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Properties of

Single Organic Molecules on Crystal Surfaces

This page intentionally left blank

Properties of

Single Organic Molecules on Crystal Surfaces Editors

Peter Grütter

McGill University, Canada

Werner Hofer

University of Liverpool, UK

Federico Rosei

INRS-EMT, Université du Québec, Canada

ICP

Imperial College Press

Published by Imperial College Press 57 Shelton Street Covent Garden London WC2H 9HE Distributed by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.

The editors and publisher would like to thank the following authors and publisher of the journal for their permission to use the image on the book cover: S. Dobrin, K. R. Harikumar, R. V. Jones, N. Li, I. R. McNab, J. C. Polanyi, P. A. Sloan, Z. Waqar, J. (S. Y.) Yang, S. Ayissi and W. A. Hofer, "Self-assembled molecular corrals on a semiconductor surface", Surface Science Vol. 600, pp. 43–47 (2006).

PROPERTIES OF SINGLE ORGANIC MOLECULES ON CRYSTAL SURFACES Copyright © 2006 by Imperial College Press All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.

For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher.

ISBN 1-86094-628-3

Typeset by Stallion Press Email: [email protected]

Printed in Singapore.

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Contents

Preface

vii

Authors’ Biographies

xi

Part I

Introductions Basic Properties of Metal Surfaces A. L. V´ azquez de Parga and R. Miranda Basic Properties of Silicon Surfaces M. J. Butcher and M. Y. Simmons

Part II

29

Experimental Methods Scanning Tunneling Microscopy and Scanning Force Microscopy S. Hembacher and F. Giessibl Optical Detection of Single Molecules at Interfaces B. Hecht

Part III

3

69 89

Theoretical Methods Ab Initio Modeling of Molecular Electronics D. Roubtsov, N. Sergueev and H. Guo Perturbation Methods in Scanning Tunneling Microscopy W. A. Hofer

v

121

147

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Part IV

Contents

Spectroscopy of Single Molecule(s) on Surfaces Properties of Single Molecules: Manipulation, Dissociation and Synthesis with the Scanning Tunneling Microscope K.-F. Braun and S.-W. Hla Single-Molecule Vibrational Spectroscopy and Chemistry J. I. Pascual and N. Lorente

Part V

Mobility of Complex Organic Species at Metal Surfaces J. V. Barth Molecular Monolayers on Silicon Surfaces G. P. Lopinski and D. D. M. Wayner Functionalization of Semiconductor Surfaces by Organic Layers: Concerted Cycloaddition versus Stepwise Free-Radical Reaction Mechanisms A. Bili´c, J. R. Reimers and N. S. Hush

247

269 287

333

Electronic Properties of Single Molecules on Metal Surfaces Molecular Electronics R. Stadler Exploring the Catalytic Activity of a Noble Metal: The Ag Catalyzed Ethylene Epoxidation Reaction M.-L. Bocquet and A. Michaelides

Index

209

Local Modiﬁcation of Surfaces Induced by Adsorbed Molecules Superlattices of Atoms, Molecules and Islands H. Brune

Part VI

183

363

389

425

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Preface

In the past decade, research activities in nanoscience have grown explosively. While we are just beginning to understand the functionalities that can be accessed through the use of nano approaches, their tremendous potential to revolutionize the ways in which matter is fabricated, synthesized and processed is already evident. Presently atoms, molecules, clusters and nanoparticles can be used as functional building blocks for fabricating advanced and totally new phases of condensed matter on the nanometer length scale. The optimal size of such unit components depends on the particular property to be engineered: by altering the dimensions of the building blocks, controlling their surface geometry, chemistry and assembly, it will be possible to tailor functionalities in unprecedented ways. Within nanoscience an emerging discipline is the study of the physics and chemistry of single molecules. These investigations have been made possible by the advent of high resolution surface imaging and characterization techniques, commonly referred to as Scanning Probe Microscopes (SPM). The most widely used of such microscopes are the Scanning Tunneling Microscope (STM), the Atomic Force Microscope (AFM) and the Scanning Near Field Optical Microscope (SNOM). The properties (adsorption, diﬀusion, interaction, conformations, etc.) of individual molecules can now be investigated virtually on any substrate, by means of a suitable (scanning) probe. Molecules may be considered as the ultimate building blocks, and are therefore interesting for the development of molecular devices and for surface functionalization. Thus the interest in studying their properties when adsorbed on a (suitable) substrate (solid/crystal surface). There is in fact a double interest, from a fundamental point of view and for potential applications in nanoelectronics/molecular electronics and nanosensing. The present book is intended to serve as a textbook for a graduate level course, as well as reference material for specialized practitioners in surface

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science, nanoscience and nanoelectronics. We have invited contributions across disciplines, while keeping a coherent plan and perspective with respect to the topics we absolutely wanted to cover. Each chapter is selfcontained, and written in a fairly simple style, to be understandable by a relatively broad audience of non specialists. All the chapters have been peer reviewed. To ensure clarity and ease of understanding for broad audiences, we asked students and postdoctoral fellows in our groups and departments to help us in this task, reading and commenting on various manuscripts. From a didactic point of view, each chapter in this book may be used to cover one or more classes of a graduate level course, and in fact we had originally aimed at collecting about 12 chapters, which correspond to a full course in many North American Universities. The focus of this book is on the properties of SINGLE molecules (some chapters evidently being an exception to this general rule), since we thought this speciﬁc focus would give it an interesting and somewhat unique perspective. In this sense, we explicitly asked the authors to emphasize what is the diﬀerence between the properties of a single molecule, as opposed to ensembles of molecules. Taking it one step further in the framework of a graduate course, after each lecture the students should be able to answer the question: “What physical or chemical properties do you learn from a single molecule in this particular context?” Besides giving a personal opinion, the authors were asked to provide an outlook, describing where this ﬁeld of research is heading, and what are the critical issues and questions to be addressed. Finally, the authors were asked to present a personal, critical view/perspective of their ﬁeld of research. It is apparent that this topic is still in its infancy, too young to be considered suitable for a full, authoritative book. The ﬁeld of research is simply not mature enough yet. However, this initial academic publication outlines many important issues that have been identiﬁed while investigating the properties of complex organic molecules adsorbed at crystal (metal, semiconductor, insulating) surfaces. Each individual chapter, as well as the book as a whole, are to a large extent self-contained, yet contain generous reference lists to the recent relevant literature. We have decided to start with two very general introductory chapters (Part I) on the properties of metal and semiconductor surfaces by R. Miranda’s (Spain) and M. Y. Simmons’ (Australia) groups, respectively. We then continue the reviews with experimental methods and techniques (Part II) that are used to investigate the properties (conformation,

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ix

adsorption, etc.) of single molecules as well as molecular assemblies adsorbed at surfaces. In this section, F. Giessibl and S. Hembacher describe recent advances in AFM that allow to image various surfaces (e.g. silicon, graphite, etc.) in ultra-high vacuum conditions with atomic resolution. Secondly, B. Hecht provides a comprehensive description of optical probes and techniques, including Scanning Near Field Optical Microscopy and Confocal Optical Microscopy. Since the STM is described in great detail in many excellent reviews and books, we decided to refer the readers to these rather than include a dedicated chapter to this technique (it is partly covered in the chapter by Giessibl and Hembacher). In Part III, we decided to give appropriate space to theoretical approaches, which are very important to model, describe and understand images and spectra acquired experimentally. Here the chapter by H. Guo and coworkers describes recent theoretical advances that allow to predict the transport properties of molecule–metal junction systems. The other chapter, by W. Hofer, focuses on the use of perturbation methods to derive calculated scanning probe microscopy images. With respect to the local modiﬁcation of surfaces (Part IV), we have a “stand alone” chapter by H. Brune. This chapter gives a broad overview of nucleation and growth and how they can be inﬂuenced by the use of suitable templates. Part V focuses on single molecule chemistry at metal surfaces. Herein the chapter by S. W. Hla and K. Braun describes how the STM can be used to induce single molecule reactions, starting from bond breaking all the way to bond formation. The chapter by N. Lorente deals with atomic scale vibrational spectroscopy studies and how they allow to obtain chemical information on individual molecules. Part VI encompasses descriptions of strong molecule–surface interactions (organics on silicon) and molecule–molecule interactions (molecules on metals). In particular, the chapter by J. V. Barth focuses on cooperative eﬀects and the diﬀusivity of organic molecules on various metal surfaces. G. P. Lopinski and D. D. M. Wayner deal with functionalizing molecular interaction on Silicon surfaces. Finally, J. Reimers and coworkers describe the self-assembly of organic molecules on Silicon, mostly from a chemistry point of view. Part V describes the electronic properties of single molecules at metal surfaces. In particular, M. L. Bocquet and coworkers focus on catalysis and reaction pathways from a theoretical point of view. Finally, R. Stadler’s

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Preface

chapter deals with the possibility of using individual molecules as molecular electronic devices, and the challenges related to these endeavors. An area which is left uncovered, and which could be an excellent candidate for a sequel publication in the medium term, is the study of biological molecules (proteins, DNA, viruses, cells) at surfaces. This area is still in its infancy, and has just begun to show how fascinating and rewarding it can be. By way of a disclaimer, we emphasize that the material covered is by no means exhaustive. Rather, it aims at presenting a fairly broad, yet not all-encompassing overview of recent progress in this ﬁeld, indicating pitfalls, breakthrough results and future directions of research. We hope several readers will ﬁnd it inspiring and will follow in these footsteps in their own work. We are indebted to all the authors for their remarkable eﬀorts in writing chapters that will be readable and enjoyable at the graduate level. Editing a book like this has turned out to be a lot more diﬃcult and complicated than we had anticipated. In the ﬁrst instance, ﬁnding suitable authors was not at all easy. We invited scientists who are considered leaders in their ﬁelds, but many are so busy that they declined. Fortunately we found enough high proﬁle contributors to succeed in this project, even though we had to endure several cancellations along the way. Unfortunately, in a scientiﬁc world which is now dominated by citation indices and impact factors, book chapters suﬀer from relatively poor recognition, especially since they are “unfairly” compared to regular peer-reviewed publications. We emphasize unfairly because their role is quite diﬀerent — they are to be intended as a form of service to the community, especially with respect to teaching and training graduate students. One ﬁnal note of appreciation goes to our referees, who contributed signiﬁcantly by providing sound advice and constructive criticism, often improving the original chapters and rendering them more easy to comprehend and appreciate at the graduate level.

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Authors’ Biographies

Peter Grutter was born in Basel (Switzerland) on June 4th, 1962. He received his PhD in Condensed Matter Physics in 1989 in the group of H.-J. Guntherodt at the University of Basel with a Thesis entitled “Magnetic Force Microscopy.” After postdoctoral fellowships at the IBM Almaden Research Centre in San Jose (California) with Dan Rugar and at the IBM Zurich Research Laboratory in Ruschlikon (CH) with Urs Duerig he joined the Physics Department at McGill University (Montreal, Canada) in 1994, where he is now a Full Professor and a William Dawson Scholar. He is also Director and Fellow of the Canadian Institute of Advanced Research Nanoelectronics program as well as Scientiﬁc Director of the NSERC Nano Innovation Platform. Grutter’s research interests focus on SPM instrumentation development, determining ultimate limits and application of these tools to nanoelectronics and biology (see for more details at www.physics.mcgill.ca/∼peter). Werner Hofer was born in Salzburg in 1960. After obtaining his BSc in Technical Physics at the University of Graz in 1983 he decided to broaden his academic horizon by studying Latin and Ancient Greek at the same University. From 1988 to 1995 he worked for various companies in Austria, the last three years in a marketing department of a high-tech company specializing in energy production and distribution. After coming back to Physics in 1995 he obtained his Master in 1997 and his PhD in 1999, both with ﬁrst class honors, from the Technical University in Vienna, specializing in electron transport and the theory of scanning tunnelling microscopy. From 1999 to 2002 he was a Postdoc at University College London, working with an experimental group at NRC Ottawa on molecular modiﬁcations of semiconductor surfaces. He was later appointed Lecturer at Liverpool University in 2002. At present he is a Royal Society University Research Fellow at Liverpool University, where he holds a joint Lectureship in Chemistry and Physics. He is also a Principal Scientist of the Surface Science Research xi

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Centre at the same University. His research interests are electron transport, metal organic and semiconductor organic interfaces, and magnetic materials at the nanoscale. Together with Adam Foster from the Technical University of Helsinki he is the author of a book on the Theory of Scanning Probe Microscopes, which is published by Springer Scientiﬁc. Federico Rosei was born in Rome (Italy) on March 27th, 1972. He received a “Laurea” degree in Physics in February 1996, and a PhD in Physics in February 2001, both from the University of Rome “La Sapienza.” From October 1996 to December 1997 he was an Oﬃcer in the Italian Navy. He continued his scientiﬁc career as a Postdoctoral Fellow and Marie Curie Fellow at the University of Aarhus (DK), from November 2000 to April 2002. In May 2002 he joined the faculty at INRS Energie, Materiaux et Telecommunications, University of Quebec, as Assistant Professor. Then, in June 2004, he was promoted to Associate Professor with Tenure. Since October 2003, Dr. Rosei holds the “Canada Research Chair in Nanostructured Organic and Inorganic Materials.” Dr. Rosei’s research interests focus on fabricating, processing and characterizing organic and inorganic nanostructured materials. (see for more details at www.nanofemtolab.qc.ca).

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PART I INTRODUCTION

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BASIC PROPERTIES OF METAL SURFACES

´ A. L. VAZQUEZ DE PARGA and R. MIRANDA Departamento de F´ısica de la Materia Condensada e Instituto de Ciencia de Materiales “Nicol´ as Cabrera”, Universidad Aut´ onoma de Madrid Cantoblanco, 28049 Madrid, Spain Abstract. Clean metal surfaces often display an atomic arrangement at the surface that diﬀers from the one in the bulk. Some of these surface reconstructions show mesoscopic order and are very adequate to act as a template for the ordered growth of arrays of atoms, molecules or clusters. The electronic states at some surfaces can be prototypes of highly dense 2D electron gases where a number of fundamental properties can be addressed in detail. Localized surface states, on the other hand, are relevant in chemical processes at surfaces. The recent developments in experimental and theoretical techniques allow the exploration of these issues with unprecedented precision. Keywords: Surface reconstructions; surface states; angular resolved photoemission; scanning tunneling spectroscopy; spin polarized spectroscopy; self-organized nucleation.

Contents 1 2 3 4

5 6 7 8

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Geometric Structure: Surface Reconstructions . . . . . . . . . . Electronic Structure: Surface States . . . . . . . . . . . . . . . Free Electron-Like Surface States in Noble Metal Surfaces . . . 4.1 Angular resolved photoemission . . . . . . . . . . . . . . 4.2 Scanning tunneling spectroscopy . . . . . . . . . . . . . . Surface States in Transition Metal Surfaces . . . . . . . . . . . Spin Polarized Spectroscopy and Imaging of Magnetic Surfaces Ultrathin Epitaxial Metal Films . . . . . . . . . . . . . . . . . . Surface-State Mediated Interactions Between Adatoms . . . . .

PACS numbers: 68.37.Ef, 68.43.Bc 3

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4 4 8 8 8 11 16 17 20 23

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4

A. L. V´ azquez De Parga & R. Miranda

9 Self-Organized Nucleation on Nanostructured Metal Surfaces . . . . . . 24 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

1. Introduction Clean solid metal surfaces have been studied in Ultra High Vacuum (UHV) chambers under pressures in the low 10−10 Torr regime over the last forty years [1,2]. Experimental techniques, such as Scanning Tunneling Microscopy (STM) [3], Angular Resolved Photo-Emission Spectroscopy (ARPES) [4] or Low Energy Electron Diﬀraction (LEED) [5] and Microscopy (LEEM) [6], and theoretical developments, mostly based on the Density Functional Theory (DFT) [7] within the local approximation for the exchange and correlation contribution to the total energy, have been reﬁned to achieve an unprecedented level of accuracy in the characterization of surfaces. We can now determine with high precision the surface crystallography, i.e. the position of the atoms in the ﬁrst few layers of the solid, the layer-resolved chemical composition in the case of alloys, the atomic vibrations and the surface electronic structure, as well as the mechanical, chemical, optical and magnetic properties of surfaces. Most of these properties are vastly diﬀerent from those of the bulk. We have learned that the atoms at surfaces are not simply located at the continuation of the bulk positions, but that, in general, they occupy diﬀerent positions from their counterparts in the bulk. This is known as surface reconstructions. The atoms at the surface vibrate diﬀerently from those in the bulk, and surface phonons have been measured and calculated. The electronic eigenstates at the surface are also diﬀerent from the ones in the bulk. 2. Geometric Structure: Surface Reconstructions The energy needed to create a surface is always positive. Therefore, solids tend to minimize the surface energy. The atoms at the surface have less neighbors than the atoms in the bulk and tend to rearrange their positions trying to reduce the surface energy, originating surface reconstructions. While in semiconductors the driving force behind most reconstructions is an attempt to decrease the density of dangling bonds at the surface, in metals it is usually the increase in the number of neighbors, i.e. in the atomic density of the surface. Reconstructions are commonly observed in clean surfaces of fcc (Au, Pt, Ir) or bcc metals, like W or Mo [8]. In many cases the reconstructions only involve short range rearrangements of the atoms.

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Basic Properties of Metal Surfaces

5

22 2425 26272829 23 45 67 81 910122 1 13 14151617 18 19 021 23 FCC FCC HCP

FCC

FCC

Fig. 1. The upper panel shows an STM image of the Au(111) surface reconstruction with the long-range “herringbone” superstructure. The size of the image is ≈ 9.5 nm × 85 nm. As illustrated in the image, surface reconstructions of lower symmetry than the bulk lattice occur in several rotational or translational domains. The lower panel shows an atomic model of the reconstruction.

Paradigmatic examples of reconstructions involving long range patterns are the reconstructions of Au(100) and Au(111). Au(111) displays a most elaborate “herringbone” reconstruction, in √ which the the surface superstructure has a repeat distance of (22 × 3) unit cells [9–11]. The reconstruction is driven by the large tensile stress in the Au surface layer, and it leads to an hexagonal overlayer 4.5% denser than a (111) plane of the bulk. Figure 1 reproduces a large scale STM image of the reconstruction showing bright, pairwise-arranged parallel lines along [11¯2], which form, in turn, an additional zigzag mesoscopic structure. The lower panel shows the atomic model of the reconstruction, which is very similar to the images of Cu/Ru(0001) in Fig. 13 below. The surface atoms occupy hcp sites in a 25 ˚ A wide part of the unit cell, and fcc sites on the other part ˚ of the cell, 38 A wide. The fcc and hcp areas are separated by soliton walls which contains stacking fault lines, often called partial surface dislocations, where the atoms are near bridge sites. The soliton wall (or dislocation)

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regions constitute the bright ridges that appear 0.15–0.18 ˚ A higher than the fcc regions in STM images. Atomically resolved images show that the hcp regions appear 0.05–0.08 ˚ A higher than the fcc regions. The soliton walls form double rows with 63 ˚ A periodicity along [1¯10] and, additionally bend by 120 degrees with a period of 150–250 ˚ A along [11¯2] originating the mesoscopic “herringbone”. The reconstruction pattern is due to the stress-induced uniaxial contraction of the surface by 4.2% along [1¯10], the direction perpendicular to the zigzag ridges, plus a longer range, mesoscopic structure of the rotated uniaxial domains that appears to further reduce isotropically the strain. This complex arrangement has an inﬂuence on the surface electronic structure, as discussed below. A surface reconstruction containing the same structural elements as the one of Au(111) has been recently found in Pt(111) above 1330 K [12] or under an excess of Pt adatoms at 400 K [13]. The reconstructed surface layer has an atomic density larger than a (111) plane in the bulk. Regions of fcc and hcp stacking are separated by bright double dislocation lines along [11¯ 2], which, contrary to Au(111), can meet and form a network structure with star-like features [13]. The (100) surfaces of Au [10,14,15], Pt [16–18] and Ir [19,20] reconstruct to an incommensurate hexagonal overlayer arrangement, which produces (5×n) superstructures. Figure 2 shows STM images of Au(100), where the reconstruction unit cell is (5 × 20) (also known as “5 × 1”). In this reconstruction, a quasi-hexagonal layer with 8% higher atomic density than a (100) layer sits on a substrate of square symmetry. The hexagonal surface layer is oriented by the alignment of the compact directions of both layers. Figure 2(a) reveals an array of parallel rows along [110] extending over the whole terrace. Domains of the reconstruction with the rows running in the perpendicular direction are found in other parts of the surface. Each row is 5 unit cells wide because along the [1¯ 10] direction, six atoms from the ﬁrst layer sit on ﬁve atoms from the second layer. The complex details of the atomic arrangements inside and along the rows can be seen in the high resolution STM image of Fig. 2(b). A large tensile stress of the unreconstructed surfaces, as a result of d charge depletion at the surface, was proposed as the driving force behind these reconstructions [21]. Later on, the surface stress in the Ir(100) reconstructed surface was found to be anisotropic, i.e. smaller than in the unreconstructed case in the [110] direction, but larger in the perpendicular [1¯ 10] direction [22]. The origin of the reconstruction has been recently assigned to the tendency to increase the atomic coordination from square to hexagonal symmetry systematically found in isolated 2D metallic layers [23].

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Basic Properties of Metal Surfaces

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Fig. 2. (a) Large scale (100 nm × 100 nm) STM image of the Au(100) (5 × 20) surface reconstruction. (b) Atomically resolved STM image of the Au(100) (5 × 20) surface reconstruction. The size is 5.3 nm × 5.3 nm.

The (110) surfaces of Au [24], Pt [25] and Ir [26] display (2 × 1) LEED patterns, which are described by “missing row” reconstructions, in which every other closed-packed atomic row along [110] is missing. The driving force in this case seems to be the formation of (111) microfacets with their lower surface energy [22]. The resulting 1D channels have been used as a template for assembling molecular “wires”, e.g. of the amino acid cysteine [27].

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Some surfaces of bcc metals, such as W(100) or Mo(100), reconstruct [28]. The reconstruction occurs reversibly upon cooling the crystals below 200–250 K, and it can be viewed as a continuous, temperature-driven, orderdisorder phase transition. The room temperature phase is (1 × 1) and the low temperature phase has a c(2 × 2)p2mg unit cell involving only shortrange atomic displacements [29]. Much has been speculated with respect to the role of surface states in driving this reconstructions, but no clear evidence has been presented so far [30]. 3. Electronic Structure: Surface States The breaking of the translational symmetry perpendicular to the surface results in the appearance of a new set of electronic states: the surface states [31–33]. In 1932, Igor Tamm solved a semi-inﬁnite 1D Kronig–Penney model [34], i.e. a chain with a “surface”, and found [31] an additional solution corresponding to an electronic state located in the gap of “bulk” states at the Brillouin Zone boundary of the chain. Walter Schottky rediscovered it in a diﬀerent model in 1939 [32]. We know now that most surfaces possess a speciﬁc set of electronic states whose wave functions are strongly conﬁned to a narrow spatial region perpendicular to the surface. The surface states appear in a projected energy gap of the bulk bands. In fact, surface states are strictly orthogonal to bulk states, but defects can couple them. The gaps can be of diﬀerent character, i.e. absolute, hybridization, spin-orbit, etc. These states play an essential role in many surface properties and have been the subject of detailed scrutiny over the years. In particular, freeelectron-like surface states are prototype quasi-2D electronic states. Their charge density is physically localized at the surface, decaying quickly to the vacuum and within a few atomic distances to the bulk. The ﬁrst surface state was detected as an unexpected bump at −0.35 eV in the energy distribution of the electrons ﬁeld-emitted by a W(100) tip by Swanson and Crouser in 1966 [35]. Its surface character was claimed on the basis of the sensitivity of the bump to contaminants. It is somewhat ironic that surface resonances in sharp W tips have been recently found to jeopardize local electron spectroscopy of the surface states performed with the STM [36]. 4. Free Electron-Like Surface States in Noble Metal Surfaces 4.1. Angular resolved photoemission The technique of choice to detect occupied surface states with high energy and momentum resolution is Angular Resolved Photoelectron Spectroscopy

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(ARPES) [37,38]. Inverse Photoemission has been developed to detect empty surface states [39]. By now more than thirty surfaces have been shown to sustain surface states, but the surface states of noble metal (111) surfaces [40–42] have become a model system for detailed studies. The s-p surface states in Cu, Au and Ag (111) surfaces are all physically similar, so we concentrate in the Shockley surface state of Cu(111), originally observed by Gartland and Slagsvold [40]. This state exists in the gap along the gamma-L line in the bulk band gap of Cu as shown in Fig. 3. It constitutes a quasi-2D nearly-free electron gas with 0.04 electrons per surface atom (i.e. 7 × 1013 electrons cm−2 ), two orders of magnitude denser than the 2D electron gas at the interface of a typical semiconductor heterojunction. One has to keep in mind, however, that the mobility is four orders of magnitude smaller than in a high quality semiconductor 2D electron gas. The lower panel of Fig. 4 reproduces angle-resolved photoemission spectra [43] showing the dispersion of the state, i.e. how its BE changes with the angle of emission with respect to the normal. The dotted line in Fig. 3 shows schematically the E(k ) upwards parabolic dispersion of the surface state. The Binding Energy (BE) of the Cu(111) surface state at the center of the 2D Brillouin Zone (BZ) is −400 meV relative to the Fermi energy. The eﬀective mass for the electrons in this state is obtained from the curvature

Fig. 3. Electronic band structure of Cu projected on the (111) surface Brillouin zone. The cross-hatched region is the projected bulk continuum of states. The Shockley surface state derived from the s-p band (broken line) lies in the L-gap around the Fermi level.

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Fig. 4. Upper panel: Experimental ARPES spectra of the surface state of Cu(111) as a function of the angle of emission near the normal. The photon energy was 11.8 eV and the second peak is a replica due to a doublet in the light source. From [43]. Lower panel: High resolution ARPES spectra at normal emission of the (111) surface states of noble metals. The spectra have been measured at 30 K using photons of 21.2 eV. From [44].

of the dispersion relation and amounts to 0.412 me . The band crosses the Fermi level at a value of the momentum, called the Fermi wavevector, of −1 0.215 ˚ A . Recent, high-precision ARPES data for the surface states of noble metal (111) surfaces [44] are summarized in Table 1.

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Table 1. Properties of L-gap surface states of noble metal (111) surfaces obtained from a parabolic ﬁt to the ARPES dispersion [44]. Material

Binding energy (meV)

Eﬀective mass

−1 kFermi (˚ A )

Cu(111) Au(111) Ag(111)

−435 −487 −63

0.412 0.255 0.397

0.215 0.167/0.192 0.080

Surface-sensitive spectroscopies imply excitations of the many body electronic system. In the measurements, electrons are added or taken from the system, and the excited electron (or hole) interacts with the other electrons, renormalizing its energy with respect to the non-interacting case. The electronic excitation, if suﬃciently long-lived, is known as a quasiparticle. The lifetime of the excited state, that is, how long the quasiparticles retain their quantum state, is a fundamental concept, because it controls phenomena such as the dynamics of charge and energy transfer or electron-phonon coupling. The lifetime of the simplest quasiparticle, i.e. a hole in a surface band, can be obtained experimentally from the width of the corresponding peak in ARPES, since the spectral linewidth of a quasiparticle excitation in the energy space is inversely related to its lifetime. The lower panel of Fig. 4 shows the widths of the photoemission peaks at normal emission corresponding to the L-gap surface states. It can be shown [45] that for a 2D band such as these, the widths reﬂect the initial state (hole) lifetime. For these surface states the lifetime ranges from 30 to 110 femtoseconds (1 meV corresponds to a lifetime of 0.67 × 10−12 s). 4.2. Scanning tunneling spectroscopy The technique of choice to detect surface states with high energy and spatial resolution is Scanning Tunneling Spectroscopy (STS) [46,47]. The STM oﬀers unique opportunities of unveiling the behavior of surface electrons with unprecedented detail, since it maps the spatial distribution of the Local Density Of States (LDOS) some ˚ A above the surface. For example, topographic STM images recorded at small tunneling gap resistance display the electron interference pattern are produced by scattering oﬀ step edges and point defects [47]. Figure 5 shows the standing waves in electron density resulting from interference of surface state electrons scattering oﬀ steps in Cu(111). The wavelength of the standing waves depends on the tunneling

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Cu(111) at 75 K

E

Fig. 5. STM image of the standing waves produced by the surface electrons of Cu(111) scattered oﬀ an atomic step. The lower panel shows the tunnel spectrum, i.e. the differential conductance versus voltage, which is proportional to the LDOS of the Cu(111) surface state. The spectrum was taken at 300 K.

voltage, and, thus, the energy dispersion, E(k) of the surface state electrons can be easily measured [47]. The lower panel of Fig. 5 shows the experimental tunneling spectrum recorded in the middle of a large terrace of a Cu(111) surface. The diﬀerential conductivity at constant tip height shows an onset (deﬁned as the midpoint of the rise) at −440 ± 40 meV, which corresponds to the step-like increase in the 2D LDOS at the bottom of the free electron-like surface state. In order to compare with the experimental spectrum, the partial s-pz Density Of States (DOS) at the surface atoms has to be integrated in a region 1/4 of the size of the Brillouin Zone (BZ) around its center. This quantity can be compared to the measured tunneling conductance since the latter is given to ﬁrst-order by the DOS some ˚ A above the surface, which is dominated by s and pz states located close to the center of the BZ. The calculated shape of the surface state spectrum only reproduces the

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Fig. 6. 20 nm × 20 nm constant current STM topograph of a Cu(111) surface (raw data) displaying both the atomic lattice and the LDOS oscillations. The image has been recorded at 60 K with a sample voltage of −5 mV and a tunneling resistance of 10 MΩ.

experiment for ﬁlms thicker than 5 layers, reﬂecting the penetration of the evanescent wave function of the surface state of Cu(111) into the bulk. The Fourier transform of the standing wave pattern can be employed to get the 2D Fermi contour [48] of the surface state electrons. Figure 6 shows an STM image of a large terrace of Cu(111) displaying simultaneously the atomic resolution (i.e. the lattice of the Cu atoms) and a circular quantum mechanical interference pattern (visible as oscillations in the apparent height) due to the surface state electrons scattered by the potential associated to points defects in the terrace. The atomic corrugation in the conditions of Fig. 6 is 0.2 ˚ A, while the standing wave corrugation is 0.1 ˚ A. Since the sample voltage is only −5 mV, the oscillations correspond to electrons in the surface state right at the Fermi level. The standing waves, thus, show a period of half the Fermi wavelength, i.e. 15 ˚ A. In order to get an accurate determination of the 2D Fermi contour (see below), point scatterers are preferred to steps, since in the ﬁrst case wavevectors from all the Fermi contour contribute to form the standing wave pattern. The (unﬁltered) Fourier transform of this image is reproduced in Fig. 7. It shows a map of the k vectors that contribute to the standing wave pattern. Spots reﬂecting the reciprocal lattice of the Cu(111) surface (originating from the atomic resolution) and circles corresponding to the 2D Fermi contour, i.e. the crossing of the Fermi level by the surface state, are

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Fig. 7. Unﬁltered 2D Fourier transform of the image in Fig. 6. The rings detected around the central spot (see inset) and the other lattice spots have twice the radius of the 2D Fermi contour of the surface state. The lines in the power spectrum reﬂect the residual mechanical vibrations of the experimental setup.

seen. The 2D Fermi contour is totally equivalent to the bulk Fermi surface. Accordingly, it dictates the response of the 2D electron gas to any static or dynamic disturbance. The experimental determination of the 2D Fermi contour is important since the electronic instabilities at the surface are connected to its shape and they may lead to the stabilization of Charge Density Waves, Kohn anomalies in the phonon spectrum, Peierls distortions of the lattice, surface reconstructions and other collective behaviors. The requisite for these instabilities, the nesting of the Fermi surface, is easier to achieve in 2D than in 3D. One word of caution is needed: most of the 2D Fermi contours reported to date have been obtained from STM images not showing simultaneously the atomic resolution and standing waves [49]. In that case, any distortion in the image coming from creep in the piezos, thermal drift, etc., results in a distorted shape of the Fermi contour, which might lead to substantial mistakes in the interpretation of the physics behind [50,51]. On the contrary, the Fourier transform of an image such as shown in Fig. 6 contains an internal calibration, because the distance separating the lattice spots in the Fourier transform is related to the lateral lattice parameter of Cu(111). In this case one can determine with high precision the size of −1 A , the surface Fermi wave vector, which turns out to be kF = 0.205±0.02 ˚ i.e. a Fermi wavelength of 30 ± 3 ˚ A for Cu(111), in nice agreement with

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˚−1 ) [43,44]. This method, ARPES measurements (kF = 0.215 ± 0.01 A dubbed Fourier Transform STM (FT-STM) [48], has an energy resolution that depends on the bias voltage and temperature, and a momentum resolution that depends on the size of the image and the broadening of the Fermi contour due to the thermal decay of the standing waves. If both are selected properly this method can compete with the best ARUPS data available. Surface reconstructions provide a periodic variation of the potential felt by the quasi-free 2D electron gas of the surface electrons. Spatially resolved spectroscopy with the STM has allowed the observation of such an electronic superlattice at the surface of clean Au(111) [52]. The diﬀerential conductivity just above the onset of the surface state is higher on the hcp regions than on the fcc areas, i.e. low energy electrons in the surface state tend to localize in the hcp regions. The electron potential landscape of the “herringbone” reconstruction has been determined using a simple Kronig–Penney model with the same periodicity than the reconstruction. The potential was found to be more attractive in the hcp region than in the fcc region by 25 meV [52]. A more sophisticated approach [53] conﬁrmed these ﬁnding and yields a potential with absolute minima where atoms occupy bridge sites. Electrons are less strongly bound by 15 ± 5 meV in the hcp regions (see Fig. 1) and even less, by 37±5 meV, in the fcc regions. In a similar way, energy and wavefunctions of surface electrons are aﬀected by conﬁnement in stepped vicinal surfaces [54,55] or islands [56,57]. Figure 8 shows the onsets of noble metal Shockley surface states recorded with STM at low temperatures [58]. The widths of the onsets are inversely proportional to the lifetimes of the holes at the band minimum of the surface states. Intraband transitions within the 2D surface state

Fig. 8. dI/dV versus sample voltage tunneling spectra recorded at 4.6 K in the region of the onsets of Ag(111), Au(111) and Cu(111) surface states. The 2D surface states causes a sharp increase in the LDOS. The midpoint energy is the binding energy and the width is related to the lifetimes [58].

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A. L. V´ azquez De Parga & R. Miranda Table 2. Energy and linewidths of the L-gap surface states of noble metal (111) surfaces at the band minimum. The ARPES spectra have been recorded at 30 K [44], and the STS at 4.6 K [58]. All values are given in meV. Material

Energy

Linewidth ARPES

Linewidth STS

Cu(111) Au(111) Ag(111)

−435 −487 −63

23 21 6

24 18 6

are found to dominate the decay of the hole [58]. The lifetimes are in the range of tenths of femtoseconds, which gives phase relaxation lengths in the order of some hundreds of ˚ A. Table 2 shows that the values obtained for the (111) surfaces of noble metals compare nicely with the most recent values deduced from ARPES measurements at normal emission [44]. 5. Surface States in Transition Metal Surfaces The orbital character of the surface states can also be predominantly p or d. This happens frequently on transition metal surfaces. Obviously, the wavefunctions of surface states of d character are much more localized than those corresponding to the s-p quasi-free states mentioned above for noble metal surfaces. Figure 9 show tunneling spectra recorded on a Fe(100) surface [59]. The prominent peak at +0.17 eV reﬂect an empty surface state of minority spin character located near the center of the 2D BZ, a general feature of bcc(100) surfaces. It is located in a large hybridization gap between the bulk

Fig. 9. Left panel: Tunneling diﬀerential conductance versus voltage measurements for Fe(100) recorded at 300 K with diﬀerent tunneling distances. The right panel shows the tunneling diﬀerential conductance for Cr(100). From [59].

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bands of s and d character. This spin polarized surface state has dz2 −r2 symmetry with lobes pointing out of the surface. As discussed below, it is very useful to visualize magnetic domains by spin-polarized STM. The limited spatial extension of the d wavefunctions is reﬂected in the strong decrease in intensity of the peak as the tip of the STM is separated from the surface illustrated in the ﬁgure. Biedermann et al. have reported the position of the peak at a slightly diﬀerent energy of +0.3 eV [60]. Other occupied surface states of spin-minority character in Fe(100) at −2.40 eV have been predicted by theory [61] and detected by ARPES [62]. The right panel of Fig. 9 shows the surface state of dz2 −r2 character observed in Cr(100) right at the Fermi level [59]. Many bcc surfaces posses a similar localized surface state: in W(100) it has been found close to the Fermi level (−0.3 eV) [63], as in Mo(100) [65] (−0.2 eV). In many cases there are electronic states with a strong weight in the surface layer, but which are not located in a gap of the projected bulk band structure. The electrons in these states can decay into bulk states much faster than those occupying pure surface states. These states are known as surface resonances. One of these cases occur in the Ru(0001) surface. The upper panel of Fig. 10 shows an atomically resolved STM image of a terrace of Ru(0001) including a defect. The lower panel reproduces the STS conductance spectra recorded on clean Ru(0001). It displays a narrow peak located slightly above the Fermi level (110 ± 40 meV).a The peak is not detected in spectra recorded above the surface steps, which suggests that it is due to a surface resonance. Total DOS calculations conﬁrm that the peak corresponds to a sharp surface resonance of pz character located on the Ru atoms. The state presents an anisotropic spatial distribution, pointing towards the hcp site of the unoccupied layer above the surface, and outwards. 6. Spin Polarized Spectroscopy and Imaging of Magnetic Surfaces The electronic states of surfaces can be spin-polarized. They have been studied by means of spin-polarized ARPES for the past twenty years [66]. Recently spin polarized STM [67] has been developed as a powerful tool a The

bottom of a surface state band, as determined by Angular Resolved Ultraviolet Photoelectron Spectroscopy, corresponds to the onset of the tunneling spectrum. This has to be taken at the midpoint of the rise in diﬀerential conductivity. Often it is easier to locate the maximum in the dI/dV curve, which is then referred to as the posiition of the surface state. For Ru(0001) the midpoint of the onset is at −140 ± 60 meV and the maximum at +110 ± 40 meV.

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A. L. V´ azquez De Parga & R. Miranda

dI/dV (nA/V)

1,5

1,0

0,5

0,0 -1,5

-1,0

-0,5

0,0

0,5

1,0

1,5

Sample voltage (V) Fig. 10. Upper panel: 10 nm × 8.3 nm atomically resolved STM image of Ru(0001); Lower panel: Tunneling spectrum recorded at 300 K on Ru(0001). The tunneling gap was stabilized at 0.4 V and 0.3 nA.

not only able to characterize these states at the local scale, but also to image the spatial distribution of magnetization with unprecedented spatial resolution. If the W tip of the STM is covered in situ with a thin ﬁlm of a magnetic material (Fe, Cr, etc.), the tunnel current will depend on the relative orientation of the magnetization of tip and sample. This is the basis of the most successful approach to date to spin polarized STM [67]. Figure 11 shows the diﬀerential tunneling conductance spectra recorded on Cr(100) with a Fe-covered tip. The peak in the tunnel conductance at the Fermi energy is the d-like surface state of Cr(100) shown in Fig. 9, but note now that the intensity of the peak depends on which terrace of the surface the spectrum had been taken. The Cr(100) d -like surface state is spin split with the minority state, partially occupied and located at the Fermi level

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Fig. 11. Tunneling spectra recorded with a Fe-covered W tip on adjacent terraces of Cr(100). From [68].

Fig. 12. (a) Topographic STM image of Cr(100) and (b) simultaneously acquired dI/dV image, recorded at Vs = −270 meV. The contrast in this image reﬂects the diﬀerent orientation of the magnetization in adjacent terraces. From [69].

and the majority state, empty and located 2 eV above the Fermi energy. Cr is an antiferromagnetic material, with the magnetization direction in the (100) plane. In Cr(100), thus, the topological antiferromagnetism of Cr produces such that the surface magnetization is in opposite direction in adjacent atomic terraces. The alternate relative orientation of the magnetization of sample and tip produces a diﬀerent intensity in the peak, which can be used as a source of contrast to image the surface spin structure of Cr(100), as shown in Fig. 12 [68].

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7. Ultrathin Epitaxial Metal Films Growing ultrathin metallic layers on a (chemically diﬀerent) single crystal metal surface allows us to explore the changes in morphology and electronic structure that occurs as strain relief processes develop and relate them to the changes in reactivity, a subject of immense importance in catalysis. A model system to study the eﬀects of tensile strain is Cu on Ru(0001). Cu has a 5.5% smaller lattice parameter than Ru. Each Cu layer grown on Ru(0001) presents a speciﬁc pattern of surface reconstruction due to the layer-dependent relaxation of the strain [69]. The ﬁrst Cu layer is pseudomorphic with Ru(0001) [70], e.g. it is laterally expanded by 5.5% from a nearest neighbor distance (nnd) of 2.55 ˚ A in Cu(111) to 2.70 ˚ A. The Cu atoms occupy hcp sites (i.e. the continuation of the Ru lattice) with a Cu-Ru distance at the interface of 2.10 ˚ A as determined by LEED [71]. A 2 ML Cu ﬁlm relaxes the strain uniaxially and, thus, presents three domains of a stripe-phase reconstruction, similar to the one described above for Au(111) (but without the “herringbone”). The upper panel of Fig. 13 shows the three domains in the same terrace. The Cu packing is 6.25% denser than in the pseudomorphic monolayer for both Cu ad-layers. In this reconstruction, as in Au(111), see Fig. 1, alternating stripes of fcc and hcp stacked Cu atoms with a periodicity of 43 ˚ A along [1¯10] are separated by domain walls [69,72]. The bright double lines along [11¯2] observed in the STM image of the lower panel of Fig. 13 reﬂect the domain walls or partial dislocation lines. The darker and wider [72] regions correspond to Cu atoms occupying fcc sites, while the gray and shorter regions inside the double rows correspond to Cu atoms in hcp sites. The short range structure is Cu(111)-like, but the lattice is slightly expanded (compressed) in the fcc (hcp) regions with respect to bulk Cu. The average lateral distance among Cu atoms is 2.61 ˚ A [72]. Thicker Cu ﬁlms relax gradually displaying quasi-hexagonal atomic arrangements that originate a weakly modulated, incommensurate moir´e-like arrangement with the Cu bulk lattice [69]. Ultrathin ﬁlms of hexagonal symmetry under compressive strains (e.g. Ag/Pt(111) with a misﬁt of +4.3%) relax the strain in a similar way by forming striped-phases. The domain walls are now regions of locally lower atomic density and are imaged dark in STM [73]. The stable conﬁguration, however, consists of a trigonal network of crossed domain walls. Figure 14 shows a Cu/Ru(0001)ﬁlm presenting regions with thickness of 1 and 2 MLs and the diﬀerential tunnel conductance spectra measured on the two regions. In both cases a single peak corresponding to the s-pz “surface state” of the Cu ﬁlms is seen. Its energy shifts with the Cu

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Fig. 13. The upper panel shows a 160 nm ×127 nm STM image of a 2 ML Cu ﬁlm grown on Ru(0001). The image has been taken with a gap resistance of 2 MΩ. The brighter parts of the image correspond to subsurface Ar bubbles (see text). The lower panel shows a 10 nm × 8 nm STM image with the atomic details of the reconstruction of 2 ML of Cu on Ru(0001).

thickness: the peak corresponding to the pseudomorphic Cu layer is located 280 ± 40 meV above the Fermi level, while it is at 110 ± 40 meV for a 2 MLthick Cu ﬁlm. Spectra recorded on Cu ﬁlms of increasing thickness [74] indicate that the state shifts to lower binding energies for increasing thicknesses, crossing back to the Fermi level at 4 ML and becoming indistinguishable

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dI/dV (arb. units)

22

15:34

-0,4

0,0

0,4

0,8

Sample voltage (V) Fig. 14. The upper panel shows a 200 nm × 200 nm STM image of a Cu ﬁlm grown on Ru(0001) with local thicknesses of 1 and 2 MLs. The regions 1 ML-thick are seen ﬂat. The areas 2 ML-thick are easily recognized by the characteristic strain-relief reconstruction pattern. A fraction of the derivative of the image has been added to increase the contrast in the presence of steps. The lower panel shows diﬀerential conductance versus voltage spectra recorded on the 1 and 2 ML patches of the upper panel. The spectra have been shifted vertically for clarity.

from the Shockley surface state of Cu(111) at local thicknesses of 8 ML. The total upward shift of the state from Cu(111) to the expanded Cu monolayer amounts to +600 meV. Most of this shift is due to the tensile strain and not to the proximity of the Ru substrate. There are several reasons for an energy shift of a surface state to occur. In fact, any modiﬁcation of the potential and matching conditions of the wavefunctions at the (surface–vacuum) interface will modify the energy position (and dispersion) of a surface state. This includes the physisorption

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of noble atoms (e.g. the onset of the Cu(111) surface state is shifted upwards by +130 meV for Xe/Cu(111) [75,76]) or deposition of ultrathin layers of insulators (the shift is +230 meV for NaCl/Cu(111) [77]). Obviously, strain-induced changes in the lateral or perpendicular lattice parameters of the ﬁlm will result in modiﬁcations of the surface electronic structure. Strain-induced shifts in the energy of the surface state of Ag(111) ﬁlms grown on Si(111)7×7 have been detected by ARUPS [78]. In this case, a 1% expansion of the lattice was predicted to shift the Ag(111) surface state by +150 meV [78]. Lateral conﬁnement in 20 ˚ A-wide terraces of vicinal Cu(111) surfaces also shifts the bottom of the state +190 meV upwards [54,55]. To all these intrinsic reasons, one would have to add the expected modiﬁcations in the electronic structure of the growing ﬁlm as it thickens, due to the decreasing inﬂuence of the substrate. This can be better judged for a system that is not pseudomorphic, such as Ag/Cu(111). The large (12%) mismatch between Ag and Cu would provoke such a tremendous compressive stress for a pseudomorphic layer that the Ag layers keep their own lattice parameter from the ﬁrst monolayer on. For 1 ML of Ag/Cu(111), the surface state has been found to be 120 meV lower in energy than for bulk Ag(111) [79], and shifts with increasing Ag coverage to the bulk value. These results might have some bearing on explaining changes in the chemical reactivity of metallic ﬁlms under strain. It was demonstrated that the position of the centroid of the d band projected on the surface atoms correlates for diﬀerent metals with the binding energies of several adsorbates [80,81]. Since increasing tensile strain in a ﬁlm changes the position of the centroid of the d band [82,83], it has been suggested that tensile strain will enhance the chemical reactivity [84]. This view is supported by calculations showing an increased binding energies for CO and O2 adsorption on theoretically strained Ru(0001) surfaces [84], by observations of enhanced adsorption of oxygen and CO on top of the subsurface bubbles in Ru(0001) [85] and by calculations for oxygen [82] and hydrogen [83] adsorption on Cu surfaces under tensile strain. Recently, it has been proposed that the depopulation of the Cu(111)-like surface state for the ﬁrst two monolayers of Cu on Ru(0001) contributes to the enhanced reactivity of Cu/Ru(0001) [74]. Further work is needed to conﬁrm or discard this suggestion.

8. Surface-State Mediated Interactions Between Adatoms The 2D electron gas of the Shockley-type surface states plays also an important role in the substrate mediated interaction between adsorbed atoms.

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Low-Temperature STM showed that the distances between bulk-segregated impurities on Cu(111) were not randomly distributed [86]. On the contrary, preferred distances between adatoms dictated by the standing waves of the scattered electron gas were found. The long range interaction between Cu adatoms mediated by the surface state of Cu(111) has been conﬁrmed [87] to decay at large distances as r−2 , while oscillating in sign with a period given by the Fermi wavelength divided by 2, as predicted by Lau and Kohn in 1978 for a partially-ﬁlled surface state (cos(kF r)/r2 ) [88]. Recently, the lateral range of the interaction has been demonstrated to scale with the Fermi wavelength of the surface state for diﬀerent metallic adsorbates on Ag(111) and Cu(111) [89], excluding a possible role of elastic lattice deformation and conﬁrming the leading role of the 2D electron gas in the lateral interaction. The possibility of using a repulsive interaction due to electronic screening in a surface state to create a pseudo-ordered array of adatoms at low temperatures has been recently demonstrated for Ce/Ag(111) [90]. Ordered arrays of molecules can probably also be created at low temperatures with the help of electron mediated adsorbate–adsorbate interactions.

9. Self-Organized Nucleation on Nanostructured Metal Surfaces Metallic atoms deposited on clean metal surfaces at temperatures high enough to be mobile experience a number of diﬀerent atomistic processes: diﬀusion, nucleation, intermixing, etc., which lead to the formation of islands, and eventually to the growth of a new metallic layer. The surface diﬀusion and nucleation processes depend strongly on the anisotropic strain present in certain reconstructed surfaces and, thus, kinetically controlled growth can result in the fabrication of a self-organized array of nanoscopic particles, if the surface provides a regular pattern of nucleation centers. This is the case for mesoscopically-ordered reconstructed surfaces, such as Au(111), or for periodic strain-relief patterns, such as 2ML Cu/Ru(0001). Figure 15 shows the result of depositing Co on Au(111) [91]. The regularly distributed elbows of the dislocation lines of the surface reconstruction constitute an array of nucleation centers with a 73 ˚ A × 140 ˚ A unit cell. There, atomic exchange between the deposited atom and the substrate takes place easily. Thus, ordered arrays of 30 ˚ A-wide nanodots of Ni [92], Co [93] or Mo [94] have been grown on Au(111) with a reduced size distribution and a density of 1 × 1012 cm−2 . Mesoscopic order can also be achieved in vicinal surfaces of crystals with long range reconstructions, such as Au(788) [95]. The combination of terrace size and long range reconstruction provides a

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Fig. 15. 3435 ˚ A × 3730 ˚ A STM image of Co clusters grown on the Au(111) surface. The inset shows Co clusters nucleated at the elbows of the herringbone reconstruction [92]. −2 73 ˚ A × 39 ˚ A periodic array of nucleation centers, where 500 ˚ A Co dots have been grown with a density of 4 × 1012 cm−2 .

Acknowledgments We thank our coworkers for years of learning together. The work was supported by the Spanish Ministerio de Ciencia y Tecnolog´ıa (MCyT) through grants BFM 2001-0174 and 2000-0526, and FIS2004. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]

A. Zangwill, Physics at Surfaces (Cambridge University Press, 1988). F. Bechstedt, Principles of Surface Physics (Springer, Berlin, 2003). F. Besenbacher, Rep. Prog. Phys. 59, 1737 (1996). S. H¨ ufner, Photoelectron Spectroscopy (Springer, Berlin, 1995). K. Heinz, Rep. Prog. Phys. 58, 637 (1995). E. Bauer, Rep. Prog. Phys. 57, 895 (1994). P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964); W. Kohn and L. J. Sham, Phys. Rev. A 140, 1133 (1965). S. Titmuss, A. Wander and D. A. King, Chem. Rev. 96, 1291 (1996). J. Perdereau, J. P. Biberian and G. E. Rhead, J. Phys. F 4, 798 (1974). M. A. van Hove, R. J. Koestner, P. C. Stair, J. P. Biberian, L. L. Kesmodel, I. Bartos and G. Somorjai, Surface Sci. 103, 189 (1981). J. V. Barth, H. Brune, G. Ertl and R. J. Behm, Phys. Rev. B 42, 9307 (1990). A. R. Sandy, S. G. J. Mochrie, D. M. Zehner, G. Grubel, K. G. Huang and D. Gibbs, Phys. Rev. Lett. 68, 2192 (1992).

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BASIC PROPERTIES OF SILICON SURFACES MATT J. BUTCHER and MICHELLE Y. SIMMONS School of Physics, University of New South Wales, Sydney NSW 2052, Australia Abstract. This chapter addresses the basic fundamental properties of silicon surfaces, including structural, electronic and chemical properties. An introduction is given to STM topographic imaging and tunneling spectroscopy as applied to semiconductors. The chapter will then give a brief overview of scanning tunneling microscope studies of clean silicon semiconductor surfaces under ultra-high vacuum conditions. Particular emphasis will be placed on the most common low index Si surface and a discussion of typical adsorbates observed on these surfaces. The use of hydrogen lithography to control the atomic placement of adsorbates on silicon is reviewed. Finally the work will be put in context of the fabrication of novel nano and atomic-scale semiconductor devices using scanning tunneling microscopy. Keywords: Scanning tunneling microscopy; scanning tunneling spectroscopy; silicon surfaces; adsorption of molecules; hydrogen resist lithography and nano- and atomic-scale devices.

Contents 1 2

3 4

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Scanning Tunneling Microscopy of Semiconductor Surfaces . . . . . . . 2.1 General operation of the scanning tunneling microscope . . . . . . 2.2 Simple model of the tunnel current . . . . . . . . . . . . . . . . . . 2.3 Relating the tunnel current to the local density of states at the Fermi level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Voltage dependent imaging . . . . . . . . . . . . . . . . . . . . . . Current Imaging Tunneling Spectroscopy of Semiconductor Surfaces . . Silicon Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 The Si(100)-2 × 1 surface . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Surface preparation . . . . . . . . . . . . . . . . . . . . . . 4.1.2 Surface geometry . . . . . . . . . . . . . . . . . . . . . . . . 29

30 30 31 32 34 36 39 40 41 42 42

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4.1.3 Electronic structure . . . . . . . . 4.1.4 Surface steps . . . . . . . . . . . . 4.1.5 Surface defects . . . . . . . . . . . 4.1.6 Adsorbates . . . . . . . . . . . . . 4.2 The hydrogen terminated Si(100) surface 4.3 Si(111)-7 × 7 . . . . . . . . . . . . . . . . 5 The Role of STM in Silicon Device Fabrication 6 Conclusions . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . .

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1. Introduction Semiconductors are the most widely studied class of materials by scanning probe microscopy. In particular silicon, which forms the basis of the semiconductor industry, has received the most interest due to its technological importance for device fabrication. A fundamental understanding of the nature of the clean surfaces of silicon, whilst not only interesting in its own right, has proved invaluable to the development of more complex issues such as adsorbate interaction, diﬀusion and epitaxy. After an introduction to the theory of scanning tunneling microscopy as applied to semiconductors, the chapter will focus more speciﬁcally on detailed STM studies of the silicon (100) surface. In particular we will consider the geometry, electronic structure, common defects observed and some typical adsorbates on this surface. The importance of the hydrogen terminated silicon surface and its role in controlling the lateral position of adsorbates is discussed, before the chapter ﬁnishes with an overview of the role of STMs in silicon device fabrication. For a more comprehensive appraisal of scanning probe microscope studies of semiconductor surfaces, and not just silicon, the reader is referred to several excellent review articles and books [1–5]. 2. Scanning Tunneling Microscopy of Semiconductor Surfaces Scanning Tunneling Microscopy has proved to be a powerful and unique tool for the determination of the structural and electronic properties of semiconductor surfaces. Semiconductors are both fascinating and important because of the existence of surface and interface states and their role in electronic device applications. In general, the clean surface of a semiconductor contains surface states which arise from the unterminated surface or dangling bonds. The internal energy of the surface can be reduced by either saturating the dangling bond density by the adsorption of adatoms

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or by the rearrangement (reconstruction) of surface atoms giving a range of interesting topographies that diﬀer signiﬁcantly from the bulk. This reconstruction typically results in a complete rearrangement of the local bonding geometry and changes in the translational symmetry at the surface. A major breakthrough in our understanding of the structure of semiconductors surfaces occurred with the ﬁrst observation of the Si(111) surface using STM in 1983 [6]. Whilst numerous possible structures of this surface had been proposed it was the ability to “see” the surface with the real-space atomic resolution of the STM [7] in combination with modeling of transmission electron diﬀraction patterns of this surface [8] that allowed the ﬁnal determination of the surface reconstruction to be understood. Nowadays it is common to perform voltage dependent scanning tunneling microscopy and spectroscopy studies to gain an insight into the surface structure. This is because STM investigations generally reveal a pronounced bias dependence, where diﬀerent bonds are observed at diﬀerent energies. In the next section we will brieﬂy introduce the basic principles of operation of the scanning tunneling microscope, the most commonly used models of the tunnel current, and the important role that voltage-dependent imaging has on the determination of surface structure. 2.1. General operation of the scanning tunneling microscope Scanning tunneling microscopy is an imaging technique that can provide three-dimensional real space images of surfaces. Under optimal conditions sub atomic resolution imaging can be achieved. The principle of scanning tunneling microscopy is now well established with STM images being generated in a number of ways. The most common form of imaging is the constant current or topographic mode, shown schematically in Fig. 1. Here a sharp metal tip is brought very close to the sample surface in vacuum, allowing the wavefunctions of the tip and sample to overlap. A small bias voltage applied between the sample and tip causes a quantum mechanical tunneling current to ﬂow, the magnitude of which is exponentially dependent on the tip-sample separation. The position of the tip in all three dimensions is accurately controlled by piezoelectric drivers. The tip is scanned across the surface in the two lateral dimensions, x and y, and generally a feedback current adjusts the tip height to keep a constant current in the third dimension, z. By keeping the current constant the tip is deﬂected as it scans across the surface essentially tracing out the shape of the sample surface. The tunneling current is therefore the control parameter in most STM

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Fig. 1.

Schematic illustration of the constant current mode of STM operation.

experiments — it is set to a ﬁxed value, and the position of the STM tip relative to the scanned surface is varied via the distortions of a piezocrystal so that the current remains constant. The extreme sensitivity of the tunneling current with respect to the tip-sample distance is the basis of vertical resolution in scanning tunneling microscopy.

2.2. Simple model of the tunnel current The scanning tunneling microscope relies on a quantum mechanical eﬀect — tunneling, where the electrons from the tip have a non-vanishing probability of passing the vacuum barrier to the sample. An insight into the workings of the STM and the resolution that can be achieved can be gained from considering a simple model of quantum tunneling in one dimension. Here we consider two metal electrodes, the sample and tip with a potential (vacuum) barrier between them, see Fig. 2(a). We can calculate the transmission probability for a wave incident on the barrier in one dimension. In classical mechanics the electron cannot travel across the barrier unless it has an energy greater than that of the barrier even when a bias eV is applied (Fig. 2(b)). However quantum mechanics allows a ﬁnite probability that an electron can transverse the barrier if the thickness of the barrier, z is small. The solutions to the Schr¨ odingers equation inside the barrier have

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(a) No Applied bias VACUUM LEVEL φ EF2

EF1 z

(b) Applied bias, V

EF1 tunneling

eV= EF1-EF2 EF2

z Fig. 2. Simple one-dimensional model of quantum tunneling — a schematic illustration of the energy level diagram of two conductors, the sample and tip separated in vacuum by a distance, z with (a) no applied bias and (b) with an applied bias, V .

the form ψ(z) = ψ(0)e−κz and

2m(V − E) where m is the mass of the electron, is Planck’s constant, E is the energy of the electron and V is the potential in the barrier. In the simplest case V is simply the vacuum level, so for states at the Fermi energy (V − E) is just the work function, φ. The probability that an electron will cross the barrier is the tunneling current I, and it decays exponentially with the barrier width, z, as κ=

I ∝ e−2κz .

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Only the electrons with energies between the Fermi levels of the two materials can tunnel. For silicon and tungsten, with work functions of ∼4.5 eV we can calculate that the tunneling current changes by more than an order of magnitude when the tip–sample separation in vacuum decreases by the height of a single silicon atom (1.36 ˚ A on the Si(100) surface). From a simple consideration of the tunnel current we can see that the STM is capable of sub-˚ A resolution in the direction normal to the surface of the sample. However to produce three-dimensional (3D) images of the surface, the STM must also have good lateral resolution. It is the shape and quality of the tip that determine the ultimate lateral resolution that can be achieved using a STM. Binnig and Rohrer estimated the lateral resolution by assuming the STM tip to be spherical in shape [9]. Typically with a spherical tip of radius 100 nm a resolution of ∼4 nm could be expected. However in practice no tip can ever approximate to a smooth sphere but instead has a surface that is rough on the atomic-scale. It is this roughness that works in our favor since most of the current will tunnel through whatever atomic-scale asperity approaches closest to the surface. A model of tunneling from a single atom was ﬁrst proposed by Lang [10], and it is now generally accepted that the best STM images result when there is tunneling from a single atom on the tip. To this end there are several groups who strive to form the perfect tip by the placement of single atoms at the end of single crystal tungsten [11]. 2.3. Relating the tunnel current to the local density of states at the Fermi level In the simple treatment of 1D tunneling we have considered an electron tunneling from the sample to the tip, however from symmetry arguments an electron could just as easily tunnel from the tip to the sample. This can only happen however if there are unoccupied states available in the sample. We can estimate the tunneling current by summing over the contributions from all states within the energy interval EF 1 − EF 2 = eV, shown in Fig. 2 I∝

E F2

|ψn (0)|2 e−2κz

EF 1

where ψn (0) is the normalized incident wavefunction. If we assume that the bias is small enough such that the density of states does not vary much in the range EF 1 − EF 2 , we can express the tunneling current in terms of the local density of states of the sample at the Fermi level ρs (z, E), evaluated

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at the surface of the sample, z = 0, I ∝ ρs (0, EF )e−2κz . Further, since we can approximate the eigenfunction within the vacuum region by ψn (z) = ψn (0)e−κz we can express the tunneling current in terms of the local density of states at the Fermi level evaluated at the tip surface, z I ∝ ρs (z, EF ). Therefore, according to our simple 1D model, by scanning the tip over the surface and keeping the tunneling current constant, we are eﬀectively mapping out a constant Fermi level density of states contour of the sample surface. A more sophisticated approach to modeling the tunnel current is given by the modiﬁed Bardeen approach of Tersoﬀ and Hamann [12], based on a pertubative treatment of the tunneling, which has become the workhorse of STM theory. In reality a more exact calculation of the tunnel current would require the Schr¨ odinger’s equation to be solved in all three regions: before, in and after the barrier. For a comprehensive survey of the range of methods used to calculate the tunneling current over the last few decades the interested reader is referred to an excellent review article by Briggs and Fischer (1999) [5]. According to Bardeen, ﬁrst order perturbation theory deﬁnes the current between two electrodes (the sample and tip) as 2π [f (Es ) − f (Et )]|Mst |2 δ(Et + V + Es ) I= s,t where f (E) is the Fermi function, V is the applied voltage and Mst is the tunneling matrix element between the states ψs and ψt of the sample and tip respectively [13]. The energies Es and Et are speciﬁed with respect to the sample and tip energies respectively. If we assume small bias voltages and zero temperature, this equation simpliﬁes to 2π 2 I= e V |Mst |2 δ(Et − EF )δ(Es − EF ). s,t Bardeen showed that to derive the tunneling matrix element, which represents the amplitude of electron transfer between the sample and tip, explicit expressions for the wavefunctions of the tip and sample were

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required. Unfortunately the atomic structure of the tip is generally not known. Tersoﬀ and Hamann modiﬁed the Bardeen approach to consider the simplest model for the tip with a locally spherical symmetry, essentially choosing the tip to be a mathematical point source of current. In this model the tunneling matrix was evaluated for an s-type wavefunction, and in the limit of weak coupling between the sample and tip, the tunneling current was found to be I(rt ) ∝ |ψt (rt )|2 δ(Et − EF ) ≡ ρs (rt , EF ) where I(rt ) is the tunneling current at the tip position, rt , ψt (rt ) is the wavefunction at the point source of the tunneling current, EF is the Fermi energy and ρs (rt , EF ) is the local density of states of the sample at the Fermi energy evaluated at the tip surface [12]. Within the given simpliﬁcations and approximations of the Tersoﬀ Hamann model, this result is the 3D equivalent of the 1D model, where the tunneling current is proportional to the Fermi level local density of states of the sample, measured at the center of curvature of the tip. In this case the local density of states is calculated for the bare surface, essentially in the absence of the tip so that there is no reference to the complex tip–sample interaction. For metals, this approximation holds well, since the density of states at the Fermi energy is fairly constant so that the constant current image in STM corresponds to a smoothed representation of the surface topography. However, for semiconductor surfaces the local density of states is strongly energy (and hence bias) dependent. 2.4. Voltage dependent imaging In the discussions of theoretical treatments for tunneling so far, we have assumed that the applied bias is small. However, typically the bias voltages used to measure semiconductor surfaces and probe these states are of the order of several volts so that the assumptions built into the Tersoﬀ–Hamann theory are no longer valid. A more accurate description of the tunneling current, therefore, would consider the bias dependence of the tunneling matrix element, the tip density of states, and the electronic structure of both sample and tip. As a result Hamers suggested that in the high bias regime it is more useful to use the semi-classical Wentzel–Kramers–Brillouin (WKB) theory for planar tunneling [2]. Here the tunneling current is expressed as eV ρs (r, E)ρt (r, −eV + E)T (E, eV, r) dE I= 0

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where ρs (r, E) and ρt (r, −eV + E) are the density of states of the sample and tip at location r and energy, E, measured with respect to their individual Fermi levels. The tunneling transmission probability T (E, eV, r) for electrons with energy, E and applied voltage V is given by √ φs + φt eV 2Z 2π + −E T (E, eV ) = exp − 2 2

where ϕs and ϕt are the work functions of sample and tip respectively and Z is the tip–sample separation. At a constant tunneling current I, the contour followed by the tip is therefore a complicated function of the density of both sample and tip, together with the tunneling transmission probability. Consideration of the transmission probability shows that for a negative sample bias (eV < 0) the transmission probability will be largest when E = 0 (i.e. when electrons are at the Fermi level of the sample). Likewise, for eV > 0 (positive sample bias) the probability is largest for E = eV (corresponding to electrons at the Fermi level of the tip). For typical work function materials, where EF = 3–4 eV, most of the tunneling current will originate from within a few hundred mV of the Fermi level, but with contributions as much as 1 eV below the Fermi level. Figure 3 sketches the tunneling processes that occur in voltage dependent STM imaging for a highly doped semiconductor. In Fig. 3(a) we present the energy diagram for a sample at zero applied bias, showing the bulk and surface density of states. At positive sample bias, Fig. 3(b), the net tunneling current arises from electrons which tunnel from the occupied states of the tip into unoccupied states of the sample. As a result the contour that the STM tip follows is directly related to the spatial distribution of the unoccupied states of the sample. At negative sample bias, Fig. 3(c), the situation is reversed, and electrons tunnel from the occupied states of the sample into unoccupied states of the tip, and the STM tip follows a contour which is related to the spatial distribution of the unoccupied or empty electronic states of the tip. Whilst the tunneling current is a convolution of the tip and sample density of states, it is the energy spectra of the sample states that we try to determine. For positive biases on the sample, where electrons are injected from the tip into unoccupied sample states, the tunnel current will be dominated by electrons close to the Fermi energy of the tip. Under these conditions the density of states of the tip can be taken to be constant and the structure of the spectrum corresponds largely to the spectrum of

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TIP

(a)

VACUUM

SAMPLE

EC EF EV

BULK DOS SURFACE DOS (b)

SAMPLE: POSITIVE (Vs>0)

eV

(c) SAMPLE: NEGATIVE (Vs<0)

eV

Fig. 3. Energy diagram for a tip–vacuum–semiconductor junction at (a) zero applied bias, (b) positive sample bias, tunneling from tip to sample and (c) negative sample bias, tunneling from sample to tip. Note there is no band bending indicating that the semiconductor is highly doped.

unoccupied sample states. The situation is slightly more complex for negative biases on the sample (ﬁlled state imaging), where the density of states of the sample at the Fermi energy is largely independent of the applied voltage. Here the STM tip follows a contour which is mostly related to

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the spectrum of unoccupied tip states, and as such, it is diﬃcult to use STM for characterization of the lower-lying ﬁlled sample states that are not near the Fermi energy. This explains the large variation in occupied or ﬁlled state imaging achieved by diﬀerent investigators of the same material compared to unoccupied or empty state imaging [4]. Whilst the density of states of diﬀerent samples of the same material is expected to be nearly identical, the unoccupied spectra of the tips will vary as its composition and morphology change. Nonetheless for the past few years several models have been developed successfully to predict behavior in the forward and reverse bias regions for highly doped silicon samples. For less highly doped samples, band bending eﬀects have to be considered, and this remains an active area of investigation, see for example [14]. It is important to note that whilst only those electrons at the Fermi level can contribute to tunneling, all the electrons below the Fermi level contribute to the charge density. The STM therefore measures the electronic charge density at the Fermi level outside the surface (put another way — it images the spatial locations of the molecular orbitals) rather than the true positions of the atoms in the surface. The imaging of Si(100) surfaces provides a simple example of this diﬀerence and will be discussed later in the chapter. Whilst this electronic charge density at the Fermi level is directly related to the positions of the atoms on the surface, the theory relating these is rather complex and remains the subject of intensive debate.

3. Current Imaging Tunneling Spectroscopy of Semiconductor Surfaces So far we have discussed how the STM can be used to generate topographic maps of the surface. Scanning tunneling microscopy probes both the empty and occupied surface states depending on the polarity of the voltage applied between the sample and tip. An important application of the STM is therefore to perform spatially localized tunneling spectroscopy to map the electronic properties of the surface with atomic resolution. The use of such a technique was ﬁrst demonstrated by Hamers et al., in 1986 [15] and a good review of this subject has been written Feenstra [16]. Figure 4 shows a schematic of the current imaging tunneling spectroscopy mode of STM operation. During the time of active feedback, a constant stabilization voltage is applied to the sample, and the tip height adjusted to maintain a constant tunneling current. When the feedback system is deactivated the tip is held over a given point on the surface, and the tip–sample bias swept

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Fig. 4. Schematic illustration of the current imaging tunneling spectroscopy mode of STM operation.

over a given range whilst measuring the tunneling current, to give an I–V curve corresponding to that location. Afterwards the applied voltage is set back to the stabilization voltage and the feedback system reactivated. By acquiring the I–V curves rapidly whilst scanning the tip position, a constant current topograph and spatially resolved I–V characteristics can be simultaneously obtained. The derivative of these I–V curves, speciﬁcally (V /I)dI/dV gives a direct indication of the density of states of the sample at that location. The capability of the tunneling microscope to perform atomically localized spectroscopy in combination with a real-space imaging makes it a powerful tool to characterize semiconductor surfaces.

4. Silicon Surfaces Silicon is a material of major technological importance since it forms the basis of a vast range of electronic devices such as transistors, microprocessors and solar cells. It is also likely to be used in numerous future technologies including atomic scale devices [17,18], ultra dense storage devices [19], quantum computers [20,21] and hybrid molecular devices [22]. The surfaces of silicon are the most thoroughly studied of all semiconductor surfaces and there are numerous known surface reconstructions [23]. In this section we

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will pay particular attention to the Si(100)-2×1 surface due to its relevance to discussions in later chapters. Silicon crystallizes in the diamond structure in which all the atoms are covalently bonded to four nearest neighbor Si atoms, see Fig. 5(a). If we take a slice through the silicon surface along one of the (001) planes, we can see a schematic representation of the ideal (unreconstructed) surface, see Fig. 5(b). At this surface there are a number of broken bonds which protrude above the surface plane, known as dangling bonds. These exposed dangling bonds are highly energetic and make the surface unstable, such that when the surface is cleaved, it seeks to minimize this energy and reduce the number of dangling bonds by the rearrangement of atoms — known as reconstruction. A schematic example of this reconstruction is shown in Fig. 5(c). 4.1. The Si(100)-2 × 1 surface The Si(100) surface is used in a large majority of semiconductor devices, and has been extensively studied. The 2 × 1 periodicity of the surface shown in

Fig. 5. Schematic diagrams of (a) bulk silicon, (b) the ideal (100) surface, (c) the (100)2 × 1 reconstructed surface, (d) the 2 dangling bonds per atom on the ideal surface, and (e) the pairing of the dangling bonds to form dimers on the 2 × 1 surface. The schematics neglect dimer buckling. Figure courtesy of S. R. Schoﬁeld.

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Fig. 5(c) was ﬁrst observed in 1959 using Low Energy Electron Diﬀraction (LEED) [24], however the surface structure responsible for this periodicity remained the subject of debate for some time. A conclusive determination of the surface structure using LEED was hampered by the diﬃculty in forming a well-ordered surface [25], and by the fact that the reconstruction actually involves the distortion of the top ﬁve atomic layers [26]. The true nature of the Si(100) reconstruction came to light with the ﬁrst STM images of the surface in 1985 [27,28]. The images revealed that the Si dimer was the basic unit of the surface, as proposed by Chadi [29], and that the dimers formed rows extending across the surface. A more complete picture of the atomic structure has been established using a combination of theoretical and experimental techniques [23 and references therein]. 4.1.1. Surface preparation In order to prepare a silicon surface, allowing for atomic resolution imaging, it is necessary to carry out the experiment in the best vacuum possible, typically 10−10 mbar or better. At such low pressures it is possible to image for several hours before a gas molecule within the vacuum impinges on the surface. Common gas molecules, such as nitrogen or hydrogen, have very low sticking coeﬃcients on silicon surfaces. However the reactive silicon surface is most vulnerable to species such as oxygen and water. As such, great lengths are gone through to outgas samples, tips and the vacuum chamber itself. Metal surfaces are generally annealed and sputtered using inert gases. However the preparation of silicon semiconductor surfaces is highly orientation dependent. Generally these consist of an acid etch, followed by thermally heating the surface in vacuum for several hours, before ‘ﬂashing’ the sample to temperatures above 1100◦ C to cause sublimation of the surface oxide layer and desorbing any residual contaminants from the surface. The sample is then cooled quickly to ∼800◦ C to avoid contamination of the surface, before being cooled slowly to avoid quenching in defects. Silicon surfaces are very sensitive to metal contamination and contact of the samples by metals must be avoided. Indeed the sample holders themselves are typically made of refractory metals — molybdenum and tungsten — to avoid nickel contamination that arises when stainless steel parts are used. 4.1.2. Surface geometry A clean Si(100)-2×1 surface is formed by thermally annealing a Si(100) substrate to 1200◦ C in UHV, and on cooling the surface reconstructs to form

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the 2 × 1 structure. The reconstruction takes place with the pairing up of dangling bonds on adjacent atoms, on the ideal surface, to form dimers. In forming dimers the surface dangling bonds re-hybridize, creating a strong σ bond between the two atoms of a dimer, and leaving a single dangling bond per atom. These remaining dangling bond orbitals have a small amount of overlap, and form a weak π bond, see Fig. 5(e). In accordance with molecular orbital theory there also exists the higher energy anti-bonding orbitals, σ* and π*. The bonding orbitals are shown schematically in Figs. 5(d) and (e). Filled and empty state STM images of the clean Si(100)-2 × 1 surface are shown in Fig. 6. Both images reveal rows of dimers running diagonally across the image. In the ﬁlled state image the features appear as beanshaped features, and in empty state they appear as pairs of protrusions: the reasons for this will be explained later. Theoretical calculations have shown that the energy of the surface can be further minimized by buckling of the dimers, where one atom protrudes higher than the other [29]. This is accompanied with a transfer of charge from the lower atom to the higher atom, leading to partially empty and ﬁlled dangling bonds respectively. Dimers next to the buckled dimer also buckle, in an alternative conﬁguration, due to dipole–dipole electrostatic interaction [29]. In STM images of the surface at room temperature, the majority of dimers appear symmetric and only a few buckled dimers are

Fig. 6. Topographic STM images showing the Si(100)-2 × 1 reconstruction in (a) ﬁlled state, (−1.6 V sample bias), and (b) empty state, (+1.2 V sample bias). The lines running diagonally across the image are rows of Si dimers, and a step edge runs up the middle. Images courtesy of S. R. Schoﬁeld.

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observed. This apparent contradiction between theory and experiment was resolved in 1992 when Wolkow imaged the surface at 120 K [30] and found that, at this temperature, 80% of the dimers appeared buckled. This led to the conclusion that the surface consists of bi-stable buckled dimers in which the atoms oscillate between up and down states. The oscillation frequency at room temperature is orders of magnitude higher than the typical sampling frequency in STM image acquisition [31], leading to the appearance of symmetric dimers. There has been much debate on the low temperature phases of the buckled dimers [32], but it is generally accepted that the dimers are buckled in the ground state.

4.1.3. Electronic structure The electronic structure of the Si(100)-2 × 1 surface has been studied using experimental techniques such as photoemission spectroscopy [33–36] and scanning tunneling spectroscopy [37–39]. The full band structure of the surface has also been theoretically calculated [29,40–42]. For a simplistic understanding of the silicon surface we should ﬁrst consider the schematic energy diagram for an individual dimer (Fig. 7(a)). The dangling bonds on the neighboring Si atoms rehybridize to form a strong σ bonding orbital, that is occupied with two electrons, and an empty anti-bonding σ* orbital. The energy splitting between the two orbitals is quite large (a few eV).

Fig. 7. Energy diagrams showing (a) the isolated dimer bonding and anti-bonding orbitals (ﬁlled circles represent occupied states), and (b) the interaction between dimers gives rise to the π and π* surface bands that are located within the bulk silicon band gap.

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The weaker π-bonding orbital, containing two electrons, and the π*-antibonding orbital have a smaller energy splitting (∼0.5 eV). If a number of dimers are considered together in a periodic arrangement, then the sharp states of the individual dimers broaden into bands (Fig. 7(b)). The σ and σ* bands become resonances within the bulk silicon valence band and conduction band respectively, and the π-bonding and π*-antibonding bands are positioned within the bulk band gap. Band structure calculations determined that if only symmetric dimers were considered then the π and π* bands should partially overlap, with the Fermi energy crossing both bands, giving rise to a metallic surface [42]. However, if the buckled dimer model was taken into account then there would be no band overlap and the surface would be semiconducting, as found experimentally, and thus further supporting the dimer buckling model. It can be concluded that the electronic structure of silicon surface close to the Fermi level is dominated by the π and π* bands, i.e. the contribution from the surface dangling bonds. The diﬀerent appearance of the Si dimer in ﬁlled and empty state STM images in Fig. 6 can now be explained. At low negative sample bias voltages (ﬁlled state), close to the Fermi energy, the largest tunneling current contribution comes from the π-bond states, whereas at positive (empty state) sample bias it comes from tunneling into the π*-antibond states. When larger bias voltages are used the σ or σ* states, along with additional backbond surface resonances, can be accessed. The diﬀerence in the dimer features comes from the diﬀerence in the average spatial charge density, taking into account dynamic dimer buckling, of the bonding and anti-bonding orbitals. For the π-bonding orbital there is a signiﬁcant amount of charge density between the dimer atoms, giving rise to a bean-shape protrusion. However, the anti-bonding orbital is located away from the center of the dimer, on the dimer atoms, and is therefore imaged as a pair of protrusions. Scanning tunneling spectroscopy (STS) can be used to obtain more detailed information about the electronic structure of the surface by probing the energy dependence of the local density of states [43]. Figure 8(a) shows a spatially averaged I/V curve of the silicon surface. In order to interpret STS measurements in terms of the surface local density of states it is usual to normalize dI/dV by dividing it by I/V (known as the normalized diﬀerential conductance) [43]. Figure 8(b) shows the resulting spectrum revealing peaks which can be attributed to the π, π* and σ* backbond surface states. The spectra can be taken with atomic resolution on the surface, and Fig. 8(c) shows a section of spectroscopic data taken perpendicular to the dimer rows. In agreement with the theory, and STM images at diﬀerent

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(a)

I [nA]

0.5

Si(001)

(c)

0.0 -0.5 -2

-1

0

1

2

σ* π*

V

(dI/dV)/(I/V) [a.u.]

(b)

π

0.4 0.3

Si(001) π

0.2

π*

σ*

V

0.1

x

0.0 -2

-1

0

1

2

V Fig. 8. STS of Si(100)-2 × 1 (a) Spatially average current–voltage (I/V ) curve (b) the calculated dI/dV /(I/V ) versus V curve shows the peaks related to the surface states. (c) Cross-sectional dI/dV /(I/V ) versus V , perpendicular to dimer rows. Figure courtesy of T. C. G. Reusch.

bias voltages, it shows that the π and π* states peak above the dimers and the σ* backbond peaks between the dimers. 4.1.4. Surface steps A cleaved silicon surface will always have steps as it is impossible to cut a crystal exactly along one of the atomic planes. A misorientation of less than 2◦ away from the [100] direction results in atomically-ﬂat terraces separated by single atomic layer steps. With higher mis-cut angles the single atomic layer steps give way to double atomic layer steps [44]. An example of a surface with single atomic steps and mismatch angle of ∼0.2◦ , is shown in Fig. 9. The 2×1 dimer rows are orientated perpendicular to each other from one terrace to the next, and a step edge is a point at which one monolayer ends exposing the terrace below. There are two diﬀerent types of step on this surface, originally classiﬁed by Chadi [45], which depend on the domain orientation. Type SA has the rows on the upper terrace parallel to the step edge, whereas type SB has the rows perpendicular to the step edge. This results in type SA steps appearing smooth whereas type SB steps appear rough. Step edges introduce strain to the silicon surface which can lead to

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Fig. 9. Filled state topographic STM images showing the two types of step on the Si(100)-2 × 1 surface: (a) type SA steps and (b) type SB steps. Schematics showing the step types are shown below. Images courtesy of S. R. Schoﬁeld.

distortion of the dimers around it (note that the dimers along the type SA step edge in the ﬁgure are buckled). 4.1.5. Surface defects Generally any deviation from a perfect surface is considered a defect and can originate from several sources, those that occur naturally on the clean surface or from contaminants. It is useful to understand the most common types of defect on the surface in order to interpret STM images of deposited adsorbates. It is also important to minimize these surface defects, especially from the perspective of nanoscale device construction on Si [17,18] where defects could alter device performance. A surface, prepared using standard annealing techniques in UHV, will typically contain a defect density of a few percent. Using high-resolution STM Hamers et al. [46] ﬁrst characterized the three most common defects of the Si(100)-2 × 1 surface. The type A defect is more commonly known as the single-dimer vacancy (DV) defect. In STM images (see Fig. 10) it appears as a dark region in both polarities and is due to the absence of a dimer [47]. The type B defect is a combination of two dimer vacancies (double dimer vacancy) and also appears as a larger

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Fig. 10. STM images of two of the most common defects on the Si(100)-2 × 1 surface in the (a) ﬁlled and (b) empty states. The two defects labeled are the single dimer vacancy (1-DV, also known as a type A defect) and the type C defect. Images courtesy of S. R. Schoﬁeld.

dark depression extending over 2 dimer rows. Both the A and B defects are symmetric about the dimer row and retain the semiconducting electronic structure [48]. The type C defect is diﬀerent from the dimer vacancies in that it is not symmetrical along the dimer row and that it appears diﬀerent at diﬀerent tip–sample polarities. In the STM image it appears as two protrusions next to a dark depression. The protrusions are brighter than the surrounding dimers in the empty state and weaker than the surrounding dimers in the ﬁlled state. The defect can also induce static buckling of adjacent dimers [49]. Atomically resolved STS results show that the defect has a metallic surface state [46]. There is still some debate over the exact conﬁguration of the C defect and there are probably several types. Recent suggestions include the absence of a Si atom in the second layer [50] or the introduction of subsurface impurities such as H, O or B [51]. Most of these defects are thermodynamic features of clean surfaces. However other defects can occur that are metastable byproducts of surface preparation. These can cover the whole surface with a more or less regular pattern, as the 2 × n and c(4 × 4) reconstructions. The Si(100) 2 × n surface arises when a high density of dimer vacancies migrate at high temperatures to line up in regularly spaced trenches perpendicular to the dimer rows. The simplest way to achieve a 2 × n reconstruction is to repeatedly anneal the surface to high temperature (∼1200◦ C) and quench it [52]. However, metal contamination has also been shown to induce dimer vacancy defects, with minute amounts of Ni and W leading to the formation of the 2 × n phase [53,54]. More complex clusters of single and multiple dimer vacancies can also form as a result of metal contamination, the most commonly observed

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of which are (1 + 2)DV split-oﬀ dimer defects consisting of a single and double dimer vacancy separated by a single surface dimer [47,55]. Another common reconstruction observed is the c(4 × 4) reconstruction, which is known to result from stress caused by incorporation of impurities or adsorbates in sub-surface locations [56]. This section has provided a very brief introduction to some of the most common surface defects in silicon. However the study of defects in silicon is a rich and intensely studied ﬁeld not least due to its importance for the functionality of devices, and a more comprehensive review can be found in [23].

4.1.6. Adsorbates There are countless examples of the interactions of various atoms and molecules with the clean Si(100) surface. In addition these adsorbate– surface interactions can diﬀer with deposition conditions, such as the rate of deposition or temperature of the sample. For example, even the simplest adsorbate, hydrogen, can etch the surface at room temperature and also form a variety of ordered structures at elevated sample temperatures [57]. A number of adsorbates can form ordered structures commensurate with the surface (e.g. Ag [58], Ga [59], Bi [60]), most transition metals react with the surface to form silicides (e.g. Ni [61], Co [62], Er [63]), halogens can etch the surface at room temperature (e.g. F2 [64], Cl2 [65], Br2 [66]), some molecules dissociate on the surface (e.g. PH3 [67], B2 H6 [68], NH3 [37]) and other molecules can bond to the silicon in diﬀerent adsorption conﬁgurations but remain intact (e.g. Benzene [69], Cu-phthalocyanine [70], C60 [71]). A detailed review of a number of adsorbate-Si(100) interactions can be found in [23,72] and a more speciﬁc review relating to organic adsorbates can be found in [22]. As an example of an adsorbate-silicon system we shall here consider the adsorption of a molecule that our group has extensive experience with: phosphine. Phosphine provides an example of an important adsorbate to study since P is used for doping in the semiconductor industry. Its interaction with the Si(100) surface has been investigated for a couple of decades [73–76] but only recently has a comprehensive understanding been achieved [67,77]. The adsorption of phosphine on the surface at room temperature is quite complex and, due to the reactive nature of the Si surface, the molecule can dissociate into a number of products which are chemisorbed to the surface. Annealing the surface to 350◦ C leads to

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complete dissociation of the molecules and the incorporation of P atoms into the silicon surface. The STM image in Fig. 11 shows the Si(100)-2 × 1 surface following a low dose of PH3 . After dosing a number of new features appear on the surface compared to the clean surface. These species are identiﬁed as follows: PH2 + H, where the PH2 molecule adsorbs to one Si atom of a dimer and the dissociated hydrogen bonds to the other; PH + 2H, where the PH molecule is bound to a ‘bridge’ site between the two atoms of a Si dimer and the H atoms are each bound to the atoms of a neighboring Si dimer to form a monohydride dimer; P + 3H, where a P atom and three H atoms are bound to Si atoms of three neighboring dimers; and a hemihydride dimer, where a single H atom is bound to one atom of a Si dimer. Each of these surface species are products of diﬀerent degrees of PH3 dissociation, forming either PH2 , PH or P. A comprehensive understanding of the PH3 -Si(001) adsorption system was achieved by performing detailed STM measurements of each of the features at diﬀerent temperatures, coverages and STM imaging conditions, and by comparison of this STM data with an exhaustive library of possible structures predicted by density functional theory calculations and simulated STM images [67,77].

PH2 + H Split-off dimer defect

Surface defect P+3H B defect

Hemihydride C-defect PH+2

Fig. 11. Filled state topographic STM image showing various products due to the interaction of PH3 with the Si(100)-2 × 1 surface. Features relating to the adsorption of PH3 are the asymmetric feature (PH2 + H), the centered feature (PH + 2H) and the u-shaped feature (P + 3H). Image courtesy of N. J. Curson.

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4.2. The hydrogen terminated Si(100) surface The inert hydrogen terminated Si(100) surface is a useful substrate, not only to study the interaction of adsorbates, but also for use in the fabrication of atomic scale devices using STM lithography. The surface can be formed by exposing the clean silicon surface, at an elevated temperature, to atomic hydrogen with the resulting reconstruction depending on the temperature [57]. The most commonly used surface is the monohydride Si(100)-2 × 1:H surface which is formed at a substrate temperature of ∼600 K. The σ bonds of the dimers remain intact and the π bonds are broken so that each dangling bond can form a σ bond with a single hydrogen atom. At monolayer exposure the surface is very inert. The STM image (Fig. 12) shows the positions of the individual dimers. The bright features on the surface are Si dangling bonds which exist due to incomplete hydrogen adsorption: however, they can also be created at pre-deﬁned locations by the STM tip [78]. The STM image also shows the presence of di-hydride units. The dihydride is formed by the breaking of the Si dimer σ-bond, leaving 2 dangling bonds per atom, which are then saturated by hydrogen. There are a number of studies of various adsorbates on the patterned hydrogen terminated surface. The reactive sites on the surface are the exposed dangling bonds not terminated with hydrogen, and for the majority of deposited species these act as initial adsorption sites. A wide range of organic species in particular can be deposited onto the hydrogen terminated surface ranging from small molecules, such as styrene [79], to large organic molecules, such as nanotubes [80]. Some examples of molecular adsorbates on the patterned hydrogen terminated silicon surface are shown in Fig. 13. Perhaps the most notable for

Fig. 12. Filled state topographic STM images of the H terminated Si(100) surface. Images courtesy of S. R. Schoﬁeld.

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(a)

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(b)

(c)

Fig. 13. STM images of organic molecules on the Si(100)-2 × 1:H surface: (a) 35 nm2 image showing self-ordering of styrene molecules [79], (b) 35 nm2 image of ordered islands of C60 molecules [82], and (c) 25 nm2 3D rendered image of a carbon nanotube [80].

its self-organizational properties is the study by Lopinski et al. [79] which observed the adsorption of styrene molecules on the surface using STM. They found that at low dose the styrene initially adsorbs at single dangling bond sites, and on further exposure the molecules assemble into lines along the dimer row direction. The proposed mechanism is a chain reaction: the ﬁrst adsorbed molecule reacts with the dangling bond to form a C-Si covalent bond, which in turn creates a radical on the molecule. This radical then extracts an H atom on an adjacent dimer on the surface, exposing a dangling bond. The new dangling bond then acts as an adsorption site for the next diﬀusing molecule. And so the reaction continues with wires of up to 100 molecules being formed by this process, all covalently bonded to the surface. An example of a larger molecular adsorbate on the surface is C60 , which has a diameter of ∼1 nm. Initially the molecules also adsorb at the surface dangling bonds [81], and on further deposition they form hexagonally ordered 2D and then 3D islands [82]. In this case the molecules are weakly bound to the surface, van der Waal’s in character, and the interaction strength is estimated to be the same or even weaker than the intermolecular interaction [83]. An example of an even larger molecule is a carbon nanotube. These can be been deposited onto the surface using a dry deposition technique [80]. Individual molecules were imaged using STM and electrically characterized by STS. As for C60 they are assumed to be physisorbed to the surface. A summary of a selection of adsorbate-Si(100):H surface interactions is given in Table 1. 4.3. Si(111)-7 × 7 The most stable and famous conﬁguration of the (111) surface is the 7 × 7 reconstruction. STM images of this surface were ﬁrst achieved

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Table 1. Interactions of various adsorbates with a hydrogen terminated Si(100)-2 × 1 surface. References are primarily related to atomic scale STM investigations. Adsorbate [reference]

Nature of adsorbate interaction and potential applications

Ag [84], Al [85], Co [86], Ga [87]

Deposited atoms diﬀuse on the surface and adsorb at exposed dangling bonds. With continued deposition, clusters form around these adsorbed atoms. Potential application in the fabrication of metallic nanoscale devices.

