Carbon: The Future Material for Advanced Technology Applications (Topics in Applied Physics)

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Topics in Applied Physics Volume 100

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Topics in Applied Physics Topics in Applied Physics is a well-established series of review books, each of which presents a comprehensive survey of a selected topic within the broad area of applied physics. Edited and written by leading research scientists in the field concerned, each volume contains review contributions covering the various aspects of the topic. Together these provide an overview of the state of the art in the respective field, extending from an introduction to the subject right up to the frontiers of contemporary research. Topics in Applied Physics is addressed to all scientists at universities and in industry who wish to obtain an overview and to keep abreast of advances in applied physics. The series also provides easy but comprehensive access to the fields for newcomers starting research. Contributions are specially commissioned. The Managing Editors are open to any suggestions for topics coming from the community of applied physicists no matter what the field and encourage prospective editors to approach them with ideas.

Managing Editors Dr. Claus E. Ascheron

Dr. Hans J. Koelsch

Springer-Verlag GmbH Tiergartenstr. 17 69121 Heidelberg Germany Email: [email protected]

Springer-Verlag New York, LLC 233, Spring Street New York, NY 10013 USA Email: [email protected]

Assistant Editor Adelheid H. Duhm Springer-Verlag GmbH Tiergartenstr. 17 69121 Heidelberg Germany Email: [email protected]

Giacomo Messina Saveria Santangelo (Eds.)

Carbon The Future Material for Advanced Technology Applications

With 245 Figures, 6 in Color, and 24 Tables

123

Giacomo Messina Saveria Santangelo Faculty of Engineering Department of Mechanics and Materials University Mediterranea of Reggio Calabria 89060 Reggio Calabria, Italy [email protected] [email protected]

Library of Congress Control Number: 2006924284

Physics and Astronomy Classiﬁcation Scheme (PACS): 81.05.Uw, 81.07.-b, 60., 70., 80.

ISSN print edition: 0303-4216 ISSN electronic edition: 1437-0859 ISBN-10 3-540-29531-3 Springer Berlin Heidelberg New York ISBN-13 978-3-540-29531-0 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com © Springer-Verlag Berlin Heidelberg 2006 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: DA-TEX · Gerd Blumenstein · www.da-tex.de ockler GbR, Leipzig Production: LE-TEX Jelonek, Schmidt & V¨ Cover design: design & production GmbH, Heidelberg Printed on acid-free paper

57/3100/YL

543210

To Lorenzo Maria, my adored son, with love Saveria

To my sons Gloria and Alfonso, with love Giacomo

Preface

Carbon is a surprisingly versatile element, able to hybridise in three diﬀerent states, sp1 , sp2 and sp3 . The changes in local bonding of carbon atoms account for the existence of extremely diverse allotropic phases, exhibiting a quite broad range of physical and chemical properties. This element can crystallise as diamond (sp3 hybridisation) or graphite (sp2 hybridisation) and give rise to many noncrystalline phases (generally containing a mixture of sp1 , sp2 and sp3 hybridisations), such as fullerenes, carbon nanotubes and disordered, nanostructured and amorphous carbons. Strong tetrahedral σ bonds are responsible for the extreme physical properties of diamond, a wide gap semiconductor having the largest bulk modulus of any solid, the highest atom density, the largest room-temperature thermal conductivity, the smallest thermal expansion coeﬃcient and the largest limiting electron and hole velocities of any semiconductor. Graphite, whose sheets (graphenes), featured by strong intralayer trigonal σ bonding, are held together by weak interlayer van der Waals’ forces, is an anisotropic metal. These two crystalline allotropic forms of carbon have been known and utilised for centuries, together with other carbonaceous materials, generically identiﬁed as coals. The use of hydrocarbons and organic materials is more recent. The true turning point in the use of carbon as a material for advanced technology applications, however, occurs only in the second half of the last century. In 1953, the discovery, at Union Carbide Co., of the possibility of growing diamond ﬁlms by chemical vapour deposition (CVD), at low pressures, opened the way to the development of low-cost deposition techniques. The growth of CVD diamond ﬁlms at subatmospheric pressures, ﬁrstly reported by Derjaguin and Fedoseev in 1967 and later implemented by Matsumoto’s group, opened new perspectives in technological applications of diamond. The enthusiasm for these achievements caused further eﬀorts to be addressed to the development of low-temperature CVD techniques and stimulated the search for alternative growth methods, such as the QQC process, based on a multiplexed laser–solid interaction, announced in the 1990s by QQC Inc. (USA). Around 1969, Aisenberg and Chabot demonstrated that carbon ﬁlms with properties ranging between those of diamond (diamond-like carbon, DLC)

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and those of graphite (graphite-like carbon, GLC) can be deposited by the use of energetic carbon species. The term amorphous carbon (a-C) identiﬁes a carbon matrix with any possible mixture of sp1 -, sp2 - and sp3 -hybridised sites and no crystalline long-range order. Indeed, a wide nomenclature for the classiﬁcation of these ﬁlms does exist. Hydrogenated amorphous carbon (a-C:H) denotes an a-C ﬁlm containing up to even 60% hydrogen. The term DLC, initially introduced to identify exclusively a-C ﬁlms with hardness and transparency properties close to those of diamond, is nowadays commonly used to designate a larger class of materials, including both hydrogen-free and hydrogenated a-Cs, containing a signiﬁcant fraction of sp3 hybridised carbon sites and exhibiting a wide spectrum of properties and potentialities. Finally, the name tetrahedral amorphous carbon (ta-C) is attributed to hydrogenfree a-Cs containing up to 95% sp3 sites, sometimes also termed amorphic diamond (a-D), whose correspondent hydrogenated form is known as ta-C:H. In 1985, spectrometric measurements on interstellar dust led to the discovery of new allotropic forms of carbon, consisting of pentagonal and hexagonal rings arranged to form closed-cage molecules. However, the scientiﬁc interest in fullerenes, started only in 1990 after the invention of the method for their production in macroscopic amounts, was really fuelled by the awarding of the Nobel Prize in chemistry for this discovery in 1996. In 1989, Liu and Cohen theoretically predicted the existence of a crystalline β-C3 N4 phase with bulk modulus and hardness higher than diamond. The attempts of synthesising such a hypothetical superhard compound drew attention upon carbon nitride (CN). In spite of the lack of any agreed success on this direction, in the last years the interest in amorphous CN compounds has been renewed, due to the wide range of possible applications. The observation, in 1993, of single-walled carbon nanotubes (SWCNTs), consisting of single graphene sheets wrapped into hollow cylinders having nanometer-sized diameter, followed to the discovery, about two years earlier, of multiwalled carbon nanotubes (MWCNTs), comprising up to tens of coaxial cylinders, caused enormous interest in many ﬁelds of research. The exciting discoveries of the last decades have given great impulse to the research on carbon-based materials, oﬀered new opportunities and issued new challenges. The lengthy history of diamond as a material for advanced technology began in the 1920s with the development of photoconductive UV detectors, followed in the 1940s by the fabrication of ionising radiation detectors, both based on the use of geological diamonds. In 1979, the experiments of Himpsel, followed by those of Pate in 1986, demonstrated the high quantum eﬃciency for photoelectron emission from natural diamond crystals, starting the consideration of diamond as an emitting material in cold cathode sources and devices. Nowadays, a great variety of technological applications in ﬁelds as diverse as mechanics, lithography, optics, chemistry, electronics, takes full advantage of the extraordinary properties of higher and higher quality synthetic diamond ﬁlms, achieved thanks to the continuous advances in prepara-

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IX

tion methods. Surprisingly, however, there are even manifold applications of “damaged diamond”. These beneﬁt from the dramatic modiﬁcations of electrical, mechanical, optical and chemical properties induced on virgin material by ion-beam exposure. The realisation of ohmic contacts in diamond-based electronic devices and the production of microstructures on single-crystal diamond membranes for micromachining exploit the local complete graphitisation process. Partial graphitisation, instead, is employed for the realisation of electrodes for electrochemistry and of conductive patterns on diamond. The cheaper production costs, along with the signiﬁcant fraction of sp3 bonding conferring on DLC many of the proﬁtable properties of diamond, make it a valuable material for widespread technology applications. The ﬁrst exploitation of DLC has been as a hard protective coating. During the last 30 years, taking advantage of its low friction, the use of DLC as coating has been enlarged to the solid lubricant technology. Its good blood compatibility suggests of extending its utilisation as biomaterial in blood-contacting-devices. Nowadays, DLCs coat a surprisingly large number of unexpectedly diﬀerent objects, spanning from microelectromechanical devices to dental prostheses, from optical windows to razor blades, from orthopedic pins and screws to car parts, from medical guide-wires to disks, heads and slides used in magnetic storage technology. Recently, there has been considerable interest in the application of lowthreshold ﬁeld-emitting carbon ﬁlms for cold cathode devices and ﬂat panel displays. The interest in amorphous hydrogen-free and hydrogenated CN compounds is, instead, mainly concerned with their possible application as electrodes, IR detectors and gas sensors. Group-IV carbon-based binary alloys, like amorphous silicon and germanium carbon-alloys, are used for optoelectronic devices and for the construction of solar cells. Fullerenes, whose family comprises a large variety of isomers, are used as sorbents, as superconductors, as chromatographic stationary phases, as materials for building optical and electronic devices, hydrogen cells, photosensitive elements and electrochemical sensors. Thanks to their astonishing properties, fullerenes and their derivatives appear to be a good alternative to polymer molecules currently used in nanolithography, as well as promising candidates as antioxidants, neuroprotectors and inhibitors of bacterial growth. The unique structural features of SWCNTs and MWCNTs are reﬂected in their singular optical, electronic and mechanical properties. Thanks to the wide variety of geometrical-structure-dependent behaviours, CNTs possess great potential in many research ﬁelds, spanning from physics to chemistry, from engineering to materials science, from biology to life science. Although gaining the control of diameter and chirality of CNTs still represents the goal needed for the defect-free CNT production and the full success of the CNT-based technological applications, they are presently regarded as building blocks for various nanoscale devices. Current applications relate to mainly electronic devices, such as ﬁeld emitters, transistors and sensors, while one of

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the future challenges consists in the creation of highly integrated CNT-based cicuits. The recent fabrication of the world’s smallest motor based on CNTs has opened the way to nanoelectromechanical systems, while the realisation of the ﬁrst AFM tip using CNTs has laid the foundations for a real revolution in high-resolution imaging techniques. It appears now clear that carbon-based materials constitute a topic of huge scientiﬁc interest and great strategic importance in an interdisciplinary approach spanning applied physics, materials science, biology, mechanics, electronics and engineering. Development of current materials, advances in their applications and discovery of new forms of carbon are the themes addressed by the frontier research in these ﬁelds. The book covers all the fundamental topics concerned with amorphous and crystalline carbon-based materials, such as synthetic diamond, diamondlike carbon, carbon alloys, carbon nanotubes and cluster-assembled materials. The latest scientiﬁc results and developments in the various technological application areas of these materials are reviewed. Both theoretical and experimental aspects related to their optical, electrical, elastic, thermomechanical, structural, vibrational and electronic properties are extensively discussed. The contributions discuss subjects of great currency and huge scientiﬁc and technological interest, such as the use of carbon-based materials for energy storage, for fabrication of sensors operating in harsh environments and as biocompatible coatings for medical implants. A broad spectrum of both well-assessed and still controversial as well as newly developed aspects concerning growth and characterisation techniques are addressed, ranging from modelling of deposition processes to semiempirical methods for its control and optimisation, from investigation of diamond-nucleation and nanotubegrowth mechanisms to more comprehensive explanation of the origin of the Raman features commonly regarded as the ﬁngerprint of amorphous carbons. An accurate picture is drawn of both the present developments in research on carbon and the future prospects that may constitute a reference point for a new generation of researchers, who accept the challenge issued by the scientiﬁc community in this fascinating ﬁeld. The volume, comprising 24 contributions, is the ﬁrst comprehensive state-of-the-art review of this fast-evolving ﬁeld of research. Its preparation, to which many of the most world-famous researchers engaged in the ﬁeld have contributed, has acted as a friendly and cooperative opportunity to share the latest outstanding and exciting results in the hot topics of research on carbon. The 75 contributors, most of whom often promote scientiﬁc events and organise international meetings on carbon and related subjects, belong to a multitude of disciplines. This witnesses the interdisciplinary nature of the fundamental and technology-centred studies of carbon, a material entering everyday life, on which worldwide attention is focused for its extraordinary future potential. The contributions are presented in alphabetic order because any classiﬁcation relative to material kind (diamond, carbon alloys, carbon nanotubes,

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etc.) or to contribution type (fundamental studies, technological applications, etc.) or subject (growth techniques, characterisation tools, etc.) might be reductive for the reader. Most of the contributions, in fact, deal with aspects common to more than one of these topics. We end this preface by acknowledging all the scientists who participated enthusiastically and painstakingly to the realisation of this volume and to the Springer staﬀ for the valuable assistance provided.

Reggio Calabria, 26 August 2005

Giacomo Messina Saveria Santangelo

Contents

Aid of Scaling Laws in the Achievement of a Well-Controlled Film Deposition Process Giacomo Messina, Saveria Santangelo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A Spectroscopic Approach to Carbon Materials for Energy Storage Giuseppe Zerbi, Matteo Tommasini, Andrea Centrone, Luigi Brambilla, Chiara Castiglioni . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Carbon-Based Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Prototypical Lattices in Three, Two and One Dimensions . . . . . . . . . 2.1 Diamond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Graphite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Polyacetylene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Polyynes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 A Spectroscopic Approach to Disordered Carbon Materials . . . . . . . 3.1 1D Systems – Saturated Carbon Materials . . . . . . . . . . . . . . . . . 3.2 Polyconjugated Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 2D sp2 Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Edge Eﬀects in Graphitic Domains for Structure Diagnosis . . . . . . . 5 Approaching the Structure of Carbonaceous Materials by Vibrational Spectroscopy: Imagination and Reality . . . . . . . . . . . . . . 5.1 Carbon-Based Materials for Hydrogen Storage . . . . . . . . . . . . . . 6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Biocompatibility, Cytotoxicity and Bioactivity of Amorphous Carbon Films Sandra E. Rodil, Ren´e Olivares, Higinio Arzate, Stephen Muhl . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Film Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Film Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Cell Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

23 23 24 26 26 28 29 32 33 33 34 35 36 41 44 47 48 52

55 55 58 58 58 59

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2.4 2.5

Cytotoxicity Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bioactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.1 Morphological Assay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.2 Protein Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Film Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Cytotoxicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Bioactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Morphological Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Proteins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59 60 60 60 62 62 64 65 65 65 71 73 75

Characterisation of the Growth Mechanism during PECVD of Multiwalled Carbon Nanotubes Martin S. Bell, Rodrigo G. Lacerda, Kenneth B.K. Teo, William I. Milne . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Production of Carbon Nanotubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Plasma Composition during PECVD . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Characterisation of the Growth Mechanism . . . . . . . . . . . . . . . . . . . . . 5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

77 77 82 84 85 89 90 92

Correlation Between Local Structure and Film Properties in Amorphous Carbon Materials Giovanni Fanchini, Alberto Tagliaferro . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Electronic States in Carbon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Hybridisation and Local Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 The Various Forms of Amorphous Carbon . . . . . . . . . . . . . . . . . . . . . . 5 Phase Matching and Its Eﬀects on Materials . . . . . . . . . . . . . . . . . . . . 6 Optoelectronic and Mechanical Properties . . . . . . . . . . . . . . . . . . . . . . 7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

95 95 95 96 97 99 102 103 104 104

Defects in CVD Diamond Films from Their Response as Nuclear Detectors Marco Marinelli, Enrico Milani, Aldo Tucciarone, Gianluca Verona Rinati . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 2 CVD Diamond Nuclear Detectors: Realization and Physics . . . . . . . 108

Contents

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Analysis of the Charge Collection Spectrum . . . . . . . . . . . . . . . . . . . . 3.1 Qualitative Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Quantitative Analysis: The General Model . . . . . . . . . . . . . . . . . 3.3 The Use of Detector Thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 The Use of Penetration Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Time-Domain Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 The Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Qualitative Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Quantitative Analysis: Computer Simulation . . . . . . . . . . . . . . . 5 Temperature Eﬀects: Depumping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

111 111 115 117 119 123 123 125 126 129 133 133 135

Eﬀects of Nanoscale Clustering in Amorphous Carbon J. David Carey, S. Ravi P. Silva . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction and Bonding in Carbon . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Disorder in Amorphous Carbon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Intracluster Eﬀects in Amorphous Carbon . . . . . . . . . . . . . . . . . . . . . . 4 Intercluster Interactions in Amorphous Carbon . . . . . . . . . . . . . . . . . . 5 Field Emission from Amorphous Carbon . . . . . . . . . . . . . . . . . . . . . . . 6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

137 137 139 142 147 148 150 150 151

Elastic and Structural Properties of Carbon Materials Investigated by Brillouin Light Scattering Marco G. Beghi, Carlo S. Casari, Andrea Li Bassi, Carlo E. Bottani . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Experimental Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Derivation of the Elastic Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Brillouin Scattering from Carbonaceous Materials . . . . . . . . . . . . . . . 5 Ultra-Thin Carbon Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Nanotubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

153 153 156 158 161 162 166 170 170 173

Electrical Resistivity and Real Structure of MagnetronSputtered Carbon Films Alexei A. Onoprienko . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Substrate Temperature Eﬀects . . . . . . . . . . . . . . . . . . . . . . . . . . . .

175 175 176 177 177

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3.2 Substrate Bias Eﬀects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

181 184 185 186

Formation, Atomic Structures and Properties of Carbon Nanocage Materials Takeo Oku, Ichihito Narita, Atsushi Nishiwaki, Naruhiro Koi, Katsuaki Suganuma, Rikizo Hatakeyama, Takamichi Hirata, Hisato Tokoro, Shigeo Fujii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Synthesis Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Fullerene Clusters and Metallofullerenes . . . . . . . . . . . . . . . . . . . . . . . . 4 Onions and Nanotubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Carbon Nanocapsules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Properties of Carbon Nanomaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Photoluminescence of Carbon Nanocapsules . . . . . . . . . . . . . . . . 6.2 Magnetic Properties of Carbon Nanocapsules . . . . . . . . . . . . . . . 6.3 Possibility of H2 Gas Storage in Carbon Nanocages . . . . . . . . . 6.4 One-Dimensional Self-Organization of Nanocapsules . . . . . . . . . 7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

187 187 189 190 196 200 204 204 205 207 209 212 212 215

Hard Amorphous Hydrogenated Carbon Films and Alloys Fernando L. Freire Jr. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Film Growth and Chemical Composition . . . . . . . . . . . . . . . . . . . . . . . 3 Film Microstructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Mechanical and Nanotribological Properties . . . . . . . . . . . . . . . . . . . . 5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

217 217 220 224 229 234 235 237

Ion Microscopy on Diamond Claudio Manfredotti . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 IBIC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Lateral IBIC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 IBIL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 XBIC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

239 240 241 246 251 257 263 264 265

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XVII

Measurements of Defect Density Inside CVD Diamond Films Through Nuclear Particle Penetration Renato Potenza, Cristina Tuv´e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 1 Diamond as Radiation Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 1.1 Properties of Diamond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 1.2 Lattice Defects in Synthetic Diamond Crystals . . . . . . . . . . . . . 269 1.3 Application of Diamond to Beam and Beam Proﬁle Monitoring271 2 Mechanism of Conduction in Circuits Including Diamond . . . . . . . . . 273 2.1 Modiﬁed Hecht’s Model for Charge Transport Inside Diamond 275 2.1.1 Absorption of Carriers During Their Transport Along the Electric Field Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275 2.1.2 Edge Eﬀects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 2.2 Eﬀect of Nonuniform Bragg’s Deposit of Charge into Diamond 278 2.3 Nonuniform Distributions of Charge and Defects . . . . . . . . . . . . 279 3 Charge Collection Eﬃciencies of Diamond Detectors Under Ion Bombardment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 3.1 Experimental Procedure to Measure the Charge Collection Eﬃciencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 3.2 Corrections to the Eﬃciencies η± Needed to Into Take Account the Pulse Height Defect of Diamond for Detectors Heavy Ionizing Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 Laser Ablation-Deposited CNx Thin Films Enza Fazio, Enrico Barletta, Francesco Barreca, Guglielmo Mondio, Fortunato Neri, Sebastiano Trusso . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Modeling of the Transport Properties of Diamond Radiation Sensors Stefano Lagomarsino, Silvio Sciortino . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Models of the Polycrystalline Diamond Band Gap . . . . . . . . . . . . . . . 1.1 Band A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Trapping Centers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Carrier Lifetimes and Charge Collection Distance . . . . . . . . . . . 1.4 Location of the Trapping and Recombination Centers in the Diamond Band Gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Unipolar Conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

287 287 288 289 300 301 302

303 303 304 304 305 306 308

XVIII Contents

2

A General Model for Transport Properties of pCVD Diamond: Underlying Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Conductivity Under Exposure to Ionizing Radiation . . . . . . . . . . . . . 4 Thermal Relaxation of Uniform Trap Level Distributions . . . . . . . . . 4.1 Radiation Induced Conductivity Transient at Diﬀerent Fading Times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Persistent Radiation-Induced Conductivity . . . . . . . . . . . . . . . . . 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

309 311 316 317 319 323 325 326

Nucleation Process of CVD Diamond on Molybdenum Substrates Giuliana Faggio, Maria G. Donato, Stefano Lagomarsino, Giacomo Messina, Saveria Santangelo, Silvio Sciortino . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Raman and Photoluminescence Analysis . . . . . . . . . . . . . . . . . . . 3.1.1 Discontinuous Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Continuous Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Statistical Study of the Nucleation Process . . . . . . . . . . . . . . . . . 4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

329 329 330 331 331 332 334 336 340 341 343

Optical Characterisation of High-Quality Homoepitaxial Diamond Maria G. Donato, Giuliana Faggio, Giacomo Messina, Saveria Santangelo, G. Verona Rinati . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Optical and SEM Characterisation . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Raman Characterisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 First-Order Raman Scattering . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Second-Order Raman Scattering . . . . . . . . . . . . . . . . . . . . . 3.3 Photoluminescence Characterisation . . . . . . . . . . . . . . . . . . . . . . . 4 Discussion and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

345 345 348 348 348 350 350 351 352 355 357 358

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XIX

Pulsed Laser Deposition of Carbon Films: Tailoring Structure and Properties Paolo M. Ossi, Antonio Miotello . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Low-Pressure Deposited Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 High-Pressure Deposited Films . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Low-Pressure Deposited Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 High-Pressure Deposited Films . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

359 359 361 362 362 367 373 373 376 377 378 379

Raman Spectra and Structure of sp2 Carbon-Based Materials: Electron–Phonon Coupling, Vibrational Dynamics and Raman Activity Chiara Castiglioni, Fabrizia Negri, Matteo Tommasini, Eugenio Di Donato, Giuseppe Zerbi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Raman Spectra of Polyconjugated Materials . . . . . . . . . . . . . . . . . . . . 3 Electron–Phonon Coupling and Raman Features . . . . . . . . . . . . . . . . 3.1 Electron–Phonon Coupling in Polyacetylene . . . . . . . . . . . . . . . . 3.2 Electron–Phonon Coupling in Graphenes . . . . . . . . . . . . . . . . . . 3.3 Electron–Phonon Coupling in Carbon Nanotubes . . . . . . . . . . . 4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

381 381 383 385 385 390 395 399 400 402

Raman Spectroscopy and Optical Properties of Amorphous Diamond-Like Carbon Films Leonid Khriachtchev . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Raman Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Eﬀects Induced by Interference of Light . . . . . . . . . . . . . . . . . . . . . . . . 5 Optical Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Some Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

403 403 404 405 409 413 416 418 419 420

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Raman Spectroscopy of CVD Carbon Thin Films Excited by Near-Infrared Light Margit Ko´ os, Mikl´os Veres, S´ara T´ oth, Mikl´ os F¨ ule . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 The Raman Eﬀect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Raman Spectra of Carbon Materials . . . . . . . . . . . . . . . . . . . . . . 2 Infrared Excited Raman Spectroscopy of Amorphous Carbon Thin Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 a-C:H Thin Films Prepared from Benzene . . . . . . . . . . . . . . . . . 2.2 a-C:H Thin Layers Prepared From Methane . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

423 423 423 426 429 429 438 443 444

The Role of Hydrogen in the Electronic Structure of Amorphous Carbon: An Electron Spectroscopy Study Lucia Calliari, Massimiliano Filippi, Nadhira Laidani, Gloria Gottardi, Ruben Bartali, Victor Micheli, Mariano Anderle . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Hydrogen Incorporation in the Structure of a-C . . . . . . . . . . . . 2.2 Temperature-Induced Hydrogen Evolution from a-C:H . . . . . . . 3 Hydrogen Incorporation in the Structure of a-C . . . . . . . . . . . . . . . . . 4 Temperature-Induced Hydrogen Evolution from a-C:H . . . . . . . . . . . 5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

447 447 449 449 450 450 455 459 461 462

UV-Induced Photoconduction in Diamond Emanuele Pace, Antonio De Sio, Salvatore Scuderi . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Properties of Diamond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Synthesis of Diamond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Electro-Optical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Polycrystalline Diamond Detectors . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Single-Crystal Diamond Detectors . . . . . . . . . . . . . . . . . . . . . . . . 7 Single-Pixel Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Photodetectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Photoconductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Photodiode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Pixel Array Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1 UV Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Photolithography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

463 463 464 467 468 470 472 474 481 485 485 485 487 489 491 493 494

Contents

9.3 Space Astronomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vibrational Spectroscopy in Ion-Irradiated Carbon-Based Thin Films Giuseppe Compagnini, Orazio Puglisi, Giuseppe A. Baratta, Giovanni Strazzulla . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Irradiation of Crystalline Carbon and Carbon Alloys . . . . . . . . . . . . . 3 Irradiation of Hydrocarbons (Oligomers, Polymers and Frozen Gases) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Irradiation of sp-Rich Amorphous Carbon Phases . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521

Aid of Scaling Laws in the Achievement of a Well-Controlled Film Deposition Process Giacomo Messina and Saveria Santangelo Dipartimento di Meccanica e Materiali, Universit` a “Mediterranea” di Reggio Calabria, Localit` a Feo di Vito, I-89060 Reggio Calabria, Italy, and INFM, Unit` a di Ricerca di Roma “Tor Vergata” [email protected] Abstract. Scaling laws are proﬁtably applied in all the scientiﬁc disciplines. Approximated solutions constitute a valuable aid for the analysis of complex systems and physical processes and, generally, for handling problems involving many variables. We indicate the path for deriving a scaling law for the growth parameters, referring to the synthesis of hydrogenated amorphous carbon-nitrides (a-CN:H) by reactive sputtering as an example. Thanks to its generality, the semiempirical method utilised here can be applied to all carbon-based materials and all deposition techniques. We demonstrate the existence of an analytical dependence of the ﬁlm physical properties, as resulting from Raman analysis and Rutherford backscattering measurements, on a single dimensionless combination of the growth parameters. We give an empirical rule for tailoring the ﬁlm characteristics through speciﬁc changes of the deposition conditions. We thus achieve the capability of easily predicting and controlling the ﬁnal issue of the synthesis process.

1 Introduction The search for approximated solutions, which are useful for describing the behaviour of complex systems and processes, is a topic common to all the scientiﬁc disciplines. In this context, the majority of eﬀorts are generally devoted to the derivation of scaling laws, which play a key role in handling problems involving a great number of variables. In the last years, a semiempirical method [1], based on a modiﬁed application of the theorem on “physically similar systems” of dimensional analysis [2], has been proposed as a physical approach to approximation [3, 4, 5]. According to this method, dimensionless variable combinations (‘Q-arguments’), aimed at describing effectively the process, are generated. These combinations can be regarded as the only independent variables and represent scaling laws for the variables involved. Once the problem is reformulated in terms of Q-arguments, practical approximants to the physical laws governing the process are derived by a ﬁtting procedure to the experimental data. The process issue is, hence, ﬁnally described by analytical functions depending on few parameters, rather than on the many variables initially present. Scaling laws constitute a quite helpful tool for practically controlling and easily improving complex systems whose behaviour depends on several mechG. Messina, S. Santangelo (Eds.): Carbon, The Future Material for Advanced Technology Applications, Topics Appl. Phys. 100, 1–21 (2006) © Springer-Verlag Berlin Heidelberg 2006

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anisms of diﬀerent nature. They are, hence, proﬁtably utilised in a very wide variety of ﬁelds [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], ranging from biology to engineering, from space science to chemistry, from medicine to materials science, from genetics to physics. They also oﬀer a valuable aid in studying complicated processes, such as ﬁlm deposition [20, 21, 22, 23, 24], whose evolution and ﬁnal issue are determined by manyfold concomitant factors. Finding the scaling laws for the growth process allows us to achieve a full control of it, with the consequent possibility of optimising the preparation technique. Once the capability of tailoring the ﬁlm characteristics is acquired, high-quality ﬁlms can be straightforwardly synthesised [5, 25, 26, 27, 28]. The derivation of scaling laws, however, generally represents a diﬃcult task whose success strongly depends on how the process is modelled. For this the reason, it must be faced in the more general context of the process approximation and requires a deep understanding of the mechanisms involved. This contribution, where the ﬁlm growth approximation is addressed, intends to furnish the experimentalist with a powerful tool for acquiring the capability of readily predicting and easily driving the deposition issue, on the basis of the empirically gained know-how. By application to the previously developed method [1], a scaling law for the ﬁlm growth process is derived and approximated solutions are therein attained. The preparation of hydrogenated amorphous carbon–nitrides by reactive sputtering is considered as an example. Nonetheless, the general method utilised can be extensively applied to all growth techniques and materials. We investigate the inﬂuence of the deposition conditions on the physical properties of the grown ﬁlms. By deriving the relationships approximating the physical laws governing the process, empirical rules are achieved for driving it and tailoring the synthesised ﬁlm characteristics through speciﬁc changes of the growth conditions. We use Raman spectroscopy and Rutherford backscattering analysis, but the results of any other postgrowth diagnostic technique could be employed for deriving the scaling law by the use of the same operative procedure. In particular, experimental details are given in Sect. 2. The operative scaling law derivation procedure we develop and our outstanding results obtained are brieﬂy reviewed in Sect. 3. In Sect. 4, the very simple model of the reactive-sputtering growth process, utilised for the scaling law derivation, is illustrated. From the discussion, a deeper insight is achieved on the role played by internal microscopic variables in determining the ﬁnal issue of the a-CN:H ﬁlm sputter-deposition. Conclusions are brieﬂy given in Sect. 5.

2 Experimental Two sets of a-CN:H ﬁlms are prepared by graphite sputtering in N2 –H2 – He–Ar atmosphere using a conventional 13.56 MHz diode system. Samples of series ‘D’ are utilised for deriving the scaling law. Samples of series ‘T’ are deposited afterwards, with the purpose of testing its validity. The deposition

Scaling Laws for Film Deposition

3

Table 1. Values of the dimensionless argument Q corresponding to the growth conditions of a-CN:H ﬁlms utilised for deriving (series ‘D’) and testing (series ‘T’) the scaling law. ΦN2 and ΦH2 indicate the reactive-gas (N2 and H2 ) ﬂow rates, while ΦHe and ΦAr standing for the inert-gas (He and Ar) ﬂow rates. Note that ﬂow rates of inlet gases, chamber pressure (p) and rf power (W ) are varied so that at least the value of one of these parameters is diﬀerent from one deposition to another Film Q #

ΦN2 ΦH2 ΦHe ΦAr p W sccm sccm sccm sccm mTorr W

D1 T1 D2 D3 D4 T2 D5 D6 T3 D7

20.0 8.4 10.0 10.0 10.0 10.0 7.0 4.2 3.0 4.2

0.036 0.079 0.169 0.347 0.434 0.578 0.603 0.715 0.865 0.974

7.0 3.0 5.0 7.0 7.0 7.0 5.0 3.0 2.2 3.0

30.0 70.0 30.0 30.0 30.0 30.0 30.0 70.0 70.0 70.0

70.0 30.0 70.0 70.0 70.0 70.0 70.0 30.0 30.0 30.0

20 38 21 25 20 20 21 38 38 38

300 300 300 300 300 400 300 220 180 300

temperature is 100 ◦ C, while the gas ﬂow rates (ΦN2 , ΦH2 , ΦHe , ΦAr ), chamber pressure (p) and rf power (W ) vary as indicated in Table 1. The ﬁlm stoichiometry is investigated by Rutherford backscattering (RBS) and elastic recoil detection analysis (ERDA) measurements. Raman spectroscopy is employed for studying bonding and structural properties. Details about ﬁlm deposition and analysis, including spectra ﬁtting and interpretation, can be found in [29, 30, 31, 32, 33].

3 Results 3.1 Film Properties Figure 1 shows the Raman spectra of the ﬁlms considered. As discussed [31, 32], the shape evolution of the D band and G bands reﬂects the structural and bonding modiﬁcations, produced by the ﬁlm stoichiometry changes. The most meaningful parameters derived from Raman analysis are shown in Table 2 together with the ﬁlm chemical composition. Since six deposition parameters are independently varied during the preparation of the samples, the representation of these results leads to hypersurfaces in 7-dimensional spaces. In principle, projecting such hypersurfaces could indicate the role of each growth variable. Nevertheless, the simultaneous variation of the remaining deposition parameters actually causes a confused spreading of the projected points, with a consequent lack of a clear correlation with the changes in ﬁlm stoichiometry and related properties.

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Giacomo Messina and Saveria Santangelo

Fig. 1. Raman spectra of a-CN:H ﬁlms belonging to (a) series D, used for deriving, and (b) series T, used for testing scaling law. Excitation energy is 2.41 eV. Spectra decomposition results are shown in case of sample D6, as an example. Dotted and dashed lines represent the best ﬁts to spectrum and D band and G band, respectively

This, as demonstrated in Fig. 2, where the G band frequency position (ωG ) is plotted as a function of rf power and chamber pressure, hinders us from guessing the possible eﬀect of any variation of the growth conditions on the ﬁlm characteristics. 3.2 Operative Scaling Law Derivation Procedure A simpler picture might derive from ﬁnding a dependence of Raman descriptive parameters on a limited number (L) of dimensionless arguments in place of the initial N (L) growth variables. The search for such arguments is pursued through a semiempirical method [1], based on an extended application of the theorem on “physically similar systems” of dimensional analysis [2]. A two-way and trial-and-error approach (Fig. 3), involving the repeated comparison with the experimental data, is utilised in place of the standard one-way and necessary procedure. After replacement of dimension-

Scaling Laws for Film Deposition

5

Table 2. Results of the structural and compositional analysis carried out on the ﬁlms. Samples are listed in increasing order of Q. ωG and ID /IG stand for G band frequency position and D/G intensity ratio measured in the Raman spectra, respectively. LC denotes the average size of Csp2 clusters estimated from ID /IG values [34]. The ﬁlm C, H and N contents, as well as O contamination, resulting from ERDA and RBS measurements, are reported Film ωG # cm−1

ID /IG LC nm

C content H content N content O content % % % %

D1 T1 D2 D3 D4 T2 D5 D6 T3 D7

0.89 1.18 1.03 0.91 0.96 0.91 0.94 1.06 1.20 1.23

69.9 75.8 73.5 74.6 71.4 71.4 74.6 73.0 79.4 79.0

1575.2 1575.1 1575.0 1574.1 1573.6 1573.2 1572.3 1569.9 1563.9 1563.3

1.27 1.46 1.37 1.29 1.32 1.29 1.31 1.39 1.48 1.50

19.6 12.9 15.4 14.2 17.9 17.9 14.2 16.1 8.7 7.2

7.0 7.6 7.4 7.5 7.1 7.1 7.5 7.3 7.9 9.8

3.5 3.7 3.7 3.7 3.6 3.6 3.7 3.6 4.0 4.0

Fig. 2. Dependence of the G band frequency position (ωG ) on rf power (W ) and chamber pressure (p). The ωG points shown are obtained by projecting the 7dimensional ωG hypersurface. Their confused spreading in the W, p, ωG space is due to the simultaneous variation of the ﬂow rates of the inlet gases

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Giacomo Messina and Saveria Santangelo

Fig. 3. Scheme of the ﬂow chart used for deriving the scaling law Q. Stage 1: initialisation and testing of the argument Q. Stage 2: deﬁnition of a new argument as power product of further dimensionless variable combinations Qk . M represents the maximum number of arguments Qk entering the new formulation of Q. Stage 3: adjusting of the exponents αk and testing of the scaling law. The experimental data are approximated to a suited function of Q and exponent adjusting is pursued, in a suﬃciently high iteration number I, by minimising the standard deviation σ

ate Raman descriptive parameters with appropriate dimensionless Raman arguments, arbitrary dimensionless combinations (Q1 , Q2 , ..., QL ) of the growth parameters (G1 , G2 , ..., GN ) are generated on the basis of physical considerations, by the aid of dimensional analysis. The operative procedure [35] followed comprises three stages: Stage 1. A dimensionless argument Q1 is ﬁrstly generated (argument Q initialisation). Assuming that the Raman argument R depends on Q, the experimental data are approximated to a suited function of Q. If the standard deviation σ does not exceed the prior-established maximum allowed value σmax (argument Q testing), combination Q1 represents the scaling law searched for. Stage 2. If not, a new dimensionless argument Q2 is generated (new argument Q deﬁnition), and R is assumed to depend on Q1 and Q2 through the power product Q1 Qα 2 (exponent initialisation).

Scaling Laws for Film Deposition

7

Fig. 4. Progressive process picture simpliﬁcation achieved during the various stages of the scaling law derivation. The dependence of the dimensionless Raman variables α β Ω (a–c) and ID /IG (d–f ) on arguments Q1 , Q1 Qα 2 and Q1 Q2 Q3 (where Q1 = −1 −1 −1 −1 W · p · Φrg , Q2 = ΦAr · Φ and Q3 = ΦN2 · ΦH2 ). The numerical value, −2/3, of exponent α is empirically determined by separately minimising the data spread in plots (b) and (e). The numerical value, −3, of exponent β is attained by analogous procedure from plots (c) and (f ). As the scaling law derivation progresses, Ω and ID /IG points progressively order, so they ﬁnally show clear trends. The dashed lines represent the best ﬁts to the (c) Ω and (f ) ID /IG data relative to samples of series D

Stage 3. A new function of Q is chosen for approximating the experimental data. The value of the exponent α is optimised (exponent adjusting) by minimising the corresponding standard deviation σ(α). If σ(α) ≤ σmax (scaling law testing), the procedure is stopped. The combination so attained represents the scaling law for the growth parameters. Otherwise, stages 2 and 3 β are repeated. A further argument Q3 is generated and the form Q1 Qα 2 Q3 hypothesised for the scaling law. If σ(β) ≤ σmax , the procedure is stopped and the eﬀective dependence of the argument R on the growth parameters involved is determined. The same procedure as for R has to be followed for any other Raman argument R and/or for the ﬁlm fractional content of any composing element ξ (with k ξk = 1). However, in principle, the introduction of diﬀerent arguments (Q1 , Q2 , ...) is necessary and diﬀerent exponents (α , β , ...) are, as a consequence, attained.

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3.3 Choice of Q-arguments According to the procedure of Sect. 3.2, the G band frequency position is ﬁrst replaced with the dimensionless argument Ω = (ωsp2 − ωG )/ωsp2 (where ωsp2 = 1575 cm−1 is the value, ωG tends to in disordered CN-alloys with low C contents [31]) and the D/G intensity ratio (ID /IG ) is considered in place of the average size of Csp2 clusters (LC ). Suitable dimensionless combinations of the deposition variables are then generated on the basis of the current assessments on the synthesis of C-based ﬁlms [36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46]. It is worth noting that the same procedure as for Ω is independently followed for ID /IG , as well as for the fractional ﬁlm N-content (ξN = 0.070 − −0.098). However, since both Raman arguments reﬂect the features of Cnanostructures, that, in turn, are strongly inﬂuenced by the N-incorporation level, the same arguments are tentatively considered and successfully tested by comparison with the experimental Ω, ID /IG and ξN data. The ﬁrst argument introduced, Q1 = W · p−1 · Φ−1 rg (where Φrg = ΦN2 + ΦH2 stands for the reactive gas ﬂow rate), ideally relies on impact ion energy for depositions operated in reactive atmosphere [24]. It is chosen with the purpose of taking into account the signiﬁcant role played by impact ion energy in determining the ﬁlm characteristics [37, 39, 40, 46]. It has been demonstrated [24] that, if the ﬁlms are prepared by changing solely W , p and Φrg , the choice of Q1 as a scaling law for the growth parameters allows stopping the procedure at stage 1. In the presence of a larger number of independently varying deposition variables instead, Q1 introduces only a partial simpliﬁcation (Fig. 4a,d), calling for the successive stage running. Hence, a second argument, Q2 = ΦAr · Φ−1 (where Φ = Φrg + ΦHe + ΦAr denotes the ﬂow rate of all inlet gases), is generated. The introduction of Q1 is intended to take into account the strong inﬂuence exerted by the changes of Ar gas fraction on the deposition rate and C-atom nanostructure formation [47, 48, 49, 50]. The comparison with the experimental data in stage 3 (Fig. 4b,e) shows that the combination −1 −2/3 ) remarkably reduces the spread of both Ω and W · p−1 · Φ−1 rg · (ΦAr · Φ ID /IG points. Trying to further simplify the process picture, stages 2 and 3 are repeated. A third argument, Q3 = ΦN2 · Φ−1 H2 , ideally taking into account the antagonist action carried out by N2 against H2 in surface reactions involving growth precursor species [51, 52, 53], is ﬁnally generated.

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9

3.4 The Scaling Law for the Growth Conditions At the end of the above described procedure, the scaling law, −2/3

Q = W · p−1 · Φ−1 rg · ΦAr

3 · Φ2/3 · Φ−3 N2 · ΦH2

(1)

(with rf power, chamber pressure and gas ﬂow rates expressed in W, mTorr and sccm, respectively), is derived. This law is able to eﬀectively account for the variations of the fractional ﬁlm N-content and of considered Raman arguments with the growth conditions. At this stage, (1) actually accounts for all the changes of ξN , Ω (Fig. 4c) and ID /IG (Fig. 4f) produced by the variations of W , p, ΦAr , Φ, ΦN2 and ΦH2 in the ranges 220−−300 W, 20−−38 mTorr, 30−−70 sccm, 107−−127 sccm, 4−−20 sccm and 3−−7 sccm (under which the ﬁlms of series D are prepared). In order to further test the eﬀectiveness of Q, a new series of samples is prepared. The deposition parameters of these ﬁlms (series T) are chosen so as to obtain values of Q falling within the range investigated (even if a wider range is actually considered for some of the growth variables). The ξN , Ω and ID /IG points relative to additional samples line up along the curves drawn by points relative to ﬁlms of series D, conﬁrming the validity of the scaling law derived. This is demonstrated in Fig. 5 for the ﬁlm N-content (xN ) and in Figs. 6 and 7 for the dimensionate Raman variables ωG and LC . Argument Q, therefore, ﬁnally turns out to be able to account for all the changes of xN , ωG and LC produced by the variations of W , p, ΦAr , Φ, ΦN2 and ΦH2 in the ranges 180 − −400 W, 20 − −38 mTorr, 30 − −70 sccm, 105 − −127 sccm, 4 − −20 sccm and 2 − −7 sccm. 3.5 Resulting Simpliﬁcation of the Process Picture As demonstrated in Fig. 4, a progressive process picture simpliﬁcation is achieved once the problem is reformulated in terms of Q-arguments. This result is of crucial importance for the achievement of a well-controlled deposition process. First, ξN , Ω and ID /IG points, initially covering 7D hypersurfaces as an eﬀect of the variation of W , p, ΦAr , Φ, ΦN2 and ΦH2 , now line up along 2D curves. The reason is that, as shown, ξN , Ω and ID /IG depend on the growth parameters through a single dimensionless combination of them. In second place, by ﬁtting such curves to proper functions, the dependence of ξN , Ω and ID /IG (i.e., of xN , ωG and LC ) on the deposition variables can be explicitly determined. The choice of the functions approximating the physical laws governing the process is, to some extent, arbitrary. Nevertheless, the ﬁlm N-content is satisfactorily ﬁtted to xN (%) 7.26 + 0.85 exp[((Q/0.8)0.1 )].

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Giacomo Messina and Saveria Santangelo

Fig. 5. Dependence of ﬁlm N content (xN ) on the dimensionless argument Q. Open and ﬁlled symbols refer to a-CN:H ﬁlms utilised for deriving (series D) and testing (series T) the scaling law, respectively. The dashed line represents the physical approximant, xN 7.26 + 0.85 exp[((Q/0.8)0.1 )], to the data

The frequency position of the G band and average size of Csp2 clusters of the ﬁlms under study are well reproduced by the analytical functions ωG (cm−1 ) 1565.8 − 3.0Q + 9.5 exp[−(Q/0.8)8] and LC (nm) 1.49 − 7.59Q2 exp(−5.49Q2), whose form, empirically demonstrated by ﬁtting the experimental data, is theoretically inferred from extremely simpliﬁed models [54] that account for the inﬂuence of the microscopic growth variables on the deposition process. Finally, if the growth parameters are scaled within the ranges above indicated, according to (1), the N-incorporation level into the ﬁlm and the features of the resulting C-nanostructures do not correspondingly undergo signiﬁcant changes. In other words, xN , ωG and LC are invariant for all the simultaneous variations of W , p, ΦAr , Φ, ΦN2 and ΦH2 leaving Q unchanged. This further implies that the same xN , ωG and LC can be obtained even starting from diﬀerent conﬁgurations, provided that the deposition parameters selected give the same value of Q. Once a clear correlation is established between variations of the growth conditions and corresponding changes of the ﬁlm physical properties, the ﬁnal issue of sample preparation can be foreseen and, besides, the a-CN:H characteristics can be tailored by properly tuning the deposition parameters.

Scaling Laws for Film Deposition

11

Fig. 6. Dependence of the G band frequency position (ωG ) on the dimensionless argument Q. Symbols are the same as in Fig. 5. The dashed line represents the physical approximant, ωG 1565.8 − 3.0Q + 9.5 exp[−(Q/0.8)8 ], to the data. Note that ωG data are the same as shown in Fig. 2. The comparison between the two plots clearly demonstrates the simpliﬁcation attained after the problem reformulation in terms of argument Q

Fig. 7. Dependence of the Csp2 cluster average size (LC ) on the dimensionless argument Q. Symbols are the same as in Fig. 5. The dashed line represents the physical approximant, LC 1.49 − 7.59Q2 exp(−5.49Q2 ), to the data

4 Discussion 4.1 Reason for the Scaling Law Existence The presented results clearly show that, in the ﬁlms considered, stoichiometry and related structural properties are determined by the six independent deposition parameters through a single combination of them. The existence

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Giacomo Messina and Saveria Santangelo

Fig. 8. Average ﬁlm growth rate as a function of the dimensionless argument Q. Symbols are the same as in Fig. 5; a line is drawn as a visual help

of such an eﬀective combination suggests the possibility that, upon variation of the growth conditions, a mutual compensation takes place between the eﬀects generated on ﬁlm composition and C-nanostructures by the physical agents (impact ion energy of precursor species, inﬂuence of sputtering gas and antagonism of H2 and N2 in surface reactions), which arguments Q1 , Q2 and Q3 are related to. For instance, the simultaneous increase of rf power and ﬂow rate of sputtering gas will reﬂect onto higher impact energy of the precursor species and improved sputtering eﬃciency. The former factor favours C-enrichment of the growing layer, while, contrarily, the latter hinders Cdeposit due to the etching process carried out by Ar-atoms. Analogously, raising the nitrogen ﬂow rate, while simultaneously decreasing chamber pressure, will cause a N-incorporation enhancement and, again, an impact ion energy increase. The former agent promotes the formation of nucleation centres for Csp2 clusters, while the latter, conversely, favours the development of tetrahedrally bonded C-phase. Therefore, in both the cases, as a balance of the opposite eﬀects generated by the variation of the microscopic variables involved into the growth process, the stoichiometry and the structural and bonding properties of the deposited ﬁlm may ﬁnally undergo no appreciable change. The cited examples allow us to qualitatively understand the reason for the existence of scaling law (1) and the related invariance of the ﬁlm characteristics. Below, an alternative path for deriving the scaling law is proposed, based on the formulation of a simple theoretical model of the growth process. In this frame, the changes undergone by the microscopic variables internally ruling the ﬁlm deposition are correlated with the variations externally carried out on the growth parameters, so as the scaling law existence is semiquantitatively explained.

Scaling Laws for Film Deposition

13

4.2 Modelling of the Growth Process It is important to remember that an approximate, rather than an exact solution to the complex problem of ﬁlm deposition by reactive sputtering is here searched for. This concept should guide the reader in the present subsection, where an extremely simpliﬁed model is proposed. An exhaustive discussion about the mechanisms involved in a-C-based ﬁlm growth can be found in [46]. Here, far from regarding all the variables actually governing the ﬁlm deposition, the discussion is limited to those parameters whose variation (Table 1) is responsible for the property changes observed in the samples under study (Table 2). As commonly established [36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46], impact ion energy and amount of C-species trapped into the growing layer have a relevant inﬂuence in the synthesis of a-C ﬁlms. Since in a-CN:H preparation the C-deposit is controlled by the irreversible surface reactions, the average energy with which the N- and H-containing precursor species (CHx , C2 Hx , CNx , C2 Nx , Hx CN, . . . [55, 56, 57, 58]) impinge onto the substrate does enter the problem. On the basis of these assessments, it has been demonstrated [24] that the dimensionless combination of the deposition variables, which are able to account for the modiﬁcations of the characteristics, featuring sputtered aCN:H ﬁlms prepared by varying only W , p and Φrg , can be written as a power product of impact energy of radicals containing reactive species (Ei,r ) and deposition ﬂux towards the substrate (FC→s ), Q = (Ei,r )a · (FC→s )c ,

(2)

with a and c exponents to be empirically determined. Having elementarily modelled FC→s under proper assumptions [24], combination (2) simpliﬁes to W · p−1 · Φ−1 rg , i.e., to argument Q1 . However, in present case, because of the variation of a larger number of growth parameters, FC→s requires a diﬀerent and more sophisticated modelling. As known, in addition to impact ion energy, the structural and bonding properties of a-C based materials largely depend on the deposition rate [48, 49, 50], which, in turn, in ﬁlm preparation by sputter techniques, is strongly inﬂuenced by the sputtering gas action. The sputtering gas exerts a twofold action, resulting in simultaneous competing deposition and etching processes [59, 60], which alternatingly prevail depending on the changes made in the growth conditions. Such an alternation is evidenced, as in present case (Fig. 8), by a nonmonotonic variation of the ﬁlm growth rate. The reason for this competition is that, as the sputtering gas fraction increases, on one hand, sputtering eﬃciency improves and C-ﬂux towards the plasma enhances. Meanwhile, on the other hand, high-energy Ar-atoms etch the growing ﬁlm layer causing a diminishing deposition rate. Then, nitrogen and hydrogen bring about a competitive action in surface reactions [51, 52, 53]. The antagonism between the two reactive gases

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Giacomo Messina and Saveria Santangelo

is due to the diﬀerent sticking coeﬃcients of N- and H-containing precursor species. Radicals having energy enough penetrate into the growing layer, while the remaining ones stick to its surface and form an adsorbate layer. Nitrogenated radicals possess, on average, lower impact energies, i.e., higher sticking coeﬃcients, sn . They are, hence, generally adsorbed onto the growing layer [38]. Contrarily, more energetic hydrogenated radicals (to which lower sticking coeﬃcients, sh , pertain) penetrate into the growing layer with consequent densiﬁcation [46]. This reﬂects onto the local C-bonding and ﬁlm stoichiometry. Since terminal Cspx Nspy groups act as nucleation centres for Csp2 phase [31, 33], the adsorption of nitrogen promotes the ﬁlm clusterisation degree enhancement. The penetration of hydrogen, instead, favours the formation of hydrocarbon groups Csp3 Hx [31, 33, 61]. In addition, since hydrogen is preferentially released in ion-induced desorption (dehydrogenation) [46], H-adsorption promotes the ﬁlm C-enrichment. N-incorporation, instead, progresses at expense of the ﬁlm C-content (see [61] in this book at p. 221). Therefore, any variation of the ratio sn /sh results in changes of ﬁlm stoichiometry, as well as of the nature of nanostructures formed by C-atoms. These are the reasons why a comprehensive model of FC→s , besides to the role of the permanence time (trg ) of reactive gases into the chamber [24], should primarily take into account the action of the ﬂuxes of Ar-atoms towards target (FAr→t ) and substrate (FAr→s ), as well as of the ﬂux of reactive gases towards the substrate (Frg→s ). The eﬀects should be, then, further considered of the antagonism between N2 and H2 , ruled by the ratio (sn,h ) between the sticking coeﬃcients of nitrogenated and hydrogenated radicals. FAr→t feeds the C-ﬂux towards the plasma, favouring C-deposit. Contrarily, being responsible for the simultaneous etching process, FAr→s hinders deposition. Acting on the precursor species formation, Frg→s controls Cincorporation into the growing layer. Finally, sn,h decides the type of growth Table 3. Proportionality relationships between microscopic (internal) growth variables and measurable (external) deposition parameters. Ei,r denotes the average impact energy of radicals containing reactive species. FAr→s and FAr→t respectively indicate ﬂuxes of Ar atoms towards substrate and target. Frg→s stands for ﬂux of reactive gases towards the substrate. Finally, trg denotes the permanence time of reactive gases into the deposition chamber, while sn,h indicates the ratio, sn /sh , between sticking coeﬃcients of nitrogenated to hydrogenated precursor species Internal variable Proportionality with external parameters From refs. Ei,r FAr→t FAr→s Frg→s trg sn,h

W 1/2 · p−1 · Φ−1 rg · Φ W 3/4 · p1/4 · ΦAr · Φ−1 W 1/4 · p3/4 · ΦAr · Φ−1 W 1/4 · p3/4 · Φrg · Φ−1 p · Φ−1 ΦN2 · Φ−1 H2

[36], [41], [46] [36], [46], [62] [54] [54] [24] [54]

Scaling Laws for Film Deposition

15

precursors incorporated. Accordingly, the ﬂux of precursor species reaching and sticking to the substrate is here modelled as: FC→s ∝ (FAr→t )b · (FAr→s )−d · (Frg→s )f · (trg )h · (sn,h )−l ,

(3)

with b, d, f , h and l positive exponents to be empirically determined. FAr→s and sn,h enter expression (3) with negative exponents, which ideally take into account the hindering action, carried out by etching process and Nincorporation, against C-deposit. Such a novel expression generalises that previously derived [24]. 4.3 Physical Meaning of the Scaling Law As accurately discussed in [54], in a-CN:H preparation by rf diode systems, under the deposition conditions of Table 1, the above-considered microscopic process variables are related to the macroscopic growth parameters through the proportionality relationships reported in Table 3. Replacing such expressions in (2) and (3) allows us to write Q explicitly in terms of measurable and externally tunable parameters. The latter enter the expression of Q consequently obtained with the exponents reported in Table 4. The numerical values of these exponents can be empirically determined through the experimental data ﬁtting, so as to ﬁnally obtain: −2/3

· Φ4/3 ) · (W 1/3 · p1/3 · ΦAr (W 2/3 · p−4/3 · Φ−4/3 rg

−3 3 · Φ−2/3 · Φ1/3 rg · ΦN2 · ΦH2 ).

4/3

This product, whose ﬁrst term corresponds to Ei,r , while the second being a power of FC→s , gives combination (1). All the deposition parameters but ΦAr enter both the two microscopic factors singled out within the expression of Q, and, what is more, each of them inﬂuences more than one internal variable. Hence, varying the growth conditions causes many microscopic variables to change simultaneously and, sometimes, the opposite eﬀects, which are produced by these changes on ﬁlm stoichiometry and the nature of C-nanostructures, to compensate each other. For this reason the ﬁlm properties may appear insensitive to the changes of the deposition conditions or, more generally, their modiﬁcations may be not readily foreseeable. 4.4 The Scaling Law for the Microscopic Growth Variables Once the exponents, with which the external deposition parameters enter combination obtained by replacing (3) in (2), have been empirically determined, the explicit relationship between Q and the microscopic growth variables can be further derived by the aid of relationships of Table 4, so we ﬁnally attain Q = (Ei,r )4/3 · (FAr→t )5/6 · (FAr→s )−3/2 · (Frg→s )1/3 · (trg ) · (sn,h )−3 .

(4)

16

Giacomo Messina and Saveria Santangelo

Table 4. Exponents with which the deposition parameters enter (2), as explicitly written, in terms of measurable parameters, after replacement of relationships reported in Table 3. W and p denote rf power and chamber pressure, while Φrg and ΦAr indicate the ﬂow rates of reactive gases and sputtering gas, respectively. Φ stands for the ﬂow rate of all the inlet gases. ΦN2 and ΦH2 denote N2 and H2 ﬂow rates Deposition parameter Corresponding exponent

Numerical value

W

a/2 + (3b − d + f ) · c/4

p

−a + (b − 3d + 3f + 4h) · c/4 −1

Φrg

−a + f c

−1

ΦAr

c · (b − d)

−

Φ

a − c · (b − d + f + h)

ΦN2

−lc

ΦH2

lc

1

2 3 2 3 −3 3

As hypothesised, Q depends inversely on FAr→s and sn,h . This ﬁnding indirectly conﬁrms the property of the assumptions on which the model formulated is based. In particular, (4) demonstrates that, as hypothetically supposed by expression (3), manifold factors may simultaneously inﬂuence FC→s . Favouring and feeding the precursor species formation, longer trg and larger Frg→s make more intense the carbonaceous ﬂux towards the substrate. FAr→t assists C-ﬂux towards the plasma, thus its increase results in ﬁlm C-enrichment. Contrarily, raising FAr→t , as a result of etching enhancement, hinders the development of the growing layer. The balance between the simultaneous deposition and etching processes determines the ﬁlm growth rate [61]. However, all the internal deposition variables cooperatively participate in the occurrence of these processes. This is clearly demonstrated in Fig. 8, where the average deposition rate, as deduced from the results of joint IR and RBS ﬁlm-thickness measurements [54], is plotted as a function of Q. A nonmonotonic trend is obtained, as expected. Finally, since the incorporation of nitrogen progresses at the expense of ﬁlm C-enrichment [61], contrarily promoted by hydrogen due to the preferential desorption from the surface adsorbate layer, decreasing sn and/or increasing sh , i.e., lowering sn,h , ultimately results in ﬁlms with higher C-contents. Combination (1) provides the rules according to which the external deposition parameters, W , p, ΦAr , Φ, ΦN2 and ΦH2 , can be scaled, within the ranges considered, with no signiﬁcant changes in ﬁlm stoichiometry and nature of C-nanostructures. Correspondingly, (4) can be regarded as the scaling law for the internal growth variables, Ei,r , FAr→t , FAr→s , Frg→s , trg and sn,h .

Scaling Laws for Film Deposition

17

The existence of the latter reﬂects onto (and, thus, explains fully and deﬁnitely) the existence of the former. 4.5 A Figure of Merit for a-CN:H Film Deposition It is ﬁnally important to point out another relevant outcome emerging from the search for an approximated solution to the a-CN:H ﬁlm growth process. According to expression (2), in order to increase Q it is suﬃcient that only one of the two factors, that Ei,r - or that FC→s -related, increases due to variations in the growth conditions. On one hand, as known, increasing impact ion energy gives rise to higher sp3 /sp2 C-bonding (i.e., fourfold-/threefoldcoordinated C-atom) fractions. On the other hand, enhancing FC→s allows the deposition of C-richer ﬁlms. Since all the elements in the ﬁlms exhibit a coordination number lower than C (Nsp1 is 1- or 2-coordinated [63]; Nsp2 , if present, is 2- or, in very few cases, 3-coordinated [64]; H is 1-coordinated), the increase of relative C-content causes similarly the enhancement of the ﬁlm average coordination number (χav ). As evidenced by the G band downshift (Fig. 6), ﬁlms with improved characteristics are actually obtained at higher Q values. Hence, Q can be regarded as a “ﬁgure of merit” for hydrogenated amorphous carbon–nitride growth by sputtering. When deposition is operated in the low Q regime, the N-incorporation level remains roughly constant (Fig. 5). Under this condition, the slow ωG variation (Fig. 6) reﬂects the C-bonding evolution produced by the formation of diﬀerent hydrocarbon groups [29, 31, 33]. Porous, softer and H-richer ﬁlms are attained, with Csp2 cluster islands exhibiting progressively smaller dimensions going towards lower Q (Fig. 7). By operating at higher Q values, instead, the enhanced terminal Cspx Nspy group formation promotes the Csp2 matrix development and hinders H-incorporation [29, 31, 33]. Correspondingly, LC gradually increases, while ωG drops as an eﬀect of the changed ﬁlm stoichiometry and related χav increase.

5 Conclusion The results of Raman analysis and Rutherford backscattering measurements performed on a-CN:H ﬁlms, prepared by graphite sputtering in N2 –H2 –He–Ar atmosphere, are utilised for the derivation of a scaling law for the deposition parameters. This is accomplished by means of a semiempirical approach, based on an extended application of theorem on “physically similar systems” of dimensional analysis. The inﬂuence of the growth conditions on the ﬁlm stoichiometry as well as on the resulting features of the nanostructures formed by C-atoms is investigated. By elementarily modelling the reactive sputtering process, the crucial role played by the variables internally ruling ﬁlm deposition is

18

Giacomo Messina and Saveria Santangelo

clariﬁed. We demonstrate that impact energy of radicals containing reactive species (Ei,r ), ﬂuxes of Ar-atoms towards substrate (FAr→s ) and target (FAr→t ), ﬂux of reactive gases towards the substrate (Frg→s ), permanence time of reactive gases into the deposition chamber (trg ) and ratio between sticking coeﬃcients of nitrogenated to hydrogenated precursor species (sn,h ) enter in determining the ﬁlm properties through their combination 4/3 5/6 −3/2 1/3 Q = Ei,r · FAr→t · FAr→s · Frg→s · trg · s−3 n,h . Such a combination represents the scaling law for the process on a microscopic scale. In the frame of the growth process approximation, the changes undergone by the internal variables are therewith correlated with the variations externally operated on rf power (W ), chamber pressure (p) and ﬂow rate of all the inlet gases (Φ), of sputtering-gas (ΦAr ) and of reactive gases (Φrg = ΦN2 + ΦH2 ). As a result, the scaling law, −2/3 3 Q = W · p−1 · Φ−1 · Φ2/3 · Φ−3 rg · ΦAr N2 · ΦH2 , for the measurable and externally tunable deposition parameters is derived. The argument Q is then shown capable of accounting for all the changes of the ﬁlm N-content (xN ), of the frequency position of the G band (ωG ) and of the average size of Csp2 clusters (LC ), produced by the variations of W , p, ΦAr , Φ, ΦN2 and ΦH2 in the ranges 180 − −400 W, 20 − −38 mTorr (2.7−−5.1 Pa), 30−−70 sccm, 105−−127 sccm, 4−−20 sccm and 2−−7 sccm. By ﬁtting the experimental data relative to the ﬁlms under study, the physical approximants xN (%) 7.26 + 0.85 exp[((Q/0.8)0.1 )], ωG (cm−1 ) 1565.8 − 3.0Q + 9.5 exp[−(Q/0.8)8 ] and LC (nm) 1.49 − 7.59Q2 exp(−5.49Q2) are attained. These represent the empirical rules whose knowledge is required to be able to tailor the ﬁlm characteristics through speciﬁc changes of the deposition conditions. Acknowledgements We wish to thank Prof. A. Tagliaferro and Dr. G. Fanchini of the Physics Department, Polytechnics of Torino, who kindly provided a-CN:H samples.

References [1] G. Messina, A. Paoletti, S. Santangelo, A. Tucciarone: Microsys. Technol. 1, 23 (1994) 1, 2, 4 [2] P. W. Bridgman: Dimensional Analysis (Yale University Press, New Haven 1931) 1, 4 [3] G. Messina, S. Santangelo, A. Paoletti, A. Tucciarone: Microelectron. Eng. 34, 147 (1997) 1 [4] G. Messina, A. Paoletti, S. Santangelo, A. Tucciarone: Nuovo Cimento D 20, 1201 (1998) 1 [5] S. Santangelo, G. Messina, G. Fanchini, A. Tagliaferro: Diam. Relat. Mater. 13, 1391 (2004) 1, 2 [6] J. Bragard, G. Lebon: Transport Porous Med. 16, 253 (1994) 2

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[36] Y. Catherine: Diamond and Diamond-like Films and Coatings, Proc. of NATOASI 1990 (Plenum, New York) 8, 13, 14 [37] P. J. Fallon, V. S. Veerasamy, C. A. Davis, J. Robertson, G. A. J. Amaratunga, W. I. Milne, J. Koshinen: Phys. Rev. B 48, 4777 (1993) 8, 13 [38] J. Robertson: Diam. Relat. Mater. 3, 361 (1994) 8, 13, 14 [39] Y. Lifshitz: Diam. Relat. Mater. 5, 388 (1996) 8, 13 [40] M. Chhowalla, J. Robertson, C. W. Chen, S. R. P. Silva, C. A. Davis, G. A. J. Amaratunga, W. I. Milne: J. Appl. Phys. 81, 139 (1997) 8, 13 [41] J. Robertson: Amorphous Carbon: State of the Art (World Scientiﬁc, Singapore 1998) p. 32 8, 13, 14 [42] D. Schneider, C. F. Meyer, H. Mai, B. Sch¨ oneich, H. Ziegele, H. J. Scheibe, Y. Lifshitz: Diam. Relat. Mater. 7, 973 (1998) 8, 13 [43] R. G. Lacerda, F. C. Marques, F. L. F. Jr.: Diam. Relat. Mater. 8, 495 (1999) 8, 13 [44] M. P. Siegal, P. N. Provencio, D. R. Tallant, R. L. Simpson: Appl. Phys. Lett. 76, 2047 (2000) 8, 13 [45] K. Yamamoto, K. Wazumi, T. Watanabe, Y. Koga, S. Iijima: Diam. Relat. Mater. 11, 1130 (2002) 8, 13 [46] J. Robertson: Mat. Sci. Eng. R 37, 129 (2002) 8, 13, 14 [47] F. Parmigiani, E. Kaym, H. Seki: J. Appl. Phys. 64, 3031 (1988) 8 [48] R. Kurt, R. Sanjines, A. Karimi, F. L´evy: Diam. Relat. Mater. 9, 566 (2000) 8, 13 [49] S. Santucci, L. Lozzi, L. Valentini, J. M. Kenny, A. Menelle: Diam. Relat. Mater. 11, 1188 (2002) 8, 13 [50] J. M. Ting, H. Lee: Diam. Relat. Mater. 11, 1119 (2002) 8, 13 [51] S. R. P. Silva, B. Raﬀerty, G. A. J. Amaratunga, J. Schwan, D. F. Franceschini, L. M. Brown: Diam. Relat. Mater. 5, 401 (1996) 8, 13 [52] S. R. P. Silva, J. Robertson, G. A. J. Amaratunga, B. Raﬀerty, L. M. Brown, J. Schwan, D. F. Franceschini, G. Mariotto: J. Appl. Phys. 81, 2626 (1997) 8, 13 [53] C. Godet, N. M. J. Conway, J. E. Bour´ee, K. Bouamra, A. Grosman, C. Ortega: J. Appl. Phys. 91, 4154 (2002) 8, 13 [54] G. Messina, S. Santangelo: Diam. Relat. Mater. 14, 1331 (2005) 10, 14, 15, 16 [55] R. Kaltofen, T. Sebald, G. Weise: Thin Solid Films 118, 308 (1997) 13 [56] W. Jacob: Thin Solid Films 326, 1 (1998) 13 [57] R. L. C. Wu, K. Miyoshi, W. C. Lanter, J. D. Wrbanek, C. A. D. Joseph: Surf. Coat. Tech. 573, 120–121 (1999) 13 [58] N. Mutsukura, K. Akita: Diam. Relat. Mater. 9, 761 (2000) 13 [59] J. Hong, A. Granier, A. Goullet, G. Turban: Diam. Relat. Mater. 9, 573 (2000) 13 [60] B. Druz, Y. Yevtukhov, V. Novotny, I. Zaritsky, V. Kanarov, V. Polyakov, A. Rukavishnikov: Diam. Relat. Mater. 9, 668 (2000) 13 [61] F. Freire, Jr.: Hard amorphous hydrogenated carbon ﬁlms and alloys, in G. Messina, S. Santangelo (Eds.): Carbon, The Future Material for Advanced Technology Applications, vol. 100, Topics Appl. Phys. (Springer, Heidelberg, Berlin 2006) 14, 16

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Index a-C:H:N, 1–5, 10, 11, 13, 14, 16, 17 sp2 -bonded clusters, 5, 10, 18 cluster size, 5, 8, 10, 11, 18 sp3 /sp2 bonding ratio, 17

hydrogenated amorphous carbonnitrides, 1

approximated solutions, 1, 2, 10, 11, 13

nitrogen incorporation, 10, 12–17

carbon coordination, 17 threefold and fourfold coordination, 17 dimensionless arguments, 4–6, 8 ﬁgure of merit for growth process, 17 ﬁlm stoichiometry, 3, 11, 12, 14–17 G band, 3, 4, 8, 10, 11, 17, 18 hydrogen desorption, 14, 16

microscopic growth variables, 12–15

physical approximants, 1, 10, 11, 18 process approximation, 2, 13–15, 18 process modelling, 13–15 Q-arguments, 1, 6, 8, 9 Raman dimensionless arguments, 6–8 Raman spectroscopy, 1–3, 17 reactive sputtering, 2, 13 scaling laws, 1, 2, 15, 17, 18 derivation method, 1, 4, 7–9, 17 validity range, 9

A Spectroscopic Approach to Carbon Materials for Energy Storage Giuseppe Zerbi1,2 , Matteo Tommasini1,2 , Andrea Centrone1,2 , Luigi Brambilla1,2 , and Chiara Castiglioni1,2 1

2

Dipartimento di Chimica, Materiali e Ingegneria Chimica “G. Natta”, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy, and INSTM, Unit` a di Ricerca di Milano Centro d’Eccellenza “Nano-Engineered MAterials and Surfaces” (NEMAS), Politecnico di Milano, Via Ponzio 34/3, I-20133 Milano, Italy [email protected]

Abstract. In this Chapter we present the contribution oﬀered by vibrational spectroscopy in the characterization of carbon-based materials. The necessary conceptual tools will be introduced in Sect. 2 and Sect. 3; the basic structural and dynamical properties of the diﬀerent crystalline or ordered aggregation forms of carbon will be described. With such a background we pave the way to the spectroscopic characterization (Raman and infrared) of disordered carbon materials, such as those recently proposed for hydrogen storage. The application of the concepts and data described to the ﬁeld of new carbon materials for energy storage is presented.

1 Introduction Carbon-based materials are at present of great technological relevance as possible substances that are capable of storing hydrogen as new energy vectors in the automotive ﬁeld. In the past few years the interest in carbon-based materials for energy storage has reached very high levels as a consequence of the news reported by some laboratories [1, 2, 3] that such materials could absorb, even at room temperature, astonishingly large amounts of gaseous hydrogen. If these reports were true the “energy problem” which plagues humanity could have been easily and happily solved. Unfortunately, the data on hydrogen absorption reported were not reproduced by other authors and were later shown to be unacceptable [4, 5, 6]. Moreover, many other papers report little or negligible hydrogen absorption in diﬀerent carbon nanostructures (for a general discussion and a list of references see [7]). We became concerned with the failure of the many attempts to squeeze, in a reversible way, hydrogen inside some kind of carbonaceous materials and noticed that most of the experiments were not based on some sort of rationale in the choice of the materials. Indeed, the physics of the absorption necessarily must be strictly related to the yet unknown structure, at the molecular level, of such carbon-based materials. On the other hand, it is well known that the knowledge, at the molecular level, of amorphous carbon-based G. Messina, S. Santangelo (Eds.): Carbon, The Future Material for Advanced Technology Applications, Topics Appl. Phys. 100, 23–53 (2006) © Springer-Verlag Berlin Heidelberg 2006

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materials cannot be easily obtained because they are generally insoluble and noncrystalline solids. The above observations have inspired a group of laboratories to take a “molecular approach” to the problem of hydrogen absorption [8]. The project focussed on producing carbon-based materials of suitable structure by synthesis in controlled situations [8, 9], followed by a molecular characterization [10] and the development of ﬁrst-principle calculations that may guide the interpretation of the experimental data [11, 12, 13, 14]. Two classes of polyaromatic compounds were considered (for a general discussion see [15]), namely 1. polyaromatic dendrimers and 2. carbon-based materials (PAH) obtained from a controlled graphitization [9] of structurally well-characterized and monodisperse polyaromatic precursors. Details on these studies are reported in Sects. 4 and 5 of this Chapter. Again, such research turned out to be unsuccessful since the amount of hydrogen absorbed is still hopelessly small and sometimes negligible. This poses the basic scientiﬁc demand (of general interest) to relate the molecular nature and the electronic properties of the hydrogen molecule to the fact that it can indeed wander inside a carbon cage, but it does not ﬁnd the conditions to stick inside such a cage. We believe that the approach to the problem must systematically proceed ﬁrst with the understanding of both the ordered and disordered structures the carbon atoms are able to generate. The structures must be identiﬁed by means of experimental physical techniques, which are obviously many when the carbon materials are crystalline and ordered, while they reduce to a few techniques, sometimes vague, when the materials become disordered. Firstprinciple calculations may provide the clue, or a hint, to the understanding of such structural data. This line of thought inspires the discussion that follows in this Chapter. Our approach aims at presenting how molecular and lattice dynamics (and, by consequence, infrared and Raman spectroscopy) can play a role in the ﬁeld of carbon-based materials. We wish to present the state of the art and the recent development of molecular dynamics and vibrational infrared and Raman spectroscopy (theory and experiments) (i) as a probe of ordered and disordered carbon-based materials and (ii) as a probe of hydrogen pushed into the interatomic spaces in such carbon-based materials. 1.1 Carbon-Based Materials The deﬁnition of “carbon-based materials” is indeed quite vague, and we shall try to draw some boundaries dictated by the kind of analysis we are going to discuss. In the formation of any kind of covalently bonded network of carbon atoms, each carbon may act in one of its three states of hybridization, namely Csp3 , tetrahedral, Csp2 , plane trigonal and Csp, linear. The duty of organic chemistry is to strictly control the reaction process directing carbon atoms to preassigned positions in a given molecule under construction and with a

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preassigned hybridization state (hence in a given valence state). The molecular architecture and the derived physical and chemical properties follow from the result of the reaction process. Recently physics has moved into the ﬁeld of carbon and proposed very interesting and potentially useful new ways to obtain networks of carbon atoms generated by collisions of carbon atoms subjected to welldeﬁned kinetic and thermodynamic conditions [16]. Various kinds of diamond-like or graphite-like materials have been produced which show very interesting new mechanical and electrical properties. The precise control of the physical conditions have also allowed for the generation of structurally ordered carbon networks like fullerenes [17] and carbon nanotubes [18], which are at present matter of strong interest in science and technology. While a whole set of physical techniques of characterization can be exploited in the case of simple organic materials practically in any physical phase, the chore of structural characterization, at the so-called molecular level, of structurally highly disordered, insoluble and sometimes unstable systems becomes an exciting challenge to physics and chemistry. We review and discuss some of the aspects of the role of molecular dynamics and vibrational infrared and Raman spectroscopy and its achievements in the study of disordered carbon-based materials. A warning is necessary at the beginning of this Chapter. Our whole experience in molecular and lattice dynamics and spectroscopy has developed based on a molecular approach [19, 20]. In this approach, the vibrating objects are made with atoms of a known mass, connected by valence bonds in a given chemically acceptable architecture and subjected to an intra- or intermolecular potential which can be conveniently described by a “valence force ﬁeld” originating from electrons building up the chemical bonds. Intermolecular interactions will generally be represented by some kind of Van der Waals forces [21, 22, 23]. In other words, we will stick as much as possible to a molecular modelling of both our ordered or disordered systems made up by carbon atoms. Our chemical background allows us, when nature makes it possible, to look at the systems as inﬁnite lattices or as ﬁnite systems. Consideration of ﬁnite systems opens the window to the very rich class of oligomeric molecules which have been made (or can be made on purpose) by chemists as models of larger, but chemically extremely similar systems. Consideration of the dynamics of ﬁnite (even if very large) molecules [24] does not allow us to overlook the existence of surface eﬀects (or end eﬀects), which may aﬀect, to diﬀerent extents, the electronic properties, the dynamics and the spectra of the systems studied. As a typical case of identiﬁcation of end eﬀects we quote the case of the spectra of the oligomers of pyrrole up to polypyrrole [25]. The examples presented in this Chapter witness the relevance of oligomers in such a kind of studies. The striking case is that of the use of infrared spectroscopy on a series of polymethylene chains, CH3 –(CH2 )n –CH3 , which

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has allowed plotting, with great accuracy, all the phonon dispersion curves of polyethylene considered as a one-dimensional lattice [26, 27]. This goal has never been reached by any, even modern, neutron scattering experiments.

2 Prototypical Lattices in Three, Two and One Dimensions In the introductory paragraph we referred to the three states of hybridization of carbon atoms as basic units that can generate ordered or disordered networks uniquely made up by carbon atoms. Before proceeding we feel it necessary to introduce in the discussion some additional “basic lattices” that will be encountered later in our discussion. Let us consider the extreme structures of various ordered organizations of carbon atoms all in a unique state of hybridisation. 2.1 Diamond The ordered linking of Csp3 generates diamond, which has been treated by hundreds of papers from solid state physics to applied industrial technology [28]. Diamond is an indirect band-gap material with an energy gap of 5.49 eV. In diamond Csp3 atoms are joined by single σ bonds. The threedimensional (3D) lattice of diamond consists of two interpenetrating facecentered cubic lattices, displaced one from the other by 1/4 of the principal diagonal of the cube. Each atom of one lattice is at the centre of a tetrahedron formed by its four neighbours of the other lattice. The crystallographic translational unit cell contains eight atoms and displays the whole cubic symmetry Oh . The smallest translational unit cell (primitive cell) contains only two atoms. These two atoms generate six branches in the phonon dispersion relation [29]. The phonons that propagate along the symmetry directions of the ﬁrst Brillouin zone belong to well-deﬁned symmetry species and determine the number of phonon branches experimentally observed (by neutron scattering) along a chosen symmetry direction. At Γ the three optical branches are triply degenerate (F2g symmetry), while the triply degenerate translational mode at ν = 0 is of F2u symmetry. For our kind of discussion most of the dynamic properties of diamond are already available [30, 31]. Accurate phonon dispersion curves are available, and they have been nicely accounted for by a six-parameter valence force ﬁeld reﬁned by least squares ﬁtting over an extremely large number of phonon frequencies derived from neutron scattering data [29]. As seen in Table 1, the statistical dispersions of the calculated valence force constants are generally very small, thus supporting the physical meaning of the calculated numbers. The information we feel relevant for this Chapter derives from the values of the valence force constants reported in Table 1:

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Table 1. Six-parameter valence force ﬁeld and relative uncertainties for diamond crystal. Units: stretching and stretching–stretching force constants are expressed in (mdynes/˚ A), bending and bending–bending in (mdyne ˚ A/rad2 ), stretching–bending in (mdyne/rad)

KR HΛ FR FRΛ FΛ FΛ

= 3.831 ± = 0.872 ± = 0.164 ± = 0.392 ± = −0.015 ± = 0.173 ±

0.023 0.121 0.017 0.012 0.010 0.043

(i) The diagonal and oﬀ-diagonal valence force constants are fully comparable with those derived from similar studies of n-alkane chains and polyethylene [26, 27], thus showing that the ‘chemistry’ of the C–C bonds is very similar (as expected) in the two classes of materials. (ii) The intramolecular potential for σ-bonded C–C systems is very localized mostly to its ﬁrst neighbour, and it feels only a slight perturbation by A/rad2 ). This is the second neighbour (FΛ = 0.173 ± 0.043 mdyne ˚ again in agreement with the ﬁnding of molecular dynamics of n-alkane chains [26, 27], of the lattice dynamics of polyethylene [32] and of similar simple polyoleﬁns [33]. The highest optical frequency of F2g symmetry is observed in the Raman spectrum at 1338 cm−1 . For a perfect crystal no other one-phonon transitions are predicted to be observable in the optical spectra. However, as soon as the crystal contains defects, the translational symmetry is broken and many of the lattice modes gain some dipole moment change, thus giving rise to weak absorption bands in the infrared. One-phonon and two-phonon densities of states are available both from calculations and experiments [29]. Oligomeric molecules for diamond were not known for quite a while. The ﬁrst cage molecule, adamantane [34], was discovered in 1933 and only recently has research on nanostructured materials revealed that a whole class of oligoadamantanes or diamondoids can be obtained from petroleum [35, 36, 37]. Their physical properties are under intense study, and their molecular dynamics and spectra are in too early a stage to teach us something relevant for the understanding of ‘end eﬀects’ of ﬁnite diamond lattices. Contrary to what we will discuss below for Csp2 and Csp systems, we expect that the

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dynamical perturbations by the end eﬀects for diamond will die oﬀ quickly moving into the crystal because only the nearest neighbours are involved in the vibrations, as mentioned above. 2.2 Graphite Next we consider Csp2 , which can form a two-dimensional (2D) lattice of graphite or a one-dimensional (1D) lattice as in the case of polyacetylene. In such a state of hybridization each carbon atom must be linked to its neighbours with three σ bonds in a trigonal planar geometry and with one π bond located at either side of the plane of the σ bonds. Because of the existence of a large set of interacting 2pz orbitals, a whole new physics has been developed in order to account for the delocalization in 2D or 1D lattice of such electrons and for the variety of new physical processes that are generated. The ﬁrst consequence of such delocalization is that the intramolecular interactions of π electrons extend over large distances as revealed in many experiments and as indicated by ﬁrst-principle calculations. The prototypical case of a Csp2 lattice in 2D is graphite, which at present is matter of active theoretical and experimental studies. Graphite is a layered material consisting of superimposed sheets made up by carbon atoms in sp2 hybridization. Each sheet has a honeycomb structure that can be viewed as the limiting case of a polycondensed aromatic system of inﬁnite size. The intermolecular interactions between layers are of Van der Waals type, whereas the bonds within each layer are covalent σ and π bonds. The π component gives rise to an extended 2D polyconjugated system with a peculiar semimetallic electronic structure [38, 39, 40]. The Fermi surface degenerates to a point in reciprocal space, named K. This is the corner of the hexagon that deﬁnes the ﬁrst Brillouin zone (six equivalent K points are therefore present). The conduction properties of graphite and related compounds such as nanotubes [18] are given by the Bloch electrons in the vicinities of the K point. Similarly to what happens in polyacetylene and its oligomers [41] (which will be discussed below), a strong electron–phonon coupling is present in graphite also [42]. This is responsible for the Kohn anomaly recently demonstrated in graphite [43]. The coupling of π → π ∗ electronic transitions with phonons allows us to successfully use resonant Raman spectroscopy to characterize graphite and the related compounds. In particular, for graphite a peculiar phonon with wavevector K (named A phonon) is normally Raman-silent since it does not satisfy the q = 0 selection rule. Because of the strong electron–phonon coupling of the A phonon [42, 43], as soon as the q = 0 selection rule is removed (by the presence of defects and/or conﬁnement such in microcrystalline graphite [44, 45]) the A phonon becomes resonantly activated in the Raman [13, 46, 47]. This gives rise to the so-called D band of defective graphite and related compounds, observed in the Raman in the 1300 cm−1 frequency range [41]. Moreover, the frequency of the D band shows a dispersion with respect to the energy of the laser in resonance condition [13, 44, 45].

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It has been recently proposed [42, 43] that the coupling of π → π ∗ electronic transitions with the A phonons (with a wavevector close to the K point) is ultimately responsible of the observed D peak behaviour. The interested reader can found additional information about the phonon structure and the electron–phonon coupling in graphite and nanotubes in the Chapter by Castiglioni et al. (pp. 381–402). 2.3 Polyacetylene The simplest 1D lattice made up by a linear sequence of Csp2 is polyacetylene (PA), (−CH=CH−)n , which appeared in modern soft matter physics and chemistry only relatively recently, and in the year 2000 generated a Nobel Prize in chemistry to Shirakawa, McDiarmid and Heeger. For sake of simplicity, with the acronym PA we refer here to the most stable, and most known, form of PA, namely trans-polyacetylene as obtained from thermal isomerization of cis-polyacetylene (which is the form chemistry provides ﬁrst during the synthesis) [48,49,50]. The molecular structure of trans-polyacetylene has been the subject of many works. The best oriented samples were obtained by the Durham route with a very high draw ratio [51], which has also been improved by a modiﬁcation of the original preparation of the Shirakawa polymer which reached a draw ratio of 6.5 and which shows a very high anisotropic electrical conductivity when doped (up to 105 Ω−1 cm−1 , almost like copper) [52]. Polyacetylene, in a ﬁrst approximation, can be considered a 1D lattice with a band gap Eg ≈ 1.4 eV consisting of a translational unit (−CH=CH−) that repeats itself in a linear zig-zag polymer chain. The existence of a band gap tells us that PA is not a metal, but is instead a semiconductor. Accepting the language of chemistry, PA is a long polyene chain with conjugated π electrons, while physics describes PA as a dimerized Peierls-distorted sequence of CH units. Because of strong electron delocalization, short-chain polyene molecules (including the large class of carotenoids [53]) become extremely interesting models for understanding physical properties of PA. Figure 1 shows the vibronic spectra of a series of conjugated oligoenes where (in a one-electron picture) the strong dependence of the HOMO–LUMO energy gap with the number of conjugated double bonds appears clearly. By increasing the number of conjugated double bonds, the Kuhn’s limit of a metallic system is not reached, but the energy gap opens at a certain length of the chain because Peierls distortion sets in [54]. As discussed in several review articles, in these polyconjugated 1D systems the motions of electrons are strongly coupled with the nuclear motions. It has been shown that for speciﬁc normal modes (which can be found by lattice dynamics calculations) a strong electron–phonon coupling takes place [56], which strongly enhances the Raman cross section, thus generating an extremely strong and characteristic scattering line in the frequency range of the skeletal stretching, near 1500 cm−1 [56]. The molecular approach taken

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Fig. 1. UV–Vis absorption spectra of oligoenes of increasing chain lengths (n = 3, 5, 6, 8, 10 represents the number of double C=C bonds). Horizontal axis is wavelengths (nm), left vertical axis is the absorbance (10−3 units) for n = 3, 5, 6; right vertical axis is the absorbance for n = 8, 10. Taken from [55]

in this work has brought to the interpretation of the electron–phonon coupling and Raman enhancement in terms of the so-called R− mode1 [57], which can be related to the approach presented by the school of Horovitz [58, 59]. The electron–phonon coupling depends on the HOMO–LUMO energy gap, hence on the eﬀective conjugation length (ECL) of the molecule. In the dynamical treatment in terms of a molecular model, such a mode is indicated by R− . It has been shown experimentally and accounted for by theory and ﬁrst principle calculations that the frequency and the intensity of the R− mode is conjugation length-dependent. Since a real sample of PA from any reaction process consists of a mixture of molecules (or chain segments) with varying ECL, by selecting various exciting laser lines in a Raman experiments it is possible to match the energy gap of various eﬀective conjugation lengths (resonance condition), thus enabling us to probe the “conjugational polydispersivity” of any real sample [56]. At present, a reliable valence force ﬁeld for PA is available [41]. Obviously the use of such a force ﬁeld for shorter oligomeric models has to consider that the eﬀective electron–phonon coupling is a function of the conjugation length, as clearly shown experimentally and theoretically in the case of a series of polyenals CH2 =CH–(CH=CH)n −CHO [60]. PA can be considered a prototypical system of a very large class of polyconjugated 1D systems (oligomers and polymers). While PA is very unsta1

The symbol R− replaces for typographical restrictions the symbol commonly used in the previous literature, namely the letter “ya” of the Cyrillic alphabet.

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ble, other 1D systems are chemically stable and can be suitably treated for attaining technologically relevant properties, such as electrical conductivity, electrochromism, photochromism, electroluminescence, photoconductivity, nonlinear optical responses, etc. [49, 50, 61]. Of particular interest in this discussion are the 1D lattices made up by aromatic rings (e.g., polyparaphenylene (PPP) [62], polyparaphenylene vinylene (PPV) [63, 64], polythiophenes [65,66], rylenes [67] and, more recently, functionalized acenes [68,69]). For a review on the vibrational properties of polyconjugated systems see [70]. At this point of our analysis we need to highlight a structural feature that strongly determines π electron delocalization in these polyconjugated systems. Conjugation means a distribution of π electrons along the carbon skeleton that is made possible through the overlapping of adjacent 2pz orbitals, which exist in this class of molecular systems. Maximum coupling takes place when the two adjacent 2pz orbitals are parallel and any rotation about the single C–C bond decreases the extent of overlapping. In more technical structural words, if ϕ is the dihedral angle of the two 2pz orbitals about the single C-C bond, coupling is maximum at ϕ = 0◦ and is minimum at ϕ = 90◦ . A cosine law may be guessed for the extent of overlapping as function of ϕ; the consequent electronic and dynamical properties derive from the ϕ dependence. In turn, the value of ϕ depends on the conformation of the system [71]. The geometrically driven coupling of 2pz orbitals allows us to classify polyconjugated systems as ‘ﬂexible’ (F) and ‘rigid’ (R). Typical cases are PPP and PPV, which are certainly F, while the classes of rylenes, linear polyacenes and generally of ladder polyconjugated polymers and, ﬁnally, graphite and its oligomers can be classiﬁed as R molecules. The conformational structure of F molecules in the solid is the result of energy minimization of inter- and intramolecular interactions, which may change dramatically when the system is dissolved in various solvents or it is mixed in a blend with another material. Innumerable are the calculations presented in the literature, with increasingly sophisticated theoretical approaches, which try to evaluate the various intramolecular contributions that give rise to the potential barrier supervising the intramolecular conformational ﬂexibility of F systems. The weakness of such calculations lies in the fact that they can easily treat molecules isolated in vacuo, but have a much harder time dealing with the reality of systems which do interact in three dimensions (either as crystals or in liquid and solution states). For R molecules one can safely think, in a ﬁrst approximation, that the electronic properties (and the many relevant consequent physical properties) remain constant per each given chain length; on the contrary for F systems, even for a ﬁxed chain length, the conformational ﬂexibility becomes a puzzle in the eﬀort of rationalizing structure and properties of a given system. Bond length alternation (BLA) loses its precise meaning, and necessarily the concept of a torsional dependent eﬀective BLA (EBLA) needs to be introduced.

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In polyconjugated systems intramolecular 2pz –2pz coupling has been considered mostly for a single molecule in vacuo (as in most of the cases considered by ﬁrst-principles calculations). Nowadays increasing importance is being given to intermolecular 2pz –2pz interactions mostly in the case of R systems. Indeed self-assembling in solution and formation of liquid crystal phases have been recently considered for ﬂat rigid oligomeric molecules that show interesting properties (e.g., intermolecular electrical conductivity), which occur because of intermolecular 2pz –2pz interactions [72, 73, 74]. 2.4 Polyynes The last structural unit to be considered is the linear repetition of Csp units named by chemists as polyynes, (−C≡C−)n . Not much is known on the dynamical and spectroscopic properties of polyynes, and their chemistry has enjoyed a recent revival of which spectroscopy will certainly proﬁt; see, for instance, [75, 76]. Depending on the hybridization state of the terminal carbon atoms, ﬁnite linear carbon chains can in principle consist of alternating single and triple bonds, or consecutive double bonds (cumulenes). The ﬁrst case is typical of H−(C≡C)n −H linear structures (terminal carbons in sp state), whereas the cumulenic case is typical of H2 Cn H2 structures (terminal carbons in sp2 state). The molecules of allene and acetylene are the ﬁrst in the series of cumulenes and polyynes, respectively. We have seen that in polyacetylene the Peierls distortion sets in, giving an alternate structure of single and double bonds. It is likewise reasonable to suppose a similar behaviour also for an inﬁnite linear chain of carbon atoms. Under this regard, for the inﬁnite linear chain, the cumulenic structure is expected to be less stable than the alternance of single and triple bonds (acetylenic structure). In fact, ring-shaped clusters of carbon atoms have been theoretically studied showing signatures of Peierls distortion and Kohn anomaly and softening of the dimerization phonon [77], similarly to polyacetylene. Recently, thanks to a new synthetic procedure [78, 79], solutions of a distribution of linear carbon chains H−(C≡C)n −H (3 < n < 8) have become available for Raman and SERS characterization [80]. While the Raman/SERS data for each single and isolated chain length are not yet available, the theoretical analysis of the experimental data (through density functional theory calculations) shows a deﬁnite softening of the most active vibration in the Raman with respect to the increasing length of the linear chain. This is consistent with previous independent theoretical studies [77].

