The Molecule-Metal Interface E-Book

• Herausgeber: Wiley-VCH
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 458

Veröffentlichungsjahr: 2013

Beschreibung

Reviewing recent progress in the fundamental understanding of the molecule-metal interface, this useful addition to the literature focuses on experimental studies and introduces the latest analytical techniques as applied to this interface.
The first part covers basic theory and initial principle studies, while the second part introduces readers to photoemission, STM, and synchrotron techniques to examine the atomic structure of the interfaces. The third part presents photoelectron spectroscopy, high-resolution UV photoelectron spectroscopy and electron spin resonance to study the electronic structure of the molecule-metal interface. In the closing chapter the editors discuss future perspectives.
Written as a senior graduate or senior undergraduate textbook for students in physics, chemistry, materials science or engineering, the book's interdisciplinary approach makes it equally relevant for researchers working in the field of organic and molecular electronics.

Leseprobe

Contents

Preface

List of Contributors

1 Introduction to the Molecule–Metal Interface

1.1 From Organic Semiconductors to Organic Electronic Devices

1.2 Role and Function of Interfaces in Organic Electronic Devices

1.3 What Will We Learn about the Interfaces?

1.4 The Fermi Level and Related Fundamentals

Part One Theory

2 Basic Theory of the Molecule–Metal Interface

2.1 Introduction

2.2 The Molecule Energy Gap Problem: Image Potential Effects

2.3 The Unified IDIS Model: Charge Transfer, Pauli Exclusion Principle (“Pillow”) Effect and Molecular Dipoles

2.4 DFT Calculations for a Single Molecule on a Surface

2.5 From a Single Molecule to a Monolayer

3 Understanding the Metal–Molecule Interface from First Principles

3.1 Introduction

3.2 A Brief Overview of Density Functional Theory

3.3 Electronic Structure of Metal–Molecule Interfaces from Density Functional Theory: Challenges and Progress

3.4 Understanding Metal–Molecule Interface Dipoles from First Principles

3.5 Two Examples of Collective Effects at Metal–Molecule Interfaces

3.6 Concluding Remarks

Part Two Atomic Structure

4 STM Studies of Molecule–Metal Interfaces

4.1 Introduction to Scanning Tunneling Microscopy

4.2 Factors Affecting Molecular Packing on Perfect Surfaces

4.3 Influence of Inhomogeneity at Metal Surfaces

4.4 Manipulation of Molecules Using STM

4.5 Summary

5 NEXAFS Studies of Molecular Orientations at Molecule–Substrate Interfaces

5.1 Principles of NEXAFS

5.2 Molecular Orientations at Interfaces: the Effect of Molecule–Substrate Interactions

5.3 Molecular Orientations at Interfaces: the Effect of Strong Intermolecular Interactions

5.4 Molecular Orientations of Self-Assembled Monolayers

5.5 Summary and Outlook

6 X-Ray Standing Waves and Surfaces X-Ray Scattering Studies of Molecule–Metal Interfaces

6.1 Introduction

6.2 X-Ray Standing Wave Theory

6.3 X-Ray Standing Wave Experiments

6.4 Examples: Organic Monolayers on Metals

Part Three Electronic Structure

7 Fundamental Electronic Structure of Organic Solids and Their Interfaces by Photoemission Spectroscopy and Related Methods

7.1 Introduction

7.2 General View of Electronic Structure of Organic Solids

7.3 Electronic Structure in Relation to Charge Transport

7.4 Electronic Structure at Weakly Interacting Interfaces

7.5 Summary

8 Energy Levels at Molecule–Metal Interfaces

8.1 Introduction

8.2 The Organic–Electrode Interface

8.3 Gap States

8.4 Metal Electrodes

8.5 Tuning of Charge Injection Barriers

8.6 Conductive Polymer Electrodes

9 Vibrational Spectroscopies for Future Studies of Molecule–Metal Interface

9.1 Introduction

9.2 Selection Rules for Infrared and Raman Spectra

9.3 Raman/IR Application in Organic Films

10 General Outlook

Index

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The Editors

Prof. Norbert Koch

Humboldt Universität zu Berlin

Institut für Physik

Berlin, Germany

[email protected]

Prof. Nobuo Ueno

Chiba University

Graduate School of Advanced Integration

Science

Chiba, Japan

Prof. Andrew T.S. Wee

National Univ. of Singapore

Department of Physics

Singapore

Cover Picture

Lowest unoccupied molecular orbital of 5,7,12,14-pentacenetetrone on the Au(111) surface as calculated by density-functional theory. The illustration was created with VMD. VMD was developed by the Theoretical and Computational Biophysics Group in the Beckman Institute for Advanced Science and Technology at the University of Ilinois at Urbana-Champaign. Courtesy of G. Heimel.

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Preface

Organic electronics is a branch of electronics that utilizes carbon-based entities such as semiconducting polymers and molecules as its basic building blocks. This is in contrast to traditional electronics that use inorganic semiconductors, for example, silicon, to fabricate the basic microelectronic components such as the transistor. Significant progress has been made in the field of organic electronics over the past few decades, driven largely by lower cost manufacturing methods and the use of flexible substrates. Organic devices are already in use today as photoconductors in copiers and laser printers, and newer applications such as organic light emitting diodes (OLED), organic solar cells (OSC) and organic field effect transistors (OFET) have already reached the market.