TiCl4 [88], Fe(CO)5 [89], Au precursor [90]

Metal CVD precursors react with dangling bonds at elevated sample temperature to form regions of metal adsorbates. Potential application in the fabrication of metallic nanoscale devices.

Si [91]

Adsorption at dimer bridge site forming SiH2 clusters. Hydrogen on surface changes the growth mode in comparison to the clean surface.

O2 [78], NH3 [92]

Adsorbs at dangling bonds. Shows that passivated surface remains unaﬀected by dosing. Potential use as thin oxide or nitride layers for nanoscale devices.

PH3 [93]

Molecules adsorb at dangling bonds and adsorption is self-limiting. Subsequent annealing can incorporate and electrically activate P dopant atoms into the surface. Applications in doped atomic scale devices [18] and quantum computation [20].

Atmosphere, water and liquid solvents [94]

Paper outlines the conditions required for putting down organic molecules, which are in solution, onto the inert Si(100)-2 × 1:H surface with minimal contamination.

Organic Molecules: Styrene [79], Vinylferrocene [95]

Initial adsorption at dangling bond and chain reaction assembly of molecular wires along dimer row direction that are predicted to permit charge transport [96].

Copper phthalocyanine [97], Cobalt phthalocyanine [98]

Adsorption at dangling bonds. Molecules expected to act as 2D wires with a central conductor atom and molecular insulator.

Biphenyl [99]

Adsorbs at dangling bonds. Molecule expected to be a good molecular conductor.

Norbonadiene [100], Azanorbornadiene [101]

Molecules adsorb at dangling bonds. The Norbonadiene molecule acts as an anchor — having a hydrogen atom that can be substituted with a functional group; azonorbornadiene is an example of this.

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Table 1. Adsorbate [reference]

(Continued) Nature of adsorbate interaction and potential applications

TEMPO molecule [102]

Adsorbs at single dangling bonds. Used as a barrier molecule for restricting the growth of styrene chains.

C60 , C59 N [82]

Initial adsorption at dangling bonds, then at higher coverage molecule-molecule interactions dominate with island growth. An insight to the molecule-molecule interaction can be gained.

Poly (3-hexylthiophene) [103]

Pulse valve injection of macromolecules in solution. Another way of depositing molecules onto the surface that cannot be evaporated.

Nanotubes [80]

Molecules have a van der Waals interaction with the surface. The dry deposition technique of isolated nanotubes with minimal surface contamination could be applied to other delicate nonvolatile molecules.

simultaneously with the invention of the technique in 1983 [6] and were found to be in excellent agreement with the commonly accepted dimer adatom stacking fault (DAS) model [8]. It is formed in a similar way to the (100) surface, and on cooling there is a phase transition at 860◦ C from a (1 × 1) structure to the energetically more stable (7 × 7) structure. The stability of the surface comes with the reduction of surface dangling bonds. Figure 14 shows the DAS model for the (7 × 7) reconstruction proposed by Takayanagi et al. [8]. The model consists of 49 surface atoms. The 12 top layer atoms, adatoms, each tie up three dangling bonds from the lower layer. This leads to a single dangling bond on each adatom. The adatoms are locally arranged two lattice parameters apart with a 7×7 periodicity. In the second layer there are 48 atoms. Six of these atoms are triply co-ordinated: these are known as restatoms and each contains a single dangling bond. The remainder of the second layer atoms are involved in Si dimer formation, which surround the triangular adatom sub units. The lowest level is the Si bilayer, which is the same as the (1 × 1) bulk termination. At the corners of the unit cell there are vacancies called corner holes. The corner holes each contain a dangling bond from the bilayer level. The total number of dangling bonds at the surface is 19, compared with 49 on the unreconstructed (1 × 1) surface. The left triangular sub unit contains a stacking fault. This can be understood by examining the side view of the reconstruction in Fig. 14. The

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Fig. 14. The Si(111)-7 × 7 surface. The schematic shows the DAS model. Atoms within the (111) layers have circle sizes depending on the layer they are in. The STM images show the surface in (a) the empty state and (b) the ﬁlled state. Images courtesy of M. J. Humphrey.

silicon layers in the right-hand triangle are stacked regularly so that the next atom directly below is in the fourth layer. For the left-hand triangle the rest atoms are directly above the atoms in the second layer below: this is the faulted half. STM images of the Si(111)-7 × 7 surface show 12 protrusions and one depression per unit cell. These protrusions are attributed to the dangling bonds on the adatoms and the depression is due to the corner hole. As the dangling bonds on the adatoms are partially ﬁlled they contribute to both the ﬁlled and empty states images. In the ﬁlled state image it is possible to determine the stacking fault, as one half on the cell appears higher. In the case of this surface the STM images reveal the direct positions of the atoms on the surface. Scanning tunneling spectroscopy [7] measurements show that the Si(111)-7 × 7 surface has states near the Fermi level and is therefore metallic. The spectra reveal that these states are related to the adatoms of the reconstruction. Although the Si(111) surface is not so important from a microelectronic device perspective, it has still been studied in great detail and is the basis for numerous adsorption studies. This is because the 7 × 7 surface is easy to

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prepare, is thermodynamically stable, and is easy to image in STM experiments. Due to the arrangement of atoms at the surface there are a number of chemically diﬀerent sites which gives rise to interesting adsorbate interactions [23,72].

5. The Role of STM in Silicon Device Fabrication Silicon has played a major role in the semiconductor industry, due to the success of metal-oxide semiconductor (MOS) technology. Each year cheaper and faster microprocessors are fabricated, achieved by the continued miniaturization of the individual components on a silicon chip. Current state-of-the-art optical lithography used in commercial semiconductor manufacturing produces feature sizes down to ∼90 nm. However if device miniaturization continues at the same rate then by 2017 commercial device sizes will reach the sub nanometer scale. Scanning probe microscopes allow the manipulation of matter at the atomic level and could therefore be adapted to allow patterning of individual components on a silicon chip down to the atomic-scale. The use of STMs to control the positioning of atoms has been particularly successful in the manipulation of absorbates on metal surfaces [104]. However the manipulation of atoms on a semiconductor surface is much more diﬃcult due to the strong covalent bonds involved. The recent work of Lyding et al. provides a method to achieve atomic resolution lithography in silicon by using the scanning tunneling microscope to pattern a hydrogen resist layer on the silicon surface — analogous to conventional optical lithography [78]. Once the surface of silicon is passivated with atomic hydrogen, the tip of a STM can be used to remove hydrogen atoms from the resist with atomic precision [105], thereby exposing the reactive underlying silicon surface. Dopant atoms or conducting molecules can then be patterned into the surface simply by ﬂooding the vacuum with the appropriate gas species. As such there has been a growing interest to incorporate STM-based lithography into proposals for atomic-scale semiconductor device fabrication [17,21,22,106]. One such approach is the use of phosphine as a precursor dopant source in silicon in combination with STM lithography and low temperature silicon molecular beam epitaxy [17,21]. Here single P atoms have been incorporated into the silicon surface with atomic precision [93], and encapsulated in epitaxial silicon with minimal segregation/diﬀusion [107,108]. Whilst the ability to fabricate nanometer and atomic-scale electronic device structures in silicon by STM has long been promised, the realization of robust devices has been a diﬃcult goal

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to attain because of the engineering problem of making electrical contact to the STM-patterned buried dopant layer. The problem is that once the sample is removed from the ultra-high vacuum where STM lithography has taken place, the actual location of the structure is lost. This is particularly the case when the nanostructured regions are buried under several layers of epitaxially grown silicon. Several diﬀerent strategies have been employed to overcome this limitation to make electrical contact to the STM patterned device, including the use of etched registration markers [18], ion implanted markers [109] and predeposited metal contacts [110– 112]. However of these only a few have allowed electrical measurement of STM-patterned devices [18,109,112,113]. One reason for this is that any pre-patterning of the surface typically requires the use of an optical resist which must be completely removed before ultra-high vacuum surface preparation to ensure atomic resolution and avoid contamination of the surface. A complete fabrication process for a nanoscale, buried phosphorus doped wire, using etched registration markers is shown in Fig. 15 [18]. Using this technique 90 nm wide phosphorus doped wires were fabricated with four terminal resistances of ∼10 KΩ resistance at 4 K, demonstrating the success of the registration based contact technology. Since this time wires down to ∼25 nm width have been fabricated that still exhibit ohmic behavior with four terminal resistances of ∼50 kΩ at 4.2 K [114]. Such etched markers will also allow nano-scale surface electrodes to be aligned to the active region of buried devices. The ability to correlate atomic to nanometer scale structural characterization of the surface with electrical transport measurements will provide valuable information on the detailed relationship between atomic-scale properties and device behavior. At present the use of the highest resolution scanning probes for electronic device fabrication is a serial process and, whilst nowhere near commercial production, is a very active ﬁeld with signiﬁcant progress being made in the sub 10 nm regime. In addition the potential merger of molecular electronics with silicon based technology oﬀers the creation of exciting new hybrid devices with enhanced functionality [22,81].

6. Conclusions An overview of the basic operation of a STM and of STM of silicon surfaces has been presented. In particular, as scanning probe technology continues to improve it has been shown that it is possible to not only image surfaces with atomic-resolution, but to controllably place and manipulate atoms

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Fig. 15. An outline of a fabrication strategy for the creation of nano-scale devices in silicon using scanning probe microscopy. Left: (a)–(e) Cross-sectional schematics of the essential fabrication steps, and (f) 3D sketch of ﬁnal device. Right: Corresponding (a) SEM image of registration markers with STM tip (white), (b) STM image of a lithographically-patterned wire in Si(100):H, (c) STM image of P-incorporated wires, and (d) the same surface after hydrogen resist removal and (e) after 25 nm MBE Si overgrowth and (f) an optical microscope image of the ﬁnal device with contact wires (f). Images courtesy of F. J. Ruess.

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on the surface. The chapter concludes with a discussion of how scanning probe technology can be adapted to create electronic devices in silicon using STM-based lithography. As the characteristic dimensions of semiconductor devices continue to decrease, the need for detailed atomic and nanoscale characterization of semiconductor surfaces using scanning probe techniques will continue to grow. Despite a relatively short history, the study of semiconductor surfaces using scanning probes promises to be a fertile ground for innovation and exploration in the coming years. Acknowledgments The authors would like to thank T. C. G. Reusch and F. Ratto for a critical reading of the manuscript. The authors acknowledge support from the Australian Research Council, the Semiconductor Research Corporation and the US Advanced Research and Development Activity, National Security Agency and Army Research Oﬃce under contract DAAD19-01-1-0653. MYS acknowledges an Australian Research Council Federation Fellowship. References [1] R. S. Becker and R. W. Wolkow, Semiconductor surfaces, in Scanning Tunneling Microscopy, eds. J. A. Stroscio and W. J. Kaiser (Academic Press, 1993) p. 149. [2] R. J. Hamers, STM on semiconductors, in Scanning Tunneling Microscopy I, eds. H.-J. G¨ untherodt and R. Wiesendanger (Springer-Verlag, 1994) p. 83. [3] H. Neddmeyer, Scanning tunneling microcopy of semiconductor surfaces, Rep. Prog. Physics 59, 701 (1996). [4] J. A. Kubby and J. J. Boland, Scanning tunneling microscopy of semiconductor surfaces, Surface Science Reports 26, 61 (1996). [5] G. A. D. Briggs and A. J. Fischer, STM experiment and atomistic modeling hand in hand: Individual molecules on semiconductor surfaces, Surface Science Reports B 33, 1 (1999). [6] G. Binnig, H. Rohrer, Ch. Gerber and E. Weibel, 7 × 7 Reconstruction on Si(111) resolved in real space, Phys. Rev. Lett. 50, 120 (1983). [7] R. S. Becker, J. A. Golovchenko, D. R. Hamann and B. S. Swartzentruber, Real space observation of surface states on Si(111)-7 × 7 with the tunneling microscope, Phys. Rev. Lett. 55, 2032 (1985). [8] K. Takayanagi, Y. Tanishiro, M. Takahashi and S. Takahashi, Structural analysis of Si(111)-7 × 7 by UHV transmission electron diﬀraction and microscopy, J. Vac. Sci. Technol. A 3, 1502 (1985). [9] G. Binnig, H. Rohrer, Ch. Gerber and E. Weibel, Surface studies by scanning tunneling microscopy, Phys. Rev. Lett. 49, 57 (1982).

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[81] M. C. Hersam, N. P. Guisinger and J. W. Lyding, Silicon-based molecular nanotechnology, Nanotechnology 11, 70 (2000). [82] M. J. Butcher, F. H. Jones, P. H. Beton, P. Moriarty, B. N. Cotier, M. D. Upward, K. Prassides, K. Kordatos, N. Tagmtarchis, F. Wudl, V. Dhanak, T. K. Johal, C. Crotti, C. Comicioli and C. Ottaviani, C59 N monomers: Stabilization through immobilization, Phys. Rev. Lett. 83, 3478 (1999). [83] D. Sanvitto, M. De Seta and F. Evangelisti, Growth of thin C-60 ﬁlms on hydrogenated Si(100) surfaces, Surf. Sci. 452, 191 (2000). [84] M. J. Butcher, F. H. Jones and P. H. Beton, Growth and modiﬁcation of Ag islands on hydrogen terminated Si(100) surfaces, J. Vac. Sci. Technol. B 18, 13 (2000). [85] T.-C. Shen, C. Wang and J. R. Tucker, Al nucleation on monohydride and bare Si(001) surfaces: Atomic scale patterning, Phys. Rev. Lett. 78, 1271 (1997). [86] G. Palasantzas, B. Ilge, L. J. Geelings and J. M. M. de Nijs, Diﬀusion, nucleation, and annealing of Co on the H-passivated Si(100) surface studied by UHV-STM, Surf. Sci. 509, 412 (1998). [87] T. Hashizume, S. Heike, M. I. Lutwyche, S. Watanabe and Y. Wada, Atom structures on the Si(100) surface, Surf. Sci. 386, 161 (1997). [88] T. Mitsui, R. Curtis and E. Ganz, Selective nanoscale growth of titanium on the Si(100) surface using an atomic hydrogen resist, J. Appl. Phys. 86, 1676 (1999). [89] D. P. Adams, T. M. Mayer and B. S. Swartzentruber, Nanometer-scale lithography on Si(001) using adsorbed H as an atomic layer resist, J. Vac. Sci. Technol. B 14, 1642 (1996). [90] J. W. Lyding, K. Hess, G. C. Abeln, D. S. Thompson, J. S. Moore, M. C. Hersam, E. T. Foley, J. Lee, Z. Chen, S. T. Hwang, H. Choi, Ph. Avouris and I. C. Kizilyalli, Ultrahigh vacuum-scanning tunneling microscopy nanofabrication and hydrogen/deuterium desorption from silicon surfaces: Implications for complementary metal oxide semiconductor technology, Appl. Surf. Sci. 130–132, 221 (1998). [91] T. Hashizume, H. Kajiyama, Y. Suwa, S. Heike, S. Matsuura, J. Nara and T. Ohno, Adsorption of Si atom on H-terminated Si(001)-2 × 1 surface, Appl. Surf. Sci. 216, 15 (2003). [92] J. W. Lyding, T.-C. Shen, G. C. Abeln, C. Wang and J. R. Tucker, Nanoscale patterning and selective chemistry of silicon surfaces by ultrahigh-vacuum scanning tunneling microscopy, Nanotechnology 7, 128 (1996). [93] S. R. Schoﬁeld, N. J. Curson, M. Y. Simmons, F. J. Ruess, T. Hallam, L. Oberbeck and R. G. Clark, Atomically precise placement of single dopants in Si, Phys. Rev. Lett. 91, 136104 (2003). [94] A. S. Baluch, N. P. Guisinger, R. Basu, E. T. Foley and M. C. Hersam, Atomic-level robustness of the Si(100)-2×1:H surface following liquid phase chemical treatments in atmospheric pressure environments, J. Vac. Sci. Technol. 22, L1 (2004).

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[95] P. Kruse, E. R. Johnson, G. A. DiLabio and R. A. Wolkow, Patterning of vinylferrocene on H-Si(100) via self-directed growth of molecular lines and STM-induced decomposition, Nano Letters 2, 807 (2002). [96] J.-H. Cho, D.-H. Oh and L. Kleinman, One-dimensional molecular wire on hydrogenated Si(001), Phys. Rev. B 65, 081310 (2002). [97] M. C. Hersam, N. P. Guisinger and J. W. Lyding, Isolating, imaging and electrically characterizing individual organic molecules on the Si(100) surface with the scanning tunneling microscope, J. Vac. Sci. Technol. A 18, 1349 (2000). [98] L. Liu, J. Yu, N. O. L. Viernes, J. S. Moore and J. W. Lyding, Adsorption of cobalt phthalocyanine on Si(100)2×1 and Si(100)2×1:H surfaces studied by scanning tunneling microscopy, Surf. Sci. 516, 118 (2002). [99] A. J. Mayne, L. Soukiassian, N. Commaux, G. Comtet and G. Dujardin, Molecular molds, Appl. Phys. Lett. 85, 5379 (2004). [100] G. C. Abeln, S. Y. Lee, J. W. Lyding, D. S. Thompson and J. S. Moore, Nanopatterning organic monolayers on Si(100) by selective chemisorption of nobornadiene, Appl. Phys. Lett. 70, 2747 (1997). [101] B. Wang, X. Zheng, J. Michl, E. T. Foley, M. C. Hersam, A. Bilic, M. J. Crossley, J. R. Reimers and N. S. Hush, An azanorbornadiene anchor for molecular-level construction on silicon (100), Nanotechnology 15, 324 (2004). [102] R. Basu, N. P. Guisinger, M. E. Greene and M. C. Hersam, Room temperature nanofabrication of atomically registered heteromolecular organosilicon nanostructures using multistep feedback controlled lithography, Appl. Phys. Lett. 85, 2619 (2004). [103] Y. Terada, B.-K. Choi, S. Heike and M. Fujimori, Injection of molecules onto hydrogen terminated Si(100) surfaces via a pulse valve, J. Appl. Phys. 93, 10014 (2003). [104] D. M. Eigler and E. K. Schweizer, Positioning single atoms with a scanning tunnelling microscope, Nature 344, 524 (1990). [105] M. C. Hersam, J. Lee, N. P. Guisinger and J. W. Lyding, Implications of atomic-level manipulation on the Si(100) surface: From enhanced CMOS reliability to molecular electronics, Superlattices and Microstructures 27, 583 (2000). [106] Y. Wada, Atom electronics: A proposal of atom/molecule switching devices, Surf. Sci. 386, 265 (1997). [107] T.-C. Shen, T.-Y. Ji, M. A. Zudov, R. R. Du, J. S. Kline and J. R. Tucker, Ultra dense phosphorus delta layers grown in silicon from PH3 molecular precursors, Appl. Phys. Lett. 80, 1580 (2002). [108] L. Oberbeck, N. J. Curson, M. Y. Simmons, R. Brenner, A. R. Hamilton, S. R. Schoﬁeld and R. G. Clark, Encapsulation of phosphorus dopants in silicon for the fabrication of a quantum computer, Appl. Phys. Lett. 81, 3197 (2002). [109] T.-C. Shen, J. S. Kline, T. Shenkel, S. J. Robinson, J. Y. Ji, C. Yang, R. R. Du and J. R. Tucker, Nanoscale electronics based on two-dimensional dopant patterns in silicon, J. Vac. Sci. Technol. B22, 3182 (2004).

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[110] A. W. Dunn, B. N. Cotier, A. Nogaret, P. Moriarty, P. H. Beton and S. P. Beaumont, Molecular scale alignment strategies: An investigation of Ag adsorption on patterned fullerene layers, Appl. Phys. Lett. 71, 2937 (1997). [111] M. R. Zuiddam, S. Rogge, L. J. Geerlings, E. van der Drift, B. Illge and G. Palasantzas, Contact and alignment marker technology for atomic scale device fabrication, Microelectron. Eng. 41, 567 (1998). [112] M. Fujimori, S. Heike, Y. Terada and T. Hashizume, Fabrication of fourprobe ﬁne electrodes on an atomically smooth Si(100)-2 × 1:H surface, Nanotechnology 15, S333 (2004). [113] M. Y. Simmons, F. J. Ruess, K. E. J. Goh, T. Hallam, S. R. Schoﬁeld, L. Oberbeck, N. J. Curson, A. R. Hamilton, M. J. Butcher, R. G. Clark and T. C. G. Reusch, Scanning probe microscopy for silicon device fabrication, Molecular Simulation 31, 505 (2005). [114] F. J. Ruess, L. Oberbeck, K. E. J. Goh, M. J. Butcher, E. Gauja, A. R. Hamilton and M. Y. Simmons, The use of etched registration markers to make four-terminal electrical contacts to STM-patterned nanostructures, Nanotechnology 16, 2446 (2005).

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PART II EXPERIMENTAL METHODS

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SCANNING TUNNELING MICROSCOPY AND SCANNING FORCE MICROSCOPY STEFAN HEMBACHER∗ and FRANZ GIESSIBL Lehrstuhl f¨ ur Experimentalphysik VI, University of Augsburg Center for Electronic Correlations and Magnetism 86135 Augsburg, Germany ∗ [email protected] Abstract. Scanning tunneling microscopy (STM) and atomic force microscopy (AFM) are vital tools for the study of single organic moelcules on surfaces. In particular, a combination of these tools allows to compare images derived by forces to those derived by measuring tunneling currents. Operation at low temperatures enables to measure even the weak forces acting between organic molecules at an excellent signal-to-noise ratio, because the thermal drift that plagues highprecision measurements at room temperatures is essentially absent at liquid helium temperatures (4 K). However, the implementation of combined STM/AFM instruments is challenging. In this article, we describe the essential component parts, the functionality and the limitations of traditional microscopes and compare them to a new design that incorporates the qPlus sensor, a stiﬀ cantilever based on a quartz tuning fork that greatly facilitates combined STM/AFM. First, results of simultaneous STM and AFM measurements on graphite, a material that can be viewed as a prototype of an organic molecule, are presented. The complementary nature of STM and AFM data and the value of access to both data sources is outlined. Keywords: Atomic Force Microscopy (AFM); Scanning Tunneling Microscopy (STM).

Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . 2 The Principle of a Scanning Probe Microscope 3 Operating Modes of AFM’s . . . . . . . . . . . 4 Imaging Organic Molecules . . . . . . . . . . . 5 Conclusions and Perspectives . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . 69

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1. Introduction The properties of single organic molecules on solid surfaces are a result of the interactions between molecule and substrate on an atomic scale. Therefore, “seeing” the molecules in real space provides a direct access to the physics of single molecules. While we have, at least up to now, not studied single molecules on surfaces, we illustrate the techniques of scanning tunneling microscopy (STM) and atomic force microscopy (AFM) with the example of a simultaneous imaging of graphite, a ‘huge molecule’ in STM and AFM modes. Imaging individual atoms was an elusive goal until the introduction of the scanning tunneling microscope (STM) in 1981 by Binnig, Rohrer, Gerber and Weibel [1]. This humble instrument has provided a breakthrough in our ability to investigate matter on the atomic scale. For the ﬁrst time, the individual surface atoms of ﬂat samples could be made visible in real space. G. Binnig and H. Rohrer were rewarded with the Nobel Prize in Physics in 1986. Within one year of its invention, the STM helped to solve one of the most intriguing problems in surface science: the structure of the Si(111)-(7×7) surface [2]. With the spectacular spatial resolution of the STM, a large number of metals and semiconductors have been investigated on the atomic scale and marvelous images of the world of atoms were created. Today the STM is an invaluable asset in the surface scientist’s toolbox. But only electrical conductive samples can be investigated with an STM, because it uses the tunneling current which ﬂows between a biased tip and a sample. As a consequence, most of the investigated surfaces have to be clean on an atomic scale, ruling out operation in ambient conditions. Except when looking at extremely inert surfaces like graphite, WSe2 and TaSe2 , sample preparation and imaging have to be done in an ultrahigh vacuum (UHV). In 1986, the atomic force microscope (AFM) was introduced by Binnig, Quate and Gerber [3]. With an AFM any suﬃciently ﬂat surface can be imaged with high spatial resolution, independent of electric conductivity and cleanliness. The original paper on the AFM [4] has been cited more than 4400 times (October 2005) and ranks among the 10 most cited articles of Physical Review Letters. Thousands of AFMs are in use in university, public and industrial research laboratories all over the world. Most of these instruments are operated under ambient conditions, and AFM studies in vacuum allowing true atomic resolution on a routine basis have only recently become possible. To study surfaces on the atomic level, a UHV environment is required, where it is more diﬃcult to operate an AFM than an STM. Moreover, it is also possible to measure the tunneling current and the force

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simultaneously on conducting samples and to obtain two diﬀerent types of atomic information at the same time. The concept of the STM has initiated, besides the AFM, a huge family of scanning probe microscopes (SPM), including lateral force microscopes and scanning near ﬁeld optical microscopes. All these instruments are built up in a very similar way and diﬀer only in the detected interaction between the probe and the sample. We start our discussion with a summary of the common essential parts of all SPMs. 2. The Principle of a Scanning Probe Microscope A schematic view of a SPM is given in Fig. 1. The major task of a SPM is to scan the surface by a probe line by line in three dimensions. This is regularly done by a ﬁne positioning system made out of piezoelectric ceramics. The scanning is usually performed by using a computer-controlled saw tooth voltage in the fast and the slow scanning direction. A relative movement of the probe and the sample with a precision of several pm can be achieved. During the operation of the instrument, the distance between the centers of probe and sample atoms is of the order of 3 to 8 ˚ A (1 ˚ A = 10−10 m). At the beginning of the measurement the probe sample distance is in the order of mm and must be reduced stepwise by using a coarse positioning device, until the ﬁne positioning system controls the scanning.

Fig. 1. The principle of a scanning probe microscope. The sample surface is scanned line by line with a probe by using a ﬁne positioning system (scanner). With a coarse positioning device, the distance between the sample and the probe is stepwise reduced until the interaction regime is reached and the ﬁne positioning system rules the scanning of the surface. The vibration isolation shields the micrscope from external vibrations.

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Because the gap between tip and sample in SPMs has to be kept steady within fractions of an atomic diameter, a damping device is often used to isolate the instrument from external vibrations. The SPMs are distinguished by the measured interaction or the used probe. In this article we will discuss the two prime representatives of the SPM family, the STM and the AFM. The Scanning Tunneling Microscope. An STM uses a sharp metallic tip as a probe for the measurement. The tunneling tip is typically a wire that has been sharpened by chemical etching or mechanical grinding. W, Pt/Ir, or pure Ir are often used as the tip material. A schematic view of an STM is shown in Fig. 2. The sample and the tip are connected by an external voltage source VT . If the distance between the tip and sample is in the order of a few angstroms, a tunneling current IT ﬂows between the tip and the sample. This current is used as the feedback signal in a z-feedback loop. Two diﬀerent operation modes are commonly used. In the topographic mode, images are created by scanning the tip in the xy plane and recording the z position required to keep IT constant. A three dimensional map z(x, y, IT = const.) is recorded. In the constant height mode, the probe scans the surface while the signal at the z-scanner is kept constant, and a three-dimensional image IT (x, y, z = const.) is created. In a rather simplistic model the tunneling current IT is given by √ (1) IT = I0 exp(−2κz) κ = 2mΦ/,

Fig. 2. Principle of a scanning tunneling microscope. Once the gap between tip and sample is about as small as the diameter of an atom, a tunneling current ﬂows between the conductive tip and the sample.

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where Φ is the work function, m is the electron’s mass, is Planck’s constant and z is the distance between tip and sample. I0 is a function of the applied voltage and of the density of states in both tip and sample. A typical value for the work function Φ is 4 eV, yielding a decay length κ of about 1 ˚ A−1 . Therefore, if the distance z is increased by one angstrom, then the current drops by an order of magnitude. As a consequence, the tunneling current is focused only on the nearest atoms of the tip and the sample. The tunneling current is measured with a current-to-voltage converter and is used to measure the distance between the tip and the sample. The current noise sources in the current-to-voltage converter have to be small enough such that the corresponding vertical noise δzIT is considerably smaller than the atomic corrugation of the sample. A simple form of such a circuit is shown in Fig. 3. It uses a low noise operational ampliﬁer and a feedback resistor (Rfb ) with a typical impedance of R = 100 MΩ. To get a maximum signal-to-noise ratio the bandwidth should be maximized while the noise should be as small as possible. The bandwidth of the complete circuit is limited by the bandwidth of the operational ampliﬁer and the parasitic capacitance of Rfb , while the main noise source is given by the Johnson noise density nRfb of the resistor Rfb : nRfb =

4kB T Rfb ,

(2)

where kB is the Boltzmann constant and T is the temperature of the resistor. At room temperature (T = 300 √ K) and with a feedback resistor Rfb = 100 MΩ, the voltage noise is nRfb · B = 40 µV (typical acquisition bandwidth for STM: B = 1 kHz), which corresponds to a current noise of

Fig. 3.

Current to voltage ampliﬁer. The output voltage is given by −IT Rfb .

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δIT = 0.4 pA. The current noise is connected to the vertical noise 4kB T B/R δIT , δzIT = ∂IT = 2κ|IT | ∂z

(3)

which amounts to 0.2 pm in the present example. Therefore, the thermal noise of the preampliﬁer circuit in STM measurements is not critical. The spectacular spatial resolution and relative ease of obtaining atomic resolution by scanning tunneling microscopy rests on three properties of the tunneling current: • Since the tunneling current is strongly distance dependent, it is possible to reach atomic resolution even with blunt tips; • The tunneling current can be measured easily and with a suﬃcient signal to noise ratio; • The monotonic dependence of the tunneling current as a function of the distance facilitates the establishment of a feedback loop that controls the distance between the tip and the sample. None of these properties hold for the tip sample forces, the imaging signal of the AFM, and therefore substantial hurdles had to be overcome before atomic resolution by AFM became possible. The Atomic Force Microscope. The principle setup of an AFM is comparable to that of an STM, except that the tunneling tip is replaced by a force sensor (cantilever). A schematic view of an AFM is shown in Fig. 4. A sharp, not necessarily conductive tip, is mounted on the end of a spring.

Fig. 4. Principle of a atomic force microscope. A sharp tip is brought close to the sample. The forces acting between tip and sample lead to a deﬂection of the spring.

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The measured deﬂection of the spring is proportional to the force between the tip and the sample. With an AFM even insulating surfaces can be investigated with atomic resolution. The potential tip-sample energy Vts involves a z component of the tip-sample force Fts = −∂Vts /∂z and a tip-sample spring constant kts = −∂Fts /∂z. Depending on the mode of operation, the AFM uses Fts or some entity derived from Fts as imaging signal. Unlike the tunneling current, Fts has long- and short-range contributions, which are characterized by range and strength. In vacuum, there are short-range (fractions of nm) chemical forces and van der Waals, electrostatic and magnetic forces with a long range (up to 100 nm). In ambient conditions, meniscus forces formed by adhesion layers on the tip and sample (water or hydrocarbons) can also be present. To achieve high resolution with an atomic force microscope it is necessary to focus only on the short range forces. In Fig. 5 the distance dependence of the tunneling current and a short range force (modeled by a gradient of a Morse potential) is compared. The distance dependence of chemical bonding forces can be modeled by a Morse interaction deﬁned by

(4) Fts (z) = 2κEB e−2κ(z−σ) − e−κ(z−σ) , EB = 3.5 eV ˚ σ = 2.3 A −1

κ = 1.5 ˚ A

: binding energy : equilibrium distance : decay length.

The tunneling current is a monotonic function of distance. A distance feedback with a setpoint of e.g. 3 nA would withdraw the tip for an actual current of 4 nA and approach for an actual current of 2 nA.

Fig. 5. Comparison of the distance dependence of a short range force with the tunneling current.

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In contrast, the Morse force is not monotonic. For a force setpoint of e.g. −1 nN, two solutions are possible: z ≈ 2 ˚ A and z ≈ 4 ˚ A. The slope of the force curve is diﬀerent for the two solutions. Assume that we wish to operate the AFM at a distance of 4 ˚ A and a corresponding force of −1 nN. We would have to wire up the feedback such that it approaches if the actual force is greater than −1 nN, and withdraws if the actual force is smaller than −1 nN. However, if the tip would encounter an upward atomic step of ∆z = 2˚ A, the actual force would be ≈ +10 nN. Because this value is greater than the setpoint, the feedback would inevitably drive the tip into the sample, leading to a premature and unintended end of the experiment. Force sensors. The central element of a force microscope and its major instrumental diﬀerence from a STM is the spring which senses the force between tip and sample. For sensing normal tip-sample forces, the force sensor should be rigid in two axes and relatively soft in the third axis. This property is fulﬁlled with a cantilever beam, and therefore the cantilever geometry is typically used for force detectors. Most AFM cantilevers are made of silicon with spring constants ranging from 0.01 to 50 N/m. They are etched from single-crystal silicon with a base part of approx. 2 × 5 × 0.5 mm3 and a diving-board geometry cantilever with a length of about 100 µm, a width of about 10 µm and a thickness of approximately 5 µm. Their resonance frequency is typically several hundred kilohertz and the Q-factor in vacuum can reach several 100 000’s. The sharp tip at the end of the cantilever is also etched from the same Si crystal and generally points in a [001] crystal direction. Figure 6(a) shows a schematic view of a classical silicon cantilever, while in Fig. 6(b) another type of probe, the qPlus-Sensor [4], is sketched. The qPlus-Sensor is made of a quartz tuning fork. One prong of the tuning fork is ﬁxed such that the tuning fork is rendered to a cantilever geometry. In comparison with silicon cantilevers, the qPlus-Sensor has several advantages. The quartz forks are large and therefore a wide selection of tips can be mounted on a tuning fork with the mere help of tweezers and a stereoscopic microscope — sophisticated micromachining equipment is not needed. Tips made from tungsten, diamond, silicon, iron, cobalt, samarium, CoSm permanent magnets, and iridium have been built in our laboratory for various purposes. The qPlus-sensor is self-sensing and does not need optical setups for the detection of its vibration amplitude (see below). The original motivation for using the qPlus-Sensor was its great stiﬀness (1800 N/m for our favorite type of tuning forks). We have calculated the optimal parameters

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Fig. 6. (a) Schematic view of a classical silicon cantilever and (b) of the qPlus-Sensor with its typical dimensions.

for force sensors [5] and found that for low noise and high resolution measurements, a cantilever with a stiﬀness of several 100 N/m should be used. In the predominantly used frequency modulation (FM) operation mode (see section: Dynamic atomic force microscopy), the frequency change of the cantilever should only be caused by the interaction between the tip and the sample. The stability of the frequency of a cantilever as a function of the temperature is crucial for the achievable accuracy. A further advantage of the qPlus-sensor is displayed by its frequency stability versus temperature variations. Since the material properties that are pertinent to the mechanical eigenfrequencies of cantilevers are anisotropic in quartz, it is possible to stabilize the eigenfrequency of the tuning fork against the variations of the temperature by cutting the crystal in certain directions. The material properties of silicon are instead isotropic, and therefore a silicon cantilever cannot be compensated against temperature variations. Deﬂection detection devices. To measure the force between the tip and the sample the deﬂection of the cantilever must be determined. Normally, the silicon cantilevers need additional equipment for detecting the deﬂection of the cantilever. Several deﬂection detection devices have emerged over the two decades in the development of AFM. As an example, Fig. 7 shows two commonly used techniques for measuring the deﬂection of a silicon cantilever under diﬀerent conditions. Microscopes working under ambient conditions often use the laser beam technique shown in Fig. 7(a) to measure the deﬂection of the cantilever. The bending of the cantilever causes a change in the light intensity distribution

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Fig. 7. (a) Laser beam deﬂection detection systems as often used in ambient AFMs. (b) Interferometric cantilever detection system, a popular choice for low-temperature AFMs.

on a segmented photodiode. Many AFMs working at low temperatures and under UHV conditions normally use an optical interferometer to detect the deﬂection of the cantilever (see Fig. 7(b)). The incident light is reﬂected at the end of the optical ﬁber and at the back of the cantilever. Both reﬂected signals are superimposed and the intensity of the interfering beams indicates the deﬂection of the cantilever. The qPlus-sensor does not need optical components for measuring its deﬂection — it is self-sensing. Figure 8 shows the qPlus-sensor and the used preampliﬁer circuit, which is similar to the preampliﬁer of an STM shown in Fig. 3. Compared with silicon cantilevers using optical deﬂection methods the qPlus-sensor has a negligible power consumption, which makes it very attractive for low temperature applications [6].

Fig. 8.

The self sensing qPlus-sensor and its preampliﬁer circuit.

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3. Operating Modes of AFM’s Static mode operation. In AFM, the force Fts that acts between the tip and the sample is used as the imaging signal. In the static mode of operation, the force translates into a deﬂection q = Fts /k of the cantilever. Because the deﬂection of the cantilever should be signiﬁcantly larger than the deformation of the tip and the sample, restrictions on the useful range of k apply. In the static mode, the cantilever should be much softer than the bonds between the bulk atoms in the tip and the sample. Interatomic force constants in solids are in a range from 10 N/m to about 100 N/m — in biological samples, they can be as small as 0.1 N/m. Thus typical values of k in the static mode are 0.01–5 N/m. The eigenfrequency f0 should be signiﬁcantly higher than the desired detection bandwidth, i.e., if ten lines per second are recorded during imaging a width of say 100 atoms, f0 should be at least 10 × 2 × 100 s−1 = 2 kHz in order to prevent resonant excitation of the cantilever. While the experimental realization of static atomic force microscopy is diﬃcult, the physical interpretation of static AFM images is simple: the image is a map z(x, y, Fts = const).

Dynamic atomic force microscopy. In the dynamic operation modes, the cantilever is deliberately vibrated. The cantilever is mounted on an actuator to allow the external excitation of an oscillation. There are two basic methods of dynamic operation: amplitude-modulation (AM) and frequencymodulation (FM) operation. In AM-AFM [7], the actuator is driven by a ﬁxed amplitude Adrive at a ﬁxed frequency fdrive , where fdrive is close to but diﬀerent from f0 . When the tip approaches the sample, elastic and inelastic interactions cause a change in both the amplitude and the phase (relative to the driving signal) of the cantilever. These changes are used as the feedback signal. The change in amplitude in AM mode does not occur instantaneously with a change in tip-sample interaction, but on a time scale of τAM ≈ 2Q/f0 . With Q-factors reaching 100 000 in vacuum, the AM mode is very slow. Albrecht, Gr¨ utter, Horne, and Rugar [8] solved this problem by introducing the FM mode, in which the change in the eigenfrequency occurs within a single oscillation cycle on a time scale of τFM ≈ 1/f0 . Both AM and FM modes were initially meant to be “non-contact” modes, i.e., the cantilever was far away from the surface and the net force between the front atom of the tip and the sample was clearly attractive. The AM mode was later used very successfully in ambient conditions at a

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closer distance range where intermittent contact prevails (“tapping mode”) [9] and is now widely used because of the great reduction of lateral forces. Using the FM mode in vacuum improved the resolution dramatically and atomic resolution was obtained even on chemically reactive samples. In this article we focus on FM mode atomic force microscopy. In FM-AFM, a cantilever with eigenfrequency f0 and spring constant k is subject to controlled feedback such that it oscillates with a constant amplitude A as illustrated in Fig. 9. The deﬂection signal ﬁrst enters a bandpass ﬁlter. Then the signal splits into three branches: one branch is phase shifted, routed through an analog multiplier, and fed back to the cantilever via an actuator; one branch is used to compute the actual oscillation amplitude — this signal is used to calculate a gain input g for the analog multiplier; and one branch is used to feed a frequency detector. The frequency f is determined by the eigenfrequency f0 of the cantilever and the phase shift φ between the mechanical

Fig. 9. Block diagram of the frequency-modulation AFM feedback loop for constant amplitude control and frequency-shift measurement. Three physical observables are available: frequency shift, damping signal, and (average) tunneling current.

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excitation generated at the actuator and the deﬂection of the cantilever. If φ = π/2, the loop oscillates at f = f0 . Caused by the interaction between the tip and the sample, the oscillation frequency f changes by

∂Fts (z) kts (z) with kts (z) = , (5) ∆f (z) = f0 2k ∂z where k is the spring constant of the cantilever and kts (z) is the weighted average of the force gradient. If the force gradient is constant for the z-range covered by the oscillating tip, the frequency change is simply given by ∆f = f0

kts . 2k

(6)

This is a good approximation for the initial implementation of FM-AFM detecting magnetic long-range forces [8] with a range large compared to the oscillation amplitude. However, in classic atomic-resolution FM-AFM, kts varies by orders of magnitude during one oscillation with amplitude A, and the averaged force gradient is now 2A A 2 2 − q 2 dq := k (z −q ) A w(z , A)kts (z + z )dz . kts (z) = ts πA2 −A 0 (7) The frequency shift is now proportional to the integral over the weighted force gradient. The weight function w(z , A) is a semicircle with radius A divided by the area of a semicircle Γ = πA2 /2. Figure 10 shows the convolution with the proper normalization factor, and it is immediately apparent from this ﬁgure how the use of small amplitudes increases the weight of the short-range atomic forces over the unwanted long-range forces. The amplitude in FM-AFM allows one to tune the sensitivity of the AFM to forces of various ranges. 4. Imaging Organic Molecules The study of organic molecules on surfaces has been an early application of STM. Smith [10] has found that liquid crystal molecules can be adsorbed on graphite and imaged with atomic resolution by STM in ambient conditions. Organic molecules were also studied by STM in vacuum [11–13]. After true atomic resolution by AFM became feasible, several groups imaged molecules in vacuum by AFM [14–16].

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Fig. 10. ∆f is a convolution of the weight function w with the tip-sample force gradient. For small amplitudes, short range interactions contribute heavily to the frequency shift, while long-range interactions are attenuated.

So far, we have not studied organic molecules in our laboratory. However, we have imaged a crystalline form of carbon: highly oriented pyrolytic graphite (HOPG). Graphite provides a nice example to illustrate the imaging characteristics of STM and AFM. Carbon, the backbone material of life on earth, comes in three modiﬁcations: diamond, graphite and fullerenes. Diamond develops tetrahedral sp3 bonds forming a cubic crystal structure, while graphite and fullerenes are characterized by planar sp2 bonds. Polycrystalline graphite is the basis for many products of everyday life: pencils, lubricants, batteries, arc lamps and brushes for electric motors. In crystalline form, highly oriented pyrolytic graphite is used as a diﬀracting element in monochromators for x-ray- and neutron-scattering and as a calibration standard for scanning tunneling microscopy. The graphite surface is easily prepared as a clean atomically ﬂat surface by cleavage. This feature is attractive and it is used in many laboratories as the surface of choice for ‘seeing atoms’. In spite of the proverbial ease of imaging graphite by STM with atomic resolution, every second atom in the hexagonal surface unit cell remains hidden, and STM images show only a single atom in the unit cell. Here we present measurements with a novel low-temperature atomic force microscope [17] with pico-Newton force sensitivity that reveal the hidden surface atom [18]. With the capability of measuring such tiny forces, it should be possible to investigate very soft materials such as biological specimens.

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Fig. 11. Crystal structure of graphite. The unit cell is shaded in green. (a) Top view of the surface layer. The hexagonal surface lattice is deﬁned by two unit vectors u and v in the xy-plane with a length of 246 pm and an angle of 120◦ forming a honeycomb web of hexagonal rings. The basis of the lattice consists of two carbon atoms α (white) and β (red) with a distance of 142 pm. (b) Perspective view, showing the layered structure. The distance between layers is 2.36 times the next-neighbor distance of atoms within one layer, and the bond between layers is weak. The α-atoms (white) are directly above an α-atom in the layer directly underneath at a distance of 334.8 pm; the β-atoms (red) are over hollow sites (h). The unit vector w is parallel to the z-axis with a length of 669.6 pm.

Structure of Graphite. Figure 11 displays the structure of graphite, a layered structure with a hexagonal lattice of carbon atoms linked by strong sp2 bonds with a next neighbor distance of only 142 pm. The layers are stacked such that three of the six atoms within a hexagon have a direct neighbor in the layer underneath at a distance of 334.8 pm. The electronic state of the valence electrons in graphite diﬀers from the atomic ground state conﬁguration in atomic carbon (1s2 2s2 2p2 ): one of the 2s electrons is promoted to a 2p state and three electrons in the 2s, 2px and 2py states hybridize to sp2 states lying in the xy-plane. The fourth valence electron is in a 2pz -like state [19,20]. The 2pz states have the lowest bonding energy. For a single sheet of graphite, the 2pz states at the α and β positions have the same energy [20]. However, for crystalline graphite the overlap of the 2pz states centered at the α-sites leads to a lower bonding energy, leaving the 2pz states centered at the β-sites as the highest occupied (and lowest unoccupied) electronic states. Adjacent atoms at the α- and β-sites are connected by extremely strong bonds, forming very durable layers that are parallel to the x-y plane. However, in the z-direction these layers are only weakly coupled. The force constants parallel and perpendicular to the

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x-y plane can be estimated from Raman scattering data of graphite. Nicklow et al. [21] found a frequency of 48.6 THz for the optical phonons parallel to the x-y plane and 4.2 THz in z-direction. Thus, for a pair of carbon atoms the force constant is estimated as 14 N/m in z-direction and 900 N/m in the x-y plane. Because of the softness of the lattice in z-direction, the normal forces acting between tip and sample have to be kept extremely small to avoid distortions of the graphite sample. The Surface of Graphite at Low Temperatures. Figure 12(a) shows an STM image of graphite recorded in a constant-height mode. In this STM image, only one maxima per surface unit cell appears. Theory predicts [19– 23] that these maxima correspond to the β-atoms. In our experiments, we have shaped the tip by ﬁeld emission as well as controlled collisions until relatively spherical atom images resulted and defects and steps could be imaged clearly. The sharpness of the tip also manifested itself in topographic images with a corrugation of only 20 pm — it is well established that imaging graphite with blunt tips ensues large forces resulting in giant corrugations [24,25]. Figure 12(b) is an AFM image of graphite, recorded with weak repulsive forces. In agreement with theory, the image shows both α-atoms and β-atoms. Dynamic AFM measurements provide an additional clue that allows one to assess the atomic sharpness of the tip. In the AFM image shown in Fig. 12(b), the energy required to maintain a constant oscillation amplitude A is measured simultaneously with the frequency shift and the average tunneling current. In the data presented here, the extra energy required for keeping A constant when the tip oscillates close to the sample was negligible, while ﬂat tips with a large contact area to the sample caused

Fig. 12. (a) STM image of graphite. The hexagonal unit cell of graphite has two atoms in its basis, but STM shows only one of the two, forming a triagonal lattice. (b) AFM image of graphite. The hexagonal carbon rings are visible, and the complete surface lattice is imaged.

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unstable tip oscillations and required signiﬁcant energy for maintaining a constant amplitude. As an estimated result one ﬁnds that the total interaction force is 248 pN over the carbon atoms at the α sites, 250 pN over the β sites, and 223 pN over the hollow sites. It is interesting to note that the force over β sites is slightly larger than over α sites. A simple analysis would lead one to expect the opposite, because the α sites have a direct neighbor underneath and thus should be harder. However, Whangbo et al. [26] found that for large tip atoms such as tungsten, the β sites appear to be harder, because when pressing on a ‘soft’ β site in the center, the front atom also soon touches the three surrounding ‘hard’ α sites, while for pressing on one ‘hard’ α site in the center surrounded by three ‘soft’ β sites, the net stiﬀness is lower.

5. Conclusions and Perspectives Scanning tunneling microscopy has long been established for studying single molecules on surfaces. Atomic force microscopy is making great progress towards that goal. Impressive results have already been obtained in the imaging of molecules by AFM with atomic or near-atomic resolution. The attenuation of long-range forces is a challenge, in particular for looking at adsorbed molecules, because the long-range forces are mainly caused by the interaction between tip and substrate, and the long-range contributions become signiﬁcantly smaller when the tip has to scan over a molecule. The introduction of small amplitude techniques promises to facilitate the imaging of non-ﬂat surfaces such as isolated adsorbed molecules. The spatial resolution of an AFM has reached a level where the electronic conﬁguration of tip and sample atoms is discernable in the images. Therefore, the tip should have a spatially conﬁned and well-characterized charge distribution. The use of tip materials with small, i.e. light atoms (like carbon) is desirable for a further increase in resolution. In addition to minimizing the size of the tip’s front atom, a search for a physical imaging signal that is even more sensitive to short-range forces than the frequency shift using small amplitudes is indicated. A direct mapping of higher derivatives of the tip sample potential would provide such a signal. Recently, it has been shown that the detection of higher harmonics of the cantilever oscillation directly couples to higher force derivatives and that recording these higher harmonics provides greater resolution [27,28]. Figure 13(a) shows a light atom probe interacting with a surface with the four-leafed clover shaped charge distribution of a tungsten surface atom. The electronic states in a

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Fig. 13. (a) Front section of a tungsten AFM/STM tip. A part of the graphite sample is shown on the top. In the bulk, each atom is surrounded by eight atoms. Because the tip atom only has four next neighbors, four local minima in the charge density appear. (b) Measured higher harmonics of the cantilever vibration, demonstrating a lateral resolution of 77 pm [28].

single atom of the tungsten tip are detected by an atomic state of a carbon atom of the graphite surface (for details see [28]), and the role of tip and sample is reversed. The image shown in Fig. 13(b) is a map of the higher harmonic amplitudes of the cantilever. Subatomic features with a lateral resolution of 77 pm are clearly visible. For the ﬁrst time it is now possible to study the covalent parts of the chemical bonding in a metal atom. In spite of the impressive results provided by STM in the study of surface nanostructures [29], there are ample examples where the spurious conductivity of molecules hampers their observation by STM, opening a bright future for AFM experiments on single molecules. The progress of smallamplitude AFM and the further use of light atom probes in combination with higher harmonic detection of the cantilever deﬂection is expected to reveal exciting views of nature on a picometer length scale. References [1] G. Binnig, H. Rohrer, Ch. Gerber and E. Weibel, Surface studies by scanning tunneling microscopy, Phys. Rev. Lett. 49, 57 (1982). [2] G. Binnig, H. Rohrer, Ch. Gerber and E. Weibel, 7 × 7 reconstruction on Si(111) resolved in real space, Phys. Rev. Lett. 50, 120 (1983). [3] G. Binnig, C. F. Quate and Ch. Gerber, Atomic force microscope, Phys. Rev. Lett. 56, 930 (1986). [4] F. J. Giessibl, High speed force sensors for force microscopy and proﬁlometry utilizing a quartz tuning fork, Appl. Phys. Lett. 73(26), 3956 (1998).

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[5] F. J. Giessibl, H. Bielefeldt, S. Hembacher and J. Mannhart, Calculation of the optimal operating parameters in non-contact atomic force microscopy, Appl. Surf. Sci. 140, 352 (1999). [6] S. Hembacher, F. J. Giessibl and J. Mannhart, Evaluation of a force sensor based on a quartz tuning fork for operation at low temperatures and ultrahigh vacuum, Appl. Surf. Sci. 188, 445 (2002). [7] Y. Martin, C. C. Williams and H. K. Wickramasinghe, Atomic force microscope-force mapping and proﬁling on a sub 100-˚ A scale, J. Appl. Phys. 61(10), 4723 (1987). [8] T. R. Albrecht, P. Gr¨ utter, D. Horne and D. Rugar, Frequency modulation detection using high-Q cantilevers for enhanced force microscope sensitivity, J. Appl. Phys. 69(2), 668 (1991). [9] Q. Zhong, D. Innis, K. Kjoller and V. B. Elings, Fractured polymer silica ﬁber surface studied by tapping mode atomic-force microscopy, Surf. Sci. 290, L688 (1993). [10] D. P. E. Smith, J. K. H. H¨ orber, G. Binnig and H. Nejoh, Structure, registry and imaging mechanism of alkylcyanobiphenyl molecules by tunneling microscopy, Nature 344, 641 (1990). [11] T. A. Jung, R. R. Schlittler and J. K. Gimzewski, Conformational identiﬁcation of individual absorbed molecules with the STM, Nature 386, 696 (1997). [12] R. Berndt, R. Gaisch, J. K. Gimzewski, B. Reihl, R. R. Schlittler, W. D. Schneider and M. Tschudy, Photon-emission at molecular resolution induced by scanning tunneling microscope, Science 262, 1425 (1993). [13] F. Rosei, M. Schunack, P. Jiang, A. Gourdon, E. Laegsgaard, I. Stensgaard, C. Joachim and F. Besenbacher, Organic molecules acting as templates on metal surfaces, Science 296, 328 (2002). [14] B. Gotsmann, C. Schmidt, C. Seidel and H. Fuchs, Molecular resolution of an organic monolayer by dynamic AFM, Eur. Phys. J. B 4(3), 267 (1998). [15] C. Loppacher, M. Guggisberg, O. Pfeiﬀer, E. Meyer, M. Bammerlin, R. Luthi, R. Schlittler, J. K. Gimzewski, H. Tang and C. Joachim, Direct determination of the energy required to operate a single molecule switch, Phys. Rev. Lett. 90(6), 066107 (2003). [16] H. Yamada, Non Contact Atomic Force Microscopy, S. Morita, R. Wiesendanger and E. Meyer, eds. (Springer Verlag, 2002), pp. 193–213. [17] S. Hembacher, Simultane Rasterkraft- und Rastertunnelmikroskopie bei 5 K im Ultrahochvakuum, PhD Thesis (Augsburg University, 86135 Augsburg, Germany, 2003). [18] S. Hembacher, F. J. Giessibl and J. Mannhart and C. F. Quate, Revealing the hidden atom in graphite by low-temperature atomic force microscopy, Proc. Natl. Acad. Sci. USA 100, 12539 (2003). [19] H. A. Mizes, S. Park and W. A. Harrison, Multiple-tip interpretation of anomalous scanning-tunneling-microscopy images of layered materials, Phys. Rev. B 36, 4491 (1987). [20] H. A. Mizes, Interpretation of Scanning Tunneling Microscopy Images of Graphite, PhD thesis, (Stanford University, 1987).

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[21] R. Nicklow, N. Wakabayashi and H. G. Smith, Lattice dynamics of pyrolytic graphite, Phys. Rev. B 5, 4951 (1972). [22] I. P. Batra, N. Garcia, H. Rohrer, H. Salemink, E. Stoll and E. Tosatti, A study of graphite surface with STM and electronic structure calculations, Surf. Sci. 181, 126 (1987). [23] D. Tom´ anek, S. G. Louie, H. J. Mamin, D. W. Abraham, R. E. Thomson, E. Ganz and J. Carke, Theory and observation of highly asymmetric atomic structure in scanning-tunneling-microscopy images of graphite, Phys. Rev. B 35, 7790 (1987). [24] J. B. Pethica, Comment on “Interatomic forces in scanning tunneling microscopy: Giant corrugations of the graphite surface”, Phys. Rev. Lett. 57, 3235 (1986). [25] M. Herz, F. J. Giessibl and J. Mannhart, Probing the shape of atoms in real space, Phys. Rev. B 68, 45301 (2003). [26] M. H. Whangbo, W. Liang, J. Ren, S. N. Magonov and A. Wawkuschewski, Structural and electronic properties of graphite and graphite intercalation compounds MC8 (M=K, Rb, Cs) govering their scanning tunneling microscopy images, J. Phys. Chem. 98, 7602 (1994). [27] U. D¨ urig, Interaction sensing in dynamic force microscopy, New J. Phys. 2(5), 1 (2000). [28] S. Hembacher, F. Giessibl and J. Mannhart, Force microscopy with light atom probes, Science 305, 380 (2004), published online June 10 2004 (10.1126/science.1099730). [29] F. Rosei, Nanostructured surfaces: Challenges and frontiers in nanotechnology, J. Phys.: Condens. Matter 16, S1373 (2004).

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OPTICAL DETECTION OF SINGLE MOLECULES AT INTERFACES

B. HECHT Nano-Optics Group, National Center of Competence for Research in Nanoscale Science Institute of Physics, University of Basel, Klingelbergstr. 82 CH-4056 Basel, Switzerland [email protected] Abstract. This chapter deals with optical detection of single ﬂuorescent molecules inside and close to the boundary of complex media. After discussing the fundamentals of single-emitter detection based on luminescence detection, experimental set-ups and methods are introduced. Advantages and disadvantages of scanning near-ﬁeld optical microscopy and scanning confocal optical microscopy are discussed in view of applications for single-emitter studies. The remainder of the chapter is devoted to the discussion of selected applications of singleemitter experiments including their use as deterministic single-photon sources, and applications as minimally invasive probes and labels in biology and material science. Keywords: Single-molecule detection; single emitters; confocal microscopy; scanning near-ﬁeld optical microscopy.

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Introduction . . . . . . . . . . . . . . . . . . . How is it Possible to Detect Single Molecules? 2.1 Signal of a single molecule . . . . . . . . 2.2 Signal-to-background considerations . . Single-Molecule Optical Microscopy . . . . . 3.1 Near-ﬁeld optical microscopy techniques 3.2 Far-ﬁeld optical microscopy techniques . 3.2.1 Confocal microscopy . . . . . . . 3.2.2 Wide-ﬁeld microscopy . . . . . . 89

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Applications . . . . . . . . . . . . . . . . . . . 4.1 Single emitter photon emission statistics 4.1.1 Time trace analysis . . . . . . . . 4.1.2 Arrival time analysis . . . . . . . 4.2 Single-emitter probes and labels . . . . 4.2.1 Single-emitter probes . . . . . . . 4.2.2 Single-emitter labels . . . . . . . 5 Conclusion . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . .

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1. Introduction The ability to detect and interact with single molecules will have a major impact on modern science and technology. While Schr¨ odinger still had to contemplate about the impossibility of experimenting with single molecules or atoms [1],1 today we are very much used to doing just that: we are able to selectively address and probe single quantum emitters on surfaces or inside the bulk of a (semi)transparent complex and heterogeneous medium as well as in artiﬁcial electromagnetical traps of diﬀerent types.2 The beneﬁts and possibilities that arise from single-emitter experiments are manifold. First of all, detailed insight into the fundamentals of lightmatter interaction can be gained. Second, the fact that one is dealing with individual quantum objects can be exploited for applications in quantum information processing [3,4] and quantum cryptography [5,6]. Third, the ability to detect single emitters embedded in complex media allows the use of them as markers and probes, i.e. as spies for their local nano environment and for the investigation of local interactions. Using molecular probes enables the study of static and dynamic heterogeneities on molecular length scales, during short times, deep inside complex materials which provides an arsenal of possibilities unrivaled by any other technique employed in the study of complex systems. Since each individual molecular probe sees its own nano environment, distributions of individual properties may be obtained rather than just ensemble averages. However, measuring distributions implies, according to the ergodicity theorem (if it is applicable) that 1 “. . . we

never experiment with just one electron or atom or (small) molecule . . . In thought-experiments we sometimes assume that we do; this invariably entails ridiculous consequences . . . In the ﬁrst place it is fair to state that we are not experimenting with single particles any more than we can raise Ichthyosauria in the zoo . . . .” 2 not covered in this chapter, for a recent review see [2].

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either the same measurement has to be repeated on the same molecule or many diﬀerent molecules have to be probed. This additional information is mandatory for instance in tracing dynamic molecular (re-)organization and interactions in complex systems on the level of individual molecules. In the emerging ﬁeld of ‘systems biology’ as well as in the ‘material sciences’ [7] this will be of major importance. In particular, experiments with single emitters can reveal rare or transient events, like blinking, bleaching, and conformational switching of individual molecules in the presence of a strong background of uninteresting events. In ensemble experiments such rare events can never be observed unless their occurrence can be synchronized in time. Finally, with the detection of single analyte molecules the fundamental limit of sensitivity in analytical chemistry has been reached [8,9]. This means that we no longer need to determine concentrations of analyte molecules but we may rather endeavor to count the number of analyte molecules present in a certain sample. Obviously this will have tremendous impact on optical sensing applications for future medical diagnostics and pharmacological applications. Historically, a change of paradigms in our perception of the atomic and molecular world came about with the development of scanning tunneling microscopy (STM) [10] and atomic force microscopy (AFM) [11]. These techniques allowed us ﬁrst to view and later also to manipulate single atoms and molecules on solid interfaces [12–14]. Around the same time it had become possible to trap single ions in electromagnetic traps in vacuum and probe their interaction with laser light. These achievements, simply lowered the psychological barrier that prevented researchers from attempting single-emitter experiments, although the technological means to do so (lasers, ﬁlters, photomultipliers, photon counting, . . . ), in principle, were long available. Hence, it is no surprise that around the same time optical techniques were being developed that were able to look at ever smaller and smaller subensembles of a population of impurity molecules in solid host matrices [15,16]. Stokes-shifted ﬂuorescence was starting to be used as a signal since it provides extreme selectivity due to the possibility of eﬃciently discriminating red-shifted radiation from residual excitation light and Rayleigh-scattered background. These “small-ensemble” methods were the predecessors of even more advanced optical techniques that were able to selectively address individual impurity centers in crystalline hosts at cryogenic temperatures. In these experiments, molecular crystals were used as hosts and dye molecules were used as impurities and consequently, single-molecule spectral signatures were detected by optical means

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in such a system for the ﬁrst time [17,18]. Optical techniques oﬀer the great advantage over AFM and STM that it is easy to achieve very high spectral (energy) resolution and selectivity. These experiments triggered an avalanche-like development that led up to today’s state of research where single molecules, semiconductor nanocrystals and other quantum emitters, like ions and metal nano particles, can be detected and investigated routinely by various optical microscopy techniques also, and in particular, at ambient conditions. The development and the current status of experimental techniques is well documented in books and reviews [19–24]. The goal of the present chapter is to serve as a primer in single-molecule detection. It should provide the reader with some basic background necessary for the understanding of optical single-molecule detection and its possible applications. 2. How is it Possible to Detect Single Molecules? The key issue in detecting a single molecule by optical means is the possibility of achieving a suﬃciently high signal-to-noise ratio in the detected signal. For visible light, we beneﬁt from the fact that individual photons can be detected with a quantum eﬃciency of up ∼90% using silicon avalanche photodiodes and back-thinned CCD chips. Optical ﬁlters with sharp cutoﬀ edges and very high suppression levels (>10−6 ) in the stop bands allow the very eﬃcient suppression of scattered excitation light. At the same time, selected spectral regions can be transmitted with very high eﬃciency (>80%). This means that we may generally neglect background arising from residual excitation light and we only need to consider sources of background due to radiation that is as much red-shifted with respect to the excitation as the ﬂuorescence, and hence falls within the spectral detection window deﬁned by the optical ﬁlters. 2.1. Signal of a single molecule We start out by determining the rate at which a single quantum system can emit photons. This will put us into a position to estimate the orders of magnitude of signal and background we may expect. To this end, we approximate the manifold of electronic states of the quantum systems3 by just two eﬀective states, which for example could be the highest 3 The

reader may think, e.g. of an organic molecule. Also other quantum emitters, such as semiconductor nano crystals, will behave in a similar way.

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occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). The excitation laser is assumed to be close to resonance with these levels which justiﬁes neglecting all other, nonresonant, levels. In addition we still consider a third level, a general dark state, which could for example be a so-called triplet state in the case of an organic molecule (see Fig. 1). The molecular triplet state is populated if the electron excited to the LUMO undergoes a spin ﬂip. This happens with a small but non-negligible probability, e.g. by spin-orbit coupling within a molecule. In a classical view this is described by the notion that the orbital magnetic moment exerts a torque on the electronic spin. The energy of the triplet state is slightly lowered with respect to the LUMO since the two aligned spins avoid each other according to Hund’s rule, thus lowering their eﬀective electrostatic repulsion. While transitions between HOMO and LUMO level are allowed transitions with an excited state lifetime in the ns-range, the transitions into the triplet state and triplet relaxation are spin-forbidden and therefore occur at much lower rates (ms). By using the simpliﬁed energy diagram of Fig. 1, we neglect very fast relaxation within the vibrational manifold superimposed to the electronic states. Those can be safely ignored since the related relaxation timescales (∼ps) are small compared to the electronic transition rates. We thus end up with an eﬀective system of three levels: the singlet ground state (HOMO), the singlet ﬁrst excited state (LUMO) and the triplet state denoted by 1, 2 and 3 as indicated in Fig. 1, that can describe much of the phenomena of lightmatter interaction for a single emitter. Let us assume that the population4

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1 Fig. 1. Single-quantum system approximated by a system of three levels with occupation probabilities pi interconnected by transition rates kij . A third level is taken into account in order to accommodate transitions to triplet or other dark states. 4 Population

here either means the probability of a level to be occupied (for a single system) or the fraction of three-level systems that occupy the respective state (for a number N of systems).

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of the three levels are determined by excitation and relaxation rates according to the processes that we have just described. We can now formulate a system of diﬀerential equations for the change of the populations pi , i = {1, 2, 3}: p˙1 = −k12 p1 + (kr + knr )p2 + k31 p3 p˙2 = k12 p1 − (kr + knr + k23 )p2 p˙3 = k23 p2 − k31 p3

(1)

1 = p 1 + p2 + p 3 . The last equation ensures that the emitter is in one of the three states at any time. The rate k21 is divided into a radiative contribution kr and a nonradiative contribution knr such that k21 = kr + knr . Nonradiative relaxations typically prevail in the relaxation of larger excited molecular systems. Only in special cases, e.g. for good dye molecules and high-quality semiconductor nano crystals, emission of photons is observed. To quantify the quality of a ﬂuorophore in this sense, we introduce the quantum eﬃciency for emission of a photon η = kr /(kr + knr ). For the experts we should note that by writing down Eqs. (1) we assume that coherence is lost in the excitation/relaxation cycle, e.g. due to dissipative coupling to the environment. This is a very good approximation at room temperature and for nonresonant or broadband excitation [25]. At cryogenic temperatures, with near-resonant narrowband excitation, or for isolated atoms and ions, the full quantum mechanical master equation approach must be employed. Such an approach will also include coherence eﬀects that show up, e.g. as Rabi oscillations of the populations of ground and excited state. Such eﬀects are not included in the present, simpliﬁed discussion that is only valid in the limit of strong dephasing. However, some phenomena, such as photon antibunching and sub-Poissonian photon statistics, related to the quantum nature of the single emitter can still be described within the present theoretical approach. To derive the steady-state solution of Eq. (1) we assume that the populations are constant in time and consequently their time derivatives can be set to zero. This leads to a set of 4 equations for the equilibrium populations pi , i = {1, 2, 3} of the three states involved. We are interested in the rate R at which the system emits photons. This rate is evidently given by R = p2 kr ,

(2)

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the population of the excited state p2 multiplied by the known radiative decay rate kr . If we solve Eq. (1) for the population p2 , we arrive, after some manipulation, at the following relation R(I) = R∞

I/IS , 1 + I/IS

(3)

where I is the intensity of the excitation light entering via k12 = σI/(ω)

(4)

with σ being the absorption cross section of the transition. Actually, I is the eﬀective intensity, i.e. the absolute square of the electric ﬁeld component projected onto the direction of the absorption dipole moment. For example, the system cannot be excited if illuminated with light polarized perpendicular to the absorption dipole moment. The constants R∞ and IS are functions of the transition rates and can be written as k31 kr k23 + k31 (kr + knr + k23 )k31 · ω. IS = σ(k23 + k31 )

R∞ =

(5)

Equation (3) describes the typical saturation behavior of the emission rate of a single emitter, visualized in Fig. 2. This kind of nonlinearity, which is a quantum eﬀect in itself, is expected to occur for a single quantum emitter since its excited state has a ﬁnite lifetime which limits the shortest average time between two emitted photons. The saturation behavior is characterized by the two parameters, R∞ and IS , deﬁned by Eq. (5). The ﬁrst describes the maximum emission rate which is achieved at inﬁnitely strong excitation intensity. The second is the intensity at which the emission rate equals R∞ /2 (see Fig. 2). Typical values for R∞ and IS for organic dye molecules at room temperature are R∞ = 6 · 106 s−1 and IS = 7.5 · 1021 photons/s ≈ 3 kWcm−2 at 500 nm wavelength, respectively. Taking into account an overall collection and detection eﬃciency of the experimental apparatus of about 10%, we can expect a maximum photon count rate at the detector of roughly 6 · 105 photons/s from a single dye molecule. Typically, a moderate excitation power of 1 µW focused to a spot of 250 nm in diameter, e.g. in a confocal microscope, is suﬃcient to saturate a molecule.

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Fig. 2. Saturation of the emission rate of a single molecule as a function of the excitation intensity. Both axes are normalized.

2.2. Signal-to-background considerations A count rate of some 105 photons/s seems to be a generous signal. This is, however, not the full story since typically we will not detect a quantum emitter in vacuum but rather in the presence of a complex environment consisting of a huge amount of other, hopefully non-ﬂuorescent molecules which will still generate some background. As pointed out above, we have to consider only such background signals that are red-shifted with respect to the excitation. The most prominent and omnipresent source of red-shifted photons is Raman scattering. Raman scattering is a process by which an incident excitation photon may loose a portion of its energy to molecular vibrations. To quantify the importance of Raman scattering as a source of background in single-molecule experiments, we need to compare the cross sections of the non-resonant Raman scattering to that of ﬂuorescence. For a typical good dye molecule at room temperature with a ﬂuorescence quantum yield near unity, for example Rhodamine 6G, the absorption cross-section for ﬂuorescence reaches values of around 10−16 cm2 which corresponds to about the physical area of the molecule. This value can even be increased at cryogenic temperatures where dephasing is reduced [21,26]. On the other hand, a typical Raman cross section for an organic solvent molecule like benzene is only about 10−28 cm2 . This means nothing else but that we are able to distinguish the signal of a single ﬂuorescent molecule in the presence of up to 1012 solvent molecules that act as Raman scatterers. Now, if we stay with benzene as a model solvent to complete our

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calculation, we may use its density of about 0.8 g/mL and its molar mass of 78 g/mol to obtain a volume of 0.1 fL or 1 µm3 that is occupied by 1012 solvent molecules. This deﬁnes the way we should conduct a single-emitter experiment: we must not illuminate a volume that is much larger than what we have calculated, if we want to detect the presence of a single molecule inside this volume. If we are able to reduce the excitation volume, we also reduce the background. Consequently the secret behind optical singlemolecule detection is a small enough excitation volume and the avoiding of saturation! This can be easily achieved by combining near-ﬁeld and far-ﬁeld optical microscopy with suitable sample preparation techniques, e.g. using thin ﬁlm processing or sub-monolayer coverage of molecules of interest on e.g. glass interfaces. Diﬀerent optical microscopy techniques applicable to single-molecule detection will be the topic of the following section. 3. Single-Molecule Optical Microscopy 3.1. Near-ﬁeld optical microscopy techniques In 1993, the ﬁrst repeatable optical detection of individual ﬂuorescent molecules embedded in a thin polymer ﬁlm became possible at ambient conditions. At that time this was achieved by minimizing the excitation volume to a subwavelength size using aperture scanning near-ﬁeld optical microscopy (SNOM) [27] (for a review see [28]). In aperture SNOM, laser light is coupled into an optical ﬁber5 which has a metal-coated taper at its far end. The taper results in a tip, suitable for scanning probe microscopy, having a subwavelength light source at its apex. Inside the taper region the light is reﬂected to a great extent and dissipated into heat. Only a small portion of light escapes the subwavelength aperture at the tip apex. However, due to its near-ﬁeld character this light is enhanced with respect to the intensity measured in the far ﬁeld of the aperture. Thus it is still easily possible, for example, to saturate single molecules in the near ﬁeld of such an aperture probe [29]. The near ﬁeld only extends roughly up to a distance of the aperture radius away from the aperture. This is why an auxiliary gapwidth regulation mechanism, i.e. shearforce detection, is employed to ensure constant gapwidth [30]. Locally excited ﬂuorescence from beneath the aperture probe is usually detected using a conventional optical microscope with a high numerical 5 The

ﬁber has to be kept short because otherwise Raman scattering in the ﬁber can contribute signiﬁcantly to the background!

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aperture microscope objective at its heart. The collected light is spectrally (and spatially) ﬁltered and further directed to a detection device. A typical setup is sketched in Fig. 3. Indeed, as expected from our discussion in the previous section, the signal-to-noise ratio in SNOM measurements of single molecules is favorable owing to the conﬁned illumination. What is particulary intriguing about SNOM images of individual molecules [27,29] is the fact that obviously not only the molecule is imaged by the probe but that each single molecule is mapping the ﬁeld distribution in the aperture. By relying on the known ﬁeld distribution in the close vicinity of a subwavelength aperture [31,32], it is possible to determine not only the position of a molecule but also the orientation of its transition dipole moment, and thus also the orientation of the molecule itself. Since the component of the electric ﬁeld parallel to the metal boundary must be small because of the free charges in the metal, the electric ﬁeld shows a distinct pattern with prominent features close to the rim of the aperture along the polarization direction. Figure 4(a) shows a rough sketch of the electric ﬁeld pattern beneath an aperture. Figure 4(b) compares expected and measured ﬁeld patterns for molecules oriented along the probe axis and for molecules in the sample plane.

Fig. 3. Typical setup of a scanning near-ﬁeld optical microscope. Excitation light is coupled into a single-mode ﬁber with a metal coated taper at its far end. The light emitted by the aperture illuminates a region of the samples whose size is determined by the aperture diameter and the distance between probe and sample. Light from the interaction region is collect using a conventional optical microscope.

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Fig. 4. Detection of single molecules by near-ﬁeld techniques. (a), (b) SNOM images of single molecules embedded in a polymer ﬁlm with random orientations, from [29]. (c) Sketch of the ﬁeld distribution in the near ﬁeld of the aperture. (d) Comparison of measured ﬁeld distributions to calculated, once for both fundamental orientations, from [27]. (e) Eﬀect of an optical antenna on the emission of a single emitter [36].

The experimental results were so convincing and promising that they inspired an enormous number of researchers to make use of the new possibilities with all their possible applications. However, it was noted soon that the ultrahigh conﬁnement of aperture SNOM is not really a necessary condition to detect single ﬂuorescent molecules at ambient conditions. Very similar results could be obtained by using diﬀraction-limited excitation spots, with diameters larger only by a factor of 2.5 than a 100 nm aperture, and with much less experimental eﬀort. Also, it was found that the proximity of the near-ﬁeld probe to a molecule can inﬂuence important molecular properties, such as the lifetime of its excited state, its emission characteristics, and its quantum yield [33–35]. To cut a long story short, the overwhelming majority of single-molecule experiments up to the present day has not been done using aperture SNOM but rather using scanning confocal and wide-ﬁeld

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optical microscopy. This is mainly attributed to the fact that these latter techniques are much easier to use, faster, and less invasive. Before we continue to discuss these two far-ﬁeld optical microscopy methods, it is important to point out that using far-ﬁeld optical techniques for the imaging and detection of single molecules is a compromise. The large discrepancy between the molecular length scale and the diﬀractionlimited spatial resolution allows us to study such systems only by farﬁeld microscopy that contain chromophores at very low concentrations. Although very often important insights can be gained this way, it should be kept in mind that numerous realistic samples cannot be diluted arbitrarily since a high density of chromophores is often crucial for their function. A typical example are systems that exhibit excitonic coupling between molecules, e.g. photosynthetic complexes. Furthermore, apart from singlemolecule studies, local spectroscopic measurements always require a spatial resolution that is as high as possible to discriminate unwanted background from neighboring structures [37]. Recently, a solution to this dilemma has been proposed that suggests the use of resonant antenna-like metallic nano structures [38], e.g. for high-resolution imaging of single emitters [36]. Here, the unavoidable interaction of the single emitter with the near-ﬁeld probe is turned into a beneﬁt in the sense that the emission of a single emitter is strongly enhanced and directed into chosen directions when placed in the subwavelength feed gap of an optical antenna probe as compared to the free emitter. The situation is sketched in Fig. 4(c). 3.2. Far-ﬁeld optical microscopy techniques The two most important types of far-ﬁeld optical microscopes shall be described here in brief: the confocal and the wide-ﬁeld conﬁguration. 3.2.1. Confocal microscopy Figure 5 shows the setup of the simplest type of a scanning confocal optical microscope (SCOM). Its beam path is ﬁxed and the sample is raster scanned to record an image. In such an instrument light from a laser source in a ﬁrst step is spatially ﬁltered, e.g. by sending it through a single-mode optical ﬁber or a pinhole. The purpose of the spatial ﬁltering is to arrive at a beam with a perfect Gaussian beam proﬁle. A well-deﬁned beam proﬁle is important since it directly inﬂuences the ﬁeld distribution in the focal spot, as we will see. After spatial ﬁltering the light is collimated by a lens. The focal distance of the lens should be chosen such that the beam diameter is

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Fig. 5. Scanning confocal optical microscopy for single-molecule detection. Sample scanning conﬁguration. The ﬁber exit and the active area of the SPAD serve as confocal pinholes. S: sample, O: high-NA microscope objective, DM: dichroic mirror, L1,L2 lenses, F: Filters.

large enough to overﬁll the back-aperture of the microscope objective used to focus the light onto the sample.6 The diﬀraction-limited spotsize ∆x at the sample depends on the numerical aperture NA of the objective and the wavelength used for illumination λ , (6) NA where λ is the light wavelength. For NA = 1.4 the lateral spotsize for green light (λ = 500 nm) is about 220 nm, slightly better than λ/2. To practically achieve this lower limit it is important to note that the demagniﬁed image of the illumination spot, i.e. the ﬁber core or pinhole, on the sample should be smaller than the diﬀraction limit when neglecting diﬀraction eﬀects. The demagniﬁcation factor is given by the ratio of the focal lengths of the objective and the collimating lens. Once a diﬀraction-limited excitation spot is achieved, the same microscope objective that is used for illumination can also be used to collect light from the sample similar to the case of SNOM. If the incoming beam of light is collimated, the beam of collected light is also collimated for a chromatically corrected microscope objective. The use of collimated beams ∆x = 0.61

6 It

is advantageous if the microscope objective is designed to work with collimated beams. Such objectives are called ‘inﬁnity corrected’.

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makes it possible to introduce ﬁlters anywhere into the beam path without introducing oﬀsets. As in the case of SNOM the collected light has to be separated from the incoming light using dichroic mirrors and ﬁlters as depicted in Fig. 5. The ﬁltered beam of collected light is now focused by a second lens onto a pinhole in front of a detector. Certain detectors such as the widely-used single photon counting avalanche photodiodes have rather small active areas. They can be used without an additional pinhole. The role of the pinhole in front of the detector is to minimize contributions to the detected light from outside the focal spot, both along the optical axis and perpendicular to it. The size of the detection pinhole must be correctly matched to the diameter of the focal spot produced by the second lens in order to eﬃciently reject out-of-focus signals. The minimum diameter of the pinhole or the detector active area, respectively, is given by the size of the Airy disc in the focus of the second lens whose central maximum should not be cut. A larger pinhole diameter deteriorates the rejection of out-of-focal-plane signals but can help to optimize the eﬀective transmission of light through the pinhole. It is found that a spotsize two times smaller than the pinhole diameter still yields good results both for lateral resolution and out-of-focal-plane rejection. From another point of view, the lateral spotsize out of which, to a good approximation, light is eﬃciently and uniformly collected through the pinhole, corresponds to the size of the demagniﬁed image of the detection pinhole in the focal plane of the microscope objective which should optimally not exceed about 1 µm2 . The demagniﬁcation factor is again given by the ratio of the two focal distances of the objective and the lens focusing to the pinhole, respectively. Due to the eﬃcient rejection of out-of focus photons, confocal microscopy can gain a factor of ∼1.3 in resolution compared to a conventional optical microscope. More important, however, is another beneﬁt of the confocal geometry: it is possible to perform optical slicing of thick, transparent objects by simply shifting the focal plane to diﬀerent positions along the optical axis and recording an image at each of these positions. For an excellent review on confocal microscopy see [39,40]. Figure 6 shows a typical SCOM image of single ﬂuorescent molecules of DiI embedded in a 20 nm PMMA ﬁlm on glass. The molecules show up as bright diﬀraction-limited spots with peak count rates as expected from our previous analysis. The dark pixels inside the molecular spots correspond to quantum jumps of the molecule into the triplet state. They become visible since the pixel integration time is comparable to the triplet relaxation rate.

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Fig. 6. SCOM images of single molecules of DiI embedded in a 20 nm thin ﬁlm of PMMA for excitation polarizations as indicated by the white arrows. Excitation intensity was 1 kW/cm2 (a), (b) and 5 kW/cm2 for (c) and (d).

A distinct advantage of SNOM is the possibility to determine the orientation of molecular absorption dipole moments from the observed image patterns. For SCOM, looking at Fig. 6(a), we observe that the spots are all more or less round. Only the peak intensity varies slightly due to varying in-plane components of the absorption dipole along the direction of the incoming polarization. Such behavior would be expected if we focus a Gaussian beam using a not too high numerical aperture (NA) such that the beam waist is still larger than the wavelength. However, this is not the case when using a high NA where the spotsize is smaller than λ/2 (see above). The strong focusing results in depolarization eﬀects in the focus. In other words: when we focus a linearly polarized Gaussian beam using a high-NA microscope objective, notable ﬁeld strength occurs in the two directions perpendicular to the incoming polarization [41] while of course the ﬁeld component along the incoming polarization still dominates. The fact that such depolarization ﬁelds occur and start to become more and

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more prominent with increasing conﬁnement of the light can be simply proven by considering that the divergence of the electric ﬁeld has to vanish in the absence of sources. Considering time harmonic ﬁelds reduce the spatial derivatives to simple multiplication with the respective wavevector components. Hence, if one of the three Cartesian components of the electric ﬁeld is nonzero, then at least one of the other ﬁeld components must also be nonzero. Its magnitude then depends on the ratio of the wavevector components along the relevant directions. This ratio becomes sizable for strongly focused beams or otherwise conﬁned optical ﬁelds. To visualize the depolarization ﬁelds we may consider the following idea: assume we ﬁnd a molecule with its absorption dipole moment in the plane of the sample. We now adjust the polarization of the excitation beam such that the ﬂuorescence is maximized. We may assume that this happens if the electric ﬁeld vector in the focus is parallel to the dipole moment. Now, if we turn the incoming polarization by 90◦ the dominant electric ﬁeld component will not be able to excite the molecule and the presence of other ﬁeld components should become visible as weak, but distinctly non-circular spots. Figure 6 shows the result of such an experiment. In Fig. 6(b) the polarization has been turned by 90◦ as compared to (a) as indicated by the white arrows. The bright spots become dim and their symmetry changes to a four-lobed structure. These weak structures can be made visible if the excitation intensity is increased by a factor of ﬁve [see Figs. 6(c) and (d)].

Fig. 7. Depolarization by high-NA focusing. (a) Geometrical optics explanation of the depolarization due to the focusing of an annular beam leading to the three displayed characteristic patterns for the ﬁeld components in x, y, and z direction. (b) Confocal imaging using a focused annular beam. Suitably oriented molecules recover the fundamental patterns as indicated by the white labels.

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Now the four-lobed and other asymmetric spot shapes become prominent [see Fig. 6(d)]. The spatial distribution and the relative strength of the depolarization ﬁeld components can be explained in a geometrical optics picture. Consider the situation depicted in Fig. 7(a). Here a linear polarized beam is focused by a lens. The lens is assumed to be homogeneously illuminated by the beam. Some particularly interesting rays have been drawn as black lines. It is easy to see that for some of the beams the orientation of the ﬁeld vector is not changed by the refraction at the lens while others are strongly inﬂuenced. Clearly those rays will contribute to ﬁeld components along the optical axis. In the geometrical focus and along a line parallel to the y-axis including the geometrical focus, the contributions to longitudinal ﬁeld components cancel out leading to a corresponding knot line with zero longitudinal ﬁelds. When moving away from the geometrical focus this destructive interference is no longer complete and ﬁnite ﬁeld components are observed. This ﬁnally leads to the generation of a doubled-lobed spatial distribution of longitudinal ﬁelds. For the generation of ﬁeld components in the y-direction similar arguments can be applied and the occurrence of a four-lobed clover leaf can be explained by similar arguments [42]. It is clear that rays at the outer rim of the lens contribute most to the depolarization eﬀects. To exploit the depolarization eﬀects for the same type of orientational imaging observed for the SNOM, it has been proposed to use ring-like (annular) illumination [43]. An annular beam can be easily created by removing the central part of the excitation beam using a simple beam stop as symbolized by the black disk in Fig. 7(a). The resulting confocal scan images show very nicely the diﬀerent eﬀective patterns that can be attributed to diﬀerent absorption dipole orientations. Some of the patterns are labeled by the respective orientation (see Fig. 7(b)). For details see [42,43].

3.2.2. Wide-ﬁeld microscopy While SCOM has the great advantage that thicker samples can be imaged slice by slice thus gaining three-dimensional information about a sample after oﬀ-line image reconstruction, the scanning motion is inherently limited in speed since the data acquisition is a serial process. For certain applications, in particular the tracking of fast diﬀusing molecules, it is mandatory to push the temporal resolution to its limits. A typical setup that allows to do just this is shown in Fig. 8. It is very similar to the confocal setup of

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Fig. 8. Wide-ﬁeld optical microscopy for single-molecule detection. A single lens is introduced in addition to the setup for SCOM of Fig. 5 and the SPAD is exchanged by a fast CCD camera. L1, L2, L3: lenses, S: sample, O: microscope objective, DH: dichroic mirror, F: ﬁlter.

Fig. 5, but the beam is slightly prefocused before the microscope objective by introducing the lens L3 into the excitation beam path. This results in a slightly larger illuminated sample area which may now contain several molecules in parallel. In order to detect all of these molecules at the same time, the image is projected onto a sensitive CCD camera. For fast imaging (video rate and beyond) the CCD camera should be equipped with either electron multiplying technology or with an image intensiﬁer (see, e.g. Andor, Ireland, or Roper Scientiﬁc, USA). Also, with a standard slow scan CCD high quality images of single molecules can be recorded; however, at higher frame rates the camera read-out noise dominates all other sources of noise and eventually deteriorates the signal to noise ratio. If single molecules emit in the sample they show up as bright spots on the camera. The magniﬁcation of the microscope is adjusted in such a way that the Airy disc formed on the CCD by a single emitter typically is extended over several pixels which simpliﬁes later analysis. A typical single molecule

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Single molecules of DiI in PMMA imaged by wide-ﬁeld optical microscopy.

wide-ﬁeld image is shown in Fig. 9. It can be clearly seen that the signal-tobackground ratio is no longer as good as in Fig. 6. From the discussion in the introduction it is clear that this must be due to the increased illumination volume. From the spatial distribution of the background one can also see that the excitation spot is not homogeneous, but that it has a Gaussian shape. In a typical experiment images are recorded as a kinetic series, as in the case of Fig. 9 with a rate of 10 frames/s, if the camera system allows without any dead times.7 4. Applications We now proceed with the discussion of some selected applications of singlemolecule detection at surfaces. Our selection will be by no means complete but only reﬂects a tiny part of the actual work done. Wherever possible we will give references to the original literature. 4.1. Single emitter photon emission statistics The temporal pattern in which photons emitted by a single emitter are detected, reﬂects the complete information on the relevant transition rates 7 Frame-transfer

cameras move the image quickly to a protected area on the CCD chip where it can be read out while the next image is recorded.

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characterizing the emitter introduced in Fig. 1. This can be seen as follows. Imagine that the molecule initially resides in the ground state. This can be made sure simply by waiting until a ﬂuorescence photon has been emitted. Now, the molecule has to be re-excited. The time this takes is the inverse excitation rate k12 which depends on the excitation intensity I and −1 the molecule the cross-section σ [see Eq. (4)]. Eventually, after a time k12 will be in the excited state 2. There are three possibilities for the further development: the molecule can either decay nonradiatively to the ground state, which means that no photon would be emitted until the next excitation, or the molecule could undergo intersystem crossing to the triplet state, which means that no photon is emitted until the molecule returns to the singlet ground state and is re-excited again. Fortunately, for good ﬂuorophores both of these events only occur with a small probability and in most of the cases molecules in the excited state decay by emission of a photon after a time on the order of the excited state lifetime that has passed. The resulting pattern of photon arrival times is sketched in Fig. 10(a).

Fig. 10. Photon arrival time statistics of single emitters. (a) Schematic description of the temporal structure of single-emitter emission. (b) Simulated timetraces for diﬀerent intersystem crossing rates as indicated. (c) Start-stop measurement yielding and anticorrelation, so called antibunching, at zero delay (the oﬀset is due to diﬀerent lengths of cables for both detectors). (d) Same measurement for pulsed excitation. Thick line: Single emitter with missing peak at zero time delay. Thin line: scattered laser light signal for comparison.