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3 A Spectroscopic Approach to Disordered Carbon Materials In the previous section we considered carbon-based materials that possess a highly ordered and well-deﬁned structure. Single crystals with supposedly perfect structure have been produced and carefully studied for diamond and graphite. The structure of trans-polyacetylene is suﬃciently well known, while an ‘inﬁnite’ polyyne chain has not yet been obtained. Moving into the world of real materials, we must accept the unavoidable existence of structural small or large defects, and the coexistence, in a given solid material, of amorphous (or disordered) and crystalline domains; sometimes the system is fully disordered. Following our line of thought we consider it an unavoidable step in the structural analysis of carbon-based materials to dwell on our present knowledge of the structure of these systems. In other words, ﬁrst we need to know how to handle a few structural defects. Then one can proceed from slightly disorded to fully amorphous systems. 3.1 1D Systems – Saturated Carbon Materials The understanding of defects in 1D systems received a great deal of attention during the golden age of chemistry and physics of classical polymers which, in most of the cases, consist of σ-bonded carbon atoms in sp3 hybridization (and this makes life easier). All conceivable theoretical and experimental techniques have been applied to understand the conformational structure and the corresponding physico-chemical and mechanical behaviour of common polymers such as polyethylene, polypropylene, polytetraﬂuoroethylene, etc., in their ideally perfect or defect-containing structures. The energies necessary for generating conformational defects labelled as G (gauche), T (trans) and of their combinations (GG, GTG, GTG , GGTGG, etc.) have been evaluated, and physical tools to detect them in the various polymers have been developed. In a similar way, chemical defects as well as stereochemical defects have been treated. From the viewpoint of molecular and lattice dynamics of polymers as 1D systems, a considerable eﬀort has been made to oﬀer vibrational spectroscopies (infrared and Raman) as useful tools for identifying such defects in real polymeric materials [81, 82]. Necessarily in disordered lattices of any dimension, the overall symmetry of the system is lost, group theory becomes useless, phonons become very perturbed and all vibrational transitions may become spectroscopically active. The concept of vibrational density of states g(ω) for a disordered system becomes then essential, and numerical tools were developed for the calculation of the vibrational eigenvalues of extremely large dynamical matrices [82, 83]. As shown in Sect. 2.1, for Csp3 systems intramolecular interactions are very localized and die oﬀ as soon as the second neighbour. This situation makes the calculation of 1D systems with defects much simpler and faster,

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since the dynamical matrices turn out to be practically band matrices with a very few codiagonals. One can then aﬀord huge calculations in reasonably short computer times [84]. We remind the reader that the comparison of the calculated g(ω) with the experimental spectrum suﬀers of an extremely relevant limitation, namely g(ω) is not transition-moment-weighted in the infrared or in the Raman, and we have no ground to predict whether a given strong singularity or a weak feature in the calculated g(ω) may give rise to a strong or weak transition in the vibrational spectra. Correlations with some known model molecules, with the results from ab initio calculations and with the studies on infrared and Raman intensities [85, 86] on simple systems turned out to be of help for the analysis of real systems. The dynamical situations previously elaborated by solid state physics for very simple defect-containing 3D inorganic lattices [87, 88] have been found also for organic 1D classical polymers. Depending on the atomic masses, geometry and vibrational potentials, highly localized out-of-band or gap modes as well as strongly collective resonance modes have been calculated and identiﬁed as originating from defects in 1D polymers [82, 83]. From the study of localized and/or quasi-localized modes, spectroscopic signals correlated with speciﬁc defects have been identiﬁed and widely used in the diagnostic analysis of the conformational, chemical and stereochemical disorder of a given real classical organic polymer system of industrial relevance. The spectra of disordered 1D classical polymers have been treated in the literature and have been used for detailed structural analysis of the simplest polymers of industrial relevance, such as polyethylene, polytetraﬂuoroethylene and polyvinylchloride [82, 83]. 3.2 Polyconjugated Polymers The problem becomes more complex when moving to sp2 polyconjugated systems. As discussed in Sect. 2.3, because of delocalization, interactions extend to large intramolecular (and, who knows, intermolecular) distances. EBLA must be considered because of the torsional ﬂexibility of F systems, cross links as well as Csp3 may truncate delocalization, and many other chemical and structural impurities of unknown type may occur. It has to be remembered that even the simplest PA in a real sample is thought (but never unquestionably shown) to contain cross links and CH2 defects that strongly perturb delocalization. As to the knowledge of the interaction distance along the 1D polyconjugated chain, great expectations were put in ﬁrst-principle calculations which necessarily must take into account the molecular reality of the systems in one, two and three dimensions. Aﬀording such enormous calculations requires powerful computing capabilities; on the other hand, data from simplistic approaches may lead to wrong conclusions. As a simple example we quote the problem tackled a few years ago on the eﬀect on delocalization by a CH2 group separating two sections of polyene chains. Old-fashioned simpliﬁed

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quantum mechanical calculations (CNDO, MNDO) have indicated that CH2 completely breaks conjugation and builds a huge barrier to the tunnelling of π electrons through the barrier [89]. Concerning the experimental indication of long range interactions in 1D polyconjugated systems we consider of extreme interest the experiments on nonlinear optics of a series of polyacetylene-like chains with growing lengths [90, 91] from which the ﬁnal answer is that certainly conjugated double bonds interact at least up to ≈ 60 neighbours [91]. 3.3 2D sp2 Systems For graphitic-like systems the issue of local and/or collective normal modes needs to be updated. We neglect in this discussion the case of defects due to the chemical synthesis of the material, namely chemical groups or atoms (functional groups) dangling from the main graphitic lattice or stemming out of the peripheral bonds. When the ideal view of an inﬁnite graphite lattice is abandoned and a real graphitic domain is considered, the number of atoms at the periphery becomes sizeable, no matter of the shape of the domain. Dynamics tells us that the normal modes at the periphery are many and may behave like gap modes (highly localized or quasi-resonance modes) or resonance modes (collective motions) depending on the dynamical conditions which deﬁne the intramolecular coupling and depending on their energies which may occur away, near or inside a phonon branch [82, 83]. The second kind of possible defects of a lattice of graphite is the distortion of the sp2 skeleton by some kind of strain induced during the chemical reaction. In this case the work of imagination becomes almost free to conceive many kinds of either small or large defects. The simplest case is consideration of a few Csp3 atoms which necessarily generate localized or extended corrugation; one can go further by introducing strained rings or even holes where dangling bonds are lingering ready to react. Our fundamental questions are the following: (i) Is there any unquestionable experimental direct evidence of such corrugated structures? (ii) Assuming that corrugations and wrinkles occur, where and how could one locate their normal modes in infrared and/or Raman and/or neutron scattering spectroscopies? Eﬀorts have been made to work out theoretical models [92,93,94], but matching with unquestionable experimental data has yet to be found. In the opinion of the writers, plenty of work still needs to be done on the dynamics and experimental spectra of these systems in order to provide clear relationships between the structures and the relative signatures in the infrared and Raman. From the viewpoint of molecular vibrational dynamics-high-energy local modes (such as C–H stretchings) arising as defects from boundaries or holes, in a ﬁrst approximation, can be overlooked and the attention should

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be focused on C–C stretchings, C–H in-plane bendings, CCC bendings and CCCC out-of-plane modes (from 1600 cm−1 downward). These modes may be generated by the defects, which are necessarily coupled to the phonons of the main lattice, thus generating collective resonance modes. It is obvious that in- and out-of-plane motions in harmonic approximation for a planar graphitic-like lattice are orthogonal and no coupling takes place. From previous experience with aromatic molecules [95, 96], we know that when corrugating defects are introduced such separation is lost, all modes can couple and the intensities are shared between two or among several coupled modes (just as expected for resonance defect modes). Since, in absence of chemical substitution (i.e., in absence of highly polar bonds) the vibrations of the CC skeleton cannot generate large transition dipole moments, characteristic signals in infrared are not likely to occur. On the other hand, CC bonds are highly polarizable and their stretching may show up in the Raman spectra as weak features. Calculations of transition moments in the infrared and cross sections in the Raman may be the clue to locate meaningful and characteristic vibrational transitions that may provide a partial picture of the disorder inside the carbon systems under discussion in this Chapter. There are no studies that have clearly shown the activation in the Raman of vibrations localized on sp3 -induced corrugations. It has to be considered that in any case the Raman spectra of defective graphite has a strong band around 1300 cm−1 , the so-called D band. The spectral region is unfortunately too close to the usual frequencies found for the C–C stretching vibrations characteristic of a sp3 carbon system. Therefore the future search for Raman signatures of skeletal sp3 -induced corrugations in graphitic domains has necessarily to take into account the fact that for visible laser excitation the Raman cross section originating from the sp2 component overrides the Raman cross section originating from any sp3 -induced corrugation. This is why recent Raman investigations on such graphitic systems have been pursued using UV excitations. In the following section we will focus on the D band and its behaviour, and we will introduce a theoretical explanation of the Raman signal that is based on model molecules mimicking conﬁned sp2 regions of graphite.

4 Edge Eﬀects in Graphitic Domains for Structure Diagnosis A clean contribution to the study of carbon materials supposed to consist of graphitic domains is given by the class of polycyclic aromatic hydrocarbons (PAHs) that have been recently made available from new synthetic processes [15]. The electronic and vibrational spectra of PAH molecules with well-deﬁned shape (hence symmetry) and size have been studied, revealing many interesting aspects related to the conﬁnement of π electrons in two-dimensional domains with a size in the nanometer range [41]. The fundamental

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(a)

37

(b)

Fig. 2. (a) Raman frequencies of G and D line of a microcristalline graphite sample, as obtained with diﬀerent exciting laser energies (from [44, 45]); (b) Modeling of the Raman frequency dispersion of a disordered graphite sample, according to [13]

understanding of the resonant Raman spectroscopy of PAHs [14] opens the way to the interpretation of the multiwavelength Raman spectra of nanostructured graphitic materials. In particular, it becomes possible to eﬀectively use the D band as a powerful diagnostic tool for obtaining information about the distribution of domains in a nanostructured graphitic material. Disordered and nanostructured graphite is a very wide class of materials (ranging from annealed amorphous carbons, microcystalline graphites, graphite ﬁbers and whiskers, and carbons obtained from controlled pyrolysis of molecular precursors). All these materials are characterized by the presence of a nonnegligible amount of sp2 carbons that give rise to islands that can be correlated (in terms of structure and also in terms of their Raman response) to an ideally perfect crystal of graphite. Their ﬁrst-order spectra show two main signatures: ﬁrst, a band located at about 1580 cm−1 , which is known as the graphite (G) band, since it is the only feature observed in the ﬁrstorder Raman spectrum of highly ordered crystalline graphite. The second band (D band) appears at about 1350 cm−1 and it is a characteristic feature of disordered samples of graphite (e.g., nanocrystalline and microcrystalline graphites) and amorphous carbon materials containing sp2 graphitic islands. The fundamental experiments made by P´ ocsik et al. [44, 45] on microcrystalline graphites and those performed by Ferrari et al. [97, 98] on ﬁlms of amorphous carbons showed a marked resonance behavior and frequency dispersion of the D line when changing the energy of the exciting laser line used in the Raman experiments. This behaviour is illustrated in Fig. 2. The presence of the G band can be immediately related to the existence of structures like graphite in the samples (it corresponds to the Raman active E2g phonon at the Γ point in the ﬁrst Brillouin zone of graphite). On the other hand, the understanding of the physical mechanism lying behind the activation of the disorder induced D band has been a matter of debate in the

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literature. An original interpretation of the origin of the D line in graphitic materials has been proposed based on a molecular approach [99] built on the spectroscopic data obtained from a wide series of samples of PAHs identiﬁed as realistic models of nanosized sp2 domains in disordered carbon materials. The correlation experimentally found between the Raman bands of graphite and the Raman-active modes of PAHs has been conﬁrmed and rationalized on the basis of quantum chemistry [14]. In particular, the analysis of the theoretical results clariﬁes the origin of the large Raman cross section for the few (D) bands near 1300 cm−1 observed (and calculated) for all the PAHs examined. The relevant fact is that the existence of nonequivalent C–C bonds in PAHs is essential for the activation of normal modes in the D-band region. The existence of nonequivalent C–C bonds is the very consequence of the conﬁnement of π electrons in a domain of a few nanometers. The extension of these fundamental ﬁndings on PAHs to nanostructured graphite is straightforward: nanosized sp2 clusters of condensed aromatic rings have to be associated to some equivalent PAHs characterized by a similar structural relaxation driven by the conﬁnement of π electrons in a ﬁnite domain. The spectroscopic signature of this relaxation is just the appearance of the D line in the Raman spectrum. Because of the eﬀects of conjugation, the optical absorption of these nanodomains (thus the resonant Raman condition) are size-dependent. In particular, a decreasing trend of the energy of the lowest optical transition is found while increasing the size of the nanodomain (graphite being a zero-gap material corresponding to the limiting case of inﬁnite size). On the other hand, because of the strong electron–phonon coupling (see the Chapter by Castiglioni et al. in this book, pp. 381–402) it turns out that also the frequency of the vibrational mode in the D-band region for each nanodomain is size-dependent. In other words, the vibronically coupled π → π ∗ optical excitations in graphitic nanodomains are size-dependent because of π-conjugation; this fact induces a size dependence also on the vibrational frequency of the Raman-active vibrations (in the D-band region) via a strong and vibration-selective (A phonon) electron–phonon coupling [42]. The consequence for multiwavelength resonant Raman spectroscopy of the D band of nanostructured graphite is dramatic: For each given laser only the nanodomains characterized by a suitable optical gap (i.e., size) are contributing to the signal in the D region; moreover their vibrational frequency for the above reasons will be size-dependent. In particular, a softening of the D-band frequency is found for an increasing size of the nanodomains. This explains the increase of the D-band frequency with respect to the energy of the resonating laser line found in the experiments carried out by P´ ocsik et al. [44, 45]. This kind of behaviour of the D band in the multiwavelength Raman spectra of nanostructured graphite closely resembles the behaviour of the ECC band in polyacetylene and related 1D polyconjugated compounds. It is not by accident that the ECC vibration is characterized by a strong electron–

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phonon coupling that drives a gap opening through the Peierls distortion exactly as the relaxation of the geometry of graphite along the D-band phonon (A phonon) induces a gap opening at the K point at the border of the ﬁrst Brillouin zone [42]. The case of microcrystalline graphite could at ﬁrst seem fairly diﬀerent, since no apparent presence of sp2 nanodomains can be foreseen. Recent studies carried out through STM and Raman spectroscopy [100] show that in this case the variety of diﬀerent π electron conﬁnement situations does not come from a plethora of nanodomains, but more precisely from the peculiar electronic structures close to the edges of the graphitic planes. Such edge electronic states can be mapped by STM and, thanks to ab initio calculations, they can be correlated with the frontier orbitals of model molecules such as rylenes, whose Raman spectra show precisely the expected behavior in a P´ ocsik diagram [100]. According to STM measurements, such edge states extend for a few nanometer far from the edge and are extremely sensitive to the topology of the edge [100]. The theoretical analysis illustrated above allows us to discuss the multiwavelength Raman behaviour of two pyrolyzed materials obtained in diﬀerent conditions from a molecularly well-deﬁned precursor [9]. Figure 3 illustrates the experimental results and the comparison with the outcome from a model of the resonant Raman response produced by a distribution of graphitic nanodomains (according to the method described in [13]). In Fig. 3a we can observe that in the case of the sample pyrolysed at 800◦ C, the frequencies of the D line undergo shifts with the energy of the exciting laser. The observed frequencies follow the empirical law experimentally determined by P´ ocsik et al. [44, 45]. As illustrated by the simulation reported in Fig. 3a, it is possible to predict this behavior using as input of the model [13] a homogeneous distribution of nanodomains ranging from very small size (6 carbons) up to a large size (384 carbons). A completely diﬀerent behavior is experimentally found for a sample obtained from the same precursor but pyrolysed at a lower temperature (600◦ C, see Fig. 3b). In this case one does not observe frequency shifts with laser excitation in the visible range. The behavior is markedly diﬀerent from that of disordered graphite, and it can be correctly predicted only if a diﬀerent distribution of nanodomains is used as input in modeling the Raman response. In particular, the observed behaviour is found when domains containing at least 150 carbon atoms are selected in the model of the Raman response (see Fig. 3b). Accordingly, we can conclude that this sample is structurally more controlled and it keeps memory of the precursor molecule. This is consistent with the milder pyrolysis conditions (600◦ C as opposed to 800◦ C).

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(a)

(b) Fig. 3. Multiwavelength Raman spectra of a pyrolytic carbon sample obtained from hexaphenylbenzene (HPB) pyrolysed at 800◦ C (a) and 600◦ C (b) [9]. Comparison with P´ ocsik data [44,45] and with the results from a modeling of the Raman response according to [13]. The Raman frequencies of the D peak are reported in a P´ ocsik diagram [44, 45] for the three excitations used (1.96, 2.41, 2.71 eV, corresponding, respectively, to the red, green and blue spectra represented) to compare with the dispersion of the D peak of microcrystalline graphite

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5 Approaching the Structure of Carbonaceous Materials by Vibrational Spectroscopy: Imagination and Reality It is well known that experimental solid state physics has tremendously contributed to the development of the ﬁeld of carbon-based materials by inventing various techniques (e.g., arc discharge, chemical vapour deposition, laser ablation, plasma-assisted vapour deposition, molecular beam deposition, etc.) for the generation of clusters of carbon atoms that are then deposited onto a surface. The physical properties of such deposits are of relevant interest in modern technology. These pioneering works have also generated well-deﬁned and important molecules such as fullerene, fulleroids and nanotubes. All these techniques are discussed in detail in specialized publications. Our previous lengthy systematic approach towards the understanding of the structure of disordered carbon-based materials is aimed at discovering the structural reason why hydrogen cannot be ‘adsorbed’ in such systems. Necessarily when a hydrogen molecule enters such complicated structures it must ﬁnd a ‘cavity’ where weak interatomic interactions favour its settling inside the cavity itself. The description of the amorphous surrounding may be represented by the following two extreme cases. (i) Amorphous carbon materials with a diﬀerent degree of local organization, such as the models proposed in [101] or [102], are the results of sophisticated large-scale atomistic simulations. The systems consist of a large variety of structural entities that ﬁnd carbon atoms bonded to each other in various disordered and irregular geometries (quite often away from their canonical states of hybridization). During the numerical calculations the system may have reached a minimum energy structure as a balance of all sorts of internal strains and stresses. In these models we ﬁnd a whole variety of strained small rings, cross links, curled chains of various lengths; necessarily a random distribution of voids (or cavities) of various sizes occurs in such materials. If this is the ‘real’ disorder of the materials we are considering, spectroscopy can give little help in characterizing the system, since all possible kinds of vibrational motions may occur, thus generating a very broad vibrational spectrum with no particular features. Fortunately, the system may evolve locally towards islands of more stable forms of aggregation, characterized by carbon atoms in a given hybridization state. These can be considered as clusters of diamond, graphite, or segments of polyacetylene or polyyne. In this case spectroscopic signatures should be found, and are indeed found, which nicely correlate with the known spectroscopic behaviour of the parent crystalline systems [103, 104, 105] as discussed in the previous pages of this Chapter. By suitable annealing such metastable systems may evolve towards graphitisation [97, 98]. (ii) An alternative picture is to consider a graphitic system consisting mostly of intermingled graphitic nanodomains with holes and imperfections em-

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(I)

(II)

(III)

Fig. 4. Sketches of the chemical structures of HPB (I ), HBC (II ) and halogenated HPB (III )

bedded in ‘amorphous’ surroundings. This has been the inspiring idea underlying the project denominated “Molecular Approach to Carbon based Materials for Energy Storage” – MAC-MES [8]. While materials obtained from vapour phase deposition, arc discharge, etc., and also simply as carbon soot, etc., may possess a structure as in (i) (which we already know does not adsorb hydrogen), systems as in (ii) were obtained only recently and provided new spectroscopic probes for the exploration of their structure and of their capability to adsorb hydrogen [7,8,9,10]. As a contribution towards a systematic understanding of the structural features of disordered carbon-based materials, we have recently reported on the infrared and Raman spectra of materials obtained from thermodynamically controlled pyrolytic processes of model aromatic molecules suitably selected and prepared as precursors of structurally controlled graphitic materials. Hexa-phenyl-benzene (HPB, (I) in Fig. 4) has been taken as the most relevant precursor molecule to be pyrolyzed at various temperatures under controlled conditions [10]. The concepts underlying our work were the following: It was previously shown [15] that polyphenyl precursors, with appropriate topology, can be smoothly transformed into ﬂat polycyclic aromatic hydrocarbons by an intramolecular cyclodehydrogenation. Typical is the case of HBC, which when treated with FeCl3 , produces hexa-pery-hexabenzocoronene ((II) in Fig. 4). It was thought that a pyrolytic treatement may cause two main processes: (a) intramolecular dehydrogenation thus generating molecules of type II, and (b) intermolecular dehydrogenation coupling various HBC units which could then undergo intramolecular dehydrogenation as in (a). Suitable halogenation (with halogen X, X=Cl, Br, I) in para position of each benzene ring in HPB ((III) in Fig. 4) could favour the intermolecular linking with elimination of the corresponding acid HX before entering the process as in (a). Pyrolysies were carried out at 450, 500, 600 and 800◦ C for various lengths of time (from 1 to 5 days). The typical morphology of the carbonaceous graphitic material obtained is given in Fig. 5.

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First, from the observation of dominant G and D lines in the Raman spectra, it was veriﬁed that the systems obtained were mostly graphitic (see Sect. 4). Then the chemical structure of the boundaries of the graphitic domains obtained were studied in terms of the dynamics and spectra of the peripheral C–H bonds, which show localized out-of-plane deformation modes (decoupled from the skeletal modes). These modes become speciﬁc of the local chemical structure as given in Table 2 [10]. As an example of application of these spectroscopic correlations, we show the structural evolution of the boundaries of the graphitic domains as revealed by the infrared spectra of HPB heated at 450, 500 and 600◦C (Fig. 6). Table 2. Top: description of SOLO, DUO, TRIO and QUATRO structures. Bottom: patterns of absorption bands in the infrared to be associated to speciﬁc sets of adjacent aromatic C–H groups belonging to “fused” benzene rings (frequency ranges are given in cm−1 )

SOLO DUO TRIO QUATRO

860–910 800–810 750–770 730–750

– 810–860 770–800 750–770

– – 800–810 –

A further interesting structural observation has been derived from these studies. Let us assume that during the pyrolysis HPB molecules are not broken up, but are only forced to ‘condense’ and/or link to each other. Ideally we can construct two main repeating ‘motives’, which show borders we label as ‘regular’ (reg) and ‘irregular’ (irreg, see Fig. 7). In absence of any regionselective reactions, simple statistical reasoning shows that the growing of reg structures becomes less and less probable favouring the formation of irreg structures. As shown in Fig. 7, irreg clusters necessarily contain ‘holes’ where six atoms are missing and are replaced by six hydrogens. Whenever the size of the clusters increases, the relative population of TRIO structures decreases in favour of SOLO and DUO. In principle, we can distinguish reg or irreg clusters by the relative population of SOLO and DUO, namely for reg structures the ratio (number of DUO/number of SOLO) is always one. For irreg structures with holes, the population of SOLO is larger than the population of DUO. As an example, we compare in Fig. 6 the infrared spectra of HPB heated for one day at 450, 500 and 600◦ C. The SOLO and DUO bands increase relative to

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Fig. 5. SEM images of HPB-800-1d at increasing magniﬁcations

Fig. 6. Infrared spectra of HPB pyrolysed at increasing temperatures (450, 500, 600◦ C)

the TRIO band, thus indicating that the sizes of the clusters have increased.

5.1 Carbon-Based Materials for Hydrogen Storage The last question which needed to be answered is whether the graphitic materials suitably prepared as described previously in Sect. 5 were able to adsorb hydrogen. Experiments were done with the usual techniques [4, 5]. In addition, a spectroscopic method based on Raman scattering was developed that provides many interesting details on the physics of the ‘adsorption’ of hydrogen in these materials [7]. A special cell for Raman scattering experiments

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Fig. 7. Examples of regular and irregular structures with diﬀerent relative TRIO/SOLO/DUO weigths: (a) regular, TRIO/SOLO/DUO = 5/2/2; (b) irregular, TRIO/SOLO/DUO = 2/1/1; (c) regular, TRIO/SOLO/DUO = 5/2/2; (d) irregular, TRIO/SOLO/DUO = 2/2/1

Fig. 8. Raman spectra of hydrogen adsorbed on a pyrolysed carbon (HPB-550-3d) recorded at 40 ± 2 K at pressures ranging from 4 to 62.5 bar (from [7])

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Fig. 9. The eﬀect of a uniform static electric ﬁeld along the bond axis of the hydrogen molecule. The ﬁeld is generated by the array of point charges depicted in the top-left panel. Comparison with the polarization eﬀects on the bond lengh, vibrational frequency and infrared absorption induced by the benzene molecule. Data from [106], according to density functional calculations (B3LYP/6-311G**). Notice that these calculations show only the softening (downshift of the vibrational frequency) of the H–H bond induced by interactions with aromatic carbon atoms. Actually the theory of the interaction also predicts an upward shift [7], as also revealed experimentally in the Raman spectrum of H2 under pressure (see Fig. 8)

was designed and built; this cell is capable of operating at very low temperature (40 K) and both in high vacuum or high pressure (up to 100 bars) with relatively high resolution. We could easily record the vibrorotational and rotational Raman spectra of hydrogen as function of temperature and pressure in absence or in presence of carbon-based materials described in (i) and (ii) in Sect. 5. Typical Raman spectra of hydrogen adsorbed on a pyrolysed carbon are shown in Fig. 8. As discussed in [7], we do observe signatures of interaction of hydrogen with carbon materials both in cases (i) and (ii) for a small relative amount of the total hydrogen introduced in the cell. Clear indications are found that no charge transfer phenomena are involved in the interaction with the absorbing material (contrary to [3]), but only a simple physisorption takes place; no indication of chemisorption has been noticed.

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The lesson we learned from these studies is that hydrogen does not ﬁnd the suitable energetic and sterical conditions to be squeezed into the ‘cavities’ of any carbon-based materials (so far known or tested), including carbon nanotubes, even at low temperatures and high pressures. This information from experiments weakens the validity of several theoretical elaborations presented in the literature. From our side, attempts at understanding such failure consisted ﬁrst in the application of classical potentials for describing the interaction of H2 with carbons. It turned out that the the potential function is extremely ﬂat with a very shallow potential minimum, which indicates a very weak interaction with the surrounding carbon atoms within the cavity. Next, a quantum mechanical modelling of the interaction of the hydrogen molecule with its surrounding has been attempted; interatomic distances, vibrational frequencies, infrared and Raman vibrational intensities have been calculated for hydrogen interacting with benzene (taken as a model of aromatic carbons). The results from this computation have been compared with the results obtained by acting on the hydrogen molecule with a static electric ﬁeld mimicking the interacting carbon substrate (see Fig. 9 and [106]). The ﬁnal relevant information which derives from these works is that in order to keep hydrogen inside the cavity, a stronger interaction, which may induce a larger dipole in the H–H bond, has to be obtained by introducing highly polarizing atoms in the cavity. The idea was empirically conceived during the synthetic part of the work, and precursors containing various nitrogen atoms were prepared and then pyrolyzed [9, 10]. Unfortunately, no real positive results were obtained on these materials. The results from these studies have suggested to set aside the idea that carbon cages (of the average size existing in the material discussed in the previous pages) may be able to store hydrogen. Smaller carbon cages or new cavities with highly charged atoms (i.e., those that are strongly polarizing) should be conceived. Recently a whole new class of more ordered organic/inorganic materials with tailored cages has been synthesized [107], and the Raman spectra of deuterium adsorbed in one of these materials has been obtained and studied [108]. It is very pleasing to realize that from an interdisciplinary collaboration between chemists, physicists and spectroscopists new routes for future studies on hydrogen storage have been indicated.

6 Conclusions We hope the reader has developed a feeling about the complexity and the yet unsolved problem in understanding the structural properties of the carbon-based materials that are now being considered as relevant for technological applications. Basically we suggest that, so far, hydrogen cannot yet be stored in a useful amount for automotive applications in the carbon-based materials presently available. However, new hopes arise with new classes of

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organic/inorganic cage molecules. The problem of hydrogen storage has motivated the development and use of the physical techniques presented here, which may ﬁnd a broader application in the ﬁeld of the characterization of materials. Acknowledgements We acknowledge all the members of the MAC-MES consortium [8] for fruitful exchange of ideas and constructive collaboration. In particular, we thank Prof. K. M¨ ullen and Dr. C. Mathis for their contributions in the ﬁeld of graphenes and Dr. L. Gherardi of Pirelli Labs for many discussions on hydrogen absorption. Part of this work was supported by a grant from MURST – Italy (FIRB project “Carbon-based micro- and nanostructures”, RBNE019NKS) and by the MAC-MES contract (European Commission, Fifth Framework Programme, Research Project “MAC-MES: Molecular Approach To Carbon Based Materials for Energy Storage” – G5RD-CT200100571).

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[70] G. Zerbi, M. Gussoni, C. Castiglioni: Vibrational spectroscopy of polyconjugated aromatic materials with electrical and nonlinear optical properties, in J. L. Br´edas, R. Silbey (Eds.): Conjugated Polymers (Kluwer, New York 1991) p. 435 [71] M. Rumi, G. Zerbi: Chem. Phys. 242, 123 (1999) [72] A. M. van de Craats, J. M. Warman, A. Fechtenk¨ otter, J. D. Brand, M. A. Harbison, K. M¨ ullen: Adv. Mater. 11, 1469 (1999) [73] M. Carminati, L. Brambilla, G. Zerbi, K. M¨ ullen, J. Wu: Nanoscale architectures for molecular electronics: Vibrational spectroscopy and structure of solid hexa-n-dodecyl-hexa-peri-hexabenzocoronene, J. Chem. Phys. 123 (14) (2005) [74] A. Milani, L. Brambilla, M. Del Zoppo, G. Zerbi: manuscript in preparation [75] T. Luu, E. Elliott, A. D. Slepkov, S. Eisler, R. McDonald, F. A. Hegmann, R. R. Tykwinski: Organic Letters 7, 51 (2005) [76] S. Eisler, A. D. Slepkov, E. Elliott, T. Luu, R. McDonald, F. A. Hegmann, R. R. Tykwinski: J. Am. Chem. Soc. 127, 2666 (2005) [77] M. Saito, Y. Okamoto: Phys. Rev. B 60, 8939 (1999) [78] F. Cataldo: Carbon 42, 129 (2004) [79] F. Cataldo: Tetrahedron Lett. 45, 141 (2004) [80] A. Lucotti, M. Tommasini, M. Del Zoppo, C. Castiglioni, G. Zerbi, F. Cataldo, C. S. Casari, A. L. Bassi, V. Russo, M. Bogana, C. E. Bottani: Raman and SERS investigation of isolated sp carbon chains, Chem. Phys. Lett. 417 (1-3) (2006) [81] G. Zerbi: Probing the real structure of chain molecules by vibrational spectroscopy. Some recent aspects, in Advances in Chemistry Series, vol. 203 (American Chemical Society 1983) p. 487 [82] G. Zerbi: Vibrational spectroscopy of very large molecules, in R. Clark, R. Hester (Eds.): Advances in Infrared and Raman Spectroscopy, vol. 11 (Wiley-Heyden, New York 1984) p. 301 [83] G. Zerbi, M. D. Zoppo: Vibrational spectra as a probe of structural order/disorder in chain molecules and polymers, in G. Zerbi (Ed.): Modern Polymer Spectroscopy (Wiley-VCH, Weinheim 1998) p. 87 [84] M. Tasumi, G. Zerbi: J. Chem. Phys. 48, 3813 (1968) [85] M. Gussoni: Infrared and Raman intensities from electrooptical parameters, in R. Clark, R. Hester (Eds.): Advances in Infrared and Raman Spectroscopy, vol. 6 (Heyden, London 1964) p. 96 [86] M. Gussoni, C. Castiglioni, G. Zerbi: Vibrational intensities: Interpretation and use for diagnostic purposes, in J. Chalmers, P. Griﬃth (Eds.): Handbook of Vibrational Spectroscopy, vol. 3 (Wiley, New York 2002) pp. 2040–2077 [87] A. A. Maradudin: Solid State Physics – Advances in Research and Applications, vol. 18 (Academic 1966) [88] A. A. Maradudin: Solid State Physics – Advances in Research and Applications, vol. 19 (Academic 1967) [89] J. T. L. Navarrete, G. Zerbi: Solid State Commun. 64, 1183 (1987) [90] I. D. W. Samuel, I. Ledoux, C. Dhenaut, J. Zyss, H. H. Fox, R. R. Schrock, R. J. Silbey: Science 265, 1070 (1994) [91] I. Ledoux, I. D. W. Samuel, J. Zyss, S. N. Yaliraki, F. J. Schattenmann, R. R. Schrock, R. J. Silbey: Chem. Phys. 245, 1 (1999)

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Index sp2 -bonded clusters, 38 annealing, 41 bond length alternation (BLA), 31 eﬀective BLA (EBLA), 31, 34 conﬁnement, 28, 36, 38, 39 conjugation length, 30 eﬀective conjugation length (ECL), 30 cumulene, 32 D band, 36–38 D-band dipersion, 37 D-band, 38

defects, 27, 28, 33–35 density functional theory (DFT), 32 diamond, 26, 41 diamond-like carbon (DLC), 25 dispersion phonon dispersion, 26 eﬀective conjugation coordinate theory (ECCT), 38 electron–phonon coupling, 28, 30, 38 ﬁrst principle calculations, 24, 28, 30, 32, 34 fullerene, 25, 41 G band, 37

A Spectroscopic Approach to Carbon Materials for Energy Storage graphite, 28, 41 graphite-like carbon (GLC), 25 graphitization, 41 HOMO–LUMO gap, 29, 30 hydrogen adsorption, 42, 44, 45 hydrogen desorption, 42 hydrogen storage, 44 infrared (IR) spectroscopy, 24, 25, 33–36, 42

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Peierls distortion, 29, 32, 39 polyacetylene (PA), 28, 29, 32, 41 polyconjugated systems, 31 polycyclic aromatic hydrocarbons (PAHs), 36–38, 42 polymers, 29, 30, 33, 34 polyconjugated polymers, 30, 31, 34 polymethylene, 25 polyyne, 32, 33, 41 pyrolytic carbons, 37, 42

Kohn anomaly, 28, 32

quantum chemistry, 38

lattice dynamics, 24, 27, 29, 33

Raman scattering, 35 Raman cross section, 29, 36 Raman intensity, 34 resonant Raman scattering, 28, 30 selection rules, 28 Raman spectroscopy, 24–28, 32–36, 42

molecular approach, 24, 29, 38 molecular dynamics, 24, 27, 33, 35 multiwavelength Raman spectroscopy (MWRS), 37–40 nanotubes, 25, 28, 41 oligomers, 25, 27, 28, 30–32

surface enhanced Raman spectroscopy (SERS), 32

P´ ocsik diagram, 37, 39, 40

valence force ﬁeld, 25–27, 30

Biocompatibility, Cytotoxicity and Bioactivity of Amorphous Carbon Films Sandra E. Rodil1 , Ren´e Olivares2 , Higinio Arzate2 , and Stephen Muhl1 1

2

Instituto de Investigaciones en Materiales, Universidad Nacional Aut´ onoma de M´exico, Circuito Exterior s/n, CU, MEX-04510 M´exico D. F. Facultad de Odontolog´ıa, Universidad Nacional Aut´ onoma de M´exico, Circuito Exterior s/n, CU, MEX-04510 M´exico D. F. [email protected]

Abstract. In this work we investigate the possibility of using an amorphous carbon layer as a bioactive coating that promotes bone ingrowth for medical implants in direct contact with bone. The initial step was to conﬁrm the tissue compatibility of the amorphous carbon coatings by studying cellular adhesion, proliferation and viability with human osteoblasts and ﬁbroblasts, cultured on the carbon surface. To investigate the bone-bonding capabilities of the sputtered a-C coatings, “in vitro” mineralisation studies were performed. For the biomineralisation assays, human osteoblasts were grown on a-C samples for periods up to 14 days, leading to the formation of mineralised structures that were morphologically and biochemically investigated by the scanning electron microscope and X-ray microanalysis, respectively.

1 Introduction There is an increasing interest in the development of novel coatings or surface modiﬁcation treatments to improve the bone-bonding ability of metal implants [1]. An essential condition for an artiﬁcial material to bond directly to living bone is the formation of bone-like apatite on its surface. Direct boneimplant joint formation is important since if the ingrowing bone is separated from the implant by an intervening soft tissue layer, excessive micromovements in the interface may occur. These micromovements are known to produce negative reactions such as destruction of the surface oxide layer and wear of the implant surface, and these can be accompanied by corrosion and wear debris accumulation, causing the subsequent failure of the implant [2]. The parameters that are important for long-term implant life include the biocompatibility of the chosen implant material, the surface chemistry and physics, the macro- and microstructure, the surgical implant procedure, the time and mode of implant loading and the implantation bed itself. Therefore, the biocompatibility of an implant is only one of parameters inﬂuencing the tissue response to an implant material; other factors must be satisﬁed for a device to be suitable for implantation. Particularly, for bone ingrowth many factors have been shown to be important: (a) mechanical factors, such as micromotion and loading; (b) geometrical factors: the surface of ingrowth ﬁxation G. Messina, S. Santangelo (Eds.): Carbon, The Future Material for Advanced Technology Applications, Topics Appl. Phys. 100, 55–75 (2006) © Springer-Verlag Berlin Heidelberg 2006

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implants must have a geometry that accommodates the bone ingrowth, and therefore noncemented porous coated implants have been proposed where the pore size and the interface gap play major roles; and (c) materials factors: the composition of the surface layer is a very important determining factor [3]. Porous coatings on titanium (Ti) and cobalt–chrome (Co–Cr) alloys are the most commonly used materials for odontological and orthopedic implants. However, the failure rates today demonstrate that there is still scope for improvement [4]. Other potential implant materials include mostly ceramics, such as, hydroxyapatite [5], tricalcium phosphate [6] and carbonbased ceramics (pyrolitic carbon, glassy carbon) [7]. All have been shown to be conducive to bone ingrowth (osteoinductive), but they have not been used for load-bearing implants due to strength concerns. Here is where the surface modiﬁcation comes into play; by modifying the surface chemistry of an implant, it is possible to retain the mechanical and geometrical conditions needed to assure the long-term stability of the implant, together with enhancing a particular biological response such as bone ingrowth [8]. Both pyrolitic and glassy carbon have been shown to be osteoinductive, but they are not mechanically stable. Therefore carbon-based coatings having graphite-like properties deposited on mechanically stable substrates are interesting systems to evaluate for their potential to enhance bone ingrowth. Amorphous carbon (a-C) and diamond-like carbon (DLC) ﬁlms are known as bioinert materials with no toxic reactions with living organism [9, 10]. Furthermore, the combination of high hardness, low coeﬃcient of friction, high wear and corrosion resistance, with the bioinert character is a good reason for selecting carbon ﬁlms as a surface ﬁnish on biomedical implants. Previous studies have shown that these ﬁlms exhibited good compatibility with diﬀerent cell types, including macrophages, ﬁbroblasts, human myeloblasts and human embryo kidney cells [11, 12, 13, 14, 15, 16]. They have also shown excellent haemocompatibility, reduced platelet adhesion, activation and aggregation, which are good indicators of reduced thrombus formation [17, 18, 19]. Another important factor in favor of the amorphous carbon ﬁlms as a biocompatible surface is that their properties (surface energy, electrical conductivity, tribological properties, etc.) can be tailored by the deposition conditions or doping/bonding using additional elements to induce speciﬁc biological responses [20, 21]. Today, two main biomedical applications of carbon-based coatings can be seen: those of DLC in blood-contacting devices (stents and heart valves); and the use of DLC to reduce wear in load-bearing joints. Coronary artery stents and heart valves are aﬀected by platelet activation due to blood contact with the biomaterial or the release of metallic ions. This activation is an important trigger for thrombosis. To solve this situation, the use of coatings on metallic stents and heart valves has been suggested. Of these coatings, carbon coating is the most frequently used. In vitro studies [22, 23] have shown that DLC signiﬁcantly reduces the release of metal ions and diminishes the platelet activation, therefore lower rates of acute and subacute thrombosis

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are expected. Although, recent clinical trials showed no statistical diﬀerences between metal bare and coated stents [24, 25, 26]. While, for coated heart valves, clinical trials have demonstrated that the most bio-haemocompatible material is pyrolitic carbon, either as a solid or a coating [27, 28]. On the other hand, the use of diamond-like carbon for orthopedic implants has been motivated by the low coeﬃcient of friction, high wear resistance and hardness of the ﬁlms. These properties are needed to improve the lifetime of total hip or knee replacements. The standard design of a hip replacement comprises a metal or sometimes a ceramic head running against an ultra-high-weight polyethylene acetabular cup. This can last for up to 15 years, which is not enough for young, active patients, and moreover, early failures are usually reported. The failure is mainly a consequence of generation of polyethylene wear debris resulting from the relative movement of the femoral head and the acetabular cup. Thus, coatings to prevent such wear have been suggested and DLC is one of the potential candidates [29, 30]. Minor applications of carbon ﬁlms in the biomedical ﬁeld include coating of polymer-based medical products, such as catheters, drainage tubes or polymer contact lenses [31]. Not much research has focused on studying the bone-related cell responses of amorphous carbon ﬁlms. The studies of the bone-forming activity have been performed on cell populations extracted from bone tissue: osteoblasts. Du et al. [32] studied the morphological behavior of osteoblast on DLC and amorphous carbon nitride deposited on silicon substrates, showing that cells were able to attach, spread and proliferate on the surfaces without apparent impairment of cell physiology. However, the ability of carbon surfaces to promote bone growth or biomineralization has not been studied. The formation and maintenance of viable bone in close proximity to the surface of biomaterials are essential for the stability and clinical success of noncemented orthopedic/dental implants. The osteoblast is the cell type responsible for the deposition of bone within the interfacial zone between the implant and host tissue. A better knowledge of the osteoblasts’ function could enhance current understanding of the cellular/molecular events that occur at the tissue–implant interface, and with this information one could produce biomaterials engineered to elicit speciﬁc responses, such as enhanced osteoblastic mineral deposition. The bone-forming activity of osteoblasts entails an initial phase of attachment, proliferation, differentiation and extracellular matrix synthesis, and a second phase of bone matrix mineralization. Mineralization in osteoblasts, cultures in vitro can be demonstrated in two main ways: detection of calcium and phosphate deposits in the cell layer or detection of bone-matrix proteins that are known to regulate “ex novo” bone formation. For example, bone sialoprotein is speciﬁcally expressed by osteoblasts depositing bone ex novo [33]. Osteoblasts cells are anchorage-dependant, and their development depends strongly on the initial cellular attachment [34]. In this paper we investigate cellular adhesion and subsequent cellular functions: proliferation and deposition of a mineralized matrix. The cellular adhesion and proliferation in conjunction with

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viability tests constitute the best combination of cytotoxicity–biocompatibility tests, while the analysis of the production of mineralized matrix on the implant materials represents the most appropriate bioactivity test for bonebonding applications. The bioactivity was monitored by direct observation of the morphology of the deposited mineralized matrix, as well as the expression of some biochemical parameters of osteoblastic phenotypes: alkaline phosphatase (ALP) activity and bone sialoprotein (BSP).

2 Experimental Details Two sets of experiments were realized to evaluate the biocompatibility and bioactivity of the a-C coatings. In the ﬁrst set, we studied the cytotoxicity using 1 cm2 stainless steel (AISI316L) squares as substrates. From proﬁlometer measurements the surface roughness was between 0.05–0.1 µm with randomly distributed scratches. The second set, used to evaluate the bioactivity, was of stainless steel discs of 15 mm in diameter: the same size as that of the wells in the culture plates. The surface of the discs was sand-blasted with SiO2 particles to obtain a uniform average roughness of 2 µm. In an earlier study we conﬁrmed that human osteoblast attachment on amorphous carbon ﬁlms was enhanced on substrates with an average surface roughness greater than 1 µm [35]. 2.1 Film Deposition Prior to deposition, the substrates were ultrasonically cleaned in acetone and isopropanol for 30 min, respectively, and then air-dried. A thin layer of titanium was deposited as an interface layer to increase the adhesion between the amorphous carbon ﬁlm and the stainless steel (SS) substrate. The Ti layer was deposited using a pulsed magnetron sputtering system using argon as the precursor gas and a high-purity, 99.99%, Ti target. The a-C were deposited using a high purity hollow cathode graphite target, 7 cm2 , in a DC magnetron sputtering system and an argon plasma. The Ti/SS substrates were initially cleaned by an argon plasma for 10 min. The base pressure prior deposition was less than 2 · 10−4 Pa and the carbon ﬁlms were deposited at 4 Pa using 0.4 A and argon ﬂow rate of 20 sccm for 5 min, giving a ﬁlm thickness of 150 nm. For the characterization of the ﬁlm properties, a-C ﬁlms under the same conditions were deposited on silicon and quartz substrates. All layers were deposited at room temperature. 2.2 Film Characterization The ﬁlms deposited on silicon substrates were used to obtain the thickness using a DEKTAK proﬁlometer. The optical absorption in the ultraviolet–visible

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range was measured for the samples deposited on quartz using an UV–VIS UNICAM spectrometer in the range 1.5–3.5 eV. Spectroscopic ellipsometry was also used to study the optical properties and thickness of the ﬁlms. The energy range was 1.5–5 eV, and the ellipsometric parameters were obtained using a Jobyn Yvon photoelastic modulated ellipsometer. The optical constants were obtained by ﬁtting spectroscopic ellipsometry measurements with a two-oscillator Tauc–Lorentz model [36]. Surface composition was investigated with X-ray photoelectron spectroscopy using a Thermo Scientiﬁc Multilab and Al Kα-radiation. 2.3 Cell Preparation Human alveolar bone-derived cells (HABDC) were obtained by a conventional explant technique [37]. The cells were cultured in 75 cm2 ﬂasks in a standard culture medium composed of: Dulbecco’s Modiﬁed Eagle’s Medium (DMEM), supplemented with 10% fetal bovine serum (FBS) and antibiotic solution (Streptoycin 100 mg/ml and penicillin 100 U/ml, Sigma Chem Co.). The cells were incubated in a 100% humidiﬁed environment at 37◦ C in an atmosphere of 95% air and 5% CO2 . 2.4 Cytotoxicity Test The cytotoxicity was evaluated on the a-C ﬁlms, the SS substrate, the Ti coating and a plastic positive control. All samples were sterilized by autoclave. The cytotoxicity study include three diﬀerent tests: adhesion after 24 h, proliferation and viability up to 7 d. The HABDCs were plated at an initial density of 1 · 104 /well and left to adhere for 3 h. After this time, 600 µl of the culture medium were added. For the adhesion tests the cells were kept for 24 h and for the proliferation and viability assays the cells were left in the culture plates for 1, 3 and 7 d. The experimental and control cultures were treated every 2 d with fresh media. To determine the number of attached cells, we followed the same procedure in each case; that is, after incubation, the unattached cells were removed with a phosphate buﬀered saline solution (PBS) and the attached cells were ﬁxed with 3.5% paraformaldehyde. The evaluation of the number of attached cells was performed by staining the cellular membranes and measuring the optical density at the corresponding color. To perform the staining, the ﬁxed cells were incubated with 0.1% toluidine blue dye for 3 h. The dye was extracted with sodium dodecyl sulfate (SDS) and the optical absorption measured with a microplate enzyme-linked immune assay (ELISA) reader at 600 nm. The number of cells was then determined by correlating the absorbance of the experimental samples with a standard correlation curve. For the proliferation test we followed the same procedure for each incubation time. On the other hand, for the cell viability the conversion of the yellow dye (3-[4,5-dimethylthiazolyl-2-y]-2,5-diphenyltetrazolium bromide, MTT) to

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blue formazan was used as a marker of cell viability or cell enzymatic activity (mitochondrial). The cells were plated and incubated as described above. After each term 10 µl of MTT were added and incubated for 3 h. Then, the supernatant was removed and 600 µl of dimethyl sulfoxide (DMSO) were added to each well. After 60 min of slow shaking the absorbance was read at 570 nm which gives a reading directly proportional to the number of viable cells. 2.5 Bioactivity Evaluation of the biomineralization consisted of the morphological examination of the mineralized extracellular matrix and the evaluation of a selection of proteins involved in the bone-formation process. 2.5.1 Morphological Assay The samples (a-C, Ti, SS and positive control) were cultured in the same way as for the proliferation assay until they reached conﬂuence. Then, we added the mineralization medium: 50 µg/ml of ascorbic acid, 10 mM of β-glycerophosphate and 100 nM of dexamethasone. These compounds are known to accelerate the mineralization process. The media was changed every 2 d. Biomineralization was evaluated after 7, 14 and 21 d. Following cultivation the samples were prepared for observation in the scanning electron microscope (SEM) in the following way: cell cultures were ﬁxed with 4% formaldehyde in 0.1 M phosphate buﬀer solution (pH 7.3), then dehydrated in graded ethanol and ﬁnally sputter-coated with gold. The microscope was a CAMBRIDGE-LEICA STEREOSCANN 440 SEM. 2.5.2 Protein Synthesis Alkaline Phosphatase Activity In this case, the cells were incubated in the culture medium, i.e., no mineralization medium was added, for 3, 7 and 14 d. The alkaline phosphatase activity was determined in cell lysates, obtained by treatment of the cultures with 0.1 Triton X100 in PBS. The lysates were analyzed by measuring the release of p-nitrophenol from p-nitrophenyl phosphate in an alkaline buﬀer solution, and the colorimetric determination of the product (p-nitrophenol). Alkaline phosphatase catalyzes the cleavage of a phosphate group from a variety of compounds, including p-nitrophenyl phosphate, which is colorless. However, one product, p-nitrophenol, is yellow in basic solutions. The appearance and intensity of yellow color thus indicates the degree to which the substrate has been acted upon by the enzyme. Normalizing the results to the time and the total protein concentration gave us information about the

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speciﬁc activity of the ALP in each of the surfaces. The total protein content of the lysates was determined using a commercially available kit (Macro BCA, Pierce Chemical Co.). The ALP activity is reported as nanomoles of p-nitrophenol produced per minute normalized to the milligrams of total protein content (nmol min−1 mg protein−1 ). The samples were produced in triplicate and the measurements repeated at least three times, giving a total of nine data values for each incubation period. Western Blot Analysis of Bone Sialoprotein Similarly, the HABDCs were plated on surfaces in triplicate at an initial density of 1 · 104 /well in a culture medium in 24-well culture plates; control cells were cultured directly on tissue culture polystyrene. The cells were cultured for 7 and 14 d. Western blots allowed us to determine the molecular weight of the protein and to measure the relative amounts of the protein present in the diﬀerent samples. The proteins were separated by gel electrophoresis. The proteins were transferred to a sheet of special blotting paper called nitrocellulose. The proteins retained the same pattern of separation they had on the gel. The blot was incubated with a generic protein (such as milk proteins) to bind to any remaining sticky places on the nitrocellulose. An antibody was then added to the solution which is able to bind to its speciﬁc protein. The antibody has an enzyme (e.g., alkaline phosphatase or horseradish peroxidase) or dye attached to it that cannot be seen at this time. The location of the antibody is revealed by incubating it with a colorless substrate that the attached enzyme converts to a colored product that can be seen and photographed. The bandwidth is proportional to the quantity of the protein, so the analysis gives us a qualitative assessment of the protein content. The relative level of the protein was assessed by measuring the integrated density of all pixels in each band, excluding the local background and normalizing to the area of the reference. The results are expressed as intensity per mm2 . Bone Sialoprotein Inmunoﬂuorescence For this test, the cells were culture for 14 and 21 d in the culture medium. After the incubation period, cells were ﬁxed using 4% paraformaldehyde for 15 min. After washing with PBS they were processed for immunoﬂuorescence: cells were permeabilized with 0.5% Triton X-100 in PBS for 15 min followed by blocking with 1% ovalbumin in PBS for 30 min. A primary monoclonal antibody to BSP was used, followed by corresponding Alexa Fluor 488 (green ﬂuorescence) conjugated goat secondary antibody. The samples were examined by epiﬂuorescence under a conventional ﬂuorescence microscope.

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Fig. 1. (a) Absorption coeﬃcient determined by three diﬀerent techniques: analysis of reﬂectance and transmittance spectra, photothermal deﬂexion spectroscopy and ellipsometry spectroscopy. (b) Refractive index and extinction coeﬃcient as a function of energy

3 Results 3.1 Film Properties Because of the diversity of properties that amorphous carbon ﬁlms exhibit, it is very important to perform as complete as possible a characterization of the type of ﬁlm used. The results of this evaluation for the present study are described below. The average surface roughness remained nearly constant at 2 µm after coating the substrate. In a previous paper, we reported the energy loss spectra of amorphous carbon ﬁlms [38] deposited by magnetron sputtering and demonstrated that the ﬁlms are nearly 100% sp2 bonded, although a quantitative sp2/sp3 fraction could not be obtained since the π peak was

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Fig. 2. Visible Raman spectra. Results of the decomposition using two Gaussian peaks for G and D

too wide, indicating that more than one conﬁguration was present and thus impeding the area calculation [39]. It is well known that the optical and electrical properties of amorphous carbon depend not only on the quantity of sp2 bonds but also on their distribution or conﬁguration. The optical measurements showed that the ﬁlms were highly absorbing for energies above 1 eV, having a Tauc optical gap of about 1 eV. The absorption coeﬃcient as a function of the energy, as determined by three independent techniques, is shown in Fig. 1a. The E04 falls below the measured range, and therefore we only report the√Tauc gap that results from an extrapolation to zero of the line ﬁtting the α × energy vs. energy spectra in the high energy range. Typical data of the refractive index and extinction coeﬃcient are shown in Fig. 1b. The existence of the small gap is in agreement with a small degree of clustering of the sp2 phase detected by the analysis of the Raman spectrum, shown in Fig. 2 together with the results of the decomposition of the Raman spectra into two Gaussians: D and G peaks. The XPS analysis demonstrated that the surface composition consisted predominantly of carbon, and oxygen as a surface contaminant (Fig. 3). We checked for the presence of metal atoms from the substrate or the Ti coating but no signal was found, indicating that the a-C ﬁlm completely and uniformly covers the substrate. According to this characterization we can conclude that the ﬁlms were uniformly deposited on the rough stainless steel substrates, copying the surface topography. The physical and structural properties, optical gap, refractive index and bonding characteristics of the ﬁlms suggest that the ﬁlms used for this investigation are graphite-like amorphous carbon ﬁlms.

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Fig. 3. XPS spectra of the sample, general view

3.2 Cytotoxicity In vitro methods provide a necessary and useful adjunct to “in vivo” studies for selecting materials as candidates for implants or biomaterials. This study includes two stages; the ﬁrst, cytotoxicity tests, is carried out to detect any toxic eﬀects of the potential materials. The second stage allows a more thorough evaluation of the biocompatibility of the material in relation to its end use, in our case the biomineralization tests. The cytotoxicity of amorphous carbon ﬁlms has been tested with diﬀerent cell lines, and in general it is catalogued as a biocompatible material. However, considering the diﬀerences in ﬁlm properties and the importance to test the material using cells speciﬁc for the proposed application of the medical device, we decided to evaluate the cytotoxicity using primary human osteoblasts on the sputtered a-C ﬁlms. Toxicity in vitro is a negative or deleterious eﬀect that induces changes in the cellular response, such as cell death, reduced cell adhesion and proliferation, altered cellular morphology, and inhibition of biosynthetic functions. All of these processes were evaluated. Cell death was not observed during the period of evaluation up to 7 d. The cellular adhesion, on the other hand, which is very important for this speciﬁc type of cells, was actually improved by the ﬁlms in comparison to either the stainless steel substrate, the Ti coating and the positive control. This is observed in Fig. 4, in which we plot the number of attached cells after 24 h on each surface. The a-C had the highest number of attached cells compared to all other materials (ANOVA p < 0.05). Cell proliferation was evaluated for periods up to 7 d. Figure 5 shows that the number of cells increased as a function of the incubation time for all surfaces. The number of cells on the a-C ﬁlms doubled at three d of incubation, while the doubling time for the Ti ﬁlms was about 7 d. On the stainless steel the number of cells remained constant at about 1.2 · 104 even after 7 d.

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These results were further conﬁrmed by the cell viability assay (MTT test), which is very important since the combined proliferation/metabolic test is a way of providing information about the cell growth and metabolic activity of the cells. The results of the MTT assay (Fig. 6) are presented as the optical absorbance at 570 nm. We found high levels of MTT conversion (higher absorbance, high metabolic activity), compare to the control, for Ti and aC ﬁlms, and this increased with time. This increment reﬂects the increased number of cells on the surfaces and therefore conﬁrms that there are a greater number of both dividing and metabolically active cells. In accordance to the lower proliferation rate measured for the SS substrate, the enzymatic activity of the osteoblasts cells on SS is lower. Finally, scanning electron microscopy allowed the observation of the cell morphology. Osteoblasts with dorsal rufﬂes close to each other connected by ﬁlopodia, attached and spread on the substrate were observed during the diﬀerent incubation times (not shown). The results of the cytotoxicity tests suggested that the amorphous carbon and titanium coatings have no negative aﬀect on cell adhesion, viability and proliferation. The cell number and absorbance values obtained for a-C and Ti resulted signiﬁcantly higher with respect to the positive control and the SS substrate, indicating the absence of toxic eﬀects. Morphologically, the cells were in good condition and well attached to the surfaces. 3.3 Bioactivity 3.3.1 Morphological Analysis Secondary electron image examination at 14 and 21 d of cultured osteoblasts on the surfaces revealed a continuous cell multilayer and an extracellular matrix that completely covered the surface. Figure 7 shows the images at diﬀerent magniﬁcations for the a-C surfaces at 14 and 21 d. Figure 8 shows corresponding images for SS and Ti coatings. The extracellular matrix was composed of both noncollagenous and collagenous components, with small (< 1µm) spherical structures or mineral deposits. These mineral deposits were seen interspersed among the osteoblast cell layer or within the ﬁbrillar matrix. The images are similar to those reported in other works [40, 41, 42], although the incubation periods used in our work are relatively shorter. By comparing Figs. 7 and 8 we can observe that similar results were obtained for the SS substrate, a-C and Ti coatings. Therefore, by simple morphological analysis of the mineralization process it is impossible to determine any substrate-dependent eﬀect, emphasizing the importance of making quantitative measurements, such as those obtained by the analysis of speciﬁc proteins.

3.3.2 Proteins Chemical reactions in living organisms occur rapidly at moderate temperatures and under mild conditions primarily because of the catalytic action of

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Fig. 4. Number of attached cells after 24 h of incubation for the SS substrate, a-C and Ti coatings and the plastic culture dish

a-C SS Ti Control

Number of Cells

24000

20000

16000

12000

8000

0

1

2

3

4

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Days Fig. 5. Osteoblast proliferation for 1, 3 and 7 d of incubation. The initial plated cells was 1 · 104 per surface

specialized proteins called enzymes. Each step in the chain of a biochemical reaction is usually catalyzed by a speciﬁc enzyme. A large number of proteins are involved in preparing the matrix for mineralization: phosphatases that regulate extracellular phosphate concentrations, kinases that regulate matrix protein phosphorylation and metalloproteinases that degrade the extracellular matrix. In order to mineralize, osteoblasts express these compounds into the extracellular matrix, speciﬁcally alkaline phosphatase, bone sialoprotein, osteocalcin and osteopontin. The rate of an enzyme-catalyzed reaction may be measured by (a) the disappearance of substrate, which is the substance acted upon by the enzyme and changed to the product, or (b) the appear-

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2.0 a-C SS Ti Control

Absorbance at 570 nm

1.8 1.6 1.4 1.2 1.0 0.8 0.6 3

4

5

6

7

Days Fig. 6. Cell viability (MTT test) expressed as the absorbance at 570 nm

ance of the product. The ALP activity was measured by the product quantity as described above. The levels of this enzyme in the various surfaces are shown in Fig. 9, as a function of the incubation time. ALP plays a vital but yet undeﬁned role in bone mineralization. It is thought to regulate phosphate transport. The enzyme is glycosylated and attached to the cytoplasmic membrane on its external surface, where it interacts with extracellular matrix proteins. The results showed that all the cultures presented a signiﬁcant induction of the ALP activity, which is in some way expected since we use osteoblasts, which produce high ALP concentrations. However, the activity was signiﬁcantly higher for the amorphous carbon coatings compared to the other surfaces (ANOVA p < 0.05). An increase in the activity and expression of ALP is a strong marker of both the osteoblast phenotype and mineralization. The other bone-related protein investigated in this work was bone sialoprotein (BSP), a phosphorylated glycoprotein. BSP is a major structural protein of the bone matrix that is speciﬁcally expressed by fully diﬀerentiated osteoblasts. The expression of BSP is normally restricted to mineralized connective tissue of bones and teeth, where it has been associated with mineral crystal formation and is considered a potent nucleator of hydroxyapatite. Western blot analysis was performed to determine the expression of bone sialoprotein on the surfaces. Semiquantitative information about the level of BSP expression was obtained by densitometric studies, and both images are shown in Fig. 10. BSP was expressed on all surfaces after 7 and 14 d of culture. For a-C, SS and Ti we observed a progressive increase in BSP expression with time, while in the tissue plastic control, the level decreased. Remarkably, the level of BSP expression was much higher on a-C than in any other surface. Because of the diﬃculty in analyzing the samples to obtain the composition of the mineralized matrix, particularly of the small spherical nodules,

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Fig. 7. SEM images of the mineralized matrix in the amorphous carbon surfaces after A, B 14 d. C and D 21 d. Bar: A 2µm, B 10µm, C 2µm, D 30µm

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Fig. 8. SEM images of the mineralized matrix in the SS substrate after A 14 d, B 21 d. SEM images of the mineralized matrix in the Ti coatings after C 14 d and D 21 d. Bar: A, 10 µm; B, 2 µm; C, 30 µm; D, 2 µm

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Fig. 9. Alkaline phosphatase (ALP) activity

Fig. 10. Western blot analysis of bone sialoprotein (top) and densitometric analysis of the bands, showing the intensity per µm2 (bottom)

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we determined the distribution of bone sialoprotein on the surfaces by immunoﬂuorescence labeling. This technique allowed us to conﬁrm that the small nodules shown in the SEM images corresponded to mineral deposits containing high concentrations of BSP. Figure 11 shows the diﬀerent images of the BSP distribution on the a-C coating, and similar images were obtained for the other surfaces (not shown). An important proportion of the cells were immunoreactive to BSP for all the time periods (14 and 21 d). BSP was present in both the cell layer and the extracellular matrix. Active osteoblasts contain BSP in a large juxtanuclear mass reminescent of the Golgi region, so the underlying cellular layer was clearly seen. However, ﬂuorescence intensity was stronger in the spherical nodules that appeared at 14 d of incubation and grew into big mineral deposits, forming large mineralized layers, as those observed in Figs. 9d and 7a by SEM.

4 Discussion The present study describes an in vitro model to study the response of human osteoblasts to well-characterized a-C coatings in comparison with titanium coatings and the stainless steel substrates. We performed both short- and medium-term studies to determine the cytotoxicity and the biomineralization of the diﬀerent surfaces. We observed an enhanced cellular adhesion and proliferation/viability on the a-C coatings, demonstrating the biocompatibility of the material. Moreover, we demonstrated the formation of a calciﬁed matrix with bone sialoprotein and alkaline phosphatase being expressed. By comparison between the diﬀerent surfaces, we showed that osteoblast cells respond diﬀerently to biomaterial in both short- and medium-term cultures. The SEM examination of the osteoblast cultures in the presence of β-glycerophosphate, dexamethasone and ascorbate revealed the formation of a stratiﬁed matrix mixed with cell layers and the mineralized nodules. The ALP activity and Western blot were performed to determine the time development and levels of two important proteins, ALP and BSP, associated with the mineralization process. Our results showed diﬀerent responses to the biomaterial, and in both cases the amount of protein expressed on the a-C surfaces was larger, suggesting that the ﬁlm properties promote the diﬀerentiation and mineralization of human osteoblast. A good correlation between proliferation and mineralization results was obtained. It is well established that proliferation stops when the mineralization process is initiated [43] and that mineralization initiates once the cells have formed a certain amount of extracellular matrix. This is clearly reﬂected in our results. Figure 4 shows that cell proliferation attained a saturation level at about 7 d, after which the ALP activity increased dramatically (Fig. 9). This was important to establish the moment at which the mineralization medium should be added to the culture, since once the culture medium is

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Fig. 11. Distribution of the bone sialoprotein on the amorphous carbon surfaces after A, B 14 d. C, D 14 d. A, C and B 10X; D 20X

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rich in phosphate ions, mineralization will occur, but without the appropriate matrix, the mineralization obtained is dystrophic and does not necessarily resemble the bone formation in vivo. Human osteoblast cultures may be regarded as a potential in vitro model to study biomaterial/bone tissue interactions. However, in order to determine the diﬀerences between biomaterial-induced responses, morphological analysis of the cell layers grown on the surface is not suﬃcient. If possible, structural characterization of the mineral deposits must be performed, but standard immunoﬂuorescence or staining techniques are more appropriate to quantitatively compare the response of the osteogenic cells to the diﬀerent materials. In conclusion, we have shown that graphite-like amorphous carbon is a potential candidate for further research as a bioactive coating to induce bone formation. Many issues must still be investigated, for example, ﬁlm properties, and more important, ﬁlm–substrate adhesion must be improve to the point that no failure is possible in long-term applications. Mechanical tests associated with the torque resistance that the coating should support during the insertion of the implant into the bone must be performed. Similarly, other biological tests, such as genotoxicity and in vitro bone growth, need to be carried out.

References [1] X. Liu, P. K. Chu, C. Ding: Mat. Sci. and Eng. R 47, 49 (2004) 55 [2] J. M. Hollis, C. Flahiﬀ: Factors aﬀecting bone ingrowth, in D. Wise, D. Trantolo, D. Altobelli, M. Yaszemski, J. Gresser, E. Schwartz (Eds.): Encyclopedic Handbook of Biomaterials and Bioengineering (Marcel Dekker, New York 1995) pp. 799–821 55 [3] B. Ratner: J. Biomed. Mater. Res. 7, 837 (1993) 56 [4] A. Buford, T. Goswami: Mater. and Design. 25, 385 (2004) 56 [5] W. R. Laceﬁeld: Bioceramics: Materials Characterization versus In Vivo Behaviour (New York Academy of Science, New York 1988) p. 72 56 [6] D. B. Burr, S. Mori, R. D. Boyd, T. C. Sun, L. Lane, J. D. Blaha, J. Parr: Trans. Orthop. Res. Soc. (USA, Japan, Canada) p. 8 (1991) 56 [7] S. D. Cook, L. P. Patron, S. L. Salkeld, J. J. Klawitter, R. D. Beckenbaug: Pyrolitic carbon as an implant for small joint replacement, in D. Wise (Ed.): Biomaterials and Bioengineering Handbook (Marcel Dekker, New York 2000) p. 383 56 [8] A. Bolz: Applications of thin-ﬁlm technology in biomedical engineering, in D. Wise, D. Trantolo, D. Altobelli, M. Yaszemski, J. Gresser, E. Schwartz (Eds.): Encyclopedic Handbook of Biomaterials and Engineering (Marcel Drekker, New York 1995) pp. 1287–1330 56 [9] F. Z. Cui, D. J. Li: Surf. Coat. Technol. 131, 481 (2000) 56 [10] R. Hauert: Diam. Relat. Mater. 14, 78 (2003) 56 [11] S. Linder, W. Pinkowski, M. Aepfelbacher: Biomaterials 23, 767 (2002) 56

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[38] S. E. Rodil, S. Muhl, S. Maca, A. C. Ferrari: Thin Solid Films 433, 119 (2003) 62 [39] A. C. Ferrari, A. Libassi, B. K. Tanner, V. Stolojan, J. Yuan, L. M. Brown, S. E. Rodil, B. Kleinsorge, J. Robertson: Phys. Rev. B 62, 11089 (2000) 63 [40] E. Parker, A. Shiga, J. E. Davies: in J. Davies (Ed.): Bone Engineering (em squared, Toronto 1999) pp. 63–77 65 [41] M. J. Coelho, M. H. Fernandes: Biomaterials 21, 1095 (2000) 65 [42] M. W. Squire, J. L. Ricci, R. Bizios: Biomaterials 17, 725 (1996) 65 [43] G. S. Stein, J. B. Lian: End. Rev. 4, 290 (1995) 71

Index a-C, 55 sp3 /sp2 bonding ratio, 62 alkaline phosphatase (ALP), 58–61, 66, 67, 70, 71 bioactivity, 55, 58, 60, 65, 73 biocompatibility, 55–58, 64, 71 biomaterials, 57, 64, 73 biomedical implants, 55–57, 64, 73 bone sialoprotein (BSP), 57, 58, 61, 66, 67, 70–72 coatings, 56–58, 67, 71–73 bioactive coatings, 55 biomedical coatings, 57 cytotoxicity, 58, 59, 64, 65, 71

G band, 63 haemocompatibility, 56, 57 hardness, 56, 57 mineralization, 57, 60, 64–67, 71 MTT test, 65, 67 optical properties, 59 proliferation, 57, 59, 64, 65, 71 Raman spectroscopy, 63 refractive index, 63 scanning electron microscopy (SEM), 60, 65, 68, 69, 71

D band, 63 diamond-like carbon (DLC), 56, 57

tribological properties, 56

electrical properties, 63

viability, 58, 59, 65, 71

friction coeﬃcient, 56, 57

wear resistance, 56, 57

Characterisation of the Growth Mechanism during PECVD of Multiwalled Carbon Nanotubes Martin S. Bell1 , Rodrigo G. Lacerda2, Kenneth B.K. Teo1 , and William I. Milne1 1

2

Engineering Department, University of Cambridge, Cambridge CB2 1PZ, UK [email protected] Universidade Federal de Minas Gerais, Departamento de F´ısica, BR-30123-970 Belo Horizonte, MG, Brasil

Abstract. The growth mechanism of multiwalled carbon nanotubes has been a subject of considerable research interest. Published results show that nanotubes may be formed by a variety of methods using diﬀerent combinations of carbonrich gases and etchant gases. We present an overview of diﬀerent forms of carbon, showing how nanotubes relate to other carbon structures and how they may be produced. The use of plasma-enhanced chemical vapour deposition (PECVD) for growing vertically aligned nanotubes for electronic device applications is reported, including an analysis of the species present in the plasma during PECVD. It is shown that the presence of a reactive species such as ammonia suppresses decomposition of carbon feedstock gas and favours the formation of carbon nanotubes. It is further shown that gas-phase reactions remove excess carbon, allowing the production of nanotubes without unwanted amorphous carbon deposits, which is essential for electronic applications. Plasma analysis is used to determine an optimum carbon-source to etchant gas ratio, which is veriﬁed by postdeposition analysis.

1 Introduction Carbon is a fascinating material due to the ability of carbon atoms to bond with each other in diﬀerent ways, giving rise to materials as varied as diamond and graphite. Carbon has six electrons, arranged as (1s)2 (2s)2 (2p)2 . It forms covalent bonds with other carbon atoms, using the outer four electrons. To form these bonds, one of the 2s electrons is promoted to a 2p level. The hybridisation of these electron orbitals allows carbon to form diﬀerent structures. In diamond, sp3 hybridisation produces four identical and very strong bonds. Each atom bonds to four others, giving rise to a tetrahedral structure, symmetric in three dimensions. In graphite, the remaining 2s electron hybridises with two of the 2p electrons, giving three sp2 orbitals, which are located in an (x, y) plane, separated by 120◦ . The remaining 2p electron orbital is perpendicular to this plane, hence it is known as a pz orbital. The sp2 orbitals form strong σ-bonds beG. Messina, S. Santangelo (Eds.): Carbon, The Future Material for Advanced Technology Applications, Topics Appl. Phys. 100, 77–93 (2006) © Springer-Verlag Berlin Heidelberg 2006

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A B Fig. 1. AB stacking in graphite

Fig. 2. C60 molecule

tween the carbon atoms in the plane. Graphite consists of a series of these parallel “graphene” planes. The pz (or π) orbital perpendicular to the plane provides a weak van der Waals bond that binds the planes together. The weakness of these π-bonds allows the graphene planes to be easily separated. In high-quality “Bernal” graphite, the graphene sheets are stacked ABAB. . . (Fig. 1). These graphene sheets have an interlayer spacing of approximately 0.334 nm. The presence of defects in the graphene sheets gives rise to a larger interlayer spacing (≈ 0.35 nm), and to a random rotation of the graphene layers with respect to one another. This less-crystalline form is known as turbostratic graphite. A third structure observed in carbon is C60 , also known as “buckminsterfullerene” after the architect Buckminster Fuller, who is famous for his geodesic dome designs. The C60 molecule is an icosahedral structure made up of 20 hexagons and 12 pentagons (Fig. 2). Each carbon atom is joined to

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a2 a1

Fig. 3. Unit vectors in the graphene plane

three others, so it is predominantly σ-bonded, like graphite. There are similar molecules containing more carbon atoms (e.g., C70 ). The discovery of C60 in 1985 [1] may be identiﬁed as the ﬁrst key step along the path which led to the synthesis of carbon nanotubes. Carbon nanotubes themselves were identiﬁed in 1991 [2]. A single-walled nanotube is simply a graphene sheet rolled up into a cylinder. The dangling bonds at the extremities of the sheet join together, completing the cylinder. The size of the nanotube and its electrical properties are determined by the “chiral vector”, which links the two points in the graphene sheet that join up to complete the nanotube. The chiral vector is deﬁned as c = ma1 + na2 , where a1 and a2 are the unit vectors in the graphene plane (Fig. 3). The nanotube, of course, requires not just sides but a cap at the end to eliminate the dangling bonds. The cap is an icosahedral structure made up of pentagons and hexagons, like a C60 molecule. A nanotube is classiﬁed according to its chiral vector, and referred to as an (m, n) tube. There are two special cases that exhibit particularly high symmetry. These are known as “armchair” and “zig-zag” nanotubes. For an armchair nanotube, n = m, whilst for a zig-zag tube, n = 0. In these cases, the chiral vector is perpendicular to the nanotube axis (Fig. 4). For the two speciﬁc nanotubes shown, the cap in each case is half of a C60 molecule. More generally, if n = 0, and n = m, a “chiral” nanotube is formed, where the hexagons are arranged helically around the nanotube. Single-walled nanotubes typically have diameters in the range 1–5 nm. They may be metallic (0 eV band gap) or semiconducting (typically 0.4–0.7 eV band gap) depending upon the chiral vector. The band gap is also inversely proportional to the diameter [3, 4, 5]. A multiwalled nanotube consists, in essence, of a series of concentric single walled nanotubes. As discussed above, the interlayer spacing in well-ordered ABAB graphite is 0.334 nm. For the ABAB structure to be replicated in a multiwalled nanotube would require successive nanotube circumferences to

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Fig. 4. “Armchair (5,5)” and “zig-zag (9,0)” nanotubes (top and bottom, respectively)

diﬀer by an integer multiple of (2π × 0.334 nm), as well as requiring wellordered individual nanotubes. Measurements have shown that the intershell spacing in multiwalled nanotubes can range from 0.34 to 0.39 nm, with the spacing decreasing as nanotube diameter increases [3, 6]. The geometrical constraints in forming the seamless graphene cylinders cause the layers to be uncorrelated with respect to one another. Multiwalled nanotubes therefore resemble the less-ordered turbostratic form of graphite rather than the higher-quality Bernal form. Multiwalled nanotubes typically have outer diameters in the range 50– 100 nm. Electrical conduction can take place within each of the individual shells of a multiwalled nanotube. However, if a multiwalled nanotube is contacted on the outside, the electric current is conducted through its outermost shell only [7]. Where conduction occurs through this outer shell, the band gap approaches 0 eV due to the relatively large diameter and the nanotube acts as a metallic conductor. Before we go any further, it is worth mentioning a related structure, namely carbon nanoﬁbres. Carbon nanoﬁbres are another kind of graphitic ﬁlament, which diﬀer from nanotubes in the orientation of the graphene planes. The graphene planes in a carbon nanotube are parallel to the nanotube axis; in a nanoﬁbre, the graphene layers are not parallel to the axis, but are rather arranged in a stacked form (layers perpendicular to the ﬁbre axis) or herringbone form (layers at an angle to the axis). These nanoﬁbres are illustrated in Fig. 5, with the nanoﬁbre axis indicated by an arrow in each case. Nanoﬁbres have many useful properties in common with carbon nanotubes and share some potential applications. They do not, however, share all of the beneﬁcial properties of nanotubes that derive from their structure. When carbon nanotubes were discovered, it was realised that because the graphene planes are parallel to the ﬁlament axis, they would inherit

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Fig. 5. “Stacked” and “herringbone” nanoﬁbres (top and bottom, respectively)

several important properties of graphite. In particular, a nanotube exhibits high electrical conductivity, thermal conductivity and mechanical strength along its axis. As there are very few open edges and dangling bonds in the structure, nanotubes are also very inert, and species tend to be physically adsorbed onto the graphene walls rather than react with them. As carbon nanotubes are completely covalently bonded, they can be excellent electrical conductors which do not suﬀer from electromigration, a limiting factor for metals. Carbon nanotubes have been investigated for a wide range of applications. A nanotube can behave as a high-aspect-ratio electrical conductor with micron-scale length and nanometre-scale diameter. Structures of this type are highly desirable as ﬁeld emission tips for applications such as ﬁeld emission displays [8, 9], X-ray tubes [10], electron sources for microscopy and lithography [11], gas discharge tubes [12] and vacuum microwave ampliﬁers. The high aspect ratio and small diameter of the nanotube is also useful for scanning probe tips [13, 14]. Semiconducting single-wall carbon nanotubes have been investigated for use as transistors or logic elements [15, 16]. The electronic properties of the carbon nanotubes are highly sensitive to adsorbed species [17, 18], which is a challenge for logic circuits, requiring the nanotubes to be suitably encapsulated. However, this sensitivity may be utilized in chemical or biological sensors for gas detection. The coherent nature of electron transport in crystalline nanotubes makes these structures potentially suitable for spin-electronic devices [19]. Carbon nanotubes may also be used as electromechanical sensors as their electrical characteristics change in response to mechanical deformation of their structure [20]. Conversely, nanotubes can mechanically deﬂect under electric stimulation (e.g., due to charge induced on the nanotubes) making them useful as cantilevers or actuators [21, 22]. Aside from applications which exploit the properties of individual nanotubes, there are a further range of applications which utilise the large surface

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area to volume ratio of carbon nanotubes and nanoﬁbres when manufactured in bulk. One interesting application for these structures is as electrodes in electrochemical supercapacitors [23, 24]. It has been shown that such structures could lead to higher charge storage than conventional capacitors and batteries [21, 25]. The high electrical conductivity and relative inertness of nanotubes also make them potentially useful as electrodes in electrochemical reactions [26, 27]. Nanotubes can support reactant particles in catalytic conversion reactions [28, 29]. It has been proposed that hydrogen could be stored amongst and inside nanotubes/nanoﬁbres for fuel cell applications [29, 30], although results show that the amount of hydrogen stored is not as high as originally anticipated [31]. The use of nanotubes and nanoﬁbres as ﬁlters or membranes for molecular transport has also been proposed [32]. Nanotubes and nanoﬁbres can be added to polymers to improve their strength and stiﬀness, and can also add electrical conductivity to polymerbased composite systems [33, 34], which has proved useful in the automobile industry for the electrostatic painting of components. Carbon nanotubes are ideal reinforcing ﬁbres for composites due to their high aspect ratio and axial strength [35]. Single-wall carbon nanotubes are preferred to multiwall nanotubes because the inner layers of the multiwall nanotubes contribute little under structural loading, and thus would reduce the stiﬀness for a given volume of nanotubes [35, 36].

2 Production of Carbon Nanotubes There are a number of known methods for producing carbon nanotubes. Between them it is possible to produce nanotubes with diﬀering properties and in diﬀerent forms. The most common methods used for the production of nanotubes are arc discharge [37, 38], laser vaporisation [39] and chemical vapour deposition. The ﬁrst nanotubes were produced in an arc discharge arrangement [2]. In a typical arc discharge apparatus, two graphite electrodes are held a short distance apart inside a vacuum chamber. The chamber is held at high vacuum and a ﬂow of helium is supplied. A DC voltage is applied across the two electrodes, and a large arc current ﬂows, removing carbon atoms from the anode in the process. The position of the anode is adjustable so that as the anode is consumed, the gap between the two electrodes can be held constant. A carbon deposit forms on the cathode; this deposit contains nanotubes as well as larger carbon nanoparticles. In a high-quality arc discharge, the deposit can contain 70% nanotubes. These nanotubes typically exhibit a good crystalline structure and are very straight, due to the very high temperatures (3000◦ C) developed during the arc discharge. However, in order to make use of these nanotubes in an electronic device, they must be separated from the cathode, puriﬁed and manipulated onto a substrate.

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Like arc discharge, laser vaporisation is a short-duration, high-temperature technique for nanotube production. A graphite target is heated to around 1200◦C in a horizontal furnace whilst an inert gas ﬂows across it. A high-power laser is then used to vaporise the graphite target. The vaporised material is carried by the gas onto a cooled collector, where it condenses. As with arc discharge, the material contains a mixture of nanotubes and nanoparticles, and once again the material must be separated, puriﬁed and manipulated in order to fabricate devices. Laser vaporisation can produce up to 90% nanotubes, however, unlike arc discharge, its use is limited to small-scale production. In both of these cases, a block of solid graphitic carbon is heated to a very high temperature and carbon atoms are separated from the block, reassembling either on the cathode in the case of arc discharge or on a cooled collector in the case of laser vaporisation. It is during this reassembly that the highly ordered nanotubes are formed. Catalytic chemical vapour deposition is very diﬀerent. Instead of beginning with a block of carbon, the feedstock is a hydrocarbon gas, which dissociates either thermally (thermal CVD) or in the presence of a plasma (plasmaenhanced CVD). Once again, the dissociated carbon atoms self-assemble into highly ordered nanotubes; however, in this case the nanotubes form on a substrate, which may be made of any material which can withstand the deposition temperature (e.g., silicon or glass). The self-assembly is facilitated by catalyst nanoparticles deposited on the substrate surface, which seed the nanotube growth. These catalyst nanoparticles determine both the location and diameter of the nanotubes formed. This ability to deposit nanotubes selectively based upon the location of catalyst particles opens the door to lithography and a range of possibilities for direct deposition of nanotube devices. Thermal CVD requires high temperatures (800–1000◦C) and has two disadvantages. First, the nanotubes produced are not just randomly oriented, but also they are not straight. Second, the high temperature rules out the use of many desirable substrate materials (e.g., glass). Plasma-enhanced CVD (‘PECVD’) is a technique used extensively in the semiconductor industry to allow CVD at lower temperatures. In this case, energy in the plasma replaces some of the heat energy, allowing gas dissociation and nanotube formation to take place at lower temperatures (600–700◦C). PECVD has a further advantage: the electric ﬁeld aligns the nanotubes during growth [40, 41]. There are a number of diﬀerent techniques available for creating the plasma. These include rf-PECVD [42], microwave PECVD [43], inductively coupled PECVD [26] and DC glow discharge PECVD [44]. For an electronic device, it is essential to be able to make good electrical contact to the nanotubes. Silicon is often selected as an appropriate substrate. Also, for an electronic device, it is important that the synthesis of nanotubes is performed without the deposition of amorphous carbon (“a-C”), which

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prevents the formation of nanotubes by poisoning the growth catalyst and can cause short circuits on the substrate surface. One method that has been shown to prevent the deposition of a-C is to combine the carbon source (a hydrocarbon gas) with a hydrogen-rich gas (typically NH3 or H2 ), which produces reactive species in the plasma that remove any excess carbon.

3 Plasma Composition during PECVD We have seen that we can form carbon nanotubes using several diﬀerent techniques. In the case of arc discharge and laser vaporisation, carbon is liberated from a graphite source before reassembling in nanotube form. In the case of CVD, it is not clear if carbon itself is present in the chemical vapour, or if carbon is extracted from hydrocarbon molecules in a reaction at the surface of the metal catalyst. Diﬀerent conditions for nanotube synthesis yield diﬀerent results: Under certain conditions we get well-deﬁned nanotubes; at other conditions we get amorphous carbon. What is the mechanism that determines this? In order to answer these questions, we conducted an analysis of the plasma composition during PECVD of carbon nanotubes [45]. Multiwalled carbon nanotubes were grown using a DC glow discharge PECVD setup with the substrate located on a resistively heated graphite stage. It has been reported that C2 H2 is the most eﬃcient carbon feedstock for the growth of carbon ﬁlaments [46], and we selected C2 H2 to be the carbon feedstock gas for our carbon nanotube growth. NH3 was added to generate reactive species, which have been shown to help prevent formation of a-C. The gases were fed into the chamber through a metal pipe that acted as an anode for the plasma discharge. A DC plasma was generated between this pipe and the tungsten heaters within the graphite stage. The chamber was maintained at vacuum using a rotary pump. Si substrates coated with a thin catalyst ﬁlm were placed on the graphite stage and heated to 520◦ C in NH3 . At this temperature, the thin ﬁlm catalyst agglomerates into particles suitable for seeding nanotube growth. The DC plasma was then initiated and C2 H2 added into the gas ﬂow as the carbon feedstock. The temperature was maintained at 650◦C throughout the deposition, and the chamber pressure was maintained at 5.3 mbar. The plasma DC bias was maintained at 600 V, with current typically around 100 mA. The volume ﬂow-rate proportion of C2 H2 in the NH3 :C2 H2 plasma was varied between 0% and 70% whilst maintaining other parameters at their standard settings. Mass spectrometry was performed on species extracted 15 mm from the graphite stage. Neutral molecules were extracted from the plasma and analysed using residual gas analysis (RGA). Positive ions were extracted and analysed using secondary-ion mass spectrometry. An RGA mass spectrum

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Fig. 6. RGA and positive ion mass spectra (top and bottom, respectively)

for neutral species and a mass spectrum for positive ion species at 23% C2 H2 are shown in Fig. 6. The species in the RGA spectrum are consistent with the cracking patterns of C2 H2 (base peak at amu 26) and NH3 (base peak at 17 amu) and also indicate the presence of H2 , HCN, H2 O, N2 and CO2 [47]. This is consistent with data reported by other authors [48]. The dominant ions detected were + + + + + NH+ 3 and C2 H2 . Other detected species were NH2 , NH4 , HCN and C2 H .

4 Characterisation of the Growth Mechanism The results obtained by growing carbon nanotubes in this particular conﬁguration have previously been reported [49]. It was demonstrated that wellaligned nanotubes were grown for C2 H2 concentrations between 4–20%, that at 29% C2 H2 the nanotubes became more obelisk-like, and that by 38% there are no longer any tubes at all. These results are shown in Fig. 7. It was also reported that the nanotube growth rate peaked at around 20% C2 H2 content. This growth condition gave a clean, a-C-free substrate [50]. We ﬁrst investigated the nature of the carbon precursor for the formation of nanotubes. We were unable to detect C2 , CH4 or other higher carbon species even after acquiring data for a prolonged period, and thus concluded that C2 H2 is the dominant precursor for nanotube formation. This conclusion is supported by other authors [51], who have detected the presence of C2 H2

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Fig. 7. Scanning electron microscope images of carbon nanotubes grown at diﬀerent gas ratios

catalyst particle

C xH y C C C Cx Hy barrier layer

(a) weak interaction

C C

C xH y

catalyst particle

barrier layer (b) strong interaction

Fig. 8. Growth models

in a CH4 /H2 /NH3 plasma yielding nanotubes. For this to be the case, our growth model must include a reaction at the catalyst surface to extract carbon from C2 H2 . The catalyst takes the form of a transition metal (Fe, Ni, Co or Mo), which may be applied chemically from a solution containing the catalyst [52] or directly by using techniques such as thermal evaporation, ion beam sputtering [53] or magnetron sputtering [54]. For our experiment we used magnetron sputtering to give us a well-controlled Ni ﬁlm. When heat is applied to the substrate bearing the ﬁlm, the increased surface mobility of the catalyst atoms causes the ﬁlm to coalesce into nanoclusters [55]. The thickness of the catalyst ﬁlm, temperature and time determine the size of these nanoclusters [49, 56, 57]. There is a further consideration with respect to the catalyst layer. This is the chemical interaction between the catalyst and substrate when heat is applied. If there is a reaction, the catalyst material will dissipate, ending its usefulness for seeding nanotube growth. This is a problem when using Si as a substrate with transition metals, as they would diﬀuse into the substrate

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at the temperatures used. In order to eliminate this problem, a thin diﬀusion barrier of SiO2 was sputtered onto the Si substrate before the metal catalyst layer was deposited. Depending upon the strength of the interaction between the catalyst metal and the barrier layer upon which it is deposited, two diﬀerent growth models have been proposed [58]. These two models are illustrated in Fig. 8. In each case, carbon is extracted from the hydrocarbon feedstock gas and diﬀuses through the catalyst particle before taking its place in the forming nanotube. The growth model when there is weak interaction between the catalyst particle and the barrier layer is known as “tip growth”, as the catalyst particle stays at the tip of the nanotube. The model when there is strong interaction is known as “base growth”, as the catalyst particle remains anchored to the barrier layer at the base of the nanotube. For nickel on SiO2 , interaction is weak, indicating tip growth. Indeed, bright catalyst particles can clearly be seen at the tips of the nanotubes in Fig. 7. These growth models are widely accepted in the nanotube community, but there is a puzzle concerning the diﬀusion of carbon through the catalyst particle. The temperatures achieved during PECVD are well below the melting point of the catalyst metals, yet it is thought that the catalyst particle must be in the liquid phase for this diﬀusion to take place. An explanation for this is that the saturation of the metal with carbon atoms causes a signiﬁcant decrease in the melting point for the catalyst particles, allowing the particle to melt and the diﬀusion to take place [59]. Figure 7 shows that varying the gas ratio produces diﬀerent structures, with carbon nanotubes deposited at low C2 H2 ratios and a-C deposited at high C2 H2 ratios. In order to understand why this is the case, we must examine the role of NH3 in the plasma. The production of a-C-free nanotubes requires a controlled deposition of carbon, which can then self-assemble into an energetically favoured nanotube form. This controlled deposition rate is achieved through the combination of two reactions: the dissociation of a carbon-rich gas (in our case C2 H2 ) and the removal of excess carbon that would otherwise lead to amorphous carbon deposits. It has been widely reported that atomic hydrogen is the active species for the removal of excess carbon. Both H2 and NH3 have been reported to act as sources for atomic hydrogen through electron impact dissociation in plasma [51, 60]. Generation of H from an NH3 :C2 H2 DC plasma has also been shown in simulations [61]. It has further been shown that NH3 is a more eﬀective generator of atomic hydrogen than H2 [51]. NH3 therefore has a key role in removing any excess carbon through the generation of reactive species which combine with and carry away carbon atoms. The eﬃcacy of NH3 in nanotube production has been further attributed to the preferential decomposition of NH3 suppressing the decomposition of C2 H2 . This is because the chemical bonds that hold the NH3 molecule together are weaker than those which hold C2 H2 together. It has also been

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Fig. 9. H2 RGA signal for varying gas ratio

Fig. 10. HCN RGA signal for varying gas ratio

suggested that nitrogen is incorporated into catalyst particles, forming nitrides and changing the composition of the catalyst surface [62]. This may also help to explain the diﬀusion puzzle. We can clearly see the preferential decomposition of NH3 in our RGA data. A graph of the RGA signal for H2 for varying gas ratio is shown in Fig. 9. H2 is generated by the decomposition of both NH3 and C2 H2 . To the left of the ﬁgure, where the plasma is predominantly NH3 , the amount of H2 increases as NH3 increases. In this region, the H2 is derived from decomposition of NH3 . To the right of the ﬁgure, where the plasma is predominantly

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C2 H2 , the amount of H2 increases as C2 H2 increases. In this region, the H2 is derived from the decomposition of C2 H2 . At high NH3 ratios, NH3 decomposes preferentially over C2 H2 . This causes the C2 H2 to decompose slowly, generating the small amounts of carbon necessary for nanotubes to self-assemble. At high C2 H2 ratios, there is insuﬃcient NH3 to eﬀectively suppress C2 H2 decomposition, resulting in high levels of carbon generation and deposition of excess carbon as a-C. NH3 therefore has two key roles in the formation of carbon nanotubes: not only does it generate atomic hydrogen species to remove any excess carbon, but it also suppresses the decomposition of C2 H2 , limiting the amount of carbon generated in the ﬁrst place. Our observed minimum in H2 is close to our previously reported peak in clean nanotube growth rate at around 20% C2 H2 . At this ratio, carbonremoving species are at a minimum and C2 H2 decomposition is low, giving rise to controlled deposition of clean nanotubes. Interestingly, ion intensities peak at around 40% C2 H2 , where a-C is deposited. The optimum condition for nanotube growth is therefore not the condition of maximum ion intensity. This contrasts with most thin ﬁlm growth, where the condition with maximum ionisation is preferred. Further work [63] has shown that the plasma during the nanotube deposition is suﬃciently energetic for endothermic ion-molecule reactions to take place. In many applications, these reactions can and have been ignored as they require signiﬁcant pressures and ion energies. However, in this case the high pressure and DC bias present the perfect condition for these reactions. The process for the removal of excess carbon by atomic hydrogen species should give rise to products including both carbon and hydrogen. The principal reaction product we detected in our RGA data was HCN. A graph of the RGA signal for HCN with varying gas ratio is shown in Fig. 10. This shows that HCN is generated where both C2 H2 and NH3 are in abundance. The Figure also shows that a purely NH3 plasma does not generate significant HCN. This conﬁrms that the reactions that remove excess carbon are predominantly taking place in the gas phase. If there was a strong surface reaction, we would see HCN arising from reactions between the active species and the graphite stage, even in the absence of C2 H2 .