Nobel laureate Herbert Kroemer coined the phrase the interface is the device when he referred to heterogeneous inorganic semiconductor structures. As is the case with inorganic semiconductors, the most important components of the organic device are its interfaces. In particular, the interactions between the organic semiconductor and electrodes critically determine the properties of the organic device, and hence the molecular-metal interface is chosen as the theme of this book. For example, in an OLED, the injection of electrons and holes from the electrodes is a crucial process, and formation of a molecular exciton via the formation of a bound state of an electron and hole gives rise to light emission. In an OSC, where the function is basically the reverse of the OLED, electrons and holes, resulting from exciton dissociation at relevant organic–organic interfaces, are separated in the interfacial band bending regions that also depend on the organic–metal electrode interfaces. Hence, a fundamental understanding of the molecule–metal interface and its associated electronic structure forms the basis for improving the device performance. In the subfield of molecular electronics, which involves the use of single molecules as building blocks for the fabrication of electronic components, an understanding of the molecule–metal interface is even more critical. Molecular electronics provides a device miniaturization pathway to extend Moore’s Law beyond the limits of silicon-integrated circuits, since a single molecule device is inherently in the nanometer scale.

This book is intended to serve as a textbook for a graduate level course, or as reference material for researchers in organic electronics, molecular electronics, and nanoscience. It does not duplicate the many excellent books already written on organic electronics, but focuses on the science at the molecule–metal interface. The chapters are written by leading experts in the various subfields, and are organized into three parts. In Part A, the basic theory and first principles theoretical studies of the molecule–metal interface is presented. In Part B, state-of the-art experimental techniques that elucidate the atomic structure of the molecule–metal interface are described, namely scanning tunneling microscopy (STM), near-edge X-ray adsorption fine structure spectroscopy (NEXAFS), X-ray standing wave, grazing incidence X-ray diffraction (GIXRD) and X-ray reflectivity (XRR) studies. In Part C, the fundamental electronic structure of organic solids and their interfaces elucidated by photoemission spectroscopy and related methods, as well as energy levels at molecule–electrode interfaces are discussed. Finally, infrared and Raman spectroscopies, as well as the future outlook are presented.

This book attempts to give a concise coverage of important topics in the science of the molecule–metal interface, but as a disclaimer, we emphasize that the coverage is by no means exhaustive. The selection of the materials is limited for space reasons, and unavoidably reflects the research interests of the chapter authors. Nevertheless, the key concepts are presented so that the reader is given an overview of the recent progress in the field, important results in a few molecule–metal systems, and future directions of research.

This book came about as a result of the co-editors’ collaborative links between our respective institutions in Germany, Japan and Singapore. We are indebted to all our contributing authors for their efforts in writing chapters that are informative and enjoyable reading for researchers in organic and molecular electronics, surface science, nanoscience and related fields. We truly hope that we have achieved our goal of writing a book that would become a useful reference for researchers and graduate students interested in the fascinating science at the molecule–metal interface.

