(ref.
28,
x,
30) have a l s o i n v e s t i g a t e d two o c c u p i e d a n t i b o n d i n g
305 hands l o c a t e d between t h e Cu d-bands and EF.
13 ( l e f t )
Fig. to)
.
The s u r f a c e c o o r d i n a t e s
t h e Cu-0 c h a i n s ,
nearly
polarized
while
7
T y p i c a l s p e c t r a a r e reproduced i n
y(x) a r e
o r i e n t e d along (perpendicular
i s d e f i n e d a l o n g t h e s u r f a c e normal.
l i g h t and t h e a p p r o p r i a t e n o n r e l a t i v i s t i c
li-
Using
dipole
selection
r u l e s , t h e o r b i t a l symmetry o f a l l f i v e occupied bands c o u l d be u n i q u e l y d e t e r -
6
alonq
the
even
mined. I n t h e upper p a r t of F i g . 13 s - p o l a r i z e d l i g h t ( v e c t o r p o t e n t i a l
-
X)
was
used t o p r o j e c t o u t t h e odd s t a t e s .
o r b i t a l since p-polarized r a d i a t i o n
(A
i n z-plane)
a l l experimental dispersion curves along o r b i t a l symmetry a t
f
'i ( f i l l e d ) .
and
proposed
was i n c i d e n t .
is shown i n F i g .
- - -
13
A summary o f (right).
The
f r o m b o t t o m ( - 7-8 eV) t o EF i s y , z , x ( f i l l e d symbols),
Also i n c l u d e d i s an empty band observed by i n v e r s e
e m i s s i o n spectroscopy ( r e f . periodicity
The l o w e r p a r t r e v e a l s
o f t h e substrate l a t t i c e constant along
s t r u c t u r e models.
photo-
2 9 ) . Note t h a t t h e s e d i s p e r s i o n c u r v e s e x h i b i t t h e
7,
i n agreement w i t h
Note a l s o t h a t t h e bonding bands a r e i n
all
excellent
agreement w i t h t h o s e i n F i g . 12. The a d s o r p t i o n s i t e is r e f l e c t e d i n t h e number
of
bands:
the
Cpv p o i n t group symmetry o f t h e l o n g - b r i d g e
s p l i t t i n g o f t h e 2px and 2 p y l e v e l s a t
I
I
I
I
Cu(llOl:p(2xllO
I
7 ,which
site
dictates
a
i s c l e a r l y observed.
I
I"
hv=21.2eV/vpoint
x
c m
C a, C
4-
-
-6
-8
-L
-2
EF=O
Energy below E,(eV) 0.5
Wavevector K,,l(zwa)along [ 0011
F i g . 13. L e f t : point o f the From r e f . 30. i.e. along
m,
ARP s p e c t r a t a k e n w i t h l i n e a r l y p o l a r i z e d He1 r a d i a t i o n a t t h e s u r f a c e B r i l l o u i n zone. For d e f i n i t i o n o f c o o r d i n a t e s see t e x t . R i g h t : D i s p e r s i o n of bonding and a n t i b o n d i n g oxygen-induced bands a l o n g t h e oxygen c h a i n s . From r e f . 28.
306 F i g . 13 ( r i g h t ) i m m e d i a t e l y shows t h a t t h e observed d i s p e r s i o n curves r e p r e s e n t an oxygen-copper bond: i n case o f an e x c l u s i v e l i n e a r 0-0 bond a l l t h r e e oxygen bonding ( o r a n t i b o n d i n g ) bands would n o t r u n i n p a r a l l e l .
derived al.
(ref.
et
28) have shown t h a t a l l s i x d i s p e r s i o n curves may b e modelled assu-
ming 02p and Cu3d bonds i n a l i n e a r 0-Cu c h a i n a l o n g
7,which
even n e g l e c t s t h e
outward p o s i t i o n o f t h e oxygen i o n s w i t h r e s p e c t t o t h e Cu row. the
Courths
- _
a r e formed by 0 2 p ~ - C u 3 d(~o r pz-dzy) c o u p l i n g
n-states
I n t h i s model, between
neighbours,
w i t h predominant p ( d ) - l i k e c h a r a c t e r i n t h e bonding
bands.
o-bands,
The
with
nearest
(antibonding)
a d i s p e r s i o n t h r e e t i m e s as l a r g e as t h a t o f t h e
TI
bands r e p r e s e n t 02p-Cu3d,4s i n t e r a c t i o n s .
On a d s o r p t i o n
Chemisorbed a t o m i c oxygen has a l s o been i n v e s t i g a t e d on A g ( l l 0 ) .
a t 300 K , c h a i n s o f oxygen atoms a r e formed i n t h e [OOl] d i r e c t i o n . The spacing between (nxl)
c h a i n s v a r i e s w i t h coverage t o g i v e LEED p a t t e r n s d e s c r i b e d
these
2n2
7
with
2 (ref.
31).
Thus we expect e l e c t r o n i c s t a t e s
as
close
in
In f a c t , r e c e n t ARP i n v e s t i g a t i o n s
analogy t o t h e 0-Cu system d i s c u s s e d above.
by P r i n c e e t a l . ( r e f . 32, 33) show s t r o n g l y (1.5 eV) d i s p e r s i n g oxygen-derived a n t i b o n d i n g bands a l o n g
above t h e Ag4d bands,
i n d i c a t i n g s t r o n g Ag-0 i n t e r -
a c t i o n s i n t h e [ O O l ] d i r e c t i o n . I n c o n t r a s t , no d i s p e r s i o n c o u l d be f o u n d a l o n g
-
rX,
i.e. i n the
mental
error,
[no]
azimuth p e r p e n d i c u l a r t o t h e c h a i n s . A l s o , w i t h i n e x p e r i -
t h e observed d i s p e r s i o n along
i s i d e n t i c a l f o r t h e (2x1) and
t h e (3x1) oxygen o v e r l a y e r s ( r e f . 33, 3 2 ) . Thus we f i n d a c l o s e analogy between atomic oxygen on C u ( l l 0 ) and on A g ( l l 0 ) . t w o systems i s , '
A s i g n i f i c a n t d i f f e r e n c e between
makes a q u a n t i t a t i v e comparison d i f f i c u l t . The l a r g e d i s p e r s i o n a l o n g occupied of
the
however, t h e absence o f r e c o n s t r u c t i o n on t h e Ag s u r f a c e . T h i s
a n t i b o n d i n g band on Ag,
of the
as c o n t r a s t e d t o t h e r a t h e r s m a l l d i s p e r s i o n
t h e occupied a n t i b o n d i n g bands on Cu,
i n d i c a t e s t h a t on Ag t h e
predominant 0 2 p - c h a r a c t e r i s l a c a t e d above t h e s u b s t r a t e d-bands.
band
with
This conclu-
s i o n i s s u p p o r t e d by r e c e n t c l u s t e r c a l c u l a t i o n s ( r e f . 3 4 ) . 2.4 Halogens on n o b l e m e t a l s Halogen
atoms on n o b l e m e t a l faces r e p r e s e n t i n t e r e s t i n g model systems,
since
b o t h t h e s u b s t r a t e and t h e a d s o r b a t e photoemission f e a t u r e s a r e i n t e n s e , s u f f i c i e n t l y narrow and i n g e n e r a l r a t h e r e a s i l y s e p a r a t e d and i d e n t i f i e d ( r e f . 35 45).
Moreover,
materials
t h e c l e a n low-index s u r f a c e s o f t h e n o b l e m e t a l s a r e among t h e
i n v e s t i g a t e d most o f t e n by ARP and t h e y a r e understood
in
conside-
rable detail.
A
prototype
system i s t h a t o f atomic c h l o r i n e on
Cu(100). coverage-dependent
normal e m i s s i o n s p e c t r a t a k e n w i t h He1 r a d i a t i o n a r e reproduced i n F i g . 14. For that
experiment c h l o r i n e was produced i n s i t u by s o l i d s t a t e
electrolysis
of
AgCl i n an e l e c t r o c h e m i c a l c e l l ( 4 6 ) . T h e r e f o r e t h e C 1 2 dose i s measured i n mAs
307
1 25-fold saturation
exposure
I
++--a
XI
OO
02
DI
05
coverage (ML) F i g . 14 ( l e f t ) . Normal e m i s s i o n s p e c t r a t a k e n w i t h He1 r a d i a t i o n f r o m Cu(100) as a f u n c t i o n o f coverage w i t h a t o m i c c h l o r i n e . The spectrum f o r t h e c l e a n s u b s t r a t e has been drawn reduced i n i n t e n s i t y by a f a c t o r o f t w o . From r e f . 37. F i g . 15 ( r i g h t ) . Amplitudes o f some peaks observed i n F i g . 14 v e r s u s c h l o r i n e coverage. From r e f . 37.
( c u r r e n t t h r o u g h c e l l t i m e s exposure t i m e ) , a q u a n t i t y t h a t i s d i r e c t l y p r o p o r t i o n a l t o t h e number o f
C12 molecules f r o m t h e c e l l .
i n d i c a t e d a t a C 1 dose o f 4mAs, tral
changes can be observed.
A s a t u r a t i o n behaviour i s
s i n c e f o r doses up t o 100 mAs no f u r t h e r specThe s a t u r a t i o n i s accompagnied by a v e r y
sharp
~ ( 2 x 2 )LEED p a t t e r n and from s t r u c t u r a l i n v e s t i g a t i o n s ( r e f . 38, 47) i t is w e l l known
t h a t t h i s corresponds t o h a l f a monolayer o f atomic c h l o r i n e i n f o u r f o l d
symmetrical hollow s i t e s , 1.60 Therefore
1 above
0.03
t h e outermost Cu p l a n e ( r e f . 4 7 ) .
a coverage c a l i b r a t i o n was s t r a i g h t f o r w a r d u s i n g XPS c o r e l e v e l
tensities.
I t i s evident from F i g .
in-
14 t h a t a l r e a d y a t r a t h e r low C 1 coverages
d r a s t i c i n t e n s i t y changes a n d / o r energy s h i f t s o f c h a r a c t e r i s t i c s p e c t r a l
sub-
s t r a t e f e a t u r e s do o c c u r , most prominent t h e a t t e n u a t i o n o f t h e s h a r p peak a t -
2.8 eV ( o f A5 symmetry). A t s a t u r a t i o n , f o u r adsorbate-induced new f e a t u r e s can be
c l e a r l y i d e n t i f i e d a t -1.9,
-3.5,
-5.4 and about -6.3 eV.
a m p l i t u d e s o f some o f t h e peaks observed i n F i g .
It we p l o t t h e
1 4 versus coverage, we o b t a i n
t h e r e s u l t s o f F i g . 15. Not unexpected, we see an a l m o s t l i n e a r i n c r e a s e of t h e -5.4 eV ( a t s a t u r a t i o n ) peak, and an a t t e n u a t i o n of t h e s u b s t r a t e e m i s s i o n a t 2 . 8 eV.
However, t h e two f e a t u r e s observed ( a t s a t u r a t i o n ) a t -1.9 eV and -3.5
308
eV
e x h i b i t d i f f e r e n t behaviour:
around
a
coverage
of
they d e f i n i t e l y appear with a
0.3 m o n o l a y e r s .
This
observation
delayed
shows
appearance is c o r r e l a t e d with t h e formation of t h e ordered overlayer.
0.3
around
suddenly. lands
but
probably, gas.
onset
that
their
In fact,
monolayer c o v e r a g e a l s o b r i l l i a n t ~ ( 2 x 2 )LEED s p o t s a p p e a r We c o n c l u d e t h a t C 1 a d s o r p t i o n d o e s n o t s t a r t i n s m a l l ,
w i t h an e s s e n t i a l l y s t a t i s t i c a l d i s t r i b u t i o n on t h e
rather
o r d e r e d is-
surface.
Very
C1 on Cu(100) i s a l s o a p h y s i c a l r e a l i z a t i o n o f a h a r d - c o r e l a t t i c e -
Such l a t t i c e - g a s b e h a v i o u r h a s been o b s e r v e d e x p e r i m e n t a l l y ( r e f . 48) f o r
C 1 chemisorbed on A g ( 1 0 0 ) , a s y s t e m v e r y s i m i l a r t o C 1 on C u ( 1 0 0 ) . S i m u l t a n e o u s
we o b s e r v e i n F i g . 14 a s p l i t t i n g o f t h e peak seen
w i t h t h e o n s e t of o r d e r i n g , around
-6 eV a t t h e l o w e s t c o v e r a g e i n t o t h e t w o f e a t u r e s o b s e r v e d a t
tion.
satura-
We c o n c l u d e t h a t n e a r a c o v e r a g e of one t h i r d o f a monolayer t h e l a t e r a l
i n t e r a c t i o n becomes e f f e c t i v e d u e t o t h e s m a l l e r a v e r a g e C 1 - C 1 d i s t a n c e and t h e We mention t h a t no o r d e r e d ~ ( 2 x 2 )structure
20 o v e r l a y e r bands d e v e l o p .
could
e v e r be o b s e r v e d on C u ( 1 0 0 ) .
lcl, 0
/[ 2
clean Cu11001
, L
Energy below
"n@,
6 E, (eV1
8
F i g . 1 6 . Normal e m i s s i o n s p e c t r a t a k e n w i t h u n p o l a r i z e d r a d i a t i o n C u ( l O O ) c ( 2 ~ 2 ) C l and ( c ) c l e a n Cu(lOO), and w i t h s - p o l a r i z e d l i g h t ordered overlayer. The
from from
i n t e r p r e t a t i o n o f t h e C1-induced p e a k s on Cu(100) is d e m o n s t r a t e d i n
(a) the
Fig.
16. As mentioned a b o v e , t h e p e a k s l a b e l e d A, E , G and H i n F i g . 16a a r e i n d u c e d
by
t h e c ( 2 x 2 ) C l - o v e r l a y e r . If we change from u n p o l a r i z e d r a d i a t i o n t o l i g h t p o l a r i z e d p e r p e n d i c u l a r t o t h e s u r f a c e normal ( s - p o l . ) we o b s e r v e an
linearly almost
complete
quenching
of t h e e m i s s i o n p e a k s E and H .
According
to
the
309
nonrelativistic features.
d i p o l e s e l e c t i o n r u l e s t h i s proves Al-symmetry
Consequently,
the
for
these
l i n e s l a b e l e d A and G a r e o f A5-symmetry,
two since
A and A i n i t i a l s t a t e s con c o n t r i b u t e p h o t o c u r r e n t i n n o r m a l e m i s s i o n 1 5 under t h e C4v p o i n t group symmetry o f t h e Cu(100) s u r f a c e . Thus t h e r e s u l t s o f
only
F i g . 1 G t e l l u s t h a t peaks E and H o r i g i n a t e from A, orbital
in
character
s-like,
i n i t i a l states, i . e . t h e i r
p z - l i k e o r 3z2-r2 ( d - l i k e ) .
The
further
di-
s t i n c t i o n can be made u s i n g d i f f e r e n t photon e n e r g i e s a t k,, = 0 ( r e f . 49): From the
dependence
(ref.
o f t h e a t o m i c p h o t o e x c i t a t i o n m a t r i x elements on
hw
and i t drops t o almost z e r o above ho = 40 eV.
around 20 eV,
know
we
t h a t e m i s s i o n from t h e C 1 3p o r b i t a l s shows a prominent
50-52)
maximum
I n contrast,
the
c r o s s - s e c t i o n f o r Cu 3d e m i s s i o n remains f i n i t e above 30 eV. Also, t h e e m i s s i o n probability (ref.
3 s - s t a t e s o f atomic C 1 i s i n v i s i b l y s m a l l as compared t o
from
3p
5 3 ) . Experiments performed a t normal e m i s s i o n demonstrate ( r e f . 49) t h a t
peak A o f F i g .
16 i s c l e a r l y r e s o l v e d a t ho = 40.8 eV.
I n c o n t r a s t , peak G i s
d r a s t i c a l l y reduced i n i n t e n s i t y a t t h i s p h o t o n energy,
and peak H i s quenched
c o m p l e t e l y . We t h u s conclude t h a t H e x h i b i t s almost p u r e C 1 3 p z - c h a r a c t e r . Peak G i s e s s e n t i a l l y o f C 1 3px, 3p - c h a r a c t e r w i t h some a d m i x t u r e s of C u - c h a r a c t e r , Y and peak A i s t h e c o r r e s p o n d i n g occupied a n t i b o n d i n g c o m b i n a t i o n o f predominant
d - c h a r a c t e r w i t h some C1 p x , p -admixtures. O b v i o u s l y , peak A i s s p l i t dxz, YZ Y o f f t h e s u b s t r a t e d-bands under t h e i n f l u e n c e o f t h e o r d e r e d - o v e r l a y e r p o t e n t i a l . We m e n t i o n t h a t H appears r a t h e r broad as compared t o G. T h i s m i g h t be an indication
s t r o n g c o u p l i n g between t h e 3pz o r b i t a l s o f C 1 t o
for
the
Cu
3s
band. Several 38,
authors
have t r e a t e d t h e C u ( l O O ) c ( 2 ~ 2 ) C ls u r f a c e t h e o r e t i c a l l y
54-57). B u l l e t t was a b l e t o i n t e r p r e t t h e peaks l a b e l e d A , G and H i n F i g .
16 on t h e b a s i s of a n o n - s e l f - c o n s i s t e n t lation (ref. peak
(ref.
G
t i g h t - b i n d i n g density-of-states calcu-
i n accord w i t h t h e e x p e r i m e n t a l o b s e r v a t i o n s ,
a r i s i n g f r o m t h e bonding i n t e r a c t i o n of t h e C 1
as
oriented
54).
parallel
to
t h e surface w i t h d
and dxz Cu YZ
t o w a r d s t h e a d s o r b a t e s i t e f r o m t h e f i r s t (or second) l a y e r . c o r r e s p o n d i n g a n t i b o n d i n g peak. substrate s,
3px,
orbitals
he
explains
py
orbitals
which
point
F e a t u r e A is
the
The C 1 3pz o r b i t a l s i n t e r a c t s t r o n g l y w i t h t h e
p - e l e c t r o n s , t h u s p r o d u c i n g t h e r a t h e r broad e m i s s i o n band H. The
peaks A , G and H were a l s o reproduced by Kar ( r e f . 55) who a c t u a l l y performed a one-step-model isostructural
l a y e r KKR photo-emission c a l c u l a t i o n f o r t h e i s o e l e c t r o n i c system Cu(100)c(2x2)Br,
and by C i t r i n e t
l a t t e r a u t h o r s a l s o d e t e r m i n e d , by a s e l f - c o n s i s t e n t d i s p e r s i o n w i t h k,, o f A , surface
Brillouin
emission, (ref.
zone.
al.
(ref.
38).
and The
f i l m LAPW c a l c u l a t i o n , t h e
G and H a l o n g t h e t w o main symmetry d i r e c t i o n s o f t h e To
interpret
the region o f
the
substrate
d-band
i n p a r t i c u l a r t h e prominent peak l a b e l e d E i n F i g . 16, Krewer e t a l .
57) used a l a y e r KKR f o r m a l i s m t o c a l c u l a t e ,
on t h e f o o t i n g o f t h e same
310
e f f e c t i v e p o t e n t i a l , p h o t o e m i s s i o n a t k , , = 0 f o r photon e n e r g i e s between 13 and l a y e r - p r o j e c t e d d e n s i t y o f s t a t e s and b u l k band s t r u c t u r e . It t u r n s o u t
4 5 eV, that
E a r i s e s from t h e i n t e r a c t i o n between t h e C 1
peak
essentially
3dz2-like
3pz-orbitals
and
s u b s t r a t e s u r f a c e s t a t e c a l c u l a t e d a t -3.5 eV on
an
clean
Cu(100).
i x
P aJ c
01
F i g . 1 7 . Two-dimensional a d s o r b a t e b a n d s d e r i v e d f o r ~ ( 2 x 2 )o v e r l a y e r s o f B r ( d a t a p o i n t s and s o l i d l i n e s ) and o f C 1 (dashed l i n e s ) on C u ( 1 0 0 ) . Squares: h a = 1 6 . 8 eV, c i r c l e s : hw = 2 1 , 2 eV. F u l l symbols r e p r e s e n t p r o m i n e n t p e a k s , open symbols weaker f e a t u r e s . From r e f . 40.