5 Conclusion We have shown that carbon nanotubes have many exciting features and potential applications. Nanotubes can be made using several diﬀerent techniques, and PECVD is particularly suitable for the fabrication of electronic devices. During PECVD, carbon is extracted from C2 H2 in a gas-phase reaction at the catalyst surface, where it self-assembles into nanotube form. We have

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explained why varying the gas ratio during deposition yields diﬀerent structures and shown that there is an optimum ratio for clean nanotube growth. This enables the fabrication of a-C-free devices for electronics applications, which we believe opens up an enormous range of potential applications. A vast amount of research eﬀort has been conducted into carbon nanotubes, and we have an increasingly clear understanding of their properties and how these can be manipulated to give desirable devices. Whilst nanotubes have made only limited forays into commercial products to date, we believe that over the next decade the remarkable promise they have shown in the research arena will be realised in the wider world.

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Index a-C, 83 arc discharge, 82 buckminsterfullerene, 78, 79

C60 , 78, 79 C70 , 79 catalytic chemical vapour deposition (CVD), 83

Growth Mechanism During PECVD of Multiwalled Carbon Nanotubes chemical vapour deposition (CVD), 83 chiral vector, 79 glow discharge, 84 graphene, 78–80 laser vaporisation, 82 mass spectrometry, 84, 85 nanoﬁbres, 80, 82 herringbone nanoﬁbres, 81 stacked nanoﬁbres, 81 nanotubes, 77–85, 87–89 armchair nanotubes, 79, 80 chiral nanotubes, 79

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chiral vector, 79 growth mechanism, 85 multiwalled nanotubes (MWNTs), 77, 79, 82, 84 single-walled nanotubes (SWNTs), 79, 81, 82 zig-zag nanotubes, 79, 80 plasma, 83 plasma-enhanced chemical vapour deposition (PECVD), 77, 83, 84, 87, 89 residual gas analysis (RGA), 84, 85, 88, 89

Correlation Between Local Structure and Film Properties in Amorphous Carbon Materials Giovanni Fanchini1,2 and Alberto Tagliaferro2 1

2

Present address: Ceramics and Material Engineering Dept., Rutgers University, 607 Taylor Road, Piscataway, NJ-08854, USA Dipartimento di Fisica and LAQ Intese, Politecnico di Torino, Via Duca degli Abruzzi 24, I-10129 Torino, Italy [email protected]

Abstract. A discussion of the various amorphous carbon and amorphous hydrogenated carbon ﬁlms is presented. A link between sp2 , sp3 and H contents and the mechanical and optoelectronic properties is established using some characteristic lengths of the structure deﬁned in a previous paper. These lengths describe the average size of the sp2 agglomerates, the distance between such agglomerates, the decay length of π states and the accommodation length of sp2 clusters in the sp3 network.

1 Introduction Several of the Group IV elements have a crucial role in our life. If silicon and its semiconductor relatives are at the basis of the modern life, carbon is the basis of life itself. Moreover, carbon in its various forms and alloys has a relevant role in the various aspects of modern life, too. Diamond is coveted because of its appealing appearance and emotional value. Graphite is used in mechanical applications. Carbon-based fuels are still running the world, and plastics and polymers are everywhere around us. Even the more “humble” amorphous forms of carbon have crucial importance in modern life. For instance, amorphous carbon is a protective layer in the majority of computer hard disks. Amorphous carbon can be grown at room temperatures in thin ﬁlm form, even on curved layers. It can be alloyed with other elements (H, N, Si) to obtain materials having diﬀerent properties. The present work aims at providing a better understanding of the role and perspectives of the various types of amorphous carbon and hydrogenated amorphous carbon ﬁlms. This work is based on the correlation between local structure and ﬁlm properties.

2 Electronic States in Carbon The peculiarity of the carbon atom that determines its multiform impact on reality is its ability to form either σ- or π-bonds. It is customary to describe G. Messina, S. Santangelo (Eds.): Carbon, The Future Material for Advanced Technology Applications, Topics Appl. Phys. 100, 95–105 (2006) © Springer-Verlag Berlin Heidelberg 2006

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molecular orbitals as a superposition of atomic orbitals pertaining to neighbouring ions [1]. In this light, σ orbitals arise from the hybridisation of 2s and 2p carbon atomic orbitals. If the p states (px , py , pz ) of the neighbouring ions mix with their s states, we have four bonding and four antibonding σ orbitals and the so-called sp3 hybridisation. This type of hybridisation can be found, for instance, in diamond crystals. If the s states mixes with two corresponding p states for each atom we have three bonding and three antibonding σ orbitals. The remaining p states hybridise to form a π state. This is the sp2 hybridisation, of which graphite is a typical example. Finally, if the s states mix with one p state for each neighbouring atom, we have two bonding and two antibonding σ orbitals and two additional π states. This is the sp1 hybridisation and is found, for instance, in acetylene. The σ and π orbitals have very diﬀerently shaped electron clouds. σ orbitals have the highest density of the electron cloud along the axis connecting the two neighbouring nuclei and form a strong, almost always covalent, bond between the ions. Each π orbital has its electron cloud formed by two lobes symmetric with respect to a plane containing the axis connecting the two nuclei and absent on such plane. The π-bonds formed between two nuclei are generally quite weak. Hence the energy spacing between π-bonding and antibonding states is much lower than that between σ-bonding and antibonding states. Although this is the situation for a pair of carbon ions, things can be quite heavily modiﬁed if the collection of ions is enlarged. In such a case, several additional eﬀects come into play due to the delocalisation of π orbitals. For instance, if we analyse a benzene ring, we found that all π orbitals arising form the six carbon ions have merged to form a delocalised orbital containing all π electrons. This orbital now forms a strong additional bond between all atoms of the ring. It becomes very costly in term of energy to break a single π-bond, as it is fused with the others so that the structure is overall much more stable. π orbitals have other peculiar properties that are of relevance in organic chemistry and in life itself. For instance, the resonance plays a relevant role in determining the properties of aromatic and aliphatic structures. However, we will focus on this and other peculiarities only if they will become relevant to our discussion.

3 Hybridisation and Local Structure In the previous paragraph we reviewed the various type of hybridisations. Here we analyse how the hybridisation aﬀects the local and the overall structures of carbon materials. We will start our discussion from the viewpoint local structure, i.e., of the distribution of neighbouring carbon ions. Obviously, the spatial orientation of the various bonds is determined by the minimisation of the free energy of the system. Hence, diﬀerent medium- and long-range structures can be found, even if the local structure remains almost the same.

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sp3 hybridisation leads to a tetrahedral local structure, in which the reference carbon ion is placed in the centre of the tetrahedron and the four bonds connect it with the vertexes of the tetrahedron where the neighbouring ions sit. The resulting structure is tridimensional, and by the repetition of this block the diamond structure is built. The distance between neighbouring atoms in diamond is 0.154 nm. sp2 hybridisation leads to three σ-bonds lying in the same plane and forming 120◦ angles between any two of them. The repetition of this block leads to a bidimensional planar structure based on hexagonal blocks: the graphene sheet. The distance between neighbouring atoms is 0.142 nm, shorter than in diamond. This is due to the presence of π orbitals that strengthen the bond between neighbouring ions. In-plane bonding is hence determined by a concurrence of σ and π orbitals. We would like to focus on the point that undistorted sp2 hybridised structures tend to be bidimensional. The out-ofplane bonding between graphene sheets in graphite is due to weak Van der Waals forces, and this justiﬁes the prompt delamination of graphite. sp1 hybridisation leads to two σ bonds lying on a line, which can be straight or kinked depending on the case [1]. The presence of foreign atoms can modify this picture. For instance, monovalent H or F become bond terminators and can lead to linear structures (such as polymeric chains), even for sp2 hybridised ions.

4 The Various Forms of Amorphous Carbon In the previous paragraphs we have very brieﬂy discussed crystalline structures and polymers. Now we move on to the ﬁeld of our interest, i.e., amorphous structures, in the attempt to clarify a few items. The misuse of the term diamond-like carbon is quite common in literature. So we will spend a few lines to detail and justify the categorisation we make use of. As it is customary to enlarge the phrase amorphous carbon to encompass hydrogenated ﬁlms too, we will extend our classiﬁcation to such ﬁlms. In amorphous carbons the various hybridisations (sp3 , sp2 , sp1 ) are present in diﬀerent amounts and in diﬀerent spatial arrangements. It is customary [2] to disregard the role of sp1 states. In this general discussion we will stick to this point of view, but it should be remembered that each sp1 hybridised carbon ion provides the same amount of π and σ states and hence even limited quantities of sp1 hybridised atoms might have an impact on the properties. An interesting point on which we will elaborate later is that at a given sp3 /sp2 ratio (i.e., a given percentage of sp3 hybridised atoms) we can obtain ﬁlms having different properties since the spatial arrangement of the sp2 and sp3 hybridised ions can be diﬀerent. Although one may naively think that a statistical distribution in space of hybridisations is possible among the various atoms of a structure, it is by far not energetically favourable [3]. It was shown quite a while ago that the system is stabilised if sp2 hybridised ions are clustered [3].

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The form of these clusters can be diﬀerent depending upon the case, ranging from conglomerates of benzene-like rings to linear chains [2]. Most of the amorphous carbon materials that we will discuss below can be considered as multiphase systems, in which sp3 - and sp2 -coordinated regions coexist. The fact that sp2 regions are basically bidimensional while sp3 ones are tridimensional has interesting consequences on the structure of amorphous carbons. In fact, the sp3 fraction needed to reach percolation threshold in the sp3 phase (∼ 0.3) is much lower than that needed for percolation of the sp2 phase (∼ 0.8 [4]). Hence, in most cases, the sp3 regions are interconnected in an overconstrained network that hosts sp2 coordinated clusters. The sp3 network will constitute the (more or less rigid, following H incorporation in it) backbone of the material, strongly aﬀecting its mechanical properties. Only in very special cases (glassy carbon) the material backbone is made by sp2 network in which sp3 regions are dispersed. Nonhydrogenated ﬁlms can be labelled as follows [5]: – Glassy carbon (GC). They have such a high sp2 content that the various sp2 regions are made of entangled and interconnected benzene-like rings. The spare sp3 regions are diluted in the network and have a negligible eﬀect on the material properties. The fact that sp2 regions are entangled leads to mechanical properties (hardness, . . . ) diﬀerent from those of graphite [2]. – Tetrahedral amorphous carbon (ta-C). ta-C ﬁlms are highly constrained sp3 -rich ﬁlms having mechanical properties close to those of diamond. sp2 regions are mainly formed by sp2 paired up or diluted in the sp3 matrix. – Amorphous carbon (a-C). This broad class contains all ﬁlms that have properties and characteristics intermediate between the previous ones. The inclusion of hydrogen aﬀects the structure and the properties of the ﬁlms in many ways. Generally speaking, it decreases the local coordination number [6] and hence makes the structure more “ﬂoppy”. The ﬂoppiness or rigidity of the material obviously correlates with the amount of hydrogen and its spatial distribution. As an sp3 -coordinated region has a higher average coordination number than an sp2 -coordinated one, a higher hydrogen content is needed to bring it to ﬂoppiness. A role is played by the number and spatial distribution of the sp2 sites. Benzene-like rings are rigid and can be distorted to a high cost in energy as a collection of bonds has to be distorted [7]. Basically, all hydrogenated amorphous carbon ﬁlms can be assigned to one of the following categories: – Tetrahedral hydrogenated amorphous carbon (ta-C:H). ta-C:H have a limited hydrogen (20–25 at %) and high (> 2) sp3 /sp2 ratio coupled with a small amount of sp2 inclusions [2], which are probably organised more in chains than in rings. This structure leads to mechan-

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ical properties closer to those of diamond than for all other types of hydrogenated amorphous carbon. – Diamond-like hydrogenated amorphous carbon (DLHC). DLHC originally bore the name of diamond-like carbon (DLC), although some authors still apply this term to all type of amorphous hydrogenated carbon, generating quite a deal of confusion in the reader. Compared to ta-C:H ﬁlms, these have lower sp3 /sp2 ratios (∼ 1) and similar hydrogen contents. The larger sp2 content is organised in larger clusters, which require larger distortions of the sp3 network to be accommodated. – Graphite-like hydrogenated amorphous carbon (GLHC). Although the hydrogen content is similar to that of the previous two categories, the sp3 /sp2 ratio is much lower (< 0.5). The average coordination number is reduced close to the ﬂoppiness limit [5]. – Polymer-like hydrogenated amorphous carbon (PLHC). These ﬁlms are hydrogen rich (> 40 at %), and their sp2 phase is mainly organised in chains. These features lead to a ﬂoppy system. The careful reader has surely noticed that some combination of H, sp3 , sp values are intermediate between the various classes. Our categorisation is aimed at usefulness and to have a limited number of classes. Hence it cannot be exhaustive and does actually leave some shadowed regions. Materials belonging to those regions have properties and characteristics bridging those of neighbouring classes. 2

5 Phase Matching and Its Eﬀects on Materials If we attempted to compare the medium- and long-range structures of the amorphous carbon ﬁlms grown around the world, we would probably ﬁnd that all of them are more or less diﬀerent. This might suggest that the quest for general rules to help in understanding and maybe predicting ﬁlm properties might be without hope. Nevertheless, it has been shown that by developing a few simple concepts [5] a reasonable understanding of ﬁlm properties can be achieved. Let us review the basics of that model and later expand its consequences to encompass mechanical properties too. As most of the optoelectronic properties of amorphous carbon ﬁlms are determined by π states [2], it is crucial to focus on those aspects of the structure that aﬀect the spatial and energy distribution of these states. In particular, it is crucial to analyse the role of “phase matching”, i.e., the distortions induced in the local bonding at the boundaries between sp3 and sp2 regions. In order to describe these eﬀects the following parameters were deﬁned (see Fig. 1) [5]: Lc

is the diameter of a given sp2 cluster, assumed for sake of simplicity to be planar and circular in shape. However, the general features of the discussion will hold for chain-like clusters too.

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Fig. 1. Characteristic lengths in amorphous carbon ﬁlms [5]

Lc−c is the distance between the borders of two neighbouring clusters. Lπ is the distance from the cluster border at which the π wavefunction becomes negligible. We can roughly estimate this parameter to be of the order of a few tenths of nanometres [2]. Before the deﬁnition of the last parameter, let us hypothesise that we insert an sp2 cluster in a fully sp3 -coordinated network. The structure of the sp3 region near the inclusion needs to be modiﬁed in order to accommodate the cluster. If we go far enough, however, no eﬀect of the inclusion on the sp3 structure will be detected: Lac is the “accommodation length”, i.e., the maximum distance from the cluster at which the modiﬁcation induced in the sp3 network is present. In most cases these modiﬁcations consist in distortions of the bonds, which can be labelled as structural disorder [2]. For a given cluster size the actual value of Lac depends on the rigidity of the sp3 network, which is correlated to the local coordination number [1]. The detailed discussion of the cases that can arise by varying the relative values of the various lengths is reported in [5]. Here we will brieﬂy discuss the various form of amorphous carbon in the light of these parameters. As said in the previous paragraphs, in most cases the backbone of the material is constituted by the (more or less hydrogenated) interconnected sp3 phase. The various possibilities are described in Fig. 2: 1. Noninteracting clusters (Fig. 2a). When the sum 2Lac of the accommodation distances of two neighbouring clusters is lower than their distances Lc−c, the two clusters have neither direct nor indirect interaction. The sp2 clusters behave almost like an ensemble of independent molecules embedded in a medium instead of dispersed in vacuum. π states are localised in the clusters, and π and π ∗ bands are made of localised states [5]. 2. Overlapping accommodation regions (Fig. 2b). The interaction between clusters is indirect since the distortions due to phase matching aﬀect the energetic distribution of π states [8]. π and π ∗ bands are still made of localised states, but their shape is distorted [5].

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Fig. 2. The various local structures (see text) [5]

3. Overlapping π states (Fig. 2d). When the sp2 content approaches the value for sp2 phase percolation, we reach a condition in which the π states, whose wavefunction decays outside the clusters, overlap. Part of the π and π ∗ bands is made of localised states, and part is made of extended (better: overlapping) ones [5]. 4. Percolating sp2 phase (Fig. 2c). When the sp2 regions percolate they become the interconnected backbone of the material. The sp3 inclusions will not even aﬀect the mechanical properties. π and π ∗ bands are made of extended states, and their diﬀerences from graphite ones are mainly due to disorder [5]. In order to better understand the implication of what we have just discussed, we note that the presence of hydrogen in the sp3 network reduces its local average coordination number and the backbone rigidity [9]. This should help in understanding why we attribute PLHC to case 1 above. The high hydrogen content of the sp3 phase strongly reduces Lac and the distortions related to phase matching at the boundaries between sp2 clusters and hydrogenated sp3 backbone. For GLHC a similar discussion can be made, although the decrease in the average coordination number has to be attributed more to the high sp2 amount [10] than to the relatively low H content. However, the higher sp2 content leads to larger cluster sizes and this aﬀects the optoelectronic properties (see below). In DLHC ﬁlms, because of the low hydrogen content and the relatively high sp3 content, the accommodation regions highly overlap (case 2). The low sp2 content prevents case 3 from occurring. In ta-C:H we have a similar situation, although sp2 clusters have a more likely aliphatic rather than aromatic character [2]. In nonhydrogenated ﬁlms, the absence of hydrogen increases, at a given sp3 /sp2 ratio, the local coordination number and Lac with respect to hydrogenated ﬁlms. Both ta-C and a-C can then be ﬁtted in case 3. However, the large diﬀerence in the sp3 content leads to a large diﬀerence in the

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2Lac /Lc−c ratio and the local coordination number. As a consequence, the sp3 phase of ta-C is much more distorted. Finally, GC can be attributed to case 4 because of its very high sp2 content, which leads to sp2 phase percolation.

6 Optoelectronic and Mechanical Properties We have already noticed that in amorphous carbon ﬁlms the optoelectronic properties are mainly determined by the π states and the mechanical ones by the backbone (usually the sp3 phase). We will now analyse more in detail how the peculiarities of the structure of each type of ﬁlm will reﬂect on its properties. GC. The percolation of the sp2 phase would suggest that the mechanical properties will be close to that of graphite. The fact that the graphene strips [11] are entangled prevents delamination and gives a certain, although limited, hardness [2] to the material. The optoelectronic properties diﬀer from those of graphite because the long-range order of graphene sheets and the consequent semimetallic behaviour are absent. Nevertheless, the graphene strips have macroscopic size so that their optical gap is in the far infrared, making the material optically black. Because of the presence of π and π ∗ extended states close in energy [5], the electrical conductivity is high and is weakly dependent on temperature. ta-C. The high sp3 content and the absence of hydrogen give rise to a rigid backbone so that the mechanical properties of this material are close to those of diamond [12, 13]. Still the optical properties in the visible range are determined by the highly distorted sp2 inclusions, and the absorption coeﬃcient has a rather slow increasing trend as photon energy is increased [14]. The high level of distortions also leads to a high spin density [14]. Although the optical gap can reach high values because of the spread of energy levels of sp2 inclusions due to distortions, the electrical conductivity is much higher than in other materials having similar gaps and no π states. a-C. The presence of a rich sp2 phase with medium-sized (up to a few nanometres) sp2 inclusions reduces the distortions of the previous cases and leads to intermediate properties. The fact that sp2 clusters are smaller than in GC opens the optical gap [2] and makes electronic conductivity lower and with a higher activation energy [15]. The lack of long-range entanglement makes the material softer with mechanical properties of no relevance [11, 12]. The high cluster density leads to a high ESR signal, even in absence of relevant distortions.

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ta-C:H. The presence of H makes the sp3 backbone less overconstrained (i.e., rigid) than in ta-C. This decreases distortions and degrades the mechanical properties with respect to ta-C, although they remain the highest in the a-C:H class [13, 16]. Less distortions in the sp2 clusters lead to steeper absorption coeﬃcient trends in the visible region, even if a higher sp2 content is present [17]. Electronic properties are improved, and in some cases photoconductivity is detected [18]. The ESR signal is reduced with respect to ta-C and DLHC as a consequence of the less distorted sp2 clusters [5]. DLHC. Despite the presence of hydrogen these materials are highly distorted because of the size of the clusters and rigidity of the sp3 backbone. This leads to the better mechanical properties among “non-ta-C:H” hydrogenated amorphous carbon ﬁlms [15]. Distortions also have a crucial impact on optical properties, reducing the optical gap, and ESR signal, giving rise to a very large spin density [5]. Electrical conductivity is higher than in ta-C:H [15, 18] because of the higher sp2 content, which leads to a reduced distance between sp2 regions, and the greater size and higher distortions of the sp2 phase that reduce the gap [5, 19]. GLHC. The larger amount of sp2 content compared to the previous case deteriorates mechanical properties [15]. Despite such sp2 increases, the optical gap increases because distortions are reduced [2]. The reduction in distortions greatly reduces the spin density too [5, 20]. PLHC. The relevant hydrogen content leads to ﬂoppy materials with mechanical properties of no interest [15]. The transparency of the hydrogenated sp3 phase and the limited size of sp2 inclusions, mainly arranged in chains, highly increases the optical gap [2]. These materials become almost insulating [2, 19] but highly photoluminescent [2] because the absence of distortions prevents nonradiative recombination paths to proliferate [2]. The spin density is orders of magnitude lower than in the other cases [5].

7 Conclusion We have discussed the various types of amorphous carbon and the role of the main structural parameters in determining their properties. The overall picture was obtained by using a few simple parameters (cluster size, distance between neighbouring clusters, decay length of π states, accommodation length of sp2 clusters) previously introduced in [5]. We have established a qualitative link between structure and mechanical and optoelectronic properties. The present paper will, of course, be more useful if a link between deposition methods and parameters and local structure could be established. However, as such link is thoroughly discussed in [2], we address the reader to that paper to ﬁnd information on this aspect.

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References [1] R. McWeeny: Coulson’s Valence (Oxford University Press, Oxford, UK 1979) 96, 97, 100 [2] J. Robertson: Mater. Sci. Eng. R 37, 129 (2002) 97, 98, 99, 100, 101, 102, 103 [3] J. Robertson, E. P. O’Reilly: Phys. Rev. B 35, 2946 (1987) 97 [4] J. Robertson: Phil. Mag. B 76, 335 (1997) 98 [5] G. Fanchini, S. C. Ray, A. Tagliaferro: Diam. Rel. Mat. 12, 891 (2003) 98, 99, 100, 101, 102, 103 [6] J. C. Philips: J. Non-Cryst. Solids 34, 153 (1979) 98 [7] J. Robertson: Diam. Rel. Mat. 4, 298 (1995) 98 [8] G. Fanchini, A. Tagliaferro: Appl. Phys. Lett. 85, 730 (2004) 100 [9] F. Jansen, J. C. Angus: J. Vac. Sci. Technol. A 6, 1778 (1988) 101 [10] J. Robertson: Phys. Rev. Lett. 68, 220 (1992) 101 [11] J. Robertson: Adv. Phys. 35, 17 (1986) 102 [12] G. M. Pharr, D. L. Callahan, S. D. McAdams, et al.: Appl. Phys. Lett. 68, 779 (1996) 102 [13] A. C. Ferrari, J. Robertson, M. G. Beghi, C. E. Bottani, et al.: Appl. Phys. Lett. 75, 1893 (1999) 102, 103 [14] K. B. K. Teo, A. C. Ferrari, G. Fanchini, S. E. Rodil, et al.: Diam. Rel. Mat. 11, 1086 (2002) 102 [15] P. Koidl, C. Wagner, B. Dischler, J. Wagner, et al.: Mat. Sci. Forum 52, 41 (1990) 102, 103 [16] M. Weiler, S. Sattel, K. Jung, H. Ehrhardt, et al.: Appl. Phys. Lett. 64, 2797 (1994) 103 [17] S. Sattel, J. Robertson, H. Ehrhardt: J. Appl. Phys. 82, 4566 (1997) 103 [18] A. Ilie: Diam. Rel. Mat. 10, 208 (2001) 103 [19] D. Dasgupta, F. Demichelis, A. Tagliaferro: Phil. Mag. B 63, 1255 (1991) 103 [20] F. Giorgis, A. Tagliaferro, M. Fanciulli: Amorphous Carbon: State of the Art (World Scientiﬁc, Singapore 1998) p. 143 ﬀ 103

Index π states, 95–97, 99, 100, 102, 103 σ states, 95–97 a-C, 98 sp2 -bonded clusters, 95, 98–103 cluster size, 103 distorted clusters, 102, 103 undistorted clusters, 97 sp1 hybridisation, 96, 97 sp2 hybridisation, 96, 97 sp3 backbone, 98–103 sp3 hybridisation, 96, 97 sp3 /sp2 bonding ratio, 97–99, 101 ta-C, 98

ta-C:H, 98 accommodation length, 100, 101, 103 amorphous carbon, 95, 98 characteristic lengths, 99, 100 carbon coordination, 98–101 cluster–cluster interaction, 100 clustering, 97 diamond, 96, 97 diamond-like carbon (DLC), 97, 99 disorder, 100, 101 distortions, 98–103

Correlation Between Local Structure and Film Properties electrical conductivity, 102, 103 electron spin resonance (ESR) ESR signal, 102, 103 electronic properties, 95

105

mechanical properties, 98, 99, 101–103 optical gap, 102, 103 optical properties, 102 optoelectronic properties, 99, 101–103

ﬂoppiness, 98 glassy carbon, 98 graphene, 97, 102 graphite, 96, 97

percolation, 98, 101, 102 percolation threshold, 98 photoconductivity, 103 rigidity, 98, 100

hydrogenated diamond-like carbon (DLC:H), 99 hydrogenated graphite-like carbon (GLC:H), 99 hydrogenated polymer-like carbon (PLC:H), 99

spin density, 102, 103 tetrahedral amorphous carbon, 98 tetrahedral hydrogenated amorphous carbon, 98

Defects in CVD Diamond Films from Their Response as Nuclear Detectors Marco Marinelli, Enrico Milani, Aldo Tucciarone, and Gianluca Verona Rinati Dipartimento di Ingegneria Meccanica, Universit` a di Roma “Tor Vergata”, Via del Politecnico 1, I-00133 Roma, Italy [email protected] Abstract. CVD diamond ﬁlms can be used to realize nuclear detectors with outstanding working capability in harsh environments. Since eﬃcient particle detection requires high drift lengths of the carriers produced by the ionizing particle, the presence of defects severely limits the performance of these detectors. This is a major issue because the fabrication technology of CVD diamond is much less advanced than that of more conventional materials like silicon. The diﬀerent kinds of defects in CVD diamond and their inﬂuence on the detector response are discussed. The connections between the microscopic structure of CVD diamond and the priming (or pumping) eﬀect, which is widely used to increase CVD diamond detector performance, are elucidated. The analysis of the response of CVD diamond-based detectors is used to extract qualitative and quantitative information on the properties of defects limiting the free movement of charge carriers in the detector (e.g., carrier type for which the traps are active, activation energies, geometrical distribution in the ﬁlm, etc.).

1 Introduction Diamond’s extreme properties [1] extend over diﬀerent areas (electrical, mechanical, thermal, etc.). As a consequence, applications in many ﬁelds could in principle beneﬁt from the utilization of diamond as the primary material for device realization. The use of natural samples is almost always not feasible, because of their cost and lack of standard properties. Diamond crystals grown by high-pressure, high-temperature methods (HPHT), on the other hand, generally have small dimensions and contain signiﬁcant amounts of impurities. For this reason, the demonstration in 1986 of the possibility to grow diamond ﬁlms by chemical vapor deposition (CVD) by exciting a plasma in a hydrogen/hydrocarbon gas mixture at low pressure (about 100 mbar) and relatively low temperatures (about 750◦ C) using silicon wafers as the growth substrate created very high expectations. As is often the case, the initial enthusiasm cooled down when it was realized that the new technique had some limitations, especially in terms of reproducibility and quality. Therefore, while in some areas CVD diamond devices are now commercially available, for many applications the growth technique is still not adequate. In particular, electronic applications of CVD diamond are severely limited by the polycrysG. Messina, S. Santangelo (Eds.): Carbon, The Future Material for Advanced Technology Applications, Topics Appl. Phys. 100, 107–135 (2006) © Springer-Verlag Berlin Heidelberg 2006

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tallinity of the grown ﬁlms and by their impurity content, so that they are particularly demanding in terms of sample quality (the so-called electronic grade diamond). The presence of grain boundaries and of traps limits the mean free path of charge carriers, thus strongly aﬀecting the amplitude and the homogeneity of the response of CVD diamond-based electronic devices. We will review here some experimental techniques that can be used to investigate the type and distribution of electrically active defects in CVD diamond ﬁlms, using the response of nuclear particle detectors built using these ﬁlms. The information provided by these techniques is reported for high-quality polycrystalline CVD diamond ﬁlms grown in our laboratories. Clearly, other samples will give diﬀerent results, but the approach that we present here can be used on any sample. Special attention will be devoted to the so-called pumping or priming eﬀect, i.e., the increase in the detector response after preirradiation with ionizing radiation, a phenomenon which is characteristic of diamond detectors. Although the pumping process is reversibile (by annealing or by exposure to strong visible light sources), the pumped state remains stable over at least several weeks at room temperature, provided that the sample is not exposed to strong light sources. Exposure to normal ambient light results in no measurable depumping on this time scale. The proposed experiments will disclose the physical grounds of the pumping process and discriminate its eﬀect on electron and hole motion in the detection process. Besides their scientiﬁc interest, these techniques could be of practical interest since the knowledge of defect properties and of the defect distribution could be very useful in understanding how changes in the growth parameters (gas composition, substrate temperature, pregrowth nucleation process, etc.) aﬀect the structure of the ﬁlms, thus in principle allowing researchers to obtain more eﬃcient devices.

2 CVD Diamond Nuclear Detectors: Realization and Physics A detailed description of the various techniques to grow CVD diamond ﬁlms is beyond the scope of this contribution. For short reviews the reader may refer to refs. [2, 3, 4, 5]. In the following we will give only the basic information necessary to understand the content of the rest of the article. In low-temperature CVD growth, carbon is fed in the growth reactor, generally in the form of hydrocarbons (e.g., CH4 ) strongly diluted in H2 atmosphere. Some sort of energy is then transmitted to the gas mixture to create a plasma. Under appropriate conditions (gas composition, plasma temperature and pressure) if a substrate (e.g., a silicon or molybdenum slab) is exposed to the plasma, a thin ﬁlm of diamond is obtained. A pretreatment (such as scratching) of the substrate surface is required to promote diamond nucleation.

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Fig. 1. SEM image of a cross section of a CVD diamond ﬁlm showing the columnar nature of the growth

The standard deposition conditions used for the ﬁlms grown in the Roma Tor Vergata University laboratories (to which we will often refer in the following) are as follows. The reactor is a NIRIM-type microwave tubular reactor, suitably modiﬁed to increase ﬁlm quality [6]. The gas mixture is 1% CH4 in H2 at a pressure of about 130 mbar, with a substrate temperature of about 700–750◦C. The substrates are 0.5 mm thick silicon slabs, pretreated by scratching. The growth rate is about 0.7 µm/h. The high crystalline quality of these ﬁlms is demonstrated by their excellent Raman spectra and very low luminescence background [7]. The heteroepitaxial nature of CVD diamond growth on silicon substrates, and the fact that nucleation takes places in the form of randomly oriented seeds, leads to the growth of polycrystalline ﬁlms. A peculiar characteristic of these ﬁlms is their so-called columnar growth, well-evidenced visually in Fig. 1, which shows a scanning electron microscope view of a cross section of a CVD diamond ﬁlm. As the thickness increases during the growth, some of the grains stop growing, while others become bigger and bigger, so that grain size increase from the diamond–substrate interface to the growth surface. On the growth surface of a CVD diamond ﬁlm therefore, the grain dimension is roughly proportional to the ﬁlm thickness. For ﬁlms in the 10–200 mm thickness range surface grain size is typically about 1/4 to 1/3 of ﬁlm thickness. Obviously all ﬁlm properties which depend on the presence of grain boundaries are not uniform along the ﬁlm cross section.

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The realization of a nuclear particle detector from a CVD diamond ﬁlm is very simple: it is suﬃcient to deposit on both sides of the ﬁlm a metal contact [8] and apply to these contacts an appropriate voltage so as to create an electric ﬁeld inside the ﬁlm perpendicular to the ﬁlm surface. Since the detector has the geometry of a thin slab, a so-called parallel plate detector is obtained. In the following, “positive” bias (or polarity) will refer to the case of the contact on the ﬁlm growth surface being at a higher voltage than the contact on the Si substrate, the opposite being referred to as “negative” bias. Typically, a 1 V/µm electric ﬁeld is applied. The working principle of the device is as follows. The nuclear particle creates in the detector a (generally) great number of electron–hole pairs, and the electric ﬁeld drives the generated carriers towards the two electrodes, according to charge sign. In the presence of trapping centers, the electron and hole will not necessarily reach the electrodes, and we will call lc the total distance that the electron and hole move apart (clearly, lc ≤ D, D being the detector thickness). Using Ramo’s theorem [9, 10], each electron–hole pair created by an ionizing particle induces in the measuring circuit a charge qc = elc /D, e being the electronic charge. The amplitude of the voltage pulse measured by the external circuit is proportional to the total collected charge Qc (i.e., the sum of qc over all electron–hole pairs produced by the ionizing particle). The ratio η = Qc /Q0 between Qc and the total charge Q0 generated by the ionizing particle in the detector is the detector’s eﬃciency, one of the most widely used parameters to identify the detector performance. Introducing Le and Lh as the average of the distances le and lh (with le + lh = lc ) that charge carriers move apart from the generation point, we obtain: Le + Lh . (1) η= D The experimentally accessible information is η, since the detector output is proportional to Qc , but like Le and Lh it depends on the system geometry through the sample thickness (i.e., interelectrode spacing) and the penetration depth of the ionizing particles. The physically relevant parameters, related to the defect distribution, are the mean free distances λe = µe τe E and λh = µh τh E, where µ is the carrier mobility, τ is the time before the carriers being trapped and E is the applied electric ﬁeld. The charge collection distance (CCD) is deﬁned as the sum of the mean free distance of charge carriers within the material: δ = λe + λh .

(2)

A direct relationship between the experimentally accessible information (η) and the intrinsic material properties (λe and λh ) can be obtained through the Hecht theory [11]: η=

[λ2 e−D/λh (eG/λh − 1) + λ2e e−D/λe (eG/λe − 1)] Le + Lh − h , D DG

(3)

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where G is the penetration depth of the particles to be detected. Assuming λe = λh = δ/2, (3) becomes η=

δ 2 (1 − e−2G/δ )(1 − e2(G−D)/δ ) δ − . D 4DG

(4)

Equations (3) and (4) or their approximate (for λe , λh D) counterpart η δ/D are often used to get an estimate of δ from eﬃciency measurement. However, they are valid only in the case of uniform distribution of the charge created by the ionizing particle along the penetration path, and homogeneous trap distribution, which is not the case of polycrystalline CVD diamond. We will see in a later section how to extend this formula to the general case. Obviously, the Hecht formula tends to saturate, so that η → 1 for δ → ∞. A peculiar feature of CVD diamond particle detectors is the increase in their eﬃciency after irradiation with ionizing radiation, a process called priming or pumping. The increased eﬃciency is believed to be due to a saturation of deep traps [12], leading to increased carrier mean free paths. Typically, irradiation with X-rays or β-particles is used to reach the pumped state. In addition to the increase in eﬃciency, pumping greatly extends the temperature region in which the detector can be operated without signiﬁcant performance degradation [13, 14]. Ion Beam Induced Current measurements showed that in CVD diamond samples the collection eﬃciency is not homogeneously distributed, and pumping increases the size of the high collection eﬃciency regions, making the response spatially more homogeneous [15]. In CVD diamond particle detectors a crucial role is played by their thickness. Because of the columnar nature of CVD diamond growth, the crystal quality is much worse close to the substrate interface than at the growth surface. In particular, the CCD has been found to increase with ﬁlm thickness [8, 16]. CCDs up to about 300 µm have been reported [17] in millimeterthick synthetic diamond after removing about half of the sample thickness from the poor-quality substrate side.

3 Analysis of the Charge Collection Spectrum 3.1 Qualitative Analysis As reported in the previous section, each particle impinging on the detector produces a signal connected to the CCD of the detector. Because of inhomogeneities in the density of defects, electric ﬁeld distribution, etc., diﬀerent particles will give signals of diﬀerent amplitudes. The statistical distribution of the amplitudes of the pulses generated by the incoming radiation is referred to as the charge collection spectrum (see Fig. 2 for a typical spectrum of our detectors in the as-grown and pumped states), easily generated using a multichannel analyzer. Its average value gives the the average amplitude of

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Fig. 2. Typical collection spectra of a high-quality CVD diamond detector in the as-grown (left peak ) and pumped (right peak ) states. Solid lines are Monte Carlo simulations

the response (that is, the induced charge and therefore the detector’s average eﬃciency and CCD), while its width gives the inhomogeneity of the response (i.e., the energy resolution). The spectrum is reported as a function either of the channel number in the multichannel analyzer or (when the multichannel scale has been calibrated through the response of a silicon detector, which has 100% eﬃciency) of the eﬃciency or of the “collected energy”, simply deﬁned as Ec = ηEd , Ed being the energy deposited by each particle in the detector. (For example, 241 Am α-particles deposit all their 5.5 MeV energy in the detector provided the detector thickness exceeds their penetration depth G 14 µm.) From Fig. 2 it is clear that even very high quality polycrystalline CVD diamond detectors cannot be compared to Si-based ones, either in terms of eﬃciency (100% for a silicon detector) or especially in terms of energy resolution (in the case of silicon detectors the FWHM of the charge collection spectrum is well below 1% of the peak position). The spectra reported in Fig. 2 show that in this case priming changes not only the position of the peak, but also its shape, from a right-asymmetric (positive skewness) to a left-asymmetric (negative skewness) one, with a sort of cut-oﬀ at high eﬃciency values. This behavior can be related to the different distribution of the two factors limiting the response of CVD diamond particle detectors, namely in-grain defects and grain boundaries. Because of the columnar growth, the latter strongly increase in concentration towards the substrate side of the sample, while the former ones can be considered to be homogeneously distributed. If we assume that priming only acts on in-grain defects, we have a qualitative explanation of the spectra [18]. In the as-grown state the response is limited by the homogeneously distributed in-grain de-

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fects (hence the positive skewness), since the low average eﬃciency implies that the generated charges do not reach the grain boundary region close to the substrate. Indeed, the detector used in Fig. 2 is D = 115 µm thick, while the charges are generated within the penetration depth G 14 µm of the 5.5 MeV α-particles used. From from η δ/D we have therefore δ 6 µm, so that G + δ D. After priming, the increase in eﬃciency is due to the deactivation by priming of the in-grain defects, creating a “defect-free” layer before the grain boundary region located close to the diamond–silicon interface, which produces the high eﬃciency cut-oﬀ. A Monte Carlo simulation quantitatively support this view [18], since both the primed and unprimed charge collection spectra can be perfectly reproduced considering that only in-grain defects can be deactivated by priming. In-grain defects are modelled by a homogeneous distribution of random trapping centers, and grain boundaries by a density distribution D(x) = A exp(−x/b), where x is the distance from the diamond–substrate interface normalized to the thickness of the sample, and A, b are parameters. The MC simulated response curves shown in Fig. 2 are obtained including in the simulation both in-grain defects and grain boundaries in the as-grown case, and only grain boundaries, with the same distribution utilized in the former curve, in the primed case. It is not possible to reproduce the leftasymmetric primed curve without introducing a grain boundary distribution strongly peaked at the substrate side as required by the columnar growth. The negative skewness appears, therefore, to be characteristic of high crystalline quality samples where in-grain defects are substantially inactivated by pumping, leading to high values of η. In the following, the average eﬃciency calculated from the charge collection spectrum will be referred to simply as the eﬃciency. To eﬀectively separate the contribution of in-grain traps and grain boundaries, the ﬁlm thickness must be substantially higher than both the extension of the grain boundary region (otherwise the grain boundary defects dominate the in-grain traps even in the as-grown state) and the penetration depth of the radiation (otherwise the carriers would be generated over the whole sample thickness, and even in the as-grown state would “sample” in their motion the grain boundary region). More evidence can indeed be collected varying the detector thickness. For thin samples, where the grain size is comparable to (or smaller than) the mean free path due to in-grain defects, only a moderate eﬀect is to be expected from the pumping process, since grain boundaries are the main obstacle to high CCD values even in the as-grown state. As the ﬁlm thickness (i.e., grain size) increases, however, substantial improvements in the eﬃciency and CCD of the detectors can be anticipated on the basis of the model because of the saturation of in-grain defects. Figure 3 shows the charge collection eﬃciency under positive bias of several ﬁlms grown in the same conditions (i.e., same crystal quality) with thickness from about 20 µm (i.e., just above the penetration depth of 5.5 MeV

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Fig. 3. Experimental eﬃciency data in the as-grown and pumped state for positive bias polarization. The solid lines are the best ﬁts obtained with the extended Hecht model (see Sect. 3.3)

Fig. 4. Collection spectra for positive and negative bias in the pumped state and in the as-grown state (inset)

α-particles) to about 160 µm [19]. The curves relative to the as-grown and pumped states show a markedly diﬀerent behavior. The initial eﬃciency increase with thickness in as-grown samples is followed for D > 40 µm by a decrease roughly following a 1/D law, while in the pumped state the eﬃciency steadily increases up to a thickness of 100 µm, and then slightly decreases.

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A quantitative explanation of the data in Fig. 3 will be presented in next section, but we can understand them qualitatively [19, 20]. For very low thickness values (D < 40 µm) the microgranularity of the substrate interface layer prevents signiﬁcant drift lengths of the carriers, so that the eﬃciency is very low. Since priming does not act on grain boundary traps, the asgrown and pumped η(D) curves are superimposed. As the ﬁlm thickness increases, so does the grain dimension, and the free path of carriers sharply increases until eventually (D > 40 µm) the grain size becomes larger than the mean free path due to in-grain defects. Now grain boundaries play a minor role and the eﬀect of pumping, which partly saturates in-grain traps, becomes increasingly evident. In the normal state the CCD is limited by the substantially homogeneous distribution of in-grain defects, as demonstrated by the 1/D decrease law of η: the approximation η δ/D is indeed valid (δ D), correctly leading to a δ value independent from thickness, with a value close to 10 µm. In the pumped state, when grain boundaries still play a role because of the partial deactivation of in-grain traps, the increase in grain size (i.e., δ) compensates thickness variation in (4), leading to a more pronounced increase of η. Eventually, of course, the eﬃciency must reach a limiting value. Another procedure that allows us to extract valuable information from the collection spectrum is to make the measurement both in positive and in negative polarity. Indeed, the geometry of the detection process may not be symmetric between the two contacts, e.g., because the ionization produced in the detector is not uniform, or because of the columnar structure of the ﬁlm. As a consequence, the contribution of the two type of carriers (ﬂowing towards opposite electrodes) to the signal will not be the same. Comparison of the collection spectra measured under both positive and negative bias could give information on the contribution of each type of carrier. Consider the idealized situation in which λh is comparable to ﬁlm thickness, λe λh , and the penetration depth of the ionizing particles is small (G D). Practically no signal would be observed under negative bias, since neither electrons (having negligible mean free path) nor holes (blocked by the negative contact) would move in the detector, while a strong signal due to holes would be detected under positive bias. Figure 4 reports typical detection spectra obtained irradiating our CVD diamond detectors with 5.5 MeV α-particles, both in the as-grown and pumped states for each polarization. In the as-grown state the eﬃciency does not change substantially with bias polarity, while in the pumped state the eﬃciency is much higher in positive polarity. As discussed in [21, 22], this implies that in the as-grown state λe ≈ λh , and that λe does not change with the pumping procedure, while λh strongly increases. 3.2 Quantitative Analysis: The General Model We pointed out that (3) is only valid when the distribution of the charge created by the ionizing particle along the penetration path and the trap

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distribution are uniform. Because of the columnar growth of polycrystalline CVD diamond, and the Bragg distribution of the energy released by a ionizing particle, both these requirements are not fulﬁlled in our case. Following [19], we now extend the Hecht theory to take into account inhomogeneous CVD diamond samples and nonuniform ionization proﬁles. We will then apply this model to extract information on the inhomogeneous defect distribution and on the defect properties from the detector response. The shape of the electron and hole trap distribution, as a function of the distance x from the growth surface, is taken as: we,h (x ) =

1 + b · e(x −D)/c , λe,h

(5)

where the ﬁrst term on the right refers to the in-grain defects (i.e., the intrinsic properties of diamond crystals), while the second terms models grain boundaries (i.e., the columnar nature of the ﬁlm). The mean distances covered by charge carriers from the generation points, lh and le , depend on the distance x of the generation point from the top electrode and can be deﬁned by considering the probability P that a charge carrier moves at least through a distance s. In a positive bias conﬁguration: s s − w (x +s ) ds − w (x −s ) ds Pe (x , s) = e 0 e (6) Ph (x, s) = e 0 h

D−x

lh (x) =

Ph (x, s) ds

le (x) =

0

x

Pe (x, s) ds

(7)

0

in which the integration limits take into account that s cannot exceed the distance of the charge generation point from the corresponding collection electrode. The average drift distances Le and Lh of all the charge carriers generated by an ionizing particle are calculated by averaging le (x) and lh (x) over the distribution function u(x) of the generation points: Lh = lh u(x) ,

Le = le u(x) .

(8)

For analytical treatment, the Bragg ionization distribution u(x) can usually be very well approximated by the exponential function u(x) = A+B ex/C with a cut-oﬀ at the penetration depth G. In the case of 5.5 MeV α-particles, for example, the above formula works ﬁne using as parameter values (obtained by the nuclear physics simulation program SRIM [23]) A = 267.7 keV/µm, B = 11.17 keV/µm, C = 3.45 µm and G = 13.54µm. After calculating Lh and Le using (5)–(8), the eﬃciency η can be ﬁnally derived from (1). Obviously, in the case of a negatively polarized detector, the role of electrons and holes must be exchanged.

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Combining (1), (5)–(8), therefore, the quantitative relationship between the intrinsic properties λe and λh and the experimentally accessible quantity η can be derived. Clearly, η depends on a number of intrinsic properties of the ﬁlm (λe , λh , b and c) in a very complicated way. Direct inversion of the equations to extract these parameters from the measured η values is not possible. Rather, it is possible to measure η as a function of other quantities such as the penetration depth G of the radiation, or the sample thickness D (from which λe , λh , b and c do not depend) and to ﬁt the obtained curves with the above proposed formulae. 3.3 The Use of Detector Thickness As an example, we will now apply this model to the analysis of the η(D) curves reported in Fig. 3. Since CVD diamond properties are diﬀerent in the as-grown an pumped state, in principle we should consider four ﬁtting parameters for each of the two η(D) curves. However, we have seen that (at least for the ﬁlms used in [18, 19, 20, 21, 22]) in the as-grown state λe ≈ λh , and only λh signiﬁcantly increases after pumping. Moreover, the pumping procedure does not inﬂuence the grain-boundary defects (described through the b and c parameters in (5)) [18, 19]. Therefore the trap distribution in CVD diamond can be described with good approximation by four parameters only. These are b, c, λe whose values are the same both in the as-grown and pumped state, and the λh value in the pumped state (in the as-grown state λh is substantially equal to λe ). A reduced number of parameters obviously puts more constraints on the ﬁt, therefore increasing its reliability. The simultaneous ﬁt of both the η(D) data sets in Fig. 3 with the theory is represented by the continuous lines, and the corresponding ﬁtting parameters are reported in Table 1. The goodness of the ﬁt is an indirect proof that the assumptions made are substantially correct, so that the charge collection distance δ = λe + λh increase after pumping from 14 µm to 62 µm is really due only to the large variation of λh , λe being by hypothesis unaﬀected by priming. In the case of negative bias the η(D) values are very similar to those measured under positive bias in the as-grown state, irrespective of the sample being in the normal or primed state. In this case, in fact, the increase in λh with pumping does not strongly aﬀect η because holes can only move an average distance G/2 (roughly equal to λe ) before being stopped by the negative contact. Table 1. Best-ﬁt parameters for the eﬃciency vs. thickness curves in Fig. 5 λh λe b c µm µm µm−1 µm−1 As-grown 7 Pumped 55

7 7

1.1 1.1

10 10

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Fig. 5. Charge collection distances for the as-grown and pumped state obtained with the homogeneous Hecht model (solid lines) and with the extended Hecht model (dashed lines)

An interesting result is the identiﬁcation of the strongly defective region near the Si–D interface, due to the columnar growth. We can divide CVD diamond ﬁlm in two regions, a “homogeneous” one where the action of uniformly distributed in-grain defects predominates on grain boundaries, and an “inhomogeneous” one, closer to the substrate, where the opposite is true. The borderline between them depends on the values of the b and c parameters, and, from (5), corresponds to a distance yB = D − xB from the substrate interface, where 1 1 + = 2b · e(xB −D)/c = 2b · e−yB /c . λh λe

(9)

A value yB = 26 µm was obtained from the data reported in Table 1, in the pumped state. When D = yB grain boundaries are always dominant over ingrain defects, and no eﬀect of pumping is expected at all. This is conﬁrmed by measurements performed on ﬁlms of thickness lower than about 30 µm. In literature the CCD values for CVD diamond ﬁlms are often derived from eﬃciency measurements using (5), i.e., the homogeneous Hecht model. Despite being widely used, this procedure is clearly incorrect. In the general model the δ value is correctly treated as an intrinsic property of the material, and as such is independent of ﬁlm thickness. As a consequence, the plot of δ as a function of the ﬁlm thickness D is given by a constant value (continuous lines in Fig. 5). The dependence of η on D is due to the diﬀerent relevance of in-grain and grain boundary defects for ﬁlms of diﬀerent thickness, according to (5). The analysis of the η(D) curves by the homogeneous model is totally diﬀerent. Since in (4) there would be no adjustable parameters, the η(D)

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curves simply cannot be ﬁtted. The only way to obtain δ would require a point-to-point eﬃciency data conversion by means of (4), however, obtaining a nonphysical, variable δ value (dashed line in Fig. 5). This value tends to the correct one, obtained by the inhomogeneous model, only for D high enough to make the inﬂuence of grain-boundaries negligible with respect to in-grain defects. As in the pumped state in-grain defects are partially ﬁlled, the asymptotic value of the CCD is higher for the pumped state than for the as-grown one. 3.4 The Use of Penetration Depth Another way to highlight the diﬀerent action of in-grain and grain boundary defects, besides varying the ﬁlm thickness, would be, of course, to change the penetration depth G of the detected particles for a given ﬁlm, and use the method outlined above to ﬁt the η(G) curves. For such an experiment to be meaningful, G should be varied in a wide region (for example, 0.1< G/D < 0.8) so that a variable energy beam source would be necessary (Van De Graaf generator, tandem accelerator, etc.). Some results can be found in [24, 25], but to limit ourselves to techniques which only require normal laboratory equipment, we will here discuss a simpler use of the penetration depth, which requires a more limited range of values for G and can still provide useful information. We will no longer be able to reconstruct the trap distribution, but could quantitatively evaluate the mean free distances λe and λh . When the ﬁlm thickness is signiﬁcantly higher than both the penetration depth and the carrier mean free path, the grain boundaries will have no eﬀect at all on the detector response, which only depends on G, λe and λh . Varying G, the contribution of one type of carrier (depending on bias polarity) gradually decreases as the penetration depth of the incident particles is reduced, so that the η(G) curves for the two polarities depend on the mean free path of each carrier type in a diﬀerent way, allowing us to separately extract the desired information. To control the α-particle penetration depth in the CVD diamond, two diﬀerent approaches have been proposed [22]. The obvious way is to vary the energy of the incident particles (variable energy method, VEM) by using an absorbing layer of appropriate thickness. Air can be used as the absorber for 5.5 MeV α-particles, since their energy is halved by a 2.5 cm layer, and the source-to-sample distance can therefore be easily controlled. As an alternative, the incidence angle θ of the α-particles with respect to the sample surface can be varied, the system being kept in vacuum to leave the incident energy of the particles at 5.5 MeV (variable incidence method, VIM). In this case, G is reduced by a factor cos θ with respect to the normal incidence value G0 = 13.54 µm. A particle incidence angle in the 0◦ –80◦ range can be controlled with a beam collimator, corresponding to 0.17 < cos θ < 1. The beam divergence prevents reaching signiﬁcantly higher incidence angles.

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Fig. 6. Eﬃciency curves as a function of the penetration depth G for air measurements in positive (square) and negative (circle) bias polarity; (a) in the pumped state, (b) in the as-grown state. Solid lines are the ﬁt curves

In Figs. 6b and 7b the η(G) curves are reported when the sample is in the as-grown state using VEM and VIM, respectively. The same curves are plotted for the pumped state in Figs. 6a and 7a. Although VEM and VIM techniques lead to qualitatively similar behaviors, at lower penetration depths (i.e., thicker absorbing layer) the energy released in the sample by the ionizing radiation is reduced in the VEM case, and the spectrum is shifted to the lower energy side, partly overlapping with the noise shoulder. The signalto-noise ratio decreases, eventually making measurements impossible. In the VIM measurements the total energy released by the impinging particles is constant for all the θ values, so that both the shape and the peak position of the spectra are not greatly aﬀected. Lower penetration depths can be reached with approximately constant error bars on the eﬃciency measurements using VIM. In the analysis of the curves, (5)–(8) can be simpliﬁed because grain boundaries play no role. Equation (5) becomes we,h = 1/λe,h and (6)–(8) can

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Fig. 7. Eﬃciency curves as a function of the penetration depth G for tilt measurements in positive (square) and negative (circle) bias polarity (a) in the pumped state, (b) in the as-grown state. Solid lines are the ﬁt curves Table 2. Transformations of the parameters A, B, C and G used in the ﬁts of Figs. 6 and 7

A B C G

(keV/µm) (keV/µm) (µm) (µm)

Normal incidence VEM

VIM

A0 B0 C0 G0

A0 G0 /G B0 G0 /G C0 G/G0 G (from SRIM)

= 267.7 = 11.17 = 3.45 = 13.54

A0 B0 e[(G0 −G)/C0 ] C0 G (from SRIM)

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be analytically calculated. For positive bias [22] we have Ph (s) = exp(−s/lh ), Pe (s) = exp(−s/le ) and lh (x) = λh (1 − e−(D−x )/λh ),

le (x ) = λe (1 − e−x /λe ).

(10)

Averaging over all the electron–hole pairs, using the energy density u(x) = A + B exp(x/C) (with a cut-oﬀ at the penetration depth G), the eﬃciency η for positive polarization one ﬁnds: λe + λh 1 Le + Lh = − η= D D D[AG − BC(eG/C − 1)] (1/C +1/λh )/G e(1/C −1 /λe )/G − 1 −1 −D/λh e × BC λe + λh e 1 − C/λe 1 + C /λh +

A[−λ2e (e−G/λe

− 1) +

λ2h e−D/λh (eG/λh

− 1)] ,

(11)

while for negative polarization the role of electrons and holes is to be exchanged. In the standard case (normal incidence in vacuum) the parameters A = A0 , B = B0 , C = C0 and G = G0 (Table 2) were calculated by ﬁtting the SRIM-simulated Bragg energy distribution with the function u(x) described in the previous section. When the α-particle penetration depth changes, the function u(x) is modiﬁed, leading to suitable changes of the parameters A, B, C and G as reported in [22] (see Table 2). The η(G) curves relative to both positive and negative polarization can be simultaneously ﬁtted by (9) using the proper transformations of A, B, C and G (Figs. 6 and 7) and the very same values of λe and λh for all four curves (Table 3) to increase the ﬁtting constraints. Consistent values of the two ﬁtting parameters are obtained from the two methods, the lower errors in VIM conﬁrming the superior accuracy of this method as compared with VEM. The pumping process is much more eﬀective on hole conduction, since λh becomes much greater than λe after pumping, in contrast with the situation before pumping, when λe λh . Table 3. Best-ﬁt parameters for the eﬃciency vs. penetration depth curves in Figs. 6 and 7 VEM VEM VIM VIM (as-grown) (pumped) (as-grown) (pumped) λe (µm) 8.6 ± 1.0 λh (µm) 8.1 ± 1.0

8.3 ± 1.3 8.6 ± 0.6 36.1 ± 1.5 6.8 ± 0.6

8.4 ± 1.0 37.6 ± 1.1

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4 Time-Domain Analysis 4.1 The Background As a direct consequence of Ramo’s theorem, the charge induced by a single generated carrier in the measuring circuit in a time dt is dq = edx/D = (ev/D)dt, where v is the drift velocity of the carrier. Therefore the time evolution of the detector signal reﬂects the dynamics of carriers generated by the ionizing radiation in the detector. Carrier dynamics are in turn related to the nature and concentration of the traps present in the ﬁlm. That is why a deep insight on the dynamics of charges generated in the detector and the identity of defects existing in CVD diamond can be obtained from the time development of single pulses. Zanio et al. [26] and Martini and McMath [27] showed how this time behavior changes when detrapping and/or trapping events occur in the detector, and applied this analysis to conventional Si detectors. This analysis was then extended [21, 28] to describe the more complex behavior of CVD diamond detectors. In the original model of Martini and McMath, a single kind of defect is considered, i.e., the situation found in Si detectors, and a single carrier type (the ionizing radiation was a focused γ-ray beam directed close and parallel to one of the electrodes, so that only one type of carrier was free to move towards the opposite electrode, contributing to the output signal of the detector according to Ramo’s theorem). In the absence of trapping defects the total distance traveled by a single electron–hole pair (before being collected at the electrodes) amounts exactly to D. In this case the detector’s eﬃciency is 100%. If deep traps are present in the detector, which capture a fraction of the carriers and do not allow their thermal release (detrapping), the collected charge and the eﬃciency are accordingly reduced, but the collection process is still completed within the transit time. When shallow traps are involved, 100% eﬃciency may still be achieved, but the time response is now slower because carriers experiencing trapping–detrapping have their motion delayed by a time on the order of the detrapping time constant, so that the charge collection process extends beyond TR . A so-called slow component appears, as opposed to the fast one due to the ballistic motion of untrapped carriers. For a 100 µm thick diamond detector working under an external ﬁeld E = 104 V/cm, TR = D/v ≈ D/mE ≈ 1 ns, so that in most cases the fast component is not experimentally accessible because of the response time of the instrument used to trace pulse shapes. Charge collection for the slow component is ruled by the detrapping time constant, which can be much longer than a few nanoseconds, so that it can be experimentally measured. For t < TR no charge reaches the electrode, and an analytical solution for the rate equation exists [27]. Unfortunately, the time evolution of the slow component cannot be calculated analytically even in this simple case involving a single type of trapping centers and a single type of carriers generated

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Fig. 8. Time evolution of the pulses measured in the as-grown state for positive and negative polarities

Fig. 9. Time evolution of the pulses measured in the pumped state for positive and negative polarities

at one electrode. For diamond detectors under α- or β-particle irradiation, the released charge Q0 is not concentrated at one electrode but is distributed along the particle penetration depth, ranging from several microns to the whole sample thickness. Consequently, both electrons and holes can in principle contribute to charge collection. In addition, we will show in the following that more than a single type of defect must be introduced to explain experimental results in the case of CVD diamond detectors. A computer simulation can be used to quantitatively describe trapping–detrapping eﬀects once a qualitative picture of the trapping centers present in the detectors is available.

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4.2 Qualitative Analysis The experimental time evolution of a diamond detector output before pumping, i.e., in the as-grown state, is reported in Fig. 8 for positive and negative ﬁeld polarity [21]. The pulses have diﬀerent amplitudes, reﬂecting the width of the charge collection spectrum, but similar amplitudes are observed for positive and negative polarity. In all cases the saturation value is immediately reached, the collected charge being constant after the 10 ns rise time of the digital oscilloscope. This implies that once trapped by a defect, electrons and holes are not detrapped, so that the defects limiting the detector’s response in the as-grown state can be identiﬁed as deep ones. No signiﬁcant diﬀerence is observed between positive and negative polarity because CCD (and therefore both electron and hole mean free paths before trapping) is lower (see below) than the penetration depth G 15 µm of 5.5 MeV αparticles in diamond. As a result, the growth surface boundary plays a very limited role. Further, since the ﬁlm thickness D d, the substrate interface boundary plays no role at all. Therefore, even if electrons and holes should have diﬀerent mean free paths, no diﬀerence would be observed between negative and positive polarity. In principle only one kind of traps for electrons and holes is necessary to explain the behavior in the as-grown state. This picture changes when examining the pulse shapes for the same sample in the pumped state (Fig. 9). No signiﬁcant eﬀect of pumping is found in the case of negative polarity. A dramatic change, on the other hand, can be seen for positive ﬁeld polarity. Not only is the amplitude of the pulses greatly enhanced, reﬂecting the large increase of eﬃciency due to pumping, but a signiﬁcant slow component develops, breaking the symmetry between positive and negative polarity. It appears, therefore, that pumping saturates most of the deep defects responsible for hole trapping without detrapping, leading to a greatly enhanced mean free path of holes in the pumped state, while not signiﬁcantly aﬀecting electron traps [21, 29]. Thus, shallower defects existing in a lower concentration than saturated, deeper ones, now become important. Since they allow detrapping, they do not limit the overall amplitude of the pulse, but slow down the charge collection process. For negative polarity, the limited changes in the pulse amplitude and shape with respect to the as-grown state show that no signiﬁcant saturation of electron traps occurs. Holes are in principle substantially free to move, but since 5.5 MeV α-particles only ionize within their penetration depth G 15 µm (much less than the hole mean free path), holes can move only a few microns before being collected at the surface electrode. They therefore cannot give a great contribution to charge collection according to Ramo’s theorem, nor can they be trapped and detrapped since their mean free path is now much higher than the real path to the electrode. Therefore the slow component substantially does not show up, and at the same time the fast one does not increase signiﬁcantly with respect to the as-grown case.

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4.3 Quantitative Analysis: Computer Simulation A computer simulation can be developed [21] to calculate, according to this model, the pulse shape Q(t) in a discrete time approximation. For each carrier type, the detector thickness D is divided into N laminae, the transit time of a carrier in each lamina being ∆t = D/N v = TR /N , where v is the drift velocity. For each carrier type (electrons and holes) deep (type-A) and shallow (type-B) defects are taken into account, having trapping time constants τA+ , τB+ and detrapping time constants τAD , τBD , respectively. Carriers can be free, ni (tj ) being the number of free carrier in the i-th lamina at time tj , or trapped in each of the two trapping centers, nAi (tj ), nBi (tj ) being their corresponding numbers. In the time interval ∆t = tj − tj−1 , free carriers either move to the next layer contributing by ev∆t/d = e/N to the induced charge, or are trapped in either defect. In the same time interval, trapped carriers can be released and move to the next layer or remain trapped. We have therefore at ﬁrst order approximation in ∆t: 1 1 + ni (tj ) = ni−1 (tj−1 ) − ni−1 (tj−1 )∆t (12) τA+ τB+ ∆t ∆t + nA(i−1 ) (tj−1 ) D + nB(i−1 ) (tj−1 ) D , τA τB ∆t ∆t (13) nAi (tj ) = nAi (tj−1 ) − nAi (tj−1 ) D + ni (tj−1 ) + , τA τA ∆t ∆t (14) nBi (tj ) = nBi (tj−1 ) − nBi (tj−1 ) D + ni (tj−1 ) + , τB τB (release and trapping of a carrier in a single time interval ∆t and other second-order eﬀects can be neglected for suﬃciently large N values). The total charge induced by each type of carrier is then e ni (ti ). (15) + Q(tj ) = Q(tj−1 ) + N i This procedure is repeated twice (for electrons and holes, respectively), and the results are summed. Direct recombination eﬀects have been neglected since electrons and holes rapidly separate under the external electric ﬁeld, and the concentration of charges generated along the α-particle track is estimated to be lower than that of trapping centers. The simulation parameters are the + + + + D D D , τeB , τeA , τeB and τhA , τhB , τhA , carriers’ velocity v and the time constants τeA D τhB for electrons and holes, respectively. However v only deﬁnes the value of ∆t, i.e., the time scale of the process. In fact, all time constants only appear in (12)–(14) through their ratio with ∆t, so that their values are relative to ∆t. A reasonable value v = 5 · 106 cm/s [8] has been chosen, resulting in TR = d/v = 2 ns. According to the qualitative discussion reported in the previous section, + = ∞). Also, type-A defects there are no type-B defects for electrons (i.e., τeB

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Fig. 10. Comparison of measured pulses with the simulation based on the trapping–detrapping model in the as-grown and pumped states + + + D D D do not allow detrapping (τeA , τhA = ∞). Only τeA , τhA and τhB , τhB must therefore be determined. Since the CCD is more easily visualized in terms of carrier mean free path, the trapping time constants are transformed into + + + , λhA = vτhA , λhB = vτhB due to type-A or the mean free paths λeA = vτeA type-B defects for electrons and holes, respectively. In contrast to the time constants, the mean free path values do not depend on the arbitrary choice of ∆t (which cancels out in the product with the corresponding time constant), and are therefore real ones. In Fig. 10 simulated pulses are compared with experimental ones for positive polarity (the negative polarity case is a trivial one, since the slow component is always very small). Because of the scaling property of the pulses [21], a single pulse for the as-grown and pumped states has been selected, chosen in the middle of the eﬃciency distribution determined by the α-particle collection spectra (about 8% in the as-grown state and 40% in the pumped state). To ﬁnd the best agreement with the measured pulses, the as-grown, positive polarity curve alone is simulated ﬁrst. As discussed above, the lack of a slow component means that the density of deep (A) traps for holes is much higher than that of shallow (B) traps, so that the only parameters to be determined are in this case λeA and λhA , the value of λhB being almost irrelevant. When, as in the present case, the eﬃciency is so low that the total CCD is lower than the penetration depth of α-particles, the only accessible information is the sum of electron and hole mean free paths and not their separate values. Setting λeA = λhA , the as-grown state pulse is simulated + + using λeA = λhA 4.5 µm (δ = 9 µm), corresponding to τeA = τhA = 0.09 ns with the chosen value for v. The pulse measured in the pumped state has then been simulated, introducing also shallow (detrapping) hole traps (i.e., λhB ) and, as already argued in the preceding section, a substantially lower

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Table 4. Parameter values used in the simulation of Fig. 10 As-grown Pumped λeA (µm) 4.5 4.5 λhA (µm) λhB (µm) 35 D τhB (ns) 200

4.5 50 35 200

concentration of eﬀective deep hole traps (i.e., a higher value for λhA ) as a consequence of pumping. The concentrations of deep electron traps (i.e., λeA ) is kept unaltered. In order to reproduce the experimentally observed amplitude ratio between fast and slow components, it turns out that λhA = 50 µm + (i.e., τhA = 1 ns), so that the pumping process reduces the density of eﬀective hole deep trapping centers by one order of magnitude, while λhB = 35µm (i.e., + = 0.7 ns), much higher than the 4.5 µm as-grown value of λhA , which τhB conﬁrms the validity of the initial assignment λeA = λhA 4.5 µm based upon neglecting hole type B traps in the simulation of the as-grown pulse. The parameter values used are summarized in Table 4. In agreement with the model, in thin ﬁlms (D < 35 µm) a signiﬁcant slow component is not detected even after pumping, since holes are trapped at the highly defective region close to the ﬁlm–substrate interface before travelling distances much in excess of 10 µm. D The time evolution of the slow component is well described when τhB = 200 ns. A rough estimate of the activation energy ED of shallow defects D responsible for hole trapping and detrapping can be made since 1/τhB = 12 −1 s exp(−ED /kT ). Using s ≈ 10 s for the attempt frequency s (to which ED is anyway relatively insensitive), we obtain ED 0.3 eV. A more quantitative evaluation of ED can be obtained by measuring the thermally activated detrapping time constant at various temperatures [28]. The slope of the linear dependence of ln(τD ) on 1/T gives then the activation energy ED . Using the estimated value ED 0.3 eV, we see that a 20% decrease in T is expected to increase τ D by a factor of 15. Temperatures ranging from about −40◦C to about 20◦ C should therefore correspond to values of τ D in the range 200–3000 ns, well accessible experimentally. This temperature range is easily covered using Peltier elements. In Fig. 11 the pulse shapes of the detector in the pumped state and under positive bias are reported, measured at various temperatures and normalised to unit amplitude for better comparison. The systematic speed-up of the response with temperature conﬁrms that the slow component is due to thermally activated detrapping from relatively shallow defects. Similar curves are obtained under negative bias. In the normal state the slow component is strongly reduced, as expected, its residual being attributed to an incomplete “depumping” process. In Table 5 the values of ED calculated by ﬁtting the τ D (T ) curves with (1) are reported in all four cases (positive and negative polarity, as-grown and

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Fig. 11. Pulses measured in the pumped state for positive polarity at temperatures −40◦ C, −30◦ C, −15◦ C, 0◦ C, 20◦ C (from slowest to fastest). The amplitudes are normalised to unity

Table 5. Values of the activation energy of shallow traps calculated from the temperature dependence of the detrapping time constant As-grown+ EA (meV) 280

As-grown−

Pumped+

Pumped−

370

340

337

pumped state). A value ED = (0.35 ± 0.02) eV is found, with the exception of the case of positive polarity in the normal state, probably as a consequence of an imperfect temperature control.

5 Temperature Eﬀects: Depumping The method described in the previous section is not suitable to measure the activation energy of deep traps, since temperatures should be raised beyond the working range of the detector to have measurable detrapping times. To circumvent this problem, the α-particle response of a diamond ﬁlm was recently measured [30,31] after successive annealing steps performed at diﬀerent temperatures in the 180–230◦C range. The measurement is therefore carried out at room temperature, and only the annealing treatment is performed at temperatures beyond those at which the detector works properly. If before each annealing curve at a given temperature the sample is driven to its fully pumped state, the eﬀect of thermal annealing is to promote thermal detrapping of carriers from occupied trapping centers, i.e., a partial depumping. The increase in the number of active (i.e., not ﬁlled) traps lowers the carrier mean free path before trapping, and the detector eﬃciency.

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Table 6. Detrapping time constants τ for the various annealing temperatures, as extracted from the ﬁt of curves reported in Figs. 12 and 13 T (◦ C) τ (h) Deeper trap (Fig. 13)

180 190 206 220 228 Shallower trap 125 (Fig. 14) 138 165

373 159 71.1 14.7 6.9 140 48.7 4.5

With reference to type-A and type-B traps for holes discussed above, let nA and nB be their concentrations, respectively. The total number per unit volume n∗A of active (not ﬁlled) type-A defects after an annealing step depends on the annealing time t as n∗A (t) = nA (1 − e−t/τ ), where τ is the detrapping time constant. The collection distance of holes depends therefore on nA and nB as λh (t) =

1 σA nA (1 −

e−t/τ )

+ σB nB

,

(16)

where σA and σB are the capture cross sections of type-A and type-B defects, respectively. Introducing λh0 and λh∞ as the hole charge collection distances in the fully pumped and completely depumped state, respectively, we have λh0 = λh (t = 0) = 1/σB nB , and λh∞ = λh (t = ∞) = 1/(σA nA + σB nB ). Substituting back in (16), we obtain λh (t) =

λh0 . 1 + (λh0 /λh∞ − 1) · (1 − e−t/τ )

(17)

It is therefore possible to calculate the activation energy EA by extracting τ from the λh (t) dependence and using 1/τ = s exp(−ED /kT ), provided we calculate λh from the detector eﬃciency η using, e.g., the VIM or VEM techniques discussed above. Since we are interested in λh only (pumping only acts on hole traps), a simpliﬁed procedure can be used, consisting in performing the α-particle irradiation at a single high incidence angle (80◦ ) with respect to the detector’s surface normal [30, 31]. The λh (t) curves were obtained at ﬁve diﬀerent temperatures ranging from 180◦ C to 228◦ C, as reported in Fig. 12. Equation (17) ﬁts these curves very well, exception made for the ﬁrst point in each curve. The fast decrease of about 5 µm in the value of λh observed in each ﬁrst annealing step can be attributed to the existence of other traps with lower activation energy, i.e., shorter time constants, that are not resolved in this temperature range and time scale. To isolate the contribution of the ﬁrst (deeper) trapping center, the

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Fig. 12. Time evolution of the thermal depumping for the deeper defect. Annealing temperatures are 180◦ C (), 190◦ C (), 206◦ C (•), 220◦ C () and 228◦ C ()

Fig. 13. Time evolution of the thermal depumping for the shallower defect. Annealing temperatures are 125◦ C (), 138◦ C (•) and 165◦ C ()

experimental data were ﬁrst ﬁtted with (17) considering only data with t > 1 h, when the initial drop is completed. The second (shallower) defect clearly requires lower annealing temperatures to be investigated (see below). The best-ﬁt time constants for each temperature, cycle are reported in Table 6. Plotting (Fig. 14) the detrapping time constants in logarithmic scale as a function of the inverse of the annealing temperature a good linear trend is observed, conﬁrming the validity of the adopted model. The activation energy of the defect is Ea1 = 1.62 ± 0.15 eV with an attempt frequency s01 = 3.5 · 1011 Hz. A similar procedure was employed to investigate the lower energy defects, using a 125–165◦C temperature region. More careful experimental procedures

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Fig. 14. Detrapping time constant τ as a function of the inverse of the annealing temperature. The activation energies are calculated through the best ﬁts (solid lines) with 1/τ = s exp(−ED /kT )

Fig. 15. Decay of the detector eﬃciency after two hours annealing time vs. the annealing temperature

should be adopted because of the smallness of the eﬀect observed [31]. The results are reported in Fig. 13 and the best-ﬁt time constants reported in Table 6 were extracted. At these temperatures the detrapping time constant of the deeper traps would be, as calculated from the τ values in Table 6, on the order of months, so that there is no “mixing” of the two eﬀects. The activation energy of these shallower traps is (Fig. 14) Ea2 = 1.33 ± 0.06 eV, s02 = 5.7 · 1010 Hz.

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The existence of two traps involved in the pumping–depumping mechanism is evidenced, plotting (Fig. 15) the ratio λh (t = 2h)/λh (t = 0) as a function of the annealing temperature. The double step shows that a ﬁrst kind of trap produces a moderate detrapping in a 2 hour time scale at temperatures around 130◦ C, while another, deeper one comes into play in the same time scale only at a temperature of about 210◦ C. A plateau exists in between, when the ﬁrst trap has been fully depumped after two hours while detrapping from the other one is not yet eﬀective on this time scale.

6 Conclusion There is a great variety of experimental techniques that allow us to extract information on the properties of defects present in CVD diamond ﬁlms. We reviewed here a number of them, characterized by the fact of being based on the analysis of the response of nuclear detectors built from the samples to be analyzed to irradiation with ionizing particles. Both the realization of nuclear detectors from the ﬁlms and the setup of the experiments are relatively simple. Since basically all these techniques make use of the response of a solid state nuclear detector, which depends on carrier dynamics, they can only give information on electrically active defects, i.e., defects acting as traps for electrons and holes. Within this ﬁeld, however, they are a simple and powerful tool to obtain information ranging from the type and distribution of defects in the ﬁlm to their activation energy, the type of carriers on which they act, the trapping and detrapping times, and the mean free paths of the carriers.

References [1] J. Field (Ed.): The Properties of Diamond (Academic, London 1979) 107 [2] C. P. Klages: Appl. Phys. A 56, 513 (1993) 108 [3] B. Dischler, C. Wild: Low-Pressure Synthetic Diamond. Manufacturing and Applications (Spinger, Berlin, Heidelberg 1998) 108 [4] S. Matsumoto: Thin Solid Films 368, 231 (2000) 108 [5] M. Werner, R. Locher: Rep. Prog. Phys. 61, 1665 (1998) 108 [6] M. Marinelli, E. Milani, E. Pace, A. Paoletti, M. Santoro, S. Sciortino, A. Tucciarone, G. V. Rinati: Photoresponse of CVD diamond ﬁlms in the 100–300 nm spectral range, J. Electr. Soc. Proc. 97–32, 556 (1998) 109 [7] M. G. Donato, G. Faggio, M. Marinelli, G. Messina, E. Milani, A. Paoletti, S. Santangelo, A. Tucciarone, G. V. Rinati: Europ. Phys. J. B 20, 133 (2001) 109 [8] S. Zhao: Characterization IF the Electrical Properties of Polycrystalline Diamond Films, Phd thesis, Ohio State University (1994) 110, 111, 126 [9] W. Shockley: Journ. Appl. Phys. 9, 635 (1938) 110 [10] S. Ramo: Proc. of the I.R.E. 27, 584 (1939) 110

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[11] K. Hecht: Z. Phys. 77, 235 (1932) 110 [12] T. Benke, A. Oh, A. Wagner, W. Zeuner, A. Bluhm, C. P. Klages, M. Paul, L. Shaefer: Diam. Relat. Mater. 7, 1553 (1998) 111 [13] Y. Tanimura: Nucl. Instr. Meth. in Phys. Res. A 443, 325 (2000) 111 [14] M. Marinelli, E. Milani, A. Paoletti, A. Tucciarone, G. V. Rinati, M. Angelone, M. Pillon: Nucl. Instr. Meth. in Phys. Res. A 476, 701 (2002) 111 [15] C. Manfredotti, F. Fizzotti, P. Polesello, E. Vittone: Nucl. Instr. Meth. in Phys. Res. A 426, 327 (1999) 111 [16] D. Kania: Diamond radiation detectors, in A. Paoletti, A. Tucciarone (Eds.): The Physics of Diamond (IOS, Amsterdam 1997) 111 [17] W. Adam, et al.: Nucl. Instr. Meth. in Phys. Res. A 511, 124 (2003) 111 [18] M. Marinelli, E. Milani, A. Paoletti, A. Tucciarone, G. V. Rinati, M. Angelone, M. Pillon: Appl. Phys. Lett. 75, 3216 (1999) 112, 113, 117 [19] A. Balducci, M. Marinelli, E. Milani, M. E. Morgada, G. Pucella, G. Rodriguez, A. Tucciarone, G. V. Rinati, M. Angelone, M. Pillon: Appl. Phys. Lett. 86, 22108 (2005) 114, 115, 116, 117 [20] M. Marinelli, E. Milani, A. Paoletti, A. Tucciarone, G. V. Rinati, M. Angelone, M. Pillon: J. Appl. Phys. 89, 1430 (2001) 115, 117 [21] M. Marinelli, E. Milani, A. Paoletti, A. Tucciarone, G. V. Rinati, M. Angelone, M. Pillon: Phys. Rev. B 64, 195205 (2001) 115, 117, 123, 125, 126, 127 [22] M. Marinelli, E. Milani, G. Pucella, A. Tucciarone, G. V. Rinati, M. Angelone, M. Pillon: Appl. Phys. Lett. 82, 4723 (2003) 115, 117, 119, 122 [23] J. F. Ziegler, J. P. Biersack, U. Littmark: The Stopping and Range of Ions in Solids (Pergamon, New York 1985) 116 [24] R. Potenza, C. Tuv`e: Measurements of defect density inside cvd diamond ﬁlms through nuclear particle penetration, in G. Messina, S. Santangelo (Eds.): Carbon, The Future Matrial for Advanced Technology Applications, vol. 100, Topics Appl. Phys. (Springer, Berlin, Heidelberg 2006) 119 [25] C. Tuv`e, V. Bellini, R. Potenza, C. Randieri, C. Sutera, M. Marinelli, E. Milani, A. Paoletti, G. Pucella, A. Tucciarone, G. V. Rinati: Diam. Relat. Mater. 12, 499 (2003) 119 [26] K. Zanio, W. Akutagawa, J. W. Mayer: Appl. Phys. Lett. 11, 5 (1967) 123 [27] M. Martini, T. A. McMath: Nucl. Instr. Meth. in Phys. Res. 79, 259 (1970) 123 [28] M. Marinelli, E. Milani, A. Paoletti, G. Pucella, A. Tucciarone, G. V. Rinati, M. Angelone, M. Pillon: Diam. Relat. Mater. 12, 1733 (2003) 123, 128 [29] C. Manfredotti, E. Vittone, A. L. Giudice, C. Paolini: Diam. Relat. Mater. 11, 446 (2002) 125 [30] M. Marinelli, E. Milani, M. E. Morgada, G. Pucella, G. Rodriguez, A. Tucciarone, G. V. Rinati, M. Angelone, M. Pillon: Appl. Phys. Lett. 83, 3707 (2003) 129, 130 [31] A. Balducci, M. Marinelli, E. Milani, M. E. Morgada, G. Pucella, G. Rodriguez, A. Tucciarone, G. V. Rinati, M. Angelone, M. Pillon: Phys. Stat. Sol. (a) 201, 2542 (2004) 129, 130, 132

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Index activation energy, 128–132

fast component, 123, 128

carrier mobility, 110, 116 charge collection distance (CCD), 110, 117, 118, 130 charge collection spectrum, 111–113, 125 chemical vapour deposition (CVD), 107–112 columnar growth, 109, 111–113, 115, 116, 118

Hecht theory, 110, 111, 114, 116, 118 high-pressure high-temperature (HPHT), 107

defects, 108 defects distribution, 108, 110–113, 115–117, 119, 133 grain boundaries, 108, 109, 112, 113, 115, 116, 118–120 grain boundaries distribution, 112, 113, 116, 118 in-grain defects, 112, 113, 115, 116, 118, 119 in-grain defects distribution, 112, 113, 115, 118 detector eﬃciency, 110 detectors, 108 detrapping, 123–129, 131 diamond, 107

Monte Carlo simulation, 113 penetration depth, 112 polycrystalline diamond, 108, 109, 112, 116 Ramo’s theorem, 110, 123–125 slow component, 123–125, 127–129 time constant, 123, 126, 128–132 trap, 108 depumping, 108, 128, 129 priming, 108, 111–113, 115, 117 pumping, 108, 111, 113, 115, 117, 122, 124, 125, 128–130 trapping, 110, 113, 123–131 variable energy method (VEM), 119–122, 130 variable incidence method (VIM), 119–122, 130

Eﬀects of Nanoscale Clustering in Amorphous Carbon J. David Carey and S. Ravi P. Silva Nanoelectronics Centre, Advanced Technology Institute, School of Electronics and Physical Sciences, University of Surrey, Guildford, GU2 7XH, UK [email protected] Abstract. In this review the eﬀects of clustering associated with the sp2 and sp3 phases of amorphous carbon thin ﬁlms are examined. We highlight that many of the optical and electronic properties of these ﬁlms can be explained by consideration of disorder in the sp2 phase. Within the context of topological and structural disorder, we explain the variation of the visible Raman line width, Raman shift, Tauc gap and Urbach energy as a function of deposition conditions. We further go on to describe how intra-sp2 cluster interactions are responsible for the narrowing of the electron paramagnetic resonance line width with increasing spin density and how this intracluster interaction can be extended to the intercluster transport properties, in particular, for electron ﬁeld emission from the ﬁlms. We also examine how the mechanical properties of carbon ﬁlms are aﬀected by clustering which can be enhanced by thermal annealing.

1 Introduction and Bonding in Carbon Crystalline carbon is unique amongst the elements of the periodic table, being able to form one of the hardest naturally occurring materials, diamond, and also one of the softest, graphite. From an electronic point of view these two materials possess, respectively, a 5.5 eV energy band gap and a zero band gap, making the electronic properties vary between those found in an insulator and those of a semimetal. This very diﬀerent behaviour can be traced to the bonding and the bond hybridization that are present (Fig. 1). In the case of sp3 hybridization, four σ bonds, arranged at 109.5◦ to each other, allow for the tetrahedral bonding of diamond. These four bonds are responsible for the high hardness and large energy band gap. By contrast, in the case of sp2 -hybridised carbon there are three σ bonds bonding in-plane to three other carbon atoms at 120◦ to each other. In addition, there is one pz orbital perpendicular to the plane of the threefold bonding. This anisotropy in the bonding distinguishes the in-plane electronic properties of graphite from the properties perpendicular to the basal plane. Whilst there is a strong inplane interaction, the weaker out-of-plane interactions are responsible for the lubricant properties of graphite. These bond hybridizations are not restricted to the crystalline forms of carbon and are available to form amorphous carbon ﬁlms (Fig. 1), which have G. Messina, S. Santangelo (Eds.): Carbon, The Future Material for Advanced Technology Applications, Topics Appl. Phys. 100, 137–152 (2006) © Springer-Verlag Berlin Heidelberg 2006

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Fig. 1. A schematic representation of diﬀerent types of hybridised bonding and the resultant crystalline and model amorphous structures

a wide range of properties, some of which are presented in Table 1. It is important at the outset to distinguish between the diﬀerent types of amorphous carbon. For example, from Table 1 the physical and electronic properties of tetrahedral amorphous carbon (ta-C) are very diﬀerent from hydrogenated diamond-like carbon (DLC:H), even though they both have a similar sp3 fraction. In the case of the former, the sp3 content is mainly made up of C–C bonds, which results in a high-hardness thin ﬁlm, whereas in the latter the sp3 content also contains C–H bonding in addition to C–C bonding. In this review the terms amorphous carbon, a-C, and hydrogenated amorphous carbon, a-C:H, will be used as generic terms for disordered carbon, either Hfree or H-containing. For speciﬁc types of ﬁlms, terms such as diamond-like carbon or polymer-like carbon will be used [1]. One of the main driving forces for the technological use of amorphous carbon thin ﬁlms is the ability to grow thin ﬁlms over large area, at low temperatures with excellent uniformity. The low-temperature deposition, often performed using plasma-enhanced chemical vapour deposition (PECVD), allows the growth onto nonconventional substrates such as organics or glass substrates. The excellent uniformity of the physical and electronic properties is also matched by the mirror-smooth quality of the ﬁlms. Extensive atomicforce microscopic studies of a-C and a-C:H ﬁlms have shown that they typ-

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Table 1. Physical properties of diﬀerent forms of a-C thin ﬁlms Category Polymer-like a-C Graphitic-like a-C Diamond-like a-C Tetrahedral a-C

sp3 %

Optical bandgap H eV at. %

PAC 60–80 2.0–5.0 GAC 0–30 0.0–0.6 DLC 40–60 0.8–4.0 ta-C 65–90 1.6–2.6

40–65 0–40 20–40 0–30

Density Hardness g cm−3 GPa 0.6–1.2 1.2–2.0 1.5–3.0 2.5–3.5

Soft Soft 20–40 40–65

ically have a rms roughness of less than 1 nm. This makes a-C ﬁlms ideal for microelectromechanical systems and for hard disk coatings. In addition, a-C is believed to exhibit excellent biocompatibility and a-C-coated surgical implants have been demonstrated. Less success has been forthcoming in the development of active electronic applications of a-C and a-C:H ﬁlms [2], and as a consequence it is necessary to examine the electronic properties and the eﬀects of disorder and localization at a nanometer level. To that end, this article ﬁrst deals with the physics of the disorder associated with the sp2 phase and then extends the discussion to the intercluster transport properties of the ﬁlms. Finally, ﬁeld emission from the carbon system is discussed.

2 Disorder in Amorphous Carbon Amorphous carbon can be considered as a disordered mixed-phase material consisting of a conductive sp2 phase, embedded in a less conductive sp3 matrix. The sp2 -hybridised carbon atoms are usually in the form of nanometersized clusters, mainly in the form of rings or olephinic chains. These sp2 clusters give rise to occupied π and unoccupied π ∗ bands with the separation between the bands being related to the size of the cluster. The sp3 component tends to be in the form of aliphatic chains of C atoms with C–C and C–H bonding being present. The optoelectronic properties of a-C and a-C:H ﬁlms can be described in terms of transitions between the occupied π states to the unoccupied π ∗ states. Previous studies have shown [3] that it is possible to represent the occupied π and unoccupied π ∗ bands by Gaussian functions centred at Eπ(π∗ ) . The σ and σ ∗ states, which are associated with sp3 C bonding, lie further separated from each other. By deposition on suitable transparent substrates, such as Corning glass, it is possible to extract the parabolic Tauc gap and the exponential Urbach energy. • The Tauc band gap corresponds to optical transitions between extended states, and for the a-C system in the absence of disorder, the Tauc gap is given by the separation between the π–π ∗ bands with a magnitude of 2 Eπ . The larger the average size of the sp2 cluster, the smaller the Tauc gap.