Humboldt-Universität zu Berlin

Chiba University

National University of Singapore

February, 2013

Norbert Koch

Nobuo Ueno

Andrew T.S. Wee

List of Contributors

Christoph Bürker

Universität Tübingen

Fakultät für Physik

Auf der Morgenstelle 10

72076 Tübingen

Germany

Wei Chen

National University of Singapore

Department of Chemistry

3 Science Drive 3

Singapore 117543

Singapore

Wei-Yang Chou

National Cheng Kung University

Institute of Electro-optical Science and

Engineering

Tainan 701

Taiwan

Fernando Flores

Departamento de Física Teórica de la

Materia Condensada

Facultad de Ciencias

Modulo C-V

Universidad Autónoma de Madrid

28049 Madrid

Spain

Alexander Gerlach

Institut für Angewandte Physik

Universität Tübingen

Auf der Morgenstelle 10

72076 Tübingen

Germany

Takuya Hosokai

Department of Material Science and

Engineering

Iwate University

Ueda 4-3-5

Morioka 020-8551

Japan

Han Huang

Department of Physics

National University of Singapore

2 Science Drive 3

Singapore 117542

Singapore

Antoine Kahn

Department of Electrical Engineering

Princeton University

Princeton, NJ 08544

USA

Kaname Kanai

Department of Physics

Faculty of Science and Technology

Tokyo University of Science

Yamazaki 2641

Noda 278-8510

Japan

Satoshi Kera

Graduated School of

Advanced Integration Science

Chiba University

Inage-ku

Chiba 263-8522

Japan

Norbert Koch

Humboldt-Universität zu Berlin

Institut für Physik

Newtonstr. 15

12489 Berlin

Germany

Leeor Kronik

Weizmann Institute of Science

Dept. of Materials and Interfaces

Rehovoth 76100

Israel

Yoshitada Morikawa

Department of Precision Science and

Technology

Graduated School of Engineering

Osaka University

Japan

José Ortega

Departamento de Física Teórica de la

Materia Condensada

Facultad de Ciencias

Modulo C-V

Universidad Autónoma de Madrid

28049 Madrid

Spain

Dong-Chen Qi

Department of Physics

National University of Singapore

2 Science Drive 3

Singapore 117542

Singapore

Frank Schreiber

Universität Tübingen

Fakultät für Physik

Auf der Morgenstelle 10

72076 Tübingen

Germany

Nobuo Ueno

Chiba University

Graduate School of

Advanced Integration Science

1-33 Yayoi-cho

Inage-ku

Chiba 263-8522

Japan

Andrew T.S. Wee

Department of Physics

National University of Singapore

2 Science Drive 3

Singapore 117542

Singapore

Swee Liang Wong

Department of Physics

National University of Singapore

2 Science Drive 3

Singapore 117542

Singapore

1

Introduction to the Molecule–Metal Interface

Nobuo Ueno, Norbert Koch, and Andrew T.S. Wee

1.1 From Organic Semiconductors to Organic Electronic Devices

In 1954, Inokuchi coined the term organic semiconductors for polycyclic aromatic compounds with a molecular structure similar to fragments of graphene. He confirmed the notion that such organic materials are electrically conductive [1] through a number of careful experiments by himself and other pioneers [2]1)2). As such, it is generally accepted that organic semiconductors were discovered in the mid-twentieth century. Following their pioneering work in this period, much of the research concentrated on revealing the nature of the electrical conduction in molecular single crystals, which exhibited charge carrier mobility values of a few cm2/Vs at room temperature, and much higher values at low temperature, as shown in the work of Karl et al. [5]. So far, the highest mobility (40 cm2/Vs) was reported for rubrene single crystals in organic field effect transistors [6]. For practical device applications, however, organic semiconductor thin films, comprised of evaporated small-molecule compounds or polymers processed from solution, are more viable.

Organic semiconductors are already widely used today as photoconductors in copiers and laser printers, and have recently gained much attention because of their potential applications in electronic and optoelectronic devices, such as organic light emitting diodes (OLEDs) [6–11], organic solar cells (OSCs) [12, 13] and organic field effect transistors (OFETs) [10, 11, 14–17]. OLEDs are already used in displays of mobile phones and are just entering the commercial lighting market. As a result of the continuous drive to fabricate organic electronic devices on lightweight, large-area plastic substrates by low-cost processing techniques, organic electronics is fast-tracked for applications that help overcome general energy problems and global warming. Following this trend, OSCs and OTFTs have developed rapidly over the past decade. Many potential applications of OFETs have been demonstrated, ranging from flexible displays [18] and sensor systems [17, 19] to radio frequency identification tags [20], and some of these systems are now close to commercialization.

Figure 1.1 Evolution of reported charge carrier mobility of OFETs employing the organic semiconductor pentacene (adapted from [23, 24]).

Organic semiconductors have other unique physical properties that offer numerous advantages compared to their inorganic counterparts: (i) The extremely high absorption coefficient of many organic molecules in the visible wavelength range offer the possibility of very thin, and therefore resource-efficient, photodetectors and solar cells. (ii) Many fluorescent molecules emit light efficiently. However, charge transport in organic semiconductors is often limited by low intrinsic carrier density and mobility. Therefore, controlled and stable doping, in full analogy to doping of inorganic semiconductors for increasing carrier density, is desirable for reaching higher efficiency of many organic-based devices [11, 21, 22]. In addition, if one succeeds in shifting the Fermi level toward the transport states upon doping, this could reduce Ohmic losses at contacts, improve carrier injection from electrodes, and increase the built-in potential of Schottky or p–n junctions.

To understand the recent progress and expansion of organic electronics we show the temporal evolution of reported charge carrier mobility of OFETs employing the organic semiconductor pentacene in Figure 1.1 [23, 24], and the progress of OSC efficiency compared with different solar cell technologies in Figure 1.2 [25]. The rapid improvement of device performance is undeniably related to the progress in the science of interfaces and the availability of techniques to control interfaces.

Figure 1.2 Efficiency progress of different solar cell technologies (Source: L.L. Kazmerski, National Renewable Energy Laboratory (NREL), Golden, CO).

1.2 Role and Function of Interfaces in Organic Electronic Devices

As organic semiconductors generally have a wider band gap and narrower band-width than their inorganic counterparts, the density of thermally excited charge carriers in organic films is not sufficient to sustain high current density. We thus need injection of carriers into organic films from electrodes to achieve sufficiently high current in organic devices. This requirement is directly linked to the energetics at electrode–organic and organic–organic interfaces that exist in devices, thus control of the interfacial energy level alignment is the key technology required for the fabrication of organic electronic devices with high efficiency [21, 22, 26–29].

Typical examples for the electronic structure at interfaces in an OLED, an OSC, and an OFET are schematically shown in Figure 1.3. In the OLED, electrons are injected into the electron transporting layer (ETL) from the right electrode and holes are injected to the hole transport layer (HTL) from the left electrode. The injected charges are transported to the ETL/HTL interface when a potential is applied between the two electrodes. In modern OLED devices, more than just two organic layers are used to realize highly efficient light emission. The injection of electrons and holes from the electrodes is more important than high carrier mobility in OLEDs, and the molecular exciton, produced via the formation of a bound state of an electron and hole at the ETL/HTL interface, yields light emission upon radiative decay. In the OSC, the physical process is essentially the reverse of the OLED. In the OSC it is necessary that photogenerated bound electron–hole pairs (molecular excitons) in the organic layer are dissociated to generate mobile electrons and holes, which are further separated in the band-bending region, which depends on the electronic structure of the organic/electrode interface. As the electric current that can be used in an external circuit necessitates good charge transport to the electrodes, one needs high carrier mobility in the organic layer in OSCs. The elucidation of the interfacial electronic structure therefore forms the basis for understanding and improving the performance of these devices. In particular, the organic/metal interfaces have attracted much interest in relation to the rapid development of organic electronic and optoelectronic devices, since organic/metal interfaces are crucial for realizing efficient charge exchange between the organic layer and the external circuit.