Experimental dispersion
curves of adsorbate-induced bands a r e
reproduced
in
F i g . 1 7 f o r c ( 2 x 2 ) B r , d a t a p o i n t s and s o l i d l i n e s , and c ( 2 x 2 ) C 1 , d a s h e d l i n e s , on C u ( 1 0 0 ) . S i n c e t h e r a d i u s o f Br i s e x p e c t e d t o b e l a r g e r t h a n C1, t h e stronger
adsorbate-adsorbate overlap increases t h e dispersion e f f e c t s .
shows
a d i s p e r s i o n of a b o u t 0.3 eV when g o i n g from
value
found
for Cl/Cu.
The s p l i t t i n g of t h e p x ,
symmetry p ) and f ( p x ) a t
FAis
of
d i s p e r s e s from
C1.
Y Also band g (p,)
B r and C 1 ,
respectively.
7 t o FA, p
Y
about
Band a
twice t h e
d e r i v e d Br b a n d s
e
(of
n e a r l y 1 . 9 eV, t o be compared t o 1.3 eV i n c a s e
However,
r t o xA by a b o u t 0.9 eV o r 0 . 4 eV w i t h
w h i l e b a n d s a , e , f and g o f Br show c l e a r
energy s h i f t s a s compared t o C1, no s u c h s h i f t c a n b e r e s o l v e d f o r band c . T h i s observation that
band
s t r o n g l y s u p p o r t s t h e i n t e r p r e t a t i o n o f Krewer e t c i s due t o a c o p p e r s u r f a c e s t a t e which i s o n l y
al.
(ref.
modified
by
57) the
adsorbate overlayer. D i s p e r s i o n c u r v e s E(k,,) and ARP s p e c t r a from h a l o g e n o v e r l a y e r s have a l s o
been
r e p o r t e d f o r s e v e r a l c o m b i n a t i o n s o f adsorbate/substrate-orientation on s i l v e r . In
p a r t i c u l a r Ag(100) is o f i n t e r e s t i n o u r c o n t e x t ,
s i n c e C1,
B r and I
all
form an a t o m i c ~ ( 2 x 2 )o v e r l a y e r . T h i s a l l o w s t h e o b s e r v a t i o n of c h e m i c a l t r e n d s
311 a t f i x e d ( l a t e r a l ) geometry. I n c o n t r a s t t o Cu, t h e h a l o g e n - d e r i v e d 20 bands o f
For
predominant p - o r b i t a l c h a r a c t e r appear e n e r g e t i c a l l y above t h e Ag d-bands. d e t a i l s see eg. r e f . 43. Taking t h e example o f C u ( O O l ) c ( 2 ~ 2 ) C lwe
f i n a l l y m e n t i o n t h e f r e q u e n t observa-
t i o n o f adsorbate-induced s c a t t e r i n g processes. atomic induced rated
levels.
occur
out
of
adsorbate
These a r e i n g e n e r a l e a s i l y i d e n t i f i e d i f t h e y a r e w e l l sepa-
i n energy f r o m s u b s t r a t e
changes
The m a j o r i t y o f ARP s t u d i e s on
focuses on t h e e m i s s i o n of e l e c t r o n s
chemisorption
however,
drastic
a f t e r chemisorption j u s t w i t h i n t h e substrate emission
emission
features.
Often,
region,
and i t i s n o t always e v i d e n t , whether "new" peaks a r e due t o o c c u p i e d a d s o r b a t e due t o changes i n t h e s u b s t r a t e e l e c t r o n i c s t r u c t u r e , or due t o a d s o r -
levels,
bate-induced have
m o d i f i c a t i o n s o f t h e ARP mechanism.
been
reported.
L i n d g r e n and Walldgn ( r e f .
Several
such
modifications
58) observed t h a t a f t e r
s o r p t i o n of Cs on C u ( l l 1 ) t h e a n g u l a r dependence i s much reduced and t h e
adspec-
t r a a r e q u i t e s i m i l a r t o t h o s e o b t a i n e d f r o m p o l y c r i s t a l l i n e Cu. They a s s o c i a t e this
b e h a v i o u r w i t h a s t r o n g i n c o h e r e n t s c a t t e r i n g by t h e
results
a r e r e p o r t e d f o r oxygen ( r e f .
in
significant sorbed
33) and C s ( r e f .
adsorbate.
43) on
o u r c o n t e x t a r e d i f f r a c t i o n e f f e c t s caused by
overlayers
(ref.
59 - 6 1 ) .
Similar
Ag(ll0). ordered
Most chemi-
Such " s u r f a c e umklapp" c o n t r i b u t i o n s
may
+
occur
s i n c e d u r i n g e l e c t r o n t r a n s m i s s i o n t h r o u g h t h e s u r f a c e k,, i s conserved + + -L t o k,,(v) = k,,(b) + g,,, where i s any r e c i p r o c a l l a t t i c e v e c t o r
GI,
according parallel
to
transitions
t h e s u r f a c e and v,
b d e f i n e k,, i n vacuum and b u l k .
Direct
f r o m u n r e c o n s t r u c t e d s u r f a c e s a r e g e n e r a l l y dominated
by
bulk
transi-
t i o n s w i t h g,, = 0 (no umklapp). However, an o r d e r e d o v e r l a y e r may i n t r o d u c e new g,,-vectors
that
can
r e d i s t r i b u t e t h e kl-conserving
bulk
substrate
emission
i n t e n s i t i e s i n k-space by umklapp processes. A t y p i c a l example i s reproduced i n Fig.
18.
Brillouin normal about
The
left
zone.
from
s i d e shows d a t a t a k e n a l o n g t h e rXUL p l a n e
Curve
(a)
Cu(OOl)c(2x2)Cl.
of
shows t h e ARP spectrum t a k e n a t 0 = 70' A spectrum
t a k e n from t h e c l e a n
pretation
structures (b) tals.
i n t o the direction 0 =
70'.
at to
It does o n l y
o f a l l f e a t u r e s observed i n (a) i s g i v e n by umklapp w i t h gl
a r e c i p r o c a l v e c t o r of t h e adsorbate mesh. I n f a c t , g ll b)
due
the
However, a complete i n t e r -
2.46
=
i s a b l e t o umklapp
t h e s u b s t r a t e e m i s s i o n observed f r o m c l e a n Cu(OO1) a t 0 = T 25' curve
off
t h e same k,, v a l u e i n t h e m i d d l e o f t h e d-band r e g i o n ( a t 0 = 65'
e x p l a i n some o f t h e peaks observed i n spectrum ( a ) .
bulk
substrate
adsorbate-induced change i n work f u n c t i o n ) i s g i v e n by c u r v e ( c ) .
R-',
the
(reproduced
It i s e v i d e n t from t h e d a t a t h a t
observed i n ( a ) a r e w e l l e x p l a i n e d by t h e s u p e r p o s i t i o n
of
in
all
curves
and ( c ) e x c e p t for f e a t u r e s A and B w h i c h a r e d e r i v e d f r o m a d s o r b a t e o r b i S i m i l a r r e s u l t s a l o n g rXWK a r e shown i n t h e r i g h t p a r t of F i g . 18, where
312
C , D and E a r e d u e t o a d s o r b a t e s t a t e s . I n g e n e r a l , a d s o r b a t e i n d u c e d umklapp p r o c e s s e s may b e s a f e l y i d e n t i f i e d p r o v i d e d a s u f f i c i e n t l y l a r g e d a t a b a s e i s
available. of
Their frequent appearance,
however, i n d i c a t e s t h a t t h e c a l c u l a t i o n
ARP d i f f e r e n c e c u r v e s ( c o v e r e d minus c l e a n ) may l e a d t o s e v e r e m i s i n t e r p r e -
t a t i o n i f umklapp c o n t r i b u t i o n s a r e n o t c a r e f u l l y c o n s i d e r e d , see e . g . refs. 61 and 62 f o r d e t a i l s .
F i g . 18. He1 s p e c t r a t a k e n a t p o l a r a n g l e s i n d i c a t g d from ( a ) C u ( O O l ~ c _ ( 2 ~ 2 ) C 1 and ( b , c ) c l e a n Cu(OO1). Left: rXUL m i r r o r p l a n e (rX); r i g h t : TXWK (TM). Data from r e f . 6 1 .
2 . 5 Halogens on s e m i c o n d u c t o r s The i n t e r a c t i o n o f h a l o g e n s w i t h s e m i c o n d u c t o r s u r f a c e s is o f i n t e r e s t
both
For e x a m p l e , c h l o r i n e a d s o r p t i o n f o r m s s t a b l e chemisorbed l a y e r s on v a r i o u s s e m i c o n d u c t o r s u r f a c e s ( r e f s . 6 3 - 6 6 ) , which rein
pure
and a p p l i e d p h y s i c s .
p r e s e n t w e l l - o r d e r e d model systems f o r t h e o r e t i c a l i n v e s t i g a t i o n s . F o r e x a m p l e , d i s s o c i a t i v e a d s o r p t i o n of C12 g a s on a S i s u r f a c e is a n i m p o r t a n t s t e p o f
the
dry etching r e a c t i o n s .
T h e r e f o r e h a l o g e n a d s o r p t i o n on s e m i c o n d u c t o r s h a s been
s t u d i e d by s e v e r a l a u t h o r s b o t h by e x p e r i m e n t and t h e o r y ( r e f s . 6 3 - 7 8 ) . As a p r o t o t y p i c a l system we w i l l now d i s c u s s C 1 on S i ( l l l ) - ( 7 x 7 ) . S c h n e l l e t
al.
( r e f . 65) were a b l e t o d i s t i n g u i s h (by s u r f a c e - s e n s i t i v e c o r e - l e v e l p h o t o -
emission) one,
two,
of a n d t h r e e C 1 atoms t o a s u b s t r a t e s u r f a c e a t o m ) . After a n n e a l i n g t o
three
d i f f e r e n t bonding g e o m e t r i e s a t room t e m p e r a t u r e (bonding
about
40OoC a l l C 1 a t o m s a r e found a s a m o n o c h l o r i d e s p e c i e s ,
layer
showing a (1x1) LEED p a t t e r n w i t h r e l a t i v e l y h i g h background
For t h i s system an ARP s t u d y was p e r f o r m e d ( r e f .
65).
w i t h i n an
over
intensity.
T y p i c a l normal e m i s s i o n
313
Energy (eV1
Binding energy lev1
F i g . 19. Normal e m i s s i o n ARP r e s u l t s t a k e n from C 1 on S i ( 1 1 1 ) - ( 7 x 7 ) a t p h o t o n e n e r g i e s h+w = 2 1 eV a n d 34 eV. The p h o t o n l i n e a r p o l a r i z a t i o n c o u l d b e changed from A,, (A p a r a l l e l s a m p l e s u r f a c e ) t o mixed p o l a r i z a t i o n A,,, Al ( r e f . 6 5 ) . F i g . 20. C a l c u l a t e d l o c a l d e n s i t y o f s t a t e s w i t h i n a C 1 monolayer and t h e t o p m o s t S i l a y e r o f S i ( l l l ) ( l x l ) - C l . P a n e l ( a ) c o r r e s p o n d s t o a d s o r p t i o n on t o p of a S i s u r f a c e a t o m , w h i l e ( b ) c o r r e s p o n d s t o a d s o r p t i o n i n a h o l l o w p o s i t i o n ( r e f . 77)
s p e c t r a , and t h e i r i n t e n s i t y d e p e n d e n c e on t h e l i g h t p o l a r i z a t i o n , a r e shown i n F i g . 1 9 . A l r e a d y t h e f i r s t i n s p e c t i o n shows t h a t t h e ( C l - i n d u c e d ) p e a k s B and C do
n o t s h i f t i n b i n d i n g e n e r g y w i t h photon e n e r g y .
character. component
T h i s d e m o n s t r a t e s t h e i r 20
As i s a l s o e v i d e n t t h e e x c i t a t i o n o f C i s s t r o n g e s t w i t h t h e A,,+ ( A - p a r a l l e l t o s a m p l e s u r f a c e ) w h i l e B is a t t e n u a t e d w i t h A,,-radia-
tion.
On t h e b a s i s o f t h e n o n r e l a t i v i s t i c p o l a r i z a t i o n s e l e c t i o n r u l e s we con-
clude
t h a t t h e i n i t i a l s t a t e c o r r e s p o n d i n g t o B i s t o t a l l y symmetric w i t h
s p e c t t o t h e s u r f a c e normal under p o i n t group o p e r a t i o n .
symmetry i s o f U(p ) - c h a r a c t e r .
re-
Therefore its o r b i t a l
S i n c e t h e C - s t a t e i s e x c i t e d by A,,, it must be
a t t r i b u t e d t o n ( p X , p ) - d e r i v e d s u r f a c e b a n d s . F i g . 19 a l s o shows t h a t peak B Y i s n o t c o m p l e t e l y quenched when o n l y t h e A,g-component i s p r e s e n t . T h i s o b s e r v a t i o n may be e x p l a i n e d by t h r e e e f f e c t s :
F i r s t , t h e applied storage-ring radia-
t i o n was n o t 100% l i n e a r l y p o l a r i z e d . S e c o n d , t h e n o n r e l a t i v i s t i c d i p o l e s e l e c t i o n r u l e s are correct o n l y i f s p i n - o r b i t i n t e r a c t i o n is c o m p l e t e l y
neglected.
T h i r d , t h e o b s e r v e d ( 1 x 1 ) LEE0 p a t t e r n was n o t v e r y b r i l l i a n t , which f a c t might
314
i n d i c a t e incomplete s u r f a c e order. vectors
different
I n consequence,
reciprocal surface l a t t i c e
t h o s e of t h e (1x1) o v e r l a y e r may m i x i n
from
(by
surface
umklapp) e m i s s i o n - i n t e n s i t y from s t a t e s w i t h k,, f 0.
I O B 6 6 2 0
Binding
1 0 8 6 6 2 0
energy lev)
F i g . 2 1 . ARP s p e c t r a from C 1 on S i ( 1 1 1 ) - ( 7 x 7 ) f o r t h e PKW and fRf d i r e c t i o n s o f t h e s u r f a c e B r i l l o u i n z o n e . The s p e c t r a a r e p l o t t e d i n p o l a r a n g l e i n t e r a l s A 0 = 3'. Data from r e f . 6 5 . F i g . 22. E x p e r i m e n t a l e n e r g y d i s p e r s i o n E(k,,) of s u r f a c e b a n d s i n d u c e d by C 1 a d s o r p t i o n on S i ( 1 1 1 ) - ( 7 x 7 ) . Data from r e f . 6 5 .
Based on a p s e u d o p o t e n t i a l c a l c u l a t i o n S c h l u t e r e t a l .
(refs.
7 1 , 77) have
d e t e r m i n e d t h e l o c a l v a l e n c e d e n s i t y of s t a t e s f o r C 1 on S i ( l l l ) - ( l x l ) , d i f f e r e n t geometries. cates
t h a t p, and p x ,
position.
In
a t two
T h e i r r e s u l t is shown i n F i g . 2 0 . The bottom p a n e l i n d i -
contrast,
p
Y
a r e degenerate f o r adsorption i n a
threefold-hollow
o(p ) a p p e a r s a t c l e a r l y h i g h e r b i n d i n g
energy
than
p ) i f C1 bonds i n a o n e f o l d s i t e on t o p o f a S i s u r f a c e atom. The Y e x p e r i m e n t a l results a r e o n l y c o n s i s t e n t w i t h t h e l a t t e r c o n f i g u r a t i o n , which n(px,
h a s a l s o been f o u n d from SEXAFS e x p e r i m e n t s ( r e f . 7 4 ) . From a n g l e - d e p e n d e n t s p e c t r a , of which t y p i c a l c u r v e s a r e r e p r o d u c e d i n F i g . 2 1 , t h e 2D b a n d s were mapped and t h e c o r r e s p o n d i n g E(k,,) r e s u l t s ( r e f . 65) are shown i n F i g . p , p -band X
Y
22. While t h e o band shows no d i s p e r s i o n w i t h k,,, t h e d e g e n e r a t e
splits
o f f - n o r m a l i n b a n d s o f odd ( n - ) and e v e n
symmetry. An a d d i t i o n a l band l a b e l e d s is o b s e r v e d a r o u n d
(71')
mirror
plane
< and i. A comparison
315
of
these
data w i t h a recent self-consistent
Schluter panel)
et al.
(refs.
69,
pseudepotential
78) i s displayed i n Fig.
assumes chemisorption of atomic C 1 on an i d e a l
23.
calculation
by
The theory ( r i g h t
Si(ll1)-(1x1) surface.
band l a b e l e d u i s c a l c u l a t e d t o be of predominant C1(pz)-Si(pz) c h a r a c t e r ,
The
while s i s of C l ( p z ) - S i ( s ) o r i g i n . However,
( l e f t panel). persion
Both
0
and s a r e observed i n t h e experiment
t h e c a l c u l a t e d binding e n e r g i e s and t h e degree of d i s -
w i t h k,, a r e somewhat overestimated.
The agreement between
calculated
Fig. 23. Comparison of experimental ( l e f t ) s u r f a c e energy bands of C 1 on with Si(111)-(7x7) theoretical r e s u l t s ( r i g h t ) of a self-consistent pseudepotential calcu l a t i o n f o r C 1 on S i ( l l 1 ) - ( 1 x 1 ) . Data from r e f . 65.
observed
and
dispersion
bands appears t o be much b e t t e r .
of
We conclude t h a t t h e observed
t h e C1-derived bands can be r a t h e r well described
a
by
(1x1)
overlayer mesh. T h i s supports s t r u c t u r e models w i t h s u f f i c i e n t l y l a r g e a r e a s of an i d e a l (1x1) s u r f a c e geometry.
I n t h i s example we observe again t h e i n t i m a t e
between e l e c t r o n i c a l a n d geometrical parameters a s revealed by
connection
ARP
spectra.
3 . OUTLOOK This
article
sorption. science
Also,
does not pretend t o have covered a l l t o p i c s of atomic space
limitation
d i d not allow t o d i s c u s s a l l
behind t h e few s e l e c t e d examples.
the
chemisurface
Nevertheless I hope it p r e s e n t s
o f how much d e t a i l e d information on adsorption systems may
impression
be
an ob-
t a i n e d from t h e a p p l i c a t i o n of A R P . Which many
improvements
and developments can we expect i n t h e near
future?
places around t h e world new synchrotron r a d i a t i o n sources a r e
construction. undulators,
They and
are
they
now
based on magnetic i n s e r t i o n devices l i k e wigglers w i l l o f f e r i n t e n s i t y and b r i g h t n e s s s e v e r a l
magnitude higher than presently a v a i l a b l e .
These sources w i l l allow
At
under
orders
or
of
spatially
316 resolved
ARP experiments w i t h sub-micron r e s o l u t i o n f r o m inhomogeneous c r y s t a l
surfaces
or
from very s m a l l s i n g l e c r y s t a l s .
concerns " r e a l - t i m e " a
function
of
time
ARP.
T h i s a l l o w s e.g.
and t e m p e r a t u r e ,
Another
point
of
development
t o i n v e s t i g a t e r e a c t i o n dynamics as
or t o
study
diffusion
processes
in
c o n s i d e r a b l e d e t a i l . Two approaches seem f e a s i b l e : Time-modulated r e a c t i v e beam techniques
may
adsorbates
and i n t e r m e d i a t e s p e c i e s .
reached
or
be combined w i t h ARP,
g i v i n g time-resolved i d e n t i f i c a t i o n
of
A t i m e s c a l e down t o picoseconds may
be
by u s i n g t h e p u l s e s t r u c t u r e o f s y n c h r o t r o n l i g h t f r o m s t o r a g e
i n two-photon a b s o r p t i o n experiments where one o f t h e p h o t o n sources
rings, is
a
pulsed l a s e r .
