Electronic Structure (eBook)

K. Horn, M. Scheffler (Herausgeber)

eBook Download: PDF | EPUB

2000 | 1. Auflage
1072 Seiten
Elsevier Science (Verlag)
978-0-08-053075-8 (ISBN)

Infos

This book is the second volume in the Handbook of Surface Science series and deals with aspects of the electronic structure of surfaces as investigated by means of the experimental and theoretical methods of physics. The importance of understanding surface phenomena stems from the fact that for many physical and chemical phenomena, the surface plays a key role: in electronic, magnetic, and optical devices, in heterogenous catalysis, in epitaxial growth, and the application of protective coatings, for example. Therefore a better understanding and, ultimately, a predictive description of surface and interface properties is vital for the progress of modern technology. An investigation of surface electronic structure is also central to our understanding of all aspects of surfaces from a fundamental point of view. The chapters presented here review the goals achieved in the field and map out the challenges ahead, both in experiment and theory.

Inhalt

Front Cover 1
Electronic Structure 4
Copyright Page 5
General Preface 6
Preface to Volume 2 8
Contents of Volume 2 10
Contributors to Volume 2 12
Chapter 1. Fundamentals of the Electronic Structure of Surfaces 14
Chapter 2. Electronic Structure of Semiconductor Surfaces 106
Chapter 3. Electronic States on Metal Surfaces 222
Chapter 4. Electronic Structure of Adsorbates on Surfaces. Adsorption on Semiconductors 260
Chapter 5. Theory of Adsorption on Metal Substrates 298
Chapter 6. Experimental Probes of the Surface Electronic Structure 370
Chapter 7.Electronic Structure of Semiconductor Surfaces 396
Chapter 8. Surface States on Metal Surfaces 446
Chapter 9. Magnetism at Surfaces and in Ultrathin Films 524
Chapter 10. Adsorption on Metals 682
Chapter 11. The Metal–Semiconductor Interface 762
Chapter 12. Electronic Structure of Adsorbates on Semiconductors 876
Chapter 13. Some Properties of Metal Overlayers on Metal Substrates 912
Chapter 14. Many-body Effects in Photoemission 966
Author index 1002
Subject index 1062

Textauszug

Chapter 1

Fundamentals of the Electronic Structure of Surfaces

E. Wimmer    Institut Supérieur des Matériaux du Mans and Materials Design s.a.r.l. 72000 Le Mans, France

A.J. Freeman    Department of Physics and Astronomy Northwestern University Evanston, IL 60208-3112, USA

1.1 Introduction

The richness of physical and chemical properties of surfaces finds its fundamental explanation in the arrangement of atoms, the distribution of the electrons, and their response to external changes. For example, surface reconstructions such as that of the Si(001) surface are driven by electronic structure effects; the work function of a metal surface is determined by the extent to which electrons spill out into the vacuum region; enhanced magnetism at the surfaces of Fe and Ni is the consequence of surface-induced changes in the electronic structure of the metal atoms at the surface; adsorption, chemisorption, and chemical reactions on surfaces are the result of the fascinating dynamic relationship between positions of atoms, electronic structure, and total energy.

Therefore, the understanding and quantitative prediction of the electronic structure takes a central and fundamental role in today’s concept of surfaces. As in the investigation of bulk solids and molecular systems, the quality and reliability of any electronic structure theory of surfaces hinges on the ability to describe the many-body interactions accurately enough to allow quantitative predictions of physical properties. On the other hand, the theory has to allow practical calculations at a reasonable computational effort on systems which are large enough so that realistic surface models can be studied. These two requirements, accuracy and practicality, continue to present a tremendous challenge to the theoretical/computational physicist and chemist.

Since the formulation of quantum mechanics in the 1920’s, two major theoretical and computational approaches have emerged, namely Hartree–Fock theory and density functional theory. A third approach, quantum Monte Carlo, is promising but, so far, has remained limited to rather small systems. Because of its applicability to a wide range of systems including metallic, semiconducting, and insulating materials and its good balance between accuracy and computational efficiency, density functional theory has become the dominant approach for electronic structure calculations of surfaces. Therefore, this chapter focuses on density functional methods and their applications to surface problems. However, the reader should be aware that Hartree–Fock based approaches have also been successful in describing surface phenomena such as chemisorption using small clusters as surface models. Furthermore, Dovesi et al. (1992) have developed a Hartree–Fock program for periodic systems that can also be used to study surfaces. These approaches and their applications will not be discussed here. In addition, one should keep in mind that in the modeling and simulation of surface phenomena, electronic structure aspects constitute the most fundamental and deepest level of theory of atomic-scale simulations, but the study of surface phenomena involving hundreds of thousands of atoms and time-scales of microseconds and longer require radically different theoretical and computational approaches. These approaches remain also outside the scope of this chapter.