Figure 1.3 Schematic electronic structure of OLED (a), OSC (b) and OFET (c). As the bands derived from the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) have very narrow bandwidth, they are represented by lines. HTL and ETL in the OLED stand for hole transport layer and electron transport layer, respectively. In the OFET, as the hole injection barrier (Δh) is smaller than the electron injection barrier (Δe), holes are injected and transported near the surface of the gate insulator to the source electrode (p-type OFET). The Fermi level (EF) is not defined across the structures, because the electron systems are not in thermodynamic equilibrium but in a steady state with current flowing. Therefore EF in the figures indicates the Fermi level position in the metals before device operation.

1.3 What Will We Learn about the Interfaces?

Fundamental interface phenomena, which are the subject of study in interface science, may be understood by investigating the difference between Figure 1.4a,b: Figure 1.4a the metal and the organic semiconductor are in direct contact, and Figure 1.4b the metal and the organic are just wired. For Figure 1.4b we assume that the wire acts only for exchanging electrons between the two solids. Both systems thereby allow exchange of electrons between the two solids to achieve thermodynamic equilibrium. Figure 1.5 compares the electronic states of the two cases. Since the electrons fill the energy levels strictly following Fermi–Dirac statistics, it is required that an interface system consisting of two different materials must have a single Fermi level (EF) throughout the system when the electrons are in thermodynamic equilibrium. This concept is always valid for electron systems in thermodynamic equilibrium, and is thus also valid for the cases in Figure 1.5a,b. It can be convincingly shown, however, that there are some differences between Figure 1.5a and Figure 1.5b, which are related to what we will discuss in this book.

Figure 1.4 What do we need to consider for the interface? Two cases of interacting solids: (a) metal and organic semiconductor are directly contacted to form an interface, where the electronic coupling is not zero even for the interface with an extremely weak interaction; (b) metal and organic semiconductor are wired only to allow for the exchange of electrons, and the two surfaces face each other without direct contact.

Figure 1.5 Hypothetical energy level alignment at thermal equilibrium of the electron system for the two cases from Figure 1.4a,b, direct contact (a) and contact by wiring (b), both of which allow for charge exchange between organic and metal. VL, CPD and Vbi stand for the vacuum level, contact potential difference, and built-in potential, respectively. A continuum media model is assumed and an n-type organic semiconductor with a donor level is used. The interface dipole exists at the direct contact interface. There must be difference between (a) and (b) due to the electronic coupling at the interface in (a), see text.

When we discuss interfaces with organic semiconductors, we divide them into two groups, (i) strongly interacting interfaces and (ii) weakly interacting ones. In the former case (i), new electronic states appear at or near the interface due to strong electronic coupling or chemical reactions between the two materials, which result in changes of the energy level alignment. The latter case (ii), where by and large no new states at the interface occur, may also be adapted to organic/metal interfaces that are not atomically clean. This is highly relevant for practical device fabrication that proceeds in moderate vacuum conditions or involving solvents. For instance, exposing metal surfaces, which in general are chemically reactive, to air during device fabrication may passivate the surfaces. To comprehensively understand the energy level alignment at organic/metal interfaces, one needs the help of theoretical studies in addition to experimental work. This book covers theoretical methods that unravel the interface electronic states in Chapters 2 and 3. However, experimental results have demonstrated that EF moves in the organic band gap upon contact of the two materials though the new electronic state density may be considered negligible. In some cases, theory is incapable of explaining experimental results, when, for example, the results are related to structural and/or chemical imperfections (Chapter 7). Cumulated experimental evidence has triggered the introduction of an intuitive idea, that there must be yet unidentified impurity molecules/atoms, which control the position of EF in the HOMO-LUMO gap of the organic semiconductor, in analogy to the physics of inorganic semiconductors. A very low concentration (~ ppm) of impurities is sufficient for inorganic semiconductors to control EF and thus to realize n- or p-type properties effectively, while a much higher dopant concentration (~ %) is required for organic semiconductors [10, 11, 21, 22]. Why do we need such high doping concentrations? The answer may be related to the nature of molecules, molecular solids, molecule–molecule heterocontacts (intermolecular interaction between different molecules), and to yet unknown electronic states in the gap. This book tries to offer a clearer insight into these issues.

1.4 The Fermi Level and Related Fundamentals

1.4.1 Definition of the Fermi Level in this Book

As mentioned above, it is important to adhere to the concept of the electronic states of interacting solids and the resulting energy level alignment. The occupation probability of electronic states by electrons in solids is given by the Fermi–Dirac distribution function, f (E),

(1.1)

Figure 1.6 Relation of the Fermi–Dirac distribution function [f (E)], density of states [D(E)] and electron density [n(E)] in a semiconductor without impurities (dopants) at T > 0.