Once s p a t i a l r e s o l u t i o n a n d / o r t i m e r e s o l u t i o n w i l l be a v a i l a b l e
routinely
combination
in
with
h i g h photon i n t e n s i t i e s
and/or
high
energy
r e s o l u t i o n , a f u r t h e r boom o f ARP can be a n t i c i p a t e d . Acknowledoement The
continuous
s u p p o r t o f my work by t h e Deutsche
Forschungsgemeinschaft
g r a t e f u l l y acknowledged. REFERENCES
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319
Chapter 9
MOLECULAR CHEMISORPTION
H.4. FREUND and M. NEUMANN
INTRODUCTION The study of adsorption of molecules on surfaces with photoelectron spectroscopy starts in the vicinity of 1971 with the landmark paper by Eastman and Cashion (ref. 1) on the system CO/Ni. Still much of present research on molecular adsorption is being done on CO adsorbates or co-adsorbates with electronegative and electropositive additives. The adsorption behaviour of other diatomics, e.g. Nz and NO, has also been investigated thoroughly by ARUPS as reviewed in (refs.2,3). During the last 15 years, larger molecules have been studied by means of ARUPS, for example unsaturated hydrocarbons like acetylene, ethylene, benzene just to name a few (ref. 4 ) . Reactive systems have been investigated using ARUPS with varying success. None of these adsorbate systems has been analysed in any such detail as CO adsorbates. This means that much of the fundamental aspects of ARUPS of molecular chemisorption systems can be demonstrated using experimental results on CO adsorbate systems. Therefore, we use CO adsorbates to illustrate some basic principles. On these grounds we then discuss specific aspects of ARUPS on molecular adsorbates and co-adsorbates by using examples of more complicated systems. In an attempt to order the various aspects of ARUPS on molecular chemisorption systems we have devided the present review into two parts, i.e. one covering the molecular aspects including co-adsorption, and a second one dealing with intermolecular interaction in connection with the formation of two-dimensionally ordered overlayers. A subdivision in this manner is natural because molecular chemisorption is determined essentially by these two types of interactions. Fig.1 illustrates on the basis of one-electron level diagrams how the molecule substrate and the intermolecular interactions 1.
320
ONE ELECTRON SCHEME OF AN ADSORBATE
w i Mic
r
Fig. 1. Schematic one-electron level diagrams for diatomic molecules (CO) interacting with a transition metal surface. The level scheme for a molecule-metal cluster (right) is correlated with the band scheme of a free unsupported molecular layer (extreme left) and the band scheme of the quasi-twodimensional adsorbate (middle). The band structure of the metal projected onto the surface is schematically shown as the hatched area. affect the electronic states of the adsorbate. It shows on the right hand side a one-electron level diagram for a single isolated CO molecule correlated with a level diagram of a CO molecule interacting with a single metal atom or a small metal cluster. The electronic states of the system can be classified according to the point group of the CO-metal cluster. On the left hand side the band structure of an isolated CO overlayer is shown and compared in the middle with the full band structure of the CO adsorbate on a fcc(ll1) single crystal metal surface. In this case the point group of the local CO-metal site is not sufficient to characterize the electronic states of the system. The full global space group of the periodic arrangement has to
32 1
20
15
10
5
O-E,
Fig. 2. Set of normal emission CO adsorbate spectra (refs. 13). s.u.: shake up satellite.
8-
be considered. Clearly, the relative magnitudes of moleculesubstrate and intermolecular interaction potential determine whether local or global symmetry dominates. Since ARUPS, as will be shown further below, allows us to study symmetry properties of the electronic states of adsorbate systems, it may be possible to disentangle via ARUPS in favourable cases which of these two types of interactions and how they are active in the adsorbate. We note at this point that all of our examples refer to adsorbate systems on transition metal single crystal surfaces, because the majority of data is available for these systems. There are very few examples for ARUPS studies of molecular adsorbates on semiconductor surfaces (ref. 5 ) .
322
2.
MOLECULAR ASPECTS Let us start with the "molecular aspect" of the COmolecule-substrate interaction, i.e. the right hand side of Fig.1. What happens electronically can easily be explained in terms of the so called Blyholder model (ref. 6 ) : The carbon lone pair is donated into empty d or s levels of the metal atom, establishing a u metal-molecule interaction. Synenergetically, metal n-electrons are donated into empty molecular orbitals (2n*) of CO forming a n metal-molecule interaction. From the view point of the molecule we can look at this process as a udonation-n-back-donation process. This means that the distribution of electrons among the subsystems, i.e. CO molecule and metal atom, in the metal-CO-cluster is considerably different as compared with the non-interacting subsystems. For example, the electron configuration of the metal atom in the cluster may be different from the isolated metal atom, or the electron distribution within the CO molecule bonded towards the metal atom may look more like the electron distribution of an "excited" CO molecule rather than the ground state CO molecule (ref. 7). Nevertheless, as a consequence of the relatively weak moleculesubstrate interaction only certain electronic levels of the subsystems are strongly influenced, so that it appears to be justified to classify the electronic levels of the interacting adsorbate system according to the nomenclature used for the isolated subsystems. Naturally, the distortions of the molecular as well as the metal levels are reflected by changes in the ionization energies of those levels, their ionization probabilities, and the line shapes of the ionization bands. Fig.2 shows a set of angle resolved, normal emission valence electron spectra of CO adsorbates on different single crystal surfaces (refs. 8-13). The binding energy (EB=hu-EKio) refers to the vacuum level. (Often the binding energy is referenced to the Fermi-level ( E F ) of the system. The binding energies with respect to the Fermi and to the vacuum levels are connected via the workfunction 0 of the adsorbate system.) The region where we expect emission from the three outer valence levels of CO, 5.e. the 50, In, and 4a levels (see Fig.1) is shown, and most of the following discussion will concentrate on these levels. From the bottom to the top the heat of adsorption increases from 19kJ/mol to 142 kJ/mol (refs. 14-18). This is accompanied by changes in the adsorbate spectra as compared to the gas and solid phase
323
spectra which are shown for comparison. There are several interesting differences in binding energies, line intensities and line shapes between gas, condensed and adsorbate phases, which we shall comment on in the following. In order to do so we have
to
cover
many
different
aspects
such
as
symmetry
considerations, relaxation energies, line widths, shake-up satellites, and so on. We shall use Fig.2 as a guide line to discuss the various aspects as they occur in going from the gas phase via weakly chemisorbed to strongly chemisorbed adsorbates. In CO/Ag(lll) at T=20K CO is physisorbed as documented by the small E s d = 1 9 kJ/mole (ref. 15). This explains why a spectrum similar to condensed CO is observed for this adsorbate. The splittings in the 40
and 50 emissions are connected with the
formation of a two dimensional overlayer as will be discussed in the second part of this review. In comparison with the gas phase, however, rather dramatic changes are observed upon condensation and physisorption, namely a shift of about 1 eV towards lower binding energies and a considerable increase in line width which destroys the vibrational structure observed in the gas phase. Chiang et al. (ref. 19) found shifts by comparing the photoelectron spectra of CO, adsorbed on a metal surface (Al(111)), and of CO adsorbed on the same surface precovered with a monolayer of Xe, so to say as a spacer between metal and CO. Fig.3 shows the spectra as a function of increasing thickness of the Xe spacer. Clearly, the bands shift towards higher binding energies, and appear to exhibit smaller line widths when well separated from the surface. Theories have been developed that allow one to understand these observations on the basis of hole hopping and relaxation together with adsorbatesurface vibrations within the condensed quasi-two- or threedimensional molecular solids (refs. 20-22). The shift of the band to lower binding energy is a consequence of the electronic relaxation in the final ion state, which is considerably more pronounced when the molecule is bound to a readily polarizable medium, because metal electrons screen the positive charge introduced by the ionization process more effectively than do the electrons on the isolated molecule. The more pronounced screening stabilizes the final hole state relative to the initial state, which lowers the binding energy as observed. Measured temperature dependences of line widths in molecular solids and model systems support the developed theoretical ideas
324
l
20
I
~
I
l
I
l
CLEAN ,AI(Ill4 1
15 BINDING ENEiiGY (eV) (Evnc
I0
=O)
Fig. 3 . Spectra of CO interacting with a clean and Xe precovered Al(111) surface (ref.19). The number of precovered Xe layers is indicated. (refs. 22-23). It is likely that other processes, for example Auger decay or other radiationless decay mechanisms, contribute to these line widths as well. If the heat of adsorption increases to about 4 7 kJ/mole (ref. 16) (weakly chemisorbed), like, for example, in the case of a CO adsorbate on a Cu(ll1) surface, the features in the spectrum shift and the intensities of the lines are altered considerably with respect to the physisorbate. The line widths, on the other hand, are quite comparable in both systems. Three lines are still found, but their assignment is, as we shall see further below, quite different from the one for the condensed molecular
325
B
A
hw
C
I+Y,IP
AIY,$
11111
Q . 0 . -
"allowed"
Fig. 4 . CO 4 0 emission intensity from CO/Pd(lll) as recorded with an elliptical mirror analyser (ref. 30). a) polar diagram, the direction of the light polarization vector is indicated by an arrow. b) intensity distribution pattern. Light regions correspond to high emission current. c) Quasi three dimensional representation of the relation between geometric structure of the adsorbate and the measured 4a emission intensity as a function of 0 and 8 . The emission intensity is given by the shaded areas. solid. Before we discuss how ARUPS establishes this assignment let us first turn towards the spectra of the strongly chemisorbed adsorbate systems, i.e. CO/Ni(lll) and CO/Pd(lll)- which are
326
only two examples out of a wealth of experimental data (refs. 24-40). In the case of strong chemisorption the spectra show two bands, the binding energies of which are rather independent of the particular system under consideration, but are shifted by more than 2 eV to lower values with respect to the gas phase. ARUPS has been instrumental to show that these two CO induced bands are really caused by three CO ion states, and that the CO molecules are oriented with their axis parallel to the surface normal (ref. 24). Fig. 4b shows an angular distribution pattern for the 4a ion state intensity of a CO/Pd(lll) adsorbate as recorded with an elliptical mirror analyser employing polarized synchrotron light (ref. 30). The polarization plane is placed along the Oo /180 -azimuth, i. e. the horizontal line in the angular coordinate diagram shown in Fig. 4a. With respect to the Pd(ll1) surface this corresponds to a mirror plane of the system. Figure 4c shows a quasi-three-dimensional plot of the emission intensity distribution (shaded areas on the halfsphere) as a function of azimuthal ( # ) and polar ( 8 ) angles in direct relation to the geometric structure of the molecular adsorbate. The angular distribution pattern clearly shows how the symmetry of the adsorbate wavefunction with respect to this mirror plane determines the angular distribution of the emitted electron current. The reason for this remarkable behaviour has been discussed long before by several groups (refs. 24,25,41) on the basis of symmetry considerations for the photoemission matrix element (refs. 42-43): I a l < Y r I p l Y i > I * (1) and we shall briefly repeat the arguments: Firstly it has to be remembered that Y f is the final state after electron excitation consisting of the ion state N - " t ' e , ~ and the emitted electron @e (n), and Yi represents the neutral ground state of the system. Since p is a one electron operator the matrix element can be rewritten as (ref. 44): 1 a I Z,
<#e(n)Ipnl#lr(n)><~-~Y~.~lar~~>l~
(2)
k,E where ak and @k (n) are the annihilation operator and the oneelectron wave function of the electron that is being emitted, respectively. These @k (n) are called initial states in the following. The first matrix element determines the angular distribution pattern, the second matrix element defines the absolute value and contains the internal degrees of freedom of
327
the system, e.g. the line widths. The sum takes all possible ion states N - - ' Y e , ~ into account and explains the existence of satellite structure (ref. 44). Since we are interested in ARUPS, much of the discussion will concentrate on the first matrix element. Secondly, in order to evaluate whether this matrix element is finite, and thus leads us to expect a finite photoelectron current into a specific direction in space, symmetry arguments can be used. In principle the space group of the adsorbate under consideration has to be chosen, and then we have to classify the wavefunctions according to its irreducible representations. Often, it is sufficient to consider one specific symmetry operation belonging to the point group, instead of all possible symmetry operations, in order to predict the angular variations of electron emission. In the present case we refer to one of the mirror planes of the Pd(ll1) surface. If we classify the wavefunctions of the electron Oe and a k , as well as the momentum operator p "even" or "odd" with respect to this mirror plane, we are in the position to differentiate between "even" and "odd" initial states by choosing certain light polarizations and detecting the angular distribution pattern as long as spin orbit interaction is not important (ref. 45). For the above given situation the light polarization direction is within the mirror plane. This corresponds to even symmetry of the momentum operator. Therefore, initial states with even symmetry will emit into the direction of the mirror plane because the final states have to be even in order for the matrix element not to vanish. In principle, one would expect a finite emission probability along the whole mirror plane. In the present case, however, one has to take into account the cylindrical symmetry of a CO molecule, bonded linearly towards the metal surface. Even initial states of a cylindrical molecule cannot emit into a direction given by the plane perpendicular to the mirror plane which contains the light polarization vector. This latter property can easily be understood if we remember that any plane in a cylindrical system containing the cylindrical axis is a symmetry plane. Combining this property with the fact that the momentum operator is odd with respect to this second plane means that there cannot be any emission of even states into this direction. Therefore, in order to fulfill both conditions simultaneously, we do not expect an intense CO-40 emission along the surface normal for
I
.
,
,
,
, . .
,
,
I
.*
.
forbidden
'.9..
;*:-*...',..,...w,.'. .. .
5
\ y
4 .L
?ex=
allowed"
Fig. 5 . ARUP-spectra of CO/Pd (111) in "forbidden" and "allowed" geometry (see text). The CO induced features are marked. Pd emissions show strong symmetry related intensity variations as well (ref. 13). The light polarization was placed along a Pd(210) mirror plane. light polarized in the surface plane. 4u emission along the surface normal can only be achieved by using a light polarization perpendicular to the surface plane because in this case the momentum operator is even with respect to any plane perpendicular to the surface plane. If we combine the considerations so far we verify the above angular distribution pattern. As a consequence of the outlined behaviour of even initial states, we expect a complementary behaviour of odd initial states. This is exactly what is observed experimentally and is shown as a set of electron distribution curves- which is the usual way to look at ARUP-spectra-in Fig.5. In this figure the complementary behaviour of u- and remissions, which was first observed by Plummer and coworkers (ref. 24) is obvious: If we
329
record a spectrum perpendicular ( s o called "forbidden" geometry) to the incidence plane we do not observe emission in the region of the 40 level but only in the region of the 5o/ln levels. Note, that the In-ion state of CO has two degenerate components, one of which always transforms according to the even representation. Thus, we expect to see the one odd component of the In-ion state. A spectrum recorded with the analyser placed within the incidence plane, the so called "allowed" geometry, show all states with even symmetry. From Fig.5 it is clear that the band at 8 eV below the Fermi energy (Fig.2) contains two states, i.e. the In and the 50 ion states. Their energies are, in contrast to the gas phase, nearly (within a few tenths of an eV) degenerate in the adsorbate. This is a situation, predicted by the simple one-electron level scheme in Fig.1. It is due to the donation of the 50 carbon lone pair into empty metal levels, thus stabilizing the CO 50 level with respect to the In level which is not as intimately involved in the molecule metal interaction for linear metal-molecule bonding. The logic s o far has been that we have assumed a geometry of the adsorbate site, thus knowing the symmetry of the system, i.e. CO perpendicular to the surface plane, and have verified this via an analysis of the angular photoemission spectra. Usually, the arguments are turned around, namely, the observed angular behaviour is used to deduce an adsorbate site symmetry. The adsorbate induced features exhibit, in addition to the described angular dependences (ref. 4 6 1 , characteristic photon energy dependences, which, when recorded in an angle dependent fashion, can be used to get further information about adsorbate site geometry (ref. 2 4 ) . Fig.6 shows a plot of the intensity of the 40 ion state as a function of photon energy. The data have been recorded for the system CO/Co(OOOl) (ref. 27) for three different electron emission angles. The observed resonance feature is caused by the so called shape resonance, which is well known from CO gas phase studies (ref. 4 7 ) . It can be traced back to a molecular final state of a symmetry in the ionization continuum, quasi-bound by a centrifugal barrier in the molecular potential. Its symmetry confines the electron emission direction to the molecular axis, and directs the 4 0 emission out of the oxygen end of the molecule. This means that for the case of a molecule oriented along the surface normal, carbon-end bound to the surface, the resonance should peak along the surface normal.
I
r
I
I
4
I
I
I
I
I
4cr SHAPE RESONANCE c o / c o (0001) ROOM TEMPERATURE 15 NORMAL EMISSION
.