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Confocal microscopy has the distinct advantage that it can be used to isolate the emission of a single emitter and detect the time course of the photons being emitted with a time resolution only limited by the detector dead time. If the usual single detector is replaced by a suitably arranged pair of detectors, then the time resolution, as we will see, becomes virtually unlimited. There are two possibilities to record so-called emission time traces of single emitters: (i) the number of detected photons per time interval can be recorded for successive intervals thus forming a continuous account of the momentarily emitted photon ﬂux, a so-called time trace, (ii) the individual photon arrival times may be stored with high precision. 4.1.1. Time trace analysis Examples of typical (simulated) time traces are shown in (b) for slightly diﬀerent intersystem crossing parameters as indicated in the ﬁgure caption. The qualitative diﬀerence in their general appearance is striking. Quantitative information can be gained by creating histograms of the duration of the ‘on-times’ as well as histograms for the duration of the ‘oﬀ-times’. Both will exhibit an exponential decaying probability for the occurrence of very long on- or oﬀ-times. An exponential ﬁt of the on-time histogram to a good approximation yields the branching ratio k23 /k21 of the probabilities in the excited state, whereas the ﬁtting of the oﬀ-time histogram directly yields −1 . For application examples see [44,45]. the inverse triplet relaxation rate k31 Similar information can be extracted by calculating the autocorrelation function of time traces [19,20]. 4.1.2. Arrival time analysis A topic of recent interest is the generation of triggered sources of single photons for applications in quantum cryptography and quantum information processing. Interestingly, a single emitter, like a molecule, does nothing else but emit single photons one at a time, with a zero probability of emitting two photons at the same time. This feature can be very nicely visualized by plotting the histogram of interphoton times which can be readily generated if accurate arrival times are stored for each photon [43] or by performing start-stop measurements [46]. A two-detector setup is necessary in both cases. Figure 10(c) shows the dip towards zero in the histogram of interphoton times, the so-called antibunching dip, which proves that there is only a single emitter in the detection volume. To exploit this behavior to build a source for single photons on demand, pulsed excitation using a pulsed laser

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is usually employed. Figure 10(d) shows the eﬀect of pulsed excitation on the shape of the histogram of interphoton times. Now the observed interphoton times are grouped in bunches separated by the laser repetition rate. However, since the same single molecule cannot be excited twice during the same laser pulse, which is short compared to the excited-state lifetime, the peak at zero time delay is missing. This observation together with the occurrence of peaks in the histogram of interphoton times qualiﬁes a single emitter as a triggerable source of single photons [5,6,47]. 4.2. Single-emitter probes and labels 4.2.1. Single-emitter probes Single emitters may be used as probes for their immediate nano environment. At cryogenic temperatures, where the molecular zero-phonon absorption lines are narrow, this becomes immediately evident in a molecular property called spectral diﬀusion. Here, tiny rearrangements of molecules or pairs of molecules in the immediate neighborhood of a probe molecule lead to signiﬁcant shifts of its zero-phonon line. These shifts can be probed by narrow band tunable lasers thus allowing us to observe molecular scale dynamic processes [19]. While spectral diﬀusion is most prominent at cryogenic conditions, another example of a single-molecule property that is inﬂuenced by the environment is the excited-state lifetime. Changes in the excited-state lifetime can be understood in terms of the opening or closing up of decay channels for the molecule, e.g. by the presence or absence of an energy acceptor in the molecules near-ﬁeld [48] or by a modiﬁed available density of states or ﬁeld modes that a ﬂuorescence photon can be emitted into [49]. One particular example is lifetime variations of single molecules close to a dielectric interface. Here, both the distance to the interface and the relative orientation of the molecules emission dipole play an important role. The behavior is summarized in Fig. 11(a). In a Gedanken experiment a molecule is moved from the air side far away from the interface, to close to the interface and then into the glass. The normalized decay rate of the emitter is plotted for both fundamental dipole orientations, parallel and perpendicular to the interface. For large distances to the interface the decay rate is largely independent of the orientation. The limiting values on both sides are in accordance with the diﬀering dielectric constants of air and glass. However, when the emitter comes close to the interface, deviations between the two orientations become obvious. In particular, for the perpendicular dipole, the decay rate jumps from a large value outside the interface to a

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Fig. 11. Environment-dependent single-emitter excited-state lifetimes. (a) Calculation of the decay rates of a single emitter at variable distance to the interface for parallel and perpendicular orientation of its dipole moment. (b) Annular illumination SCOM images for two orthogonal polarizations revealing the orientation of single emitter dipoles embedded in thin ﬁlm of PMMA. (c) Examples of two ﬂuorescence decays for circled spots A and B in (b). For more details see [50].

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small value inside.8 On the other hand, for the parallel dipole, the transition between the two limiting decay rates is continuous. As a matter of fact, inside a thin layer close to the interface there is a pronounced diﬀerence in lifetime between the two orientations which can be observed if molecules are placed inside a thin layer of PMMA which has the same refractive index as glass. The expected diﬀerence in decay rate can be measured by directly exploiting the depolarization ﬁeld patterns obtained by annular illumination. To do this, we have to ﬁrst identify molecules with dipoles parallel to the interface and perpendicular to the interface. Both can be recognized by very speciﬁc image patterns, a four-lobed pattern in the ﬁrst case and a two-lobed pattern in the second case. Figure 11(b) shows SCOM images with annular illumination where two molecules with pure orientations have been marked. Figure 11(c) shows the respective ﬂuorescence decays which were obtained by time-correlated single photon counting. The expected difference in decay rates is clearly recovered. These results show the sensitivity of single emitters on environmental factors such as the presence of inhomogeneities in the immediate environment.

4.2.2. Single-emitter labels Another important application of single emitter detection is to use them as minimally invasive labels. The human and several other eukaryotic and prokaryotic genomes have now been completely sequenced, and the mechanisms that translate a gene into a protein are largely understood at atomic detail. We also know much about the structure and function of membranes and proteins that make up a living system. What remains an enormous challenge, however, is how these diﬀerent parts interact with each other and how these interactions lead to the complex function we observe in living organisms. Rising to this challenge will be at the core of future developments in biology and medicine. The emerging ﬁeld of ‘systems biology’ concentrates on answering these and similar types of questions. Wide-ﬁeld singlemolecule microscopy can be used to track the motion of single diﬀusing molecules in various environments with a time resolution down to a few ms [51–53] and a precision down to a few nm [54]. These abilities qualify single-molecule tracking to become a powerful tool to investigate molecular interactions in living systems, such as cells or bacteria.

8 Non-continuous

inﬁnitely sharp.

behavior follows from the fact that the boundary is assumed to be

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While it is easy to see that a high temporal resolution in imaging can be achieved by the use of an appropriate experimental apparatus, it is not so clear why the precision of determining the position of a single molecule should be a few nm although the diﬀraction limited resolution is only about half a wavelength. The explanation is however simple enough. If we need to determine the position of a luminescent spot in Fig. 9, we simply perform a nonlinear ﬁt of the spot to a two-dimensional Gaussian.9 The origin of the Gaussian determined from the ﬁt then deﬁnes the position of the molecule. If there was no noise in the data, the precision at which we can determine the origin is unlimited. The presence of noise introduces an uncertainty that limits the precision [55,56]. This precision, however, does not allow us to distinguish nearby identical molecules. Based on this principle various applications of single-molecule tracking in living organisms have been demonstrated. Most of the applications track the diﬀusion of dye-labeled lipids or proteins in the cell membrane [51–53]. Others follow the motion of dye labeled particles inside the body of the cell [57]. If diﬀerently labeled structures can be followed at the same time, then interactions can be observed by means of dual-color co-localization [55,56]. The latter is not only of interest for the probing of protein-protein interactions in living organisms but also for the evaluation of ultrasensitive assays at the single molecule level [9]. Figure 12 shows an example of data obtained by tracking the motion of individual G-protein coupled receptors marked by a ﬂuorescently labeled ligand [47] in the membrane of living HEK cells overexpressing the receptor. A setup very similar to the one in Fig. 8 was used. The top of Fig. 12 shows sub-areas of larger images that contain a selected protein. The sub-areas were extracted from a movie recorded at a rate of 10 frames/s. The singlemolecule ﬂuorescence spots are ﬁtted within the sub-areas as described above, yielding the position and its uncertainty along with several other parameters, such as local background and the signal amplitude. The ﬁrst two parameters can be used to reconstruct the trajectory of the protein in the cell membrane (see Fig. 12, inset). The spot shape and size is related to the uncertainty of the position determination. From a trajectory as the one shown in Fig. 12, it is possible to determine the mean square displacement 9 To

be precise, we would have to ﬁt an Airy pattern to account for the correct shape of the spot. It turns out, however, that usually in tracking applications signal-to-noise ratio is sacriﬁced with respect to increased time resolution. Hence, usually the diﬀerence of the ﬁtting quality between an Airy pattern and a Gaussian is negligible while the latter is much easier to handle.

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Fig. 12. Imaging of a single-chromopore labeled G protein coupled receptors diﬀusing in the membrane of a living HEK cell. The plot shows the mean square displacement (MSD) vs. time interval for a typical protein trajectory. The error bars: standard deviation of the MSD for each time interval. Top: Fluorescence spots recorded at 100 ms intervals (raw data). Resulting diﬀusion trajectory obtained from Gaussian ﬁts is shown as inset. The spot sizes in the trajectory represent the uncertainties of the position of each spot. Each ﬂuorescence image at the top has a dimension of 1.67×1.67 µm2 and is a sub-image taken from a larger image of a whole cell. Only the ﬁrst 20 images are shown. From [47].

of the diﬀusing protein as a function of the time interval. For the particular case shown here a conﬁned diﬀusion is observed for longer times. 5. Conclusion Now we have come a long way, but have by no means reached the end. In particular, in the ﬁeld of biological sciences and quantum information technology, the number of single emitter experiments is exploding. What we have covered here is but a small part of the extensive literature that exists. However, we hope to have conveyed some basic and important insights to the reader. We have seen that the detection of single emitters is (easily) possible using conventional optical microscopy techniques in combination with dedicated detection devices. We have discussed the basic theoretical approach that allows us to assess the signal size and saturation behavior of single emitters. We have seen how the internal structure of the emitter can inﬂuence the time pattern in which single photon emission takes place. Finally, we have seen how the environment can inﬂuence the properties of a single emitter. Being aware of these factors, we introduced the application of single emitters as labels with special emphasis on tracking experiments

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in complex (living) systems. For those who wish to get a deeper insight into the technique we recommend the cited reviews and books for further reference. Acknowledgments The author is grateful to H. J. G¨ untherodt for continuous support and to D. W. Pohl for inspiration and friendship. Furthermore, helpful discussions are acknowledged with H.-J. Eisler, A. Lieb, Y. Lill, J. Y. P. Butter, J. N. Farahani, S. Karotke, M. Kreiter, P. M¨ uhlschlegel, and J. Toquant. Financial support by the Swiss National Science Foundation via the National Center of Competence in Research (NCCR) in Nanoscale Science and a professorship for the author is gratefully acknowledged. References [1] E. Schr¨ odinger, Are there quantum jumps? Brit. J. Philos. Sci. 3, 109 (1952). [2] D. Leibfried, R. Blatt, C. Monroe and D. Wineland, Quantum dynamics of single trapped ions, Rev. Mod. Phys. 75, 281 (2003). [3] T. Stievater, X. Li, D. Steel, D. Gammon, D. Katzer, D. Park, C. Piermarocchi and L. J. Sham, Rabi oscillations of excitons in single quantum dots, Phys. Rev. Lett. 87, 133603 (2001). [4] X. Li, Y. Wu, D. Steel, D. Gammon, T. Stievater, D. S. Katzer, D. Park, C. Piermarocchi and L. J. Sham, An all-optical quantum gate in a semiconductor quantum dot, Science 301, 809 (2003). [5] P. Michler, A. Kiraz, C. Becher, W. Schoenfeld, P. Petroﬀ, L. Zhang, E. Hu and A. Imamoglu, A quantum dot single-photon turnstile device, Science 290, 2282 (2000). [6] B. Lounis and W. E. Moerner, Single photons on demand from a single molecule at room temperature, Nature 407, 491 (2000). [7] W. Trabesinger, A. Renn, B. Hecht, U. P. Wild, A. Montali, P. Smith and C. Weder, Single-molecule imaging revealing the deformation-induced formation of a molecular polymer blend, J. Phys. Chem. B 104, 5221 (2000). [8] T. Schmidt, G. Sch¨ utz, H. Gruber and H. Schindler, Local stoichiometries determined by counting individual molecules, Anal. Chem. 68, 4397 (1996). [9] W. Trabesinger, B. Hecht, U. P. Wild, G. J. Sch¨ utz, H. Schindler and T. Schmidt, Statistical analysis of single-molecule colocalization assays, Angew. Chem. 73, 1100 (2001). [10] G. Binnig and H. Rohrer, Scanning Tunneling Microscopy, Helv. Phys. Acta 55, 726 (1982). [11] G. Binnig, C. F. Quate and C. Gerber, Atomic force microscope, Phys. Rev. Lett. 56, 930 (1986). [12] E. Heller, M. Crommie, C. Lutz and D. Eigler, Scattering and absorption of surface electron waves in quantum corrals, Nature 369, 4646 (1994).

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[13] T. A. Jung, R. R. Schlittler, J. K. Gimzewski, H. Tang and C. Joachim, Controlled room-temperature positioning of individual molecules: Molecular ﬂexure and motion, Science 271, 181 (1996). [14] J. Gimzewski and C. Joachim, Nanoscale science of single molecules using local probes, Science 283, 1683 (1999). [15] K. Rebane, Impurity Spectra of Solids (Plenum Press, New York, 1970). [16] W. E. Moerner, ed., Persistent Spectral Hole-Burning: Science and Applications, vol. 44 of Topics in Current Physics (Springer Verlag, Berlin, 1988). [17] W. E. Moerner and L. Kador, Optical detection and spectroscopy of single molecules in a solid, Phys. Rev. Lett. 62, 2535 (1989). [18] M. Orrit and J. Bernard, Single pentacene molecules detected by ﬂuorescence excitation in a p-terphenyl crystal, Phys. Rev. Lett. 65, 2716 (1990). [19] T. Basch´e, W. E. Moerner, M. Orrit and U. P. Wild, eds., Single–Molecule Optical Detection, Imaging and Spectroscopy (VCH Verlagsgesellschaft, Weinheim, 1997). [20] R. K. C. Zander and J. Enderlein, eds., Single–Molecule Detection in Solution (Wiley-VCH Verlag GmbH, Weinheim, 2002). [21] T. Plakhotnik, E. A. Donley and U. P. Wild, Single-molecule spectroscopy, Annu. Rev. Phys. Chem. 48, 181 (1997). [22] X. S. Xie and J. K. Trautman, Optical studies of single molecules at room temperature, Annu. Rev. Phys. Chem. 49, 441 (1998). [23] W. E. Moerner and M. Orrit, Illuminating single molecules in condensed matter, Science 283, 1670 (1999). [24] Ph. Tamarat, A. Maali, B. Lounis and M. Orrit, Ten years of single-molecule spectroscopy, J. Phys. C. 104, 1 (2000). [25] R. Loudon, The Quantum Theory of Light, Oxford Science Publications (Oxford University Press, Oxford, 1983). [26] B. Hecht, Nano-optics with single quantum systems, Proc. R. Soc. Lond. A 362, 881 (2004). [27] E. Betzig and R. Chichester, Single molecules observed by near-ﬁeld scanning optical microscopy, Science 262, 1422 (1993). [28] B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin and D. W. Pohl, Scanning near-ﬁeld optical microscopy with aperture probes: Fundamentals and applications, J. Chem. Phys. 112, 7761 (2000). [29] J. Veerman, M. Garc´ıa-Paraj´ o, L. Kuipers and N. van Hulst, Single molecule mapping of the optical ﬁeld distribution of probes for near-ﬁeld microscopy, J. Microsc. 194, 477 (1999). [30] K. Karrai and R. Grober, Piezoelectric tip-sample distance control for near ﬁeld optical microscopes, Appl. Phys. Lett. 66, 1842 (1995). [31] H. Bethe, Theory of diﬀraction by small holes, Phys. Rev. 66, 163 (1944). [32] C. J. Bouwkamp, On Bethe’s theory of diﬀraction by a small hole, Philips Res. Rep. 5, 321 (1950). [33] R. X. Bian, R. C. Dunn, X. S. Xie and P. T. Leung, Single molecule emission characteristics in near-ﬁeld microscopy, Phys. Rev. Lett. 75, 4772 (1995).

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[34] H. Gersen, M. Garcia-Paraj´ o, L. Novotny, J. Veerman, L. Kuipers and N. van Hulst, Inﬂuencing the angular emission of a single molecule, Phys. Rev. Lett. 85, 5312 (2000). [35] H. Frey, S. Witt, K. Felderer and R. Guckenberger, High-resolution imaging of single ﬂuorescent molecules with the optical near-ﬁeld of a metal tip, Phys. Rev. Lett. 93, 200801 (2004). [36] J. N. Farahani, D. W. Pohl, H.-J. Eisler and B. Hecht, Single quantum dot emitter coupled to a scanning optical antenna: A tunable superemitter, Phys. Rev. Lett. 95, 017402 (2005). [37] A. Hartschuh, E. S´ anchez, X. Xie and L. Novotny, High-resolution near-ﬁeld Raman microscopy of single-walled carbon nanotubes, Phys. Rev. Lett. 90, 095503 (2003). [38] D. Pohl, Near ﬁeld optics seen as an antenna problem, in Near-Field Optics: Principles and Applications, M. Ohtsu and X. Zhu, eds. (World Scientiﬁc, Singapore, 2000), pp. 9–21. [39] R. Webb, Confocal optical microscopy, Rep. Prog. Phys. 59, 427 (1996). [40] J. Pawley, ed., Handbook of Biological Confocal Microscopy 2nd edn. (Plenum Press, New York, London, 1995). [41] L. Novotny, E. Sanchez and X. Xie, Near-ﬁeld optical imaging using metal tips illuminated by higher-order Hermite-Gaussian beams, Ultramicroscopy 71, 21 (1998). [42] B. Sick, B. Hecht, U. P. Wild and L. Novotny, Probing conﬁned ﬁelds with single molecules and vice versa, J. Microsc. 202, 365 (2001). [43] B. Sick, B. Hecht and L. Novotny, Orientational imaging of single molecules by annular illumination, Phys. Rev. Lett. 85, 4482 (2000). [44] C. G. H¨ ubner, A. Renn, I. Renge and U. P. Wild, Direct observation of the triplet lifetime quenching of single dye molecules by molecular oxygen, J. Chem. Phys. 115, 9619 (2001). [45] J. A. Veerman, M. F. Garcia-Parajo, L. Kuipers and N. F. van Hulst, Timevarying triplet state lifetimes of single molecules, Phys. Rev. Lett. 83, 2155 (1999). [46] R. H. Brown and R. Q. Twiss, Correlation between photons in two coherent beams of light, Nature 27, 4497 (1956). [47] Y. Lill, K. L. Martinez, M. Lill, B. H. Meyer, H. Vogel and B. Hecht, Kinetics of the initial steps of G-protein coupled receptor mediated cellular signaling revealed by single molecule imaging, Chem. Phys. Chem. 6, 1633 (2005). [48] L. Stryer and R. Haugland, Energy transfer: A spectroscopic ruler, Proc. Natl. Acad. Sci. USA 58, 719 (1967). [49] E. Purcell, Spontaneous emission probabilities at radio frequencies, Phys. Rev. 69, 681 (1946). [50] M. Kreiter, M. Prummer, B. Hecht and U. P. Wild, Orientation dependence of ﬂuorescence lifetimes near an interface, J. Chem. Phys. 117, 9430 (2002). [51] G. Harms, L. Cognet, G. Blab, P. Lommerse, H. Kahr, R. Gamsjger, H. Spaink, N. Soldatov, C. Romanin and Th. Schmidt, Single-molecule imaging of L-type Ca2+ channels in live cells, Biophys. J. 81, 2639 (2001).

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[52] W. E. Moerner, Optical measurements of single molecules in cells, Trends in Analytical Chemistry 22, 544 (2003). [53] P. H. M. Lommerse, G. A. Blab, L. Cognet, G. S. Harms, E. B. SnaarJagalska, H. P. Spaink and T. Schmidt, Single-molecule imaging of lipidanchored proteins reveals domains in the cytoplasmic leaﬂet of the cell membrane, Biophys. J. 86, 609 (2004). [54] A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman and P. R. Selvin, Myosin V walks hand-over-hand: Single ﬂuorophore imaging with 1.5-nm localization, Science 300, 2061 (2003). [55] L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, in press, 2005). [56] T. Lacoste, X. Michalet, F. Pinaud, D. Chemla, A. Alivisatos and S. Weiss, Ultrahigh-resolution multicolor colocalization of single ﬂuorescent probes, Proc. Natl. Acad. Sci. USA 97, 9461 (2000). [57] G. Seisenberger, M. U. Ried, T. Endress, H. B¨ uning, M. Hallek and C. Br¨ auchle, Real-time single-molecule imaging of the infection pathway of an adeno-associated virus, Science 294, 1929 (2001).

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PART III THEORETICAL METHODS

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AB INITIO MODELING OF MOLECULAR ELECTRONICS DAN ROUBTSOV, NIKOLAI SERGUEEV and HONG GUO Center for the Physics of Materials and Department of Physics McGill University, Montreal, P.Q., Canada H3A 2T8 Abstract. In this Chapter, we review a state-of-the-art theoretical formalism for modeling quantum transport properties of molecular scale conductors. The formalism is based on carrying out density functional theory (DFT) analysis within the Keldysh non-equilibrium Green’s function (NEGF) framework. It allows predictions of nonlinear and nonequilibrium charge transport through nano-electronic devices without using phenomenological parameters. We present relevant details to the physical, mathematical, and numerical backgrounds of this formalism. An example will be given to illustrate the application of this technique. Keywords: Density functional theory (DFT); Green’s functions; Keldysh non-equilibrium Green’s functions (NEGF); linear combination of atomic orbitals (LCAO); tunnel junction; metal-fullerene-metal junction; density of states (DOS); transmission function; Landauer formula; renormalized molecular levels (RMLs); I-V curves.

Contents 0 1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Theoretical Formalism . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Open boundary conditions . . . . . . . . . . . . . . . . . . 1.2 Kohn–Sham Hamiltonian within Keldysh Green’s functions 1.3 Practical issues . . . . . . . . . . . . . . . . . . . . . . . . . 2 Au-C60 -Au Molecular Tunnel Junction . . . . . . . . . . . . . . . 3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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0. Introduction Using nano-scale conductors for electronic device application [1–3] has attracted intensive work in recent years, driven by the desire of achieving faster, cheaper, and more powerful electronic devices. In particular, using molecules as functional units of devices is a very interesting perspective and a possible goal of nano-electronics. Indeed, if the Si based microelectronic technology continues along the Moore’s law [4] of size scaling, individual devices will reach molecular scale in a not-too-distant future. It is believed that the micro-electronic technology at its present form will not function well at the nano-scale when quantum eﬀects become important. While hybrid micro-nano systems may provide some breathing room, it may not provide a fundamental solution. It is these requirements which drive the nano-electronics research to discover a fundamentally new device paradigm based on quantum phenomena. Impressive progress has been achieved in fabricating and understanding nano-scale systems, among many others the carbon nanotubes [5], fullerenes [6], molecular wires [1], switches [7], nanoscale magnetic systems [8], fabrication techniques based on massive selfassembly [9] and/or bio-technology [10]. Work in this ﬁeld has clearly demonstrated that many of the important molecular device characteristics relate speciﬁcally to a strong coupling between the atomic and the electronic degrees of freedom, i.e., microscopic details of a device play very important roles. These details have proved diﬃcult to control experimentally. Theoretical investigations are, therefore, useful in providing understandings to the device physics at nano-scale. In order to be predictive, a theory for molecular devices must include the relevant microscopics. In this regard, tight-binding (TB) models have provided very important contributions [11–15]. Nevertheless, a TB model involves phenomenological parameters which are diﬃcult to obtain, or whose validity is diﬃcult to determine. Hence a more fundamental theoretical framework that comes to mind is the density functional theory (DFT) [16,17]. In DFT, the quantum many-body physics involving a large number of N electrons which are coupled via Coulomb interaction, is treated within a mean ﬁeld theory where each electron is moving inside an eﬀective potential Veﬀ (r) produced by the other electrons. Namely, instead of solving an N -body problem, DFT solves N one-body problems. Because DFT solves quantum mechanic model including all atomic details, it has been applied to many diﬀerent problems to predict structural and mechanical properties of materials, optical and electronic properties of matter, molecular modeling in chemistry, biological and drug-design applications, etc.

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When attempting to apply DFT to model nano-electronic devices, one has to solve some new problems not confronted before. Recall that most of the previous DFT-based simulations [18,19] solve two types of problems: (i) ﬁnite systems such as isolated molecules and clusters; and (ii) periodic systems consisting of super-cells. On the other hand, a molecular electronic device is neither ﬁnite nor periodic. Typically, it has open boundaries which are connected to long and diﬀerent electrodes extending to electron reservoirs far away, and external bias potentials are applied to these reservoirs. In other words, calculations of ﬁnite or periodic systems do not include the correct transport boundary conditions necessary for device modeling. It is also important to realize that when there is a current ﬂow driven by a bias voltage, the system is in a non-equilibrium state. Therefore, in device modeling we are dealing with an open boundary problem in non-equilibrium. There have been several DFT based approaches for transport modeling, including combining DFT with the Lippmann–Schwinger scattering equation [20–22]; combining DFT with the transfer matrix solution of the scattering states [23,24]; combining DFT with equilibrium Green’s functions [25,26]; and ﬁnally, combining DFT with the Keldysh non-equilibrium Green’s functions (NEGF) [27–34]. In this Chapter, we focus on the theoretical and practical issues of the NEGF-DFT technique which is very powerful in predicting nonlinear and non-equilibrium transport properties of molecular devices involving as many as several hundred atoms in the device scattering region. As an example, we apply the NEGF-DFT approach to investigate a C60 molecule connected to two gold electrodes. The rest of this Chapter is organized as follows. In Sec. 1, we discuss the NEGF-DFT formalism in detail. In Sec. 2, the transport properties of an Au-C60 -Au tunnel junction is investigated. Section 3 is reserved for a short summary, and some technical details are given in Appendix.

1. Theoretical Formalism We consider a model of a two-probe molecular device which is schematically shown in Fig. 1 where a C60 molecule is contacted by two semi-inﬁnite gold electrodes [35,36]. One can replace the C60 by other molecules, atomic clusters, thin ﬁlms, semiconductors, and other materials. The theoretical formalism for dealing with such a molecular device is the NEGF-DFT which has two diﬀerent kinds of implementations. The implementation in [27,32,33] adopts a cluster approach in which the device scattering region (called “extended molecule”) is calculated within DFT while the device leads are treated within tight-binding models. The main

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Fig. 1. Schematic plot of a molecular electronic device in the Metal-Molecule-Metal conﬁguration. The device consists of a scattering region connected to external sources through metallic leads. The scattering region (the extended molecule) contains the molecule and several layers of the metal leads. The molecule is placed between lines 2 and 3, the metal layers of the scattering region are placed between lines 1 and 2, and 3 and 4. The leads extend to reservoirs at z = ±∞ of the horizontal axis. The leads to the left of line 1 and to the right of line 4, are maintained at constant electro-chemical potentials µL and µR , respectively. A current ﬂows through such a device if µL − µR = eVb where Vb is the voltage bias. A gate voltage may be applied to the device by a metal gate capacitively coupled to the scattering region.

advantage of this approach is the usage of well-tested quantum chemistry codes for DFT. The main disadvantages are the artiﬁcial surface eﬀect due to the connection of TB leads to the extended molecule, as well as the possible incompatibility of the TB parameters and DFT. Such problems can be reduced if a very large extended molecule is included in the DFT analysis; this has not yet been done due to the large computational eﬀort that is required. The other implementation of the NEGF-DFT, reported in [30,31,34], deals with atoms in the scattering region and in the leads on equal footing, thereby without the artiﬁcial surface problem mentioned above. We will focus on this implementation in the rest of this Chapter. To calculate the electronic states of such devices, two problems should be solved. First, the inﬁnitely large problem (due to the electrodes) must be reduced to a ﬁnite one which is manageable on a computer. This means that one has to solve an open boundary problem. Second, within DFT, one needs to ﬁnd charge density ρ(r) of the molecule and electrodes under a bias voltage across the open device. We will assume that µL − µR is not

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very large so that we can treat such density ρ(r) as a perturbed ground state density, i.e., we can disregard the contribution of excited many-body electronic states when calculating current ﬂow. The vibrational quanta can however be excited at small µL −µR = 0, but these processes can be treated within the NEGF-DFT formalism [37] presented here, although we will not include its discussion in this Chapter. Furthermore, we assume that strong bonding between the molecule and the metal gives rise to large charge ﬂuctuations in the scattering region so that Coulomb Blockade eﬀect [38] is irrelevant and the DFT mean ﬁeld analysis is adequate. From the computational point of view, it is convenient to divide a system into three parts: a scattering region (a molecule plus some portions of electrodes) and two metal electrodes. This is shown by the vertical lines in Fig. 1, and these three parts constitute a total computation box. Although the electrodes are inﬁnitely long, extending to z = ±∞, they are consisted of repeated unit cells which are ﬁnite. The electrodes in Fig. 1 have a ﬁnite cross section in the lateral plane (x, y) so that it is more like a quasi-1D quantum wire with a sub-band structure in its energy spectrum, ε = εα (kz ) where α is a band index. Another electrode model is represented by an inﬁnitely large slab of atoms arranged in a crystalline structure, and ε = εα (kz , k⊥ ). Such a model can be analyzed using a super-cell technique in the (x, y) direction [31] if images of the molecules are far apart so that they do not interact. 1.1. Open boundary conditions How can one reduce the inﬁnitely large open device system into one that can be computed? The solution is to treat the transport open boundary condition properly. It was discovered in [30] that for a molecular device, the eﬀective Kohn–Sham (KS) potential [39] Veﬀ [ρ(r)] = VH [ρ(r)] + Vxc [ρ(r)] deep inside the semi-inﬁnite left (or right) lead is very close to the corresponding bulk KS potential of the inﬁnite left (or right) lead. Here VH is the electrostatic Hartree energy and Vxc the exchange-correlation energy. This is approximately true due to an eﬀective screening by the metal layers so that electronic states deep inside a lead are not inﬂuenced by the molecule. This “screening” approximation makes it possible to write the boundary conditions in the following form [30,31]:   Vl,eﬀ (r) = Vl,bulk (r), z ≤ zl , (1) Veﬀ (r) = Vc,eﬀ (r), zl ≤ z ≤ zr ,   Vr,eﬀ (r) = Vr, bulk (r), z ≥ zr ,

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where the planes z = zl (r) are the left (right) limits of the scattering region (see Fig. 1). Note that Vl, bulk (r) and Vr, bulk (r) can be computed by conventional DFT solutions of periodic structure because the leads are assumed to be perfect solids. Once Vl, bulk (r), Vr, bulk (r) are calculated, they serve as the boundary conditions according to Eq. (1). In practice, within DFT one only needs to match the Hartree potential UH = eVH at the boundaries [30]. This can be accomplished by solving a Poisson equation for UH (r) inside the scattering region, zl < z < zr , with the “bulk” boundary condition in the same form as Eq. (1). Once the Poisson equation is solved this way, one can show that Veﬀ (r) will be matched [30] perfectly at the boundaries, i.e., Eq. (1) is satisﬁed. Importantly, when Veﬀ (r) is matched across the boundaries, the charge density ρ(r) is automatically matched. A plot of such a matching can be found in [30]. When there is a bias potential Vb applied to a lead, we simply shift the lead’s Hartree potential by Vb before carrying out the matching procedure; this is justiﬁed because a metal lead can be considered equalpotential. On a technical note, one can eﬃciently solve the 3D real space Poisson equation using a multi-grid method. The real space solution, in addition to handling the leads which may or may not be formed with the same material (e.g. left lead is a gold wire and right lead is a nanotube), also allows the application of a gate voltage Vg through an additional electrostatic boundary condition. The screening approximation discussed here is such that one neglects any inﬂuence the scattering region might give to the leads. If the portion of leads included inside the scattering region is long enough, such an approximation is well controlled. On the other hand, the semi-inﬁnite leads do contribute to the potential of the scattering region; this is handled by the self-energies in the Green’s function of the scattering region (see below).

1.2. Kohn–Sham Hamiltonian within Keldysh Green’s functions In order to determine the KS Hamiltonian of the molecular device, one needs to calculate charge density in non-equilibrium. This is accomplished by the Keldysh non-equilibrium Green’s functions (NEGF). The advantages of using NEGF to construct density are at least three-fold. First, NEGF treats bound states and scattering states on equal footing. Second, the analytical properties of NEGF give great eﬃciencies in numerical computation. Third,

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NEGF naturally takes care of the non-equilibrium transport conditions. These advantages are crucial for any practical application. We begin by recalling the conventional method for constructing charge density in DFT. One starts by solving the well-known Kohn–Sham equation [39]: ˆ KS [ρ]|Ψs = Es |Ψs , H

Ψs |Ψs = δss ,

(2)

ˆ KS [ρ] is the KS Hamiltonian, where H ˆ KS [ρ] = H0 + Vps + VH + Vxc . H

(3)

Here H0 is the kinetic energy operator of valence electrons; Vps is the pseudopotential [40,41] which deﬁnes the atomic core. VH = eUH (r) is the Hartree energy which satisﬁes the Poisson equation ∆r UH (r) = −4πeρ(r) with proper boundary conditions as discussed in the previous subsection. The last term is the exchange-correlation potential Vxc [ρ] which is a functional of the density. Many forms of Vxc exist and we use the simplest one which is the local density approximation [42] (LDA). One may also consider the generalized gradient approximation (GGA) [43,44] which can be implemented for transport calculations without too much diﬃculty [45]. ˆ KS Importantly, a self-consistent solution of Eq. (2) is necessary because H is a functional of the charge density ρ. One constructs ρ from the KS states ∞ ρ|r = s=1 ns |Ψs (r)|2 , where ρˆ is the density matrix, Ψs , ρ(r) = r|ˆ ρˆ =

∞

ns |Ψs Ψs |,

(4)

s=1

and ns is the occupation number of the KS state Ψs at zero temperature. In ˆ KS · · · until ˆ KS → ρ → H practical calculations, one iterates the cycle ρ → H ˆ KS . numerical convergence. Physical quantities are then obtained from H These DFT details can be found in standard text books [39]. For open device problems, a part of the summation in (4) becomes integration over energy: because the scattering states are continuum states. Such an energy integral is very diﬃcult to do numerically due to the many van Hove singularities in the continuum density of states (DOS) [30,31]. For instance, when there is a sharp resonance in a scattering state at some energy, a very ﬁne energy mesh must be used in the energy integration. For molecular devices, there are indeed many resonances due to the molecule as well as the electronic structure of the leads. Furthermore, the bound states are also very diﬃcult to calculate for open systems [30], and they become

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almost impossible to be found if they happen to sit in continuum.a For these reasons, Eq. (4) is not the way to go for transport calculations. An alternative way to compute density matrix is to use NEGF. ˆ KS [ρ], Recall that quantum mechanics of the stationary Hamiltonian H Eq. (2), can be solved equally well through the so-called retarded (R) and advanced (A) Green’s functions, GR and GA . Using an appropriate basis set {φµ }, GR is calculated by inverting the Hamiltonian matrix: −1 GR (E) = (E + i0+ )I − HKS , where I is the identity matrix, 0+ is a positive inﬁnitesimal, and HKS ˆ KS |φν . The is the Hamiltonian matrix whose elements are Hµν = φµ |H advanced Green’s function is obtained by GA (E) = GR † (E). In addition, Green’s function formalism provides a very useful and powerful tool for calculating observables in many-particles systems [46], and in particular, it can be combined with DFT for analyzing molecular electronic devices [30] which we now describe. For a device structure, the Hamiltonian matrix HKS is “inﬁnitely” large because the device leads are “inﬁnitely” long. But using the screening approximation [30] discussed in the previous subsection, the inﬁnitely large Hamiltonian matrix is reduced to a ﬁnite one deﬁned inside the scattering region. The contribution due to the semi-inﬁnite leads to the electronic structure of the scattering region, is included through a quantity called “self-energy”. Therefore, for transport problems the Green’s function becomes [47] R −1 , (5) GR (E) = EI − HKS − ΣR l − Σr where HKS is now a ﬁnite matrix deﬁned in the device scattering region, R(A) and Σl(r) is the retarded (advanced) self-energy of the left (right) lead. For semi-inﬁnite leads with a periodic lattice structure, the self-energy can be calculated exactly within DFT using a number of techniques [48–50], and is related to the “surface” Green’s function of the leads. Some details of the derivation of Eq. (5) are contained in the Appendix. The self-energy matrix is also a ﬁnite matrix because only a ﬁnite number of atoms in the leads will interact eﬀectively with those atoms inside the scattering region. Therefore all the matrices on the right-hand side are ﬁnite, and GR can be computed by matrix inversion. The power of Green’s function theory can a A bound state can sit in continuum if its wavefunction is orthogonal to that of the electrodes.

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be made even clearer by noting that the interaction of the electrons inside the scattering region with other physical factors, such as phonons, can also be cast into the form of a self-energy [37]. For equilibrium problems, the imaginary part of the retarded Green’s function determines the charge density ρ [46]. For transport problems, ρ(r) can still be computed by Green’s functions — the Keldysh non-equilibrium Green’s functions [51]. The formula is [51]: ∞ 1 dE G< (E), where G< (E) = GR (E) Σ< (E) GA (E). (6) ρˆ = 2πi −∞ Here G< (E) is the NEGF, Σ< (E) is the lesser self-energy, and charge density is calculated as a trace to the density matrix ρ(r) = r|ˆ ρ|r. In Eq. (6), Σ< can be easily evaluated within mean ﬁeld theory such as DFT, Σ< (E) = ifL (E, µL )Γl (E) + ifR (E, µR )Γr (E), where fL(R) (E) is the Fermi distribution function of the left (right) leads. The quantities Γl,r describe coupling strength between the leads and the scattering region. They are related to the self-energies of the leads [47,51], A A Γr (E) = i ΣR Γl (E) = i ΣR l (E) − Σl (E) , r (E) − Σr (E) , R† < is not a simple Fermi distriwhere ΣA l(r) (E) = Σl(r) (E). Note that Σ bution: it is a linear combination of the Fermi functions of the two leads, reﬂecting the non-equilibrium nature of the transport problem. Indeed, in general the chemical potentials of the leads µL = µR and a current are ﬂowing through, i.e., the scattering region is in a non-equilibrium state. We emphasize that the density matrix calculated from Eq. (6) is equivalent to that from Eq. (4), but Eq. (6) is much easier to compute for open systems. To see why this is so, let us consider zero temperature and assume µL − µR = eVb > 0. Then, in the energy range −∞ < E < µR the Fermi functions fL = fR = 1. Because the Fermi functions are equal, no information about the non-equilibrium statistics exists and the NEGF must reduce to the equilibrium Green’s function GR . In the range µR < E < µL , fL = fR and NEGF must be used in Eq. (6). A more careful mathematical manipulation shows that this is indeed true [30], and Eq. (6) can be written as a sum of two terms: µL 1 1 µR R dE Im G (E) + dE GR (E)Γl (E)GA (E). (7) ρˆ = − π −∞ 2π µR

The ﬁrst integral, which has the largest integration range, is easy to calculate even though there are many van Hove singularities in the integrand.

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This is because the poles (the singularities) of GR , which come from bound states or scattering states, are on the real energy axis or in the lower half of the complex energy plane [46]. Hence the integral can be completed by a contour (see next subsection). The second integral still has to be done directly along the real energy axis, but its integration range is small and this usually does not pose a very large numerical problem. Finite temperature can also be included by slightly altering the integration limits in Eq. (7), namely by adding a few temperature scales to the limits. In the NEGF-DFT formalism, Eq. (7) is used to calculate the density matrix ρˆ, then the usual ˆ KS · · · is numerically iterated until convergence. ˆ KS → ρ → H cycle ρ → H

1.3. Practical issues Practically, in order to calculate the Green’s function from Eq. (5) by matrix inversion, one must control the size of the matrix. If one uses large basis sets such as planewaves, the matrix becomes too large to invert. Hence it is most convenient to use a minimal {s, p, d, . . .} LCAO (linear combination of atomic orbitals) basis set [19]. The LCAO basis, denoted by {φµ (r)}, corresponds to the valence eigenstates of an isolated atom where µ = s, p, d , . . . . Extensive research has been devoted [19] in generating small basis sets which can give reasonably accurate results. In the NEGFDFT formalism, all operators — Hamiltonian, density matrix, self-energies, Green’s functions, electronic wavefunctions, etc., are all expanded in terms of {φµ (r)}. For example, the scattering wavefunction of a molecular device can be constructed as Ψ(r) = j,µ Ajµ φµ (r − Rj ), where Rj is the position of the jth atom in the device. The coeﬃcient Ajµ can be calculated by the KS Eq. (2) after the KS Hamiltonian has been obtained from the NEGFDFT iterations. Since this is a non-orthogonal basis, the overlap matrix Sjµ;kν = φjµ |φkν = δjk , and it is a function of the distance Rj − Rk . With the non-orthogonal basis, the identity matrix I in Eq. (5) should be replaced by the overlap matrix S. One can also conﬁrm that the linear dimension of the matrix in Eq. (5) is equal to the number of atoms in the device scattering region multiplied by the number of basis functions in the set {φµ (r)}. ˆ KS |φν , i.e., the Within the LCAO basis, one can construct Hµν = φµ |H Hamiltonian matrix of the device scattering region. By inverting a matrix according to Eq. (5), one obtains the retarded Green’s function matrix GR (E) for each energy E. The density matrix is then constructed using Eq. (7) by numerically integrating over E, and charge density is obtained

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as ρ(r) = ˆjµ;kν φµ (r − Rj )φν (r − Rk ) where the sum is over all jµ;kν ρ atoms in the device scattering region and its immediate neighborhood. In this procedure, a critical step is the energy integration in Eq. (7). As discussed in the previous subsection, a direct numerical computation is ineﬃcient as very large number of energy points are needed to ensure accuracy due to the poles of the Green’s functions (van Hove singularities). The problem is solved as follows. Because GR has no poles on the upper half complex energy plane, the ﬁrst term on the right-hand side of Eq. (7) can be computed by a contour integration very eﬃciently, namely µR dE GR (E) = dZ GR (Z), −∞

sc

where sc means a semi-circle in the upper half plane Z (see Fig. 2). This is because, along the complex contour, the integrand is very smooth without any singularity. Since the Green’s function GR can be constructed for any energy including complex energy, the contour integral trick can be easily applied. If one were to use wavefunctions to construct density matrix, as in Eq. (4), one would have to ﬁnd wavefunctions with complex energy in order to use this trick — a task impossible to accomplish in general. In practical implementations [30], the lower energy limit on the left-hand side of the last equation is replaced by a very large cutoﬀ Ec such that no states exists below Ec (Fig. 2). The contour integration trick drastically reduces the number of integration points. In practice, for scattering regions involving about a hundred atoms, ∼50 complex energies suﬃce to converge the integration. Finally, the second integral in Eq. (7) must still be calculated along the real energy axis. For small bias voltages (µL − µR = eVb 1 eV), the numerical convergence is easily obtained for most devices examined so far.

Fig. 2. Contour for integration in the complex energy plane Z. As any retarded Green’s function is analytic in the upper half-plane Z, the analytic continuation GR (E) → GR (Z), Re Z = E, and Im Z > 0 is well deﬁned. The semi-circle C and the real line (µR , µL ) are used to calculate ρˆ = dE G< (E)/2πi if µL − µR = eVb > 0.

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In the NEGF-DFT algorithm, the total number of valence electrons is ρS). Here the trace is over all the orbitals obtained by Ne = dr ρ(r) = Tr(ˆ included into the computation box. It is often useful to perform a Mulliken population analysis by representing Ne as a summation: Ne = Nj , where Nj = ρˆjµ;kν Skν;jµ . j:atoms

µ;kν

Nj can be interpreted as an average number of the valence electrons at atom j. In general one can expect Nj = NNA, j where NNA, j is the number of valence electrons in the neutral atom. Another useful quantity for analyzing molecular devices is the charge transfer to/from the molecule, i.e. the excess charge, which can be calculated as δQ = e j (Nj − NNA, j ) where j runs over atoms of the molecule. δQ is often a function of external voltages. When the molecule is in good covalent contact with the metallic leads, δQ is usually not even an integer. This means that the actual number of electrons in the molecule ﬂuctuates around an averaged value. One can interpret the integrand of Eq. (7) as the density of states of the scattering region. Such a DOS(E) often has many peaks at various energies E. The peaks mark the scattering states or quasi-bound states of the scattering region, and their origin can be investigated by the so-called Renormalized Molecular Levels and Orbitals (RMLs and RMOs) [52] as follows. After the KS matrix HKS is self-consistently determined, one digs out the sub-matrix from HKS that corresponds to the molecule and solves an eigenvalue problem: Hνµ ΨRMO = ERML Sνµ ΨRMO . (8) µ µ µ

µ

Here, again, the sum runs over the atoms of the molecule and ν, µ are their orbital quantum numbers, respectively. Obviously, the obtained eigenlevels and orbitals are diﬀerent from those of the free molecule because the interaction with the leads is taken into account in Eq. (8) through Hµν . The correspondence to the free molecule levels and orbitals can be found onto the orbitals of the free molecule. This way, the by projecting ΨRMO kµ terms “HOMO-derived” or “LUMO-derived” levels can be used for the corresponding groups of renormalized molecular levels. The NEGF-DFT method discussed above has been implemented in the simulation packages McDCal (McGill Device Calculator) [30] and Transiesta [31]. A similar package has also been implemented recently [34]. A ﬂowchart of the McDCAL package is shown in Fig. 3. In the ﬂowchart, the electrode calculation determines the potential of the leads which is later

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Fig. 3. The NEGF-DFT program ﬂowchart. The basic steps of computational procedure are shown schematically in this ﬁgure. To calculate HKS [ρ] and ρ(r) self-consistently, we use the Green’s function technique. In the block called “Analysis”, the transmission coeﬃcient and I-V curve of the scattering region are calculated.

used for matching the open device boundaries as discussed in Subsection 1.1; it also determines the self-energies as discussed in Subsection 1.2; ﬁnally it computes the Fermi energy F of the leads which is used as the Fermi energy of the equilibrium device. The electrode calculation solves a periodic problem of unit cells, and several hundred k-points are necessary to sample the Brillouin zone. After the electrode calculation is completed, one starts the self-consistent NEGF-DFT loop as shown in Fig. 3. Once a pre-speciﬁed convergence criterion is reached, one proceeds to the last box labeled “Analysis” in Fig. 3 where physical quantities are determined. For transport problems, the basic interests are the currentvoltage (I-V) curves and conductances. For coherent quantum conductors, one applies the Landauer formula [47,53], e I= h

dE T (E, Vb )[fL (E, µL ) − fR (E, µR )],

(9)

where the transmission coeﬃcient T (E, Vb ) describes the probability for an electron with energy E to traverse the device under a bias voltage Vb .

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T (E, Vb ) is determined by the Green’s functions [47,53]: T (E, Vb ) = Tr Γl GR Γr GA ,

(10)

where all quantities on the right are functions of energy E. At equilibrium, i.e., Vb = 0, the conductance of the device G is easily obtained from Eq. (9), G = Go T (εF ).

(11)

Here Go ≡ 2e2 /h is the quantum of conductance and the factor 2 is due to spin degree of freedom. The current determined by Landauer formula is the elastic current. Indeed, we did not include any interactions leading to inelastic transport channels into the Hamiltonian. 2. Au-C60 -Au Molecular Tunnel Junction As an example of the NEGF-DFT formalism discussed in the last section, we now report an analysis on the transport properties of an Au-C60 -Au molecular tunnel junction whose device structure is shown in the lower panel of Fig. 1. So far a considerable amount of eﬀort has been devoted to investigate transport properties of C60 and other fullerene molecules both experimentally [54–59] and theoretically [25,60–62]. However, to obtain a complete picture of the transport properties of such junctions, many details have yet to be clariﬁed, including how conductance and I-V curves depend on the lead material and geometry, and on the position and orientation of the C60 molecule. C60 tunnel junctions with Au leads have not been studied before. The device consists of a C60 molecule ﬁxed in the middle of two atomic scale gold leads, and the c2 symmetry axis of the molecule coincides with the horizontal axis (z-axis), see Fig. 1. Two distances between the electrodes are considered, 11.7 ˚ A and 13.7 ˚ A. They correspond to the minimum distance between an Au atom of the left (right) lead and a C atom of the C60 at 2.3 ˚ A and 3.3 ˚ A, respectively. Each electrode consists of repeated unit cells with nine Au atoms in the (100) direction and extended to z = ±∞. We do not consider the Coulomb blockade eﬀect because the C60 is strongly coupled to the electrodes at these small electrode separations. For the Au-C60 -Au junctions at Vb = 0, the density of states near the Fermi energy is presented in Figs. 4 and 5 (the Fermi level is shifted to εF = 0) as a function of energy. The DOS near εF is dominated by large and relatively sharp features which are shifted up or down in energy by a gate voltage. These sharp features in DOS result from the molecular states in the tunnel junction, and can be analyzed using the renormalized

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Fig. 4. Density of states of the Au-C60 -Au junction as a function of energy. The electrode separation is 11.7 ˚ A, bias voltage Vb = 0. The curves are for diﬀerent gate voltages. Solid line: Vg = 2.7 V; dashed line: Vg = 0 V; dash-dotted line: Vg = −2.7 V. Positions of the molecular levels (RMLs) of the C60 molecular junction are depicted over the peaks of the DOS(E), the triangles, circles, and squares correspond to Vg = 2.7 V, Vg = 0 V, and Vg = −2.7 V, respectively. These levels roughly align with the DOS peak, and are LUMO-derived states although the original LUMO degeneracy of a free C60 is lifted by the presence of the leads. Inset: the excess charge δQ (in units of e) inside the C60 versus gate voltage. At zero gate voltage, there is a net charge transfer from the leads to the C60 : for this system the equilibrium excess charge is ≈ 0.7 e. At Vg = 2.7 V, δQ ≈ e, and at Vg = −2.7 V, δQ ≈ 0.

molecular levels, see Eq. (8). These levels are indicated by the symbols on top of the DOS curves and reside near the DOS peak. Note that the RML analysis of Eq. (8) gives the energy levels with zero width, because these levels were obtained by diagonalizing a ﬁnite Hamiltonian matrix. When the molecule is contacted by leads, the scattering states acquire a ﬁnite width due to coupling to the leads, as indicated by the DOS curves. Hence, several RMLs may merge into one DOS peak. Recall that a free C60 has a ﬁlled HOMO (highest occupied molecular orbital) and an empty LUMO (lowest unoccupied molecular orbital), and the LUMO is a threefold degenerate level (six-fold with spin). Due to the presence of the Au leads, the level degeneracy can be lifted as shown by the several RMLs near the DOS peak. Our analysis indicates that these RMLs are largely LUMO-derived. The inset of Figs. 4 and 5 plots the excess charge δQ inside the C60 versus an applied gate voltage. Note that even at zero Vg , there is a ﬁnite amount

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Fig. 5. Density of states of the Au-C60 -Au junction versus energy, for electrode separation of 13.7 ˚ A, Vb = 0. The curves are for three diﬀerent gate voltages. Other system parameters are the same as in Fig. 4. Positions of the molecular levels are depicted over the peaks of DOS(E): the triangles, circles, and squares correspond to Vg = 2.7 V, Vg = 0 V, and Vg = −2.7 V, respectively. The degeneracy of the original LUMO level is removed due to the presence of Au leads. Inset: excess charge δQ (in units of e) in the C60 versus gate voltage. Due to the wider electrode separation, the equilibrium excess charge is smaller, ∼0.5 e, and the DOS features are sharper due to a weaker coupling of the C60 to the leads.

of excess charge. This has been known before [60] as due to the charge transfer from the metal leads to the more electro-negative C60 molecule. Importantly, since a free C60 has a ﬁlled HOMO, this excess charge must occupy the LUMO: the reason why the RMLs are found to be LUMOderived. A positive Vg is found to increase δQ linearly to ﬁll up the LUMO, shifting the DOS peak toward the Fermi level of the electrode. A negative Vg depletes the excess charge until δQ = 0. Afterwards, making Vg more negative starts to deplete the charges on the HOMO (not shown). As a result, a negative Vg shifts RMLs upward in energy as shown in Figs. 4 and 5. The transmission coeﬃcients T (E, Vb ) obtained from Eq. (10) are presented in Figs. 6 and 7 as a function of the electron energy E for three different bias voltages and a zero gate potential. A resonance peak is clearly seen, and the peak at Vb = Vg = 0 aligns well with the corresponding peak in the DOS plots, see Figs. 4 and 5. At a ﬁnite bias, these peaks are also aligned well with the corresponding RMLs as shown in these ﬁgures by the symbols. We therefore conclude that the resonance originates from the LUMO-derived state of the C60 . At Vb = 0, this resonance lies slightly

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above the Fermi level of the leads. As the bias voltage is applied, the position of this peak shifts toward higher energies. For this system we found that the transmission peak position shifts by about ∼0.15 eV when Vb is increased by 0.2 V, i.e., the applied voltage drops more on one side than on the other side of the C60 . A plot of the voltage drop across the device is shown in Fig. 8. The I-V curves of the Au-C60 -Au devices are calculated by Eq. (9), and shown in the insets of Figs. 6 and 7. These I-V curves show a metallic behavior with a ﬁnite slope across Vb = 0, due to the alignment of the LUMO to the Fermi level of the leads. One can easily calculate the equilibrium conductance G of the junction for the linear regime −0.25 V < Vb < 0.25 V, by Eq. (11). The results of G versus Vg are shown in Fig. 9 for the two electrode separations. As discussed above, a positive gate potential changes the occupancy of the LUMO-derived energy levels, and we can expect a strong dependence of G on Vg . It appears that the conductance increases with the gate voltage in the plotted range, with some additional features due to the resonance behavior discussed above. The gate voltage shifts the LUMO-derived levels to align or misalign with the Fermi level of the leads, giving rise to the additional features. In addition, some features appear to correlate with

Fig. 6. Transmission coeﬃcient T (E, Vb ) versus electron energy E. The electrode separation is 11.7 ˚ A, Vg = 0. The three curves correspond to three diﬀerent bias voltages Vb . In each curve, a transmission peak dominates. This peak results from resonance transmission through LUMO-derived molecular levels (RMLs) which are depicted as symbols over the peaks of T (E, Vb ). The circles, triangles, and squares correspond to Vb = 0 V, Vb = 0.2 V, and Vb = 0.4 V, respectively. The inset shows the calculated I-V curve from which the metallic behavior of the junction is evident.

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Fig. 7. Transmission coeﬃcient T (E, Vb ) versus electron energy E. The electrode separation is 13.7 ˚ A, Vg = 0. The three curves correspond to three diﬀerent bias voltages Vb . Due to a larger electrode separation, a sharper peak is obtained. Again, the LUMOderived RMLs align very well with the transmission peaks, indicating a resonance behavior. The inset shows the calculated I-V curve.

Fig. 8. Voltage drop Vb (y, z) in the scattering region is presented for bias of 0.5 V applied to the left Au electrode. The electrode separation is of 11.7 ˚ A, and the C60 sits in the middle of the tunnel junction. Here, we deﬁne the voltage drop in the scattering region as Vb (r) ≡ VH (r; Vb )−VH (r; Vb = 0). The presented Vb (y, z) is an average over the horizontal planes, i.e., xxt dx Vb (x, y, z)/(xt −xb ), where xb and xt are the coordinates of b the bottom and top of the computation box in the x direction. The dashed vertical lines highlight the C60 location in the molecular junction. We project the positions of the left and right electrodes and the molecule onto the surface Vb (y, z). The corresponding edges are shown by the bold solid lines.

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Fig. 9. Equilibrium conductance G is plotted as a function of the gate voltage Vg for the electrode separations of 11.7 ˚ A (the upper panel, circles) and 13.7 ˚ A (the lower panel, squares). Note that G ≈ 0.94Go at Vg = 0 V and G ≈ 0.25Go at Vg = 0 V for the electrode separations of 11.7 ˚ A and 13.7 ˚ A, respectively.

an integer occupancy of the LUMO-derived RMLs. For example, at the electrode separations of 11.7 ˚ A, the conductance “plateau” near Vg ≈ 5 − 7 V can be associated with the average excess charge δQ ≈ 2e inside the C60 , whereas the small peak near Vg ≈ 13 − 14 V can be associated with an average excess charge of δQ ≈ 3e. A similar situation is also seen for electrode separations of 13.7 ˚ A, shown in the lower panel of Fig. 9. Here, the ﬁrst peak, plateau, and the second peak can be associated with the average excess charge of δQ ≈ 2e, 3e, 4e, respectively. Similar metallic behavior has been reported before [60] for Al-C60 -Al junctions at the electrode separation of 9.3 ˚ A (it corresponds to the minimum distance between an Al atom and C atom of ≈1.1 ˚ A); see also [25]. Recall that the work function of Al (100) is ≈ 4.41 eV, whereas the work function of Au (100) is ≈ 5.47 eV [63]. At Vb = Vg = 0, it was reported δQ ≈ 3 e, G ≈ 2.2 Go for the Al-C60 -Al junction [60]. Here, δQ ≈ 0.7 e, G ≈ 0.94 Go for the Au-C60 -Au junction (the electrode separation of 11.7 ˚ A). This diﬀerence is also seen in the current. Experimentally, the characteristic value of the tunneling current through a C60 molecule was found to be 1 − 3.8 µA in STM measurements with the C60 sitting on an gold surface, where the tip-gold surface separation was 10 ˚ A and Vb = 0.05 V [54–56]. Our calculated value of current, therefore, is at the same order of magnitude as these measurements. Given the many unknowns in the

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experimental device structures and idealized theory model used here, such a consistency is quite good indeed. The interesting physics for the Au-C60 -Au tunnel junction is that despite the relatively large HOMO-LUMO gap of a free C60 ( 1.8 eV [64]), one predicts a metallic transport characteristic for such a device. This is due to a strong charge transfer from the metal leads to the C60 cage, and it partially ﬁlls the (empty) LUMO of the free C60 . In other words, charge transfer from the electrodes to C60 aligns the LUMO to the Fermi energy of the leads. As a result, a large resonance conductance and a metallic I-V curve arise [60]. Finally, the transport features can be well understood by analyzing the nature of the scattering states using the RMLs analysis, and these features can be controlled by both the bias and gate voltages.

3. Summary In this chapter, we reviewed a ﬁrst principle formalism for predicting nonlinear and non-equilibrium charge transport properties of molecular devices. The formalism is based on carrying out DFT atomistic analysis within the NEGF framework. The novelty of this formalism is in constructing electron charge density via non-equilibrium Green’s functions for open boundary problems, and the very eﬀective screening approximation. It is realized that modeling electronic devices requires a new formalism since a device has open boundaries and works at non-equilibrium conditions. The NEGFDFT formalism solves these features conveniently. From a quantum transport theory point of view, many problems can be solved within the NEGF theory [47,51], and thereby numerically computed using the NEGF-DFT formalism for devices where atomistic details are important. Numerically, the entire NEGF-DFT algorithm is based on evaluating Green’s functions: as distant atoms do not have large orbital overlaps, the Hamiltonian matrix is block-diagonal and its inversion scales as O(N 2 ) [65]. Furthermore, since one only requires a small portion of the Green’s function matrix element in constructing charge density (the diagonal elements), even faster algorithms are possible. As an example, some details of transport features of Au-C60 -Au molecular tunnel junctions were discussed. The physical mechanism of resonance transmission through the molecule was responsible for most of the transport properties. The resonance is mediated by the LUMO-derived states, and charge transfer plays a very important role. The I-V curves show metallic

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behavior, and the calculated current is in the µA range at small biases, consistent with the existing STM measurements. The entire transport features can be controlled by the external voltages. It appears that details of excess charge depend on device geometry, chemistry, and lead material. These details are readily analyzable using the atomistic model presented here. Although the NEGF-DFT formalism as developed to date [30,31] can explain and predict interesting phenomena in quantum transport, many further developments are still needed. For example, it would be useful to include spin into the DFT part of the method so that molecular scale spintronics can be studied from ﬁrst principles. Another extension of the NEGFDFT formalism is to analyze molecular vibrational spectra during current ﬂow. We have recently shown [37] that dynamic matrix can be entirely constructed from NEGF so that the vibrational spectra of the molecule (or extended molecule) can be obtained at non-zero applied bias with a current ﬂow. The vibrations can also be experimentally determined using tunneling spectroscopy which is contained in the second derivatives of the I-V curve. A more diﬃcult theoretical issue is concerned with heat generation in nanoelectronics. The theory with elastic scattering is not able to describe heating and quantum dissipation at all. These problems may be attempted by including molecular vibration and phonon scattering into the Hamiltonian of the scattering region, and solving a quantum statistical physics problem. As an electron tunnels through a molecular device, it can loose or gain some amount of energy due to interaction with the quantized molecular degrees of freedom. This is the basic idea of inelastic tunneling, and technically it can be described by including proper self-energies in the Green’s function. Furthermore, additional inelastic corrections to the elastic transmission function and current can be derived and included into the NEGF-DFT formalism [37]. Nevertheless, at non-equilibrium with µL −µR = eVb = 0, these are not easy tasks. Indeed, how a nano-scale device is actually heated is not clear and this is an area of active research [66,67]. It will be very useful to extend the NEGF-DFT formalism to address time-dependent problems. Since the ultimate goal of molecular electronics is in the application domain of nanotechnology, one of the most important questions which has yet to be answered is how fast or how slow can a device turn on/oﬀ a current. In other words, if one applies a square voltage pulse, what is the time-dependent current I(t)? What is I(t) for other shapes of the time-dependent voltage? These questions should be answered before one can attempt to judge if a particular switching device is technologically viable. We have made a preliminary investigation on these issues recently

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[68] within the NEGF formalism, but a full atomistic analysis has yet to be done. Finally, in the present NEGF-DFT formalism [30,31], a mean ﬁeld theory (DFT) is used to approximate the electron correlation and interaction. In particular, the expression for Σ< (see Subsec. 1.2) used here does not hold beyond the mean ﬁeld theory. There are classes of transport problems in which strong interactions cause strong correlations between electrons, for these problems the NEGF-DFT formalism cannot be applied. At present, there is no general approach which can make quantitative predictions for strongly correlated transport problems at atomic level, although the NEGF theory is usually the starting point for such an analysis [51]. For these situations, perhaps a combination of NEGF with exact diagonalization [69] or quantum Monte Carlo methods [70] can provide a powerful tool where chemical details can still be included. These and other issues provide a rich ﬁeld of future research. Acknowledgment We gratefully acknowledge ﬁnancial support from NSERC of Canada, FQRNT of Quebec, and NanoQuebec. We gratefully acknowledge collaborations with Dr. Jeremy Taylor, Dr. Brian Larade, Dr. Hatem Mehrez, Dr. Pawel Pomorski and Dr. Chao-chen Kuan, for their contributions throughout the work presented here. Appendix In this Appendix, we present some details for computing the self-energies Σl,r and the derivation of Eq. (5) in terms of the Green’s function of the leads. As discussed in the main text, we divide a device into three parts: the left lead (L), the central scattering region (C), and the right lead (R). Note that the central scattering region includes the molecule and several layers of the leads from the both sides. Within the LCAO basis where the atomic orbitals have a ﬁnite cut-oﬀ radii in real space, the KS Hamiltonian and the overlap matrices have the following form [30,31]:     0 HLL HLC 0 SLL SLC   H =  HCL HCC HCR  , S =  SCL SCC SCR  . 0 SRC SRR 0 HRC HRR Here, to simplify notation, the Hamiltonian matrix elements correspond to the matrix H(E) = (E + i0+ )S − HKS so that the equation for the retarded

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Green’s function becomes H(E) GR (E) = I, where I is the identity matrix. Note that the matrix H(E) is actually inﬁnitely large due to the electrodes which are accounted for by the inﬁnitely large blocks HLL , HRR . The block HCC , corresponding to the matrix block of the scattering region, is ﬁnite. We are interested in GCC (E), i.e., in the retarded Green function of the central scattering region. Explicitly, from H(E) GR (E) = I, we have the following system: HLL (E)GLC (E) + HLC (E)GCC (E) = 0, HCL (E)GLC (E) + HCC (E)GCC (E) + HCR (E) GRC (E) = ICC , HRC (E)GCC (E) + HRR (E)GRC (E) = 0. Solving these equations for GCC (E), we obtain:

R R HCC (E) − ΣR L (E) − ΣR (E) GCC (E) = ICC , R which is actually Eq. (5) of the main text. The matrices ΣR L (E) and ΣR (E) are the self-energies, and we derive: −1 ΣR L (E) ≡ HCL (E)HLL (E)HLC (E), −1 ΣR R (E) ≡ HCR (E)HRR (E)HRC (E).

As a result, the self-energies are given by the coupling matrices HCL , HCR , −1 and the surface Green’s functions of the semi-inﬁnite leads, HLL (E) and −1 HRR (E). Explicitly, these surface Green’s functions are: −1 −1 + GR , (A.1) LL (E) ≡ HLL (E) = (E + i0 )SLL − HLL −1 −1 R + GRR (E) ≡ HRR (E) = (E + i0 )SRR − HLL , (A.2) where we have restored the explicit notation of the KS Hamiltonian in the right-hand side. There are well-developed simple methods for computing these surface Green’s functions for periodic structures [30,48–50], and we refer interested readers to them and the references therein. The simplest idea (but a slow algorithm) is starting from one unit cell of the lead, computing its Green’s function directly from Eqs. (A.1), (A.2), and repeatedly applying the Dyson equation for additional unit cells of the periodic lead until numerical convergence. References [1] A. Aviram and M. A. Ratner, Chem. Phys. Lett. 29, 277 (1974). [2] J. R. Heath and M. A. Ratner, Physics Today 56(5), 43 (2003). [3] A. Nitzan and M. A. Ratner, Science 300, 1384 (2003).

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PERTURBATION METHODS IN SCANNING TUNNELING MICROSCOPY WERNER A. HOFER Surface Science Research Centre University of Liverpool Liverpool L69 7ZH, UK [email protected] Abstract. With the availability of ﬁrst principles methods to simulate the operation of a scanning tunneling microscope (STM), theory has moved from the qualitative and topographic to the quantitative and dynamic. Simulations in eﬀect predict the inﬂuence of a model-tip or chemical interactions between tip and sample in the actual imaging process. By comparing experiments and simulations, the information about the analyzed system can be substantially extended. We give an overview of recent work, where the combination of ﬁrst principles simulations with high resolution measurements was decisive in arriving at consistent results. Keywords: Electron transport; low-conductance transport; non-equilibrium transport; perturbation theory; density functional theory; scanning tunneling microscopy.

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Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . Theory: Uniﬁed Approach for Scattering and Perturbation 2.1 Zero order . . . . . . . . . . . . . . . . . . . . . . . 2.2 First order . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Interaction energy . . . . . . . . . . . . . . . 2.2.2 Current . . . . . . . . . . . . . . . . . . . . . 2.2.3 Corrections to the Tersoﬀ–Hamann approach Performing Simulations . . . . . . . . . . . . . . . . . . . 3.1 The surface . . . . . . . . . . . . . . . . . . . . . . . 3.2 The tip . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Tip-surface interaction . . . . . . . . . . . . . . . . . 3.4 Generating a theoretical surface image . . . . . . . . 147

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3.5 Assumptions . . . . . . . . . . . . . . 3.6 Criteria of agreement . . . . . . . . . 4 Studying Metal Surfaces . . . . . . . . . . . 4.1 Chemical interactions . . . . . . . . . 4.2 Adsorbates on surfaces . . . . . . . . 4.2.1 O on Fe(100) surface . . . . . . 4.3 O on Ru(0001) . . . . . . . . . . . . . 5 Silicon(001) . . . . . . . . . . . . . . . . . . 5.1 Saturation of Si(001) by hydrogen . . 6 Adsorbates on Si(001) . . . . . . . . . . . . 6.1 Acetylene C2 H2 on Si(001) . . . . . . 6.2 Benzene C6 H6 on Si(001) . . . . . . . 6.3 Maleic anhydride C4 O3 H2 on Si(001) 7 Conclusion and Outlook . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . .

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1. Introduction While STM images provide important information about the arrangement of atomic or molecular features at a surface, their relation to physical surface properties is far from obvious. Even though experimental images do convey the impression that we look directly at the atoms of a surface, we have to clarify what property of an atom is actually causing a feature in an STM image. This seems obvious: since we measure the transition of electrons from the surface into the tip, the electrons at the surface of our metal or semiconductor will have something to do with it. However, even in this case the electron will experience quite diﬀerent physical conditions in a tunneling junction than within the structure of a metal or semiconductor. For one, an applied bias will change the potential in the local environment of the electron. Near the surface of the material, such a potential can be seen as roughly constant: the only eﬀect on the electronic structure would be a shift of the electron states to lower values. However, we also encounter a potential from the opposite side of the tunneling junction, so that the two subsystems are no longer disconnected. In this case one would have to treat the combined surface and tip system as one quantum mechanical system. The third eﬀect theory needs to address is the change of a system due to charge transport within it. Fortunately, most of these eﬀects play minor roles and can be conveniently neglected. The current within a tunneling junction, for example, is very low: at a current of one nA, it takes about 10−10 seconds from one electron impinging on the drain, to the next. At this rate every electron can

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be thought of as decoupled from the previous one, such that cumulative eﬀects, which could lead to the heating of a sample and therefore dramatically changed conditions, are not observed. Interface eﬀects on electron transport, e.g. through a molecule, cannot be completely neglected, but since the resistance in the interface is commonly much lower than in the vacuum barrier, these only lead to small errors, which can be accounted for by using multiple scattering techniques. The eﬀect of an STM tip potential onto the electronic structure and the decay lengths of surface electrons is still problematic, because the eﬀect can only be properly addressed by treating the whole system of surface and tip in a common model, which creates enormous obstacles in the description of heterogeneous junctions composed of an arbitrary surface and tip, which do not possess the same symmetry. Perturbation methods for the description of tunneling processes in a scanning tunnneling microscope (STM) are based on the assumption that the two subsystems, the surface and the STM tip, can be described separately, without taking into account the detailed changes arising from the vicinity of the two objects. Experimentally, this assumption is justiﬁed by the low conductances observed in tunneling experiments. Theoretically, by the fact that the result of perturbation theory is the lowest order expansion in the multiple scattering approach, which treats tunneling as a dynamic process of one electron propagating across the barrier. In the next section, we shall describe the outline of a uniﬁed treatment of perturbation and scattering approaches, based on standard density functional theory (DFT). Theoretical progress in the past has relied to a large extent on the existence of precise and fast DFT codes. Until very recently, however, one could observe a distinct separation of the community into two diﬀerent paradigms. One, which most DFT groups favored, consisted of utilizing precise descriptions of the surface topography and electronic structure, while the actual tunneling process remained unconsidered. Instead of treating the electron as a dynamic entity propagating in the interface, which is scattered and proceeds along a multitude of diﬀerent pathways, it was seen as a basically static distribution of charge, which due to the overlap with other static distributions of charge changed its location under certain conditions. It has to be emphasized that time did not enter the picture at all in this model, since all transition amplitudes were calculated for inﬁnite intervals. The other, which was favored by tight-binding groups and a number of specialists in transport theory, consisted of a precise analysis of the

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actual process of tunneling, which was quantiﬁed using either the Landauer– B¨ uttiker relation, or a time-dependent formulation of the problem based on non-equilibrium Green’s functions, which reduces to the Landauer–B¨ uttiker formulation for the time-averaged currents [1]. In this case the main emphasis is generally put on the multiple scattering events in the interface. In both treatments atomic relaxations due to the onset of chemical bonding are generally omitted. This is justiﬁed as long as the coupling between surface and tip electrons does not lead to the formation of chemical bonds between the two surfaces. However, this eﬀect plays a major role in high resolution experiments on metal surfaces, which are generally considered the most successful ﬁeld of STM analysis. For example, the apparent height of Cu atoms on Cu(111), and of Au atoms on Au(111), in the range of 10–30 pm as well as the giant corrugations on Al(111) of more than 70 pm, can only be understood on the basis of substantial atomic displacements during STM scans [2]. An additional problem is that many events observed experimentally are unique and are not subject to statistical averaging. Due to these diﬃculties, theory till recently has been mainly concerned with qualitative predictions. However, continuous reﬁnement of experimental and theoretical methods makes quantitative comparison increasingly possible. This requires determination of parameters for comparison, formulation of criteria of agreement, and common calibration for theory and experiment. Today, experimental research is increasingly focused on subtle eﬀects. One reason for this change of emphasis is the continuing integration of solid state physics, chemistry, and biology into a common framework of understanding, based on atomic models. This poses unprecedented challenges on the precision of theoretical methods. It is within this framework that the increasingly sophisticated methods of density functional theory have been at the forefront of theoretical progress. Subtle physical phenomena can only be modelled if the minute energy diﬀerences of site-speciﬁc adsorptions (0.1 to 0.5 eV), surface eﬀects (20–50 meV), or magnetic anisotropy (1–10 meV) can be accurately described. If STM theory is to be used to elucidate the experimental results in this range, it seems necessary to utilize the same method. A number of review papers in the last few years have provided an overview of theoretical methods, their application and limitation in the context of present experiments. Here, we wish to point out the relevant theoretical developments, which are most likely to aid the analysis of experimental results for the purpose of this volume.

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2. Theory: Uniﬁed Approach for Scattering and Perturbation The most comprehensive description of the tunneling problem is based either on a self-consistent solution of the Lippman–Schwinger equation [3] or on the non-equilibrium Green’s function approach [4–8]. Inelastic eﬀects within e.g. a molecule-surface interface can be included by considering multiple electron paths from the vacuum into the surface substrate [9]. The current between two leads with the chemical potentials µA and µB is given by the energy integral: e µB +eV > > < I= dE Tr Σ< (1) S (E)G (E) − ΣS (E)G (E) . h µB −eV Here, the Σ(E) and G>(<) (E) denote the self-energies of the leads and the non-equilibrium interface Green’s functions, respectively. For experimenters and also theorists who are not familiar with transport theory, these symbols often look forbiddingly complex. However, their physical content is quite simple. Consider a tunneling junction connected to two inﬁnite leads. The main problem then is to describe the path of an electron from the end of one inﬁnite lead through the barrier and to the end of the other inﬁnite lead. No theoretical model could actually do that, due to the sheer size of the system. So we may look at it somewhat diﬀerently: the vacuum barrier itself is seen as an interface, and the two inﬁnite leads are only included in the picture as boundaries: after the boundaries, the transition probability of electrons is supposed to be one. These boundaries are what we call the self-energies. The reason for this term is that boundary conditions alter the Schr¨ odinger equation, and every alteration of the Schr¨ odinger equation can be interpreted as an energy. So that self-energies are just a general quantum mechanical form of a boundary condition. Similarly, one could think of all the ways that a system can react to an impinging electron. Let’s say we write all these possible reactions in a very large table, which comprises the exact information, how the electron impinges, and the exact reaction of the system. A Green’s function is just such a very large table. The reason it is widely used in transport theory is that it can generally be calculated from electronic properties, and theorists know quite well how to calculate electronic properties. Now we have Green’s functions and self-energies, and we know how to compute the current. At this point, the problem is still unsolvable, because we would have to include all interaction processes like electron–phonon or electron–electron interactions, which can lead to the excitation of lattice vibrations or charge density waves, into the picture.

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Again, a tunneling junction is a much simpler system, which does not force us to solve the problem in full generality. Within the vacuum barrier itself, inelastic eﬀects play an insigniﬁcant role. Then the problem can be reduced to the description of the tunneling current between two leads — the surface S and the tip T — thought to be in thermal equilibrium. The bias potential of the circuit is in this case described by a modiﬁcation of the chemical potentials of surface and tip system, symbolized by uttiker µS and µT . This reduces the tunneling problem to the Landauer–B¨ formulation [5,10]: I=

2e h

+∞

dE[f (µS , E) − f (µT , E)] × Tr ΓT (E)GR (E)ΓS (E)GA (E) −∞

(2)

where f denotes the Fermi distribution function, GR(A) (E) is the retarded (advanced) Green’s function of the barrier, and ΓS , ΓT are the surface and tip contacts, respectively. These new symbols are just diﬀerences of the old self-energies, so they also account for the boundary conditions at the interfaces to the two leads. However, this is still a non-equilibrium formulation of the problem, since the chemical potentials µ account for the non-equilibrium condition of nonzero bias voltage. The only additional assumption in this formulation of the tunneling problem, compared to the general formulation above, is that the leads remain in thermal equilibrium. The expression can be calculated using a standard eigenvector expansion of surface and tip Green’s functions: R(A)

(r1 , r2 , E) =

R(A)

(r1 , r2 , E) =

GS GT

ψi (r1 )ψ ∗ (r2 ) i + (−)iη , E − E i i χj (r1 )χ∗j (r2 ) . E − Ej + (−)i j

(3) (4)

At this point it may help the reader to simplify the Green’s functions by setting r1 = r2 . In this case the numerator is just the density of charge. So we ﬁnd that the reaction of a system is related to the electron density. If r1 = r2 then this entity describes how an electron, injected at r1 , is changing the physical situation at r2 . It can therefore be said to propagate a cause at r1 to an eﬀect at r2 . For this reason Green’s functions are often called propagators, in particular in ﬁeld theoretical models.

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There exists a general relation between the contacts Γ, and surface and tip Green’s functions [5]: A R A (5) i GR S(T ) (E) − GS(T ) (E) = GS(T ) (E)ΓS(T ) (E)GS(T ) (E). The second theoretical tool needed is called a Dyson series. It comes from the realization that one may start from an initial guess for the Green’s function and reﬁne it by a series of terms which successively incorporate the real physical situation by way of a physical potential. The great discovery of Dyson was that such a series actually converges to the exact solution of the problem. One can therefore construct the interface Green’s function starting from the sum of the two components, or the zero order Green’s function: R(A)

R(A)

G(0) (r1 , r2 , E) = GS

R(A)

(r1 , r2 , E) + GT

(r1 , r2 , E).

(6)

Improving the result successively with the help of the Dyson equation gives: R R R GR (1) = G(0) + G(0) V G(0) .

(7)

An outline of this method can be found in [11]; a comprehensive presentation of the theoretical model including the multiple scattering terms in the ﬁrst order current is presently in preparation. 2.1. Zero order From the zero order Green’s function the evaluation of expressions is straightforward. The exponential decay of surface and tip wavefunctions allows the conversion of the fourfold volume integration contained in the trace of Eq. (2) into surface integrals. An evaluation of the trace as well as the energy integral then leads to a modiﬁcation of the standard Bardeen expression: 4πe f (µS , Ek ) − f (µT , Ei ) I(0) = ik

E − E M 2

ik k i (8) × δ Ei − Ek κ2i − κ2k where κi(k) is the exponential decay of surface (tip) states, and Mik is described by the usual Bardeen matrix element: Mik = dS χ∗i (r)∇ψk (r) − ψk (r)∇χ∗i (r) . (9)

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The decay constants for zero bias voltage are proportional to the electron eigenvalues Ei(k) , according to (see Fig. 1(b)): Ei(k) = −

2 2 = Ei(k) (V = 0). κ 2m i(k)

(10)

In this case we recover the result by Feuchtwang [12], that the Bardeen method is just the zero order approximation to a full scattering treatment [13,14], 4πe [f (µS , Ek ) − f (µT , Ei )] I(0) = ik 2 2 Mik δ(Ei − Ek ). × − (11) 2m

STM tip VT

~

Vacuum

nS + nT

~

Surface Integral

(a)

Surface VS

~

Surface Integral

~

This result and its interpretation in terms of scattering theory is well accepted. Here, it shows once more that the choice for the zero order Green’s function of the interface is justiﬁed. In case of non-zero bias the scattering approach leads in addition to a bias dependent term, which increases the current and leads to a quadratic relation between current derivative dI/dV and bias V . Though this result has been well documented in experiments,

(b) U = eV

-eV/2

Ek E'k

E'i

+eV/2 Ei

Fig. 1. (a) The system under consideration, and the surface integrals used in deriving the zero order current. (b) The eﬀect of ﬁnite bias potentials: in this case the eigenvalues are shifted by ±eV /2.

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it is however completely beyond the usual Bardeen method. We shall deal with the explicit voltage dependency in the ﬁrst order approximation below. 2.2. First order The ﬁrst order Green’s function, from the Dyson series and taking into account the exponential decay of electron states, contains two discrete terms, which can be written of the Bardeen matrix elements Mik

in terms

± using the shortcut fik = E − Ei ± iη E − Ek ± i : R(A)

G(1)

R(A)

= G(0)

−

∗ ∗ χk (r2 ) + χk (r1 )Mki ψi∗ (r2 ) 2 ψi (r1 )Mki . +(−) 2m f i,k

ik

It is evident that each subsequent iteration in the interface Green’s function can also be formulated in terms of Bardeen matrix elements: in principle, the Green’s function and thus the current can therefore be evaluated to any order. 2.2.1. Interaction energy The interaction energy between the surface and the tip in the low coupling limit can be calculated from the ﬁrst order Green’s function. It has been shown recently by an analysis of ﬁrst order perturbation expressions for the tunneling current and the interaction energy, that the two variables should be linear with each other. From the ﬁrst order Green’s function we may construct the density matrix n ˆ = i/2π(GA − GR ). Here, the reader may remember that above we related the Green’s function to charge density by setting r1 = r2 . The diﬀerence between advanced and retarded Green’s functions is just the sign of the imaginary part in the denominator. Their diﬀerence then can be shown to amount to a delta functional times charge density. Generalizing the concept of charge density for r1 = r2 one arrives at the concept of a density matrix. Performing the integration and the trace we get: 2 |Mki |2 4 2 . (12) Eint = − π m |Ei − Ek + eV | i,k

The absolute value of the denominator is due to integrating the inﬁnite energy interval in two steps, and taking each result separately as a contribution to the interaction energy. The calculation of the interaction energy only involves the computation of the tunneling matrix elements. As

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shown previously, the interaction energy will therefore be proportional to the tunneling current [14]. 2.2.2. Current The ﬁrst order current involves a number of multiple scattering terms, described by multiplications of the Mik matrices. So far these terms remain unconsidered. However, we also obtain terms with |Mik |2 in the ﬁrst order expression, which lead to a modiﬁcation of the result for ﬁnite bias voltage. These terms amount to a tunneling current: 4πe I(1) = [f (µS , Ek ) − f (µT , Ei )] ik 2 2 eV − × (13) Mik δ(Ei − Ek + eV ). 2m κ2i − κ2k 2.2.3. Corrections to the Tersoﬀ–Hamann approach The additional approximation in the Tersoﬀ–Hamann approach concerns only the shape of the tip orbital, in particular the substitution of the matrix element Mik by: −

2 2 Mik ∝ ψi (R) 2m 2m

(14)

where R is the position of the STM tip. Since this does not aﬀect the rest of the derivation, we also obtain a modiﬁed formulation for the tunneling current with changing bias voltage under the condition that the tip wavefunction χi decays radially with a decay constant κT . The correct Tersoﬀ–Hamann approximation therefore reads: 2 eV 2 eV . − dE (R) (15) ψ ITH (R, V ) ∝ i 2m κ2 − κ2 0 i T i 3. Performing Simulations Within perturbative methods, where surface and tip are initially thought to be separate entities, a simulation is generally split in three discrete steps: (i) calculating the surface electronic structure, including atomic relaxations and surface adsorbate interactions; (ii) calculating the electronic structure of a model tip; and (iii) calculating the ensuing STM images and spectra using the theoretical models described in the previous section, with the optional correction for chemical interactions (see further down).

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3.1. The surface The ﬁrst stage of the modelling process is establishing a good representation of the surface being studied. The wealth of experimental methods of surface preparation is to a certain extent responsible for the wealth of surface eﬀects which are studied by atomic probe instruments. In the simplest cases, and if a clear consensus on the surface structure has been established previously, then this can be used directly. If there is no clear consensus, then an accurate structure in some cases can be found from a combination of other experimental techniques and theoretical methods. The most diﬃcult situation arises when establishing the unknown surface structure is the sole purpose of STM experiments. Notwithstanding the famous example of the Si(111) surface, where SPM revealed the (7 × 7) reconstruction [15], this is not a trivial task. In view of the ambiguities of the experimental results, alternative surface models should be used and checked, before an agreement is sought from a broad set of experimental data. Preliminary models of the surface topography, for example, can be determined by atomic-probe methods, ion-scattering, electron diﬀraction, or Auger spectroscopy. The chemical bonds of adsorbates can be estimated from infrared spectroscopy. The surface electronic structure is accessible by photoelectron emission techniques. In case the surface structure is known, its electronic structure has to be computed with sophisticated methods, where existing codes more and more rely on ﬁrst principles density functional theory (DFT) [16–18], or, in case of tight-binding models [19], they obtain their parameters from a ﬁt to DFT data [20]. The ﬁt is not without ambiguities, since it is unknown whether the density of states used for the ﬁt is really unique. 3.2. The tip It is well known that contact between the bottom of the tip and the sample surface will not be between two smooth, regular surfaces. In particular, the bottom of the tip may contain many asperities, and one of these asperities will serve as the probe. In STM experiments the most common tip is made from a tungsten poly-crystalline wire, and other tip materials are commonly transition metals (platinum, iridium, alloys) [21]. It is generally agreed today that only a very sharp tip with a single atom at its pinnacle is suitable to obtain atomic resolution on close-packed surfaces. But, such a tip is highly unstable. Therefore, the fabrication and characterization of deﬁned tips, e.g. by ﬁeld ion microscopy, have not been achieved, nor can it

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be expected for the near future. The most likely STM-tip model is chosen according to the experimental situation. On metal alloy surfaces, for example, it is likely that the apex of the STM tip is composed either of atoms of the tip material (e.g. tungsten), or of single atoms of the scanned surface, because it comes frequently in very close contact with the surface. The eﬀect of single STM tips can be studied qualitatively by analyzing their surface electronic structure. If it is composed to a high degree of single electron states (Kohn–Sham states), which protrude far into the vacuum within a small area, then the electron tunneling from the sample to the tip will be far more localized: the tip, in this case, resolves the surface electronic structure very well. The opposite is true if the wave-functions are very delocalized: then the conductance for one state will cover a large area and sample the surface electronic structure in a statistical manner. The detailed information about the surface in this case is lost. To obtain realistic tip models, DFT calculations of the electronic structure of fully relaxed tungsten ﬁlms with one or two surface layers of either tungsten atoms or adsorbates have proven to be the most suitable choice [22,23]. The adsorbates so far considered include most transition metals. In single cases, where the (STM) tip was covered by 10–20 layers of Fe, the tip has been modeled by a Fe(100) ﬁlm covered by one atom or a layer plus one atom of sample surface atoms [24].

3.3. Tip-surface interaction The force can be split into two general components: (i) the microscopic chemical force between atoms in the tip and surface, and (ii) the macroscopic force between the tip and surface, which always includes the van der Waals and various other (electrostatic) interactions depending on the speciﬁc tip/surface combination studied. Extensive modelling suggests that only the short-range chemical forces are responsible for atomic resolution [25–27], whereas the macroscopic forces can be treated as a background attractive force. This background force is important to reproduce experimentally observed frequency changes in AFM, but is independent of the identity of the atom under the tip and does not play a role in atomic displacements. Therefore it is generally irrelevant for STM experiments. In terms of STM modelling, this means that only microscopic forces have to be considered in speciﬁc situations (high resolution scans); in general (low resolution, semiconductors) even these forces can be neglected and the theoretical model can be reduced to perturbation theory.

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3.4. Generating a theoretical surface image Shifting the position of the STM tip laterally and vertically produces, by the above procedure, a map of tunneling currents. The current maps are used to extract the contours of constant current. In a further step the maxima and minima of the current contours for a speciﬁc current value are determined: this corrugation amplitude is then directly compared to images. It is clear from the procedure that speciﬁc tunneling conditions (bias voltage and tunneling current) uniquely determine a constant current contour and a corrugation amplitude. In this sense the calculation does not involve any parameter or ﬁt to experimental data. Therefore, it can be said to be fully ab initio. 3.5. Assumptions No model can reproduce all features of a physical environment. In this sense every model depends crucially on basic assumptions. These are, in the present context: • The groundstate properties of a system are equal to the properties at ﬁnite temperatures (e.g. in an ambient environment); • there is a hierarchy of interactions, which allows separation of diﬀerent eﬀects in the theoretical models (no inclusion of e.g. cumulative or timedependent interactions); • macroscopic interactions do not aﬀect the tunneling current; • the resistance in the STM-circuit is only due to the tunnel-barrier; • the current cross-section is centered at the apex atom of the tip; • current ﬂow does not change the properties of a system. The last point has recently been analyzed by Todorov et al. [28], and it was found that the current ﬂow slightly changes the position of the surface atoms. 3.6. Criteria of agreement The control parameters in STM experiments are the bias voltage and the tunneling current. The results of an experiment are the shape and the dimensions of atomic or molecular structures on the surface, and their apparent height compared to the surface environment. Generally, it has been found that apparent heights are not uniquely determined by a set of control parameters. The shape and dimensions of atomic structures are thus

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usually a better indication of the experiment. Given this uncertainty, the agreement between experiment and simulation can, pending future reﬁnements, be considered suﬃcient, if the values are in qualitative agreement. This is still largely a topic of discussion. A disagreement in the shape of a structure is commonly an indication of simulations based on unrealistic assumptions. Therefore this has to be seen as the primary criterium. The apparent height in experiments is usually a statistical distribution around a mean value. In this case the criterium is less forceful. However, disagreements exceeding 30% of the base value obtained in simulations are usually an indication that an important feature of the system has been neglected, e.g. the electronic structure of the STM tip or the interactions between tip and surface. As the methods of simulations proceed, and the experimental descriptions of the actual experiments become more precise, this value should be subject to revision in the near future.

4. Studying Metal Surfaces The emphasis in this section will be on demonstrating how simulations extend the experimental method. Only by simulating STM scans do the physical origins of measured eﬀects become accessible. In particular we shall focus our demonstration on model calculations to review the following widely discussed problems: (i) relaxation of tip/surface atoms and their eﬀect on the tunneling current on the gold surface, (ii) the eﬀect of tip potentials on the surface electronic structure from oxygen contaminated iron surface, and (iii) the eﬀect of the tip structure on STM images for oxygen adsorbed on ruthenium. Simulations (i) and (ii) also demonstrate the exact limitations of the perturbation approach: in the ﬁrst case it breaks down, where the chemical forces between the separate systems substantially shift the surface atoms out of their groundstate positions; in the last case it ceases to be applicable, where the potential of the STM tip severely distorts the electronic properties of the crystal surface. Metal surfaces have been widely studied by STM. The main results include: (i) reconstructions, or surfaces with a diﬀerent arrangement of surface atoms than in the bulk; (ii) relaxations, or the trend for surface layers to possess a diﬀerent interlayer spacing than bulk crystals; and (iii) surface states, or electron states trapped in the surface region due to the potential boundary [29,30]. The surface chemical composition plays an important role in STM imaging of metal surfaces. It is a well-known fact in STM experiments that

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oxygen or carbon atoms on a surface change the image locally in a decisive way [25,31]. Both atoms usually appear in STM images as distinct depressions, even though their actual position is sometimes well above the surface plane. Hence, one of the main problems in STM experiments on metals is the contamination of the bulk with carbon. On the other hand, oxygen on a surface can lead to stable reconstruction of the entire surface, and this eﬀect may be used to render imaging actually easier than on a clean metal surface. These are very drastic examples of chemical eﬀects changing the tunneling current on surfaces. Similar eﬀects, even though not as drastic, change the apparent image of single atoms on a surface depending on the chemistry of their neighbors [32]. It took about ten years from the invention of the STM [33–35] for the instruments to be precise enough to be able to discriminate not only between substrate atoms and adsorbates, or diﬀerent adsorbates, but even between diﬀerent substrate e.g. metal atoms [36]. The experiments marked an important point, because they made the concept of a chemical atom visible for the ﬁrst time. An atom, henceforth, could be seen as a small sphere in some shade of grey. But if the chemical nature of a substrate atom can change the observed STM image, then also the chemical nature of the tip apex can have a decisive role. This eﬀect changed the focus in STM theory somewhat from the discussion about single tip-orbitals (most theoretical work previously assumed that the representation of a tip by one orbital would be suﬃcient), to the chemistry of the STM tip. This is still a very lively topic today, not least because subtle eﬀects are more and more dominant in experimental practice.