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• An alternative band gap that is sometimes employed is to measure the energy at which the absorption coeﬃcient is 104 cm−1 ; this is known as the E04 gap. Values associated with the E04 gap tend to be larger than the Tauc gap, as the absorption at 104 cm−1 tends to occur in states beyond the π and π ∗ band edges. E03 and E05 gaps are also sometimes quoted in the literature. • Transitions between extended-to-localised states in amorphous semiconductors are usually characterised by the Urbach energy, E U . The value of E U is found by ﬁtting an exponential function to the slope of the absorption edge and has been used as a measure of disorder in other material systems. For example, in the case of low defect density a-Si:H, the valence band tail has an exponential slope of about 45 meV, whereas the slope of the conduction band is 25 meV. In this manner the observed Urbach energy of 55 meV for a-Si:H is mainly associated with the valence band and with low-lying defect states. Fanchini and colleagues have, however, suggested that while the experimentally observed values can be extracted, the validity of this approach for this dual mixed-phase system may be too simplistic. As a result, care must be exercised in the interpretation of the Tauc band gap and the Urbach energy that are obtained [4]. A second measure of disorder, based upon bond angle distortion, is the full width half maximum of the Raman active G band, Γ G . This Raman signal is found at around 1580 cm−1 and originates from the E 2g vibration between sp2 C bonds [5]. Several complementary optical [6,7,8] and Raman studies [7, 9] have revealed that as the Tauc gap increases the Urbach energy increases monotonically, but that the width of the G band undergoes a maximum of about 1.5 eV (Fig. 2). In this respect, if the Urbach energy and the width of the G band are valid measures of disorder in the a-C:H system, then they must measure diﬀerent aspects or types of disorder. Robertson previously proposed that the Urbach energy is a measure of an inhomogeneous disorder associated with diﬀerent sp2 cluster sizes, whereas the G band width has been attributed to a homogeneous disorder associated with bond angle disorder [10]. However, such an interpretation is unable to explain: (i) why the largest values of E U are observed at the highest Tauc gaps (Fig. 2a), since the cluster sizes are smallest there is only a small limited number of diﬀerent cluster conformations possible; (ii) the observation of a maximum in the G-band line width with Tauc gap (Fig. 2b); (iii) why the G-band position is also dependent on the excitation wavelength, with the G-band position tending to saturate at ∼ 1600 cm−1 for excitation wavelengths below 350 nm and the peak shifting to lower energies at longer wavelengths, as shown in Fig. 3a;

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Fig. 2. Variation of (a) Urbach energy and (b) linewidth of Raman G band for diﬀerent a-C ﬁlms as a function of optical Tauc gap. The diﬀerent symbols refer to diﬀerent sets of ﬁlms (see [2])

(iv) the observation that the G-band line width depends on the excitation wavelength with the narrower values of Γ G observed at increasing excitation energy as seen in Fig. 3b. Since the Raman spectra are a result of resonant excitation of sp2 clusters, dispersion of the G peak reﬂects excitation of clusters with diﬀerent band gaps. The saturation of the G-band position at ∼ 1600 cm−1 in Fig. 3a reﬂects the maximum possible Raman shift for C atoms bonded in sp2 rings. The observation of dispersion of the Raman line width implies that there is an inhomogeneous distribution present in the bond angle disorder. Furthermore, the reduction of the G width with increasing excitation energy implies that there is a narrower distribution of higher-gap sp2 states, in contradiction with the proposal that there must be a larger distribution of sp2 states required for the large Urbach energy. The increase in the Urbach energy with increasing π–π ∗ separation and small numbers of possible sp2 cluster conﬁgurations, coupled with the dispersion in the G line width have lead Fanchini and Tagliaferro to conclude that the Urbach energy in amorphous carbon is not a good measure of disorder [11]. Furthermore, they went onto propose two types of disorder: (i) A structural disorder associated with clusters of the same size but with diﬀerent amounts of distortion. This type of inhomogeneous disorder would increase the Urbach energy as well as broaden the G-band line width. (ii) A topological disorder arising from undistorted clusters but of diﬀerent sizes. This would also broaden the Urbach energy but have no eﬀect on the G line width.

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Fig. 3. Variation of (a) G-band Raman shift and (b) G-band linewidth for a series of polymer-like a-C:H ﬁlms (), diamond-like a-C:H () and graphitic carbon (•) thin ﬁlms as a function of Raman excitation wavelength (see [5])

As a consequence, the diﬀerences between distorted and undistorted sp2 clusters needs to be explored. The location of the sp2 clusters in the energy gap depends on two factors: whether they consist of even or odd numbers of carbon atoms and whether they are distorted. Undistorted even-numbered clusters will give rise to states near the Fermi level (E F ) only if they are suﬃciently large. This diﬀers from the case of odd-numbered clusters, which can give rise to gap states even if composed of a small number of atoms. In general, distorted clusters give rise to states that are closer to E F than undistorted clusters. One method that is able to distinguish between the diﬀerent types of cluster is to measure the density of unpaired electron spins arising, for example, from odd-numbered clusters. Such states can be measured by electron paramagnetic resonance (EPR), also called electron spin resonance (ESR). A high concentration of paramagnetic defects (1020 cm−3 ) is typically found in ﬁlms deposited under energetic conditions. Such energetic conditions include samples deposited on the driven electrode of a PECVD system [12]. Low defect densities, typically ∼ 1017 cm−3 , tend to be found under less energetic conditions [13]. The term “defect” is a misnomer since the ESR active species are generally agreed to result from diﬀerent conﬁgurations of sp2 clusters. In this manner, ESR can give a measure of the density of sp2 states at the Fermi level, provided that a majority of these states have a net unpaired electron spin present. It should be noted that ESR spin densities do not themselves measure the sp2 content.

3 Intracluster Eﬀects in Amorphous Carbon Several studies have examined the variation of spin density with deposition conditions, though rarely in terms of relating spin density to localisation of

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Fig. 4. Variation of (a) spin density and (b) peak-to-peak linewidth with negative self-bias for three series of a-C:H ﬁlms (see [2])

the wavefunction [2]. The variation of the spin density, N s , and peak-to-peak line width, ∆B pp , with negative self-bias for three diﬀerent series of ﬁlms are shown Fig. 4. It is evident that the spin density rises from a low value of ∼ 1017 cm−3 and tends to saturate at 1020 cm−3 . The ESR line width initially increases, often as the spin density increases, but at higher biases the line width decreases. In this regime the line shape of the ESR signal is Lorentzian. Furthermore, in these high-bias conditions, the spin densities are typically ∼ 1020 cm−3 , corresponding to ∼ 1 at. % of the ﬁlm. As a result, the ESR signal can be considered as originating from a dilute paramagnetic material. Abragam’s formulism may be used to calculate the contribution to the peak-to-peak line width, ∆B pp , from the dipole–dipole interaction between like spins [14]. Such a broadening mechanism will produce a Lorentzian ESR line shape, which is consistent with the ESR line shapes observed. Assuming a spin concentration N s , measured in cm−3 , the contribution to the dipolar interaction ∆B pp , measured in mT, can be given as [12] ∆B pp =

4π2 g µB N s . 9

(1)

Barklie et al. applied (1) for a typical C-related g value of 2.0025 to obtain the expression ∆B pp = 8.12 × 10−21 N s . The variation of ∆B pp against N s directly for the same three data sets reported in Fig. 4, as well as the predicted line width (dashed line) based solely on dipolar broadening using (1) is shown in Fig. 5. It is apparent that signiﬁcant reductions in ∆B pp are observed at high spin densities, indicating an additional mechanism is responsible for reductions in the line width. This additional interaction is due to the motional averaging of the electron wavefunction within the sp2

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Fig. 5. Variation of peak-to-peak linewidth with spin density for a data in Fig. 4. The dashed line represents the predicted dipolar contribution to the linewidth based on (1)

cluster. As the sp2 cluster increases in size, the probability of the electron being associated with a particular atom decreases. This spreading or delocalization of the wavefunction as the cluster size increases is accompanied by a general reduction in the Tauc gap. Further evidence of delocalization can also be found in an examination of the spin resonance relaxation times. The spin–lattice relaxation time, T1 , decreases from 3 × 10−5 s for polymer-like ﬁlms down to 2 × 10−7 s for DLC ﬁlms, which implies a greater interaction between the spin system and lattice [12]. At the same time, the spin–spin relaxation times increase, reﬂecting a change in the exchange frequency. It has been reported that in ﬁlms with a high sp2 content that the exchange frequency is approximately ∼ 1010 rad s−1 . In addition to the concentration of the sp2 clusters, the size of the sp2 clusters is therefore an important feature of this description. Indeed, there have been attempts to infer the cluster size and shape using visible Raman spectroscopy [15]. As a result, considerable interest was generated by the report [16] of an apparent anisotropy in the ESR signal of defects in DLC ﬁlms measured at high frequency and low temperature. A fully amorphous material with a single spin 12 paramagnetic centre should exhibit a single isotropic line. In [16] it was proposed that the ESR signal could be assigned to the sum of an anisotropic powder spectrum with axial g values of g ∼ 2.005 and g⊥ ∼ 2.0025, and one symmetric unresolved line with g = 2.0025. From previous ESR studies of nanocrystalline graphite, it is known that the

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g tensor is anisotropic and the g values depend on the average crystallite size. A value of g of 2.005 was associated [17] with a crystallite of a size less than 7.5 nm. In this way, it was believed that ESR was providing a way to quantify the size of the nanoclusters. This is an extremely attractive feature since it has been proposed that the ratio of the intensities of the G and D Raman bands (the D band being located at 1350 cm−1 and associated with the A1g breathing mode of 6-fold sp2 rings) can be related to the in-plane correlation length of disordered graphite. The reason that no anisotropy was observed at the more conventional 9 GHz room-temperature measurement was due to the strong exchange narrowing. Unfortunately, in this analysis the role of demagnetizing ﬁelds, which at room temperature and “low” magnetic ﬁelds are negligible, but must be included when operating at 4 K and especially at higher resonance ﬁelds, required at the higher microwave frequencies [18, 19]. When demagnetizing ﬁelds are taken into account, an apparent anisotropy of the resonance can occur since the demagnetizing ﬁeld results in an eﬀective shift downwards of the eﬀective g value when the applied Zeeman magnetic ﬁeld is perpendicular to the ﬁlm and results in an up-shift when the applied ﬁeld is parallel to the plane. Apart from changes in deposition conditions, such as self-bias or the addition of N, nanoclustering within a-C ﬁlms can be adjusted via thermal annealing. Siegal et al. annealed nonhydrogenated a-C ﬁlms produced by pulsed laser ablation and reported the presence of regions 3–5 nm in size which were 5–10% more dense that the surrounding regions [20]. The as-deposited ﬁlms has stresses of 5–7 GPa and a ﬁlm density of 3.0 g cm−3 , but near-complete stress relief had occurred and the density had dropped to 2.8 g cm−3 with thermal annealing to 600◦ C. Over the same annealing temperature range the optical transparency of the ﬁlm decreased, demonstrating that clustering of the sp2 within the ﬁlm has occurred. By considering diﬀerent bonding topologies on the basis of Raman spectroscopy, Siegal et al. concluded that the as-grown ﬁlms consist of small and isolated sixfold clusters, but that above annealing temperatures of 300◦ C the fraction of ﬁve-membered rings begins to increase. The presence of ﬁve-membered rings was attributed to the newly formed π-bonded atoms, rather than a reduction in the population of the six-membered rings themselves. Despite the reduction in the ﬁlm’s density, nanoindentation measurements showed that the nanocomposite ﬁlms were 15% harder than the as-deposited ﬁlms. Computational studies showed that within this nanocomposite ﬁlm, the residual stress consists of an inhomogeneous stress distribution where the three-fold coordinated atoms are under tensile stress, but that the four-fold atoms are under a smaller compressive stress [21]. During annealing small regions of high stress relax, leading to the preferential generation of three-fold coordinated atoms. The stress relief is as a result of fourfold sp3 C bonds being replaced by threefold sp2 C bonds. This change to the shorter sp2 C bond is irreversible under normal conditions. If the near-zero stress is achieved due to

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high temperature annealing, care must the exercised to prevent an excessive thermal stress being introduced into the ﬁlm on cooling back to room temperature. The thermal stress can be eliminated by growing the ﬁlm at above room temperature, which introduces some tensile stress. Further evidence of the formation of clustering in ta-C ﬁlms was reported in the ﬂuctuation microscopy studies recently undertaken by Chen et al. [22]. Annealing up to 600◦ C resulted in the increase in locally ordered regions, but the formation of graphitic ordering did not occur until annealing to 1000◦ C. Much of the research for stress relief in hard a-C ﬁlms, especially ta-C ﬁlms, is driven by the development of carbon-based microelectromechanical systems. Evidence for mixed-phase components in a-C has also been obtained by examining the proton and 13 C relaxation times using nuclear magnetic resonance (NMR). J¨ ager et al. used cross-polarization 13 C NMR to measure the eﬀects on the proton relaxation times in diﬀerent environments of ﬁlms deposited from acetylene and benzene [23]. A two-component 1 H spin–lattice relaxation with time constants of 14 and 120 ms was found and interpreted as being due to the presence of two diﬀerently relaxing proton systems. The shorter relaxation time originates from CH groups in the sp2 and sp3 matrix and the longer T1 time originating from short CH2 polymer units with an sp3 conﬁguration. In this description the two environments are separated by regions of nonhydrogenated sp2 C. It is was further found that for ﬁlms grown by rf glow discharge from benzene at a self-bias voltage of −200 V, the proton relaxation time of ∼ 10 ms was virtually independent of temperature. This temperature independence of the shorter T1 component was interpreted in terms of nuclei being relaxed via spin diﬀusion to paramagnetic centers. It is therefore the degree of electron aggregation or clustering around these paramagnetic centers that determines the proton relaxation. The inﬂuence of spin diﬀusion to paramagnetic centers as an explanation of the temperature independence of the spin–lattice relaxation times implies that an understanding of the factors that aﬀect the spin density and line width are important. Tamor et al. estimated from NMR measurements the protonated and nonprotonated C concentration with either sp2 or sp3 hybridisation [24]. At a self-bias of −500 V, the H content was estimated to be 36 at. % and the fraction of protonated sp3 C atoms to be 0.16, nonprotonated sp3 C atoms to be 0.20, protonated sp2 C atoms to be 0.25, and nonprotonated sp2 C atoms to be 0.37. For a ﬁlm density of 1.7 g cm−3 , this result suggests there are 5.1 × 1022 sp2 C atoms cm−3 in the ﬁlm. If the signal observed from ESR is associated with sp2 C centers, then for a value of N s of 1020 cm−3 , this corresponds to 1 spin per 510 sp2 C atoms, or equivalently to 1 spin per 300 atoms of nonprotonated sp2 C atoms. If these spins were randomly distributed throughout the ﬁlm, cooperative eﬀects, such as exchange, should not occur. Since exchange eﬀects have been attributed to ﬁlms grown at high bias, the combined use of NMR and ESR conﬁrms and quantiﬁes the clustering of the sp2 phase has taken place.

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4 Intercluster Interactions in Amorphous Carbon The increase in intracluster delocalization also manifests itself in changes that can be associated with intercluster interactions. Various transport studies of a-C ﬁlms reveal a commonality in behaviour with high resistivity associated with samples with large Tauc gap. The resistivity decreases as the Tauc gap decreases and the conductivity associated with various mechanisms such as variable range hopping in the more conductive DLC ﬁlms [1]. In the case of resistive polymer-like amorphous carbon, the conductivity has been attributed to a space charge-induced current mechanism [1]. Improvements in the conductivity have also been reported with nitrogen incorporation and attributed to a weak “doping” eﬀect [25] or to a reduction of the band gap through graphitization [26]. In terms of post-deposition processing, transport studies of annealed ﬁlms also reveal an improvement in the conductivity. However, this is almost always accompanied by signiﬁcant modiﬁcation to the structure of the ﬁlm at a microscopic level. In this respect furnace annealing results in an improvement in electrical properties but is accompanied by global changes to the ﬁlm. Ion implantation as a method of injection of thermal energy is therefore an alternative process to modify the ﬁlm properties in a highly controlled manner with precise depth control by the correct choice of ion species, ion energy and dose. Using high-dose B+ implantation into polymerlike ﬁlms, it is possible to reduce the low-ﬁeld resistivity from 2 × 1014 Ω cm (unimplanted) to 6 × 1012 Ω cm (2 × 1014 B+ cm−2 ). Over the same range the Tauc gap remained constant at about 2.6 eV, indicating that no signiﬁcant increase in the mean sp2 cluster size has occurred. For doses greater than 2 × 1014 cm−2 , a fall in the optical gap ﬁnally ends with a total collapse to 0.2 eV at a high dose (2 × 1016 B+ cm−2 ), and the resistivity concomitantly decreases to 5 × 106 Ω cm. The improvement in the electrical characterization has been attributed to improvements in the cluster–cluster interaction via a hopping related mechanism (Fig. 6). During low-dose implantation, localized heating results in localized sp2 clusters, which remain small (as evidenced by the absence of a reduction in the Tauc gap). Before the formation of damage cascades, the concentration of the induced sites will be proportional to the ion dose. This nanoclustering of the sp2 sites, which maintains the wide gap, increases the conductivity by decreasing the hopping distance. At higher doses, nanostructuring of the bulk of the ﬁlm occurs and the band gap decreases. As a result, ion implantation demonstrates that it is possible to improve the conductivity without inducing extensive graphitizing of the ﬁlm. Further evidence for the idea of dielectric inhomogeneity of conductive sp2 clusters embedded in a more insulating matrix can be found in the highresolution scanning tunneling microscope (STM) for a DLC ﬁlm, where the STM results show that there are nanometer-sized regions of higher conductivity surrounded by other regions of lower conductivity [2]. Similar localized regions of conductivity have also been recently reported in an STM study of

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Fig. 6. Schematic of how the diﬀerent bias growth conditions can give rise to a change in the size and concentration of sp2 clusters

sulphur-containing ultrananocrytalline diamond (UNCD) ﬁlms [27]. UNCD ﬁlms consist of nanometer-sized grains surrounded by graphitic grain boundaries. The surface density of states was determined from the normalized differential conductivity, which for sulphur-rich ﬁlms showed an oscillatory behaviour. In UNCD ﬁlms, it was reported that the sulphur acts both to dope the ﬁlms but also to introduce localized defects. In both cases increasing the concentration and size of the clusters results in improved localized electrical conductivity. This is an important result since conventional “large-area” contacts used in current–voltage characteristics would mask the localized nature of the conductivity.

5 Field Emission from Amorphous Carbon The implication of this “dielectric inhomogeneity” can also be extended to examine the ﬁeld-induced electron emission from a-C:H ﬁlms. Application of an applied electric ﬁeld can result in electron emission from the surface. In the case of PAC, ﬁlms it has been reported [28] that the threshold electric ﬁeld for emission exhibited a dependence with the ﬁlm thickness with a minimum threshold observed for a thickness of 65 nm. This behavior was attributed to the eﬀects of internal high electric ﬁeld eﬀects within the ﬁlm and the absence of any signiﬁcant screening of the applied electric ﬁeld. Such an explanation is possible when one considers that the electric ﬁeld from the anode will terminate on the “more conductive” sp2 clusters. At a low density (∼ 1017 cm−3 ) screening of the bulk of the ﬁlm will not occur. In

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such a situation the controlling step in the electron emission process is at the ﬁlm/substrate. A diﬀerent situation will result for ﬁlms grown at higher biases when the defect density increases. For two ﬁlms deposited at −90 V and −265 V self-bias, it was observed [29] that there was little dependence on the ﬁlm thickness and the lowest threshold ﬁeld was reported for the ﬁlm grown at the highest bias, consistent with the model presented in Fig. 6. Here, the ﬁlm with the largest bias has the greatest intercluster interactions since the clusters are larger and the cluster–cluster separation will be the lowest. This gives rise to an emission mechanism that is dominated by the front surface properties of the ﬁlm. Furthermore, the local electric ﬁeld in the neighbourhood of the clusters is enhanced, resulting in lower than predicted threshold ﬁelds for emission. Finally, it has been reported in several studies that the onset of stable ﬁeld emission, often in more resistive samples, occurs only after several voltage cycles [30,31]. This conditioning behaviour often results in lower threshold ﬁelds. It has been shown that it is possible to condition a PAC ﬁlm by current stressing, by intentionally passing a current of suitable magnitude through the ﬁlm [31]. Mercer et al. performed a similar experiment using a scanning tunneling microscope tip to generate a highly spatially localized electric ﬁeld and eﬀectively current stress ta-C ﬁlms [32]. They observed that after ramping the tip–sample bias and current, nanostructures of about 100 nm in extent form. By using high-resolution spatially-resolved electron energy loss spectroscopy (EELS), they showed that the predominant bonding conﬁguration changes from predominately fourfold coordinated C to threefold coordination. Changes in the sp2 bonding have also been reported for heavy ion irradiation of S-doped UNCD ﬁlms [33]. High-energy (GeV/amu) Fe and Si ions were used, and it was reported that there was a reduction in the threshold ﬁeld after implantation for irradiated ﬁlms and this improvement in threshold ﬁeld was accompanied by changes in the sp2 phase as inferred from by Raman spectroscopy. The net eﬀect of the conditioning, current stressing or heavy ion treatment is to generate conductive sp2 -rich areas or ﬁlaments through localized Joule heating. These conductive regions can then be viewed as either isolated sp2 clusters or a continuous sp2 network that can lead to high ﬁeld enhancement factors, which result in reduced threshold ﬁelds. Further evidence of the importance of the sp2 phase in ﬁeld emission comes from a comparative study of the threshold ﬁeld with the ratio of the I D /IG bands found in Raman spectroscopy. For a range of diﬀerent types of a-C ﬁlms (including ta-C, ta-C:N, ta-C:H and DLC ﬁlms [16] and S-doped UNCD ﬁlms [34]), it was observed that the threshold ﬁeld is correlated with the in-plane correlation length, suggesting sp2 cluster sizes of around 1–2 nm. The in-plane correlation length is inferred from the ratio of the intensities of D and G Raman bands.

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6 Conclusions In conclusion, the disorder inherent in amorphous carbon ﬁlms plays a major role in determining the electronic properties. An understanding of the role of disorder is important. PAC ﬁlms have small clusters with a small distribution of cluster sizes and are dominated by topological disorder in which the Urbach energy is not a good measure of disorder and topological disorder dominates. In DLC ﬁlms a reduction in the Tauc gap and blue shift of the G-band implies a higher concentration of larger clusters is present. Furthermore, the increase in spin density (1020 cm−3 ) coupled with the increase in the G band width implies more distorted clusters are present. At the higher spin density the ESR line width is no longer determined by the dipole interaction, with intracluster exchange interactions determining the line width. In this regime, both topological and structural disorder are present and can eﬀect the stress in the ﬁlm. The disorder is dominated by structural disorder with little topological disorder, thereby reducing the line width of G band. The clustering can be adjusted by thermal annealing or ion implantation. In addition, the sp2 phase plays an important role in the ﬁeld emission from these ﬁlms. Acknowledgements The authors acknowledge funding from the EPSRC, and JDC acknowledges the funding of an Advanced Research Fellowship from the EPSRC.

References [1] S. R. P. Silva, J. D. Carey, R. U. A. Khan, E. G. Gernster, J. V. Anguita: Handbook of Thin Film Materials (Academic Press, New York 2002) and reference therein 138, 147 [2] J. D. Carey, S. R. P. Silva: Phys. Rev. B. 70, 235417 (2004) 139, 141, 143, 147 [3] D. Dasgupta, F. Demichelis, C. F. Pirri, A. Tagliaferro: Phys. Rev. B. 43, 2131 (1991) 139 [4] G. Fanchini, S. C. Ray, A. Tagliaferro: Diam. Relat. Mater. 12, 891 (2003) 140 [5] A. C. Ferrari, J. Robertson: Phys. Rev. B. 61, 14095 (2000) 140, 142 [6] J. Ristein, J. Schafer, L. Ley: Diam. Relat. Mater. 4, 509 (1995) 140 [7] A. Zeinert, H.-J. von Bardeleben, R. Bouzerar: Diam. Relat. Mater. 9, 728 (2002) 140 [8] F. Giorgis, F. Giuliani, C. F. Pirri, A. Tagliaferro: Appl. Phys. Lett. 72, 2520 (1998) 140 [9] M. A. Tamor, W. C. Vassell: J. Appl. Phys. 76, 3823 (1994) 140 [10] J. Robertson: Mater. Sci. Eng. R 37, 129 (2002) 140 [11] G. Fanchini, A. Taliaferro: Appl. Phys. Lett. 85, 730 (2004) 141

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[12] R. C. Barklie, M. Collins, S. R. P. Silva: Phys. Rev. B. 61, 3546 (2000) 142, 143, 144 [13] M. Collins, R. C. Barklie, J. V. Anguita, J. D. Carey, S. R. P. Silva: Diam. Relat. Mater. 9, 781 (2002) 142 [14] A. Abragam: Principles of Nuclear Magnetism (Clarendon, Oxford 1996) 143 [15] A. Ilie, A. C. Ferrari, T. Yagi, J. Robertson: Appl. Phys. Lett. 76, 2627 (2000) 144 [16] H. J. von Bardeleben, J. L. Cantin, A. Zeinert, B. Racine, K. Zellama, P. Hai: Appl. Phys. Lett. 78, 2843 (2001) 144, 149 [17] G. Wagoner: Phys. Rev. 118, 647 (1960) 145 [18] B. Druz, I. Zaritskiy, Y. Evtuikhov, A. Konchits, M. Y. Valakh, S. P. Kolesnik, B. D. Shanina, V. Visotskij: Mat. Res. Soc. Symp. Proc. 593, 249 (2000) 145 [19] B. J. Jones, R. C. Barklie, G. Smith, H. E. Mkami, J. D. Carey, S. R. P. Silva: Diam. Relat. Mater. 12, 116 (2003) 145 [20] M. P. Siegal, D. R. Tallant, P. N. Provencio, D. L. Overmyer, R. L. Simpson, L. J. Martinez-Miranda: Appl. Phys. Lett. 76, 3052 (2000) 145 [21] P. C. Kelires: Phys. Rev. B. 62, 15686 (2000) 145 [22] X. Chen, J. P. Sullivan, T. A. Friedmann, J. M. Gibson: Appl. Phys. Lett. 84, 2823 (2004) 146 [23] C. J¨ ager, J. Gottwald, H. W. Spiess, R. J. Newport: Phys. Rev. B. 50, 849 (1994) 146 [24] M. A. Tamor, W. C. Vassell, K. Carduner: Appl. Phys. Lett. 58, 592 (1991) 146 [25] G. A. J. A. S. R. P. Silva: Appl. Phys. Lett. 68, 2529 (1996) 147 [26] R. U. A. Khan, J. D. Carey, S. R. P. Silva, B. J. Jones, R. C. Barklie: Phys. Rev. B. 63, 121201 (2001) 147 [27] S. Gupta, B. R. Weiner, G. Morell: J. Appl. Phys. 97, 094307 (2005) 148 [28] R. D. Forrest, A. P. Burden, S. R. P. Silva, L. K. Cheah, X. Shi: Appl. Phys. Lett. 73, 3784 (1998) 148 [29] J. D. Carey, R. D. Forrest, S. R. P. Silva: Appl. Phys. Lett. 78, 2339 (2001) 149 [30] A. A. Talin, T. E. Felter, T. A. Friedmann, J. P. Sullivan, M. P. Siegal: J. Vac. Sci. Technol. A. 14, 1719 (1996) 149 [31] J. D. Carey, S. R. P. Silva: Appl. Phys. Lett. 78, 347 (2001) 149 [32] T. W. Mercer, N. J. DiNardo, J. B. Rothman, M. P. Siegal, T. A. Friedmann, L. J. M. Miranda: Appl. Phys. Lett. 72, 2244 (1998) 149 [33] A. Gonzalez-Berrios, D. Huang, N. M. Medina-Emmanuelli, K. E. Kristian, O. O. Ortiz, J. A. Gonzalez, J. D. Jesus, I. M. Vargas, B. R. Weiner, G. Morell: Diam. Relat. Mater. 13, 221 (2004) 149 [34] S. Gupta, B. R. Weiner, G. Morell: Appl. Phys. Lett. 80, 1471 (2002) 149

Index a-C, 137, 149

cluster size, 139–141, 144, 147

a-C:H, 138

distorted clusters, 142

2

sp -bonded clusters, 137, 139, 142

intercluster interaction, 137, 147

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intracluster interaction, 137, 142, 150 undistorted clusters, 142 sp2 -chains, 139 sp2 -rings, 139, 141, 145 ﬁve-fold rings, 145 six-fold rings, 145 ta-C, 138, 149 ta-C:H, 149 ta-C:N, 149

G band, 140, 141 G-band, 150 G-band, 145, 149 graphite-like carbon (GLC), 139, 142 graphitization, 147 hydrogenated diamond-like carbon (DLC:H), 138, 142, 149 nitrogen incorporation, 147

amorphous carbon thin ﬁlms, 137 cluster-cluster interaction, 147 cluster-cluster separation, 149 clustering, 137, 145, 146 D band, 145, 149 D/G-band intensity ratio, 145, 149 defects, 142, 144, 148 diamond-like carbon (DLC), 138, 139, 144, 147, 149, 150 disorder, 137, 139–141, 150 homogeneous disorder, 140 inhomogeneous disorder, 140, 141 electron paramagnetic resonance (EPR), 142 electron spin resonance (ESR), 142–144, 146, 150

optical properties, 137 plasma-enhanced chemical vapour deposition (PECVD), 138, 142 polymer-like carbon (PLC), 138, 139, 142, 144, 147 Raman spectroscopy, 137, 140–142, 144, 145, 149 scanning tunneling microscopy (STM), 147 Tauc gap, 137, 139–141, 144, 147, 150 tetrahedral amorphous carbon, 139 ultrananocrytalline diamond (UNCD), 148, 149 Urbach energy, 137, 139–141, 150

Elastic and Structural Properties of Carbon Materials Investigated by Brillouin Light Scattering Marco G. Beghi, Carlo S. Casari, Andrea Li Bassi, and Carlo E. Bottani NEMAS-Center for “Nano-Engineered MAterials and Surfaces”, and Dipartimento di Ingegneria Nucleare, Politecnico di Milano, Via Ponzio 34/3, I-20133 Milano, Italy [email protected] Abstract. Brillouin light scattering (BS) is a nondestructive technique exploited to investigate collective excitations in solids: acoustic phonons, spin waves, magnons and density ﬂuctuations. In particular, it permits users to characterize dynamical structural and nanomechanical properties of materials through the detection of thermally excited surface and bulk acoustic phonons. This gives access to information about both surface and bulk structural properties in the spatial range from a few nanometers to several hundred nanometers. Here we show how BS has been widely and successfully used to study various carbon-based materials ranging from ultrathin tetrahedral amorphous carbon ﬁlms to carbon nanotubes. These materials are interesting for both technological applications and fundamental research.

1 Introduction Carbon-based materials are currently exploited, or being considered, for a variety of applications. Suitable characterization techniques are therefore needed in order to investigate a wide spectrum of properties, in particular mechanical and structural properties are of paramount interest to study structural materials and ﬁlms for coating applications. Brillouin scattering (BS) permits us to characterize dynamical structural and mechanical properties of materials through the detection of thermally excited surface and bulk acoustic waves. This gives access to information about both surface and bulk structural properties at the mesoscale (from a few nanometers to several hundred nanometers). Here we show how BS has been widely and successfully used to study a large variety of carbon-based novel materials, of interest for both technological applications and fundamental research aspects. Inelastic scattering of visible light is a contactless, nondestructive measurement technique that can be employed to investigate various types of collective excitations in solids. Measurements are performed by illuminating a sample with a focused laser beam and analyzing the spectrum of the scattered light. Most of the light is elastically scattered and remains at the laser frequency, while the light that interacts with some kind of excitation undergoes a frequency shift. G. Messina, S. Santangelo (Eds.): Carbon, The Future Material for Advanced Technology Applications, Topics Appl. Phys. 100, 153–174 (2006) © Springer-Verlag Berlin Heidelberg 2006

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In Raman scattering a photon interacts with a single optical phonon, i.e., an oscillation of local, atomic degrees of freedom, and thus provides information mainly on local order at an atomic scale. In carbonaceous materials Raman scattering involves frequency shifts in the 102 –103 cm−1 range, i.e., phonons of frequencies ranging from a few THz to one hundred THz. In BS a photon interacts with an acoustic phonon having wavelength of the same order of the optical wavelength, i.e., a bulk or surface acoustic wave of submicron wavelength [1, 2, 3, 4, 5]. The involved frequency shifts are the frequencies of the acoustic waves of such wavelengths; they depend on material properties and on the type of acoustic mode, and typically lie in the GHz to one-hundred GHz range, i.e., a fraction to a few cm−1 . These frequencies are determined by the elastic properties at the wavelength scale, and thus provide information on material properties at such a scale. Interactions with single phonons, i.e., traveling excitations, give Stokes– anti-Stokes doublets: couples of down-shifted and up-shifted peaks, at welldeﬁned frequencies. Interactions can also occur with nontraveling excitations (quasi-elastic scattering), or involving more phonons (multiphonon Raman scattering). Both these mechanisms give a single broad peak centered at null frequency shift, having width typically comparable to the Brillouin shifts [6]. Other techniques to measure the characters of acoustic waves, like quantitative acoustic microscopy [7] and the so-called laser acoustic technique [8] are based on the excitation of acoustic waves, respectively by a piezoelectric transducer and by a laser pulse, and on the observation of their propagation over millimeter distances. Such techniques typically operate in the tens to hundreds of MHz frequency range. BS measurements do not involve the excitation of acoustic waves, but exploit the spontaneous thermal ﬂuctuations of the acoustic modes. The amplitude of these ﬂuctuations is small and requires longer measurement times (tens of minutes up to some hours), but the acoustic modes are observed at higher frequencies (tens of GHz) and locally. Light scattering occurs in the focusing spot of the laser and does not imply acoustic wave propagation over macroscopic distances. These characteristics qualify BS as a nondestructive, contactless testing technique that is also applicable to small samples. BS can occur by interaction with either bulk acoustic waves, in transparent or semitransparent media, or surface acoustic waves (SAWs), at the surface of any kind of material. Bulk waves are characterized by their wavevector k, while SAWs have a wavevector k parallel to the surface. When acoustic waves are detected, their velocity is measured: the wavevector is determined by the scattering geometry (see Sect. 2), the circular frequency ω is measured from the spectrum, and the acoustic velocity v = ω/k or v = ω/k is immediately obtained. In homogeneous solids the acoustic velocities are independent of wavelength, while they depend on the mode polarization and, in anisotropic media, on the propagation direction. At the surface of a homogeneous solid only one type of SAW exists: the Rayleigh wave, of velocity v R . The dis-

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placement ﬁeld of this type of wave decays exponentially with depth, the decay length being of the same order of the wavelength 2π/k . The Rayleigh wave can be considered the prototype of the various SAW types. In layered solids, beside a Rayleigh wave modiﬁed by the layered structure, other types of SAWs can be present, depending on layer thickness and properties: Sezawa waves, Love waves, pseudo surface waves [9]. Diﬀerently from homogeneous solids, layered media have an intrinsic length scale; consequently, the velocity of all the modes supported by layered structures generally depends on wavelength, and the dispersion relation v(k ) can be measured. In particular, for a single supported ﬁlm of thickness h on a homogeneous substrate, the velocity of SAWs is a function of the nondimensional product k h [2, 3]. The acoustic properties of materials or of layered structures are the direct outcome of BS measurements. The acoustic properties are of direct interest only for speciﬁc applications, but they provide a useful tool to probe other properties, namely the elastic properties, which are of interest in various cases, like, e.g., for coatings. Indentation techniques directly give the hardness, and instrumented indentation supplies one combination of the elastic moduli [10, 11]. However, also in the simplest case, the isotropic medium, the full characterization of the elastic properties requires two independent parameters, to be chosen among Young’s modulus E, shear modulus G, bulk modulus B, Poisson’s ratio ν, or among the elements Cij of the elastic constants tensor. Any pair of these parameters uniquely determines all the others. BS can be exploited to measure these parameters. This Chapter is mainly, although not exclusively, devoted to a discussion of the measurement and data analysis techniques. The velocity of bulk acoustic waves is easily computed as a function of the mass density ρ and the elastic constants Cij of the material supporting them. The velocity of SAWs in layered media can be computed as a function of the material properties and the thickness of all the layers. The properties of the layer(s) can be derived by ﬁtting the computed dispersion relations to the measured ones. In reality the available information is generally not suﬃcient to derive all the mentioned properties; the most frequent applications concern either bulk nonmetallic samples or single supported ﬁlms. In the ﬁrst case the mass density is independently measured and the elastic constants are obtained [4, 12, 13, 14]. In the second case one exploits the substrate properties and values of ﬁlm thickness and mass density independently obtained, e.g., by X-ray reﬂectivity measurements, to derive the ﬁlm elastic constants [5, 15, 16, 17, 18]. It can be noted that, since the probed acoustic wavelengths are submicrometric, in ﬁlms having thickness of a few micrometers the bulk waves are fully present and measurable (if the material is suﬃciently transparent), while SAWs are entirely conﬁned within the ﬁlm, and are unaﬀected by its ﬁnite thickness. In other words, from the point of view of BS, ﬁlms having thickness above a couple of microns are indistinguishable from a semiinﬁnite medium [19, 20], except for the acoustic modes having a wavevector normal to the surface [21].

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Fig. 1. Scheme of the experimental set-up for Brillouin scattering experiment in the backscattering conﬁguration. Sp: specimen; θi : incidence angle; M: mirror; L1– L4: lenses; P: pinhole for spatial ﬁltering; FP: Fabry–Perot interferometer (a single interferometer is shown, for clarity, instead of the tandem multipass interferometer actually exploited); D: light detector

In the following sections the experimental and data analysis techniques are ﬁrst discussed. A general overview of the applications of BS to various types of carbonaceous materials is then presented. Two speciﬁc cases are ﬁnally reviewed in more detail to show the potential of the technique: the measurement of the elastic constants of ultra-thin (down to 2 nm) tetrahedral amorphous carbon ﬁlms of high density and stiﬀness, and the characterization of single-walled nanotubes (SWNT).

2 Experimental Technique As mentioned above, BS measurements are performed illuminating a sample with a focused laser beam, collecting the scattered light and analyzing its spectrum. The incidence and collection directions deﬁne the scattering geometry. In the backscattering conﬁguration the two directions coincide and are at an angle θi from the normal to the specimen surface (Fig. 1). This conﬁguration is the most common one, since it has some advantages: it maximizes the acoustic wavevector k, and it exploits the same lens to focus the incident laser beam and to collect the scattered light, instead of needing two separate optics. In the scattering event, energy conservation has the form Ω s = Ω i ± ω,

(1)

where Ω i and Ω s are the circular frequencies of the incident and scattered light, respectively. The + and − signs refer to anti-Stokes (phonon annihilation) and Stokes (phonon creation) events, respectively. The spectrum of scattered light is dominated by the light at the same incident frequency Ω i ,

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elastically scattered by static inhomogeneities. As indicated by (1) it also contains one or more doublets, symmetric with respect to Ω i . In scattering by bulk waves, wavevector conservation has the form q s = q i ± k,

(2)

where q i and q s are the wavevectors (in the material) of the incident and scattered light; the sign refers again to anti-Stokes and Stokes events. In scattering by SAWs the absence of translational invariance in the depth direction leads to the nonconservation of the wavevector component in that direction: (2) holds only for the two components parallel to the surface, in the form q s = q i ± k .

(3)

Obviously, Ω i = (c/n) |q i | and ω = v |k|, where v is the velocity of the acoustic wave and (c/n) is the velocity of light in the material, c being its velocity in vacuum and n being the refractive index. Since (2) and (3) imply that |k| and k are at most of the same order of |q i | and q i , it follows that ω/Ω i is at most of the same order of the ratio v/(c/n) 1. This means that Ω s Ω i and, accordingly, |q s | |q i |: the modulus |q i | = n (2π/λ0 ) being determined by the laser wavelength λ0 , in a given experiment the probed acoustic wavevector is fully determined by incidence and scattering directions. For backscattering by bulk waves, |q i | = 2 (2π/λ0 ) n. This marks a diﬀerence with the other techniques to measure the acoustic properties [7, 8]: in these techniques the experiment selects the frequency, and the wavelength is determined by the material properties. Consequently, hard materials, which are acoustically fast, are probed at longer wavelength. In BS experiments the acoustic wavelength is instead selected, irrespective of the material properties, and the latter determine the acoustic frequency. It must be remembered that Snell’s law means that upon refraction the parallel component of the optical wavevector remains unchanged. Consequently, q i and q s are completely determined by the incidence and scattering angles θi and θs , and are independent of the refractive index n. Therefore the analysis of surface Brillouin scattering (SBS) results does not require the value of n. In backscattering k = 2 |q i | sin θi = 2 2π sin θi , λ0

(4)

and the relative diﬀerence |Ω s − Ω i | /Ω i = |q s − q i | /q i reaches its maximum value (for scattering by SAWs) 2 (v SAW /c) sin θi , which is, for any material, well below 10−4 , down to below 10−6 . A typical experimental set-up for this scattering conﬁguration is presented in Fig. 1. The laser beam is directed onto the specimen by a small mirror and focused onto the specimen surface by a lens, which also collects the scattered light. Spatial ﬁltering by a pinhole

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is typically needed, and the ﬁltered scattered beam goes to the spectrometer. A more complete analysis would consider the ﬁnite collection solid angle: the lens collects all the scattered wavevectors belonging to a cone around the nominal backscattering direction q s = −q i . Computation of the average exchanged wavevector leads to a correction to (4) [3, 22]. The analysis of Brillouin spectra is diﬃcult because the doublets to be measured (1) have, as noted above, a very small relative frequency shift ω/Ω i from the elastic peak at Ω i , whose intensity is larger by several orders of magnitude. Diﬀraction gratings are not suﬃcient, and surface Brillouin spectra became observable with the introduction of the tandem multipass Fabry– Perot interferometer [1, 23, 24]. The interferometer is operated as a narrowbandwidth, high-contrast tunable band-pass ﬁlter [2, 25], and light is ﬁnally detected by a photomultiplier, operated in the single-photon counting mode.

3 Derivation of the Elastic Constants A Brillouin spectrum gives the velocities v = ω/k and/or v = ω/k of the bulk and surface acoustic waves which give spectral doublets. SAWs are of particular interest for supported ﬁlms. Since the value of k is determined by the incidence angle (4), a set of measurements at diﬀerent incidence angles allows us to measure several points of the dispersion relation v SAW (k ). The bulk wavevector |k| is instead independent of the incidence angle (except at most for anisotropy eﬀects), but this is not a limitation because, since bulk wave velocities do not depend on |k|, the measurement of a dispersion relation is not needed. In the simplest case, the isotropic medium, longitudinal and transverse bulk waves exist. Their velocities are simply given by C11 /ρ and C44 /ρ, respectively, and the two moduli are immediately obtained if both types of waves give measurable spectral peaks and if the mass density is known. In an isotropic medium the whole tensor of the elastic constants is completely determined by only two independent quantities, and the elastic behavior of the material is thus fully characterized. In anisotropic media (single crystals) the number of independent elastic constants is higher, and there are generally three diﬀerent bulk waves, because the two diﬀerent transverse polarizations are no longer equivalent. The velocities of these waves have more complex expressions, functions of the propagation direction. In the case of bulk crystals the complete elastic characterization depends on the speciﬁc crystal symmetry and typically needs measurements with diﬀerent directions of k, possibly requiring crystals with diﬀerent cuts. The behavior of bulk waves has to be kept in mind also for the analysis of ﬁlms, because, as noted in Sect. 1, for ﬁlm thicknesses above about one micrometer, data analysis can be performed as for a semi-inﬁnite medium; this also means that in this case a precise knowledge of ﬁlm thickness is not required.

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In the case of a semi-inﬁnite medium, either isotropic or anisotropic, only one type of SAW generally exists: the already-mentioned Rayleigh wave. It is a true surface wave, meaning by this that its velocity is lower than that of any bulk wave, that its displacement ﬁeld vanishes at increasing depth (for the Rayleigh wave it declines exponentially) and that its energy ﬂow (the acoustic Poynting vector) is strictly parallel to the surface. In the case of layered media other types of SAWs can exist [9, 26, 27, 28]. Considering in particular a single supported ﬁlm, the Rayleigh wave generally exists, modiﬁed by the presence of the ﬁlm (modiﬁed Rayleigh wave, MRW) but preserving its main character. If the ﬁlm is acoustically slower than the substrate it can act as a waveguide, supporting guided modes (Sezawa waves), which are reminiscent of the acoustic modes in free-standing plates (Lamb waves) and have the character of true surface waves. Both the Rayleigh and the Sezawa waves are polarized in the sagittal plane, deﬁned by the propagation direction and the normal to the surface. Transverse waves, polarized in the surface plane (Love waves) also exist. Along a stress-free boundary pseudo surface waves (PSAWs) can also exist. They do not have the character of true surface waves: their velocity is not lower than that of any bulk wave, and they radiate part of their energy towards the interior of the medium; accordingly, their displacement ﬁeld does not vanish at inﬁnite depth. However, when their displacement ﬁeld is still mainly conﬁned in the vicinity of the surface and the rate at which they lose energy towards the bulk is low, they resemble to true SAWs, and in BS measurement they give doublets exactly as true SAWs. Of particular importance in the case of ﬁlms acoustically faster than the substrate is the wave called “leaky longitudinal surface wave” or longitudinal resonance: it is a PSAW that, at the surface, is longitudinally polarized. The velocities of all these waves can be computed, as functions of the mass density and the elastic moduli of all the layers, and of the thickness of the layers (of the product k h for a single supported ﬁlm). If the dispersion relation v SAW (k ) is measured for a set of values of k , obtaining a set of values {vi meas. }, the same set of velocities can be computed as function of some free parameter, namely the elastic moduli Cj , obtaining the values {vi comp.(Cj )}. The free parameters Cj are then identiﬁed by a standard least squares minimization procedure. The sum of squares is computed: vi comp. (Cj ) − vi meas. 2 χ2 (Cj ) = , (5) i σi where the general case has been considered, in which the variances σi of each vi meas. can be individually estimated. Following standard estimation theory, the minimum of χ2 (Cj ) identiﬁes the most probable values (C j ) of the parameters in the (Cj ) space, and the isolevel curves of the ratio χ2 (Cj )/χ2 (C j ) identify the conﬁdence region at any predetermined conﬁdence level [17, 29]. If the minimum of χ2 (Cj ) is well deﬁned, the isolevel curves identify a limited region in the (Cj ) space, resulting in a rather precise measurement of

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the Cj parameters [16, 17, 18]. In other cases the function χ2 (Cj ) has relatively low values in a broad region [30]; for instance, in a two-dimensional (Cj ) space, it can have the shape of an elongated valley [31]. In such cases precise measurements of the Cj parameters are not achieved, although in some cases a combination of the parameters exists, which is identiﬁed with a better precision than the individual parameters [18]. The information that can be obtained on the Cj moduli depends obviously on the amount of information available from the dispersion relations. If only the modiﬁed Rayleigh wave is observed, the Cj parameters are generally not identiﬁed with good precision, but if further acoustic modes are observed, either Sezawa waves [32] or longitudinal guided modes [33, 34], the precision of the measurement of the Cj moduli increases signiﬁcantly [15,16,18,29,31,35]. In particular, in isotropic materials the longitudinal guided mode has a wavevector parallel to the surface, and the same velocity of the longitudinal bulk wave: without needing the value of the refractive index, it directly supplies the value of the C11 elastic constant [33]. The information that can be derived when only the modiﬁed Rayleigh wave is detected was assessed by a sensitivity analysis [36]. For the representative model case of an isotropic ﬁlm on a silicon substrate, it was found that the modiﬁed Rayleigh wave velocity is indeed sensitive to the values of the Young modulus E and the shear modulus G, but very slightly sensitive to the Poisson’s ratio ν, the bulk modulus B and the C11 elastic constants. This means that both E and G can be determined with good precision, and that a similar precision cannot be achieved for ν, B and C11 . This is not contradictory with the fact, remembered above, that in an isotropic medium the values of two elastic constants are suﬃcient to determine all the others. The moduli ν, B and C11 , viewed as functions of E and G, are functions characterized by steep slopes. Consequently, even a small region in the (E, G) plane, corresponding to a good identiﬁcation of these two parameters, corresponds to wide intervals of ν, B and C11 , corresponding to a poor identiﬁcation of their values. For Poisson’s ratio ν the interval can be numerically not very wide, but easily covers a substantial fraction of the range (0, 0.5) which is the meaningful range for this parameter. The same analysis showed that the sensitivity to the ﬁlm thickness and mass density is not high. This is an interesting result, as it means that, for the precise measurement of the elastic moduli, extremely accurate values of thickness and mass density are not crucial. It must be remembered that not all the (E, G) plane is physically meaningful. Since ν = E/2G − 1, in the (E, G) plane the ν = const lines are straight lines through the origin, and the ν = 0.5 and ν = 0 lines are the G = E/3 and G = E/2 lines. These lines delimit the triangle that is fully meaningful. The condition ν ≤ 0.5 is required for thermodynamic stability; the condition ν ≥ 0 is not strictly required (thermodynamic stability only requires ν ≥ −1), but is violated only in extremely rare and peculiar cases.

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4 Brillouin Scattering from Carbonaceous Materials BS has been extensively used to characterize carbonaceous materials, although in several cases their scattering cross section seems to be relatively low. In the case of diamond this possible limitation is overcome by the high thermal conductivity, by which the samples can withstand a high incident laser power without being damaged. In other cases long measurement times allow researchers to reach a suﬃcient counting statistics also with weak signals, but for some types of “diamond-like carbon” the scarcity or absence of published BS measurements is probably to be ascribed to the low scattering cross section. A synthetic overview of published BS results is given here. In crystalline graphite the elastic constants had already been measured by ultrasonic techniques, but these techniques had proven to be unable to reliably measure C44 , due to dislocation motion at the achievable ultrasonic frequencies. Attempts to avoid this problem had been made by performing measurements on graphite irradiated to pin the dislocations. BS avoids this problem by operating in a much higher frequency range. The values of C44 obtained by BS by diﬀerent authors [37, 38] are in reasonable agreement among them, and similar to the values obtained from neutron scattering, but signiﬁcantly higher than those found by ultrasonic techniques. The remaining diﬀerence among the BS results can be ascribed to crystallite size eﬀects [39]. If the crystallites are not much larger than the acoustic wavelength, and the measurement spot encompasses several, not perfectly aligned crystallites, their boundaries have a signiﬁcant inﬂuence on propagation properties [38]. If instead the crystallites are much larger than the the acoustic wavelength and the measurement spot, the boundaries have no eﬀect [37, 39]. In crystalline diamond the most accurate measurements were performed by Grimsditch’s group, who also reviewed previous works [4, 13]. They measured with great precision the elastic constants of natural composition diamond and isotopically enriched diamond [13], ﬁnding, for natural composition diamond, C11 = 1080.4 GPa, C12 = 127 GPa and C44 = 576.6 GPa. These values correspond to a bulk modulus B = 444.8 GPa. The temperature dependence of these moduli was also measured [14], ﬁnding a decrease of only 8% for temperatures up to 1600 K. Various measurements have been performed on CVD polycrystalline diamond ﬁlms. Measurements on 400 µm thick ﬁlms, in which the crystallite size is much larger than wavelength, give values of the elastic moduli in agreement with those found for crystalline diamond, with a Rayleigh velocity v R = 10326 ± 470 m/s, consistent with the (110) texture of the ﬁlm [40]. Measurements on diﬀerent ﬁlms give results that depend signiﬁcantly on ﬁlm quality [20]. Exploiting a peculiar Brillouin scattering conﬁguration and known values of the stress coeﬃcients for diamond single crystals, Kr¨ uger et al. were able to evaluate the internal stresses in CVD diamond [41]. They found stresses up to several GPa, without a clear diﬀerence between the nucleation side (nanocrystalline) and the growth side (microcrystalline).

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The ability of BS to perform measurements on submillimeter-sized samples was exploited to measure the elastic constants for two types of materials that can be obtained only in small samples: fullerite fcc crystals [19] and the hard amorphous carbon phases which can be synthetized, at high temperatures and pressures, from fullerite [42]. In the latter case BS found, for both bulk acoustic waves and SAWs, velocities that approach those of diamond, up to around 90% of diamond values [42]. Hydrogenated amorphous carbon ﬁlms were characterized by BS [43]. Measurements performed in conjunction with nanoindentation [44] were analyzed with an a priori assumption about the value of Poisson’s ratio, while in other cases [34] such an assumption was not needed. Films of nonhydrogenated amorphous carbon, with diﬀerent fractions of sp3 bonding, were characterized by various authors [33, 34, 45]. In these works, besides the Rayleigh wave, other surface or pseudo surface acoustic modes could be measured. For ﬁlms acoustically slower than the substrate it was a Sezawa wave [45], while for ﬁlms acoustically faster than the substrate it was a pseudo surface mode, the so-called longitudinal guided mode [33, 34]. In both cases the additional information coming from the second mode allowed a better determination of the elastic constants. Ultra-thin ﬁlms (down to 2 nm) of tetrahedral amorphous carbon ﬁlms of high density and stiﬀness only perturb the Rayleigh wave of the substrate, without adding other modes; nevertheless this perturbation could be measured, allowing researchers to characterize the ultra-thin ﬁlms, as reviewed in the next section. The characterization by BS of low-density nanostructured carbon ﬁlms deposited by low-energy cluster beam deposition was also possible [46], despite the relatively high porosity and roughness of such ﬁlms. At least for some types of such ﬁlms acoustic phonon propagation is supported, and their detection is possible for ﬁlms deposited on highly reﬂective aluminum substrates. Single-walled nanotubes (SWNT) are a peculiar type of carbon material. BS from aligned nanotubes could be detected, allowing a characterization of the graphene sheet forming the tube wall, as reviewed below.

5 Ultra-Thin Carbon Films Ultra-thin diamond-like carbon ﬁlms, of thickness down to 2–5 nanometers, have been developed as protective coatings of magnetic hard disks and the corresponding reading/writing head. The distance between the recording head and the magnetic material has to be decreased, in order to further increase the storage density [47], and a reduction of the thickness of the protective coatings of the disk and the head is required. Carbon coatings are already a current choice to provide protection against corrosion, grafting sites for the lubricant molecules and mechanical protection [47]. In order

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to achieve a storage density of 100 Gbit/in2 , coatings having thickness reduced to 2–5 nanometers, but maintaining the peculiar properties of thicker diamond-like ﬁlms, are needed; coatings of even lower thickness are currently being investigated. The characterization of such thin ﬁlms is a challenging task. The measurements achieved by BS are discussed here. With thicker ﬁlms the inﬂuence of ﬁlm properties on the modiﬁed Rayleigh wave velocity is higher: several cases in which the ﬁlm properties could be determined were mentioned above. Ultra-thin ﬁlms induce instead only a small perturbation of the wave velocity, which remains mainly determined by the substrate properties. The ability to detect these perturbations and to interpret them is a good proof of the potential of the technique. Ultra-thin carbon ﬁlms are amorphous, and therefore isotropic: as already noted, only two independent parameters are suﬃcient to fully characterize their stiﬀness. For ultra-thin ﬁlms their measurement becomes diﬃcult. Mechanical characterization is often performed by instrumented indentation, which directly gives the hardness, and one combination of the elastic moduli [10,11]. However, when the ﬁlm thickness is reduced to tens of nanometers or even less, the requisite that indentation depth be signiﬁcantly smaller than ﬁlm thickness cannot be met, and the results are determined by the substrate rather than by the ﬁlm. Other means have then to be exploited to measure the elastic moduli. As discussed above, SBS, allowing the measurement of acoustic waves of wavelength down to a quarter of a micron, is a precious tool. We review here BS measurements performed on tetrahedral amorphous carbon (ta-C) ﬁlms deposited using an S-Bend Filtered Cathodic Vacuum Arc (FCVA) with an integrated oﬀ-plane double bend (S-Bend) magnetic ﬁlter; the deposition chamber was evacuated to 10−8 Torr. This deposition method proved able to deposit ta-C ﬁlms with particle area coverage of less than 0.01% and uniform thickness [48]. Samples of thickness ranging from 2 to 8 nm were considered, together with a bare silicon substrate, which is in reality covered by a thin layer of native oxide due to exposure to air. The thickness and mass density of the ﬁlms were obtained by X-ray reﬂectivity measurements, performed on a Bede GXR1 reﬂectometer with CuKβ radiation. Reﬂectivity curves for supported ﬁlms typically consist of a critical angle peak, followed by a long decay. Superposed on this decay are oscillations (interference fringes) due to the interference of waves reﬂected from the surface and the substrate interface. Usually, the density is directly derived from the critical angle [48]. However, for thickness below about 20 nm the X-ray evanescent wave reaches the substrate; consequently, the critical angle turns out to be determined by the substrate rather than by the ﬁlm. The ﬁlm density must then be derived by a ﬁt of the whole experimental reﬂectivity curve to a simulated scattering curve computed from model structures [49]; this was performed by the Bede REFS-MERCURY code [50]. For low thickness the interference fringes on the decay become wider, and their number is

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reduced. However, comparison of the reﬂectivity proﬁles from the bare silicon and from the coated samples shows evidence of at least one broad fringe, from which the thickness can be measured. It is known from measurements on thicker ta-C ﬁlms [51] that in this kind of ﬁlms the properties can have a gradient in proximity of the outer surface and the inner interface, the mass density declining when approaching the two surfaces. Also in these nanometric ﬁlms the X-ray measurements gave indications of such a gradient: the ﬁt to the experimental reﬂectivity curve improved if a three-layer model was considered, with thin layers of lower density on the two sides of the main carbon ﬁlm. However, adopting such a three-layer model the individual layer properties could not be identiﬁed with good precision. Furthermore, characterization of the elasticity of a three-layer model requires six independent parameters, and their identiﬁcation would remain an undetermined problem. In order to avoid these complexities, both the X-ray and SBS results were interpreted in a consistent way, modeling the ﬁlms as single homogeneous equivalent ﬁlms, with a sharp interface with the substrate. SBS measurements were performed at room temperature exploiting the 514.5 nm line of an Argon ion laser and a 3 + 3 passes tandem interferometer [2], the type of spectrometer most commonly adopted in Brillouin spectrometry. Measurements were performed in backscattering, with incidence angle ranging from 30◦ to 70◦ . SAW propagation was along the [100] direction on the (001) face of the Si substrate. The incident light was p-polarised, the scattered light being collected without polarisation analysis. The incident power on the specimen was around 100 mW, focused into a spot of the order of 103 µm2 ; irradiation did not induce ﬁlm modiﬁcations. Films of such low thickness do not alter the spectrum of SAWs of the substrate: the Rayleigh wave undergoes a slight modiﬁcation of its velocity, but remains the only type of SAW supported by this structure. As indicated in Sect. 3, its velocity was computed [9] as a function of the elastic constants and mass density of both the ﬁlm and the substrate, of ﬁlm thickness and of the wavevector k . The anisotropy of crystalline silicon was fully taken into account; accepted values of its properties (C11 = 166 GPa, C12 = 63.9 GPa, C44 = 79.6 GPa, ρ = 2.33 g/cm3 [52]) were adopted. The ﬁlm thickness and mass density were obtained by X-rays, as indicated above, and the SAW wavevector k was determined by the laser wavelength and the scattering geometry. The Rayleigh wave velocity remained thus a function of the unknown elastic constants of the ﬁlm. The ﬁlm being isotropic, the elastic properties were represented, as indicated in Sect. 3, by the (E, G) couple of moduli. The velocity for each value of k is computed (see (5)) as vi comp. (E , G), obtaining a sum of squares χ2 (E, G) whose minimum identiﬁes the most probable values of E and G, and whose isolevel curves identify the conﬁdence regions.

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Fig. 2. 90%, 95% and 99% conﬁdence regions, having a valley shape, obtained ﬁtting DLC ﬁlms dispersion relation in the E, G plane. Continuous lines: ν = 0 and ν = 0.5 physical limits and ν = 0.1, 0.2, 0.3, 0.4 isolevel lines; dashed lines: B = 100, 200, 300, 445 GPa isolevel lines. The line B = 445 GPa = B diam is taken as the physical upper bound delimiting the acceptable part of the conﬁdence regions

The χ2 (E, G) function turns out, in this case, to have the shape of a valley that extends from the neighborhood of the ν = 0.5 line into the region in which ν < 0. The bottom of this “valley” is relatively ﬂat and does not reliably identify a small region in the (E, G) plane; instead, it identiﬁes a “strip” running through wide ranges of E and G, and also of B and ν. In order to delimit the range of acceptable results, only the part of any conﬁdence region is considered that corresponds to positive values of Poisson’s ratio (see Sect. 3) and to values of bulk modulus B below a predetermined upper limit. The bulk modulus of diamond, B diam = 445 GPa, was adopted as physically plausible upper limit for B. The conﬁdence regions run across the region delimited by these acceptability limits, meaning that ν and B remain essentially undetermined, while the part of the conﬁdence region compatible with these limits corresponds to reasonably well deﬁned intervals of E and G. The acceptable part of the conﬁdence regions must be seen as the meaningful information that can be obtained from the SBS measurements. Further resolution within the conﬁdence regions does not have real signiﬁcance. The values of the elastic constants corresponding to the center of the 90% conﬁdence region allow us to ﬁt the measured dispersion relations, as shown in Fig. 2. The dispersion relations computed by the most probable parameter values are compared to the measured ones in Fig. 3.

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Fig. 3. Measured and computed dispersion relations for six thin ﬁlms on silicon substrate. Dispersion relations presented as function of the nondimensional product k h are independent from ﬁlm thickness and depend only on ﬁlm properties. From bottom to top: ∗ and ×, two ﬁlms of native silicon oxide of diﬀerent thickness and indistinguishable properties (they fall on the same line); and , two DLC ﬁlms of 3.5 nm and 4.5 nm thickness, of very similar properties (they fall on nearby lines); ◦, DLC ﬁlm of 15 nm thickness. , DLC ﬁlm of 8 nm thickness, stiﬀer than all the other ﬁlms

6 Nanotubes Single-wall carbon nanotubes (SWNT) can be thought as formed by warping a single graphitic layer into a cylindrical object [53]. Beyond possessing unique electronic properties, depending on the symmetry, or chirality, of the carbon lattice, nanotubes also attract much attention because they are expected to be very strong and to have high elastic moduli. The Young’s modulus of a carbon nanotube was estimated observing by transmission electron microscopy (TEM) the vibrations of the free end of a nanotube clamped at the other end [54], and by observing the nanotube bending by an atomic force microscope (AFM) [55]. These estimates (values up to 1.25 TPa) are consistent with the exceptionally high values of the Young’s modulus measured for a graphene sheet, i.e., about 1 TPa; such values imply very high stiﬀness-to-weight ratios. Acoustic vibrational properties are strictly related to elastic properties of SWNT, and acoustic vibrational modes in carbon nanotubes have been calculated both by ab initio calculation (lattice dynamics, e.g., [56]) and by continuum elastic models [57]. AFM and TEM measurements, beside being destructive, suﬀer from lack of precision in determining the SWNT diameter, length, temperature and vibrational fre-

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Fig. 4. Left: AFM image of the (top) oriented SWNT sample surface, and of the (bottom) nonoriented SWNT sample surface. Square area is 1 µm × 1 µm, z range is 1 nm. Right: scattering geometry with respect to the nanotube direction

quency; furthermore, the tendency of SWNT to form bundles complicates the analysis. Dynamic light scattering from longitudinal acoustic modes in aligned SWNT, with a wavelength of the order of hundreds of nm, has been measured by means of Brillouin spectroscopy; a model for the description of the phenomenon and for the calculation of the scattered intensity was also proposed. The model is based on a shell mechanical model and a surface elasto-optic eﬀect coupling the incident light to the tube thermal strains [58,59]. The sample was a free-standing ﬁlm of aligned SWNT, produced by the laser-oven method, puriﬁed and aligned with a strong magnetic ﬁeld [60]. SWNT are present in bundles or ropes, with a preferential orientation, as shown in Fig. 4. SWNT have instead a complete random orientation in nonaligned samples. The typical tube free length is on the order of several hundreds nanometer. BS measurements were performed exploiting the λ0 = 514.5 nm line of an Ar+ ion laser. The incident light was p-polarized, with a power of 40 mW; the scattered light, collected without polarization analysis, was analyzed by a Sandercock interferometer with a free spectral range of 100 GHz. Measurements were performed in backscattering, with the scattering geometry shown in Fig. 4: the scattering plane (determined by the scattering wavevector k = q s − q i and the normal z to the sample surface), the sample surface plane and the nanotube direction x ; α is the angle between the SWNT direction and the scattering plane xz; θi is the incidence angle, between incident light q i and z; β is the angle between x and q i (cos β = sin θi cos α). The incidence angle θi was varied in the range 30◦ –70◦ in order to vary the scattering wavevector k; measurements were performed with α = 0◦ and α = 90◦ (scattering plane parallel and perpendicular to the nanotube direction).

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Fig. 5. (a) Brillouin spectra for the oriented SWNT sample along the tube direction (α = 0◦ ; θi = 30◦ , 70◦ ), and perpendicularly to the tube direction (α = 90◦ ; θi = 30◦ ). (b) Brillouin spectrum of a nonaligned SWNT (θi = 50◦ )

The experimental results show that scattering does not occur from SAWs as in thin ﬁlms, but from longitudinal acoustic modes of the single tube, having a wavevector k ph parallel to the tube axis. In spectra from the oriented SWNT sample (θi = 30◦ , 70◦ ), with α = 0◦ , a broad peak is detected at about 45 GHz (Fig. 5), and its position is independent of the incidence angle. When the scattering plane is instead perpendicular to the SWNT direction (α = 90◦ ), the feature disappears (Fig. 5). A spectrum from a randomly oriented SWNT sample is also shown (θi = 50◦ ), with a broad feature at about 40 GHz. This feature does not change as the sample is rotated by 90◦ (α = α + 90◦ ), showing the in-plane isotropy of the ﬁlm. The absence of scattering from aligned tubes for α = 90◦ and the peak shift and width for α = 0◦ conﬁrm the relative independence between the tube bundles, and that the material is not an eﬀective medium where acoustic waves can propagate in all directions, at least at the scale of the laser wavelength λ0 . A cylindrical shell model provides an adequate description for this scattering phenomenon. For a long cylindrical thin shell the elastodynamic equations can be written in cylindrical coordinates (x , r, φ) and a membrane approximation can be used [61]. This model, described by 2D stress conditions and membrane elastic constants having the dimension of a force per unit length, is precise enough to describe thermally excited modes along the tube axis,

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with frequency in the range 1–100 GHz, responsible for the observed BS. The elastodynamic equations admit plane wave solutions traveling along the axial direction with wavevector k ph , i.e., ux = A u0 exp[i(k ph x − ωt + mφ)], with m an integer. The mode frequency ω depends on the 2D Young’s modulus E 2D , the surface density ρ2D , the Poisson’s ratio ν, and the SWNT radius R. For an inﬁnitely long tube these are the appropriate solutions; for tubes of ﬁnite length L the proper boundary conditions aﬀect the form of the solution and the corresponding frequencies. A surface elasto-optic eﬀect is assumed, coupling the light to the tube thermal phononic strains and producing a ﬂuctuating surface polarization density that radiates the scattered photons. The intensity of the light scattered by a single tube is related to the Fourier transform of the dielectric susceptibility tensor and to the polarization of the incident light. It results from the computed cross section that, in backscattering, only longitudinal modes with m = 0 contribute to the scattered intensity, provided that the component k = (4π/λ0 ) cos β = (4π/λ0 ) sin θi cos α of the scattered wavevector k parallel to the tube is not zero (there must be a nonvanishing component of transferred wavevector, i.e., the scattering plane must not be perpendicular to the SWNT orientation). In the case of an inﬁnite tube (L 2π/k ph ) the cross section is nonzero only if the parallel wavevector is conserved (k = k ph ). This would be a coherent “line Brillouin scattering”, with only one longitudinal wave (determined by the selected value of k ph ) contributing to the scattered intensity, and the corresponding peak position depending on the incidence angle (dispersion of the modes). Instead, in the measurements published in [58], the θi dependence of the peak position is negligible, because the free SWNT length is of the order of 1 µm or less: the tubes cannot be considered as inﬁnite with respect to the wavelength (λ = λ0 /2 cos β L) of the modes selected by BS. Thus, all longitudinal modes (ﬁxed end boundary conditions) with m = 0 contribute to scattering, due to conﬁnement eﬀects, with relative weights given by the computation. This kind of scattering is often called low-frequency Raman scattering. Contributions from tubes of diﬀerent lengths (0.5–1.5 µm) were considered, and assuming ρ2D = 7.6 × 10−7 kg/m2 , R = 6 × 10−10 (by Raman spectroscopy measurements) and ν = 0.2, a feature with a shape similar to that observed was obtained, independent of the scattering angle. The broadening of the peak can be related to length and orientation distributions, tube interactions, and real boundary conditions. The 2D Young’s modulus can be estimated by ﬁtting the computed peak position to the measured one and a value E 2D = 100 N/m is obtained, on the order of magnitude of the C–C atomic force constant in a graphite plane [62]. Taking into account the thickness of a graphite layer, the estimated E 2D value corresponds to a Young’s modulus for the curved graphitic sheet of the order of 1 TPa, compatible with known values of C11 for graphite [37].

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7 Conclusions We have presented Brillouin scattering (BS) as a nondestructive, contactless, powerful characterization technique capable of studying structural and mechanical properties of bulk materials, thin ﬁlms and nanostructures. In particular elastic properties are accessible through the observation of thermally excited acoustic modes propagating in the medium. The experimental technique and the derivation of the elastic constants have been described together with some results on diﬀerent carbon materials in order to show the capabilities of this technique. In conclusion, BS turns out to be an interesting tool which proved to be able to characterize a wide variety of materials, and namely carbon-based materials.

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Index ta-C, 162, 163

graphite, 161

acoustic phonon, 154 acoustic waves, 153 acoustic wave velocity, 154, 155, 157, 159, 160, 163 surface acoustic waves (SAWs), 154, 155, 157–159, 162, 164, 168 pseudo surface waves (PSAWs), 159 SAW velocity, 154, 155, 159 amorphous carbon thin ﬁlms, 163

hydrogenated amorphous carbon, 162

Brillouin scattering, 153–159, 161–164, 167–170 surface Brillouin scattering, 157, 163–165 diamond, 161 diamond-like carbon (DLC), 162, 164–166 dispersion, 166

inelastic scattering, 153 light scattering, 154 low-frequency Raman, 169 mechanical properties, 153 nanostructured carbon, 162 nanotubes, 166 single-walled nanotubes (SWNT), 166, 167 single-walled nanotubes (SWNTs), 156, 162, 167–169 quasi- elastic scattering, 154

elastic constants, 155, 156, 158, 160–162, 164, 165, 168 elastic moduli, 155, 159–161, 163, 166 elastic properties, 154, 155, 170 elastic scattering, 153

Raman scattering, 154 Rayleigh wave, 154, 155, 159, 162, 164 modiﬁed Rayleigh wave, 159, 160 modiﬁed Rayleigh wave velocity, 160, 163 Rayleigh wave velocity, 154, 161, 162, 164

fullerite, 162

Sezawa wave, 155, 159, 160, 162

graphene, 162

ultra-thin carbon ﬁlms, 156, 162–166

Electrical Resistivity and Real Structure of Magnetron-Sputtered Carbon Films Alexei A. Onoprienko Institute for Problems of Materials Science, National Academy of Sciences of Ukraine, 3 Krzhyzhanovsky St., UA-03142 Kiev, Ukraine [email protected] Abstract. The resistivity and structure of DC magnetron-sputtered carbon ﬁlms is studied. The ﬁlm structure is examined by Raman spectroscopy, transmission electron microscopy, and electron diﬀraction. The ﬁlms reveal prominent resistivity anisotropy relating to ﬁlm structure. In the range of deposition temperatures 20– 450◦ C, ordered regular aromatic rings and graphite-like clusters form. In the range 450–650◦ C, the growth mechanism changes and graphite phase forms directly on the substrate. Annealing of ﬁlms in the range 50–300◦ C results in transformation of distorted aromatic rings into regular ones, and in ordering them without formation of graphite fragments. Further increase in the annealing temperature causes little changes the ﬁlm structure. Ion bombardment in the range of substrate bias voltage −20 ≤ V bias ≤ −150 V decreases cluster size and results in disordering in their internal structure. At V bias > −150 V the cluster structure tends to be more ordered towards graphitization. The results obtained open the way for deposition of carbon ﬁlms with controllable electrical properties.

1 Introduction The great interest in diamond and diamond-like carbon (DLC) ﬁlms as promising materials for microelectronics stems from their speciﬁc electrical properties. However, when using diamond ﬁlms, problems arise connected with their polycrystalline structure. Diamond ﬁlms have a well-developed net of grain boundaries that aﬀect the electrical properties of ﬁlms. In this respect DLC or amorphous carbon (a-C) ﬁlms are preferable since they are smooth and do not contain well-developed grain boundaries. In many studies [1, 2, 3, 4, 5, 6, 7, 8, 9], it has been shown that the substrate temperature and energy of carbon species constituting the growing ﬁlm are the parameters that govern the structure and properties of carbon ﬁlms the most. Depending on the deposition method and conditions, the carbon ﬁlms can be deposited with a variety of properties ranging from diamond-like to graphite-like. The ﬁlm resistivity, being a structure-sensitive property, is also dependent on deposition conditions. However, in spite of the fact that a number of works deal with the eﬀects of deposition [1,2,3,4,5] and heat treatment temperature [10, 11, 12, 13] and ion energy [5, 6, 7, 8, 9] on the microstructure and properties of a-C ﬁlms prepared by various techniques, there do not seem to be any systematic studies on the electrical resistance of a-C ﬁlms. G. Messina, S. Santangelo (Eds.): Carbon, The Future Material for Advanced Technology Applications, Topics Appl. Phys. 100, 175–186 (2006) © Springer-Verlag Berlin Heidelberg 2006

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Fig. 1. Schematic draw of specimen with Ni contacts (1–1 and 2–2 ) and carbon ﬁlm for resistance measurements

In the aforementioned studies, the electrical resistance was measured only as a subsidiary parameter along with other properties of a-C ﬁlms. Moreover, in all of them the resistance (or conductivity) was measured only in one direction: either parallel or perpendicular to the substrate surface. Conversely, in our previous study [14] we reported, for the ﬁrst time, the phenomenon of prominent resistivity anisotropy in a-C ﬁlms deposited by DC magnetron sputtering, the extent of which depends on deposition temperature. The present study focuses on the relationship between structure and electrical resistivity evolution with substrate temperature and ion bombardment (IB) intensity of carbon ﬁlms, which may favour understanding the mechanism of ﬁlm microstructure formation. Electron diﬀraction (ED) and Raman scattering were chosen as the methods sensitive to the structure. These studies were supplemented by measurements of ﬁlm resistivity and by transmission electron microscopy (TEM).

2 Experimental The a-C ﬁlms were sputter-deposited using a planar DC magnetron system of balanced type with graphite target, and argon at pressure of 1 Pa as a sputtering gas. As substrates, cleavages of NaCl single crystals (for electron diﬀraction and electron microscopic studies) and polished platelets of Si–Ti– Al–O ceramics (for Raman spectroscopy and resistance measurements) were used. For resistance measurements, specially conﬁgured 150 nm thick nickel ﬁlm contacts (1–1 and 2–2 , Fig. 1) were magnetron sputter-deposited onto substrates before (1–1 ) and after (2–2 ) C-ﬁlm deposition. Three series of specimens were prepared for study. In one series, ﬁlms were deposited onto substrates preheated to a given temperature in the range 20 − 650◦C. In the second series, the carbon ﬁlms were deposited onto substrates approximately at room temperature followed by annealing for 1 h in a vacuum of 1.3 × 10−3 Pa at diﬀerent temperatures in the range 50–650◦C. During deposition in the above two series, the substrates were at a ﬂoating potential of approximately V bias −20 V. In the third series, carbon ﬁlms

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were deposited onto substrates at room temperature, but DC negative bias voltage in the range V bias = −25 V to −175 V was applied to lower metal contacts (1–1 in Fig. 1) during ﬁlm deposition. It has to be noted that carbon ﬁlms in all series were deposited at low magnetron power in order to prevent uncontrollable heating of the substrates by plasma radiation [15]. The resistance of C-ﬁlms was measured in two directions: parallel (R ) and perpendicular (R⊥ ) to substrate surface (see Fig. 1). Film resistivities ρ and ρ⊥ were calculated from the measurements of R and R⊥ , the surface area and thickness of carbon ﬁlm between respective metal contacts. The resistivity anisotropy coeﬃcient was deﬁned as κ = ρ⊥ /ρ . The ﬁlm thickness was measured with an optical interferometer, 400– 600 nm, on ceramic substrates. Thickness of the ﬁlms deposited onto NaCl for TEM and ED was 60–80 nm. Raman scattering was induced by the λ = 514.5 nm line of argon laser. The recorded spectra were ﬁtted to the sum of two Gaussian-shape lines (G band centered at approx. 1580 cm−1 and the D band centered at approx. 1360 cm−1 ) and a linear background term.

3 Results and Discussion 3.1 Substrate Temperature Eﬀects Figure 2a shows the dependence of logarithm ρ⊥ on the substrate temperature during deposition (T dep) and annealing (T ann ) temperature (T ann ). As seen, ρ⊥ decreases with increase in both T dep and T ann , but this change is not large. At the same time, those dependencies for ρ exhibit an essentially diﬀerent character (Fig. 2b). An increase in T dep results in immediate decrease in ρ at T dep ≥ 50◦ C. It decreases with temperature change up to T dep ≈ 400◦C, but with further increase in T dep up to 650 ◦C it remains unchanged. Contrary to this, a-C ﬁlms deposited at room temperature and further annealed exhibit constancy of ρ in the range T ann = 50 to 300◦ C, and only at T ann > 300◦ C does ρ decrease with the increase in annealing temperature. In Fig. 2c the dependence of the logarithm of resistivity anisotropy coefﬁcient on T dep and T ann is shown. For ﬁlms deposited at diﬀerent values of T dep, κ increases in the range of deposition temperatures 20–400◦C and then slightly decreases at higher deposition temperatures. For ﬁlms deposited at room temperature and annealed at diﬀerent temperatures, κ is nearly constant in the range 50–300◦C and then it increases with further increase in T ann . In Fig. 3a the dependence of integral intensity ratio I D /I G of D and G peaks on the T dep and T ann is shown. For ﬁlms deposited at diﬀerent substrate temperatures, I D /I G increases in the range 20–400◦C and then decreases with further increase in T dep. For ﬁlms deposited at room temperature and then annealed, the intensity ratio I D /I G increases rapidly with increase

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Fig. 2. Carbon ﬁlm resistivity ρ⊥ (a), ρ (b), and resistivity anisotropy coeﬃcient κ = ρ⊥ /ρ (c) as a function of (1) deposition and (2) annealing temperatures

in annealing temperature in the range 50–300◦C, but then it increases at a lower rate. Figure 3b shows the dependence of the G-peak position on temperatures T dep and T ann. With increase in temperature of deposition or annealing, the G-peak position shifts towards higher frequencies in both cases. Electron diﬀraction revealed that carbon ﬁlms deposited at room temperature and then annealed in the range 50–650◦C were amorphous, and ED patterns consisted of three–four diﬀused halos corresponding to d ∼ = 0.30, 0.20, 0.16, 0.11 nm that are close to the interplanar distances of a graphite (0.338, 0.212, 0.169, 0.115 nm, respectively). The carbon ﬁlms deposited at substrate temperatures in the range 20–400◦C were also amorphous. Only at T dep > 500◦ C were halos transformed into broadened diﬀraction lines peculiar to the structure of polycrystalline graphite. The observed anisotropy and the character of changing electrical resistance in carbon ﬁlms studied can be explained in terms of C-ﬁlm microstructure. In accordance with the model proposed earlier [14], upon magnetron sputtering the C-ﬁlms form with predominantly sp2 -bonds that are distrib-

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Fig. 3. Integral intensity ratio I D /I G (a) and G-peak position (b) as a function of (1) deposition and (2) annealing temperatures

uted chaotically within the ﬁlm volume. ED shows that ﬁlms deposited at low (room) temperature are amorphous. However, the presence of a D peak in the Raman spectra indicates that a-C ﬁlms contain aromatic rings [16]. At the same time, the coeﬃcient of resistivity anisotropy κ ∼ = 1 for such ﬁlms (Fig. 2c) is peculiar to isotropic structure. On the basis of this, it can be assumed that aromatic rings that form within the structure of C-ﬁlms at low temperature are strongly distorted and mutually disordered. Such a model of a-C ﬁlm microstructure is justiﬁable since there is information that C-ﬁlms deposited by DC magnetron sputtering and laser ablation of graphite at low temperature also contain distorted ﬁvefold and sixfold rings [17, 18]. As deposition temperature increases in the range 20–400◦C, the formation of regular (nondistorted) aromatic rings becomes more probable and ordering of them into sp2 -bonded clusters takes place. This is supported by growth of I D /I G (Fig. 3a) in this temperature range because, as pointed out in [16], the intensity of the D peak increases with the number of aromatic rings with sixfold symmetry and degree of ordering them. The number of sp2 -bonded clusters increases with an increase in T dep, and the ﬁlm forms with a more graphite-like structure, which is indicated by increase in κ (Fig. 2c). Shifting of the G-peak position towards higher frequencies with increase in T dep (Fig. 3b) also indicates graphitization of the a-C ﬁlm. The graphitization of

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C-ﬁlms deposited by various techniques at elevated substrate temperatures was also observed in [2, 4, 18, 19]. Since electron diﬀraction patterns from C-ﬁlms deposited at diﬀerent substrate temperatures in the range 20–400◦C are similar (halos), it is clear that: (i) the short-range atomic order in a-C ﬁlms with a structure based on sp2 bonding remains unchanged, and (ii) the sizes of graphite-like clusters are so small that structural changes within the clusters are below the sensitivity limit of the method used (ED). The graphite crystallites of very small size (nanocrystallites) have been also detected in electron microscopic and scanning tunnelling microscopic examination of a-C ﬁlms deposited by DC magnetron sputtering and laser-arc evaporation at elevated substrate temperatures [17, 20]. Further increases in T dep over 400◦C results in direct nucleation and growth of a ﬁne-grained graphite phase onto the substrate. This is indicated by ED patterns, which contain broadened lines peculiar to a polycrystalline graphite phase, and also the temperature dependence of ratio I D /I G and Gpeak position at elevated temperatures (Figs. 3a, 3b). Nucleation and growth of graphitic ﬁlms at high temperatures is supported also by near constancy of the resistivity anisotropy coeﬃcient at T dep ≥ 450◦ C (Fig. 2c). The nature of changes in the microstructure of a-C ﬁlms annealed at various temperatures diﬀers from that of ﬁlms deposited at diﬀerent substrate temperatures. As seen from Fig. 2a, the dependence of ρ⊥ on temperature and the respective values of resistivity are virtually the same for both deposition and annealing. This means that structural changes are similar in ﬁlms of both types in the direction perpendicular to substrate surface. At the same time, annealing in the range 50–300◦C does not appreciably change ρ , but its absolute value remains higher than for ﬁlms deposited at the same temperatures. Only at T ann > 300◦ C does ρ decrease (Fig. 2b). Accordingly, the dependence of κ on T ann is diﬀerent: up to 300◦ C coeﬃcient κ is nearly constant and then changes similarly to the case of ﬁlm deposition at various temperatures. The ratio I D /I G increases with increase in T ann up to ∼ 300◦ C and then changes little (Fig. 3a). This indicates that postdeposition annealing also results in changing a-C ﬁlm microstructure towards graphitization. However, in contrast to the ﬁlms deposited at various temperatures, in this case only transformation of distorted aromatic rings into regular ones occurs. This process is the most intense in the annealing temperature range 50–300◦C. An increase in the number of regular aromatic rings in the ﬁlm structure, in accordance with ideas stated in [16], should give an increase in D-peak intensity and a shift of G-peak position towards higher frequencies, as actually observed in Figs. 3a, 3b. However, lengthy graphite fragments do not form in this case, and it is only at T ann > 300◦ C that the formation of graphite-like fragments seems to occur, reﬂected in the corresponding variation of κ with temperature (cf. Fig. 2c). Since the energy required for structure rebuilding with cluster formation is higher than for their formation

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during deposition, then the microstructure of a-C ﬁlms changes little with further increase in T ann, corresponding to the dependence for κ and I D /I G in that temperature range. This conclusion is also supported by the results of the electron diﬀraction study: even after annealing at 650◦ C the respective ED pattern contain very diﬀused halos. 3.2 Substrate Bias Eﬀects In this set of experiments NaCl single-crystal cleavages with Ni contacts (1–1 in Fig. 1) were used as substrates, and DC bias voltage in the range V bias = −25 V to −175 V was applied to contacts during ﬁlm deposition. Because NaCl is essentially a low-conductivity material, such a conﬁguration resulted in bombardment with ions of growing ﬁlm on contacts and in a close vicinity of contacts, while areas far from contacts were not subject to ion bombardment (IB) [21]. In Figs. 4a, 4b the TEM micrographs of carbon ﬁlm deposited at V bias = −175 V are shown for the areas in which the ﬁlm was subject and was not subject to IB, respectively. As can be seen, the microstructures of these parts of the C-ﬁlm are quite diﬀerent. The C-ﬁlm area grown without the IB consists of round-shaped partially faceted “grains” (Fig. 4b), whereas the ﬁlm area grown under intense IB consists of elongated “grains” with clearly seen internal structure (Fig. 4a). ED patterns from both areas are similar and coincide with those for amorphous carbon ﬁlms. However, in some cases ED patterns taken from ﬁlm areas aﬀected by intense IB contained an additional halo with d ∼ = 0.30 nm that is close to the d-spacing of graphite (002) basal plane. Note that such a prominent diﬀerence in ﬁlm structure was observed only at V bias > −100 V. Raman spectra were taken from the area in the middle between the contacts for the ﬁlms grown at diﬀerent values of substrate bias [21]. Analysis of Raman spectra recorded for the ﬁlms deposited at diﬀerent V bias revealed a nonmonotonous dependence of I D /I G on bias voltage (Fig. 5). The I D /I G ratio increases with increased bias voltage and reaches a maximum value at V bias ≈ −150 V, and then drops to the initial level at −175 V. It was not possible to investigate the dependence of resistivity anisotropy of C-ﬁlms on V bias due to particularities of the ﬁlm microstructure and variation of the thickness of such ﬁlms caused by the IB [21]. Only the ρ⊥ resistivity of these ﬁlms could be measured. The ρ⊥ values of C-ﬁlms deposited at diﬀerent V bias are listed in Table 1. From these data one can see that the IB results in an increase of ρ⊥ by more than an order of magnitude. Based on the interpretation of Raman spectra developed in [16, 22, 23], it is possible to assert that the increase in I D /I G with increasing bias voltage in the range of −25 < V bias < −150 V indicates the bond-angle disorder of internal structure of graphite-like clusters along with a decrease in their size. This is indicated also by an increase in ﬁlm resistivity ρ⊥ in this V bias

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Fig. 4. TEM micrographs of carbon ﬁlms subject to (a) and not subject to (b) intense IB during deposition

Fig. 5. Integral intensity ratio I D /I G as a function of substrate bias voltage V bias

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Table 1. Resistivity values for C-ﬁlms deposited in diﬀerent bias conditions Substrate bias V bias Resistivity ρ⊥ V Ω · cm Floating −100 −150 −175

1.5 × 104 1.2 × 105 2.9 × 105 2.2 × 105

range. An increase of V bias over −150 V results in a decrease in I D /I G and simultaneously in a decrease in ﬁlm resistivity ρ⊥ (drop-down branch on the plot in Fig. 5, and data in Table 1). The critical value of V bias ∼ = −150 V for maximum resistivity in our work is close to that found in [6, 24] for maximum values of various ﬁlm properties (optical gap, atomic density, etc.). The eﬀect of a decrease in both I D /I G and ρ⊥ with increasing IB intensity (above V bias = −150 V) relates to a certain bond-angle ordering within the graphite-like clusters (i.e., their graphitization) and to some increase of their size. A similar dependence of I D /I G on V bias was observed during a-C ﬁlm deposition by ion-beam sputtering of a graphite target with simultaneous bombardment by argon ions of the growth surface [25]. It was revealed that at low ion energy both ﬁlm density and sp3 concentration are low. The maximal value of the ﬁlm density and the minimal size of ﬁlm-forming clusters were achieved at about 100 eV. A further increase in the ion energy promoted the decrease of ﬁlm density, and the appearance and increase in the size of graphite regions together with local microstructural ordering within them. The most probable reason for these eﬀects could be the development of local high-temperature spikes caused by the collision cascades arising during enhanced IB [26]. TEM investigations of our ﬁlms allow us to assume that the dense, roundshaped or partially faceted “grains,” observable in Fig. 4b, are the crosssections of the columns disposed normally to the substrate, which form the ﬁlm in the area where the IB is almost absent. The “grains” observable in micrographs taken from a-C ﬁlm area subject to intense IB also have columnar structure (Fig. 4a), but in contrast to Fig. 4b, these columns are strongly tilted to the substrate. As it follows from the micrographs, the column width in Fig. 4a is approximately equal to the diameter of the columns in Fig. 4b. This means that the columns from both areas are similar. At the same time, on some of ED patterns from an area of ﬁlm subject to intense IB the halo appeared with d -spacing of about 0.30 nm, which is close to (002) d -spacing of graphite. This halo was never observed in ED patterns from ﬁlm that was not subject to IB. The (002) reﬂection in the transmission ED pattern indicates that the graphite-like planes are arranged nearly parallel to the electron beam, i.e., these planes are perpendicular to the substrate. In other words, the “c-axis” of graphite-like clusters forming the columns that are arranged

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along the substrate (columns in Fig. 4a) is parallel to the substrate surface, whereas the graphite-like clusters forming the columns arranged perpendicular to the substrate (Fig. 4b) have “c-axis” directed perpendicular to the substrate surface.

4 Conclusion On the basis of the results obtained, it is possible to deduce what follows. Magnetron-sputter deposition at low temperature results in the formation of amorphous carbon ﬁlms with predominantly sp2 bonds between atoms. The microstructure of such ﬁlms consists of chaotically displaced and distorted aromatic rings and graphite fragments. This structure is close to an isotropic one, so there is virtually no resistivity anisotropy. As the deposition temperature is raised in the range 20–450◦C, more regular sixfold aromatic rings and graphite-like clusters form on the substrate. The extent of aromatic ring ordering and cluster growth is greatest at T dep ∼ 450◦C. Graphitization of the ﬁlm occurs mainly in the direction parallel to the substrate surface that is indicated by electron diﬀraction patterns and the dependence of resistivity on the deposition temperature. An increase in deposition temperature above 450◦ C results in changing the formation mechanism for carbon ﬁlms, and the nuclei of the graphite phase form directly on the substrate. Increasing the temperature in the range 450–650◦C also results in growth of clusters with an ordered inner structure. This is evidenced by the drop in the dependence of I D /I G on deposition temperature, the appearance of ED patterns peculiar to ﬁne-grained polycrystalline graphite, and the stabilization of the resistivity anisotropy coeﬃcient at maximum level. Annealing in the range 50–300◦C of a-C ﬁlms deposited at room temperature results in the intense transformation of distorted aromatic rings into regular ones, and in ordering them in the substrate plane without formation of graphite fragments. Further increase in the annealing temperature up to 650◦ C has little inﬂuence on the structural changes in ﬁlm, and graphite-like clusters do not form in this case. This inference is supported by the dependencies for ρ and κ, and the absence of “graphite” lines in the ED patterns over the entire annealing temperature range studied. Ion bombardment of growing C-ﬁlm aﬀects its structure and therefore resistivity. In the range of substrate bias voltage −20 < V bias < −150 V the size of graphite-like clusters within C-ﬁlms decreases and simultaneously increases their internal structural disorder. At V bias > −150 V the cluster structure tends to be more ordered towards its graphitization. The microstructure of C-ﬁlms is of columnar type, and columns are built of packs of graphite-like clusters that are ordered somehow within the columns. When the intensity of IB is low (or absent) the c-axis of these clusters is oriented predominantly perpendicular to the growth surface, while the enhancement of the IB promotes the reorientation of the c-axis predominantly along the

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growth surface. The observed variations in C-ﬁlm resistivity occur according to ﬁlm microstructure changes.