x 40. OFF NORMAL 0 50’ OFF NORMAL
*
'4
a
10
-
a
**
m
5
@
X
m-
O2
I
30
,
,
,
,
l
,
,
,
,
40
l
50
PHOTON ENERGY ( e V ) Fig. 6. Intensity variations of the 4 0 intensity in CO/Co(OOOl) as a function of photon energy. Filled circles refer to normal emission, open circles and crosses to off-normal emission as indicated (ref. 27). Experimentally, we find in Fig.6 the expected behaviour, i.e. a pronounced attenuation of the resonance intensity for off normal emission, which corroborates the assumed adsorbate orientation. Another interesting property of this resonance is its coherentforward-emission character (ref. 4 8 ) . Coherent-forward-emission leads to an oscillatory behaviour of the photoionization crosssection. The periodicity is determined by the distance of the interfering sources, which are in the present case the carbon and oxygen atoms participating in the ion state wavefunction under consideration ( 4 ~ ) . Examples are shown in Fig.7 for the system CO/Pd(lll) and CO+Na/Pd(llll (ref. 4 9 ) . At a photon energy of 35 eV the resonance corresponding to the one shown in
331
P
A
Pd(ll1)llL CO
co L O
B Pd(111)/75s NallL CO
CO LO
30
L'O ' 50
60 70 80 90 100 Photon energy (eV)
Fig. 7. Intensity variations in normal emission of the CO 4a intensity in (a) CO/Pd(lll) and (b) CO+Na/Pd(lll) as a function of photon energy between 25 eV and 110 eV (ref. 4 9 ) . Fig.6 is found. As predicted by theoretical calculations (ref. 4 8 1 , at about 9 5 eV a second feature with larger width and smaller amplitude is observed. Potentially, the energy separation can be used to estimate the CO bond length in adsorbates as proposed by Gustafsson (ref. 4 8 ) . Very similar results as those discussed so far for the 4a ion state are found for the 50 ion state. A comparison of the resonance positions in different CO systems shows (refs. 49-51) that it is not so much dependent on the specific system, as was originally expected, and its absence is somewhat surprising on the basis of current theoretical models. If we apply the geometry sensitive experiments, just presented, to investigate the geometric structure of physisorbed
332
molecules, for example CO/Ag(111) (ref. 101, Fig.2 or CO/A1(111) (ref. 191, Fig.3, we find that the orientation of the molecular axis is not, like in the chemisorbates perpendicular, but rather parallel to the surface. The reason is that due to the electronic structure of the substrate, not enough energy can be gained via the above mentioned a-donor-n-acceptor interaction, for which a vertical orientation is a neccessary prerequisite. As we shall see further below, intermolecular interactions are rather important to understand the electronic structure of physisorbates. . At this point we can return to the assignment and analysis of the spectra of the weakly chemisorbed system. The assignment of the spectrum of the CO/Cu(lll) system, given in Fig.2 indicates that the considerations presented so far are not complete and sufficient to explain all experimental findings. It has been shown theoretically that for weakly chemisorbed systems so called shake up excitations accompanying the "normal" electron emission have to be considered (refs. 52-56). These shake up excitations are manifestations of the fact that the ionization process is a rather complicated many-electron process (refs. 4 4 , 57). They can be assigned to electron excitations in addition to electron emission. Their intensity is determined by the second matrix element in equation (2) whose magnitude is governed by the projection of the wavefunction of the shake-up state N - i Y e , E onto the "frozen" ion state arli . Shake-up intensities are rather low for chemisorbed and for physisorbed systems but reach the maximum for intermediate metal-molecule coupling, 1.e. weak chemisorption (refs. 53-58). Again, ARUPS can be employed to support the assignment as given in Fig.2 for the CO/Cu(lll) system. If the most intense CO features were due to In emission, as might be suspected by comparing the spectra of the CO/Cu(lll) system with CO/Ag(lll), a resonance behaviour for this particular peak would not be allowed. Horn et al. (ref. 59) showed that both bands at higher binding energy are due to states of u symmetry by investigating the shape resonance discussed above. The 40 ion state as well as the accompanying shake up transition exhibited parallel resonance behaviour as expected according to the assignment in Fig.2. A spectrum rather similar to the one of the CO/Cu system, but with even slightly more intense satellite structure, has been found for the system CO/Au (ref. 60). In the latter system the adsorption energy is
333
Ni (110) I CO (2x1) PZmg normal emission
A
I
I
1
I
I
I
I
> c
.-It C
a
c
C Y
Binding energy (eV)
Fig. 8 . ARUP-spectra in normal emission for different light polarization directions of CO(2xl)p2mg/Ni(llO) (full lines) in comparison with the clean Ni(ll0) surface (broken lines) in the region of the metal emissions (ref. 63). between the one for C O / A g and CO/Cu which leads us to expect more intense satellites, and corroborates the ideas presented. In our discussion so far we have only considered the molecule induced peaks at binding energies higher than the metal states, i.e. those states that correspond to "molecular" ion states. However, as is obvious from Fig.1 there are levels of the adsorbate system within the region of the metal projected density of states, due to the coupling of unoccupied molecular states to occupied metal states. There have been several attempts to identify these states (refs. 61-63). The most recent one was done on the system CO(2xl)p2mg/Ni(llO), whose structure will be discussed in detail in connection with intermolecular interactions (ref. 26). The symmetry and high CO density of this system allows to measure the adsorbate induced
334
peaks in the d-band region of the Ni substrate (ref. 63). Fig.8 shows a selected set of spectra that demonstrate the intensity, symmetry and energy position of the CO induced, d-like states for this system. The spectra of the clean surface are given as dashed curves for comparison. The usually dominant CO molecular ionizations (ref. 26) are not shown in this figure. The various peak intensities are strongly polarization dependent, and, together with the measured dispersion, discussed in the section intermolecular interactions, support an assignment of these features to CO-2n-Ni-3d states, To summerize the results so far, the ARUP-spectra are found to reflect the bonding with the surface. It is possible to differentiate between physisorbed, weakly chemisorbed, and strongly chemisorbed CO adsorbates. However, the differences in the habit of the spectra for various chemisorbed systems are rather unpronounced which limits the applicability of photoemission with respect to fingerprinting. On the other hand, ARUPS is sensitive to the local site symmetry via the angular emission pattern, as well as the angular dependence of resonance features in the ionization cross-section. For special cases the back-bonding states in the region of the metal substrate states can be identified. In order to appreciate in more detail how these aspects of photoemission have been used to study molecule surface interactions under the influence of variations of the substrate and co-adsorbed species we briefly review selected results of adsorbates on clean and precovered surfaces: 2.1
Pure adsorbates
2.1.1 Hz
Even though HZ adsorbates have a lot of appeal to be the model system to study molecular adsorption very little has been done with respect to the application of ARUPS. The reason is, of course, that in general, at routinely accessible temperatures hydrogen adsorbs dissociatively to form atomic adsorbates. To our knowledge only angle integrated spectra have been published for adsorbed molecular H2 (ref. 6 4 ) . Whether one should look at hydrogen adsorbates with coverage 8 = 2 as containing atomic (2H) or quasimolecular HZ is probably a matter of semantics. Christmann et al. (ref. 6 5 ) have studied these systems with ARUPS and observed band dispersions as large as 4 eV and binding
335
energies for the hydrogen induced features close to 10 eV below EF .
4? 50/l~
.-
:?.
0.5L; T = 240K hw = 36eV
Fig. 9. ARUP-spectra of CO/Fe(lll) for various light incidence and electron emission angles as indicated in the inset ( E n i n in eV). Top and bottom panels differ by the CO exposure. The top panel corresponds to saturation coverage (ref. 66). 2.1.2 co As documented in the previous section the adsorption of CO has been extensively investigated with ARUPS. The orientation of the CO molecule has been found to be parallel to the surface in the case of Ag(ll1) (ref. 101, and upright in many chemisorbed systems (refs. 24-40). Recently, some systems have been studied where CO shows photoemission patterns different from the usual behaviour. Fig.9 presents spectra for CO/Fe(lll) (ref. 6 6 ) . The 5a/ln-band is clearly split, and the 4 0 intensity is not
336
completely attenuated in the forbidden geometry indicating a possible tilt of the CO molecules or a strong distortion of the 4 0 wavefunction. Spectra have been reported for CO/Cr(llO) (ref. 2 9 ) and CO/Fe(100) (refs. 67) where the authors claim flat lying CO. These are the only cases where strongly chemisorbed CO appears to be oriented parallel to the surface.
I
.
FellllVN,
; T*llK
1.
2-pol .?'
Fclllll/N,
2- pol nornol
normal emission
cmission
..., ...
-._ . '
.
%
4 ! LZSN
32 5rv 30 0.v 275.v ZI5.Y
-I
1
bl
b2
ho 17 5SV
LZ 5rv
37 5."
32 I*
17%"
-
I pol 60'off nwmol
E,
emission -
2
L
6
6
10
12
E,,"l*'
Fig. 10. ARUP-spectra of Nz /Fe(lll) for grazing light incidence and normal emission (left panel), and s-polarization (near normal incidence, right panel) and two electron emission angles (bl: normal emission; b2: off-normal(600) emission). For each measurement geometry typical spectra at different photon energies are plotted (ref. 72).
337
2.1.3 Nz Nz on Fe(ll1) has been the model system to investigate the mechanism of ammonia synthesis (ref. 68). It is known that NZ dissociation is the rate limiting step, and that there exist molecular precursor states for dissociation where NZ has been presumed to be side-on bonded to the iron surface (ref. 69). Via ARUPS a strongly inclined NZ species was identified (ref. 70) in addition to a vertically bound Nz species which only exists at lower temperature. Fig.10 shows a set of angle resolved spectra at low temperature (vertically bound N2) and higher (T=llOK) temperature (Nz bound inclined). Fig.lOa reveals the a-shape resonance in normal emission for z-polarized light at T<77K. Fig.lOb shows a a resonance, but only in off-normal emission for s-polarized light (compare left and right part of this figure) at T=llOK, supporting the proposed inclined geometry in the second case. A more detailed discussion including the theoretical aspects of the two Nz bonding modes is given in ref.70. Another interesting feature can be demonstrated on the basis of the present results. Both, the 309 as well as the 20" state exhibit the shape resonance behaviour. while in the gas phase the ag resonance is symmetry forbidden. The reason is very simple: The inversion symmetry of the homonuclear NZ molecule is broken upon adsorption which makes the final resonance state accessible to both a states. This was demonstrated earlier by Horn et al. (ref. 71) for the system Nz/Ni(llO). In contrast to the case Nz/Fe(111) where NZ dissociates at low temperature (T>140 K), Nz-metal coupling is usually rather weak (refs. 34, 71-74). This leads to the existence of rather intense shake up structure as noted for several Nz-transition metal systems (refs. 34,71-76). The experimental findings are corroborated by several theoretical calculations (refs. 34, 71-76). 2.1.4 0 2 Only a small number of ARUPS studies have been reported on molecular 0 2 adsorption, which is probably due to the relatively high reactivity of the system leading to dissociative adsorption. A prominent example for molecular adsorption is the system Oz/Ag(110) (ref. 77) where at T-20 K 0 2 was found to be physisorbed, and even more interesting a chemisorbed 0 2 dissociation precursor state has been detected below 170 K. Only for Oz/Pt(lll) (refs. 78-79) similar conclusions have been
338
reached. Whether the chemisorbed 0 2 species must be looked at as an open-shell 0 2 or a closed shell peroxo-species appears to be the interesting question. 2.1.5 CN Very recently Conrad, Bradshaw and coworkers (ref. 80). and Netzer et al. (ref. 81) published ARUP-spectra of adsorbed CN. The adsorbate was prepared by decomposition of (CN)Z as previously reported (ref. 82). The analysis reveals that CN must be adsorbed parallel to the surface plane, and that the species is basically a CN-anion. For example, the 40 intensity is weak in normal emission which must be expected for a flat lying molecule. Since CN- is isoelectronic with CO and Nz one would have expected a similar adsorption geometry for CN, i.e perpendicular to the surface. The theoretical studies published so far (refs. 83-84) assume a linear metal CN bond geometry. These calculations reveal that 2n back donation plays a minor role in CN bonding which is due to the relatively high energy of the antibonding 2n level. This is expected because the electron affinity of a CN-anion is very low. Thus one of the prerequisites for linear molecule-metal bonding according to the o-donation-n-back-donation model is missing, which leads to the flat bonding geometry found experimentally. 2.1.6 NO Although NO has been studied for a long time with various methods (ref. 85) only very few ARUPS studies (refs. 86-88) have been published. The axis of the NO molecule appears to be oriented parallel to the surface normal in the case of the c(4x2)NO/Ni(lll) (ref. 87) system but not in all cases. This corresponds to the bonding geometry known from NO-transition metal complexes (ref. 89). There are basically two bonding modes known for NO, the nature of which depends on the charge transfer between the molecule and the surface. Two extreme cases are considered: i) NO+, which is isoelectronic with CO, and thus exhibits similar bonding characteristics, ii) neutral NO, which has an additional electron in the 2n* level, leading to a weakening of the metal-NO bond and a bent metal molecule complex.
339
COz, NOz, NzO The adsorption of these molecules has been studied in detail using photoelectron spectroscopy (refs. 90-92), but only very few ARUPS studies have been reported so far. COZ adsorption has been treated recently on several substrate surfaces (refs. 9395) where the molecule was found to dissociate below 2 0 0 K into adsorbed CO and oxygen. A series of normal emission spectra of the system COz/Ni(110) (ref. 93) in Fig.11 indicates the usefulness of ARUPS to identify reaction intermediates in favourable cases. A t low temperature COZ adsorption leads to 2.1.7
1L
O,, 7.293
I
2LCq. 1=293K
2L
co,
ZL CO,
-r:2001 ,1=lLOK
2LCO,.T=llL K
2L CO,. T = 80 W clean
i
6
6
io
i2
iL
EBln(eVI
Fig. 11. ARUP-normal-emission-spectra of COz/Ni(llO) as a function of temperature (spectra b-f) in comparison with the clean Ni(ll0) surface (spectrum a) and a 0-adsorbate (spectrum g) and a CO adsorbate (spectrum h) (ref. 92). mixed chemisorbed/physisorbed layers (spectrum b)), and the physisorbed species desorbs selectively by elevating the temperature (spectra b)-el). Around 200K a spectrum of the pure
340
chemisorbed species is found which shows three features marked with arrows. One additional feature around 5eV (see arrow) is forbidden in normal emission indicating CZV symmetry of the adsorption site. Comparison with results of cluster calculations (ref. 96) shows that this is a bent anionic COz- species. Whether the COZ- species is carbon or oxygen bound to the surface cannot be decided on the basis of the present results. Above 200K (spectrum f)) this species dissociates into CO and 0, both adsorbed on the surface, as is clear from a comparison with the spectra of pure CO and 0 adsorbates (spectra g)-h) ) . It was concluded from this study that COz- is an intrinsic precursor for COZ dissociation. Note that COzis isoelectronic and isostructural to N O Z , which is known to dissociate rapidly upon adsorption also at low temperature (ref. 91). COz is known to react on Ag(ll0) surfaces with co-adsorbed oxygen to form a carbonate COa species. ARUPS has been employed (refs. 97-98) to study the COa orientation. It is found that COS assumes an orientation with Cs symmetry and the plane along the (110) direction a mirror plane. 2.1.8 HCOOThe adsorption of formic acid often leads to the formation of
formate anions. Recently, several groups have studied the adsorption of HC02- on Cu(ll0) with ARUPS (refs. 99-100). Fig. 1 2 taken from the work of Hofmann and Menzel (ref. 99) shows a set of ARUP-spectra of this system for various orientations of light polarization relative to the Cu(ll0) surface azimuths, but all taken in normal emission. For normal emission the selection rules are particularly simple, because the final electron state cPe in the present case belongs to the representation a1 in CzV The x,y,z-components of the dipole operator transform like bl , b2, and a1 , respectively. Since the light always impinges under a finite angle ( a = 2 0 ° ;small z-component and 6 5 O ;large zcomponent), there is always a z component, but bi and bz are selected by going from the (110) to the (001) azimuth. Therefore, bl and bz initial states can be selected in the two azimuths. Comparing spectra a and b we identify bi derived levels at 4.8 eV and 9.5 eV, and a bz derived level at 7.7 eV. Increasing the z-component in spectra c and d shows a1 derived levels at 5.0eV, 9.7 eV, and 13 eV. The a2 level indicated on the basis of theoretical calculations (ref. 101) is dipole
.
341
'ORMATE ICu(Il0) normal
emission
hw=28eV '0 RM ATE MO's Lb,6a,1b23b, Sa, La,
a
x
along
(iiol 10011
[UOlI
tit01
I
E,
I
,
I
I
l
l
I
2 4 6 8 10 12 1L Energy below E,(eVl
Fig. 12. ARUP-normal-emission-spectra as a function of light polarization for HCOz-/Cu(llO) (ref. 99). Explanation see text. forbidden. The observed intensity variations are compatible with a formate ion oriented along the (110) azimuth. The observed influence of binding the anion to the substrate on the topmost three molecular levels is compatible with oxygen coordination to the surface. It appears that formate coordination is similar to COP- coordination. 2.1.9 HzO HzO interaction with metal surfaces has been a topic of interest for a long time because this adsorbate system could be a model to understand processes at and on electrodes (ref. 102). Often, water adsorption leads to bonding configurations that can be derived from that of HzO in ice. Recently, Benndorf and Madey (refs. 103-104) have published a series of investigations on the system HzO/Ni(110) among which are ARUPS studies (ref. 1031, indicating the formation of HzO dimers oriented along the (001) surface azimuth. Cluster formation seems to be an important
342
ingredient to understand HzO adsorption, and has been postulated in almost all studied H2O adsorption systems. 2.1.10 NH3 Ammonia adsorption (refs. 105-107) represents one of the few molecular adsorption systems where azimuthal angle distribution patterns (ref. 105) were used to try to unravel molecular orientation. Fig.13 shows azimuthal patterns from the NH3 le level, 11.3 eV below the Fermi energy. The detector was [iizl
[iizl
“1121 [I@]‘
Fia. 13. Azimuthal variations of the off-normal ( 4 2 - 4 5 O ) emission intensity of the le emission of NH3/Ir(lll) at two different photon energies. The data have been measured for a 120 azimuthal sector (circles), and then symmetrized to 3600 (squares) (ref. 105). positioned off-normal ( 4 2 - 4 5 O ) . and the sample was rotated about the surface normal. Light impinges at 4 5 O . The observed intensity of the le level is recorded and plotted in Fig.13. It is clear that the three N-H bonds of the NH3 molecules must be locked into one fixed orientation on the surface. By comparison with theoretical calculations (ref. 108) it was concluded that the exact orientation of NH3 could not be derived from the experimental data. 2.1.11 Hydrocarbons Acetylene (ref. 1091, ethylene (refs. 109-1111, and benzene (refs. 112-119) adsorption have been studied extensively in the past. As is obvious from the above discussion ARUPS is particularly useful if the symmetry of the adsorbate site is
343
reasonably high, so that selection rules can be defined. For hydrocarbons this is not always the case. As an example, where the selection rules can be applied favourably, we consider here a series of studies on benzene adsorption published by Netzer and collaborators (refs. 113-118). It was deduced that on the group VIII transition metals (Ni,Pd,Pt,Rh) benzene adsorbs basically unperturbed in CSV symmetry with surface bonding occurring through the n-electrons of the intact aromatic ring. On other transition metals the aromatic ring appears to be distorted, for example on Os(OOO1) (ref. 116), as was shown via ARUPS. On Os(oOO1) C6Hs undergoes chemical reactions as a function of temperature, finally forming hydrocarbon fragments on the surface. ARUPS (ref. 119) indicates that before the carbon ring is cracked precursor states are populated on the surface. One of these precursor states is proposed to be a aryne-like C6H4 species with a carbon ring system oriented by about 45O inclined with respect to the surface normal (ref. 119). Preferential azimuthal orientation of benzene molecules on Rh(ll1) has been reported (ref. 120): On Pd(ll1) ARUPS has been used to study the low temperature formation of benzene via cyclotrimerization of CzH2 (refs. 121-122). The spectra of the benzene formed did not show the typical shift of the n-electron states known from chemisorbed C6H6 (refs. 112-120). This was attributed to the co-adsorption of the reacted acetylene. Very recently, the adsorption and orientation of large aromatic molecules like anthracene and tetracene has been studied by Koch and his group via ARUPS (ref. 123). The remarkable intensity variations between o and n electrons, oriented in and out of plane of the aromatic ring plane, observed in these cases are documented in Fig. 14 for tetracene. The spectra indicate that the tetracene plane is oriented perpendicular to the surface plane. 2.2 Co-adsorbates ARUPS has been used in the past, and will be even more frequently employed in the future, to investigate the electronic structure of co-adsorbates. The adsorption of atomic hydrogen induces marked changes in the electronic structure of co-adsorbed CO on Ni(100), as was recently shown with ARUPS by Bradshaw and his group (ref. 1241. This is shown in Fig. 15 where spectra of a pure CO (a), a H+CO
344
18 16 14 12 10
8
Binding Energy (eV)
6
4
2
0
Evac = 0
Fig. 14. ARUP-spectra of a tetracene/Cu(lOO) adsorbate in two measurement geometries as indicated (ref. 123). adsorbate, with both gases exposed to saturation coverage (b), and a H+CO adsorbate, so called I-state (c), where the hydrogen coverage is lower than in case ( b f are shown. The spectra are taken with polarized synchrotron radiation in the forbidden geometry. In spectra (a) and (b) we find the normal behaviour documented in Fig.5. This is typical for CO molecules oriented perpendicular to the surface plane. In spectrum (c), however, the emission intensity of the 40 state is not suppressed, which is consistent with a slightly tilted bonding geometry or a strong distortion of the 4 0 ion state wavefunction. Also, the normal emission spectra with zpolarization are different from a pure CO adsorbate, and there are indications of weak satellite structure on the high binding energy side of the 40 ionization. This is in line with the finding that the adsorption energy (ref. 125) of the I-state of CO+H/Ni(100) is considerably weaker as compared to CO/Ni(lOO), and is similar to CO/Cu(lOO) (ref. 1261, where we expect intense satellite structure similar to CO/Cu(lll) (ref. 11) discussed
345
.t-co -.
c-
CO/H/Ni11001 h w z 3 2 e V a = ( e.50’ k
.... :.: .....-...’c-
LX
..i.
.._
..H+CO
.-..... ’...-.’
........ 1-
..
-..-......
.........
..........
L..,
..’
......... ..b ...... .... ........--..-.. . . .-.--*.<... .,<’., ....
..........
4; 4;
,.co ....