If a semiconductor is free of impurities or dopants, and the DOS of the conduction band [Dc(E)] and the valence band [Dv(E)] are approximated by the model of free-electron-like DOS near the band edges, one obtains [32]

(1.2)

where me* and mh* are the effective mass of electron and hole, respectively, Ec is the energy of the bottom of the conduction band and Ev is the energy of the top of the valence band. Using Eqs. (1.1) and (1.2), the charge neutrality condition, where the density of thermally excited electrons (ne) is the same to that of holes (nh), is given as

(1.3)

EF is obtained from Eq. (1.3) as

(1.4)

where Eg is the band gap energy. If , EF is located exactly in the middle of the energy gap independent of T. As often , EF indeed is found near the middle of the gap.

Impurity doping yields occupied (electron donor) or unoccupied (electron acceptor) levels in the gap, thus EF moves in the gap depending on the density of these levels, their energy position, and temperature [33]. As the mechanism of doping in organic semiconductors may be different from their inorganic counterparts, and still is under investigation, one should be aware of possible shortcomings in applying this model for organic systems.

1.4.2 Measuring the Fermi Level of Organic Semiconductors

An important issue in studying organic/metal interfaces is to consider thermodynamic equilibrium of electrons throughout the system [34]. If thermodynamic equilibrium is achieved after contact, the Fermi level in the organic layer aligns with that of the metal by electron exchange, which results in shifts of the energy levels and band bending in the organic layer. A measurement of the EF position in the HOMO-LUMO gap is critically important, since the EF position dominates various electronic properties of the interface system. However, the experimental difficulty is that ultraviolet photoemission spectroscopy (UPS) cannot directly measure the EF position for materials with a band gap, such as organic semiconductors, because there are no electrons at EF. In this case, we assume thermodynamic equilibrium for the organic/metal systems and use EF measured for the metal substrate also as that in the band gap. In practice, this is achieved by measuring film thickness-dependent UPS spectra of an organic semiconductor on a metal substrate as shown in Figure 1.7. Note that possible (positive) surface charging of the organic film upon photoionization has to be prevented. Charging decreases the electron kinetic energy in the measurement, thus increasing the binding energy in UPS. It can be identified by looking carefully at time-dependent changes in spectral position and/or spectral shape especially, near the vacuum level. The latter is because the energy distribution of electrons with small kinetic energies is sensitively influenced by the nonuniform surface potential due to the charging. Note that charging-induced changes can occur on time scales smaller than the time required for accumulating a spectrum. Therefore, initial studies with much reduced photon flux are very useful. If photoelectrons emission is observed above EF in UPS of an organic film, one must consider that the organic/metal system is not in thermodynamic equilibrium, or may suffer from photovoltage effects during UPS measurements [35].

1.4.3 The Work Function and the Vacuum Level of a Solid with Finite Size

The work function is defined as the energy difference between the Fermi level and the vacuum level. The vacuum level refers to the energy of a zero-velocity electron that is placed in vacuum. Here we consider an “empty” vacuum to be where the electrostatic potential is constant. However, we should be aware of electrostatic potential variations in vacuum in reality due to the omnipresence of charge distributions if the material exists in vacuum. We first consider a biased semiinfinite metal in this vacuum and discuss the potential at a position away from the infinite surface (case I). In this case we know from classical electrostatics that there is a constant potential independent of the position in the half space. When we put a similarly biased small metal in this vacuum (case II), it is also clear that there is an electrostatic potential, which is similar to that of case I near the surface, and the potential becomes 0 at a position infinitely far away from the surface. As the vacuum level is a property of the electron and free space, the vacuum level is defined as the level, where the kinetic energy of an electron is 0, to avoid problems between the cases I and II. The vacuum level can be used as a common reference level for the energy levels of two different materials before contact. It is particularly important to understand the meaning of the vacuum level, and therefore the work function, for the design of organic device components, such as cathodes and anodes. In the following, we discuss a bit further the vacuum level/work function defined for a small metal or solid that is actually used in experiments.

Consider a hydrogen atom in vacuum, the simplest atom that consists of a proton (the nucleus) and an electron with a positive and a negative elementary charge (±e), respectively. Assuming point charges for both, the potential energy U(r) of the electron at distance r from the nucleus is given by

(1.5)

where V(r) is the electrostatic potential by the nucleus, and ε0 is the vacuum permittivity. U(r) becomes 0 for r → ∞, which means that an electrostatic potential in vacuum at ∞ is selected to be 0. This energy level, U(r → ∞), is defined as the vacuum level (VL∞). Therefore, if the kinetic energy (Ek) of the electron is 0 at r → ∞, the total energy of the electron is 0 at VL∞ because we have chosen the potential to be 0 at r → ∞ (see Figure 1.8).

Figure 1.8 The vacuum level defined for a simple atom, hydrogen. The electrostatic potential [V(r)] of an electron in the field of the nucleus and the electron potential energy [U(r)] are 0 for r → ∞, where the electrostatic potential in vacuum is chosen to be 0. If the electron is at VL∞, its kinetic energy (Ek) is 0.