References [1] N. H. Cho, D. K. Veirs, J. W. Ager III, et al.: J. Appl. Phys. 71, 2243 (1992) 175 [2] E. Mounier, F. Bertin, M. Adamik, et al.: Diamond Relat. Mater. 5, 1509 (1996) 175, 180 [3] J. Koskinen, J. P. Hirvonen, J. Keranen: J. Appl. Phys. 84, 648 (1998) 175 [4] B. K. Tay, X. Shi, E. J. Liu, et al.: Thin Solid Films 346, 155 (1999) 175, 180 [5] M. Chhowalla, J. Robertson, C. W. Chen, et al.: J. Appl. Phys. 81, 139 (1997) 175 [6] P. J. Fallon, V. S. Veerasamy, C. A. Davis, et al.: Phys. Rev. B 48, 4777 (1993) 175, 183 [7] Y. Lifshitz, G. D. Lempert, S. Rotter, et al.: Diamond Relat. Mater. 3, 542 (1994) 175 [8] M. Gioti, S. Logothetidis: Diamond Relat. Mater. 7, 444 (1998) 175 [9] F. Rossi: Chaos, Solitons & Fractals 10, 2019 (1999) 175 [10] L. G. Jacobson, R. Priorli, F. L. Freire Jr., et al.: Diamond Relat. Mater. 9, 680 (2000) 175 [11] T. A. Friedman, K. F. McCarty, J. C. Barbour, et al.: Appl. Phys. Lett. 68, 1643 (1996) 175 [12] S. Anders, J. W. Ager III, G. M. Pharr, et al.: Thin Solid Films 308-309, 186 (1997) 175 [13] A. C. Ferrari, B. Kleinsorge, N. A. Morrison, et al.: J. Appl. Phys. 85, 7191 (1999) 175 [14] A. A. Onoprienko, L. R. Shaginyan: Diamond Relat. Mater. 3, 1132 (1994) 176, 178 [15] A. A. Onoprienko, V. V. Artamonov, I. B. Yanchuk: Surf. Coat. Tech. 200, 4174 (2006) 177 [16] A. C. Ferrari, J. Robertson: Phys. Rev. B 61, 14095 (2000) 179, 180, 181 [17] B. Marchon, M. Salmeron, W. Siekhaus: Phys. Rev. B 39, 12907 (1989) 179, 180 [18] S. Bhargava, H. D. Bist, A. V. Narlikar, et al.: J. Appl. Phys. 79, 1917 (1996) 179, 180 [19] M. A. Capano, N. T. McDevitt, R. K. Singh, F. Qian: J. Vac. Sci. Technol. A 14, 431 (1996) 180 [20] I. Alexandrou, H. J. Scheibe, C. J. Kiely, et al.: Phys. Rev. B 60, 10903 (1999) 180 [21] L. R. Shaginyan, A. A. Onoprienko, V. F. Britun, V. P. Smirnov: Thin Solid Films 397, 288 (2001) 181 [22] S. Fujimaki, M. Kitoh, K. Furusawa, et al.: Diamond Films and Technol. 2, 17 (1992) 181 [23] D. Beeman, J. Silverman, R. Lynds, M. R. Anderson: Phys. Rev. B 30, 870 (1984) 181

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[24] J. Ishikawa, Y. Takeiri, K. Ogawa, T. Takagi: J. Appl. Phys. 61, 2509 (1987) 183 [25] F. Rossi, B. Andre, A. van Veen, et al.: J. Appl. Phys. 75, 3121 (1994) 183 [26] L. K. Cheah, X. Shi, B. K. Tay, E. Liu: Surf. Coat. Tech. 105, 91 (1998) 183

Index a-C, 175, 176, 181 sp2 -bonded clusters, 179–181, 183

graphitization, 175, 179, 180, 184 ion bombardment (IB), 176, 181–184

annealing, 175–180, 184 clustering graphite-like clusters, 175, 180, 181, 183 D band, 177, 179, 180 D/G band intensity ratio, 177, 179–184 diamond-like carbon (DLC), 175

magnetron sputtering, 176 microstructure, 175, 176, 178–181, 183, 184 graphite-like structure, 179, 183 Raman spectroscopy, 176, 179–181 resistivity, 175–178, 180, 181, 183 resistivity anisotropy, 175–181, 184

electron diﬀraction (ED), 176–181, 183, 184

substrate bias, 181

G band, 177–180 graphite-like carbon (GLC), 175

transmission electron microscopy (TEM), 176, 177, 181–183

Formation, Atomic Structures and Properties of Carbon Nanocage Materials Takeo Oku1 , Ichihito Narita1 , Atsushi Nishiwaki1 , Naruhiro Koi1 , Katsuaki Suganuma1 , Rikizo Hatakeyama2, Takamichi Hirata2 , Hisato Tokoro3, and Shigeo Fujii3 1

2 3

Institute of Scientiﬁc and Industrial Research, Osaka University, Mihogaoka 8-1, Ibaraki, Osaka 567-0047, Japan Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan Hitachi Metals Co. Ltd., Advanced Electronics Research Laboratory, Mikajiri 5200, Kumagaya, Saitama 360-0843, Japan [email protected]

Abstract. Various carbon nanocage fullerene materials (clusters, metallofullerenes, onions, nanotubes, nanohorns and nanocapsules) were synthesized by electron-beam irradiation, chemical reaction, hybrid arc discharge, and self-organization. Atomic structures and structural stability of these materials were investigated by highresolution electron microscopy, molecular dynamics, and molecular orbital calculations. Photoluminescence as well as magnetic and electronic properties of these fullerene materials were also investigated. The present work indicates that the new carbon nanocage fullerene materials with various atomic structures and properties can be produced by various synthesis methods, and a guideline for designing the carbon fullerene materials is summarized.

1 Introduction Carbon has various hollow-cage nanostructures such as C60 , giant fullerenes, nanocapsules, onions, nanopolyhedra, cones, cubes, and nanotubes [1, 2, 3, 4, 5, 6, 7]. These C structures show diﬀerent physical properties, and have the potential of studying materials of low dimensionality within an isolated environment. In particular, cluster-included fullerene materials are intriguing for both scientiﬁc research and device applications such as cluster protection, cluster separation, nano-ball bearings, nano-electronic–magnetic devices, gas storage, and biotechnology [8, 9, 10, 11, 12, 13, 14]. By controlling of the size, layer numbers, helicity, compositions, and included clusters, the cluster-included C nanocage structures with band-gap energy of 0–1.7 eV and nonmagnetism are expected to show various electronic, optical, and magnetic properties such as Coulomb blockade, photoluminescence, and superparamagnetism, as shown in Fig. 1a. Possible applications of the C fullerene materials are also shown in Fig. 1b. The direction of the research on carbon nanocage materials is threefold. The ﬁrst is to prepare the new C nanocage fullerene materials. In the present G. Messina, S. Santangelo (Eds.): Carbon, The Future Material for Advanced Technology Applications, Topics Appl. Phys. 100, 187–216 (2006) © Springer-Verlag Berlin Heidelberg 2006

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Fig. 1. (a) Structures and properties of C fullerene materials. (b) Applications and future of C fullerene materials

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work, various methods such as electron-beam irradiation, chemical reaction, hybrid arc discharge, and self-organization techniques were selected for the formation of the fullerene materials. Nanocapsules and onions are expected to form at low temperatures compared to the ordinary arc-discharge method. Au clusters were selected for the C nanocapsule formation. Arc-discharge, electron-beam irradiation and chemical synthesis techniques were applied for the fullerene formation. One-dimensional carbon nanocage arrangement was also tried by using self-organization of metal nanoparticles with a size below 10 nm. Gold colloids have been used for the formation of single-electron transistors [15, 16]. In the present work, Au nanoparticles were selected because of easy control of cluster size [17]. Fabrication of one-dimensional Au nanodots and nanowires encapsulated in carbon nanocage structures was tried by annealing the one-dimensional self-organized nanoparticles on carbon thin ﬁlms. The second direction is to understand the formation mechanism and microstructure of these C nanocage fullerene materials from high-resolution electron microscopy (HREM), which is a powerful method for structure analysis at the atomic scale [18, 19, 20]. Energy dispersive spectroscopy (EDS) was carried out for composition analysis the fullerene materials. In order to conﬁrm the atomic structure proposed by HREM, theoretical calculations by molecular mechanics, molecular dynamics, and molecular orbital calculations were carried out. The third direction is to understand the various properties of the C nanocage materials. Photoluminescence (PL), electronic properties and magnetic properties of these fullerene materials were investigated. Downsizing of these materials is expected to show the various properties [21]. These studies will give us a guideline for design and synthesis of the fullerene materials, which are expected for the future nanoscale devices.

2 Synthesis Methods Carbon nanocapsules and clusters were produced by the following method [22, 23]. β-SiC nanoparticles (Sumitomo Cement), were dispersed in deionized water with polyvinyl alcohol (PVA-706, Kuraray) at 60◦ C. This polymer is a copolymer of polyvinyl alcohol and polyvinyl acetate. The solution with clusters and polyvinyl alcohol was dried in a drying oven prior to loading into the vacuum chamber. The annealing chamber was ﬁrst evacuated to 1 × 10−6 Pa, and the samples were annealed at 400–800◦C for 30 min in an Ar atmosphere of 0.12 MPa. Commercially available a-Fe2 O3 (hematite, 99.7%) and graphite carbon (99.5%) powders were also used as starting materials [24, 25]. Their particle sizes were 30 nm and 5 µm, respectively, which were measured by using a particle counter (HORIBA LA-920). Samples for Fe nanoparticles coated with C nanolayers were prepared by annealing mixtures of a-Fe2 O3 and C powders at 1000◦C for 2 h in the same manner. Ratios in weight of a-Fe2 O3 to B

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were varied from 7 : 3 to 3 : 7. Those of a-Fe2 O3 to C were from 8 : 2 to 5 : 5. Each mixture was mixed in a V-shape mixer. The temperature elevation rate was 3◦ C min−1 at annealing. For the formation of carbon onions, amorphous carbon produced from with polyvinyl alcohol (PVA-706, Kuraray) was used [26, 27]. Carbon nanocapsules were also prepared by a direct current and radiofrequency (DC-RF) hybrid arc discharge using pair anodes in order to enhance the Ge and Si evaporation [28, 29]. A graphite hollow cylinder (0.6 cm in diameter, 30 cm in length) is used for the main DC arc discharge. The gap distance between the main discharge electrodes is approximately 0.4 cm. A subanode of a carbon cylinder (1.5 cm in diameter, 10 cm in length) with the semiconductor (Si or Ge) powder is used, and a main anode of a carbon rod is partially mixed with the semiconductor powder. The DC arc discharge is initiated between a cathode electrode and the pair anodes. An RF antenna of water-cooled spiral copper pipe is installed 3 cm above the arc point to generate auxiliary plasma produced by an RF discharge around the DC arc plasma. When RF power is applied to an antenna through a matching circuit, the antenna DC current is also generated. The experimental parameters are as follows: DC arc current, 100 A; subanode current, 80 A; RF power, 600 W (13.56 MHz); helium gas pressure, 100 Torr. A detailed illustration of the apparatus was provided in the previous work. The plasma produced by this DC-RF hybrid discharge is much more voluminous than that by the ordinary DC arc discharge. Au nanoparticles (ULVAC) with a size of ca. 5 nm are selected in the present work for the one-dimensional positioning of carbon nanocapsules [30, 31]. The surface of these nanoparticles was stabilized by α-terpineol (C10 H18 O) in toluene solution. The solution with Au nanoparticles was dispersed on holey carbon grids with thickness ca. 15 nm (Oken Syoji.). After drying the specimens, they were loaded into the vacuum chamber, and annealed at ∼ 200–400◦C for 30 min in vacuum of ca. 7 × 10−4 Pa.

3 Fullerene Clusters and Metallofullerenes Hollow carbon clusters with diameters in the range of 0.7–1.0 nm are often on the carbon nanocapsules. Two of the carbon clusters are shown in Figs. 2a and 2b. The size of the carbon cluster in Fig. 2a is in the range of 0.5–0.7 nm, which corresponds to that of C36 [32,33]. The high-resolution image of Fig. 2b also shows a carbon cluster with the size of 0.7–0.8 nm, and the number of carbon atoms would be ∼ 70 (C70 ) [1], which could be estimated from the size of the cluster. In addition, dark contrast is observed inside the cluster, which would indicate the existence of several atoms inside the carbon cluster. The carbon cluster is directly connected at the step edge of the graphite sheets, which results in the stabilization of the carbon cluster. These C36 and C70 carbon clusters have elliptical structures [1,32,33], which agrees well with the

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Fig. 2. HREM images of (a) C36 and (b) C70 clusters. Atomic structural models of (c) C36 and (d) C70 clusters

present high-resolution observation. Structure was optimized by molecular orbital method using MOPAC software (Fujitsu). The possibility of direct detection of doping atoms in C60 solid clusters by HREM was investigated using calculated residual indices (RHREM ) and diﬀerence images [1, 34, 35]. The light element nitrogen (Z = 7) and heavy element rubidium (Z = 37) were selected as doping atoms in the present work. It was reported that nitrogen atoms were included at the center of the C60 clusters [36], which was detected by electron paramagnetic resonance [37]. It was also reported that Rb atoms were doped at the octahedral sites of C60 solid clusters, which were determined by X-ray diﬀraction [38]. Based on the crystal structure of C60 solid clusters, diﬀerence images between C60 and doped C60 (C60 /doped C60 ) were calculated for image analysis using residual indices. HREM images of C60 doped with nitrogen (N) and rubidium (Rb) atoms were calculated as functions of accelerating voltage of microscope, crystal thickness, and defocus values. The structure models and calculated images are shown in Fig. 3. Diﬀerence images of N@C60 /C60 and RbC60 /C60 showed N and Rb atomic positions clearly at high accelerating voltage and large crystal thickness. RHREM values of RbC60 are strongly dependent on accelerating voltage and crystal thickness, which would be due to the dynamical diﬀraction eﬀect of Rb atoms. Defocus values also inﬂuence the RHREM

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Fig. 3. Structural models of C60 , N@C60 , and Rb@C60 , and HREM simulated images

values, and the Scherzer defocus would be the best for atomic detection. The present work indicates that the doping atoms at the inside and interstitial site of C60 solid clusters could be detected by HREM with diﬀerence images and RHREM values. Various types of endohedral C clusters have been discovered and investigated. Metallofullerenes, which have atoms (such as La, Y, Sc, Li, Na, N, and other lanthanoids) inside the C60 , C82 , C84 , and other giant fullerenes, are expected as superatoms with various structures and physical properties [39, 40]. In addition, encapuslation of Sc [41], La [42], Ba [43], Ca [40, 44], Eu [45], Gd [46], Y [47], Sm [47] and Tb [47] atoms inside the C74 cluster have been reported. Silicon (Si) atoms have also been successfully introduced in carbon clusters by using the DC-RF hybrid arc discharge. Mass analysis of the soot indicated high-yield production of C74 [48] and existence of Si@C74 [28], as shown in Fig. 3a. The C74 fullerene has D3h symmetry satisfying the isolated pentagon rule, and the possibility of inserting a Si atom inside the C74 cage was investigated by using ab initio molecular dynamics simulation [49]. Hollow carbon clusters with diameters of ∼ 0.8 nm are often observed on carbon nanotubes and nanocapsules. A HREM image of a carbon cluster on a carbon nanotube is shown in Figs. 3b and 3c is an enlarged image of the carbon cluster. The carbon cluster has an elliptical structure, and the size is ∼ 0.8 nm, which agrees well with the size of Si@C74 [50]. Dark contrast is often observed in the carbon clusters. This indicates the existence of Si atoms inside the carbon clusters, which was also supported by the mass spectra analysis.

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Fig. 4. (a) Mass spectra of the soot indicated high-yield production of C74 . (b) HREM image of Si@C74 on a carbon nanotube. (c) Enlarged HREM image of the Si@C74 cluster. Calculated HREM images of (d) C74 and (e) Si@C74 clusters, as a function of defocus values, respectively

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Table 1. Calculated values for carbon clusters Total steric energy Heat of formation εHOMO

C60 C70 C72 C74 Si@C74 C76

kcal mol

kcal mol · atom

kcal mol

kcal mol · atom

179 177 197 170 168 182

2.98 2.53 2.74 2.30 2.24 2.39

811 886 928 950 994 937

13.5 12.7 12.9 12.8 13.3 12.3

eV −1.527 1 −1.503 9 −1.399 6 −0.468 3 −0.564 9 −1.106 3

εLUMO

Energy gap

eV

eV

0.606 4 0.454 1 0.572 9 −0.369 8 −0.466 6 0.272 8

2.133 5 1.958 0 1.972 5 0.098 5 0.098 3 1.379 1

The cluster structures are calculated theoretically, and the structure models of the C74 and Si@C74 are shown in Figs. 4d and 4e, respectively. The structures are optimized by molecular orbital calculations using PM3. Based on the projected structure models, image calculations on the C74 and Si@C74 clusters were carried out for various defocus values to investigate the imaging condition of the HREM images, as shown in Figs. 4d and 4e, respectively. The Scherzer defocus value of the present 300 kV electron microscope is ∼ 41 nm. The experimental data agree well with HREM images calculated at the defocus values in the range of −40 to −50 nm, which indicates the observed HREM images were taken close to the Scherzer defocus. Electronic structures of C74 , Si@C74 , and a single Si atom were investigated by DV-Xa, as shown in Figs. 5a–c, respectively. Calculated results for the structural stability and electronic structure are listed in Table 1. The C60 shows a large energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). Although the HOMO–LUMO gap of C60 is calculated to be 2.134 eV, the energy gaps of C74 and Si@C74 are 0.099 and 0.098, respectively. The energy gap of a single Si atom was also calculated to be 0.452 eV. The C2p orbital is strong around the energy gap for C60 and C74 , and the Si3p orbital shows the density of states (DOS) around the energy gap for Si@C74 . The Si@C74 cluster in Fig. 4b is directly connected on the carbon {002} sheets, which would result in the stabilization of the carbon cluster. Total energies of the C clusters were calculated as listed in Table 1, and 60–76 total steric energy of the Si@C74 was the lowest in the present calculation, which indicates that the insertion of the Si atom into the C74 cluster stabilizes the structure. Heat of formation per carbon atom for the Si@C74 is almost the same as that of C60 cluster, which indicates the structure is fairly stable. It has been reported that the energy gap of C74 clusters is small (∼ 0.2 eV) compared with the ordinary C60−80 fullerenes [19]. In the present work, the energy gaps of the C74 and Si@C74 were calculated to be 0.0985 and 0.0983 eV, respectively. Although the Si3d orbital aﬀects the energy levels of the C74 , the Si@C74 shows almost the same HOMO–LUMO gap. For the metallofullerenes such as Sc@C74 , La@C74 , Ca@C74 , Eu@C74 , and Gd@C74 ,

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Fig. 5. Energy level diagram and density of states of (a) C74 , (b) Si@C74 , and (c) a single Si atom

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encapsulated atoms are ionized and change the electronic states. In the present work, the energy gap of a single Si atom is calculated to be 0.452 eV, as shown in Fig. 5c, and electronic state of the Si atom is isolated by the C74 cluster. The Si atom would keep the original electronic state inside the C74 cluster, which would be interesting for investigation of atomic properties of Si.

4 Onions and Nanotubes Carbon was formed from polyvinyl alcohol after annealing at 400◦ C in Ar, and the carbon matrix was found to have an amorphous structure from the HREM image, as shown in Fig. 6a. The amorphous carbon was irradiated by an electron beam for 20 min under a beam current of 100 A/cm2 at 1250 kV. This beam current is ∼ 20 times higher compared to that of the ordinary HREM observation. Graphitization of amorphous carbon is observed, which is conﬁrmed by the lattice fringes of carbon layers with a spacing of ∼ 0.34 nm, as shown in Fig. 6b. Two carbon onions were produced from amorphous carbon as shown in Fig. 6b. Lattice fringes of the carbon {002} planes are observed. Figure 6c is an HREM image of tetrahedral carbon onion produced from that of Fig. 6b [27]. By electron-beam irradiation for 10 min on the onions of Fig. 6b, a carbon onion with tetrahedral structure was formed as shown in Fig. 6c. The edge lengths of the ﬁrst and second internal shell of the tetrahedral carbon onion are approximately 0.8 and 1.4 nm, respectively. The distance between onion layers is 0.35 nm. Although a similar structure consisting of C264 @C660 @C1248 was calculated [15], the size of the present tetrahedral carbon onion is smaller compared to the C264 . Figure 6d is a six-layered onion structure, and the outside is calculated to be C2160 from the equation 60n2 (n is the number of the shell). The lattice fringes of the carbon {002} planes are smeared at the edges of the onions with pentagonal carbon bonding, as indicated by arrows. “Atom clouds” [51, 52], which have vague contrast, are also observed at the vertices of onion edges as indicated by arrows. The carbon “vibration” was also observed at the surface of the onions. The shell structure is not perfect, but has some defects. The same onion after 60 s is shown in Fig. 6e. Change of the vertices into spherical structure is observed on the onion surface. At the center of the onion, there would be a C28 cluster from the size of ∼ 0.4 nm. Although this structure would be unstable, the C28 cluster would be stabilized by compressive tension of outer onion. The structure model is proposed as shown in Fig. 6f. At the center of the onion in Fig. 6c, there would be a tetrahedral carbon cluster and the basic arrangements of carbon atoms are proposed, as shown in Fig. 7a. Each vertex consists of a hexagonal ring (as indicated by a star mark), and three pentagonal rings exist around the vertex along the edge. Other parts consist of only hexagonal rings. Edge lengths of the C84 and

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Fig. 6. (a) HREM image of as-prepared amorphous carbon. (b) Two carbon onions produced from amorphous carbon (a) by electron-beam irradiation for 20 min. (c) Tetrahedral carbon onion produced from (b) by electron-beam irradiation for 30 min. (d) HREM images of onion structures. (e) Six-layered carbon onion; 60 s after (d). (f ) Structure model of C24 @C84

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Table 2. Calculated values for tetrahedral carbon onions

Calculation method Layer number Edge length (nm)

C84 Td (No. 20)

C168

C276

PM3

PM3

MM3

MM3

MM3

PM3

1

2

3

4

1, 3

–

0.8

1.0

1.4

C408 C84 @C276

C84 D2 (No. 22)

2.0

1.4

–

Interatomic distance of pentagonal rings (nm)

0.1445 0.1444 0.1399 0.1399

–

0.1438

Interatomic distance of hexagonal rings (nm)

0.1452 0.1429 0.1407 0.1406

–

0.1464

Total steric energy (kcal/mol)

362

395

389

345

823

335

Total steric energy (kcal/mol · atom)

4.31

2.35

1.41

0.85

2.29

3.99

Heat of formation (kcal/mol)

991

1413

–

–

–

967

Heat of formation (kcal/mol · atom)

11.8

8.41

–

–

–

11.5

C276 in optimized structures are 0.8 and 1.4 nm, respectively. The total numbers (N ) of carbon atoms of the present tetrahedral onions are represented by the equation N = 12(n + 2)2 − 24 (n = 1, 2, ...). Edge lengths of the C84 and C276 agree with the ﬁrst and second internal shells of tetrahedral carbon onion in the HREM image, respectively. Steric energy by molecular mechanics calculations and heats of formation by semiempirical molecular orbital calculations on tetrahedral carbon clusters are summarized in Table 2. On the basis of the projected structure model of Fig. 7c, image calculations on the C84 @C276 cluster were carried out for various defocus values to investigate the cluster structures. The smallest tetrahedral onion in the HREM image in Fig. 6c agrees well with the calculated images of C84 @C276 in Fig. 7c. In this optimized model, the distance between layers is close to the observed value of 0.35 nm. Further reﬁnement has to be carried out in which the van der Waals interaction is considered. Energy levels and density of states of C84 were calculated, as shown in Fig. 7b. Energy gaps of C60 , C84 , and C168 clusters were calculated to be 2.13, 2.06, and 1.44 eV, respectively. The experimental energy gap of C60 is 1.7 eV [53]. Since the diﬀerence between the present calculation and the experimental data is approximately 0.4 eV, the energy gap of a C84 cluster would be approximately 1.6 eV, which is a little smaller compared to that of the C cluster. The increase of numbers of the 60 carbon atoms decreased energy gaps of the clusters, as calculated for C186 (1.44 eV). In addition, DOS for C186 is broader than that of C84 . The formation mechanism can be described with three eﬀects: cutting of car-

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Fig. 7. (a) Proposed structure models of tetrahedral carbon onions: C84 , C168 , C276 and C408 (◦, pentagonal ring; , vertex (hexagonal ring)). (b) Energy level diagram and density of states for C84 . (c) Structure model and (d) calculated HREM images of C84 @C276 onion as a function of defocus values

bon bonds by electron irradiation, knock-on of carbon atoms, and increase of sample temperature. In the present work, bonding cuts and knock-on eﬀects would be important. These eﬀects cause ﬂuidization of the structure, which provides a spherical structure by the surface tension. In Fig. 6b, two onions were observed and their collision would occur during onion formation. The onion would be formed from the outside because C84 is too unstable to be fabricated, compared to C60 and related giant fullerenes. The outsidemost layer would be formed ﬁrst, and inside layers would be formed gradually. In the end, the number of remaining carbon atoms is important to construct the structure at the center of the onion, so that C84 would be formed in the present work. Concerning the shape and the size of the onion, the center of the onion would be C84 , and the onion would have any eﬀect from the carbon

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layer located outside. There are two important theorems of the Euler rule [54] and the isolated pentagon rule (IPR) [55] in the formation of the fullerene. Even if the closed fullerene size becomes larger, the number of pentagonal rings is always 12 by the Euler rule. Pentagonal rings do not adjoin to others based on the IPR rule when the size becomes bigger than C60 . There are 24 structural isomers in C84 [56], and C84 D2 and C84 D2d with the ratio of 2 : 1 are the main structural isomers. The ﬁrst inside shell of the tetrahedral carbon onion is equivalent to the C84 Td structural isomer. Heats of formation of C84 D2 and C84 D2d by the PM3 calculation are 967 and 968 kcal/mol, respectively. This means that a spherical structure is more stable than the tetrahedral structure (heat of formation 994 kcal/mol), and the Stone–Wales transformation [57] would be introduced during the growth of C84 Td to satisfy the Euler rule and the IPR rule. The position of the pentagonal ring can be moved by this transformation keeping the fullerene size. Although this tetrahedral structure (C84 Td ) might transform into spherical structure (C84 D2 and C84 D2d ), the energy barrier between them would prevent the transformation. The barrier would be the van der Waals force from outside shell and distortion due to the collision of two onions. The smallest carbon nanotube with a diameter of 0.4 nm was reported in [58]. They showed a HREM image of the multiwalled carbon nanotube, and they proposed an atomic structure model of C20 for the cap structure. However, the nanotube was not an isolated single-walled nanotube. Figure 8a is an HREM image of isolated carbon mininanotube on the carbon layers. The diameter and length of the nanotube are 0.5 and 3.1 nm, respectively. Figure 8b is a proposed atomic structure model of carbon mininanotube C180 . The size of the C180 agrees well with the observed image of Fig. 8a. The cap of the nanotube consists of a part of the structure of a C36 cluster, which are indicated by dark gray. Figure 8c is a 30◦ -rotated model of Fig. 8b along the nanotube axis. The atomic structure model of the C180 carbon mininanotube along the nanotube axis is shown in Fig. 8d. Carbon atoms corresponding to C36 clusters are indicated by dark gray. A structure model of C36 is also shown in Fig. 8e. The distortion of the mininanotube would be mitigated by the surface of the carbon layers, which may stabilize the cap structure.

5 Carbon Nanocapsules Although many carbon nanocapsules with various elements and compounds have been prepared by an ordinary arc-discharge method, a few nanocapsules ﬁlled with Ge and SiC have been reported. A HREM image of Ge nanoparticles encapsulated in graphite sheets is shown in Fig. 9a. In Fig. 9b, the Ge nanoparticle is surrounded by one to three graphite sheets. Figure 9c is a HREM image of a Ge nanowire encapsulated in a carbon nanotube with one to two graphite sheets. The diameter is 10 nm,

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Fig. 8. (a) HREM image of carbon mininanotube on the carbon layers. (b) Proposed atomic structure model of carbon mininanotube C180 . (c) 30◦ -rotated model of (b) along nanotube axis. (d) Structure model of C180 carbon mininanotube along nanotube axis. (e) Structure model of C36

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Fig. 9. (a) HREM image of Ge nanoparticles encapsulated in carbon sheets. (b) Enlarged image of the nanocapsule. (c) Ge nanowire encapsulated in carbon nanotube. HREM images of (d) carbon nanocapsules with SiC nanoparticles, (e) carbon nanocapsule and nanohorn. (f ) Enlarged image of SiC cluster encapsulated in carbon cage

and the length is 70 nm. The Ge nanowire has microtwin structures, and the growth direction of the nanowire is < 111 > of Ge [29]. A HREM image of carbon nanocapsules with SiC nanoparticles is shown in Fig. 9d. SiC nanoparticles with sizes of 6–10 nm are observed. All SiC nanoparticles are encapsulated in graphite sheets, and the number of graphite sheets was in the range of three to ten layers. A HREM image of the carbon nanocapsule and nanohorn is shown in Fig. 9d. Five to six graphite layers are observed around the nanoparticle, and the size of the carbon nanocapsule is

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Fig. 10. Structure models for carbon nanohorns. Three and ﬁve pentagonal C rings are introduced for model (a) C67 and (b) C74 , respectively. (c) Density of states for C74 nanohorn

4 nm. Lattice fringes with a distance of 0.25 nm, which corresponds to the distance of the {111} planes of β-SiC, are observed in the cluster. A carbon nanohorn with three graphite sheets is observed. The tip of the cage is smeared. Figure 9e is a HREM image of a carbon nanocapsule ﬁlled with a SiC nanocluster of size 2 nm. In this work, a special DC-RF arc-discharge method was used, which results in their formation. The SiC nanoparticles would be formed by reaction of Si and C atoms in the arc plasma. The DC-RF arc-discharge plasma would be eﬀective for the formation of semiconductor nanoparticles encapsulated in graphite sheets. In the present work, the sizes of the semiconductor Ge and SiC nanoparticles were reduced down to 10 nm, which indicates that the widening of the band-gap energy is expected by quantum size eﬀects, and peculiar optical properties will be expected. Ge nanowires encapsulated in carbon nanotubes are also expected as one-dimensional devices. Si oxide and Ge oxide layers are not observed at the surface of the SiC and Ge nanoparticles, which indicates that the carbon nanocapsules are eﬀective for cluster protection against oxidation in air. Figure 10 show structure models for carbon nanohorns observed in Fig. 9e. Three and ﬁve pentagonal C rings are introduced for model Figs. 10a and 10b, respectively, and the model in Fig. 10b is equivalent to the previously proposed model [59]. Heats of formation of the C67 and C74 clusters were calculated to be 22.18 and 20.53 kcal/mol · atom, and the stability of C74 is higher than that of C67 . DOS of C74 nanohorns were calculated, as shown in Fig. 10c. Energy level diagram of C74 nanohorn shows narrow energy gaps of 0.49 eV between the HOMO–LUMO gap. Carbon nanohorns are expected as catalytic elec-

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Fig. 11. (a) HREM image of carbon nanocapsules with SiC cluster. (b) Photoluminescence spectrum of (a). (c) HREM image of surface of carbon nanocapsule with SiC together with calculated image based on the proposed interfacial model (d)

trode materials for fuel cells in next generation, which separate hydrogen and electrons from methanol [8].

6 Properties of Carbon Nanomaterials 6.1 Photoluminescence of Carbon Nanocapsules SiC nanoparticles prepared with polyvinyl alcohol were annealed at 500◦ C in an Ar atmosphere. The particle size of SiC is in the range of 5–50 nm. All the SiC particles are surrounded by graphite sheets, and the number of graphite sheets is in the range 1–6. An enlarged HREM image of a carbon nanocapsule is shown in Fig. 11a. Lattice fringes with a distance of 0.25 nm, which corresponds to the distance of {111} planes of β-SiC, are observed in the nanoparticle. Two {002} planes of graphite grow on the β-SiC nanoparticle.

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The PL spectrum of the carbon nanocapsules encasing SiC clusters is shown in Fig. 11b [12]. A luminescence peak is observed at 382 nm, which corresponds to ∼ 3.2 eV. The bulk SiC has an energy gap of 3.00 eV. The present carbon nanocapsules with SiC clusters have higher energy compared to the bulk SiC, which would be due to the quantum size eﬀect of SiC as shown in Fig. 11a. A HREM image of the surface of a carbon nanocapsules with SiC nanoparticle is shown in Fig. 11c. Carbon {002} planes grow epitaxially on the SiC {111}, but disordered carbon structure is observed on the SiC {200}. Epitaxial growth of carbon {002} on the β-SiC {111} planes was often observed at the nanocapsule/nanoparticle interfaces in the present work. A similar epitaxial relationship was observed at the carbon/β-SiC in previous study [60]. The information on atomic arrangement at the carbon/SiC interface was obtained from the HREM images in the present work, and two structural models of the carbon/SiC interface were constructed, as shown in Fig. 11d. In Fig. 11d, carbon atoms that belong to the SiC structure connect with carbon atoms of the graphite. From the present high-resolution observation, the carbon {002} is parallel to the SiC {111}, and carbon [1,−1,0] is nearly parallel to SiC [0,1,−1]. (If the incidence is parallel to carbon [0,1,0], two-dimensional lattice fringes should be observed.) The distance between the SiC crystal and graphite layer was assumed to be 0.335 nm, which is the same as that of graphite {002} planes. Based on these models, HREM images are calculated as shown in Fig. 11c as an inset. In the observed images, the distance between the dark contrast of the ﬁrst carbon layer and the top of the SiC crystal is almost the same as that of carbon {002}, which indicates that carbon atoms of the graphite-type structure directly connect with carbon atoms that belong to the SiC structure. Graphitization of amorphous carbon on SiC {111} planes would be easier compared to the SiC {200}. It is believed that the carbon surface of SiC would have a low activation energy for graphite growth, which results in the heterogeneous nucleation growth of graphite. 6.2 Magnetic Properties of Carbon Nanocapsules Magnetic nanoparticles are suitable for potential applications like high-density magnetic recording media [61], magnetic ﬂuids [62], electromagnetic wave absorbing materials [63], magnetic carriers in clinical cures, and other novel magnetic devices. Iron (Fe) or Fe-based alloy nanoparticles have an advantage of high saturation magnetization for these applications, whereas deterioration by oxidation has kept them from practical usage. To overcome this problem, nanocoating techniques for the metal nanoparticles have been reported [24, 25]. Carbon nanocapsules encapsulated Fe are shown in Fig. 12a. Fe nanoparticles with 100–200 nm diameters are observed as shown in Fig. 12a. An EDX spectrum of the nanoparticles conﬁrmed that they are Fe nanoparticles. HREM makes it clear that the Fe nanoparticles are coated with well-oriented

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Fig. 12. Morphology of C-coated Fe particles. (a) TEM image of C wire with Fe particle. (b) Microstructure of coating layers encapsulating Fe particle. (c) Magnetic hysteresis loops of C-coated Fe particles with maximum DC applied ﬁeld of 0.8 MAm−1 . (d) Dependence of magnetization on temperature for commercially available carbonyl Fe, BN-coated Fe and C-coated Fe particles. Magnetization at each temperature is normalized with reference to that at 25◦ C

layers of ∼ 5 nm in thickness (Fig. 12b). The spacings of the lattice fringes in the layers revealed that the crystal structure is graphitic carbon with the spacing of 0.34 nm of {002} plane. The C-coated Fe nanoparticles also grew nanotubes of 50–100 nm in diameter, ∼ 1 µm in length, and ∼ 10 nm in wall thickness (Fig. 12a). Detailed observation of these tubes reveals that they have a multiwalled structure with something like joints inside. Multiwalled carbon nanotubes have been formed with diameters in the range from 1.4 nm to at least 100 nm [64,65]. So, the carbon nanotubes in this sample have large diameters. The magnetic properties of C-coated Fe nanoparticles in Fig. 12c were measured at room temperature. A magnetic ﬁeld higher than 0.6 MAm−1 must be applied in order to saturate magnetizations, because the demag-

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netizing factor of Fe nanoparticles would be larger than that of bulk Fe. Coercivities are very low, so the samples exhibit soft magnetic properties. Magnetization (Ms ) and coercivity (Hc ) values of the sample were measured to be 193 Am2 kg−1 and 1.1 kAm−1 under an applied ﬁeld of 1.6 MAm−1 . The Ms value is 87% of the value of bulk Fe [66]. Ms values of Fe or Co nanoparticles with C nanocoatings have been reported to be 40–60% of those of the bulk metals, and the Hc values are around several hundred oersteds (∼ 20 kAm−1 ) [67, 68]. In particular, the C-coated Fe nanoparticles in this work have much higher Ms values than the reported values. The Hc values of the C-coated Fe nanoparticles are lower as well. Herzer showed that the Hc of soft magnetic metal particles depends on the particle size [69]. Lower Hc values would be due to large particle sizes. The particle sizes in this work are 100–500 nm, about ten times larger than reported nanoparticle sizes. Considering that coercivity disturbs soft magnetic properties, it is obvious that this C-coated Fe nanoparticles is excellent as soft magnetic materials. In order to investigate resistance to oxidation, Ms values were measured, heating the C- and BN-coated Fe nanoparticles from 27◦ C to 800◦C in air (Fig. 12d). Commercially available carbonyl Fe powders, which have an average diameter of 3 mm, were also measured as a reference. The Ms values of all three samples decrease gradually as temperature increases, and fall to zero abruptly at elevated temperatures. The Ms of the carbonyl Fe disappears at ∼ 600◦ C. The BN- and C-coated Fe samples still keep their Ms at more than 60% of the initial value even at 600◦ C, and decrease to zero at ∼ 800◦ C. As the Curie temperature of magnetite (Fe3 O4 ) is 587◦ C (‘T1’ in Fig. 12d), the degradation of Ms in carbonyl Fe could be explained as oxidation and transformation of Fe into Fe3 O4 . The temperature of ∼ 800◦ C coincides with the Curie temperature of iron (767◦ C, indexed as ‘T2’ in the ﬁgure). Accordingly, the BN- and C-coated Fe nanoparticles exhibit resistance to oxidation. 6.3 Possibility of H2 Gas Storage in Carbon Nanocages Clean hydrogen energy is expected as substitute for oil energy in twenty-ﬁrst century. LaNi5 H6 is already used as H2 gas storage material. However, the H2 gas storage ability is only 1 wt. % because of large atomic number of La and Ni. On the other hand, fullerene materials, which consist of light elements such as boron, carbon, and nitrogen, would store more H2 gas compared to the metal hydrides. It was reported that H2 gas was stored in alkali-doped carbon nanotubes under ambient pressure and moderate temperature [70]. Collision between C60 and alkali-metal ions was also calculated to investigate a possibility of Li@C60 by molecular dynamics calculations [71]. Here, the possibility of H2 gas storage in fullerene materials was investigated. The condition of H2 gas storage into C60 cage and H2 gas discharge from C60 were calculated by molecular dynamics software (MASPHYC). The conditions were set as follows: pressure (p) and temperature (T ) are constant, or volume (V ) and temperature are constant. H2 gas storage into C60

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Fig. 13. (a) Molecular dynamics calculation of H2 gas storage in C60 cage. (b) Atomic structure models of C186 nanotube. (c) Structure models wherein the H2 molecule passes from pentagonal and hexagonal rings of C60 . (d) Structural model of H atom chemisorbed on C60

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cages is shown in Fig. 13a. This model is calculated under the condition of V = 8.0 × 10−27 m3 and T = 150 K. The H2 molecules pass through the hexagonal rings of C60 cage at 20 ps. After introducing H2 molecule into the C60 cluster at 40 ps, H2 is stored and stable in C60 . The condition of H2 gas discharge from C60 is similar to that of H2 gas storage, which is as follows: T = 300 K and p = 0.15 GPa. Although electronic structure calculation of hydrogen in C60 was reported [72], the present work showed the molecular dynamics of H2 molecule storage in C60 cluster. The H2 molecules are considered to enter from the cap of nanotubes, where the curvature is ﬁnite, as shown in Fig. 13b. The possibility of H2 gas storage in C nanotubes was investigated by using ﬁrst-principle calculations. In the present work, C60 was used to calculate the end-cap structure of the nanotube. In this case, only cap structures should be in the calculations. In the nanotubes, H2 molecule would invade from the cap of tube in the same way because of coulomb barriers of the tube wall. C60 clusters would have energy barriers for H2 molecules to pass through pentagonal and hexagonal rings. Figure 13c shows structure models wherein the H2 molecule passes from pentagonal and hexagonal rings of C60 . Single-point energies were calculated with changing set points of H2 molecule from the center of the cage at intervals of 0.1 nm. Energy barriers were calculated for H2 molecules to pass through pentagonal and hexagonal rings, and they are 23 eV and 16 eV, respectively [73]. Figure 13d is a structural model of hydrogen atoms chemisorbed on a C60 cluster. Atoms bonded with hydrogen are moved outside from the clusters. The hydrogenated energies for C60 H and C60 H2 were calculated to be −0.18 and 0.6 eV, respectively [74]. Hydrogen bonding with a carbon atom of C60 is more stable than C60 . When two hydrogen atoms were chemisorbed on carbon clusters, energies of carbon clusters increased. To investigate stability of H2 molecules in clusters, energies were calculated for H2 molecules placed in the center of a C60 cluster, as summarized in Table 3. Structural models are shown in Fig. 13e. When more than 22 H2 molecules were introduced in C60 , hydrogen atoms chemisorbed inside the cluster [75]. When more than 26 H2 molecules were introduced in the C60 clusters, 22 H2 molecules were in the cluster and 8 hydrogen atoms chemisorbed inside the clusters and the C–C bond was broken. 6.4 One-Dimensional Self-Organization of Nanocapsules The recent speed-up of ultra-large scale integrated circuits (ULSI) of semiconductor devices is based on the minimization of the design rule. New properties are also expected by the formation of low dimensional arrays of quantum dots. The photolithography technique is used for the formation of these nanostructures, and the ULSI with 0.07 µm rule will be produced in 2009 [76]. However, the limit of the design rule is reported to be 0.05 µm (= 50 nm) by using extreme ultraviolet lithography [77]. It is believed that establishment

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Table 3. Energy of C60 cluster with hydrogen. A C–C bond was broken in case of 8 chemisorbed hydrogen atoms (∗ ) Introduced Optimized Heat of formation Hydrogen atoms Hydrogen storage H2 (eV) chemisorbed (wt. %) H2 inside cluster 0 20 22 25 26 30

0 20 22 25 26 24

35.21 127.54 143.01 164.87 169.63 165.59

0 0 0 4 8 (∗ ) 4

0 5.6 6.1 6.9 7.2 6.7

of nanostructure-formation techniques by self-organization of nanoparticles is worth pursuing in order to overcome the lithography limit. Spontaneous formation of well-organized nanostructures is intriguing for both scientiﬁc research and future electronic-device application. However, dimensionality of this self-organization has been two and three [78, 79], and one-dimensional self-organization has been needed for the formation of “nanowiring” for the future ULSI devices. Gold nanoparticles and nanowires encapsulated in carbon nanocapsules and nanotubes were spontaneously formed from one-dimensional selforganized gold nanoparticles on carbon thin ﬁlms by annealing at low temperatures of 200–400◦C, as shown in Figs. 14a–c [30, 31]. The gold crystals inside the nanotubes are distorted by the crystal growth of the nanowires, as shown in Figs. 14d and 14e. Lattice expansion and reduction are observed parallel and perpendicular to the growth axis, respectively. It is believed that the distortion of the nanowire would be due to the coalescence of nanoparticles along the growth direction at the low temperatures. A conductivity (dI/dV ) curve of a single carbon nanocapsule with Au nanoparticles is shown in Fig. 14f, which indicates the V-shape behavior with the gap of ∼ 0.5 V [80]. This would be due to the disordered carbon layers at the carbon/Au interface as shown in Fig. 14g. A schematic illustration of self-organized Au nanoparticles, carbon nanocapsules, and carbon nanotube is shown in Fig. 14h. For the one-dimensional positioning, adhesive force due to the step edge and substrate are mainly used. The ordinary ordering mechanism for nanoparticle self-organization is due to the internanoparticle force by α-terpineol and adhesion by the substrate. The width of the one-dimensional line could be controlled by the interactive force of α-terpineol. The present result indicates that the onedimensional arrangement is strongly dependent on the atomic step edge of the substrate. The diﬀerence in the formation of carbon nanocapsules and nanotubes would be due to the distance between the gold nanoparticles. Although the atomic step edge is formed by the common sample preparation

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Fig. 14. (a) Low-magniﬁcation image of one-dimensional self-organized carbon nanocapsules with Au nanoparticles on amorphous carbon ﬁlm. (b) Alternate arrangement of diﬀerent size of carbon nanocapsules with gold nanoparticles. (c) HREM image of Au nanowire in carbon nanotube. (d) Fourier transform of nanotube. (e) Structure model of Au{111}/C{002} interface. (f ) Conductivity curve of a single carbon nanocapsule with Au nanoparticle. (g) Enlarged HREM image of carbon/Au interface. (h) Schematic illustration of one-dimensional selforganized Au nanoparticles, carbon nanocapsules and carbon nanotube

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technique in the present work, the atomic step could be controlled by ordinary lithography techniques such as electron beam, and is expected as a nanofabrication technique for future electronic devices. The present result is expected as a future fabrication technique for self-assembled ULSI nanowires and quantum dots protected by nanocapsules and nanotubes at scales beyond the limits of current photolithography.

7 Conclusion Various C fullerene materials were synthesized by polymer pyrolysis, chemical reaction, DC-RF hybrid arc discharge, and electron-beam irradiation. Atomic structure and formation mechanisms were investigated by HREM, and structural models were proposed. Measurements of PL and magnetic properties of C nanocapsules showed a higher energy shift of luminescence and good soft magnetic properties. The present work indicates that the new C fullerene materials with various atomic structures and properties can be produced by various synthesis methods, and are expected to be the future nanoscale devices. Acknowledgements The authors would like to thank T. Hirano, M. Kuno, H. Kitahara, K. Hiraga, E. Aoyagi, H. Kubota for their useful discussion, experimental help, and collaborative work.

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Index atomic structures, 187 C168 , 198, 199 C180 , 200, 201 C186 , 198 C20 , 200 C2610 , 196 C264 , 196 C276 , 198, 199 C276 :C84 , 198, 199 C28 , 196 C36 , 190, 200 C408 , 198, 199 C60 , 187, 191–194, 198, 200 C60 :Li, 207 C60 :N, 192 C60 :Rb, 192 C60 with hydrogen, 207–211 doped C60 , 191 C67 , 203 C70 , 190, 194 C72 , 194 C74 , 192–195, 203 C74 :Ca, 194 C74 :Eu, 194 C74 :Gd, 194 C74 :La, 194

C74 :Si, 192–195 C76 , 194 C82 , 192 C84 , 192, 198, 199 C84 :C24 , 197 C84 D2 , 198, 200 C84 D2d , 200 C84 Td , 198 C84 Td , 200 carbon clusters, 194 endohedral clusters, 192 fullerene, 187–192 fullerene materials, 188, 189, 207 giant fullerene, 192, 199 graphitization, 205 high-resolution electron microscopy (HREM), 191, 192 highest occupied molecular orbital (HOMO), 194 HOMO-LUMO gap, 194, 203 hybrid arc-discharge, 187, 189, 190, 192, 203 hydrogen storage, 207–209, 211

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lowest unoccupied molecular orbital (LUMO), 194 metallofullerene, 187, 190, 192 molecular dynamics, 207 nanocages, 187, 189, 207 nanocage materials, 189 nanocapsules, 187, 190, 192, 200, 202–205, 207–211 self-organization, 187, 209 one-dimensional self-organization, 209 nanohorns, 187, 202, 203 nanoparticles, 210 gold nanoparticles, 210, 211 nanostructures hollow-cage-nanostructures, 187 nanotubes, 187, 192, 196, 201–203, 208, 210, 211

mininanotube, 200 multi-walled nanotubes (MWNTs), 200 multiwalled nanotubes (MWNTs), 206 single-walled nanotubes (SWNTs), 200 nanowires, 200, 203, 210, 211 onions, 187, 196–199 tetrahedral onions, 196–198 photoluminescence (PL), 187, 189, 204 SiC, 200, 202–205 ultra-large scale integrated circuits (ULSI), 209 self-assembled ULSI, 212

Hard Amorphous Hydrogenated Carbon Films and Alloys Fernando L. Freire Jr. Pontif´ıcia Universidade Cat´ olica do Rio de Janeiro, Departamento de F´ısica Rua Marquˆes de S˜ ao Vicente 225, Rio de Janeiro, BR-22452-900, RJ, Brazil [email protected] Abstract. Hard hydrogenated amorphous carbon ﬁlms are presently being used in a wide variety of applications as protective coatings. The properties of the carbon ﬁlms are essentially controlled by the ratio between the number of carbon atoms in sp2 and sp3 hybridization states. The properties of the ﬁlms, which are closely related to the ﬁlm microstructure, can be tuned by the deposition technique employed and by the growth conditions, with the energy of the impinging species playing the main role in the control of the carbon bonding hybridization. Another way to improve the properties of carbon ﬁlms is through the incorporation of several elements. In this work, the attention is focused on ﬁlms deposited by plasma-enhanced chemical vapor deposition, discussing the eﬀects of nitrogen and ﬂuorine incorporation on the ﬁlm microstructure and on the mechanical and tribological properties.

1 Introduction Amorphous carbon ﬁlms are nanostructured materials made of clusters of sp2 -hybridized carbon atoms, with a typical size of a few nanometers, connected to each other by sp3 -hybridized carbon atoms. The electronic and optical properties of these materials are mainly controlled by the size of the sp2 clusters, while the mechanical properties are given by the degree of interconnectivity of the amorphous skeleton, i.e., the fraction of sp3 -hybridized carbon atoms present in the matrix [1]. Film properties can be tuned by choosing the deposition technique with the appropriated deposition conditions. Among the diﬀerent deposition parameters, the energy of the impinging ions plays the more important role and controls the sp2 /sp3 -hybridized carbon atoms ratio. The subplantation model suggests that the deposition of hyperthermal carbon species is a shallow implantation process, where the incorporation of carbon species in subsurface layers followed by internal stresses is the dominant mechanism, responsible for the formation of a sp3 -carbon-rich dense phase, the diamondlike phase [2]. Recently, this model was improved with the inclusion of the role of the interstitials, which are physically and energetically diﬀerent from the bulk sp2 and sp3 carbon atoms [3]. In this way, ﬁlms with properties typical of polymers, graphite or diamond can be synthesized. Carbon ﬁlms are used in a wide variety of applications as protective G. Messina, S. Santangelo (Eds.): Carbon, The Future Material for Advanced Technology Applications, Topics Appl. Phys. 100, 217–238 (2006) © Springer-Verlag Berlin Heidelberg 2006

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coatings. In particular, ﬁlms deposited by magnetron sputtering, plasma-enhanced chemical vapor deposition (PECVD) and ﬁltered cathodic vacuum arc (FCVA) are used as overcoats for biomedical implants [4], computer hard disks [5] and as spacer tools for electron guns of cathode ray tubes [6]. The incorporation of hydrogen in the amorphous skeleton also plays an important role. The amorphous hydrogenated carbon ﬁlms (a-C:H) can be deposited by both sputtering and PECVD techniques in a large range of sp2 /sp3 -hybridized carbon atom ratios. The hydrogen content in these ﬁlms can vary from 0 to 50 at. %. Depending on the deposition conditions, substrate bias voltage, substrate temperature, and pressure and gas precursor atmosphere, they can be either diamond-like (sp3 -rich ﬁlms) or graphitic-like (sp2 -rich ﬁlms). However, a-C:H ﬁlms with high H content and high fractions of carbon atoms with sp3 hybridization have a polymeric character. It was shown that the subplantation model could also be applied to describe the mechanisms of a-C:H growth by PECVD. In fact, the internal stress and hardness of a-C:H ﬁlms deposited by rf-PECVD in pure methane atmosphere show a dependence with the self-bias voltage that is well described by the subplantation model [7]. One of the ways of changing, in a controlled way, a-C:H ﬁlm properties is through the incorporation during the ﬁlm growth of diﬀerent elements, such as nitrogen (N), ﬂuorine (F), silicon (Si) and many metals, for example, titanium (Ti). The incorporation of Si, for example, seems to stabilize sp3 carbon bonds and to improve the thermal stability of a-C:H ﬁlms [8]. On the other hand, the incorporation of one or more of these elements can induce the formation of new nanostructured materials, as the fullerene-like carbon ﬁlms, ﬁlms with strongly interacting curved graphene planes. The fullerenelike structure results from the curving of the graphene planes induced by nitrogen incorporation and is similar to that found in carbon nanotubes and fullerenes [9]. In recent years, an important fraction of the research eﬀort was dedicated to the study of nitrogen incorporation on carbon ﬁlms [10]. The main reason of this eﬀort was the intention to synthesize the C3 N4 , proposed by Liu and Cohen [11], to have mechanical properties comparable to those of crystalline diamond. In spite of this, no clear experimental evidence of the formation of C3 N4 has been presented until now [12]. Nitrogen incorporation into a-C:H ﬁlms was found to modify the structure [13] and the mechanical properties [14] of these ﬁlms, as well as their electrical and optical properties [15]. In fact, the fraction of carbon atoms in sp3 hybridization state decreases upon nitrogen incorporation [16]. In terms of the mechanical properties, a reduction on the internal compressive stress was observed, with minor changes in the mechanical hardness [14]. Concerning the modiﬁcation of electrical and optical properties, it was found that nitrogen could electronically dope a-C:H ﬁlms, with the simultaneous reduction of the electronic defect density [15]. This reduction makes possible the use of a-C:H:N ﬁlms as

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a semiconductor material. In addition, a-C:H:N ﬁlms deposited by PECVD showed a promising performance as electron ﬁeld-emitters [17]. The incorporation of ﬂuorine in a-C:H ﬁlms has also attracted interest [18]. In spite of the lubricant properties of poly(tetraﬂuoroethylene) (PTFE) the recent research on the ﬂuorine incorporation into a-C:H ﬁlms was mainly motivated by its electrical properties. In fact, to improve the switching performance of future ultra-large scale integrated circuits (ULSI), insulator ﬁlms with dielectric constants less than that of SiO2 are needed to reduce the capacitance of interlayer insulators [19]. Fluorinated amorphous carbon (a-C:H:F) ﬁlms have been proposed as possible candidates due to their dielectric constant [20]. These ﬁlms can be plasma deposited in a wide compositional range, the ﬁlm ﬂuorine content being determined primarily by the atmosphere during deposition [21]. It has been found that the dielectric constant decreases with the increase of the F/H ratio of the precursor atmosphere for ﬁlms deposited by PECVD [22]. Notwithstanding the interest in the dielectric properties of ﬂuorinated amorphous carbon ﬁlms, few attempts to combine the mechanical properties of a-C:H ﬁlms with the tribological characteristics of PTFE have been made. The eﬀect of ﬂuorine incorporation on the mechanical [23] and tribological [24] properties of a-C:H ﬁlms has received more attention only in the last few years. As expected, ﬂuorine incorporation increases the surface hydrophobicity and reduces the friction coeﬃcient [25]. Besides, the eﬀect of ionic bombardment during a-C:H:F ﬁlm growth has not been investigated in detail [26]. Up to now, only a few studies have concentrated on the simultaneous incorporation of F and N into a-C:H ﬁlms [27]. They were focused to the structural characterization and the electrical properties of the ﬁlms [28]. In a recent investigation, it was shown that N atoms were incorporated into the aromatic rings and as electronegative groups directly bonded to sp2 -carbon in a-C:H:F ﬁlms deposited by PECVD [29]. The incorporation of nitrogen, which occurs at the expense of carbon atoms, induces modiﬁcations on the surface hydrophobicity and friction behavior of the ﬁlms, indicating a route to control the surface wettability of these ﬁlms [30]. In this review, a comparative study of the incorporation of N and F into a-C:H ﬁlms deposited by PECVD using CH4 –N2 and CH4 –CF4 mixtures as precursor atmospheres is presented. The eﬀects on the ﬁlm microstructure and mechanical properties will be discussed emphasizing the role of the energy of the bombarding species. Tribological properties will also be discussed, as well as the thermal stability of those ﬁlms. Results of an investigation on the incorporation of N into a-C:H:F ﬁlms deposited by PECVD using CH4 –CF4 – N2 mixtures as precursor atmospheres will also be presented, with special attention to the tribological properties of a-C:H:F:N ﬁlms.

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Fig. 1. Nitrogen and ﬂuorine content in a-C:H:N and a-C:H:F ﬁlms as a function of the methane partial pressure

2 Film Growth and Chemical Composition a-C:H:N and a-C:H:F ﬁlms were deposited by the plasma-assisted decomposition of CH4 –N2 and CH4 –CF4 mixtures, onto Si substrates mounted on the water-cooled copper cathode feed by an rf power supply (13.56 MHz). In this method, the capacitive coupling allows the development of an average in time DC negative potential at the powered electrode, the self-bias potential, V b , which extracts and accelerates ions from the plasma towards the powered electrode. For deposition chamber pressure around 10 Pa, the mean energy of those ions is around (1/3)eV b , where e is the electron charge [1]. Results obtained from two series of ﬁlms will be presented. In the ﬁrst set of samples, during the deposition V b was kept ﬁxed at −350 V, while the CF4 and N2 pressures were changed from 0 to 80% and 0 to 50%, respectively. For the second series, V b ranged from −100 V to −700 V with the N2 partial pressure ﬁxed at 40% of the total pressure for a-C:H:N ﬁlms, while the partial pressure of CF4 was 67% in the case of a-C:H:F ﬁlm deposition. For the sake of comparison, a-C:H ﬁlms were deposited in pure methane atmosphere in the same range of self-bias voltage. The desired V b value was adjusted by changing the rf power in the range of 10–80 W. The total gas inlet ﬂux was ﬁxed at 3 sccm. The pressure in the deposition chamber was 10 Pa. A 10 nm thick a-C:H buﬀer layer was deposited without breaking the vacuum prior to the deposition of the ﬁlm in order to enhance the ﬁlm adhesion. Without the buﬀer layer, the a-C:F:H ﬁlms peel oﬀ. Details of the experimental apparatus can be found elsewhere [23]. The ﬁlm composition was determined by ion beam analysis (IBA): Rutherford backscattering spectrometry (RBS), elastic recoil detection analysis (ERDA) and nuclear reaction analysis (NRA) [31].

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Fig. 2. Deposition rate of a-C:H:N and a-C:H:F ﬁlms as a function of the methane partial pressure

The chemical compositions of the ﬁlms deposited while changing the precursor atmosphere are shown in Fig. 1, where the nitrogen and ﬂuorine content of a-C:H:N and a-C:H:F ﬁlms, respectively, were plotted as functions of the partial pressure of methane. An increase of the F and N content in the ﬁlms occurs upon the the increase of the partial pressure of CF4 and N2 . While in the case of a-C:H:N ﬁlms the nitrogen incorporation occurs at the expenses of the carbon content of the ﬁlms, the hydrogen concentration remaining constant within experimental errors around 20 at. %, in the case of a-C:H:F ﬁlms the incorporation of ﬂuorine occurs at the expenses of the hydrogen content, which decreases from 19 at. % to 1 at. %, in the range of partial pressures considered in Fig. 1. The observed upper limits for the incorporation of nitrogen and ﬂuorine in the ﬁlms have diﬀerent reasons and can be understood with the help of Fig. 2, where the deposition rates of a-C:H:N and a-C:H:F ﬁlms are plotted as functions of the methane partial pressure. The a-C:H:N deposition rate presents a sharp decrease when nitrogen partial pressure increases, while the deposition rate of a-C:H:F ﬁlms increases by a factor of 2 when the partial pressures of CF4 increases from 0 to 80% of the total pressure. For higher CF4 partial pressures, no ﬁlm deposition but substrate erosion occurs. It is important to note that for both a-C:H:N and a-C:H:F ﬁlm deposition, in order to keep V b constant at −350 V, the power applied to the plasma is almost constant in the entire range of partial pressures (CF4 or N2 ) studied, around 50 W. The deposition rate reduction due to nitrogen incorporation observed in a-C:H:N ﬁlm deposition was attributed to the onset of a kind of chemical sputtering process arising from energetic N+ 2 ion bombardment of the ﬁlm growing surface [32]. In fact, it was found that low-energy N+ 2 ion bombardment of pure amorphous carbon results in

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carbon atom removal, at a rate of about 0.5 C atom per N+ 2 ion [33]. However, there is no justiﬁcation for the absence of the symmetric situation in carbon– nitrogen ﬁlm deposition process, i.e., nitrogen atoms being sputtered out by carbon-carrying ions. We must consider both processes in the simulation of ion beam deposition of carbon–nitrogen ﬁlms. Besides, the possibility of N2 evaporation during ﬁlm growth must be included. This situation is likely to occur since N-atom subsurface penetration must favour N–N bond formation with N atoms already in the ﬁlm. The formation of other volatile species, such as CN can also occur. These mechanisms are increasingly more probable for deposition conditions that result in increasing nitrogen contents, reducing the deposition rates. Therefore, the growth kinetics of carbon–nitrogen ﬁlms may be pictured as a competition between aggregation and erosion resulting from the impinging of diﬀerent species on the ﬁlm-growing surface [34]. The increase of the deposition rate of a-C:H:F ﬁlms with higher CF4 partial pressure can be explained as follows: the growth of a-C:H ﬁlms is mainly due to the physisorption of hydrocarbon radicals onto the surface followed by chemisorption of such radicals induced by energetic processes such as ion bombardment. The existence of dangling bonds at the surface is expected to enhance the sticking probability of carbon-carrying radicals [35]. As the partial pressure of CF4 increases, the hydrogen concentration in the plasma decreases together with the increase of the ﬂuorine concentration. Fluorine atoms can react on the surface by chemically eroding H from hydrocarbon radicals, forming volatile HF and leaving a dangling bond on the surface. In fact, a similar mechanism for dangling bond formation during the deposition of a-C:H ﬁlms has been reported [36]: atomic hydrogen chemically erodes hydrogen bonded on the surface of the growing ﬁlm, leaving a dangling bond and enhancing the sticking probability of CH3 radicals by a factor of 100. The hydrogen erosion induced by ﬂuorine atoms is expected to be more eﬃcient than that induced by hydrogen atoms due to their much higher electronegativity. In this way, the higher the CF4 concentration, the higher the probability of hydrocarbon radicals sticking onto the surface. Besides, the higher the CF4 partial pressure, the higher the probability for large molecule formation in the gas phase due to the agglomeration of CFx radicals [37], providing a new channel for the formation of a ﬂuorinated ﬁlm up to the limit where there are not enough hydrocarbon radicals to prevent F-induced substrate etching, which occurs for CF4 partial pressure higher than 80%. The a-C:H:N ﬁlm composition is almost constant, within experimental errors, for samples deposited in CH4 –N2 mixtures with N2 partial pressure of 40% and with V b in the range of −100 V to −700 V. The nitrogen content is around 12 at. %, while the hydrogen content is typically 20 at. %. On the contrary, ﬂuorine and hydrogen contents in a-C:H:F ﬁlms show a strong dependence with the self-bias voltage, as shown in Fig. 3. An increase of the ﬂuorine content for higher V b was observed. Since the sum of the ﬂuorine and hydrogen concentrations is roughly constant around 20 at. %, these results

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Fig. 3. Fluorine and hydrogen content in a-C:H:F ﬁlms as a function of the self-bias voltage

Fig. 4. Deposition rate as a function of the self-bias voltage

suggest that ﬂuorine is incorporated by substituting hydrogen. On the other hand, the deposition rate increases with the increase of V b , as one can see in Fig. 4. It can be understood as a result of the higher degree of plasma dissociation due to the higher power needed to achieve higher V b . Also, the contribution to a higher generation rate of nucleation sites on the ﬁlm surface due to the more energetic ion bombardment should be taken into account.

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Fig. 5. Atomic density of a-C:H:N and a-C:H:F ﬁlms as a function of the methane partial pressure

3 Film Microstructure The inﬂuence of the nitrogen and ﬂuorine incorporation on the ﬁlm microstructure was usually investigated following a multitechnique approach. Raman and X-ray photoelectron (XPS) spectroscopies [38], as well as, infrared absorption spectroscopy (IR), electron energy loss spectroscopy (EELS) [16] and thermal-induced gas eﬀusion experiments were used to probe ﬁlm microstructure [39]. The atomic density can be evaluated by combining the areal atomic density provided by IBA and the thickness of the samples, determined by stylus proﬁlometry [31]. The modiﬁcations in the ﬁlm microstructure are illustrated by the results of the atomic density presented in Fig. 5. In this range of nitrogen incorporation, the atomic density remains constant, but for ﬂuorine content higher than 15 at. % (corresponding to a-C:H:F ﬁlms deposited in a CH4 –CF4 atmosphere with 33% of partial pressure of methane) the atomic density decreases from 1.3 to 1.1 × 1023 atoms/cm3 , indicating the occurrence of structural modiﬁcations in these ﬁlms. As will be discussed in more detail below, this more opened and relaxed structure has a polymeric character. Three representative Raman spectra obtained from ﬁlms deposited at the same V b (−350 V) are shown in Fig. 6. The two spectra at the bottom part of the ﬁgure obtained from a-C:H and a-C:H:N ﬁlms are typical of a diamond-like ﬁlm, while the one at the top, obtained from a ﬁlm with ﬂuorine content of 19 at. %, has a larger luminescence background, characteristic of a polymer-like material [21]. The main features of the Raman spectra are the two partially overlapping bands characteristic of all a-C:H ﬁlms. They are usually referred as the D (disorder) and the G (graphite) bands. The ﬁrst

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Fig. 6. Raman spectra obtained from a-C:H, a-C:H:N (11 at. % of N) and a-C:H:F (19 at. % of F) ﬁlms. The position of the D and G bands are indicated by arrows

band, centered at around 1370 cm−1 , corresponds to the so-called D band and is associated with disorder-allowed zone edge modes of graphite that become Raman active due to the lack of long-range order [40]. The second one, which peaks around 1550 cm−1 , is known as the G band and is attributed to E 2g -symmetry optical modes occurring at the Brillouin-zone center of crystalline graphite [40]. This band is usually observed in the Raman spectra of the a-C:H ﬁlms as well as in ta-C ﬁlms, but it may peak at slightly different energies in the two forms of amorphous carbon, depending on their sp3 fractional content [41]. No other band besides the second-order Raman was observed in the spectra. We can interpret the Raman results according to the approach adopted by Dillon et al. for the analysis of the spectra obtained from a-C ﬁlms [42]. Recently, Ferrari et al. discussed in details the Raman results obtained from carbon nitride ﬁlms. This work is also taken into account in the present analysis [43]. It was proposed that both the increase in the ratio of the intensities of the D and G bands (I D /I G ) together with the shift to higher frequencies of the position of the maximum and the decrease of the width of the G band are indications of an increase in the size of the sp2 -hybridized carbon domains. To obtain the evolution of these

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Fig. 7. (a) I D /I G intensity ratio and (b) sp2 fraction as functions of the incorporated nitrogen. The lines are eye-guides only

bands against the changes in the ﬁlm composition, the Raman spectra were decomposed using two Gaussian functions, after the removal of the luminescence background by means of a polynomial best-ﬁt procedure [44]. In the case of a-C:H:F ﬁlms, a continuous shift of the position of the maximum of the G band from 1538 to 1556 cm−1 (typical ﬁtting errors of 5 cm−1 ) and an increase of the I D /I G ratio by a factor of 2 was observed, together with a decrease of the G bandwidth. The Raman results obtained from the a-C:H:N ﬁlms show a similar trend [13]. These results are presented in Fig. 7, together with the sp2 fraction as a function of the nitrogen content in the ﬁlms. The G band position shifts from 1538 to 1550 cm−1 and the G bandwidth reduces from 165 to 153 cm−1 , while I D /I G increases by 60% upon nitrogen incorporation up to 11 at. %. These results are interpreted as being due to an increase of the size of the sp2 clusters. The increase of the fraction of sp2 -hybridized carbon atoms measured by EELS (Fig. 7b) supports this interpretation. The increase of CF4 and N2 partial pressures, and consequently the incorporation of F and N, induces an increase in the size of the sp2 -hybridized carbon domains. However, it should be pointed out that visible Raman spectroscopy is 50–230 times more sensitive to sp2 sites than to sp3 sites [45]. In this way, the above analysis cannot completely describe the structural modiﬁcations induced by changing the deposition conditions. To this aim, more information can be obtained, perhaps, from the evolution of the luminescence background, underlying the a-C:H:F Raman spectra. In fact, while the luminescence intensity is negligible in the spectra obtained from a-C:H:N ﬁlms or a-C:H:F ﬁlms with ﬂuorine contents up to 14 at. %, it increases in ﬁlms with greater ﬂuorine contents. The increase in the luminescence background has

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Fig. 8. XPS spectrum obtained from an a-C:H:F ﬁlm with 20 at. % of F. The main features of the spectrum are indicated by arrows

been discussed in terms of a structural rearrangement towards a polymer-like structure [21], and this interpretation is reinforced by both the reduction of the a-C:H:F ﬁlm density upon ﬂuorine incorporation and the XPS identiﬁcation of C–F2 bands, characteristic of ﬂuorinated polymers, observed in the ﬁlms containing about 20 at. % of ﬂuorine. The C1s XPS spectrum shown in Fig. 8 can be ﬁtted using four bands: C–C and C–H at 285.1 eV, C–CF at 287.1 eV, C–F at 289.3 eV and C–F2 at 291.5 eV [38]. The ﬂuorine peak at around 690 eV does not provide any information about the diﬀerent chemical bonds. XPS spectra taken from ﬁlms deposited at lower CF4 partial pressure are not shown in this ﬁgure. However, they show that higher CF4 partial pressures lead to a relative increase in the intensity of ﬂuorinated carbon peaks. In fact, only for ﬁlms with 20 at. % of ﬂuorine, we observed the bands corresponding to both C–F and C–F2 bonds. These trends are in good agreement with the infrared results, which show an increase in the intensity of the C–Fx bands when the ﬂuorine content increases [23]. As discussed above, the ionic bombardment during a-C:H ﬁlm growth controls the ﬁnal ﬁlm properties. According to mass spectrometry measurements in CH4 and CF4 low-power rf capacitively coupled plasmas, the main + ionic species in our plasmas are expected to be CF+ 3 and CH3 ions [46]. In + the case of N2 plasma, N2 is the more important ionic species [47]. For V b on the order of several hundred volts, these molecular ions promptly break up upon colliding with the ﬁlm surface. From simple mechanical arguments, it is possible to show that the energy sharing between the atoms is proportional to the mass ratio of the atom and the molecule. Clearly, for CH+ 3 ions this energy is almost totally concentrated in the carbon atom, while for CF+ 3 ions it is more equally divided between all atoms. In a few words, the CF+ 3 bom+ or even N ions. In bardment is much less eﬀective than that due to CH+ 3 2 the case of CF4 –CH4 atmospheres, when the methane partial pressure in the plasma is reduced, the eﬃciency of the ionic bombardment is also reduced, resulting in ﬁlms with polymeric character.

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Fig. 9. Atomic density as a function of V b

Fluorinated a-C:H ﬁlms were also investigated by thermal-induced gas eﬀusion [39]. A structural transition from diamond-like to polymer-like ﬁlms as a result of the incorporation of ﬂuorine could be inferred from the eﬀusion spectra. At low ﬂuorine contents (up to 10 at. %) the material is relatively compact and the eﬀusion of hydrogen-related species (hydrogen molecules and hydrocarbons) dominates. As the ﬂuorine content is increased, hydrogen-related eﬀusion is progressively substituted by the eﬀusion of CF4 -related species, conﬁrming that ﬂuorine atoms substitute hydrogen ones in the amorphous network. For high enough ﬂuorine concentrations a strong change in the eﬀusion characteristics indicates that an interconnected network of voids is present. Strong eﬀusion of CF4 -related species is consistent with a surface desorption process and can only be observed when CF2 and CF3 bonds are present in the ﬁlm microstructure and the void dimensions are large enough, i.e., for ﬁlms with the highest ﬂuorine contents. Thermal-induced gas eﬀusion experiments are also used to study the thermal stability of the ﬁlms. Gas evolution experiments performed on a-C:H:N ﬁlms showed that any possible application for such ﬁlms is limited to temperatures below 300◦ C. Above this temperature H and N losses provoke severe structural changes [48]. These results conﬁrm a previous study performed on ﬁlms annealed in vacuum, which reveals a decrease in thermal stability when the amount of nitrogen incorporated in the ﬁlm increases [49]. It was shown that a-C:H ﬁlms deposited by PECVD are thermally stable up to 450◦C, compared with the 350◦C determined for a-C:H:N ﬁlms with 8 at. % of N. The thermal stability of a-C:H:F was also studied and the incorporation of ﬂuorine in the amorphous skeleton reduces the thermal stability of the ﬁlms [50]. Concerning the application of a-C:H:F ﬁlms as interconnect dielectric materials, the thermal stability of low-κ materials is of major importance since they are submitted to thermal annealing during subsequent integrated circuit manufacturing steps. Among other requirements, such as gap-ﬁll capability, adhesion and minimal moisture absorption, thermal stability up to 400◦ C is necessary. However, despite some claims that plasma-deposited carbon ﬂu-

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orinated ﬁlms are thermally stable at those temperatures, the usefulness of a-C:H:F ﬁlms have yet to be proved by integration in an ULSI structure. The eﬀects of the self-bias voltage are illustrated in Fig. 9, where the ﬁlm density of a-C:H, a-C:H:N and a-C:H:F ﬁlms are presented as functions of V b . Our results for low-V b depositions correspond to low-density ﬁlms. Also, these ﬁlms present high luminescence Raman background, while IR results show important contents of CHn groups. These features are characteristic of a polymer-like structure, with high concentration of saturated sp3 carbons. As the self-bias is increased, the ﬁlm properties change. Within the self-bias range from −100 V to −300 V, the most remarkable structural changes occur. They can be identiﬁed by the densiﬁcation of the structure as a result of the higher generation rate of nucleation sites on the ﬁlm surface due to the more energetic ion bombardment. These ﬁlms have a diamond-like character, with high hardness and high internal stress. Films deposited at higher V b have a slightly lower density.

4 Mechanical and Nanotribological Properties The study on the nanometer scale of the physical phenomena related to the interaction of surfaces in contact and in relative motion, nanotribology, was made possible with the invention of the atomic force microscope in 1986 [51]. These phenomena are extremely important in situations like manipulation of atoms and molecules in surfaces, as well as in the operation of electromechanical devices. In the last decade, with the development of friction force microscopy, the study of wear and friction properties of materials has received increasing attention [52]. In spite of that, the study of the lubricant and tribological properties of carbon-based ﬁlms and other carbon-nanostructured materials is still in the beginning [53]. The friction and wear measurements at nanometer scale that are discussed in this section were carried out using an atomic force microscope (AFM) operated in the lateral force mode. During the experiments the temperature and the relative humidity were kept constant at 23◦ C and 40%, respectively. The cantilever normal force was obtained by multiplying the measured cantilever bending by its normal bending constant. In order to obtain the absolute values of the friction coeﬃcients, the cantilever bending constant was calibrated using the formula of Neumeister et al. [54], while the AFM was calibrated with the method proposed by Liu et al. [55]. In this section we present both the internal stress and ﬁlm hardness results. The internal stress determination was made by measuring the curvature of the substrate by means of stylus proﬁlometry and by applying Stoney’s equation, as described in detail elsewhere [56]. The hardness of the ﬁlms was measured employing a nanoindenter. The ﬁlm hardness was obtained according to the Oliver and Pharr method [57].

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Fig. 10. (a) Compressive internal stress and (b) hardness as functions of the incorporated nitrogen

The discussion in the previous section shows that a-C:H:N ﬁlms with up to 11 at. % of nitrogen retained their diamond-like properties, despite the progressive graphitization induced by nitrogen incorporation. The compressive internal stress and hardness are presented in Fig. 10 for a-C:H:N ﬁlms. It is well known that the high internal compressive stress observed in a-C:H ﬁlms may be viewed as a result of the material overconstraining. This means that the relatively high carbon sp3 fraction observed in hard a-C:H ﬁlms causes the mean atomic coordination number to be higher than the ideal value predicted for a fully constrained network [58]. In this scheme, any stress relief process may be strongly coupled to a reduction of the coordination number. In the case of a-C:H:N ﬁlms, the important decrease in the internal compressive stress upon nitrogen incorporation (Fig. 10a) is conceived as a combination of the chemical composition, since nitrogen atoms admit a coordination number equal to 3 at most, and hybridization states. Besides the nitrogen incorporation itself, which occurs at the expense of the carbon content, the sharp increase in the fraction of carbon atoms in sp2 -hybridization state is a source of decrease in the mean coordination number. Thus, for 9 at. % of nitrogen content in a-C:H:N ﬁlms, the hardness shows only a slight reduction (Fig. 10b), while the internal stress is reduced by a factor of two [14]. The ﬁlm hardness and the internal stress of a-C:H:F ﬁlms were shown in Fig. 11. Fluorine-poor ﬁlms present high hardness and high compressive internal stress, which is typical of diamond-like materials. As the amount of incorporated ﬂuorine increases, the magnitudes of these quantities decrease. Films with ﬂuorine content of 22 at. % are nearly stress-free and their hardness was reduced by a factor of 3 when compared to a-C:H ﬁlms. This hardness is still more than a factor of 10 higher than the values obtained for PTFE. Further incorporation of ﬂuorine leads to soft ﬁlms with slightly ten-

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Fig. 11. (a) Compressive internal stress and (b) hardness as functions of the incorporated ﬂuorine

Fig. 12. Contact angle as a function of the ﬂuorine content of the ﬁlms

sile stress. The reduction of the internal stress in a-C:H:F can be explained by the more relaxed and less dense polymeric structure of these ﬁlms [23]. The hydrophobicity of these ﬁlms was investigated by contact angle measurements. The results indicate an increase in the contact angle as the ﬂuorine content of the ﬁlms increases (Fig. 12). The increase in the contact angle in ﬂuorinated amorphous carbon materials was attributed not only to a higher incorporation of ﬂuorine but mostly to the presence of CFn groups on the surface [59]. In fact, the ﬂuorine richest ﬁlms have a F/C ratio of only 0.5

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Fig. 13. Friction coeﬃcient as a function of the contact angle

but present contact angles of 95◦ . On the other hand, PTFE has a F/C ratio of 2 and presents contact angles in the range 104–111◦ [25]. From the results presented in Fig. 13, the importance of the surface wettability on the friction mechanism is clear. In this ﬁgure, the friction coeﬃcients were plotted as function of the contact angle and show a nearly linear decrease. This result is in good agreement with previous observation of the inﬂuence of the surface hydrophobicity on the friction forces for a-C:H ﬁlms [60]. The importance of the nitrogen incorporation to surface hydrophobicity and friction processes was also veriﬁed when the nitrogen incorporation into ﬂuorinated carbon ﬁlms was studied [27]. In Fig. 14, the friction coeﬃcients and the contact angles were plotted as functions of the nitrogen content in the ﬁlms. It is clear from the ﬁgure that the friction coeﬃcient and the contact angle have an opposite tendency. The observed correlation between the contact angle and the friction coeﬃcient reinforce the importance of the capillary condensation kinetics in the friction process that occurs at nanometer scale: the greater the surface hydrophobicity, the less important is the water vapor condensation for the nanoscale friction process. In a recent publication [61], it was suggested that the sliding friction forces are determined by two competitive processes. Depending on the surface wettability, one of the processes can dominate. The ﬁrst one is the thermally activated stick and slip behavior, and friction is due to the cohesive forces between the two surfaces in contact. The second contribution comes from the formation of capillaries at the nanoasperities contact points between tip and ﬁlm surface due to water vapor condensation, which must be taken into consideration especially for measurements performed in air. In fact, the role of the water condensation was investigated

Contact angle (

o

)

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80

72

64

Friction coefficient

56 0.24

0.20

0.16

0.12 0

5

10

15

20

Nitrogen content (at.%) Fig. 14. Contact angle (upper part) and friction coeﬃcient (lower part) as functions of the nitrogen content in the ﬁlms. The a-C:H:F:N ﬁlms are represented by black dots, while the open dots correspond to values measured in a-C:H ﬁlms deposited in pure methane atmosphere

from the velocity dependence of the friction force, and the results revealed the importance of the surface energy [25]. In this case, the kinetics of capillary condensation of water vapor in the contact area causes a decrease of friction with increasing velocity, since for higher scanning velocities there is no time for capillary formation [61]. In the case of hydrophilic surfaces, this mechanism can predominate. Nano- and microscale wear behavior of a-C:H, a-C:H:N and a-C:H:F ﬁlms deposited by PECVD have been studied with the use of atomic force microscopy and the sliding sphere test [62]. At the nanometer scale, the wear depth is observed to increase linearly with the increase of the tip surface normal force. An analysis of the minimum force necessary to scratch the surface, obtained by extrapolating the wear versus load force curve, as well as the wear rates and the scratch depth test results, show that the wear is strongly related to the ﬁlm hardness and microstructure. This fact has been observed either in a very low force regime, in the range of µN using the AFM, or with

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Fig. 15. Wear rate and critical force to scratch the ﬁlms as functions of the hardness. For sake of comparison, the wear rate obtained for the Si substrate is 20 × 103 mm3 /Nm. The lines are only eye-guides

forces in the range of mN with a sphere abrasion equipment, since a similar trend is observed in both scales. Even though the range of forces and the wear process in both tests are quite diﬀerent, we are led to the conclusion that the hardness of the ﬁlms plays the dominant role in determining their wear performance in both nano- and microscales [62]. From Fig. 15, it is seen that the wear rate of the polymeric a-C:H:F ﬁlm is higher than the values obtained for the a-C:H ﬁlm. The results show that when the ﬁlm hardness decreases, an increase in the wear rate, as determined by a sphere test, is observed. At the micrometer scale, the hardness of the ﬁlms appears to be the dominant factor in determining the wear resistance. In this ﬁgure we also plot the critical force to scratch the ﬁlm surface using the AFM tip as a function of the ﬁlm hardness. In this last set of data, the hardness also appears as a good parameter to present the data.

5 Conclusion We found that a-C:N:H ﬁlms with up to 11 at. % of N retained their diamondlike properties, despite the progressive graphitization induced by nitrogen incorporation. In this case, the reduction of the internal stress without substantial changes in the ﬁlm hardness was attributed to the reduction of network connectivity. On the other hand, the increase of the ﬂuorine content results in polymer-like ﬁlms, with smaller internal stress and hardness. A structural

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transition from diamond-like to polymer-like ﬁlms as a result of the incorporation of ﬂuorine could be inferred. As a general rule, ﬁlms deposited with low values of self-bias voltage result in polymeric materials. In which concerns the ﬁction properties, surface hydrophobicity plays an important role in the friction properties. One can control the friction behavior of a-C:H ﬁlms and their alloys by changing the surface energy via the incorporation of ﬂuorine (increases the surface hydrophobicity) or nitrogen (reduces the surface hydrophobicity). In this way, the friction coeﬃcient and the contact angle have an opposite tendency. On the other hand, the wear rate is nearly independent of the chemical composition of the ﬁlm, but is directly proportional to the ﬁlm hardness. Acknowledgements The author is very grateful for the fruitful discussions with D.F. Franceschini, G. Mariotto, R. Prioli, L.G. Jacobsohn and M.E.H. Maia da Costa. This work is partially supported by the Brazilian agencies: Funda¸c˜ao de Amparo a` Pesquisa do Estado do Rio de Janeiro (FAPERJ), Conselho Nacional de Desenvolvimento Cient´ıﬁco e Tecnol´ogico (CNPq) and Coordena¸c˜ao de Aperfei¸coamento de Pessoal de N´ıvel Superior (CAPES).

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Index a-C:H, 218–220, 222–224, 227–230, 232–234 a-C:H:F, 219–224, 226, 228–234 a-C:H:F:N, 219, 233 a-C:H:N, 218, 220–224, 226, 228–230, 233 sp2 -bonded clusters, 217 cluster size, 226 annealing, 228

atomic force microscopy (AFM), 229, 233, 234 carbon coordination, 230 coatings protective coatings, 218 D band, 224, 225 D/G band intensity ratio, 225, 226 density, 224, 227–229 diamond, 217

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diamond-like carbon (DLC), 218, 224, 228–230, 234 diamondlike carbon (DLC), 217

nanotribology, 229 nanotubes, 218 nitrogen incorporation, 217–219, 221, 224, 226, 228, 230, 232, 234

electrical properties, 218, 219 electron energy loss spectroscopy (EELS), 224, 226

optical properties, 218

ﬂuorine incorporation, 217–219, 223, 224, 226–228, 230, 231 friction coeﬃcient, 219, 229, 232, 233 fullerene, 218

plasma-enhanced chemical vapour deposition (PECVD), 218, 219, 228, 233 polymer-like carbon (PLC), 224, 227–229, 234 polymers, 217

G band, 224, 225 graphene, 218 graphite, 217 graphite-like carbon (GLC), 218 graphitization, 230, 234 hardness, 218, 229–231, 233, 234 hydrogen incorporation, 218 hydrophobicity, 219, 231, 232, 235 infrared (IR) spectroscopy, 224, 227, 229 internal stress, 217, 218, 229–231, 234 ion beam analysis (IBA), 220, 224 mechanical properties, 217–219, 229 microstructure, 217, 219, 224, 228, 233

Raman spectroscopy, 224–226, 229 silicon incorporation, 218 subplantation model, 217, 218 thermal stability, 218, 219, 228 thermal-induced gas eﬀusion, 228 tribological properties, 217, 219, 229 ultra-large scale integrated circuits (ULSI), 219, 229 wear resistance, 229, 233, 234 wettability, 219, 232 x-ray photoemission spectroscopy (XPS), 224, 227

Ion Microscopy on Diamond Claudio Manfredotti Dipartimento di Fisica Sperimentale and Centro d’Eccellenza “Nanostructured Interfaces and Surfaces” (NIS), Universit` a di Torino, Via P. Giuria 1, I-10125 Torino, Italy [email protected] Abstract. Because of its physical properties (strong radiation hardness, wide energy gap with a consequent extremely low dark current, very large electron and hole mobility) diamond is a very good candidate for nuclear particle detection, particularly in harsh environments or in conditions of strong radiation damage. Being commonly polycrystalline, diamond samples obtained by chemical vapour deposition (CVD) are not homogeneous, not only from the morphological point of view, but also from the electronic one. As a consequence, as it was indicated quite early starting from 1995, charge collection properties such as charge collection eﬃciency (cce) are not uniform, but they are depending on the site hit by incoming particle. Moreover, these properties are inﬂuenced by previous irradiations which are used in order to improve them and, ﬁnally, they are also dependent on the thickness of the sample, since the electronic non uniformity extends also in depth by aﬀecting the proﬁle of the electrical ﬁeld from top to bottom electrode of the nuclear detector in the standard “sandwich” arrangement. By the use of focussed ion beams, it is possible to investigate these non uniformities by the aid of techniques like IBIC (Ion Beam Induced Charge) and IBIL (Ion Beam Induced Luminescence) with a space resolution of the order of 1 µm. This relatively new kind of microscopy, which is called “ion microscopy”, is capable not only to give 2D maps of cce, which can be quite precisely compared with morphological images obtained by Scanning Electron Microscopy (generally the grains display a much better cce than intergrain regions), but also to give the electric ﬁeld proﬁle from one electrode to the other one in a “lateral” arrangement of the ion beam. IBIL, by supplying 2D maps of luminescence intensity at diﬀerent wavelength, can give information about the presence of speciﬁc radiative recombination centers and their distribution in the material. Finally, a new technique called XBIC (X-ray Beam Induced Charge), which makes use of very collimated (to 0.1 µm) x-ray beams from high energy electron synchrotrons, opens new ways to map cce with a less damaging radiation and with a better energy resolution. In this paper we resume recent and less recent work carried out by our group by using these techniques, a work that has been undertaken afterwards also by other research groups in the world. In particular, topics such as the better homogeneity obtained by “priming” and the eﬀects of “light priming”, together with a certain “complementarity” between IBIC and IBIL maps, giving evidence that radiative recombination centers along the grain boundaries or in damaged regions are important in aﬀecting cce, will be presented and discussed in some details. The conclusion is that ion microscopy is a powerful and essentially unique method for the investigation of diamond and other semiconductor materials proposed for nuclear detection. G. Messina, S. Santangelo (Eds.): Carbon, The Future Material for Advanced Technology Applications, Topics Appl. Phys. 100, 239–265 (2006) © Springer-Verlag Berlin Heidelberg 2006

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1 Introduction Ion microbeams [1] represent a powerful tool for investigating the physical and chemical properties of solids. Even if the spatial resolution is still lower than for electron microscopy (SEM, TEM), the types of measurement with ions (protons, helium) are wider and their accuracy is much better. In eﬀect, ion microbeams in the energy range between 2 and 10 MeV or more allow for: (1) trace elements analysis and chemical composition measurements down to ppma range [2] and below (particle-induced X-ray emission, PIXE), due to the absence of bremsstrahlung radiation background; (2) measurement of transport properties [3] of semiconductors (charge collection distance or drift length, mobility-trapping time product) and for the acquisition of the relevant maps over regions as wide as 2 mm or more (ion beam-induced charge, IBIC); (3) measurement and mapping of luminescence properties [4] down to a thickness of 100 µm or more, with respect to 1 µm depth reached by CL (ion beam-induced luminescence, IBIL); (4) measurement of doping levels down to 1 ppma with a depth resolution of 1 nm (Rutherford, RBS backscattering) or light elements distribution proﬁles with the same resolution (elastic recoil diﬀusion, ERD). The precise deﬁnition of the range, the very low Coulomb scattering and lateral straggling keep the spatial resolution at the same level as the ion spot diameter, while the possibility of getting a trigger signal allows for the realization of time-resolved measurements, which give information about time behaviour of the measured parameter, such as radiative recombination lifetime with IBIL. The number of charges released by ions is so large to allow for the possibility of getting a map just in one pass over the selected area without getting problems with radiation damage, which, of course, is heavier with ions than with electrons. Even if this technique is much younger than electron microscopy, there are now on the market apparatuses which are technologically advanced and which are to some extent as user-friendly as SEM or TEM. In this paper we shall concentrate only on IBIC and IBIL measurements on diamond, both CVD and natural, because diamond is a very interesting material for the realization of nuclear and other kinds of detectors (very large resistivity, complete depletion over thick regions at low voltages, extremely high resistance to radiation damage). Still, diamond has the problem of being mainly polycrystalline and, as it will be shown, this structural property is reﬂected in material nonhomogeneity with respect to radiation response or charge collection eﬃciency (CCE). Change collection eﬃciency is deﬁned as the fraction of generated charges which are contributing to the current pulse released by the nuclear particle or by some ionising radiation crossing the sample. IBIC [5, 6, 7, 8] represents, in fact, the only simple way to map CCE over suitable region sizes, while with IBIL it is possible to select the regions which limit CCE by giving rise to a strong radiative recombination, which characterizes by its blue light emission the luminescence properties of the purest, detector grade, diamond.