4.1. Chemical interactions Another issue acknowledged in STM research nearly from the beginning is that chemical forces must play an important role in the imaging process [37–41] on metal surfaces. The strong adhesion interaction between an atomically deﬁned W(111) tip and an Au(111) sample has been studied using AFM [42]. However, the exact mechanism, and more importantly, the quantitative eﬀect of the tip-surface chemical interaction in STM images, could not be conclusively determined. It was, for example, unclear whether these forces would lead to a contrast reduction, an enhancement only in the low distance regime, or no eﬀect at all for scanning on close packed metal surfaces. The so-called “giant corrugation” on Au(111) or Al(111) especially remained a puzzle for over ﬁfteen years.

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To study the problem of chemical forces on a model surface, a combined tip-sample system consisting e.g. of an Au(111) surface and a W(111) tip was simulated [25]. By reducing the unit cell in the z-direction the approach of an STM tip to a sample surface can be described. The results of DFT calculations of the interaction energy between diﬀerent surfaces and the STM tip in connection with calculations of the tunneling current was then used to parametrize the ratio between interaction energy and tunneling current, which is constant to ﬁrst order, in terms of the Wigner–Seitz radii of surface and tip atoms [2,14]. The parametrization captures the essential physics of chemical bonding between surface and tip atoms. Within an elastic approximation for atomic displacements, the actual position of a surface atom during a scan with tunneling current I can then be calculated, and the constant current surface corrected, for atomic displacements. The results of these simulations for close packed Au(111), Cu(111) and Al(111) surfaces are shown in Fig. 2. The most astonishing feature of the images is that the chemical interactions and subsequent atomic displacements are actually dominating the STM images on Cu(111). For example, the Tersoﬀ–Hamann model arrives at positive corrugations of Cu(111), while the Bardeen model, using a tungsten tip, clearly does not (see Fig. 2(b)); it must be concluded that in this case the error from neglecting the STM tip is canceled by the omission of chemical interactions. The qualitative results in both the TH model and

1 nA 0.5 nA

0.5 nA 0.4 pm

2 nA

2 nA 4 pm

0.5 nA 0.5 nA 12 pm -0.2 pm

Au(111)

15 nA

20 pm

-1 pm

b

1 nA 3 pm

5 nA

2 nA

24 pm 2 nA

5 nA

4 nA

a

14 pm

15 pm

1 pm

7 pm

-0.1 pm

8 pm

0.2 pm

37 pm

70 pm

10 pm 5 nA

Cu(111)

10 nA

c

45 nA

Al(111)

Fig. 2. The eﬀect of chemical interactions in STM scans on three close-packed metal surfaces: (a) Au(111), (b) Cu(111), (c) Al(111). The left frames show a constant current contour without corrections due to chemical interactions, current and corrugation values, while the right frames show constant current contours with the corrections.

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a b

500pm

Corrugation [pm]

50pm

100

163

Difference x 10 fcc hollow hcp hollow

50

10 5

-20mV 0.1 2 1 Conductance [MΩ-1]

c 0.01

Fig. 3. Resolution of subsurface atomic positions in STM scans on Al(111) and comparison with experiments. The diﬀerence in apparent height between the fcc hollow site and the hcp hollow site of about 5 pm in experiments (a) and (b) is fully accounted for in the simulations (c).

the Bardeen model, including interactions, are the same, but the physical reason is quite diﬀerent. In the ﬁrst case it is the electronic structure of the surface that is responsible, in the second case it is the onset of chemical bonding. A fully quantitative comparison for Al(111) shows the defect of the TH model quite drastically (see Figs. 2(c) and 3). In this case the measured corrugation is one order of magnitude higher than the corrugation from the electronic structure of surface and tip by itself: in the simulations agreement for the actual corrugation value (up to 70 pm) and the diﬀerence between the fcc and the hcp hollow sites can only be obtained with a model including the onset of chemical bonding and the subsequent displacement of surface atoms. The reason that Al(111) shows giant corrugations, whereas Au(111) or Cu(111) lead to more moderate values, is that the elastic constant for atomic displacement on Al(111) is only a fraction of the value for Cu(111) or Au(111) [2].

4.2. Adsorbates on surfaces Adsorption on surfaces has been studied with diﬀerent methods well before the invention of STMs [43]. However, due to the real space image of STMs and their potential to study the processes in real-time, analytical methods become more and more focused on this instrument. In this context it is interesting to determine what an STM can tell us about the changes electron orbitals undergo during adsorption processes.

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4.2.1. O on Fe(100) surface The question as to how the electric ﬁeld of the STM tip aﬀects the vacuum barrier of the surface electronic structure, and thus the decay length of the tunneling current, has been a widely discussed topic since the invention of the STM. In particular the role of image forces, which should lead to a lowering of the potential barrier, remained unclear [44,45]. Related to this problem is the question of when a perturbation approach to tunneling becomes insuﬃcient. In general, the regime of ﬁeld interactions is not accessible to STM experiments, as will be seen. However, by measuring a 3-dimensional map of currents on a Fe(100) surface in such a way that the tip-position is adjusted from the outset, the transition from the tunneling regime to point contact can be studied experimentally [46]. From the 3D current map the corrugations can be extracted in a straightforward manner. In addition, the apparent height of atoms can be determined by adsorbing e.g. oxygen on a surface. Since the position of the adsorbant is known (e.g. for oxygen on Fe(100) the preferred site is the fourfold hollow site), its position with respect to the maxima and minima of the constant current contour can be determined. The measurements revealed the following behavior: (i) the positions of the Fe atoms on the surface are imaged as protrusions for z ≥ 400 pm, (ii) these positions are imaged as depressions if z ≤ 400 pm, (see Fig. 4) (iii) the corrugation height is in all cases very small and below 2 pm, and (iv) the 3D current maps were generally obtained with a stable tip and in one single sweep. The measurement with a stable tip suggested that the tip was not contaminated. For this reason the STM tip chosen in the simulations was a clean tungsten tip. Since the surface orientation at the apex of the

Distance > 4 A: O hollow

Distance < 4 A: O on-top

Fig. 4. STM images of Fe(100) with an adsorbed oxygen atom. Oxygen appears to be adsorbed at the hollow site of the surface for distances above 4 ˚ A (correct), but it appears to be at the on-top site for distances below 4 ˚ A (incorrect). The conclusion from the experiments is a reversal of surface corrugation in the low distance regime.

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polycrystal is a priori unknown, simulations were performed with all three low index surfaces, (100), (110), and (111). The surface electronic structure of sample and tip were calculated with a full potential DFT code [46], the surfaces were represented by free standing ﬁlms in a vacuum. The results were also checked with a Fe terminated tungsten tip; in this case agreement was not obtained between experiments and simulations, therefore this tip model was ultimately excluded. The current was calculated for nine positions of the STM tip on the Fe(100) surface: the top site, the bridge sites, and the hollow sites. From the distance dependent current curves the corrugation amplitudes were extracted. The results of the calculations are shown in Fig. 5(a). The ﬁrst conclusion to be drawn from the simulations is therefore that the tip most likely used in the experiments was a clean tungsten tip. The positive corrugation on an anticorrugated surface in this case arises from the high contribution of dxz and dyz states in the electronic structure of the tip. Which, in itself, is one more conﬁrmation that the electronic structure of tungsten tips is not accurately described by a single orbital of dz2 symmetry [47,48]. While the simulation agrees well with the experimental results in the distance range above 400 pm, it does not agree at all in the distance regime below 400 pm. Experimentally, the positions of the Fe atoms are imaged as depressions, in simulations they appear as protrusions. The reason for this obvious disagreement can only be that the tip interacts with the surface. Neglecting the eﬀects of chemical forces, since they generally lead

W(100) W(110) W(111) TH

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a 400 500 Distance z [pm]

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15 Corrugation [pm]

Corrugation [pm]

20

10

Unqu ench ed

5 0 -5 300

b 400

500

600

Distance z [pm]

Fig. 5. Simulated corrugation of Fe(100) surface with three diﬀerent tungsten tips (left), and simulation of scans of the same surface if the surface states are quenched due to the STM tip potentials (right). The quenching of surface states due to the tip in the very close distance regime leads to a corrugation reversal, which is actually observed in the experiments.

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to a corrugation enhancement and thus would further increase positive corrugation, the only possibility is that the ﬁeld of the tip inﬂuences the surface electronic structure. This eﬀect can be simulated by an applied bias potential on the Fe(100) surface. On Fe(100) a substantial contribution to ¯ the tunneling current originates in a surface state near the Γ-point of the Brillouin zone [49]. Surface states are generally an expression of the boundary conditions at the vacuum boundary of a crystal. Their existence thus depends on the existence of this boundary. If a tip approaches the surface then the tip-potential will gradually lower the vacuum potential barrier. The surface layer gradually loses its surface characteristics, leading to the loss of surface states. In principle, such a behavior can be simulated by a distance dependent quenching of the surface state density. Since surface states on Fe(100) are states in the minority spin band, we have simulated the quenching by reducing the contributions from the minority band during an approach. Numerically, this was done by a polynomial of second order, and the results are shown in Fig. 5(b). The percentage describes what part of the minority states density was quenched in the simulation for a distance of 300 pm. Comparing experiments with simulations we see that a quenching of about 50%–70% is suﬃcient to reproduce the measurements.

4.3. O on Ru(0001) Considering adsorbed oxygen layers or oxide surfaces, experimental reports claim that, depending on the system and the state of the tip, either the O or the metal atoms appear as bright features in the STM images. In the case of isolated oxygen atoms adsorbed at metal surfaces, their observed shape (a depression) is well understood. But even in this case, the tunneling conditions can reverse the contrast of an STM image as seen in the previous section. In dense, ordered arrays of adsorbed oxygen the situation is even more unclear. Because the geometric and electronic structure of the surface, as well as the chemical state of the tip, play a role in determining the corrugation, contrast and shape of the image, it is necessary to perform ab initio calculations to interpret STM images. A thorough experimental investigation of oxygen adsorption on Ru(0001) over a wide range of tunneling conditions and with two diﬀerent tips has been undertaken by the group of Miranda [50]. Corresponding high-resolution STM simulations with two diﬀerent tips, a clean tungsten tip and a tip contaminated by oxygen, reveal that not only the actual contrast, but also the shape of surface features, depend on the STM tip and the tunneling conditions.

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The experimental results are shown in Fig. 6. In this case the tunneling conditions aﬀect the shape of the ensuing surface superstructures quite drastically, while the apparent height of the structures does not change. This points to a characteristic of the surface electronic states themselves, which are composed of Fourier components of diﬀerent symmetry in diﬀerent distance ranges from the surface. To answer the question whether oxygen in this case is seen as a protrusion or as a depression, STM simulations with a clean tungsten tip were performed. The results of these simulations for two distinct tunneling resistances and the comparison with experimental data is shown in Fig. 7. Changing the resistance by one order of magnitude changes the shape of the depressions at the oxygen positions from circular to triangular. The simulation thus not only answers the questions as to how the speciﬁc experimental results relate to the position of surface atoms, but also how the diﬀerent decay of Fourier coeﬃcients of electron states aﬀects the images. Carrying the comparison between experiments and simulations one step further, one can model the STM tip by a tungsten ﬁlm covered by single oxygen atoms. This mimics the situation when the STM tip comes too close to the surface and an oxygen atom is transferred from the surface to

(a)

(b)

(c)

Fig. 6. Experimental results of oxygen adsorbed on Ru(0001) with half a monolayer coverage. While the clean surface has hexagonal symmetry (a), the oxygen covered surface shows a 2 × 2 superstructure (b). The shape of the ensuing features depends on the tunneling conditions (c): it changes from circular to triangular as surface and tip move closer together.

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(a)

(b)

(c)

Fig. 7. Simulated results with a clean tungsten tip (a), (b), and comparison between simulated contours with a clean and oxygen-contaminated tip (c). The shapes change when the tunneling resistance is changed from 300 (a) to 30 (b) MΩ. The contrast is reversed when the tip is contaminated by oxygen: (c), top and bottom frames.

the STM tip. Under ambient conditions, such an atomic transfer is quite frequent and is thought to account for most sudden changes in STM images, observed daily by experimentalists. 5. Silicon(001) The surface of Si(100) reconstructs in dimer rows along the (011) direction, the Si-Si dimer bond is 2.2 ˚ A long, adjacent dimers are 3.8 ˚ A apart [51]. The dimer reconstruction was the subject of intense dispute around 1990, since photoemission spectra suggested a buckled dimer [52], while STM images clearly revealed a ﬂat dimer structure [53]. The riddle has been solved by a combination of experimental and theoretical techniques. Experimentally, it was realized, that a tilted dimer in fast ﬂip-ﬂop motion would appear ﬂat in STM images due to the low time-resolution of the STM. At temperatures below 90 K the motion of dimers is frozen, and individual dimers under these conditions appear tilted, as Wolkow showed in 1992 [54]. The same feature is observed if the buckling is pinned down by surface defects. The additional information, gained by STM simulations under zero temperature conditions, compared to charge density contour plots (see Fig. 8) is the

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Apparent height [nm]

Fig. 8. Simulation of the buckled Si(001) surface. Adjacent dimers in one row are buckled in the opposite direction (left). In this case we simulated a 2 × 2 unit cell, which leads to the same buckling in adjacent rows. The charge density contours show that only one of the Si atoms is actually visible (right).

0.8 Linescan 0.75 0.7 0.65

0.5

1.0

1.5

2.0

2.5

Position [nm]

Fig. 9. Constant current contour plot for a bias voltage of −2 V and a current value of 50 pA. Adjacent Si-dimers are buckled in the opposite direction, the zig-zag pattern as well as the apparent height of about 0.6 to 0.8 ˚ A is conﬁrmed by experimental data [54].

exact distance range under experimental conditions (see Fig. 9). We also note that the agreement between the shape of the current contours in STM experiments and simulations is improved signiﬁcantly. It seems that the question of dynamic buckling is still to some extent discussed in the literature, even though the variable temperature experiments seemed to have proven beyond doubt that the ﬂat dimer structure in room temperature experiments is a dynamic eﬀect. Given the large distance between tip and surface, the assumption of current induced buckling [55] or buckling due to tip-surface interactions [56] lack experimental and theoretical conﬁrmation.

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5.1. Saturation of Si(001) by hydrogen A silicon surface is very reactive. This is due to the dangling bond of the Si-dimer atoms, which reaches far into the vacuum and thus provides an adsorption site for atoms and molecules in the gasphase. The extent of the dangling bond can be estimated if the silicon surface is saturated by hydrogen. In this case the electron charge in the vacuum range is substantially reduced. Saturating the whole surface with hydrogen by deposition from the gas phase leaves a basically inert surface. However, if a single hydrogen atom is removed from the surface by an STM tip, then the surface contains only one speciﬁc adsorption site for molecules. This fact can be used to position a molecule very accurately on the surface. Furthermore, if a chemical reaction is induced, which removes another hydrogen atom from the surface during adsorption, then a self-directed growth process with in principle a well-deﬁned growth direction can be initiated. Just why a dangling bond is so reactive can be seen from simulations of charge density and constant current contours. As the current at a speciﬁc location is proportional to the interaction energy (see previous chapters), we can study the eﬀect by analyzing simulated density and current contours. To this end we simulated a 4 × 6 Si(001) unit cell, where all but one of the silicon atoms were saturated by hydrogen. The size of the cell is necessary to avoid an overlap between neighboring dangling bonds. The setup of the unit cell is shown in Fig. 10. It can be seen that the additional

Fig. 10. Silicon (001) surface saturated by hydrogen but for a single location. This location, the dangling bond, is marked by a red arrow (left). A constant charge density contour shows the local extent of the dangling bond, which covers an area of about 1 nm × 1 nm (center). A constant charge density contour has a diﬀerent shape than the current contour, the apparent height of the dangling bond at a bias voltage of −2 V and a current value of 50 pA is about 1.5 ˚ A (right).

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hydrogen atom, due to the change of its surface charge distribution, removes the buckling of the surface, which consists now of ﬂat dimers saturated by hydrogen. The charge density contour (center) contains only the charge of the dangling bond, which is situated in the bandgap of Si(001), somewhat below the middle (it is 0.6 eV above the valence band and 0.8 eV below the conductance band in simulations with standard DFT codes). The constant current contours also contains to some extent the contributions from the valence band of the surface. But as the vacuum of the saturated surface contains only very little charge, compared to the clean surface, these contributions should be minor. However, we observe a change of shape of the dangling bond: the peak becomes narrower and higher than the peak in the density contours. We attribute this eﬀect to a genuine tip eﬀect: as the overlap is a maximum, if the tip is centered at the position of the dangling bond, the slope of the protrusion must necessarily increase once the STM tip is included in the simulation. The apparent height of the dangling bond under normal tunneling conditions (−2 V/50 pA) is about 1.5 ˚ A. 6. Adsorbates on Si(001) Since the surface of Si(001) is highly reactive it has been used as a template for studying adsorption processes. The additional advantage of silicon is that the covalent bonds are very localized and that diﬀusion barriers for the propagation of molecules from one adsorption site to another are forbiddingly high. It is therefore possible to study most processes under ambient conditions, while the large apparent height of the silicon dimers makes it possible to determine the location, the conformation, and the exact bonding site with great precision. 6.1. Acetylene C2 H2 on Si(001) The simplest hydrocarbon molecule is acetylene HC≡CH, which in vacuum possesses a triple carbon carbon bond. If this molecule attaches to a clean silicon surface, it has essentially two options: it can either adsorb on the tip of a silicon dimer, where the C-C bond in this case is reduced to a double bond; or it can attach to two adjacent dimers, if the C-C bond is reduced to a single bond. There was some controversy, a few years ago, about the preferred adsorption site. Diﬀerent methods seemed to reach a diﬀerent conclusion concerning the actual adsorption geometry under different thermal conditions (for an outline of the discussion, see [57]). There were essentially two diverging opinions: (i) There are only two adsorption

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sites, one on top of an Si dimer (called a cyclo-addition reaction), and one midway between two dimers. (ii) There are three adsorption sites, one on top of the dimer; one midway between two dimers, even though the orientation of the molecule — the C-C bond either parallel or perpendicular to the dimer rows — was under discussion; and a third one, which showed the same depression as the second one, but in addition an asymmetric feature (these three sites are shown in frame (A) of Fig. 11). The main question, which arose from STM experiments, was the nature of the diﬀerence between the two adsorption sites, covering the area of two silicon dimers. In the experimental images, these two sites are clearly distinguished (feature II and III, see Fig. 11(A)). Since the C-Si bonds of organic molecules on silicon are very localized, the electronic structure remains quite unperturbed at short distances from the adsorption site. This makes it possible to use relatively small unit cells. But in addition, the silicon lattice is very elastic. If, therefore, a molecule induces strain in the silicon lattice, the strain will shift Si atoms out of their groundstate position. The energy diﬀerences, arising from lattice strain, can be quite substantial and reach, in speciﬁc cases, values of about 0.5 eV. Together with the slight diﬀerences from exchange-correlation potentials, energy cutoﬀ and k-space sampling, this makes for a large variety of adsorption energy values found in the literature (for a compilation, see [57]). Here, we are mainly concerned with topographic images and the comparison between experiments and theory. It can be seen that the simulated image (C) 1, of Fig. 11 agrees well with the experimental image. A more thorough analysis also revealed that the apparent depression of about 0.3 to 0.4 ˚ A is in line with experimental ﬁndings. The rotated conﬁguration (C) 2 does not seem to appear in experiments, presumably because the adsorption energy in this case is lower by 0.1 eV. Concerning the adsorption sites with two-dimer footprints, the simulated images show a deeper depression than in the ﬁrst case, but due to the small size of the unit cell, the question whether there is a diﬀerence between conﬁgurations 3 and 4, which would in one case show up as a slight asymmetry in the calculated constant current contour, had to be left open [59]. Recently, the question was taken up by another group, which used a slight modiﬁcation of the Tersoﬀ–Hamann approach to calculate the STM contours, obtaining quite similar images to the ones presented here [60]. The authors interpreted features II and III of the experimental scans in a quite diﬀerent manner: feature II supposedly arises from an end-bridge conﬁguration (see (C) 2 of Fig. 11), while feature III is thought to be due to two

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Fig. 11. Adsorption of acetylene on Si(001). The experimental STM scans show three diﬀerent adsorption conﬁgurations, labeled I-III (A). They are due to the possibility of restructuring of the carbon bond to either a double bond (conﬁgurations (1) and (2) in frame (B)), or to a single bond (conﬁgurations (3) and (4)) in frame (B)). The resulting STM images (frame (C)) in the simulation agree quite well with three of the conﬁgurations found in the experiments ((A), features I, II, and III). The experimental images were taken from [58].

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acetylene molecules adsorbed at the same dimer. From an energetic point of view, the interpretation is tempting, since it removes the problem of the large diﬀerence in adsorption energies between the bonding conﬁgurations (about 1 eV [57]), which makes it quite unlikely that the two species could exist in the same thermal environment for the interval it takes to perform an experimental scan. From the viewpoint of STM experiments, it is far less convincing, since the depression in features II and III of the experimental scans is much larger (about 0.8 compared to 0.4 ˚ A) than that of feature I. It has to be concluded that at present the experimental features cannot be uniquely assigned to speciﬁc adsorption geometries.

6.2. Benzene C6 H6 on Si(001) While acetylene is the smallest organic molecule, benzene is the smallest molecule with a ring-like structure: its carbon ring is the building block of many organic molecules used in chemical synthesis. The carbon ring also provides a ready signature in STM images, because the delocalized π-electrons above and below the carbon nuclei provide the main overlaps with STM tip wavefunctions. These features have made the study of benzene quite attractive, and a large number of experimental and theoretical papers describe the adsorption of benzene on many metal and semiconductor surfaces (a survey from the experimental point of view can be found in [61,62]). Acetylene, as shown above, can attach to one or two dimers of the silicon surface. This feature is linked to the restructuring of the carboncarbon bond. In benzene, each carbon atom is attached to two neighboring atoms and a hydrogen atom. This leaves only one electron per atom, which is either delocalized, or can form a double bond, or it bonds to the dangling bond of a silicon surface. Due to the geometry of the molecule, which has a diameter of about 5 ˚ A, it cannot attach to two adjacent silicon dimer rows. As the diameter across the carbon ring is about 3 ˚ A, it will induce considerable strain into the silicon lattice if it adsorbs in a conﬁguration where its central axis is parallel to a surface dimer. This makes it clear that the adsorption sites and their energetics are somewhat limited by the shape of the molecule itself. Consequently, one observes only three adsorption sites: (A) The ‘butterﬂy’, where the molecule straddles a single dimer; (B) the ‘Tight Bridge’, where it attaches to two adjacent dimers, and the part of the ring, which remains unbounded, is tilted upwards; and (C) a rotated ‘Tight Bridge’ (see Fig. 12 (left)). Energetically, the

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Tight bridge Butterfly

8 Height [A]

175

7 6 5 4

Butterfly

Experiments 0

4

8 12 Position [A]

16

Tight bridge

Fig. 12. Benzene C6 H6 on Si(001). One observes three distinct adsorption sites for the molecule in experimental scans (left): (A) butterﬂy, (B) tight bridge, (C) rotated tight bridge. Two of the conﬁgurations have been simulated (center); the ensuing line scans agree qualitatively with the STM images, but the actual corrugation values are, however, too high (right).

‘Tight Bridge’ site is favored by about 0.3 eV [51], which means that the ‘Butterﬂy’ will be transformed into a ‘Tight bridge’ quite rapidly. It should thus be the exception, rather than the rule, that both features can be observed in the same experiment. Benzene shows up as a protrusion in STM experiments. This is contrary to the result for acetylene. The reason is the size of the molecule. While single atoms like oxygen, or small molecules like acetylene deplete the surface charge of the contributions due to either dangling bonds (silicon) or surface charge (metals), they do not possess enough delocalized charge to lead to a substantial overlap with tip wavefunctions. The main eﬀect is thus the reduction of charge. Benzene, however, possesses a ring of delocalized π electrons, which overlap with tip states; this ring is, moreover, substantially elevated compared to the substrate surface. STM simulations reveal one interesting diﬀerence to STM experiments: while on metals it is usually found that the simulated corrugation values are at the lower end of the experimental results, they are substantially higher than measured values on this surface (see Fig. 12 (right)). To date, the reason for this diﬀerence is not quite clear. Disregarding the potential eﬀect of a too small unit cell, which is evident from the constant current contour of the tight bridge, it seems that the most likely origin of this deviation is either the interface between molecule and silicon substrate, or due to neglecting the bias dependency in these calculations (see the modiﬁcations of the Bardeen equation, if it is derived from the Keldysh formalism, in the theory section of this chapter).

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6.3. Maleic anhydride C4 O3 H2 on Si(001) As a ﬁnal example, let us consider the adsorption of a highly polar molecule on silicon. Here, it was observed in STM experiments that maleic anhydride adsorbs predominantly in the troughs between silicon dimer rows [63,64]. In this case the energy component resulting from the strain of the silicon lattice plays a major role in the preferred adsorption site. As the lattice strain depends strongly on the coverage, the ensuing distributions of above trough and above dimer adsorption sites can change substantially with a variation of coverage. The STM images show a protrusion by 0.07 nm (−1.8 V) and 0.12 nm (−2.7 V) at the position of the molecule (see Fig. 13 (left)), which is well reproduced in the simulations (Fig. 13 (right)). Please note that the linescans in the ﬁgure are for two adjacent unit cells. In this case the interesting feature in the scan is the increase of the molecular height by 0.05 nm if the bias voltage is increased by 0.7 V. The silicon surface itself will possess states in this energy range, so that the total contribution of the surface will be slightly enhanced and the current contour is about 0.03 nm higher (Fig. 13 (right)). But the molecule itself increases its height by nearly double this amount. As a detailed analysis of the electronic structure of the molecule shows, this large increase is due to only a single molecular state. In eﬀect, in

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6 5

5

10 15 20 Position [A]

25

- 2.7 V

- 1.8 V

Si

C

O

H

Fig. 13. Maleic anhydride on Si(001). Experimental images of scans at −1.8 V and −2.7 V, respectively (left). Current contours for the experimental values (right, bottom), and linescans across two unit cells (right, top). The increase in this range is due to only one molecular state [63].

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passing the threshold of −2.5 V an additional state comes into play, which lights up the molecule’s position. Passing the threshold, one therefore tunes into a single molecular state [63]. 7. Conclusion and Outlook Quantitative methods developed for analysis of STM images reﬂect the change of the ﬁeld from the earliest experiments on Si(111) surfaces until today. The cutting edge in theory is now an exact description of currents, forces, and inelastic eﬀects. The most striking results are achieved where experiment and theory can combine to really reveal the atomic processes being imaged. However, this requires immense sophistication from both sides and has so far rarely been achieved. Further progress in this ﬁeld should eventually allow us to study not only surface topography, but also surface dynamics, excitations, and chemical processes. An essential ingredient to the successful characterization of any surface process remains the development of methods for a quantitative comparison between theory and experiment. Although the theoretical methods used to simulate STM can vary widely, the most important simpliﬁcations include the inability to treat truly the real structure of the tip. Even though theoretical analysis has proved to be very useful in determining the tip sample separation in STM experiments, it still remains problematic. As yet, no reliable error estimation of simulation methods exists. Tip and surface atomic relaxation have proved to be so crucial to imaging that they are increasingly included. Only in this way can the distance dependent contrast observed in STM be accounted for. Acknowledgments The article gives an overview of recent advances in STM theory, which involved a number of scientists in Liverpool, London, San Sebastian, Madrid, and Vienna. The author would like to thank K. Palotas and A. Garcia-Lekue in Liverpool, A. J. Fisher in London, A. Arnau and P. M. Echenique in San Sebastian, A. Vazquez de Parga and R. Miranda in Madrid, and G. Kresse in Vienna for their contributions and helpful discussions.

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W. A. Hofer, A. J. Fisher and R. A. Wolkow, Surf. Sci. 475, 83 (2001). F. Wang, D. C. Sorescu and K. D. Jordan, J. Phys. Chem. 106, 1316 (2002). R. A. Wolkow, Annu. Rev. Phys. Chem. 50, 413 (1999). G. Held, J. Phys: Condens. Mat. 15, R1501 (2003). W. A. Hofer, A. J. Fisher, T. Bitzer, T. Rada and N. V. Richardson, Chem. Phys. Lett. 355, 347 (2002). [64] A. Bilic, J. R. Reimers, W. A. Hofer and N. S. Hush, Chem. Phys. Lett. 385, 341 (2004). [59] [60] [61] [62] [63]

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PART IV SPECTROSCOPY OF SINGLE MOLECULE(S) ON SURFACES

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PROPERTIES OF SINGLE MOLECULES: MANIPULATION, DISSOCIATION AND SYNTHESIS WITH THE SCANNING TUNNELING MICROSCOPE KAI-FELIX BRAUN∗ and SAW-WAI HLA Department of Physics and Astronomy Nanoscale and Quantum Phenomena Institute Ohio University, Athens, OH-45701, USA ∗ [email protected] Abstract. The fascinating advances in the manipulation of single atoms and molecules with the scanning tunneling microscope tip allow scientists to build atomic scale structures and to probe chemical and physical properties of matters at an atomic level. Due to these advances, the basic steps of a catalyzed chemical reaction such as dissociation, diffusion, adsorption, re-adsorption and bond formation processes can be performed by using the STM-tip. Here a short review of these steps and the techniques involved is presented. The lateral manipulation is used for the controlled positioning of atoms/molecules whereby only the tip– atom/molecule forces are employed. By measuring the tip-height signal during the manipulation, diﬀerent modes of motion of the adparticle can be distinguished. Lower corrugated surfaces exhibit more complex motions than higher corrugated surfaces where the adparticle movement is conﬁned to one dimension. Molecules have more degrees of freedom which allow a rotational motion or change in conﬁguration. Even internal degrees of freedom can be detected and manipulated. The vertical manipulation not only allows the pick-up of adparticles and the subsequent transfer back to the surface, but also the manipulation of fragments of larger molecules. Eﬀects due to the tunneling curent can be used for a controlled dissociation of chemical bonds as well as for the formation of new bonds. The combination of these manipulation techniques can induce chemical reactions at a single molecule level and construct new molecules. These achievements in STM manipulation of molecules open up new opportunities in nanochemistry and nanochemical technology. In this article, various STM manipulation techniques used for the single

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molecule reaction process are reviewed, and their impact on the future of nanoscience and nanotechnology is discussed. Keywords: STM; nanotechnology.

manipulation;

reaction;

dissociation;

synthesis;

Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 2 Lateral Manipulation . . . . . . . . . . . . . . . . . . . . 3 Vertical Manipulation . . . . . . . . . . . . . . . . . . . 4 Single Bond Formation . . . . . . . . . . . . . . . . . . . 5 STM-Tip Induced Single Molecule Chemical Reaction . 6 Future Prospects of Single Molecule Chemical Reactions References . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1. Introduction Since its Nobel award winning invention by Binnig and Rohrer in the early 1980s the scanning tunneling microscope (STM) has developed into a celebrated tool for surface imaging. Soon after its invention it was realized that the imaging itself causes undesirable changes to the tip or/and surface structure through the interaction of the tip with adsorbates and surface atoms. Eigler et al. [1] were ﬁrst to demonstrate that this interaction can be exploited for a controlled positioning of single atoms with a precision of a single adsorption site (Fig. 1a). This technique proved to be applicable for metal atoms, rare gas atoms as well as for small and large molecules. Advances in scanning tunneling spectroscopy led to a detailed insight to the vibrational and electronic structure of molecules — a requirement for

Fig. 1. (a) The ﬁrst successful work of artiﬁcial atomic structures created by manipulation with STM. The logo of IBM written with single Xe atoms on Ni(110) [1]. (b) The basic steps involved in the STM lateral manipulation.

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the controlled dissociation of molecules. The ultimate control of matter at the atomic level was ﬁnally achieved by creating new chemical bonds. In this article, a broad introduction to atomic manipulation will be given, followed by a detailed explanation of all steps included in the single molecule synthesis. For reviews about atomic and molecular manipulation see also [2,3]. Manipulation of single adparticles or surface atoms can be achieved by tuning the electric ﬁeld, by varying the tunneling current or by changing the tip–surface distance. Each of these parameters has a speciﬁc outcome — (1) the electric ﬁeld acts on static and induced electric moments of the adparticle, (2) the tunneling current can be used for the dissociation or creation of a chemical bond, and (3) variation of the tip–surface distance can change the interaction forces between them. Manipulation processes can be diﬀerentiated as vertical manipulation processes where the adparticle is transferred between tip and surface and lateral manipulation processes where the adparticle moves on the surface. The main diﬀerence between the two modes of manipulation is that in the case of lateral manipulation the adparticle remains bonded to the surface whereas in the vertical manipulation process the adparticle is bonded to the tip. An adsorbate-substrate system suitable for a manipulation experiment should not exhibit thermally activated diﬀusion of the adsorbates. Moreover, it is necessary to have binding energies low enough to avoid tip-apex structure changes due to the counterforces acting on the tip. The choice of substrates for the experiments was restricted to mainly low corrugated metal surfaces like Cu(111), Ag(111), Ag(110), Cu(100) and Cu(211). The crystal surfaces were cleaned in an ultra high vacuum (UHV) environment by means of several cycles of sputtering with noble gas ions followed by annealing at high temperatures. Small amount of gas adsorbates were dosed at low temperature onto the sample located either in the STM chamber or in a separate sample preparation chamber. For deposition of metal atoms and heavier molecules, thermal evaporators were used. The controlled manipulation of single atoms and molecules demands a higher stability and lower thermal drift of the STM than that required for surface imaging. Most experiments up to now have been performed at low temperatures since instrumental eﬀects like piezo creep, hysteresis and thermal drift are then negligible. Due to the above-mentioned requirements a much lower precision was achieved in the experiments at room temperature than at low temperature. Nevertheless vertical manipulation can be done with atomic precision at room temperature as well.

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2. Lateral Manipulation An STM manipulation technique to create an artiﬁcial diﬀusion process of single atoms and molecules across a surface is known as lateral manipulation. It applies tip–atom/molecule interactions to laterally move the atom or molecule. This procedure involves approaching the tip towards a target atom/molecule at its initial location to increase the tip–atom/molecule interaction force, and then scanning the tip along a desired path until it reaches its ﬁnal place (Fig. 1(b)). The atom/molecule moves along with the tip and is left behind on the surface when the tip retracts back to the normal imaging height. One of the signiﬁcant aspects of this technique is that one can extract further information — such as how the atom or molecule moves and what kind of interactions are involved during manipulation — from the corresponding STM feedback or tunneling current signal. Based on the tip– adparticle interaction, three basic lateral manipulation modes pushing, pulling and sliding can be distinguished [4]. These manipulation modes are shown in Fig. 2. Pb, Cu and also other metal atoms can be manipulated via an attractive tip–adatom interaction in which they follow the tip discontinuously by hopping from one adsite to the next. This is the pulling mode of lateral manipulation, (Figs. 2(a), (b), (e)–(g)). By applying a larger force than that required for pulling, Pb atoms could also be manipulated attractively in a continuous way, known as the sliding mode, (Fig. 2(c)).

Fig. 2. Tip height curves during manipulation of (a) a Cu-atom, (b, c) a Pb-atom, (d) a CO molecule and (e–g) a Pb-dimer along step edges on Cu(211). The tip is moved from left to right and respective tunneling resistances are indicated. The vertical dotted lines correspond to fcc sites next to the step edge. The initial sites of the manipulated particles are indicated. Notice that in the attractive manipulation modes (a,b,e,f,g: pulling and c: sliding) the particles ﬁrst hop towards the tip and then follow it, whereas in the repulsive mode (d: pushing) the particle performs hops away from the tip [4] (image supplied by L. Bartels).

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In this mode, the tip–adparticle interaction is increased so strongly that the tip–adparticle system scans the corrugation of the substrate, while the adparticle–substrate interaction is still strong enough to keep the particle on the substrate. Finally, single CO molecules as well as rows of several CO molecules could be reliably manipulated via repulsive interaction, referred to as the pushing mode, (Fig. 2(d)). In this ﬁgure, the intrinsic step edges on top of which the CO molecules are bound, act as guiding trails for manipulation. Note that a CO molecule is imaged as a depression, therefore the manipulation curve has to be ﬂipped upside down for a direct comparison with the manipulation curve of the pulling mode. On the close-packed metal surfaces the direction of the adparticle movement can be freely chosen, and here the atom movement depends on the direction in addition to the nature of the tip–atom interaction [5]. An example is illustrated in Fig. 3 where a single silver atom is manipulated in various directions on a Ag(111) surface. For simplicity, the manipulation direction is deﬁned by means of an angle φ from the surface close-packed row directions, i.e. [110] directions. The φ = 0◦ signal shows a pulling mode with single site hops of the atom along a close-packed row. At φ = 5◦ , the smaller steps in the center of the curve are due to fcc-hcp site jumps of the atom. In the φ = 10◦ curve two series of small steps are separated by large steps in between, a similar situation as with the previous angle. At φ = 15◦ and φ = 20◦ , the periodic appearance of the deep minima in the tip-height signal is due to a jump of the atom to the next close-packed row to follow

Fig. 3. A sphere model (a) illustrates the tip paths encountered during the lateral manipulation on a fcc(111) metal surface. (b) Single atom manipulation signals taken on a Ag(111) surface show a sudden transition from various pulling modes to a sliding mode at φ = 30◦ [5].

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the tip. The φ = 30◦ signal includes two consecutive bumps 0.18 nm apart followed by another two bumps at a distance of 0.33 nm. The surface geometry along this path includes repeating units of three hollow sites. First, the atom moves in a sliding mode between the ﬁrst two sites. Then, instead of moving directly to the next site, the atom moves in a semicircle around the tip to end up in front of it. At φ = 25◦ the manipulation signal includes both the signatures of φ = 20◦ and 30◦ . An intriguing ﬁnding from this experiment is the observation of a sudden transition from the pulling mode to the sliding mode when the atom is manipulated along the [211] direction of Ag(111) surface. This detailed picture of the movement of the atom during manipulation was achieved with the aid of simulations [6]. The atom moves in a local potential minimum on the surface. This potential is the sum of the surface potential and the tip potential. The surface potential can be expressed by the migration barrier while the tip potential describes the direct interaction via chemical or electrostatic forces. The local potential minimum is not identical with the adsorption site, in the limit of close tip–atom separation this minimum always resides below the tip resulting in the sliding mode. The atom is slowly pushed/pulled by the tip out of the adsorption site until it jumps into the next local potential minimum. The jump to the next potential minimum proceeds on a timescale of picoseconds [7,8] whereas typical tip speeds are of the order of 0.5–2.5 nm/s. The tip–atom interaction during a lateral manipulation process was investigated in detail for the case of single Ag atoms adsorbed on a Ag(111) surface. In Fig. 4(a) the probability for a successful atom manipulation as a function of tunneling current at a ﬁxed voltage of −45 mV is shown. It can be seen from the ﬁgure that the probability abruptly changes from ∼0 below 147 nA to ∼1 above 250 nA, and the average threshold current is determined as 200 nA. Figure 4(b) illustrates the threshold current plotted versus the tunneling voltage. Each data point here is acquired by measuring a curve similar to the curve in Fig. 4(a). The plot in Fig. 4(b) clearly displays a linear dependence between the tunneling voltage and the threshold current, independent of the bias polarity. In this low bias range (from ±10 to ±55 mV), the inﬂuence of the electric ﬁeld in the manipulation process is negligible. From the slope of the plot in Fig. 4(b), a tunneling resistance of (184 ± 8) kΩ has been measured. This linear relationship unambiguously reveals that the tunneling resistance is the ultimate parameter to move an atom within the bias range used in this experiment. This tunneling resistance value corresponds to an absolute tip–atom distance of (1.9 ± 0.2) ˚ A. In this range a chemical bond is formed due to a large overlap of the atomic

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Fig. 4. (a) The probability for an Ag atom to move with the STM tip versus the tunneling current at a ﬁxed voltage of −45 mV. (b) The threshold currents between ±55 mV determined by 3857 automated atomic manipulations show a linear dependence on the tunneling voltage.

orbitals. Therefore metal adhesion forces are dominant in this voltage and current regime, which would allow the same kind of manipulation experiment to be performed with an atomic force microscope. An investigation of the lateral manipulation of Au atoms on Ag(111) over a larger voltage interval again showed a linear relationship between the current threshold and the applied voltage for low biases. Above ±70 mV tunneling voltage, Au atoms start to move already at larger tip–atom separation, and this can be attributed to a current eﬀect [9,10]. The most common application of lateral manipulation is the assembly of larger atomic structures on a surface. Figure 5 shows an example where 98 Ag atoms are arranged to form two Chinese letters. By using closed geometries the surface electrons can be conﬁned to the interior forming quantum corrals with a highly modulated local density of states. Inside such quantum corrals surface electrons can be trapped and form resonances comparable to eigenstates of isolated systems. The electronic structure and associated properties have been investigated in detail [11,12]. Due to the non-spherical shape of most of the molecules and their multiple degrees of freedom, the interpretation of the lateral manipulation signals of molecules is not straightforward. In most cases, the recorded lateral manipulation signals reveal complex and sophisticated molecular movement [13,14]. C60 molecules are rigid and resemble the spherical symmetry of single atoms, therefore they can be manipulated analogous to single atoms. They bind covalently on a Si(100)-2 × 1 surface and have been laterally

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manipulated at room temperature. These molecules can be pulled, moving in steps of 1–3 lattice constants (Fig. 6(a)). At smaller tip–surface distances the tip–molecule interaction is repulsive and the C60 molecules are moved in a pushing mode in single lattice constant steps (Fig. 6(b)). The probability for a successful manipulation can, in this case, reach ∼100% (Fig. 6(c)). In spite of the rather high electric ﬁelds (tunneling voltages ranging from −1 to −5 V) chemical forces are suggested to dominate the manipulation [15]. Other rigid molecules with a lower symmetry oﬀer more possibilities for the manipulation with STM. The manipulation of the polar molecule phosphangulene adsorbed on a Ag(111) surface was investigated in detail at low temperature. By lateral manipulation and vertical manipulation the

Fig. 5. By means of lateral manipulation 98 Ag atoms have been arranged on a Ag(111) surface to form two chinese letters, the logo of the JiJing university [16,17] [(40 × 40) nm, I = 1 nA, U = −30 mV]. (image supplied by N. Pertaya)

Fig. 6. Manipulation curves of C60 molecules on a Si(100)-2 × 1 surface demonstrating (a) pulling and (b) pushing mode. (c) Probability distribution for successful attempts as a function of relative tip–surface separation (initial parameters U = −3 V and I = −0.1 nA) [15].

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molecule could be switched between three diﬀerent binding conﬁgurations, which were identiﬁed by electron scattering quantum chemistry calculations (ESQC). The lateral manipulation of the three-lobed molecule is shown in Figs. 7(a,b). At tunneling resistances of 0.5 MΩ pushing, sliding and pulling modes were observed, whereas, at higher resistances up to 10 MΩ only pulling mode was possible. Experiments with diﬀerent bias polarity indicated that the molecular dipole has a minor eﬀect on the lateral manipulation. Usually the lateral displacement was accompanied by a rotation of the molecule visible in Figs. 7(a,b). The interconversion between diﬀerent binding conﬁgurations is also possible with lateral manipulation (Figs. 7(c–f)) [18] but can be achieved via an electric force mechanism too [19]. The internal degrees of freedom of molecules can be manipulated and their motion can be detected in the manipulation curves (Fig. 8). As an example, manipulation of sexiphenyl on Ag(111) surface is discussed. Sexiphenyl is composed of six π-rings connected to form a linear chain. Sexiphenyl preferentially aligns along the surface close-packed directions with alternately twisted π-rings. From the measured atomic registry, it was determined that shifting the molecule forward by half of the nearest-neighbor silver atom distance, i.e. hcp-fcc sites, ﬂips the π-rings from one tilted position to another. To understand the molecule propagation mechanism, the internal conformation changes of sexiphenyl were directly measured by laterally moving it with the STM tip. To observe the π-ring movement, the STM-tip is positioned above a π-ring edge and the molecule is dragged along the tip in a constant-current mode, where the tip-height is maintained by the feedback loop. The recorded tip-height signal (Fig. 8(b)) shows two contours of unequal height periodically repeating at 0.145 nm, which is half of

Fig. 7. (a,b) STM images showing the lateral manipulation of a phosphangulene molecule which usually results in a rotation at the same time. (c–f) STM images showing the interconversion between diﬀerent conformations induced by lateral manipulation [18].

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Fig. 8. Molecular conformation changes of sexiphenyl: (a) Sexiphenyl preferentially align along the surface close-packed directions. The dotted line indicates the long molecule axis. The π-ring edge is tilted up when the two carbon atoms sit on top of a single surface atom (light balls) and tilted down when they sit on two surface atoms (dark balls). Moving the molecule (upper drawing) for a half-atomic distance forward (hcp-fcc sites) will switch the π-ring position relative to the surface atoms (lower drawing). The up-site π-ring edge will now become down-site and vice-versa resulting in the π-ring ﬂipping. The tip is positioned (white circle) 0.27 nm above the π-ring edge and moved along the arrow pointed direction. (b) Periodic low-high peak tip-height signal repeating at every half of the silver atom distance is observed during lateral manipulation. (c) A low-height manipulation signal is recorded when the tip is in the low-site of the π-rings; the higher height signal is obtained when the π-ring edge is lifted up (d) (as indicated by the arrows) [Manipulation parameters: Vt = 49 mV, Rt = 600 kΩ] (image supplied by Saw Hla).

the nearest-neighbor silver atom distance. This reveals the π-ring ﬂipping at every hcp-fcc site as follows: When the STM-tip encounters the down site of the π-ring (Fig. 8(c)) it produces a lower height signal while the up-site of the π-ring causes the higher height signal (Fig. 8(d)). An interesting application of molecular manipulation in combination with metal atoms is shown in Fig. 9. By using lateral manipulation the restructured metal surface beneath the adsorbed Lander molecules C90 H98 can be revealed. The Lander molecules were adsorbed onto a Cu(110) surface at room temperature. Subsequent imaging and manipulation experiments were performed between 100 K–200 K where the thermally activated diﬀusion is suppressed. Figure 9 shows a manipulation sequence where a molecule is removed from a step edge making thereby a double row of Cu atoms visible. The molecule diﬀuses toward the step edges at RT and reshapes the ﬂuctuating Cu step adatoms into a toothlike structure. Theoretical calculations showed a higher energy gain for this conformation than

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Fig. 9. (a–d) Manipulation sequence of the Lander molecules from a step edge on Cu(110). (e) Zoom-in smooth-ﬁltered STM image showing the characteristic two-row width of the tooth-like structure (right corner) after removal of a single Lander molecule from the step edge. The Cu rows are visible as well [20].

the energy required for the creation of the Cu rows [20]. This restructuring by self-assembly has an important potential application for the parallel production of molecular contacts [21].

3. Vertical Manipulation An STM manipulation mechanism related to the adsorption and desorption processes of single atoms and molecules is known as vertical manipulation (Fig. 10). This process involves transfer of single atoms or molecules between the tip and substrate and vice versa (Fig. 10(a)). An atomic switch realized by the repeated transfer of a Xe atom between the STM tip and a Ni(110) substrate is the ﬁrst example of vertical manipulation [22]. The atom/molecule transfer process can be realized by using an electric ﬁeld between the tip and sample, or by multiple excitations with inelastic tunneling electrons, or by making mechanical contact between the tip and atom/molecule. This transfer mechanism can be modeled by using a double potential well as shown in Fig. 10(b). At an imaging distance, approximately 6 ˚ A between tip and surface, the atom/molecule has two possible

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Fig. 10. Atom/molecule transfer process between the tip and the sample (a) and double well potential model (b). In (b), the solid black, the dashed black and the gray curves represent the shape of potentials at an imaging height, under an electric ﬁeld and at the tip–atom/molecule contact, respectively.

stable positions, one on the surface and one at the tip–apex. Each position corresponds to a local potential minimum separated by a barrier in between (Fig. 10(b), solid black line). If, additionally, an electric ﬁeld is applied, one of the minima deepens and the barrier between the minima reduces (Fig. 10(b), dashed line). In this case the barrier even vanishes and the atom moves to the potential mimimum located at the tip leading to the transfer of the atom to the tip. Upon the reversal of polarity of the tunneling bias voltage, the minimum of the potential well can be changed to the surface side i.e. the dashed potential curve reverses from right to the left. The atom is then transferred back to the surface. In case of vertical manipulation by mechanical contact, the tip-height is reduced until the tip– apex and atom/molecule contact has been achieved. At this distance, the two potential wells overlap resulting in one well (Fig. 10(b), gray curve). The atom resides in this minimum which changes back to two potential wells upon increasing the tip–surface distance. By doing so, the atom can switch to the other minimum and is transferred between the tip and the surface. Vertical manipulation has been mainly applied to the extraction of single atoms from semiconductor surfaces or single atoms adsorbed on top of them [23–28]. Using this technique an artiﬁcial structure was made by Hosaka et al. [29] on the MoS2 surface by extracting single sulfur atoms.

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In the case of vertical manipulation of CO molecules, a temporary tunneling electron attachment into a 2π ∗ anti-bonding state of CO leads to the breaking of the CO-Cu bond and the resultant excited CO molecule can either jump to the nearby Cu surface sites [30] or towards the tip [31]. The CO can be transferred back to the surface using the same process. Further work on vertical molecular manipulation includes transfer of C6 H6 and C3 H6 between the tip and surface [32] and the desorption of NH3 [33]. One useful application of vertical manipulation is to modify the STM tip. The sharpness of the tip and the chemical element that forms the tip– apex are extremely critical for STM applications. A single atom/molecule tip can be fabricated by deliberately transferring an atom/molecule to the tip apex. This improves the tip sharpness and thus the image contrast is enhanced. Additionally, the tip is better deﬁned with respect to its chemical constitution. The application of functionalized tips is of great virtue in STM imaging for molecular recognition. For example, CO and oxygen can be distinguished when CO functionalized tips are used [31]. All the CO molecules undergo a contrast reversal (Fig. 11(c)), whereas the oxygen atom in the upper left part of Fig. 11(b) retains its identity as a depression. A further step towards the implementation of a molecular switch is to use manipulation techniques to reversibly modify the molecular conformation. The switching of a single leg in and out of the porphyrin plane is possible by lateral and vertical movement of the tip to push the leg down. By measuring the current passing through a single leg in real time during its

Fig. 11. (a) Schematic picture demonstrating the ﬂipping of a CO molecule upon vertical transfer from the substrate to the tip. (b) Demonstration that chemical contrast is obtained for CO molecules with a CO-tip, whereas oxygen remains unaﬀected. The blue arrow denotes the CO molecule, which was transferred deliberately towards the tip [31].

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Fig. 12. (a,b) Sketch of the approximate molecular conformation for a Cu-TBPP molecule showing one leg rotated out of the porphyrin plane and all legs in plane. (c) Current through a single leg versus the tip–surface distance during a vertical manipulation process leading to a leg’s rotation. STM images of the molecule before and after the manipulation are shown in the inset. The black dot in the left image shows the exact position of the tip during the vertical manipulation [34].

rotation it was shown that the tunneling current through one leg strongly depends on the extent of its rotation (Fig. 12). Molecular mechanics calculations show that a rotation of 90◦ should induce a change in resistance of over six orders of magnitude [34]. A recent development is the ability to measure the energy required for such a rotation by using a noncontact AFM. In this measurement frequency vs. distance curves were recorded above the molecule and above the bare surface. Short range tip–molecule forces were extracted from the diﬀerence between these two measurements. In combination with theoretical calculations it was deduced that an upper limit of 100 zJ (zeptojoule, 10−21 J) is required to rotate a di-phenyl-butyl leg [35]. Molecule Dissociation. One of the fundamental steps in a metal catalyzed reaction is the dissociation of molecules. The resultant molecular

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fragments are then joined to form new chemical products. After adsorption of molecules on the substrate, the molecule–substrate binding weakens the intra-molecular bonds and thermal activation can break the molecules. In some cases, the molecule can fragmentize upon landing on the surface due to a collision impact. Low substrate temperatures are favored in an STM tip-induced bond breaking process to avoid thermal dissociation of the molecules. To dissociate a molecule using an STM-tip, the necessary energy for the dissociation is supplied by injecting tunneling electrons into the molecule. Based on the electron energy, the STM-tip induced molecule dissociation process can be separated into the ﬁeld emission regime and inelastic tunneling regime. High electron energies (roughly above 3 eV) are used in the ﬁeld emission regime, where the tip acts as an electron emission source. In the early 1990s, Avouris and coworkers demonstrated the dissociation of B10 H14 and O2 molecules on Si(111) using high STM bias voltages (≥4 V and ≥6 V respectively) [36,37]. The dissociation involving inelastic tunneling (IET) processes uses lower STM bias voltages and controlled bond breaking can be achieved. Dissociation of Single Molecules Using IET Process. In an IET dissociation process, low energy tunneling electrons are injected into the molecule via an adsorbate-induced resonance state (Fig. 13). The tunneling electron energy can be transferred to the molecule by means of a temporary electron attachment to the molecule which increases the bond distance, leaving the molecule in an excited state after detachment. IET processes are classiﬁed as single excitation and multiple excitations. In a single excitation process the energy transferred from one tunneling electron is suﬃcient

Fig. 13. Schematic illustration of the IET dissociation process. (a) Inelastic electrons are injected into the molecule through the adsorbate-induced resonance state. (b) The energy required for a dissociation can be supplied by single- or multiple-excitation processes.

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to break the molecular bond (Fig. 13(b)). In case of multiple excitations, several electrons are involved in the bond breaking process. These processes can be explained by using a harmonic oscillator-like model (Fig. 13(b)). The energy transfer of an electron excites the molecule to a higher energy level and subsequent energy transfer by other electrons causes further excitation in a sequential process. The molecule dissociates when it exceeds the dissociation barrier. Experimentally, an IET dissociation process is realized by positioning the STM-tip above the location of the molecular bond at a ﬁxed height and then low bias voltage pulses are applied to inject tunneling electrons into the molecule. The electrons can be injected either from the tip or the substrate depending on the bias polarity. The corresponding tunneling current can be monitored. The changes in the current are related to the dissociation event, and the dissociation rate can be determined. In most cases, the change in the tunneling current indicates the displacement of the molecular fragments upon dissociation. A variation of the tunneling current, i.e. a variation of the number of tunneling electrons passing through the molecule, will change the dissociation probability and rate. It is possible to determine the number of tunneling electrons involved in a bond-breaking process from the dissociation rate vs. tunneling current relationship given by, R ∝ IN ,

(1)

where R is the dissociation rate, I is the tunneling current and N is the number of electrons involved in the IET dissociation process. In the case of oxygen dissociation on Pt(111), in a pioneering work of IET dissociation [38] both single and multiple excitation processes have been successfully demonstrated. Controlled Dissociation of Polyatomic Molecules. Controlled dissociation of polyatomic molecules using tunneling electrons is more complex than that of diatomic species such as O2 . The reason for this is the variety of bonds in polyatomic molecules. Hence the tunneling process may involve more than one bond. Selective bond breaking of polyatomic molecules has been reported for the HCCH, C6 H6 , C6 H5 I and C6 H4 I2 dissociations [38–43]. As an example, the controlled step-by-step dissociation of iodobenzene (C6 H5 I) molecules is presented in this article. The iodobenzene molecule is formed by an iodine atom attached to a π-ring (Fig. 14(a)). Altogether 12 atoms and three diﬀerent types of bonds,

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Fig. 14. Selective bond breaking of single iodobenzene molecule at a Cu(111) step-edge. (a) Structure of an Iodobenzene molecule. (b) An adsorbed iodobenzene molecule at lower part of a Cu(111) step-edge appears as an asymmetric shape with a larger bump at the right side which is contributed by the iodine atom of the molecule. (c) After breaking the C-I bond of the iodobenzene, both the resultant phenyl (larger protrusion with roughly a triangular shape) and iodine are adsorbed at the Cu step-edge. (d) The tunneling current signal recorded during this dissociation procedure shows an abrupt drop, which is caused by the C-I bond-breaking event. (e) Single-molecule I-V spectroscopy curve of an iodobenzene showing the abrupt decrease in tunneling current at ∼1.5 V caused by the C-I bond breaking event [3].

C-C, C-H and C-I constitute the molecule. Their bond strength ratio in the gas phase is approximately 3:2:1, respectively, with the carbon π bonds having the highest strength and the σC-I bond the weakest. The selective C-I bond dissociation using the STM-tip is illustrated in Fig. 14. One of the experimental diﬃculties encountered during the selective bond breaking of polyatomic molecules is the knowledge of the exact strength of a particular bond. The internal bond strengths can be altered after adsorption of the molecule on a substrate depending on the adsorption sites. The threshold energy necessary to break a single bond inside a polyatomic molecule can be determined by using single molecule I-V spectroscopy (Fig. 14(e)). To measure the C-I bond-breaking energy, the STM-tip was positioned above the molecule with a ﬁxed height and then the tunneling voltage was ramped from 0.5 to 2 V. The resulting I-V spectrum shows a sudden drop of current around 1.5 V caused by fragmentation of the molecule into iodine and phenyl. Thus the C-I bond breaking energy is determined as 1.5 V. In an IET dissociation process, the probability of the electron energy transfer exponentially decreases with increasing bond strengths [44]. Thus, breaking of the weakest bond inside the iodobenzene, C-I is, by several orders of magnitude, favored over the two and three times stronger bonds of C-H and C-C. By gradually increasing the tunneling electron energy, the

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C-I bond is broken ﬁrst when the energy transfer exceeds its dissociation barrier. As soon as the molecule dissociates, the resultant phenyl and iodine atom are displaced from the original location of the molecule under the tip. As a result, the tunneling current intensity passing through the phenyl and iodine is decreased. This greatly reduces the probability for further dissociation of phenyl and leaves the whole π-ring intact. Similar I-V spectroscopy is used to determine the threshold bond breaking energy of phenyl. The phenyl can be dissociated by applying tunneling voltages higher than 3.0 V in agreement with the benzene dissociation on Cu(100). In conclusion, by proper choice of a molecular system, speciﬁc bond breaking can be performed. By using an IET selective bond-breaking procedure, unnecessary parts of a molecule can be cleaved oﬀ and thereby active sites can be created. Such molecular fragments can be used as building blocks to join with other speciﬁcally tailored species to build a new molecule.

4. Single Bond Formation The use of catalysts in chemistry increases reaction speed and lowers reaction temperatures. Metal catalysts are commonly used in many technologies — the detailed knowledge of catalyzed reaction steps can be used to improve eﬃciency or ﬁnd new reaction pathways. Bond formation is the reverse process of bond breaking and constitutes an important basic step in a metal catalyzed reaction. In the simplest case, the transfer of an atom/molecule between the sample and the tip in the vertical manipulation procedure involves both bond breaking and bond formation processes. In this case, the substrate–atom/molecule bond is broken and a new bond between the atom/molecule and the tip–apex atom is formed or vice-versa [45]. Such a bond formation was demonstrated by Lee and Ho [46]. They deposited two CO molecules over an adsorbed Fe atom on a Cu(100) surface using the vertical manipulation procedure. Because an adsorbed Fe atom on this surface can accommodate two CO molecules, an Fe(CO)2 iron carbonyl was produced. Complex mechanisms are involved in the formation of a bond between two adsorbed molecular fragments on a surface. In order to join the two molecular fragments to form a bond between them, the electronic wave functions of their reactive parts need to overlap signiﬁcantly. Hence they have to be in close proximity to each other, in addition to a proper alignment of their reactive parts, to allow for a bond formation [39]. After dissociation

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from the parent molecule, the reactive part of a molecular fragment is in most cases bonded to the metal substrate. For example, in case of a phenyl molecule produced from the dissociation of an iodobenzene molecule, the free carbon atom bond is attached to the Cu substrate. This bonding results in tilting of the π-ring about 45◦ away from the surface plane on the terrace (Fig. 15(a)). At the step-edge however, the free carbon atom can be directly attached to a Cu step atom so that the π-ring is lying ﬂat on the lower terrace (Fig. 15(b)). Here phenyls can be aligned more easily than on the terrace since only the distance in between them varies as they are moved, while on the terrace they can also be rotated. When the two phenyls bonded to the step edge are in very close proximity to each other, the hydrogen atom repulsion causes a rotation (Fig. 15(c)). This position weakens the C-Cu bonds as compared to the isolated phenyls. Calculations for the C-C coupling mechanism on a surface explain that this slightly rotated position of the two C atoms can already produce a σ ∗ anti-bonding state, an important indicator for a σC-C bond formation. Further rotation of the two π-rings until their reactive C atoms face each other will complete formation of the C-C bonds while simultaneously severing the C-Cu bonds. This rotation requires an activation energy to overcome the coupling barrier. Naturally, this process is thermally activated. However, at very low substrate temperatures, the thermal activation process is negligible and thus, the C-C bond

Fig. 15. (Left) Adsorption geometry of phenyl. (a) Tilted π-ring position on the Cu terrace to form C-substrate bonding and (b) ﬂat-lying π-ring position at the step edge. When the two phenyls are in close proximity at the substrate step edge, the π-rings are rotated owing to the H repulsion (c). Further rotation into the direction shown by arrows results in the joining of the two reactive C atoms. (Right) A background subtracted STM image with a phenyl couple in its center. The upper and lower parts correspond to the stages before and after the chemical association. The tip height proﬁle across the centers of the synthesized biphenyl molecule is indicated. (Image parameters: +100 mV, 1.3 nA; 24 × 7 ˚ A2 ) [3,39].

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formation may not be completed. In the STM experiments, the two phenyls do not join at this substrate temperature of 20 K even though they are closely located to each other. The coupling of the two phenyls can succeed only when an additional amount of energy is supplied by injecting 0.5 eV tunneling electrons from the tip to the phenyl couple. This electronic excitation with tunneling electrons completes the C-C bond formation process. Figure 15 (right) visualizes the chemical association of two phenyls that were moved as close as possible to each other. The upper half of this image was acquired before association. The tip was positioned right above the center of the phenyl couple and the bias was raised to 500 mV for 10 seconds. Then the voltage was reduced to its original value of 100 mV and the STM tip continued to scan the lower half of the image, which corresponds to the post-association stage. The distance between the phenyl centers changes upon association to 4.4 ± 0.05 ˚ A (Fig. 15), which is consistent with the distance of 4.3 ˚ A between the two centers of the π rings for biphenyls in the gas phase. The observed process can only be initiated by using voltages greater than 0.5 V. Since the bias required for association is as small as 0.5 V, dehydrogenation during the association process can be ruled out.

5. STM-Tip Induced Single Molecule Chemical Reaction Using a combination of manipulation techniques together with tunneling spectroscopy measurements, a number of chemical reactions have been induced on single molecules leading to the synthesis of new chemical products [39,47,48]. A CO oxidation reaction was induced with STM on Ag(110) by Hahn and Ho. Single oxygen atoms were prepared by dissociation of an oxygen molecule using tunneling electrons. Then a CO molecule was moved towards an oxygen atom either by vertical manipulation after picking it up with the tip apex, or by inducing a lateral hopping on the surface upon application of repeated voltage pulses. After inducing the formation of CO2 , the product immediately desorbed [48,49]. By injecting electrons into the trans-2-butene (C4 H8 ) molecule, a transformation into 1,2-butadiene (C4 H6 ) was induced. This required electrons of suﬃcient energy to excite a speciﬁc vibrational mode to an amplitude such that two hydrogens were shaken oﬀ. The parent molecule as well as the product were identiﬁed both by their appearance in the STM images and by their vibrational spectra [47].

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Okawa and Aono [50] demonstrated under ambient conditions a diacetylen chain polymerization induced in a self assembled monolayer of 10,12-nonacosadiyonic acid on graphite. First an artiﬁcial defect was created with the STM tip by applying a positively pulsed sample bias, the polymerization of a single diacetylene monolayer chain was initiated at another surface location with a negative voltage pulse. After progression of the chain reaction, the polymer chain was terminated at the artiﬁcial defect site. Wolkow et al. [51] generated molecular lines on a H-terminated Si(100) surface by creating dangling bonds at the surface and exposing them to styrene vapor. A carbon centered radical is formed which is stabilized by H-abstraction from the neighboring Si-H site. Thus, the propagating species, the dangling bond, is regenerated. The process leads to the formation of lines with potential use as molecular wires. In the following section, the synthesis of a biphenyl molecule from two iodobenzene molecules adsorbed on a Cu(111) surface using single molecule manipulation techniques with the STM-tip is presented as example. Ultimate Ullmann Reaction. Almost a century ago, Ullmann and coworkers discovered that heating a mixture of C6 H5 I liquid and Cu powder to ∼400 K resulted in formation of C12 H10 [52]. From this experiment, they derived the following formula;

There are three elementary steps involved in this reaction after adsorption of C6 H5 I on Cu: dissociation of C6 H5 I into phenyl (C6 H5 ) and iodine, diffusion of phenyl to ﬁnd its reaction partner, i.e. another phenyl, and ﬁnally, association to form a biphenyl. The Cu surface acts as a catalyst in this reaction process. Naturally, the Ullmann reaction is triggered by thermal excitations. Dissociation of C6 H5 I occurs at ∼180 K and biphenyls are formed at ∼400 K. Thus it is necessary to conduct single molecule experiments at low temperatures to avoid thermal inﬂuences. All the STM manipulation procedures described in the previous sections are systematically applied to create each reaction step in the above sequence. An STM image sequence of a tip-induced Ullmann reaction is presented in Fig. 16. Two iodobenzene (C6 H5 I) molecules adsorbed at the lower part of a Cu(111) step-edge (Fig. 16(a)) have been selected as the initial ingredients for this reaction. The dissociation of molecule is realized by injecting

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Fig. 16. Three dimension STM images showing the basic steps of the tip induced Ullmann reaction. Two adsorbed iodobenzene molecules at the lower terrace of the Cu(111) step-edge (a). Iodine is abstracted from the molecules by injecting tunneling electrons (b). Iodine atoms (small) and phenyl molecules (large) are further separated by lateral manipulation (c). The iodine atom located between the two phenyls is removed onto the lower terrace to clear the path between the two phenyls (d). The phenyl molecule at the left side is moved close to the right phenyl and then 500 meV voltage pulses are supplied by the STM-tip to form a biphenyl molecule (e). [Image parameters: +100 mV, 0.53 nA; 70 × 30 ˚ A2 ] [3].

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1.5 eV tunneling electrons from the tip to each molecule. A single tunneling electron energy transfer to the molecule causes breaking of the C-I bond. After dissociation, both iodine and phenyl are adsorbed at the lower part A denoting of the Cu step edge and are separated by 2.5a0 (a0 = 2.55 ˚ the Cu nearest-neighbor distance), i.e. two and a half Cu atom distances (Fig. 16(b)). To prove that they are actually dissociated, the iodine atoms and phenyl fragments are further separated by lateral manipulation with the tip (Fig. 16(c)). After this, the iodine atom located between the two phenyls is relocated to a terrace site with the tip to clear the diﬀusion path of phenyl (Fig. 16(d)). The phenyl at the left side of the image is then moved along the Cu step edge to the right side until the two phenyls meet and then 500 meV tunneling electrons are injected into the phenyl couple to join them (Fig. 16(e)). The ﬁrst image (Fig. 16(a)) shows two adsorbed C6 H5 I molecules on Cu exactly representing the left side of the Ullmann equation. The ﬁnal image (Fig. 16(e)), illustrating a biphenyl molecule and two iodine atoms on Cu, exactly represents the right side of the equation. Thus, the whole chemical equation can be visualized step by step with individual reactants. Additionally, the important role of step edges in catalytic reactions is reﬂected in this atomic scale reaction sequence. In 1929, one-dimensional defects were proposed as the catalytically active sites in the ‘Adlineation Theory’ by Schwab and Pietsch [53]. Since then only a few detailed studies for metal catalyzation at step edges have emerged. During this experiment, it was found that it is much easier to induce the reaction at Cu step edges, especially at very low molecule coverages for the following reasons: (1) Adsorption: Due to their mobility, most C6 H5 I molecules are adsorbed at the Cu step-edges even at ∼20 K. Therefore, they are easy to locate. (2) Dissociation: Due to the stronger binding at the step edges than on the terrace, the phenyls attach to the step edges after dissociation. (3) Diﬀusion: Again due to the stronger binding, it is easier to laterally manipulate the phenyls along the step edge without losing them. Step edges are also used as navigation aids for the manipulation paths. Moreover, there is a higher probability for phenyls to meet a reaction partner, another phenyl, at the step edges. (4) Association: Because the step edge locks the closely located phenyl couple, it is easier for them to join.

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6. Future Prospects of Single Molecule Chemical Reactions By inducing chemical reactions with the STM tip, various underlying reaction processes can be studied on a molecular level. Chemical reactions like the Ullmann equation can be conﬁrmed. New chemical reaction pathways can be discovered. However, care needs to be taken in making direct relationships between the natural and tip-induced reactions. Under the inﬂuence of the tip, reactions can be induced which otherwise may not occur in nature. But this is exactly the advantage for nanotechnology since the synthesis of individual man-made molecules, never before seen in nature nor made in chemical reactors, may eventually become a possibility. Construction of single molecules on a one-at-a-time basis using the STM-tip as an engineering tool [55] may require creation of basic building blocks, bringing them together to an assembling place and then joining them to form a desired molecule. This entire process is somewhat similar to the assembly of automobiles or electronic commodities such as TV’s, computers, etc. in a factory production line. Basic blocks for construction of a molecule can be atoms, molecules or radicals. By selective bond breaking with an STM-tip, unnecessary parts of a molecule can be cleaved oﬀ and thereby active sites can be created. Such molecules can be used as basic blocks to join with other tailormade species to build a new molecule. The individual molecules may also be constructed with the STM tip and collected for further use as basic blocks to assemble larger molecules. The ability to bring these basic blocks to an assembling place with atomic scale precision is an important and integral part of the process. A crucial step in the bond formation procedure is the proper alignment of molecular blocks so that they can be joined in a correct geometry. For this an accurate reorientation and repositioning of molecules is necessary. At sufﬁciently low temperatures, this can also be achieved by using the STM tip. Molecules with speciﬁc functions, to be used in nanoelectronic and nanomechanical devices, can be constructed, and their physical and chemical properties can be studied in situ with STM spectroscopy techniques on an individual basis. Even though the direct industrial application of single molecule construction may not be possible in the near future, the knowledge can help initiate a mass scale production. Thus, with these achievements in molecular manipulation possibilities with the STM, a new dimension for future nanoscience and technology is now open.

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[31] L. Bartels, G. Meyer and K.-H. Rieder, Appl. Phys. Lett. 71, 213 (1997). [32] G. Meyer, S. Z¨ ophel and K.-H. Rieder, Appl. Phys. A 63, 557 (1996). [33] J. I. Pascual, N. Lorente, Z. Song, H. Conrad and H.-P. Rust, Nature 423, 525 (2003). [34] F. Moresco, G. Meyer, K.-H. Rieder, H. Tang, A. Gourdon and C. Joachim, Phys. Rev. Lett. 86, 672 (2001). [35] C. Loppacher, M. Guggisberg, O. Pfeiﬀer, E. Meyer, M. Bammerlin, R. L¨ uthi, R. Schlittler, J. Gimzewski, H. Tang and C. Joachim, Phys. Rev. Lett. 90, 066107 (2003). [36] G. Dujardin, R. Walkup and P. Avouris, Science 255, 1232 (1992). [37] R. Martel, P. Avouris and I.-W. Lyo, Science 272, 385 (1996). [38] B. C. Stipe, M. A. Rezaei, W. Ho, S. Gao, M. Persson et al., Phys. Rev. Lett. 78, 4410 (1997). [39] S.-W. Hla, L. Bartels, G. Meyer and K.-H. Rieder, Phys. Rev. Lett. 85, 2777 (2000). [40] L. J. Lauhon and W. Ho, Phys. Rev. Lett. 84, 1527 (2000). [41] L. J. Lauhon and W. Ho, J. Phys. Chem. 104, 2463 (2000). [42] S.-W. Hla, G. Meyer and K.-H. Rieder, Chem. Phys. Lett. 370, 431 (2003). [43] S.-W. Hla, G. Meyer and K.-H. Rieder, Chem. Phys. Chem. 2, 361 (2001). [44] J. W. Gadzuk, Surf. Sci. 342, 345 (1995). [45] L. Bartels, G. Meyer, K.-H. Rieder, D. Velic, E. Knoesel et al., Phys. Rev. Lett. 80, 2004 (1998). [46] H. J. Lee and W. Ho, Science 286, 1719 (1999). [47] Y. Kim, T. Komeda and M. Kawai, Phys. Rev. Lett. 89, 126104 (2002). [48] W. Ho, J. Chem. Phys. 117, 11033 (2002). [49] B. Stipe, M. Rezaei, W. Ho, S. Gao, M. Persson and B. Lundqvist, Phys. Rev. Lett. 78, 4410 (1997). [50] Y. Okawa and M. Aono, Nature 409, 619 (2001). [51] G. Lopinski, D. Wayner and R. Wolkow, Nature 406, 48 (2000). [52] F. Ullmann, G. M. Meyer, O. Loewenthal and O. Gilli, Justus Liebig’s Annalen der Chemie 331, 38 (1904). [53] G. M. Schwab and E. Pietsch, Z. Phys. Chem. Abt. B 2, 262 (1929). [54] L. Bartels, G. Meyer and K.-H. Rieder, Appl. Phys. Lett. 71, 213 (1997). [55] S.-W. Hla, in Nanoscale Spectroscopy and Its Application to Semiconductor Research, eds. Y. Watanabe, S. Heun, G. Salviati and N. Yamamoto, Lecture Notes in Physics (Berlin, Springer, 2002), p. 222.

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SINGLE-MOLECULE VIBRATIONAL SPECTROSCOPY AND CHEMISTRY J. I. PASCUAL Instut f¨ ur Experimentalphysik Freie Universit¨ at Berlin Arnimallee 14, D-14195 Berlin, Germany N. LORENTE∗ Laboratoire Collisions Agr´ egats R´eactivit´e UMR 5589, IRSAMC Universit´e Paul Sabatier, 118 route de Narbonne 31062 Toulouse C´ edex, France [email protected] Abstract. The ultimate characterization of a single molecule relies on its chemical identiﬁcation. Single-molecule vibrational spectroscopy has been a major breakthrough in the development of individual molecule handling. On one hand it provides a tool to characterize local structure and bonding; on the other it provides a methodology to manipulate single molecules by activating speciﬁc vibrations. Here we introduce the topic of single molecule vibrational characterization with the scanning tunneling microscope (STM) and its speciﬁcities with regards to the excitation and detection of local vibrations. We will expound how inelastic electrons can serve to this end, and how to interpret the results of such a technique. An important consequence of exciting localized modes is the enhanced control that the excitation grants over possible molecular reaction paths. Keywords: Vibrational spectroscopy; scanning tunneling microscopy and spectroscopy; conductance; inelastic conductance; single-molecule chemistry; controlled manipulation; mode-selective reactivity.

Contents 1 2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 How Does Single-Molecule Vibrational Spectroscopy Work? . . . . . . . 211

∗Corresponding

author. 209

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3 Experimental Issues of Inelastic Tunneling Spectroscopy 4 Theoretical Basis of Inelastic Tunneling Spectroscopy . 5 What Can We Learn from Theory? . . . . . . . . . . . . 6 Single Molecule Vibrational Chemistry . . . . . . . . . . Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1. Introduction Scanning tunneling microscopy (STM) and spectroscopy (STS) are the most suitable techniques to image and measure a single adsorbed molecule. However, since the initial development of this technique, an intrinsic lack of chemical sensitivity became apparent. As an imaging technique based on electronic interactions between an adsorbate/surface system and a probe, its chemical sensitivity depends on the possibility to recognize the identity of a single adsorbate from measurements of its topography plus its electronic conﬁguration. This is in practice a very diﬃcult task, especially with an adsorbate, since its electronic conﬁguration is strongly distorted upon adsorption, and includes states from both the surface and the adsorbate itself. In surface science, molecular vibrations are the chemical ﬁngerprints suitable for the identiﬁcation of adsorbed species. When binding with a surface, changes in molecular conformation plus reduction in symmetry lead to partial rupture of degeneracies, to combination of modes into new vibrational states, and to partial shifting of the vibrational frequencies as a response to the interaction with the surface. In general, the molecule’s vibrational ﬁngerprint can be recognized from both experiments and theoretical simulations. Thus, the measurement of molecular vibrational modes with the spectroscopic mode of STM [1] allows the chemical characterization of a single adsorbate to be ﬁnally accomplished. An important aspect intrinsically associated with the excitation of molecular vibrations is that they provide a means to individually manipulate a single adsorbate. On a surface, local molecular excitations do generally damp quickly due to the continuum of excitations provided by the substrate. However, alternative quenching pathways may take place involving intra- or extra-molecular movement. With the advance of singlemolecule vibrational spectroscopy, several works have provided interesting points of view of this phenomenon, in many circumstances involving complex channels of energy transfer between diﬀerent vibrational coordinates.

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In this chapter, we review important concepts regarding vibrational spectroscopy with the STM. First, the basis of the technique will be introduced, together with some of the most relevant results produced up to date. It will be followed by a short description of experimental issues. The third section introduces theoretical approaches employed to simulate the vibrational excitation and detection processes. The theory provides a molecular-scale view of excitation processes, and can foresee the role of various parameters such as molecular symmetry, adsorption properties, or electronic structure of the adsorbate. Finally, we will describe current approaches to understand quenching dynamics via internal molecular pathways, leading to several kinds of molecular evolution. This has been named single-molecule chemistry.

2. How Does Single-Molecule Vibrational Spectroscopy Work? Single-molecule vibrational spectroscopy uses a measurable change in conductance across the onset for vibrational excitation of the diﬀerent modes of an adsorbed molecule to identify its vibrational ﬁngerprint. The tip of an STM is placed on the molecule and the voltage is ramped up. When the energy given to the electrons matches a quantum of vibration, the conductance changes abruptly; the STM has measured the frequency of a mode of an adsorbed molecule. Vibrational spectroscopy is based on two fundamental processes: excitation and detection. As we shall see later in this chapter, they are not equivalent, and indeed both have to be treated to understand the origin of active modes in the spectra. The excitation is based on inelastic scattering processes, thus connecting initial and ﬁnal states with diﬀerent energy. The detection relies on the eﬀect of the new inelastic channel on experimentally observable magnitudes, i.e. the junction conductance. In this section, we introduce the working principle of vibrational spectroscopy. It will be compared with a “parent” technique called Inelastic Electron Tunneling Spectroscopy, which was developed in the 60’s. Although the working principle is similar in each of them, the speciﬁc nature of electron–vibration interaction diﬀers. We shall conclude this section by reviewing the most important achievements of single-molecule vibrational spectroscopy. The inelastic channel: A current is created when two electron reservoirs are connected. In equilibrium no-electron ﬂow takes place; the chemical potential (i.e. the Fermi energy at T = 0) is well deﬁned. When a bias

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voltage is applied between the tip and sample electrodes, their chemical potential is no longer deﬁned. The voltage drop will take place in the small region connecting both electrodes. In the case of tunneling junctions the voltage drop happens in the insulator layer: the vacuum in STM. Electrons can ﬂow because the ﬁnal states will be empty; the chemical potentials of each electrode diﬀer by the applied bias voltage times the charge of the electron. When the bias voltage corresponds to chemical potential shifts smaller than the quantum of vibration the electron cannot yield its energy to the vibration because there is no ﬁnal state at the surface electrode available (Fig. 1(a)). At T = 0, the excitation happens suddenly when the bias voltage energy is larger than the quantum of vibration. The inelastic electron can continue its propagation into an empty electronic state now available above the sample Fermi level. In this case, a new channel for electronic transport has been open; this is called the inelastic channel (Fig. 1(b)).

Fig. 1. (a, b) Energy-distance diagrams of the tunneling processes with an applied bias V . The molecular vibrator is represented by a harmonic oscillator located in the vacuum gap. When the electron energy eV is smaller than the vibrator eigenenergy, the ﬁnal state of an inelastic transition would be a sample ﬁlled state (a); the inelastic channel is closed. Hence electrons tunnel without interaction with the oscillator. When eV reaches the mode energy ω, empty ﬁnal states at the sample’s Fermi energy become accessible; the inelastic channel is open. The opening of the inelastic channel causes (c) a sharp increase ∆G in the tunneling diﬀerential conductance dI/dV or (d) peaks in the second derivative d2 I/dV 2 . The activation of the inelastic channel takes place indistinguishably of the bias polarity.

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Detection of the inelastic signal: To probe the vibrational structure of an adsorbate, the modes have to change their excitation state. When the inelastic channel is opened, a small fraction of electrons (fi ) tunneling through the adsorbate are susceptible of inducing these excitations. The inelastic channel acts in addition to those scattering (transport) processes in which initial and ﬁnal electronic states have equal energy, i.e. the elastic channels. Hence, as a ﬁrst approximation, the eﬀect of the vibrational excitations will be a slight increment ∆G ∼ fi × G of the junction diﬀerential conductance G ≡ dI/dV (Fig. 1(c)). Since the intrinsic width of a vibrational mode is smaller than 1 meV, the measurement of a vibrational spectrum can be then achieved with high energy resolution by detecting changes in the tunnel junction conductance as the onset energy for vibrational activation is surpassed. However, as we shall see later, the eﬀect of the channel opening on the conductance is more complex, and ∆G is usually reduced due to many-body eﬀects in the transport, causing only a few modes to be active to the observation with the STM. The eﬀect of the opening of the inelastic channel on the diﬀerential conductivity (dI/dV ) of the molecular junction may be understood by using a water analogy, used in [2]. The water ﬂow (tunneling current) through a water pipe increases steadily with the water pressure (voltage). If at a certain pressure a crack in the pipe opens (inelastic channel), a sudden increase in the rate of water ﬂow will take place. The opening of the crack is an additional channel for the ﬂow of water, producing a decrease of the tube’s resistance. In practice, the inelastic fraction fi is a small number, typically smaller than 0.1. A change in conductance smaller than 10% can be detected only under very extreme conditions of stability and energy resolution. To help with the detection of such small signal, the second derivative of the tunneling current, d2 I/dV 2 = dG/dV , is usually measured. A d2 I/dV 2 vs. V spectrum will show sharp peaks at energy values of a vibrational excitation onset = E/ (Fig. 1(d)). Integration of the peak gives an estimation of the normalized change of conductance ∆G/G, thus, a lower limit for the inelastic fraction of a speciﬁc inelastic channel. Symmetry of the spectra: A clear characteristic of the spectra is that narrow peaks, centered at certain values in the positive (sample) voltage axis, are reproduced as similar narrow dips at the opposite polarity. Such symmetric position of the vibrational peaks with respect to the zero bias point is a general feature for every spectrum measured, and it is used as a test of the vibrational origin of a measured peak (see Fig. 1(d)). This

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symmetry implies that the inelastic channel is open similarly for electrons tunneling in both directions. Strong asymmetries of the electrode’s density of states might introduce a variation of the peak intensity, as the inelastic channel depends on the number of ﬁnal states available. However, the position of the vibrational peaks should not be aﬀected. Whenever the chemical potential of the molecule/surface electrode is constant (good chemical/electrical interaction) the position of the vibrational peaks is fully deﬁned as an energy loss process between an initial ﬁlled state and a ﬁnal empty state, and thus independent of polarity. The magnitude of the Stark eﬀect in the energy position of the vibrations is also negligible [3]. IETS vs. STS: The strategy to obtain the vibrational structure of a single molecule is based on a traditional vibrational spectroscopy technique called Inelastic Electron Tunneling Spectroscopy (IETS) [2]. In 1966, Jacklevic and Lambe [4] observed that tunneling electrons were able to excite and resolve vibrational modes of a thin layer of molecules buried between two metallic electrodes and an oxide layer (Fig. 2(a)). The latter represents a tunneling barrier for the electronic transport between the metallic electrodes. Such tunnel junction conﬁguration is easily reproduced by the STM (Fig. 2(b)), where the oxide layer is substituted by the tip-sample vacuum gap. In STM, the molecules under investigation are adsorbed on an atomically clean metal surface with a well-deﬁned geometry, and do not interact with any other atomic object. Thus STM works under the same controlled conditions as other classical surface chemistry

(a) IETS

(b) IETS-STM

Fig. 2. (a) IETS conﬁguration vs. (b) STM conﬁguration. The former measures a macroscopic amount of species buried between the electrodes and the oxide layer of typically 3 nm, while STM resolves vibrations on a single molecule on atomically clean conditions.

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techniques, but with a quantitative gain in the spatial resolution of the adsorbate’s vibrational structure. Besides, there are other important diﬀerences between the so-called inelastic STS (ISTS or IETS-STS) and traditional IETS. A gross comparison between them is shown in Table 1 for the sake of illustration. Regarding the experimental technique, ISTS employs larger current densities — typically in the order of 1 nA per molecule. However, IETS averages information on a large amount of molecules, and additionally, its stability allows for larger time averaging periods. This causes IETS to be more sensitive, being able to detect changes of conductance smaller than 1%. ISTS, on the contrary, fails to resolve signals smaller than 1%; in the STM conﬁguration, the tunnel junction is subjected to small changes during the measuring process due to small instabilities or drifts of the system. Hence, the measurements need to be performed in a shorter timescale (usually in the order of one minute) before readjusting the vacuum gap size with the feedback loop. The lower sensitivity of ISTS could have prevented the resolution of vibrational ﬁngerprints if the excitation mechanism had been merely based on the dipolar coupling between tunneling electrons and the molecular bonds, as is the case in IETS. In IETS, infrared as well as Raman active modes induce a change in conductivity smaller than 1%, which is suﬃcient to produce clear signals in the spectra. G. Binning et al. [5] predicted a change of conductance for infrared active modes in the order of 1%, for current densities and geometry of the STM conﬁguration, by using the dipole Table 1. Gross comparison between IETS and ISTS: The entries are illustrative of the diﬀerences between two techniques. IETS is more sensitive due to averaging for larger time window and larger number of molecules; therefore, it may reach also better energy resolution. ISTS reaches higher spatial resolution by detection of signal on a single molecule, and employing a shorter tunneling barrier. Data for IETS are representative parameters, from [2].

Information from Current Tunnel resistance Current density Tunnel barrier Sensitivity (∆G/G) Time Bias modulation Energy resolution

IETS

ISTS

molecules mA’s ∼100 Ω ∼10−1 A/cm2 3 nm 0.1–1% ∼30 min ∼1 mV ac ∼2.6 meV (21 cm−1 )

1 molecule nA’s ∼100 MΩ ∼105 A/cm2 0.5 nm 1–10% ∼2 min >3 mV ac >6 meV (54 cm−1 )

1010

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approximation. Later on, Persson and Baratoﬀ [6,7] predicted that due to the proximity of the electron source to the molecule, resonance and impact scattering might dominate over dipole scattering. With this type of interaction, changes in conductance as large as 10% could be induced, thus lying in the range of sensitivity of the STM. Additionally, in STM the electron ﬂux is now focused on a single molecule, and the spatial resolution is conﬁned to the extension of molecular resonances, being more localized than if the electron-molecule interaction would have been mediated by dipolar moments.

3. Experimental Issues of Inelastic Tunneling Spectroscopy The intrinsic width of a vibrational mode is less than 1 meV. In order to detect the inelastic signal, high resolution in energy is required. Since we are working with tunneling electrons, such resolution may be only accomplished working at cryogenic temperatures. Thermal broadening of the vibrational peaks is in the order of 5 kT; at 10 K this corresponds to 4 meV. Although there is no ﬁxed temperature limit for the detection of the inelastic signal, it becomes extremely diﬃcult to resolve the peaks from the background above some tens of degrees. Thermal drift worsens this upper limit considerably. Lauhon and co-workers [3] succeeded to detect the signal of the C-H stretch mode in acetylene at temperatures up to 60 K. To detect the weak d2 I/dV 2 signal, lock-in techniques are usually employed. These techniques are implemented by adding a small ac modulation with frequency w to the bias voltage and by detecting the response of the molecular tunneling junction. The resulting tunneling current can be then Fourier decomposed in the base of the applied modulation frequency w: I(V, t) = I0 (V ) + ε

ε2 d2 I dI cos(wt) + cos(2wt) + · · · dV 4 dV 2

(1)

where ε is the ac voltage modulation with frequency w, and t is the time. Non-linearities in the current vs. bias (I vs. V ) plot give rise to higher harmonics in the response of the tunneling current to an ac voltage. Following expression (1), the magnitude of the response oscillating with frequency 2w yields a value proportional to d2 I/dV 2 . This value is outputted by modern lock-in instruments, which can measure a large number of diﬀerent harmonics of the modulation frequency w. To take a spectrum, the dc sample bias is scanned along the energy window of interest, searching for sharp variations of the d2 I/dV 2 magnitude.

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To enhance the signal to noise ratio, the measurements have to be performed slowly; for each data point the time scale of the measurement should be large compared to the period of the bias modulation. This requires a very stable tunnel junction. Usually, the measurement of one spectrum takes times in the order of 60 seconds. At the low temperatures mentioned above, such higher stability of the tunnel junction can be attained since the whole STM head is in thermal equilibrium with a liquid He bath or ﬂow. Based on speciﬁc conditions of stability, it is advisable to maximize the temporal averaging of the measurements, i.e. the ratio between the lock-in time constant ﬁlter and the modulation period, as well as the time spent at each bias value. To improve the quality of the spectra, it is also usual to average several individual measurements obtained sequentially; in this case, the size of the tunnel junction gap is re-established to its initial value by connecting the feedback loop for a short time interval between each spectrum. This improves the aspect of the spectrum, albeit the signal should be clear in every voltage scan. A detailed description of experimental methods for acquiring the inelastic signal can be found in [2] and [3]. Achievements: Examples of vibrational spectra are shown in Fig. 3. ISTS is sensitive to both signal from internal (e.g. Fig. 3(a)) and external (e.g. Fig. 3(b)) modes. In every case, the number of modes detected is small, and does not follow any selection rule known for Raman or infrared active modes. Modes involving movement of a large number of atoms are

Fig. 3. (a) Vibrational spectra of C2 H2 on Cu(100): the peak at ±356 mV is due to excitation of the C-H stretch vibration (ν(C-H)). (b) Vibrational spectra of CO on Cu(100): the peaks at ±5 mV and ±35 mV are due to excitation of the CO frustrated rotation (R(CO-Cu)) and translation (T(CO-Cu)) respect the Cu(110) surface; thus they are external modes. (c) Vibrational spectra of C60 on Ag(110): the two clear peaks at ±55 mV are associated to a breathing mode of the fullerene cavity (Hu (2) mode). The insets show topography of a single molecule.