1.2 Basic concepts of density functional theory

1.2.1 The Kohn–Sham equations

Hohenberg and Kohn (1964) and Kohn and Sham (1965) formulated a rather remarkable theorem which states that the total energy of a system such as a bulk solid or a surface depends only on the electron density of its ground state. In other words, one can express the total energy of an atomistic system as a functional of its electron density

=E[ρ].

  (1.1)

The idea of using the electron density as the fundamental entity of a quantum mechanical theory of matter originates in the early days of quantum mechanics (Thomas, 1926; Fermi, 1928). However, in the subsequent decades, it was rather the Hartree–Fock approach (Hartree, 1928; Fock, 1930a, b) which was developed and applied to small molecular systems. Calculations on realistic solid state systems were then out of reach. Slater (1951) used ideas from the electron gas with the intention to simplify Hartree–Fock theory to a point where electronic structure calculations on solids became feasible. Slater’s work, which led to the so-called X α method (Slater, 1974), has contributed tremendously to the development of electronic structure calculations. Today, Slater’s X α method can be seen as an early, simplified form of density functional theory. The X α method is hardly used in present electronic structure calculations and therefore will not be further pursued in this chapter and we return now to the explanation of density functional theory.

The electron density is a scalar function defined at each point r in real space,

=ρ(r).

  (1.2)

The electron density and the total energy depend on the type and arrangements of the atomic nuclei. Therefore, one can write

=E[ρ(r),{Rα}].

  (1.3)

The set {Rα} denotes the positions of all atoms α in the system under consideration. Equation (1.3) is the key to the atomic-scale understanding of electronic, structural, and dynamic properties of matter. If one has a way of evaluating expression (1.3), one can, for example, predict surface reconstructions, the equilibrium geometry of molecules adsorbed on surfaces, and the cohesive energies of solids.

Furthermore, the derivative of the total energy (1.3) with respect to the nuclear position of an atom gives the force acting on that atom. This enables the efficient search for stable structures and, perhaps more importantly, the study of dynamical processes such as diffusion or the reaction of molecules on surfaces. Most of the considerations discussed in this book are based on the Born-Oppenheimer approximation in which it is assumed that the motions of the electrons are infinitely faster than those of the nuclei. In practice this means that the electronic structure is calculated for a fixed atomic arrangement and the atoms are then moved according to classical mechanics. This is a fairly good approximation for heavy atoms like W, but can cause significant errors for light atoms like H or Li.

In density functional theory, the total energy (1.1) is decomposed into three parts, a kinetic energy, an electrostatic or Coulomb energy, and a so-called exchange–correlation energy,

=T0+U+Exc.

  (1.4)

The most straightforward term is the Coulomb energy U. It is purely classical and contains the electrostatic energy arising from the Coulombic attraction between electrons and nuclei, the repulsion between all electronic charges, and the repulsion between nuclei

=Uen+Uee+Unn

  (1.5)

with

en=−e2∑αZα∫ρ(r)|r−Rα|dr

  (1.6)

ee=e2∬ρ(r)ρ(r′)|r−r′|drdr′,

  (1.7)

nn=e2∑αα′ZαZα′|Rα−Rα′|,

  (1.8)

where e is the elementary charge of a proton and Zα is the atomic number of atom α. The summations extend over all atoms and the integrations over all space. Once the electron density and the atomic numbers and positions of all atoms are known, expression (1.6)-(1.8) can be evaluated by using the techniques of classical electrostatics.

The kinetic energy term T0 is more subtle. In density functional theory, the “real” electrons of a system are replaced by “effective” electrons with the same charge, mass, and density distribution. However, effective electrons move as independent particles in an effective potential, whereas the motion of a “real” electron is correlated with those of all other electrons. T0 is the sum of the kinetic energies of all effective electrons moving as independent particles. Often, one does not explicitly make this distinction between real and effective electrons.

If each effective electron is described by a single particle wave function ψi then the kinetic energy of all effective electrons in the system is given by

0=∑ini∫ψi*(r)[−ħ22m∇2]ψi(r)dr.

  (1.9)

Expression (1.9) is the sum of the expectation values of one-particle kinetic energies; ni denotes the number of electrons in state i. By construction, dynamical correlations between the electrons are excluded from T0.

The third term of Eq. (1.4) includes all remaining complicated electronic contributions to the total energy and is called...

Produkt-Details

• Erscheint lt. Verlag: 19.7.2000
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Chemie ► Physikalische Chemie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Thermodynamik
• Themenwelt: Technik ► Maschinenbau
• ISBN-10: 0-08-053075-3 / 0080530753
• ISBN-13: 978-0-08-053075-8 / 9780080530758