A metal single crystal has various values for the vacuum level, and thus the work function, depending on the surface crystal plane. Some examples are collected in Table 1.1. This phenomenon occurs because electrons form a solid tail into vacuum at the surface, which yields an electric dipole layer at the surface, as the charge neutrality condition does not hold near the surface. Figure 1.9 shows such a surface dipole layer of a metal using the Jellium model [36]. Thus the vacuum level and the work function depend on the specific surface of a crystal due to the electrostatic potential generated by the surface dipole layer (see Table 1.1). Another surface phenomenon related to the anisotropy of the work function of metals was introduced by Smoluchowski [37]. The effect, called after Smoluchowski, originates from a redistribution of the electron cloud on a metal surface with a strong corrugation. Figure 1.10 illustrates this smoothing effect of the electron cloud, where the surface charge redistribution is represented by the wavy curve. The electron density redistributes from the “mountains” into the “valleys” to result in a net positive charge on the “mountain” and a negative charge in the “valley”. This charge distribution depends strongly on the surface atomic structure. For a close-packed surface, like (111) surfaces of face-centered cubic [fcc(111)] crystals, this mechanism does not have a momentous effect, whereas the surface charge distribution of an open surface, like (110) surfaces of simple cubic [sc(110)] crystals (see Figure 1.10), or a stepped surface, like fcc(311), is strongly effected. Work function values of various metals are summarized in [38]. Note that these work function values are only relevant for atomically clean surfaces; any adsorbates, like organic semiconductor molecules or contaminants from air, change the charge distribution at the surface and thus the work function.

Table 1.1 Surface dependence of work function of metals.

Figure 1.10 Schematic of the Smoluchowski effect using a simple cubic (sc) metal. Electrons near a bumpy surface redistribute to result in surface dipole layer as illustrated here for the (011) surface.

When we discuss interacting electron systems, we need to use the Fermi level as an energy reference. This is because the Fermi level can then be drawn as a horizontal line on a vertical energy axis, and the work function changes are represented by vertical shifts of the vacuum level, depending on the surface dipole potential changes. Thus, it is convenient to redefine the vacuum level at close proximity to the surface (the distance from the surface should be smaller than the lateral extensions of the surface, and larger than the range of the electron density tailing into vacuum, see above), where the kinetic energy of an electron is 0. Figure 1.11a depicts the vacuum levels and work function for two different surfaces, A and B, of a small metal single crystal with a finite surface area. Here we choose the Fermi level as the energy reference. Therefore, the vacuum level near the surface A is different from that of surface B due to differences of the surface dipole layer potentials. It would be a good exercise to consider what happens when we connect surface A with surface B.

Figure 1.11 (a) Direction dependence of the vacuum level and the work function (ϕ) for a metal with the Fermi level as the energy reference, and (b) direction dependence of the vacuum level and ionization energy (IE) for nonpolar perfluoropentacene (local dipole effects). In (b) small local dipoles due to spatial spread of π electrons perpendicular to the molecular plane are neglected. One should be careful with ionization energy that is measured for gas phase and solid phase samples. For the gas phase the ionization energy refers generally the vacuum level at r → ∞ (VL∞ in Figure 1.8) that does not involve the local dipole potential, while for the solid phase it refers the vacuum level near the surface that involves the local (surface) dipole potential.

An analogous electrostatic effect regarding the vacuum level being dependent on the surface electron density distribution occurs also at nonmetal surfaces, for example, even for a nonpolar organic molecule with intramolecular electric dipoles [39, 40]. As shown in Figure 1.11b, the ionization energy of perfluoropentacene, which does not have a permanent molecular dipole, depends on the direction that an electron escapes to vacuum. As a local dipole exists at each –Cδ+ –Fδ− bond, this yields an electrostatic potential, and an electron from inside the molecule needs additional energy to escape to vacuum along C–F bonds compared to the direction perpendicular to the molecular plane. This situation can indeed be understood in analogy to the surface plane-dependent work function of a metal single crystal. Therefore, the orientation of molecules at interfaces plays a crucial role for the energy level alignment, even at weakly interacting interfaces comprising nonpolar molecules.

As is apparent from this short introduction of a few important concepts and mechanisms that must be considered when describing organic/metal interfaces, obtaining a comprehensive understanding of these interfaces requires thorough efforts. The following chapters of this book are intended to help acquiring the necessary prerequisites for mastering the organic/metal interface challenge.

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1) For history before 1988 see [3], where review articles by (I) D.D. Eley (p. 1), (II) H. Inokuchi (p. 23), (III) N. Karl (p. 31), (IV) L.E. Lyons (p. 53), (V) C. Pecile et al. (p. 69), (VI) M. Pope (p. 89), (VII) Z.D. Popović (p. 103), (VIII) R. Qian (p. 117), (VX) E.A. Silinsh (p. 135), and (X) J. Sworakowski and S. Nešpurec (p. 145) are available.

2) See also [4].

Part One Theory

2

Basic Theory of the Molecule–Metal Interface

Fernando Flores and José Ortega

2.1 Introduction

The study of the molecule–metal interface is of fundamental importance in diverse fields such as molecular electronics, organic electronics, catalysis, surface photochemistry, and so on. Thus there is very active research in these areas to investigate the properties of molecules interacting with metals, research that is further stimulated for its important technological implications [1–6].