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also observed. Figure 3(c) shows a cavity breathing mode of a C60 molecule adsorbed on a Ag(110) surface [8]. Among the 46 distinct vibrational eigenfrequencies, the authors ﬁnd only one clear peak associated to a breathing mode of the icosahedral cavity. Several issues come out from these sample spectra; the most obvious one is the lack of sensitivity for many of the molecular modes, which remain inactive, or undetected. No relation with excitation selection rules from other techniques (IR, Raman, EELS) can be deduced. The initial results of ISTS point to the fact that active modes depend on the symmetry and conﬁguration of the adsorption geometry. Although the exact origin of excitation-detection selection rules are unknown, there is general agreement that they lie behind the resonant mechanism for excitation, and in any case being strongly dependent on the electronic conﬁguration of the adsorbate-surface ensemble at the Fermi energy. The most clear demonstration of the predictions of a resonant mechanism of vibrational excitation was provided by Hanh et al. [9]. The authors ﬁnd a decrease in the conductance associated with the onset of activation of an O-O stretch mode, for O2 on Ag(110). Such reversed behavior follows predictions made by Persson et al. [10] for those systems with narrow molecular resonances around the Fermi level (EF ). The theoretical fundaments of these and related issues will be discussed later in this chapter. Attached to the idea that the activation of a mode depends on electronic states at EF , the symmetry of the adsorption conﬁguration, which dictates orbital degeneracies surviving from the free molecule, also aﬀects the activation of speciﬁc modes. Lauhon and Ho found that benzene on copper activates a C-H stretch mode only when the molecule is tilted by removing two of the hydrogen atoms [11]. A similar eﬀect is found both on physisorbed and chemisorbed benzene on Ag(110): undetected modes become detectable in molecules with a distorted adsorbed conﬁguration due to the presence of a surface step [12]. On C60 the eﬀect of the adsorption symmetry was the opposite one, since the detected cavity breathing mode could only be observed on those molecules keeping a symmetric orientation with respect to the surface [8,13]. Clearly, there is not a uniﬁed response to all these issues; we cannot even rely on the existence of ﬁxed set of selection rules that predict the intensity of a speciﬁc mode in the spectra. However, Lorente and co-workers found some group theory arguments based on the symmetry of initial and ﬁnal electronic states participating in the inelastic channel [14], which will be reviewed in the following section.

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One of the most impressive achievements of ISTS is the high spatial resolution, which allows localization of vibrational ﬁngerprints with subnanometer resolution. By tuning the dc sample bias to the energy of a speciﬁc mode, the STM can resolve spatial variations of the inelastic signal around the molecular structure. The question thus arising is how focused this signal is in real space. Stipe and co-workers [15] observed that the excitation of the C-H (or C-D) stretch modes of single deuterated acetylene (C2 HD) is well localized to the chemical bond being probed (Fig. 4(a)). However, whenever a resonance located close to the Fermi level mediates the excitation, its spatial shape will be inherently represented in the inelastic maps. Hanh et al. [9] found that the distribution of the O-O stretch signal in O2 on Ag(110) follows the shape of the 1πg resonance about the Fermi level, whose ﬁlling upon chemisorption leads to longer O-O bonds. In many cases the electronic states at the Fermi level are derived from the tails of several resonances crossing the Fermi level. For benzene on Ag(110) [12, 13], several external modes detected in an energy window of barely 40 meV follow diﬀerent distributions along the molecule, as indication of excitation mechanisms

Fig. 4. Spatial distribution of inelastic signal in (a) C2 HD on Cu(100) (from [15]) and (b) C6 H6 on Ag(110) (from [13]). The plots show the corresponding vibrational spectra: (a) peaks appear at the energy of ν(C-H) and ν(C-D) modes; (b) peaks reveal the excitation of 3 external modes at 4, 19 and 39 meV (from [13]). In (a) the signal at 270 mV (360 mV) is localized at the C-D (C-H) bond. In (b) the inelastic signal is plotted as a function of energy (vertical axis) and distance across the molecule, i.e. x axis. The mode at lower energy (4 meV) has a minimum of intensity right at the center of the benzene molecule (appearing as a depression in the accompanying (x vs. y) topography. The other two external modes are distributed with a bell shape centered at the molecule.

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mediated by molecular resonances with diﬀerent symmetry (Fig. 4(b)). All in all, the spatial mapping of the inelastic signal is a powerful tool, with no equal in other spectroscopies.

4. Theoretical Basis of Inelastic Tunneling Spectroscopy A current is created when two electron reservoirs are connected. In equilibrium no-electron ﬂow takes place: the chemical potential (i.e. the Fermi energy at T = 0) is well-deﬁned. When a bias voltage appears between the electrodes, the chemical potential is no longer deﬁned. If the electrodes are large enough we can consider them to be in equilibrium, and the voltage drop will take place in a small region connecting both electrodes. In the case of tunneling junctions the voltage drop happens in the insulator layer: the vacuum in STM. Electrons can now ﬂow because the ﬁnal states will be empty: the chemical potential of both electrodes diﬀer by the applied bias voltage times the charge of the electron. When the bias voltage corresponds to chemical potential shifts smaller than the quantum of vibration, the electron cannot yield its energy to the vibration. Let us assume that the temperature is very low (less than 10 K) such that the probability of ﬁnding the vibrator in an excited state is negligible. In this case the electron will not gain energy from the vibrator but will cede its energy. In order to yield its energy the ﬁnal state of the electron has to be empty, in other words, the ﬁnal channel must be open. The only way of opening the channel is that the bias voltage energy is larger than the quantum of vibration. In this case the electron can excite the vibration and continue its propagation in an electronic state above the Fermi level of the second electrode: the vibration opens a new channel. The inelastic channel: When a vibration is excited by an electronic current, new channels contribute to the electron ﬂow. The conduction process is described as a scattering process: electrons enter the interaction region through well-deﬁned channels. A channel is deﬁned by the solution of Schr¨ odinger’s equation in the region well before the interaction so that the solution is exactly known. Each of the possible solutions before and after the interaction deﬁnes the initial and ﬁnal channels. Figure 5 shows a scheme with diﬀerent channels entering an interacting region. In the present context, the interacting region is given by the place where (or the time when) the electron–vibration interaction is no longer negligible. Figure 5(a) shows a case of elastic scattering. It corresponds to the ballistic regime in which the electrons ﬂow through the interaction region without

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Fig. 5. Scheme of the lowest-order contributions to electron transport through an interacting region. Two initial and ﬁnal asymptotic channels are represented joining the interaction region. The electronic trajectory is represented by an arrow entering and exiting through the diﬀerent channels. Case (a) corresponds to the zero order contribution where the electron–vibration interaction is not present and the electron stays in its corresponding elastic channel. Cases (b) and (c) are the ﬁrst non-zero contributions in the electron–vibration interaction (second order). In case (b) one electron changes channel, corresponding to a purely inelastic process. In case (c) the interaction mediates electron exchange, giving an extra contribution to the elastic channel.

scattering. The initial and ﬁnal channel energies are the same. The channels themselves can change: the initial electrode is diﬀerent from the ﬁnal one. Figure 5(b) shows the case when an electron is scattered by the vibration changing its channel. Newly open channels lead to an increase of the electron current. The inﬁnite electron reservoirs act as a pressurized container: whenever an electron can leak from the reservoir, it will. Hence the increase of ﬁnal electron channels leads to an increase of the electron current. The picture just given is not accurate. It actually depends on what type of coupling exists between the vibrator and the ﬂowing electrons. Caroli et al. [16] give a formal but complete account of the diﬀerent scenarios leading to a rich variety of behaviors of the current with the excitation of localized vibrations. In their analysis of metal-insulator-metal junctions they consider diﬀerent types of coupling where the vibrator (molecular impurity) lies within the junction. If the impurity lies inside the insulator layer, then the above picture turns out to be correct; the vibrational excitation is an opening of a new channel and the current increases. If the impurity is in contact with one of the electrodes the case is much more complex, and particular details on the impurity-metal interaction need be taken into account. The reason behind this classiﬁcation is that the electron–vibration scattering in the insulator layer is a one-electron process equivalent to the electron-molecule scattering problem. In contact with the metal, many-body features appear. The states are multielectronic and the

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vibration mixes them eﬃciently. The simple channel-opening picture is no longer valid. As a matter of fact, Caroli et al. [16] show that the current can actually decrease. Prior to the work by Caroli et al. [16], Davies [17] did some model calculations where the deﬁning parameter of the type of electron–vibration coupling was the distance of the vibrator to the metal contacts. He reached some conclusions in the line of the more systematic and profound description by Caroli et al. [16]. Namely, he showed that the main many-body eﬀect is the anti-symmetry of the many-body wave function. In order to take this anti-symmetry into account, he considered Slater determinants of the one-electron wave functions, and then performed perturbation theory on the electron–vibration interaction. The eﬀect of the electron–vibration coupling is to mix up the electronic states; the states of the full Hamiltonian contain the electron and vibration coordinates. One way of putting this mixing is to claim that “virtual” phonons are emitted and reabsorbed. This is a description that comes from perturbation theory in which electrons and vibrations are treated separately and they are mixed gradually through perturbation theory. Indeed, what it means is that the actual ground state contains vibration contributions that one cannot neglect. These contributions are very eﬃcient in mixing two-electron coordinates with the vibration coordinates in the full-system wave function. Our initial picture of one-electron channels needs to be reconsidered in certain cases. When tackling the task of developing a theory for the description of IETS with the STM, a many-body approach is thus unavoidable. The work by Davies [17] shows that one can actually get away with a simple manybody theory in which only the anti-symmetry of electron states is needed. The mandatory question is what a theory should account for. In order to answer this we need to re-consider what the IETS-STM technique is. By measuring the change in conductance, IETS-STM gives information on the localized vibrations of the STM junction. Hence there are two processes: the electron propagation and the vibration excitation. IETS-STM is performed at low temperatures (typically below 10 K) and at low currents (in the nano Amp`ere range). These are conditions that allow an identiﬁcation of vibration excitation by single electrons; the vibrator is probably in its ground state and the time between electrons is much longer than the lifetime of the vibrations. A theory should just consider electron propagation with a weak probability of exciting a vibration. Perturbation theory seems to be justiﬁed due to the smallness of the electron–vibration coupling (Migdal’s

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approximation), and the dynamics of the process (excitation and deexcitation) is considerably simpliﬁed by the above experimental conditions. Basically, there are two approaches to describe the vibration excitations: approaches that compute the probability of vibration excitation by an electron current, and approaches that compute the change in conductance by vibration excitation. In the ﬁrst case the accent is put on the description of the excitation, the change in conductance being a secondary process. In the second case, the conductance description is emphasized. Approaches based on scattering theory: The process of vibrational excitation is described with great detail in these approaches. The underlying idea is to calculate transition times (or excitation rates), and from there to obtain the contribution to the current coming from the inelastic process. A current can be seen as the transition time between electrodes times the charge of the electron. In this way, these theories expect that the inelastic contribution to the current be the rate of vibration excitation times the charge of the electron. This simplistic picture is wrong and theories taking into account inelastic eﬀects in electron transport are complicated (see e.g. [18,19]). Nevertheless, in the tunnel regime these theories turn out to be good approximations. In the tunneling regime, one can basically picture the electron transport as single-electron conduction events, where the static electronic structure is not strongly modiﬁed by transport itself. Persson and Baratoﬀ [6] have been the ﬁrst to estimate the inelastic contribution to the current by using a scattering-like approach. They show that fundamental aspects of the transport problem can be taken into account only if the propagation of the electron is treated on the same level as the vibration excitation. Similar approaches are those by Gata and Antoniewicz [20], and Spataru and Budau [21]. All of these approaches start by writing a Newns-Anderson type Hamiltonian: VakL,R c+ ckL,R + H.c. εkL,R c+ H = εa c+ c + kL,R ckL,R +

kL,R

+ Ω b+ b +

1 2

+

kL,R + Vµ,ν c+ µ cν (b + b).

(2)

µ,ν

The ﬁrst term of Hamiltonian (2) refers to the molecular orbital a, which is just the energy of the corresponding level when the state is populated (this is the meaning of the creation and annihilation couple c+ c). The second term refers to the extended electron states in the left (kL ) and right (kR ) electrodes. The third term is the coupling between the molecular and electrode states, given by the matrix element VˆakL,R . H.c. stands for hermitian

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conjugate. Hence, this term sets the width of the molecular resonance in contact with the electrode continua. The fourth term is the corresponding vibrational Hamiltonian for the local vibration of single frequency Ω. The creation and annihilation operators of one quantum of vibration are denoted by b+ and b respectively. The last term is the electron–vibration coupling where µ and ν are in principle any electronic states of the full system. This term permits an electronic transition induced by a vibrational one and vice versa. In Appendix, we comment on the way of calculating this term and its implications. These theories assume that there is an electronic state of the molecular impurity that will be populated and will induce the vibration excitation. This description is usually called resonance scattering because the active electronic state (a in Hamiltonian (2)) becomes a resonance in presence of the electrode’s continuum of states. In the gas-phase formulation [22,23] a negative ion resonance is formed. This negative ion has in general a diﬀerent conformation from the neutral molecule, hence when the ion resonance decays into the neutral molecule, the molecule is left in a vibrationally excited state. This process is very eﬃcient in producing the coherent multiple excitations of molecular modes [24]. However, it is quite diﬀerent from what the above theories using Eq. (2) try to model. In Eq. (2), resonance scattering means that there is basically a single molecular orbital that determines much of the relevant electronic structure. In the gas phase, the above exciting mechanism is dealt with the impact-scattering approach, also called sudden approximation. One can understand the excitation as caused by the brief appearance of an extra electron in the system which leads to the mixing of the diﬀerent states of the quantum oscillator (the molecular modes). Indeed, the residence time of an electron in a chemisorbed molecular resonance is orders of magnitude smaller than the typical times involved in any vibrational quantity. This is diﬀerent from the negative-ion resonance excitation in the gas-phase where the resonance lifetime is of the order of the vibrational period. The impact scattering or sudden mechanism has been used to explain the vibrational excitation of chemisorbed molecules in electron energy loss spectra (EELS). See in particular the reference by Tong et al. [25]. The above approaches estimate the excitation rate by using either second-order perturbation theory [6] or a re-summation to all orders in perturbation theory [20,21]. In order to be able to sum the inﬁnite series of perturbation theory references [20,21], we use an orthogonal basis-set of the model Hamiltonian (2) (the creation and destruction operators need to

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be canonical in order to use Green’s function perturbation theory). This approximation leads to the neglect of the mixing of electronic states in the electrode due to the molecular vibration. Despite the more approximate treatment of [6] this coupling is not neglected. The outcome is that [20,21] neglect many-body eﬀects that explain the decrease of conductance in certain systems, as Persson and Baratoﬀ predicted in the case of IETS-STM [6]. In the case of metal-insulator-metal junctions the decrease in conductance had been predicted two decades earlier by Davis [17]. The weakest point of these approaches is the diﬃculty to ﬁnd parameters for the initial Hamiltonian that are reliable and realistic enough for predictions and analyses. Approaches based on conductance calculations. More direct, these approaches focus in the measured quantity: the conductance. There are two main groups of theories. One is based on a tight-binding description of the transport processes where the electron current ji,j between to adjacent sites i and j, is evaluated by using [26–28]: 2e (3) Im(ψj∗ tj,i ψi ), where ψi is the electronic wave function for the site i, and tj,i is the Hamiltonian matrix element between adjacent sites or hopping matrix element. This approach allows for a complete calculation of transport in the presence of vibrations and interacting with them. In this way, the eﬀect of temperature (through phonon population, i.e. degree of excitation of the vibrations) and multiple excitations is taken into account. The inclusion of multiple electronic channels permits them to go beyond the above resonance models: the molecule can have several orbitals contributing to the conductance and to the coupling with its vibrations [28]. Emberly and Kirczenow [29] have included explicitly the eﬀect of exchange in the evaluation of inelastic transport in the above approach. As we saw above, the eﬀect of exchange is fundamental to understanding the decrease in conductance when a vibration is excited (i.e. a phonon is emitted). However Mingo and Makoshi [27] claim that the formalism of Bonca and Trugman [26] includes exchange eﬀects if the formalism is used with Green’s functions instead of wave functions. They claim that the expressions of [6] are recovered if they developed perturbatively their own expressions. The other type of theory uses non-equilibrium Green’s functions. Green’s functions are more tractable in a localized basis set, such as the one ji,j =

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corresponding to a tight-binding description [16]. Nevertheless an extended basis description is also possible [30]. The use of tight-binding implies the simpliﬁcation of the problem to Hamiltonian Eq. (2), hence having the same problems of pertinence and accuracy as we mentioned above. The real space or extended basis description has the advantage of building upon accurate results from plane-wave calculations of the electronic structure [30]. Nevertheless, electronic structure calculations based on localized basis sets can become as accurate and predictive as plane-wave based results [31]. Plane-wave based calculations have the diﬃculty of how to transpose the calculated electronic structure into a form useful for transport calculations. Transport calculations are better suited for description in localized basis sets, hence transport based on ab initio localized basis codes are turning to be the best tool [32]. When a tunneling calculation is undertaken, many simpliﬁcations render the task easier than a complete transport calculation such as the one of [32]. Let us take the formulation by Caroli et al. [16] using the change induced by the vibration in the spectral function of the lead. In this description, the current and thus the conductance are proportional to the density of states (spectral function) of the leads (here tip and substrate). This is tantamount to using some perturbational scheme on the electron transmission amplitude between tip and substrate. This is what Bardeen’s transfer Hamiltonian achieves. The main advantage of this approximation is that one can use the electronic structure calculated by some standard way, for example planewave codes, and use perturbation theory to account for the inelastic eﬀect. In [33], a careful description of the Bardeen approximation in the context of inelastic tunneling is given, and how the equivalent of Tersoﬀ and Hamann theory [34,35] of the STM is obtained in the inelastic case. The Tersoﬀ and Hamann theory [34,35] says that the tunneling conductance, σ, is proportional to the local density of states (LDOS) evaluated at the tip’s center, r0 , and at the Fermi energy, εF : σ∝ |ψν (r0 )|2 δ(εν − εF ) (4) ν

The LDOS is then a sum over all the one-electron eigenstates given by the label ν, of the square of the wave function of each eigenstate, ψν , times a Dirac’s delta function that selects those eigenstates at the Fermi energy. This quantity is then a density of states (the Dirac’s delta gives the number of states per unit energy at the Fermi level) times an electron density (the contribution of each eigenenergy to the density of states

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is weighed by the spatial distribution of the corresponding eigenstate). The Tersoﬀ and Hamann theory is a simple and powerful way of identifying a constant current STM image with the electronic structure of the surface. The bias voltage between tip and substrate does not enter because it is assumed that the STM operates in the linear regime. A result of linear theory is that the transport properties are ﬁxed by the electronic structure at the Fermi level: there is no room for the bias voltage. This approximation will fail when the current is not linear with voltage. The tip structure does not enter in this theory explicitly. This is due to the assumption that the electronic structure of the tip is totally symmetric about the tip’s apex. This is equivalent to saying that the electronic wave functions have angular components that only contain the spherical harmonic Y00 . This does not imply that the electrons of the tip’s atoms are s-electrons. Indeed, one can have a tip made out of s-electrons, and the overall wavefunction has other spherical harmonics in their composition; this is so because the spherical harmonics are centered about the tip’s apex and not about each atom’s center. The corresponding generalization to inelastic tunneling takes on a very simple form (see [33] for a complete description beginning in Bardeen’s approach). It basically says that the inelastic contribution to the change in conductance will be caused by the change in the LDOS due to the vibration. Now the problem is complicated by the many-body aspects of the theory. There is a ﬁrst term that can be traced back to a transfer of a quantum of vibration by the impinging electron. This is called the inelastic contribution to the change in conductance [16,17,30,36]: |∆ψν (r0 )|2 δ(εν − εF ). (5) ∆σinel ∝ ν

This equation says that there is an increase of conductance due to the modulation of the wave function by the vibration. The spatial resolution of the wave function carries the information of the exponential decay in vacuum of the tunneling probability. Hence, during the vibration this tunneling probability will be modulated, in a way given by the change of the wave function. The change of wave function is calculated in perturbation theory: µ|V |ν ψµ (r0 ) . (6) ∆ψν (r0 ) = − εµ + i0+ ε ν µ

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We approximate the principal part of ∆ψ by its ﬁnite diﬀerence: δQ δQ − ψ r0 , Q0 − , ℘∆ψ(r0 , Q0 ) ≈ ψ r0 , Q0 + 2 2

(7)

0 is the vector of atomic positions and δ Q is the eigenvector corwhere Q responding to the displacement of the molecule’s atoms for a given mode. The modulus of this vector is the root mean square displacement of the vibration (in the case of a vibrating single atom of mass m, we have

δQ = 2mΩ where Ω is the mode’s frequency; see Appendix for a more complete account). The electron–vibration matrix elements, µ|V |ν, can be obtained from Eq. (5): µ|V |ν = ψµ |∆ψν . Notice that Eq. (6) is not evaluated directly because the metallic states are a continuum, here taken care of by the inﬁnitesimal element 0+ . The principal part, Eq. (6), corresponds to the real part of the denominator in Eq. (6). The second contribution to the change in conductance at the same order in the electron–vibration coupling, µ|V |ν, has been termed the elastic contribution. The name originates from the fact that the initial and ﬁnal electron states are at the same energy, they do not diﬀer in a quantum of vibration as in the inelastic term, Eq. (5). The origin of this term is the many-body character of electron transport in the presence of vibrations. In the absence of vibrations one can approximate the many-body wave functions in terms of one-electron wave functions that are solutions of an eﬀective one-body Hamiltonian. When the electron–vibration coupling, µ|V |ν, is included the one-electron wave functions are no longer eigenstates of the Hamiltonian. The vibration mixes them up. The complexity appears because the full wave function needs to be antisymmetric under electron exchange, i.e. two electrons cannot be in the same quantum state. The elastic contribution reﬂects the exchange of two electrons mediated by the electron–vibration interaction. This exchange term gives a negative contribution to the change in conductance due to the antisymmetric character of the wave function. Figure 5 shows a scheme with the two interfering paths due to exchange of two electrons with the same spin in the transport process. Exchange is made possible by the excitation of the vibration. Otherwise the Fermi occupation and the one-electron states are an excellent approximation in the transport problem.

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The elastic contribution is given by: 2 2 ψν (r0 )µ|V |νδ(εµ − εν ) δ(εµ − εF ). ∆σelas ∝ −π ν

229

(8)

µ

The notation is the same as in Eq. (5). There are two fundamental diﬀerences between Eq. (5) and Eq. (8). The ﬁrst one is the sign. The elastic contribution, Eq. (8), is negative. It is the term responsible for the decrease in conductance as we have announced. The second diﬀerence is the range of evaluation of the inner summation over ν. In Eq. (8) this summation is restricted to states at the Fermi level, while in Eq. (5) it extends over all energies. Hence the elastic contribution Eq. (8) will become particularly important when the density of states is very high at the Fermi level: namely, in the case of a sharp resonance at the Fermi level. The total change in the conductance will be determined by the sum of the two contributions Eqs. (5) and (8): ∆σ = ∆σinel + ∆σelas . Hence the outcome of the vibration excitation on the conductance is too complicated to predict. This is particularly true when there is a strong mixing of molecular states with metallic states. In this case, the interplay between the elastic contribution (exchange eﬀects) and the purely inelastic one (increase of tunneling probability) is diﬃcult to assess except after complete electronic structure calculations. The conditions of applicability of this simple extension of the Tersoﬀ and Hamann theory into the inelastic regime are usually in good agreement with the experimental conditions. Namely the conditions are: 1. Linear regime: small tip-surface bias voltage as compared with the electronic structure of the surface. This is usually the case since vibrational quanta are one order of magnitude smaller than the energy spacing between electronic resonances. 2. Highly symmetric tips, ideally with s-wave symmetry for its electronic structure at the Fermi level. 3. Low current regime: the time between tunneling electrons should be much larger than the vibrational lifetime. The theory only assumes one excitation at a time. 4. For reason 3, the temperatures should be low. The excitation probability depends on the phonon population; hence the theory assumes that the molecule is in its vibrational ground state. Advantages are the accuracy of the electronic structure and of the vibration calculation yielding quantitative results, plus the simplicity of

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the theory that allows an understanding of the basics behind an IETS-STM spectrum.

5. What Can We Learn from Theory? As in many areas of science, a good theoretical understanding is needed for the full exploitation of the technique not only from the point of view of enhancing and optimizing the amounts of information obtained, but also from the point of view of obtaining some useful information at all. As we have shown in the experimental technique, the STM vibrational spectroscopy has good energy and spatial resolutions. The change in conductance can be mapped spatially. The geometrical pattern of the variation of conductance has relevant information that theory can exploit. Ideally, any theoretical approach should then be able to account for the change in conductance at a given location of the STM tip and at a given surface-tip bias voltage. In this way, the mode at the origin of the change in conductance can be identiﬁed. In the following paragraphs, we analyze how to do so. The ﬁrst issue is when and why there is a measurable change in conductance. This leads us to analyze the possible cancellations in the inelastic current. Secondly, once a change in conductance is obtained, we address the problem of how the mode’s signature shows in the experimental data. Elastic−Inelastic cancellations. Inelastic electron tunneling spectroscopy is a technique that combines the exciting with the detecting probes. Theory shows that the probability of exciting the vibration by the electron current is not directly connected with the change in conductance at the bias voltage threshold of the vibration. Indeed, the excitation probability can be high and the change in conductance negligible. The situation thus becomes quite complicated because the absence of inelastic signals may come from the absence of excitation or from the absence of change in conductance. In the case of sharp resonances at the Fermi level (situation encountered in the case of magnetic impurities), the elastic contribution to the change in conductance will likely be the largest one, leading to a decrease of conductance above the vibration threshold. When the change of conductance is large (in the range of 10%) the elastic contribution will be negligible in front of the elastic one. Only in this case can the change of conductance be directly linked to the probability of excitation of the vibration. The relative change of conductance can be assigned to the fraction of electrons leading to an excitation; it is the

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inelastic fraction (see “How does single-molecule vibrational spectroscopy work”, above). Mode assignment and symmetry selection rules. Equations (5) and (8) contain the matrix element µ|V |ν. When this matrix element is zero, the conductance at the vibration threshold will be zero. Hence, the symmetry of the electronic states µ and ν, and of the vibration can determine when this matrix element will be zero. The electron–vibration coupling V has the same symmetry of the vibration. This is because the Hamiltonian is totally symmetric under transformations of the point group of the ensemble molecule plus substrate. In Appendix we give further details; in particular Eq. (A4) shows that in order to preserve the invariance of the Hamiltonian under transformation of the nuclear coordinates, the electronic coordinates must transform in the same way [37]. Hence, if a symmetric mode is excited, the electron–vibration coupling will also be symmetric in the electronic-coordinate transformations. Thus only electronic states of the same symmetry will give non-zero matrix elements for a symmetric vibration. This kind of reasoning can be used over the diﬀerent vibrations of the molecule. Reference [14] shows unequivocally that the change in tunneling conductance in the spectra of one deuterated acetylene molecule chemisorbed on Cu(100) originates in the antisymmetric mode of the C-D stretch. The experimental vibrational spectra were recorded on a deuterated acetylene molecule (C2 D2 ) because its rotation rate under the STM tip was lower, and hence it was easier to obtain meaningful spatial maps of the inelastic signal. Chemisorbed acetylene can have two almost-degenerate modes for the C-D stretch: an antisymmetric mode in which the D-atoms move out of phase, one approaching its corresponding C-atom while the other one elongates from its C-atom (calculated frequency 275 meV), and a symmetric mode in which the D-atoms elongate or contract the C-D bond in phase (calculated frequency 281 meV). The calculation shows that the maximum change of conductance was 9.6% for the antisymmetric mode. The maximum change of conductance was 1.4% for the symmetric one. Experimentally, the energy resolution was better than 6 meV (the calculated mode frequency mismatch) and the maximum of the signal was 8 ± 1%. The conclusion is that the antisymmetric C-D stretch mode is being detected. Equations (5) and (8) give information on the mode symmetry without performing a complex electronic structure calculation. Equation (5) gives us the spatial distribution of the change in conductance. It basically tells us that the tip will plot the state ψµ (r0 ) of Eq. (6). We see that the matrix

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element is between the states, ψµ (r) and ψν (r). This last state, ψν (r), is just the state at the Fermi energy of the molecule plus the surface electronic system, following Eq. (5). Hence we can have some indirect information about the symmetry of all relevant states through: (i) the constant current image (related to states at the Fermi energy, here ψν (r), Eq. (4)), and (ii) the spatial distribution of the change in conductance (related to the states ψµ (r), Eqs. (5) and (6)). This information is indirect because it refers to the modulus square of the wave function rather than the wave function itself. Due to the reduced symmetry of the molecule on the surface, there are only a few symmetry elements that survive after chemisorption. Generally, these elements are mirror planes and molecular axes both perpendicular to the surface. We are dealing with symmetry in 2D. In the case of deuterated acetylene, the constant current image presents a depression in the plane perpendicular both to the surface and to the C-C axis. The origin of this depression lies largely in the antisymmetry of the ψν (r) states at the Fermi level. As is shown in [14], the plane of the depression is indeed a nodal plane of ψν (r). The calculated spatial mapping of the change in conductance presents no depression and is symmetric with respect to the diﬀerent elements of symmetry of the local point group. This means that contrary to ψν (r), the states ψµ (r) are symmetric. The electron–vibration coupling V has to be antisymmetric, so that the product antisymmetric times antisymmetric times symmetric is symmetric. Put in group theory terms, the product of the representations of the terms in the matrix element must contain the identity [37]. This same kind of reasoning can be applied to more complex systems. In the case of the measured changed of conductance in C60 spectroscopy [38], the mode giving the largest change in conductance at a bias voltage of 54 meV (432 cm−1 ) was assigned to the breathing mode Hg (ω2 ). In order to reach this conclusion we can use symmetry arguments plus the energy resolution of the measured spectra. From the constant current STM images we know that the states at the Fermi level have a strong molecular character. This character coincides with the LUMO (lowest unoccupied molecular orbital) of the C60 molecule [8]. The inelastic signal mapping has a worse resolution, but one can conclude that it probably has LUMO character, since the HOMO would have a much more symmetrical aspect than the experimental images plotted in [8]. The irreducible representation of the C60 LUMO is Γ2 (F1 ). For the direct product of this representation, we ﬁnd Γ2 ⊗ Γ2 = Γ1 + Γ2 + Γ5 = A + F1 + H (see for example [39]). Hence, by

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using the above symmetry selection rule, the vibration can only have one of the A, F1 or H representations. Due to the small adsorption interaction, the free-molecule frequencies are probably not terribly shifted upon adsorption of C60 on a metal surface. If we take the free-molecule frequencies, we have only one mode within ±5 meV of the 54 meV peak: the Hg (ω2 ). Three paradigmatic cases. We have shown that the excitation of a molecular vibration under an STM tip does not entail a measurable change in conductance. First case: the conductance increases by 10% [1] or more [40]. This is notably the case of the C-H stretch of acetylene on Cu(100) where an extremely broad resonance straddles the Fermi level. This resonance is directly aﬀected by the vibration. The vibration modulates the amounts of electrons that can tunnel into the substrate, hence increasing the transmission probability [30]. The rest of the modes involve many states at the Fermi energy, leading to large elastic–inelastic cancellations. A similar case is found in the CO molecule [36], where the tunneling through 2π ∗ is strongly aﬀected by the frustrated rotation mode. Hence, there is a large positive increase of the conductance at the frustrated rotation threshold. The 2π ∗ is a large resonance across the Fermi level. Second case: the conductance decreases by some percent. This is the case of the O2 molecule. The molecule keeps some magnetic moment when chemisorbed on a typical metallic surface (Ag(110) in the case of [9]). In addition, the moleculesurface interaction is extremely weak. This means that there is a narrow resonance appearing at the Fermi level. This is the origin of the spin polarization of the molecule on the surface. The elastic contribution originating in the exchange term (see above) leads to a reduction of the conductance, as obtained experimentally [9]. Two concurring circumstances are found in this case: a half-ﬁlled resonance, and a very sharp one. Third case: The electronic structure about the Fermi level has no molecular signature. This is the case of ammonia chemisorbed on metals (for the calculations of NH3 on Cu(100) see [41]). In this case the change in conductance is well below 1% since there is little coupling between the conducting states and the molecular vibrations. The smallness of the change in conductance has nothing to do with elastic–inelastic cancellations in this last case. Connection with vibrational lifetime on surfaces. The decay of molecular vibrations in the excitation of the electron-hole pairs of metallic surfaces have been identiﬁed with the mechanisms of vibration excitation by tunneling electrons [42]. Intuitively this may seem so. Indeed, an excited vibration may couple to the surface electronic excitations through the same electron–vibration matrix elements of Eqs. (2) and (4). The surface

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electronic density of states and the molecular states’ width seem to be common ingredients to the process of excitation by tunneling electrons and the electronic decay of molecular vibrations; but, the processes are quite diﬀerent. The molecular decay involves only surface quantities: a substrate electronic state is excited with an electron from the substrate. In the second case, it is the tunneling electron exciting the vibration that ends up in a hot substrate state. The starkest contrast between both processes is that in the tunneling excitation, elastic contributions (exchange mediated as we saw above) can be extremely important, making it impossible to reconcile the inelastic current with the probability of vibrational excitation. In the case of vibration decay, only the probability of de-excitation enters in the picture. The diﬀerences are more serious indeed. Calculations show that even in the case where elastic contributions are negligible, the behavior of molecular excitation by tunneling electrons and molecular de-excitation in electronhole pairs follow diﬀerent trends [36]. The reason after this discrepancy can be found in the initial and ﬁnal electronic states (see discussion about Eq. (10) below). In the tunneling process the electron ends up in a state above the Fermi level. In the de-excitation one, the electron ends up in a state above the Fermi level after having left a hole behind. This shows in the diﬀerence in the equations leading to the evaluation of both processes [36]. The possibility of inducing controlled evolutions of a molecule on a surface has been greatly enhanced by the possibility of promoting the reaction from the excitation of speciﬁc vibrations of the molecule [43]. In the following section we will brieﬂy present this new ﬁeld, and the many opportunities that it contains from a theoretical point of view.

6. Single Molecule Vibrational Chemistry As stated by their own deﬁnition, inelastic tunneling electrons are a tool to donate energy into an adsorbate. During the acquisition of vibrational spectra, the excitation of a molecular mode may trigger a change in a molecule, such as bond dissociation, if the energy is placed in an internal coordinate, or molecular motion, when the mode excited is a hindered one. Key experiments during the past years have demonstrated that chemistry at the single-molecule scale provides complementary information to classical surface chemistry techniques for the investigation of reaction dynamics producing either molecular dissociation [44–46], or molecular motion (desorption, rotation, translation) [47–51] when speciﬁc vibrational states of the adsorbate are excited.

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With the typical operation parameters of STM (i.e. 1 nA and 1 V) the power applied to a molecule/surface system is in the range of 1 nW per molecule, which is in the low limit of the typical power applied by photochemistry techniques. This allows investigation of reaction dynamics, since we can control the energy of the excitation source, i.e. the electron energy, and the ﬂuence (in photochemistry deﬁned as power per unit area), here corresponding to the tunneling current. Thus, inelastic electrons can be also considered as a useful excitation source to induce and investigate controlled chemical reactions in a single adsorbate. Given a fraction of tunneling electrons fi scattering inelastically oﬀ an adsorbate, the rate of excitation from the ground state to the ﬁrst state is R0→1 = fi ·It /e = fi /t. The probability of ﬁnding the molecule in the n = 1 state is (fi · τ /t), where τ is the lifetime of the n = 1 state. Approximating the vibrational potential with a truncated harmonic oscillator (Fig. 6), the rate of excitation from a level n − 1 to a level n is given by R(n−1)→n = (n − 1) · fi /t, and the population of level n is Pn = (fi · τ /t)n = (P1 )n [24]. Such population follows a quasi-Boltzmann distribution with an associated vibrational temperature of ≈11 E1 /Ln[fi · τ /t], where E1 is the energy

Fig. 6. Schematic of mechanisms for accumulation of vibrational energy on a vibrator. DIMET refers to multiple one-step excitations, thus dominating when the excitation (dashed arrows) rates are comparable to decay rates. DIET refers to one step gain of several quanta. This mechanism is mediated by anharmonicities of the vibrational potential. In general, a transition of several quanta at once has lower probability, but since the total number of steps is so decreased, it dominates over a DIMET mechanism for suﬃcient low excitation rates.

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between vibrational levels. Associated with this vibrational temperature, there will be a probability of reaction inducement which evolves following the Boltzmann statistics. To have an idea of the magnitude of these eﬀects, we consider that a tunneling current of 1 nA implies an average time between successive tunneling electrons of 160 ps. This time is larger than characteristic lifetimes of vibrational modes, typically a few ps, and much larger than any electronic excitation of the adsorbate-surface complex. Thus, during tunneling processes, the adsorbate remains in its vibrational and electronic ground states. Typically, the vibrational temperature under these circumstances barely reaches a few degrees, which in most chemisorption systems is insufﬁcient to eﬀectively induce a reaction. DIMET vs. DIET: When the tunneling current is increased up to a few tens of nano-Amp`eres the time between electrons approaches the vibrational time scale, and vibrational heating eﬀects become important. As soon as the excited vibrational wave-functions gain importance in the dynamics of a reaction, the anharmonicities of the vibrational potential become eﬀective to couple diﬀerent vibrational coordinates (which would be orthogonal in harmonic oscillator models), spreading the vibrational energy among different molecular vibrational coordinates. This corresponds to the so-called vibrational heating regime, in which as a thermal-like mechanism the reaction will proceed along the lowest activation barrier. This regime can be treated as if the adsorbate establishes a new equilibrium with the excitation source, just as if it were a thermal source. The eﬃciency of the reactions increases exponentially with temperature, but it is diﬃcult to ﬁnd a close relation between the excited mode and the reaction coordinate. In general, these reactions will proceed along the pathway having the lowest activation barrier. This is the mechanism acting in the Xe atom switch experiment by Eigler et al. [47]. From photochemistry results, this mechanism is called Desorption Induced by Multiple Electronic Transitions (DIMET), generally used to describe such multiple excitation processes. Due to the exponential decrease of the population of vibrational levels with their index n, in the regime of very low excitation rate, a DIMETlike reaction pathway competes with a process in which a single excitation process excite several vibrational quanta at once, i.e. coherently as in Desorption Induced by Electronic Transitions (DIET) (Fig. 6). This is of course true if the tunneling electron energy is large enough to induce the adsorbate to react; otherwise, it may still compete with other DIMET processes involving a lower number of excitations, such as those climbing the barrier in

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sequences of several steps. The general idea is that coherent excitations may become relevant to understanding reaction mechanisms since it involves a low number of excitations [24]. The eﬃciency of this mechanism is of course low, but it posses the advantage of the adsorbate being in its ground state, thus vibrational heating or thermal-like processes do not apply here; it is possible for the reaction to proceed through a diﬀerent activation barrier other than in a barely thermal process. Intramolecular decay pathways: Let us imagine that we provide sufﬁcient energy with a single electron to induce a speciﬁc bond cleavage. If the bond is an external one, connected with a coordinate describing molecular motion, we could provide the energy directly into that coordinate by exciting the ﬁrst unbounded level above the activation barrier. In general, the probability of coherent excitation of a higher overtone n by tunneling electrons decreases exponentially [24]. In certain cases, an indirect mechanism of pumping energy into that coordinate might be more eﬀective. Several examples in the literature demonstrate this point, which has become of extreme importance in connection with single molecule chemistry. Stipe et al. [48] found that excitation of one quantum of C-H stretch mode induced rotational movement of acetylene on Cu(100) between two equilibrium positions. The barrier for rotation is about 169 meV [52], smaller than the fundamental energy of the C-H stretch (360 meV), but large compared with the rotational mode energy. Thus, the energy to rotate is more eﬀectively pumped into the molecule via excitation of one single quantum of an internal coordinate, rather than exciting directly — coherently or incoherently — several quanta of rotational levels. Similar results were found by Komeda et al. [51] and Pascual et al. [43] for the diﬀusion CO and NH3 respectively. In both cases, molecular motion was activated by excitation of internal stretch modes. By modeling theoretically the coupling between internal and external modes, these works gave a magnitude for the relevance of such internal pathways compatible with experimentally measured reaction yields. Intermode coupling: All of these experimental ﬁndings reveal the existence of internal pathways of energy transference between modes which eventually become eﬃcient due to non-negligible coupling between the excited internal mode and the mode directly actuating in the reaction coordinate. In the gas phase, the coupling between modes having diﬀerent energy is small because the energy between initial and ﬁnal states must be conserved. For an adsorbate, the decay of a given molecular vibration into a

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group of other molecular vibrations is greatly enhanced in the presence of electron-hole pairs. The excitation of electron-hole pairs absorbs the excess energy in the transition, thus allowing energy conservation in the full process and reduces considerably the number of lower-energy modes needed to match the energy of the decaying high-energy mode. Anharmonicity is also a key aspect in intermode coupling. In the gas phase, the nuclear potentials are usually more harmonic than for the adsorbed phase, also reducing intermode coupling in the gas-phase case with respect to the adsorbed one. The calculation of the damping rate into diﬀerent low-energy vibrations assisted by electron-hole pairs can be carried on in a similar way to the calculation of mode damping in electron-hole pairs [36]. Indeed, we can present the decay rate as a Taylor expansion on normal coordinates. The increasing number of diﬀerent modes coupled via electron-hole pairs, correspond to an increasing order in the expansion. Thus, the decay of a high-energy mode into one type of low-energy mode corresponds to second-order. The decay into two diﬀerent types of low-energy modes is tantamount to a third-order expansion. The simple decay into electron-hole pairs is a ﬁrst-order process. i, The small parameter of the expansion is the mode displacement δ Q because it is always evaluated for the mode ground state or a low-energy i of the state. Both are very localized. Let us consider the eigenvector Q mode i. Then the Hamiltonian can be expanded in a Taylor series on the i: displacements δ Q 2 ∂H i + 1 i ∂ H δQ + ··· · δQ δQ (9) H = H0 + i i∂Q j j 2 ∂Q ∂Q i

i,j

The perturbation H-H0 can be used in Fermi’s Golden rule to calculate various transition rates. Hence the leading term in a single mode transition, i.e. the damping of the mode i of frequency Ωi from the ﬁrst excited level into the ground state by electron-hole pair excitation is given by the ﬁrst term (see for example [36]):

2 ∂H 1 2π fλ (1 − fµ ) 1, λ · δ Qi 0, µ δ(ελ − εµ + Ωi ) (10) = τ ∂ Qi λ,µ where fλ is the Fermi occupation factor for the electronic state λ. Hence fλ (1 − fµ ) explicitly shows the excitation of an electron-hole pair in the transition; both λ and µ are electronic states indices. This contribution is identically zero when two modes are coupled via electron-hole pairs. The ﬁrst contribution is given by the last term in the expansion Eq. (9). The

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probability of de-exciting one mode i from its ﬁrst excited level to its ground state, while exciting another mode j from its ground state to a level n of the j mode in the presence of electron-hole pair excitation is then: 2 2π 1 ∂2H j 0, n, µ fλ (1 − fµ ) 1, 0, λ δ Qi δQ = i∂Q j τ ∂Q λ,µ × δ(ελ − εµ + Ωi − Ωj (n)).

(11)

In this last expression we take into account that the excitation of n quanta of the j mode will be an anharmonic process, and hence the transferred energy may not be simply proportional to the mode frequency Ωj . The anharmonic coupling becomes readily apparent if we simplify the matrix element in Eq. (11): ∂2H ∂2H i |0 λ j |n. 0, n, µ = 1|δ Q 1, 0, λ δ Qi δQ µ 0|δ Q i∂Q j j i∂Q j ∂Q ∂Q (12) In the harmonic approximation only the term n = 1 is diﬀerent from zero. It is then the anharmonicity that allows the coupling between the initial state and ﬁnal states n > 1. The second-order derivative of the Hamiltonian does not pose any particular problem and can be evaluated in the same way as the ﬁrst derivative (see above). Full calculations of the anharmonic terms are very diﬃcult due to the large number of coordinates involved. Whenever is possible to approximate the ﬁnal coordinate to one single variable, for example molecular motion on 1D, the estimation of the magnitude of the anharmonic terms can be reasonably obtained. For example, calculation for NH3 on Cu(100) shown in Fig. 7 estimates the probability for exciting frustrated translational modes m along a 1D external potential upon decay the ﬁrst N-H stretch quantum [41,43]. According to our calculations at a bias of ∼420 mV between tip and substrate, the symmetric stretch N-H can be excited. The N-H stretch can decay into electron-hole pairs while exciting one quantum of the frustrated translation mode. As expected, we ﬁnd that the leading-term in the decay is simply the damping into electron-hole pairs without other vibration excitation. The excitation of higher states in the frustrated translation mode, eventually leading to the translation of the molecule, can be calculated by i |m for the frustrated numerically evaluating the matrix element 0|δ Q translation mode. If the harmonic case would exclusively apply here, only transitions exciting the m = 1 mode (plus the rest of the N-H stretch

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Fig. 7. (a) Scheme and one-dimensional potentials of internal energy transference pathway leading to diﬀusion of a NH3 molecule on Cu(100) by excitation of internal N-H stretch (from [43]). 420 meV electrons excite the N-H stretch mode (dashed arrow). Upon decay of the vibrational excitation there is a ﬁnite probability of exciting hindered translational states via anharmonic inter-mode coupling. Population of states m > 30 produces molecular motion above the 301 meV barrier for diﬀusion. (b) Probability Pm to ﬁnd the molecule in a translational mode m after excitation of the νs (N-H) mode, vs. the energy of the ﬁnal translational state m. The vertical dashed line marks the location of the barrier from translation along (011) directions. States with larger energy (m > 30) are unbounded. The tilted dashed line refers to the probability of populating the m levels on the full harmonic approximation. In this case, only transitions of one quantum are 0,1 m . allowed, and thus, the population scales as the power law P1,0

energy to substrate excitations) would be diﬀerent from zero. In this case, the barrier can be overcome only by DIMET processes. The tilted dashed line in Fig. 7 quantiﬁes the population of levels m in this fully harmonic case, showing a negligible probability of inducing motion above the 300 meV translational barrier (i.e. negligible vibrational heating). In our procedure, we solve Schr¨odinger’s equation in 1D for the PES of the center of mass.

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When anharmonic terms of the vibrational potential are introduced in the calculation, the probability of reaching each level m directly upon N-H stretch decay (points in Fig. 7) becomes non-negligible. Above 300 meV the molecule can translate classically into other sites. The classical threshold is attained at m = 30 state of the anharmonic frustrated translation mode. The change in wavefunction above the threshold leads to an extra kink in the decay rate function. The probability of populating states above the 300 meV diﬀusion barrier is in the order of 10−5 , compatible with yield values found in experiments [43]. The few experiments available to date about single-molecule chemistry have provided a diﬀerent view of understanding the complexities behind excitation and relaxation of vibrational in adsorbates. Certainly, more than a tool for technological processing, it will develop concepts and strategies for selectively studying catalytic reactions.

Appendix Hamiltonian (2) is a very useful simpliﬁcation to treat the interplay between electrons and vibrations in condensed matter systems. More complete approaches use some electronic structure calculation to go beyond the approximation of Hamiltonian (2). Nevertheless they remain at the same level of approximation concerning the electron–vibration coupling term: ∗ Vµ,ν c+ (A.1) µ cν (b + b). µ,ν

All of the approaches reviewed in this article rely on two approximations: the adiabatic one for the electronic structure calculation, and the linear one in the electron–vibration coupling Eq. (A.1). The adiabatic approximation means the neglect of the nuclear motion in the Schr¨ odinger equation. The electronic structure is thus calculated for a set of ﬁxed nuclear coordinates. This approach can in principle be exact if one uses the set of wave functions for ﬁxed nuclear coordinates as a basis set for the full Schr¨ odinger equation, and solves the nuclear motion on this basis. The adiabatic approximation stops at the step before. (The Born– Oppenheimer approximation assumes a speciﬁc classical behavior of the nuclei and hence it is more approximate than the adiabatic approximation.) Yet, the information about the electron–vibration coupling is known because the adiabatic approximation has parametrized the electronic structure for each nuclear conformation.

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This parametrization can be very demanding, hence one goes a step further and only calculates the electronic structure at equilibrium and the leading term in a Taylor expansion on the nuclear coordinates; the electron– vibration interaction is linearized. Equation (A.1) is then determined following these two approximations. Let us look into the electronic part of the Hamiltonian for a given nuclear and approximate it by its Taylor expansion: conformation Q, ˆ · δ Q. ˆ ˆ 0 ) + ∇H H(Q) ≈ H(Q

(A.2)

Hence the only term mixing electronic and nuclear coordinates is the second one in (A.2). We can now express it in a second quantization. If we consider one only mode of frequency Ω, there is only one annihilation (creator) operator b (b+ ) for the mode. Thus, εp (b+ + b), δQ = (A.3) 2m Ω p p where ε is the unitary displacement vector of the nucleus p in the mode, and mp its mass. So ﬁnally, Eq. (A.1) is retrieved by making ˆ εp . Vµ,ν = µ|∇H|ν · (A.4) 2mp Ω p This expression can be easily and accurately calculated by using a DFT electronic structure code. First, one can make use of the Hellman–Feynman theorem to extract the gradient from Eq. (A.4). Second, one can use ﬁnite diﬀerences to estimate the gradient on the electronic Hamiltonian matrix elements following the explanation of the theory section above. Due to Eq. (A.3) the above theories only permit the excitation of one quantum of vibration at a time (b and b+ connect vibrational states where their populations diﬀer by only one quantum). This is a consequence of the linear approximation because the nuclear coordinates deviate slightly from the equilibrium situation; the molecule can only change its vibrational state by the smallest of the allowed quantities: one quantum. In order to account for the excitation of several quanta at a step (coherent excitation) one needs to use other kind of theories (see for example [24]). Nevertheless, the presented approaches permit the sequential excitation of quanta in a ladder climbing fashion (incoherent excitation). The approaches analyzed in the theory section use the smallness of the matrix element, Eq. (A.4), to do perturbation theory. This is one more

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approximation without connection to linearizing the electron-phonon interaction as in Eq. (A.2). References [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] [31] [32] [33] [34] [35]

B. C. Stipe, M. A. Rezaei and W. Ho, Science 280, 1732 (1998). P. K. Hansma, Tunneling Spectroscopy (Plenum, New York, 1982). L. J. Lauhon and W. Ho, Review of Scientiﬁc Instruments 72, 216 (2001). R. C. Jacklevic and J. Lambe, Phys. Rev. Lett. 17, 1139 (1966). G. Binnig, G. Garc´ıa and H. Rohrer, Phys. Rev. B 32, 1336 (1985). B. N. J. Persson and Baratoﬀ, Phys. Rev. Lett. 59, 339 (1987). B. N. J. Persson and J. Demuth, Solid State Comm. 57, 769 (1986). J. I. Pascual, J. G´ omez-Herrero, D. S´ anchez-Portal and H. P. Rust, J. Chem. Phys. 117, 9531 (2002). J. R. Hahn, H. J. Lee and W. Ho, Phys. Rev. Lett. 85, 1914 (2000). B. N. J. Persson, Phys. Scripta 38, 282 (1988). L. J. Lauhon and W. Ho, J. Phys. Chem. A 104, 2463 (2000). J. I. Pascual et al., Surface Science 502–503, 1 (2002). J. I. Pascual et al., Phys. Rev. Lett. 86, 1050 (2001). N. Lorente, M. Persson, L. J. Lauhon and W. Ho, Phys. Rev. Lett. 86, 2593 (2001). B. C. Stipe, H. A. Rezaei and W. Ho, Phys. Rev. Lett. 82, 1724 (1999). C. Caroli, R. Combescot, P. Nozi`eres and D. Saint-James, J. Phys. Part C: Solid State Physics 5, 21 (1972). L. C. Davis, Phys. Rev. B 2, 1714 (1970). Y. Meir and N. S. Wingreen, Phys. Rev. Lett. 68, 2512 (1992). H. Haug and A. P. Jauho, Quantum Kintetics in Transport Optics of Semiconductors (Springer, Berlin, 1996). M. A. Gata and P. R. Antoniewicz, Phys. Rev. B 47, 13797 (1993). C. Spataru and P. Budau, J. Physics-Condensed Matter 9, 8333 (1997). W. Domcke and L. S. Cederbaum, Phys. Rev. A 16, 1465 (1977). J. P. Guayacq, Dynamics of Negative Ions (World Scientiﬁc, Singapore, 1987). G. P. Salam, M. Persson and R. E. Palmer, Phys. Rev. B 49, 10655 (1994). S. Y. Tong, C. H. Li and D. L. Mills, Phys. Rev. Lett. 44, 407 (1980). J. Bonca and S. A. Trugman, Phys. Rev. Lett. 75, 2566 (1995). N. Mingo and K. Makoshi, Surface Science 438, 261 (1999). N. Mingo and K. Makoshi, Phys. Rev. Lett. 84, 3694 (2000). E. G. Emberly and G. Kirczenow, Phys. Rev. B 61, 5740 (2000). N. Lorente and M. Persson, Phys. Rev. Lett. 85, 2997 (2000). J. M. Soler et al., J. Physics-Condensed Matter 14, 2745 (2002). M. Brandbyge et al., Phys. Rev. B 65, 165401 (2002). N. Lorente, Applied Physics a-Materials Science & Processing 78, 799 (2004). J. Tersoﬀ and D. R. Hamann, Phys. Rev. Lett. 50, 1998 (1983). J. Tersoﬀ and D. R. Hamann, Phys. Rev. B 31, 805 (1985).

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[36] N. Lorente and M. Persson, Faraday Discussions 117 (2000) p. 277. [37] L. D. Landau and E. M. Lifshitz, Mec´ anica Cu´ antica (Editorial Revert´e S. A., Barcelona, 1967). [38] M. S. Dresselhaus, G. Dresselhaus and P. C. Eklund, Science of Fullerenes and Carbon Nanotubes (Academic Press, San Diego, 1996). [39] A. J. Heinrich, C. P. Lutz, J. A. Gupta and D. M. Eigler, Science 298, 1381 (2002). [40] N. Lorente and J. I. Pascual, Phylosophical Transactions 362, 1227 (2004). [41] N. Mingo, K. Makoshi, T. Mii and H. Ueba, Surface Science 482, 96 (2001). [42] J. I. Pascual et al., Nature 423, 525 (2003). [43] Y. Kim, T. Komeda and M. Kawai, Phys. Rev. Lett. 89, 126104 (2002). [44] S. W. Hla, L. Bartels, G. Meyer and K. H. Rieder, Phys. Rev. Lett. 85, 2777 (2000). [45] B. C. Stipe et al., Phys. Rev. Lett. 78, 4410 (1997). [46] D. M. Eigler, C. P. Lutz and W. E. Rudge, Nature 352, 600 (1991). [47] B. C. Stipe, M. A. Rezaei and W. Ho, Phys. Rev. Lett. 81, 1263 (1998). [48] B. C. Stipe, M. A. Rezaei and W. Ho, Science 279, 1907 (1998). [49] L. Bartels et al., Chem. Phys. Lett. 313, 544 (1999). [50] T. Komeda et al., Science 295, 2055 (2002). [51] L. J. Lauhon and W. Ho, J. Chem. Phys. 111, 5633 (1999).

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PART V LOCAL MODIFICATION OF SURFACES INDUCED BY ADSORBED MOLECULES

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SUPERLATTICES OF ATOMS, MOLECULES AND ISLANDS

H. BRUNE Institut de Physique des Nanostructures Ecole Polytechnique F´ed´erale de Lausanne (EPFL) CH-1015 Lausanne, Switzerland Abstract. We describe the state-of-the-art in the creation of ordered superlattices of adsorbed atoms, molecules, semiconductor quantum dots, and metallic islands, by means of self-assembly during atomic-beam growth on single crystal surfaces. These surfaces often have long-period reconstructions or strain relief patterns which are used as template for heterogeneous nucleation. However, repulsive adsorbate-adsorbate interactions may also stabilize ordered superlattices, and vertical correlations of growth sequences of buried islands will be discussed in the case of semiconductor quantum dots. We also present new template surfaces considered as particularly promising for the creation of novel island superlattices.

Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Stabilization of Superlattices by Friedel Oscillations in Surface States 3 Order in Vertically Stacked Quantum Dots . . . . . . . . . . . . . . . 4 Decorating Mesoscopically Ordered Surface Reconstructions . . . . . . 5 Templates — Dislocation Networks and Ordered Domains in Biphases 6 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1. Introduction In this chapter we describe several means to create ordered superlattices of adsorbed atoms, molecules, semiconductor quantum dots, and metallic

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islands, and ﬁnally we describe templates which might be used in the future to create novel island superlattices. In most cases the approach is based on kinetically controlled growth by means of molecular beam epitaxy (MBE) onto a low-index single crystal surface. The creation of order is based on the hierarchy of activation energies of the atomic and molecular displacements, and on the variation of the binding energy as a function of lateral position on the surface, inducing a directional variation in the diﬀusion barriers and thereby a diﬀusion current directed to particular surface sites. In a few cases kinetically controlled growth can be followed by gentle annealing enabling the formation of energetically favored structures or sizes, so-called magic islands. The interest in growing large ensembles of nanostructures with welldeﬁned sizes is the investigation of their physical and chemical properties as a function of size and composition, ideally in an atom-by-atom, or molecule-by-molecule way. Many properties can so far only be investigated with spatially integrating techniques, requiring high densities of uniform particles. As an example, the methods presented here have already unravelled the spectacular increase of the orbital magnetic moment and magnetic anisotropy energy of Co islands on Pt(111) with decreasing size [1]. A second aim of creating molecular, atomic, or island superlattices is to study the properties speciﬁc of the ensemble, i.e., the properties emerging from their mutual interactions. One example is a superlattice of Kondo scatterers [2,3], or dipolar interactions between magnetic particles [4]. At ﬁrst glance the attempt to create long-range ordered periodic and almost monodisperse structures seems impossible due to the statistics in time and space inherent in deposition and in the Brownian motion of the adsorbed species. On homogeneous substrates this leads to interdependent spatial and size distributions of the islands with width and shape given by well-known scaling laws of nucleation [5–8]. In the temperature regime where dimers are stable on the time scale of deposition, the half-width at half-maximum (HWHM) of the size distribution is 0.55 times the average size, which is rather polydisperse. We shall show below that heterogeneous nucleation on equidistant sites leads to much better results and therefore, to some extent, one may create order out of randomness. We ﬁrst discuss atomic and molecular superlattices which are stabilized by interactions due to electronic screening in a two-dimensional (2D) electron gas of a surface state. In this case the perfect lattice distance represents a shallow minimum in total energy. Diﬀusion has to be activated to reach this minimum; however, it also creates Brownian motion

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and a liquid-like-state, such that the degree of order depends on the ratio between interaction energy and diﬀusion barrier. Our second example will be strain-mediated vertical stacking of buried semiconductor quantum dots. The spacer layers covering the quantum dots are inhomogeneously strained leading to correlations in the nucleation of the quantum dots grown on-top. With an increasing amount of quantum dot and spacer layers, the order is increased since the strain ﬁelds of too close dots coalesce, and randomness leads to nucleation of new dots between two dots which are too far apart. The best size distributions have a HWHM of 0.08, and the dot distance can to some extent be tuned by the thickness of the spacer layers. Then we turn our attention back to two-dimensional systems where elastic interactions mediated by the substrate lead to mesoscopically periodic surfaces. Such surfaces represent long-range modulated potential energy surfaces for deposited species to which their periodic structure may be transferred. The focus is on recent work and the reader is referred to the literature for former work on the nucleation on strain relief patterns [9]. We close by showing a few template surfaces which have been discovered very recently and have not yet been employed as templates for the growth of ordered superlattices.

2. Stabilization of Superlattices by Friedel Oscillations in Surface States An impurity atom in a solid induces a variation in the potential acting on the host conduction electrons, which they screen by oscillations in their density. Friedel introduced such oscillations with wave vector 2kF to calculate the conductivity of dilute metallic alloys [10]. In addition to the pronounced eﬀect on the relaxation time of conduction electrons, Friedel oscillations may also be a source of mutual interactions between impurity atoms through the fact that the binding energy of one such atom in the solid depends on the electron density into which it is embedded, and this quantity oscillates around another impurity atom. Lau and Kohn predicted such interactions to depend on distance as cos(2kF r)/r5 [11]. We note that for isotropic Fermi surfaces there is a single kF -value, whereas in the general case one has to insert the Fermi vector pointing into the direction of the interaction [12,13]. The electronic interactions are oscillatory, and their 1/r5 -decay is steeper than the monotonic 1/r3 -decay of elastic interactions [14]. Therefore elastic interactions between bulk impurities dominate the electronic ones from relatively short distances on.

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This situation is quite diﬀerent in 2D. The pair interaction energy between two impurities caused by screening in a 2D electron gas was predicted to be proportional to cos(2kF r)/r2 [11]. This relatively slow decay implies that electron mediated interactions in 2D dominate elastic and dipolar ones, giving rise to interactions between impurities which oscillate between attraction and repulsion as a function of distance. The ﬁrst experimental observation indicative of long-range interactions, possibly mediated by 2D Friedel oscillations, came from equidistant bulk segregated impurities on Cu(111) [15]. However, the quantitative determination of the interaction energy as a function of distance became possible only very recently [16,17]. The required 2D nearly free electron gas is realized in Shockley type surface states of close-packed surfaces of noble metals. These states are located in narrow band gaps in the center of the ﬁrst Brillouin zone of the (111)-projected bulk band structure. The fact that their occupied bands are entirely in bulk band gaps separates the electrons in the 2D surface state from those in the underlying bulk. Only at structural defects, such as steps or adsorbates, is there an overlap of the wave functions, opening a ﬁnite transmission between the 2D and the 3D system. The fact that the surface state band is narrow implies extremely small Fermi wave vectors and consequently the Friedel oscillations of the surface state have a signiﬁcantly larger wave length than those of bulk states. Scanning tunneling microscopy (STM) images taken at low bias directly reﬂect the oscillating quantity, namely the LDOS close to EF , thus enabling direct observation of Friedel oscillations [18]. Figure 1(a) shows Friedel oscilA−1 [19] lations on Ag(111) which has a surface state with kF,surf = 0.083 ˚ −1 A [20]). There are two substitutional defects (compare kF,bulk = 1.2 ˚ appearing as protrusions on the otherwise clean surface. They induce a smooth modulation in the apparent height of the Ag atoms extending over the entire image. These are the surface state Friedel oscillations [21] which are readily detectable up to more than 100 ˚ A distance in the large scale STM image Fig. 1(b). Figure 1(c) shows Friedel oscillations around Cu atoms adsorbed onto −1 A [21]). a Cu(111) surface, which equally has a surface state (kF = 0.21 ˚ The STM image is taken out of a sequence of images recorded at 13.5 K where Cu adatoms readily diﬀuse (for videos see the author’s website under gallery). Despite the fact that the atoms quite often come close to each other, they do not form islands but remain isolated during the observation time of several hours. This is remarkable for a metallic system and can only be reconciled by a signiﬁcant short-range repulsion. For the present

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Fig. 1. (a) Two substitutional defects on Ag(111) (Vt = −5 mV, It = 8 nA, T = 9 K). A around (b) Large view of (a) showing the long-range oscillations with λ = π/kF = 38 ˚ 4 point defects on Ag(111) (Vt = 24 mV, It = 0.5 nA, T = 9 K). (c) Still from time sequence of STM images recorded to trace diﬀusing Cu atoms on Cu(111) (coverage Θ = 1.4 × 10−3 ML, 1 ML is deﬁned by one adatom per atom of the substrate surface, Vt = 100 mV, It = 0.5 nA, T = 13.5 K). From [17].

system, no cluster formation was observed during annealing at 16.5 K for 20 min. On the other hand, almost all the monomers formed islands during annealing at 22 K for a comparable time. From these observations the shortrange repulsion has been estimated to be between 10 and 14 meV [22]. This energy can only partly be caused by surface state Friedel oscillations. Its main origins are more likely dipole-dipole, elastic, or bulk-electron mediated interactions. Such short-range interactions have been studied by means of ﬁeld ion microscopy (FIM) [23] and STM [24,25]. We note here that their existence is mandatory for the observation of the long range interactions we are after, since they stabilize the adatom gas and prevent nucleation. Inspection of Fig. 1(c) reveals that there are a few pairs of atoms with a preferred distance. Analysis of many such images in terms of site occupation probabilities as a function of adatom distances revealed signiﬁcant deviations from a random distance distribution, and the existence of adsorbate interactions which indeed oscillate with a wave vector of 2kF [16]. The decay followed the 1/r2 -prediction only for large distances, while signiﬁcant deviations were observed at distances below 20 ˚ A and interpreted as a shortcoming of theory [16]. However, an independent study, carried out in parallel, focused on two body interactions only, i.e., the authors counted only those distances r from a selected atom to a nearby atom where no third scatterer (adatom or impurity) was closer than r [17]. This way, many body interactions were eliminated and the interaction energy E(r) yielded perfect

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agreement with the theoretically predicted decay down to 5 ˚ A distance. The energy was of the form E(r) = −AE0 (2 sin δπ)2 sin(2qr+2δ)/((qr)2 +(qc)2 ), with A the scattering amplitude, δ the scattering phase [26], and c a ﬁt parameter. The wave vectors q were found to be in perfect agreement with the Fermi-vectors of the respective host surface states, for Co atoms diffusing and interacting on Ag(111), and for Co and Cu atoms on Cu(111) [17]. The theoretically predicted oscillatory long-range interactions between adsorbates were experimentally conﬁrmed. Note, however, that the interaction energy is very small; for example the depth of the ﬁrst energy minimum in the pair potential of Cu/Cu(111) amounts only to 2 meV [17]. This energy is small compared to the diﬀusion barrier of 40 ± 1 meV [17] implying ﬁrst that the atoms always reside on surface lattice sites, and second that high temperatures are needed to reach the shallow minimum. Too high temperatures, on the other hand, lead to irreversible nucleation due to the limited short range repulsion of 12 ± 2 meV, thus determining a narrow temperature window for the pair interactions to be studied. Early attempts to use these interactions for the formation of atomic superlattices failed [16,17]. Figure 2(a) shows the case of Cu/Cu(111) where chains of equidistant atoms are formed but there are only small patches of hexagonally close packed atomic superlattices. This was also the case for Co on the same substrate, whereas Co/Ag(111) showed quasi hexagonal lattices, which were, however, not well-ordered [17]. The breakthrough came for the system Ce/Ag(111) where the Ce atoms are forming well-ordered hexagonal superlattices with a lattice constant of 32 ˚ A, (a)

(b)

300 Å

(c)

10 Å

Fig. 2. (a) For Cu/Cu(111) the surface state mediated long-range interactions favor atomic chains with inter-atomic distances of 12 ˚ A, but not hexagonal lattices (Θ = 6 × 10−3 ML, T = 15 K, Vt = −0.3 V and It = 2.0 nA). (b) and (c) STM images of wellordered Ce superlattices formed on Ag(111) (Θ = 8 × 10−3 ML, T = 3.9 K, Vt = 0.1 V and It = 10 pA). Figures (b) and (c) are kindly provided by W. D. Schneider.

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see Figs. 2(b) and (c) [2]. Note that Ce atoms on Ag(111) are Kondo scatterers, thus Fig. 2(c) shows a superlattice of Kondo impurities which may interact also electronically via the 2D surface state electron gas [2,3]. The dilute atomic superlattices are most nicely ordered at 3.9 K, whereas the atoms start to diﬀuse around their ideal positions at 4.8 K, corresponding to a 2D dilute liquid, and the lattice is destroyed by irreversible nucleation of Ce islands at 10 K. The question why superlattices could be formed for Ce/Ag(111) and not for the other systems studied before is at present not fully settled. Let us point out a few diﬀerences between the systems and discuss their possible consequences. For Ce/Ag(111), the ﬁrst minimum in the pair potential is 0.8 meV deep and the diﬀusion barrier 12 meV, therefore the relative strength of the long-range interaction is slightly larger (1/15) than for Cu/Cu(111) (1/20). The relative stability toward irreversible nucleation is also slightly larger for Ce/Ag (10 K/12 meV vs. 22 K/40 meV). This enables one to reach higher relative temperatures bringing the system closer to the total energy minimum. Note, however, that temperature also creates disorder; in the case of Ce/Ag one can even melt the dilute solid before it collapses into an island. A third item favoring Ce/Ag over Cu/Cu is its scattering phase of δ = (0.37 ± 0.05)π vs. δ = (0.50 ± 0.07)π. The phase determines the position of the ﬁrst interaction maximum and thereby the surface area around an adatom in which deposited atoms become irreversibly attached to the adatom. This area is smaller when the phase is smaller, favoring Ce/Ag. A second order eﬀect of the phase is to deter√ mine whether the 3 distance appearing as second neighbor distance in hexagonal lattices is favored. The arguments above are for pair interactions. Once a germ of a hexagonal lattice is formed, these interactions add up and lead in the case of Ce/Ag to an energy minimum of (4.9 ± 0.5) meV for a six-fold coordinated Ce atom, and to a repulsion of (11.8 ± 1.2) meV when it approaches one of its six neighbors [2]. These energies compare favorably with the diﬀusion barrier and suggest that having used higher coverages may well have helped to create superlattices as well for Cu or Co/Cu(111). For Co/Ag(111) the interaction was comparable to Ce, and also the scattering phase; however, the diﬀusion barrier was much larger (in the range of 50 meV [27]). Let us discuss a few more consequences of the fact that repulsive adsorbate–adsorbate interactions add up. The formation of superlattices may be hampered by adding up interactions since this may favor attachment to the ends of elongated structures compared to their sides. In the

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extreme case, this leads to the formation of straight 1D chains, as was ﬁrst observed by means of FIM for interactions of intermediate range [28]. Ir atoms were reported to diﬀuse at some distance along Ir chains on W(110), and attach exclusively to their ends. Calculations for Ag on compressively strained Ag(111) and Cu/Cu(111) reported strongly anisotropic repulsive barriers around elongated islands (dimers, linear trimers) favoring attachment to their ends [29]. A similar phenomenon has been reported to hold also for the long-range interactions. For Co/Cu(111) the individual interactions were shown to add up leading to an attachment barrier of 22 meV for atoms approaching from the side to a chain of Co atoms sitting on the distance favored by the interations, whereas there was no attachment barrier to the chain ends [30]. This is in agreement with the preference for linear structures over compact ones observed in experiment for Cu and Co on Cu(111) [17]. However, the precise role of the scattering phase and of multiple interactions in the formation of superlattices is not yet settled and would be worth further exploration. A particular promising way are ab initio calculations of long-range interactions fed into kinetic MonteCarlo (KMC) simulations. Recent calculations of the long-range interactions of 3d elements on Cu(111) will stimulate experiments since they predict particular superlattice stability for a number of elements, most spectacularly for Ti [31]. Calculating the diﬀusion barriers for these systems could enable KMC simulations of the kinetics of superlattice formation and stability. A further consequence of intermediate-range interactions adding up are very high almost isotropic repulsive barriers around compact clusters. This has consequences for the density scaling [32] and favors small islands with more narrow distributions of sizes and spacings than the ones obtained without interactions [29]. We ﬁnally note that atomic superlattices with smaller lattice constant may be stabilized by dipolar interactions of relatively short range. The most prominent examples for such interactions are alkali metals on metal surfaces. A phase transition from a dilute liquid into √ √ a well-ordered solid has been reported for Cs/Ag/Si(111)-( 3 × 3) [33]. The example of Ce/Ag demonstrates that the surface state electron mediated adsorbate–adsorbate interactions may well be employed for the creation of ordered atomic and possibly also molecular superlattices. In principle the lattice constant can be adjusted by the surface state band structure.

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3. Order in Vertically Stacked Quantum Dots There is considerable eﬀort to create 2D and 3D superlattices of semiconductor quantum dots (QDs). This interest is driven by the desire of size uniformity leading to uniform electronic properties evolving from quantum conﬁnement, such as sharp photoluminescence peaks [34]. One of the anticipated applications are quantum dot lasers which have lower threshold currents through the conﬁnement of the current into the active material and are expected to have higher band width. Alternatively to sequential processing techniques involving high-resolution lithography and etching, the spontaneous formation of 3D coherent islands in the Stranski–Krastanow growth mode of lattice-mismatched heteroepitaxial layers has evolved as a novel approach for quantum dot fabrication [35,36]. The formation of 3D islands on-top a wetting layer is driven by the fact that islands allow for an eﬃcient relaxation of elastic energy through their lateral expansion or compression. Because of the statistical nature of growth, these self-assembled dots are usually not very uniform in size, shape, and spacing. The size uniformity can be improved by growing superlattices with uniform spacings since the distribution of spacings is correlated to the one of sizes [8,39]. A successful way to create such lattices consists of strainmediated nucleation on-top of islands buried by a spacer layer. Figure 3(a) shows an atomic force microscope (AFM) image of the uppermost uncapped island layer of a growth sequence of Six Ge1−x quantum dots separated by Si(100) spacer layers burying the QDs. Ge has a 4.2% larger lattice constant than Si, thus the Si spacer is strained to a slightly larger lattice constant on-top of a buried quantum dot, whereas it has its intrinsic lattice constant in-between. The nucleation rate of islands is an exponential function of the nucleation barrier, which depends sensitively on strain [40]. This barrier is lowest where strain in the surface reduces the lattice mismatch between surface and islands. Therefore Six Ge1−x –alloy islands nucleate preferentially where the Si lattice is expanded, i.e., on-top of a buried island, leading to vertical island correlations in bi-layer stacks. In addition, the following error correction scheme is operative. If by statistical ﬂuctuations two dots are too far apart, there will be a high probability of nucleating one in-between; if two buried dots are too close the strain ﬁelds in the Si spacer overlap and only one new QD nucleates on-top, see Fig. 3(b). Repetition of the growth sequence of quantum dots and spacer layer 20 times yields to increased order, as evidenced by Fig. 3(a) [37].

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(a)

(b)

SixGe1-x

(c) 2000

Si 200

Si(100)

10 5 2 1

5000 Å

0

40

x (D)

80

5000 Å

Fig. 3. (a) Ordered arrays of Si0.25 Ge0.75 quantum dots on Si(100) produced by 20 sequences of Stranski–Krastanov growth of dots and subsequent capping with Si spacer A). (b) One-dimensional layers (spacer thickness D = 100 ˚ A, Si0.25 Ge0.75 coverage 25 ˚ model showing the creation of order by strain ﬁelds inducing nucleation on-top of the buried QDs in such a way that statistical variations in QD spacings and sizes (heights of vertical lines) are corrected (distances are given in units of the spacer thickness D, number of growth sequences increases from bottom to top panels as indicated). (c) AFM image of the last PbSe layer of a 60-period PbSe/Pb1−x Eux Te dot superlattice grown on PbTe(111) (x = 5 − 10%, PbSe coverage 5 ML, D = 450 ˚ A, 360◦ C growth temperature). The inset shows the 2D power spectrum of the AFM image. (a) and (b) from [37], (c) from [38].

In our example the HWHM of the distribution of island diameters goes from σ = 55% for the ﬁrst island layer down to σ = 15% after 20 growth sequences [41]. For diﬀerent material systems, diﬀerent types of island correlations have been observed, ranging from vertically aligned dot columns for InAs/GaAs [42–44] and SiGe/Si superlattices [37,41], to trigonal dot lattices with fcc stacking for IV–VI superlattices [38]. The lateral island spacing L can be tuned to some extent by the spacer thickness D. There is a linear relationship between the two and the slope depends on the misﬁt and on the elastic constants. In the model one ﬁnds a slope of 3.5, whereas it is larger in the SiGe/Si experiments, and lower for IV–VI superlattices. Order gets better with increasing the number of QD-spacer sequences. The theoretical model in Fig. 3(b) predicts a monotonic increase of order with increasing bi-layer number, though with decreasing slope. It predicts that one may reach σ = 5% in island volumes after 2000 stacking sequences [37]. For spherical islands this corresponds to σ = 1.7% in diameter (with V = 4π/3 r3 one ﬁnds dV /V = 3 dr/r). However, the stress accumulated with increasing number of bi-layers sets an upper limit to the number of stacking sequences on which misﬁt dislocations normally

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start to form. Figure 3(c) shows an example of an entirely strain symmetrized superlattice overcoming this limitation [38,45,46]. This is achieved by adjusting the spacer composition (here Pb1−x Eux Te) to exactly compensate the tensile stress in the Stranski–Krastanov QD layers (here PbSe). This allows for up to 100 stacking sequences resulting in for semiconductor QDs unprecedented uniformity of σ = 6% in island spacing and σ = 10% in height [38,45]. In the present case the dots are arranged in an fcc-like vertical stacking sequence, due to the (111) growth direction and to the high elastic anisotropy of the material. We note that this system can be grown also with QD correlations parallel to the growth direction by reducing the spacer thickness [46], however, the increase of order with increasing number of stacks is better for the fcc stacking. The buried QDs form a 3D crystal where the lattice constant can be tuned continuously over several tens of nanometers by the thickness of the spacers, and the size and spacing uniformities increase with number of stacking sequences. For the size uniformity it is essential to distinguish diameter, area, and volume since they typically diﬀer by factors of 2, respectively, 3. Some physical properties may depend on volume, some on area, and some on diameter, thus reﬂecting the polydispersity in a diﬀerent way. For instance, the quantization energies are dominated by the smallest dimension of the QDs, which is the height in the cases discussed above.

4. Decorating Mesoscopically Ordered Surface Reconstructions Surface reconstructions can have large unit cells of up to 25 atoms in length. In addition, the reconstruction may have rotational domains which may be ordered on an even larger length scale into mesoscopic periodic patterns. These surfaces can be used as templates for the heterogeneous nucleation of island superlattices, or for the regular arrangement of single molecules or molecular clusters. One example of mesoscopic order is the herring√ bone pattern of the Au(111)-( 3 × 22)-reconstruction [47]. Other examples of relatively long-range 2D periodic surfaces are Au(111)-vicinal surfaces. When miscut towards the [¯ 211]-azimut, these surfaces present the energetically favored {111}-faceted steps. For a limited range of miscut angles [48] this makes them stable against faceting, and elastic step repulsions give rise to regularly spaced steps [49]. Thus the step distance is solely given by the miscut angle (35 ˚ A on Au(788) and 50 ˚ A on Au(11,12,12)), while the surface period parallel to the steps is caused by the reconstruction of

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the (111)-terraces and ﬁxed to about 70 ˚ A. The advantage of vicinals with respect to low-index surfaces is that the superlattice is not perturbed by the steps, and thus phase-coherent over the entire crystal. The Si(111)-(7 × 7)reconstruction [50] and the (15×15)-termination of the reduced Fe3 O4 (111) surface [51] are examples of large period semiconductor and oxide surface reconstructions, respectively. The surfaces mentioned so far have a long-range periodicity in their pristine state, leaving only limited room for adjustment of period, or symmetry. This is diﬀerent in periodic strain relief patterns created in ultrathin single crystalline ﬁlms on single crystal substrates, where the period of the superlattice can be adjusted by the misﬁt between ﬁlm and substrate. Such incommensurate adlayers exist for metals on metals [9,52–55], dielectrics on metals [56–62], semiconductors on semiconductors [63,64], metals on semiconductors [65], and ﬁnally for adsorbates changing the reconstruction of metal ﬁlms on metals [66]. In principle, one can achieve a continuous tuning of the superlattice period by growing alloy layers for which the lattice constant can be adjusted linearly through the alloy composition, as described by Vegards law. This has been realized for the surface alloy between Au and Ni on a Ni(111) surface [67]. Depending on the lateral stiﬀness of the ﬁlm with respect to the corrugation of the substrate potential, one observes moir´e patterns with a smooth transition between diﬀerent stacking sites, or narrow domain walls, which can also be called partial surface dislocations. These long-range periodic surfaces have been used with success for the heterogeneous nucleation of ordered island superlattices. They have in common the characteristic that nucleation takes place on predeﬁned periodically arranged sites. Therefore the size distribution is given by the statistics of the deposition, leading to a binomial distribution of island volumes with √ σ = (1 − θ)/θ/ n with n the area of the superlattice unit cell expressed in atoms, and θ as usual the coverage expressed in monolayers [68]. Note that this can lead to quite narrow size distributions obtained in a single deposition step, e.g. σ = 4% for half a monolayer deposited onto a surface with a (25 × 25) unit cell! For a more detailed description of these systems we refer to the literature [9,48,69–82], and here focus on one case which emerged recently and which seems to be particularly promising. Ordered strain relief patterns with a large period are most often formed on hexagonally close-packed surfaces since they have a small corrugation of the substrate potential, and the overlayer is relatively stiﬀ since it is

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close-packed. For many reasons one is interested to also create square superlattices of islands, atoms, or molecules. One case where this has been achieved with reasonable success is metal decoration of a Cu(100) surface having been prestructured by nitrogen islands. Figure 4(b) shows that chemisorbed N forms c(2 × 2)-reconstructed square islands with quite uniform size [83]. The fact that islands are formed indicates attractive interactions between chemisorbed N-atoms. The ideal island size is caused by an optimum between strain and edge energy. These islands exhibit long-range elastic interactions mediated by the substrate [84]. They repel each other at very long distances, they attract each other over intermediate distances, and they repel each other again at very short distances prohibiting island coalescence. The resulting scenario with increasing N-coverage is quite complex, but in brief it can be seen as follows. Once two islands approach each other into the attractive regime, they form a dimer to which further islands can only be added along its axis, whereas laterally approaching islands are repelled. This leads to island chains which can be compressed with increasing N coverage to a very regular lattice of quadratic N-covered islands separated by thin stripes of bare Cu, see Fig. 4(a) [48,83]. Since this lattice is stabilized by elastic relaxations in the substrate it is expected that the lattice constant of the N/Cu(100) template can be adjusted by working with

(a)

(b)

300 Å

(c)

100 Å

500 Å

Fig. 4. (a) Quadratic areas of N-covered c(2 × 2)-reconstructed Cu(100) form a regular lattice leaving only small stripes of bare Cu in-between (θN = 0.9 ML of the c(2 × 2) structure, dosage of N2 dissociated with ﬁlament, Tads = 630 K). (b) STM image showing the c(2 × 2) structure atomically resolved (θN = 0.74 ML of the c(2 × 2) structure). (c) Nucleation of Au islands at the intersection of the clean Cu stripes (θAu = 0.67 ML, Tdep = 300 K, θN = 0.92 ML of the c(2 × 2) structure). (a) from [85], (b) and (c) from [83].

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Cu ﬁlms of varying thickness on-top of a more rigid and lattice matched substrate. Deposition of Au onto this surface leads to the nucleation of Au islands at the intersection of clean Cu stripes thus leading to a square island lattice with a period of 50 ˚ A [83,86–88]. The N-covered Cu(100) surface has also been used for the growth of so far less well-ordered lattices of Fe and Cu [89], Co [90–92], Ag [93,94], and Ni [95]. We note that square lattices can in principle also be created on Au(14,15,15) since this miscut leads to 70 ˚ A step distance, which is equal to the reconstruction period. However, the steps are already far apart reaching the limit of the elastic step repulsions which may render global order diﬃcult. Finally we note that another interesting alternative square √ template, although with smaller lattice constant, is presented by the (3 3 × 5)-phase of V-oxide on Rh(111) [96]. 5. Templates — Dislocation Networks and Ordered Domains in Biphases Above we discussed surfaces which may serve as templates to grow square lattices. Here we present one more such example, however, with a larger lattice constant. Figure 5(a) shows the square lattice of misﬁt dislocations formed by 9 ML PbTe deposited onto PbSe(100) [97]. The system exhibits a (a)

(b)

1000 Å

(c)

200 Å

200 Å

Fig. 5. (a) STM image of a regular square array of misﬁt dislocations for 9 ML of PbTe on PbSe(100) (Tgrowth = 380◦ C). (b) 2D crystal of Ag vacancy islands obtained by deposition of S onto 1 ML Ag on Ru(0001) (θS = 0.10 ML, T = 300 K). The inset shows that the vacancies are entirely covered by the chemisorbed sulfer. (c) STM image of a boron-nitride nanomesh formed by high-temperature decomposition of borazine on a Rh(111) surface (exposure 40 L (HBNH)3 at 1070 K sample temperature, Vt = −1.0 V and It = 2.5 nA, brighter spots are related to Ar bubbles in the near-surface region of the substrate). (a) from [97], (b) from [98], and (c) from [99].

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high dislocation mobility since the dislocation glide plane is parallel to the surface; in addition, the dislocations nucleate in a homogeneous way, and ﬁnally they strongly repel each other. These factors lead to the well-ordered superlattice with a lattice constant of 101 ± 12 ˚ A. Domain patterns evolving from the spinodial decomposition of two surface phases are often very well-ordered due to long-range repulsive dipolar elastic interactions. One example is N/Cu(100) discussed above, where the two phases are the c(2 × 2)-structured islands of chemisorbed N, and the clean Cu(100) surface. For close-packed surfaces one observes, with increasing coverage of one phase at the dispense of the other, a transition from droplets to stripes to inverse droplets, as reported for the Ag/Pt(111) surface alloy [100], and for a Pb overlayer coexisting with a PbCu alloy-phase on Cu(111) [101]. Here we focus on another example where S is adsorbed onto a Ag covered Ru(0001) surface [98]. S binds strongly to the Ru substrate and therefore displaces Ag, by which it compresses the Ag layer. This leads to a hexagonal lattice of islands of chemisorbed S which repel each other by the compressive stress in the Ag layer, see Fig. 5(b). The islands are 24 ± 4 ˚ A in diameter and the lattice parameter is 53 ˚ A. The last example we would like to discuss is a lattice of holes formed in stoichiometric hexagonal (h) BN double layers on Rh(111), see Fig. 5(c) and [99]. The lattice is composed of holes in the BN-bilayer with a diameter of 24 ± 2 ˚ A, and an average distance of 32 ± 2 ˚ A. The holes in the upper layer are oﬀset with respect to the smaller holes in the lower layer. We note that well-ordered superstructures with a large period have already been observed some time ago by means of LEED for borazine adsorption onto Re(0001) [102], while borazine adsorption onto other close-packed metal surfaces, such as Pt(111), Pd(111), and Ni(111), leads to the self-limiting growth of commensurate h-BN monolayers [103,104]. For BN/Rh(111) it is not clear at present whether the Rh(111) substrate is exposed at the bottom of the holes. If this was the case the surface would not only be periodic in morphology but also in chemistry, and therefore would constitute a very useful template for the growth of ordered superlattices of metals, semiconductors, and molecules.

6. Outlook We were discussing various ways to create ordered superlattices of atoms, molecules, and islands. Atomic superlattices are monodisperse and can be

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stabilized by electronic screening in a 2D electron gas. Also, metal islands on Si(111)-(7 × 7) are monodisperse. In these systems the metal atoms form strong bonds with Si surface atoms creating Mx Siy -silicide clusters with preferred size, see the example of Al6 Si3 presented in [78–80]. The islands created by heterogeneous nucleation on periodic surfaces and the vertically stacked QDs are not monodisperse, however, they can potentially reach size distributions down to a few % in width. All superlattices are metastable structures created by the diﬀusion of adspecies on long-range modulated potential energy surfaces. The stability is lowest for the atomic superlattices which, upon annealing, ﬁrst nucleate small islands which then Ostwald ripen to larger islands [105,106] until eventually these islands also decay to form a seam at the substrate steps. Adsorbates forming alloys with the substrate may even disappear into the bulk upon annealing. The examples given here concern atoms and islands, and in most cases were not yet extended to molecules, which will be very interesting to explore. Many of the templates presented here have not yet been used for the creation of superlattices. It will be interesting to investigate how, for example, the BN-lattice will behave when depositing metals, semiconductors, or molecules on top (C60 molecules have already been adsorbed [99]). For larger distances the PbTe/PbSe(100) dislocation network will be a good candidate, and for small distances, for example of catalytic particles, the reconstructions of bulk oxide surfaces and the ones of thin epitaxial oxide-ﬁlms are promising templates. Following the approaches used in 3D supramolecular chemistry, one has realized 2D molecular superlattices with cavities exposing the underlying metal substrate [107–111]. These lattices may in the future also be employed as templates for metal or semiconductor deposition. Future work into this direction will have to address the stability of the molecular lattice towards the highly reactive diﬀusing adsorbates, and the challenge of obtaining a ﬁlling factor of 1 for the molecular superlattices, since up to now in many cases only half of the surface is covered with the superlattices. Regular lattices of 1D stripes may also be achieved with molecules [112], and recently it was shown that a striped biphase surface can be used as template for molecular decoration [113]. We hope that the present overview inspires future work in the creation of well-deﬁned atomic, molecular and island superlattices at surfaces, opening up the investigation of the novel properties also with spatially integrating experimental techniques.

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MOBILITY OF COMPLEX ORGANIC SPECIES AT METAL SURFACES JOHANNES V. BARTH Advanced Materials and Process Engineering Laboratory Departments of Chemistry and Physics & Astronomy University of British Columbia, Vancouver, BC V6T 1Z4, Canada Institut de Physique des Nanostructures Ecole Polytechnique F´ed´erale de Lausanne CH-1015 Lausanne, Switzerland Abstract. Concepts, recent developments and achievements in investigations addressing the mobility of complex organic molecules on welldeﬁned metal surfaces are reviewed. Keywords: Adsorption; surface diﬀusion; molecular rotors; self-assembly; metal surfaces; Scanning Tunneling Microscopy; molecular nanoscience.