.’...... .. i.
,:
.-.-
.i..
,.,.:.
.:......a .._...
5
...,... .
*--a a...>.,.-.
-2.
.r.
. ..... . -...-
*.-
.....
.-.:.,, .. ...-
..
.-....’%
:
.
-.....-.-.
...-....*..
16
1L
12
8 6 I 2 Energy below E,(eVI
10
E,
Fig. 15. ARUP-spectra of CO-, and CO+H-co-adsorbates on Ni(100) taken in the forbidden geometry (ref. 124). above. CO-alkali-co-adsorbates (ref. 127) are the most frequently tackled co-adsorbate systems with ARUPS. Several different metal surfaces have been studied (ref. 127). The most complete sets of ARUP-spectra exist for Ru(001) and Cu(100) surfaces (refs. 128134. Some important conclusions have been drawn from these studies which were partially in contrast to existing models of CO-alkali interaction at the time (ref. 127). As monitored by the angular distribution pattern and the peaking of the shaperesonance the CO orientation with respect to the surface normal does not change upon alkali-CO-adsorption independent of alkalicoverage, except for a thick alkali film (refs. 128-1341, In the case of the alkali-C0-co-adsorbates on Cu surfaces (ref. 129), interesting variations in the shake up structure have been observed by Heskett and Plummer (ref. 129) as shown in Fig.16, where both the pure CO and the co-adsorbate spectra are presented for comparison. As outlined above, the decrease of the satellite intensity can be a sign of stronger or weaker metal-C0 coupling. Since, however, there are still only two CO bands we must conclude that the metal-CO-bond strength actually increases. In addition to this variation of the CO-metal bond
346
C O + K / C U (100) hw=37eV
e1 =L5'
-
p POLAR1 2 ATION 15OOFF NORMAL EMISSION 2L CO AT 110K I
I
C
K ICU(100) 8,-0.:
Lo ri
h
a
CLEAN Cu(100) L
22
,
,
,
I
,
18
,
,
I
14
,
,
,
I
I0
.
,
.
I
6
,
.
,
I
.
,
2 E= ,O
BINDING ENERGY (eVI Fig. 16. ARUP-spectra for CO/Cu(lOO) (8~0=0.5,curves b and c), and CO+K/Cu (100) (€h= O . 3 , 8 o~=O . 3 ) in comparison. The spectra of the systems before CO adsorption (curves a and d) are shown as broken lines. The peak around 18 eV is due to K3p emissions (ref. 129). CO induced peaks are marked. The spectra were taken for light incidence angle 81=45O and 15O off-normal emission. strength direct CO-alkali short range interactions involving the alkali-s- and
the
CO-ln-orbitals have been
postulated
(ref.
128). Fig.17 shows two sets of spectra, one for the pure CO adsorbate, equivalent to Fig.5, and another one for the alkalico-adsorbate. The spectra in the s o called "allowed" geometry are fairly similar, but in the "forbidden" geometry they are substantially different. The In peaks in spectra b and c are located at different energies and the 4a peak for CO/K has more residual intensity than expected for an unperturbed, perpendicularly adsorbed CO molecule. The shift of the In level in the CO/K-system to lower binding energy is similar to that observed on Pt(ll1) (ref. 135) or on Fe(ll0) (ref. 136). The fact that a states are visible in the "forbidden" geometry may be caused by a slight tilting of the CO molecule or be due to
347
allowed
> u
?=
C
a.
+ C c
c
Fig. 17. ARUP-spectra in "allowed" and "forbidden" geometry (20 off-normal) for CO/Ru(001) and CO+R/Ru(OOl) ( 8 ~ = 0 . 3 3 ) (ref. 128). the immediate vicinity of the K species, such that the symmetry of the coadsorbed CO molecule is broken. The spectra of the R/CO system are interestingly similar to those of systems like CO/Fe(lll) (ref. 6 6 ) . This may mean that in the latter case similar interactions, i.e. between the CO In and the metal surface are active. Very often alkali co-adsorption leads to stronger molecule-surface interactions (ref. 127). but there are cases where the opposite effect is observed. For example, small amounts of alkali precoverages lead to a very strong repulsive interactions with Nz and attenuates Nz adsorption by a factor of 4 while the electronic structure of the adsorbed Nz
348
appears to be the same as without alkali precoverage (ref. 135). ARUPS was used to prove this (ref. 1371, and it has been interpreted as an indication for long range alkali-Nz repulsion. Tentatively, a lack of d-n-backdonation in the case of NZtransition metal bonding has been argued to be the reason for this behaviour (ref. 137). Many other alkali co-adsorbates have been studied using photoelectron spectrosopy (ref. 127). A use of angular resolution, on the other hand, has been rather scarce in these cases. ARUPS has been used recently to study the interaction of COZ and alkali co-adsorbates (ref. 138), benzene with alkali-coadsorbates (ref. 139) on transition metals, and CN-alkali coadsorbates (ref. 140). COZ dissociates into CO and 0 at very low temperatures (T<110 K) when Pd(lll), for example, is predosed with Na (ref. 138). On clean Pd(lll), on the other hand, COP does not adsorb. On thick alkali metal films different COZ reaction channels, i.e. towards the formation of COS are opened (ref. 138). The CN-alkali co-adsorbates (ref. 140) are interesting because they allow direct comparison of the photoemission characteristics with bulk cyanide salts (ref. 141). It is clear that an ionic phase is formed on the surface (ref. 140). Interesting results have been obtained on mixed Nz and rare gas atom layers at low temperatures by Umbach, Menzel and collaborators (ref. 74). A monolayer of NZ on Ni(ll1) consists of two states one of which is chemisorbed and vertically bound to the surface, while the other is physisorbed and probably lies flat on the substrate between the chemisorbed molecules. If such a layer is exposed to Ar, the physisorbed Nz layer is replaced. Research activities on co-adsorbates involving electronegative co-adsorbed species, like oxygen or halogens have been much less intense. There are several reports on photoelectron spectroscopic studies but only a few ARUPS studies have been reported (ref. 142-1931. Again the influence of oxygen co-adsorption on CO-Cu-adsorbates has been studied under the aspect of studying the influence on satellite intensities and absorption geometries (ref. 142). These studies point to specific CO-0 interactions or oxygen induced variations in the CO-metal interaction. In other cases like CO+O on Pd(ll1) the
349
experimentally found results can be considering CO-0 interactions (ref. 143).
understood
without
3.
INTERMOLECULAR INTERACTIONS IN ORDERED OVERLAYERS Intermolecular interactions are always present in real adsorbate systems. Intermolecular interactions determine among other things the chemical reactivity between adsorbed species and also the ordering of the adsorbed overlayers. The present section is dedicated to cover this latter aspect because ordering leads to a two dimensionally periodic arrangement of adsorbed particles. As mentioned in the introduction and illustrated in Fig.1 we can assign a certain space group to this arrangement, and then classify the electronic band states of the system according to the space group. Experimentally, molecular band dispersions were first observed by Horn et al. (refs. 31, 144) for CO overlayers, and interpreted in terms of tightbinding calculations (refs. 31,145) on free unsupported two dimensional CO arrangements. 3.1 Pure adsorbates As an introduction to
the quasi two dimensional band structure of molecular overlayers we discuss the band dispersions and the symmetry properties of a hexagonal overlayer (ref. 27) of CO molecules on a fcc(ll1) surface as shown in Fig.1. If the intermolecular interaction potential is large enough to demand consideration of the two-dimensional crystal periodicity, the overlap of adsorbate wavefunctions is sufficient to produce two-dimensional Bloch states Yk and to make a band description of the electronic structure more appropriate. Then the wave function at a lattice site R1 is related to the wave function at site RZ by: (3) Yk (Ri) = exp[ik(Ri-R~)l’fk ( R z ) where exp [ik (RI-Rz ) I gives the phase difference between the two sites for a state specified by the two-dimensional wave vector k. Before we consider the changes in the band structure introduced by the substrate we will briefly discuss the qualitative behaviour of the band dispersion of a hypothetical support free molecular layer (ref. 145) as shown on the left of Fig.1. We can illustrate the qualitative features of the dispersion by plotting schematically the real parts of a tightbinding wave function in real space for values of k
350
RECIPROCAL SPACE
REAL SPACE 0 0
0 Q-0-
0
0
A T-R MIRROR PLANE SYMMETRY
kz7.O
G (0')
EVEN
0 0 0 0
n
10')
EVEN
PPPP n b"1 ODD
B Fig. 18. (a) Schematic representation of the real and reciprocal space structures of a hexagonal (J3xJ3)R30 CO overlayer-. (b) Schematic representation of a two-dimensional a- wavefunction and two two-dimensional n-wavefunctions at two points of high symmetry in the Surface Brillouin Zone (ref. 27). corresponding to high symmetry points in reciprocal space. Fig.18a shows the real- and reciprocal-space unit cells for the hexagonal structure. The real and reciprocal lattices have two mirror planes, one along the r-M-r line (in reciprocal space), -- - and the other one along the line r-K-M-K. The wave functions along these lines will be even (a’) or odd (a"). Fig.18b illustrates the phases of a o and the two n states at and 8. At ( k = O ) all the wave functions at the different lattice sites are in phase. This results in a strongly bonding configuration for the a state (top row), but an anti-bonding configuration for both n states because the individual n functions change sign about the molecular axis. The n functions have been chosen so that one is even and one is odd with respect to the mirror plane. Because at the wave functions transform according to
---
35 1
co/co (0001) LOW T DISPERSION 4a
5v
hv=40ev,0:55:k,,* 20. 2.12f '
hv=37eV,@:450kl,: 1.62,1.72
d"
hv=35eV,8=30',kl,. 1.09 ,117
8"
hv=3leV,8=30~k,,:096, 1.06
12
11
10
9
8
7
6
5
4
3
2
1
O E,
8"
(ev)
BINDING ENERGY E,
Fig. 19. ARUP-spectra of a (2J3x2J3)R3O0C0 overlayer on Co(OOO1) for different values of the two-dimensional wave -.rector k ,I as indicated in the figure. The positions of the CO induced features are marked with arrows (ref. 27). C6v,
the two n components are degenerate. Therefore, at I; we
have a strong bonding o band and a degenerate antibonding n band. Along the mirror plane k increases from 0 at P to n/(acos30° ) at the zone boundary R . The second column shows the wave functions at A where the arrow indicates the direction of
k. All rows of atoms parallel to k have the same phase but each row has a phase change of n. The result for the o states is that each atom is surrounded by four atoms of opposite phase (antibonding) and two bonding atoms. The o bands therefore disperse upward from ? to T?. In contrast, the even n state is strongly bonding since each lobe of the molecular n orbitals sees only bonding nearest neighbours. The even n band disperses downward from to with the largest difference in the n band is just slightly more bonding than energy. The odd n state at the n state at P since the overlap of the lobes in a line perpendicular to k is antibonding but the overlap between the lines of atoms is bonding. This means that at fi the two n derived bands are no longer degenerate as a consequence of the lower symmetry of the fi point. Thus we have explained the direction qualitative features of the dispersions in the 7 to shown in Fig.1. Analogously the dispersions in the other
w
352
10 0-
COlCO IO001) LO
101-
I26 "26I R 30.
10 2-
B
10 3-
10 L-
10 5-
I
Fig. 20. Measured (circles) and calculated (full lines) kll dispersions of the 40 level in two hexagonal CO overlayers on Co(OOO1). Filled circles refer to the (J3xJ3)R30 structure, open circles to the (2J3x243)R300 structure (ref. 27). directions of high symmetry in the Surface Brillouin Zone can be explained, and we refer to the literature for a more detailed discussion (ref. 27) . Such dispersions can be determined via ARUPS as shown in Fig.19, where spectra of a (243 x 2J3)R30 CO/Co(OO01) overlayer for different values of the wave vector k are plotted. The wave vector is varied by varying the photon energy and the emission angle within the direction of the considered surface azimuth as noted in the figure. The connection between k and the varied quantities is given by: k,, = ( 2 m e h - Z E r i ~ ) 1 / sine 2 (4) where k,, is the wave vector parallel to the surface, which is the conserved quantity. Fig. 20 shows a comparison of calculated dispersions for the 4a-derived band with measured 4 0 dispersions - of CO/Co(OOOl) adsorbates in , r-M direction in two hexagonal ( J 3 x J 3 )R30 and (2J3x2J3)R30 layers (partially based on Fig.19).
353
1.8
\
'\*\
.
A+ AA }Pt (100)
v
c0100011
Ir(ll1)
w Pdi100)
1.4
8 0 0
Pd(ll1) O/Pd(fll) Ni (100) Ni(ll0) Ni(111)
o 0
Fe(1001 CU(ll1)
v
Ru(0001) KIRu(100)
w
A
1.0
\ -t \
\
B(r1=3.65 EXP (- r /I251
0.6
\ &
0.2
I
I
3
L
\
I
5 CO NEAREST NEIGHBOUR DISTANCE
(A1
Fig. 21. Plot of the 4a band widths of various CO overlayers as a function of the CO-CO separation (refs. 11,25-28,30-31,3334,39,143-148). The CO-CO separation has been estimated on the basis of published structure models used to explain the observed LEED patterns. We have artificially set the lengths of the two Brillouin zones equal for a more convenient comparison. Due to the smaller CO-CO distance in the (2f3 x 2J3)R30 layer, the overlap of the 4a CO wave functions increase, and concommitantly, the band width increases. Fig.20 illustrates that the increase in band width can be quantitatively reproduced by simple tight binding calculations in the case of 4a derived bands. In the present case the comparison can be made directly because the number of nearest neighbours is the same in both systems. If, on the other hand, we want to compare dispersions in hexagonal and quadratic systems, the observed band widths have to be corrected for the different number of nearest neighbours. Such a correction is straightforward on the basis of simple tight binding considerations. The result of such a comparison for several different adsorbate systems is shown in Fig.21 (refs. 11, 25-28,
354
30-31, 33-34, 39, 143-148). The data points follow an exponential dependence on the nearest neighbour distance with a decay length on 1.25 A if we disregard the CO-K co-adsorbate for the moment. This strongly supports the conclusion that the 4 0 dispersion is caused by direct CO-CO overlap. Intuitively, this is reasonable, because the 4 0 CO level is not strongly involved in the metal substrate bonding. At the same time we expect a completely different behaviour for the 50 level, because in this case the interaction with the substrate as indicated in the middle of Fig. 1 should have a marked influence on measured dispersion. There is no such linear dependence of the observed band width as a function of CO-CO distances as for the 4a level (ref. 34). A similar plot as for the 40 level exhibits no particular functional dependence, which may be an expression of the participation of indirect through substrate interactions in intermolecular interaction. Care has to be exercised not to jump to this conclusion prematurely, because, due to the stabilization of the 50 level into the region of the In level (see Fig.1) we expect strong 5o/ln hybridization effects which have to be taken into account in the prediction of band dispersions (ref. 27). There are only very few cases, where the complete band structure in the 5a/ln region has been determined. One such example, which shall be considered in the following, is the system CO(2xl)p2mg/Ni(llO) (ref. 2 6 ) . In this system the coverage is 8=1, and the lateral stress is particularly demanding. Fig.22 shows a model of this structure. The interesting structural feature is the glide plane along the densely packed rows ((110) azimuth) of the Ni(ll0) surface. The unit cell of this overlayer contains two CO molecules, which leads to peculiar consequences for the ARUP-spectra. Fig.23 shows the measured dispersions and a calculated tight binding band structure for comparison. A doubling of the number of bands is found. Therefore we observe eight, instead of 3(if In is degenerate) or 4, features for the r point in the Surface Brillouin Zone. The eight features are classified in Fig.23 according to the wave function character of the parential molecular ion state (40, 5 0 , In), and even and odd behaviour with respect to operation of the glide plane (40+, 40-, etc.). Due to the twofold symmetry of the adsorbate, the two components of the In level ( Inx, pointing along the (110) azimuth;
355
Fig. 22. Structure model of the CO(2xl)pZmg/Ni(llO) adsorbate (ref. 26). lny,pointing along the (100) azimuth) are not degenerate. All bands are degenerate pairwise at the X-point which is required by symmetry of the p2mg non-symmorphic space group (ref. 149). The important point is that the p2mg system allows a detailed assignment and comparison with calculations in the region of the 5a/ln band system. Fig.24 shows schematic representations of the In and 5a wave functions at F . The two Inx orbitals in the unit cell interact strongly due to the short distance along the (110) azimuth and split by more than 2 eV. The Iny orbitals interact much less strongly and split only by 0.7 eV. The 5a orbitals split by more than 1 eV. Without the theoretical calculation one is trying to determine the 50 band width by taking the splitting between the 5ot and the Inx- bands which is only 0.6 eV. The observed band dispersion is caused by hybridization of the crossing I n x - and the 5ot bands, which along F belong to the same irreducible representation in the p2mg space group. The values used to correlate 5 0 band widths versus CO-CO distance as mentioned above have been determined without detailed knowledge of 5a/ln hybridization. Therefore we reach the conclusion
356 I
Ni IllO)/CO (2x1) p2mg
Y
-
r r x
A WAVE VECTOR
Fig. 23. Comparison of measured (circles) and calculated (full lines) quasi-two-dimensional band structure of the C0(2xl)p2mg/Ni(llO) system (ref. 26). before that not several such detailed theoretical analysis for various systems have been undertaken, an exponential decay for the 50 band widths cannot be excluded. There is, yet, another interesting aspect of the p2mg band structure: The splitting between the two Inx derived bands at i? is a strong function of the CO tilt angle with respect to the surface normal. Band structure calculations (ref. 26) as a function of the tilt angle showed that the optimum theoretical fit of the measured band structure can be obtained for a tilt angle of 17+2a. This value is in excellent agreement with results of other structure sensitive methods (refs. 150-151). It shows that similar to the gas phase, where photoelectron spectroscopy has been extensively used to determine, e.g. ring conformations (ref. 152),
357
adsorbate photoemission can be extract structural information. -
r
r
used
in
favourable cases to
r
r
Fig. 24. Schematgc representation of a C O - a , and the two CO-n wavefunctions at r of a p2mg structure (ref. 26). The examples for dispersions in quasi two dimensional systems were chosen so far from the many examples of strongly chemisorbed systems. One question is what happens to the dispersions when weakly chemisorbed or physisorbed systems are considered. The latter case is easy: Fig.25 shows the dispersions measured via ARUPS for the system CO/Ag(lll) (ref. 10). We know from the previous section that in this system the CO molecules are oriented with their axis parallel to the surface. It is known from LEED studies that CO molecules physisorbed on graphite form herring bone structures (ref. 153) as shown in the inset in Fig.25. Such structures again belong to nonsymmorphic space groups with two molecules in the unit cell. This is the reason why the molecular ionization bands appear as split in two components, i.e. a bonding and an antibonding combination at r . From symmetry considerations it is clear that these two bands are degenerate at the zone boundary. The splitting is larger for the u levels than for the n level, which is not unreasonable on the basis of intermolecular overlap considerations. A particularly interesting observation has been made or this system if the temperature is increased. These physisorbed overlayers are known to undergo order-disorder transitions (ref. 153). The CO molecules are then no longer locked into a herring bone structure but rotate freely on their
358
r
K'
K
8.3n
>
-
Q,
Y
m
8.7-
9.1L
Fig.
25.