From a fundamental point of view, the study of the molecule–metal Interface is at the frontier of two separate scientific kingdoms – solid-state physics and molecular science – fields where different paradigms are used to describe and investigate the properties of metals and molecules. In a metal the atoms are held together by metallic bonding in which electrons are delocalized over the whole crystal [7]. The atoms are arranged in a periodic array and the electron energy levels form continuous bands of energy (i.e., the energy bands); the Fermi energy (or Fermi level) EF lies within the range of one or more energy bands, that are thus partially filled and there is no gap of energy between occupied and empty states. On the other hand, in a molecule the atoms form strong intramolecular covalent bonds and are not arranged periodically. The electronic states are localized, the molecule presents discrete energy levels and there is a gap in energy between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) [8].

Molecules can bind to other molecules via noncovalent bonding (e.g., van der Waals forces, hydrogen bonds, etc.) and form molecular solids (see Figure 2.1). This is the case of organic semiconductors that are made up of organic molecules. In these materials electrons in π-conjugated systems are delocalized inside each molecule and the intermolecular interactions allow the motion and delocalization of these electrons among neighboring molecules. In this way the discrete energy levels of the molecules transform into weakly dispersive energy bands.

The growing field of organic electronics relies on the use of organic conjugated molecules as components of multilayer devices. The performance of these devices depends critically on the energy barriers that control the carrier transport between layers, where energy barriers are determined by the relative alignment of the molecular levels at metal–organic or organic–organic interfaces [1–3, 9]. In the metal–organic case, the interaction between molecules is typically small and understanding the barrier formation at these interfaces implies understanding first the interface between individual molecules and the metal surface, and then including the long-range interaction between molecules on the surface (see Figure 2.2).

Figure 2.1An organic semiconductor is made up of organic molecules. The LUMO and HOMO levels are shown in the figure as well as the Fermi level EF, the energy gap , and the Ionization I, and affinity A, energies (VL is the vacuum level).

Figure 2.2 The geometry of a PTCDA monolayer on Au(111) [10]; the molecules are weakly interacting with each other.

When a molecule is interacting with a metal the electronic coupling of the molecular orbitals with delocalized states in the metal broadens the molecular levels into resonances (see Section 2.3); also, the charge rearrangement due to the molecule–metal interaction creates a potential between molecule and metal that shifts the molecular levels relative to the metal Fermi energy [11, 12] (see Figure 2.3). Energy level alignment at the molecule–metal interface is also influenced by the metal polarization response to added electrons or holes in the molecule (i.e., image potentials, see Section 2.2).

Figure 2.3 Band alignment at a metal–organic interface. (a) For very weak interaction limit, there is no induced dipole at the interface and the vacuum levels are aligned. (b) In general, an interface dipole ∆, is induced between the two crystals.

In this chapter we introduce the basic concepts relevant for the analysis of the energy level alignment in molecule–metal interfaces: as mentioned above, the position of the molecule’s energy levels (especially the HOMO and LUMO) with respect to the metal Fermi energy, as well as the electronic coupling of these states to extended states in the metal, determines the charge transport across the metal–molecule interface as well as other important properties of the system. We start with a discussion of the molecule energy gap problem and the effect of the metal polarization response: in Section 2.2.1 we show that the molecule energy gap problem is related to the molecule self-interaction energy as described by the molecule charging energy U, while in Section 2.2.2 we analyze the image potential effects that appear when a molecule is brought into contact with a metal due to image charges. In Section 2.3 we present the unified induced density of interface states (IDIS) model [13–15] for energy level alignment at molecule–metal interfaces. The concept of charge neutrality level (CNL) of the molecule is introduced; the CNL is related to the charge transfer between molecule and metal. Due to this charge transfer there appears an induced potential VIDIS that shifts the molecular levels with respect to the Fermi level of the metal. In this section two other contributions to the potential between molecule and metal are also considered: Pauli repulsion (or “pillow” effect) and molecular dipoles. In Section 2.4 some examples for a single molecule on a metal are discussed, showing how the ideas introduced in Sections 2.2 and 2.3 can be applied in a density functional theory (DFT) calculation to understand the energy level alignment in these systems. In particular, we analyze the molecules C60, TCNQ and TTF on Au(111). Finally, in Section 2.5 we discuss how the ideas presented before for the interface of a single molecule and a metal can be extended to the case of a monolayer (or fraction of a monolayer) of molecules on the metal surface.

2.2 The Molecule Energy Gap Problem: Image Potential Effects

The molecule–metal interaction is, in principle, amenable to DFT calculations; however, using the local density approximation (LDA) or the generalized gradient approximation (GGA) for the exchange–correlation functional might not allow an accurate determination of the charge transfer at the interface, since molecular energy gaps in the gas phase can be underestimated by several eVs [16–18] (the situation at interfaces will be discussed below). This problem is related to the fact that Kohn–Sham eigenvalues (as calculated in LDA or GGA) are not a proper representation of quasi-particle excitation energies: in conjugated organic molecules, the difference between the HOMO and LUMO Kohn–Sham eigenvalues is significantly smaller than the transport gap measured experimentally [19–21] (optical gaps are smaller than transport gaps due to excitons, the coupling between the excited electron and the hole left behind). This discrepancy largely arises from the fact that the Kohn–Sham DFT gap refers to an N-electron calculation, while the transport gap, Et, involves total energy differences with the molecule in a charged state, either N + 1 or N – 1.