Contents 0 1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . Basics and Methodology . . . . . . . . . . . . . . . . . . 1.1 Tracer diﬀusion and the hopping model . . . . . . 1.2 Concentration gradients and mass transport . . . 1.3 Rotation of adsorbed molecules . . . . . . . . . . . 1.4 Laser-induced thermal desorption . . . . . . . . . 1.5 Scanning tunneling microscopy . . . . . . . . . . . 2 Case Studies Addressing Mobility of Complex Molecules at Metal Surfaces . . . . . . . . . . . . . . . . . . . . . . 3 Future Perspectives . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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0. Introduction The motion of complex organic molecules plays a decisive role in the positioning of functional molecular species at selected sites of templates and the self-assembly of supramolecular nanostructures or layers at surfaces. Both translational and rotational motions need to be considered, and moreover, 269

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conformational changes may interfere. The detailed understanding of such phenomena is a mandatory issue in the present race for nanoscale control of matter and the development of future nanostructured functional materials, nanofabrication methodologies and devices. But also from the fundamental research point of view this ﬁeld is rewarding, because it comprises new horizons and challenges in the exploration of the molecular world. The ﬁrst ideas about molecular mobility at surfaces date back to the 1920’s [1–3]. Notably, detailed light microscopy observations in the crystallization of benzophenone provided indirect evidence that ‘molecules can migrate on the surface by virtue of thermal motion’ [3]. Based on these and other observations, Volmer suggested ‘the following conception of the mechanism of the spreading over solid surfaces: at low enough temperatures the adsorbed molecules . . . are mostly bound to the ﬁxed atoms of the underlying material, and like these only oscillate around their equilibrium positions. When, with rising temperature, the amplitude of the oscillations is increased, it will occur more and more often that an adsorbed molecule, because of an occasional elongation, jumps into the unoccupied ﬁeld of an adjacent atom. The process therefore requires a deﬁnite energy of activation and its velocity will increase as the temperature rises in accordance with an exponential law’ [3]. This interpretation is in agreement with the thermionic observations from Becker and Taylor, which were at the origin to associate surface diﬀusion with ‘hopping atoms’ [4,5]. These basic conceptual views are valid to date. However, in the last decades, tremendous progress has been made in both the experimental characterization and theoretical understanding of surface mobility, and the foundations and advances of this ﬁeld have been extensively reviewed [6–21]. With the advent of modern surface and nanoscience experimental tools, comprehensive investigations of the motion of complex molecular adsorbates at atomically clean surfaces under ultra-high vacuum conditions (UHV) became possible. In initial studies integral techniques such as laserinduced thermal desorption (LITD) were employed to create concentration gradients in organic layers at well-deﬁned metal substrates and measure their temporal decay [22]. The invention of the scanning tunneling microscope (STM) [23], which revolutionized surface science and was key in the development of nanoscale science, introduced the possibility to perform observations at the single molecule level. 1. Basics and Methodology Molecules coming from the gas phase into contact with a metal surface thermalize with the phonon heat bath of the crystal upon adsorption. The

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Fig. 1. STM images resolving (a) the hexagonal atomic structure of the close-packed fcc(111) surface and (b) the anisotropic fcc(110) surface of Ag. The surface unit cells and high symmetry directions are marked. (c) Schematic one-dimensional potential energy surface experienced by a simple individual adsorbate along a high-symmetry surface direction (Em : migration energy barrier; Eb : bonding energy; a: surface lattice constant).

admolecule similarly experiences the periodic corrugation of the substrate atomic lattice, which is illustrated in Fig. 1. The binding energy is thus subject to lateral variations with local minima corresponding to energetically favorable positions. These adsorption sites are separated by energy barriers being usually signiﬁcantly smaller than the energy barrier for desorption. For isolated adspecies the minimum energy diﬀerence between adjacent sites is called the migration energy barrier Em . In the case of anisotropic surfaces direction dependent migration barriers along principal crystal axes can be present [20]. The excitation and damping of the thermal motion of an adsorbate is predominantly mediated by the coupling to the substrate phonon bath. The typical frequency of the phonons is ∼1012 –1013 s−1 , with surface atom vibrational amplitudes of ∼0.1 ˚ A at room temperature. The magnitude of the thermal energies with respect to the migration energy barrier is decisive for the lateral transport of adsorbates on the surface. In most practical situations the condition kB T Em is obeyed. When the thermal energies are very small, the adsorbates are conﬁned to speciﬁc sites, corresponding generally to high-symmetry positions on the surface. A temperature can be

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identiﬁed where the adspecies can be considered immobile with respect to a time scale of interest (quantum mechanical tunneling transport is not considered here, cf. Refs. [13,19,20]). For temperatures exceeding this value, surface migration is driven by the continuous energy exchange between adsorbate and substrate. The corresponding energy ﬂuctuations result in random jumps from one energy minimum to another, i.e., a stochastic hopping mechanism is operative. Most of the time the adsorbates remain in the adsorption well, where they are vibrating, and only rarely the energy necessary to overcome the migration barrier is accumulated. Hence it is frequently assumed that subsequent jumps are uncorrelated, i.e., that hopping is a Markov process. Upon averaging over many events, a hopping rate can be deﬁned. On the one hand the aleatoric thermal mobility of adsorbed particles is called surface diﬀusion. This 2-D brownian motion is a stochastic process reﬂecting the never ceasing energy ﬂuctuations of a system in thermal equilibrium in the absence of external forces at ﬁnite temperature. When the particles are adsorbed on a homogenous surface and do not interact with each other, this leads to random walks. On the other hand, a directed ﬂux of adsorbates can be induced by the variation of their density or chemical potential at the surface. This corresponds to a gradient-driven transport phenomenon for a system which is not in thermodynamic equilibrium. In its simplest form it can be described by Fick’s law, where the concentration gradient is the driving force. With increasing time, the resulting 2-D directional diﬀusion smears out an initial concentration proﬁle. When eventually equilibrium is attained, there is a uniform adsorbate distribution on the surface and no further net surface mass transport takes place; nevertheless the aleatoric thermal mobility persists. In both cases there is a strong temperature dependence. The higher the temperature, the more active the adsorbate motion and the faster the gradient decay. 1.1. Tracer diﬀusion and the hopping model In the hopping model, the migration of an isolated adspecies corresponds to an aleatoric walk from adsorption site to adsorption site for a system in thermodynamic equilibrium. Upon denoting the starting point of the motion at t = 0 as ro + (xo , yo ), the mean jump length along the x, y directions as λx , λy and the corresponding hopping frequencies as Γx , Γy , the mean square displacement of the atom is: (r(t) − ro )2 ≡ (∆r)2 = (Γx λx 2 + Γy λy 2 )t

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which reduces for an isotropic surface to: (∆r)2 = Γh λ2 t. A characteristic property of surface migration is that (∆r)2 varies linearly with time. Note that the very deﬁnition of a hopping frequency Γh tacitly implies statistic averaging over many hopping events. The time diﬀerence between the individual jumps of a speciﬁc particle varies stochastically. The corresponding tracer diﬀusion coeﬃcient is deﬁned as: (∆r)2 t→∞ 2dt

D∗ = lim

where d is the dimensionality of the diﬀusion process (d = 1, 2 at surfaces). Combining the above equations it follows that D∗ can be expressed in terms of the hopping rate Γh and the mean jump length λ: D∗ =

1 λ2 Γh . 2d

When kB T Em , the tracer diﬀusion coeﬃcient obeys an Arrhenius law and accordingly the following relation holds: D∗ =

1 λ2 νo exp[−βEm ] ≡ Do∗ exp[−βEm ] 2d

where νo is designated as the attempt frequency, Do∗ as the pre-exponential factor (or prefactor ) of the tracer diﬀusion, β = [kB T ]−1 . A unique migration barrier is posed. This equation is fundamental in surface migration. When nearest-neighbor jumps prevail, λ is equal to the surface lattice constant a. Since a ∼ 3 ˚ A and since the attempt frequency can be associated with the vibrational frequency of the atom in the adsorption well (typically 1013 s−1 [24]), the pre-exponential factor is expected to be ∼10−3 cm2 s−1 , which is frequently considered as a universal value.

1.2. Concentration gradients and mass transport Gradient-driven diﬀusion phenomena at ﬁnite coverages are usually described in macroscopic terms via an adsorbate ﬂux density in two dimen˜ is accordingly sions. The chemical or collective diﬀusion coeﬃcient D deﬁned through Fick’s laws. The ﬁrst of these empirical laws describes the diﬀusion ﬂux density j across a borderline, which results from a coverage

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gradient in a continuum: ˜ j = −D(Θ)∇ r Θ(r, t) upon combination with the continuity equation −∂t Θ(r, t) = ∇r j, Fick’s second law is obtained: ˜ ∂t Θ(r, t) = ∇r · D(Θ)∇ r Θ(r, t). The collective diﬀusion coeﬃcient is thus relevant for the mass-transport at surfaces in systems, which are not in thermodynamic equilibrium. It generally depends on coverage. The above diﬀusion equation is widely employed ˜ since the adsorbate concentration is a measurable quanto determine D, tity. In practice, frequently the decay of an adjusted coverage gradient is analyzed and diﬀusion equation is solved numerically or analytically for a given geometry. This task is considerably simpliﬁed when diﬀusion coeﬃcients independent of coverage exist or may be assumed and: ˜ 2r Θ(r, t). ∂t Θ(r, t) = D∇ Collective diﬀusion on homogenous substrates usually obeys an Arrhenius law under conditions where it can be conveniently measured. Accordingly, the data are analyzed assuming that energetics and dynamics can be factorized, i.e.: ˜ ˜ o exp[−βEd ]. D(Θ) =D The barrier for chemical or collective diﬀusion Ed is then obtained using the relation: ˜ Ed = −∂β ln D. It is important to note that the migration barrier Em of isolated adsorbates and the barrier encountered in collective diﬀusion Ed are a priori unequal, although they are related and become identical in the zero coverage limit [13,20]. 1.3. Rotation of adsorbed molecules For the case of adsorbed complex molecules, which generally have a preferred orientation with respect to the substrate atomic lattice in their energy minimum conﬁguration, the possibility of 2-D molecular rotations needs to be considered. These rotations require thermal activation, analogous to lateral transport. In the simplest case they imply the overcoming of a unique rotation energy barrier Er , which may be higher, equal or lower than the

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diﬀusion or migration barrier. Er is associated with a corresponding rotational prefactor. As an exemplaric study with a simple molecular adsorbate, we refer to a recent STM study of C2 H2 on Cu(001) where both molecular rotation and diﬀusion could be monitored [25]. Each process was found to obey an Arrhenius law. The activation energy for diﬀusion (rotation) is 530 ± 10 meV (169 ± 3 meV) with a prefactor of 1013.6±0.2 s−1 (1011.8±0.2 s−1 ). At lower temperatures, rotations induced by the tunneling current could be monitored (cf. Fig. 2(a)). It was proposed that they are mediated by the coupling of vibrational excitations to the rotational motion [26,27]. An STM study with the complex species hexa-tert-butyldecacyclene (HBDC) on Cu(100) provided evidence for continuous rotation of a single molecule at room temperature laterally conﬁned in a vacancy of an organic layer, as schematically illustrated in Fig. 2(b) [28,29].

Fig. 2. (a) Frustrated rotational motion of C2 H2 adsorbed on a Cu(001) surface induced by tunneling electrons at 8 K. The model shows top and side views of the molecular adsorption site with the C-C bond parallel to the surface and the preferred angular orientations. In the corresponding STM data the conﬁgurations of a speciﬁc C2 H2 molecule at the same adsorption site with respect to the Cu substrate (indicated as a square lattice) are illustrated [26]. (b) Model illustrating the rotation of the complex molecule hexa-tert-butyldecacyclene on a square substrate [29].

1.4. Laser-induced thermal desorption In the 1980’s a versatile technique based on laser-induced thermal desorption (LITD) was introduced for the investigation of surface diﬀusion phenomena [30]. LITD is conceptionally straightforward. A speciﬁc homogeneous concentration of adsorbates is established on a surface.

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Subsequently a well-deﬁned area at the surface is depleted from the adsorbate layer by a focused laser pulse. Since thermal equilibrium at the surface is rapidly recovered, the bare spot can be reﬁlled only by surface diﬀusion of adsorbates from the surrounding areas [31]. A second laser impulse is applied to desorb the transported adsorbates after a time interval t from the ﬁrst pulse. The corresponding amount of material can be quantiﬁed by mass spectrometry. For the idealized case of a circular depletion region, with a step-like coverage gradient and a concentration-independent diﬀusivity, the time-dependent reﬁlling from Fick’s ﬁrst law is [32,33]: ∞ 2 r ˜ r 2 J1 ( ro ) r Dt S(t) =1−2 exp − 2 d r S(∞) ro r o ro o ro where S(t) is the measured signal, ro is the radius of the depleted area and J1 is a Bessel function of order 1. ro is typically in the 100 µm range. Upon measuring the fractional reﬁlling for several time intervals at a given temperature, the diﬀusivity can be determined from ﬁts using the above equation or analogous expressions for other geometries to the experimental data. Experiments performed with diﬀerent initial coverages provide trends for the coverage dependence of the diﬀusivity. LITD has been employed for investigating surface mobility of adsorbed gases and large molecules on single crystal surfaces. Among this technique’s advantages are the possibility to study virtually all adsorbates and coadsorbate systems which can be thermally desorbed and detected by mass spectrometry. A frequently discussed problem is the possible eﬀect of substrate imperfections in the area under investigation, which may be even created upon irradiation [34]. Diﬀusion over atomic steps is of course inevitable for the mesoscopic mass transport in the experiments. Coverage-independent diﬀusivities are frequently assumed for the data interpretation, and it was pointed out that the concentration variation in the depletion area aﬀects the corresponding results [35–37]. 1.5. Scanning tunneling microscopy STM measurements can be employed to systematically study tracer diffusion by following adsorbate migration at the atomic level in situ. This was achieved for a variety of systems, including adsorbed gas atoms and molecules at metal surfaces [20]. Moreover, STM allows for detailed investigation of the bonding geometries and 2-D rotational motions. The temperature dependence is conveniently investigated by variable-temperature

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instrumentation [38–42]. In most cases, hopping frequencies were determined from a statistical analysis of series of STM images, whence the corresponding activation energies and prefactors can be extracted from Arrhenius plots. With favorable systems the mean square displacement of adatoms can be determined and the jump mechanims elucidated [43,44]. The recently presented ‘atom tracking’ method allows to follow the migration path of an individual moving adsorbate [45]. With very sophisticated instruments, surface mobility can be even recorded at video rates and visualized by STM movies [43,46]. The complete analysis and interpretation of such data can only be achieved with the development of adequate computer techniques [43,47]. Care must be taken to exclude the possible eﬀect of tipsurface interactions in STM experiments. Both theoretical and experimental studies indicate a modiﬁed migration energy barriers under the STM tip [48–53]. However, such eﬀects are negligible or can be largely excluded by working at large tunneling electrode distances. Among the limitations of STM studies are also the rather low diﬀusivity ranges accessible and its principal application to small adsorbate concentrations. The striking advantages of STM are atomic resolution, its conceptional transparency and versatility, and the appeal of direct visualisation. STM can be applied to study anisotropic surface mobility, diﬀusion on inhomogeneous surfaces, or adsorbate interactions and collective transport eﬀects on a local scale. It also a technique where a simultaneous characterization of tracer and chemical diﬀusion on single crystals is feasible [54]. Surface mobility studies using STM are currently progressing rapidly.

2. Case Studies Addressing Mobility of Complex Molecules at Metal Surfaces A fair number of studies on the surface mobility of adsorbed complex molecules can be found in the literature. Techniques applied so far are LITD and STM. The investigated adsorbates cover the range from small molecules with simple adsorption conﬁgurations to large organic molecules which exceed by far the dimensions of the respective substrate unit cells. In any case additional degrees of freedom need to be considered. These include rotational motions or the occupation of multiple adsorption sites. With large and ﬂexible species moreover conformational changes may be of importance in adsorption [55–58] and hence interfere in the surface transport properties [59]. Exemplaric investigations are discussed in the following.

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Systematic observations on the mobility of n-alkanes (propane, n-butane, n-pentane and n-hexane with the chemical formula Cn H2n+2 ) on Ru(001) were performed with LITD [22]. Arrhenius behavior is obeyed in all cases and it was found that the diﬀusion barrier increases linearly with the alkane chain length from 130 ± 10 to 210 ± 10 meV, whereas only small variations in the prefactors (∼0.15 cm2 s−1 ) exist [22] (cf. Fig. 3). The observed diﬀusion coeﬃcients are quite independent of coverage, indicating small lateral interactions. It was suggested that the n-alkanes move in a rigid conﬁguration on the surface [22]. Related investigations employing pentane isomers revealed diﬀusion barriers scaling inversely with the degree of branching of the isomers [60]. Upon ﬂuorination of n-butane both the diﬀusion barrier and the prefactor were found to be lowered [61]. Recent Helium atom scattering (HAS) observations with octane on Ru(001) indicate that electron-hole pair creation is involved in the damping of the molecular motion [62]. The observations of the n-alkane diﬀusion triggered extensive theoretical investigations, mostly employing Monte Carlo (MC) and Molecular Dynamics (MD) simulations [63–69]. From systematic simulations of a series of nalkanes (n-C3 H8 , n-C6 H14 , n-C10 H22 and n-C20 H42 ) on W(001) the trends observed experimentally on Ru(001) were conﬁrmed in the 300–1000 K

Fig. 3. Arrhenius plots of the surface diﬀusion coeﬃcients for a series of n-alkanes adsorbed on Ru(001) at θ = 0.2θsat . LITD results [22].

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range (i.e., Arrhenius behavior, increase of Em with the chain length), albeit with signiﬁcantly smaller prefactors close to 1 × 10−3 cm2 s−1 [63]. In a recent detailed transition state theory (TST) study of n-alkane (n-butane — n-decane) diﬀusion on Pt(111) the respective diﬀusion mechanisms were addressed in detail. It was found in particular that the hopping between nearest neighbor sites is not strictly obeyed and directional anisotropy can be induced by the molecular orientation [66]. In addition, the motion of larger molecules involves transient occupation of local minima. Some typical diﬀusion paths are illustrated in the model shown in Fig. 4. Again, the theoretical prefactors were found to be close to the universal value. In related theoretical studies the diﬀusion and spreading of chain-like molecules on solid surfaces was considered [70,71]. Chains were modeled as connected segments occupying sites on a square lattice, whereby the chain ﬂexibility and attractive interactions can be varied [70]. The coverage and interaction dependence of tracer and collective diﬀusion coeﬃcient calculated from MC simulations have been obtained. Further aspects are considered in Refs. [72–74]. A systematic STM study was reported for the thermal migration of the complex molecule PVBA (4-trans-2-(pyrid-4-yl-vinyl) benzoic acid) on Pd(110) [75]. This rigid and large organic molecule interacts strongly with the Pd substrate and binds diagonally to two neighboring Pd troughs (cf. Fig. 5). No changes in the adsorption geometry exist at diﬀerent coverages [76]. The diﬀusion of single molecules is strictly 1-dim in [1¯10], i.e., along the Pd surface atom rows, whereby the molecular orientation is strictly

Fig. 4. Selected molecular conﬁgurations involved in (a) n-hexane and (b) n-butane and n-octane hopping on Pt(111) along easy migration paths. The molecular motion follows the sequence 1-2-3 in (b). Filled (open) circles indicate the carbon backbone position of the molecule at the binding site (transition state), diamonds correspond to Pt surface atoms [66].

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Fig. 5. Surface diﬀusion of the rigid rodlike molecule 4-trans-2-(pyrid-4-yl-vinyl) benzoic acid on Pd(110). In (a) and (b) two consecutive STM images taken at 361 K are shown which demonstrate the 1-dim motion. Arrows indicate molecules whose position changed; circles mark fractionally imaged molecules moving under the STM tip in the course of the measurement. (c) Model for the ﬂat adsorption geometry explaining the two observed molecular orientations in the STM data. The length of the molecule is 12.5 ˚ A. (d) Arrhenius plot of single molecule hopping rates [75].

retained, as demonstrated by the data reproduced in Fig. 5. It obeys an Arrhenius law with a diﬀusion barrier of 830 ± 30 meV and a prefactor of 7.6 × 10−6±0.4 cm2 s−1 [75]. In subsequent related investigations the motion of individual buckyballs adsorbed on Pd(110) system was investigated. The migration barrier for 1-D motions along the substrate furrows of adsorbed C60 monomers was determined to 1.4 ± 0.2 eV with a prefactor of 1014.4±0.4 s−1 [77]. It was not possible to determine possible buckyball orientational changes during the motion, which eﬀectively might ‘roll’ over the surface. An intricate diﬀusion limited scenario was observed in the lowtemperature aggregation of PVBA and the related species PEBA (4-[(pyrid-4-yl-ethynyl)]-benzoic acid) on Ag(111) [78,79]. The operation of anisotropic hydrogen bonding between the molecular endgroups in conjunction with the smoothness of the substrate leads to the formation of molecular networks, as demonstrated by the STM data in Fig. 6. At higher

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Fig. 6. (a) Diﬀusion limited aggregation of 4-trans-2-(pyrid-4-yl-vinyl) benzoic acid lying ﬂat on Ag(111). The hydrogen bonding between the molecular endgroups stabilizes a molecular network upon adsorption at T = 125 K. (b) For the H-bond mediated selfassembly of molecular twin chains in equilibrium (∼250–400 K) both rotational and translational molecular mobility is required [78,79].

temperatures, the PVBA molecules self-assemble at the surface to extended molecular twin chain gratings (2-D islands), which are again stabilized by hydrogen bonding. The formation of such superstructures provides indirect evidence of both rotational and translational molecular rearrangements [78,79], which are similarly operative in the self-assembly of other hydrogenbonded supramolecular nanostructures on other substrates [80–85]. A detailed comparative STM study on the motion of the related molecules HBDC and decacyclene (DC) on the Cu(110) surface revealed that with this system long jumps, i.e., hopping events spanning multiple lattice spacings are dominating the 1-D tracer diﬀusion of these species [86] (a STM movie can be found at http://www.phys.au.dk/ camp/stmmovies.shtm). The chemical structure, exemplaric STM observations and Arrhenius plots for hopping rates are shown in Fig. 7. Both molecules comprise an aromatic π system and adsorb in a ﬂat geometry on the substrate, whereby the presence of the additional tert-butyl aromatic side groups in HBDC is expected to raise the aromatic system away from the surface. This geometrical diﬀerence goes along with marked differences in the migration barriers, prefactors and mean jump lengths λ for DC (HBDC) molecular displacements along the [1¯10] direction, which were determined to 0.74 ± 0.03 (0.57 ± 0.02) eV, 1013.9±0.7 (1013.5±0.4 ) s−1 and 3.9 ± 0.2 (6.8 ± 0.3) substrate spacings, respectively. The intriguing possibility exists that the diﬀusion of such species could be coupled to a disk-like rotation [58].

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Fig. 7. (a), (b) The complex molecules decacyclene (DC) and hexa-tert-butyldecacyclene (HBDC). (c) Stills from an STM movie of HBDC migration on Cu(110) — arrows indicate displacement directions for molecules in the subsequent image (T = 194 K; 50 × 50 nm2 ; ∆t = 13.9 s). (d) Arrhenius plots of the hopping rates and tracer diﬀusion constants for both molecules [86].

Finally we address an STM study providing direct insight into the formation of coordination compounds at a Cu(100) surface, whereby translational and rotational molecular motions are involved. Towards this goal a molecular building block — 1,3,5-benzenetricarboxylic acid (trimesic acid, tma) — was deposited on the copper substrate. At room temperature the carboxylic acid mo¨ıeties deprotonute and the resulting trimesate admolecules bind ﬂat on

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Fig. 8. tma-molecules bond in a ﬂat adsorption geometry at a copper surface and are resolved as equilateral triangle in STM. The sequence of STM images reveals how the thermal motion of molecules at the surface proceed: following tma rotational motions and displacements a Cu atom is captured whereupon a cloverleaf-shaped Cu(tma) 4 coordination compound evolves (second image for t = 80 s, central Cu atom highlighted in red) [87].

the surface, where they coexist with a 2-D gas of highly mobile Cu adatoms, originating from the continuous atom evaporation at atomic steps. These Cu adatoms can bind to the reactive ligands of the molecule, i.e., the carboxylate groups. In STM image sequences, such as the one reproduced in Fig. 8, the movements of single molecules were monitored revealing how rotating tma molecules act as dynamical atom trap for individual Cu atoms. Thus single events of association and dissociation of cloverleaf-shaped Cu(tma)4 coordination compounds were directly observed. Furthermore it turned out that the lifetime of the complexes depends crucially on the local chemical environment [87]. 3. Future Perspectives The comprehensive investigation and understanding of the mobility of complex adsorbed molecules is a challenging and fruitful ground for experimental and theoretical investigations. The examples presented on the previous pages reveal that the pertaining research is currently at an early stage. Much remains to be learned about the detailed nature of the mechanisms underlying the motion of complex adsorbed species, notably when they include conformational adaptation, rotations or substrate rearrangements. The most promising experimental technique in this respect is at the present stage temperature controlled STM, especially when instrumentation with high data acquisition rates is employed. With systematic investigations a general phenomenological description of the molecular motion may emerge. Furthermore, in view of the recent progress in computational science, the interplay between experiment and modeling is expected to heavily contribute to a comprehensive understanding and may even culminate in the

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development of a rationale to predict properties or at least trends for any system of interest. It is thus believed that studies advancing this ﬁeld will be a continuous source of further scientiﬁc insight and inspiration. Moreover, the current trends in nanoscale science and technology suggest that supramolecular assemblies built up from appropriate molecular building blocks will play an important role in the future development of highly organized functional materials and nanosystems. When suitable processes are conducted using appropriate building blocks at surfaces or prestructured templates, entirely novel low-dimensional architectures can be realized. In this case the motions and interactions of the adsorbed complex species are decisive elements to rationalize and steer the respective self-assembly protocols. Hence we expect that the basic understanding elaborated today will be useful for the design of tomorrow’s materials and devices.

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[61] M. V. Arena, E. D. Westre and S. M. George, J. Chem. Phys. 94, 4001 (1991). [62] G. Witte et al., Phys. Rev. Lett. 80, 121 (1998). [63] D. Cohen and Y. Zeiri, J. Chem. Phys. 97, 1531 (1992). [64] M. Silverberg, J. Chem. Phys. 99, 9255 (1993). [65] D. Huang, Y. Chen and K. A. Fichthorn, J. Chem. Phys. 101, 11021 (1994). [66] J. S. Raut and K. A. Fichthorn, J. Chem. Phys. 108, 1626 (1998). [67] J. S. Raut, D. S. Sholl and K. A. Fichthorn, Surf. Sci. 389, 88 (1998). [68] J. S. Raut and K. A. Fichthorn, J. Chem. Phys. 110, 587 (1999). [69] A. A. Tarasenko, L. Jastrabik and C. Uebing, Phys. Rev. B 57, 10166 (1998). [70] T. Hjelt, S. Herminghaus, T. Ala-Nissila and S. C. Ying, Phys. Rev. E 57, 1864 (1998). [71] T. Ala-Nissila, S. Herminghaus, T. Hjelt and P. Leiderer, Phys. Rev. Lett. 76, 4003 (1996). [72] T. Hjelt and I. Vattulainen, J. Chem. Phys. 112, 4731 (2000). [73] J. M. Lahtinen, T. Hjelt and T. Ala-Nissila, Surf. Sci. 454–456, 598 (2000). [74] J. M. Lahtinen, T. Hjelt, T. Ala-Nissila and Z. Chvoij, Phys. Rev. E 64, 021204 (2001). [75] J. Weckesser, J. V. Barth and K. Kern, J. Chem. Phys. 110, 5351 (1999). [76] J. Weckesser et al., Surf. Sci. 431, 268 (1999). [77] J. Weckesser, J. V. Barth and K. Kern, Phys. Rev. B 64, 161403 (2001). [78] J. V. Barth et al., Angew. Chemie Int. Ed. 39, 1230 (2000). [79] J. V. Barth et al., J. Am. Chem. Soc. 124, 7991 (2002). [80] T. Kawai, H. Tanaka and T. Nakagawa, Surf. Sci. 386, 124 (1997). [81] M. B¨ ohringer et al., Phys. Rev. Lett. 83, 324 (1999). [82] A. Dmitriev et al., J. Phys. Chem. B 106, 6907 (2002). [83] T. Yokoyama et al., Nature 413, 619 (2001). [84] J. A. Theobald et al., Nature 424, 1029 (2003). [85] J. V. Barth et al., Appl. Phys. A 76, 645 (2003). [86] M. Schunack et al., Phys. Rev. Lett. 88, 156102 (2002). [87] N. Lin et al., Angew. Chem. Int. Ed. 41, 4779 (2002).

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MOLECULAR MONOLAYERS ON SILICON SURFACES

G. P. LOPINSKI and D. D. M. WAYNER Steacie Institute for Molecular Sciences 100 Sussex Dr., Ottawa, Ontario, Canada Abstract. Formation of organic molecular monolayers on silicon surfaces oﬀers the promise of enhancing the functionality of existing silicon-based materials and devices. These monolayers can function as passivating layers, stabilizing the properties of the underlying substrate, or used to tailor its physical, chemical and electronic properties. Monolayers can also impart new functionality to the silicon surface, such as molecular recognition capability. In this chapter we review the methods that have been developed for the formation of molecular monolayers via reactions with hydrogen terminated silicon, and summarize the current understanding regarding the mechanisms behind these reactions. A variety of chemical approaches have been employed to form alkyl monolayers covalently attached to the surface via Si-C, Si-O or Si-N linkages. Multi-step reactions have been developed to build up more complex chemical functionalities as well as for the attachment of biomolecules such as DNA and proteins. The characterization of the resulting monolayers, employing a wide variety of surface science probes, will be discussed. Investigations of the electronic properties of these layers with both electrochemical and solid-state approaches are summarized. Attempts to demonstrate the utility of these monolayers for molecular electronic and chemical/bio sensing applications are critically reviewed.

Contents 1 2 3 4 5

Introduction . . . . . . . . . . . . . . . . . . . . . . . Methods and Mechanisms for Monolayer Formation Monolayer Functionalization . . . . . . . . . . . . . . Monolayer Structure and Physical Properties . . . . Electronic Properties . . . . . . . . . . . . . . . . . .

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6 Challenges and Opportunities . . . . . . . . . . . . . . . . . . . . . . . . 323 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327

1. Introduction The controlled formation of organic molecular monolayers on inorganic substrates oﬀers tremendous opportunities to enhance the functionality of a variety of conventional solid-state structures and devices. The synthetic tunability and diversity of properties of organic molecules suggests a range of promising applications for hybrid organic/inorganic structures. At the simplest level, molecular monolayers can serve to passivate the surface, protecting the underlying substrate or structure from unwanted reactions or processes which degrade its properties. This is especially important in the case of micro and nanoscale devices where the surface properties can play a dramatic role in inﬂuencing the performance (e.g. micro-mechanical (MEMS) and microﬂuidic systems, porous materials, nanowires, quantum dots, etc.). However, molecular monolayers can be much more than passive protective coatings. Molecular layers can be used to controllably alter the properties of a surface or structure, imparting new functionality to bulk materials. For example, monolayers with molecular recognition properties oﬀer opportunities for the development of novel sensing platforms based on electrical, optical or mechanical transduction of chemical binding events. Incorporation of biologically active elements into these ﬁlms opens up a wide range of biosensing possibilities as well as the prospect of improved technologies for both passive and active medical implants and prosthetic devices. Another intriguing area of application is that of molecular scale electronics which envisages the use of molecular systems to furnish analogs of insulators, interconnects, switches and memory elements. The possibilities outlined above have led to an explosion of research in the area of molecular monolayers and organic/inorganic interfaces over the past 30 years. While early work in this area employed Langmuir–Blodgett ﬁlms, the development of so-called “self-assembled” monolayers (SAMs) in the 1980’s enabled a higher degree of control over the structure and properties of these molecular layers. The ﬁrst SAMs (deﬁned as “molecular assemblies which form spontaneously by the immersion of an appropriate substrate into a solution of an active surfactant in an organic solvent” [1]) were actually formed on oxidized silicon surfaces via the reaction of chloro or alkoxy silanes with surface hydroxyl groups [2]. This method produces molecular layers which are covalently linked to the oxidized silicon surface

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via Si-O-Si bonds. A subsequent breakthrough was the discovery that alkanethiols could form dense, ordered monolayers on gold [3,4]. The ability to form ordered monolayers with reasonable ease has led to these thiol-based SAMs on Au becoming the system of choice for exploring fundamental issues in the physics and chemistry of molecular layers as well as for the development of applications in molecular scale electronics and biosensing. Silicon is of particular interest as a substrate for the formation of molecular monolayers due to its extensive use in the microelectronics industry. Covalent attachment of molecules directly to the silicon surface (without an intervening oxide layer) opens up the possibility of hybrid devices that complement and/or extend the functionality of conventional microlectronic devices. For example, molecular switches on silicon surfaces could be seamlessly integrated with conventional CMOS-based ampliﬁers to create hybrid high density memory and/or logic. In addition, one can envision device concepts in which the molecule is not the active current-carrying component but acts to “gate” electronic transport in the underlying substrate, much like the application of a voltage to the gate of a conventional CMOS transistor. This type of gating eﬀect is unique to semiconductors and could be particularly useful for electrical detection of chemical and biochemical processes. Apart from electronic applications, silicon substrates are used extensively for microﬂuidics, MEMS and optical waveguides (taking advantage of the exhaustive microfabrication processes developed for this material). Controlled formation of molecular monolayers on silicon is expected therefore to enable a wide range of diverse applications. In 1993, Linford and Chidsey reported the formation of molecular monolayers covalently attached directly to silicon surfaces, with no intervening oxide layer [5]. This approach involved radical initiated reactions with atomically ﬂat hydrogen terminated Si(111). These H/Si(111) surfaces, which can be generated by a relatively straightforward wet chemical etching procedure [6], are stable enough to permit some degree of manipulation in air as well as in a number of organic solvents. Studies of the reactivity of H/Si(111) have led to the development of a variety of approaches for the attachment of a wide range of functional groups to the silicon surface. Many of these reaction schemes have been developed based on analogies with the well-developed organic chemistry of organosilanes (although not without some surprises along the way), illustrating some of the potential that is presented by the convergence of organic chemistry with surface science. In this chapter we review progress in the development of methods for the formation of molecular monolayers on silicon and summarize what is known

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regarding the properties of the resulting surfaces. Signiﬁcant progress in this area has led to a diversity of reaction schemes, enabling the formation of surfaces with almost any desired functionality. Surfaces for the controlled attachment of biomolecules (DNA, proteins) have been developed. The difﬁcult task of fully characterizing the properties of the resulting surfaces and attempting to evaluate the suitability of these interfaces for the longenvisaged applications discussed above is now well underway. While many issues remain to be resolved, early indications are that interfaces with controllable electrical properties can be made. The utility of these monolayers in some rudimentary molecular device and sensing applications has been demonstrated. This chapter will focus on organic/silicon interfaces formed via solution phase reactions using hydrogen-terminated crystalline silicon surfaces as a starting point. While some of the surface chemistry issues have been reviewed previously [7,8], more recent developments will be emphasized here. We will not discuss the considerable literature of reactions with porous silicon [8], or studies of molecules reacting with clean silicon surfaces under ultrahigh vacuum (UHV) conditions [9–11] which have been reviewed elsewhere. The remainder of this chapter is divided into ﬁve sections. First we review the methods that have been developed for the covalent attachment of molecules to H-terminated silicon surfaces, summarizing what is currently known regarding the mechanism of these reactions. Section 3 discusses procedures for building up more complex functionalities on the surface (including attachment of biomolecules) via sequential reactions. Section 4 discusses monolayer structure and physical properties while Sec. 5 summarizes progress in investigating the electronic properties and exploring the suitability of these layers for molecular device and sensing applications. The ﬁnal section is entitled “Challenges and Opportunities” and presents our view of the future outlook for this ﬁeld.

2. Methods and Mechanisms for Monolayer Formation Methods for the direct organic functionalization of silicon using wet chemical methods usually begin with H-terminated silicon surfaces. This is because the H-terminated surface is reasonably stable and thus can be handled in various solvents, facilitating the attachment of a variety of molecules via solution phase chemical reactions. While both H-terminated Si(111) and Si(100) surfaces have been used as starting points for organic

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functionalization reactions, the former is preferred as atomically ﬂat, monohydride terminated surfaces can be prepared via etching in ammonium ﬂuoride [6]. In contrast, H-terminated Si(100) surfaces formed by wet chemical etching are always atomically rough and contain a mixture of monohydride and dihydride sites, complicating the reactivity of these surfaces. Atomically ﬂat, monohydride terminated Si(100) surfaces can only be prepared in UHV by exposing a clean reconstructed 2×1-Si(100) surface to atomic hydrogen at an elevated temperature (300◦ C) [12]. Linford and Chidsey ﬁrst reported the formation of organic monolayers on H-terminated Si(111) surfaces via pyrolysis of diacyl peroxides [5]. In a subsequent study, this group found that these peroxides could be used to initiate the reaction of 1-alkenes (and alkynes) with the H/Si(111) surface [13]. In order to explain the preferential reaction of alkenes even in the presence of a high concentration of the peroxide initiator, they postulated a radical chain reaction process, based on similar reactions known in gas phase organosilane chemistry [14]. In this mechanism, depicted schematically in Fig. 1, a small number of silyl radicals (Si dangling bonds) are formed by the initiator (presumably via peroxide radicals abstracting H atoms from the surface). Alkenes can then react readily with this dangling bond, breaking the carbon-carbon double bond and creating a carbon-based radical. This radical can then abstract a hydrogen atom from an adjacent silicon creating a new reactive site, continuing the process. Thermal [13], and photochemical (at wavelengths <300 nm) [15] initiation were also found to yield alkyl R H

H

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R CH2 CH2

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H

Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si

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Fig. 1. Schematic of the radical chain reaction mechanism for alkenes reacting with isolated dangling bonds on H/Si(111) proposed by Chidsey and co-workers [13].

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monolayers and it is often assumed that these reactions also proceed via the same mechanism. The existence of such a molecular chain reaction of alkenes at isolated dangling bonds on a silicon surface has been conﬁrmed in UHV scanning tunneling microscopy (STM) studies [16,17]. Single dangling bonds lead to the growth of extended structures consisting of up to 100 molecules, where each of the molecules is covalently attached to the silicon substrate. Since the abstraction process for simple alkenes is expected to occur from adjacent sites, the geometry of the substrate dictates the shape of these structures as seen in Fig. 2. On the hexagonal lattice of Si(111) no directional preference for the abstraction process is expected (apart from steric constraints and other intermolecular interactions with the molecules that are already attached to the surface), leading to the formation of irregularly shaped islands arising from a random walk like the progress of the chain reaction [17,18]. On Si(100), the dimer rows of the reconstructed surface lead to the formation of molecular lines along the dimer row direction [16]. While the observation of a chain reaction under UHV conditions illustrates the plausibility of this mechanism, it does not prove that this mechanism is operative for the solution phase attachment reactions. Recent developments regarding the photochemical reactivity of Hterminated Si(100) and Si(111) surfaces have raised interesting questions about the mechanism of these hydrosilylation reactions. Zuilhof and coworkers have shown that alkylation reactions can be stimulated by visible

Fig. 2. STM images of molecular nanostructures of styrene on H-terminated silicon surfaces resulting from reaction at single dangling bonds via the radical chain mechanism depicted in Fig. 1. This process leads to the growth of molecular lines on H/Si(100) and irregularly shaped islands on H/Si(111).

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light (up to 650 nm) [19,20]. The observation of alkylation under milder photochemical conditions is important in the context of attaching molecules (i.e. biomolecules, molecular switches) that may degrade upon UV irradiation. This observation also has signiﬁcant mechanistic implications as homolytic cleavage of the Si-H bond in a single photon process requires wavelengths of less than 365 nm. STM images (shown in Fig. 3) following the progress of the visible light reactions on Si(111) have demonstrated that this reaction proceeds via the growth of irregularly shaped islands [21] (as in the case of alkenes reacting with single dangling bonds under UHV conditions). These measurements also facilitated an estimate of the eﬃciency of the photochemical reaction. From the number of islands generated in the

Fig. 3. A series of STM images (40 nm×40 nm) incompletely reacted H/Si(111) surfaces upon irradiation (447 nm) in a solution of 1-decene for 3 (top left), 15 (top right), 30 (bottom left) and 120 (bottom right) minutes. Images were acquired in constant current mode at 20 pA and sample biases of –2.7 to –3.8 V. Reprinted from [21].

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initial stages of the reaction, it was determined that each photon (@447 nm) has a ∼4×10−7 probability of nucleating an island. The observation that the visible light reaction proceeds via a surface chain reaction could account for the observation that monolayer formation is considerably slower on Si(100) than on the Si(111) surface [20]. For the photochemical reaction conditions employed by Sun et al., formation of a complete monolayer was observed to take about 10 hours on Si(100), whereas only 5 hours was required on Si(111). On the rough HF-etched Si(100) surface with its mixture of mono and dihydride sites, the chain-length (i.e. the number of sequential reactions after a single nucleation event before the process is terminated) is expected to decrease considerably as the abstraction process cannot cross steps and dihydride sites appear to favor abstraction perpendicular to the dimer row direction [22]. Although the data shown in Fig. 3 clearly indicate that this reaction proceeds via a chain mechanism, it is not clear how this reaction is initiated. Possible mechanisms that must be considered include exciton-based schemes involving surface localized holes that facilitate the attack of the alkene nucleophile (such as proposed for the white light alkylation of porous silicon [23]). However, given the low eﬃciency of the initiation process it is diﬃcult to completely rule out the role of photogenerated radicals from impurities in solution, even when high purity reactants are used. An intriguing aspect of the photoreactivity of H-terminated silicon surfaces that has not yet been fully explored is the possible role of substrate doping. Diﬀerences in reactivity with type (n or p) and/or level of doping could shed light on the reaction mechanism. In addition such diﬀerences would open the possibility of dopant selective functionalization that could prove useful in the fabrication of hybrid devices. Cai et al. have reported doping dependent reactivity in visible light (514 nm) initiated reactions of alkenes with iodine terminated Si(111) [24]. In this case, reaction on n-type substrates was found to be considerably more facile than on p-type substrates, which the authors suggested was consistent with a hole-mediated reaction mechanism. On these substrates, photogenerated electron hole pairs have been determined to separate in the near surface region resulting in the near surface accumulation of holes on n-type substrates and electrons on p-type material. More recently, Sun et al. have reported similar variations in the eﬃciency of the visible light induced reactions of alkenes with H-terminated Si(100) and Si(111) substrates [20]. For both substrates and for several diﬀerent wavelengths, heavily p-doped (p+ ) substrates appear to react more slowly than n-doped samples. While the authors argue that this

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is possible evidence for a hole-related mechanism, it is not at all clear that similar band-bending will be present on iodine and H-terminated surfaces. Furthermore Sun et al. have relied on contact angle measurements, which may depend on other factors such as surface roughness and therefore may not be the most reliable monitor of the reaction rate. Nonetheless this is an intriguing result requiring further investigation with other probes. On the other hand, Miramond and Vuillaume ﬁnd, from atomic force microscopy (AFM) and electrical measurements, that octadecyl monolayers made (via 254 nm initiation) on n+ substrates are more disordered [25]. In this case the authors speculate that the position of the Si Fermi level is important in determining the occupancy of the Si dangling bond state and hence its reactivity. In the case of n+ substrates, the Si dangling bonds are postulated to be fully occupied, decreasing their reactivity and leading to a higher probability of unwanted impurity reactions. This prediction could easily be tested by systematic STM studies of doping type and level on the reactivity of isolated dangling bonds. While dopant eﬀects on the photochemical hydrosilylation reactions are still somewhat speculative and remain to be ﬁrmly established, oxidation of the surface does adversely aﬀect the rate of these reactions [26]. Once oxygen insertion into the Si-Si backbonds is complete, the photochemical initiated reaction is slowed signiﬁcantly, even if a substantial number of Si-H bonds are still present on the surface (i.e. the surface is not fully hydroxylated). This eﬀect has been exploited to create patterned functionalized surfaces. In this patterning procedure the H-terminated surface is exposed to 185 nm light in ambient air through a contact mask. This patterned photoxidized surface is then photoreacted with alkene A, resulting in the formation of a monolayer only in the pristine H-terminated regions. This surface can then be dipped in HF to etch away the oxide in the unreacted areas (the covalently attached organic monolayer is not aﬀected by this procedure) followed by reaction with alkene B. Compared with direct approaches involving irradiation through a mask [24,27], this patterning approach has the advantage that the patterning step (photoxidation) is reagentless, and thus is compatible with conventional clean room processing. Besides its practical utility, the lack of a photochemical reaction on the photo-oxidized surface also raises interesting mechanistic questions. We note that oxygen insertion into the backbond acts to strengthen the Si-H bond (as evidenced by an upshift in the Si-H stretching vibration) and is expected to reduce both the rate of nucleation and the rate of hydrogen atom transfer from silicon to carbon. Furthermore, oxidation of the surface

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can also induce electrically active defects which will shift the energy levels at the surface (as discussed in more detail in Sec. 5) and may act as recombination centers for photogenerated electron-hole pairs. All of these processes could aﬀect the rate of the photochemical hydrosilylation reaction. Alkyl monolayers can also be formed by a thermal reaction at temperatures >140 C◦ [13,28,29], It has been suggested that this is also a radical reaction, initiated via the thermal generation of Si dangling bonds [8,13]. However, simple considerations indicate this is highly unlikely. Heating a H-terminated silicon surface in the absence of impurities will result in the desorption of molecular hydrogen (generating pairs of dangling bonds). Based on the known activation energy for this process (∼2.3 eV) we can estimate that generation of even only 0.01 ML of dangling bonds will take >25 years! Therefore, it is highly unlikely that the thermal generation of Si dangling bonds plays a signiﬁcant role and that impurity related mechanisms are likely responsible. Thermal alkylation of the HF etched Si(100) surface in the gas phase (160◦ C, 30 mTorr 1-decene) has been reported by Kosuri et al. [30]. These authors used FTIR to follow the reaction in situ, and found that both the growth of the C-H stretch and the disappearance of the Si-H stretch follow Langmuir kinetics and require ∼90 minutes to approach completion. The observation of a gas phase thermal reaction is interesting as the role of impurities is likely diminished. The authors argue that their data is consistent with a chain reaction but oﬀer no suggestion as to the initiation step (apart from also dismissing the possibility of thermal initiation). An alternate route to formation of alkyl monolayers is via Lewis acid catalyzed reactions of alkenes with the hydrogen terminated surface. In this approach, a catalyst such as ethyl aluminum dichloride is used to mediate the hydrosilylation reaction of an alkene (or alkyne), resulting in the same type of product as in the case of the photochemical or thermal reactions. This type of reaction is well known based on molecular organosilane chemistry and has also been used successfully to alkylate porous silicon [31]. Although this route has been shown to work on H/Si(111), the resulting monolayers are found to have lower coverages than those achieved using the photochemical or thermal approach [29]. Another concern with this approach is the possibility of trace metal residues from the catalyst that could adversely aﬀect the electronic properties of these surfaces (even when present at levels below the detection limit of most common surface analysis techniques). Alkyl Grignards (i.e. RMgBr) have been used to form alkyl monolayers via a two-step process [32]. First, a halogen terminated surface is formed by

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photochemical or thermal reaction of molecular halogens or suitable halogenating agent (i.e. PCl5 ), with the H-terminated surface. The Grignard reagent then reacts readily with this halogenated surface, resulting in the formation of Si-C bonds. Recently reported methods for the generation of high quality halogenated surfaces may improve the properties of surfaces prepared via this route [33,34]. While the reaction of Grignards with halogenated surfaces is expected based on the analogy with organosilane chemistry, the surprise is that these reagents also react directly with the H-terminated surface [29]. The mechanism of this direct reaction is still in debate, but may involve alkyl halide impurities in the Grignard solution [35]. While these Grignard routes appear to yield high quality monolayers, they preclude formation of a monolayer with a reactive terminal functionality that can be utilized for further reaction. Electrochemical routes to the formation of monolayers have also been demonstrated. Allongue et al. have demonstrated formation of aryl monolayers via the electroreduction of arene diazonium salts [36]. This reaction proceeds via the generation of aryl radicals which can then react with the H-terminated surface. Oxidation processes can also lead to radical initiated monolayer formation, as demonstrated by the methylated Si(111) surface obtained via the electrochemical oxidation of methyl magnesium iodide [37]. Cathodic electrografting of alkynes, as demonstrated by the Buriak group on porous silicon and H/Si(111), represents another unique approach for the attachment of organic moieties [38,39]. Although the mechanism is not yet determined, it is thought to involve deprotonation of the alkyne as there is evidence that the C-C triple bond remains intact. This is in contrast to the case of the photochemical or thermal hydrosilylation reactions of alkynes with the surface where the triple bond is reduced to a double bond upon Si-C bond formation. The maintenance of the triple bond is of interest for structural rigidity of the attached molecules as well as for possible improvements in the electronic coupling across the organic/silicon interface. This electrografting method has also been implemented using a conducting AFM tip as the electrode, facilitating “writing” of nanoscale molecular features [39]. The formation of alkyne monolayer lines with a width of 40 nm has been demonstrated, as seen in Fig. 4. Although reactions resulting in the formation of monolayers attached to the surface via Si-C bonds have received the bulk of the attention, some work aimed at varying the nature of the silicon-molecule link has been reported. For example, alcohols have been observed to react thermally with H/Si(111) and are thought to result in the formation of Si-OR monolayers

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Fig. 4. Nanopatterning of alkynes using a conducting AFM tip for cathodic electrografting on H/Si(111). The process is shown schematically at the left while representative line scans after electrografting with diﬀerent alkynes are shown on the right. The observed heights in the AFM scans correlate well with the expected heights. Adapted from [39].

[40,41]. The properties of these monolayers are similar to the alkyl monolayers discussed above, although no direct evidence of Si-O bond formation has yet been put forward. Aldehydes also react thermally with the H/Si(111) surface, resulting in monolayers with similar properties to those formed via the alcohol reactions. A noticeable diﬀerence between the properties of the monolayers formed from the reaction of alcohols and aldehydes is their stability in boiling water. Aldehyde derived monolayers are stable with respect to this procedure while alcohol derived ones are not [41]. This could suggest diﬀerences in the structure of the monolayer or in the nature of the bond to the surface. Reactions of alcohols and amines with chlorinated surfaces, forming Si-OR and Si-NHR monolayers, have also been reported [42,43].

3. Monolayer Functionalization In most of the reactions discussed above the resulting monolayers are terminated by a methyl group. While these types of monolayers are useful for passivation and chemical stabilization, the low reactivity of the terminal group makes further manipulation of the surface physical or chemical properties diﬃcult. In order to incorporate more complex organic or bio-organic structures at the interface, new strategies for coupling these molecules to the surface are required.

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In some cases direct attachment of biomolecules to the silicon surface in one step can be achieved. For example, Zuilhof’s group has demonstrated the covalent attachment of saccharides via the visible light initiated reaction of acetyl-protected β-glucose functionalized alkene with the H/Si(100) surface [44]. Although attachment of this class of biomolecules is signiﬁcant, opening up the possibility of attaching oligosaccharide receptors capable of selective recognition of antibodies, this type of attachment chemistry is not expected to be widely applicable for larger more complex biomolecules such as proteins. Attaching these type of species will likely require multistep processes resulting in the formation of functional monolayers capable of forming covalent links to the biomolecule. One approach to this problem is to start with the alkyl terminated surfaces and carry out chemical transformations of the methyl end group. Chidsey and co-workers employed this approach by forming sulfonyl chloride terminal groups via a photoinitiated free radical reaction of Cl2 and SO2 with the original methyl-terminated monolayer [45]. These were then converted to sulfonamides by reaction with amines. Schematically this twostep reaction scheme can be written as; Si-RCH3 + Cl2 + SO2 + hν → Si-RCH2 SO2 Cl + HCl Si-RCH2 SO2 Cl + R NH2 → Si-RCH2 NHR + HCl. This approach was shown to facilitate the attachment of a diverse range of amines including n-butyl amine, amine-tagged DNA fragments and an amine terminated poly aromatic ether dendrimer [45]. An alternative approach is to attach bifunctional molecules to the surface, permitting one to couple molecules to the unreacted terminal group. However, with bifunctional molecules it is necessary to carefully study the reactivity of both ends of the molecule in order to ensure selectivity of binding. If both ends of the molecule are reactive it is possible that both ends will link to the surface, leaving no groups available for reaction. Alternatively, if both ends react with comparable eﬃciency, a ﬁlm of mixed termination may result. In some cases it is necessary to protect one of the terminal groups in order to obtain the desired functionality. For example, amino-terminated monolayers are useful for the binding of biologically relevant molecules such as DNA and proteins. However, since the amine group is expected to react directly with the H-terminated surface, particularly under UV irradiation, it must be protected. A common protecting group is tert-butoxycarbonyl (t-Boc), which can be removed by treatment in tri-ﬂuoro acetic anhydride (TFA). Amine terminated monolayers made by this route have been used to

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attach thiol-modiﬁed DNA oligomers to the silicon surface using a heterobifunctional cross-linker [46]. Alternative protection strategies for achieving amine terminated monolayers have been demonstrated by Sieval et al. [47]. Another protection/de-protection approach to building up functionality on the silicon surface has been demonstrated by Pike et al. [48]. These authors reacted dimethoxytriphenylmethyl (DMT) protected ω-undecanol thermally with H/Si(111). The unprotected alkene end reacted with the surface resulting in a monolayer with protected alcohol terminal groups. The alcohol functionality was recovered by removing the DMT protecting groups using anhydrous methylamine (CH3 NH2 ) (the standard deprotection treatment involving aqueous ammonia was found to result in pitting of the surface). The alcohol functionalized monolayers were then used as a base for the on-chip synthesis of DNA. Oligonucleotides were synthesized at these modiﬁed surfaces with base phosphoramidites using a DNA synthesizer. Alkene esters on the other hand do not require protection as they appear to react primarily via the alkene end, allowing standard chemical transformations to be carried out as summarized in Fig. 5. For example, the terminal esters can be hydrolyzed to form a carboxylic acid terminated surface, or reduced with LiAlH4 to form an alcohol modiﬁed surface [28]. A concern in carrying out these transformations is that the rather harsh conditions required have the potential to degrade the silicon substrate. Boukherroub and Wayner demonstrated further chemical manipulation of

O Si-C10H20C OH O

l HC

Si-C10H20C OC2H5

LiAlH4 RM gB r

Si-C10H20 OH OH R Si-C10H20C R

Fig. 5. Schematic of end group transformations that have been demonstrated for monolayers with terminal ester groups. The terminal acid group has been used to couple amino acids to the surface while the “branched” structure that results from the Grignard reaction is expected to result in more stable, passivated surface.

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the terminal ester group to create novel types of monolayers. For example ester-terminated monolayers were reacted with alkyl Grignards, resulting in two alkyl chains attaching to every initial alkyl chain attached to the surface [49]. The formation of these “branched” monolayer structures is expected to more fully block the surface, increasing the stability. The esters have also been shown to react with thienyl Li, producing thienyl terminal groups on the monolayer. This thienyl terminated monolayer has been used as the starting point for the photoelectrochemical growth of polythiophene [50,51]. Polymer ﬁlms grown from this functionalized surface are smoother and more adherent than ﬁlms grown directly on the H/Si(111) surface. This scheme has been shown to be useful for the formation of electrical contact to the monolayers (discussed in more detail in Sec. 5). By using the photoxide patterning strategy discussed in the previous section to create a patterned thienyl-terminated surface, it is possible to localize polymer growth and form micron scale “contact pads” to the molecular layer, as shown in Fig. 6 [52]. Undecylenic acid has also been shown to react with the surface preferentially at the alkene end, leaving the terminal carboxylic acid group free for further reaction [53]. This result was somewhat unexpected as the Si-H sites are considered to be somewhat acidic and the oxophilic nature of silicon should thermodynamically favor reaction with the hydroxyl group of the acid. The preferential reactivity with the alkenyl end is consistent with a free radical, rather than a nucleophilic mechanism. The acid function can be activated with N-hydroxy succinimide (NHS) to facilitate coupling with amine tagged molecules. Schematically, Si-RCOOH + NHS → Si-RCOONHS Si-RCOONHS + R NH2 → Si-RCONHR . This strategy has been used to attach DNA as well as methoxytetraethylenegycol (TEG) (a compound known to inhibit non-speciﬁc binding of biomolecules to surfaces) [Voi04]. FTIR is a particularly eﬀective probe of this reaction sequence as seen in Fig. 7. The carbonyl stretching mode is observed to undergo characteristic changes upon NHS activation from a single adsorption at 1715 cm−1 , characteristic of a free acid, to peaks at 1815 cm−1 , 1787 cm−1 and 1744 cm−1 assigned to the succinimidyl ester. Upon reaction with TEGamine the NHS peaks are seen to disappear with the appearance of new peaks at 1650 cm−1 and 1550 cm−1 , assigned to the carbonyl and CNH vibrations of the amide. The TEGamine terminated surface also exhibits N-H stretch modes at ∼3300 cm−1 .

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(a)

(b)

h S

S

S

S

S

S

S

S OH

S OH

S OH

(c)

Fig. 6. Patterning of polythiophene growth on silicon; (a) scanning Auger image (with representative line scan) of sulphur on a patterned thienyl terminated surface made via the photooxidation patterning approach discussed in the text, (b) schematic of photoelectrochemical polymerization on patterned surface and (c) optical micrograph of surface after polymerization to grow 50 nm polythiophene ﬁlm. Adapted from [52].

For the attachment of biomolecules or other larger complex molecules it is useful to have the ability to control the density of reactive sites. This has been demonstrated in the case of reactions of alkene esters [49] or protected ω-amino-1-alkenes [47] where the density of reactive groups was controlled simply by diluting the “active” molecule in a solution of 1-alkene. While the incorporation of the reactive group has been shown to approximately correspond to concentration of “active” molecule in solution, an open question is whether these reactive groups are dispersed or clustered on the surface. 4. Monolayer Structure and Physical Properties Molecular monolayers made via solution phase chemical reactions with H/Si(111) are often referred to as “self-assembled” monolayers on silicon

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0.010

Absorbance (a.u.)

0.005 a 0.000 b -0.005 c

-0.010 d -0.015 3500

3000

2500

2000

1500

Wavenumber (cm-1) Fig. 7. Baseline-corrected ATR-FTIR spectra through the NHS activation sequence discussed in the text; (a) freshly prepared H/Si(111), (b) after functionalization with undecylenic acid, (c) surface (b) reacted with NHS/EDC for 1 hour at room temperature and (d) surface (c) after reaction with TEGamine. The background used is the spectrum of a clean oxidized ATR Si(111) crystal for (a) and the spectrum of a Si(111)-H surface for (b) and (c). Reprinted from [53].

surfaces. However in contrast to the thiol-based SAMs on gold surfaces, these layers are not ordered. While the observation of solid-like infrared C-H stretch frequencies close to 2920 cm−1 have often been used to argue that these ﬁlms are close-packed and well-ordered, molecularly resolved STM images of these surfaces indicate that this is not the case. For example, the STM image in Fig. 8 shows a 10 nm × 10 nm area of a decyl terminated Si(111) surface made via photochemical initiation at 447 nm [54]. In contrast to the initial H/Si(111) surface which shows the expected ordered (1×1) structure, the image of the alkylated surface shows that even though a reasonably dense layer of molecules has been formed there is no long-range or, for that matter, even local order. For surfaces made via photochemical initiation, this can be explained on the basis of the random walk process by which the monolayer is formed as discussed above. However regardless of the method used to form the monolayer there is the additional problem of the mismatch between the distance between Si atoms on Si(111) (0.385 nm) and the diameter of an alkyl chain (0.42 nm). Thus it is obvious that alkyl

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Fig. 8. STM images (10 nm × 10 nm) of an H/Si(111) surface (left) and a decyl terminated surface (right) prepared by photochemical initiation at 447 nm. Counting the density of molecular features in the image on the right-hand side leads to a coverage estimate of ∼0.3 ML.

chains will not be able to bind to every Si site. An exception to this is the case of methyl groups which may be expected to occupy all the surface sites, forming an ordered (1 × 1) structure. This expectation has been conﬁrmed very recently by molecularly resolved STM imaging of methyl terminated Si(111) surfaces produced via reaction of methyl Grignards with Cl/Si(111) [55,56]. An ordered (2 × 1) structure has been reported for a C6 H4 Br Si(111) surface formed by the electrochemical reduction of 4-bromobenzene diazonium tetraﬂuoroborate [57]. While there has been some suggestion that longer chains may also adopt this (2 × 1) structure, no experimental evidence for such ordered conﬁgurations has been reported. The lack of order observed for longer alkyl chain systems also extends to monolayers made via the Grignard route. Decyl and hexadecyl modiﬁed Si(111) made via reactions of RMgBr directly with H/Si(111) exhibit molecularly resolved images similar to that of the photochemically alkylated surface in Fig. 8. The density (coverage) of these monolayers has been the subject of some debate. Molecular mechanics simulations of the structure of decyl monolayers suggest that the optimal coverage that reproduces experimentally determined tilt angles (angle of the alkyl chains with respect to the surface normal) is 0.5 ML (i.e. 50% substitution of the surface hydrides) [58]. However, these calculations use an ordered unit cell as a starting point whereas the STM images show that such high symmetry is not achieved in reality. Chidsey and co-workers have devised a scheme for determining surface coverage combining ellipsometry and X-ray photoelectron spectroscopy (XPS)

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data [18]. Coverages estimated by this method depend on the molecule and method of preparation but fall in the range of 0.35–0.45 ML. However this method depends on assuming values of poorly known parameters such as the inelastic mean free path and index of refraction of the molecular layer. STM oﬀers the possibility of directly determining the coverage by counting the density of molecular features. Applying such an analysis to the image in Fig. 8, for example results in a coverage estimate of ∼0.3 ML although it is apparent that it is diﬃcult to unambiguously count the molecular features. A coverage of 0.4 ML on Si(111) corresponds to an area per molecule A2 that can be of 32 ˚ A2 . This is considerably less than the density of ∼21 ˚ achieved for SAMs on gold substrates or in close-packed Langmuir–Blodgett ﬁlms [1]. Vibrational spectroscopy has been used extensively to characterize these monolayers, with FTIR in the attenuated total reﬂection (ATR) geometry being the most used experimental method. While IR absorption in silicon usually limits this approach to the observation of modes >1500 cm−1 , it has provided important information regarding the C-H stretch modes as well as transformations of terminal functional groups in the sequential coupling reactions discussed in Sec. 3. One of the mysteries regarding FTIR spectroscopy of these monolayers has been the complete “disappearance” of the Si-H stretch mode upon alkylation of the surface. This is despite the fact that, as discussed above, at least 50% of the surface hydrogen remains unreacted. This apparent contradiction has been resolved by experiments which show that physisorbed molecular layers on the H/Si(111) surface can broaden the Si-H stretch mode from ∼1 cm−1 to >20 cm−1 FWHM, making it diﬃcult to resolve from the background [59]. The presence of a residual Si-H stretch on alkylated surfaces has been conﬁrmed in vibrational spectra of the surface obtained by high resolution electron energy loss spectroscopy (HREELS) as shown in Fig. 9. Unfortunately, the quantitative interpretation of HREELS spectra is complicated by multiple scattering mechanisms and screening eﬀects, precluding quantitative analysis of the Si-H stretch intensity to estimate coverage. However, the frequency of this Si-H stretch is a useful monitor of the chemical stability of molecularly modiﬁed surfaces as this mode is known to shift upon oxidation. HREELS measurements have also facilitated observation of modes below 1500 cm−1 (including the important “ﬁngerprint” region) not accessible in the ATR-FTIR experiments. Most notably, HREELS has been used to detect the Si-C stretch at 670 cm−1 on methyl [60] and hexyl [61] terminated surfaces, conﬁrming the presence of a covalent link to the silicon surface.

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Fig. 9. HREELS spectra of functionalized silicon surfaces prepared via photochemical reactions with H/Si(111). In each case R represents a saturated alkyl chain (9 or 10 carbon atoms long) covalently attached to the Si surface. The methyl and acid terminated surfaces were prepared via reactions with decene and undecylenic acid respectively while the thienyl terminated surface was prepared by reaction of thienyl Li with an ester terminated surface. The dashed line at 1500 cm−1 represents the typical low frequency cut-oﬀ for ATR-FTIR measurements on silicon.

While the detection of the Si-H and Si-C modes indicates HREELS can probe the “buried” molecule/silicon interface, in general this method will be most sensitive to the terminal groups at the vacuum/monolayer interface. This is illustrated in Fig. 9 where spectra for several modiﬁed surfaces with diﬀerent terminal functionalities are shown. In each case this terminal group is tethered to the surface via a C10 alkyl linker yet the spectra are signiﬁcantly diﬀerent. This is particularly evident in the spectra for the thienyl terminated surface in which the aromatic C-H stretch is clearly observed. In contrast this mode is quite small in the FTIR spectra, which are dominated by the contributions of the alkyl linker chain [51]. The observation of strong terminal group modes in the HREELS spectra indicates that these functional groups are likely present at the surface of the ﬁlm and not buried back towards the H-terminated surface. This is consistent with their availability for sequential reactions as discussed in the previous section. One of the key problems in the functionalization of silicon via solution methods is the possibility of unwanted side reactions, most notably oxidation. Silicon surfaces are known to be highly susceptible to oxidation. XPS spectra of even carefully prepared surfaces invariably show a signiﬁcant O1s

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core level signal, corresponding to 0.1–0.5 ML of oxygen [18], which likely arises from oxygen insertion into Si-Si backbonds. The absence of a shifted Si2p core level at ∼103 eV is often cited as an indication of an absence of silicon oxidation. However, this feature is associated with formation of SiO2 (Si in a +4 oxidation state) and is therefore indicative of the later stages of oxidation. It is important to note, however, that insertion of an oxygen atom into one out of the three available backbonds for each Si atom (i.e. 1 ML of oxygen) will only shift the Si2p level by ∼1 eV which would be diﬃcult to resolve in most reported spectra. As even low levels of oxidation can give rise to surface states (see the next section), the reduction of oxygen concentrations in these monolayers remains a challenge. While all molecular monolayers prepared to date exhibit some level of oxygen incorporation, this can be reduced to ∼0.1–0.05 ML provided appropriate care is taken in preparation [25]. As in the case of SAMs on gold, monolayer formation on silicon can be used to “tune” the wetting properties from hydrophobic to hydrophilic. Contact angle is a quantitative measure of the wetting properties of a solid surface by a liquid, with values near 90◦ and higher indicating a hydrophobic surface. Water contact angles for the H-terminated surfaces are typically in the range of 85–90◦ and increase to ∼110◦ upon formation of a methyl terminated monolayer [13,28]. On the other hand ester monolayers exhibit contact angles in the range of 70–80◦ [28]. Monolayers with terminal amino or acid functionality are considerably more hydrophilic, yielding contact angles in the 45–60◦ range [47,62]. When used in conjunction with chemical patterning methods, such as the photo-oxidation method discussed above, it is possible to pattern hydrophilic and hydrophobic domains on the surfaces [26]. Liu et al. have studied contact angle variations in mixed monolayers [62]. As the percentage of ester in the alkyl monolayer is varied from 0 to 100% the contact angle is observed to go from 104◦ to 82◦ . The authors also reported contact angle changes after hydrolyzing the terminal ester groups in which case the contact angles varied from 90◦ to 45◦ reﬂecting the more hydrophilic acid termination. The fact that a contact angle change is observed even for the surface with no ester groups indicates that the hydrolysis treatment is having a detrimental eﬀect on the monolayer. The chemical stability of these layers has been tested by various “torture tests” including boiling and sonication in various solvents (water, chloroform, HCl, HF, etc.) [13,29]. Monolayers formed via Si-C links are reasonably stable to all these treatments, whereas molecules thought to be linked via Si-OR bonds do not survive HF treatment. While the alkyl

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monolayers themselves are not removed by these treatments, possible degradation of the silicon surface has received less attention. While alkyl termination does signiﬁcantly slow down the oxidation relative to the unpassivated H-terminated surface, oxidation is still observed, particularly in aqueous environments. This is not surprising in view of the fact that the monolayer is disordered and not closely packed, but suggests a possible problem for using these monolayers for biosensor applications that would likely involve immersion in aqueous solutions. The thermal stability of alkyl monolayers in vacuum has been studied by HREELS where it was shown that the ﬁlms are stable up to 615 K [63]. Recently there have been a couple of studies reporting on the UV induced decomposition of alkyl monolayers on silicon [64,65]. Prolonged irradiation is found to decompose the monolayer via Si-C bond cleavage in the absence of oxygen while irradiation in an oxygen atmosphere results in oxidation (formation of carbonyl species) and decomposition [64]. This eﬀect has been exploited for patterning [65] but also has additional implications in terms of the quality of monolayers prepared via the photochemical route. If UV light is to be used to initiate the reaction, irradiation time should be kept to the minimum required to achieve full coverage; further irradiation beyond this point could degrade the monolayer quality.

5. Electronic Properties As discussed in the introduction, a major motivation for the development of methods to controllably functionalize silicon surfaces is the opportunity to create novel hybrid organic/silicon devices. By integrating organic molecules with silicon substrates it should be possible to expand the functionality of conventional microelectronic devices. Possibilities include highdensity molecular memory and logic as well as chemical and biochemical sensors. Realization of these opportunities requires not only the development of the attachment chemistries, as discussed in the previous sections, but also detailed studies of the electronic properties of the resulting surfaces. In discussing possible hybrid molecular devices it is useful to categorize them broadly into two types — one in which the current ﬂows directly through molecules, and another where the molecules act to gate the electronic transport in the underlying substrate. The ﬁrst type are the ones most often considered, and have been the focus of studies in the thiolbased SAMs on gold. However on a semiconductor substrate, surface bound species can have long-range eﬀects on the electronic properties through

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electric ﬁeld eﬀects. This is because, in contrast to metals, electric ﬁelds can penetrate substantial distances into semiconductors, shifting energy levels in the near surface region. Charged or polar molecules on the surface may be expected to shift the electronic states, altering the conductivity of the substrate, in a manner analogous to the way that an external electric ﬁeld is used to control conductivity in a ﬁeld eﬀect transistor (MOSFET). To understand how this occurs, consider the case of an n-type semiconductor whose surface has become negatively charged as depicted in Fig. 10. This could result from adsorption of a negatively charged species or trapping of an electron in a surface state. This surface charge induces an electric ﬁeld in the semiconductor substrate that will repel free electrons from the near surface region, depleting it of majority carriers. As a result, the ionized dopant atoms (donors) near the surface are no longer compensated by the free electrons they contributed to the lattice. The extent of this depletion region is determined by the charge neutrality condition — equating the

Conduction band (empty)

Ef

Valence band (full)

Surface States

Ef +

+

-

+

Fig. 10. Schematic showing how the energy levels of a semiconductor can be shifted in the near surface region (band-bending). This diagram depicts the case for an n-doped semiconductor in which the conduction band is partially occupied with electrons and the Fermi level is close to the conduction band). In the absence of surface states or external electric charges or ﬁelds, the energy level positions at the surface are the same as in the bulk, as in the top diagram. However, negative charge on the surface resulting from a partially occupied surface state band results in an upward shift in the energy levels in the near surface region and depletion of the free carrriers (electrons). In equilibrium the uncompensated dopant atoms (positive charge) balance the negative charge on the surface.

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surface charge (negative) with these ionized dopant atoms (positive charge). In the energy band diagram of Fig. 10, the penetration of the electric ﬁeld is seen to shift the energy levels in the depletion region, bending the bands upwards. This phenomena of surface charges shifting the electronic states in the substrate is termed band-bending. While upward band-bending on n-doped semiconductors results in the depletion of majority carriers, if the bands bend far enough the valence band will begin to approach the Fermi level, resulting in the generation of holes (minority carriers). The situation where the minority carrier concentration at the surface exceeds the majority carrier concentration in the bulk is known as inversion. On the other hand, if the surface of this same n-type substrate becomes positively charged, downward band-bending will result, leading to the accumulation of majority carriers at the surface. We have spent some time introducing the concept of band-bending as it is extremely important in understanding the properties of organic/ semiconductor interfaces. This band-bending phenomena explains why the electronic properties of molecular monolayers will be very sensitive to details in the method of preparation. Defects at the surface can give rise to allowed electronic states in the gap of semiconductor. These so-called surface states can act as traps for electrons and/or holes, leading to the possibility of the surface becoming charged, resulting in band-bending. Extremely small densities of these electrically active trap (surface) states (corresponding to coverages <1×10−5 ML) can result in measurable changes in band-bending. For rather high densities of surface states, such as clean Si surfaces produced in UHV, the surface states are numerous enough to “buﬀer” any attempts to alter the electronic states of the substrate by applying charge to the surface (via an external electric ﬁeld or adsorption of charged species). In this situation the band-bending remains ﬁxed at a certain level, a condition known as Fermi level pinning. Conversely if there are no (or minimal) surface states in the gap, there will be very little initial band-bending. Surfaces of this type (often referred to as electronically well-passivated) will exhibit the maximum sensitivity to the subsequent adsorption of charged species or application of external electric ﬁelds, making them most suitable for device and sensor applications. While all real surfaces have some measurable density of surface states, H-terminated silicon surfaces (produced by careful etching in HF or NH4 F) are examples of electronically well-passivated surfaces with minimal band-bending [66,67]. As the Si-C bond is not very polar, alkyl monolayers are expected to preserve the electronic passivation while increasing the chemical stability of these surfaces.

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Non-contact methods such as surface recombination velocity and surface photovoltage can be powerful probes of the quality of the interfaces, particularly with regards to the introduction of surface states. Lewis and co-workers have used photoconductivity decay measurements to extract surface recombination velocities for alkyl modiﬁed silicon surfaces [67,68]. This quantity reﬂects the density of electrically active defects (recombination centers) at the surface. Freshly prepared H/Si(111) surfaces show low recombination velocities but degrade rather rapidly in air. In contrast, methylated Si(111) surfaces, prepared via the two step chlorination/alkylation route [32] discussed above, were shown to exhibit low surface recombination velocities even after air exposure for more than a month [67]. In subsequent work this group examined relative electrical quality and stability for alkylated (Cn H2n+1 , n = (1, 2, 6, 8)) surfaces prepared via several diﬀerent routes including: reactions of alkyl Grignards with Cl/Si(111), Lewis-acid catalyzed reaction of terminal alkenes with H/Si(111) and electrochemical oxidation of CH3 MgI [68]. The alkylated surfaces prepared by the chlorination/alkylation route exhibited relatively long charge carrier lifetimes and hence low surface recombination velocities (100–500 cm ·s−1 ) that remained reasonably stable for an extended period of time. Surfaces formed by the Lewis-acid route were found to have somewhat higher recombination velocities that degraded more quickly, perhaps related to the lower coverages on these surfaces noted previously. Relating the measured recombination velocities to a density of electrically active surface traps or defects yielded an estimate to the order of 5 × 1010 cm−2 or approximately 1 atom in every 105 surface sites. It is important to point out however, that surface recombination velocity can underestimate the density of electrically active defects. As has been discussed by the Lewis group, band-bending can actually decrease the measured recombination velocity as electrons and holes will be separated by the internal electric ﬁeld, making it more diﬃcult for them to recombine [69]. Sieval et al. [70] have used modulated free carrier absorption (MFCA) measurements to investigate the passivating properties of alkylation reactions. Surfaces modiﬁed via a thermal reaction of methyl undecylenate (CH2 =CH-C8 H16 -C(=O)-O-CH3 ) with the H-terminated surface were found to exhibit rather long minority carrier lifetimes (>130 µs) corresponding to surface recombination velocities less than 120 cm/s (similar to those reported by the Lewis group). Somewhat surprisingly the minority carrier lifetime was found to increase under illumination, and a slow surface trapping process was suggested to account for this observation. In addition a

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Kelvin probe was used to measure the surface photovoltage. Surface photovoltage (SPV) measures band-bending directly by measuring the diﬀerence in surface potential in the dark and under illumination. Photogenerated electron hole pairs act to screen the surface charge responsible for any bandbending, ﬂattening the bands (provided the light intensity is high enough). The SPV was measured to be ∼100 mV (for p-type samples with a doping density of 1016 cm−3 ). This corresponds to a density of surface charge of ∼3 × 1012 cm−2 , considerably higher than that extracted from the recombination velocity measurements. Evidence for trapping/de-trapping of electrons in surface states were also observed in the photovoltage measurements. Most of the initial studies of electron transfer in these systems have employed electrochemical methods. Current-voltage characteristics give information regarding charge transfer through the monolayer while AC impedance measurements provide further insight into the integrity of the layer and its eﬀect on the underlying silicon substrate. The ability of alkyl monolayers on silicon to block electron transfer, as in the case of alkanethiol SAMs on gold, was tested in electrochemical measurements by Chidsey and co-workers [71]. Reproducible current versus potential curves were observed for alkyl, ﬂuorinated alkyl and alkoxy monolayers on Si(111) in tetrahydrofuran (THF) while signiﬁcant variability was noted when the measurements were preformed in acetonitrile or methanol. Current for 1-octene modiﬁed Si(111) was observed to be 3 orders of magnitude lower (in THF) than the H-terminated surface. The absence of a diﬀusion-limited peak on alkyl terminated surfaces (observed on the H-term surface) indicated that electron transfer is much slower (i.e. the monolayer acts as a tunneling barrier, as expected). Fluorinated alkyl and alkoxy monolayers were found to not block current as eﬀectively as the alkyl monolayers, presumably due to a lower surface coverage. In a subsequent study the same group also studied the distance dependence of electron transfer on alkyl modiﬁed silicon electrodes [72]. The electron transfer rate was shown to exhibit the expected exponential dependence on distance (characteristic of a tunneling mechanism), with a decay constant (β) of ∼1/methylene unit — in agreement with measurements on alkyl monolayers on metal electrodes. In contrast, Yu and Wayner observed diﬀerent behavior using acetonitrile as the solvent [73]. In this case, the electron transfer was found to be almost independent of chain length (β = 0.05), suggesting that the solvent was penetrating the ﬁlm, facilitating electron transfer at the silicon/organic interface. Further information regarding the insulating properties of these alkyl monolayers has been obtained through electrochemical impedance

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Fig. 11. Diﬀerential capacitance versus voltage curves for alkyl monolayers of diﬀerent chain lengths on Si(111). The curves were obtained in an electrochemical cell with 0.1 M H2 SO4 + 2% HF. The circuit model used to ﬁt the observed behavior is also shown. Reprinted from [74].

measurements [74]. Capacitance versus voltage characteristics were obtained that could be modeled as in Fig. 11. The various circuit elements represent the silicon space charge region, the organic layer and the Helmholtz double-layer. For capacitors adding in series the total capacitance will be dominated by the smallest capacitor. In depletion, the total capacitance is dominated by that of the silicon space charge layer (the uncompensated ionized dopant atoms). In this regime, a plot of C−2 vs. V is linear, and the slope can be used to extract the doping density, and the intercept corresponds to the ﬂat band potential. In accumulation, the double layer and organic layer capacitances should dominate. If it is assumed that the double layer is the same for H and alkyl terminated surfaces, the capacitance of the organic layer can be extracted. By plotting C−1 vs. thickness, the eﬀective dielectric constant of the layer was determined to be 3.3 ± 0.6. This dielectric constant is somewhat larger than that of polyethylene, but consistent with studies of SAMs on Au (2.6). The slightly higher

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value of ε suggests partial penetration of solvent into the ﬁlm. Modeling the surface as a uniform layer with vacancies occupied by the solvent, a “ﬁlling factor” of 0.85 is obtained (1 would correspond to a closely-packed alkyl monolayer). This penetration of the layer by solvent is not too surprising given the estimates of the coverage of these monolayers which indicate that the density is considerably less (50–60%) than that of a close-packed alkyl ﬁlm (see Sec. 4). Going beyond simple alkyl chains to molecules with more complex functionality, the electrochemistry of electroactive molecules covalently bound to the silicon surface has also been examined. The initial study of this type was from the group of Horrocks and Houlton, and involved an H-terminated Si(100) electrode modiﬁed with ferrocenyl (hydroxy-methyl) phosphine and ferrocenylmethanol. Both these molecules are thought to attach to the surface via formation of a Si-O link and have exhibited similar cyclic voltamograms, although the monolayer derived from ferrocenylmethanol appeared to be more stable to repeated cycling, which did result in loss of molecules from the surface in both cases [75]. More recently Roth et al. [76] have studied electron transfer rates of ferrocene and Zn porphyrins attached to silicon. They have pointed out that these electroactive molecules possess properties that are potentially useful for the construction of molecular based memories, most notably their ability to store charge for extended periods (tens of minutes) in the absence of an external potential. Benzyl alcohol linkers were used to attach the molecule to the surface via formation of a Si-O bond. In contrast to the previous work these monolayers are reported to exhibit robust, reversible voltammetric behavior. As seen in the cyclic voltamogram in Fig. 12, the porphyrin monolayer exhibits two redox states. Charge can be stored in the ﬁlm after a potential suﬃcient to oxidize the molecule has been applied. Re-connecting at the open circuit potential (after a set time) results in a transient current as the molecules that have remained oxidized become reduced. Integrating this transient yields a measure of the charge retained in the ﬁlm. Figure 12 shows that substantial charge is stored in the ﬁlm even 5 minutes after disconnection. Charge retention times are found to be strongly coverage dependent 2 ranging from about 10 s at low coverage (5 × 1011 mol/cm ) to >150 s at 2 13 high coverage (3 × 10 molecules/cm or 0.03 ML). The authors also compare the characteristics reported for their monolayers with state of the art dynamic random access memory (DRAM) cells and conclude that molecular devices based on this system may compete favorably with this technology. To address the prevelant skepticism that molecular systems could withstand

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Fig. 12. (A) Zn poryphyrin molecule with benzyl alcohol linker. (B) Cyclic voltamograms for the molecule in (A) tethered to a Si(100) microelectrode at scan rates 10, 25, 50, 75 and 100 V s−1 . (C) Reductive current transients after selected disconnect times and reconnection at the open circuit potential. (D) Charge density in the monolayer obtained by integrating the curves in (C). The charge retention time t1/2 is determined to be 150 s. Reprinted from [76].

the extreme conditions required to function as practical devices, this group has also demonstrated that their monolayers maintain their electrochemical activity even after heating to 400◦ C in an inert atmosphere and after being subjected to a large number of read-write cycles (1012 ) [77]. Some changes in the voltamogram are observed for an initial “burn-in” phase of ∼1 × 107 cycles, after which the response stabilizes. Over 90% of the charge is retained in the ﬁlm even after 1010 cycles. While electrochemical experiments provide useful information regarding electron transport through these molecular monolayers, construction of real devices requires formation of a top contact so that solid-state transport measurements can be made. The fabrication of contacts to molecular layers has been the major obstacle to the development of molecular electronic devices, whether based on thiol-based SAMs on gold or covalently attached molecules on silicon. The most popular approach to making contacts involves evaporation of metals onto the molecular layer, which is likely to result in at least partial penetration of the monolayer, and may possibly damage the molecules in the layer.

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Despite these potential diﬃculties, Vuillaume and co-workers have reported electrical characteristics of octadecyl (C18 ) monolayers on Si(111) using evaporated Al contacts [25,78]. These metal/monolayer/silicon junctions exhibit the expected capacitance–voltage characteristics for these types of junctions. Figure 13 shows the measured C-V curves for moderately

Fig. 13. (a) High frequency (1 MHz) capacitance-voltage curves for Al/octadecyl/ Si(111) structures formed on n- and p-doped substrates showing the typical accumulation (acc), depletion (dep) and inversion (inv) regimes. (b) Capacitance-voltage curves (1 MHz) in the dark (circles) and under white illumination (squares) for a structure formed on a p-doped substrate. The increase in capacitance under illumination in positive bias is characteristic of the formation of an inversion layer. Reprinted from [25].