CO/Ag(111)
I
I
I
1.0
0.5
0
I
0.5
k,,I A-7
I
I
1.0
1.5
I
dispersion of the 5a levels for the system (ref. 101. The inset shows the assumed herring bone
kll
structure. site. This destroys the nonsymmorphic structure and, concommitantly, the splitting of the a levels disappears. CO/Ag(lll) is a system where ARUPS can be used to study phase transitions in quasi-twodimensional systems (ref. 10). In the case of weakly chemisorbed systems the situation is slightly more complicated: The reason for this complication is the shake-up structure identified in the previous section (ref. 11). Fig.26 shows the dispersions for the system (J7xJ7)CO/Cu(lll), for which Fig.2 showed an electron distribution curve (ref. 11). In this case the CO molecules are oriented perpendicular to the surface as in the case of the strongly chemisorbed systems. While the integrated 5a/ln dispersion is compatible with other CO overlayer systems, the 40 dispersion is considerably smaller than expected for the given intermolecular separation. The observed value is represented in Fig.21 by the dashed circle. The shake-up which is- as noted above- associated with the 4 0 ionization shows almost no dispersion, but a slight variation in relative intensity with respect to the 4 0 ionization. There are sum-rules (ref. 154) relating intensity and ionization energy of
359
the peaks in the observed spectral function with the quasiparticle energy. These sum-rules are of the type:
ir:
oA(w,k)dw
=
ErnF
(5)
We can apply this sum rule to the observed data and regain a dispersion shown as the open circles in Fig.26. This renormalized 4a band widths can now be favourably compared with the values measured for the strongly chemisorbed systems. This shows that it is the ionization process that introduces the deviations in the observed band widths and not a different intermolecular interaction potential in this case.
-
'"_I- -
11.8 12.0I
I
I l l
I
I
I
I
I1
2.0 1.21 0.40 0.4 l.?
M K
,,
K
I l l
I
I
2.0 M
(El)
Fig. 26. kl, dispersions of the CO induced features (filled circles) for the system CO(J7xJ7)/Cu(lll) (ref. 11) including the 40 satellite (see text). The dispersion calculated via the analysis of the spectral function according to equation ( 5 ) is shown as open circles (ref. 11). way to investigate the substrate mediated intermolecular interactions may be the analysis of the dispersion of the above mentioned molecule induced changes in the region of the metal substrate ionizations (see solid lines in the region of the A
1.0
1 7
I 0.5 0 0.5 1.0 Wave vector Fig. 27. kll dispersions of the Ni3d-CO2n-back-bonding states in the region of the metal emissions in the system CO(2xl)p2mg/Ni(llO~ (ref.63). The full lines are the results of qualitative tight-binding estimations. projected band structure in Fig. 1). Such an analysis has been carried out for the CO(2xl)p2mg/Ni(llO) system (ref. 61). Before the dispersions are analysed we have to ensure that the bands are really localized at the surface of the so1id.i.e. the C02nNi3d features should not exhibit a dispersion as a function of photon energy in normal emission, which is the usually applied criterion for a surface state. Once this has been done, we can determine the dispersion via off normal emission and vary the photon energy such that we choose an appropriate cross section of the feature under consideration. The result of such a -very tedious- analysis has been carried out by Kuhlenbeck et al. (ref. 63) and is shown in Fig.27 for two directions of the Surface Brillouin Zone. There are two important qualitative features of the dispersion curves. First there are no band gaps at zone boundary f , which -as Hund pointed out in 1936 (ref. 155)- is a consequence of the glide plane in the P direction. Secondly, the lower well resolved band can be fitted very well
361
with a tight binding type curve (full lines). A detailed discussion, for which we refer to the original literature (ref. 63), reveales a rather clear picture of the nature of the C02nNi3d interaction. For the case Ni (110) this interaction creates new surface resonances positioned from 1 to 2.7 eV below the Fermi energy with the appropriate symmetry and intensity. This picture seems to be quite incompatible with the Newns-Anderson model (ref. 156) of CO chemisorption, where the C02n orbital is resonantly broadened by interaction with the metal. The tails of this broadened band would extend below the Fermi energy and therefore create a degree of 2n occupancy. In contrast to the inadequacies of the Newns-Anderson model (ref. 156), it i s quite easy to understand the data on the basis of the Blyholder model (ref. 4 ) used to explain Fig.1. In this model we have a 2n level, the width of which is not very important, far above the Fermi energy as the molecule approaches the surface. This level ( or the symmetry adapted combination of levels ) mixes into the metal levels because there is a finite overlap between them. Since the overlap is a matter of symmetry it determines which of the metal bands will couple with the C02n. The question which of the an-induced bands are actually observed is then determined by the strength of the CO2n-metal coupling, and will depend upon the nature of the metal, the crystal face, and the structure of the CO layer. Summarizing this section so far we have shown that ARUPS allows the observation of level specific dispersions. For those levels not strongly involved in the molecule-substrate interaction we can describe the measured dispersions by through space intermolecular interactions that depend exponentially on the intermolecular separation with a decay length of 1.25 A independent of whether they are strongly or weakly chemisorbed. Chemisorbed systems cannot be compared with physisorbed systems because the adsorption geometry changes from perpendicular to parallel orientation. The observed dispersions reflect the global symmetry of the adsorbed layer, and can, in favourable cases, be used to obtain structural information of the adsorbed molecules. In certain systems the dispersion of metal-moleculebackbonding states can be observed. Quasi-two-dimensional level dispersions have so far mainly been investigated for pure CO overlayers. Very recently, several
362
groups have started to study other systems. For example, the dispersions in Nz overlayers on Ni(100) (ref. 73) and on Ni(ll0) (ref. 157) have been determined. Ordered NO adsorbates have recently been studied with ARUPS (refs. 158,159). Steinruck et al. (ref. 158) report on an interesting comparison of the size of the 40 dispersions in the c(4x2)NO/Ni(lll) and the c(4x2)CO/Ni(lll) systems. They find relatively larger 40 dispersions in the CO adsorbate. 3.2 Co-adsorbates Some studies (refs. 34, 143, 147, 160-161) on co-adsorbate systems have been published very recently. In the following we briefly review what is known about band dispersions in ordered co-adsorbates. The first molecular co-adsorbate system that has been studied with ARUPS with respect to level dispersions were ordered K/CO overlayers (refs. 34, 143, 161). The bandwidth found for the 40 level is included in Fig.21 as the filled triangle. Unfortunately, the structure model for the co-adsorbate is not unique (ref. 160). The CO-CO distance used in the present case is based on the assumption that a (J3xJ3)R3Oo CO overlayer is co-adsorbed with a (J3xJ3)R300 K overlayer, which leads to the observed (3x3) overlayer structure (ref. 160). There are other structures possible, which would give shorter CO-CO distances, but the result would always lead to a relatively large band width as compared with pure CO overlayers. Obviously, the coadsorption of K causes the 40 wave function to change considerably, in the sense that the CO-CO interaction is mediated via the co-adsorbed potassium. Very recently, an ordered CO/O co-adsorbate on Pd(ll1) has been studied using ARUPS (ref. 143). Early angle integrated photoemission results (ref. 162) were basically reproduced. The co-adsorption of oxygen shifts the positions of the 40 and 5a/ln bands to higher binding energies. This has been taken as evidence for a strong oxygen CO interaction. The ARUPS study shows that the 40 dispersion, as presented in Fig.21 is in line with those of pure CO adsorbates. Therefore, if there is any distortion of the wavefunction it is smaller than in the case of K/CO adsorbates. Further comparison with other pure CO adsorbates on Pd(ll1) revealed that the observed chemical shift of the CO peaks can be explained exclusively via CO-CO
363
interaction. Therefore, the reason for the high tendency of the CO+O/Pd(lll) system to form COZ well below room temperature (ref. 162) must be due to CO-CO and 0-0 repulsive interactions rather than strong attractive CO-0 interactions within the adsorbate. SYNOPSIS AND OUTLOOK The present chapter shows that ARUPS is a very powerful tool to study the interaction of molecules on and with surfaces, with respect to geometric and electronic structure. Even relatively large molecules like aromatic hydrocarbons and their chemical reactions on surfaces have been successfully studied with this method in the past. Often ordered molecular adsorbates can be used as model systems to study effects of more general physical importance. One promising area concerns the study of the influence of electronic correlations, i.e. many body effects, on energy-vs.momentum disperions in periodic systems: In weakly chemisorbed, ordered molecular adsorbates particular ionizations exhibit intense satellite structure which leads to a breakdown of the band-like behaviour, while other ionizations in the same system may still show pronounced "normal" band dispersions (ref. 11). Our feeling is that more quantitative work should be done in this direction in the future. Another interesting area of research in connection with molecular chemisorption is the study of many-electron-effects accompanying ionizations in the inner valence electron regime. Photoemission has not provided us s o far with detailed spectroscopic information on this region where it is known from the gas phase that the simple one-electron picture of photoemission is known to break down. Although there have been some attempts (ref. 163) to study the inner valence electron regime, results have not been too promising. One reason for the problem may be that substrate emissions swamp the adsorbate features. Therefore experiments at the so called Cooper minimum (ref. 164) of the substrate cross sections could be appropriate to suppress such effects. Several groups have choosen a different approach (refs. 165-173): Angle resolved electron spectroscopy of ion states via autoionization of highly excited states of the adsorbate (sometimes unfortunately called
4.
364
"Resonant Auger Decay"). Certainly, this will be one of the future directions to tackle this problem. Also, we would like to mention a field which has been abandoned after some early work (ref. 174), namely the study of vibrational structure in photoemission of adsorbates. Especially for physisorbates at low temperature in connection with the study of phase transitions and desorption phenomena it should be possible to look for interesting aspects of the coupling between electronic and vibrational states. The investigation of molecular HZ adsorbates could be of interest in this respect. As mentioned in the introduction molecular chemisorption on semiconductor, metal oxides, and multi-component-system surfaces has not been studied with ARUPS to the same extent as metal surfaces. These, even technologically interesting systems should attract some attention in the near future. Finally, with the advent of high brilliance and high flux light sources (ref. 175) it should be possible to excite photoelectrons in a highly localized spot on the adsorbate surface and still have sufficient intensity to do ARUPS of the emitted electrons. This may allow us to move towards the study of more realistic "adsorbate systems" and of adsorption at defects . ACKNOWLEDGEMENTS We would like to thank many colleagues and students for their help and support in carrying out some of the reviewed work. Among the many people we would like to mention in particular: B. Bartos, W. Eberhardt, G. Ertl, H.H. Graen, F. Greuter, M. Grunze, D. Heskett, G. Hohlneicher, G. Illing, H. Kuhlenbeck, R.P. Messmer, K. Muller, G. Odorfer, E.W. Plummer, H. Pulm, D. Saddei, W.R. Salaneck, D. Schmeisser, J. Wambach, G. Wedler. Mrs. H. Koslowski, Mrs. C. Risse, and Mr. H. Rayess are gratefully acknowledged for their technical support. H. Hamann has helped us by carefully reading the manuscript. Without the financial support of the Deutsche Forschungsgemeinschaft, the Bundesministerium fur Forschung und Technologie. and the Fonds der Chemischen Industrie most of our own work could not have been carried out.
365
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123 P. Yannoulis, E.E. Koch, M. Lahdeminhi, Surf. Sci. 182, 299 (1987). 124 R. Klauser, M. Surman, Th. Lindner, A.M. Bradshaw, Surf. Sci. 183,L279 (1987). 125 D.W. Goodman, J.T. Yates. T.E. Madey, Surf. Sci. 9 3 , L 135 (1980). 126 C.L. Allyn, T. Gustafsson, E.W. Plummer, Sol, State Comm. 24, 531 (1977). 127 K P . Bonzel, Surf. Sci. Rep. t3, 43 (1988 128 W. Eberhardt, F.M. Hoffmann, R. DePaola, D. Heskett, I. Strathy, E.W. Plummer, H.R. Moser, Phys. Rev. Lett. 54, 1856 (1985). 129 D. Heskett, E.W. Plummer, Phys. Rev. B33 2322 (1986). 130 D. Heskett, I. Strathy, E.W. Plummer, R.A. Depaola, Phys. 6222 (1985). Rev. 131 D. Heskett, E.W. Plummer, R.A. Depaola, W. Eberhardt, Phys. Rev. m, 5171 (1986). 4863 (1984). 132 J.J. Weimer, E. Umbach, Phys. Rev. 133 J.J. Weimer, E. Umbach, D. Menzel, Surf. Sci. 159, 83 (1985). 134 W. Wurth, J.J. Weimer, E. Hudeczek, E. Umbach, Surf. Sci. 173, L 619 (1986). 135 T K i s k i n o v a , G. Pirug, H.P. Bonzel, Surf. Sci. 133, 321 (1983). 136 G. Broden, G. Gaffner, H.P. Bonzel, Surf. Sci. 84, 295 (1979). 137 R.A. DePaola, F.M. Hoffmann, D. Heskett, E.W. Plummer, to be published. 138 J. Wambach, G. Odorfer, H.-J. Freund, H. Kuhlenbeck. M. Neumann. Surf. Sci. to be published. 139 G. Rosina, G. Rangelov, E. Bertel, H. Saalfeld, F.P. Netzer, Chem. Phys. Lett. 140, 200 (1987). 140 R. Hemmen, M.E. Kordesch, H. Conrad, Surf. Sci. , to be published. 141 H. Pulrn, B. Marquardt, H . 4 . Freund,R. Engelhardt, K. Seki, U. Karlsson, E.E. Koch, W. v. Niessen, Chem. Phys. 9 2 , 457 (1985). 142 E.W. Plummer, private communication. 143 G. Odorfer, E.W. Plummer, H.-J. Freund, H. Kuhlenbeck, M. Neumann, Surf. Sci. 198, 331 (1988). 144 K. Horn, M. Scheffler, A.M. Bradshaw. Phys. Rev. Lett. 41, 822 (1978). 145 I.P. Batra, K. Hermann, A.M. Bradshaw, K. Horn, Phys. Rev. 801 (1979). 146 C.W. Seaburg, E.S. Jensen, T.N. Rhodin, Sol. State Comm. 37, 383 (1981). 147 Heskett, private communication. 148 C. Schneider, H.-P. Steinrfick, P. Heimann, T. Pache, M. Glanz, K. Eberle, E. Umbach, D. Menzel, Verhdl. DPG 0-24.4 (1988). 149 A review collecting experimental information gained via photoemission on systems belonging to non-symmorphic space groups has recently been published by K.C. Prince, J. Electr. Spectr. Rel. Phen. 42, 217 (1987), and we refer to this paper for details. 150 W. Riedl, D. Menzel, Surf. Sci. 163, 39 (1985). 151 Very recent X-ray-photoelectron diffraction results by D. Wesner, F.P. Koenen, H.-P. Bonzel Phys. Rev. Lett. 6 0 , 1045 (1988), and U. Buskotte, M. Neumann to be published confirm this angle.
m,
m,
m,
370 152 R.S. Brown, F.S. Jorgensen in "Electron spectroscopy" Vol 5 (Ed. D.A. Baker, C.R. Brundle), Acad. Press, London 1984) p.2. 153 R.D. Diehl, S.C. Fain, Surf. Sci. 125, 116 (1983). 154 L. Hedin, Phys. Sci. 2 l , 477 (1979); B.I. Lundquist, Phys. Kond. Mater. 6 , 193, 203 11967), and 1, 117 (1968), and 2, 2236 (1969). 155 F. Hund, 2 . Phys. 99, 119 (1936). 156 D.M. Newns, Phys. Rev. 178, 1123 (1969). 157 H. Kuhlenbeck, M. Neumann, H.-J. Freund, unpublished. 158 H.-P. Steinruck, C. Schneider, P. Heimann, T. Pache, E. Umbach, D. Menzel, Surf. Sci., to be published. 159 G. OdBrfer, R. Jaeger, H. Geissler, H. Kuhlenbeck, H.-J. Freund, M. Neumann, unpublished results. 160 J.J. Weimer, E. Umbach, D. Menzel, Surf. Sci. 159, 83 (1985). 161 H.P. Steinriick, E. Umbach, D. Menzel, private communication. 162 H. Conrad, G. Ertl, J. Kuppers, Surf. Sci. 76, 323 (1978). 163 H . 4 . Freund, F. Greuter, D. Heskett, E.W. Plummer, Phys. Rev. 828, 1727 (1983). 164 J.W.Cooper, Phys. Rev. 128, 681 (1962). 165 C . T . Chen, Thesis, University of Pennsylvania (1985). unpublished. 166 E.W. Plummer, C.T. Chen, W.K. Ford, W. Eberhardt. R.P. Messmer, H.-J. Freund, Surf. Sci., 158,58 (1985). 167 C.T. Chen, R.A. DiDio, W . K . Ford, E.W. Plummer, Phys. Rev. B32, 8434 (1985). 168 T M e n z e l , P. Feulner, R. Treichler, E. Umbach, W. Wurth, 166 (1987). Phys. Scr. 169 W. Eberhardt, Phys. Scr. 28 (1987). 170 G. Loubriel, T . Gustafsson, L.I. Johansson, S.J. Oh, Phys. Rev. Lett. 49, 571 (1982). 171 W. Wurth, R. Treichler, E. Umbach, D. Menzel, Phys. Rev. m, 7741 (1987). 172 W. Wurth, C . Schneider, R. Treichler, D. Menzel, E. Umbach, Phys. Rev. 8725 (1988). 173 G. Illing, T. Porwol, H.-J. Freund. H. Kuhlenbeck, M. Neumann, S. Bernstorff, Proc. 3rd Surf. Sci. Symp., Kaprun, Austria, p.81 (1988). 174 W. Eberhardt, E.W. Plummer, Phys. Rev. Lett. 4 7 , 1476 (1981). 175 Technical Report:"BESSY 11- Eine optimierte Undulator/Wiggler Speicherring Lichtquelle fur den VUV und XUV-Spektralbereich.(Eds. A.Gaupp, E.E. Koch, R. Maier) (1986).
m,
m,
m,
371
Chapter 10 METALLIC FILMS ON METALLIC SUBSTRATES K. JACOB1
1
INTRODUCTION There i s p r a c t i c a l and basic i n t e r e s t i n t h i n m e t a l l i c f i l m s on m e t a l l i c
substrates. F i r s t , one might t h i n k o f such processes as m e t a l l i z a t i o n , by which r e a c t i v e m e t a l l i c compounds l i k e s t e e l o r brass are protected against c o r r o s i o n by t h i n l a y e r s o f chromium or n i c k e l . The thickness o f such m e t a l l i c coatings i s i n the range o f several pm, i.e.
the f i l m s have the p r o p e r t i e s o f bulk met-
als. The aim o f t h i s review goes beyond t h i s thickness range t o thicknesses of up t o several monolayers (ML), a range which can be q u a n t i f i e d by most o f t h e known s u r f a c e - a n a l y t i c a l techniques, As we w i l l show, i t i s a l s o t h e range i n which the t r a n s i t i o n i n e l e c t r o n i c s t r u c t u r e from atom t o b u l k occurs. Recently, w i t h extension o f the development o f e l e c t r i c a l devices i n t o t h e submicron
range, one r e a l i z e s the importance o f understanding and c o n t r o l l i n g t h e growth
o f u l t r a t h i n metallic films.
The
same i s t r u e
also
for
photovoltaic
and
magnetic devices w i t h t h e i r great promise. I t seems t h a t t h e f i e l d o f u l t r a t h i n m e t a l l i c f i l m s i s bound t o become ever more important. M e t a l l i c f i l m s on m e t a l l i c substrates have been i n v e s t i g a t e d so f a r under various aspects, i n c l u d i n g the geometrical s t r u c t u r e o f t h e adlayer,
t h e bind-
i n g energy o f t h e adsorbed metal atom, or number d e n s i t i e s and morphology o f the n u c l e i . Auger e l e c t r o n spectroscopy (AES),
low-energy e l e c t r o n d i f f r a c t i o n
(LEED), and thermal desorption spectroscopy (TDS) have been used f o r t h i s purpose. The pioneering work was performed by Palmberg and Rhodin (1). Studies o f t h i s k i n d have been undertaken since then by many other groups, e t a l . (2-4),
Bauer e t a l . (5-9) o r Venables e t a l .
e.g.
by Rhead
( 1 0 , l l ) . The reader i s r e -
f e r r e d t o several e x c e l l e n t review a r t i c l e s (3,6,9,10). R e l a t i v e l y few atttempts have been made t o evaluate t h e e l e c t r o n i c s t r u c t u r e o f d i f f e r e n t m e t a l l i c adsorbates, e.g.
by photoemission. A pioneering work
was performed by Eastman and Grobman i n studying t h i n Cu and Pd f i l m s on an Ag substrate (12). It has been w e l l recognized t h a t t h e e l e c t r o n i c s t r u c t u r e p l a y s an important r o l e i n several nucleation phenomena. Thus,
i n discussing the
a s t o n i s h i n g l y l a r g e d i f f e r e n c e s between Ag and Au on W(110) and Mo(ll0) subs t r a t e s Bauer and Poppa (7) have mentioned the e l e c t r o n i c s t r u c t u r e as a poss i b l e explanation. For basic research one important aspect i n studying t h i n m e t a l l i c f i l m s i s the t r a n s i t i o n from t h e atomic t o t h e bulk state.