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Fig. 1. The proton microbeam set up at AN-2000 electrostatic accelerator in Legnaro National Laboratories (LNL) of National Institute for Nuclear Physics (Italy)

2 IBIC There are more than 50 ion microbeam apparatuses around the world and many of them are in Europe. One such apparatus, that at the National Laboratories of Legnaro, Italy, National Institute for Nuclear Physics, is illustrated in Fig. 1, which shows the last part of AN-2000 electrostatic accelerator [6] with the focusing system (three quadrupoles) and the scattering chamber. The spot diameter can be reduced down to about 1 µm, and the scanned area can be as large as 2 mm × 2 mm, but is typically much lower (400 µm × 400 µm). With a dwell time of few ms, the time taken for a full image 258 × 258 pixels is on the order of few minutes. Beam intensities are kept very low, much less than a fA. By limiting the counting rate to 100 cps, for instance, it is possible to get one event per pixel. At larger counting rates local trapping may create space charge in the pixel and reduce the charge collection eﬃciency. Some details of the scattering chamber are shown in Fig. 2. Several ports at the periphery can be used for signal outputs related to the collected charge (IBIC), induced luminescence (IBIL, with monochromator and phototube), charateristic X-rays revealed by a Si(Li) detector suitably cooled by a liquid nitrogen dewar (PIXE), ions backscattered from the sample as revealed by a Si surface barrier detector (RBS). Downstream a similar detector may be used for scanning transmission ion microscopy (STIM) and other similar detectors may be used for other techniques (a Faraday cup can be used for detection of secondary electrons to obtain secondary electrons ion microscopy

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Fig. 2. Details of the scattering chamber used in LNL for IBIC/IBIL measurements

(SEIM) images. A scintillator is used to detect beam position and to align the samples under investigation. An IBIC setup is schematically shown in Fig. 3. The acquisition is carried out event-by-event in a ﬁle (x, y, collected charge) giving the possibility to replay the events in order to follow some speciﬁc behaviour (polarization, for instance). IBIC could be used both in standard frontal geometry and also in “lateral” geometry [9, 10], on a cross section of the sample (Fig. 4). There are a number of important advantages for lateral IBIC. First, carriers are immediately swept apart by the electrical ﬁeld and plasma recombination is avoided. In addition, CCE can be proﬁled as a function of depth, giving information concerning diﬀerent regions in inhomogeneous samples, like CVD diamond. Third, some CCE loss under the electrodes can be suitably monitored. Finally, proﬁles of the electrical ﬁeld could be obtained under some reasonable assumptions. The drawbacks of obtaining a cross section of the sample, of getting in general large dark currents and some fringing ﬁeld effects, are overcome in CVD diamond by cleaving the sample (dark currents remain very low) and by using protons of a suitable energy in order to place the Bragg’s peak at a depth large enough to be sure to have a real bulk electric ﬁeld. In frontal IBIC [7,11] it is possible to obtain CCE maps with the maximum contribution given by carriers generated at the depth of Bragg’s peak, which ranges from 25 µm (2 MeV protons) up to more than 100 µm for 9 MeV protons (shorter thicknesses are reached with few MeV helium ions). Frontal IBIC may present some problems in thicker CVD diamond samples with drift lengths of both carriers much longer than thickness. In eﬀect, with respect

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Fig. 3. Layout of a typical IBIC experiment

Fig. 4. Description of the geometry of irradiation and signal collection in a lateral IBIC measurement. In frontal IBIC the microbeam hits one of the two electrodes

to the minimum ionising particles (mips), as may be deﬁned for almost all the particles coming out from high-energy experiments, ionisation density is more than 100 times larger (0.7 MeV/mm for mips and 80 MeV/mm for 2 MeV protons, on average). Taking into account the lateral diﬀusion of charge, created by δ-rays, assuming carrier lifetimes in diamond on the order of 0.1 ns, the ionisation given by low energy protons can give rise to an

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Fig. 5. A frontal IBIC map carried out on a CVD diamond sample biased at +600 V (front electrode) together with the relevant multichannel pulse spectrum. The proton energy is 2 MeV. The electrode diameter is 2 mm. Previous X-ray priming of the sample amounted to 10 Gy

instantaneous carrier density on the order of 1013 –1015 cm−3 , which is much larger than the equilibrium one (about 105 cm−3 ) in diamond. Mips create much more energetic δ-rays, and local ionisation density along the track is lower by some orders of magnitude. With respect to mips, it is expected that frontal IBIC maps could be aﬀected by polarization eﬀects, even if priming with X-rays is used in order to ﬁll the traps and make the response of the sample more homogeneous. One example is given in Fig. 5, which shows a CCE map together with the relevant multichannel spectrum obtained on a CVD diamond detector 600 µm thick in which a charge collection distance (CCD) of 75 µm was measured by using mips. CCD, which is deﬁned as the average distance between electrons and holes, as averaged over the thickness of the sample, is obtained simply by multiplying the average CCE by the thickness. It has been proved by the “linear model” that it increases linearly from the back to the growth face of the sample. In our case, even if the average CCE is between 10 and 15%, in agreement with data obtained with mips, the spatial distribution is very inhomogeneous, with large regions of the sample in which, because of strong polarization, no events were recorded. In fact, after 2 hours of measurement, the event rate dropped down to zero, while it started at more than 100 cps. The homogeneity of the response [12] is quite important in tracking applications, since the precise event position is reconstructed as a center of mass

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Fig. 6. A frontal IBIC map carried out on the same CVD diamond sample biased at −600 V (front electrode) and under illumination, together with the relevant multichannel pulse spectrum. The scan region is the same as in Fig. 5

by means of the collected charge in nearby strips or pixels and, if CCE is not uniform, the position is badly reconstructed. In IBIC maps there are small regions with CCE as large as 30–35%, which should correspond to CCD values of about 200 µm, the best it is possible to get in similar samples. As a matter of fact, these regions are corresponding to almost perfect diamond monocrystals, as evidenced in maps obtained on thin samples by X-rays. By illuminating the sample with blue light (400 nm) or with white light and by switching the polarity to negative bias (Fig. 6) the situation changes drastically: high-eﬃciency spots are still there, but now the large “blind” region among these spots has got CCE values of about 10%, i.e., CCD values of 60 µm, close to those obtained by mips. If these regions are disordered regions with grain boundaries and dislocations, with a lot of ﬁlled dangling bonds and a distributed space charge with very low electric ﬁelds, now this optically induced detrapping eliminates, at least partially, this space charge and the relevant polarization and thereby improves CCE. Since these data were obtained by 2 MeV protons (25 µm penetration depth) and with a negative bias voltage applied at the front electrode, we can immediately attribute this beneﬁcial eﬀect to electrons, which are giving the main contribution to the charge signal according to Ramo’s theorem. In fact, this theorem states that a charge contributes with the fraction of the covered path with respect to the extension of the electrical ﬁeld (sample thickness in this case, as evidenced by lateral IBIC and discussed in the next section).

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Fig. 7. Lateral IBIC CCE proﬁle on a cross section of a CVD diamond sample 200 µm thick. Bias voltage (+400 V) is applied at the growth side (left). The proﬁle was averaged over a region 450 mm wide. Black squares are the experimental data, the continuous line is the ﬁt, empty and ﬁlled circles are holes and electrons contributions, respectively

Fig. 8. Lateral IBIC CCE proﬁle on a cross section of the same CVD diamond sample 200 µm thick. Bias voltage (−400 V) is applied at the growth side (left). For symbols see Fig. 7

3 Lateral IBIC Lateral IBIC [9,10,13,14,15] has been used in order to test the “linear model” and to throw some light on the electric ﬁeld depth distribution, which is generally assumed to be uniform. Moreover, from CCE depth proﬁles obtained

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now without polarization eﬀects and therefore in conditions not diﬀerent from the mips case, it is possible to evaluate CCD from experimental data and compare it with data obtained with mips. In order to do this, charge collection distance or charge collection length should be better deﬁned as drift length µτ E, i.e., the product of (mobility)×(trapping time)×(electric ﬁeld), which is a local value and can be diversiﬁed for the two carriers. Then the average value of the sum of µτ E for electrons and holes over the sample thickness, taking into account that ionisation for mips is uniform, can be compared with CCD. This is what will be done in what follows. We can start from CCE distributions (Figs. 7 and 8) for positive and negative bias voltages, respectively (the voltage is applied on the left, which is also the growth side) in the case of a sample 200 µm thick. It can be observed that these distributions do depend on the bias voltage polarity, essentially because mobility lifetimes are diﬀerent for the two carrier types and also because the electric ﬁeld distribution is diﬀerent due to the electric contacts. In eﬀect, by looking at both curves, one observes that peak CCE is closer to the negative contact. This means, by Ramo’s theorem, that the main contribution in this case is given by electrons, which have at their disposal a much longer path towards the anode. It is possible to express CCE by Ramo’s theorem as a double path integral for each carrier as a function of hit point of the beam and to obtain CCE distribution in terms of µτ E depth distribution separately for each carrier. In order to reduce the number of parameters, one can make a more physical “linear model” assumption in terms of a linear dependence of µτ on depth, increasing from the back (substrate) side, a constant ratio of µτ between the two carriers and a suitable parametrization of the electrical ﬁeld with as few parameters as possible [3]. Apart from electrical ﬁeld, all the other parameters are kept constant for all the bias voltages investigated (seven in total). From Figs. 7 and 8 it can be deduced that eﬀectively the largest contribution to CCE (about ten times) is given by electrons, which display an almost uniform value of µτ of about 5 × 10−7 cm2 V−1 , with a resulting ﬁt to experimental data that can be considered quite good (not only in this, but also in all the other cases). The electric ﬁeld distribution is, however, diﬀerent, with a peak at the positive front side and a much more penetrating behaviour in the case of a negative front side. The eﬀect of the electric ﬁeld is that of giving a similar behaviour to drift lengths of both carriers (Fig. 9), with an average value of 100 µm for electrons at −400 V and with a decay at both electrodes. The ﬁnal result is to get a combined drift or mean collection length, averaged over the sample thickness and deﬁned here as Le + Lh , similar to CCD and symmetric with respect to the bias voltage (Fig. 10). The same behaviour resulted from mips data, with a quite close value of 50 µm for CCD at 200 V, i.e., at an ohmic electrical ﬁeld of 1 V/µm and of 100 µm at 2 V/µm. Apart from the details of the deconvolution of CCE in terms of diﬀerent contributions of electrons

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Fig. 9. Electron and hole drift lengths (L) as a function of depth derived from previous ﬁgure, together with the proﬁle of the electric ﬁeld

Fig. 10. Behaviour of mean collection length L for electrons (ﬁlled circles), holes (open circles) and both carriers (ﬁlled squares) as a function of bias voltage obtained by simulating the behaviour of a mip

and holes, this result is given directly from ﬁgures like Figs. 7 and 8, and it proves the validity of lateral IBIC in deriving CCE depth distributions. In the same way, it is possible to observe the eﬀect of priming or pumping (see [16] at p. 93), i.e., with irradiations of the sample with X-rays or highenergy electrons, in order to stabilize the performances of the detector. After a priming dose of 46 Gy (Fig. 11), the CCE proﬁle has a higher and broader peak and it is much improved in the right part at lower values of CCE. This is an average over a cross section region of 450 µm. By considering now the single paths connecting the two electrodes (called here “columns”), one

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Fig. 11. Lateral IBIC CCE proﬁles on a cross section of the same CVD diamond sample 200 µm thick, as obtained before (top) and after (bottom) a priming dose of 46 Gy. Bias voltage (−300 V) is applied at the growth side (left)

obtains distributions of CCE like those reported in Fig. 12, which measures the average increase of CCE or CCD given by priming. Since peak eﬃciency increases from 0.153 to 0.283 after priming, the improvement amounts to a factor 1.8, which is exactly the same as that obtained with mips [16]. What can be observed in more detail is that this improvement is really “local”, as clearly shown in Fig. 13, which refers to the detailed efﬁciency proﬁle obtained along the border of the top (or front) electrode and derived from the averages along the “columns”, as it was for Fig. 12. The exact comparison with the results concerning uniformity of CCE obtained by mips, which have been here simulated by starting from CCE proﬁles across the sample, will be reported in what follows. It is clear that in our case we got uniformity along a line, while with mips the uniformity refers to an area, which is, of course, impossible to obtain by our approach. However, it has to be noted that the nonuniformity, obtained as a standard deviation from ﬁts reported in Fig. 12, is decreased by priming from 32.7% to

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Fig. 12. Distributions of CCE as obtained from the same data as Fig. 11 and averaged over the diﬀerent straight lines connecting the two electrodes (called “columns”): these distributions simulate CCE as viewed from mips with hit points along a straight line (the border of top electrode). The ﬁt has been obtained with two Gaussian curves for the nonirradiated or unprimed case (mean 0.153, FWHM 0.059 for the ﬁrst peak, mean 0.283 and FWHM 0.035 for the second one) and one Gaussian line for the primed case (mean 0.292, FWHM 0.077)

Fig. 13. Proﬁle of CCE as viewed by mips along a segment of top electrode, for the primed and unprimed case

22.2%. This result conﬁrms those reported more qualitatively in Figs. 5 and 6: the improvement is due to the strong increase of the number of pixels showing CCE values around 10–15%, but also to the analogous increase around 30% of CCE. It is conﬁrmed that, as observed in Figs. 5 and 6, those regions were already present in a smaller number in the nonirradiated sample.

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Fig. 14. Layout of IBIL apparatus, with ellipsoidal mirror, the monochromator and the phototube

4 IBIL With the same proton microbeam, it is also possible to carry out IBIL measurements [3, 4, 17, 18, 19] and to map the luminescence eﬃciency produced by the beam itself. When, as occurs in diamond, the radiative recombinations are important and at least comparable with the nonradiative ones, IBIL maps are indicative of regions with lower CCE. As a consequence, by the examination of the relevant wavelength spectra, it is possible to infer which are the recombination centers responsible for the low values of CCE. A IBIL schematic setup is given in Fig. 14. The microbeam enters a small hole (diameter of 1 mm) of an ellipsoidal metal mirror, which allows for the beam scanning, and the light is collected by a vacuum light guide without dispersions or absorptions (two photos of mirror and monochromator in Fig. 15). With a 0.25 m focal length monochromator it is possible to reach a good wavelength resolution in the interval 300–900 nm, which is also the region of the maximum quantum eﬃciency of the phototube. Two retractable mirrors give the possibility of also carrying out panchromatic images. With respect to standard cathodoluminescence (CL), the electronic chain works in pulse conditions: the signal from the phototube is ampliﬁed by a gated ampliﬁer (gate of 70 ms at each microbeam position), and the pulses are collected and simply counted (no pulse height analysis is carried out) until the beam moves to the next position. Taking into account the microbeam intensities, which are here much higher than for IBIC (about 700 pA), the luminescence eﬃciency of the sample, the solid angle viewed by the mirror, its reﬂectivity, the optical band pass, etc., we are led to the conclusion that we are just counting the photons, i.e., one event per pixel and no pile-up problems. As a consequence, the maps are intended to be maps in photon number, instead of CCE or electron number as in IBIC. In any case, the map signals are not to be quantitatively related by a direct proportionality to the luminescence inten-

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Fig. 15. Photographs of parts of IBIL apparatus

sity coming from the relevant pixels. The advantages with respect to CL are that the luminescence is a real bulk luminescence, i.e., it comes mainly from a deﬁned depth due to the Bragg’s peak and time-resolved measurements can be carried out by this approach. An example of the complementarity between IBIC and IBIL maps is given in Fig. 16. The maps were carried out on the same sample cross section (and therefore are to be quoted as lateral). As expected, IBIC CCE is higher in the upper part of the map, which is on the growth side and contains larger and better quality grains, while IBIL is higher in the bottom region, in which the grains are smaller and the defective regions are wider. Of course, there are exceptions, such as the big luminescent region at the center-left extending towards the upper contact, as there are regions completely white, in which

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Fig. 16. Top: Lateral IBIC maps on a cross section of a CVD diamond sample 600 mm thick. The growth side is on the top, the region is about 400 mm wide. Proton energy 2 MeV. Bottom: Lateral IBIL map on the same cross section. The substrate side is more visible at the bottom. Proton energy 2 MeV

Fig. 17. Frontal IBIL spectra on a CVD diamond sample of good electronic quality. The spectra are decreasing in intensity at increasing proton doses. Proton energy 2 MeV

both CCE and luminescence are low or absent. It could also be that the two maps, which were carried out without moving the sample, the scan size and the beam position (but, of course, focusing or collimation had to be changed because of higher intensity needed by IBIL) are not exactly coincident and that the complementarity could be better than what “rigidly” observed. It is suggested that IBIL maps are indicative of the “non-detector quality” regions present in the sample; what therefore are the defects responsible for the worsening of CCE? The answer is clearly given in Fig. 17, which reports

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Fig. 18. Frontal IBIL spectrum on a CVD diamond sample of bad electronic quality. The spectra are decreasing in intensity at increasing proton doses. Proton energy 2 MeV

a wavelength spectrum obtained on a CVD diamond sample of good quality: the presence of the blue A-band at about 440 nm (2.8 eV), attributed to dislocation networks, is indicative of the facts that the main contribution to the decrease in CCE is given by the disordered regions in which a lot of dislocations are present and that these regions occupy the space between the “good grains” (the other band at 515 nm, 2.41 eV is the H3 center, probably created by irradiation itself). The IBIL spectra were taken subsequently and it is seen that radiation damage probably converts radiative regions to nonradiative ones (or also creates vacancies in N–N groups that decorate A-band regions by converting them in H3 centers, which are believed to be N–V–N centers). Figure 18 shows the same spectra for a non-detector quality CVD diamond sample. It appears that there is another broad band at about 600 nm, which also strongly decreases as a function of radiation damage. The damage-induced decay of the A-band is shown in Fig. 19, which reports the area under the peak as a function of proton dose. The decay is observable after doses on the order of 1015 p/cm2 , which are obtained in few minutes of measurement. The decay seems to be exponential with the dose, which could suggest some kind of “positive reaction”, i.e., the presence of damage itself seems to facilitate the production of damage. The problem of attributing the space distribution of the luminescent centers can be solved also by CL maps, which display a better spatial resolution, as shown in Fig. 20. There are – for the same cross section of the sample to which Fig. 17 refers – respectively a SEM secondary electron image, and three CL images (panchromatic and monochromatic at 440 nm and 600 nm). Apart from the consideration that CL, which is more sensitive to dislocations, gives a brighter image of the columnar structure of CVD diamond cross section, it

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Fig. 19. Decay of intensity of blue A-band at 433 nm as a function of proton dose

Fig. 20. SEM micrograph (secondary electrons) and three CL maps of a cross section of a CVD diamond sample of good electronic quality (monochromatic at 440 nm, at 600 nm and panchromatic)

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Fig. 21. SEM micrographs (secondary and backscattered electrons) and two CL frontal maps on a sample of bad electronic quality

can be clearly observed that luminescence at 440 nm (blue A-band) gives the main contribution also in this case, while the luminescence at 600 nm, apart from some spots, is not spatially well correlated with dislocated regions. A better view is given in Fig. 21, in which single grains have a sharper appearance. Here a micrograph by backscattered electrons is also included, since it gives a sharper identiﬁcation of single-crystal grain dimensions in depth. It can be observed that while the luminescence at 440 nm reproduces exactly the borders of the two main squared grains at the center of the image, the luminescence at 600 nm is much broadly distributed in the volume of the sample. According to our interpretation, this band is due N– V complexes distributed in the sample and created by lower temperatures at which the mobility of the species at the surface is lower. These centers should be responsible for the short CCD of holes in non-detector quality diamond: when ﬁlled during priming, they could allow for a longer CCD of holes themselves. These should be therefore mainly in-grain centers. Centers responsible for A-band luminescence are certainly intergrain centers, and they could be responsible for electron recombination, which is mainly radiative. By illuminating the sample at around 400–440 nm, these centers are emptied and the space-charge, due to electron capture, disappears, strongly improving CCD of electrons, which are now able to reach CCD values above the grain dimensions and to overcome grain boundaries.

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Fig. 22. The ID21 beam line of ESRF and the scanning X-ray microscope, with a layout of XBIC

5 XBIC The recent availability of X-ray microbeams has opened the possibility of carrying out IBIC measurements (referred here as XBIC) with a much better spatial resolution [20, 21]. This turned out to be possible at ID21 line at ESRF of Grenoble (see Fig. 22, which shows in some detail the scanning X-ray microscope (SXM)). The nominal diameter of the X-ray spot is well below 1 µm in this case, the measurements are carried out in air, pixel size is 1 µm and the dwell time of the beam in each pixel can be varied from 100 to 400 ms. Time-resolved measurements were not possible due to the very tight time structure of the beam, and therefore the measurements were carried out in current by using a picoamperometer. The nominal photon intensity at 5.5 KeV was about 108 photons/s. The synchronous acquisition of the photocurrent signal and of the signal coming from the sample micropositioning system allowed for image formation on a pixel-by-pixel basis as in proton IBIC. There are two main diﬀerences, however, with respect to IBIC: one is related to the diﬀerent energy loss of electrons and protons and the other to the output signal. With respect to 2 MeV protons, 5.5 KeV X-rays display a much lower energy loss (Fig. 23) and an exponential absorption, which lets them penetrate thicknesses of much more than 100 µm. As a consequence, carrier generation may be assumed to be roughly uniform across the sample for thicknesses on the order of 100 µm. Space charge and polarization problems are experimentally absent in XBIC. The photocurrent is a DC signal which may include gain, and carrier generation represents a strong perturbation with respect to

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Fig. 23. Energy absorption coeﬃcient for 5.5 KeV X-rays and percent stopping power of 2 MeV protons as a function of depth in diamond

Fig. 24. XBIC map of a diamond sample (the same as in Figs. 5 and 6): X-ray energy, 5.5 KeV, bias voltage +200 V applied at the back side (substrate). The small square indicates a 100 × 100 µm2 region over which the maps and spectra of Figs. 25 and 26 were obtained

the IBIC proton case, even if also with protons the local perturbation is not small. In any case, the photocurrent is another way to get CCE values, and it will reported in eﬀect as photoconductive gain with respect to dark current in arbitrary units, since quantitative estimates of CCE are not possible. An example of an XBIC map is given in Fig. 24, which refers to the same sample as Figs. 5 and 6. The circular electrode is clearly visible, and the black spot at the center is due to a drop of silver paste used for gluing the wire to

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Fig. 25. XBIC photocurrent maps obtained at diﬀerent (positive and negative) bias voltages over the region indicated by a square in Fig. 24

the electrode. The nonuniformity of the current is due to the nonhomogeneity of the electronic properties of the sample, being the electrode, as observed by an optical microscope, perfectly smooth. An idea of the much better spatial resolution achievable is given in Fig. 25, which shows the maps at diﬀerent negative and positive bias voltages obtained in the small square indicated in the previous ﬁgure. “Grains” of dimensions much smaller than 20 µm are visible in particular at low bias voltages, while the overall uniformity and the average photocurrent increases with bias voltage. It seems that uniformity is better at positive bias; in eﬀect this observation is conﬁrmed by Fig. 26, which reports the “multichannel spectra” of the photocurrent obtained by sampling during the dwell time. These spectra are displayed here in terms of numbers of pixels instead of counts, in order to make a better comparison in terms of uniformity. Since the bias is applied on the back side with respect to the incoming beam and since X-ray absorption is much larger in the ﬁrst 100 µm (Fig. 23), it can be assumed that the main contribution is given by electrons, which have at their disposal a much longer path. This conclusion is in agreement with what was reported for the same sample in the discussion concerning lateral IBIC. In eﬀect, the spectra of Fig. 26 are narrower at positive bias voltages with respect to negative ones, and this means that spatial uniformity is better, even if the mean photocurrent is larger at negative bias. The logarithmic grey scale used in these ﬁgures is used to improve the contrast between nearby regions in order to observe “structures” given by the photocurrent signal and to obtain a better correspondence with the morphology of the material. Since the sample is quite thick (0.6 mm) and since also since the penetration depth of X-rays is quite large, this correspondence is not easily seen (and in eﬀect it can be and it has been observed in much thinner samples). However, with respect to a colour-based IBIC map, a map graphically obtained with a suitably selected logarithmic grey scale can give a detailed and more visible structure (Fig. 27,

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Fig. 26. XBIC photocurrent spectra of the maps reported in Fig. 25

which has been obtained with the same data of Fig. 6, in which grains of a clear geometrical structure make their appearance). One question could be given by the diﬀerent “grain” size observed in XBIC with respect to IBIC maps. This could be related to the shorter penetration depths of protons in IBIC with respect to X-rays in XBIC and to the larger grain sizes at the growth side of the sample. As already stated, one of the main applications of IBIC/XBIC is the investigation of the uniformity of the electric response in terms of CCE. It

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Fig. 27. IBIC map obtained from the same data as Fig. 6 by a suitably selected grey scale

is possible to quantitatively deﬁne the uniformity vj by dividing the selected area in bins of square size and by calculating the ﬂuctuations between the average values in the bins and the average value over the total area, according to the following equation: 2 1 i (sij − s) , (1) vj = 1 − s Nj where s is the overall average signal, sj is the average signal of the ith bin of bin size j and Nj is the number of bins of bin size j (j indicates the square root of the bin area). This exercise is presented in Fig. 28 for the central bottom region, 480 × 480 µm2 wide, of Fig. 27. The results, which are compared with the results obtained by a similar exercise carried out on an XBIC map of the same size and on the same sample, are reported in Fig. 29. It is seen that there is a relatively good agreement between the two, even if the selected regions are not the same. It has to be noted that in the case of IBIC the homogeneity has been improved by blue light illumination (Fig. 6 and the relevant part of the discussion in Sect. 3). These results are also in agreement with those obtained directly by mips in a much more cumbersome way (see [16] at p. 162) by placing two position-sensitive detectors (two couples of silicon strip detector with crossed strips), by triggering the event and by reconstructing the track across the diamond detector by a suitable analysis of the event. It has also

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Fig. 28. IBIC maps of a region 480 × 480 mm2 wide, in which CCE has been averaged over bins of increasing surface areas

Fig. 29. Eﬃciency uniformity, as deﬁned by (1), as a function of bin size, obtained in the same way from XBIC and IBIC maps

been noticed that X-ray priming improves homogeneity: this was not possible to obtain by frontal IBIC, because of the polarization eﬀect, but it has been observed by lateral IBIC by a suitable “simulation” of a mip. This result, obtained by following the lines depicted in the illustration of Fig. 12, is shown in Fig. 30. These results prove that, at low size bins at least, eﬀectively priming improves CCE uniformity.

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Fig. 30. Eﬃciency uniformity, as deﬁned by (1), as a function of a linear bin size, obtained from lateral IBIC maps as reported in Fig. 12, both for a primed and an unprimed state

6 Conclusions A new kind of ion microscopy, applied in this case to qualify CVD diamond as a nuclear detector, or even simply as an electronic material, has been described both in terms of capabilities and of speciﬁc results obtained on samples of diﬀerent quality. IBIC and IBIL can be used together with other beam techniques like PIXE, ERD or RBS in order to make a correlation with chemical impurities. The direct comparison between IBIC and IBIL maps leads to the conclusion that the morphologically polycrystalline CVD diamond is in eﬀect also “electronically” polycrystalline, i.e., the largest values of CCE and CCD are found in the central part of speciﬁcally “good” single crystal grains or columns and that the main defects responsible for the low CCE values found in CVD diamond are due to the radiative recombination defects, which are distributed along the grain boundaries. The speciﬁc contribution of the two carriers types to CCE can be separated by lateral IBIC and the proﬁle of the electrical ﬁeld across the sample can be suitably calculated, by putting in evidence the still unsatisfactory quality of the electrical contacts. The eﬀects both of standard priming and of blue light illumination have been also evidenced in terms of improvement of the homogeneity of the response, both at the surface and along the thickness of the sample. Time-resolved IBIC and IBIL may supply in the future even more powerful methods of investigation of CVD diamond, both in terms of material and of a speciﬁc detector. Improvements are under way in order to obtain a value of lateral resolution better than 1 mm and may be to reach a value of the order of 100 nm, by a more accurate design of focusing quadrupoles. If this will be the case, ion microscopy could enter the class of more standard and much more widely used electron microscopies, even if the experimental apparatus is

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much more cumbersome. In any case, it must be emphasized that the amount of information given by this kind of microscopy and the variety of techniques which can be applied is much wider, as exempliﬁed in this work. Acknowledgements The author acknowledges the important and direct contributions given by E. Vittone, A. Lo Giudice, F. Fizzotti, P. Olivero and C. Paolini, during various periods of IBIC, IBIL and XBIC measurements from 1995 to 2004, concerning data acquisition, analysis and interpretation. Many IBIC measurements reported in this review were carried out at Ruder Boskovic Institute in Zagreb (Croatia), with the professional help of M. Jaksic, S. Fazinic and I. Bogdanovic.

References [1] M. B. H. Breese, D. N. Jamieson, P. J. C. King: Materials Analysis Using a Nuclear Microprobe (Wiley, New York 1996) 240 [2] N. P. O. Homman, C. Yang, K. J. Malmquist: Nucl. Instr. Meth. A 353, 610 (1994) 240 [3] C. Manfredotti, F. Fizzotti, P. Polesello, E. Vittone, M. Truccato, A. L. Giudice, M. Jaksic, P. Rossi: Nucl. Instr. Meth. B 1333, 136–138 (1998) 240, 247, 251 [4] C. Manfredotti, G. Apostolo, G. Cinque, F. Fizzotti, P. Polesello, E. Vittone, M. Truccato, A. L. Giudice, G. Egeni, V. Rudello, P. Rossi: Diamond Relat. Mater. 7, 742 (1998) 240, 251 [5] C. Manfredotti, E. Vittone, P. Polesello, F. Fizzotti, M. Jaksic, I. Bodganovic, V. Valkovic: Scanning ion beam microscopy – a new tool for mapping transport properties of semiconductor nuclear detectors, in J. Duggan, I. Morgan (Eds.): CP392, Application of Accelerators in Research and Industry (AIP, New York 1997) pp. 705–708 240 [6] F. Cervellera, C. Donolato, G. P. Egeni, G. Fortuna, R. Nipoti, P. Polesello, P. Rossi, V. Rudello, E. Vittone, M. Viviani: Nucl. Instr. Meth. B 130, 25 (1997) 240, 241 [7] C. Manfredotti, F. Fizzotti, E. Vittone, M. Boero, P. Polesello, S. Galassini, M. Jaksic, S. Fazinic, I. Bogdanovic, M. Valkovic: Nucl. Instr. Meth. B 100, 133 (1995) 240, 242 [8] P. J. Sellin, M. B. H. Breese, A. P. Knights, L. C. Alves, R. S. Sussmann, A. J. Whitehead: Appl. Phys. Lett. 77, 913 (2000) 240 [9] C. Manfredotti, F. Fizzotti, P. Polesello, E. Vittone, P. Rossi, G. Egeni, V. Rudello, I. Bogdanovic, M. Jaksic, V. Valkovic: Nucl. Instr. Meth. B 130, 491 (1997) 242, 246 [10] C. Manfredotti, F. Fizzotti, A. L. Giudice, P. Polesello, E. Vittone, R. Lu, M. Jaksic: Diamond Relat. Mater. 8, 1597 (1999) 242, 246 [11] C. Manfredotti, F. Fizzotti, E. Vittone, P. Polesello, F. Wang: Phys. Stat. Solidi A 54, 327 (1996) 242

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[12] C. Manfredotti, F. Fizzotti, A. L. Giudice, C. Paolini, E. Vittone, R. Lu: Nucl. Instr. Meth. B 187, 566 (2002) 244 [13] E. Vittone, F. Fizzotti, A. L. Giudice, C. Paolini, C. Manfredotti: Nucl. Instr. Meth. B 446, 161–163 (2000) 246 [14] C. Manfredotti, F. Fizzotti, P. Polesello, E. Vittone: Nucl. Instr. Meth. A 426, 156 (1999) 246 [15] R. Lu, C. Manfredotti, F. Fizzotti, E. Vittone, A. L. Giudice: Mater. Sci. Eng. B 90, 191 (2002) 246 [16] D. Meier: Diamond Detectors for Particle Detection and Tracking, Phd thesis, University of Heidelberg, Heidelberg (1999) 248, 249, 261 [17] C. Manfredotti, F. Fizzotti, A. L. Giudice, P. Polesello, E. Vittone, M. Truccato, P. Rossi: Diamond Relat. Mater. 8, 1592 (1999) 251 [18] C. Manfredotti, E. Vittone, A. L. Giudice, C. Paolini, F. Fizzotti, G. Dinca, V. Ralchenko, S. V. Nistor: Diamond Relat. Mater. 10, 568 (2001) 251 [19] A. L. Giudice, G. Pratesi, P. Olivero, C. Paolini, E. Vittone, C. Manfredotti, F. Sammiceli, V. Rigato: Nucl. Instr. Meth. B 210, 429 (2003) 251 [20] E. Vittone, A. L. Giudice, C. Paolini, F. Fizzotti, C. Manfredotti, R. Barrett: Diamond Relat. Mater. 11, 1472 (2002) 257 [21] E. Vittone, A. L. Giudice, C. Paolini, P. Olivero, C. Manfredotti, R. Barrett, V. Rigato: Nucl. Instr. Meth. B 210, 159 (2003) 257

Index cathodoluminescence (CL), 251 charge collection distance (CCD), 244, 245, 247, 249, 256, 263 charge collection eﬃciency (CCE), 240, 242, 244–254, 258, 260, 262, 263 CCE maps, 242, 244 CVD diamond, 242, 244, 254, 263 detectors, 240, 241, 244, 248, 253, 254, 256, 261, 263 ion beam induced charge (IBIC), 241–243, 245–252, 257, 258, 260, 261, 263 frontal IBIC, 242–244, 262 IBIC maps, 244, 245, 252, 259–263

lateral IBIC, 242, 243, 245–250, 253, 259, 262, 263 ion beam induced luminescence (IBIL), 240–242, 251–256, 263 frontal IBIL, 253, 254, 256 IBIL maps, 251–253, 255, 256, 263 lateral IBIL, 252, 253 ion beam-induced charge (IBIC), 240 ion beam-induced luminescence (IBIL), 240 Ramo’s theorem, 245–247 X-ray beam induced charge (XBIC), 257–263 XBIC maps, 258–262

Measurements of Defect Density Inside CVD Diamond Films Through Nuclear Particle Penetration Renato Potenza and Cristina Tuv´e INFN and Dipartimento di Fisica e Astronomia, Universit` a di Catania, Via S. Soﬁa 64, I-95123, Catania, Italy [email protected] Abstract. Fast nuclear particles (light or heavy ions), passing through a diamond ﬁlm, deposit energy by ionization. It is possible to collect the developed charges by applying an electric voltage through both sides of the ﬁlm. Experimental results show that the positive hole charges and the negative electron charges have very diﬀerent mean free paths inside a real diamond ﬁlm. Holes travel more deeply than electrons, so that the charges collected under a given voltage and under the opposite one are very diﬀerent, as a suitable “two ﬂuid” microscopic model of electrical conduction of the ﬁlm can show. Furthermore, using fast particles of diﬀerent penetration produced by a Tandem accelerator, it is possible to obtain a “photograph” of the diﬀerential charge collection, which can show the distribution of charge production (through the Bragg’s ionization curve) and destruction (through the defects, and therefore on defect density along the particle path). Minimization of this defect density allows us to optimize the deposition procedure of CVD diamonds.

1 Diamond as Radiation Detector 1.1 Properties of Diamond Diamond is a solid with a density ρ = 3.51 g/cm3 . It shows a gap of 5.47 eV between valence and conduction bands, compared to that of 1.12 eV of silicon (Fig. 1). So, while silicon can be called a semiconductor, diamond is intrinsically an insulator. Its resistivity at room temperature is in fact ρD > 1012 Ω cm, more than 4 · 106 times that of pure silicon (ρSi = 2.3 · 105 Ω cm [1]) and more than 5 · 1017 times that of a good conductor such as copper with ρCu = 1.7 · 10−6 Ω cm. Diamond does not need doping to act as a nuclear detector. There is no need of an artiﬁcial depletion region; it is always totally depleted. It simply does not conduct in both directions, unless an ionizing particle crosses it. In this case electron–hole pairs are formed in the bulk of the material, and they can become carriers of electric charge for a short time and can give rise to a pulse like in other solid state detectors, but with the characteristic property of an insulator. That is, a pulse can be produced both for positive or negative polarization of the crystal. The mean energy required to create an electron–hole pair in diamond is = 13.3 eV, while in silicon it is only 3.6 eV (Fig. 1). The minimum energy resolution width of a detector is G. Messina, S. Santangelo (Eds.): Carbon, The Future Material for Advanced Technology Applications, Topics Appl. Phys. 100, 267–286 (2006) © Springer-Verlag Berlin Heidelberg 2006

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Fig. 1. Gap and pair production energies in diamond and silicon

given by the statistical ﬂuctuations in the number of carrier pairs N c created by the passage of the ionizing particle. That is: √ ∆N c ∆E 1 (1) = = √ =√ , E Nc Nc E where N c = E/ and assuming valid Poisson’s statistics. E means here the energy released by the particle into the detector. Since is rather higher for the diamond, it is certainly worse than the silicon as a radiation detector from the point of view of the energy resolution. Diamond has, however, a great advantage and conversely a great disadvantage with respect to silicon. The advantage consists in its much stronger hardness to radiation damage. The disadvantage is given by the fact that good natural diamonds cost a great deal and that synthetic ones have an energy resolution much worse than foreseen by (1) because lattice defects cause independently both an increase of the dispersion ∆N c and a decrease of the value of N c with respect to the theoretical ones. The radiation hardness of diamond has been extensively tested through charged particle bombardment [2] and in some cases also through neutron bombardment [3]. The results obtained with charged particles are all in agreement and show that diamond, instead of being damaged, is in many cases improved by the bombardment. This eﬀect is called pumping and is obtained by irradiation for a given time with ionizing particles, frequently β-particles. It is discussed in another paper in this volume [4] and seems to

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diffuse crystal defects

a)

b)

2.4 cm

c)

0

1320.0

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1332.5

4000 -1

-1

1345.0

6000

Wavenumber shift (cm )

Fig. 2. Raman spectra of diﬀerent diamond specimens in order of increasing purity of the CH4 –H2 vapour mixture

be due to the saturation of some type of lattice defects by means of the many electrons and holes produced by a strong ﬂux of ionizing particles. Neutron eﬀects are still under study, but also for them diamond seems to be suﬃciently hard. In eﬀect recent measurements [5] suggest that diamond detectors could advantageously replace silicon detectors as neutron ﬂux monitors in the core of the experimental nuclear fusion reactor at JET, Culham, U.K., due to the much longer life of diamond with respect to silicon detectors of comparable volumes. 1.2 Lattice Defects in Synthetic Diamond Crystals Lattice defects in diamonds can be detected using Raman scattering techniques. Figure 2 shows some results obtained on synthetic diamonds grown by chemical vapour deposition (CVD), that is, condensation of carbon from a CH4 (1%)–H2 (99%) gas mixture [4] onto silicon crystal substrates. Let this technique be called CVD heteroepitaxial growth (polycristalline, pCVD). As one can see in the ﬁgure, the Raman spectra clearly detect the presence of graphite, the allotropic crystalline state of the carbon, the presence of diﬀuse lattice defects and impurities, and, of course, the sharp peak produced by diamond at ∆k = ∆(1/λ) = 1332.7 ± 1.2 cm−1 . Both graphite and diﬀuse crystal defects can be decreased, improving the purity of the vapour mixture so as to avoid as much as possible nitrogen and oxygen. The spectra in Fig. 2 are taken in conditions of increasing purity.

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Renato Potenza and Cristina Tuv´e 350 Negative bias

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250 200

Positive bias

150 100 50 0

0

20

40

60

80

h (%) Fig. 3. Pulse height eﬃciency η = Qc /Q 0 of a “pure” diamond specimen for αparticles of 5.5 MeV. Qc is the collected charge and Q0 is the charge really produced inside the diamond. This has been subject to β-irradiation before being used.

Fig. 4. Scheme of the circuit in which the diamond sensor is inserted. The reported case is that of positive polarization of the diamond (Au electrode is positive)

One can note that in the specimen in the spectrum (c) there are no more defects or impurities detectable with Raman technique, that is, the specimen can be considered “pure”. Only these specimens will be considered as nuclear detectors in this paper. However, they contain still many defects which inﬂuence their quality as nuclear radiation detectors, as Fig. 3 shows for the spectra produced by 241 Am α-particles in a similar diamond specimen for both polarizations. The spectra are reported in Fig. 3 as functions of the charge collection eﬃciency: η=

ph meas Qc = , Q0 ph max

(2)

Defect Density Measurements Inside CVD Diamond Films

271

where Qc is the charge detected in the external charge-sensitive electrical circuit, and Q0 is the charge produced inside the diamond by the passage of the ionizing particle, so that phmeas and phmax refer to the measured and maximum obtainable pulse height, respectively. To detect the spectra in Fig. 3 and all the other ones with which this paper will deal, it is necessary to adapt the diamond crystals to an external electrical circuit. To do this one must distinguish between the substrate side of the diamond crystal, where it is in contact with the semiconductive silicon substrate, and the growth side, where the free CVD diamond surface appears. Figure 4 shows the schematic drawing of a pCVD diamond inserted in the circuit which allows us to record the electrical signals produced by the passage of a nuclear particle. A thin (500 ˚ A) gold deposit, sometimes done above a ﬁrst, also thin (100 ˚ A) titanium deposit, assures electrical contact on the growth side. The silicon substrate itself assures the contact on the substrate side. A charge-sensitive ampliﬁcation chain allows us to record the signals from the diamond. The bias voltage is applied to the growth side, so that positive or negative polarization means that the growth surface, that is, the gold electrode, is respectively positive or negative with respect to the silicon substrate. Figure 4 reports the case of positive polarization, as one can see from the indicated directions of electron and hole motion. Referring again to Fig. 3, remembering that for a silicon detector η ≈ 1 with very good approximation, one clearly sees that the spectra produced by the diamond detector not only show mean values of the pulse heights signiﬁcantly less than the maximum possible and in any case much less then those from equivalent silicon detectors, but also that the widths of the spectra are very large, though the specimen could be considered “pure”, that is, detector grade, from the point of view of a Raman spectrum. The resolution widths are much larger than the minimum foreseen by (1). So one must conclude that the inﬂuence of crystal defects is still large as it concerns the qualities of a detector and, since the Raman spectrum is already ﬂat, these defects can be detected by now essentially using other probes. The proposal is to use as probes the same nuclear particles one would like to detect. 1.3 Application of Diamond to Beam and Beam Proﬁle Monitoring Before discussing in more detail how to use nuclear radiation to measure the defect distribution in “pure” diamond crystals, it is worthwhile to discuss how these diamonds behave when bombarded with very high nuclear particle intensities, say I > 1 pnA = 6.25 · 109 p/s, that is, intensities for which the crystal cannot resolve each single particle from the others within its intrinsic resolving time τ r ≈ 1 ns. In this case the response of the detector is a direct current in the external circuit, where the charge-amplifying chain is replaced by a direct current ampliﬁer. If the gold contacts (see Fig. 4) are designed in the form of a network of pixels, the insulating properties of the diamond

272

Renato Potenza and Cristina Tuv´e

assure that each pixel collects, without detectalbe cross-over among pixels, the current produced in the cylindrical column traced along electric ﬁeld lines between the gold pixel on one side and its projection on the substrate on the other side. So such a pixel detector bombarded by a beam of particles from an accelerator impinging along the electrical ﬁeld lines inside the diamond can give very good information about the beam proﬁle after an easy internal calibration made by moving the detector so that the same part of the beam can impinge on diﬀerent pixels. Using such a direct current ampliﬁcation circuit, we obtained the results shown in Fig. 5 [6]. In that ﬁgure the response of a diamond detector is compared with the measurement of the intensity of a 26 MeV proton beam in the Faraday cup at the end of the pipe of the 15 MV Tandem accelerator of the National Southern Laboratories (LNS) of National Institute of Nuclear Physics (INFN) in Catania (Italy). As can be seen in Fig. 5, the diamond follows instantaneously, in the time scale of the ﬁgure, the changes of beam intensity. Moreover, the ﬂuctuations in the measurement are much less for the diamond, as seen from the fact that the electron–hole current is much larger than the original proton current. Taking into account the ampliﬁcation factor of the circuit, it was estimated that the ratio between proton and related electron–hole currents was 1/23 000 [6], so that possible inﬂuence from secondary electron emission, which is a cause of detectable error in the measurements of currents with Faraday cup, is absolutely negligible. The diamond used in these measurements was only 50 µm thick, so that a simple calculation, taking into account that 26 MeV protons lose 0.33 MeV in passing through and remembering the energy required per carrier pair, tells us that the charge collection eﬃciency at the used polarization voltage, 150 V, is about 60%. Other less rough evaluations through the so-called restricted energy loss [7] or the computation through the standard electron–hole pair number produced by minimum ionizing particles (MIP) [8] give the same values within a 10% variation. As will be seen below, because the protons pass over the diamond, there is almost no diﬀerence between the eﬃciency for positive or negative polarization. This is again conﬁrmation that pCVD diamonds have eﬃciency signiﬁcantly less than 1, which is diﬀerent from that of silicon detectors. The diamond detector we used is transparent to low-energy protons and also to other low-energy ions of intermediate mass. This means that if one removes by lapping the substrate and makes a second gold–titanium contact on the substrate side of the diamond, the new detector oﬀers a very good measurement of beam intensity and proﬁle without appreciably perturbing the beam itself, which can be monitored continuously during the applications. This is very important, e.g., in medical applications of nuclear radiation or in monitoring fast neutron ﬂuxes in the cores of nuclear reactors, particularly fusion reactors. And this quality is well exploited by the high hardness to radiation, proved by the fact that the diamond specimen used in [6] lasted several hours under a current of 10 pnA of 26 MeV protons, that is, a ﬂuence

Defect Density Measurements Inside CVD Diamond Films

273

Diamond sensor

26 MeV protons

TANDEM Accelerator

5 mm Collimator Faraday cup A to pump

current (µA)

0.06

Diamond detector

0.04

0.02

0.00

Faraday cup

current (pA)

0.2

0.1

0.0

560

630

700

770

840

910

t (sec)

Fig. 5. Intensity vs. time (bottom) for a 27 MeV proton beam from the 15 MV Tandem accelerator of LNS in Catania (Italy), measured simultaneously through a diamond detector and the Faraday cup shown at the top

φ ≈ 1015 p/cm2 , without any sign of deterioration, whereas a good silicon detector would have been damaged by a ﬂuence one hundredth as large [2, 3].

2 Mechanism of Conduction in Circuits Including Diamond Let us consider the electrical circuit of Fig. 4 containing a diamond. Call V − the applied voltage, and let 2Q0 = Q+ 0 − Q0 = 2N c e be the charge produced at a point x by the passage of a particle through the diamond. Let dU = + + −Q+ 0 dV = −Q0 Edx be the energy gained by the charge Q0 during its movement along a length dx parallel to the ﬁeld E. The work needed to supply this energy is done by the electromotive force of the generator, which moves the induced charge of opposite sign dQ− ind in the external circuit, maintaining a constant applied voltage V = EL, where L is the thickness of the diamond. − This work is given by dW = −V dQ− ind = −ELdQind .

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Renato Potenza and Cristina Tuv´e

Taking the x-axis going from the substrate to the growth side of the diamond, one has: − −dU = Q+ 0 Edx = −dW = ELdQind .

(3)

That is, + dQ− ind = Q0

dx v+ µ+ = −Q+ dt = −Q+ Edt, 0 0 L L L

(3a)

from which: −Q− ind = −

+ dQ− ind = Q0

d+ E + + c ≤ Q+ µ τ c ≤ Q+ 0 0, L L

(3b)

and three similar equations with the appropriate signs for the negative charge − + Q− 0 , where Qi → −Qi and all the superscripts + → −. In (3b) and its ± ± ± equivalent d± c ≤ λc = µ τ c E ≤ L are the mean actual distances, in a crystal of ﬁnite thickness, covered by the charges Q± 0 travelling inside under the action of the applied ﬁeld and subject to: (i) absorption from donor or acceptor defects along the path, which is responsible for the ﬁnite λ± c , the charge collection distances of the carriers in that crystal; (ii) abrupt interruption of the path for the surviving carriers able to reach the contacts, ± ± which makes d± c ≡ dc (x) < λc near the contacts themselves. Strictly related + to the λ± are the mobility µ = v + /E and the charge collection time τ + c c . Equations (3), (3a) and (3b) are expression of the so-called Ramo’s theorem, demonstrated by S. Ramo in 1939 [9]. Noting that when an ionizing particle passes through a solid state detector − it is always, at a given x, Q+ 0 = −Q0 ≡ Q0 ≡ Q0 (x), one can now deﬁne the corresponding collected charge as − − Qc (x) = Q+ ind − Qind = −Q0

d− d+ c (x) c (x) + Q+ 0 L L

(4)

+ (d− c + dc ) ≤ Q0 (x), L and the charge collection eﬃciency at the same x (see (2)) as:

= Q0

η(x) =

Qc (λ− + λ+ (d− + d+ c ) c ) < c . = c Q0 L L

(5)

It is clear that if the mean free paths λ± c are both equal to or bigger than L, taking into account the interruptions of carrier paths at contact surfaces, where moving and induced charges neutralize each other, one has: +x , −Q− ind = Q0 L

Defect Density Measurements Inside CVD Diamond Films

275

and − Q+ ind = −Q0

(L − x) . L

As a result, Qc = Q0 , from (4), as happens in the depletion barriers of all good semiconductors such as silicon. When, on the other hand, acceptor or donor defects present in the material forbid long free paths for charge carriers, − then not only is Qc < Q0 , but also it can happen that λ+ c = λc . This is just the case of the pCVD diamonds, as various recent results show [4, 10, 11]. Of course, the charge collection eﬃciency η for a whole crystal is a mean value of η(x), as said below. 2.1 Modiﬁed Hecht’s Model for Charge Transport Inside Diamond This section follows, with modiﬁcations, the treatment given in [12]. 2.1.1 Absorption of Carriers During Their Transport Along the Electric Field Lines Because of the ﬁniteness of the specimen, the values of the d± c (x)’s which . If the specimen appear in (5) are less than those of the mean free paths λ± c can be considered inﬁnite, that is, L λ± , then edge eﬀects can be neglected c ± ± and the d± c ’s reduce to the λc . To compute the values of the dc ’s in a ﬁnite specimen it is, however, possible to start from the situation in the inﬁnite specimen. The general expression of a mean free path for particles in a medium is given by λ± c =

1

(6)

N ± σ±

where σ is the cross section of the absorption centres and N is their concentration (volume−1 ). There is no need that the values of σ or the N be the same for electrons and holes, so it will be assumed that N + = N − and σ + = σ − . There is also no need that they be constant with position inside the ± specimen, so that in general λ± c ≡ λc (x, y, z). However, it is useful to assume ± for the moment that λc = const. Now, referring to Fig. 4 with the direction of the x-axis going from bottom to top, as shown also in Fig. 6, that is, from substrate to growth side of the diamond along the lines of the applied ﬁeld, − assume that an incident particle creates at the level x, N + c (x, 0) = N c (x, 0) carriers of both signs. Following the deﬁnition of the absorption cross section σ, one has that after a displacement of a given type of carriers ±

± (−N d σ N± c (x, ) = N c (x, 0)e

±

)

= N± c (x, 0)e

−

± λc

,

(7)

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Renato Potenza and Cristina Tuv´e

because at every

1 dN ± c ± ± = − ± N± c (x, ) = −p (x, )N c (x, ), d

λc

(7a)

where 1/λ± c is just the constant probability of absorption per unit length p± (x, ) for positive or negative carriers, constant here since one is speaking of inﬁnite homogeneous specimens. Note that N ± c (x, ) is just the number of surviving carriers at a depth away from the point at coordinate x. To compute the mean free path of the carriers inside an inﬁnite and homogeneous medium, one can write: ∞ − λ± ∞ ±

N (x,

)d

e c d

c = 0 = λ± λ = 0∞ ± c . ∞ − λ± 0 N c (x, )d

c d

e 0

(7b)

2.1.2 Edge Eﬀects Trying now to compute the charge collection distances d± c for ﬁnite specimens, one must note that carriers that succeed in reaching the edges of the specimen, that is, the surfaces at = x moving towards the substrate side, or = L − x moving in the other direction, do not proceed anymore since they are all absorbed at these values of . So the mean value of the path length becomes: ap± d± c

=

0

± ∞ ±

N ± c (x, )d + ap ap± N c (x, )d

∞ ± 0 N c (x, )d

ap± =

0

e

−

± λc

d + a± p

∞ 0

= λ± c

1−e

−

e

± ap ± λc

− ± λc

∞

ap±

e

−

± λc

d

d

< λ± c ,

(8)

where a± p can take the value of x or L − x depending on both the type − of carriers and the polarization p. More precisely, a+ + = a− = L − x and + − a− = a+ = x, where subscripts refer to polarizations and superscripts to ± carriers. Because of the dependence of the a± p on x, the dc depend on x also in this simple model of ﬁnite homogeneous specimens. The total number of carriers that succeed in escaping absorption in diamond is just: 1 ∞ ± ± N c (x, )d ≡ Np> . ± λ± c ap

Defect Density Measurements Inside CVD Diamond Films

277

That is, ± Np> = N ± (x, 0) −

≡

1 Λ±

∞

1 Λ±

a± p

N± c (x, )d

0

N± c (x, )d −

0

1 Λ±

a± p

N± c (x, )d .

(8a)

0

Λ± is a normalization constant, equal to λ± c only for inﬁnite homogeneous media; its value depends on the deﬁnition of p± (x, ) outside the edges of the specimen. p± (x, ) has, in fact, physical meaning only inside the specimen, but it can be convenient to extrapolate it outside. How to do the extrapolation does not matter, because of the appearance in (8) of Λ± , which depends on p± (x, ) in order to compensate for diﬀerent arbitrary choices of the nonphysical part. If the charge Q0 were all produced at the point x then substitution of (8) in (5) would give the charge collection eﬃciency η. But when an ionizing particle impinges on the detector, charges are produced all along a path which begins at the entrance edge and goes through up to the end of the range R, or even passes over the detector if the particle energy is suﬃciently high. So, in the simple case actually being discussed, the charge produced between x and x + dx inside the detector, neglecting the nonuniform deposit due to Bragg’s distribution, is given by Q0,tot Q0,tot dQ0 (x) = = = const, dx min[Rcosθ, L] min[G, L]

(9)

where G is the penetration depth of the particle along the lines of the electric ﬁeld and θ is the angle of incidence on the growth surface. One obtains, using (5), (8) and (9): Qc,tot η= = Q0,tot

min[G,L] 0

η(x) dQ dx dx min[G,L] dQ dx dx 0

min[G,L] (d+ − c (x)+dc (x)) =

0

L

Q0,tot (L−x) min[G,L] − min[G,L] + − + − x− λc λc λc 1 − e λc 1 − e dx + 0 dx 0

=

=

Q

0,tot · min[G,L] dx

L · min[G, L]

− (λ+ c + λc ) − L

2 (λ+ c )

L−min[G,L] min[G,L] − − L+ − + − − 2 λc λc λc −e e + (λc ) 1 − e ,

L · min[G, L] (10)

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Renato Potenza and Cristina Tuv´e

for positive polarization (the case reported in Fig. 4); for negative polarization − λ+ c and λc interchange between each other to give η− . When it happens that − δ (λ+ c + λc ) ≡ , 2 2 (10) reduces to the original Hecht formula [13]:

2min[G,L] 2(min[G,L]−L) δ δ − δ δ 1+e 1−e η= . 1− L 4G − λ+ c = λc =

(10a)

However, there is an enormous diﬀerence between (10) and (10a). Equation (10), in fact, foresees diﬀerent eﬃciencies of the same detector for the same particles when the polarization is reversed, that is, when the growth side is positive or negative with respect to the substrate side, due to the − + − diﬀerent values of λ+ c and λc . If one supposes for a moment that λc > λc , the eﬃciency for low penetrating particles in negative polarization is deﬁnitely less than that in positive polarization. In fact, when the particles have G λ± c < L, either because they have low energy or because they impinge with high incident angle, in positive polarization one has − L+ + − λc + λc λc e − L+ λ+ (λ+ + λ− c ) − = c 1 − e λc , η+ ≈ c L L L and in negative one has − L− − + λc λc e + λc − L− λ− (λ− + λ+ c ) − = c 1 − e λc < η+ , η− ≈ c L L L − provided that L > λ+ c > λc .

2.2 Eﬀect of Nonuniform Bragg’s Deposit of Charge into Diamond The nonuniform production of charge carriers inside the diamond due to the Bragg’s curve B(s) of speciﬁc energy loss along the trajectory of the particle is easily taken into account by changing (9) to x dQ0 (x) = B[x(s)] = B , (9a) dx cosθ where θ the incidence angle as above. Equation (10) becomes min[G,L] η(x) dQ dx Qc,tot η− = = 0 min[G,L] dx dQ Q0,tot dx 0

dx

− min[G,L] (d+ c (x) + dc (x)) dQ0,tot

=

0

and η+ and η−

L dx dx , Q0,tot can be computed numerically.

(10b)

Defect Density Measurements Inside CVD Diamond Films

279

Fig. 6. Schematic representation of in-grain and grain-boundary defects in diamond

2.3 Nonuniform Distributions of Charge and Defects In ﬁnite and inhomogeneous diamond crystals the measurement of charge collection eﬃciency for both polarizations of the crystal is a very powerful tool to obtain the distribution of defects responsible for the quality of the crystal, and consequently to allow the optimization of the growth parameters of the crystals themselves. In such specimens the probabilities of disappearance of carriers p± (x, ) in (7) is no longer constant. So the solution to (7a) becomes the more general: − p(x,)d ± 0 N± (x,

) = N (x, 0)e , (11) c c and the collection distances become: a± ± ∞ ± p

N ± N c (x, )d

c (x, )d + ap a± 0 p ± ∞ ± dc = 0 N c (x, )d

a± p =

0

e

−

0

p± (x,)d

∞ 0

e

d + a± p

−

0

∞ a± p

p± (x,)d

e

−

0

p± (x,)d

d

,

(12)

d

formally identical to (8). The probability of disappearance p± (x, )d of a given carrier in the path between and + d is, of course, proportional to the product N ± σ ± of (6). Assuming that the cross sections for the various processes that give rise to the absorption of a given type of carriers are constant at every point inside the diamond, p± (x, ) is directly proportional only to the local concentrations of defects N ± . Now, these last can be divided into two types [4], as shown in Fig. 6: those distributed all along the diamond (the so-called in-grain defects), which depend on the impurities and on random accumulations of vacancies, and those which depend on the mismatch between the reticular constants of diamond and of the substrate, which are located preferentially in the columnar structure [4], that is, in the ﬁrst part of the deposit, near the

280

Renato Potenza and Cristina Tuv´e

substrate surface (border-grain defects). As said below, the in-grain defects seem to aﬀect the two types of carriers diﬀerently, with a greater inﬂuence on the electrons, while the border-grain ones, being essentially structural defects, less dependent on impurities in the crystal, seem to aﬀect both carriers in a similar way. So a suitable way to write the probability of disappearance seems to be: p± (x, ) =

1 1 − (x∓) + e Λ p = ±1, λ λ± b g

(13)

where p = ±1 is the polarization given to the crystal, assuming that the concentration of border-grain defects goes down exponentially from substrate to growth surface. Now, substituting N ± (x, 0) with B(x) (9a) and using p± (x, ) given by (13) in (11), one can ﬁnally compute numerically the correct charge collection eﬃciency η± for positive and negative polarizations of a diamond specimen bombarded with diﬀerent penetrating particles. The integration must be done numerically because (11), with the mentioned substitutions, contains combinations of Γ and γ incomplete functions [14]. One can expect that also in specimens considered pure from the point of view of Raman scattering the two curves η± vs. G should be signiﬁcantly diﬀerent since the defects still inﬂuence the quality of the diamond, as shown, e.g., by energy resolution. So, the comparison of the results of the measurements of the η’s in both polarization states can give much better information about the distribution of defects inside the diamond than Raman eﬀects, as shown in the next section.

3 Charge Collection Eﬃciencies of Diamond Detectors Under Ion Bombardment The results of typical measurements of mean charge collection eﬃciencies η± (for positive and negative polarization) in thin pCVD diamond detectors are reported in Figs. 7 and 8. In the ﬁrst case the employed method shows a specimen that is suﬃciently good. In fact, the theoretical curves computed with the simple model of (10) with uniform distribution of defects (mirrored by −1 ) are very near to the curve computed the constant values of p(x, ) = (λ± c ) with the complete model; the length Λ in the exponent of (13) is large, so that the defects are almost uniformly distributed. This specimen is practically the best that one can hope to obtain from the technique of pCVD, though it is still not satisfactory as a detector, because of the big diﬀerence between λ+ c and λ− c and the fact that the resolution width is still on the order of 35% in both states of polarization (compare with Fig. 3). The eﬃciencies reported in Fig. 8 denote a worse specimen. The eﬃciency for G > L is low (on the order of 5%), the curves given by (10) are very diﬀerent from those given by the complete model and the defect density is high in the uniform terms as in the

Defect Density Measurements Inside CVD Diamond Films

281

Fig. 7. Charge collection eﬃciency of a ﬁrst 55µm thick diamond detector bombarded with 12 C at various energies. The penetration depths of 12 C particles are also shown. Upward pointing triangles: positive polarization; downward pointing triangles: negative polarization. Theoretical curves: (a) simple model (10) with − λ+ c = 17 µm and λc = 0.5 µm; (b) same model with account of Bragg’s curve; (c) − complete model (13) with λ+ g = 33 µm, λg = 0.8 µm, λb = 25 µm and Λ = 37 µm

exponential one. As is said below, these diﬀerent results can be associated with diﬀerent values of the parameters of the reactor in which the CVD diamonds are produced and can be used to optimize these parameters. However, the best results for thin specimens (L < 300 µm) are not much better than those of the diamond represented in Fig. 7. At this point it seems useful to pay attention to some interesting characteristics of the complete model that can be seen in Figs. 7 and 8. First, the simple model gives eﬃciencies that change smoothly from those at G ≈ 0 to those at G > L, where both η’s become equal. The complete model instead gives a cross between η+ and η− at G ≈ L, after which both η’s tend to the same asymptotic value as well. This value is about the mean between those at low penetrations. The ﬁgures clearly show this eﬀect, which is produced by the nonuniform production of charge given by Bragg’s curve. It is essentially an edge eﬀect due to the fact that the Bragg’s peak moves towards the substrate edge, so that the eﬃciencies again feel the inﬂuence of the diﬀerent values of the λ± c . Second, we must note that the points at the lowest measured values of the penetration G for positive polarization are systematically higher than foreseen by the best ﬁtted curves. As said below, this depends on the fact that, for crystals with a large number of defects, though not visible in Raman spectroscopy, a non-negligible pulse

282

Renato Potenza and Cristina Tuv´e

penetration depth (µm) 10

20

20

30

40

50

60 positive bias negative bias simple model Bragg curve defects

15

η(%)

c 10

5

a b

0

0

10

20

30

40

50

60

70

80

90

100

Beam Energy (MeV) Fig. 8. Same as Fig. 7 for a second 55µm thick diamond detector. Theoretical − curves: (a) simple model (10) with λ+ c = 3.7 µm and λc = 0.05 µm; (b) same model with account of Bragg’s curve; (c) complete model (13) with λ+ g = 13 µm, λ− g = 0.3 µm, λb = 0.33 µm and Λ = 8 µm

height defect is to be foreseen and a correction must be introduced into these data, which can be considered only rough data. 3.1 Experimental Procedure to Measure the Charge Collection Eﬃciencies The experimental setup for bombardment with 12 C or other accelerated ions is similar to that shown in Fig. 5 and reported in Fig. 9. A collimated beam of accelerated ions (typically I ≈ 1–3 pnA) from the 15 MV Tandem accelerator of the LNS in Catania impinged on a ≈ 300µg/cm2 thick gold target. The machine voltage varied between 6.8 MV and 14 MV. These values allowed the energy of the ions to be varied between a minimum of 18 MeV for 6 Li to a maximum of 110 MeV for 16 O; for 12 C in particular the energy was varied between 22 MeV and 91 MeV. Scattered ions were detected either through a silicon detector placed at θ = −20◦ with respect to the beam or by diamond detectors placed at +20◦ ≤ θ < +30◦ at the other side of the beam. The calibrations were done with respect to Si detector. Target and detectors were contained in a high-vacuum scattering chamber. Pulses from Si and diamond detectors were ampliﬁed through conventional charge preampliﬁers followed by ampliﬁers, converted to digital signals and registered on disc to be analyzed oﬀ-line afterwards. The setup used for irradiation with the 5.4 MeV α-particles from an 241 Am source was, of course, simpler in that the

Defect Density Measurements Inside CVD Diamond Films

283

Fig. 9. Experimental setup for bombardment of diamond detectors with ions accelerated by the Tandem accelerator at LNS in Catania (Italy)

experiment was done in air and the energy of the α-particles was varied by simply changing and carefully measuring the distance between the Am source and the detectors, that is, using air as the absorber. The electronics were essentially the same. 3.2 Corrections to the Eﬃciencies η± Needed to Into Take Account the Pulse Height Defect of Diamond for Detectors Heavy Ionizing Particles Figure 10 reports the charge collection eﬃciencies measured for the same diamond specimen with α-particles and with 12 C of various penetrations G in their lower range. The eﬃciencies measured with α-particles are deﬁnitely higher than those obtained with carbon at the same penetration. Moreover, there is a diﬀerence ∆η asymp ≈ 15% between the asymptotic values of eﬃciencies for α-particles and 12 C. The best hypothesis seems that this diﬀerence is a measure of the pulse height defect in diamond between diﬀerently ionizing particles. As is well known [15, 16], every detector is subject to the phenomenon of pulse height defects. It consists essentially in the fact that when the local charge density produced by the ionizing particle in its passage is too high, a spatial charge forms, which lowers the local electric ﬁeld. This last becomes less eﬀective in separating rapidly carriers of opposite signs, so that they can recombine, with a consequent reduction of the output pulse. The reduction of the local ﬁeld depends on the angle θ between the incident particle and the applied electric ﬁeld, because when the electric ﬁeld is just along the line of production of carriers, these last tend to pack together, making recombination easier. The pulse height defect ∆E shown by a given diamond detector for given incident ions of energy E0 can be deﬁned empirically as the absolute value of the diﬀerence between the mean signal actually given by the detector hit by

284

Renato Potenza and Cristina Tuv´e 40

Pos 35

Neg

0° 60° 75°

α

30

Efficiency (%)

α 25

α asymptotic

20

asymptotic pulse height defect

12C

15 10

12C asymptotic

α

12C

5 0 0

5

10

15

20

25

30

Penetration depth (µm)

Fig. 10. Eﬃciencies at low penetrations of a 130µm thick diamond in positive (full symbols) and negative (empty symbols) polarization for α-particles and 12 C ions at various angles of incidence

those ions and the mean signal expected for α-particles that can create the same charge inside the detector, that is: ∆E =

Q0 |η ion − η α |, e

(14)

where Q0 can be computed from the Bethe–Bloch energy loss formula [7] or obtained experimentally from measurements with a silicon detector, making allowance for the diﬀerent values of in (1). The value of ηα can be obtained by ﬁtting appropriate curves from (5) (using (12) and (13) in it) to the points taken for positive and negative polarizations at low penetration for α-particles and allowing these curves to cross just at G = L. The implicit assumption under this deﬁnition is that the pulse height defect for light particles is negligible. A preliminary study of this phenomenon has shown [17] that the pulse height defect ∆E deﬁned as above can be well represented by an empirical formula with the form of a power law in the energy E ≤ E 0 lost inside the specimen: ∆E = AE b (1 − e−c · cosθ ),

(15)

where b = 1.2 (as in silicon detectors [15]) is the same for all particles and diamond detectors, while A and c depend on both the detector and the incident particle. A can be usefully derived from the ∆η asymp between η±,α and η ±,ion ion at about the energy for which G = L; that of c from, e.g., η +,ion vs. θ at constant E.

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4 Conclusions With the application of the corrections foreseen in Sect. 3.2, the model is complete and is applicable to various types of detector-grade pCVD diamond, as deﬁned in Sect. 1.2. Using this model means: (i) bombard diamond detectors under test in both states of polarization with α-particles in order to know their maximum charge collection eﬃciencies. (ii) If the maximum available energy of α-particles gives G > L it is enough to do measurements of η±,α , changing either the incident energy or the incident angle: where ∆E = 0 changing the incidence angle does not aﬀect the ηα ’s. (iii) If α-particles cannot penetrate the whole thickness L of the diamond, use penetrating ions from an accelerator; measure always both rough η± , compute the pulse height defect, if any, and correct the rough data as said above. At this point ﬁtting to the points giving the η ±,corr ’s vs. G the curves computed from (5), (12) and (13) will give a reliable measurement of the defect distribution inside the specimen, allowing one to compare diamonds obtained by diﬀerent methods. That is: pCVD without and with lapping from the substrate side; as-grown or pumped CVDHG diamonds [4] (pumping improved the values of η+ increasing λ+ g in (13)); eventually also some new CVD diamonds grown on natural diamond (homoepitaxial growth). It remains to explore the consequences of a given defect distribution on the behaviour of diamond as a beam proﬁle monitor, mainly to see how it is possible, from a priori knowledge of the defect density, to foresee the current ampliﬁcation factor that one must expect.

References [1] M. Friedl: Diamond Detectors for Ionizing Radiations, Diploma thesis, University of Technology, Vienna (1999) 267 [2] D. Meier, (RD42 Collaboration): Nucl. Instr. Meth. Phys. Res. A 426, 173 (1999) 268, 273 [3] D. Husson, (RD42 Collaboration): Nucl. Instr. Meth. Phys. Res. A 388, 421 (1997) 268, 273 [4] M. Marinelli, E. Milani, A. Tucciarone, G. V. Rinati: in Chap. 6 268, 269, 275, 279, 285 [5] M. Angelone, M. Pillon: EFDA Fusion Newsletter 2004/1, 8 (2004) 269 [6] M. Marinelli, E. Milani, A. Paoletti, A. Tucciarone, G. V. Rinati, S. Albergo, V. Bellini, V. Campagna, C. Marchetta, A. Pennisi, G. Poli, R. Potenza, F. Simone, L. Sperduto, C. Sutera: Diamond Relat. Mater. 10, 706 (2001) 272 [7] P. D. Group: Review of particle physics, Phys. Lett. B 592, 1 (2004) 272, 284 [8] O. Madelung, et al. (Eds.): Kristall und Festk¨ orperphysik, Band 22, Halbleiter, Landolt–Bornstein and Zahlenwerte und Funktionen Halbleiter (Springer, Berlin, Heidelberg 1987) 272 [9] S. Ramo: Proc. of the I.R.E. 27, 584 (1939) 274 [10] M. Marinelli, E. Milani, A. Paoletti, A. Tucciarone, G. V. Rinati, M. Angelone, M. Pillon: Diamond Relat. Mater. 10, 645 (2001) 275

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Renato Potenza and Cristina Tuv´e

[11] C. Tuv´e, V. Bellini, R. Potenza, C. Randieri, C. Sutera, M. Marinelli, E. Milani, A. Paoletti, G. Pucella, A. Tucciarone, G. V. Rinati: Diamond Relat. Mater. 12, 499 (2003) 275 [12] G. Pucella: Phd thesis, Rome (2003) 275 [13] K. Hecht: Z. Phys. 77, 235 (1932) 278 [14] I. S. Gradshteyn, I. M. Ryzhik: Table of Integrals, Series and Products (Academic, New York 2000) 280 [15] E. C. Finch, M. Asghar, M. Forte, G. Siegert, J. Greif, R. Decker: Nucl. Instr. Meth. Phys. Res. 142, 539 (1977) 283, 284 [16] M. Ogihara, Y. Nagashima, W. Galster, T. Mikumo: Nucl. Instr. Meth. Phys. Res. A 251, 313 (1986) 283 [17] G. Pucella, et al.: private communication 284

Index charge collection eﬃciency (CCE), 280–285 chemical vapour deposition (CVD), 269 CVD heteroepitaxial growth (pCVD), 269 defects defects distribution, 279, 280 diamond

defects in diamond, 269, 270 diamond detectors, 267–273, 277, 278 transport in diamond, 273–279 Hecht’s model, 275 Hecht theory, 275, 278 Ramo’s theorem, 274

Laser Ablation-Deposited CNx Thin Films Enza Fazio1 , Enrico Barletta1 , Francesco Barreca1, Guglielmo Mondio1 , Fortunato Neri1 , and Sebastiano Trusso2 1

2

Dipartimento di Fisica della Materia e Tecnologie Fisiche Avanzate, Universit´ a di Messina, Salita Sperone 31, I-98166 Messina, Italy [email protected] CNR – Istituto per i Processi Chimico-Fisici sezione di Messina, Via La Farina 237, I-98123, Messina, Italy

Abstract. Amorphous CNx thin ﬁlms were deposited at room temperature by pulsed laser ablation of graphite targets in a controlled atmosphere using both N2 and N2 /Ar gas mixtures. The structural and electronic properties of the samples were investigated by means of X-ray photoelectron, reﬂection electron energy loss and Raman spectroscopy. Nitrogen contents as high as 32% have been estimated. The overall results show a progressive transformation of the C–C sp3 bonds into sp2 hybridized C–N ones with the development of sp2 carbon clusters upon increasing the gas pressure values. By means of fast photography measurements, diﬀerent regimes of the laser-induced plasma expansion dynamics have been evidenced. The results indicate that the electronic and structural properties of the laser ablationdeposited CNx ﬁlms depend strongly on the regime under which the plasma expansion takes place, not simply on the overall nitrogen content. In this respect the role played by the gas composition and pressure are of fundamental importance.

1 Introduction Carbon nitride materials have been the focus of considerable experimental and theoretical attention since Liu and Cohen proposed that β-C3 N4 should have a hardness comparable to that of diamond [1]. Subsequent calculations have shown that other crystalline C3 N4 structures should have stability comparable to or greater than that of β-C3 N4 , and that many of these structures should be very hard (e.g., the cubic form). The only exception is represented by the energetically most stable form, rhombohedral C3 N4 , which has a graphite-like structure and is expected to be quite soft [2, 3]. From the experimental point of view, most of the thin ﬁlms deposited with very diﬀerent preparation techniques have been shown to have an amorphous or disordered phase although there are several reports of crystalline phases dispersed in the amorphous matrix [4, 5]. Nevertheless, nonstoichiometric carbon nitride thin ﬁlms have also shown promising technological applications in the ﬁelds of optical and electronic engineering due to their peculiar mechanical, optical and electronic properties, which can be tailored as a function of the nitrogen content x [6]. The eﬀect of nitrogen insertion on the structure of amorphous carbon thin ﬁlms is not yet completely and easily interpreted due to the variety of diﬀerent local chemical environments allowed for nitrogen atoms in G. Messina, S. Santangelo (Eds.): Carbon, The Future Material for Advanced Technology Applications, Topics Appl. Phys. 100, 287–302 (2006) © Springer-Verlag Berlin Heidelberg 2006

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such a structural context. Usually, ﬁve possibilities based on diﬀerent nitrogen bonding conﬁgurations are considered: incorporation in aromatic rings, sp with one carbon neighbour, sp2 with two or three carbon neighbours and sp3 with three carbon neighbours. The identiﬁcation of such diﬀerent local chemical environments has been generally performed by means of diﬀerent spectroscopic techniques such as X-ray photoemission spectroscopy (XPS), reﬂection electron energy loss (REELS), Fourier transform infrared (FTIR) and Raman spectroscopy [7, 8, 9, 10, 11, 12, 13, 14, 15]. Many diﬀerent preparation techniques can be adopted to deposit CNx thin ﬁlms [16, 17, 18, 19]. Their properties vary considerably, depending both on the technique adopted and the deposition parameters for a given technique. Among others, pulsed laser ablation (PLA) has been widely used due to its particular characteristics: the production of high-energy species and great ﬂexibility in the control of several deposition parameters (laser ﬂuence and wavelength, target composition, substrate temperature, target–substrate distance and the possibility of performing the process in an inert or a reactive background-controlled atmosphere) [20, 21, 22]. Since the PLA technique involves high-energy species, one can expect to observe interesting, from an application point of view, C–N stoichiometries and structural conﬁgurations, even for materials deposited at room temperature (RT). For this reason, in this work we report the studies on CNx thin ﬁlms deposited at RT by means of pulsed laser ablation of graphite targets in a controlled nitrogen atmosphere. The eﬀects of the gas pressure and composition were also taken into account by depositing some samples in the presence of a N2 /Ar gas mixture. Indeed, generally, there is a heavy correlation between plasma dynamics and the structural properties of the deposited ﬁlm, thus the study of characteristics of the plasma can contribute to a better understanding and control of the deposition process itself. The dynamics of the expansion laser-induced plasma were investigated by means of fast photography measurements, while the stoichiometry and the structure of the samples were obtained by means of optical and electronic spectroscopy.

2 Experiments Carbon nitride thin ﬁlms were grown in a high vacuum chamber with a residual pressure down to approximately 1 × 10−4 Pa. High-purity graphite targets were ablated by focusing the beam of a KrF excimer laser (wavelength 248 nm, pulse width 25 ns, repetition rate 10 Hz) onto the surface with an incident angle of 45◦ , and the estimated energy density was 2 J/cm2 . The samples were deposited onto crystalline silicon and Corning 7059 glass substrates kept at room temperature and placed at 40 mm from the target, which is positioned on a rotating holder in order to avoid craterization phenomena. A mass ﬂow controller was used to introduce high-purity nitrogen gas during the deposition process, reaching partial pressure values up to 66.7 Pa. Moreover, two

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samples were grown in a N2 /Ar gas mixture with a total pressure of 13.3 and 66.7 Pa and a N2 /Ar partial pressure ratio of 1/9 and 1/49, respectively. The investigation of both the stoichiometry and the structural properties of the samples were performed by means of XPS, REELS and Raman spectroscopy. In particular, REELS and XPS measurements were carried out using a VG ESCALAB vacuum system. REEL spectra were obtained by a VG LEG61 electron gun in conjunction with a VG CLAM 100 hemispherical analyzer. The primary electron energy was Ep = 2.5 keV, and the incidence angle α was about 40◦ from the normal to the sample surface. The gun current was about 10 µA, and the pass energy of the analyzer was set to 7.5 eV. The acceptance angle β of the analyzer was about 3◦ . The same analyzer, with the same pass energy, was used to measure X-ray photoelectron spectra excited by the Al Kα radiation (1486.6 eV) of a conventional twin-anode Al/Mg Kα source. To take into account any possible charging eﬀects, a tiny silver paint droplet has been deposited on the sample surface for referencing the binding energy scale to the Ag 3d5/2 line. The relative concentrations of nitrogen and carbon atoms were estimated by the areas under the N1s and C1s peaks weighted by the relative sensitivity factors. Raman scattering measurements were performed by means of an U1000 Jobin Yvon monochromator coupled with an Olympus BX-40 microscope. The 514.5 nm line of an Ar+ laser was focused on the sample surface through the 100× objective of the microscope. The backscattered radiation was collected by the same microscope optics and dispersed by a 1000 mm double monochromator, equipped with two holographic gratings (1800 lines/mm). The dispersed radiation was detected by means of a LN2 -cooled CCD sensor. During the ﬁlm deposition process, the light emitted from the laser-induced plasma was collected at a right angle with respect to the plume expansion direction by means of an optical system. A fast intensiﬁed charge-coupled device (Andor Technology iStar iCCD) with a variable gate (∆t ≥ 2 ns) was used to detect the optical emissions from the plasma and then to acquire the images of the expanding plasma. A time gate of 2 ns was adopted in the initial stage of the expansion and then progressively increased up to 50 ns to acquire the images of the expanding plasma at diﬀerent time delays after the laser pulse arrival.

3 Results and Discussion The chemical bonding states and the relative atomic contents in CNx thin ﬁlms were investigated by means of X-ray photoelectron spectroscopy and low-energy reﬂection electron energy loss spectroscopy. In fact, in the case of CNx materials, these spectroscopic techniques are thoroughly sensitive to local coordinations of carbon and nitrogen atoms. In particular, changes in the carbon microstructure can be well evidenced from the modiﬁcations occurring in both the subband structures and the chemical shifts of the C1s

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Fig. 1. Behavior of the nitrogen N/C ratio as a function of the gas pressure for samples grown in pure nitrogen atmosphere. Line is a guide for the eye

and N1s core level photoemission peaks. Taking into account both the experimentally determined and the literature-reported sensitivity factors [23], a compositional analysis was performed and the N/C atomic ratio x was obtained from the integrated areas of the carbon and nitrogen photoelectron peaks. In Fig. 1 is shown the compositional parameter x as a function of the nitrogen partial pressure. The results (see also Table 1) show that, under the ablation conditions chosen, increasing P N2 up to 13.3 Pa, the nitrogen content reached a value close to x = 32 % and then decreased down to about 17% at P N2 = 66.7 Pa. In Fig. 2a are shown the C1s XPS lineshapes of some of the investigated samples grown at diﬀerent pure nitrogen partial pressures: a clear modiﬁcation is evident. The eﬀects of the increasing gas pressure are an asymmetric broadening and a shifting towards higher binding energies of the C1s peak, with respect to the position observed for pure carbon systems (284.5 eV). These eﬀects, also evident for the lowest nitrogen partial pressure (P N2 = 0.1 Pa), indicate the occurrence of changes in the carbon chemical bonding structure due to the formation of nitrogen–carbon bonds. It is not possible to unambiguously deconvolve the C1s core level photoelectron peak since an accurate determination of the diﬀerent contributions is diﬃcult to give. Nevertheless, it is quite well established that the main contribution detected at 284.5 eV is attributed to pure carbon (C–C bonds in a-C network), while the asymmetry on the high binding energy side depends on the local environment of the carbon atoms into C–N sp3 and C–N sp2 bonding coordinations located at 286 eV and 287 eV, respectively [24].

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Fig. 2. Experimental C1s and N1s XPS spectra of CNx ﬁlms grown at diﬀerent nitrogen partial pressures

In Fig. 2b are shown both the experimental and the numerically ﬁtted N1s XPS spectra of CNx ﬁlms. To check the bonding states of carbon in the samples, the N1s peak was deconvolved by using two Gauss–Lorentzian bands positioned around 398.5 eV and 400 eV [21]. These two bands are assigned to diﬀerent nitrogen bonding states in C–N bonds and, more precisely, to N bonded to sp3 -hybridized C and to N bonded to sp2 -hybridized C, respectively. Nitrogen–carbon triple bonds have been excluded due to the absence of their characteristic resonance at about 2200 cm−1 in the infrared transmission spectra. Overall, the results of the ﬁtting procedure show that the 400 eV N1s photoemission peak exhibits a slight, but deﬁnite, growth upon increasing the nitrogen partial pressure. The XPS results, by themselves, do not give a complete information about the carbon–carbon bond reorganization, nevertheless, combining them with REELS data, an estimate of the various C–N and C–C bonding types concentration can be obtained. In the following, according to the literature [25], the short notations [C–Csp2 ], [C–Csp3 ], [N–Csp2 ] and [N–Csp3 ] have been used to indicate the concentrations of diﬀerent bonds type in a-CNx . From the analysis of energy loss spectra [10, 12], the low-energy plasmon Eπ is known, and a shift of the main plasmon peak towards lower energies

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Table 1. Results of XPS and REELS spectra analysis: x(%) is the relative nitrogen content with respect to carbon, [N–Csp2 ] (%) and [N–Csp3 ] (%) are the fractional contributions to the C–N bond, Ep (eV) and Eπ (eV) are the high- and low-energy plasmons, ρ is the calculated mass density, and sp2 and sp3 are the relative fraction of sp2 and sp3 bonds Sample #

P N2 /P A Pa

x %

[N–Csp2 ] %

[N–Csp3 ] %

Ep eV

Eπ eV

ρ g cm−3

sp2 %

sp3 %

22 40 37 47 49 42 24 45 39 38 48

0.0/– 0.1/– 1.3 1.3/12.0 1.3/65.0 6.5 12.8/– 13.3/– 17.0/– 26.6/– 66.7/–

0.0 2.7 8.6 9.0 3.0 7.3 25.0 32.0 11.9 12.2 16.0

0.0 1.4 5.1 6.0 1.8 5.1 12.0 24.4 9.2 8.5 14.1

0.0 1.3 3.5 2.9 1.3 2.2 13.0 6.7 2.7 3.7 3.5

26.9 27.1 26.7 – 21.8 26.2 24.0 23.7 26.1 25.5 23.4

5.1 5.2 4.9 – 5.3 5.2 4.2 4.4 5.0 4.8 5.4

2.61 2.65 2.57 – 1.71 2.46 2.05 1.99 2.44 2.32 1.96

50.5 53.7 53.8 – 75.6 61.5 58.8 67.7 60.6 58.0 90.1

49.5 46.3 46.2 – 24.4 38.5 41.2 25.6 39.4 42.0 9.9

(from 26.9 to 24.0 eV) is also evident, increasing the x values (see Table 1). Applying the Drude formula, this trend can be related to a reduction of the valence electron density and interpreted in terms of a reduction of mass density ρ of the samples. Moreover, to simplify, we assume that our samples are essentially built up by only threefold and fourfold coordinated carbon atoms bonded to other carbon or nitrogen atoms. So, we can state: [N–Csp2 ] + [C–Csp2 ] + [N–Csp3 ] + [C–Csp3 ] = 1,

(1)

where the concentrations of N–Csp2 and N–Csp3 bonds are known from the XPS quantitative analysis of the N1s photoemission peaks, while the total concentration of the C–Csp2 bonds can be calculated by applying the Drude formula to the low-energy plasmon resonance Eπ , [Csp2 ] = [C-Csp2 ] + [N-Csp2 ] = 7.25 × 1020

Eπ2 , sNC

(2)

where NC is the density of carbon atoms and s = 0.28 is a static screening factor which takes into account the screening eﬀects on the π electrons due to the remaining σ electrons [10, 26, 27]. Thus, using the previous relations (1) and (2), it is possible to calculate the remaining bond fraction [C–Csp3 ]. All the results (see Table 1) show the continuous growth of the sp2 bond fraction and the contemporary decrease of the sp3 one with an increase of the nitrogen partial pressure (see Fig. 3a). Moreover, both [N–Csp3 ] and [N– Csp2 ] slightly increase at the same rate. This behavior indicates a progressive material graphitization which proceeds at expense of the [C–Csp3 ] concentration. It seems that nitrogen could preferentially substitute carbon atoms

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Fig. 3. Behavior of the partial contributions [N–Csp2 ], [N–Csp3 ], [C–Csp2 ] and [C–Csp3 ] as a function of the gas pressure

bonded in a fourfold coordination, inducing an increase of the graphitic islands of the samples. From Fig. 3b is also evident a slow and smooth variation of the estimated mass density ρ. The density values of our samples are not comparable to those reported in literature for CNx samples with low nitrogen content [28, 29]. Nevertheless, in our opinion, the bonding conﬁgurations present in the CNx ﬁlms are strongly dependent not only on the nitrogen content, but also on the starting sp3 /sp2 bonding ratio, which, in turn, is determined by the samples preparation conditions. Additional details about the change in the carbon bonding structure were also evidenced by the evolution of the D and G bands in vibrational Raman spectra. In fact, visible Raman spectroscopy is sensitive to the carbon sp2 phase due to the resonance with π–π ∗ transitions which occurs in sp2 domains while σ–σ ∗ transitions, occurring in both sp2 and sp3 domains, are in resonance with UV light. Then, visible Raman spectroscopy can only indirectly probe the evolution of an sp3 phase through the evolution of the sp2 one. In particular, the sp3 /sp2 bonding ratio can be indirectly evaluated from the ratio between the intensity of the two contributions (the so-called D and G bands). Indeed, the G band is connected with the relative motion of sp2 carbon atoms, while the D peak is related to the breathing mode of the aromatic rings [30]. The evolution of the D band is indicative in microcrystalline graphite of a disordering process which produces smaller and smaller crystalline domains, while in diamondlike carbon system its appearance is related to the development of an sp2 phase with the creation of sixfold aromatic rings.

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PN =6.5 Pa

Intensity (arb. un.)