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doped n and p-type substrates, indicating that accumulation, depletion and inversion regimes are all obtained. Particularly signiﬁcant is the observation of the capacitance characteristic of strong inversion under white light illumination, which is the hallmark of good insulating properties of the monolayer and a low density of interface states [25]. The measurement of capaci2 tance in accumulation (8–9 × 10−7 F/cm ) compares well with the expected value for a monolayer of thickness 2.3 nm (as determined by ellipsometry) if the dielectric constant is 2.2–2.5. These dielectric constants are similar (slightly lower) than those observed for alkanethiols/Au but considerably lower than that obtained in the electrochemical impedance measurements discussed above, providing further evidence for the likelihood of solvent penetration in the latter. Capacitance data can also be used to extract interface state densities for these monolayers [78]. On p-type substrates the interface state density was found to be rather low, <3 × 1011 cm−2 V−1 . The surface state densities on n-type substrates are somewhat higher (up to 1012 cm−2 V−1 ). These values correspond favorably with those obtained for Si/SiO2 interfaces, particularly when it is noted that these interfaces are formed on the Si(111) surface (interface state densities of Si/SiO2 interfaces on (111) are typically an order of magnitude higher than (100)) and at room temperature with no post-anneal. Leakage currents in these mono2 layers were in the range of 10−6 to 10−8 A/cm for applied voltages of ±1 V. Considerably higher (two orders of magnitude) leakage currents were observed on heavily n-doped substrates, which the authors interpreted in terms of a poorer quality monolayer [25]. One approach to making gentle contact to molecular monolayers is the use of liquid metals such as Hg. Hg drop electrodes have been used to make measurements on SAMs on Au, and have recently been applied to organic monolayers silicon surfaces by Yu and co-workers. This group has published a series of papers in which they report the electrical characteristics of Hg/alkyl/silicon junctions [79–81]. The Hg drop electrode approach facilitates repeated measurements on diﬀerent parts of a sample, enabling collection of an extensive set of experimental data and reporting of statistical variations in the measurements, giving a handle on the reproducibility of the current–voltage characteristics [81]. Current–voltage (I/V) curves (an example of which is shown in Fig. 14) exhibit rectifying behavior, as expected for metal-insulator-semiconductor (MIS) junctions, and are relatively well described by the diode equation based on thermionic emission theory. It is important to note that this rectifying behavior is not related to the presence of a molecular layer but arises from the presence of a Schottky

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Fig. 14. Schematic of the Hg drop electrode set-up and current-voltage characteristics for a Si(111) substrate modiﬁed by a decyl monolayer (C10 ) and with a clean native oxide (SiO2 ). The decyl monolayer was formed by a thermal reaction of decylmagnesium bromide with H/Si(111). The contact areas of the Hg drop were measured optically and were typically ∼2 × 10−3 cm−2 . Reprinted from [81].

barrier at the organic/silicon interface. The Schottky barrier arises from the mismatch in work functions of the silicon and the top metal contact. In the absence of surface states this barrier height corresponds to the work function diﬀerence, although in general it is somewhat smaller than this value and depends on the surface state density. Ideality factors of these Hg/alkyl/silicon diodes are found to be ∼1.3 [81]. Ideal diodes have an ideality factor of 1 [82], while considerably larger ideality factors (in the range of 1.5–3) have been reported previously for organic semiconductor junctions [83–86]. The ideality factors derived from the I/V curves can be used to estimate the density of surface states at the organic/silicon interface, yielding values in the range 1–3 × 1012 cm−2 . The authors have also used the Hg drop approach to observe a systematic trend in the I/V characteristics as the alkyl chain length is varied. A plot of the eﬀective barrier height, extracted from the I/V data, versus chain length was found to be linear with a slope corresponding to a β of 0.63 ± 0.1/CH2 unit [79]. This is considerably smaller than the value obtained in the electrochemical measurements discussed earlier [72]. We note however, that since the eﬀective barrier height in this analysis will also contain the Schottky barrier height, this analysis assumes that this barrier does not vary with chain length. A separation of the tunneling and Schottky barrier eﬀects on the I/V curves requires temperature dependent measurements not attempted in these studies. We note that this Schottky barrier eﬀect

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may also account for the observed behavior in Fig. 14 where the alkyl layer exhibits lower current densities than observed for a native oxide layer. From the I/V curves alone it is not possible to ascertain whether this is due to the alkyl monolayer being more resistant to electron tunneling or rather to the presence of a smaller Schottky barrier for the Hg/oxide/silicon junction. While the Hg drop electrode approach is useful for fundamental studies of the electrical properties of molecular monolayers, it is not a practical method of making contacts for real device applications. As an alternate approach to making a “top” contact one can consider growing conducting polymer from the attached organic layer. This has the added advantage of forming covalent linkages at both top and bottom interfaces, which should improve the electronic coupling at this junction. Laibinis and co-workers reported current voltage characteristics of polypyrole/silicon junctions [85]. Electrodeposited polypyrole ﬁlms were formed on both chemically modiﬁed H/Si(111) surfaces with covalently attached pyrrole units as well on surfaces with the native oxide intact. While diode characteristics were observed in both cases, those on the former exhibited higher current densities and lower ideality factors. More recently, Fabre et al. have reported using photoelectrochemical growth on thienyl terminated substrates as outlined in Sec. 3 to make electrical contact to molecular monolayers [51]. Four probe measurements determined that the conductivity of AuCl− 4 doped polythiophene ﬁlms made in this way were ∼25 S cm−1 , lower than typically reported for conducting polythiophene but suﬃciently conducting to serve as an adequate contact to the layer. Current–voltage curves through these polythiophene/alkyl/silicon junctions follow the expected diode behavior, although the characteristics are far from ideal. Capacitance measurements revealed the expected linear behavior of C−2 vs. V in depletion although the ﬂatband potential is 1.2 eV, considerably larger than expected. Surface photovoltage studies of these junctions (the polythiophene layer is suﬃciently thin to allow transmission of light to the Si) conﬁrm that this high value of the ﬂat-band potential is due to a substantial surface state density (∼5 × 1012 cm−2 ) at the Si/organic interface, which results in a substantial voltage drop across the insulating layer. For an MIS structure with such a thin insulating layer (∼1.5 nm), the voltage should drop almost entirely across the semiconductor. This can also account for the rather high nonideality factors of these diodes. We note however that the initial thienyl terminated surface has a much lower (∼1 × 1011 cm−2 ) surface state density. It remains to be seen whether this increase in the surface state density

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is due to extrinsic defects arising from the electrochemical growth process, or rather is an intrinsic property of these structures (although the former appears more likely). An interesting result of the photovoltage studies is that increasing the work-function of the polymer contact by ∼200 mV (by doping with AuCl− 4 ) led to an increase of ∼100 mV in band-bending in the silicon. This indicates that the surface state density is insuﬃcient to “pin” the Fermi level so that it is possible to tune the Schottky barrier height of these junctions by varying the work function of the top contact. We note that Schottky barrier heights for metal/silicon contacts exhibit little variation with metal work function due to Fermi level pinning eﬀects [82]. In the case of alkyl monolayers discussed above, the molecular layer is thought to electronically passivate the surface, ideally maintaining the minimal band-bending of the H-terminated surface. However, attachment of polar functional groups should induce band-bending in the substrate, opening up the possibility of purposely tailoring the electronic properties of the substrate via chemical modiﬁcation. For example, recent studies have demonstrated that chlorination of a H/Si(111) surface substantially increases its surface conductivity. This eﬀect has been attributed to strong upward band-bending due to the electron withdrawing nature of the chlorine atoms, resulting in the formation of an inversion layer [87]. Although Cl/Si(111) is an interesting model system for studying these band-bending eﬀects, it does not provide the tunability or stability of molecular systems. Cohen et al. have previously demonstrated less dramatic band-bending eﬀects for molecules attached to oxidized silicon surfaces [88]. By exploiting the chemistry for directly modifying silicon surfaces, where the molecular species will be closer to the silicon interface, it should be possible to increase these eﬀects. Hartig et al. [89] have observed the modiﬁcation of band-bending on H/Si(111) using electrochemical grafting of nitrobenzene. Nitrobenzene monolayers on Si(111) were formed by reaction of nitrobenzenediazonium tetraﬂuoroborate with the H-terminated surface. The electrochemical grafting reaction was shown to be accompanied by a reduction of the photovoltage and a drop in the photoluminescence intensity. In a subsequent paper [90], the authors reported a study of the band-bending eﬀects of aryl groups with diﬀerent substituents, which resulted in diﬀerent dipole moments at the surface. As seen in Fig. 15 diethylaniline was found to increase the photovoltage slightly (∼20 mV) but all other compounds studied (bromo, chloro, methoxy and nitro) resulted in decreases in the photovoltage (relative to the H-terminated surface). The largest eﬀect is for nitrobenzene where the SPV decreases by 100 mV. Methoxybenzene has a

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Fig. 15. The ﬁgure on the left shows the time dependence of the current density (A), pholuminescence intensity (B) and the change in photovoltage (C) during the grafting of various diazonium compounds at a potential of –1.2 V. The ﬁgure on the right plots the observed photovoltage changes as a function of the calculated eﬀective dipole moment perpendicular to the surface. Reprinted from [90].

small eﬀect. Plotting the observed change in SPV versus the eﬀective dipole moment of the molecule perpendicular to the surface, as seen in Fig. 15, yields a linear correlation with a slope of ∼25 mV/Debye. It must be noted that the linear ﬁt indicates the SPV to be –30 mV when the eﬀective dipole moment is zero. The authors attribute this observation to the eﬀect of the dipole moment of the Si-H bond, although the possible role of extrinsic surface defects should be taken into account as well. The observation that it is possible to control band-bending at the silicon surface by introducing appropriate functional groups paves the way for the use of chemical modiﬁcation to alter the electronic states, and hence the conductivity, of the underlying silicon substrate. When combined with various techniques for chemical patterning, it should be possible to use these eﬀects to construct low-dimensional conducting channels on silicon for fundamental studies of transport as well as for interconnects in future molecular devices. These band-bending eﬀects can also be exploited for chemical and/or bio sensing applications. An example of how molecularly modiﬁed silicon surfaces can be used to detect gas phase chemical species has been demonstrated by Mitchell et al. [91]. Hydrazide functionalized surfaces

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were produced from carboxylic acid terminal groups via the activated ester (N-hydroxy succinimide) route described in Sec. 3. These hydrazide modiﬁed surfaces exhibit reversible changes in band bending upon exposure to oxygen. This intriguing eﬀect was ﬁrst observed in non-linear optical studies of these surfaces, where an enhanced second harmonic signal was attributed to an electric ﬁeld induced (EFISH) response. Molecular oxygen trapped in the ﬁlm is thought to act as an electron trap, with this charged species (O− 2 ) inducing substantial band bending in the underlying silicon substrate. These band bending eﬀects have also been recently conﬁrmed in surface photovoltage studies using a Kelvin probe [92]. However, similar band-bending eﬀects are noted for exposure to iodine, indicating the need for alternative chemical strategies that will increase the selectivity of these ﬁlms for chemical sensing applications. Hamers and co-workers have illustrated the potential use of organically modiﬁed silicon surfaces for electrically based detection of biochemical processes [93]. Electrochemical impedance measurements were used to investigate the changes that occur when DNA modiﬁed surfaces are exposed to complementary and non-complementary DNA molecules in solution. Reproducible impedance changes were reported with the substrate biased into depletion. Opposite changes were recorded on n- and p-type substrates, consistent with band bending eﬀects. The impedance data was modeled with an equivalent circuit (similar to that in Fig. 11) in which the organic layer was represented by a leaky capacitor (Corg ) where the leakage resistance (Rorg ) reﬂects penetration of the electrolyte through this layer. In series with this is the contribution of the silicon space charge region (characterized by CSi and RSi ). As seen in Fig. 16, the highest sensitivity to hybridization is observed at high frequencies (>104 Hz). On n-type silicon, hybridization results in a slight increase in RSi , consistent with an increase in the silicon space charge region. Conversely on p-type substrates RSi is seen to decrease, consistent with a decrease in the depletion region. The observed behavior is consistent with the negative charge of DNA as hybridization will increase the eﬀective negative charge on the surface. Increased negative charge on the surface will increase the width of the depletion region on n-type semiconductors and decrease it on p-type. The observed changes were reversible upon denaturation and could be cycled through several hybridization/denaturation cycles. The work discussed above demonstrates that it is possible to use molecular monolayers on silicon for label-free electrical detection of DNA hybridization. More work remains to fully understand the details of the observed response, optimize the sensitivity of this approach and benchmark it with respect to ﬂuorescence detection methods. However, this work points

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Fig. 16. Electrochemical impedance and ﬂuorescence data for DNA modiﬁed Si(111) upon hybridization and de-hybridization. The real (a) and imaginary (b) parts of the impedance (sample biased into depletion) are shown as a function of frequency. The various curves show the response of the initial surface modiﬁed with single stranded DNA (16-mer), after exposure to the complementary sequence S2 and de-hybridization. Exposure to a non-complementary sequence S3, did not signiﬁcantly change the impedance. A plot of the real versus imaginary parts of the admittance is shown in (c), more clearly showing the hybridization induced changes. The ﬂuorescence image shown in (d) conﬁrms hybridization and de-hybridization, the central bright region corresponds to the area of the sample exposed to the DNA solution in the electrochemical cell. Reprinted from [93].

to the viability of potentially low-cost, silicon-based electronic DNA chips which would obviate the need for expensive optical readers required with the current microarray technology. Ultimately, the big payoﬀ for label-free detection methods of this type is expected to be in the fabrication of protein arrays, where tagging with ﬂuorescent dye molecules may be expected to interfere with their activity. 6. Challenges and Opportunities As evidenced by the discussion in this chapter, considerable progress has been achieved in learning how to prepare molecular monolayers with a wide range of terminal functionalities on silicon surfaces. Using hydrogen

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terminated silicon as a starting point, a number of diﬀerent reaction routes leading to the covalent attachment of molecules have been developed. This diversity of reaction schemes is useful in oﬀering ﬂexibility in the design of schemes for tailoring the properties of the surface, allowing the method most appropriate for attaching a given molecule to be chosen. Sequential reactions have been used to build up more complex functionalities on the surface and to attach larger, more complex organic species, including biomolecules such as DNA, saccharides and proteins. Molecular monolayers on silicon formed by these approaches are reasonably dense and chemically stable, although disordered on the molecular level. Provided that appropriate care is taken in processing, samples with rather low densities of surface states (<1012 cm−2 ) can be made. A continuing challenge here is to reduce the level of oxygen incorporated at the silicon/organic interface, particularly in monolayers prepared via photochemical initiation. Despite the fact that over ten years have elapsed since the pioneering experiments from the Chidsey group, many of the mechanisms underpinning the reactions leading to the formation of these monolayers are not yet ﬁrmly established. While the known molecular chemistry of silanes has often been used to guide observations on silicon surfaces, several of the surface reactions have no molecular precedent. In particular the visible light induced hydrosilylation and the direct reaction of alkyl Grignards with the H-terminated surface are not observed in organosilane molecular model compounds (such as tris-trimethylsilyl silane). Although the Si-H bond is similar on the surface and in the model compound, there are also major diﬀerences such as the fact that silicon has a band-gap of 1.1 eV while the molecular HOMO-LUMO gap is in the range of 8–11 eV. Another major difference is the potential role of free carriers, either photo or dopant induced, which of course are absent in the organosilane molecules. Developing a deeper understanding of the mechanisms responsible for the reactions of organic molecules with H-terminated surfaces will require more detailed kinetic studies, which have been largely lacking up to now. These kinetic studies should examine the role played by substrate parameters such as doping type and level as well as seeing how diﬀerent molecular properties, most notably ionization potential, aﬀect the rate of reaction. The progress in developing controlled attachment chemistries has opened up a range of opportunities for designing and fabricating molecular scale electronic devices based on these monolayers. Electrical transport through alkyl monolayers on silicon has been relatively well studied, particularly using electrochemical methods and Hg drops. The work of

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Vuillaume’s group using evaporated metal contacts is encouraging [25], but the role of pinholes and metal penetration in these measurements must be carefully investigated. Use of conducting polymer to make electrical contact to the monolayer eliminates the possibility of metal penetration and/or damage to the ﬁlm as well as oﬀering the advantage of covalent links at both “terminals” of the device. The less rigid polymer contact may also be advantageous in terms of incorporating “switching” molecules into the layer that may undergo conformational change. While there have been some attempts to compare transport through alkyl monolayers on silicon with that through alkanethiol SAMs on gold, we note that this requires that Schottky barrier eﬀects be taken into account. Temperature dependent measurements are clearly needed to fully characterize transport through organic/silicon junctions. Although alkyl monolayers are relatively easy to prepare and thus serve as useful model systems, demonstration of molecular switching on silicon will require incorporating more complex molecules into these monolayers. In terms of designing molecular switches two general approaches can be envisioned — tailoring the electronic structure so that resonant tunneling and/or charge trapping phenomena will result, or considering molecules whose conformation will change in response to an external stimulus (light, ﬁeld, current, heat, pH, etc.). An example of the ﬁrst approach has been demonstrated in the case of the porphyrin modiﬁed silicon electrodes which exhibit charge storage [76]. While this demonstration is the closest thing to a molecular electronic “device” on silicon, it remains to demonstrate this interesting behavior in an actual solid-state structure. Molecular devices in which the current passes through the molecule are always going to be subject to stability concerns, particularly in the case of molecular switches where the switching can lead to unwanted side reactions and, ultimately, degradation of the molecule. Thus the use of molecules to gate electronic transport in the silicon warrants more attention. While some ability to tailor the band-bending in silicon via chemical modiﬁcation has been demonstrated, this requires further exploration. While the quest to build molecular scale switches and other molecular electronic devices is intellectually stimulating and is leading to the generation of interesting knowledge regarding electrical transport in molecular systems, many practical hurdles must be overcome for these systems to be viable for memory and logic applications. In addition, the potential advantages over conventional CMOS devices are not entirely clear. Although molecular scale memories represent the ultimate limit in terms of high

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density, taking advantage of this high density will require novel schemes for wiring up these devices. Assuming CMOS scaling continues down to 30 nm, use of single molecules (of 0.5–1 nm dimensions) as memory elements may not yield substantial advantages in terms of density. Remarkable gains are possible if use of molecular elements enables three-dimensional integration, perhaps utilizing silicon nanowires as interconnects. Another intriguing possibility is taking advantage of speciﬁc molecular properties, such as multiple redox states, to implement multi-state logic. In our opinion, a more promising area for practical applications of these molecular layers, at least in the short term, is in the area of chemical and biochemical sensing. By functionalizing the silicon surfaces appropriately to selectively bind chemical or biochemical species, novel sensors based on any number of transduction schemes can be envisioned. For example, selective binding on the surface of functionalized Si-based MEMS devices could be detected through changes in the resonant frequency or quality factor. Very recently, Si micro-cantilevers functionalized with terminal triethyl ammonium groups (made via photochemical hydrosilylation) have been used to demonstrate the sensing of chromate ions in solution [94]. Silicon based waveguides can be functionalized to fabricate evanescent ﬁeld sensors. In addition, working on silicon surfaces oﬀers interesting possibilities for electrical transduction of chemical and biochemical species through the “gating” eﬀects we have discussed extensively. Applications of this eﬀect to sensing molecular oxygen [91,92] and DNA hybridization [93] have already been demonstrated. In this context, it should be possible to integrate the surface chemistry for functionalizing silicon with commercial CMOS processes, enabling the development of low-cost sensors. Low-cost label free detection of DNA and, more importantly, proteins, has the potential to lead to the development of revolutionary medical technologies. While the discussion in this chapter has focused on molecular layers on single crystal silicon surfaces, the attachment chemistries discussed here could easily be applied to functionalize silicon nanowires or nanoparticles. Silicon nanowires have been shown to exhibit interesting electrical transport characteristics and have been used to fabricate nanoscale pn junctions [95], ﬁeld eﬀect transistors [96] and biochemical sensors [97–100]. However, all these interesting phenomena have been reported on oxidized silicon nanowires. It is likely that better control over the surface properties, as could be achieved by employing some of the chemistry discussed here, could signiﬁcantly improve the performance of these nanowire-based devices. From another perspective, silicon nanowires could prove extremely

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useful in “scaling-down” organic/silicon junctions based on the monolayers discussed here. One can envision a nanoscale junction formed by bringing an H-terminated silicon nanowire in contact with one which has been modiﬁed by alkyl chains with terminal alcohols. A thermal reaction would then presumably result in a junction with ∼1000 molecules that are covalently attached at both contacts. Another potentially interesting extension of the current work is to the other group IV semiconductors, Ge and diamond. While there has been some work on these substrates, they have received much less attention than silicon. Germanium is of interest due to its high electron mobility (twice that of silicon). It has been overlooked for device applications largely because it lacks a stable oxide to serve as a passivating layer. As we have seen in this chapter, alkylation of the silicon surface can provide an interface with good electrical properties and reasonable chemical stability. If this chemistry can be transferred to Ge surfaces it may oﬀer a potential solution to the surface passivation problem. Although a report of alkylation of Ge(111) dates back to 1962 [101], there have only been a couple of more recent studies [102,103]. In terms of biosensing applications, diamond is of particular interest due to the fact it is less susceptible to oxidation than silicon. Hamers and coworkers have reported attachment of DNA to diamond surfaces [104]. In summary, the future for molecular monolayers on silicon and related materials appears to be full of possibilities, both for fundamental scientiﬁc studies and practical applications. While much progress has been achieved, many open questions remain. We expect that this ﬁeld will continue to be a vibrant one, continuing to illustrate some of the potential made possible by the convergence of surface science and organic chemistry. Acknowledgements The authors would like to thank their colleagues, Steve Mitchell and Robert Wolkow as well as all the postdocs, students, visitors and collaborators (too numerous to list here) that have been part of the Molecular Interfaces group at the Steacie Institute for many fruitful debates, ideas and insights over the past eight years. References [1] A. Ulman, An Introduction to Ultrathin Organic Films (Academic Press, 1991). [2] J. Sagiv, J. Am. Chem. Soc. 102, 92 (1980).

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FUNCTIONALIZATION OF SEMICONDUCTOR SURFACES BY ORGANIC LAYERS: CONCERTED CYCLOADDITION VERSUS STEPWISE FREE-RADICAL REACTION MECHANISMS ´ ∗ , JEFFREY R. REIMERS∗,‡ and NOEL S. HUSH∗,† ANTE BILIC ∗

School of Chemistry, The University of Sydney NSW 2006, Australia † School of Molecular and Microbial Biosciences The University of Sydney, NSW 2006, Australia ‡ [email protected] Abstract. In the age when the miniaturization trend that has driven the semiconductor industry is reaching its limits, organic modiﬁcation of semiconductors is emerging as a ﬁeld that could give much-needed impetus. We review the current state of understanding of the functionalization of C(100), Si(100), and Ge(100) surfaces through chemisorption of alkenes and alkynes, focusing on adsorbate structural control. While reactions on C(100) show most of the properties expected for concerted cycloaddition reactions such as [2+2] and [4+2] (Diels–Alder) processes, reactions on Si(100) present a wide range of variant behavior, including in some cases the prominence of non-cycloaddition products. More general stepwise free-radical addition processes are seen to provide a better description of reactions on Si(100), their prominence being attributed to either the non-existence or ineﬀectiveness of π bonding within surface silicon dimers. The investigations of these systems provide not only insight into driving mechanisms for chemisorption but also motivation for the development of new techniques of organic functionalization on semiconductors. Keywords: Chemisorption; surface structure; cycloaddition; silicon dimer; semiconductor functionalization; π bonding; free-radical reactions.

Contents 1 2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334 The Semiconductor Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . 335 333

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3

Prototype Examples: The Chemisorption of Ethylene and Acetylene to the Silicon(100) Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Interpretation of the Chemisorption in Terms of Either Concerted Cycloaddition or Stepwise Free-Radical Addition Reactions . . . . . . . 5 The Chemisorption of Other Alkenes to Si(100) . . . . . . . . . . . . . . 6 Cycloaddition Chemistry at Ge(100) and Diamond(100) Surfaces . . . . 7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

337 339 342 355 356 357 357

1. Introduction Over the decades there has been a great interest in the Group IV semiconductors because of their widespread use as the building blocks for microelectronic devices. Silicon is at present the most technologically important material, and closely related germanium, diamond, and gallium arsenide also play important roles in the microelectronics industry. The rapid miniaturization trend that has driven and revolutionized the technology, however, is facing challenges. As the size of active elements in a device approaches nanometer dimensions, it follows that the functionality of the device will increasingly rely on the processes that take place on the scale of just a few atomic layers in an interface. Therefore, the interfacial chemistry research on semiconductor surfaces is certain to become an increasingly important ﬁeld. A particularly promising line of research seems to be the organic functionalization of semiconductors, that is, the modiﬁcation of semiconductor surface via the deposition of layers of organic molecules. The motivation for the incorporation of organic material at a semiconductor surface is to endow the semiconductor device with desirable properties of the organic material. Given the wealth of structures, sizes, and composition of organic molecules, the combination of organic materials with conventional semiconductors provides an opportunity to create hybrid devices that oﬀer new possibilities for electronic, optical, and mechanical functions. Such hybrid materials are being investigated for use in molecular electronics, computing, nonlinear optics, thin-ﬁlm displays, lithography and for device implantation. In recent years much progress has been made in the development of new methodologies for the generation of organic/semiconductor interfaces and in understanding of the mechanisms that govern the attachment reactions at the surface. The majority of the studies have focussed on the basic principles of attachment and bonding at the surface. This, and the great deal of

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knowledge acquired regarding the nature of the semiconductor surface, is providing the foundation for the development of future applications. The focus of this Chapter is on understanding and controlling molecular adsorption of alkenes and alkynes on semiconductor surfaces. The goal is to provide a microscopic insight into the structure and bonding of the organic/semiconductor interface. Selected examples are used to illustrate general principles of the chemistry at semiconductor surface in an eﬀort to suggest ways that will allow the hybrid properties of organic/semiconductor interfaces to be utilized. Control of surface adsorbate structure is a central issue. In particular, the usefulness of the picture of these reactions as being concerted cycloaddition reactions, say of the classic [2 + 2] or [4 + 2] (Diels– Alder) type, as opposed to stepwise free-radical reactions, is analyzed. These two views of the reaction mechanisms are similar but diﬀer fundamentally in terms of the way the reconstructed surface dimers are viewed: are they or are they not eﬀectively π bonded? They lead to diﬀerent, experimentally testable, predictions for reaction kinetics and reaction products. In order to perform our analysis, we review in detail the nature of the semiconductor surfaces, and the detailed experimental and computational evidence that illuminates the chemisorption kinetics and products.

2. The Semiconductor Surfaces Silicon is the predominant semiconductor material in the microelectronics industry. It is commercially available in the form of silicon wafers of high purity. The Si(100) and Si(111) surfaces are the most common orientations and most important for industrial applications, and therefore understanding the chemistry of these surfaces particular importance. Both surfaces undergo reconstruction, producing surface atomic geometries that diﬀer markedly from that of the bulk [1,2]. The (100) crystal faces of silicon, germanium, and diamond share a common bonding motif in which neighboring atoms pair up to form the so-called dimers along the [110] crystal direction and dimer rows along [110], which are separated by troughs. Such a surface is illustrated in Fig. 1(a). The new structure is referred to as Si(100)(2 × 1), where (2 × 1) designates the doubled size of the unit cell relative to the unreconstructed surface. The Si(111) surface exhibits a complex (7 × 7) reconstruction which contains 49 surface atoms per unit cell. The Si(100)-(2 × 1) dimers are often thought of as being connected via a double bond, i.e. a σ and a π bond [2]. Scanning tunneling microscopy (STM) images of the surface reveal occupied and empty electronic states

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Fig. 1. Models of the silicon(100) surface. (a) The clean reconstructed Si(100)-(2 × 1) surface lined with rows of symmetric dimers. (b) The tilted-dimer model of the surface. Note that the actual periodicity is c(4 × 2). (c) The monohydride-passivated Si(001)(2 × 1)-H surface, Dimers are symmetrized upon hydrogen adsorption.

having the symmetry properties that correspond to π orbitals as the highest-occupied and lowest-unoccupied electronic states [3]. The advantage of this picture is that analogies between the dimer bond and molecule double bonds, such as C=C in alkenes, can be drawn; as their reactivity is very well categorized in terms of symmetry-controlled concerted cycloaddition reactions [4], it is tantalizing to consider whether such simple correlations also hold for surface chemistry [5]. In general, it is known that π bonding in silicon compounds is weak [6–8], and the STM results can also be interpreted in terms of independent isolated silicon free radicals rather than as π bonds. If this is indeed the case, then cycloaddition reaction mechanisms would be thwarted, as discussed in detail later in Sec. 4. An additional complication aﬀecting silicon surface chemistry is the well-established fact that dimers tilt away from the symmetric position (c.f. Fig. 1(b)). Associated with dimer tilting is a charge transfer from the “down” atom to the “up” atom. Hence, the dimers exhibit somewhat zwitterionic character, with one electron-poor atom and one electron-rich atom. Such a property of the Si(100)-(2×1) surface makes it possible to use nucleophilic and electrophilic attachment reactions. At temperatures less than 120 K, dimer tilting on Si(100)-(2 × 1) can be observed in STM experiments [3,9], while at higher temperatures the direction of the tilt oscillates on a time scale faster than the order milliseconds sampling times of the STM. Upon reconstruction, both Si(100)-(2 × 1) and Si(111)-(7 × 7) are still very reactive and, if exposed to air, quickly oxidize by forming a native SiO2 layer. In order to stabilize the surface and prevent oxidation, it is hydrogenated by exposure to atomic hydrogen. At Si(100)-(2 × 1) a modest exposure to hydrogen results in the formation of the Si(100)-(2 × 1)-H monohydride phase. The hydrogen atoms react with Si surface bonds leaving the dimers still bonded and the (2 × 1) reconstruction still present, as

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illustrated in Fig. 1(c). At higher exposures a dihydride phase is formed in which each surface silicon atom bonds with two hydrogen atoms, causing the disappearance of the dimer bonds and the restoration of a (1 × 1) periodicity. On the Si(111) surface, because of certain weak Si-Si bonds that are replaced by strong Si-H bonds, hydrogenation results in a structure that does not reconstruct, but rather exhibits a bulk-like periodicity. Functionalization studies have been carried out at both clean and hydrogen-passivated surfaces. The vast majority of studies on clean silicon substrates are performed under “dry” ultra-high vacuum conditions (UHV). On the other hand, reactions at hydride-terminated silicon commonly rely on “wet” chemical methods performed in solution. Regardless of the diﬀerent environment and surface structure, common principles of the functionalization at semiconductor surfaces are emerging from these studies.

3. Prototype Examples: The Chemisorption of Ethylene and Acetylene to the Silicon(100) Surface The investigations of organic/semiconductor interfaces were initially driven by the need to generate silicon-carbide, which is a promising wide-gap semiconductor material, and diamond-like ﬁlms on the silicon substrate. For this purpose small unsaturated hydrocarbons have been adsorbed on the Si(100) surface via chemical vapor deposition. In the late 80’s most studies involved ethylene C2 H4 and acetylene C2 H2 (see [1] for a review of this work) and, more recently, other simple alkenes. These were found to adsorb readily on the surface at room temperature, in a geometry known as the “di-σ” conﬁguration [10], depicted for ethylene in Fig. 2(a). This case is of particular signiﬁcance because it turns out that analogous adsorption structures have been observed for many other alkenes. The bonding is termed di-σ because it takes place through the formation of two new σ bonds between Si and C atoms. While the reaction breaks the π bonds of the hydrocarbons and, if actually present, the Si-Si dimer, the original σ bonds remain preserved [11–13]. For ethylene a barrier to desorption of 1.65 eV (38 kcal mol−1 ) was evaluated from thermal desorption [14], which represents an upper bound to the binding energy. Density functional theory (DFT) based calculations predict slightly higher adsorption energies of 1.81–1.89 eV [13,15]; however these do not include zero-point energy corrections to the computed values which should improve the agreement between the calculated and observed quantities.

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Fig. 2. (a) Ethylene adsorbed on Si(100) in the di-σ conformation. (b) STM image of ethylene/Si(100), ﬁlled-state scan. Circle shows one adsorbed molecule. (c) Filled state scan of acetylene/Si(100). (Square) One molecule in the bridge conﬁguration. Reprinted from [16] with permission from Annual Reviews.

Initial investigations of acetylene on Si(100)-(2 × 1) that used electronenergy loss spectroscopy (EELS), low energy electron diﬀraction (LEED) and temperature programmed desorption (TPD) concluded that the adsorption geometry also corresponds to a di-σ model [17]. The molecules were found to be adsorbed undissociated, but at elevated temperatures they largely decomposed, with less than 5% desorbed intact [18]. An estimate of 46 kcal mol−1 for the adsorption energy was obtained from these. Even though the energy could not be accurately measured by thermal desorption, it is certain to be higher than that of ethylene, because it is more costly to turn a double bond into a single one than to turn a triple into a double bond. Interestingly, it was argued in a number of studies that the Si dimer bond was completely cleaved upon adsorption [18–20]. The reason for this is that on a post-hydrogenation, hydrogen attaches to the Si dangling bonds. Since both the Si-C and Si-H coexist on the surface, as well as two Si-Si bonds to the subsurface layer, the Si dimer bonds could not be preserved. The picture did not agree with computational predictions [5,21] that clearly favor the structural model with Si dimers intact. Eventually, the cleaved-dimer model has been ruled out by theoretical work [12,22] that suggests that the dimer bond is indeed broken in the presence of co-adsorbed atomic hydrogen and C2 H2 , but the bond cleavage occurs as a consequence of the posthydrogenation rather than of the initial attachment of the hydrocarbon. Surfaces exposed to ethylene and acetylene have been investigated by STM [23,24]. For ethylene the results at low coverage clearly demonstrate symmetrical adsorption atop of a dimer, as shown in Fig. 2(b), consistent with the di-σ model. The STM scans indicate that adsorbates tend to attach

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to the surface so as to avoid nearest-neighbor interactions. At around 50% of full coverage the molecules adsorb preferably on alternate dimer sites, exhibiting either (2×2) or c(4×2) local periodicity. However, these are only local domains and there is no long-range order. Once the alternate dimers are populated, the adsorption continues to ﬁll in the remaining adjacent sites [14,23,25]. For acetylene more recent STM images [26] conﬁrmed the observation of the di-σ model, but at low coverages they adopt instead the so-called bridge structure involving bridging the ends of two adjacent dimers in the same row by bonding to just one atom of each dimer. Both conﬁgurations are visible in Fig. 2(c). Since most calculations favor the di-σ model as energetically favorable, it is rather unusual that the bridge structures are so evidently dominant. Wolkow has speculated [16] that the bridge conﬁguration, while not as strongly bound, is more accessible kinetically to arriving molecules than the di-σ. According to a recent DFT study [27], the bridge structure is only 0.05 eV higher in energy at a coverage of 0.5 monolayers [ML] (one ML corresponds to one molecule per each Si dimer). The thermal stability of the bridge-bonded molecules indicates the existence of a large barrier that separates it from the energetic minimum. It has been suggested that at a high coverage the di-σ adsorption structure takes place at every other dimer [26], but an alternative interpretation [16] is that these are actually bridge adsorbed molecules. Studies based on high-resolution photoemission spectroscopy [28] and photoelectron holographic imaging technique [29] have also challenged the di-σ model of C2 H2 on Si(100). They have instead proposed a pedestal conﬁguration in which the molecule is symmetrically bonded to four Si atoms between two adjacent silicon dimers. A recent STM-based investigation [30] has identiﬁed three distinct bonding conﬁgurations: the di-σ, bridge, and fourfold-bonded conﬁgurations. DFT calculations [31] have again conﬁrmed that the di-σ adduct is the ground state at an adsorption energy of 69 kcal mol−1 , the bridge is next with a binding energy of 66 kcal mol−1 , while the fourfold bonded conﬁguration at 46 kcal mol−1 is much less stable. The simulated STM images [31] corroborate the experimental assignment [30].

4. Interpretation of the Chemisorption in Terms of Either Concerted Cycloaddition or Stepwise Free-Radical Addition Reactions While originally the reactions of ethylene and acetylene with Si(100)-(2×1) were not recognized as such, it is intriguing that they are analogous to an

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important class of reactions known in organic chemistry as “cycloadditions” [4,5]. The covalent nature of the surface suggests that its reactivity can be described through analogies with molecules: the dimers of the Si(100)(2 × 1) surface are reminiscent of organic reactants bonded by a strong σ and weak π bond. In a cycloaddition reaction, two molecules combine to form a cyclic molecule via the synchronous scission of π bonds and the creation of new σ bonds. The reaction is designated by the number of electrons on each independent moiety that participates in the process. Some classic examples including [2 + 2] and [4 + 2] (Diels–Alder) reactions, as applied to chemisorption on silicon(100), are depicted in Fig. 3; in these cases the independent moieties are the adsorbate, contributing either 2 or 4 π electrons, and the silicon dimer, contributing 2 π electrons in each case. The description of the chemisorption in terms of cycloaddition reactions is useful if it leads to reliable predictions of the reaction products: for most reactions, a variety of products are possible, yet only one will result from a particular cycloaddition mechanism. Central to the applicability of such schemes is the notion that the silicon dimers contain a weak π bond responsible for the enforced concerted motion of the two electrons involved. However, in reality there is little evidence to support the presence of even a weak π bond within the dimers. While DFT calculations that enforce spin pairing depict the bond as a singlet biradical [32], spin-polarized calculations predict a triplet ground state for the unbuckled dimer [33] with no π character whatsoever. The decoupling of the two silicon electrons means that their motion is not likely to be concerted so that a [2+2] cycloaddition reaction becomes better represented as an independent [1 + 2 + 1] process, a notation that recognizes the independence of the silicon free radicals. This mechanism is also illustrated in Fig. 3. In practice such a reaction is unlikely to proceed in a concerted fashion, and a key signature for it would be the

Fig. 3. Some examples of postulated concerted [2+2] and [4+2] cycloaddition reactions of alkenes with silicon double bonds, as well as alternate descriptions in terms of a [1 + 2 + 1] reaction with silicon free radicals that would be expected to proceed in a non-concerted fashion through the intermediate [1 + 1] adduct shown.

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detection of an unstable intermediate formed by a simple [1 + 1] radical reaction, requiring a second independent [1 + 1] reaction to complete the chemisorption; such an intermediate is also indicated in the ﬁgure. The reactions of ethylene and acetylene with Si(100)-(2 × 1) were initially described as being [2 + 2] cycloadditions, with the di-σ conﬁguration predicted by this mechanism believed to provide the dominant reaction products. A variety of alternate reaction products could actually be formed as a result of the chemisorption, with, e.g., the organic molecule spanning silicon atoms in diﬀerent dimer rows, adhering above a row oriented perpendicular to the silicon dimers, or adhering above a row and parallel to the dimers. As reviewed in Sec. 3, a variety of alternate structures have now indeed been found for chemisorbed acetylene. Hence, while the [2 + 2] cycloaddition mechanism appears apt for ethylene chemisorption, its applicability to similar processes in acetylene is questionable. A characteristic feature of [2 + 2] cycloaddition reactions is that the symmetry properties of the frontier orbitals of the reactants make them formally symmetry forbidden [4] through a symmetric pathway. As a result, the reactants must overcome an activation barrier which makes the process very slow for homogeneous reactants. In organic chemistry, photoexcitation can be used to change the nature of the frontier orbital occupation, breaking the π bond and hence facilitating the reaction, but otherwise high heat and other extreme conditions are required in order to make this type of reaction proceed. For reactions with silicon(100), chemisorption is observed to be facile for most alkenes even at room temperature [16], contrary to naive expectations based on the cycloaddition model. The symmetry rules can be relaxed due to the dynamic dimer tilting observed for the surface silicon dimers. Liu and Hoﬀmann [5] investigated the mechanism of acetylene attachment at several levels of theory. They proposed that the reaction takes place through an asymmetric pathway that reduces the symmetry and leads to an almost zero-energy barrier. In eﬀect, this mechanism assumes that the silicon dimers form a weak π bond when parallel to the surface that is broken by the reorganizational process (electron-phonon coupling) that drives symmetry breaking via dimer tilting. After tilting, the silicon atoms become independent moieties and so the [2 + 2] mechanism in fact degenerates to the more primitive [1 + 2 + 1] one, and [1 + 1] intermediates may be observed. Liu and Hamers studied the adsorption of cis- and trans-1,2-dideuterioethylene by Fourier transformed infrared (FTIR) spectroscopy and were able to interpret their results in terms of the anticipated intermediate [34].

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While the question of whether silicon dimers can be considered as having either a weak π bond or no π bond at all [32,33] is of signiﬁcance, in this case a more important feature is the ratio of the π bond strength to the strength of the tilting reorganizational process [35]. The π bond is clearly too weak to prevent tilting, a process that localizes the bonding electrons into atom-based free radicals that aﬀects all of the chemical and spectroscopic properties of the dimer. Processes of this nature dominate chemical reactivity and structure [36] and form the core of the Marcus– Hush theory [37,38] that describes electron transport through molecular and biomolecular systems [39]. 5. The Chemisorption of Other Alkenes to Si(100) Cis- and Trans-Butene. Lopinski et al. [40] have studied the chemisorption of cis-butene and trans-butene on Si(100), investigating the stereospeciﬁcity of the chemisorption. Molecules chemisorbed in the cis and trans conﬁgurations give rise to distinct STM images, allowing the fraction of each type of adsorbate to be determined for each type of reactant. They found that 2–3% of adsorbate molecules underwent cis-trans isomerization during the chemisorption process. Concerted [2 + 2] cycloaddition reactions occur by electron rearrangements at a single critical transition-state geometry, with the barrier crossing being too fast to allow for isomerization and other nuclear motions. Alternatively, stepwise reactions proceed via two distinct transition states, and following the ﬁrst reaction the system has time to allow for nuclear rearrangements before the second reaction locks the structure. Loss of stereospeciﬁcity is thus clear evidence that at least part of the reaction products arise from a stepwise mechanism: the degree of isomerization is controlled by the relative rate constants for the isomerization process and the second chemisorption reaction, with the latter determined to be of the order of a few ps. This rate is in good agreement with calculated stepwise reaction processes for [4 + 2] cycloaddition [41]. Cyclopentene. Among a number of simple alkenes reacting with Si(100)(2 × 1), one system is interesting as it provides a particularly well-ordered monolayer. Using STM and FTIR Hamers and co-workers have investigated the adsorption of cyclopentene (a ﬁve-member ring molecule, C5 H8 , sketched in Fig. 4(a)) on the surface [42–44]. It has been established that cyclopentene bonds with silicon to give the products predicted by the [2+2] cycloaddition mechanism again, making a well-ordered monolayer on the surface as shown in Fig. 4(b). Each bright oval-shaped object represents a

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Fig. 4. (a) The cyclopentene molecule. (b) STM image of cyclopentene adsorbed on Si(100). (c) STM image of cyclopentene on a vicinal (100) surface obtained by a miscut of 4◦ . The molecules remain ordered across double-height steps. Reprinted from [42] with permission from the American Chemical Society.

cyclopentene molecule. The molecules are clearly aligned in rows, suggesting that the adducts spontaneously order with very speciﬁc bonding sites. In addition, individual molecules are elongated along a direction that appears common for all, with the elongation corresponding to the direction of the ring. Therefore, the layer exhibits both translational and rotational order. The presence of some vacant sites can be attributed to steric intermolecular repulsions or missing dimer defects on the substrate. Figure 4(c) shows an STM image of cyclopentene monolayer on a vicinal Si(100) surface, oriented a few degrees away from the (100) face so as to exhibit double-height steps. It is worth noting that across the steps the molecules preserve a uniform rotational orientation, thus maintaining the orientational anisotropy. The ﬁlm is even slightly better ordered on the vicinal surface, indicating that the presence of steps relaxes sterical interactions between adjacent adsorbates. Such success in fabricating an ordered overlayer is quite unusual and remarkable considering the nature of the system. Firstly, the sticking coeﬃcient of cyclopentene, like that of ethylene, is nearly unity, which means that each molecule impinging on the surface has the probability of ∼1 of attaching to it. Secondly, given the strength of the bonds and large kinetic barriers, molecular diﬀusion on the surface is expected to be highly restricted [16,32] indicating that once the molecule is chemically bound to the surface, it will stay at that particular site. Such a frustrated surface mobility is expected to prevent or greatly reduce the ability of the adsorbates to conform in a well-ordered way. Hence, the growth of the cyclopentene layer seems to be controlled solely by the strong directional interactions at the interface that

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steer molecules towards Si dimers, with the substrate acting as a template for molecule attachment. However, the range of the steering eﬀects is presumably quite short, and given the observed fact that molecules do not necessarily stick at their point of impact [16], it is likely that a particular character of the short-lived physisorbed precursor states plays some part in the process. In conclusion, the regular dimer spacing on the surface produces the translational order in the cyclopentene ﬁlm and the directional character of the interacting π bonds imparts the rotational order of the dimers to the overlayer. Cyclopentene thus stands out as a prototypical example of the use of the alkene chemisorption reactions as a general strategy for fabricating well-deﬁned anisotropic organic ﬁlms. Its binding is in accord with predictions of the cycloaddition reaction mechanism. Maleic anhydride. One of the key challenges in the organic functionalization of semiconductor surfaces is the ability to grow multiple layers in a controllable manner. To date much of the work has focused on the ﬁrst monolayer. It has been speculated [42] that the translational and rotational order of the initial overlayer could be propagated further to successive layers through the directional character of the bonding and steric interactions at the surface as a way of controlled linking of various organic substituents to the Si(100) surface. Bitzer and Richardson [45] have demonstrated the formation of organic multilayers of polyimide on Si(100) via a Si-NH-C linkage. In a subsequent work [46] the surface was functionalized by a layer of maleic anhydride prior to the deposition of phenylene diamine, as a route of growing the polyimide ﬁlm with the Si-C linkage to the substrate. Maleic anhydride was chosen because, like cyclopentene, it consists of a ﬁvemembered, albeit heterocyclic, ring (C2 H2 -C2 O3 , sketched in Fig. 5(a)). The nature of the binding of maleic anhydride to silicon has been investigated using a range of analytical techniques [46–49]. STM images have revealed that maleic anhydride binds preferentially above the dimer troughs, i.e. by straddling two dimers in adjacent rows. This product is not in accord with the predictions of a concerted [2 + 2] cycloaddition mechanism but does provide another example of a free radical [1 + 2 + 1] addition. In eﬀect, the two dimers are broken and a new one is formed across the trough. The STM image in Fig. 5(b) taken at a coverage of 0.03 ML suggests that the above-row attached molecules make about 20% of all adducts, while the rest is above-trough. At an increased coverage of 0.12 ML, shown

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Fig. 5. (a) The maleic anhydride molecule. (b) Occupied-state STM image of maleic anhydride on Si(100) at a coverage of 0.03 ML. (c) STM image taken at a coverage of 0.12 ML. Reprinted from [47] with permission from the American Chemical Society.

in Fig. 5(c), 98% of the species are adsorbed above trough. DFT calculations [15], on the other hand, show energetic preference for the above-row conformation at all coverages. Even though they suggest the above-trough structures become relatively more favored with the coverage, this eﬀect could not account for the observed strong preference for above-trough binding. It has been speculated [47] that the strong electrophilic character of the molecule contributes to the anomalous binding. The charge transfer from C to O atoms, experienced through the large dipole moment, leaves the C atoms electron-poor. This could bias the reaction with silicon to proceed via the bonding to nucleophilic buckled-up atoms of two Si dimers in adjacent rows. The eﬀect has been calculated to be energetically minor [15], however, and such a surface would not lie at the energetic minimum. On the other hand, when growth is kinetically controlled, this eﬀect could contribute the enhanced above-trough attachment by stabilizing the associated physisorptive precursor species and by lowering (or completely removing) the barrier to chemisorption. Norbornadiene. Hamers and co-workers ﬁrst studied the adsorption of norbornadiene (bicyclo[2.2.1]hepta-2,5-diene) [43] on Si(100); this molecule and a sample STM image are shown in Fig. 6 along with a functionally modiﬁed norbornadiene analogue [50] containing a silyl molecular rotor, which we have also investigated. Norbornadiene was in fact the ﬁrst hydrocarbon containing multiple C=C bonds to be studied in this fashion. Its two double bonds are separated by 2.4 ˚ A and are chemically independent moieties, and hence this molecule could react twice with silicon via a double

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Fig. 6. Norbornadiene, its functionalized analogue N -trimethylsilyl-7-azanorbornadiene, and the occupied-state STM image of Si(100) upon an exposure of 30 ML of norbornadiene. Reprinted from J. Vac. Sci. Technol B ([43]. Copyright 1997 AIP).

[2 + 2] cycloaddition-type reaction to bridge two adjacent dimers, separated by 3.85 ˚ A, along a dimer row. Such a binding would guarantee the azimuthal orientation and vertical placement of the apex atom relative to the surface. Functionalization of norbornadiene, at say the 7-position like the example shown in Fig. 6, would then lead to controlled architectures on the silicon surface. Abeln et al. [51,52] have also utilized norbornadiene for a selective attachment to exposed dangling bonds on the otherwise hydrogen passivated Si(100)-(2 × 1)-H surface. This approach has been envisaged as a route to nanopatterned functionalization of the surface, and has subsequently been reﬁned [53,54] so as to make possible the fabrication of templates of individual dangling bonds. Most noticeable in Fig. 6, however, is the complete lack of ordering in the STM scan, taken at a high coverage, indicating that there must be more than one type of binding site at the substrate. Four diﬀerent modes of attachment were originally proposed [43]: both C=C bonded to adjacent dimers along a row; one C=C bonded to a single dimer; both C=C bonded to two dimers in adjacent rows (that is, above a trough); and one C=C bonded above a trough. A recent DFT investigation [32] has addressed the issue of the optimum bonding geometry, considering these and a number of variants. In summary, four strongly bound norbornadiene conﬁgurations have been found, with the C-C bonds situated either above a Si-Si dimer row or trough, and oriented either parallel or perpendicular to the Si-Si bonds. When norbornadiene is adsorbed above a row with C-C parallel to Si-Si, it corresponds to the product of a double [2 + 2] cycloaddition; all other products require more general mechanisms such as the [1+2+1] free-radical

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process. The calculated binding energies are 96, 85, 81, and 72 kcal mol−1 for the perpendicular above-row and above-trough, and parallel above-row and above-trough conformations, respectively, at a moderate coverage; these results thus lead to the conclusion that the [2 + 2] mechanism does not provide proper insight into the chemisorption process. It has also been suggested [55] that the disorder in norbornadiene ﬁlms is due to the steric hindrance the adsorbate experiences when approaching the surface. Consistent with this hypothesis, DFT calculations [32] suggest that in general the observed [43] structural disorder in the norbornadiene overlayer arises from kinetic control rather than thermodynamic control of the reaction products. This control is shown [32] to be associated with large barriers in excess of 40 kcal mol−1 for surface diﬀusion and annealing. At high coverage, enhanced disorder is also predicted owing to the strong partial binding of norbornadiene via a single alkene linkage only, with the analogous four structural motifs being calculated to be very similar in energy to each other. With reference to general mechanisms for alkene chemisorption, we note that the optimum calculated [32] single-alkene-bonded conﬁguration, with an adsorption energy of 47 kcal mol−1 , corresponds to the anticipated [2 + 2] cycloaddition product, consistent with the structure for most mono-alkene adducts. The second most favorable single-alkene-bonded structure, with an energy of 45 kcal mol−1 , corresponds to the “bridge” (c.f. acetylene), i.e. above-row placement with C-C perpendicular to the Si dimers. These two reactions thus lead to similar binding energies. However, as the corresponding total norbornadiene double-binding energies are 81 vs. 96 kcal mol−1 , respectively, it is clear that addition of the second double bond when oriented parallel to the silicon dimers is far less exothermic than when oriented perpendicular. Thus the preference of the uncommon, perpendicular azimuthal orientation of norbornadiene on the surface is interpreted as arising from a cooperative eﬀect associated with the silicon-lattice relaxation required to accommodate two adjacent chemisorbed moieties. It is indeed this same eﬀect that causes the tendency for adsorbed ethylene to avoid nearestneighbor sites along a row [22,23]. Hence, in summary, we see that concerns such as these appear to be more important in determining the structure of chemisorbed alkenes to the silicon(100) surface than the symmetry constraints that are manifest in concerted cycloaddition reaction mechanisms. 1,5-Cyclooctadiene. Following the work on norbornadiene, Hovis and Hamers [55] utilized another diene, 1,5-cyclooctadiene; representative

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Fig. 7. (a) STM image of COD adsorbed on Si(100) at the saturation coverage. (b) Magniﬁed view of a smaller area of the surface. Reprinted from [55] with permission from the American Chemical Society.

images are shown in Fig. 7 whilst molecular and adsorbate structures are shown in Fig. 8. Like norbornadiene, this molecule contains two chemically independent C=C groups held rigidly separated at a speciﬁc geometry. The STM images show that at high coverage the adsorbates interact with the surface to form a highly-ordered monolayer of uniformly oriented molecules aligned in rows. The separation between the adsorbates is 7.7 ˚ A, twice the separation between adjacent dimers in a row. Such a spacing can lead to local regions of (2 × 2) or c(4 × 2) periodicity, depending on whether the molecules in neighboring rows are aligned or staggered. The observation of both types of ordering suggests that there are little direct or substratemediated interactions. The most signiﬁcant feature of the chemisorption is that, as is clear from the FTIR spectra [55], only one of the two bonds actually binds to the substrate. Since no dissociation could be observed, it follows that each molecule identiﬁed in the scans is the product of a single alkene chemisorption. The signiﬁcance of this ﬁnding is that the modiﬁed surface thus presents an array of ordered and exposed C=C bonds which can be exploited for a further functionalization. The ability to bond via one of the two equivalent C=C groups has been ascribed to the particular molecular shape of 1,5-cyclooctadiene [55].

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Fig. 8. Geometry of gas-phase and adsorbed COD. (a) Minimum-energy structure (“twisted boat”) of the free COD molecule. (b) “Endo” interaction of COD with Si(100). (c) “Exo” interaction of COD with Si(100). (d) Optimized structure of COD on a Si(100) cluster. Reprinted from [55] with permission from the American Chemical Society.

The lowest energy conﬁguration of the molecule is a twisted-boat geometry, illustrated in Fig. 8(a), in which the two C=C bonds, separated by 3.20 ˚ A, are twisted by 23◦ with respect to one another; this arrangement is quite diﬀerent from that in norbornadiene, for which the two C=C bonds are parallel. Figures 8(b) and (c) schematically show two possible ways of interaction with Si dimers, termed “endo” and “exo”, respectively. In order to bond to two adjacent dimers 1,5-cyclooctadiene makes the endo

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approach. In this scenario there is a relatively weak overlap between the π orbitals, in part due to an imperfect match in the separation of the bonds in the two subsystems (3.85 vs. 3.20 ˚ A) and also because the C=C bonds are not coplanar. On the other hand, in the exo approach a good overlap is possible without steric obstacles. In addition, the rigidity of the molecule provided by the ring structure supports the selective attachment. Therefore, steric constraints seem to be responsible for the easily controllable growth of the COD monolayer. 1,3,5,7-Cyclooctatetrene. To investigate the hypothesis that stereochemistry governs the ordered growth of 1,5-cyclooctadiene, Hovis and Hamers [56] studied the structure of 1,3,5,7-cyclooctatetrene on Si(100). This molecule, shown in Fig. 9, is symmetric and conjugated, with two sets of coplanar C=C bonds. STM images taken on a high exposure are shown in Fig. 10. The single height step from the clean surface still visible in Fig. 10(a) demonstrates that the molecules are aligned along dimer rows (the upper terrace is rotated by 90◦ with respect to the lower terrace) making a well-ordered overlayer. Again, the separation between most of them is 7.7 ˚ A. A closer look (Fig. 10(b)) shows that the majority species are elongated along the rows and appear identical (a few white protrusions are attributed to contaminants). At even higher resolution (Fig. 10(c)) a minority species, labeled “D”, can be seen. STM scans at low coverage [56] elucidate the nature of the majority type. The common features are placement above a dimer row, with the center of each molecule being midway between two dimers, and the direction of elongation along a dimer row. FTIR indicates that 1,3,5,7-cyclooctatetrene has at least two C=C bonds preserved on adsorption. Hovis and Hamers considered possible bonding geometries that are consistent with these ﬁndings and, with the help of DFT calculations [56], the geometry illustrated in Fig. 9 was identiﬁed as the most likely conﬁguration of the majority species. This structure leaves two C=C bonds exposed and amenable to further functionalization.

Si Si

Si Si

Si

Si Fig. 9. 1,3,5,7-cyclooctatetrene and its adsorption geometry on Si(100) for majority species comprising two C=C bonds reacting each in the di-σ conﬁguration with adjacent silicon dimers.

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Fig. 10. STM images of 1,3,5,7-cyclooctatetrene on Si(100) taken at a saturation coverage. (a) Molecules aligned themselves in rows on the two terraces that are separated by a single-height step. (b) Magniﬁed view showing the adsorption pattern. (c) Highresolution scan indicating the presence of a minority species, labelled “D”. Reprinted from [56] with permission from the American Chemical Society.

As in the case of norbornadiene and 1,5-cyclooctadiene, the particular reactivity of 1,3,5,7-cyclooctatetrene with Si(100) has been attributed to the molecular shape [56]. While the separation between terminal C=C bonds is slightly shorter than in 1,5-cyclooctadiene (3.1 vs. 3.2 ˚ A) and thus a poorer match for a pair of adjacent Si dimers, the C=C groups are now parallel to one another and, therefore, a better overlap of the π bonds is expected at both ends. In addition, the intermediate CH2 groups in 1,5-cyclooctadiene that could produce steric repulsions and prevent this molecule from taking up the shape needed for the attachment via both C=C bonds are replaced

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with CH ones and pushed away from the surface. It is the “antiaromatic” nature of 1,3,5,7-cyclooctatetrene (i.e. energy lower in a lower symmetry geometry than in a planar delocalized π system of 8 electrons) that provides the rigidity that prevents alternate reactions from proceeding. Compared to norbornadiene, the C=C bonds are much further spaced (3.1 vs. 2.4 ˚ A) and hence diﬀerent steric constraints are placed on the binding from the underlying silicon lattice. It would appear that these constraints result in the dramatic diﬀerence in binding topology observed for the two molecules. 1,3-butadiene, 2,3-dimethyl-1,3-butadiene, and 1,3-cyclohexediene. These molecules are dienes with one single bond separating the two double bonds. In terms of cycloaddition chemistry, two reactions with single double bonds are expected: the forbidden [2 + 2] cycloaddition reaction on a single double bond discussed previously at length, and an alternate allowed [4 + 2] cycloaddition, known as the Diels–Alder reaction, in which both double bonds react synchronously [4]; both mechanisms are illustrated in Fig. 3. As this approach predicts that the allowed process should have a much lower reaction barrier and hence should dominate, only one reactant product is expected and hence these molecules form another test of the appropriateness of the concerted cycloaddition mechanism for alkene chemisorption. The surface equivalent of the Diels–Alder reaction was ﬁrst predicted to be the most important reaction by Konecny and Doren [57,58] who used DFT calculations to investigate the adsorption of 1,3-cyclohexadiene on Si(100). They obtained binding energies of 54 kcal mol−1 for the [4 + 2] product and 39 kcal mol−1 for the [2 + 2] product, and also a negligible barrier for the [4+2] process. Concomitantly to this study, Bent and co-workers [59] carried out an infrared spectroscopic investigation of 1,3-butadiene and 2,3-dimethyl-1,3-butadiene ﬁlms which provided experimental evidence for the formation of the [4 + 2] reaction product on the surface. Subsequent results by Hovis et al. [60,61] shown in Fig. 11 support the observation of a Diels–Alder product as the majority species, which makes about 80% of the adducts. However, a minority (20%) species is also observed and is attributed to the [2 + 2] cycloaddition. Finally, experimental studies for 1,3-cyclohexadiene itself [44] were performed with the observation that only 55% products arise from the [4 + 2] cycloaddition, 35% from [2 + 2], while 10% an unknown product. Thus, the selectivity of 1,3-cyclohexadiene towards the Diels–Alder product is even poorer than that of 2,3-dimethyl1,3-butadiene. For both molecules subsequent annealing of the surface at

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Fig. 11. STM image of 2,3-dimethyl-1,3-butadiene on Si(100), with visible two reaction products, labelled “A” and “B” attributed to [4 + 2] and [2 + 2] cycloaddition products, respectively. Reprinted from [61] with permission from the American Chemical Society.

high temperature failed to convert the product distribution to the thermodynamically more stable [4 + 2] products. Hence, it has been suggested [44] that the reaction is controlled by adsorption kinetics. Viewing the reactions of these molecules with silicon(100) as occurring through concerted cycloaddition reactions is useful in that likely products are predicted, but the failure to observe almost exclusively the symmetryallowed product again indicates that this approach does not recognize the most important features governing the surface adsorption of alkenes. Simplistic ideas based on free-radical reaction mechanisms also give rise to the prediction that the [4 + 2]-like process should be energetically favored in preference to the [2 + 2]-like one, as in the second case a highly strained 4-membered ring is produced. Once again, however, kinetic concerns and possibly also surface relaxation eﬀects appear to be of greatest importance. Ab initio molecular dynamics calculations have recently been performed that model the time dependence of the reaction [41]. These clearly indicate that the [4 + 2] products forms via a stepwise mechanism. Benzene. In the context of conjugated addition reactions, one needs to consider the adsorption of aromatic systems. It was observed by Taguchi et al. [62] that benzene (C6 H6 ) chemisorbs on Si(100) at room temperature. Particularly interesting features of benzene are its ability to adsorb and desorb reversibly [62], unlike simple alkenes and dienes, and to migrate from one bonding conﬁguration to another [63]. The TPD spectra indicate the existence of two species with binding energies of 28 and 32 kcal mol−1 ,

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respectively, and the EELS spectra are consistent with a di-σ bonded structure. Based on these ﬁndings, models of binding structures were proposed that correspond to [4 + 2] and [2 + 2] cycloaddition products to a single silicon dimer as well as non-cycloaddition products involving two silicon dimers [62]. Since it was not possible to distinguish between the two possibilities, the system has been investigated by STM, FTIR, and semi-empirical calculations [16,63]. An STM image of benzene on silicon(100) is shown in Fig. 12 and contains three distinct bonding conﬁgurations labelled “S”, “B1” and “B2”. The S-conﬁguration images are the largest ones and centered above one dimer; these are preferentially occupied upon adsorption but are unstable with respect to relaxation to form B1 sites. Both chemisorption to a single silicon dimer and two adjacent silicon dimers in the same dimer row have been considered in the calculations, as illustrated in Figs. 12(b)–(f). The 1,2-single-dimer structure in Fig. 12(b) that corresponds to a single [2 + 2] reaction product is predicted to be only weakly bonded with an evaluated energy of 9 kcal mol−1 . This species is thus expected to be only transient on the surface. On the other hand, for the 1,4single-dimer conﬁguration in Fig. 12(c) a binding energy of 24 kcal mol−1 is predicted and is assigned to the observed feature labelled “S” [16]. This corresponds to the product of a [4 + 2] cycloaddition reaction. The adsorption of benzene can be considered as being analogous to that of 1,3-butadiene [57,58], with the relatively weaker binding of benzene by ∼30 kcal mol−1 being simply the consequence of the loss of aromaticity of benzene upon adsorption [64].

Fig. 12. (a) Filled-state STM image of benzene on Si(100). Single-dimer bonded molecules, and molecules in two other distinct bridging conﬁgurations are labelled “S”, “B1” and “B2”, respectively. (b–f) describe various adsorption conﬁgurations considered while (g–k) are simulated STM images of the adsorption geometries. Reprinted from [16] with permission from Ann. Rev. Phys. Chem.

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As for the non-cycloaddition conformations in which benzene reacts with two adjacent silicon dimers within the one dimer row, the structure in Fig. 12(f) was predicted to be very unfavorable, with an energy of only 5 kcal mol−1 , owing to the creation of radicals on both of the two central C atoms [16]. However, the structure in Fig. 12(d), with an adsorption energy of 26 kcal mol−1 , was predicted to be the most stable of all the examined structures and was assigned to the observed structure labelled “B1” in the STM images. The conﬁguration shown in Fig. 12(e) was also predicted to be quite stable, with a binding energy of 21 kcal mol−1 , and has been assigned to the B2 feature, a feature found exclusively in conjunction with the type-C defects [16,65] that occur on Si(100). These assignments have been veriﬁed by STM-simulated images shown in Figs. 12(g)–(k). The symmetric nature of Fig. 12(h) conﬁrms that the “S” features are indeed due to the 1,4-single-dimer bonded structure of Fig. 12(c). Also, the brighter contrast above one of the two aﬀected dimers in Fig. 12(i) agrees with that observed for the B1-type product while a similar character is observed in Fig. 12(j) rotated by 90◦ , corresponding to B2-type products. More recent studies of benzene and chlorobenzenes have also focused on chemisorbed species in which H or Cl atoms detach from the adsorbate, and on noncycloaddition products in which the adsorbates span dimer troughs [66]. In summary, non-cycloaddition products are again seen to dominate the chemisorption.

6. Cycloaddition Chemistry at Ge(100) and Diamond(100) Surfaces Both Ge(100) [2] and diamond(100) [67] surfaces undergo the same (2 × 1) reconstruction as does Si to form rows of dimers. However, there are some obvious diﬀerences in the strength and associated geometry of the dimer bonds. While on silicon, tilting on the ms STM timescale is observed only at temperatures <120 K, on germanium such structures persist to much higher temperatures [2]. While this could be attributed to slightly weaker π bonding in Ge than on Si resulting in a higher and sharper tilting interchange barrier, it is more likely due to an increased reorganization energy favoring more metallic conﬁgurations in Ge. Signiﬁcant π bonding is expected in dimerized diamond surfaces, while the reorganization energy driving localized structures with near 90◦ bond angles produced by tilting would also be greatly reduced [68,69]. These forces most likely account for the observation of symmetric dimers on the diamond surface [70].

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Adsorption of ethylene [71], cyclopentene and cyclohexane [72], and cyclohexadiene [73] on Ge(100)-(2 × 1) has been observed, but the resulting monolayers are disordered. FTIR spectra of adsorbed cyclopentene [72] imply the formation of what would be the [2 + 2] cycloaddition product, but while on Si the sticking coeﬃcient of cyclopentene is close to unity, on Ge it is only about 0.1. Conjugated polyenes react with Ge(100) to form predominantly what appear to be [4 + 2] cycloaddition products [73,74], but, in contrast to reactions on Si(100), the chemisorption is weak and reversible [74]. All of these observations of much weaker chemisorption can be rationalized by noting that the Ge-C bond is less stable than the Si-C bond by ∼10 kcal mol−1 [75]. In contrast to Si and Ge, on the diamond C(100) surface the cycloaddition of alkenes is rather slow and more in accord with what is expected for a forbidden [2 + 2] reaction. The sticking coeﬃcient of cyclopentene on C(100) is very small, of the order of 0.001 [76], also consistent with naive expectations for a [2 + 2] cycloaddition process. 1,3-butadiene has been shown to react prominently via the conjugated [4 + 2] addition [77] mechanism. While the reaction probability for this reaction is again found to be lower than that on Si or Ge, presumably owing to the presence of π bonds in diamond dimers, the eﬀect is not as large as for [2 + 2] addition of cyclopentene, so once again the symmetry properties of the reaction correlate with observed phenomena. Experimentally, it remains unknown whether the observed symmetric carbon dimers are composed of independent free radicals or form a π bond, but the applicability of cycloaddition selection rules for carbon(100) compared to their inapplicability for silicon(100) suggests the presence of signiﬁcant π-bonding character.

7. Conclusions Organic functionalization of semiconductors has become an area of increasing importance, principally owing to its prospective use in the fabrication of devices that incorporate properties of organic and inorganic matter. However, there are a number of diﬃculties that need to be overcome before it becomes a useful technology. As examples presented in this Chapter suggest, a particular weakness is the preparation process that commonly results in several competing products. Consequently, monolayers so formed are usually not well-deﬁned. A number of studies have indicated that, more often than not, the reaction system is kinetically controlled rather than thermodynamically controlled. In order to control and manipulate reaction

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products a better understanding of driving mechanisms and experimental variables that govern the adsorption process is needed. Concepts of cycloaddition reactions from organic chemistry provide a useful framework for describing certain classes of reactions of hydrocarbons with Group IV surfaces. For reactions with carbon surfaces, the observed products and kinetics may readily be predicted and interpreted using this approach, suggesting that the surface dimers display a signiﬁcant amount of π character. Silicon surfaces, however, are characterized by either no π character whatsoever, or by π bonding interactions that are too weak to prevent symmetry breaking via dimer tilting with its subsequent loss of π character. In this case, concerted cycloaddition reactions are not expected to occur, being replaced by simpler multi-step free-radical processes that are not subject to the symmetry selection rules of cycloaddition chemistry. The cycloaddition concept remains useful in that it readily allows signiﬁcant reaction products to be predicted and identiﬁed, but it fails to predict the alternate products that dominate many reactions. It now appears that aspects such as kinetic eﬀects as well as steric strain, both across the surfacemolecule junction and within the top surface layers, are more important than symmetry selection rules in determining chemisorption products. Acknowledgments The authors gratefully acknowledge Prof. Robert Wolkow (University of Alberta) and Prof. Neville Richardson (University of St. Andrews) for providing their original ﬁgures and permission to reprint them. Prof. Robert Hamers (University of Wisconsin) is gratefully acknowledged for permission to reprint his ﬁgures. We also thank the Australian Research Council for supporting this work. References [1] [2] [3] [4] [5] [6] [7] [8]

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PART VI ELECTRONIC PROPERTIES OF SINGLE MOLECULES ON METAL SURFACES

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MOLECULAR ELECTRONICS ROBERT STADLER Center for Atomic-Scale Materials Physics (CAMP), Department of Physics Technical University of Denmark, DK-2800 Lyngby, Denmark [email protected] Abstract. Molecular electronics is one of the most promising candidates currently discussed for electronic nanodevices. One big advantage of this ﬁeld is that organic molecules are well-deﬁned stable structures on an atomic scale, which in principle can be modiﬁed atom by atom in large quantities by means of chemical synthesis. This cannot in general be achieved for inorganic or more precisely non-carbon based materials, although Si-nanowires are a special case. Therefore, the use of molecules in electronic circuits might well represent the ﬁnal frontier in miniaturization. There are, however, diﬀerent approaches depending on the types and numbers of molecules used in an active device and on the ways they are connected to form a circuit. These approaches vary widely in their near future feasibility, state of development and in their ultimate limits for miniaturization and performance, and are usually difﬁcult to categorize. For this chapter recent research has been divided into (1) theory and experiments on electron transport through single small molecules, (2) design and fabrication of small circuits based on single macromolecules as active transistor elements, and (3) integrated circuits with a few thousand molecules representing one diode in a regular metallic grid structure on the nanoscale. Keywords: Molecular electronics overview; molecular circuit design, modelling and fabrication; diﬀerent length scales in molecular electronics.

Contents 1 2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electron Transport through Single Organic Molecules . . . . . . . . . . 2.1 Electron transport theory . . . . . . . . . . . . . . . . . . . . . . . 2.2 Scanning probe measurements and mechanically controlled break junctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363

364 366 366 369

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2.3

Possible applications of single organic molecules as various components in electrical circuits . . . . . . . . . . . . . . . . . . . . . . 3 Nanotubes and C60 Molecules as Active Transistor Elements . . . . . . 3.1 Carbon nanotube ﬁeld eﬀect transistors (CNTFETs) . . . . . . . . 3.2 A memory/adder model based on an electromechanical single molecule C60 transistor . . . . . . . . . . . . . . . . . . . . . . . . 4 Molecular Films as Active Elements in Regular Metallic Grids . . . . . . 4.1 Molecular switches in the junctions of metallic crossbar arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 High density integration of memory cells and complex circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Summary and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

371 372 373 376 380 380 382 384 384

1. Introduction In 1974 Aviram and Ratner introduced a concept for a molecular rectiﬁer based on the use of a single organic molecule [1]. This molecular diode consisted of a π system functionalized with a donor and an acceptor group, which were separated by a sigma-bonded tunneling bridge. In their theoretical work the electron’s movement from the cathode to the anode through the molecule was divided into three steps, namely the hopping of electrons from the cathode to the acceptor part of the molecule, from the acceptor to the donor function inside the molecule, and ﬁnally from the donor part of the molecule to the anode. The rectiﬁcation eﬀect was given by the partial polarization of the molecule due to their substituents, where electrons would have to overcome a larger energy barrier to hop on the donor function if the bias was reversed. Thirty years later, molecular electronics has become a very active ﬁeld of research [2–4]. The reasons for that can partly be found in economic necessity, since despite continuous achievements in miniaturization of CMOS technology, fundamental diﬃculties will be faced when the nanoscale is approached. Some of them, such as the irreproducibility of detailed atomic structures based on Silicon, can be solved by replacing the components of electric circuits by organic molecules, where well-deﬁned structures can be mass produced by means of chemical synthesis. Additionally, the rich variety of diﬀerent structures and functionalities in organic chemistry oﬀers the potential of a huge tool box for the implementation of logic functions on the nanoscale. Another important reason for the increase of research in this ﬁeld over the last ten years is that major breakthroughs in developing experimental techniques for studying systems consisting of a few or even single molecules have been achieved. Scanning probe techniques now

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allow the imaging, spectroscopical characterization and manipulation of single molecules adsorbed on crystal surfaces. By means of nano-lithography (see Chapter 3 of this book), metallic electrodes with a spatial gap of only a few nanometers between them can be fabricated. Advances in supra-molecular chemistry have enabled the synthesis of a variety of tailor-made complex molecules, which have been designed to meet diﬀerent requirements such as a high conductivity, the possibility of switching between two states triggered either by photons or electrons, a stiﬀ rod-like structure and good solubility. Molecular electronics has now become a very vibrant and interdisciplinary ﬁeld of science, where physicists, chemists and engineers in academia and industry work together on various aspects and levels in large scale national and international collaborations. This inevitably led to a diversiﬁcation into diﬀerent approaches, where there are as many suggestions for a categorization of the ﬁeld as there are reviews about it. One way is to distinguish between hybrid-molecular and mono-molecular electronics [2]. In the former category the molecule is just the active part of a diode or transistor and molecular units are inter-connected by an electro-mechanical metallic grid, whereas the aim in the second category is to integrate an arbitrarily large numer of logic functions including the wiring inside a single molecule. Other categorizations are based on classes of molecules, the physical process used for the implementation of 2-bit states (such as redox processes, conﬁguration change, electronic excitations, etc.) or the type of the main circuit element (diodes, transistors, qubits, etc.). For the current review the authors decided to make the size of the molecular system under study the characteristic feature for the organization of this chapter. The reason for this is that ‘larger’ molecular systems have been integrated in rather complex circuits, which can be readily compared with CMOS based electronics, whereas ‘smaller’ molecular systems are still on the level of basic research in theory and experiment, although in the long term they are showing more promise for performance enhancement. The next section gives an overview of theoretical calculations and scanning probe measurements of electron transport through single organic molecules, although this is kept deliberately short, because it overlaps with other chapters of this book. For such systems quantum mechanical eﬀects and atomistic details of the molecule/electrode interface play a decisive role. The following section focuses on small circuits, where the active elements are nanotubes or C60 molecules. Due to the larger size of these molecules and the range of conductivities they can adopt depending on their state of compression or charge

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polarization in an electric ﬁeld, their applicability as circuit components is less sensitive with regard to details of the molecule/electrode interface on an atomic scale. In the next section, circuits based on organic molecular ﬁlms are reviewed. Research in this category, where ﬁlms of ∼5000 molecules are used to implement a single diode, is so advanced that very complex circuits such as demultiplexers and large memory arrays have already been fabricated on very dense crossbar grids. Finally, a summary and outlook is given. 2. Electron Transport through Single Organic Molecules The characterization of electron transport through single molecules is demanding, both theoretically [5] and experimentally [6]. For the theoretical description, quantum mechanical equations have to be solved numerically for a non-equlibrium system with open boundaries provided by long electrodes which maintain diﬀerent chemical potentials due to an external bias. Within the framework of scattering theory, several approximations to this problem have been developed, where increased accuracy comes at the cost of increased computational expense. For experimental measurements the problem lies in the controlled and reproducible fabrication of nano-junctions, where two (or ideally three) metallic electrodes are positioned so close to each other that a molecule can be placed in the gap between them and connected to at least two of them. For this task scanning probe techniques can be used, where several problems have to be faced and a simultaneous imaging of details of the molecule-electrode contacts and measurement of the current/voltage (I/V) curves can rarely be achieved. There have been many proposals in the literature for devices based on single molecule nano-junctions, but none of them has reached a stage of development where small circuits could be designed in theory and reproducibly demonstrated in experiment. This section gives a short review of some of the latest advances in this research area. 2.1. Electron transport theory For the theoretical modelling of an electrode/molecule/electrode nanojunction, the system has to be divided into separate parts: the ﬁnite contact region, for which Schr¨ odinger’s equation is solved electron by electron, and the semi-inﬁnite leads where translational symmetry of a two-dimensional unit cell of the electrode material is assumed in the direction pointing away from the contact region. The problem can then be deﬁned in terms of plane waves entering the system through the leads and scattered by the contact region. Since atomistic and electronic details of the

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electrode/molecule interface have an inﬂuence on the conductance through the electrode/molecule/electrode junction, a few layers of the electrode are often also deﬁned as part of the contact region, which is then sometimes referred to as ‘extended molecule’. The great majority of theoretical work on the subject of electron transport through molecules deals with conditions very near to thermal equilibrium, particularly with very small voltage drop across the transporting system. These conditions are known as the linear-response regime, because the currents induced are linear in the applied voltage. A general approach to near-equilibrium transport is embodied in the Landauer formula [7], which expresses the conductance of a system at T = 0 in terms of the quantum mechanical transmission coeﬃcients calculated from a steady state scattering matrix. Despite the attention directed toward linear-response theories, they remain severely limited in the range of physical situations which they address, and in particular do not include any inelastic eﬀects such as dissipative scattering. The application of this approach for a ‘smallsignal analysis’ in the engineering sense of this term is problematic. Such an analysis studies small departures from a steady-state — but typically far from equilibrium — situation where a signiﬁcant voltage drop occurs. The linear-response theories study small departures from equilibrium, not from a non-equilibrium state. Apart from the general setup of the theoretical frame-work, in which the open-system scattering problem is deﬁned, there is also the question of how accurate the contact region is described numerically. Semi-empirical methods such as extended H¨ uckel (EH) techniques [8–10] where the Hamiltonians are parametrized, allow the modelling of rather large molecules and have now been extended to circuit simulation software, where an arbitrarily large number of electrodes can be connected to a molecule [8] (see Fig. 1). However, these methods are implementations of a linear-response theory (with the exception of [10]) and additionally operate with parametrized Hamiltonians and, therefore, they cannot describe electrostatic eﬀects such as the polarization of the electronic wavefunctions in the contact region, which might aﬀect the potential distribution along the region. For solving this problem, ﬁrst principle calculations using density functional theory based non-equilibrium Green’s function (DFT-NEG) techniques have to be performed where the coupled Schr¨ odinger and Poisson equations are solved self-consistently [11–13]. This has the advantage that the energetic position and shape of the molecular orbitals in the contact region depends on the voltage applied on the electrodes, which is necessary for a realistic non-equilibrium description of the system. Such calculations are

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Fig. 1. (a) Structure of a scattering circuit consisting of a central molecule interacting with N electrodes as developed recently based on an EH approach by S. Ami et al. [8]. (b) An example of a complex molecule attached to six electrodes, which from its original design represents a full adder, where the I/V characteristics between each combination of electrodes can be assessed using the EH technique.

computationally more expensive but can also describe current induced local forces acting on atoms in the contact region [14], thereby allowing predictions about the junctions stability for a variety of applied voltages. In order to make the computational eﬀort of such calculations more bearable, the electrodes have been modelled as jellium in early versions of this technique [11], where the positive charge of the nuclei is uniformly distributed in the region of the electrodes and the details of their atomic and electronic structure are not taken into account. The methods, where the electrodes are described atomistically [12,13], diﬀer in the way in which the semi-inﬁnite boundary conditions are deﬁned, where the matching between the ‘extended molecule’ and the leads presents a technical challenge. For a discussion of these issues see [12]. EH methods have been used to scan the conductance properties of molecular wires for a variety of chemical compositions [15] and the inﬂuence of the way they are interconnected to each other has also been addressed [16]. For the physically more complex issue of the inﬂuence of details of the molecule/electrode interface and related electron density polarization and charge transfer eﬀects, DFT simulations have been performed for chemically rather simple test systems such as dithio-phenyl radicals [17] or the original proposal for the Aviram–Ratner diode [18]. For the research in this ﬁeld in the future, it is expected that both methods will be further developed and

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are complementing rather than competing against each other, since semiempirical techniques enable quick scans of whole classes of rather complex molecules, whereas ﬁrst principle methods provide a very accurate picture of all possible physical eﬀects for small junctions.

2.2. Scanning probe measurements and mechanically controlled break junctions Molecular junctions can be investigated by scanning probe techniques, where a layer of organic molecules is adsorbed on a single crystal surface, and the adsorption sites are scanned with a scanning tunneling microscope (STM) tip, which can act as the second electrode where the surface would be the ﬁrst one [19]. This method has the advantage of providing imaging and conductance measurements for the adsorbate system, at the same time but there are a few short-comings. The surface and the STM tip have different chemical potentials due to their diﬀerence in shape even if they are made of the same material, and this creates an undesirable asymmetry in the junction that would not be present in any application with a molecule connected to two metallic nano-wires. Most molecules of interest are aromatic molecules, which are characterized by rings with conjugated double bonds. The resulting delocalized π electron system is responsible for the semi-conducting properties of this class of molecules, but also makes a planar geometry their most stable equilibrium conﬁguration. Consequently, such molecules have to be chemisorbed for STM studies of molecular conductance, because if physisorbed they would lie ﬂat on the surface due to Van der Waals interactions between its π system and the surface, and the current through the molecule from one of its atoms to another could not be measured. Usually such a chemisorbtion is achieved by using thiol-groups as ‘alligator clips’, since the sulphur atoms in these groups form strong bonds with gold surfaces, which are chosen as the electrode material for most studies. Even in the chemisorbed case it is necessary to substitute the molecules with four thiol-legs or embed them in a carpet of insulating alkanethiols to make sure that they ‘stand up’ on the surface [20]. Such an insulating matrix also allows in principle the isolation of single conducting molecules and the measurement of their conductance. To identify these single molecules, however, is not an easy task. It requires a distinction between the contributions to the conductance coming from the type and from the length of a molecule, which can be achieved by STM measurements of a surface covered

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with molecules using a combination of a conventional direct current-voltage STM with a microwave alternating current STM technique. STM techniques have an even wider range of applications in molecular electronics than the imaging of the topography of a substrate/molecule system and the measurement of conductances through molecules. They can also be used for the controlled desorption of molecules, for placing atoms individually, and as a spectroscopic tool which provides information about the electronic density of states and inelastic eﬀects such as molecular vibrations [21]. In a recent study copper(II) phthalocyanine (CuPc) molecules have been assembled on a NiAl(110) surface and have been bonded to two gold atomic chains by manipulation of single atoms [22]. The dependence of the electronic properties of this metal-molecule-metal junction on the length of the gold chain have been systematically investigated by varying the number of atoms one by one, and the inﬂuence of the detailed position of the molecule on the contacts could then also be addressed. Such experimental studies with complete control over the atomic conﬁgurations in the junction are needed to complement the theoretical work described in the last section for the understanding of the alignment of the molecular orbitals with respect to the wires’ Fermi energy, the buildup of electrostatic barriers and other issues determined by the detailed electronic structure of the system. As an alternative to STM measurements for single molecule conductance, metallic nanowires can be broken in a mechanically controlled way which allows for the formation of gaps with ∼1 nm width, and molecules deposited on top of this gap can be detected by changes in the I/V curves [23–25]. There is no way to be certain that the increase of conductance in such a junction is due to the adsorption of single molecules rather than many of them, since no microscopy technique up to now is able to observe them directly. However, this method has the advantage that, contrary to the STM measurements, the junction setup is symmetric with regard to the two electrodes, and could in principle be used for the fabrication of integrated circuits if a reproducible, reliable and cost eﬀective way for mass production would be found. The symmetry or lack of symmetry of the molecular part of the setup has been used as an argument that conductances through single molecules have been measured in some experiments. Symmetric molecules give symmetric diﬀerential I/V curves because there is no reason to assume that the conductance should change if the voltages on the two electrodes are reversed. For an asymmetric molecule that has donor and acceptor groups at diﬀerent positions, the I/V curves can

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be asymmetric. This eﬀect, however, would be statistically averaged out if more than one molecule is adsorbed inside the junction, since it is an experimental challenge to control or predict which end of the molecule bonds to which electrode, and a random behavior must be assumed, which would make the measured conductance curves symmetric again. In summary of this section, it can be said that experimental manipulations and conductance measurements on single molecules are still a big scientiﬁc challenge, and a lot of the progress that has been recently made has been achieved for particular substrate/molecule systems and can not be easily transferred to other surface materials or types of molecules. The STM is certainly the most versatile instrument for manipulations and measurements on the nanoscale but it is not very suitable for an integration into nano-electronic devices. New techniques such as mechanically controlled break-junctions will have to be further developed for this purpose in the future.

2.3. Possible applications of single organic molecules as various components in electrical circuits There have been several proposals for wires, diodes [1,27], transistors [28], memory cells [29] or logic gates [30] based on the conductance properties of small single organic molecules. Recently, Kondo and Coulomb blockade eﬀects have been observed, which could be the basis for the use of molecules as single electron transistors [31]. Similarly, observed negative diﬀerential resistance could enable resonant tunneling transistors [32]. However, in some of the theoretical work it is not clear whether the predicted device behavior is an artifact of the level of approximation chosen for the calculations. The initial Aviram/Ratner proposal for a molecular rectiﬁer, for instance, originally modeled by a 3-step hopping process, has been recently reinvestigated with DFT-NEG calculations and very poor diode characteristics were found [18]. On the other hand, there is a controversy about theoretical explanations for device eﬀects found in experiments, where negative diﬀerential resistance found in molecular wires has been explained by such diverse concepts as charging of the molecule [32] and thermally activated rotation of functional groups [33]. On the molecular scale any device eﬀect is not a property of a particular molecule but must be attributed to the electrode/molecule/electrode nano-junction, where details of the interface between the molecules and the electrodes can qualitatively change the characteristics of the system. Since atomistic details of this contact can rarely

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be observed and much less so controlled in conductance experiments, the big variety of theoretical explanations for the same measurement is hardly surprising. It is rarely addressed in the literature that for molecular versions of circuit elements to be useful, there has to be the possibility to connect them together in a way where their electrical characteristics — measured individually between electrodes — would be preserved in the assembled circuit. However, it has been recently shown that such a downscaling of electrical circuits within classical network theory cannot be realized due to quantum eﬀects, which introduce additional terms into Kirchhoﬀ’s laws and let the classical concept of circuit design collapse [16]. Circuit simulations on the basis of a topological scattering matrix approach have corroborated these results [34]. Recently, schemes for computational architectures, which make use of the quantum properties on the molecular scale rather than avoiding them, have been proposed, such as cascading CO molecules on metal surfaces [35], computing with optical excitations [36] or controlling the interference pattern of electron transport through aromatic molecules by modifying their chemical side-groups [37] (Fig. 2).

3. Nanotubes and C60 Molecules as Active Transistor Elements Single-walled carbon nanotubes are currently perceived as the main candidate for a material to replace silicon in information technology [38]. They can exhibit a large range of conductances depending on details of their structure, ranging from semiconducting to metallic, where the semiconducting ones especially can be used as active elements in ﬁeld eﬀect transistors. The nearly dissipation-free ballistic electron transport along the tubes also suggests applications as high current density interconnects. The comparatively large size of these molecules make them less sensitive to details of their contact to the electrodes and conventional device schemes, e.g. ﬁeld eﬀect transistors (FETs), small logic gates, and memory cells could be experimentally demonstrated and are theoretically well-understood. Semiconducting nanowires made from GaP, GaN, InP or Si exhibit somewhat similar properties and have also been used for the fabrication of diodes, bipolar transistors and FETs as well as simple circuits. A recent proposal for a single C60 molecule eletromechanical transistor has been used as the basis for a performance evaluation study, where a memory/adder model

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Fig. 2. A molecular data storage scheme based on an aromatic molecule (naphthalene) bonded to four gold electrodes by sulfur atoms and polyacetylene wires [37]. For the surface an insulator has to be chosen to prevent cross-talk between the electrodes. The variables X, Y and Z could either be chemical substituents or, alternatively, connections to further electrodes. Some parts of the molecule, electrodes and variables are drawn in bright colors, which is meant to indicate an active state during a particular read-out. The darker parts are considered to be inactive.

has been designed, and the signal response behavior of the corresponding circuit has been tested with standard circuit simulation software. In this section, recent progress with such devices will be reviewed.

3.1. Carbon nanotube ﬁeld eﬀect transistors (CNTFETs) Carbon nanotubes are rolled up sheets of graphene just a few nanometres in diameter that can behave as either metals or semiconductors depending on their atomic arrangement [38]. They can be deposited on source and drain electrodes, which are fabricated by lithographical means. If the substrate wafer is a material which can be capacitatively charged but is covered with an oxide layer, varying the voltage on the substrate, which then acts as a gate electrode, changes the number of charge carriers on the nanotube [39]. One of the major challenges in nanotube electronics is to ensure that the coupling between the gate and the nanotube is strong enough to amplify a

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signal, so that the variations in the output voltage of one nanotube transistor can control the input of a second transistor, which is necessary for integrating nanotubes into circuits. Recently, a new layout that resembles a conventional MOSFET structure with the gate above the conduction channel has been developed, which is characterized by a very small gap between the gate and the nanotube, thus making the resistance much more sensitive to variations in the gate voltage [40]. One way to realize this is using electron beam lithography to pattern aluminum electrodes on top of an oxidized silicon wafer, depositing the nanotubes on top, and adding gold electrodes by an evaporation technique [41]. Semiconducting nanotubes typically operate like p-type semiconductors (conducting holes rather than electrons), where the charge-transfer from the electrodes acts as ‘doping’. In this setup, molecules being adsorbed from the atmosphere onto the nanotube can aﬀect the reproducibility of the device characteristics. This molecule adsorption can be controlled by embedding the nanotubes in a ﬁlm and by applying thermal-annealing treatments in a vacuum [42]. The same techniques can be used to fabricate n-type devices, as an alternative to the current method of doping nanotubes with alkali metals. Recent progress in improving the intrinsic resistance of nanotubes as well as the contact resistance at the electrodes is due to advances in nanotube growth [43] and deposition [44] techniques and their ability to tailor the diameter (which determines the bandgap) and chirality of the tubes as well as the Schottky barriers at the molecule/electrode interface. However, the synthesis of nanotubes, which can be done by e.g. electric arc discharge [45] or chemical vapor deposition [46], in general, results in a mixture of metallic and semiconducting tubes, where only the latter can be used as a transistor element. A separation procedure has been recently proposed, where metallic tubes are ‘burnt oﬀ’ by high voltages and only the semiconducting ones remain on the substrate [47]. But to obtain transistors that can conduct the same amount of current as micron-wide silicon transistors, for example, 2D arrays of parallel tubes with exactly the right width are needed. The assembly of diﬀerent nanotubes into basic logic circuits, such as a logic NOR, a static random-access-memory cell and a ring oscillator, has been achieved [41] (see Fig. 3). In these circuits a simple inverter device consists of a nanotube FET and a large bias resistance, and the NOR gate can be realized by adding an extra FET in parallel. Any of the standard logic gates — AND, OR, NAND — can be created using diﬀerent

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Fig. 3. Experimental demonstration of one-, two- and three-transistor logic circuits with CNTFETs [41]. Output voltages as a function of the input voltage are given for (A) an inverter, (B) a NOR gate, (C) a static random access memory cell (SRAM) and (D) a ring oscillator.

arrangements of these FETs. Using thermal annealing, which can transform p-type CNTFETs into n-type tubes also locally on just a part of a tube, an inverter with complementary p- and n-FET transistors on a single nanotube bundle can also be demonstrated [48] (see Fig. 4). Nevertheless, current fabrication techniques fall far short of those needed for mass production. Most problematic, perhaps, is the lack of control when it comes to placing the tubes in predetermined positions during device fabrication, where diﬀerent approaches such as controlled deposition from solution or lattice-directed growth are currently pursued [37]. A remarkable success has been recently achieved in using DNA molecules for the construction of a single CNTFET device [49]. However, more research is needed to assess whether such a biological approach can also be used for the assembly of a large number of devices. In order to create nanotube based devices, researchers must carefully tailor their electronic properties. This is diﬃcult to achieve as described above since these properties depend on the diameter and chirality of the

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Fig. 4. (a) Atomic force microscope (AFM) image of the design and (b) measured voltage output characteristics of a complementary CNTFET inverter [49]. (a) A single nanotube bundle is positioned over the gold electrodes to produce two p-type CNTFETs in series. The device is covered by a resist and a window is opened by e-beam lithography to expose part of the nanotube. Potassium is then evaporated through this window to produce an n-CNTFET, while the other CNTFET remains p-type. (b) Open circles are raw data for ﬁve diﬀerent measurements on the same device. The thick line is the average of these ﬁve measurements. The thin straight line corresponds to an output/input gain of one.

tubes, and it is diﬃcult to separate the semiconducting from the metallic ones. The composition of semiconduncting nanowires, by contrast, where GaP, GaN, InP and Si are the most commonly used materials, is relatively easy to control. Silicon wires, for instance, can be produced by vapor-liquidsolid (VLS) growth combined with other techniques [50]. 3.2. A memory/adder model based on an electromechanical single molecule C60 transistor The physical principle of a C60 electromechanical ampliﬁer has been experimentally demonstrated with a single molecule on a gold surface compressed and at the same time electrically contacted by an STM tip [51] (Fig. 5). In such a setup the substrate and the STM tip act as source and drain electrodes, whereas the force on the tip compressing the molecule acts as gate, where the state of compression changes the conductance through the molecule by orders of magnitude. This design facilitated the experimental demonstration because the behavior of a three-terminal device (source, drain and gate) could be mimicked with two terminals only. For devices assembled into circuits, however, this would be completely impractical and a physical separation of all terminals is needed.

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Fig. 5. (a) Schematic diagram of an experimentally demonstrated electromechanical single molecule C60 ampliﬁer, where the molecule is connected between an STM tip and a surface, and the input voltage Vin actuates a piezoelectric translator. (b) The output voltage Vout (t) (solid line) is determined from the experimentally measured conductance through the C60 molecule and the characteristics of an external polarization circuit [51] and is compared with Vin (t) (dotted line).

In a later design [52] (Fig. 6(a)), which was the basis for a theoretical evaluation of the performance of C60 transistors in larger circuits [53,54], a single C60 molecule is placed in a 1.24 nm wide gap between a source and a drain electrode in a coplanar arrangement. A tip at the end of a cantilever, which is equipped with a piezolayer to control its deﬂection, can be used to compress the C60 molecule, thereby changing its conductance which gives the transistor eﬀect. The equivalent electrical circuit description (Fig. 6(b)) of the electromechanical conversion of the gate signal into a movement of the nano-cantilever follows the theoretical framework outlined in [55] and has been adapted to C60 transistors by Ami et al. [52]. The C60 molecule comes into this circuit description twice. On the one hand it acts as an electrical resistor where the value for the resistance is modulated by the compressing action of the cantilever tip. On the other hand the molecule resists its deformation elastically which has to be taken into account as a counter electromotive force in the model. Based on this design a memory/adder model (Fig. 6(c)) using 464 transistors could be constructed and evaluated on grounds of SPICE circuit simulations. Four bits of information were read from four diﬀerent memory cells, added as two 2-bit words, and the resulting 2-bit was moved through registers (clocked D-latches) to a subsequent computation. It must be noted

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Fig. 6. (a) Layout of a theoretically modeled modiﬁed C60 electromechanical transistor composed of a metal-C60 -metal nano-junction and of a small grid cantilever whose dimensions are speciﬁed. (b) Electrical equivalent circuit model of the C60 transistor in (a) used for circuit simulations, where the mechanical properties of the cantilever have been described as a RLC cell plus a counter elastic force to describe the reaction of the molecule upon compression [52]. (c) Schematic diagram of a memory/adder model, where the arrows indicate the directions in which the signals move [53].

that unlike suggestions for other nanoscale architectures [56], the described C60 microprocessor does not use any CMOS components but consists of hybrid-molecular transistors only. This demonstrates that hybrid-molecular electronics can be moved from the device to the computer architecture level without fundamental problems. A performance evaluation, however, shows that such circuits are not likely to be a competitor for current CMOS devices [54]. A comparison with current CMOS devices (R ∼ 0.01 MΩ, C ∼ 2∗ 10−16 F) shows that

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although the capacitance is a bit higher in hybrid-molecular devices, it is the high resistance of the molecule that mainly limits the clock frequency on the device level. This resistance is not only deﬁned by the conductance of the molecule as a passive device, as in a molecular wire, but also by the requirements of compatible input and output voltages as discussed in [52] and [53]. These restrictions on speed are mainly due to the delicate interplay between the molecule and the electro-mechanical grid or electric ﬁeld of the device. The dimensions of a C60 electromechanical transistor are limited by the length of the cantilever, which has to be larger than ∼200 nm in order to compress the C60 molecule eﬃciently, and therefore cannot be further reduced. If this is compared with the minimum feature size of CMOS today (∼150 nm) and extrapolated to 2012 (∼50 nm) [57], the C60 architecture will not be able to compete. One might argue that these limits are due to the electromechanical nature of the device and would not apply to transistors based on molecules in an electric ﬁeld. Quite recently, a 4-terminal CNTFET has been fabricated where two electrodes act as source and drain bridged by a nanotube, and the other two electrodes are used to apply a local electric ﬁeld [58]. By changing the ﬁeld, the conductance of the molecule was varied, which gives the transistor eﬀect. Although in [58] 2 device densities of only 0.1 Mbit/cm were realized, the authors claim that 2 100 Mbit/cm could be achieved. This would still not reach the densities 2 that are expected for CMOS technology in the near future (475 Mbit/cm for SRAM memories in 2006 [57]). Wherever electric ﬁelds are considered as the ‘non-molecular’ part of a hybrid-molecular device, the ﬁeld strength has to be large enough to change the conductance of the molecule inside the nano-junction. Since the ﬁeld strength depends on the area of the electrodes, there is a natural limit to the minimum feature size of the device for each choice of a particular molecule. From this comparison it can be concluded that on the device level there are fundamental limits for the miniaturization of hybrid-molecular electronics, which are not only governed by the size of the molecule but also depend on the size that an electromechanical or capacitative grid has to have in order to inﬂuence its energy levels. These architectural issues regarding the interfacing of a molecular device to the outside world or the assembly of many devices into larger circuits will have to be addressed to a larger extent in the near future.