There a r e several examples
372
f o r which layerwise growth has been found,
i n which case two-dimensional
(20)
c l u s t e r s can be a n t i c i p a t e d i n t h e sub ML region. Such 20 c l u s t e r s represent an intermediate s t a t e between atom and bulk. intermediate state.
Surface-analytical
The complete ML i s a l s o such an
methods l i k e LEED o r AES supply some
i n f o r m a t i o n on t h e average s i z e and shape o f 2D c l u s t e r s . Also, more r e c e n t l y , imaging methods have been developed such as t h e Scanning Tunneling microscopy
(13) and LEED microscopy (14) which open up many new ways t o study s i z e and shape o f 2D c l u s t e r s . These developments make t h e i n v e s t i g a t i o n o f m e t a l l i c f i l m s on s i n g l e c r y s t a l surfaces down i n t o t h e sub ML r e g i o n very promising f o r g a i n i n g some i n s i g h t i n t o the atom-to-bulk
t r a n s i t i o n . We w i l l show how angle-resolved UP
photoelectron spectroscopy (ARUPS)
c o n t r i b u t e s t o answer t h i s question.
This
method makes i t possible t o d i s c r i m i n a t e between atomic l i n e s , 2D bands and 30 bands i n the conduction-electron
region.
I t seems t h a t t h e t r a n s i t i o n from
atomic l i n e s t o 30 bands occurs between 0.1 and 10 ML. I n studying t h i n m e t a l l i c f i l m s , one furthermore encounters the problem o f n u c l e a t i o n and f i l m qrowth. We can touch upon t h i s important p o i n t o n l y b r i e f l y , since the i n v e s t i g a t i o n o f t h e e l e c t r o n i c s t r u c t u r e i s n o t the o n l y key t o
understand t h i s phenomenon. I t may be i n t e r e s t i n g t o note t h a t t h e s i t u a t i o n i s q u i t e d i f f e r e n t f o r the condensation o f r a r e gases (e.g.
Xe),
where one can
d i f f e r e n t i a t e beween s i n g l e Xe atoms, 2D Xe i s l a n d s and Xe i s l a n d s i n t h e second and t h i r d l a y e r on t o p o f the complete f i r s t l a y e r from t h e b i n d i n g energy (BE) o f t h e Xe 5p l e v e l s along (15-17).
Very r e c e n t l y s i m i l a r observations have
been made f o r a l k a l i metals as we w i l l discuss below. The growth o f t h i n m e t a l l i c f i l m s i s governed by l a t t i c e and svmmetry matching o f the adlayer w i t h t h e supporting substrate. From t h e case s t u d i e s we
w i l l see which range o f l a t t i c e mismatch has been observed. The r e s u l t o f mismatch i s a r a t h e r l a r g e amount o f s t r a i n w i t h i n the f i r s t l a y e r s o f t h e f i l m .
So f a r i t i s n o t c l e a r whether t h i s s t r a i n can be visualized,
e.g.
i n photo-
emission. We w i l l make t h e p o i n t t h a t f o r the ML t h e question o f s t r a i n has t o be disucssed anew i n t h e l i g h t o f a possible i n t r i n s i c ( i n general smaller) l a t t i c e constant w i t h i n the ML. Nevertheless, f o r t h i c k e r layers, p e r f e c t epit a x i a l growth c e r t a i n l y needs a l a t t i c e match o f 1 % o r b e t t e r .
It has been demonstrated already i n the foregoing chapters t h a t ARUPS i s e s p e c i a l l y w e l l s u i t e d t o evaluate a 2D e l e c t r o n i c s t r u c t u r e . Therefore, t h e ML and t h e t r a n s i t i o n from sub ML t o supra ML coverage i s very accessible t o
ARUPS.
It also has been noted t h a t the ARUPS signal comes o n l y from very few
l a y e r s near the surface ( c e r t a i n l y l e s s than 10) due t o t h e very small escape depth o f t h e photoelectrons i n the accessible range o f photon energies. Therefore, a 10 ML t h i c k f i l m , which i s s t i l l an u l t r a t h i n f i l m , i s t h i c k enough f o r studying p r o p e r t i e s o f t h e bulk metal.
373
An i n t e r e s t i n g problem a r i s e s i n t h i s context, namely t h e existence o r non-
existence o f i n t e r f a c e states.
There are o n l y some very recent examples o f
experimentally v e r i f i e d i n t e r f a c e states. The main problem here i s t o separate i n t e r f a c e from ML states,
n e i t h e r o f which i s known y e t f o r most systems.
It
may be necessary t o note t h a t i n order t o i n v e s t i g a t e ML as w e l l as i n t e r f a c e s t a t e s one needs n o t only p e r f e c t epitaxy b u t a l s o s i n g l e domains o f ordered adlayers. This i s n o t a t a l l a t r i v i a l problem, since most ML are ordered w i t h -
i n hexagonal close-packed (hcp) phases which tend t o a l i g n t h e i r t i g h t l y packed rows along or n e a r l y along t i g h t l y packed rows o f the substrate. Therefore,
a
f o u r f o l d symmetric substrate surface l i k e t h e f c c (001) surface mostly gives r i s e t o two domains which are r o t a t e d by 90" against each other. One p o s s i b i l i t y t o circumvent t h i s d i f f i c u l t y i s t o use the twofold symmetric f c c (110) sur-
face. This attempt can be successful only i n p a r t , since many o f these (110) faces are reconstructed, preventing a f l a t metal f i l m from growing
or promoting
a l l o y i n g o f t h e adatoms w i t h the substrate. On a f c c (111) substrate surface very o f t e n t h e r e i s a small r o t a t i o n a l angle a between t h e adlayer and subs t r a t e hcp l a y e r s g i v i n g r i s e then t o two adlayer domains r o t a t e d by +a against t h e substrate. The choice o f t h e substrate i s important f o r several reasons. I t determines t h e growth mode, enables or prevents i n t e r d i f f u s i o n , and obscures t h e adsorbate emission, i f substrate emission evolves a t t h e same energy.
One p o s s i b l e way t o
solve t h i s problem i s t o use an sp metal w i t h i t s nearly f l a t sp-band as subs t r a t e i n s t e a d o f a d-band metal. I n an attempt t o evaluate the t r a n s i t i o n from atom t o bulk from t h e study o f t h i n m e t a l l i c f i l m s we l i k e t o compare t h i s study w i t h c l u s t e r studies. This technique, w h i l e being most useful for a f i r s t look, encounters l i m i t i n g d i f f i c u l t i e s . So f a r i t has n o t been possible t o prepare c l u s t e r s o f one s i z e only; i n s t e a d one prepares a d i s t r i b u t i o n o f c l u s t e r s w i t h d i f f e r e n t sizes. There i s no i n - s i t u
-
i.e.
d u r i n g spectrocopy
-
access t o shape and s i z e of t h e c l u s t e r s
being analyzed. Furthermore, spectroscopy mostly i s done on c l u s t e r s f r o z e n i n t o a m a t r i x o f i n e r t gases i n order t o increase the c l u s t e r density. T h i s i n troduces t h e problem o f the so-called m a t r i x - e f f e c t ,
i.e.
how t h e m a t r i x i n f l u -
ences shape and e l e c t r o n i c s t r u c t u r e o f t h e i n d i v i d u a l c l u s t e r . Thus, c l u s t e r s on a s i n g l e - c r y s t a l l i n e surface are f o r a longer time amenable t o a wider range o f spectroscopies. But the i n f l u e n c e from the support i s a more severe problem i n t h i s case.
I n t h e f o l l o w i n g we w i l l discuss the e l e c t r o n i c s t r u c t u r e o f t h i n m e t a l l i c f i l m s on metals, which i s mainly evaluated by ARUPS.
I n a f i r s t step the t h i n
m e t a l l i c l a y e r s can be analyzed i n terms o f BE and o p t i c a l d e n s i t y o f s t a t e s and t h e i r development w i t h thickness. This step can be performed a l s o i n an angle-integrated photoemission experiment. For t h e ordered ML, ARUPS a f f o r d s a
374
wave-vector-resolved analysis of the conduction band. For this purpose the known relation for k,,
can be applied. klis the wave vector parallel to the surface layer, Ekin the kinetic energy of the emitted photoelectrons in the vacuum, and 0 the angle of emission with respect to the surface normal. Using the trivial relation between Ekin and the binding energy related to EF EsF, hw
=
I E B ~ I+ @ + Ekin,
the 20 band structure EBF(kl) can be determined. Cp denotes the work function of the surface. For greater thickness the bulk (3D) metal develops. The conduction band changes, in general it broadens. The photoemission process changes dramatically. Now the photoelectrons are excited into empty bulk states under k-conservation in the reduced Brillouin zone. As a consequence the transition becomes strongly hw dependent. This dependence is a reliable proof that the photoexcitation process occurs in the 30 bulk. From (2) one easily recognizes how the work function can be determined by photoemission. If we ask for the energy of the Fermi edge, we have IEBFI = 0 by definition, and Ekin is the kinetic energy of the photoelectrons excited from EF. Therefore, Cp is given by the difference between hw and Ekin at EF. Using a discharge lamp hw is exactly given to a few meV only. Therfore, how precisely @ can be determined depends on the precision in determining Ekin of EF. The latter is given by the difference between energies of the Fermi and the secondary-electron edge. In an AR mode these edges can be measured with an accuracy of ?lo meV, and the width of the secondary-electron edge turned out to be as sharp as the Fermi edge (20). Therefore, for an AR mode and normal emission, @ can be determined absolutely to 9 0 meV. It should be stressed also that there i s no need for any extrapolation at the secondary edge (or threshold), as is commonly performed in the A1 mode, since in the AR mode one always collects secondary electrons with k, = 0 at normal emission. For an ideal system we expect the following changes with thickness i n the ARUP spectra from conduction electrons. For isolated atoms in the sub ML region we expect atomic lines without any k-dependence of EB and being only broadened by 0.3 to 1.0 eV, as is known for the condensed state mainly due to life-time effects. If these atoms then coagulate into 20 islands, we expect a 2D band structure to build up. For two or more ML the ARUP spectra may be smeared out due to overlapping features from the 20 bands and the beginning of 3D transi-
375
t i o n s . Then, a t even higher thicknesses, we expect t h e 3D ARUP spectrum f o r a t h i c k s i n g l e - c r y s t a l l i n e f i l m t o evolve i d e n t i c a l l y t o t h a t from a bulk sample.
To our knowledge such an i d e a l system has n o t y e t been found. Only some aspects have been v e r i f i e d so far,
and several problems should be mentioned b r i e f l y .
One problem i s t o d i f f e r e n t i a t e between 20 band s t r u c t u r e and i n t e r f a c e states.
We w i l l show by comparing our own r e s u l t s w i t h others t h a t t h e character o f t h e s u b s t r a t e i s very important. I t seems t h a t d-metal substrates e x h i b i t d-derived i n t e r f a c e s t a t e s which are as intense as t h e adlayer and substrate s t a t e s themselves.
Our conclusion w i l l be t h a t the best approximation o f t h e 20 band
s t r u c t u r e o f conduction d s t a t e s i s obtained by s t a r t i n g w i t h an sp substrate. For t h e development o f an s p - l i k e ML band there e x i s t s a t the moment o n l y t h e example o f Cs. The next problem i s t o understand,
a t which thickness t h e 3D
band s t r u c t u r e develops. There are r e l a t i v e l y l a r g e d i f f e r e n c e s found between d i f f e r e n t systems.
I t w i l l be shown t h a t the work f u n c t i o n i s very i n d i c a t i v e
f o r t h i s transition. The o u t l i n e o f t h i s chapter i s as follows.
From the given arguments i t has
become c l e a r t h a t t h e c h a r a c t e r i z a t i o n o f t h e t h i n f i l m s i s important w i t h spect t o t h e i r growth mode,
thickness and alignment t o t h e substrate.
re-
There-
fore, we b r i e f l y discuss t h e experimental aspect o f determining t h e ML coverage by AES.
Then we present an overview o f t h e d i f f e r e n t systems known so f a r ,
ordered according t o t h e k i n d o f t h e adlayer metal.
We s t a r t w i t h t h e noble
metals Cu, Ag, Au, go then t o the 3d t r a n s i t i o n metals, mention Pd and P t and t u r n f i n a l l y t o t h e sp metals, e s p e c i a l l y t o the a l k a l i n e and e a r t h - a l k a l i n e metals. We do n o t discuss r a r e - e a r t h metals,
since t o o l i t t l e i s known about
these systems a t t h e moment.
We w i l l see t h a t from t h e small number o f systems studied so f a r o n l y very f i r s t and t e n t a t i v e conclusions can be drawn.
2
AUGER ELECTRON SPECTROSCOPY FOR THICKNESS ANALYSIS Most o f our knowledge o f the e l e c t r o n i c s t r u c t u r e o f t h i n m e t a l l i c f i l m s
o r i g i n a t e s from ARUPS. The discussion o f such studies w i l l f i l l t h e g r e a t e s t p a r t o f t h i s chapter.
However,
besides ARUPS data, a d d i t i o n a l i n f o r m a t i o n i s
c o l l e c t e d a l s o from o t h e r surface-analytical
techniques. The geometrical s t r u c -
t u r e and t h e alignment o f t h e adlayer i s very o f t e n determined by LEED. I n t h e f u t u r e , methods which analyze only t h e topmost l a y e r may become more important. Such methods as i o n s c a t t e r i n g spectroscopy (ISS) and photoelectron d i f f r a c t i o n
(PED) are n o t w i d e l y used a t the moment. For our t o p i c the most important subs i d i a r y technique i s AES. However, we w i l l not discuss t h a t i n g r e a t d e t a i l here, f o r we only want t o show how s t r u c t u r a l i n f o r m a t i o n can be e x t r a c t e d from
AES.
376
Mostly, the AES data are taken from the energy-distribution curve N ( E ) of the secondary electrons in its derivative mode dN/dE. For coverages up to several ML the peak-to-peak amplitude in the dN/dE curve of an Auger transition is a quantitative measure of the coverage. For the analysis of a metallic film A (from adsorbate or adlayer) on a substrate S one has available both the signal from the metal and from the substrate. The adlayer signal IA will increase and the substrate signal Is will decrease with coverage. The rate of these changes depends characteristically on the morphology of the adlayer. Let us consider first the Frank van der Merwe (FM) growth mode for which the adlayer grows layer by layer. Assuming that the change of Is(z) with thickness z is proportional to Is(z), i.e.
and that each adsorbed atom is smeared out into an infinitely thin 20 layer, one obtains Is(z)
Is(o) exp(-z/Xs).
=
(4)
A S is the mean free path for inelastic scattering of the outgoing electrons which originate from the substrate. For reasons of simplicity this and the following formulae are given for an emission direction normal to the surface. For an emission under an angle 0 with respect to the surface normal the effective layer thickness will increase by a factor (cos@)-l. The curve according to equation ( 4 ) i s given in fig. 1 by a broken line. The model calculations given in fig. 1 are performed for a ML thickness of d = 2.5 and X s = 4.0 8, the latter value being near the minimum for most substances (18). In reality the adlayer will grow laterally atom by atom and not by adding thin 20 slabs. This gives rise to straight lines with a change in slope after completion of every ML, as shown in fig. 1 by a line. The growth is described then by:
Is’(z)
=
x Is(o) exp(-nd/Xs) + (1-x) I s ( o ) ,
(9
with x the fraction of the ML, by which the substrate is covered. d is the thickness of the ML and n = 1,2, the number of the adsorbed layers. Equation (5) describes a sequence of straight lines with breaks in slope after completion of the nth layer. These breaks lie on the broken curve from equation ( 4 ) , i . e . just at the ML breaks, the continuous model ( 4 ) and the discrete model ( 5 ) coincide. In the continuous model dJ/dz is larger at the beginning and smaller
...
377
when the ML is nearly completed compared to the constant dJ/dz value for the discrete model (5). In the continuous model every additional slab weakens somewhat less than the foregoing, whereas in the discrete model each additional atom adds a whole package of thin slabs with lateral extension of only one atom and with their different weakening power thus adding a constant weakening contribution for each atom.
''hi '\
,
1
I
2
3 COVERAGE 0 (MLI
L
Fiq. 1: Auger intensities I(@) of a Auger transition of the substrate S as function of coverage @of the adlayer A in units of monolayers (ML) for the three different growth modes as indicated by the insets.
With d = 2.5 A and X s = 4.0 A the model calculations of fig. 1 exhibit nearly the strongest deviation from exponential decrease which i s possible for normal emission. For larger exit angles this deviation can be larger. Considering 0 = 80", which would be really an extreme case, z/X = 3.60 compared to value down to 0.027 at the 0.63 for 0 = 0". This would decrease the I(@)/I(o) 1 ML break resulting in a very strong deviation from the exponential curve. Under the same assumptions the adsorbate Auger intensity is given by:
for the continuous model and by
IA(z)
=
x IA(~) [ l - exp(-nd/XA)l
(7)
for the discrete model. One gets these curves by mirroring the curves of fig. 1 at the I(O)/I(o) = 0.5 line. Two useful formulae can be deduced from the above equations. From (4) the thickness of the ML can be deduced as:
Furthermore,
This equation holds for adlayer and substrate Auger intensities, By (9) deviations from the layer-by-layer growth mode can be easily detected. Besides the FM mode two other growth modes are indicated in fig. 1. In the Stranski-Krastanov mode (SK) only the first ML grows as layer on top of which 3D cluster growth continues. For the SK mode the ML break is well developed. The slope beyond the ML break depends on the size of the 3D clusters. For large clusters a horizontal line is found beyond the ML break. This can be understood easily. Let us assume that one atom covers 5 %', i.e. approximately 2x1013 atoms cover lmd. If we condense these atoms into one cube, it will cover 3.7~10-5 mm2 and is therefore far below the limit which can be detected by AES (which is 10-2 to 10-3 mm2 probing a surface area of 1 mm2). Thus, the slope in fig. 1 indicates much smaller clusters. From the change of slope a mean size of the clusters can be calculated. This is reasonable if, as sketched in fig. 1, a constant slope over several layers indicates a constant cluster size distribution. The Vollmer Weber (VW) mode is the same as the SK mode without a complete ML in the first layer. In fig. 1 a rather similar slope is taken arbitrarily for the VW and SK modes in the cluster range. In general, the cluster distribution can be quite different. It should be noted that from the experiments the SK mode turns out to be the most common case. From basic thermodynamics this is quite understandable. The quantity to be considered here is the specific surface free energy T. Neglecting edge energies as well as shape and size dependencies one has to consider
which is the difference between the specific surface-free energies of the adsorbate (A), the interface (I), and the substrate ( S ) . For A > o the VW mode is the equilibrium mode, whereas A s o holds for the SK and the FM mode. Bauer
379
(6) has pointed t o the f a c t t h a t f o r the FM ( l a y e r by l a y e r ) mode A s o has t o be f u l f i l l e d f o r each new layer. This w i l l be the case o n l y when adsorbate and s u b s t r a t e are very s i m i l a r :
TA
= TS, TI = 0. From t h i s simple argument i t be-
comes c l e a r t h a t t h e SK mode i s t h e most l i k e l y one.