2

2

P =66.7 Pa N

PN =17 Pa

2

2

1100

1300

1500

1700 1100 1300 Raman Shift (cm−1)

1500

1700

Fig. 4. Raman spectra of CNx ﬁlms grown at diﬀerent nitrogen partial pressures. The dashed lines represent the ﬁtting of the D and G peaks

The Raman spectra of some samples grown at diﬀerent nitrogen partial pressures are shown in Fig. 4. The spectra are characterized by a broad asymmetric band near 1550 cm−1 (G band), with a shoulder at 1300–1400 cm−1 (D band), typical of diamond-like carbon systems. Raman spectra were deconvoluted using a Breit–Wigner–Fano (BWF) lineshape for the G peak plus an additional Gaussian line for the D peak [31]. The BWF lineshape is described by: I(ω) = I0

[1 + 2(ω − ω0 )/QΓ ]2 , 1 + [2(ω − ω0 )/Γ ]2

(3)

where I0 is the peak intensity, ω0 is the peak position, Γ is the full width half maximum (FWHM) and Q−1 is the BWF coupling coeﬃcient. The maximum of the BWF line used to account for Raman contribution at around 1300 cm−1 due to its asymmetric line-shape lies at: ωmax = ω0 +

Γ , 2Q

(4)

where the peak position ωmax is lower than the line position of the undamped mode peaked at ω0 if Q value is negative. The positions, the linewidths and the intensities of the G and D bands were deduced from the ﬁtting procedure (see Table 2). It is evident that

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Fig. 5. Variation of I D /I G ratio of the Raman spectra vs. the gas pressure for samples grown in pure nitrogen atmosphere. The line is a guide to the eye

Table 2. Results of the deconvolution procedure performed on the Raman spectra and sp3 /sp2 bonding ratio as determined by REELS analysis Sample #

P N2 /PA Pa

x %

I D /I G

ωG cm−1

γG cm−1

sp3 /sp2

40 37 47 49 42 45 39 48

0.1/– 1.3/– 1.3/12.0 1.3/65.0 6.5/– 13.3/– 17.0/– 66.7/–

2.7 8.6 9.0 3.0 7.3 32.0 11.9 16.0

0.21 0.32 0.32 0.30 0.34 0.48 0.49 0.57

1548 1545 1574 1548 1555 1563 1575 1583

250.0 230.0 188.3 187.8 217.3 181.7 162.8 144.7

0.86 0.86 – 0.32 0.63 0.38 0.65 0.11

with increasing nitrogen partial pressure, the D band intensity increases and the G band position shifts towards higher frequencies, while its linewidth decreases. In Fig. 5 the I D /I G ratio increasing behaviour is evident, even at relatively low nitrogen gas pressures. As reported above, the I D /I G values can be used only to indirectly estimate the sp3 content. However, the values obtained from REELS and XPS results are in good agreement with Raman ones. In fact, at the lowest nitrogen partial pressure, the ﬁlms present a higher sp3 /sp2 bonding ratio and, correspondingly, low I D /I G values (the structure is characterized by oleﬁnic groups [32]). Upon increasing the nitrogen partial pressure, the sp3 /sp2 ratio decreases and, correspondingly, the I D /I G ratio increases (see Table 2). Such

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behavior is consistent with a transformation of sp3 bonded carbon atoms into sp2 ones, induced by the higher nitrogen partial pressure values. Clustering of sp2 sites gives rise to ordering and aromatic ring development, which in turn increase the D band intensity. As can be seen from Fig. 1, the nitrogen content steadily increases with the nitrogen pressure, but above a certain value, it drops drastically. Nevertheless, the I D /I G value shows a monotonic increase with the pressure. It is well known that in PLA experiments the plasma expansion dynamics is strongly aﬀected by the pressure and by the chemical nature of the gas through which the expansion takes place. Thus, the observed structural properties of the ﬁlms cannot be simply dependent on the nitrogen gas pressure but, more generally, on the expansion dynamics also. To investigate this important aspect, we prepared a set of samples in a nitrogen/argon gaseous mixture, keeping ﬁxed the nitrogen partial pressure. Just after the arrival of the laser pulse on the target surface, a plasma ball develops and starts to expand along the normal to the target surface. When such an expansion takes place in a background gas, as happens in the deposition of CNx thin ﬁlms, a shock wave can develop if some conditions are fulﬁlled. Indeed a shock wave, due to the supersonic expansion of the plasma in the gas, develops if the mass of the removed material is lower than the mass of the gas surrounding the plasma and if the pressure driving the moving front of the plasma is greater than the pressure of the gas at rest. Useful information about the expansion dynamics can be obtained by means of time-resolved fast photography of the expanding plasma. The appearance of a bright edge at the contact front between the plasma and the surrounding gas is, in fact, indicative of the development of the shock wave. Moreover, the position R of the front edge of the plasma as function of the time t, after the arrival of the laser pulse, can be obtained from these images. The expansion of the shock wave front as a function of time is given by the following relation: R = ξ0

E ρ0

1/5 t2/5 ,

(5)

where ξ is a factor related to both geometrical and thermodynamical quantities, E is the plume energy, and ρ0 the density of the gas at rest [33]. Usually, three expansion regimes are observed: a ﬁrst stage, where interaction with the gas weakly aﬀects the expansion, in which the plasma expands linearly with time, then a shock wave develops and ﬁnally the plasma expands as a sound wave. Eventually the plume stopping can also be observed. In Fig. 6 the position of the moving front of the plasma is reported as a function of time for diﬀerent ambient gas and pressure conditions, as obtained from the time-resolved images of the expanding plasma, not shown here. In particular, experiments were performed at three pure nitrogen pressures (i.e., 1.3, 13.3 and 66.7 Pa) and two N2 /Ar mixtures (i.e., 13.3 and 66.7 Pa with P N2 /P A ratios of 1/9 and 1/49, respectively). As can be seen from Fig. 6, at a pressure

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Fig. 6. Variation of the position R of the plume front edge as a function of time. Open symbols refer to expansion in diﬀerent pure nitrogen pressure, while solid ones to expansion in mixed N2 /Ar atmosphere

of P N2 = 1.3 Pa the expansion dynamics is weakly inﬂuenced by the background gas: initially a linear behavior holds and only at longer delay times deviation from this behavior can be envisaged. Interaction with the gas becomes more and more eﬀective as the nitrogen pressure is increased, and a slowing down of the plume can be clearly observed. Similar results have been obtained for the two experiments performed in the mixed N2 /Ar atmosphere. In this case the slowing down of the plume is evident also at the total pressure of 13.3 Pa. Argon atoms thus are more eﬃcient in limiting the expansion of the plasma with respect to the nitrogen molecules. When data reported in Fig. 6 were ﬁtted with relation (5) a good agreement could be obtained only in a limited time range. Arnold et al. [34] proposed an analytical model that could describe the whole expansion process in terms of the above reported temporal stages. The transitions from a temporal stage to the following one are also taken into account. The experimental data are expressed in terms of the following dimensionless variables: ˜=R R

2E P

−1/3 t˜ = tvs

2E P

−1/3 ,

(6)

where E is the plume energy, P the pressure of the gas and vs the velocity of the sound in the undisturbed gas. When the R − t experimental data are transformed using relations (6), all the curves showed in Fig. 6 collapse onto

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Fig. 7. Plot of the distance vs. time in dimensionless variables for pure nitrogen atmosphere and for the nitrogen/argon gaseous mixture case (inset)

a single master curve as shown in Fig. 7. The experimental data describing the expansion in pure nitrogen gas show two distinct slopes as a function of t˜: (i) a linear behavior typical of a free expansion regime and (ii) a region where a R ∝ t−1/3 relation holds. In the inset is shown the same plot, but for the experiments performed in the N2 /Ar mixtures. It can be clearly seen that the shock wave regime is present for all the mixtures. In Fig. 8 we report the XPS (Fig. 8a) and Raman (Fig. 8b) spectra of the samples deposited in nitrogen/argon gaseous mixture. Comparing these results with those obtained for the corresponding samples deposited at the same pressure but in an all nitrogen atmosphere, the following eﬀects are evident: (i) a growth of the concentration of the N atoms bonded to sp2 hybridized C and (ii) a blue-shift of the G band position with a decrease of its linewidth, while the D band intensity remains almost constant. The relevant nitrogen content x and the I D /I G ratio are reported in the tables. A clear correlation between the stoichiometry and the structure of the growing ﬁlms and the plasma expansion regimes emerges from these results. In fact, concerning the samples grown in a pure nitrogen atmosphere, increasing P N2 up to 13.3 Pa, the N/C content reaches a value close to 31.2% and the I D /I G ratio increases: a progressive development of the sp2 carbon clusters is induced. Nevertheless, the further increase of P N2 up to 66.7 Pa does not induce an increase in nitrogen content, since the N/C ratio is less than 20%. A further transformation of sp3 bonded carbon atoms into sp2 ones, as well

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Fig. 8. XPS (a) and Raman (b) spectra of the samples deposited in nitrogen/argon gaseous mixture

as a clustering process of the sp2 domains are observed. In such a case the dynamics of the plasma expansion plays a crucial role. As observed from the fast photography, the dynamics of the expanding plasma changed from a free expansion behavior at low pressure to a shock wave formation at the higher pressures and, in the late stage, plume stopping has also been observed. In such a case the reduced nitrogen content in the ﬁlms upon raising the pressure up to 66.7 Pa is a consequence of the reduced ﬂux of species reaching the substrates, due to the increased collision rate between the plasma species and the nitrogen molecules. The observed increase of the I D /I G ratio can be understood if the reduction of the kinetic energy of the species impinging on the substrates is considered. Concerning the sample deposited in the nitrogen/argon atmosphere, at 13.3 Pa with 1/9 N2 /Ar, the dynamics of the expansion plasma are diﬀerent from the ones observed at the same total pressure, but in pure nitrogen. In our case, in the mixed gaseous mixture the nitrogen content drops rapidly from 27% down to 3% as argon atoms are introduced in the chamber, even though the total nitrogen gas content is kept constant. Thus, the reduction of the nitrogen content has been explained considering the plasma dynamics, and

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it is expected that the reduction of the kinetic energy of the species should produce an increase of the I D /I G ratio. On the contrary, it remains constant for both the samples with values comparable to the one estimated for sample grown at 1.33 Pa in a pure nitrogen atmosphere. Really, it is important to remark that the nitrogen content of the two ﬁlms is very low (from 9% down to 3%) so that the increase of sp2 carbon phase due to the nitrogen content can be expected to be very low. Thus, the structures of the ﬁlms are more dependent on the dynamics of the plume expansion rather than on the total pressure at which they are deposited. In this respect the nature of the gas mixture must be taken into account.

4 Conclusion In summary, CNx thin ﬁlms have been deposited by means of pulsed laser ablation at diﬀerent N2 and N2 /Ar mixed partial pressures. In particular, the results obtained can be summarized as follows. Concerning the samples grown in pure nitrogen atmosphere, the nitrogen content increases upon increasing the nitrogen partial pressure up to 13.3 Pa, but when it is raised to 66.7 Pa, its value decreases. The nitrogen introduction in the amorphous carbon matrix has been found to induce an increase in the total threefold-coordination fraction with a contemporaneous lowering of the C–C fourfold-coordination concentration, as evidenced by the XPS and REELS measurements. Nevertheless, as shown by the Raman spectroscopy results, the growth of graphitic domains has also been observed when nitrogen content in the ﬁlms decreases, as happens for the samples deposited at the highest partial pressures. This behavior is explained in terms of the reduction of the kinetic energy of the depositing species, i.e., it involves the plasma expansion dynamics. Changes of the expansion dynamics from a linear expansion to a shock wave formation and, ﬁnally, to the stopping of the expansion were observed. The decrease of the nitrogen content in the ﬁlms above a certain nitrogen pressure have been related to the transition from the free expansion to the shock wave formation transition. Samples grown in N2 /Ar gaseous mixture show a nitrogen content as low as that of the sample deposited in 1.33 Pa of pure nitrogen gas. Also the trend of the structural properties, as evaluated from the I D /I G ratio, is similar, even though, considering the total pressure at which they were deposited, higher values should be expected. All these results reveal that the structure of laser ablation-deposited carbon–nitrogen thin ﬁlms depends strongly on the dynamics of the expansion plasma regime, not simply on the overall nitrogen content, and in this respect the role played by the gas composition and pressure is of paramount importance.

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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]

A. Y. Liu, M. L. Cohen: Phys. Rev. B 41, 10727 (1990) 287 D. M. Teter, R. J. Hemley: Science 271, 53 (1996) 287 S.-D. Mo, L. Ouyang, et al.: Phys. Rev. Lett. 83, 5046 (1999) 287 K. M. Yu, M. L. Cohen, E. E. Haller, et al.: Phys. Rev. B 49, 5034 (1994) 287 A. Y. Liu, R. M. Wentzcovitch: Phys. Rev. B 50, 10362 (1994) 287 M. N. Semeria, J. Baylet, et al.: Diamond Relat. Mater. 8, 801 (1999) 287 A. G. Filtzgerald, L. Jiang, M. J. Rose, et al.: Appl. Surf. Sci. 175–176, 525 (2001) 288 F. L. Normand, J. Hommet, T. Szorenyi, et al.: Phys. Rev. B 64, 235416 (2001) 288 S. Widemann, M. Knupfer, J. Fink, B. Kleinsorge, J. Robertson: J. Appl. Phys. 89, 3783 (2001) 288 A. M. Mezzasalma, G. Mondio, F. Neri, S. Trusso: Appl. Phys. Lett. 78, 326 (2001) 288, 291, 292 F. Barreca, A. M. Mezzasalma, G. Mondio, F. Neri, S. Trusso, C. Vasi: Thin Solid Films 377–378, 631 (2000) 288 F. Barreca, A. M. Mezzasalma, G. Mondio, F. Neri, S. Trusso, C. Vasi: Phys. Rev. B 62, 16893 (2000) 288, 291 N. Tsubouchi, B. Enders, A. Chayahara, A. Kinomura, C. Heck, Y. Horino: J. Vac. Sci. Technol. A 17, 2384 (1999) 288 P. Papakonstantinou, D. A. Zeze, A. Klini, J. M. Laughlin: Diamond Relat. Mater. 10, 1109 (2001) 288 E. Fazio, F. Barreca, F. Neri, S. Trusso: GNSR 2001 – State of Art and Future Development in Raman Spectroscopy and Related Techniques (IOS, Amsterdam 2002) pp. 61–67 288 H. Sjostrom, L. Hultman, et al.: J. Vac. Sci. Technol. A 14, 56 (1996) 288 B. C. Hollowaya, O. Kraft, et al.: J. Vac. Sci. Technol. A 18, 2964 (2000) 288 P. Hammer, N. M. Victoria, F. Alvarez: J. Vac. Sci. Technol. A 18, 2277 (2000) 288 B. Kleinsorge, A. C. Ferrari, J. Robertson, W. I. Milne: J. Appl. Phys. A 88, 1149 (2000) 288 D. B. Crisey, G. K. Hubler (Eds.): Pulsed Laser Deposition of Thin Films (Wiley, New York 1994) 288 E. Riedo, F. Comin, J. Chevrier, A. M. Bonnot: J. Appl. Phys. 88, 4365 (2000) 288, 291 G. M. Fuge, C. J. Rennick, et al.: Diamond Relat. Mater. 12, 1049 (2003) 288 J. F. Moulder, W. F. Stickle, P. E. Sobol, K. D. Bomben: Handbook of X-Ray Photoelectron Spectroscopy (Perkin-Elmer, Eden Prairie 1992) 290 M. Tabbal, P. Merel, S. Moisa: Appl. Phys. Lett. 69, 1689 (1998) 290 T. Kohler, G. Jungnickel, T. Frauenheim: Phys. Rev. B 60, 10864 (1999) 291 S. Bhattacharyya, C. Valle´e, et al.: J. Appl. Phys. 85, 2162 (1999) 292 G. Curr´ o, F. Neri, G. Mondio, et al.: J. Electron. Spectr. Related Phen. 72, 89 (1995) 292 S. Rodil, N. A. Morrison, W. I. Milne, J. Robertson, et al.: Diamond Relat. Mater. 9, 524 (2000) 293 J. Hu, P. Yang, C. M. Lieber: Phys. Rev. B 57, 3185 (1998) 293

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[30] K. W. R. Gilkes, H. S. Sands, D. N. Batchelder, J. Robertson, W. I. Milne: Appl. Phys. Lett. 70, 1908 (1997) 293 [31] A. C. Ferrari, J. Robertson: Phys. Rev. B 61, 14095 (2000) 294 [32] J. Schwan, S. Ulrich, V. Baton, H. Ehrhardt: J. Appl. Phys. A 80, 440 (1996) 295 [33] Y. B. Zel’dowich, Y. P. Raizer: Physics of Shock Waves and High Temperature Hydrodynamic Phenomena (Academic, New York 1966) 296 [34] N. Arnold, N. J. Gruber, J. Heitz: Appl. Phys. A 69, S87 (1999) 297

Index sp3 /sp2 bonding ratio, 293, 295

G band, 293, 294, 298

carbon chemical bonding, 290 carbon coordination, 291 threefold and fourfold coordination, 292, 296 chemical shift, 290 CNx thin ﬁlms, 289, 290, 296, 298 core level photoelectron peak, 290

plasma plasma expansion, 296, 299 plasma plume plume stopping, 297 pulsed laser ablation (PLA), 288, 296, 299

D/G band intensity ratio, 295 D/G band intensity ratio, 295, 298–300 density, 293 diamond-like carbon (DLC), 294 diamondlike carbon (DLC), 293 D band, 293, 294, 296, 298 fast photography, 287–289, 296, 299 free expansion regime, 297 graphite-like carbon (GLC), 287 graphitization, 292, 293, 299

Raman spectroscopy, 288, 289, 293–295, 298–300 reﬂection electron energy loss spectroscopy (REELS), 288–292, 295, 300 shock wave, 296, 298–300 X-ray photoemission spectroscopy (XPS), 288, 291, 292, 295, 298–300 x-ray photoemission spectroscopy (XPS), 289–291

Modeling of the Transport Properties of Diamond Radiation Sensors Stefano Lagomarsino and Silvio Sciortino Dipartimento di Energetica, Universit` a di Firenze, Via S. Marta 3, I-50139 Firenze, Italy, and INFM, Unit` a di Ricerca di Firenze [email protected] Abstract. A fully quantitative model of electronic transport in polycrystalline chemical vapour deposited (pCVD) diamond sensors is presented, predicting the conductivity behavior of diamond devices during and after exposure to ionizing radiation. The model takes into account a widely adopted qualitative picture of the diamond band gap, based on two distributions of defect levels: a mid-gap group of recombination centers and a distribution of traps closer to one of the band edges. Analytical expressions for the radiation-induced currents (RIC) and persistent radiation-induced currents (PIC) are derived from the solutions of a complete set of rate equations, and the experimental data are well ﬁtted by assuming the distribution of the trap centers to be formed from the superposition of several uniform bands, with diﬀerent cross sections, energies and concentrations. The model is validated against experimental data from a set of diamond detectors whose charge collection distance ranges over an order of magnitude (from 15 µm to 250 µm), i.e., from highly defective to the state-of-the-art material. A rationale is then proposed for the relationship between material quality and trap parameters, also with regard to the changes in the material properties caused by high irradiations of fast neutrons.

1 Models of the Polycrystalline Diamond Band Gap The simplest model for carrier kinetics in a wide band-gap material which can explain and reproduce the experimental data involves an active trap and a recombination center [1]. Deeper trap centers can also be introduced which are not active at the temperature of interest, i.e., whose activation energy is far higher than the Boltzmann factor kT . These centers can play a role only in the neutrality condition of the material, which is an underlying assumption of almost all the works found in literature, and in determining the position of the Fermi level at thermodynamic equilibrium. This picture is obviously oversimpliﬁed in the case of crystalline diamond with a band gap as high as 5.5 eV and a considerable variety of possible defect centers. The eﬀort to take into account a competition between diﬀerent trapping centers in an insulator material is due to Chen et al. [2], whilst McKeever et al. [3] have reviewed the main models proposed to describe thermally and optically stimulated luminescence phenomena. G. Messina, S. Santangelo (Eds.): Carbon, The Future Material for Advanced Technology Applications, Topics Appl. Phys. 100, 303–327 (2006) © Springer-Verlag Berlin Heidelberg 2006

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Nevertheless, a two-level model allows us to introduce basic concepts and describe processes which will be generalized in the following sections to a more satisfying model. This generalization is based on the experimental data collected for several years on polycrystalline chemical vapour deposited (pCVD) diamond. In this section, we give a short review of some relevant models presented so far, resulting in a commonly accepted qualitative description of the band-gap structure of the highest quality pCVD diamond. In Sects. 1.4 and 1.5 we will introduce experimental facts which will be useful to develop a mathematical model of the carrier kinetics. The assumptions on which the model is based will be reviewed in Sect. 2. The model will be tested on pCVD diamond devices, specially prepared as ionizing radiation detectors. Radiation-induced conductivity will be considered in Sect. 3, and thermal relaxation of trapped carriers in Sects. 4 and 4.1. In Sect. 4.2 persistent (radiation-induced) current will be treated in detail. The quality of the samples, their performances and the eﬀect of neutron irradiation will be explained in terms of the obtained values of the trap and recombination center parameters. 1.1 Band A Donor–acceptor pair recombination (DAP) has been extensively studied in natural and synthetic high-pressure high-temperature (HPHT) diamond [4] as well as in thin diamond ﬁlms [5]. In those works DAP is ascribed to recombination between levels due to boron and nitrogen, i.e., the extrinsic impurities more easily incorporated in the diamond lattice. DAP is related to well-known luminescence broad bands [6], from 1.8 eV to about 3.2 eV. Conversely, a broad band peaking at 2.8 eV, commonly referred to as band A, is believed to be originated by dislocations [5], possibly including sp2 -like structure [7]. Band A is generally prominent in the cathodoluminescence spectra in high-quality pCVD diamond [8]. Moreover, sharp photoluminescence peaks are less observed in higher quality samples, due to the absence of nitrogen and other impurities [9]. As can be expected, the band A emission disappears in some single-crystal CVD (scCVD) diamond ﬁlms, also if it is observed in homoepitaxial diamond ﬁlms with nonepitaxial crystallites [7]. Manfredotti et al. [10] have suggested, by photoconductivity (PC) and electroluminescence measurements, that the defect levels related to band A act as a recombination center inside the diamond band gap. 1.2 Trapping Centers Many conductivity investigations [11, 12] support the existence of acceptor states close to the valence band, probably related to grain boundaries. Gonon et al. [12] proposed a trapping/recombination mechanism governing the thermally stimulated conductivity (TSC) and UV photoconductivity. According

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to their scheme, acceptor states at 1 eV from the valence band (VB), partially ﬁlled in their initial state, are responsible for the conduction of unirradiated samples. As electron–hole pairs are generated by UV illumination, electrons are trapped on levels located at 1.9 eV below the conduction band (CB). During thermal annealing carriers are released from the deep electron trap to the CB and return to the initial electron state. A similar mechanism has been suggested by Vittone et al. [13], relying on thermoluminescence (TL) characterization. Diamond samples are exposed here to α-radiation and then illuminated by visible light. Finally, the TL glow curve is recorded. Optical fading of the TL signal starts at about 550 nm and is nearly full at 500 nm. In order to explain this eﬀect, the authors assume the existence of an electron trapping band at half band gap and a hole trapping level with activation energy in the range 0.98–1.13 eV above the VB. These traps are ﬁrst saturated (primed) by exposure to an α-source, then illuminated. On reaching the wavelength of 550 nm, light photons have enough energy to release trapped electrons, which tend to annihilate the still trapped holes. Souw et al. [14] independently propose a qualitative model with a defect band close to the VB, and a defect band close to half band gap, negatively and positively charged, respectively, at thermal equilibrium. Under these hypotheses they explain their photoconductive (PC) measurements from red to over band-gap UV and backwards. They observe that only holes contribute to the PC signal in their samples. Conversely, Nebel et al. [15, 16] report that nominally undoped pCVD diamond is an n-type semiconductor, but in this case the investigated samples yield a high concentration of nitrogen (∼ 1018 cm−3 ). They also propose a qualitative model of amorphous carbon-like density of states present at grain boundaries. In conclusion, there is plenty of experimental evidence of distributions of deep and shallow traps close to the band edge and recombination bands close to the mid-gap. Whether the traps are close to the valence or conduction band edge it is not well assessed. In the following we will try to give a mathematical treatment of the carrier kinetics independent from this choice. We will consider hole traps close to the VB edge, but our conclusions will hold as well for the opposite situation. 1.3 Carrier Lifetimes and Charge Collection Distance A theoretical model on natural diamond, based on transient conductivity measurements, has been proposed by Pan et al. [17, 18], to relate the defect levels inside the band gap to the carrier lifetimes. They introduce a deep donor level, acting as a recombination center for holes and electrons, which they tentatively attribute to an impurity concentration of 20 ppm of nitrogen in diﬀerent aggregate forms. Two additional trap mechanisms for holes and electrons are considered, by means of two decay times τ p and τ n . This model ﬁts very well to the experimental data, yielding the concentration, N r ∼

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1018 cm3 , and cross-section values of the recombination center σ p = 1.4 × 10−16 cm2 and σ n = 3.1 × 10−14 cm2 , for holes and electrons, respectively. The lifetime of the carriers is on the order of hundreds of picoseconds. Such a high density of defects is believed to limit the charge collection distance (CCD) in natural IIa diamond to values of 20 to 50 µm [19]. The CCD is deﬁned as the average distance electrons and holes move apart under the inﬂuence of the external electric ﬁeld, before they are trapped in the diamond material or reach the electrodes, and it is used as a major ﬁgure of merit of pCVD diamond detectors and of the material itself. In pCVD diamond the content of impurities can be strongly reduced with respect to natural or HPHT synthetic diamond. Indeed, pCVD diamond from production reactors now “regularly” exhibits 300 µm charge collection distance [20], a value which is believed to be mainly limited by grain boundaries. 1.4 Location of the Trapping and Recombination Centers in the Diamond Band Gap In order to test the outlined picture of two distributions of defect levels, and to locate their position inside the diamond band gap, we performed a set of CCD measurements on a state-of-the-art pCVD diamond after exposure to light [21]. We illuminated with photons of diﬀerent energies a diamond device produced by De Beers Industrial Diamonds (DEBID) for the RD42 collaboration (sample CDS88) [22]. The diamonds were metallized with a single electrode on one side and 256 narrow strips on the other side. The strips had a width of 25 µm and a pitch of 50 µm, which allowed the radiation to penetrate the material. All the strips were shorted to form a single electric contact. The sample was exposed to light starting from two diﬀerent initial states: – (P) “pumped” state, obtained by irradiating the sample with a 10 mCi β-radiation source to an absorbed dose of about 1 Gy. A rise of the radiation-induced current of the sample occurs due to passivation of deep traps, a phenomenon which is commonly referred to as “pumping”. Notably, a dose one tenth as large is high enough to obtain an increase in CCD, measured oﬀ-line, from about 150 µm to 230 µm. This eﬀect can endure for months in a dark environment at room temperature. – (D) “depumped” state, obtained by exposing the sample to a continuous light source such as a halogen lamp. This procedure reset the CCD of the sample to the initial value, about 150 µm. We divided the band gap into twelve intervals ∆Ei = [Ei , Ei+1 ], and exposed the sample to photons with energy spread ∆Ei . Then, we measured the CCD under exposure to relativistic β-particles, which is the standard method to test the collection eﬃciency for minimum ionizing particle (MIP) detection. The measurements were performed according to the following scheme for each energy interval ∆Ei :

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Fig. 1. Measured CCD in the depumped (dashed line) and pumped state (solid line) as a function of the photon energy of the applied luminous exposure. Model of the trapping–detrapping mechanisms. The fat arrows indicate the main transitions during the pumping and depumping processes. A tentative evaluation of the extent and position of the defects bands is also indicated

1. First, we set the sample in the P state, then we expose it to photons of energies in ∆Ei , ﬁnally we measure the CCD. 2. First, we set the sample in the D state, then we expose to photons of energies in ∆Ei , then we measure the CCD. The outcome of these measurements is presented in Fig. 1. The band gap appears to be divided into four regions (I–IV in the ﬁgure): – Starting from the D state, photons of energy in II and IV are able to pump (at least partially) the sample while photons of energy in I and III do not change the state of the sample. – On the other hand, starting from the P state, photons corresponding to region III completely depump the sample. Notably, the energies of region I and III are complementary, in the band gap, to those of region IV and II, respectively, in the sense that, if photons of energy E tend to pump diamond, photons of energy (Egap − E) tend to depump it, and vice versa. This is true except for region I, whose photons does not aﬀect the P state of diamond. We ascribe this fact to a small capture cross section for these photons of the centers responsible for the P state. These considerations lead to the conclusion that pumping/depumping processes are ruled by the ﬁlling or emptying of two bands of levels, one for each pair of regions: zone II and III relative to the band closer to mid-gap, zone I and IV to the other one. Photons with pumping energies ﬁll directly one of the bands, leaving a free carrier (hole or electron) which is trapped by the other one. Depumping photons, on the other hand, empty one of the bands, and the released carriers recombine in the other. We will assume, in the following, that the shallowest trap distribution is closer to the VB, but all our considerations hold as well when the positions are reversed with respect to half band gap.

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In order to assure neutrality, the two bands have to be either neutral or oppositely charged. The depumped state most likely corresponds to charged bands, because the capture cross sections of charged centers tend to be higher than those of the neutral ones [23]. In conclusion, there is experimental evidence supporting the picture of two bands, a deep donor and a deep acceptor center distributions, with the Fermi level situated somewhere in between, so that the two distributions are charged at thermal equilibrium (depumped state). We will refer to the deep donor distribution as “band A” because it has a maximum density in the region where the luminescence band A is peaked. This assumption is in agreement with the suggestion of Manfredotti et al. [10], that this band acts as a recombination center. We also denote the deep acceptor center as “band B”. The boundaries of the regions I–IV suggest that band A ranges from about 1.7 to 2.7 eV, where it has a maximum concentration [21], while band B is extended up to 1.7 eV. These values of energy are conﬁrmed by photoconductive responsivity measurements performed on the same sample. The lower limit of band B is not detected by this method, but it can be studied in detail with thermal spectroscopy methods (TSC or TL) or with the combined analysis of radiation-induced currents (RIC) [24] and persistent radiation-induced currents (PIC) [25], developed by the authors and presented in Sects. 4.1 and 4.2. 1.5 Unipolar Conduction As discussed before, it has been reported by several authors that the transport properties in the pCVD diamond material are due mainly to one type of carrier. This consideration, which is essential for the subsequent development of the model, has to be treated in more detail. It has been found by the RD42 CERN collaboration [26] that the collection eﬃciency of CVD diamond detectors can be strongly incremented by removing the material from the substrate side (linear model). This is due to the poorer quality of the CVD diamond ﬁlm near the substrate. As the removed thickness increases, the charge collection distance, after reaching a maximum, begins to decrease, being limited by the ﬁlm thickness. As the thickness L tends to zero, the plot of the CCD vs. L tends to approach a straight line crossing the origin. If conduction were due to both types of carriers, the straight line would have a form CCD = L (all the carriers reaching the contacts). On the contrary, if only one type of carrier contributes, then CCD = L/2, i.e., only holes or electrons reach the contacts, whilst the carriers of the other type are trapped in the vicinity where the pair is created. In intermediate cases CCD ≈ L for small L values, and its derivative approaches 1/2 for higher L values. We ﬁtted the data reported by the RD42 collaboration [26], as shown in Fig. 2, making use of the expression for the CCD calculated by assuming that the CCD is linearly increasing from the substrate to the growth side. The best

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Fig. 2. Simulation of the CCD (d) vs. material thinning at diﬀerent dn /d values. A two-carrier model yields values very distant from the experimental points. Pure single-carrier conduction is quite better. The best ﬁt is given when the electrons contribute for only 5% to the collected charge. Modiﬁed from a cited reference [26]

ﬁt of the experimental data, as shown in Fig. 2, is obtained assuming that one carrier contributes to conductivity for only 5%. Hence, in the following, we will assume conductivity to be proportional to the hole concentration, which is the choice anticipated in the previous sections.

2 A General Model for Transport Properties of pCVD Diamond: Underlying Assumptions Any theoretical modeling of transport properties of a semiconductor material requires the solution of a complete set of rate equations for the populations of both the defect levels and the conduction/valence bands. Unfortunately, the presence of two distributions of levels in the diamond band gap, both with a spread in energy and, presumably, capture cross section, can make it impossible to ﬁnd a simple, analytical solution for the rate equations of the system. Nevertheless, a few assumptions listed below make the system analytically solvable and permit us to relate the radiation induced conductivity (RIC) to the structure of the diamond band gap. 1. The centers of band B are purely hole traps, as discussed in Sects. 1.4 and 1.5, and their capture cross sections for electrons are negligible. 2. Band B is decomposable in several (m) components with diﬀerent capture cross sections for holes (σi , with 1 ≤ i ≤ m) and distinct trap concentrations per unit volume (Ni , 1 ≤ i ≤ m).

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3. The capture cross sections for electrons (σnr ) and for holes (σpr ) take constant values over the entire band A. These three assumptions alone make it possible to solve analytically the rate equations of diamond under irradiation. A further assumption, the unipolar conduction approximation, whose validity is assessed by the linear model (Sect. 1.5), makes it possible to relate directly the hole density in the VB to the conductivity of diamond. This hypothesis is expressed as: 4. The capture cross section for electrons of the A centers is much higher than that for holes: σnr σpr ≡ σr . The validity of the inequality above is based on the assumption, discussed in Sect. 1.4, that A centers are positively charged when empty of electrons. Moreover, assumption 4 is strongly suggested by comparison with the results reported by Pan et al. [17, 18] on conductivity of natural IIa diamond, discussed in Sect. 1. The authors of the cited work report two orders of magnitude of diﬀerence between σnr and σpr = σr for the recombination centers. In Sect. 3 a model of RIC is developed, based on assumptions 1–4. Moreover, the decay of the current after irradiation (persistent radiationinduced conductivity or PIC) is also related to the presence of several components of band B. This phenomenon is accounted for by hypotheses 1 and 2 and by the further assumptions: 5. Each component of band B has a spread in energy, and the density of levels per unit energy di /dE is assumed to be constant in the energy interval of interest. 6. The energy limits of each component of band B are diﬀerent and range from E1i to E2i (i = 1, . . . , m). 7. Retrapping terms are considered to be negligible with respect to recombination during thermal release of carriers from band B (ﬁrst-order kinetics [3]). We will sometimes refer to the slow carrier release from the traps caused by thermal energy as thermal fading. Then, the validity of assumption 5 is based on the fact that, in a range of 1–105 s (the range of our measured fading times) the width of the energy interval emptied by thermal fading is only about 5 × kT log 10, i.e., 0.25 eV. It is quite reasonable to assume that the density of levels is constant on this interval. In the following sections, we will develop a model of PIC based on assumptioins 5–7 and also relate these hypotheses to the partial depumping of RIC after thermal fading. In this context, assumption 7 will be justiﬁed by an a posteriori consideration (Sect. 4.1). The picture of the diamond band gap derived from assumptions 1–7 is represented in Fig. 3, by the schematics on the left.

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Fig. 3. Schematic representation of the observed radiation-induced current behaviour and of the trap states model of the pumping process, from the depumped state (left) to the pumped state (right)

3 Conductivity Under Exposure to Ionizing Radiation We consider here a pCVD diamond detector with an externally applied voltage bias and assume that it is depumped, i.e., it has been reset by irradiation with visible light of proper wavelength [13] or heated [11]. By exposing the depumped device to a continuous source of ionizing radiation (e.g., X- or βradiation), we can observe a typical rise of the induced current from an initial level to a saturation level, with a time response dependent on the dose rate. The increase of the induced current is believed to be due to a progressive ﬁlling of traps that are responsible for the degradation of carrier lifetimes. Diﬀerent samples not only show a diﬀerent rise time or saturation level, presumably dependent on the concentration of defects, but also a quite diﬀerent shape of the rise current, probably related to the details of the defect distributions. As an example, Fig. 4 shows a comparison among the responses of ﬁve samples of diﬀerent quality, exposed to β-radiation. The ﬁgure plots the sensitivity of the samples as a function of absorbed dose, deﬁned as the induced current density divided by the product of the dose rate and the electric ﬁeld. This quantity is proportional to the product of the lifetime and the mobility of the carriers, and it is directly related to the quality of the material. The considerable diﬀerence in sensitivity and time response of the ﬁve devices is clearly observable. Starting from the hypotheses introduced at the beginning of Sect. 2, we can explain the details of the conductivity increase in terms of diﬀerences in concentration and cross section of the components of band A and B. We will denote with Nr and σr the concentrations and the capture cross sections for holes of the A recombination levels, and with N1 , . . . , Nm , σ1 , . . . , σm , the same quantities relative to the m components of band B. The terms {q1 (t), . . . , qm (t)} and qr (t) represent the numeric concentrations of charged centers, i.e., the concentrations of empty centers (both A and B centers are neutral when ﬁlled with electrons and holes, respectively). The generating factor of the betas is denoted by g. The concentration of holes and their

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Fig. 4. The sensitivity of ﬁve samples as a function of absorbed β-radiation dose. CDS92, P13 and P16 are DEBID detectors; F56 and F58 were produced in Florence by pulsed DC glow-discharge under similar deposition conditions. P13 and P16 were cut from the same wafer. P16 as well as F56 were irradiated at a ﬂuence of 2 × 1015 MeV equivalent n/cm2

thermal velocity are indicated by p and vp , respectively. The rate equations for the VB and for the components of band B are the following: m dp (1) qi (t)vp σi + (Nr − qr (t)) vp σr . =g−p dt i=1

dqi = −pqi (t)vp σi . dt

(2)

In pCVD diamond, even under irradiation, the free carrier concentration is very much lower than the population of the defect centers (∼ 104 cm−3 free carriers generated by a dose rate of 1 Gy/min against no less than 1012 cm−3 capture centers). As a consequence: dp dqi . dt dt

(3)

Inequality (3) justiﬁes the “quasi-equilibrium (QE) approximation” [1], from which we can set dp/dt = 0 in (1). Accordingly, the neutrality condition can be written: m

qi (t) = qr (t) + p − n ∼ = qr (t).

(4)

i=1

In the single-carrier hypothesis 4 (Sect. 2, p. 310), the hole concentration p is proportional to the current I: p=

I , eµSE

(5)

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313

where µ is the hole mobility, e the elementary charge, S the metallization area and E the electric ﬁeld strength. If we denote the total charge collected by: t Q= I(t ) dt , 0

we can solve each (2) in terms of Q, as follows: vp σi Q . qi (Q) = Ni × exp − eµSE

(6)

Substituting (4), (5) and (6) in the rate (1), and setting dp/dt = 0 (QE approximation), we obtain for I the expression: −1 m vp eµSEg σi Q × Nr σr + Ni (σi − σr ) exp − , (7) I(Q) = vp eµSE i=1 with the neutrality condition derived from (4) calculated at t = 0: m

Ni = Nr .

(8)

i=1

Equation (7) is a simple, analytical expression of the instantaneous current I in terms of the overall collected charge Q. This theoretical expression can be ﬁtted to the measured current I, by varying the trap parameters Ni and σi , together with Nr and σr , which are the corresponding quantities for the recombination center. A qualitative interpretation of the behaviour of the induced current is shown in Fig. 3. At the beginning of the process, electrons and holes are trapped by centers A and B , respectively. As a stationary condition is attained, some A levels remain charged, while holes are mainly trapped in neutral A levels, thus providing charged recombination states for the generated electrons. A small amount of charged B levels, necessary to satisfy the neutrality condition, are mantained by thermal relaxation, which is not taken into account by our model at this stage. Analysis of (7) reveals that, if, most likely, the charged traps have a cross section for holes greater than that of the neutral recombination center, then the induced current increases monotonically with the absorbed dose. Expression (7), with a suitable choice of the number m of components of band B, accounts for the current rise of a number of pCVD diamond samples of diﬀerent qualities, grown with diﬀerent deposition methods. It also allows the interpretation of the response degradation due to high ﬂuences of neutron irradiation, in terms of structural modiﬁcations of bands A and B. As an example, in Table 1 and Fig. 5 we report the results of the analysis of RIC curves for ﬁve samples, three (CDS92, P13 and P16) grown by DEBID,

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Fig. 5. Schematic plot of the trap parameters of the samples under study, deduced from the analysis of the radiation-induced currents

presumably by microwave plasma-enhanced CVD, two (F56 and F58) grown by the authors at the University of Florence, by pulsed DC glow-discharge CVD [27]. The deposition conditions of F56 and F58 were very similar. Two of the samples (P16 and F56) were irradiated with fast neutrons at a ﬂuence of 2 × 1015 /cm2 (1 MeV equivalent). Samples P13 and P16 were cut from the same wafer, the diﬀerence between them being most likely due to the irradiation of P16. Table 1. Values of CCD, concentration and capture cross section of the recombination centers, obtained for the samples under study Manufacturer Sample

CCD (µm)

σr (10−16 cm2 )

Nr (1015 cm−3 )

DEBID

245 140 851 14 192

5.5 5 5 1 0.6 25

2.3 5 5 1 18 43

Univ. of Florence 1 2

CDS92 P13 P16 F58 F56

Measured after neutron irradiation Measured before neutron irradiation

Figure 6 shows the best ﬁt of the RIC curve of sample P16. The measurements ﬁt very well to the theoretical expression, with a χ2 on the order of some units. From Table 1 and Fig. 5 it is possible to recognize some interesting features of pCVD diamond. As far as the commercial (DEBID) samples are concerned:

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315

Fig. 6. Best ﬁt of the model to the radiation-induced current of sample P16

(a) The capture cross section of the mid-gap A centers has about the same value for all samples, i.e., there is a substantial identity of this type of center over all the DEBID diamonds investigated. (b) On the other hand, in the more recent sample (CDS92) the concentration is about half that of the others (P# samples). Interestingly, the CCD is about doubled passing from the P# batch to sample CDS92. (c) Neutron irradiation aﬀects neither the cross section nor the concentration of the recombination states (as can be seen by comparing the parameter values of P13 and P16). Thus, the variation in time response is likely related to a change in structure of the more shallow band B. (d) Indeed, neutron irradiation produces a slight change in cross-section and concentration of the low cross section tail of band B. Concerning the local samples: (e) The capture cross section of the recombination levels is very diﬀerent from that of the DEBID samples, and it is strongly aﬀected by neutron damage; (f) Neutron damage also produces a strong variation in the concentration of both recombination and trap states. With our analysis, we succeeded in separating band B in several components of diﬀerent cross sections. It is intrinsic to the method that no information can be drawn about the activation energy of the levels. In particular, we are not able to determine the position of the several components of band B in the band gap nor can we evaluate the density of levels per unit energy of the various components. This problem, left unresolved in this section, will be answered in Sects. 4.1 and 4.2 by means of independent measurements, interpreted in the framework of the same model.

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4 Thermal Relaxation of Uniform Trap Level Distributions As the radiation source is removed, each trap level releases carriers with a constant probability per unit time: E 1 = s × exp − , (9) τ kT where E is measured by taking the VB edge as a reference, τ is the mean life of the level and s is a frequency factor [1] equal to the product of the eﬀective density of states Nv , the thermal velocity vp and the capture cross section of the trap: s = Nv σvp .

(10)

In the ﬁrst-order approximation (assumption 7, p. 310), i.e., if the charge released has much more probability to recombine in the band A rather than to be trapped again, then the probability to ﬁnd a single trap of band B occupied after a time t from the removal of the radiation source is:

P (E, t) = exp −Nv σvp e−E/kT t . (11) Now, let us adopt the hypotheses 5 and 6 of Sect. 2 (p. 310), stating the presence of an almost uniform distribution of trap levels in the interval E1 < E < E2 with a density of levels per unit energy given by d/ dE. In this case, the rate of change of the distribution population is straightforwardly: exp − τt2 − exp − τt1 dq d d E2 d =− kT , (12) P (E, t) dE = dt dE dt E1 dE t where: τ1 =

E1 1 × exp , s kT

τ2 =

E2 1 × exp . s kT

(13)

If E2 − E1 kT , well inside the interval [τ1 , τ2 ] the function (12) can be approximated as: d kT dq ≈ . dt dE t

(14)

Thus, the total charge q(t) of the distribution depends on time as: q(t) = C +

d kT log t. dE

(15)

Equations (12) and (15) allow the interpretation of two diﬀerent kinds of measurements:

I (A)

Modeling of the Transport Properties of Diamond Radiation Sensors

7 10

-10

5 10

-10

3 10

-10

1 10 -10 0 0

2

4

6

8

10

12

317

14

t (10 s) 3

Fig. 7. Radiation-induced current after diﬀerent (exponentially increasing) fading times. The sample is fully depumped at the start of the measurement run

– RIC measured on a sample after diﬀerent time intervals between consecutive irradiations (Sect. 4.1) – PIC after removal of the radiation source, measured over ﬁve decades in time (Sect. 4.2) In the following sections we describe in detail the information that can be extracted by these type of measurements. 4.1 Radiation Induced Conductivity Transient at Diﬀerent Fading Times If we remove the ionizing radiation source after the RIC has attained its stationary value, and then expose the sample to the same radiation source after a variable time delay, the current does not reach immediately the stable current level. A partial emptying of the band B traps, i.e., a thermal fading, occurs, such that the radiation takes a certain time to ﬁll the traps again, dependent on the fading time between exposures. In this case, we say that the sample is partially depumped ; then, the longer is the fading time, the higher is the time necessary to reach the RIC saturation value, i.e., the pumped state. Figure 7 shows the induced current behavior during a single measurement run, under consecutive exposures to the same level of β-irradiation. The ﬁrst current step represents the response of the sample in the fully depumped state, the following exposures alternate between exponentially increasing fading times (0.33 min, 1 min, 3 min, and so on, up to 12 h). The stationary levels are the same within the limits of reproducibility of the dose rate. In Fig. 8 we report the conductivity dependence on the absorbed dose for several values of fading time. It is worthy of note that the spacing between curves is equal. Since the measurements were taken at exponentially increasing fading times, this fact suggests a logarithmic dependence on time of the trap population levels, as assessed by (15). As a matter of fact, if we perform the analysis

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Fig. 8. Radiation-induced current vs. dose behaviour at diﬀerent fading times

Fig. 9. Evolution with thermal fading of the numeric concentration of empty (charged) traps qi for two trap components of diﬀerent cross section

of the RIC at each fading time, in order to determine the dependence of the population of the traps on time, we obtain the behavior shown in Fig. 9. The concentration of empty traps tends to follow a logarithmic behavior of type: q(t) = A + B log t.

(16)

A comparison of (16) with the theoretical expression (15), allows us to evaluate the density of levels per unit energy by simply dividing the slope of the curves of Fig. 9 by the term kT . Figure 10 shows the results of this analysis performed on three samples for the traps whose uncertainties in concentration is small enough to recognize a deﬁnite time behavior. A comparison of the overall trap concentration with the density of levels per unit energy shows that they are consistent with level distributions whose width ranges over a few eV.

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319

Fig. 10. Comparison between concentration of defects (cm−3 ) and density of defect states per unit energy (cm−3 eV−1 ) for three samples under study: F56, F58, P16

The analysis of RIC at gradually increasing fading times allows us to deduce the density of levels per unit energy, but does not yield any information about the eﬀective position of the level distribution in the band gap. The study of the currents immediately after the removal of the radiation source overcomes this diﬃculty, and gives a complementary method to evaluate the density d/dE, also providing a consistency test of our model. At this stage, we can verify “a posteriori” the ﬁrst-order kinetics assumption 7, introduced in Sect. 2. In order to demonstrate that recombination play a prominent role with respect to retrapping, it suﬃces to verify the statement: qi σi (Nr − qr ) σr . (17) i

This can be easily done by making use of the data of Table 1 and Fig. 9. It appears that the inequality (17) is satisﬁed in the whole range of fading times under consideration. In fact, in the worst case, after 15 h of thermal fading, the left side of (17) is one six the value of the recombination term. 4.2 Persistent Radiation-Induced Conductivity After removing the radiation source, the electric current approaches the initial value prior to any irradiation. The time involved in reaching the original (depumped) state depends on how fast the populations of the defect levels in the band gap return to the thermal equilibrium value, and it is quite long for polycrystalline CVD diamond. As an example, Fig. 11 reports the time

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Fig. 11. Persistent radiation-induced current of each sample as a function of time. The curves are normalized to the current level under irradiation I0

evolution of the ratio of the current levels after and immediately before the removal of the radiation source, for the samples under study. A very slow evolution towards a stationary level is hardly observed, in a log–log scale, even after two days of thermal fading at room temperature. It goes without saying that the shape of each relaxation curve is related to the structure of the defect levels. In the following, we propose a method of trap characterization of CVD diamond sensors based on the analysis of this time evolution of electrical current at constant temperature (PIC). The analysis of electrical currents induced by light photons after switching oﬀ the light source (persistent photocurrent, PPC), has been studied [15, 16] by means of a ﬁtting function called stretched exponential, previously introduced to describe eﬀects related to disordered phases in solid state physics. The stretched exponential, in the form γ t , (18) i = i0 exp − τ has been tentatively related to the presence of continuous distributions of defect levels. Chen and Leung [28] ﬁtted with a stretched exponential some numeric simulations of a luminescence signal obtained in the framework of a two-level model of the band gap, but did not obtain a correlation between relevant trap parameters, such as energy or concentration or capture cross section, and the parameters of the phenomenological function. In our case, the stretched exponential appears to be a quite good approximation both of experimental data and of the simulations over one or at most two decades in time variation, but we veriﬁed that it does not ﬁt PIC data

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321

over longer periods of time. On the other hand, expression (12), giving the rate of change of the charge stored in a continuous level distribution, permits to study the PIC in terms of a sum of “limited hyperbolic” functions of the type: 1 − e− τ , t t

i = i0 τ

(19)

whose parameters, i0 and τ , are directly related to the characteristics of a continuous distribution of trap levels: capture cross section, spread in energy of the trap and density of levels per unit energy. The expression of PIC as a sum of limited hyperbolic functions follows from (12). In fact, assuming the QE approximation, the rate of change of the overall trap population is equal to the recombination rate, i.e., if qi is the concentration of the empty traps of the distribution i and p the hole concentration in the VB, then: m dqi i=1

dt

= pvp σr Nr ,

(20)

where vp is the thermal velocity of holes, σr and Nr are the capture cross section and the concentration of the recombination center, respectively. By expressing (20) in terms of Nr instead of the population of the recombination centers (Nr − qr ), we implicitly assume that during thermal relaxation of band B the recombination centers are almost entirely occupied by electrons. This implies, from (4), that during the whole process also the number density of free traps is very small compared to the overall trap population. During the previous exposure to the ionizing radiation, as the stationary state was reached, the generation rate g had become equal to the recombination rate, and therefore proportional to the population p0 of the valence band in the steady state: g = p0 vp σr Nr .

(21)

Equations (20) and (21) can be used to ﬁnd a relationship between the PIC (I(t)) and the steady current I0 just before the removal of radiation source. Since the ratio I(t)/I0 is equal to the ratio p(t)/p0 of the hole concentrations, then: I=

m I0 dqi . g i=1 dt

(22)

Hence, from [12]: t t m di exp − τ2i − exp − τ1i I0 . I = kT g dE t i=1

(23)

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Fig. 12. Best ﬁt of the persistent current for sample CDS92 to a function composed of three limited hyperbolic components (19). The PIC slowly relaxes to the initial dark current level

If we assume that the upper limit of each trap distribution is too deep in the band gap to be aﬀected by thermal fading, setting: E2 1 → ∞, (24) τ2 = × exp s kT we ﬁnd:

t m di 1 − exp − τ1i I0 , I = kT g dE t i=1

(25)

In this way, we express the PIC as a sum of limited hyperbolic terms, from which we can determine di / dE and, once the capture cross section σi is known from the analysis of the RIC (Sect. 3), we can determine E1i too. As an example, in Fig. 12 we report the ﬁt of the current curve of sample CDS92, whose behaviour has been well described by means of three components, each one corresponding to the traps represented in Fig. 5. Figures 13 and 14 complete the information of Table 1 ad Fig. 5 reporting the relationhips between d/ dE, σ and E1 for each sample under study. In conclusion, the analysis of the results of Sect. 4 yields the following conclusions. Concerning the commercial (DEBID) samples: (a) All samples have a very similar structure of band B, with a cross section decreasing as the level position becomes deeper and deeper in the band gap, starting from minimum distance above the VB of about 0.77 eV. (b) The sample with the highest CCD (CDS92) has the lowest trap concentration.

Band lower energy E1 (eV)

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323

1.00 0.95 F56 (n-damaged)

F58

0.90 0.85

P16 (n-dam.)

0.80 0.75 -16 10

CDS92

10 -15

10 -14

P13

10 -13

10 -12

10 -11

cross section (cm 2) Fig. 13. Dependence of the lower energy limit of each trap distribution as a function of the capture cross section

(c) Neutron irradiation causes an increase of the trap densities, without appreciably aﬀecting the cross sections. Concerning the local samples: (d) Band B begins at about 0.82 eV from the VB, and has a very large spread in cross section, compared to that of DEBID samples. (e) After neutron damage the energies shift upward about 0.1 eV, together with an increase of the trap density.

5 Conclusions We have brieﬂy reviewed some relevant works on modeling the diamond band gap, aimed to correlate the defect levels with the electric transport properties of pCVD diamond devices. From the present literature a qualitative or semiquantitative description can be extracted which we have used as the starting point for a quantitative model of the trapping and recombination processes. We have introduced two defect bands: a trapping center, with different components, each with distinct trap parameters, and a recombination center, described by a single value of capture cross section and concentration. The number of components of the trapping centers increases with increasing numbers of defects in the sample. We have chosen as the ﬁgure of merit of material quality the charge collection distance, since the diamond devices we have tested are specially prepared for ionizing radiation detectors. Our calculated expression for radiation-induced current, thermal relaxation between

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Fig. 14. Dependence of the trap density per unit volume and unit energy of each trap distribution as a function of the capture cross section

irradiations, persistent current after removal of the generation source, ﬁts very well to our experimental data. This has allowed us to determine defect concentrations and capture cross sections for both the recombination and trapping centers. The capture cross section of the recombination center in the state-of-the-art diamonds is in good agreement with the one reported for natural IIa diamond, suggesting that the dramatic improvement in the performances of the diamond devices during the last eight years is more due to a decreasing in the concentration of defects than to a change in their structure. This has been conﬁrmed by the results obtained on medium to high-quality pCVD diamonds where an increase of a factor two of the CCD (from about 100 µm to more than 200 µm) corresponds to a decrease of the same factor of the recombination and trapping centers. Neutron irradiation (∼ 1015 /cm2 ) seems to have a very limited inﬂuence on traps in medium quality samples whilst has a dramatic inﬂuence on low quality samples. This is consistent with the limited decrease of the CCD (about 30%) measured for the medium-quality samples and the reported strong improvement of the dynamic response in low-quality samples [29]. We have also been able to calculate the position in energy of the lower edge of the diﬀerent components of the trap center. Our analysis is limited to a narrow interval in energy, nevertheless this is the range of energy of the traps which are active at room temperature. A further investigation is required of the shallower traps, i.e., the traps within 0.75 eV from the band edge, which cannot be ﬁlled at room temperature but can, however, limit the response of the material in transient conductivity experiments or single-particle events, like in the case of charge collection measurements. Finally, homoepitaxial CVD diamond can overcome these diﬃculties since there are no grain boundaries or structural defects originating at the mid-gap

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325

centers in ideally single-crystal diamond (sCVD). However, the reproducibility of defect-free sCVD material does not seem within reach in the short term [30], and its radiation hardness is at present a subject of investigation. Moreover, further improvements in the pCVD diamond devices are still to be expected [30]. Therefore, defect modelization in CVD diamond will be most likely useful in the future. Acknowledgements The authors are deeply indepted to Stefano Mersi (INFN, Florence) who helped to perform the experiments as a diploma student and Ph.D. student, to Prof. Emilio Borchi (University of Florence) for stimulating discussions, to Dr. Fred Hartjes (NIKHEF, Amsterdam) and Prof. Raﬀaello D’Alessandro (INFN, Florence) for their support with the experimental setup. We also wish to thank the RD42 CERN collaboration for lending us their samples. The neutron irradiation of sample F56 has been performed in the framework of the experiment CONRAD, of the Italian National Institute for Nuclear Physics (INFN).

References [1] [2] [3] [4] [5] [6] [7] [8]

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A. Lewandowski, S. S. McKeever: Phys. Rev. B 43, 8163 (1991) 303, 312, 316 R. Chen, A. Lewandowski, S. Durrani: Phys. Rev. B 24, 4931 (1981) 303 S. S. McKeever, R. Chen: Radiat. Meas. B 27, 625 (1998) 303, 310 P. Klein, M. Crossﬁeld, J. A. Freitas Jr., A. Collins: Phys. Rev. B 51, 9634 (1995) 304 J. Ruan, K. Kobashi, W. Choyke: Appl. Phys. Lett. 60, 3138 (1992) 304 L. Robins, L. Cook, E. Farabaugh, A. Feldman: Phys. Rev. B 39, 13367 (1989) 304 D. Takeuchi, H. Watanabe, S. Yamanaka, H. Okushi, H. Sawada, H. Ichinose, T. Sekiguchi, K. Kajimura: Phys. Rev. B 63, 245328 (2001) 304 T. Sharda, A. Sikder, D. Misra, A. Collins, S. Bhargava, H. Bist, P. Veluchamy, H. Minoura, D. Kabiraj, D. Awasthi, P. Selvam: Diamond Relat. Mater. 7, 250 (1998) 304 K. Iakoubovskii, G. Adriaenssens: Phys. Rev. B 61, 10174 (2000) 304 C. Manfredotti, F. Wang, P. Polesello, E. Vittone, F. Fizzotti, A. Scacco: Appl. Phys. Lett. 67, 3376 (1995) 304, 308 P. Gonon, A. Deneuville, E. Gheeraert: J. Appl. Phys. 78, 6633 (1995) 304, 311 P. Gonon, S. Prawer, D. Jamieson: Appl. Phys. Lett. 68, 1238 (1996) 304, 321 E. Vittone, C. Manfredotti, F. Fizzotti, A. L. Giudice, P. Polesello, V. Ralchenko: Diamond Relat. Mater. 8, 1234 (1999) 305, 311 E. K. Souw, R. Meilunas, C. Szeles, N. Ravindra, F. M. Tong: Diamond Relat. Mater. 6, 1157 (1997) 305

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[15] C. Nebel, A. Waltenspiel, M. Stutzmann, M. Paul, L. Sch¨ afer: Diamond Relat. Mater. 9, 404 (2000) 305, 320 [16] C. Nebel: Semicond. Sci. Technol. 18, S1 (2003) 305, 320 [17] L. Pan, D. Kania, P. Pianetta, O. Landen: Appl. Phys. Lett. 57, 623 (1990) 305, 310 [18] L. Pan, D. Kania, P. Pianetta, J. W. Ager III, M. Landstrass, S. Han: J. Appl. Phys. Lett. 73, 2888 (2001) 305, 310 [19] D. Kania: Diamond radiation detectors, in A. Paoletti, A. Tucciarone (Eds.): The Physics of Diamond (IOS, Amsterdam 1997) pp. 555–564 306 [20] H. Kagan: Nucl. Instr. and Meth. A 541, 221 (2005) 306 [21] M. Bruzzi, F. Hartjes, S. Lagomarsino, D. Menichelli, S. Mersi, S. Miglio, M. Scaringella, S. Sciortino: Phys. Stat. Sol. A 199, 138 (2003) 306, 308 [22] The RD42 collaboration, IEEE Trns. Nucl. Sci. 49, 1857 (2002) 306 [23] A. Rose: RCA Rev. 12, 362 (1951) 308 [24] E. Borchi, S. Lagomarsino, S. Mersi, S. Sciortino: Phys. Rev. B 71, 104103 (2005) 308 [25] S. Lagomarsino, S. Sciortino, E. Borchi: Model of persistent radiation induced current in CVD diamond detectors, Phys. Rev. B submitted 308 [26] The RD42 collaboration, Nucl. Instr. and Meth. A 514, 79 (2003) 308, 309 [27] S. Sciortino, S. Lagomarsino, F. Pieralli, E. Borchi, E. Galvanetto: Diamond Relat. Mater. 11, 573 (2002) 314 [28] R. Chen, P. Leung: Radiat. Meas. 37, 519 (2003) 320 [29] M. Bruzzi, D. Menichelli, S. Pini, M. Bucciolini, J. M´ olnar, A. Fenyvesi: Appl. Phys. Lett. 81, 298 (2002) 324 [30] H. Kagan for the RD42 collaboration: Diamond (Radiation) Detectors Are Forever, IWORID 2004, Glasgow, UK (2004) 325

Index acceptor acceptor states, 304 donor acceptor pair recombination, 304 cathodoluminescence (CL), 304 charge collection distance (CCD), 306–309, 315 current persistent, 304, 308, 317, 319–324 radiation induced, 304, 306, 308, 311, 313 sensitivity, 311 defects in diamond band A, 304 band A, 308, 310, 311, 315, 316

band B, 308–311, 313, 321–323 neutron irradiation, 313, 315, 324 donor deep acceptor centers, 308 deep donor level, 305, 308 donor acceptor pair recombination, 304 electroluminescence, 304 fading optical fading, 305 thermal fading, 310, 317, 319 ﬁrst order kinetics, 310, 316, 319 frequency, 316 limited hyperbolic function, 321 linear model, 308, 310

Modeling of the Transport Properties of Diamond Radiation Sensors photoconductivity, 304, 305, 308 quasi equilibrium (QE) approximation, 321 quasi-equilibrium (QE) approximation, 312 rate equations, 303, 309, 312, 313

trap density per unit energy, 310, 315 depumping, 307, 310 pumping, 306, 307, 311 trap ﬁlling, 307, 311 unipolar conduction, 308–310

327

Nucleation Process of CVD Diamond on Molybdenum Substrates Giuliana Faggio1, Maria G. Donato1 , Stefano Lagomarsino2, Giacomo Messina1 , Saveria Santangelo1, and Silvio Sciortino2 1

2

INFM, Dipartimento di Meccanica e Materiali, Universit` a “Mediterranea” di Reggio Calabria, Localit` a Feo di Vito, I-89060 Reggio Calabria, Italy INFN, Dipartimento di Energetica, Universit` a di Firenze, Via S. Marta 3, I-50139 Firenze, Italy [email protected]

Abstract. Nucleation is a critical step of diamond growth by chemical vapour deposition (CVD), and its control is essential for optimising the properties of the synthesised material. In this work, diamond samples have been grown by pulsed dc glow discharge CVD onto molybdenum (Mo) substrates at diﬀerent temperatures using a CH4 –H2 gas mixture at diﬀerent methane concentrations. A thorough Raman and photoluminescence (PL) analysis has been carried out on a set of samples, whose deposition process has been stopped before the grain coalescence in order to monitor the quality of the material during the growth. Moreover, an optical characterisation of continuous free-standing ﬁlms has been performed, aimed at assessing the inﬂuence of growth and nucleation parameters on the global quality of the ﬁlms. A complementary statistical study of the nucleation process has evidenced a strong dependence of the nucleation density on CH4 concentration. A correlation between optical characterisation results and statistical analysis has been pointed out.

1 Introduction The success in growing synthetic diamond ﬁlms using chemical vapour deposition has stimulated enormous interest in diamond, not only as subject of basic research, but also as material for advanced technological applications. Nowadays, the CVD technique enables the deposition of single-crystal ﬁlms on diamond substrates (homoepitaxial growth [1]), and the growth of polycrystalline sample, of quality comparable with the best natural diamonds [2, 3] on more commonly available nondiamond substrates (heteroepitaxial growth). However, the optimisation of the nucleation process and of the early growth stages is still a developing subject [4]. It is well known that the nucleation process aﬀects the quality of the deposited ﬁlms in terms of roughness, structural defect density and nondiamond phase inclusion. Thus, it is essential to deeply understand the nucleation mechanism and its consequences on the ﬁlm quality [5, 6]. Polycrystalline diamond ﬁlms have been deposited on various nondiamond substrates, including insulators, semiconductors and metals [4]. Diamond nucleation on nondiamond substrates occurs mostly on an intermediate layer G. Messina, S. Santangelo (Eds.): Carbon, The Future Material for Advanced Technology Applications, Topics Appl. Phys. 100, 329–343 (2006) © Springer-Verlag Berlin Heidelberg 2006

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of diamond-like amorphous carbon, metal carbide or graphite formed at the substrate interface. Such intermediate layers provide nucleation sites for diamond growth enhancing diamond nucleation density and oﬀer an opportunity for controlling morphology, orientation and texture of diamond ﬁlms [4, 7]. Most of heteroepitaxial diamond ﬁlms are grown on single-crystal silicon (Si) wafers. The chief reason for the wide diﬀusion of the heteroepitaxial growth of diamond on silicon is that, among carbide-forming substrates, Si wafers are easily available and extensively used in electronics industry. However, one of the major problems associated with the growth of CVD diamond on Si or metal substrates is the low nucleation density in the absence of substrate pretreatments [8]. Thus, a scratching procedure of Si substrates with diamond powder is generally carried out for enhancing the nucleation density [9, 10]. Diamond growth on metal substrates is also of interest and exhibits appealing features [4, 11]. Unlike Si wafers, molybdenum substrates oﬀer the possibility to attain diamond nucleation without any surface pretreatment [12, 13], or to use CVD reactors operating at very high power, which results in considerably higher growth rates. Diamond nucleation on Mo substrates occurs mostly on an intermediate layer of metal carbide (Mo2 C) [4]. The nucleation density obtained is about one order of magnitude higher than on all other carbide-forming substrates under the same deposition conditions [4, 14]. In this work, the nucleation process of diamond samples grown onto molybdenum substrates by pulsed glow-discharge CVD will be studied by Raman scattering and photoluminescence spectroscopy at low temperature. The dependence of the sample quality on the most important deposition parameters will be discussed. The comparative analysis of the indications emerging from the optical characterisation of the ﬁlms and from a statistical study of grain size distribution will be carried out.

2 Experimental Polycrystalline CVD diamond ﬁlms (samples A, B, C) have been deposited onto Mo substrates by a pulsed direct current (dc) glow discharge CVD, thoroughly described in a previous work [12], using a CH4 –H2 gas mixture. No substrate pretreatment has been carried out apart from polishing with 1000 SiC paper before deposition. Aiming at clarifying the eﬀect of the methane concentration on the sample quality, the content of CH4 in H2 has been varied from 2% up to 3%. In order to investigate the nucleation process, the growth process of the three samples has been stopped before grain coalescence. Total gas pressure p, substrate temperature T s , deposition time of sample A, B and C are shown in Table 1. The surface morphology of the samples has been investigated by scanning electron microscopy (SEM). Raman measurements have been carried

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Table 1. Deposition conditions and Raman parameters for samples A, B and C Samples Deposition parameters [CH4 ] p Ts % mBar ◦ C A B C

3 3 2

315 320 320

Raman parameters

Dep. time XP h cm−1

1030 0.4 1000 1 1040 7

Γ cm− 1

1335.1 10.8 1334.5 8.3 1332.8 4.2

out using the 514.5 nm line of an Ar+ ion laser. The scattered light has been dispersed by an Instrument S.A. Ramanor U1000 double monochromator equipped with a microscope (Olympux BX40) for micro-Raman sampling. In such a conﬁguration, the laser spot is focused, by a X100 objective, to a diameter of about 1 µm. In addition, using the microscope confocal optics, a nominal focus depth of 2 µm is obtained. Photoluminescence measurements have been carried out with the same experimental setup at room and liquid nitrogen temperature, using a Linkam freezing stage. Because of the stage size, a long focal distance X50 objective has been used.

3 Results and Discussion 3.1 Raman and Photoluminescence Analysis Optical techniques, such as Raman spectroscopy and photoluminescence (PL) are commonly used for a careful and nondestructive analysis of the quality of diamond samples. Raman spectroscopy represents the most useful diagnostic technique for characterising diamond, because it allows a ready and accurate identiﬁcation of the diﬀerent carbon allotropes present in the analysed sample. Therefore, Raman scattering studies are widely used to evaluate phase purity and crystalline quality of synthetic diamond samples. Position XP and full width at half maximum Γ of the diamond Raman peak give an estimation of the crystalline quality of the synthesised material. An inhomogeneous distribution of stress, in fact, shift and broaden the diamond peak with respect to natural diamond values (XP = 1332 cm−1 , Γ = 2 cm−1 ) [15, 16]. Moreover, amorphous carbon (a-C) phases, commonly found in polycrystalline CVD ﬁlms, can be easily identiﬁed due to their characteristic band at about 1500 cm−1 . PL spectroscopy is very useful in the study of impurities incorporated in synthetic diamond during the growth process. Many impurities, in fact, form optical centres having characteristic vibronic structures in PL spectra. The detection of a zero-phonon line (ZPL) and vibronic sidebands in PL spectra allows an unambiguous identiﬁcation of the optical centre.

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Fig. 1. Micro-Raman diamond lines measured at diamond crystallites of the samples A, B and C. The peak position XP and the full width at half maximum Γ of each line have been indicated

3.1.1 Discontinuous Samples In order to clarify the role played by the deposition parameters in determining the quality of the samples grown on molybdenum, a careful micro-Raman analysis of the diamond crystallites of the samples A, B and C has been carried out. The average values XP of the position and of the linewidth Γ of the diamond peaks are reported in Table 1. Some micro-Raman peaks of the three samples are shown in Fig. 1. As a general trend, an upshift of the position of the diamond Raman lines is observed with respect to natural diamond (1332 cm−1 ), indicating the existence of compressive stress, due to a thermal expansion coeﬃcient mismatch between ﬁlm and substrate [17, 18]. Diamond crystallites of better crystalline quality are obtained at longer deposition times, as witnessed by narrower and less shifted Raman lines. In addition, sample C, grown at lower CH4 concentration, shows lower shift than samples A and B, indicating a lower stress level and, consequently, an improved crystalline quality. Owing to the restricted temperature range investigated, a clear correlation between substrate temperature and ﬁlm quality cannot be assessed. Additional information comes out from the analysis of the micro-Raman spectra (Fig. 2) measured on a wider range (800–1800 cm−1 ). The character-

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Fig. 2. Micro-Raman spectra of samples A and B grown at 3% CH4 concentration

istic diamond Raman line and two broad bands at about 1350 and 1550 cm−1 , associated to sp2 -bonded carbon phases [19, 20, 21], are visible in sample A, whereas in sample B only the diamond line is observed together with a weakly increasing photoluminescence background. Samples A and B, grown at 3% CH4 concentration and at diﬀerent deposition times, show diamond crystallites of diﬀerent quality. The SEM analysis of the growth surface of samples A, B and C showed diamond crystallites of diﬀerent average size (Fig. 3). The deposition process of sample B, in fact, has been stopped after 1 h and its diamond crystallites have grown longer than those of sample A. The total area of grain boundaries, compared to the volume of diamond crystallites, is correspondingly lower. As defects and nondiamond carbon phases are chieﬂy accumulated at grain boundaries [3, 22, 23, 24], in sample B the signal originating from grain boundary regions becomes more hardly detectable. In the light of the above consideration, the absence of nondiamond carbon band in the Raman spectrum of sample B can be attributed to the growth of diamond crystallites of larger average size and so of higher phase purity. Aiming at studying the nature and distribution of impurity-induced optical centres, PL measurements have been carried out. The comparison of the PL spectra registered at room temperature on sample B, grown at 3% CH4 concentration for 1 h, and on sample C, grown at 2% CH4 concentration for 7 h, is shown in Fig. 4a. The diamond Raman peak is clearly visible in both spectra, however, sample B exhibits a stronger photoluminescence. In order to understand the origin of this large band, PL measurements at low temperature (80 K) on sample B have been carried out (Fig. 4b). Thanks to both low temperature

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Fig. 3. SEM micrograph of the samples A (top, left), B (top, right) and C (bottom)

and greater focus depth due to the use of a long focal distance X50 objective, a richer scenario is obtained. The spectrum shows, besides the diamond Raman peak, the a-C Raman band originating from more defective layers at the substrate interface, and some PL features associated with nitrogen impurities [10, 21, 25, 26]. The peak at 2.156 eV corresponds to the ZPL of the nitrogen-vacancy [N-V]0 centre in the neutral state. In addition, the spectral features at 1.945 eV and at 1.882 eV can be attributed to the ZPL and the vibronic sideband of the [N-V]− centre. Such PL bands are commonly seen in PL spectra of nitrogen-doped CVD diamond ﬁlms [27, 28, 29]. As in [30, 31], sample B has been grown with gases nominally without nitrogen. However, the observation of nitrogen-related centres in the PL spectra witnesses the presence of residual nitrogen in the growth chamber, probably due to impurities in the gas mixture or to not perfect vacuum conditions of the chamber before the deposition. 3.1.2 Continuous Samples So far, the optical characterisation has been performed on noncontinuous samples. In order to study the global quality of CVD diamond ﬁlms grown

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Fig. 4. PL spectra of samples B and C at (a) room temperature and (b) 80 K. The energy positions of the diamond and a-C-related Raman peaks together with the PL bands have been indicated

in the same experimental conditions of the discontinuous samples previously analysed, the deposition process of two samples was continued until they coalesced into continuous ﬁlms. The two CVD diamond ﬁlms were deposited at Ts = 1000◦C and [CH4 ] = 3%, and at Ts = 970◦ C and [CH4 ] = 2%, respectively. The resulting polycrystalline ﬁlms have been made freestanding, with ﬁnal thicknesses of approximately 50 µm and 40 µm, respectively. Figure 5 shows the micro-PL spectra taken at the growth surface of the two freestanding ﬁlms. For a better comparison, the diamond peak is magniﬁed in the inset. The change in CH4 concentration from 3% to 2% results in a narrowing of the diamond line from 3.5 to 2.6 cm−1 . The PL background of the sample grown at 2% CH4 concentration is very low, without evident nitrogen-related PL bands, witnessing an excellent quality of the surface grains. At higher methane content, the PL background is higher, but still unstructured. Bergman et al. [21, 22] pointed out a correlation between broadband PL and phase purity. On the basis of this correlation, the broadband PL emission has been attributed to a continuous distribution of in-gap states introduced by sp2 carbon phases in the ﬁlm. These results indicate

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Fig. 5. Micro-PL spectra measured at the growth surface of two continuous samples, grown at [CH4 ] = 2% and [CH4 ] = 3%

that, in the range of substrate temperatures investigated, better crystalline quality and higher phase purity are obtained at lower methane concentration. Figure 6 shows the comparison between the micro-Raman spectra registered on the growth surface and the nucleation side of the freestanding ﬁlm grown at 2% methane concentration of Fig. 5. As can be seen, both the surfaces show a complete absence of nondiamond carbon phases. Only a broadening of the diamond line from 2.6 to 3.2 cm−1 is observed when the laser spot is focused from the surface to the nucleation side. This indicates that the polycrystalline ﬁlm grown at 2% CH4 concentration exhibits diamond grains of high phase purity even on the nucleation surface. 3.2 Statistical Study of the Nucleation Process A statistical study of the nucleation process of pulsed glow-discharge CVD diamond ﬁlms onto molybdenum substrates has been carried out. This study is based on an analysis of the statistical distribution of the grain sizes performed by scanning electron microscopy of the growth surface of the three samples A, B and C, previously characterised by means of Raman spectroscopy and photoluminescence. A model of a two-step nucleation process has been deduced, and a correlation between the nucleation density and the most important thermodynamic parameters, such as substrate temperature and CH4 concentration, has been assessed. Figure 7 shows the frequency distribution of the grain linear size of the sample C, whose SEM micrograph is shown in Fig. 3. The grain linear size

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Fig. 6. Comparison between the micro-Raman spectra, measured at the growth surface and the nucleation side, of a continuous sample grown at [CH4 ] = 2% concentration and Ts = 970◦ C

Fig. 7. Grain size frequency distribution of sample C. The points represent the experimental data. The ﬁt function (continuous line) is the sum of two components, related to a “fast” (dashed line) and “slow” (dotted line) nucleation process, as described by (1)

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Fig. 8. Grain size frequency distribution of samples A, B and C. The points represent the experimental data; the continuous line corresponds to the ﬁt function (1)

has been deﬁned as the greatest distance (expressed in µm) between couples of points on a same grain. The frequency distribution is quite asymmetric, composed of a sharp maximum, with a Gaussian-like tail on the right, and a broader distribution on the other side. As shown in Fig. 8, all samples exhibit a similar grain linear size frequency distribution, notwithstanding the diﬀerent deposition conditions (Table 1). If we adopt the grain size as an obvious indicator of the time elapsed after the nucleation of each grain, and consider the grain distribution smoothed by the spread in the grain growth rate, then we can explain our experimental data assuming a two-step nucleation process. – First step: “fast” nucleation. At ﬁrst, a sudden and simultaneous nucleation of a great many grains occurs, represented by the sharp maximum in the frequency distribution. – Second step: “slow” and constant nucleation. Then, other nuclei form, with constant probability per unit time, resulting in a roughly square distribution, smoothed by the diﬀerences in grain growth rate. Under this assumption, the nucleation rate, i.e., the number of nuclei that appears per unit time and unit surface, can be expressed by: f (t) = kδ(t) + νχ[0,T ] (t), where k is the surface nucleation density of the “fast” phase, δ(t) is the Dirac distribution, ν is the nucleation rate (nucleation density per unit time) of the “slow” phase and T is the deposition time, χ[0,T ](t) being the characteristic

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function of the time interval [0,T ]. If, with a reasonable approximation, we assume a Gaussian distribution g(v) for the growth rate of the grains: 1 (v − v0 )2 √ g(v) = exp − , 2σv2 σv 2π where v0 denotes the mean value and σv stands for the standard deviation of the distribution, then the experimental data shown in Fig. 7 are well ﬁtted by the function: F (x) = 0

T

1 dt f (t ) · dx

x t

+ dx t

dv g(v ),

(1)

x t

where x = vt is the statistic variable, i.e., the grain linear size. In Table 2 the parameters derived by the ﬁtting procedure are reported. Table 2. Fitting parameters entering (1) Sample Ts (◦ C) [CH4 ] (%) A B C

1030 1000 1040

3 3 2

v0 (µm/h) σv /v0 k (mm−2 ) ν (mm−2 h−1 ) 14 13 2.6

0.28 0.32 0.30

1 800 750 77

1 900 450 6.5

The evidence of a two-component grain size distribution in the three samples under consideration indicates that, in our working conditions, a quite complex nucleation pattern occurs onto Mo substrates. Although the small number of samples does not allow us to be conclusive about the dependence of the nucleation density on temperature and methane concentration, some hypotheses can be formulated. – The dependence of the nucleation density on temperature does not seem to be very critical, at least in the temperature range under consideration, as it is observed by comparison of samples A and B, grown at the same CH4 concentrations and diﬀerent temperatures. – On the other hand, by comparison of samples A and C, grown at approximately the same substrate temperature, a diﬀerence from 2% to 3% in the methane concentration produces a two-order of magnitude diﬀerence in the “slow” nucleation probability and a one-order diﬀerence in the “fast” one. The diﬀerent dependence of the two distributions on the methane concentration indicates two diﬀerent mechanisms of nucleation. The ﬁt parameter σv /v0 is quite the same in the three samples, in spite of the diﬀerences in the deposition time. This result suggests that at time t = 0, when the grain size is zero, the grain size distribution has only the Dirac delta component, i.e., the

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ﬁrst component is almost instantaneous at the beginning of the deposition process. Therefore, in the ﬁrst step of the nucleation process, nucleation sites form, whose number strongly depends on methane concentration. The slow component of the nucleation, being a process ruled by a constant probability per unit time, can be explained by the nucleation model proposed by Angus [32]. The model establishes the dependence of the nucleation rate on the concentration of active species, [CHx ], forming hydrogenated graphitic fragments, which can act as nucleation centres for diamond [33]. Given n the minimum number of carbon atoms in the fragment that acts as a nucleation center, Angus ﬁnds an expression for the nucleation rate in terms of the concentration ratio [CHx ]/[H]. This expression, in the limit of very high hydrogen concentration (which is assumed to be satisﬁed for the high temperature-high activation state of a dc pulsed-glow discharge plasma [12]) can be written: n [CHx ] , (2) rn = K · v0 · [H] where v0 is the growth rate and K depends on temperature. Moreover, if we suppose the concentration of active species [CHx ] proportional to the methane percentage, the data reported in Table 2, relative to the samples A and C, grown at approximately the same temperature, allow us to establish that the minimum number of carbon atoms in the hydrogenated graphitic fragment is approximately n ≈ 10. Interestingly enough, 10 is just the number of carbon atoms of the lightest hydrocarbon possessing the diamond unit structure, hadamantene (C10 H16 ), which is believed to be a possible precursor of diamond, produced by a homogeneous gas-phase nucleation [4].

4 Conclusions In this work, a comparative study on pulsed glow-discharge CVD diamond grown onto molybdenum substrates, using a CH4 –H2 gas mixture at diﬀerent methane concentrations has been presented. The eﬀect of the change in the deposition parameters on the nucleation and growth process has been studied by Raman spectroscopy and photoluminescence. A correlation between the results of the optical characterisation and of the statistical study of the nucleation process can be evidenced. The micro-Raman analysis carried out shows unshifted and narrow diamond lines at the growth surface of samples grown at low CH4 concentration, indicating low stress level and high crystalline quality of individual grains. Furthermore, a high phase purity of the diamond crystallites has been evidenced by the complete absence of any feature related to nondiamond carbon and by a very weak luminescence background. Micro-Raman measurements carried out on the nucleation side of free-standing ﬁlms have only evidenced

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the presence of residual stress in diamond grains. The absence of nondiamond carbon phases witnesses that the ﬁlms grown at lower CH4 concentration exhibit high phase purity even at the nucleation side. Thanks to the statistical analysis, it has been assessed that the growth parameters have a more evident dependence on the CH4 content than on the substrate temperature, at least in the temperature range investigated. Lower nucleation density has been found in the samples grown at lower CH4 concentration. On the basis of these preliminary results, it is possible to conclude that the use of a lower CH4 content in the gas mixture, inducing lower nucleation density on molybdenum, results in the synthesis of CVD diamond samples of higher crystalline quality and phase purity. The same correlation between CH4 concentration and ﬁlm quality has been found in free-standing samples. These experimental evidences may be explained as follows. Once the nucleation process onto Mo substrate has started, diamond crystallites grow larger until they coalesce into a continuous ﬁlm. Then the growth proceeds only upwards, following a columnar structure. With increasing ﬁlm thickness the size of diamond crystallites increases, and the grain boundary density correspondingly decreases, improving the ﬁlm quality. If the number of diamond crystallites per unit surface is low (low nucleation density), the grain coalescence will occur at greater crystallite size. In this way, the layer close to the interface between the diamond ﬁlm and the Mo substrate will be poorer of grain boundaries, where defects and nondiamond carbon phases are preferentially accumulated. As a consequence, the resulting ﬁlm will exhibit a good quality even on the nucleation side. However, it should be highlighted that the correlation between lower nucleation density and higher crystalline quality found in diamond ﬁlms deposited on molybdenum is strictly dependent on the substrate used. In fact, recent studies carried out on diamond samples grown on Si substrates [34] have evidenced that a lower nucleation density could have the drawback of a greater incorporation of Si atoms in the growing ﬁlm, which could strongly degrade the ﬁnal quality of the sample. Further studies are necessary to cover a large range of deposition parameters and to clarify the correlation between molybdenum substrate temperature and ﬁlm quality. Acknowledgements We wish to thank the Scientiﬁc Director of the Centro Microscopie Elettroniche, CEME-CNR, Florence, Prof. Laura Morassi Bonzi, for the availability of the SEM facilities and helpful discussions.

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[31] L. T. S. Lin, G. Popovici, Y. Mori, et al.: Diam. Relat. Mater. 5, 1236 (1996) 334 [32] J. C. Angus: in A. Paoletti, A. Tucciarone (Eds.): The Physics of Diamond, International School of Physics “Enrico Fermi”, Course CXXXV, Varenna, Italy, 1996, vol. 135 (IOS, Amsterdam 1997) 340 [33] W. R. L. Lambrecht, C. H. Lee, B. Segall, et al.: Nature 364, 607 (1993) 340 [34] M. G. Donato, G. Faggio, G. Messina, S. Santangelo, M. Marinelli, E. Milani, G. Pucella, G. V. Rinati: Diam. Relat. Mater. 13, 923 (2004) 341

Index chemical vapour deposition (CVD), 329 defects grain boundaries, 333, 341 in diamond, 329, 333, 334, 341 diamond, 329 diamond nucleation, 329, 336, 338, 339 heteroepitaxial growth, 329 homoepitaxial growth, 329

nucleation probability, 339 nucleation rate, 338 slow phase, 338 statistical study, 336–339 surface nucleation density, 338 photoluminescence (PL), 329, 331, 333–335 micro-PL analysis, 333–336

Mo substrates, 329–341

Raman spectroscopy, 329–333, 335–337 micro-Raman analysis, 331–333, 337

nucleation, 329–341 fast phase, 338, 339

scanning electron microscopy (SEM), 330, 333, 334, 336

Optical Characterisation of High-Quality Homoepitaxial Diamond Maria G. Donato1 , Giuliana Faggio1 , Giacomo Messina1 , Saveria Santangelo1 , and G. Verona Rinati2 1

2

Dipartimento di Meccanica e Materiali, Universit` a “Mediterranea” di Reggio Calabria, Localit` a Feo di Vito, I-89060 Reggio Calabria, Italy Dipartimento di Ingegneria meccanica, Universit` a di Roma “Tor Vergata”, Italy

Abstract. Recently, great eﬀort has been devoted to the deposition of homoepitaxial diamond for electronic applications. Its single-crystal nature avoids the problems due to grain boundaries in polycrystalline diamond ﬁlms, although the quality of such materials may still be very high. However, the optimisation of the deposition process of single-crystal diamond has not yet been achieved. In fact, the surface morphology of homoepitaxial diamond seems to be very sensitive to the quality of the diamond substrate and to even slight variations in the deposition parameters (composition of the gas mixture, microwave power, substrate temperature). Moreover, the growth of ﬂat samples needs very low growth rates, which are not practical for technological exploitation of the material. Thus, a deposition process at relatively high growth rates needs to be developed. In this view, characterisation studies of the material deposited play a key role, because they may give precious hints for the optimisation of a fast growth process of electronic-grade homoepitaxial diamond. In this work, we report on the characterisation of single-crystal diamond grown on diamond substrates of diﬀerent origin. The samples have been deposited by means of microwave plasma-enhanced chemical vapour deposition (MWPECVD) with a CH4 –H2 gas mixture at diﬀerent methane concentrations and at approximately 560◦ C substrate temperature. The growth rates range between approximately 1 µm/h and 4.5 µm/h. Optical and scanning electron microscopy have been used to study the surface morphology of the samples. A Raman investigation has been carried out to study the crystalline quality and the spatial homogeneity of the material, by means of accurate measurements of position and width of the diamond Raman peak at diﬀerent points in the samples. Photoluminescence (PL) has been used to investigate both the phase purity and the distribution of possible impurities in the deposited material. The results indicate that homoepitaxial CVD diamond samples having very high crystalline quality (full width of the diamond Raman peak ∼ 1.75 cm−1 ) and no impurity-related defect centers can be obtained in the adopted deposition conditions.

1 Introduction Diamond has been looked for, down the centuries, owing to its undisputed beauty and rarity. However, in recent years, the research about diamond has assumed a more scientiﬁc aspect. In fact, its optical and electrical properties, among which transparency to visible light, high breakdown ﬁeld, high radiaG. Messina, S. Santangelo (Eds.): Carbon, The Future Material for Advanced Technology Applications, Topics Appl. Phys. 100, 345–358 (2006) © Springer-Verlag Berlin Heidelberg 2006

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tion hardness and chemical inertness, would allow, in principle, the realisation of highly performing electro-optical devices, such as solar-blind UV detectors or high-energy particle detectors, which might substitute the Si-based devices in harsh environments. However, natural diamond, mainly because of lack in standardisation, cost and inclusion of impurities, is not a feasible proposal as an engineering material. For these reasons, a great eﬀort has been and is still being done to establish a highly reproducible deposition process allowing the large-scale synthesis of diamond crystals. At the beginning of the research about a suitable synthesis process, diamond crystals were obtained from graphite subjected to high-pressure hightemperature conditions (HPHT process). However, the cost of the deposition set up and, above all, the reduced size of the specimens obtained led the research towards a more convenient deposition process. In the same period, diamond synthesis was also obtained by a low pressure technique, involving decomposition of a gas mixture containing a hydrocarbon and hydrogen. Typically, in microwave chemical vapour deposition (MWCVD) a microwave discharge transforms a methane-containing gas mixture into plasma. Diamond deposition is enhanced by the presence of hydrogen, which has an eﬀective role in the etching of nondiamond carbon phases. When diamond is deposited by CVD onto nondiamond substrates (heteroepitaxy), polycrystalline ﬁlms are obtained. The most commonly used substrate is silicon, thanks to its widespread availability. Continuous progress in the deposition techniques produced diamond samples having most of the exceptional properties of natural diamond [1, 2]. However, the polycrystalline nature of such material may put some serious limitations on its technological exploitation. Grain boundaries, in fact, act [3] as preferential sites for the incorporation of defects and impurities, which, in turn, may cause a dramatic worsening in the electronic properties of the material. Anyway, polycrystalline diamond ﬁlms show values of the mobility-lifetime product of the carriers comparable to those found in GaAs and SiC [4] and, until a highly reproducible and standardised growth process of homoepitaxial diamond is achieved, polycrystalline diamond seems to be a good candidate for diamondbased electronics. If diamond substrates are used for the deposition (homoepitaxy), singlecrystal specimens are obtained. For this purpose, 100-oriented commercial HPHT diamond is commonly used. Recently [5] very high values for the electron and hole mobility measured on a CVD homoepitaxial diamond sample have opened the way to the realisation of diamond-based highly performing electronic devices. However, a deposition process which could guarantee very high electronic properties has not still achieved, as pointed out in [4]. Moreover, very often homoepitaxial samples exhibit structural defects as pyramidal hillocks or unepitaxial crystallites, which, incorporating defects and impurities, cause the deterioration of the electronic quality of the material [6].

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The problem of depositing homoepitaxial diamond having a ﬂat surface by CVD has been faced by diﬀerent authors [7,8,9,10,11,12,13]. Watanabe et al. [7, 8, 14] have shown that homoepitaxial samples having an atomically ﬂat surface can be deposited at very low (0.05 %) methane concentration. However, such a deposition process has the drawback of being extremely slow. In fact, growth rates of some tens of nanometers per hour have been obtained. Thus, the deposition of samples having suitable thickness for advanced electronic applications would require unacceptably long growth times. A moderate improvement in the growth rate (approximately 0.5 µm/h) has been obtained by Stammler et al. [9] with hot ﬁlament CVD. The authors succeeded in depositing samples exhibiting very low density of unepitaxial crystallites; however, both nitrogen and silicon atoms are incorporated in the growing material. To further enhance the growth rate, Teraji et al. [10, 11] proposed the use of quite high microwave power. They showed that at 3.8–4.2 kW microwave power, ﬂat samples can be obtained at a ratio of the methane ﬂow to the total deposition gas ﬂow [CH4 ] = CH4 /(CH4 + H2 ) = 4%. In these conditions, a relatively high growth rate (approximately 2.5 µm/h) has been achieved. Higher growth rates (up to 25 µm/h) can be obtained at even higher methane concentrations. However, the samples deposited show the inclusion of nitrogen atoms, probably coming from the hydrogen used for the deposition [10]. To suppress the formation of unepitaxial crystallites, Bauer et al. [12] grew homoepitaxial samples onto slightly oﬀ-axis substrates. Such a procedure is based on the observation that unepitaxial crystallites form at the top of the pyramidal hillocks commonly found in homoepitaxial samples, but not on their lateral faces. In order to enhance the quality of homoepitaxial CVD diamond, Tallaire et al. [13] used a two-step deposition process: before the diamond deposition, the substrates were subjected to an etching process in a hydrogen– oxygen plasma. After this pretreatment, the eﬀective diamond deposition at 3.2 kW microwave power has been carried out. In these conditions, the best quality sample has been grown at 4% CH4 with a growth rate of approximately 6 µm/h. In this work, we report on the characterisation of homoepitaxial diamond grown by the research group of the University of Rome Tor Vergata [15]. As our group has already obtained the optimisation of the deposition process of polycrystalline CVD diamond [1], approximately the same experimental conditions were used as a starting point for the deposition of single-crystal CVD diamond specimens. After the growth, the morphology of the deposited samples was studied by optical microscopy (OM) and SEM. The crystalline quality of the samples was studied by means of Raman spectroscopy. Photoluminescence(PL)at diﬀerent excitation wavelengths was used to evidence the possible presence of defects and/or impurities in the deposited material.

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The results show that homoepitaxial diamond having extremely high quality can be obtained with the deposition conditions used.

2 Experimental Homoepitaxial diamond samples have been grown onto nonselected diamond substrates by microwave plasma-enhanced CVD (MWPECVD) at the University of Rome Tor Vergata. Three samples have been deposited at 1% CH4 /H2 at a substrate temperature of approximately 560◦ C . As a test for the eﬀect of a higher concentration of methane in the deposition gas mixture, a CVD ﬁlm was deposited at 4% CH4 /H2 . For all the samples, the microwave power was 720 W. The characteristics of the samples are summarised in Table 1. The Raman scattering measurements were carried out at room temperature with an Instrument S.A. Ramanor U1000 double monochromator, equipped with a microscope Olympus BX40 for micro-Raman sampling. The 514.5 nm line of an Ar+ ion laser (Coherent Innova 70) was used to excite Raman scattering. Using a X100 objective, the laser beam was focused to a diameter of about 1 µm. A depth resolution of about 4 µm was obtained with a confocal aperture of 200 µm. Micro-photoluminescence (µ-PL) measurements were carried out at room temperature by using the same experimental setup used for micro-Raman spectroscopy. The 514.5 nm line (2.41 eV) and the 457.9 nm (2.71 eV) of the argon-ion laser were used to excite luminescence; the spectra were taken in the region 1.54–2.7 eV. Table 1. Deposition parameters of the samples analysed in this work. ND and HCVD stand for natural diamond and homoepitaxial CVD diamond, respectively Sample

Substrate [CH4 ] Ts % K

Pressure Thickness Growth rate mbar µm µm/h

SCD4 SCD5 SCD7 SCD15

ND IIb HCVD ND

149 147 147 149

1 1 1 4

560 560 550 560

171 90 52 89

1.1 1 1.1 4.6

3 Results 3.1 Optical and SEM Characterisation In their studies about the deposition of atomically ﬂat homoepitaxial diamond, Takeuchi et al. [14] proposed a map of the surface morphologies which

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Fig. 1. Optical micrographs (×10 objective) of the samples studied in this work

may be obtained at diﬀerent CH4 /H2 concentrations in the deposition gas mixture and at diﬀerent misorientation angles of the (001) diamond substrates. They found that homoepitaxial diamond can develop three diﬀerent types of surface morphology, at CH4 /H2 concentrations ranging between 0% and 2%, and misorientation angle ranging between 0◦ and 5◦ . In the region of misorientation angles lower than 1.5◦ and CH4 /H2 ratios higher than 0.05%, surface morphologies exhibiting unepitaxial crystallites and pyramidal hillocks are obtained. If the misorientation angle is higher than 1.5◦ , macro-bunching steps are observed. At the boundary between these two regions, surface morphologies with unepitaxial crystallites, pyramidal hillocks and macro-bunching steps are observed. Finally, at methane concentrations lower than 0.15%, the samples show ﬂat surfaces, independently of the misorientation angle of the diamond substrates. The optical micrographs of the samples deposited in this work are shown in Fig. 1. All the diﬀerent surface morphologies are clearly observed. In particular, whereas in sample SCD5 nearly square-shaped hillocks are clearly seen, in sample SCD7 unepitaxial crystallites are observed. Their distribution and size are diﬀerent on the surfaces of the various samples. SCD4 and SCD15, grown on the top and back side of the same diamond substrate, but at diﬀerent methane concentrations, show a bunching-step-like morphology. The diﬀerent surface morphologies are obviously observed also in SEM micrographs (Fig. 2). This analysis conﬁrms that the diﬀerent conditions of

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Fig. 2. SEM micrographs (×500 magniﬁcation) of samples studied in this work. The micrograph referring to SCD7 has been registered at lower (×250) magniﬁcation

the initial diamond substrates have a “driving” eﬀect on the morphology of the overlaying homoepitaxial diamond [14]. In particular, the diﬀerent morphologies observed in ﬁlms grown at the same methane concentrations are attributed to diﬀerent misorientation angles of the substrates. The similar morphology observed on the samples grown on the two sides of the same substrate, but at diﬀerent methane concentrations, is associated with a similar misorientation angle of the substrate surfaces. 3.2 Raman Characterisation 3.2.1 First-Order Raman Scattering Raman spectroscopy is a very powerful tool to study the crystalline quality of synthetic diamond. In fact, a perfect diamond structure has a triply degenerate optical phonon at the center of the Brillouin zone whose energy is approximately 165 meV. The inelastic light scattering from this phonon gives rise in the ﬁrst-order Raman spectrum of diamond to a sharp peak at 1332 cm−1 whose full width at half maximum (Γ ) is only approximately 2 cm−1 . The study of the crystalline quality of synthetic diamond is commonly performed by comparing the values of position and width of the measured Raman peaks with the corresponding values of natural diamond. To properly compare the measured linewidths with the narrow standard value, slit-induced broadening has to be considered. In the following, we will show diamond Raman peaks registered with only 50 µm slit aperture, determining an instrumental line broadening on the order of 0.15 cm−1 .