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4. Molecular Films as Active Elements in Regular Metallic Grids The most advanced concept in molecular electronics today makes use of recent progress in various ﬁelds, such as the tailoring of chemical functions via supra-molecular synthesis, the subsequent imprinting of metallic nanowires and molecular mono-layers using a combination of nano-lithography and molecule deposition techniques, and innovative circuit design on the basis of regular grid arrays. Molecular ﬁlms are sandwiched between metallic wires of sub-micron size, where they act as molecular switches depending on their redox state, which can be manipulated by applying external voltages on the wires [60–62]. If such metallic wire/molecular ﬁlm/metallic wire cross-junctions are fabricated in arrays, they can be used as memory cells, where the individual junctions can be addressed independently and each junction can store one bit of information. Alternatively, such crossbar arrays can be used for circuit design in the context of programmable gate logic arrays (PGLAs), where the junctions that are ‘on’ and ‘oﬀ’ represent diodes and disconnected grid points, respectively. This scheme has received a lot of attention in the last few years since researchers have managed to fabricate complex circuits such as demultiplexers and memory cells that are an order of magnitude smaller than anything that can currently be produced with CMOS technology. It must be noted, however, that this scheme is based on classical electron transport in the Boltzmann regime [2], where quantum eﬀects are averaged out statistically, and devices cannot be scaled down to the size of single molecules [34]. 4.1. Molecular switches in the junctions of metallic crossbar arrays Two-terminal devices might seem more natural for the molecular-scale systems than three-terminal ones because of the technological diﬃculties in manipulating small structures. Furthermore, chemical assembly of molecular devices usually results in a periodic structure. This observation resulted in the idea to have a two-terminal switch, electronically reconﬁgurable, where a relatively high voltage (e.g. −2 V or +2 V in [62], which uses a 2catenane-based molecule) (Fig. (7a)) is applied to close or open the switch, but a relatively low voltage to read (∼0.1 V) [60]. These molecular switches [62], a mono-layer of rotaxane molecules, are not ﬁeld-activated but can be described as small electro-chemical cells, which are characterized by

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Fig. 7. (a) Molecular structure of the bi-stable [2] rotaxane R used to form Langmuir– Blodget monolayers [62]. (b) Crossbar circuit architecture at an increasing level of complexity in terms of fabrication and function [61]. Each junction is a switching device, with black arrows corresponding to open switches and grey arrows to closed switches. In the 1D circuit, the number 0100 is stored by addressing the second device and closing the switch. In the 2D memory circuit, the number 0101 is stored by writing the second row with the second and fourths column in parallel. In the 2D logic circuit, the switches are conﬁgured in such a way that six of them are closed, so that the circuit can perform as a half adder. (c) An atomic force micrograph of the cross-point molecular device with an insert showing the details of the cross point [62].

signature voltages at which current ﬂows and the molecules switch. They are a few nanometers wide and have a dumbbell-shaped component with an interlocked ring. When the molecules sit between two wires, electrons ﬂowing through one wire can hop onto them and cross to the other wire. But if a voltage is applied to a particular crossbar-junction, the interlocked ring of its molecules slides to a new position on the dumbbell and blocks the electrical current. Once the ring slips to its new position, it cannot be moved back, making the rotaxane molecules of a particular junction a single-use switch. But since discovering the rotaxane switch, the researchers have come up with other molecular switches, including reversible ones [61]. A crossbar architecture (Figs. 7(b) and (c)) has four advantages over other circuit design concepts in nano-electronics: (i) the architecture is easily scalable at least up to the point where the dimensional limits of the Boltzmann electron transport regime begin, (ii) it requires only 2N

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communication wires to address 2N nanojunctions, which would allow a better addressability of the circuits with external CMOS circuits than a dedicated architecture, (iii) a regular architecture is reconﬁgurable, since the position of diodes is not determined by fabrication, but junctions are switched ‘on’ and ‘oﬀ’ by applying voltages to change their redox state, which compensates for a high percentage of defects, (iv) the regular structure facilitates the fabrication process. Figure 7(b) illustrates the concept with simple examples. 4.2. High density integration of memory cells and complex circuits For the fabrication of the crossbar structures described in the last section, a special lithographic technique is needed that does not have the same shortcomings as electron-beam lithography in terms of the slow writing speed and the damage that the high energy electron beams can cause in molecular devices. For this purpose an imprinting process [62] (Fig. 8) can be used, which produces sub-10-nm feature sizes and combines high throughput with low costs. This process has resulted in the highest density electronically addressable memory to date [63]. A 64-bit memory with an area of less than one square microns has been experimentally demonstrated. The researchers made the device by creating a master mold of eight 40 nm wide parallel lines and pressed this mold onto a polymer layer on a silicon wafer to make eight parallel trenches. After molecule deposition and fabrication of the top-wires, the resulting device contains 64 points where the top and bottom wires cross. A bit of memory sits at each of these points in the roughly 1000 molecules sandwiched in a single junction between a higher and lower

Fig. 8. Schematic of the procedure used for fabrication of nanoscale molecular-switch devices by imprint lithography [62]. (a) Deposition of a molecular ﬁlm on Ti/Pt nanowires and their micron-scale connections to contact pads. (b) Blanket evaporation of a 7.5 nm Ti protective layer. (c) Imprinting of 10 nm Pt layers with a mold that was oriented perpendicular to the bottom electrodes and aligned to ensure that the top and bottom nanowires crossed. (d) Reactive ion etching with CF4 and O2 (4:1) to remove the blanket Ti protective layer.

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wire. To write a bit, a voltage pulse is applied to set the molecules’ electrical resistance. Measuring the molecules’ resistance at a lower voltage allows the bit to be read. It is also possible to put logic in the same circuit by conﬁguring molecular-switch junctions to make a demultiplexer — a logic circuit that uses a small number of wires to address memory, which is essential to make memories practical. This has been the ﬁrst experimental demonstration that molecular logic and memory can work together on the same nanoscale circuits. The memories are also rewritable and non-volatile, that is, unlike today’s DRAM (dynamic random access memory) chips they preserve information stored in them after the voltage is removed. Recently, the method for the fabrication of the nanowire pattern has been reﬁned [64], where regular arrays of nanowires with a diameter of down to 8 nm can now be achieved. (Fig. 9) In spite of the overall success of this particular scheme, there are some issues which need to be clariﬁed especially when it comes to details of the structure of the electrode/monolayer/electrode crossings on an atomistic level [4]. In a recent review on the vapor deposition of metal atoms on organic monolayers [65], the complexity of the process and the subtle eﬀects of the surface structure and composition on the outcome are illustrated. A reﬂection-absorption infrared spectroscopy study [66] of a system, which is similar to the actual cross-junction, suggests undamaged organic monolayers with Ti coatings, but further research is needed for the complete characterization of these complex structures. A crossbar array based scheme is at the moment perceived as the most realistic strategy to combine nano-scale components with CMOS circuits [67], where a concept for neuromorphic networks based on molecular singleelectron transistors [68] has also been proposed.

Fig. 9. An electron microscope zooms in on an eight-by-eight nanowire grid [62]. Molecules between the grid junctions act as switches.

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5. Summary and Outlook Three diﬀerent approaches to nano-devices in molecular electronics have been reviewed in this chapter. The use of single organic molecules in such devices is the least developed of those branches in terms of possible technological applications, although it is historically the oldest. Due to the challenges that circuit design and fabrication on an atomistic scale imply, it is still on a basic science level. Much more progress has been made with macromolecules such as C60 molecules and nanotubes. With these macromolecules simple circuit elements have been demonstrated experimentally, and circuit design on a system level has been done based on their experimentally determined device characteristics. The fabrication of larger circuits, however, still remains diﬃcult due to the absence of a scheme for the fabrication of large arrays of identical devices. The most developed concept in molecular electronics so far is based on molecular ﬁlms between the cross-junctions of metallic wires, which can act as switches in memories or conﬁgurable diodes in logic circuits. In this scheme large memory cells and complex circuits have been experimentally demonstrated on the same chip in high density arrays. References [1] A. Aviram and M. A. Ratner, Chemical Physics Letters 29, 277 (1974). [2] C. Joachim, J. K. Gimzewski and A. Aviram, Nature 408, 541 (2000). [3] C. Joachim, Nanotechnology 13, R1 (2002); J. R. Heath and M. A. Ratner, Physics Today 56, 43 (2003). [4] M. Mayor, H. B. Weber and R. Waser, Nanoelectronics and Information Technology (Wiley-VCH, Weinheim), p. 501 (2003). [5] A. Nitzan, Annual Review of Physical Chemistry 52, 681 (2001); A. Nitzan and M. A. Ratner, Science 300, 1384 (2003). [6] X. D. Cui, A. Primak, X. Zarata, J. Tomfohr, O. F. Sankey, A. L. Moore, T. A. Moore, D. Gust, G. Harris and S. M. Lindsay, Science 294, 571 (2001). [7] M. B¨ uttiker, Y. Imry, R. Landauer and S. Pinhas, Physical Review B 31, 6207 (1985). [8] P. Sautet and C. Joachim, Physical Review B 38, 12 238 (1988); S. Ami and C. Joachim, Physical Review B 65, 155 419 (2002); S. Ami, M. Hliwa and C. Joachim, Chemical Physics Letters 367, 662 (2003). [9] V. Mujica, M. Kemp and M. A. Ratner, Journal of Chemical Physics 101, 6849 (1994); M. P. Samanta, W. Tian, S. Datta, J. I. Henderson and C. P. Kubiak, Physical Review B 53, R7626 (1996). [10] E. G. Emberly and G. Kirczenow, Physical Review B 60, 6028 (1999); 62, 10451 (2000).

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EXPLORING THE CATALYTIC ACTIVITY OF A NOBLE METAL: THE Ag CATALYZED ETHYLENE EPOXIDATION REACTION MARIE-LAURE BOCQUET Laboratoire de Chimie UMR 5182, Ecole Normale Sup´ erieure, Lyon, France [email protected]

ANGELOS MICHAELIDES Department of Chemistry, University of Cambridge Lensﬁeld Road, Cambridge, CB2 1EW, United Kingdom Abstract. In this chapter, we recount a recent success story in the quest for a molecular-level view of a large-scale catalytic process, namely ethylene (C2 H4 ) partial oxidation to ethylene epoxide (C2 H4 O). This selective oxidation reaction, which is catalyzed uniquely by silver, is more than sixty years old and one of the most widely studied in heterogeneous catalysis. What the microscopic mechanism of this reaction is, however, remains unclear, and why the noble metal Ag is the only metal that catalyses this process is also unknown. Traditionally, studies (and hence debates!) have centered on identifying the nature of the ‘active’ oxygen species, i.e. the one that actuates the catalysis and leads to the desired partial oxidation product. Here, we begin by describing density functional theory (DFT), scanning tunneling microscopy (STM) and STM simulation studies which have characterized the atomic level structures of O on the {111} surface of Ag. These studies have identiﬁed two types of stable phase of O on Ag: (i) Low coverage O adatom phases (θ ∼ 0.05 monolayers); and (ii) ultra-thin Agx O (x = 2) surface oxides. Following this, the relative stabilities of these overlayers are assessed at ﬁnite temperatures and pressures in order to link these ‘surface science’ ultrahigh-vacuum conclusions with the high pressure and high temperature realm of industrial catalysis. This is done through the application of thermodynamics (with a strategy now commonly referred to as “ab initio thermodynamics”) and leads to an ab initio surface phase diagram for O on Ag{111}. Next the reactivity of the phases predicted to be stable at, or close to, industrial epoxidation conditions is examined. This involves (i) a combined STM and DFT study of ethylene adsorption on 389

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one of the ultra-thin Agx O surface oxides; and (ii) a DFT study in which reaction pathways and transition states for the conversion of ethylene to ethylene epoxide have been determined. One of the key ﬁndings of the latter study is that whether on a surface oxide overlayer or on a surface with a low coverage of O adatoms, ethylene epoxidation is not a direct reaction. Instead it is a two-step non-concerted process, which proceeds via an oxametallacycle intermediate. Keywords: Atomic scale characterization; surface structure; epoxidation reaction; {111} cleaved silver; surface oxide; STM simulations; DFT slab calculations; ab initio phase diagram; free energy; non-stoichiometry; oxygen adatoms; site speciﬁcity; epoxidation mechanism; catalytic reactivity; oxametallacycle intermediate; transition state; catalytic cycle.

Contents 1 2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Theoretical Methods . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Oxygen Overlayers on Silver (111)-Cleaved Surface . . . . 2.2 Ethylene Adsorption on the Active Ag-Oxide Catalyst . . 2.3 Epoxidation Pathways . . . . . . . . . . . . . . . . . . . . 2.4 Reﬁning the Stoichiometry of the Ag-Oxide Overlayer Ag 3 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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390 394 396 404 408 413 421 422

1. Introduction It is hard to overstate the importance of molecule-solid interactions. They play a key role in many areas of science (heterogeneous catalysis, electrochemistry, corrosion etc.) as well as in many aspects of daily life. Understanding the ﬁne details of molecule–solid interactions, however, is not an easy task and requires experimentation and theoretical simulation at nanoscale dimensions. Over the last two decades this challenge has been met to some extent. Notably, the development of scanning probe techniques such as scanning tunneling microscopy (STM) now means that it is possible to ‘see’ individual atoms and molecules interacting with close-packed metal surfaces. For atomic adsorption, individual atoms are routinely identiﬁed and imaged. For molecular adsorption, however, the situation is not quite as clear-cut and experiments cannot systematically resolve the internal structure of adsorbed molecules, central to understanding the precise nature of an adsorbate overlayer. One feature of the present study is that it will show

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that by judiciously combining STM, STM simulations and density functional theory (DFT), the much sought after atomic resolution of molecular adsorption systems can readily be obtained [1]. Heterogeneous catalysis remains one of the key motivations for obtaining an atomic level understanding of molecular adsorption systems [2]. Traditionally, fundamental studies have been of the surface science type, i.e. performed on single crystal surfaces under ultra-high vacuum conditions. These studies have had a huge impact on our understanding of catalytic systems and have occasionally lead to improved catalysts (see for example Refs. [3–5]). However, recent in situ experiments and DFT calculations have indicated that the structure and chemical composition of catalytic metal surfaces may be signiﬁcantly diﬀerent under the high-pressure hightemperature conditions of industrial catalysis (see Refs. [6–8] for examples). On Ru and Pt catalysts, for example, it has been suggested that the active catalyst present under industrial conditions are metal oxides, not pure metals. Bridging these so-called “pressure and materials” gaps between catalysis and surface science is one of the grand challenges of research in this area. A second feature of the present study is that we will show how developments in theoretical methodology and improvements in computational performance allow much of the additional complexity of more realistic catalytic systems to be taken into account. The catalytic reaction discussed here is the partial oxidation of ethylene by Ag to yield ethylene epoxide (EO). This is one of the most important industrial catalytic reactions and is thus, of course, a multi-billion dollar worldwide process. United States production in 2000 was, for example, 4 billion kilograms [9]. One reason why so much EO is made stems from the fact that it is a small molecule containing two carbon atoms and an oxygen atom, all bonded to each other via single bonds, in a high-strain threemember ring conﬁguration (Scheme I). This particular structure allows easy addition of other organic functions to the epoxide unit, and hence EO O

1/2 O2

H H

(EO) Epoxidation

2 CO2 + 2 H2O

Combustion

H H

C

C

C2H4 Ag 3 O2

Scheme I. The two competing ethylene oxidation processes. The upper channel is the desired partial oxidation processes, whereas the lower channel leads to total oxidation (combustion).

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serves as a very useful chemical intermediate from which other materials (for example plastics, polyester, glycols) can be derived. Essentially the same catalyst for this process has been used for the last seventy years. It consists of silver particles dispersed on alumina (Al2 O3 ) [10]. When promoters are added to the feedstock, the selectivity of the ethylene oxidation reaction to the desired EO product can be ca. 80%. The ethylene that is not converted to EO is combusted to carbon dioxide and water (Scheme I). This represents an enormous waste of valuable feedstock. As with other catalytic processes, catalyst performance was traditionally optimized by trial and error methods. Indeed this approach has been very successful for the epoxidation process, leading directly to the current 80% levels of selectivity, from an original value of ca. 40%. However, this traditional trial and error approach is no longer paying dividends and, as with the rest of heterogeneous catalysis, it is hoped that fundamental understanding at the atomic level will provide the insight that will improve the performance of existing catalysts, or help to develop new ones. Because this is such an important reaction to the chemical industry an improvement in the selectivity by a mere 1% translates into savings of millions of dollars per annum. Ethylene epoxidation is not merely an important economic reaction. It is, in its own right, a fascinating reaction scientiﬁcally. For example, it is the simplest example of a kinetically controlled, selective heterogeneous catalytic reaction; complete combustion leading to CO2 and H2 O is the thermodynamically favored product of the reaction between ethylene and oxygen, yet kinetics dictates that EO is the majority product. Moreover, epoxidation is one of the very few reactions catalysed by a noble metal, Ag in this case. Indeed Ag is the only metal catalyst that oxidises ethylene with appreciable selectivity towards EO; other more active transition metals, such as Pd, Pt or Ni combust ethylene to yield almost exclusively total combustion products (CO2 and H2 O) [11]. However, why Ag is such a good catalyst for this reaction is still not known. One important reason why this question has not been answered yet is that it has not been possible to carry out the ethylene epoxidation reaction under ultra-high-vacuum (UHV) conditions. Under UHV conditions the reactant molecules simply desorb before the reaction barrier(s) inhibiting EO formation can be surmounted. Much of the actual debate in the literature about the epoxidation process has centered on identifying the nature of the active oxygen species, i.e. the one that actuates the catalysis. This has been, and remains, a controversial issue. The older part of the literature was mostly concerned with

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the question of whether molecular or atomic adsorbed oxygen is active for epoxidation. Chemisorbed dioxygen was ﬁrst proposed as the active species in the work of Kilty and Sachtler [12] and later by Campbell [13]. Studies by Grant and Lambert [14], however, provided evidence that atomic O was the active O species. It was shown that for both epoxidation and total combustion, the yield of adsorbed dioxygen from the substrate remained unchanged while a marked attenuation of desorption peaks related to atomic O were observed. Van Santen and de Groot lent strong support to the conclusion that atomic O was active by showing that partial oxidation could proceed in the absence of O2 [15]. Today, although occasionally asserted otherwise [16,17], a consensus has emerged that atomic oxygen and not diatomic O2 is the epoxidizing agent. The story remains complicated, however, as it has been suggested that diﬀerent types of atomic O exist with diﬀerent charge states and diﬀerent locations on the surface. For example nucleophilic O, electrophilic O, subsurface O and oxidic O species have all been proposed [18–20]. The theoretical work described here for O adsorption and ethylene epoxidation on Ag{111} has been carried out in conjunction with experiments performed in Dave King’s surface science group in Cambridge. In particular our studies rely heavily on low temperature STM experiments for O and ethylene adsorption on Ag{111} [21–23]. In the following we brieﬂy describe the theoretical methods employed and then present ﬁve subsections of results. In the ﬁrst subsection we describe how STM, STM image simulations and DFT have been used to characterize two types of adsorbed O phases on Ag{111}; namely a low coverage atomic O phase and a high coverage surface oxide phase. Following this we describe theoretical attempts to bridge the so-called pressure and material gaps which separate the ultrahigh vacuum world of surface science from the high pressure high temperature world of industrial heterogeneous catalysis. Based on these “ab initio thermodynamics” [6] calculations, a phase diagram in T-P space for O on Ag{111} is proposed. This phase diagram indicates that at the conditions typical of the industrial ethylene epoxidation process a non-stoichiometric surface-oxide phase is thermodynamically stable. With this in mind, in the third and fourth sub-sections, we then examine the reactivity of this surface oxide phase. Speciﬁcally, in part three we describe how STM and DFT have been used to identify the preferred adsorption site and binding mode for ethylene on the newly characterized surface oxide overlayer. And in part four detailed DFT studies of reaction mechanisms for the complete conversion of ethylene to ethylene epoxide are described. Possible

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reaction pathways have been identiﬁed on the characterized surface-oxide phase and for comparison on the low coverage atomic O phase on Ag{111}. An important conclusion is that ethylene epoxidation is not a direct reaction; rather it is a two-step non-concerted process, which proceeds via an oxametallacycle intermediate. In the ﬁnal subsection we describe interesting new developments that reveal that the surface-oxide overlayer is prone to further oxidation, readily accommodating atomic oxygen. This conclusion, which is consistent with in situ experiments, thus implicates a second type of atomic O, in addition to the oxidic oxygens of the surface-oxide in the ethylene epoxidation story. Before drawing some conclusions in the ﬁnal section we brieﬂy outline some avenues for future research in this area. 2. Theoretical Methods The strategy used to reach an accurate interpretation of the STM experimental results is to, whenever possible, perform DFT calculations on appropriate model adsorption systems and then to use the optimized DFT structures as input for subsequent STM image simulations [1]. We now brieﬂy describe the details of both of these types of calculation. DFT. DFT calculations were performed in periodic super-cells within the plane-wave pseudopotential formalism. Vanderbilt ultra-soft pseudopotentials [24] and the Perdew Wang ‘91 generalized gradient approximation were used [25]. Calculations were performed on three- or four-layer Ag slabs in a variety of supercells, ranging from small p(2 × 2) cells to quite large p(5×5) cells. Unless stated otherwise Monkhorst–Pack k-point meshes with 4 × 4 × 1, 3 × 3 × 1 and 2 × 2 × 1 k-point meshes were used for the p(2 × 2), p(3 × 3) and p(4 × 4)a unit cells. Calculations in the p(5 × 5) unit cell were performed with the Γ point. Two DFT codes, VASP [26,27] and CASTEP [28] were used. Most of the key structures reported here were calculated with both codes and there is good agreement between the results obtained with them. Transition states were identiﬁed with constrained minimization techniques and veriﬁed by the presence of a single imaginary mode from an additional vibrational frequency analysis [29,30]. STM simulations. STM image simulations were performed with the GREEN code [31,32]. The STM current is evaluated within a one-electron a Because of the relatively large size of the p(4 × 4) unit cell this k-point sampling was used merely to obtain energies based on structure optimizations performed with the Γ point.

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elastic scattering approximation after calculating the system’s Greens function by matching up to ﬁrst order the surface and the tip apex. The leads attached at each side of the STM interface are modeled as semi-inﬁnite bulk-like blocks. The entire system is described atom by atom as depicted in Scheme II, and we employ eﬃcient k-sampling schemes to approximate the inﬁnite lateral size of the system. The electronic structure is calculated by employing a parameterization scheme within the extended H¨ uckel theory (EHT) [33]. In particular, special care is taken with the choice of the EHT parameters at the surface sample. These are deduced by ﬁtting the EHT derived density of states, projected at the surface atoms, to those obtained from DFT. One of the strengths of the approach employed here is that we have freedom over the choice of the transition metal for the tip and also the structure of the tip employed. Usually we use Pt and W tips and represent the tip apex as a pyramid-like cluster epitaxed on a substrate that is orientated along some low Miller index crystal plane (for example, {111}, {110}, or {100} surface planes). Generally we ﬁnd that the structure of the tip has quite a big impact on the images obtained. Sharp tips, such as those constructed on Pt{100}, Pt{111} or W{100} surfaces tend to yield higher resolution images than those obtained with more ‘blunt’ tips (for example the {111} surface of (bcc) W as shown in Scheme II). However,

Z

W{111} Tip bulk

Tip apex Sample surface

Ag {111}

Sample bulk

Scheme II. Direct space representation of the STM interface. The junction is composed of two adjacent metallic blocks. Each block is divided into characteristic subparts that are stacked along the Z direction: Sample bulk, Sample surface, Tip apex and Tip bulk. For clarity, ethylene molecules are schematically drawn at the sample surface on an Agoxide overlayer. White, black, light and dark grey circles depict C, H, Ag and O atoms respectively. The tip is composed of a W{111} surface upon which a cluster of W is adsorbed to model the apex.

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Scheme III. Top view of a Pt{111} tip. The tip apex is represented by a tetrahedral Pt4 cluster adsorbed upon the Pt{111} surface. The shading changes from black to white as one moves away from the Pt atom of the apex into the underlying Pt surface.

we stress that although diﬀerent tip types and structures yield quantitative diﬀerences in calculated images, all the clean metallic tips considered yield qualitatively similar images. Only when the tips are poisoned (by, for example, an adsorbate such as CO [1]) are dramatic changes, such as inversion of the contrast, observed [34–36]. In the present study we display results obtained mostly with a tip constructed on top of a Pt{111} substrate, as represented in Scheme III. 2.1. Oxygen Overlayers on Silver (111)-Cleaved Surface High coverage surface-oxide phase. Figure 1(a) displays an experimental STM image for O on Ag{111}. For details of the experimental set-up and conditions used to obtain this image we refer the interested reader

Fig. 1. 4 K high resolution STM topographic images of O on Ag{111} prior to (a-b) and after (c) ethylene deposition. Experimental conditions: (a) V = 5 mV, I = 0.1 nA, W tip, corrugation = 0.6 ˚ A; (b) V = 1 V, I = 1 nA, W tip, corrugation = 0.4 ˚ A; (c) V = 60 mV, I = 1 nA, W tip, corrugation = 1 ˚ A. Copyright (a), (b) Ref. [22] and copyright (c) Ref. [23].

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to references [21] and [22]. Hexagonal arrays of bright bumps are clearly observed in the image and it is known that there is a (4 × 4) periodicity on this overlayer with respect to the underlying Ag{111} substrate. Throughout we shall refer to this overlayer as the high-coverage phase of O on Ag{111}. The image displayed in Fig. 1(a) is the ﬁrst STM observation of the infamous p(4 × 4) O overlayer on Ag{111}. This overlayer, which is stable in temperature programmed desorption (TPD) experiments to ca. 590 K, has become a characteristic of O on Ag{111} [37–40]. The microscopic structure of this reconstruction had, however, remained unclear. Originally the (4 × 4) pattern was interpreted in terms of the growth of a {111} orientated trilayer of Ag2 O epitaxed to the Ag{111} surface [37]. Various modiﬁcations of this original model were proposed [41]. Notably, however, they all assumed that the surface oxide reconstruction was a stoichiometric Ag2 O overlayer. Initial STM simulations, however, with simple unrelaxed Ag2 O trilayers adsorbed on top of the Ag{111} substrate call this assumption into question.b The key results are summarized in Fig. 2, which shows the structure and simulated image of an Ag2 O overlayer as well as the structure and STM image of a novel non-stoichiometric oxide overlayer.c Only the simulated image of the non-stoichiometric oxide overlayer yields satisfactory agreement with the experimental image (Fig. 1(a)). Furthermore, we can immediately see that the bright features, which dominate the STM image, are the metallic Ag ad-atoms that reside in the center of the Od -Ag-Ou oxide rings.d Some of these metallic adatom sites are indicated with a hexagon in Fig. 2 (bottom side). Since a single Ag adatom has been removed from the oxide overlayer the stoichiometry of the oxide overlayer is Ag1.8 O. The O coverage in this overlayer is 0.375 ML, which is somewhat lower than the existing experimental estimates (0.40 ± 0.02 ML [42] to 0.51 ± 0.04 ML [40,41]). We will show below that this apparent discrepancy should not be overlooked. Having proposed a model for the much debated (4×4) oxide reconstruction on Ag{111}, when it became computationally feasible to do so, it was then tested DFT. This allowed us to reﬁne the model and report the ﬁrst

b Rigid and bulk-derived structures were assumed since DFT calculations were not feasible at that time. c STM experiments in which the Ag{111} substrate and oxide overlayer were simultaneously imaged allowed us to identify the registry of the oxide overlayer with respect to the underlying substrate. See [21] for details. d Indexes on O atoms recall that the trilayer oxide is formed by two layers of O atoms, down (right above Ag substrate) and up (the outermost layer) sandwiching one Ag layer constituted by metallic and electrophilic Ag atoms.

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Fig. 2. Atomic structures (left) and associated STM topographic simulations (right) of stoichiometric (A) and silver-deﬁcient (B) silver-oxide overlayers on Ag{111}. The black and small light grey circles represent oxygen and silver atoms in the oxide ﬁlm. The large white circles represent Ag atoms belonging to the underlying {111} substrate. The diﬀerent types of Ag atoms in the oxide are labeled 1–6. Silvers labeled 1 and 2 are occasionally referred to as metallic; those labeled 3, 4, and 5 belong to the Ag-O-Ag rings and are occasionally referred to as oxide silvers. STM maximum contrasts (white regions) are exclusively located on the metallic Ag atoms (Ag-1 and Ag-2). STM conditions: V = 25 mV; I = 1 nA; corrugation (Top) = 0.7 ˚ A; corrugation (Bottom) = 0.6 ˚ A; size = 20 ˚ A × 20 ˚ A.

atomic level structure determination for the (4 × 4) oxide reconstruction. This is shown in Fig. 3 together with a comprehensive list of structural parameters obtained from VASP and CASTEP calculations. The nearest Ag-O distances of the oxide ﬁlm are close to those in the bulk oxide (2.04 ˚ A) and there is signiﬁcant buckling within the trilayer of about 0.45 ˚ A, as well as a 0.14 ˚ A rumpling of the underlying Ag{111} substrate. The STM simulation (not shown) performed on this optimized DFT structure is essentially undistinguishable from the one shown in Fig. 2 (bottom side) and thus in excellent agreement with the experimental STM image displayed in Fig. 1(a). Moreover, DFT calculations performed on the original (stoichiometric) Ag2 O oxide overlayer revealed that this overlayer was ca. 0.5 eV per (4 × 4) unit cell less stable than the non-stoichiometric Ag1.8 O overlayer. We shall return to this issue later and explain how this estimate had been made. Finally we note that, aside from the additional Ag adatom, the structures of the stoichiometric and non-stoichiometric Ag oxide overlayers are similar and the simulated STM image of the DFT optimized Ag2 O

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Fig. 3. Top (A) and side (B) views of the DFT structure of the p(4 × 4)-Ag1.83 O/ Ag{111}. Numbers 1–9 are given to representative Ag atoms, which are represented by light grey balls in the oxide overlayer and light grey sticks in the {111} substrate. Dark grey balls with u and d labels describe up and down oxygen atoms forming the O bilayer. The table on the right gives key structural parameters obtained with VASP and CASTEP.

oxide overlayer is similar to that shown in Fig. 2(a) and thus in very poor agreement with the experimental image. Low coverage atomic O phase [22,43]. Upon heating for several minutes (10–45 minutes) at 490 K the high coverage Ag-oxide phase decomposes into a second, novel phase of O (Fig. 1(b)). The O coverage estimated from the experimental STM images is 0.05 ± 0.02 ML. Not surprisingly we refer to this overlayer as the low coverage phase. In Fig. 1(b) it can be seen that the adsorbed O atoms image as depressions, ∼9 ˚ A in diameter (dark regions in the STM image). Adsorbed O atoms have before appeared with a negative contrast in STM [1]. For O on Ag{111}, however, it was suggested that these large depressions are an indication that O atoms are adsorbed beneath the top and second Ag layers at subsurface sites [22]. In order to resolve this issue and identify the nature of the O atoms in this low coverage phase we performed DFT calculations for O adsorption at the on-surface (fcc, hcp, bridge and atop) and subsurface (octahedral (Oh ) and tetrahedral (Td )) sites of Ag{111} at a wide coverage range (between 0.04 and 0.25 ML). This range straddles the reported experimental value of 0.05 ML and involved calculations in p(2 × 2), p(3 × 3), p(4 × 4) and p(5 × 5) unit cells. These calculations reveal that the most stable surface site is the fcc three-fold hollow site and that the most stable subsurface

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site is the Oh site. Of particular interest, DFT clearly indicates that in this whole coverage regime the on-surface fcc site is energetically preferred, by ca. 0.6 eV, to the subsurface Oh site. STM simulations were then performed on the optimized DFT geometries obtained for O at the fcc and Oh sites. These simulations fully support our assertion that the experimentally observed O atoms are indeed on-surface oxygens. The simulated images, at a coverage of 0.06 ML, are displayed in Fig. 4. The top side corresponds to O adsorption at the fcc site and the bottom side to O at Oh site. In Fig. 4 (the top side) large depressions, ∼8.3 ˚ A in diameter, are centered on the O atoms. This image qualitatively and semi-quantitatively resembles the observed STM depression of Fig. 1(b). The STM simulation for O at the subsurface Oh site, however, shows only a very small spatial modulation of the contrast with the absolute minima located over oxygen-free three-fold sites. Indeed the corrugation in this simulation is negligible (0.02 ˚ A), characteristic of metallic corrugation and exactly one order of magnitude less than the depth of the on-surface oxygen depression. From the combination of total energy

Fig. 4. Left: DFT structures of on-surface (top) and Oh subsurface (bottom) oxygen atoms (dark grey balls) on Ag{111} (light grey balls and sticks). Right: STM topographic simulations for each overlayer. Black crosses and circles mark the locations of Ag and O atoms. STM conditions: V = 100 mV, I = 1 nA. Corrugation: Osurf = 0.2 ˚ A, Osub = 0.02 ˚ A.

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and STM image calculations, we conclude, therefore, that O adsorption at low coverages on Ag{111} occurs at on-surface fcc sites and exhibits a large depression in STM which extends beyond the three-fold fcc adsorption site. The depression observed in the STM when O is adsorbed at the onsurface fcc sites is an electronic rather than a structural eﬀect. When O adsorbs on Ag{111}, charge is transferred from Ag toward O. At 0.06 ML a Mulliken analysis indicates that the charge on O at fcc sites is ∼ − 1.1 e. Most of this charge has come from the Ag surface atoms of the fcc site, and in the STM experiment it is this charge depletion associated with the Ag atoms that is observed; rather than the O atom itself. When O is adsorbed beneath the surface, charge is again transferred from Ag toward O (∼1.2 e.), however, this electronic eﬀect is compensated by considerable outward displacements of the top layer Ag atoms in the immediate vicinity of the subsurface O site. The three Ag atoms above the subsurface Oh site move 0.13 ˚ A above the other Ag atoms of the top Ag layer. This displacement of the Ag atoms towards the tip counteracts the depletion in electron density and yields greatly reduced variations in the density above the surface. Based on DFT calculations Scheﬄer and co-workers drew similar conclusions for atomic O adsorption at low coverages on Ag{111}. Interestingly, however, their DFT calculations revealed that at higher coverages of atomic O (> 0.5 ML), O atoms would adsorb preferentially at subsurface sites [44,45]. Extension to ﬁnite temperature and pressure; O/Ag{111} phase diagram [43]. The key issue which we aim to resolve now is the identiﬁcation of what phase, or phases, of O on Ag{111} are likely to be present under typical epoxidation conditions (10–20 at ∼550 K [10]). To do this we assess, as a function of temperature and pressure, the stability of the O adatom phases (0.04–0.25 ML) and the two Ag oxide phases identiﬁed above. This can be done equally by comparing the surface energies (γ) [46,47] or the Gibbs free energies of adsorption (∆G) of the phases considered. Here we opt for the latter because we are primarily interested in comparing the stability of structural overlayers that form upon the bare Ag surface, rather than on comparing the energies for the overall formation of these surfaces.e The Gibbs free energy of adsorption is: ∆G(T, P ) =

1 [G(O/Ag{111}) − G(Ag{111}) A − NO µO (T, P ) − NAg µAg (T, P )].

(1)

e In fact when normalized by the same surface area γ and ∆G are simply related by the surface energy of the clean Ag{111} surface.

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Here G(O/Ag{111}) denotes the total Gibbs free energy of our O or oxide covered Ag surfaces. G(Ag{111}) is the total energy of the clean four-layer Ag{111} slab. µO is the chemical potential of O, and NO is the number of O atoms in the 3D supercell. The ﬁnal (NAg µAg ) term only comes into play for the Ag oxide systems (not for atomic O adsorption), accounting for the additional Ag atoms present in the Ag oxide overlayers. For these two cases NAg is the number of (excess) Ag atoms in the Ag oxide overlayers, and µAg is the chemical potential of these Ag atoms. ∆G(T, P ) is normalized to energy per unit area by dividing through the surface area (A) of our slab. To maintain a thermodynamic equilibrium we deﬁne the chemical potential of the excess Ag atoms in the oxide overlayers by that of the bulk crystal and is thus simply our DFT computed total energy of a bulk Ag atom. The chemical potential of O is referenced to oxygen molecules in the gaseous phase for which we use the ideal gas equation.f With this approach we can now go beyond standard DFT calculations and investigate the temperature and pressure dependence of µO and thus the temperature and pressure inﬂuence on the stability of the various oxygen and oxide phases. However, in the present study we have neglected temperature and pressure eﬀects on the Gibbs free energy of all solid slabs, i.e., the Gibbs free energy G(Ag{111}) and G(O/Ag{111}) terms are approximated by their total energy at zero temperature. This approximation will certainly introduce an error in the precise location of phase boundaries [48]; however, it is largely justiﬁed because the corresponding corrections are small compared to the temperature and pressure dependence of the vapor contribution (which we include explicitly) [6,49]. Figure 5(left) shows the Gibbs energy of adsorption as a function of temperature at a typical UHV pressure (10−12 atm.). This ﬁgure reveals several important pieces of information. First, the silver deﬁcient Ag1.8 O oxide is more stable than the stoichiometric Ag2 O oxide. Since both oxide phases contain the same number of O atoms, their relative stability is independent of temperature and pressure, with the silver deﬁcient Ag1.8 O oxide favored by 0.74 and 0.46 eV per (4 × 4) oxide unit cell with CASTEP and VASP, respectively. Thus, as mentioned earlier, there is a clear preference for nonstoichiometric Ag1.8 O growth on Ag{111}. The reason for this preference is that in the ‘ideal’ Ag2 O overlayer an additional Ag atom would have f It is well known that the ideal gas equation suﬀers deﬁciencies at low temperatures and high pressures. Fortunately under the conditions we are primarily interested in (high temperatures and moderate pressures) it is a well-behaved approximation.

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Fig. 5. Left: ∆G/Area plot of trial oxide and O adlayers as a function of temperature T at PO2 = 10−12 atm; a pressure characteristic of UHV experiments. Right: an ab initio phase diagram displaying stability regions (minimum values of ∆G/Area) as a function of T and PO2 . Characteristic ‘Industry’ and ‘UHV’ pressures are indicated.

to sit at an unfavorable atop site of the underlying Ag{111} substrate.g The other important information contained within Fig. 5(left) is that it reveals which of the phases considered is the most stable at a given temperature. Indeed, at the pressure in question, three distinct phases are stable: (i) At low temperatures, up to 360 K, the Ag1.8 O phase is the most stable; (ii) over the very short range between 360 K and 370 K the 0.06 ML O adatom phase is stable; and (iii) above 370 K the clean Ag{111} surface becomes thermodynamically stable. In Fig. 5(left) we have displayed the temperature dependence of all the considered phases at a single pressure. Of more interest, however, is to identify what phases are stable over the whole range of experimentally accessible temperatures and pressures. This information is contained within Fig. 5(right), which reveals the most stable phase (of those considered) of O on Ag{111} from 1 × 10−15 atm. to 100 atm. and from 200 to 700 K. This ab initio phase diagram reveals that the only stable phases in the temperature and pressure regime investigated are the Ag1.8 O oxide, the 0.06 ML O adatom and the clean Ag{111} surface. At no stage does the lower coverage (0.04 ML) phase or any of the higher coverage O adatom (0.11 and 0.25 ML) phases become stable. The key insight, which can be gleaned from this ﬁgure, is that in the range of pressures and temperatures g ‘Non-ideal’ Ag O overlayers with the additional Ag adatom adsorbed at other sites on 2 the surface have not been investigated.

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at which industrial ethylene epoxidation is conducted the Ag1.8 O oxide phase is thermodynamically the most stable. Indeed Figs. 5(left) and 5(right) point to a crucial pressure and materials gap for Ag oxidation catalysis: on raising the pressure, at a temperature of 550 K, from UHV to industrial pressures the thermodynamically stable state of the Ag substrate is predicted to change from bare Ag{111} to Ag1.8 O oxide. Figure 5(right) is also in satisfactory agreement with the experiments of Carlisle et al. recalled above, in which oxide decomposition was probed with the STM. It was recalled above that when the oxide overlayer (high coverage phase) was heated slowly at 490 K (10–45 minutes) in vacuo it began to decompose into the low coverage (0.05 ML) O adatom phase. Although we have not attempted to model the precise two-phase system encountered experimentally it is clear that our phase diagram predicts the same qualitative behavior. Considering ﬁnally the oxide decomposition temperatures of 490 K upon slow heating and ca. 590 K with rapid heating, as conducted in a TPD experiment. The implication from our calculations is that, for these processes, kinetic barriers exist that inhibit oxide decomposition until suitably high surface temperatures are achieved. However, it is important to recognize that this apparent discrepancy may also be, in part, a result of some error in the precise values of our determined phase transitions. Indeed, because the O2 dissociative adsorption on Ag is only mildly exothermic [43,44] small variations in the relative adsorption energies of the diﬀerent overlayers can have a considerable impact on the details of the obtained phase diagram [45,48].

2.2. Ethylene Adsorption on the Active Ag-Oxide Catalyst [50] Having identiﬁed the Ag-oxide reconstructed Ag{111} surface as the best candidate for the Ag surface under industrial epoxidation conditions, the reactivity of this overlayer was further investigated. This began with STM experiments for ethylene adsorption on the high-coverage oxide phase. A typical image for ethylene adsorption on the (4 × 4) oxide overlayer is shown in Fig. 1(c). Each large bright feature (two in the image) corresponds to an ethylene molecule adsorbed on the oxide overlayer. The molecular protrusion is 0.5 to 1.0 ˚ A higher than the honeycomb oxide and shows pronounced elongation perpendicular to the hexagon perimeter of the oxide ring. Because in this image the ethylene molecules and the Agoxide overlayer are simultaneously imaged, it is possible to determine the location of the ethylene molecules on the surface. According to the site

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labels assigned in Fig. 2(a) for the Agx O oxide overlayers on Ag{111}, the ethylene molecules are adsorbed above “Ag-3” sites. These are the least coordinated Ag sites on the surface. They reside within the O-Ag-O oxide rings and are located directly above Ag atoms of the Ag{111}substrate. From Fig. 2(b) one can see that these sites are located directly between the isolated Ag adatoms (Ag-1 and Ag-2), which give rise to the bright features in the STM image. Although the binding site for ethylene can be identiﬁed with STM, the resolution of this STM image is not suﬃcient to enable a determination of the orientation or binding mode of the molecule. For this information we turn to DFT and STM simulations. For completeness ethylene adsorption has been examined at all distinct types of Ag site on the oxide and not just the experimental (Ag-3) site. Thus adsorption at sites Ag-1, Ag-3 and Ag-5 sites was considered, as shown in Fig. 6. In addition, ethylene adsorption above one of the upper oxygen atoms (Ou ) in the oxide overlayer was considered. Sites Ag-2 and Ag-4 were not considered as these only diﬀer from sites Ag-1 and Ag-5, respectively with regard to the second topmost Ag{111} layer. Unexpectedly, DFT calculations identify two stable adsorption sites on the oxide overlayer: the experimental, Ag-3 site, and also the Ag-1 adatom sites. The ethylene binding energy at both sites is about 0.3–0.4 eV. Intriguingly, there is a strong orientational dependence of the binding energy at the experimental Ag-3 site: when the C-C plane is aligned with the O-Ag-O bond, the binding

Fig. 6. Optimized DFT structures of ethylene adsorbed on four diﬀerent sites of the surface Ag1.83 O oxide. Light grey balls and sticks represent Ag atoms. O and C atoms are represented by dark grey and black balls, respectively. On one speciﬁc site, Ag-3, two orientations of ethylene relative to the Ag-O linkage (3 and 3 ) are compared.

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M.-L. Bocquet & A. Michaelides Table 1. Adsorption energy and interaction distances for ethylene adsorbed on diﬀerent oxide atomic sites. dC-oxide corresponds to the closest distance between the adsorbate and the oxide substrate, namely between one C atom of the ethylene and a Ag or Ou atom of the substrate. Site label

Ag-1

Ag-3

Ag-3

Ag-5

Ou

Eads [eV] dC-oxide [˚ A]

0.30 2.7

0.38 2.3

0.07 2.9

0.07 3.2

0.07 3.8

energy is 0.4 eV (labeled Ag-3 ). When the C-C plane is rotated by 90◦ about the surface normal the binding energy is only 0.07 eV (labeled Ag3 ). Such a strong orientational dependence is not observed at any of the other adsorption sites examined. Adsorption energies (Eads ) and bond lengths for ethylene are reported in Table 1.h Starting with the strongest adsorption, the adsorption energy for all considered models decreases in the following order: Ag-3 > Ag-1 > Ag − 3 = Ag − 5 = Ou . Three adsorption sites are essentially non-bonding or weakly physisorbed, as their structural data show no molecular distortion in comparison with gas phase ethylene and bonding distances in the physisorption range (above 3 ˚ A). Flexible oxide substrate. Closer inspection of the optimized structures for all models shows that the preferred conﬁguration (Ag-3 ) results from a local but substantial deformation of the oxide registry. This deformation is not observed when ethylene is adsorbed in the perpendicular orientation at this site (Ag-3 ), or when ethylene is adsorbed at any of the other Ag sites. On the clean oxide surface the Ag-3 atoms are at an intermediate height, located between the high lying (Ou ) and a low lying (Od ) oxygen planes. When ethylene adsorbs the surface reconstructs considerably: the Ag-3 atom is displaced outward by 0.8 ˚ A to maximize its interaction with the adsorbate. In a concerted action, the upward oxygen atom moves down toward the low-lying oxygen plane. The O-Ag-O angle, initially almost 180◦ , is thus decreased to 89◦ after adsorption (as pictured in Fig. 7). In this way, the surface is strongly reconstructed, at a moderate energy cost, to optimize molecular adsorption. An analysis of the electronic structure at the favored (Ag-3) adsorption site has been performed in order h It should be mentioned that a slightly less accurate DFT set up has been used for the calculations in this section compared to Sec. 1. Here only 3 Ag slabs have been considered instead of 4 and k-point sampling restricted to the Γ point.

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Fig. 7. Structures (left), schematic linkages (center), and schematic orbital diagrams (right) for ethylene adsorption at the Ag-5 (top) and Ag-3 (bottom) adsorption sites.

to understand this large deformation. An in-depth discussion can be found in [50]. The essential conclusion, as depicted on the right of Fig. 7, is that there is a bonding interaction between the vacant π ∗ orbitals of ethylene and occupied Ag(d)-O(p) hybrid orbitals of the substrate. To summarize, our DFT calculations show that the experimental result corresponds to a speciﬁc orientation of ethylene on the oxide overlayer. The adsorption energy at this site is signiﬁcantly greater than the ethylene adsorption energy on clean Ag{111}.i This, coupled with a non-negligible increase in the C-C bond length and some degree of sp3 hybridization in the adsorbed ethylene, indicates that the molecule is ‘activated’, to some extent, for subsequent surface reactions such as epoxidation. Finally at this stage we point out several important issues that remain to be resolved. In particular, existing STM data indicates that ethylene adsorbs exclusively at Ag-3 sites. As shown above DFT, however, indicates that ethylene should also adsorb at Ag-1 sites in addition to the Ag-3 sites. This apparent discrepancy is as yet unresolved. In addition the contrast of the ethylene molecule in the simulated STM images (not shown) is severely overestimated (by about a factor of two). See [50] for a brief discussion on this later issue. i We

have computed a binding energy of 0.04 eV for C2 H4 /Ag{111} at 1/9 ML [51].

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2.3. Epoxidation Pathways [52] Catalytic cycle on the oxide covered Ag substrate. Having characterized the ﬁrst step towards reactivity, namely the adsorption step on the thin Ag oxide, the next step is to examine how the adsorbed ethylene would react and transform into the ethylene epoxide. The key point is to identify the elementary step(s) that transform ethylene into EO. In particular it is necessary to resolve if this proceeds in a single step as a concerted process or in two steps as a non-concerted process via an intermediate molecule. We have addressed this issue with DFT and the identiﬁcation of a stable oxametallacycle (OMME) intermediate strongly suggests that this is a twostep process. The OMME intermediate is displayed on the left hand side of Fig. 8. It is named thus because the organic molecule forms a ring with surface atoms, Ag and O. Our surface OMME is similar to that characterized by Barteau and co-workers [53] on clean Ag{111} with the aid of high resolution electron energy loss spectroscopy (HREELS) and DFT based cluster calculations. Crucially it was shown that the OMME intermediate is a precursor to EO formation [54].

Fig. 8. Schematic illustrations (top panel) and real space structure (lower panel) of the oxametallacycle (OMME) intermediate and a weakly adsorbed ethylene epoxide (EO) molecule on the (4 × 4)-oxide overlayer on Ag{111}. Color codes are the same as Fig. 6. Additional small black circles are added in the ball structures to help correspondence with the schemes above. As revealed by the additional Newman projection, the most favorable structure for the OMME intermediate is when all the C substituents are staggered. Certain optimized DFT distances are given in ¨ angstroms [˚ A].

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Also shown in Fig. 8 is the adsorbed EO that is weakly bound on the (reduced) oxide ﬁlm. It can be seen that once a single O is removed from the reference oxide to create the EO, the three Ag atoms of the oxide overlayer, which had previously surrounded the extracted O, move to produce a triangle of chemisorbed Ag atoms as schematically drawn in Fig. 8. Hence on the surface, the cleavage of Ag-O bonds is compensated by the strengthening of Ag-Ag bonds and represents a transition from a local oxide to a local metal environment. The partial oxidation reaction, C2 H4 + 1/2O2 → C2 H4 O, is exothermic in the gas phase by 117 kJ/mol (Standard heat of reaction) and so, the conversion is merely inhibited by kinetics. We aim to determine with DFT accurate values for the kinetic barriers to the formation of ethylene epoxide. We use the same thickness of Ag slab (3 layers) as with the preliminary adsorption step. The energetic proﬁle for epoxidation on the high coverage Ag1.8 O oxide surface is displayed in Fig. 9. A moderate ethylene adsorption precursor is ﬁrst seen. This state has been characterized in the previous section (see Fig. 7) and shows ethylene symmetrically adsorbed above an Ag of the oxide ring. The barrier to produce the OMME from this state is 0.74 eV (0.46 eV relative to the initial C2 H4 gas phase state). At the transition state a C-O bond has been created through a lateral shift of ethylene towards an adjacent oxygen in the underlying oxide. The structure of the OMME product of this step is 0.15 eV more stable than the initial state (with C2 H4 in the gas phase). In the next step the second C-O bond is formed to produce an epoxide with a barrier of 0.74 eV. The epoxide binds weakly to the oxygen deﬁcient oxide (0.09 eV), above a triangle of Ag atoms as described above. Reaction mechanisms with ethylene adsorbed at the second type of ethylene adsorption site identiﬁed (Ag-1/2) were also investigated. However after several unsuccessful attempts to identify a stable oxametallacycle associated with this ethylene adsorption site we concluded that ethylene was not reactive at this site. This is to be anticipated given that the ethylene molecule is a considerable distance from the O atoms in the oxide ring (around 4 ˚ A). In order to mimic an entire catalytic cycle, a second O was removed from the oxide overlayer (equivalent to performing a second epoxidation cycle) and O2 dissociation was examined on this doubly reduced oxide overlayer. The most favorable dissociation route identiﬁed, with a barrier of 0.40 eV, proceeds through the transition state labeled (d) in Fig. 9, and involves O2 initially adsorbed parallel to the surface.

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Fig. 9. Relative energy diagram for the conversion of gas phase C2 H4 to epoxide on the high coverage Ag11 O6 (Ag1.83 O) surface oxide on Ag{111}. Energies shown in eV refer to the diﬀerences between adjacent equilibrium states, or between adjacent equilibrium and transition states. On the right side of the vertical dashed line, O2 dissociative adsorption on O-deﬁcient Ag11 O4 (Ag2.75 O) oxide is displayed. The panels (a)–(d) correspond to top views of the intermediate states labeled (a)–(d): (a) transition state of step 1, (b) OMME, (c) transition state of step 2, (d) transition state of the regeneration step i.e. O2 dissociation on the doubly reduced oxide. (O black circled grey, C small grey, Ag light grey, ∗ transition state). Note that the color codes are diﬀer from those used the previous ﬁgures. Copyright from [52].

At this stage it is worth pausing to consider the structure of the reduced oxide overlayer. Several trial structures with one (Ag2.2 O) and two (Ag2.75 O) oxygen atoms removed have been tested. Within the accuracy of our calculations, it costs the same energy (∼0.8 eV to yield 1/2O2 ) to remove a high-lying O (Ou ) or a low lying O (Od ) from the initial oxide overlayer. Following the removal of the ﬁrst O, a second O was then removed from the Ag oxide overlayer to produce an oxide with a stoichiometry of Ag2.75 O. Speciﬁcally, three non-equivalent systems with two O atoms

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removed have been calculated. It is found that the most stable of these three doubly reduced oxide systems is the arrangement in which a pair of adjacent O atoms is removed. It costs ∼1 eV to remove the second O atom after the ﬁrst is removed. In addition there is a greater tendency (∼0.2 eV preference) to remove a pair of O atoms that are adjacent to each other as opposed to any pair of O atoms that are next nearest neighbors or even further apart. The structure of the most stable doubly reduced Ag2.75 O oxide overlayer can be inferred from Fig. 9 (lower panel d). This structure is very interesting and it reveals that two Ag triangles matching the underlying Ag{111} have been formed. These triangular structures appear every time an O is removed and resemble, albeit on a much smaller scale, the islands observed by STM that form upon oxide decomposition [22]. The formation of a single “metallic” island by the removal of two adjacent O atoms, is favored over the formation of two separated Ag-3 triangles, because it allows an easier relaxation of these Ag atoms, with less induced surface strain upon local reduction. In conclusion we ﬁnd that epoxidation occurs through a two-step process via an OMME intermediate. On this Ag-oxide catalyst, the two steps have similar barriers, which are higher than the regenerating step of the catalyst. Since this catalyst structure only displays one kind of active oxygen atom, and bearing in mind that our phase diagram showed that the temperature and pressure boundary with the low coverage O adatom phase was close to the active high coverage phase, we also determined the energy proﬁle on the O adatom phase for the sake of comparison. Catalytic cycle on the low coverage O/Ag overlayer. As shown in Fig. 10, epoxidation on this O overlayer occurs through a similar two-step process via an OMME intermediate. The barrier for the ﬁrst step, which proceeds through an Eley-Rideal type mechanism, is reduced to 0.32 eV. This produces a chemisorbed OMME, which is 0.47 eV more stable than the initial state of chemisorbed O and gas phase ethylene. In this OMME intermediate, O is at a bridge site and the O-C-C backbone sits across a three-fold site with one of the carbons bonding directly to the surface. This OMME structure is similar to that predicted by previous cluster calculations [55]. A barrier of 0.92 eV was then identiﬁed for OMME ring closure to produce a weakly adsorbed ethylene epoxide (0.09 eV). In order to determine the energetics of the entire catalytic cycle, the dissociation of O2 on clean Ag{111} was also examined as the last regeneration step. A barrier of

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Fig. 10. Relative energy diagram for the conversion of gas phase ethylene into ethylene epoxide (C2 H4 O) via an oxametallacycle (OMME) intermediate on the low coverage atomic O phase on Ag{111}. States to the right-hand side of the vertical dashed line do not contain epoxide molecules and are simply related to O2 dissociative adsorption on clean Ag{111}. (Same color codes as Fig. 9.) Copyright from [52].

0.64 eV, relative to a weakly adsorbed O2 precursor state (Eads = 0.17 eV), has been determined for this process. Overall we see that on the two surfaces examined the epoxidation mechanisms are reasonably similar, both in terms of structures and energies. On both catalysts it is the ring closure of the OMME intermediate, which is the most highly activated step of the cycle (with a barrier of 0.74 eV on the oxide and 0.92 eV on the O adatom phase). This lower barrier to OMME ring closure on the oxide surface is readily explained by the reduced stability of the OMME intermediate on this surface. Other diﬀerences between the two substrates arise in the OMME formation step (1st step) and the catalyst regeneration step (O2 dissociation). Ethylene is ﬁrst trapped into a chemisorption state (an electrophilic Ag atom) before reacting on the oxide (high coverage phase), whereas on the O adatom phase (low coverage phase) it reacts directly from the gas phase. Finally, O2 dissociation is favored on the reduced oxide surface (Ag11 O4 in Fig. 2), with a barrier of 0.40 eV as opposed to 0.64 eV on clean Ag{111}. Given that the reduced Ag11 O4 oxide surface is unstable compared to the equilibrium Ag1.8 O oxide overlayer, a low barrier to O2 dissociation on this surface is to be anticipated.

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In conclusion we ﬁnd that on both catalysts’ epoxidation proceeds similarly via a non-concerted process. Concerted mechanisms in which O adds across the C=C bond, directly producing epoxide, have been ruled out. In both pathways a C-Ag bond is formed and further broken. The key implications are that both surfaces are active for epoxidation. This partial oxidation reaction is hence shown to take place over a wide O coverage regime characterizing two types of oxygen species. 2.4. Reﬁning the Stoichiometry of the Ag-Oxide Overlayer Ag [56] The reaction pathways just considered yielded reduced Ag-oxide overlayers, which we have shown can be readily oxidized to reform the reference Ag1.8 O oxide overlayer. Further oxidation of the oxide overlayer, which may also be crucial to its performance as an oxidation catalyst [57,58] has not yet been considered. Or, in other words, the question of the absolute stability of the reference oxide as a function of small variations of O coverage remains unanswered at this stage. The previous phase diagram (Fig. 5) does not explicitly consider the O concentration in the oxide overlayer. Since O adatoms image with a negative contrast, it is plausible that additional O atoms could be located within the large dark regions encircled by the honeycomb STM pattern. A further reason for addressing this issue is the fact that the proposed model appears to underestimate the oxygen coverage. As mentioned already the O coverage in the (4 × 4) oxide overlayer model is 0.375 ML, whilst experimental estimates of the O coverage in the (4 × 4) oxide are in the 0.4–0.5 ML range [40–42]. In this ﬁnal section, we investigate this issue, primarily with DFT, by determining structures and energies for the initial stages in the oxidation of this oxide model. In addition, by also utilizing thermodynamics and STM image simulations, we aim to improve the atomic level understanding of the Ag oxide overlayer at ﬁnite temperatures and pressures. Inventory of oxidized structures. The reference oxide overlayer is shown again in Fig. 11. It contains three hexagonal Ag-O-Ag rings per (4 × 4) unit cell. Two of the oxide rings contain an additional chemisorbed Ag adatom, whilst in the third (center of the unit cell) there is no such Ag adatom. Throughout this section we shall call the oxide rings that contain Ag adatoms ‘ﬁlled’ rings, and the oxide rings that do not contain additional Ag adatoms ‘vacant’ rings. Oxidation of the reference Ag1.83 O oxide was examined by adding chemisorbed O atoms to the system. Chemisorbed O atoms were added

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1

3 2

ACF BDE

5 4

6

B Fig. 11. Inventory of 12 available three-fold sites (stars) with respect to the underlying {111} substrate. The p(4 × 4) unit cell is recalled by the black solid parallelogram. In the vacant (Ag-free) ring, 6 positions A-E are available. The two other ﬁlled oxide rings, i.e. those that contain Ag adatoms, each have three similar adsorption sites.

to three-fold hollow sites. In each (4 × 4) unit cell there are a total of twelve threefold adsorption sites. There are three fcc and three hcp sites (indicated by the capital letters A to E in Fig. 11) inside the vacant oxide ring. There are three further hcp sites inside one of the ﬁlled oxide rings (labeled 1–3) and a further three fcc sites inside the second ﬁlled oxide ring (labeled 4–6). It should not be overlooked, however, that the six three-fold sites in the two ﬁlled oxide rings are all in the vicinity of chemisorbed Ag adatoms and are thus are not strictly three-fold symmetric. Addition of the ﬁrst oxygen atom was considered at 4 representative and non-equivalent adsorption sites: an fcc (site A) and an hcp (site E) site inside a vacant oxide ring; and an fcc (site 5) and an hcp (site 3) site inside a ﬁlled ring. It is found that O binds with a similar energy, to within ∼0.1 eV, at all four adsorption sites, and decreases on going from 5 > A > 3 > E. This indicates that small preferences exist for adsorption at fcc sites over hcp sites, and in ﬁlled rings over vacant rings. Thus we conclude that addition of the ﬁrst oxygen atom is not selective thermodynamically, and it does not have any strong energetic preference for adsorption in ﬁlled over vacant oxide rings. Adsorption in ﬁlled oxide rings is, however, accompanied by a large displacement of the chemisorbed Ag adatom. It is plausible therefore that adsorption in the ‘vacant’ rings (site A for example) where no such reconstruction is required may be kinetically favored. Indeed the inclusion of a chemisorbed O atom inside a vacant oxide ring has a negligible eﬀect on the structure of the initial Ag1.83 O oxide. The O adsorption energy at

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site A is −0.5 eV again with respect to the formation of 1/2 O2 .j We ﬁnd that, using an identical level of theory, this is 0.2 eV less than the O adsorption energy on clean Ag{111}. A consideration of the structure reveals that this is likely because the chemisorbed O is bonding with a surface Ag atom that is already interacting with oxygens in the oxide overlayer. For the adsorption of two oxygen atoms on the reference Ag1.83 O oxide, a number of combinations mixing the 12 three-fold sites are possible. Several possibilities have been considered. Let us consider them. First we consider adding two oxygen atoms to the same oxide ring. By placing an O atom at site A and a second O at site E, we ﬁnd however that there is a strong repulsion between the O atoms. Since the O adsorption properties inside vacant and ﬁlled rings are similar it is anticipated that an equally large repulsion will characterize the adsorption of two O atoms in the ﬁlled oxide rings. Strong repulsion between O atoms adsorbed in the same oxide rings is important because it establishes that if a second O is to be added to the unit cell then it is more likely to adsorb in a diﬀerent oxide ring from the ﬁrst O. If we consider arrangements of the two extra oxygens with these oxygens inside diﬀerent oxide rings, we ﬁnd that either both oxygens can adsorb in two ﬁlled oxide rings, or one can adsorb in a vacant ring and the other in a ﬁlled ring. We ﬁnd that the latter arrangement, especially when O atoms are at site A and site 1, is the most stable conﬁguration. The structure of this overlayer is shown in Fig. 13. The average adsorption energy for these two additional O atoms is ∼−0.5 eV. Noteworthy is that the stability of the various arrangements is correlated with a decrease in the nearest distance between the pair of chemisorbed O atoms. Since we know that two O atoms do not like to adsorb in the same oxide ring, adding a third oxygen atom supposes that all three oxide rings per unit cell contain a single additional chemisorbed O atom. Three alternative arrangements of the three chemisorbed O atoms were considered. We ﬁnd that the arrangement A-1-5 (Fig. 12) is clearly favored, again with an average binding energy of the three O atoms of −0.5 eV. Further oxidation of the Ag1.83 O oxide overlayer, i.e. addition of a fourth O atom to the unit cell, has ﬁnally been examined. Since there are three

j The adsorption energy (E ads ) per O atom on the Ag1.83 O oxide is calculated from: Eads = O + Ag1.83 O/Ag − Ag1.83 O/Ag − 1/2 O2(g) ; where O + Ag1.83 O/Ag and Ag1.83 O/Ag are the total energies of the Ag1.83 O oxide overlayer with and without the chemisorbed O atom, and O2 is the total energy of a gas phase O2 molecule.

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Fig. 12. O abstraction energy for each of the (4 × 4) oxide overlayers investigated. The O abstraction energy is the energy required to remove a given O atom from an oxide overlayer of a given stoichiometry in order to form 1/2 O2 . This energy is similar to a binding energy and precisely equal to the total energy of a given oxide ﬁlm deﬁned by n O atoms minus the total energy of the most stable oxide overlayer with n − 1 O atoms minus the total energy of O2 . Negative values correspond to favorable oxidation processes. Consequently, oxidation is favorable up to 9 O atoms in the unit cell. The additional O atoms are labeled according to Fig. 11. Similarly O atoms are removed from the reference Ag1.8 O oxide and labeled as follows: (a) corresponds to an Ou atom of the central oxide ring; (b), (c) and (d) to O atoms at ortho, and meta positions relative to (a).

oxide rings per unit cell, adding four oxygen atoms almost certainly requires that at least two O atoms must be added to at least one of the oxide rings. Since it was established above that two O atoms do not like to adsorb in the same oxide ring, structures with four extra O atoms become highly unstable (∼ +0.4 eV for the binding energy of the 10th O). This result is important because it indicates that with the addition of three additional chemisorbed O atoms, equivalent to the addition of 0.19 ML O atoms, the Ag1.83 O oxide overlayer becomes saturated to the addition of chemisorbed O atoms. Obviously it is always possible that further oxidation takes place by some other mechanism, for example oxide growth facilitated by penetration of O atoms into the bulk [44]. However, alternative mechanisms for oxidation are beyond the scope of the present study and have not been investigated yet.

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The relative energetics of all the investigated oxidized and reduced structures from the above sections are summarized in Fig. 12. Speciﬁcally in Fig. 12 the ‘O abstraction energy’ of certain O atoms in all the overlayers investigated are represented and compared. For example, Fig. 12 recalls that the energy required to remove O(a) from the Ag1.83 O overlayer (six oxygen atoms per cell) is ∼0.8 eV. It is clear that the oxygen abstraction energy reaches a plateau around −0.5 eV for the successive ﬁlling of available oxide rings starting from the reference oxide. This is consistent with an energetic equivalence of the O adsorption energy inside all three oxide rings in a cell. Further, the abstraction energy of the tenth O in the cell is positive, again demonstrating the onset of saturation of the Ag1.83 O oxide overlayer at the point when all three rings contain a chemisorbed O atom (Ag1.22 O). As stressed above this strong repulsion is attributed to the fact that in this conﬁguration the chemisorbed oxygen atoms must share bonding with the same Ag substrate atom. The solid line in Fig. 12 marks a possible sequential atomic mechanism when oxidizing a reduced Ag2.75 O structure. STM simulations: uncertainty of the oxide model. Having determined structures for possible oxidized Ag oxide overlayers on Ag{111}, we then performed STM image simulations on the most stable structures at each stoichiometry. The results of the simulations are shown in Fig. 13 alongside the structure of each oxide overlayer. One clear ﬁnding is that a second Ag oxide overlayer, in addition to the reference Ag1.83 O oxide, is identiﬁed that exhibits the same characteristic honeycomb image observed experimentally. This is the Ag1.83 O oxide with a single additional O adsorbed inside each vacant Ag-O-Ag ring (i.e. Ag1.57 O with O at site A). In addition the simulated images for the Ag1.83 O and Ag1.57 O oxide systems are essentially indistinguishable. As anticipated before, this is clearly related to the fact that the Ag adatoms in the ﬁlled rings, which are responsible for the STM contrast, are not signiﬁcantly perturbed by the additional O adsorbate. It is also seen from Fig. 13, however, that all the images associated with oxygen rich oxide overlayers (Ag1.37 O to Ag1.1 O) are reasonably similar to the reference honeycomb image (Ag1.8 O and Ag1.57 O). The image associated with Ag1.37 O (“A-1”) exhibits a reduced three-fold symmetry since half the metallic Ag adatoms are displaced outward by the presence of the extra oxygen atoms. Equivalent maximum current values are recovered for Ag1.2 O (“A-1-5”) where all the Ag adatoms are now aﬀected. This image is however slightly distorted with respect to the reference Ag1.83 O case. As would be expected there is no visible diﬀerence

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Fig. 13. Structures (left) and STM simulations (right) for oxide overlayers with diﬀerent stoichiometry on Ag{111}. The O coverage in each overlayer is given on the far left and the stoichiometry on the far right. Oxygen (silver) atoms appear as dark grey (light grey) balls. The black squares on the right depict the location of Ag adatoms responsible for the bright features in the STM simulations. The extra O atoms, which are in excess of those in the reference Ag1.8 O oxide (top), are circled in black.

between the image Ag1.2 O and Ag1.1 O since the only diﬀerence in their structures is the presence of a single O in the dark region of STM contrast. To conclude, the simulations indicate that it should not be possible for the STM to distinguish between the Ag1.8 O oxide and a singly oxidized version of it (Ag1.57 O). Or put another way, O adatoms adsorbed inside the vacant Ag oxide rings should be invisible to the STM. Given that the simulated

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STM images for structures with more O adatoms are also reasonably similar, it is plausible that the Ag oxide overlayer that forms on Ag{111} could well be Ag1.83 O or one of the higher coverage oxide overlayers. Indeed the higher coverage oxides display O coverages of 0.43 ML (Ag1.57 O), 0.5 ML (Ag1.37 O) and 0.56 ML (Ag1.2 O), which are in closer agreement with the reported experimental range (0.40 [42] to 0.51 [40,41] ML) for the (4 × 4) Ag oxide overlayer. On this basis, Raukema et al. [42] already suggested the presence of excess randomly absorbed oxygen prior to oxide growth. Our DFT calculations and STM image simulations support this proposal and provide clear information on the possible location of the additional chemisorbed O adatoms. Active O stoichiometry: G(T,P) analysis. Figure 14 plots the free energy of adsorption as a function of temperature for the most stable Ag oxide overlayer at each O coverage.k The pressure is 15 atmospheres, which is characteristic of the pressure used in industrial epoxidation catalysis [10]. We ﬁnd that at zero Kelvin the most stable overlayer is the Ag1.22 O overlayer, i.e. the Ag oxide with an additional O adatom inside each oxide ring PO2=15 atm 2

0

100 200 300 400 500 600 700 800

Temperature (K)

deltaG (eV)

1 0 2.75 (4)

-1 -2

2.2 (5) 1.83 (6) 1.57 (7)

-3 1.37 (8)

-4 -5

1.2 (9) 1.1 (10)

Fig. 14. Free energy of adsorption as a function of temperature for diﬀerent oxide overlayers at a ﬁxed O2 pressure. The stoichiometry (number of O atoms per 4 × 4 unit cell) is given for each overlayer.

k The computational set-up used in this section (3 layer Ag slab) diﬀers from that in Sec. 1 (4 layer Ag slab) and so we refrain from including the O adatom phases in this plot and from making a strict comparison with the phase diagram presented in Sec. 1 (Fig. 5). This will be done in a forthcoming publication [48].

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(and a total of 9 oxygen atoms in the unit cell). Indeed it is apparent from Fig. 12 that at zero Kelvin the relative stability of the various oxide overlayers simply increases with the number of oxygens present up to the Ag1.22 O oxide, after which the addition of a tenth O is unfavorable since the oxide saturates for the addition of further chemisorbed O atoms at this stage. At this pressure and at low temperature the Ag1.22 O oxide is most stable. As the temperature is raised, however, its stability compared to reduced structures (like Ag1.83 O, Ag1.57 O, or Ag1.37 O) decreases, and at 550–650 K up to four oxide overlayers (Ag1.83 O, Ag1.57 O, Ag1.37 O and Ag1.22 O) become equally stable, with the Ag1.83 O overlayer marginally favored as the clean surface stability curve (horizontal axis) is crossed at ∼680 K. At no stage do the lower oxygen ratio oxides (modeling the reduction mechanism) become the most stable phases. We also see that the relative stabilities change quite a lot as we go to higher temperatures and pressures. Precisely at the reaction temperature (around 600 K) four phases (the reference system and oxidized models) become equally stable. In addition, the phases with less oxygen tend to become more and more favorable at increasing temperature. This implies that it may cost less and less free energy to reduce the reference oxide at ﬁnite temperature and pressure. Oxidation or reduction processes between Ag1.83 O, Ag1.57 O, Ag1.37 O and Ag1.22 O proceed with almost no free energy variation in a large range around the reaction temperature. This demonstrates a remarkable ﬂexibility of this oxidized Ag surface for redox processes. The Ag1.57 O, Ag1.37 O and Ag1.22 O overlayers in particular should be the best candidates for oxidation catalysis, since O abstraction can occur with no free energy cost. To conclude this section, oxidation of the reference Ag1.83 O oxide is under certain conditions exothermic. Up to three chemisorbed O atoms can be added before the oxide becomes saturated to the addition of further chemisorbed O atoms. Moreover, the chemisorbed O atoms added do not signiﬁcantly modify the structure of the oxide overlayer. The only noteworthy structural changes upon the addition of O atoms are that the Ag adatoms get displaced upward when O atoms are added to the ﬁlled oxide rings. By combining DFT and STM simulation results, we ﬁnd that two models match quantitatively the experimental STM images. Indeed the STM simulations for Ag1.83 O with a single additional O, i.e. Ag1.57 O and Ag1.83 O, are virtually indistinguishable. Moreover, simply in terms of the STM simulations, up to four of the oxygen rich oxide overlayers match the experimental image reasonably well. To resolve this particular issue of whether additional O atoms are present in the Ag oxide overlayer will

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require a quantitative experimental analysis such as LEED. Further, assessment of the relative stability of the oxide overlayers at ﬁnite temperatures and pressures reveal that at typical industrial conditions, surface terminations with diﬀerent oxygen content have a remarkably similar stability, thus creating the ideal thermodynamic conditions for re-dox processes. This indicates that the reference Ag1.8 O oxide overlayer as well as several oxidized analogues identiﬁed here may make good oxidation catalysts. However it must be emphasized that we have only considered a gas phase atmosphere of O2 , whereas, in reality, there will be a mixture of, at least, ethylene and oxygen. What the eﬀect of other reactant gases in equilibrium with the substrate have on the precise composition (O stoichiometry) of the epoxidation catalyst remains to be seen. 3. Concluding Remarks By reﬁning the stoichiometry of the oxide overlayer in more detail as we have just done, two types of O species are now predicted to coexist on the oxidized Ag surface. Since the additional adsorbed O atoms are more loosely bound than O atoms adsorbed on bare Ag{111} and the O atoms within the oxide ring, it is likely that their reactivity will be diﬀerent. We aim at examining the reactivity of these two types of O atoms. It is possible that this will prove to be an important step towards understanding the selectivity question in the ethene epoxidation reaction. Indeed Barteau and co-workers have already made important progress on the issue of epoxidation selectivity (see [60] for example). They have concluded that the branching of the oxametallacycle into ethylene oxide or acetaldehyde is the key factor controlling selectivity, as shown in Scheme IV.

H

H

O

H H C (OMME) C H O insertion H C O

Ag Ag H migration

H

C

H (EO) H

O C (AcH)

CO2 + H2O

CH3 Scheme IV. Two possible outcomes for the adsorbed OMME intermediate. Along the upper channel ethylene epoxide (EO) is formed through O insertion (ring closure). Along the lower channel a H migration step leads to an acetaldehyde (AcH) intermediate, which subsequently reacts to yield CO2 and H2 O.

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This has in turn been related to the relative stability of the OMME compared to the ethylene reactant and the epoxide product [11]. It has been argued that the relative instability of the OMME intermediate on Ag compared to Group VIII metals is the main origin of the unique activity of Ag as an eﬀective epoxidation catalyst. Whether this simple interpretation is correct remains to be seen and will require considerable further investigations. In our current studies, we propose to shed light on the competitive partial oxidation and total oxidation channels with ab initio derived microkinetic modeling [61].

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[49] J. Xie, S. de Gironcoli, S. Baroni and M. Scheﬄer, Physical Review B 59, 970 (1999). [50] M.-L. Bocquet, P. Sautet, J. Cerda, C. I. Carlisle, M. Webb and D. A. King, Journal of the American Chemical Society 125, 3119 (2003). [51] M.-L. Bocquet, A. Rappe and H.-L. Dai, Molecular Physics 103, 88 (2005). [52] M.-L. Bocquet, A. Michaelides, D. Loﬀreda, P. Sautet, A. Alavi and D. A. King, Journal of the American Chemical Society 125, 5620 (2003). [53] G. S. Jones, M. Mavrikakis, M. A. Barteau and J. M. Vohs, Journal of the American Chemical Society 120, 3196 (1998). [54] S. Linic and M. A. Barteau, Journal of American the Chemical Society 124, 310 (2002). [55] C. Saravanan, M. R. Salazar, J. D. Kress and A. Redondo, Journal of Physical Chemistry B 104, 8685 (2000). [56] M.-L. Bocquet, A. Michaelides, P. Sautet and D. A. King, Physical Review B 68, 075413 (2003). [57] K. Reuter, C. Stampﬂ, M. V. Ganduglia-Pirovano and M. Scheﬄer, Chemical Physics Letters 352, 311 (2002). [58] C. Stampﬂ, M. V. Ganduglia-Pirovano, K. Reuter and M. Scheﬄer, Surface Science 500, 368 (2002). [59] M.-L. Bocquet, P. Fleurat-Lessard, D. Loﬀreda and A. Michaelides, in preparation. [60] S. L. Linic and M. A. Barteau, Journal of Catalysis 214, 200 (2003). [61] M.-L. Bocquet and D. Loﬀreda, Journal of the American Chemical Society, in press (2005).

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INDEX

π bonding, 333, 336, 355, 357 bond formation, 200 Brillouin zone, 133 1,3-butadiene, 352 buckling of the dimers, 43

absorption cross section, 95 absorption dipole moment, 103 acetylene, 171, 231, 337, 339 adsorbates, 49, 163 with a hydrogen terminated Si(100)-2 × 1 surface, 53 AFM feedback loop, 80 alcohols, 297 aldehydes, 298 alkene, 291, 299, 301, 311, 335 alkyl Grignards, 296, 301, 311 alkynes, 291, 335 alligator clips, 369 amines, 299 analytical chemistry, 91 annular illumination, 112 antiaromatic, 352 architectural issues, 379 atomic force microscopy, 91 atomic superlattices, 252 Au(111)-vicinal surfaces, 257 Aviram–Ratner diode, 368

C60 , 189, 232 C60 electromechanical transistor, 379 C60 microprocessor, 378 capacitance, 313 carboxylic acid, 300 catalytic cycle, 408, 409, 411 cathodic electrografting, 297 CCD camera, 106 cell membrane, 113 charge density, 126, 127, 129, 130 charge transfer, 132 charge-transfer doping, 374 chemical and biochemical sensing, 326 chemical forces, 160 chemical interactions, 161 chemisorption, 333 circuit simulations, 372 cis- and trans-butene, 342 cleaved-dimer model, 338 clock frequency, 379 clocked D-latches, 377 CO, 233 coherent multiple excitations, 224 combustion, 391 computation box, 125 conductance, 134 conductance “plateau”, 139 conductance calculations, 225 confocal microscopy, 100

ballistic electron transport, 372 ballistic regime, 220 band-bending, 309, 320 Bardeen matrix element, 153, 155 benzene, 174, 353 bias potential, 126 binomial distribution, 258 biosensing, 288 bleaching, 91 blinking, 91 BN double layers on Rh(111), 261 π bond, 340, 344 425

index

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WSPC/SPI-B346: Properties of Single Organic Molecules on Crystal Surfaces

426

conformational switching, 91 constant current mode, 31 contact angle, 307 corrugation, 163 counter electromotive force, 377 coupling matrices, 143 coupling strength, 129 crossbar arrays, 380 cryogenic temperatures, 94, 110 crystal structure of graphite, 83 current imaging tunneling spectroscopy of semiconductor surfaces, 39 current noise, 74 current to voltage ampliﬁer, 73 1,3-cyclohexediene, 352 1,5-cyclooctadiene, 347 1,3,5,7-cyclooctatetrene, 350 cycloaddition, 335, 336, 339–342, 344, 346, 352, 354, 356, 357 cyclopentene, 342 dangling bond, 171, 292 deﬂection detection device, 77 demultiplexer, 383 density functional theory (DFT), 122, 149, 337, 340, 345, 346, 350 density matrix, 155 density of states, 132, 134 desorption induced by electronic transitions (DIET), 236 desorption induced by multiple electronic transitions (DIMET), 236, 240 deterministic single-photon source, 89 DFT calculations, 394 di-σ, 337 diamond, 327, 334 Diamond(100), 355 dideuterioethylene, 341 Diels–Alder, 333, 335, 352 diﬀraction-limited excitation spot, 101 dimer reconstruction, 168 2,3-dimethyl-1,3-butadiene, 352 disorder, 347

Index

dissociation of single molecules, 197 DNA, 299, 322 DNA, proteins, 290 doping, 294 double bond, 335 dual-color co-localization, 113 dynamic atomic force microscopy, 77 dynamic buckling, 169 Dyson series, 153 eﬀective potential, 125 eigenvector expansion, 152 elastic–inelastic cancellations, 233 electrical equivalent circuit model, 378 electrochemical, 297, 312, 320 electro-mechanical grid, 379 electromechanical transistor single C60 molecule, 372 π electron system, 369 electron transfer, 312 electron–electron interactions, 151 electron–phonon, 151 electron–vibration coupling, 228, 231 electron–vibration scattering, 221 electronic states, 124 electrophilic, 345 electrostatic Hartree energy, 125 epoxidation, 392 equilibrium conductance, 137 ergodicity theorem, 90 esters, 300 ethylene, 337, 339 ethylene adsorption, 405 excess charge, 136, 139 exchange-correlation energy, 125 excitation, 211 excitation volume, 97 extended H¨ uckel, 367 extended molecule, 123, 124, 367 far-ﬁeld optical microscopy, 100 ferrocene, 314 Feuchtwang, 154 ﬁeld eﬀect transistor (MOSFET), 309 ﬁeld eﬀect transistors (FETs), 372

index

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WSPC/SPI-B346: Properties of Single Organic Molecules on Crystal Surfaces

Index

ﬁrst order current, 156 ﬁrst principles, 157 force gradient, 81 force sensors, 76 free radical, 340, 344, 346 free-radical addition, 333, 339 frequency change, 81 frequency-modulation AFM, 80 Friedel oscillations, 250 FTIR, 305 gallium arsenide, 334 Gaussian beam, 100 Ge, 327 Ge(100), 355 generalized gradient approximation, 127 geometric structure surface reconstructions, 4 germanium, 334 giant corrugation, 161 Graphite, 83 Green’s function, 151 non-equilibrium Green’s functions, 150 H migration, 421 H/Si(111), 289, 303 hexagonal lattice of islands, 261 Hg drop electrodes, 317 high current density interconnects, 372 high density integration, 382 high resolution electron energy loss spectroscopy (HREELS), 305, 308 higher harmonics, 85 highest occupied molecular orbital, 93 histogram of interphoton times, 109 Hund’s rule, 93 hybrid materials, 334 hybrid-molecular electronics, 379 hydrogen terminated Si(100) surface, 51 I/V curves, 370 IET process, 197

427

image forces, 164 imaging of magnetic surfaces, 17 impact scattering, 224 imprinting metallic nanowires, 380 molecular mono-layers, 380 nano-lithography, 380 impurity molecules, 91 inelastic, 213 inelastic channel, 220 inelastic electron tunneling spectroscopy, 211, 214 inert surface, 170 interaction energy, 155 interface eﬀects, 149 interfacial chemistry, 334 interference pattern of electron transport through aromatic molecules, 372 interferometric cantilever detection, 78 intermode coupling, 237 intramolecular decay pathways, 237 iodobenzene, 198 island superlattices, 258 jellium, 368 Johnson noise, 73 Kelvin probe, 312 kinetic control, 347 kinetically controlled, 345, 356 Kirchhoﬀ’s laws, 372 labels in biology, 89 Landauer formula, 133, 367 Landauer–B¨ uttiker, 152 Landauer–B¨ uttiker relation, 150 Lander molecules C90 H98 , 192 Langmuir–Blodgett ﬁlms, 288 laser beam deﬂection, 78 lateral manipulation, 185 lateral manipulation modes pushing, pulling and sliding, 186 lateral resolution, 34

index

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WSPC/SPI-B346: Properties of Single Organic Molecules on Crystal Surfaces

428

linear combination of atomic orbitals, 130 Lippman–Schwinger equation, 151 local density approximation, 127 local nano environment, 90 lock-in techniques, 216 long-range interactions, 250 longitudinal ﬁelds, 105 low temperatures, 84 lowest unoccupied molecular orbital, 93 macroscopic forces, 158 maleic anhydride, 176, 344 manipulation, 183 manipulation curve, 187 many-body eﬀect, 222 Marcus–Hush theory, 342 master equation, 94 memory/adder model, 372, 377 MEMS, 288 metal adhesion forces, 189 metal surfaces, 160 microelectronic devices, 334 microﬂuidic, 288 micro-mechanical, 288 microscopic forces, 158 miniaturization, 333 minimum feature size, 379 model tip, 156 molecular adsorbates on the patterned hydrogen terminated silicon surface, 51 molecular diﬀusion, 343 molecular dynamics, 353 molecular electronic, 325, 334 molecular probes, 90 molecular rectiﬁer, 371 molecular scale electronics, 288 molecular wires, 371 molecule dissociation, 196 mono-molecular electronics, 365 Morse interaction, 75 multiple scattering, 150

Index

nano-cantilever, 377 nanotube growth and deposition techniques, 374 nanowires, 288, 326 negative diﬀerential resistance, 371 NH3 , 237 non-contact mode, 79 non-equilibrium, 152 non-equilibrium Green’s function, 123, 126, 367 nonlinear optics, 334 Norbornadiene, 345 N/Cu(100) template, 259 N -trimethylsilyl-7-azanorbornadiene, 346 O insertion, 421 on-surface oxygen, 400 open boundary conditions, 125 optical detection, 89 organic functionalization, 334 organosilane, 289, 324 oscillatory long-range interactions, 252 oxametallacycle, 408 oxidation, 295, 306, 308 oxide ring, 414 oxygen, 164, 166, 167 oxygen stoichiometry, 419 performance evaluation, 378 Perturbation methods, 149 phase diagram, 401, 403, 419 phosphangulene, 190 photochemical, 291 photoexcitation, 341 photon antibunching, 94 pico-Newton force sensitivity, 82 Poisson equation, 126, 127 poles of the Green’s functions, 131 polyimide, 344 polythiophene, 301, 319 programmable gate logic arrays (PGLAs), 380

index

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WSPC/SPI-B346: Properties of Single Organic Molecules on Crystal Surfaces

Index

protein, 299, 323 pseudopotential, 127 qPlus-sensor, 76 qPlus-sensor preampliﬁer circuit, 78 quantum corrals, 189 quantum dots, 288 quantum eﬃciency, 94 quantum information processing, 90 quantum tunneling in one dimension, 32 quantum yield, 99 Rabi oscillations, 94 radical chain reaction, 291 Raman scattering, 96 reconstructions, 160 relaxation, 160 renormalized molecular levels, 132, 135 resonant antenna-like metallic nano structures, 100 resonant tunneling transistors, 371 ring oscillator, 374 RLC cell, 378 rotaxane molecules, 380 saturation, 95, 97 saturation of Si(001), 170 scanning confocal optical microscopy, 89 scanning force microscopy, 69 scanning near-ﬁeld optical microscopy, 89, 97 scanning probe microscopy, 71 scanning tunneling microscopy (STM), 69, 72, 91, 292, 303, 335 semiconductor surfaces, 30 scanning tunneling spectroscopy (STS), 11, 45 scattering region, 125, 142 scattering wavefunction, 130 Schottky barrier, 318 screening approximation, 125, 126, 128

429

selectivity, 421 “self-assembled” monolayers (SAMs), 288, 303, 308 self-directed growth, 170 self-energy, 128, 142, 143 self-organized nucleation nanostructured metal surfaces, 24 semi-classical Wentzel–Kramers–Brillouin, 36 semiconductor surfaces, 335 semiconduncting nanowires, 376 sexiphenyl, 191 shearforce detection, 97 Shockley type surface states, 250 short-range repulsion, 250 Si dangling bond, 291 Si(100)-(2 × 1), 335 Si(111)-7 × 7, 52 Si(100)-2 × 1 surface, 41, 42 silicon, 289, 334 silicon dimers, 342 silicon surfaces, 40 silver-oxide overlayer, 398 simulations, 156 single electron transistors, 371 single ﬂuorescent molecules, 89 single molecule vibrational chemistry, 234 single photon counting avalanche photodiodes, 102 single-molecule detection, 92 single-molecule tracking, 112 single-walled carbon nanotubes, 372 spatial resolution, 70 spectroscopic measurements, 100 SPICE circuit simulations, 377 spin polarized spectroscopy, 17 spin-orbit coupling, 93 spinodial decomposition, 261 square lattice of misﬁt dislocations, 260 square superlattices of islands, 259 start-stop measurements, 109 static mode operation (AFM), 79

index

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WSPC/SPI-B346: Properties of Single Organic Molecules on Crystal Surfaces

430

stepwise free-radical reactions, 335 stepwise mechanism, 353 stepwise reaction, 342 STM interface, 395 STM simulations, 400, 418 STM-based lithography, 56 STM-tip, 158 strain symmetrized superlattice, 257 subatomic features, 86 sub-Poissonian photon statistics, 94 subsurface oxygen, 400 subwavelength aperture, 98 superlattices of semiconductor quantum dots, 255 surface defects, 47 surface electronic structure, 156 surface Green’s function, 128, 143 surface mobility, 343 surface photovoltage (SPV), 311, 312, 319 surface recombination velocity, 311 surface state, 160, 166, 310 surface-state mediated interactions between adatoms, 23 surface states transition metal surfaces, 16 surface steps, 46 symmetry, 336 symmetry forbidden, 341 symmetry selection rules, 231 ‘systems biology’, 91, 112

Index

thermodynamically controlled, 356 thin-ﬁlm displays, 334 three-terminal device, 376 tight-binding, 157 time-correlated single photon counting, 112 tip-sample force, 75 tip-surface interaction, 158 topographic mode, 31 topological scattering matrix approach, 372 transient events, 91 transition state, 409, 410 transmission coeﬃcient, 133, 136 triplet state, 93 tunneling conditions, 166 tunneling current, 34, 156 tunneling junction, 148 two-probe molecular device, 123 Ullmann reaction, 203 ultrasensitive assays, 113 van Hove singularities, 127, 129 vertical manipulation, 185, 193 vertical noise (AFM), 74 vertically aligned dot columns, 256 vibrational heating, 236 vibrational lifetime, 233 vibrational temperature, 235 Wide-ﬁeld microscopy, 105

tapping mode, 80 templates, 260 Tersoﬀ Hamann model, 36 Tersoﬀ–Hamann approach, 156 theoretical surface image, 159 thermodynamic control, 347

X-ray photoelectron spectroscopy (XPS), 304, 306 zero-phonon line, 110 Zn porphyrins, 314

index