2.2.1 Molecule Self-Interaction Energy

The transport gap is given by the difference between the LUMO (εL) and HOMO (εH) levels (see Figure 2.1), defined by

(2.1)

E[Ni] being the ground state energy of the system with Ni electrons.

We are going to show how the difference between the transport energy gap and the one calculated from the Kohn–Sham eigenvalues, , can be associated with the self-interaction energy, U0, for electrons in HOMO and LUMO levels:

(2.2)

(2.3)

where define the density matrix operator with mean values niασ (niα) and niα,jβσ, respectively. The first two terms represent the electron kinetic energy plus the electron–ion interaction (εiασ is the one electron contribution to the energy of the orbital iασ; and tiα,jβ,σ the hopping term between orbitals iασ and jβσ) while the last two terms define the electron–electron interaction (Uiaβ and Jiα,jβ are, respectively, the intraatomic and interatomic electron–electron interactions).

For the sake of simplicity, we analyze the Hamiltonian equation (2.3) by means of a Hartree approximation; then, the electron–electron energy is approximated by the interaction between the mean charges niασ:

(2.4)

and Hamiltonian equation (2.3) by the effective (Kohn–Sham) one-electron Hamiltonian:

(2.5)

where . A self-consistent solution of Eq. (2.5) in the charges niασ yields the eigenvalues, , which represent the Kohn–Sham energies of the Hartree approximation to Hamiltonian equation (2.3), and the eigenfunctions, , which provide us with niασ and and . Those eigenvalues are given by

(2.6)

Notice also that, in the Hartree approximation, the total energy, E, is given by:

(2.7)

so that

(2.8)

We can now use Eq. (2.6) to calculate εH and εL, assuming that the molecular wavefunctions do not change (a kind of Koopmans approximation) nor does the geometry relax when N is changed to N + 1or N – 1. Thus, if one electron is added to the system in the LUMO level, niασ and niα,jβσ are changed with respect to the uncharged case; so, for an electron of spin σ we find:

(2.9)

then, the LUMO level is given by (see Eq. (2.1)):

(2.10)

an equation that yields:

(2.11)

In a similar way, the HOMO level is given by:

(2.12)

Equations (2.11) and (2.12) express, in the Hartree approximation, the LUMO and HOMO levels as the Kohn–Sham eigenvalues, and , corrected by the self-interaction energy (with a 1/2-factor) of the charge associated with either the LUMO or the HOMO molecular wavefunctions. Notice also that the corrections to these levels have opposite signs, so that the transport energy gap, , is given by:

(2.13)

where we have introduced the charging energies, and , of the LUMO and HOMO levels. Thus, the appropriate transport energy gap for the molecule is given as the (underestimated) Kohn–Sham gap plus the self-interaction correction . Although Eq. (2.13) has been obtained using a Hartree approximation to Hamiltonian equation (2.3), its validity holds for a very general case as shown in [4, 25]. Notice also the following (e.g., see [25]):

(2.14)

Figure 2.4 Molecular energy levels for PTCDA using (a) a LDA-DFT approach and (b) after introducing the self-interaction correction as calculated with a Koopmans approximation (see text) [13, 16]. The DOS is obtained by introducing a Gaussian broadening in the energy levels.

An argument similar to the one leading to Eqs. (2.11) and (2.12) can be used to obtain the self-interaction correction for any molecular orbital, [4], including exchange–correlation effects [13]. Figure 2.4 shows the Kohn–Sham energy levels for PTCDA using a LDA-DFT approach, as well as the final spectrum once the self-interaction correction has been included. The effect of this correction is basically to open the energy gap, shifting the occupied levels by almost a constant to higher binding energies and the empty levels practically by the same quantity to lower energies. This is also illustrated in Figure 2.5 for PTCDA and pentacene [4, 16], by showing the self-interaction correction for different orbitals around the energy gap.

In Table 2.1, we show for different organic molecules (benzene, C60, TTF, PTCDA and pentacene) the LDA-DFT transport energy gap as calculated with a plane-wave converged basis and the (εL – εH)-value obtained either from experiments or from charged configuration calculations. Notice that the (εL – εH)-gap is 3.7 ± 0.4 eV larger than the Kohn–Sham value (LDA gap) for all the molecules except for benzene, where it is 5.3 eV larger.

Figure 2.5 Value of the self-interaction correction to the Kohn–Sham energies as a function of the molecular level for (a) PTCDA and (b) pentacene [16]. Black (gray) squares correspond to states of π (σ) symmetry. Positive (negative) values correspond to empty (occupied) states.

Table 2.1 Transport gap, εL – εH, LDA gap, , and value of the charging energy, U0, for different organic molecules, in electron volts.

2.2.2 Image Potential Effects

Up to now, we have just considered the case of isolated molecules. We have seen that the molecule energy gap is substantially underestimated by LDA- or GGA-DFT and that the Kohn–Sham levels should be somehow corrected to properly represent the electronic spectrum of the molecule. When an organic molecule is near a metal surface another related effect takes place due to the image potential created by the image charge (see Figure 2.6): this is a correlation effect that opposes the self-interaction correction and tends to reduce the energy gap, making it more similar to the results of the LDA-DFT calculations [25, 33–35].