It has t o be noted t h a t
f o r p r a c t i c a l cases the above argument i s not very h e l p f u l : Exact
‘I
values are
n o t known i n most cases, and the e q u i l i b r i u m c o n f i g u r a t i o n may n o t be reached, since t h e m o b i l i t y o f the incoming atoms may n o t be l a r g e enough. Thus, pending on substrate temperature, observed,
de-
d i f f e r e n t metastable c o n f i g u r a t i o n s may be
and i t has t o he proven experimentally which growth mode occurs i n
each case.
Fiq. 2: Auger i n t e n s i t i e s from Mo substrate and Pd adl a y e r as f u n c t i o n o f evapor a t i o n steps. From (8).
5
0
10 15 NUMBER OF 1 mnn DOSES OF Pd
20
25
From an experimental p o i n t o f v i e w i t i s most d i f f i c u l t t o v e r i f y t h e FM mode, since some s c a t t e r o f experimental p o i n t s may round o f f t h e breaks i n t h e Auger
curves.
The most important p o i n t
i s to
have a l l
settings f o r
the
evaporation source, the AES detector and sample p o s i t i o n w e l l reproducible. The best curves are published by Bauer and h i s coworkers. One example i s shown i n f i g . 2. I t e x h i b i t s r e a l l y s t r a i g h t l i n e s f o r the Is(Mo) as w e l l as f o r IA(Pd). I n o t h e r cases, where a d d i t i o n a l data are c o l l e c t e d depending on thickness, t h e s c a t t e r of t h e data may increase g r e a t l y . One o f these examples i s presented i n
3, where a k i n d o f SK mode i s demonstrated f o r Ag/A1(111)
fig.
(19).
from our group
One c l e a r l y recognizes a break a f t e r one ML and a s t r a i g h t l i n e up t o
about 4 ML. By evaluating the data i n d e t a i l we found a completion o f t h e M L up t o 87% before the second l a y e r s t a r t s growing and estimated the c l u s t e r on t o p
o f t h e f i r s t ML t o be 3-4 l a y e r s t h i c k . As Rhead e t a l .
(3) have pointed out t h e r e are several o t h e r more com-
p l i c a t e d growth modes possible besides t h e three simple cases o f f i g .
1. For
380
rt
I
1
I
I
I
I
Fiq. 3: Auger intensities for Ag layers vapor deposited onto Al(111) as function of evaporation time. The kinetic energies of the Ag and A1 transitions are given in parentheses. The sample temperature was 300 K. From (19).
I
I C
200
-
LOO 600 EVAPORATION TIME I s
800
instance, it is quite possible that real exponential behavior is exhibited over the whole thickness range or starting with the second layer for the SK mode, if there is simultaneous multilayer growth. This mode can be operative for high supersaturation and low substrate temperature when the atoms may adsorb at the site, where they hit the surface, Furthermore, the discussion above breaks down, if the sticking coefficient varies with thickness (which is, on the other hand, very unlikely for metallic adsorbates and rather low substrate temperatures). Another underlying assumption is the neglect o f interdiffusion, which has to be checked in each case. NOBLE METALS The noble metals Cu, Ag and Au are the most frequently studied among the thin metal film systems. This is certainly due to the importance of these metals as electrical conductors. Besides this, the investigations are facilitated by the chemical inactivity of these metals. In the following we discuss each of the three metals separately. Some conclusions are drawn in section 3.4, where some tables of BE are presented. 3
3.1 Comer There are two major ARUPS studies of Cu on Ag(001) (21,22) which confirm pseudomorphic growth up to a thickness of 2-3 Cu layers. These Cu layers are expanded by 13 % relative to bulk Cu. The large misfit induces more strain than can be sustained by the adlayer during FM (layer-by-layer) growth. Therefore, after 2-3 ML the system switches to the SK mode as can be seen from the deterioration of the LEE0 pattern and the shallow slope of the AS curves.
381
Fiq. 4: Series of AR spectra taken along the Z azimuth for 1 ML Cu on Ag(001). The photon energy is 30 eV. Three bands of features (indicated by the tick marks) are attributed t o Cu 3d states and are seen to disperse in energy as 0 i s varied. The Cu 3d origin of the features is established by comparison with data from clean Ag and from Ag with 2-6 monolayers of Cu coverage, Emission at 0 = 40" originates near the M symmetry point. From (21).
-a
-6
-4
Energy
-2
0
(eV)
Fig. 4 exhibits a series of ARUP spectra taken in the TM azimuth for different angles of emission 0 (21). Especially, above the upper edge of the Ag 4d emission of the substrate at about 4 eV, well resolved Cu-derived peaks can be seen exhibiting some dispersion. The 20 band structure is presented in fig. 5, as it is deduced by the authors from all measured spectra including those of fig. 4. By using well suited angles and photon energies also states near 5 eV are identified as Cu states which overlap with the Ag bands from the -
-
-
Ag(OO11* 1 ML
Cu
-I
Fiq. 5: 2D band structure of the Cu monolayer. Features displaying clear A 1 or ’c2 symmetry are indicated by solid circles while open circles represent A1 or Z7 states. The remaining features are plotted as triangles or, in the case o f unresolved peaks, as error bars soannina the Drobable ’peak posit\ons. Bands are drawn through the points in qualitative agreement with theory (23,24). Bands with C2 or A2 symmetry are indicated by dashed lines. The shaded area indicates the projection o f the Ag 4d bulk band structure. From L
4
l
2
-
'.
I -4
-5 I
I5
10
05
0
05
I0
(21)
-
382
substrate. For the ML only peaks are taken, which increase in intensity also for the 2 and 3 ML thicknesses. Other Cu-induced features are not discussed, since in the Ag 4d region there is no way to differentiate between redistributed Ag features and real interface states. The former effect may arise from increased scattering due to the higher density of defects at the interface compared to the clean Ag(001) surface. Thus, it is interesting to note that (a) the derived band width of the Cu ML (3.15 eV) is essentially identical to that reported for bulk Cu (3.20 e V ) , and (b) the bands are more tightly bound than bulk Cu bands by only 0.25 eV. These findings agree best with a calculation for a Cu ML on Ni(001) (23) indicating that the lattice constant is only o f minor importance for the 20 band structure. For the same system (Cu/Ag(001)) Smith et al. (22) arrive at a somewhat different 20 band structure, which i s shown in fig. 6. There is a further band resolved nearer to EF and, more important, the total width of the ML bands is only 1.5 eV and lying completely above the substrate 4d emission. This finding led the authors to vary the result of a ML calculation (24) in order to explain their result as pointed out in the caption of fig. 6.
Fiq. 6: Energy bands of the Cu (100) mono1 ayer on Ag(100). Full curves, LCAO bands calculated by Smith et al. (24) for an isolated Cu(100) monolayer, after reducing the energy dispersion by a factor o f 1.8 in order to correct for the Cu lattice expansion and rigidly shifting the bands 1.2 eV away from the Fermi level. From (22).
I
R
r
1 X
The second well defined Cu adlayer system is Cu/Ru(0001) (25-27), which has the advantage of being composed of two immiscible components. Cu grows pseudomorphically up to one ML on the Ru(0001) surface with a 5 % tensile strain with respect to the Cu(ll1) bulk lattice, which is largely reduced compared to the Ag(001) surface. Houston et al. (25) have been able to separate a true interface state which is, according to their slab calculations, localized in the Cu and outermost Ru layers. Guided by their calculations they have been able to separate this state from the Ru substrate emission near the ?t point at 1.5 eV
383
Fiq. 7: ARUP spectra taken with He1 radiation at normal incidence and an electron emission angle of 52" for Cu on Ru(0001) are shown as functions of Cu coverage. The intensity of the various curves has been normalized at the Fermi level, EF. The individual curves are matched to their corresponding Cu coverages in monolayers by the solid lines while the saturating behavior of the interface state at approximately -1.4 eV is identified by the dashed lines. From
(25).
-6.0 -5.0 4.0 -3.0
-2.0
-1.0
0.0
BINDING ENERGY-OV
below EF, as shown in fig. 7. From this figure it is also seen that the Cu ML emission evolves at nearly the same energy as the Cu 3d emission for higher coverages. Houston et al. did not try further t o extract a 2D band structure. They stressed that for 1 ML or less "the Cu 3d levels mix stronqly with the Ru 4d states". This may become even more clear from their calculated bands as shown in fig. 8. They point out that without a strong interaction between the first Cu layer and the Ru substrate a pseudomorphic growth with a 5 % tensile strain would be difficult to understand. They felt this to be in contradiction
aa
9 s w
-20
F
-
persions along the r - K s.ymEfmetry line for a five-layer Ru(0001) film covered on both ’faces by a 1 ML 1x1 Cu overlayer. States indicated by ,. heavy lines and arrows are ’strongly weighted on the outer Cu overlayers and first underlying Ru layers of the film.
384
Fiq. 9: ARUP spectra (normal emission, mixed s/p polarization) from Cu/Ru bilayers as a function of the Cu coverage (OCU= 0.38... ? 5 ML), at a fixed photon energy of 30 eV. Since only the Cu d-band position is to be shown, the curves have not been normalized with respect to their absolute intensity. The dotted line represents the spectrum o f the uncovered Ru(001) surface. The Cu was evaporated with the substrate at 1000 K. From (26).
\
ML
038
.- _.
, - 00 I
-1 E -0 F initial energy lev 1
-8 -7 -6 -5 - L -3 -2
to the analysis o f Vickerman et al. (26), which found the Cu 3d and Ru 4d emission just added "without any hint of a stronq electronic interaction". Fig. 9 presents some of their data (26). They evaluated also a 20 band structure as shown in f i g . 10 and found their results of the ML to be in agreement with the work of Richter e t al. (27). q.0
-
,
I
1
-% -1
Fiq. 10: 20 band structure of the Cu film on Ru(0001). The open circles refer to a 0.82 ML film ( h a = 28 eV). The squares (ha= 30 eV) and the diamonds ( R w = 50 eV) refer to a 2 ML Cu film. The solid circles indicate the position of the Cu d-bands as obtained experimentally in (28) for Cu on NixCui-x(ll1). From (26).
%
m
$ -2 e
-2 -3 .-
.-C
-c
-5
P parallel momentum
ii,,
385
In order to separate the adlayer from the substrate state an interesting experiment was performed by Shek et al. (29) for Cu on Pt(ll1). From LEEO and AES they argued that the ML grows pseudomorphically, giving rise to a tensile stress of 9 %.By using synchrotron radiation at ho= 150 eV they suppressed the Pt 5d emission, since the Cooper minimum lies at this energy for Pt. They observed the Cu emission at 2.65 eV and a weak shoulder at 3.5 eV developing for coverages between 0.75 and 1.0 ML. From their core-level measurements they concluded that the Cu adatoms are essentially neutral in spite of the large electronegativity difference between Cu and Pt. The work function, as measured from the PE EDC’s, decreased by 1.26 eV during completion of the ML. We turn now to what we believe is another class of substrates - the spmetal substrates. Fig. 11 presents the result of the pioneering work of Abbati et al. (30). Cu was deposited onto a freshly cleaved Zn(0001) surface. LEEO indicated a pseudomorphic adlayer, but an AES study was not performed at that time. In agreement with their tight-binding calculation they found for the Cu ML a shift of 1.2 eV to larger binding energies and an appreciable narrowing of the 3d emission. These results have been quite consistently interpreted: The band narrowing in the ML is due to the decreased number of neighbors from 12 to 6 with respect to bulk Cu. The distance between EF and the 3d band is increased. since the average density of states in the lower part of the conduction band is decreased. Thus, the shift to higher BE may be seen as a consequence of the SP charqe decompression at the surface with respect to the bulk. The final d occupancy was found to be 9.963, i.e. larger than the value 9.886 obtained for the bulk. Thus the Cu species is more atomic in the over1 ayer
.
Fiq. 11: Energy distribution curves for (a) one Cu ordered monolayer on Zn(0001) face, (b) about one ML’ of Cu on a polycrystalline Zn film, and (c) thick Cu layer. Theoretical results are given for (d) the local density of states of a Cu overlayer and the total density o f states of (e) Cu and Zn, (f) bulk Cu, and (9) the isolated monolayer. From
-
(30)
386
It is worthwhile to explain in more detail what is meant by "sp charge decompression". It is connected to the normalized atom approach (31) pointing back to the beginning of band structure calculations (31). For example, let us consider the transition from the Cu atom with its 3d10 4s1 configuration to bulk Cu. By the interaction in the bulk both the 3d10 and the 4sl level broaden into bands and overlap strongly. Furthermore, the center of gravity of the d band is shifted to smaller energies by more than 5 eV so that the bottom of the s band (which is actually an sp band due to the admixture of states) falls well below the bottom of the d band. The local charge distribution around the atom is also changed. The sp states which are spatially more extended than the d states, are somewhat compressed into the atomic unit cell in the bulk. Introducing now a surface means a "sp charge decompression" into the vacuum. Within this model the d band should move back to higher energies as it is observed for the Cu ML here (30). It is interesting to note that a quite similar result has been found for Cu on different surfaces o f Al, which belongs also to the group of sp-metal substrates. Di Castro and Polzonetti (32) have found a ML emission peaked at 4.2 eV, which shifts to 2 eV for thicker layers. They measured on polycrystalline A1 films. From their Auger intensities as function of thickness they deduced some interdiffusion between A1 and Cu for the first layer. An ARUPS investigation for Cu on Al(111) was performed by Barnes et al. (33). From their Auger intensities versus thickness curves they concluded that
INITIAL
ENERGY
EiieV)
'
Fiq. 12: ARUP spectra at normal emission from Cu films grown on Al(111) at Ts = 300 K. Also shown is emission from a semi-infinite Cu(ll1) single crystal. Incident radiation: He1 (ha= 21.22 eV). From (33).
e s s e n t i a l l y l a y e r growth takes place below 300
K besides some i n t e r f a c i a l mix-
i n g i n t h e ML. Fig. 12 e x h i b i t s t h e main r e s u l t o f Barnes e t a l . (33). There i s a whole t r a n s i t i o n r e g i o n from the ML t o about 10 ML w i t h i n which t h e Cu 3d emission i s s h i f t e d towards EF by about 1.5 eV. The C u ( l l 1 ) 3d band has been developed o n l y a t about 10 ML. The broad ML and sharp 10 ML-ARUP spectra a r e i n good agreement w i t h t h e long-range disorder f o r t h e ML and a weak C u ( l l 1 ) LEED p a t t e r n f o r 10 ML. Finally,
i t i s i n t e r e s t i n g t o note t h a t these r e s u l t s are i n very good
agreement w i t h o l d e r angle-integrated XPS measurements (34). 3.2 S i l v e r Among t h e noble metals, Ag i s most i n t e n s i v e l y studied and t h e Ag ML i s best defined w i t h respect t o i n t e r d i f f u s i o n and a l l o y formation. Tobin e t a l . (35,36)
i n v e s t i g a t e d Ag on Cu(OO1). Ag forms a hcp ML g i v i n g r i s e t o a ~ ( 1 0 x 2 )
s t r u c t u r e as i n d i c a t e d i n f i g . 13. Normally two domains develop so t h a t t h e FR and % d i r e c t i o n s
cannot be separated i n t h e (110) plane.
For one surface t h e
authors c l a i m t h a t they have been able t o prepare a s i n g l e domain Ag adlayer (36).
I n fig.
14 some normal emission spectra are shown f o r C u ( l l l ) ,
Ag(ll1)
and Ag overlayers o f d i f f e r e n t thickness. The BE are given i n t h e 4 t o 5 eV interval for different
photon energies. For normal emission
kll= 0 and kl
is
REAL SPACE
RECIPROCAL SPACE
F i q . 13: Depiction o f one o f t h e two o r thogonal domains o f c(10x2)Ag/Cu(001) in r e a l space. The Ag atoms are shown as f i l l e d c i r c l e s and t h e Cu(OO1) surface l a t t i c e as squares. The a c t u a l r e g i s t r y w i t h t h e subs t r a t e i s unknown. The s u r f a c e - B r i l l o u i n zones of Cu(OO1) and both u n d i s t o r t e d hexagonal Ag domains as w e l l as t h e paths across each zone taken when r o t a t i n g o f f normal i n t h e Cu(OO1) planes (110) and (100) are shown. Only t h e domain associated w i t h (c) was observed w i t h LEED. From (35).
388 s-pol
23-eV Photon energy
He I
m
,
r
.-VI
L
o(
L
U C
-e Q
h .In f
m
c
E -
Binding energy (eV)
I l l 10
5
I
I
,
,
I
I 1
EF
Binding energy (eV)
Fiq. 14 (left): Mapping of the binding energies (BF) o f the silver features vs photon energy for (a) Ag(lll), (b) 5 ML, (c) 4 ML, and (d) 2 ML o f c(lOxZ)Ag/ Cu(OO1). The band i i i states (BF > 4.5 eV) at 2 ML become bands 4, 5, and 6 in Ag(ll1). The weak leading shoulder in Ag(ll1) at BF near 4.2 eV is shown with open circles and i s due to band iv. (e) Normal-emission spectra collected with hw = 23 eV for curve A Ag(lll), curve B 5 ML of c(10x2)Ag/Cu(001), curve C 4 ML, curve 0 2 ML, and curve E clean Cu(OO1). From (35). F i q . 15 (riqht): ARUP spectra taken of clean Cu(OO1) (lower member o f each pair) and 1) ML of c(lOxZ)Ag/Cu(001) (upper member of each pair), with s-polarized He1 radiation. The angle listed is the polar emission angle 0 versus the surface normal. Each spectrum is normalized to the largest Cu d-band peak. From
(36).
389
Fiq. 16: 20 band structure for Ag on Cu(100) observed at near-monolayer coverages. The triangles at BF near 4.8 eV at ?; are the averaged values of the spin-orbit split peaks observed with s- and p-polarized He1 and NeI radiation.
I
Y
10
08
06
k II
02
02
-6
I
06
04
08
I
-4
I
I
I
-2
10
I Z Z 14
k II
I
-8
a4
L 6 0 I
,
EF
INITIAL ENERGY(&)
Fiq. 17 (left): ARUP spectra from 1.2 A (1/2 monolayer) of Ag on Ni(001) taken with a photon energy ho= 22 eV and kl along Ni[llO]. The polar emission angles 0 are indicated. Features which are due to the presence of the Ag overlayer are marked with arrows. The inset shows a schematic drawing of the Brillouin zone of monolayer Ag(ll1). From (37). Fiq. 18 (riqhtl: Comparison of the 20 band structure a 0.5 ML Ag on Niflll) (data indicated by crosses: energy scale on the left-hand side) to the 2D dispersion relations from a near-monolayer coverage o f Ag on Cu(OO1) (data indicated by squares; energy scale on the right-hand side). In both cases k, is along the direction o f the Ag overlayer. The smooth solid and dashed curves are proposed band dispersions of bands 1-6. From (37).
390
varied with ho. It is necessary for a 2D band structure that the dispersion relation be independent of kl. Fig. 14 indicates that this requirement is nicely fulfilled for the 2 ML features between 4 and 5 eV. Fig. 15 presents some ML spectra for s-light from a He1 laboratory light source. The ML spectra are compared with the clean Cu(OO1) spectra indicating a fairly large overlap between Ag and Cu states down to an energy of 5 eV. Thus, this system certainly demanded some care to unambiguously figure out the 2D band structure of the Ag ML as shown in fig. 16. The investigations of this kind seem to be at the very beginning, where trends have to be figured out first. Therefore, the study of Shapiro e t al. (37) is very useful, in which they measured the Ag films on Ni(ll1) and Ni(100) substrates. Surprisingly, they found the 2D band structure to be practically identical for both substrates. With respect to the results for