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Fig. 3. Micro-Raman spectra registered on the surface of the samples studied in this work. Excitation wavelength λ = 514.5 nm. Values of position (XP ) and width (Γ ) of the peaks are also indicated

The Raman spectra shown in Fig. 3 demonstrate the extremely high crystalline quality of the deposited samples. In particular, the diamond peak registered on the sample grown at 4% CH4 /H2 (SCD15) is only 1.75 cm−1 wide. Raman linewidths registered on the samples range between 1.75 cm−1 and 2.31 cm−1 . Such linewidths are narrower than the ones obtained on the substrates and even narrower than the linewidths typically found on unselected natural diamond specimens. Lower values have been recently found on a 520 µm thick homoepitaxial diamond [13] and on a 350 µm thick freestanding sample [12]. In a recent work, Tallaire et al. [16] showed that also in homoepitaxial diamond the linewidth of the Raman peak becomes narrower as the sample thickness increases. In this regard, we remark that the thickness of our samples does not exceed 170 µm and that the thickness of the sample on which the narrowest Raman peak has been registered is only 80 µm. On the basis of these considerations, we can conclude that the linewidths measured on our relatively thin samples point out a crystalline quality comparable to that of the best quality samples reported in the literature. 3.2.2 Second-Order Raman Scattering In the previous section, we discussed the Raman scattering from the optical phonon at the centre (k = 0) of the Brillouin zone. This is the only mode

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which is Raman-active in the ﬁrst-order spectrum. When one-phonon scattering is considered, the conservation of the crystal momentum requires that the wave vector of the scattering phonon is approximately zero [17, 18]. However, if a two-phonon process is considered, the conservation of the crystal momentum requires that the two scattering phonons have equal and opposite wave vectors. The second-order Raman spectrum arises from critical points in the two-phonon density of states of diamond; moreover, to be Raman-active, the modes have to satisfy selection rules which can be deduced by group theory analysis [18]. As a consequence, the second-order Raman spectrum of diamond ranges between 1800 cm−1 and 2667 cm−1 , and is explained in terms of combinations and overtones of phonons in diamond [18]. The intensity of the second-order Raman spectrum is much lower than the intensity of the ﬁrst-order Raman spectrum, and thus it can be easily obscured by Raman or PL signals originating from defects and/or impurities in the material. In fact, Solin and Ramdas [18] measured the second order spectrum at visible excitation (488 nm) in a IIb natural diamond, whereas Wagner et al. [19] observed it in polycrystalline ﬁlms, but with a more energetic excitation (4.82 eV), to diminish the contribution originating from a PL background in the second-order Raman region. Thus, the observation, consequent to a visible excitation, of second-order bands in the Raman spectrum of diamond is an indicator of high material quality, because it requires the complete absence of any other spectral feature arising from defects and impurities. As a further conﬁrmation of the great quality of our homoepitaxial diamond samples, the spectral features due to second-order Raman scattering are clearly detected in spectra registered, at 514.5 and 457.9 nm exciting wavelengths, in the 2000–2700 cm−1 range (see inset of Fig. 7). 3.3 Photoluminescence Characterisation Photoluminescence consists in light emission following the excitation of the electronic states of the material by means of a UV–visible radiation source [20]. As the diamond band gap is 5.5 eV, PL emission in the visible range would be impossible in a perfect diamond crystal. Instead, impurityrelated defects having energy levels within the diamond band gap may determine PL emission in the visible range. Obviously, each defect centre has its typical PL emission. Thus, the study of PL spectra in diamond allows the identiﬁcation of its possible contaminants. A typical PL spectrum of a defect centre has its own characteristic structure, consisting of a sharp zero-phonon line (ZPL) and vibronic sidebands. The ZPL corresponds to the transition between the lowest vibrational state of the excited electronic state to the lowest vibrational state of the ground electronic state. The vibronic sidebands, i.e., one-phonon, two-phonon, etc., bands correspond to the transition from the lowest vibrational state of the excited electronic state to the ﬁrst, second, etc., excited vibrational state in

Normalised PL intensity (a. u.)

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x10 H3 vibronic band 2.156 eV vibronic band 1.945 eV vibronic band

0,0

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1,8

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2,6

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PL energy (eV) Fig. 4. Room-temperature micro-PL spectra registered at the same point of the sample SCD4 using two diﬀerent excitation wavelengths: 514.5 nm (black ) and 457.9 nm (light gray)

the ground electronic state. To identify optical centres, the spectral positions of both ZPLs and vibronic sidebands must be accurately measured. As overlapping multi phonon transitions are observed at high temperatures, the optical centres are usually identiﬁed by means of PL measurements carried out at low temperatures (usually 77 K or less). Nitrogen is the main contaminant of diamond. The inclusion of nitrogen in CVD diamond ﬁlms is quite commonly found in the literature results, probably due to small residual amounts of this element in the growth chamber after evacuation or to the use of not ultra pure gases. The incorporation of nitrogen during the growth gives rise to the well-known PL centre at about 2.156 eV, attributed [21] to a [N-V]0 defect centre. A diﬀerent state of charge of this defect [21] gives rise to a PL band with ZPL at 1.945 eV ([N-V]− defect centre). Another PL feature commonly associated to N impurities consists of a ZPL centered at 2.463 eV and vibronic sidebands corresponding to a phonon energy of 40 meV. This structure is attributed to the defect complex involving two nitrogen atoms and a vacancy ([N-V-N] centre), usually called H3 defect. The type of defect which is observed in PL measurements depends on the excitation energy used. In fact, only defects having energy lower than the excitation energy may be observed. For this reason, PL measurements are generally performed with diﬀerent excitation wavelengths. In our measurements we have used two excitation wavelengths: the 514.5 nm line (corresponding

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1

0,1

x10

Raman peaks

1.945 eV 2.156 eV vibronic band

0,0 1,5

1,7

1,9

2,1

2,3

0 1,6

1,8

2,0

2,2

2,4

2,6

PL energy (eV) Fig. 5. Room temperature micro-PL spectra registered at the same point of the sample SCD5 using two diﬀerent excitation wavelengths: 514.5 nm (black ) and 457.9 nm (light gray)

to an excitation energy of 2.41 eV) and the 457.9 nm (2.71 eV) line. The ﬁrst line may evidence the presence of the two nitrogen-related defects at 2.156 eV and 1.945 eV, while the second may evidence, besides these, the H3 defect (2.463 eV). However, resonance eﬀects, or selective absorption [21], may hide the presence of the PL structure related to a particular centre, so only the comparison between the spectra obtained with both the excitation energies may give a complete identiﬁcation of the defects present in the material. In Fig. 4 the spectra obtained on the same surface point of sample SCD4 are shown. From these data, the quality of the sample is evident: the main features of the spectra are the two sharp peaks corresponding to the Raman scattering from the diamond crystal. However, a weak photoluminescence background is observed, due to the inclusion of nitrogen atoms, in both the H3 [N-V-N] and in the [N-V] defect conﬁguration. The presence of both types of defect indicates a moderate inclusion of nitrogen atoms during the growth. It is interesting to observe the resonant excitation of 1.945 eV emission with the 2.41 eV excitation energy. Such an eﬀect has been already observed in polycrystalline samples [22], and it has been explained hypothesising the presence of a higher excited electronic state of the [N-V]− centre at an energy value approaching 2.41 eV. The resonant PL emission of the 1.945 eV defect centre is more impressively observed in Fig. 5, where the spectra obtained on the same surface point of the sample SCD5 are shown. When PL is excited with the green laser line (2.41 eV) the ZPL and the vibronic band of the [N-V]− defect centre are

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Raman peaks

0 1,6

1,8

2,0

2,2

2,4

2,6

PL energy (eV) Fig. 6. Room-temperature micro-PL spectra registered at the same point of the sample SCD7 using two diﬀerent excitation wavelengths: 514.5 nm (black ) and 457.9 nm (light gray)

seen, together with a weak contribution of the 2.156 eV centre. However, the more energetic laser line at 457.9 nm does not excite the centres. Moreover, the [N-V-N] defect is not seen in this sample. In Fig. 6, the spectra registered on the sample SCD7 are shown. No nitrogen-related defects are seen. Finally, in Fig. 7 the PL spectra obtained on the sample SCD15 are shown. The exceptional crystalline quality and phase purity indicated by the Raman measurements are conﬁrmed also by PL characterisation. A completely ﬂat spectrum and the second-order Raman spectrum of the diamond structure is observed with both the excitation wavelengths used.

4 Discussion and Conclusions In the previous sections we have shown measurements carried out on homoepitaxial diamond samples grown onto diamond substrates of diﬀerent origin. Optical and SEM micrographs have shown very diﬀerent surface morphologies, which have been associated with the diﬀerent conditions of the diamond substrates, and in particular with the misorientation angles of the 100 diamond substrate. Thus, we may conclude that the initial state of the diamond substrate plays a crucial role on the ﬁnal morphology of homoepitaxial diamond. This may be a problem in view of the technological

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Normalised PL intensity (a. u.)

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x10 2nd order Raman bands

1500

2500

0 0

2000

4000

6000

8000

-1

Wavenumber shift (cm ) Fig. 7. Room-temperature micro-PL spectra registered at the same point on sample SCD15 using two diﬀerent excitation wavelengths: 514.5 nm (black ) and 457.9 nm (light gray). To evidence the presence of the second-order Raman of diamond peak, data have been plotted as wavenumber shifts

exploitation of this material. In fact, an accurate and standardised preparation of diamond substrates, which are not as common as silicon wafers, may be too expensive. Moreover, the removal of diamond substrates, which are almost always of lower quality than the homoepitaxial layer, may not be easy to carry out. Anyway, the crystalline quality of the obtained samples, even if deposited onto not-selected substrates, is really exceptional: on relatively thin samples, values of Raman linewidth as low as 1.75 cm−1 are measured. Such values indicate a great crystalline quality of the material, which becomes really attractive if compared with the more easily obtainable polycrystalline diamond. However, some further improvements in the experimental setup should be done. In fact, photoluminescence measurements indicate the possible inclusion of nitrogen atoms. The incorporation of such impurities is not an easily resolvable issue, because, as other authors have observed [9, 11, 23], at high growth rates nitrogen atoms may also be incorporated in ﬁlms grown without the intentional addition of N2 in the deposition gas mixture. Thus, a further step in the optimisation of the deposition process of homoepitaxial diamond will be the individuation of the growth conditions which both limit the incorporation of nitrogen atoms and guarantee to obtain the best quality material. Finally, it seems that the sample grown at higher methane concentration (sample SCD15, 4% CH4 ) has a higher crystalline quality and no incorporation of defects and impurities. Other authors have already ob-

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served an improvement of sample quality with increasing methane concentration [11, 13]; however, their experimental conditions are very diﬀerent from ours. In fact, while Teraji et al. [11] use a high-power deposition, Tallaire et al. [13] perform the etching of the diamond substrates before the homoepitaxial diamond deposition. On the contrary, when depositing polycrystalline samples, we have observed [1], with our experimental setup, that the best quality material is obtained at lower methane concentrations. For this reason, a further systematic study on samples grown on substrates of identical quality, changing the CH4 concentration in the deposition gas mixture needs to be done, in order to assess the role of this growth variable on the quality of homoepitaxial diamond obtained. Acknowledgments The authors wish to thank the group of Prof. Aldo Tucciarone at the University of Rome Tor Vergata for kindly providing the diamond samples and performing the SEM measurements.

References [1] M. G. Donato, G. Faggio, M. Marinelli, G. Messina, E. Milani, A. Paoletti, S. Santangelo, A. Tucciarone, G. V. Rinati: Eur. Phys. J. B 20, 133 (2001) 346, 347, 357 [2] J. Alvarez, A. Godard, J. P. Kleider, et al.: Diam. Rel. Mater. 13, 881 (2004) 346 [3] L. Bergman, B. R. Stoner, K. F. Turner, et al.: J. Appl. Phys. 73, 3951 (1993) 346 [4] C. Manfredotti: Diam. Rel. Mater. 14, 531 (2005) 346 [5] J. Isberg, J. Hammersberg, E. Johansson, et al.: Science 297, 1670 (2002) 346 [6] Y. Vohra, A. Israel, S. A. Catledge: Appl. Phys. Lett. 71, 321 (1997) 346 [7] H. Watanabe, D. Takeuchi, S. Yamanaka, et al.: Diam. Rel. Mater. 8, 1272 (1999) 347 [8] H. Okushi: Diam. Rel. Mater. 10, 281 (2001) 347 [9] M. Stammler, H. Eisenbeiß, J. Ristein, et al.: Diam. Rel. Mater. 11, 504 (2002) 347, 356 [10] T. Teraji, S. Mitani, C. Wang, et al.: J. Crys. Growth 235, 287 (2002) 347 [11] T. Teraji, M. Hamada, H. Wada, et al.: Diam. Rel. Mater. 14, 255 (2005) 347, 356, 357 [12] T. Bauer, M. Schreck, H. Sternschulte, et al.: Diam. Rel. Mater. 14, 266 (2005) 347, 351 [13] A. Tallaire, J. Achard, F. Silva, et al.: Diam. Rel. Mater. 14, 249 (2005) 347, 351, 357 [14] D. Takeuchi, H. Watanabe, S. Yamanka, et al.: Diam. Rel. Mater. 9, 231 (2000) 347, 348, 350

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[15] High Resolution Single Crystal CVD Diamond Particle Detectors, presented at the 16th European Conference on diamond, diamond-like materials, carbon nanotubes and nitrides, Toulouse (France), 11–16 September 2005 347 [16] A. Tallaire, J. Achard, F. Silva, et al.: Phys. Stat. Sol. A 201, 2419 (2004) 351 [17] N. W. Ashcroft, N. D. Mermin: Solid State Physics (Saunders College, Philadelphia 1976) p. 481 352 [18] S. A. Solin, A. K. Ramdas: Phys. Rev. B 1, 1687 (1970) 352 [19] J. Wagner, M. Ramsteiner, C. Wild, et al.: Phys. Rev. B 40, 1817 (1989) 352 [20] J. Walker: Rep. Progr. Phys. 42, 108 (1979) 352 [21] A. T. Collins: The electronic and optical properties of diamond, in A. Paoletti, A. Tucciarone (Eds.): The Physics of Diamond, Proceedings of the Interna¨ tional School of Physics Enrico Fermi”, Course CXXXV, Varenna 1996 (Ios,, Amsterdam 1997) p. 273 353, 354 [22] M. C. Rossi, S. Salvatori, F. Galluzzi, et al.: Diam. Rel. Mater. 7, 255 (1998) 354 [23] A. Chayahara, Y. Mokuno, Y. Horino, et al.: Diam. Rel. Mater. 13, 1954 356

Index CVD diamond, 345–348

homoepitaxial growth, 346

defects grain boundaries, 345, 346 in diamond, 347, 352–356 detectors diamond-based detectors, 346 diamond diamond properties, 345 high-quality diamond, 347, 348, 351–357 homoepitaxial diamond, 345–348, 352, 355–357 HPHT diamond, 346 IIb type diamond, 348, 352 natural diamond, 348, 352 nitrogen contamination, 347, 353–356 silicon contamination, 347 single-crystal diamond, 345

optical microscopy (OM), 345, 347–349, 355

heteroepitaxial growth, 346 high-pressure high-temperature (HPHT), 346

photoluminescence (PL), 345, 347, 352–355 micro-PL analysis, 348, 352–356 plasma-enhanced chemical vapour deposition (PECVD), 345 polycrystalline diamond, 345–347, 352, 354, 356, 357 Raman scattering, 350, 351, 354 ﬁrst-order Raman scattering, 350 second-order Raman scattering, 351, 352 Raman spectroscopy, 345, 347, 348, 350–352, 355, 356 micro-Raman analysis, 348, 351–356 scanning electron microscopy (SEM), 345, 347–350, 355

Pulsed Laser Deposition of Carbon Films: Tailoring Structure and Properties Paolo M. Ossi1 and Antonio Miotello2 1

2

Dipartimento di Ingegneria Nucleare and Centro di Eccellenza “Nano-Engineered MAterials and Surfaces” (NEMAS), Politecnico di Milano, Via Ponzio 34/3, I-20133 Milano, Italy [email protected] Dipartimento di Fisica, Universit` a di Trento, I-38050 Povo (TN), Italy [email protected]

Abstract. Pulsed laser deposition (PLD) is a versatile technique to synthesize ﬁlms of a given material with strongly diﬀerent properties. In this chapter we discuss the microstructure and structure of carbon ﬁlms ranging from diamond-like carbon to tetrahedral amorphous carbon, to nanometer-sized cluster assembled ﬁlms, depending on PLD process parameters. All ﬁlms are hydrogen-free, as shown by FTIR spectroscopy, and result invariably structurally disordered. Carbon local hybridisation was checked by Raman spectroscopy, both visible and UV. Vacuum deposited ﬁlms undergo a transition from mainly disordered graphitic to up to 80% tetrahedral amorphous carbon above a threshold laser energy density. The microstructure and morphology of the deposited ﬁlms were studied in a complementary way by SEM and AFM. All vacuum deposited ﬁlms appear featureless. Cluster assembled glass-like ﬁlms display diﬀerent growth modes, mainly depending on the deposited energy per laser pulse and nature-pressure of the ambient gas. Film morphology is correlated with the ballistic mechanisms that occur when plasma plume constituents interact with ambient gas atoms. Cluster formation in the plume is modelled, and we estimate the average number of atoms per cluster. Model predictions agree with cluster sizes deduced by Raman spectroscopy and observed by TEM imaging.

1 Introduction Carbon displays a wide variability of structures and properties. It is a good candidate to explore the tunability of material properties that in turn make it suitable for emerging technologies. Carbon can crystallise in several forms, including, besides the most widely known diamond and graphite, fullerene molecules like C60 and carbon nanotubes, which are rolled tubules of graphite sheets. There are also many noncrystalline carbons due to the diﬀerent types of bonding and diﬀerent degrees of disorder. We are thinking of amorphous carbon and nanostructured carbon, the latter being a mixture of amorphous carbon, nanotubes, fullerenes and graphitic fragments. Amorphous carbon with a large fraction of tetrahedral, diamond-like sp3 bonds is known as diamond-like carbon (DLC). The possibility to synthesise DLC at room temperature is a great advantage with respect to diamond ﬁlms. The interesting G. Messina, S. Santangelo (Eds.): Carbon, The Future Material for Advanced Technology Applications, Topics Appl. Phys. 100, 359–380 (2006) © Springer-Verlag Berlin Heidelberg 2006

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mechanical and optical properties of DLCs lead to several applications, including magnetic hard disk coatings, wear-protective and antireﬂective coatings, ﬂat panel displays and biomedical coatings. The versatility of carbon materials is due to the critical dependence of their physical properties on the sp2 (graphite-like) to sp3 (diamond-like) bond ratio [1]. We know many types of sp2 bonded carbons with diﬀerent degrees of graphitic order, that range from microcrystalline graphite to glassy carbon. Any amorphous carbon has a mixture of sp3 , sp2 and occasionally sp1 bonds, possibly in the presence of a fraction of hydrogen that can be as high as 60%. As a rule, hydrogenated amorphous carbons have a quite small content of sp3 C–C; DLCs with the highest sp3 contents are known as tetrahedral amorphous carbon (ta-C). The electronic structure of amorphous carbons essentially consists of the strong σ bonds of sp3 and sp2 sites that form the occupied bonding states in the valence band and the empty σ ∗ antibonding states in the conduction band; a wide gap separates σ from σ ∗ states. The π bonds of sp2 and sp1 states result in the occupied π and unoccupied π ∗ states that largely lie within the σ–σ ∗ gap. Each modiﬁcation of the sp2 /sp3 fraction is associated with a change of the density of states and of the energy gap. Any technique able to synthesize carbon ﬁlms, ﬂexible enough to allow to control the above fraction, the degree of structural disorder and the extent of clustering of sp2 phase, its orientation and anisotropy, is suitable to prepare DLC ﬁlms with largely diﬀerent structural, mechanical, optical and electronic properties. In particular, ta-C is grown by deposition techniques involving energetic ion beams, or a plasma; such an energetic beam deposition is necessary to stabilise the metastable sp3 bonding. It was observed that the optimum ion energy to maximise the fraction of tetrahedrally coordinated material, around 70–80%, lies between 100 and 200 eV. In the following we discuss the synthesis of DLC and ta-C ﬁlms by pulsed laser deposition. The intrinsic conceptual simplicity of the technique is associated with the possibility to change several deposition parameters, thus tailoring ﬁlm structure and properties. Hydrogen-free ta-C is characterised by its low friction coeﬃcient and high hardness [2], optical transparency in a wide spectral range and absorbance in the UV. Such a set of properties is promising for scratch-resistant thin coatings of lenses [3]. The eﬀectiveness of pulsed laser deposition (PLD) techniques to obtain in vacuum hydrogen-free amorphous carbon ﬁlms was ascertained long ago [4]. PLD is characterised by low deposition temperatures and high deposition rates. The main process parameters that aﬀect the degree of diamond-like character of deposited ﬁlms are vacuum quality, laser wavelength λ and power density P . To obtain DLC a vacuum of at least 10−4 –10−5 Pa, and a minimum P value, which increases with λ (P ≈ 3 × 106 W mm−2 at λ = 248 nm), seem to be necessary [5]. Ultraviolet excimer lasers allow one to obtain good quality ﬁlms [6], since particulate emission is reduced and ta-C ﬁlms are obtained at comparatively

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low laser ﬂuences with respect to visible and infra-red lasers [7]. On the other hand, a dramatic change from dense, uniform, compact ﬁlms to progressively more open microstructures is observed when ﬁlms are deposited in a background atmosphere, either inert or chemically reactive. Our discussion includes the features of carbon ﬁlms deposited by PLD at high pressures of inert gas, which permit us to obtain nano-glassy ﬁlms. Here we report the morphological and structural analyses of carbon ﬁlms pulsed laser deposited in vacuum, in a reactive gas (molecular nitrogen) lowpressure atmosphere and in an inert gas (helium and argon) high-pressure atmosphere. Ablation of carbon atoms and ions from the irradiated target, plasma formation and interaction of the plume of ejected particles among themselves and with background gas lead to strong modiﬁcations of microstructure and structure of the deposited ﬁlms [8]. We performed: – scanning electron microscopy (SEM) and atomic force microscopy (AFM) to investigate ﬁlm morphology – Fourier transform infrared (FTIR) spectroscopy to assess hydrogen content – visible and UV Raman spectroscopies to study carbon atom coordination – electron energy-loss spectroscopy (EELS) on selected samples to quantify the fraction of tetrahedrally coordinated carbon – transmission electron microscopy (TEM) on selected samples deposited in inert gas to directly check the presence and size of carbon clusters A discussion of the mechanisms underlying the formation of carbon ﬁlms with largely diﬀerent properties is oﬀered.

2 Experimental Details The ﬁlms were deposited at room temperature on cleaned Si (100) substrates, in a vacuum chamber (base pressure, 10−4 Pa) either at an operating pressure of 10−2 Pa, or in diﬀerent background gases. These were a molecular nitrogen atmosphere at 1 Pa, or a helium or argon atmosphere at pressures pHe;Ar = 0.6, 30, 50, 60, 70, 250, 103 and 2 × 103 Pa. Highly oriented, highpurity (99.99%) pyrolytic graphite (HOPG) was ablated with laser pulses from a KrF excimer laser (λ ≈ 248 nm, pulse duration τ = 20 ns, repetition frequency 10 Hz, incidence angle 45◦ ), at power densities ranging from 0.25 to 19 MW mm−2 . The average deposition rate of ﬁlms prepared in vacuum and in nitrogen was about 0.6 nm s−1 , while for ﬁlms prepared in helium it was around 0.7 nm s−1 and in argon it was around 0.8 nm s−1 . More details of the deposition system are reported in [9]. We used a JEOL JSM 6300 SEM, with the primary beam accelerated at 15 keV and an incidence angle of 30◦ . After metallization, both surface and cross-sectional pictures were taken for all examined samples. A Thermo Microscopes CP Research AFM was used in

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noncontact mode; measurements were made at room temperature, in ambient air. FTIR spectra were taken at room temperature, in dry air, using a WinBio-Rad Fast Transform spectroscope over the 400–4000 cm−1 range. The spectra were recorded in transmission and corrected for substrate contributions. Unpolarized visible micro- (ﬁlms deposited in vacuum and in nitrogen; spot diameter, 1 µm; incident power at the sample surface, 3 mW) and macro- (ﬁlms deposited in helium and argon) Raman spectra were recorded in backscattering geometry for 532 nm excitation from a Nd:YAG laser using a Jobin-Yvon T64000 triple grating spectrometer with a resolution of 1 cm−1 . UV Raman spectra were collected using an UV-enhanced CCD camera on a Renishaw micro-Raman System 1000 spectrometer, modiﬁed for use at 244 nm (resolution, 4–6 cm−1 ), with fused-silica optics throughout. All UV spectra were corrected for system response signal, obtained by measuring a background spectrum with an Al mirror and normalising to atmospheric molecular nitrogen vibrations. EELS measurements were performed with a dedicated VG501 scanning transmission electron microscope ﬁtted to a spectrometer with a McMullan parallel EELS detection system.

3 Results Among the deposited carbon ﬁlms a clear a posteriori separation into two families with distinct and often opposite properties is possible. Thus it appears obvious to separately discuss the properties of samples synthesized in vacuum, or at low pressure, before presenting our results on cluster assembled (CA) ﬁlms prepared at high background gas pressure. 3.1 Low-Pressure Deposited Films The surface of all ﬁlms belonging to this family appears smooth, uniform and featureless. SEM pictures (not shown) indicate the absence of droplets, as expected when carbon is ablated with pulses in the UV region, while accidental micrometer-sized debris are sometimes observed. All ﬁlms of this family adhere well to the Si substrates. Two representative FTIR transmission spectra of DLC ﬁlms deposited in vacuum are shown in Fig. 1. In both spectra no absorption bands in the range 2800–3100 cm−1 , due to the C–Hx stretching mode, are found. This means that the ﬁlms are hydrogen-free (more precisely, H content is below the detectable limit of 0.5 at. %). The overall aspect of the spectra indicates that such ﬁlms are structurally disordered. Yet, the spectrum (curve 1) of the ﬁlm

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Fig. 1. FTIR transmission spectra of DLC ﬁlms deposited in vacuum below (curve 1 ) and above (curve 2 ) the threshold laser power density P t . Substrate contributions have been subtracted

deposited at low laser intensity (P = 0.5 MW mm−2 ), below the threshold intensity value P t = 5 MW mm−2 , shows a broad band at about 710 cm−1 , attributed to a vibrational mode observed also in visible Raman spectra discussed below. This feature coincides with a peak in the calculated vibrational density of states of a graphene sheet [10]. We believe that it can be attributed to a collective in-plane deformation of graphitic islands. Indeed, the calculated IR and Raman spectra of model polyconjugated hydrocarbons, ranging from C24 to C114 [11], display intense bands in the region between 700 and 750 cm−1 that arise from in-plane cooperative motions involving combinations of C–C stretching and C–C–C bending. An evident shoulder at about 1250 cm−1 is attributed to a stretching mode of mixed sp2 –sp3 C–C bonds, while the high-frequency shoulder at about 1550 cm−1 is due to vibrations of sp2 C=C bonds [12]. The above bands are absent in the featureless spectrum (curve 2) of the transparent ﬁlm deposited at P = 10 MW mm−2 , thus above the threshold P t . Film transparency is an indirect indication that a structural transition from disordered graphitic carbon to ta-C occurred. A set of visible Raman spectra of ﬁlms deposited in vacuum (V) and in nitrogen atmosphere (N2 ) at the same intensity, for various increasing intensities, is reported in Fig. 2. The spectra of vacuum-deposited ﬁlms indicate that the content of fourfold-coordinated carbon increases with laser intensity. Indeed, given the slight diﬀerences of ﬁlm thickness, we can compare spectra of different ﬁlms. In the ﬁlms deposited above P t the increasing intensity of the

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peaks due to the crystalline Si substrate (ﬁrst order at ∼ 520 cm−1 and second order at ∼ 970 cm−1 ) with increasing power density indicates increasing ﬁlm transparency, associated with increasing content of fourfold-coordinated carbon atoms. Two features are evident in all spectra: the D peak (∼ 1350 cm−1 ), due to breathing of hexagonal rings, and the G peak (∼ 1560 cm−1 ) due to the relative motion of sp2 carbon atoms [13]. Indeed both “peaks” are broad bands, the nomenclature coming from the literature. Inset a in Fig. 2 shows a magniﬁcation of a broad, weak band centred around 720 cm−1 in a ﬁlm deposited below P t . The nice coincidence of this feature, that is lacking in ﬁlms deposited at high power densities, with the band observed in the above-discussed IR spectra of the same ﬁlms is noteworthy. The spectra were ﬁtted to a combination of a Breit–Wigner–Fano (BWF) function for the G peak and a Lorentzian for the D peak. The evolution of relevant parameters (Raman shift at BWF maximum and D to G peak intensity ratio, I D /I G ) with increasing power density is shown (diamonds; dashed lines) in Fig. 3. We consider the Raman shift corresponding to the peak value of the BWF function to allow comparison with literature data where symmetric lineshape ﬁtting is used. Both ﬁtting parameters indicate that above the threshold intensity P t the ﬁlms consist largely of ta-C. The coincidence of an almost zero value for the I D /I G ratio and of a G peak position at a frequency above 1550 cm−1 is a suﬃcient condition to assert a high sp3 content in the ﬁlms [13]. Looking at Fig. 2, the low-frequency Raman spectra of the set of ﬁlms deposited in N2 atmosphere at a partial pressure of 1 Pa with the same power densities used for vacuum-deposited ﬁlms, can be attributed to mainly threefold-coordinated disordered carbon networks. Thus nitrogen induces qualitative changes in the dynamics of the ablation plume. Fitting the spectra to the above-discussed lineshapes results in the parameter trends shown in Fig. 3 (triangles, dashed-dotted lines) and conﬁrms that no ta-C was formed in this set of ﬁlms, even at the highest power density. This conclusion is supported by two immediate observations: ﬁrst (see inset b in Fig. 2), we ﬁnd the band around 720 cm−1 even in the ﬁlm deposited at the maximum power density P = 18.5 MW mm−2 . Second, all ﬁlms of this group are opaque, the substrate Si peaks being lacking. In these samples the I D /I G ratio is about unity and remains nearly constant, while the G peak position slightly red-shifts, in agreement with the observed trends [14]. UV Raman spectra (not reported) of ﬁlms grown in vacuum show the G peak, around 1600 cm−1 , thus blue-shifted with respect to its position in low-frequency Raman spectra. The characteristic feature is the T peak around 1100 cm−1 , attributed to all sp3 C–C bond vibrations [15]. At the lower power densities a further evident shoulder around 1400–1430 cm−1 is discernible. We believe that this feature corresponds to the D peak in visible Raman spectra [6]. The results of the peak-ﬁtting procedure are displayed in Fig. 4. We observe that, with increasing power density P , the T peak is

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Fig. 2. Visible micro-Raman spectra of DLC ﬁlms pulsed laser deposited at various laser power densities in vacuum (V) and in nitrogen atmosphere (N2 ). The insets (a) and (b) show the broad band centered around 720 cm−1 in non-ta-C ﬁlms

red-shifted and its intensity increases. Correspondingly, the G peak is blueshifted, it becomes more symmetric and its intensity in turn increases. The ratio I T /I G increases with power density up to about 0.45, then it remains constant, again indicating that a transition to ta-C occurred [13]. UV Raman spectra of ﬁlms prepared in N2 atmosphere display the T and G broad peaks and a small, narrow extra peak around 1550 cm−1 due to atmospheric oxygen. Again from Fig. 4, with increasing deposited power density the G peak around 1570 cm−1 remains asymmetric and shows no obvious position shift [14]; the position of the T peak, around 1300 cm−1 , is unchanged. The feature around 1400 cm−1 is absent in all spectra. The ratio I T /I G is around 0.35 and remains nearly constant. Looking at the trends of ﬁtting

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Fig. 3. Fitting parameters of visible Raman spectra versus laser power density: left scale, intensity ratio between G and D peaks, I D /I G ; right scale, G peak position. Diamonds, dashed lines: ﬁlms deposited in vacuum; triangles, dashed-dotted lines: ﬁlms deposited in nitrogen atmosphere. The lines are guides to the eye

Fig. 4. Fitting parameters of UV Raman spectra versus laser power density: left scale, intensity ratio between T and D peaks, I T /I G ; right scale, G peak position. Diamonds, dashed lines: ﬁlms deposited in vacuum; triangles, dashed-dotted lines: ﬁlms deposited in nitrogen atmosphere. The lines are guides to the eye

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Fig. 5. Transmission EELS spectra of a selected ﬁlm deposited in vacuum at laser power density P below P t

parameters for these ﬁlms it is evident that ta-C was not synthesized with the above process conditions. Transmission EELS measurements allow us to quantify [16] in selected ﬁlms deposited in vacuum the fraction of sp2 -hybridised, and thus also of sp3 -hybridised carbon from the ratio of the area of the sp2 peak at 285 eV to that of the (sp2 + sp3 ) peak at 290 eV. Such a ratio is about 40% (Fig. 5) in a ﬁlm prepared at P = 0.25 MW mm−2 , thus below the threshold laser intensity P t . In Fig. 6 the same ratio is about 80% in a ﬁlm deposited above P t , at P = 10 MW mm−2 . In ﬁlms deposited in nitrogen atmosphere at the same values of power density, the measured sp3 fraction slightly increases from about 40% to about 45%. Thus EELS results agree with the indications from vibrational spectroscopies concerning ta-C formation in this family of ﬁlms. 3.2 High-Pressure Deposited Films Carbon ﬁlms were deposited at room temperature in helium and in argon atmospheres at pressures of 0.6, 30, 50, 60, 70, 250, 1000 and 2000 Pa, with power intensities ranging from 8.5 to 19 MW mm−2 . Both planar and crosssection SEM observations show that columnar, nodule-like and dendritic, highly porous microstructures occur in the ﬁlms prepared in helium. Such microstructures are found according to the above sequence, mainly as a function of increasing partial gas pressure in the deposition chamber pHe and also, less sensitively, of the deposited power density. Notably, for various combinations of power density and helium pressure, columns coexist with nodes that

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Fig. 6. Transmission EELS spectra of a selected ﬁlm deposited in vacuum at laser power density P above P t

develop within the columnar structure during the ﬁlm growth. At the lowest pHe = 0.6 Pa, ﬁlm surfaces are very similar to those of DLC ﬁlms deposited in vacuum; they appear ﬂat and laterally homogeneous. The pictures in Figs. 7, 8, 9 are representative of the evolution of ﬁlm microstructure with increasing pHe . The microstructure of the ﬁlms deposited at medium-low pHe (30–70 Pa) consists of densely packed columns with several embedded spherically capped nodes that are partly agglomerated with each other. Such ﬁlms adhere well to the substrate. With increasing pHe , the number density (cm−3 ) of the nodes increases while their cap radius decreases. The calculated ratio between measured node diameters, at the top and at half of the height is equal, or very close to 21/2 ; the same value is obtained when the ratio is made between the diameter at half of the node height and that at one quarter of node height. The above diameter ratios have been found for all well-resolved nodes in all cluster-assembled ﬁlms deposited at pHe = 50, 60 and 70 Pa. This result indicates that nodes have parabolic shape. This deﬁnitely diﬀers from the conical shape predicted by ballistic growth models, where the ratio of node diameters scales with n1/2 , n being an integer greater than 2 [17]. The irregular surface in Fig. 8 is characteristic of all ﬁlms prepared at pHe = 250 Pa, irrespective of the laser power density. Columns coexist with nodes, both being loosely packed in comparison to ﬁlms deposited at lower pHe . The nodes are large, with a deﬁnite tendency to spherical geometry. The degree of intraﬁlm cohesion increases with power density. Yet, ﬁlm– substrate adhesion is worse than in ﬁlms prepared at low helium pressures, independently of the power density.

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Fig. 7. SEM micrograph cross sections of a representative cluster-assembled carbon ﬁlm. pHe = 60 Pa, P = 16 MW mm−2

Fig. 8. SEM micrograph cross sections of a representative cluster-assembled carbon ﬁlm. pHe = 250 Pa, P = 8.5 MW mm−2

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Fig. 9. SEM micrograph cross sections of a representative cluster-assembled carbon ﬁlm. pAr = 2 kPa, P = 16 MW mm−2

Fig. 10. SEM micrograph cross sections of a representative cluster-assembled carbon ﬁlm. pAr = 70 Pa, P = 19 MW mm−2

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The morphologies of cluster-assembled ﬁlms deposited in argon have many similarities to those of ﬁlms prepared in helium. Essentially, the same sequence of columns, nodes, dendritic structure is observed. The dendritic microstructure in Fig. 9 is highly porous and irregular. Although ﬁlm thickness can exceed 15 µm, at some positions on the substrate the surface is barely covered. The ﬁlm–substrate adhesion is poor. The aspect of such a ﬁlm is similar to the predictions of ballistic growth models with null atomic mobility, where strongly oﬀ-geometrical equilibrium conﬁgurations are frozen. When a comparison with ﬁlms deposited in helium under identical conditions is made, ﬁlms synthesised in argon have three features: 1. The nodes are smaller, with spherical geometry; the spatial distribution is more homogeneous and the size distribution is narrower. 2. The ﬁlm–substrate adhesion is lower. 3. The ﬁlms are thinner and laterally inhomogeneous. Furthermore, as shown in Fig. 10, a peculiar platelet morphology is found at pAr = 50, 60 and 70 Pa. The size of these particles lies between 1 and 5 µm with thickness between 400 and 500 nm, independently of argon partial pressure and laser power density. The particle spatial distribution is, however, homogeneous. Platelets initially grow normally to the substrate surface, but with increasing deposition time they show a trend to grow parallel to the substrate, and in thick ﬁlms they are included in the columnar structure. Noncontact AFM on representative ﬁlm areas of 15 × 15 µm2 was performed for ﬁlms deposited at pHe;Ar = 50, 60 and 70 Pa, whose surface was suﬃciently smooth to allow for reliable measurements. Using AFM it was possible to count the nodes and estimate ﬁlm roughness. Figures 11 and 12 show, respectively, a comparison between the depositions in He and in Ar, at the same conditions. Figure 12 shows the smaller size and narrower size distribution of the nodes in ﬁlms deposited in Ar, thus conﬁrming our SEM observations. As a general trend, when pHe;Ar changes from 30 to 70 Pa the average node size decreases, the node number density increases, the size distribution of the nodes becomes progressively broader and the ﬁlm roughness (r.m.s.) correspondingly decreases. In Fig. 13 are reported three representative Raman spectra of cluster-assembled carbon ﬁlms. All spectra consist of the G peak and a less evident D peak at lower frequency. The former is always asymmetric and broad, while the latter is well deﬁned for the ﬁlms prepared at the highest ambient gas pressure, namely pHe;Ar = 2kPa, while it decreases to a shoulder in all other spectra. Thus the ﬁlms consist of structurally disordered carbon networks with trigonal coordination. The presence of a resolved D peak in the ﬁlms showing the most irregular morphology indicates that graphitic aggregates of considerable size were assembled together. The spectra were ﬁtted using the same combination of a BWF function for the G peak and a Lorentzian curve for the D peak already adopted to ﬁt Raman spectra of ﬁlms deposited in vacuum and at low ambient gas pressure. At each power density, with increasing

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Fig. 11. AFM pictures (15 × 15) µm2 of a representative cluster assembled ﬁlm deposited at P = 16 MW mm−2 and pHe = 70 Pa. The morphology dependence on the nature of ambient gas is evident

background gas pressure, the peak intensity ratio I D /I G decreases, remaining in the range ∼ 0.93 to ∼ 0.85. Correspondingly, the G peak maximum lies between 1580 cm−1 and 1530 cm−1 . According to the Raman spectrum analysis [13], the range of values of both I D /I G and G maximum indicate that the fraction of sp3 -coordinated carbon in cluster-assembled ﬁlms does not exceed 10%. From the I D /I G ratio it is possible to estimate the coherence length La , namely the average size of cooperatively scattering domains in these carbon ﬁlms. La values for CA ﬁlms, prepared at ambient gas pressures pHe;Ar ranging from 30 to 250 Pa, evaluated by the Tuinstra–Koenig (TK) relation [18], lie in a narrow interval between 4.7 and 5.2 nm. Indeed La , calculated by the TK relation for carbon ﬁlms with diﬀerent structures, prepared by several diﬀerent techniques, is correlated to I D /I G [19]. Our data for cluster-assembled ﬁlms ﬁt well into such a correlation. Figure 14 shows that in the I D /I G interval spanned by the CA ﬁlms, La linearly scales with I D /I G , both with helium (Fig. 14a) and with argon (Fig. 14b) as the background gas. Our ﬁlms are near the lower limit of validity of the TK relation and belong to the family of nano-glassy carbon ﬁlms. In the above analysis we do not consider cluster-assembled ﬁlms deposited at the highest pHe;Ar values because only one power density value was adopted for such depositions. Cluster size

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Fig. 12. AFM pictures (15 × 15) µm2 of a representative cluster assembled ﬁlm deposited at P = 16 MW mm−2 and pAr = 70 Pa. The morphology dependence on the nature of ambient gas is evident

and structure as deduced from Raman analysis is conﬁrmed by direct TEM structural observations [20].

4 Discussion We separately discuss the mechanisms underlying ﬁlm formation in the two families of low- and high-pressure deposited ﬁlms so that qualitative diﬀerences between the experimental conditions leading to diﬀerent energetic and chemical evolution of the plasma plume can be better highlighted. 4.1 Low-Pressure Deposited Films The existence of a threshold intensity P t at which the structure of vacuumdeposited ﬁlms changes from mainly graphitic to ta-C can be associated with a corresponding threshold in the values of ablated particle energy. The plasma plume produced by laser irradiation of graphite mainly consists of C, C2 , C+ and C++ [21], where the C2 constituent most probably results from ion–atom collisions followed by charge neutralisation in the plume [21]. The critical factor to drive ta-C formation is the energy of C+ ions (and energetic neutrals)

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Fig. 13. Macro-Raman spectra of representative cluster assembled carbon ﬁlms. (a) pHe = 60 Pa, P = 16 MW mm−2 ; (b) pHe = 2 kPa, P = 16 MW mm−2 ; (c) pAr = 2 kPa, P = 16 MW mm−2

impinging on the growing C ﬁlm. The latter will be graphitic if only neutral, low-energy carbon atoms arrive at the substrate. A C+ energy threshold between 100 and 200 eV appears to be a necessary condition to obtain a high sp3 /sp2 bond ratio [16]. We observe ta-C formation once the laser power density exceeds the threshold power density P t ; this is expected, as C+ ion energy increases as a function of power density [22]. As the experimental conditions are very similar to ours, we assume the same energy values of plume particles as in [22]. High-energy C+ ions impinging on the growing carbon ﬁlm are stopped in interstitial positions at diﬀerent depths, progressively increasing with increasing ion energy. According to SRIM simulations [23] 50, 100 and 175 eV particles are stopped within 0.5, 1.5 and 2.2 nm below the surface. Each 175 eV ion produces 1.5 recoils, so that the thermal spike model to explain ta-C formation [24] is ruled out for our energy range because the required dense collision cascades do not form. Instead, our results agree with the subplantation model that predicts ﬁlm densiﬁcation and transition from trigonal to tetrahedral bond coordination with maximum eﬃciency at ion energies around 100–150 eV [25]. The presence of a reactive gas such as nitrogen during the ablation process aﬀects plasma characteristics and laser energy absorption. In general, gas

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Fig. 14. Calculated coherence length La versus I D /I G for carbon ﬁlms prepared by several techniques, in diﬀerent deposition conditions. Diamonds for data from [19]; triangles for cluster assembled ﬁlms deposited in (a) He atmosphere, (b) Ar atmosphere. Dotted interpolation lines from [19]

atoms collisionally cool down hot plasma electrons, with two consequences. First, both electron impact excitation and plasma recombination mechanisms are more eﬀective, and second, the plasma is better conﬁned at the target surface, leading to an increase of particle emission. However, both carbon neutrals and ions emitted from the target react with nitrogen in the plasma region near the target. Reaction kinetics in plasma is strongly accelerated, and a conversion of C2 to CN radical readily occurs. Indeed, the optical

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emission intensity of the C2 Swan band becomes weaker, while the intensity of the CN violet band increases with increasing nitrogen pressure [26]. CN is highly eﬀective to scatter energetic C+ ions in the plasma, thus decreasing their energy. Such a ballistic mechanism reduces C+ ion ability to trigger the transition from sp2 to sp3 bond coordination in the growing ﬁlm. Besides this, CN is transported at the growing ﬁlm surface where it is incorporated. The presence of nitrogen in the growing DLC ﬁlm results in an increase of the fraction of sp2 bonded carbon with increasing nitrogen content [14]. Thus both ballistic and chemical mechanisms inhibit ta-C formation when pulsed laser deposition is performed in the presence of nitrogen. 4.2 High-Pressure Deposited Films With respect to ﬁlm synthesis by pulsed laser deposition in vacuum, or at low ambient gas pressure, PLD at high gas pressure is a recent process. In the case of carbon ﬁlms only a few studies were devoted to the formation of cluster-assembled ﬁlms [8, 27], whose molecular structure depends on the conditions both of cluster formation during plume ﬂight and of cluster landing on the substrate. The presence of a nonreactive gas (helium, or argon, in our experiments) in the deposition chamber, at high pressure pHe;Ar from 30 Pa to 2 kPa leads to carbon cluster condensation in the plume. The net result is the above-discussed sequence of morphologies in the growing ﬁlm. The scarce amount of tetrahedral sp3 bond coordination in all ﬁlms, irrespective of laser power density, is due to relevant scattering of plume constituents from ambient gas and the associated cooling down of the plume to a plume– ambient gas equilibrium temperature. In agreement with previous results [28], with respect to plume propagation in vacuum, we visually observed: (a) enhanced visible ﬂuorescence, as induced by collisions, of the expanding plume front (b) spatial conﬁnement of the plume, associated with a drastic change of its shape Within the range of the adopted laser parameters, the growth rate of a typical carbon cluster is considerably higher than the ablation rate of carbon atoms from the target [8]. Thus the number density of carbon atoms in the plume is progressively reduced, while the average cluster size increases. Although the processes associated with the initial stage of plume expansion are highly nonlinear over the isothermal expansion regime that corresponds to the maximum plume density, it is possible to estimate the number of atoms per cluster N using average parameter values, taken over a longer time scale. In a simple ideal gas approach, N depends on: (a) The nature of the scattering gas, through the geometrical collision cross section σ. A common value σ = 10−15 cm2 is assumed for σ C−C , for σ C−He and for σ C−Ar .

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(b) The number density of the inert gas n. (c) The number density of the ablated species, na . Both plume conﬁnement and the collision rate of individual C atoms with a growing cluster increase with increasing n. Sticking coeﬃcient of 1 and identical behaviour of energetic neutrals and C+ ions are assumed. Energetic neutrals most likely arise from charge transfer reactions, each involving a fast carbon ion and a slow gas atom. (d) The average escape velocity v e of ablated species. When v e increases, the time interval between two successive attachment events of individual C atoms to a growing cluster decreases. (e) The average cluster formation time, tf . This is shorter than the target– substrate time-of-ﬂight because below a minimum value of the number density of ablated particles na the plume becomes noncollisional. On the basis of the above considerations, the number of carbon atoms in a cluster may be estimated as: N = nna σ 2 (v e tf )2 , where the product of the cross section times the number density of gas atoms, n or that of ablated atoms, na , indicates the probability of a carbon atom to be scattered by, or attached to the cluster, respectively. Ablation experiments performed in geometric and energetic conditions similar to the present ones [29] give na ∼ 1017 cm−3 . In the absence of details on plume energetics we assume tf to be half of the target–substrate time-of-ﬂight for fast species in the plume. With a target–substrate distance of 6 cm, and v e ∼ 5 × 105 cm s−1 [8], we obtain tf ∼ 5 × 10−6 s. At the lower limit of ambient gas pressure pHe;Ar = 30 Pa, n is 7.4 × 1015 cm−3 , while at the opposite limit of highest pressure pHe;Ar = 2 kPa, n is 5 × 1017 cm−3 . The average number of carbon atoms in a cluster ranges from N = 5 × 103 (pHe;Ar = 30 Pa), to N = 5 × 105 (pHe;Ar = 2 kPa). We take a value of 0.14 nm for the atomic radius of carbon, to which corresponds an estimated ﬁlm density of 1.8 gcm−3 , a typical value for porous nano-glassy carbon ﬁlms. If we assume that clusters are spherical, the data give cluster diameters of 4.7 nm and 22 nm, respectively. Although rough, such an estimate of cluster size is in agreement with the previously discussed coherence length La values deduced from the ﬁtting of Raman spectra for cluster-assembled ﬁlms deposited at pHe;Ar up to 250 Pa and with TEM observations of cluster size.

5 Conclusions In conclusion, we prepared carbon ﬁlms by pulsed laser deposition in vacuum, in a reactive, low-pressure molecular nitrogen atmosphere and in highpressure atmospheres of inert gases with diﬀerent mass, such as helium and

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argon. We investigated by vibrational spectroscopies the structure of the deposited ﬁlms. In vacuum, sp3 bond coordinated ta-C is obtained above a threshold power density P t of 5 MW mm−2 . Both ballistic and chemical mechanisms inhibit the transition from mainly graphitic to ta-C in ﬁlms deposited in the presence of nitrogen. At high inert gas pressure, clusterassembled, nano-glassy, sp2 bond coordinated ﬁlms, with strongly diﬀerent morphologies, are obtained as functions of the gas species and pressure as well as of the laser power density. Cluster sizes estimated from experiments are in agreement with those predicted by a simple model of cluster synthesis in the ablation plume. Acknowledgements The authors are grateful to M. Bonelli and P. Mosaner, Department of Physics, University of Trento; and to A.P. Fioravanti and D. Bolgiaghi, Department of Nuclear Engineering, Politecnico di Milano, for ﬁlm deposition; to V. Russo, Department of Nuclear Engineering, Politecnico di Milano, for assistance with Raman spectroscopy; and to C. Castiglioni, Department of Chemistry, Applied Chemistry and Materials, Politecnico di Milano, for useful discussions on the interpretation of vibrational spectra of carbon-based materials. A.C. Ferrari, Department of Engineering, University of Cambridge, performed UV Raman and EELS measurements.

References [1] J. Robertson: Mater. Sci. Eng. R 27, 1 (2002) 360 [2] A. C. Ferrari: Surf. Coat. Technol. 190, 180–181 (2004) 360 [3] M. Bonelli, A. Miotello, P. Mosaner, C. Casiraghi, P. M. Ossi: J. Appl. Phys. 93, 859 (2003) 360 [4] Marquardt, R. T. Williams, D. J. Nagel: in R. Chang, B. Abeles (Eds.): Plasma Synthesis and Etching of Electronic Materials, vol. 38 (Materials Research Society Symposium Proceeding, Boston 1985) p. 325 360 [5] A. A. Voevodin, M. S. Donley: Surf. Coat. Technol. 82, 199 (1996) 360 [6] M. Bonelli, A. C. Ferrari, A. P. Fioravanti, A. Miotello, P. M. Ossi: in J. Sullivan, J. Robertson, O. Zhou, T. Allen, B. Coll (Eds.): Amorphous and Nanostructured Carbon, vol. 593 (Materials Research Society Symposium Proceeding, Boston 2000) p. 359 360, 364 [7] R. F. Haglund: Laser Absorption and Desorption (Academic, London 1998) p. 15 361 [8] A. V. Rode, E. G. Gamaly, B. Luther-Davies: Appl. Phys. A 70, 135 (2000) 361, 376, 377 [9] M. Bonelli, C. Cestari, A. Miotello: Meas. Sci. Technol. 10, N27 (1999) 361 [10] C. Mapelli, C. Castiglioni, G. Zerbi, K. M¨ ullen: Phys. Rev. B 60, 12710 (1999) 363

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[11] M. Rigolio, C. Castiglioni, G. Zerbi, F. Negri: J. Molec. Struct. 79, 563–564 (2001) 363 [12] B. Dishler: in H. Hintermann, J. Spitz (Eds.): Metallurgical Coatings and Materials Surface Modiﬁcations, vol. 17 (European Materials Research Society Symposium Proceeding, Strasbourg, FR 1987) p. 189 363 [13] A. C. Ferrari, J. Robertson: Phys. Rev. B 61, 14095 (2000) 364, 365, 372 [14] J. R. Shi, X. Shi, Z. Sun, E. Liu, B. K. Tai, S. P. Lau: Thin Solid Films 366, 169 (2000) 364, 365, 376 [15] K. W. R. Gilkes, H. S. Sands, D. N. Batchelder, J. Robertson, W. I. Milne: Appl. Phys. Lett. 70, 1980 (1997) 364 [16] P. J. Fallon, V. S. Veerasamy, C. A. Davis, J. Robertson, G. A. J. Amaratunga, W. I. Milne: Phys. Rev. B 48, 4777 (1993) 367, 374 [17] Z. Czigany, G. Radnoczi: Thin Solid Films 5, 343–344 (1999) 368 [18] F. Tuinstra, J. L. Koenig: J. Chem. Phys. 53, 1126 (1970) 372 [19] D. S. Knight, W. B. White: J. Mater. Res. 4, 385 (1989) 372, 375 [20] D. Bolgiaghi, A. Miotello, P. Mosaner, P. M. Ossi, G. Radnoczi: Carbon 43, 2122 (2005) 373 [21] Y. Yamagata, A. Sharma, J. Narayan, R. M. Mayo, J. W. Newmann, K. Ebihara: J. Appl. Phys. 86, 4154 (1999) 373 [22] B. Angleraud, J. Aubreton, A. Catherinot: Eur. Phys. J. A 5, 303 (1999) 374 [23] J. F. Ziegler, J. P. Biersack: The Stopping and Ranges of Ions in Matter SRIM –2000.10 374 [24] H. Hofs¨ ass, H. Feldermann, R. Merk, M. Sebastian, C. Ronning: Appl. Phys. A 66, 153 (1998) 374 [25] Y. Lifshitz, S. R. Kasi, J. W. Rabelais: Phys. Rev. Lett. 62, 1290 (1989) 374 [26] S. Aoqui, K. Ebihara, T. Ikegami: Composites B 30, 691 (1999) 376 [27] E. Cappelli, S. Orlando, G. Mattei, C. Scilletta, F. Corticelli, P. Ascarelli: Appl. Phys. A 72, 2063 (2004) 376 [28] D. Geohegan, in D.B. Chrisey, G. Hubler (Eds.): Pulsed Laser Deposition of Thin Films (Wiley, New York 1994) p. 115 376 [29] M. Bonelli, A. Miotello, P. M. Ossi, A. Pessi, S. Gialanella: Phys. Rev. B 59, 13513 (1999) 377

Index sp2 -bonded clusters cluster size, 359, 372, 376, 377 sp3 /sp2 bonding ratio, 360, 374 ta-C, 360, 362–365, 367, 373, 374, 376, 378 atomic force microscopy (AFM), 361, 371–373 background gas, 371, 372, 376, 377 C24 , 363

C60 , 359 cluster assembled (CA) ﬁlms, 362, 368–375, 377 cluster-assembled (CA) ﬁlms, 372, 376, 378 clustering, 360 coatings, 360 biomedical coatings, 360 coherence length, 372, 377 columnar ﬁlm, 367, 368, 371 node-like ﬁlm, 367, 368, 371

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D band, 364 D/G band intensity ratio, 366, 375 D/G band intensity ratio, 364, 372 dendritic ﬁlm, 367, 371 diamond, 359 diamond-like carbon (DLC), 359, 360, 362, 363, 365, 368, 376 electron energy loss spectroscopy (EELS), 361, 362, 367, 368 friction coeﬃcient, 360 fullerene, 359 G band, 364 graphite, 359 hardness, 360 infrared (IR) spectroscopy, 361–364 nano-glassy carbon, 372, 377

nanotubes, 359 nitrogen, 374, 376, 377 optical properties, 360 plasma plasma plume, 361, 373 pulsed laser deposition (PLD), 360, 361, 376 Raman spectroscopy, 362–365, 371, 373 scanning electron microscopy (SEM), 361, 362, 367, 369–371 subplantation model, 374 T band, 364, 365 T/G band intensity ratio, 366 T/G band intensity ratio, 365 transmission electron microscopy (TEM), 361, 373, 377

Raman Spectra and Structure of sp2 Carbon-Based Materials: Electron–Phonon Coupling, Vibrational Dynamics and Raman Activity Chiara Castiglioni1 , Fabrizia Negri2 , Matteo Tommasini1 , Eugenio Di Donato1 , and Giuseppe Zerbi1 1

2

INSTM and Dipartimento di Chimica, Materiali e Ingegneria Chimica “G. Natta”, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy [email protected] INSTM and Dipartimento di Chimica “G. Ciamician”, Universit` a di Bologna, Via Selmi 2, I-40126 Bologna, Italy [email protected]

Abstract. We focus on several common features that dominate the Raman spectra of carbon materials whenever delocalised π electrons are present. A molecular approach, based on high-level quantum chemical calculations and experiments on molecular models, allows us to predict the evolution of these features with the relevant structural parameters, namely the size and topology of the conjugated domains. These results allow us to obtain insight on the eﬀect of the conﬁnement (in both one and in two dimensions) of conjugated electrons in terms of electronic structure as well as of nuclear geometries. On the other hand, the relevant physical mechanisms that govern the spectroscopic response of theses systems can be successfully predicted in a very simple and general way in the frame of the H¨ uckel theory. The generalisation of this theory to the determination of a vibrational potential for a two-dimensional (2D) crystal (graphene) and for carbon nanotubes of any diameter and chirality is presented and discussed in this work.

1 Introduction Raman spectroscopy is a widely used technique for nondestructive analysis of solid-state samples of newly developed carbon materials. These materials range from nanocristalline diamond, ﬁlms of diamond-like carbon, a variety of amorphous carbons, carbon ﬁbres and whiskers, carbon nanotubes, nanocrystalline or microcrystalline graphites, and structurally controlled graphenes. There are two aims of this research activity: (a) To obtain a characterization of the materials through the detection of spectroscopic markers, the determination of their characteristic parameters (frequency, band width and shape, line intensity) and of their changes with respect to the material synthesis and/or treatment (thermal history, G. Messina, S. Santangelo (Eds.): Carbon, The Future Material for Advanced Technology Applications, Topics Appl. Phys. 100, 381–403 (2006) © Springer-Verlag Berlin Heidelberg 2006

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annealing, mechanical treatment, laser damaging, etc.). This activity required the collection of a large amount of experimental data and the development of useful empirical correlations. (b) To obtain an understanding of the physical origin of the spectroscopic response. This kind of investigation requires the help of theory, models and simulations. As a consequence of this approach, several structure/properties relationship have been obtained that are useful as guidelines for the tailoring of the material properties through the modulation of the structural parameters at the nanoscale. An “output” of point (b) is a wide collection of computer simulations of the spectroscopic behaviour of the materials modelled, which indeed gives strong support also to the activity described in point (a). The contribution of the authors of this work mainly concerns point (b). During about ﬁve years of activity on graphitic materials, mainly based on Raman experiments on polycyclic aromatic hydrocarbons (PAHs) [1] and quantum chemical computations on molecular models [2, 3, 4, 5, 6], we have collected a lot of evidence of the intimate relationship between the molecular structure (size of the molecule, topology of the edges, bond lengths, etc.) and the electronic structure of these systems. This evidence formed the basis for the interpretation of the spectroscopic behaviour of much more complex materials whose structure is usually not known or only approximately known [6]. On the other hand, extrapolation to carbon materials requires that a bridge is built, linking the properties of molecules (oligomers) to those of their inﬁnitely extended parents, describing ideal crystals. This can be done if common theoretical models are applied for the prediction of properties both of molecules and of crystals. One of the most intriguing problem arising in the study of the vibrational spectra of polyconjugated systems is the need of knowing vibrational potentials, which are expected to be strongly sensitive to properties such as the delocalisation/conﬁnement of π electrons. Moreover, they are also inﬂuenced by bond topologies, defects, etc. In this paper we will discuss the results obtained by the generalisation of the Kakitani equations [7], developed for constructing valence force ﬁelds for a variety of conjugated molecules. The treatment is based on the simple H¨ uckel theory, ﬁrst developed for the modelling of the electronic structure of conjugated organic molecules, and can be easily extended to inﬁnite two-dimensional (graphene) and one-dimensional (polyacetylene and carbon nanotubes) crystals. On this basis we will show that the wide family of materials, characterised by the presence of carbon atoms in sp2 hybridization state, is aﬀected by common physical mechanisms which can be described in terms of simple physical models of general validity. In particular, at the basis of their spectroscopic behaviour, is the existence of an eﬃcient and selective electron–phonon coupling, which is responsible for relevant changes of the electronic structure whenever collective nuclear displacements along preferential paths take place. The introduction of the concept of electron–phonon coupling allows us to explain several experimen-

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tal results from Raman spectroscopy (activation, resonance enhancement, frequency dispersion of speciﬁc Raman transitions). Moreover, it provides a key for the interpretation of other independent experimental ﬁndings, such as, for instance, STM images recently obtained across step edges in highly oriented pyrolytic crystalline graphite (HOPG) [8]. The natural follow-up of the concepts developed is the analysis and the interpretation of the Raman spectra of carbon nanotubes, which still presents several unsolved questions. It is surprising that the same physical concepts proposed about 20 years ago for the interpretation of the vibrational spectra of polyconjugated polymers work very well also in the case of more complex systems characterised by the presence of domains formed by condensed aromatic rings (graphitic domains). These kinds of structures can be ideally thought as pieces of matter obtained from an inﬁnite graphite sheet (2D crystal), and they can be described as structurally modiﬁed graphenes. Structural modiﬁcations can be described as: (i) Conﬁnement: this happens in the case of molecules (which have indeed a ﬁnite size) and in microcrystals and/or nanocrystals by eﬀect of edges of diﬀerent topologies. (ii) Curvature: this is, for instance, the case of fullerenes and carbon nanotubes. Notice that in these cases the curvature is accompanied by conﬁnement. (iii) Defects: a variety of defects can be found ranging from those created by laser damage, ion implantation or chemical doping to those already present in the material as obtained, such as, for instance defects due to the copresence of sp3 carbon phase in amorphous carbon ﬁlms.

2 Raman Spectra of Polyconjugated Materials As illustrated in the Chapter by Zerbi et al. (pp. 23–53), the presence of delocalised π electrons in polyconjugated polymers makes their Raman response very peculiar. Raman spectra of polyenes [9] are characterised by few, strong lines (in simple all-trans polyenes and polyacetylene only two lines dominate the Raman spectrum), very sensitive to resonance enhancement when the laser energy approaches their optical energy gap. By comparison of the Raman spectra of simple polyenes of increasing chain length, one can readily verify that the Raman frequencies of the main two lines show a systematic, pronounced softening of the characteristic frequencies. In a parallel way any polyacetylene sample shows frequency shifts of the two strong Raman lines (peak maxima at 1472 cm−1 and 1060 cm−1 with near-infrared excitation) while changing the exciting laser energy [10]. Even at the beginning of the Raman investigations on polyacetylene this behaviour was ascribed to the presence of diﬀerent “conjugation lengths” in polyacetylene, each of them characterised by a given energy gap [10]. This fact is easily justiﬁed, both on

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the basis of the presence of chemical defects and as due to a wide distribution of molecular weights, which usually happens in polymer synthesis. Few chains in the distribution are selectively probed in the Raman spectrum when the laser energy fulﬁlls their suitable resonance condition: this is the origin of the observed frequencies softening while decreasing the laser energy. At a ﬁrst sight, the Raman spectrum of graphites shows few points in common with that of conjugated chains: namely, also in this case, the ﬁrst-order features are few, relatively strong and sensitive to the laser energy. Highly ordered and crystalline graphite has a very simple ﬁrst-order Raman spectrum, showing a strong G line at 1580 cm−1 , in agreement with the Raman selection rules for the 2D crystal (a perfect graphene sheet) characterised by just one optical phonon (of E 2g symmetry) at the Γ point in the ﬁrst Brillouin zone. A G band (showing sometimes modest frequency shift and line broadening) is always observed in any sample which contains some amount of carbon in the sp2 -hybridization state. However, the relevant feature in the case of graphitic materials containing some kind of structural defects (ranging from sp2 -rich amorphous carbons to microcrystalline graphites) is the appearance of a strong Raman band, the so-called D band, between 1250 and 1350 cm−1 . This feature shows a systematic frequency softening while decreasing the energy of the exciting laser and undergoing resonance enhancement [11]. The origin of the D band has been discussed for a long time in the literature. Thomsen et al. [12] developed a solid state theory approach based on a double resonant process, activated by the disorder. The authors of the present paper proposed a diﬀerent approach, mainly based on molecular spectroscopy [2, 3, 4, 5, 6]. As discussed also in the Chapter by Zerbi et al. (pp. 23– 53), the conclusions reached through the “molecular approach” brought to the idea that the D line (and its frequency dispersion) is the evidence of a distribution of conﬁned domains in disordered graphites. As in the case of polyacetylene, according to their characteristic energy gap (modulated by the conﬁnement) diﬀerent graphitic domains (showing diﬀerent D line frequency) are selectively probed by resonance while varying the energy of the exciting laser in the Raman experiment [13]. What is really new, with respect to the case of polyacetylene, is the fact that the D line is perfectly silent in the Raman when the material approaches the limit of a perfect 2D crystal. The aim of this paper is to show that it is possible to discuss analogies and diﬀerences shown by Raman spectra of conjugated chains and graphenes on the basis of the concept of electron–phonon coupling. Its main eﬀects (in terms of electronic structure, nuclear arrangement, vibrational dynamics and potential) will be described in a simple but conceptually powerful way in the frame of the H¨ uckel theory.

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(a)

(b)

ν = 1476 cm−1 I = 1.0 106 A4 /amu

ν = 1122 cm−1 I = 0.82 106 A4 /amu Fig. 1. (a) Sketch of the nuclear displacements associated with R− coordinate of polyene chains and polyacetylene (b) Sketch of the nuclear displacements associated with Raman-active normal modes (R− modes, see text) of a trans polyene chains with 22 carbon atoms. Eigenvectors, frequencies and nonresonant Raman intensities have been obtained from DFT BLYP 6.311G** calculations [14]

3 Electron–Phonon Coupling and Raman Features 3.1 Electron–Phonon Coupling in Polyacetylene Since from the ﬁrst experimental determination on polyacetylene and polyenes, the evidence of conjugation length-dependent Raman spectra suggested that the very origin of such a behaviour was the existence of a long-range, conjugation length-dependent, intramolecular potential [15]. Many valence force ﬁelds were proposed in the past to include this eﬀect. One of the most widely debated points was to establish the range of extension of interactions described by nondiagonal harmonic force constants involving CC stretching coordinates of the polyene chain. Values and extension of these interactions are indeed expected to be modulated by the degree of delocalisation of π electrons. The wide literature about polyacetylene vibrational force ﬁelds is referred to and commented on in the review by Gussoni et al. [16], to which the interested reader is addressed. In this paper we would like to recall only a few of the relevant points of this discussion. It is remarkable that, in the eﬀort to reproduce the experimental ﬁndings, several authors developed diﬀerent empirical force ﬁelds for “long chain polyacetylene” and for “short chain polyacetylene” [17, 18]. Still on the side of the empirical valence force ﬁelds we would like to mention the results of the “eﬀective conjugation coordinate theory”(ECCT) [19]. According to the ECCT, the eﬀect of the π electron delocalisation on the intramolecular potential is accounted for by the diagonal force constant (FR− ) associated with the collective valence coordinate (R− coordinate) which describes the oscillation of the bond alternation (simultaneous stretching of CC double bonds and shrinking of CC single bonds in the whole chain). As far as the conjugation length increases, the value of FR− decreases with a consequent softening of the Raman frequencies associated

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with vibrational modes involving oscillation of bond alternation. The ECCT for polyacetylene brought the following important results: – It showed that a special nuclear trajectory (along the R− direction) does exist, which is strongly sensitive to the π electron structure (Fig. 1a). – It showed that the two strong Raman lines of polyacetylene and polyenes are due to R− modes, that is, to modes with high “content” of the dimerisation oscillation (Fig. 1b). Moreover their Raman intensity and resonance enhancement is due to the large polarization change associated with this peculiar nuclear displacement. It is remarkable that until the introduction of high-level ab-initio Moller– Plesset (MP2) quantum chemical (QC) predictions [20, 21] or density functional theory (DFT) methods [14,22,23], ﬁrst-principle calculations of the Raman spectra of simple polyenes (based on Hartree–Fock approximation) [24] were unable to give a reasonable prediction of the observed Raman features. Quite localised CC stretching interactions were obtained by these methods and (as a direct consequence) a very modest frequency dispersion with polyene length was predicted for Raman-active bands. In contrast, semiempirical force ﬁelds built on the basis of a quantum mechanical description restricted to π electrons allowed one to give a correct prediction of the Raman frequencies dispersion. Among others, the best results were obtained by the QCFF-π methods [25, 26, 27]. An even simpler model that allows one to treat longrange CC stretching interactions is based on the H¨ uckel theory. In this frame, according to the derivation proposed by Coulson [28, 29, 30], Kakitani [7] developed expressions for valence force constants involving CC stretching at any distance along a polyconjugated chain (1): ∂2E ∂2E σ ∂2E π = + ∂Ri ∂Rj ∂Ri ∂Rj ∂Ri ∂Rj 2 2 ∂β ∂ β = kσ + 2 2 pi δij + 2 Πij ∂R ∂R ∗ ∗ ∗ ∗ (Cλo Cµe + Cλe Cµo ) (Cνo Cσe + Cνe Cσo ) = + c.c. εo − εe o,e

fij ≡

Πλµ,νσ

(1) (2)

The “ingredients” that appear in the Kakitani expressions are: (a) Bond–bond polarizabilities (Πij ), which can be simply calculated from molecular orbital coeﬃcients for π states as obtained according to the diagonalisation of the H¨ uckel Hamiltonian for the chain considered (2). In (2) the symbols λ, µ and ν, σ refer to the pair of carbon atoms which deﬁne, respectively, the bond i and the bond j. Πij terms are obtained in units of β (the H¨ uckel hopping integral between adjacent atomic sites, which at the 0th-order approximation is assumed to be a constant of identical value (β0 ) for each pair of adjacent carbon atoms).

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(b) Kσ : a force constant relative to the (localised) contribution of σ electrons, which can be treated as an adjustable empirical parameter (σ contributions are described as classical springs which aﬀect only the diagonal CC stretching force constant). (c) The electron–phonon coupling term, namely the parameter (∂β/∂R) which describes the modulation of the electronic states (through the hopping integral) by the stretching of CC bonds. (d) A term consisting of the product of the second derivative of the hopping integral and the bond order pi . This parameter aﬀects only the diagonal force constants and can be combined with Kσ in order to deﬁne an “effective” adjustable diagonal parameter Fi (ﬁrst term in parethesis, (1)). According to (1) and (2), H¨ uckel theory allows us to determine CC stretching interactions between the bonds i and j at any given distance, provided that the molecular orbital coeﬃcients for the π states are calculated. The introduction of a few empirical parameters, namely β0 , ∂β/∂R and Fi , is required in order to obtain the harmonic intermolecular potential involving the CC stretching coordinates. The remaining force constants (involving CH stretching, bending and bending/stretching interactions) can be assumed independent from conjugation length and described by short-range interactions in terms of a set of a few empirical parameters. Notice, moreover, that in its simpler form the theory makes use (for the deﬁnition of the Hamiltonian, which in turn determines the Πij parameters) of just one average hopping integral between adjacent sites, namely β0 . It is, however, possible to choose diﬀerent values for βij in order to explicitly consider the existence of a bond alternation in the equilibrium structure. In the case of equilibrium structures showing alternation of double and single bonds, as in the case of polyacetylene, this choice can be expressed through the deﬁnition of β1 and β2 parameters for the single and the double bonds, respectively, which in turn can be written (within a linear approximation of β(R)) as: β1 = β0 + 1/2(∂β/∂R)∆R and β2 = β0 − 1/2(∂β/∂R)∆R. Notice that in this case another empirical parameter is required, namely the value of equilibrium bond alternation ∆R (otherwise referred to as “dimerisation parameter”, u). Kakitani formulas have been extended to the case of an inﬁnite chain (i.e., polyacetylene, regarded as an inﬁnite one-dimensional crystal) by Piseri et al. [31, 32], obtaining a valence force ﬁeld with seven empirical parameters. This has been done considering that polyacetylene orbitals now have the form of Bloch functions. Accordingly, the 2 × 2 H¨ uckel Hamiltonian of the perfect crystal (which indeed corresponds to a simple one-electron tight binding Hamiltonian for π electrons) gives wave vector-dependent coeﬃcients of the π states (θ and θ in (3) represent the phase associated with k in the one-dimensional (1D) crystal according to the relationship θ = k · d, where d is the unit traslation parameter and k varies in the ﬁrst Brillouin zone (BZ) of the reciprocal lattice).

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Equation (3) gives the expressions so obtained in [32] for the mutual polarizabilities, where θ and θ label, respectively, Bloch states in the valence (occupied π orbitals, o) and in the conduction (unoccupied π orbitals, e) electronic bands: π π Aλµ (θ, θ )Bνσ (θ, θ ) 1 dθ dθ + c.c. Πλµ,νσ = (2π)2 −π −π εo (θ) − εe (θ ) ∗ ∗ (θ)Ceµ (θ ) + Coµ (θ)Ceλ (θ )] Aλµ (θ, θ ) = [Coλ ∗ ∗ (θ ) + Coσ (θ)Ceν (θ )] . Bνσ (θ, θ ) = [Coν (θ)Ceσ

(3)

In [32] the above formalism has been used in order to obtain semiempirical phonon dispersion relations for polyacetylene. Since long-range interactions are modulated by the parameter (∂β/∂R), they obtained diﬀerent dispersion curves while varying the strength of the electron–phonon interaction. Notice that in [32] for any choice of (∂β/∂R), four adjustable parameters of the ﬁeld were determined in such a way that the frequency values observed for “long-chain polyacetylene” (lower limit of the observed Raman lines) were predicted. In this way the change of (∂β/∂R) results in a deeper and deeper dispersion of the two phonon branches associated with the strongest Raman active transitions (R− phonons). No softening is allowed for k = 0 modes, due to the procedure followed for the reﬁnement of the adjustable parameters. On the other hand, if the empirical parameters diﬀerent from (∂β/∂R) are kept ﬁxed, frequency calculations also give a remarkable softening of k = 0 modes of R− branches as the electron–phonon coupling parameter increases in value. This softening is still associated with an increase of the positive slope of such phonon curves. This last result can be put in relation with the ECCT and rationalised with the introduction of the following expression for the diagonal collective force constant FR− for polyacetylene: FR− =

1 (K C=C + K C−C ) − [−f n C=C − f n C−C + 2f n C=C,C−C ] , (4) 2 n

where f n C=C (f n C−C ) are nondiagonal CC stretching force constants between double C=C (single C–C) bonds at distance n along the chain; these constants are always negative. f n C=C,C−C are nondiagonal CC stretching force constants describing interactions between single and double bonds at distance n and result in positive values. According to (4), it can be realized that an increase in the values of the constants in the squared brackets and/or an increase of the range of interactions (number of the terms of the sum) give rise to a higher positive sum. Notice that as far as the sum increases in value, we obtain a decrease of FR− since the sum enters with a minus sign in (4). If now we reconsider interaction force constants (1) as obtained according to the Kakitani relationships, we can immediately correlate the softening of FR− with conjugation length (as prescribed by ECCT) to two possible effects: (i) increase in value of the electron–phonon coupling parameter (which

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450 400 350 300

Raman CC stretching parameter

250 200 150 100 50 0 -50 -100 -150 -200 -250 -300 -350 -400 -450 1

2

3

4

5

6

7 8 9 10 11 12 13 14 15 CC bond position (odd positions are C=C)

16

17

18

19

20

21

Fig. 2. Local Raman CC stretching parameters (α = 1/3 Tr(∂α/∂RCC )) as predicted according to DFT 6.311G** calculations for a polyene chain with 22 carbon atoms [14]. Units are bohr2 . Notice the change of the sign while passing from double to single CC bonds

gives rise to an increase of the values of all nondiagonal interactions) and (ii) widening of the range of interaction (increasing the number of terms in the sum). Notice that in the case of polyenes (i.e., for molecules with a ﬁnite size), this range is necessarily determined by the number of bonds forming the chain. In conclusion, with the help of the simple H¨ uckel theory applied to polyacetylene we can predict: – the existence of a long-range, conjugation length-dependent, intermolecular potential, involving interaction of CC stretching coordinates – the consequent softening of two peculiar Raman-active modes which are characterised by a large content of the bond alternation oscillation (R− modes) – the origin of the eﬀective conjugation force constant FR− in terms of electron–phonon coupling It is important at this point to stress that one of the key points in the physics of polyacetylene is the existence of an energy gap due to Peierls distortion of the 1D crystal structure [33]. In terms of H¨ uckel theory this gap opening is just expressed as: E gap = 2

∂β · u = 2∆β, ∂r

(5)

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where u represents the equilibrium bond length alternation, i.e., the “distortion” (along R− ) from a perfectly “equalised” metallic structure to a “dimerised” equilibrium structure. In other words, (5) states that a peculiar trajectory in the vibrational space (namely the trajectory described by R− ) does exist, which is coupled to π electrons to such extent that it determines a transition between a metal (ideal polyacetylene, with u = 0) and a semiconductor. According to this statement, it is obvious why ECCT works so well. Indeed, in ECCT the explicit introduction of the R− coordinate in the description of the molecular dynamics allows one to “summarize” in just one parameter (FR− ) the eﬀect of the electron–phonon interaction and its dependence on the conjugation length of the chains. The evidence of bond alternation is also preliminary to any discussion regarding Raman activities of R− modes. According to DFT calculations performed on many simple polyenes of diﬀerent length [14], we demonstrated that local Raman parameters (polarizability changes associated with the stretching of individual CC bonds) are characterised by opposite sign according to the character of the CC bond considered (single or double), as shown in Fig. 2. This sign rule has the eﬀect of determining a huge polarization change with the bond alternation oscillation, namely during R− modes. On the other hand, if we ideally remove bond alternation, we expect to obtain a vanishing polarization change during R− according to the new vibrational selection rules (the crystal symmetry at k = 0 passes from C 2h to D2h , and R− modes become infrared-active and silent in the Raman spectrum). This fact can also be explained in terms of local stretching Raman parameters which, because of the symmetry, are forced to be equal (same sign and value!) for all the CC stretching of the “metallic” chain. 3.2 Electron–Phonon Coupling in Graphenes The idea is now to extend the simple treatment illustrated in Sect. 3.1 to the case of graphenes. In [2] the Kakitani approach has been applied to a perfect graphite sheet (2D crystal) and to several PAH molecules, seen as oligomers of 2D graphite. The force ﬁeld used is that derived by Ohno [34] for small PAHs, following the same derivation proposed by Kakitani. In the Ohno treatment long-range interaction CC stretching force constants are expressed through three adjustable parameters according to the following equations: fii = f1 + f2 (pi − p0 ) + f3 (Πii − Π0 ) , fij = f3 Πij i = j,

(6)

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where p0 and Π0 are the “reference” bond order and self-polarizability of the benzene molecule. Equation (6) can be put in correspondence with Kakitani formulas to obtain (7). ∂2β f1 = kσ + 2 2 p0 + 2 ∂R ∂2β f2 = 2 2 . ∂R 2 ∂β . f3 = 2 ∂R

∂β ∂R

2 Π0 .

(7)

The important point is to notice that the constant f3 is determined by the value of electron–phonon coupling parameter ∂β/∂R. Also in the case of Ohno ﬁeld, the range of interaction (and its decreasing law with bond distance) is then determined by the mutual polarizabilities, as obtained in the frame of the H¨ uckel theory. In the case of graphite these terms have to be calculated taking advantage of the translational symmetry, as illustrated in [2] and starting from (8): π π π π fλµ,νσ (θ1 , θ2 , θ1 , θ2 ) 1 dθ dθ dθ Πλµ,νσ = 1 2 1 , θ ) dθ2 + c.c. 4 (2π) −π ε (θ , θ ) − ε (θ o 1 2 e −π −π −π 1 2 fλµ,νσ (θ1 , θ2 , θ1 , θ2 ) = gλµ (θ1 , θ2 , θ1 , θ2 )hνσ (θ1 , θ2 , θ1 , θ2 ) ∗ ∗ (θ1 , θ2 )Ceµ (θ1 , θ2 ) + Coµ (θ1 , θ2 )Ceλ (θ1 , θ2 )] gλµ (θ1 , θ2 , θ1 , θ2 ) = [Coλ

∗ ∗ (θ1 , θ2 ) + Coσ (θ1 , θ2 )Ceν (θ1 , θ2 )] . (8) hνσ (θ1 , θ2 , θ1 , θ2 ) = [Coν (θ1 , θ2 )Ceσ

Here, θ1 and θ2 are the phases associated with displacements along a1 and a2 , respectively, in the 2D graphite crystal (θ1,(2) = 2πk1,(2) ; k = k1 b1 +k2 b2 , where b1 and b2 are primitive vectors of the reciprocal 2D lattice of graphite). The use of the complete set of adjustable Ohno parameters gave the phonon dispersion curves published in [2]. In Fig. 3 we illustrate the eﬀect of the change of the electron–phonon coupling constant (through the f3 parameter) on the dispersion relation of graphite phonons. The f3 value as reﬁned by Ohno [34] and used in [2] corresponds to the red plots. It is apparent that the more relevant eﬀect obtained by changing the value of f3 is on the higher frequency branch near K point, to which belong the socalled A phonon of A1 symmetry at K (Fig. 4). According to the “molecular approach” described in [2, 3, 4, 5, 6], this vibration has been associated with the strong D line, shown by the Raman spectra of defected graphites and disordered carbon phases. Moreover, the phonon curve showing strong electron–phonon coupling dependence in Fig. 3 has been indicated as that involved in the doubleresonant process proposed by Thomsen [35]. This same phonon branch has been recently investigated by high-level DFT calculations, which revealed a

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Fig. 3. In plane phonon dispersion curves obtained for a 2D graphene crystal according to Ohno force ﬁeld [2]. Diﬀerent colors correspond to diﬀerent choices of the f3 parameter (diﬀerent electron–phonon coupling constant). Blue: f3 = 2.000 mdyne/A; green: f3 = 3.000 mdyne/A; red: f3 = 3.646 mdyne/A

strong Kohn anomaly, driven by electron–phonon coupling [36]. According to these observations we can state that H¨ uckel theory applied to the construction of long-range interaction valence potential of graphite immediately indicates that the totally symmetric phonon at K is heavily aﬀected by interactions with π electrons. This fact suggests that the selective and strong activation of A modes (D line) in the Raman spectra of graphite samples containing some disorder (e.g., microcystalline graphites, see [11], or conﬁnement, as in PAH molecules) has its origin in a mechanism similar to that found in the case of R− modes of polyacetylene and polyenes. In a recent paper [37] we have shown an alternative, independent demonstration of the eﬃcient electron–phonon coupling of the A phonon with π electrons at K. With a treatment still based on the simple H¨ uckel theory, we have described the eﬀect on the electronic dispersion curves of a graphene crystal, of a nuclear relaxation along the A phonon. As illustrated in Fig. 5, this relaxation (to which a new crystal structure corresponds, described by a threefold unit cell (six carbon atoms) with CC bond characterized by two diﬀerent bond length), is responsible for a gap opening at K point, that is, of a transition from a metallic to a semiconducting phase. The diﬀerence with respect to the case of polyacetylene is the fact that for graphene, the stable phase is the metallic one.

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(a)

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C114 ν = 1291 cm−1 I = 51128 A4 /amu (b)

Fig. 4. (a) Sketch of the nuclear displacements associated with the A phonon (K wave vector, see text) of graphite. (b) Sketch of the nuclear displacements associated with the Raman active transition giving rise to the D band of a PAH molecule with 114 carbon atoms. Eigenvectors, frequency and nonresonant Raman intensities have been obtained from DFT BLYP 6.31G calculations [4]

In presence of defects (or simply in presence of conﬁnement) the graphene structure locally relaxes (preferentially in the direction of the maximum electron–phonon coupling), giving rise to a new crystal structure characterised by a threefold cell. This observation is corroborated by equilibrium structure predictions on model molecules (PAHs) [6], but also by experimental evidence from STM analysis of graphite near to step edges, which indeed shown a periodic superstructure which can be correlated to the structural relaxations described above [8]. Another very important result which can be obtained considering the “dimerised” graphite structure described by the threefold lattice is the consequence of the lattice relaxation on the Raman selection rules. It can be easily seen according to the standard zone folding procedure that the K point of the usual (nonrelaxed) graphene is “folded” on Γ if the lattice relaxes according to the threefold cell. This implies that the totally symmetric phonon at K becomes symmetry-allowed for Raman transition, thus giving an elegant explanation for the activation of the D line as a consequence of disorder (conﬁnement) induced relaxation of the lattice [5]. Another very impressive analogy with the case of polyacetylene can be found considering DFT studies carried out on molecular species (PAHs) [4] aimed at the understanding of their Raman activity in the D band region (A modes). Also in this case the Raman stretching parameters obey a sign

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Fig. 5. (a) Blue curves: electronic structure (π bands) of “regular” graphite (idenuckel tical hopping integral β0 for any CC bonded pair) as obtained according to H¨ theory and considering the conventional graphite cell (2 atoms). Red curves: Same calculation (identical hopping integral β0 for any CC bonded pair) referred to a threefold cell (see text). (b) Electronic structure (π bands) of dimerised graphite (two diﬀerent hopping integrals β1 and β2 for CC bonded pair belonging to the two diﬀerent classes originating by the deformation along the A phonon). The cell considered is the minimal one for the distorted structure with shorter (heavy lines) and longer (light lines) CC bonds (threefold cell, 6 carbon atoms, see sketch (c)). The ﬁrst Brillouin zone of the “regular” graphite and of “dimerised” graphite are represented in the sketch (d)

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rule determined by the bond order of the CC considered. CC bonds in the molecules are indeed arranged according to two diﬀerent classes. In the case of the PAHs characterised by armchair topology of the edges, this “bond dimerisation” gives rise to an equilibrium structure which obeys the so-called Clar’s rule [38] (see Fig. 5c): shorter bonds form six-membered rings and show positive stretching polarizablity parameters; the longer ones, connecting the benzenoid rings, show negative stretching polarizability parameters. During A vibration (which can be described as a collective breathing of the benzenoid rings, Fig. 4b) bonds belonging to a given set (i.e., the shorter ones, forming the rings) oscillate out of phase with respect to (longer) bonds of the second set, with a consequent cooperation in building up a very large change of the total molecular polarizability. Notice that this sign rule cannot be “transferred” to the case of the perfect crystal of graphite because of symmetry: equilibrium structure of graphite is indeed characterised by identical CC bond length (metallic structure) for which the A oscillation is at K point (and then it is forbidden in the Raman). On the other hand, structure relaxation (as, for instance, induced by defects and/or conﬁnement) can make active this peculiar phonon by virtue of the consequent symmetry decrease. The experimental fact that the activation of the A phonon is so selective (no other new and strong features are observed in graphites with defects) strongly supports the existence of a selective electron– phonon coupling and of a preferential path of relaxation of the atoms toward a structure which can be schematically described in terms of the threefold lattice illustrated above. Another look at Fig. 3 indicates that also the phonon responsible for the G band is coupled with π electrons: a softening of the Raman frequency with f3 is indeed observed also for the relative phonon branches, near to the Γ point. In the next section we will report on some preliminary results on carbon nanotubes where this coupling is predicted to determine very peculiar features. 3.3 Electron–Phonon Coupling in Carbon Nanotubes The many works dealing with Raman spectra of single-wall carbon nanotubes (SWNTs) always focus attention on the two major features of the ﬁrst-order spectrum: – the so-called radial breathing modes (RBM) bands, which belong to the lower frequency region of the spectrum (usually observed between 400 and 100 cm−1 ) and show clear, widely discussed and well rationalised frequency dependence on the nanotube diameter and species [39, 40] – the region near 1600 cm−1 , commonly ascribed to phonons related to the G band (Γ = 0, E 2g symmetry) of a perfect graphite crystal Experiments on individual SWNT showed that the frequency degeneracy of the G line (dictated by symmetry in the case of graphite) is removed (as

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expected by the symmetry lowering) in nanotubes, giving rise to two components, usually referred as “G+ ” and “G− ” bands. While the peak position of the higher frequency component (G+ ) seems practically insensitive to tube diameter and chirality, the G− peak shows a frequency decrease while decreasing the tube diameter. Moreover, according to [41] a markedly diﬀerent trend for G− is observed in the case of semiconducting carbon nanotubes with respect to the case of the metallic ones, which show a more pronounced frequency softening while decreasing the tube diameter. It is diﬃcult to imagine a vibrational force ﬁeld which is able to account for these experimental features, using the same force constant values for diﬀerent nanotubes. In order to be quantitative about this point, we have computed the phonon frequency of many diﬀerent SWNTs [42] by transferring the valence force ﬁeld previously derived from graphite [2]. Calculations were performed on the basis of internal vibrational coordinates within the GF Wilson’s formalism [43], taking into account the real “curved” geometry and the full symmetry of any tube. Symmetry considerations allow us to treat the dynamical problem in terms of phonon coordinates built on the basis of the few degree of freedom of the minimal structural unit, which coincides with the graphene cell (only two carbon atoms). On one hand, the advantage of the treatment lies in the fact that phonon frequencies and eigenvectors can be obtained through the diagonalization of a small dynamical matrix (i.e., a 9×9 problem, based on the 9 valence coordinates of the structural unit). On the other hand, and even more important, we obtain a formally identical problem (same dimension, identical mathematical structure) for any nanotube (characterised by the indexes n, m) we would like to consider. According to our treatment, the phase diﬀerence between structural units along the tube are described in terms of a pair of two phase parameters (θ1 , θ2 ) which have exactly the same meaning as for graphite (see Sect. 3.2). However, θ1 and θ2 now obey well-deﬁned quantization relationships, dictated by the structure of the nanotube considered, according to (9): k · C h = 2πµ k · T = ξ,

(9)

where k is the wave vector in the reciprocal space, C h the chiral vector (C h = na1 + ma2 , for a n, m nanotube), T is the proper translation vector along the tube axis. θ1 and θ2 can be written in the form described by (10): 2π(2n + m)µ + mdR ξ . 2(n2 + nm + m2 ) 2π(2m + n)µ − ndR ξ θ2 = . 2(n2 + nm + m2 ) θ1 =

(10)

Notice that the index µ can assume only integer values (µ = 0, 1, . . . , 2(n2 + nm + m2 )/gcd((2n + m), (2m + n)), while value ξ assumes rational values between −π and π.

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Explicit calculations of the (k = 0) phonon frequencies in the 1500– 1600 cm−1 range done using a force ﬁeld with common parameters for many nanotubes of diﬀerent chiralities clearly show the degeneracy removal of the G line frequency [42]. This is the direct consequence of the introduction of the appropriate geometries of the nanotubes considered. However, the results obtained with a common ﬁeld do not allow us to account for the experimental frequencies trends observed for G+ and G− lines by Jorio et al. [41]: the predicted range of frequency variation results indeed are very narrow (about 10 cm−1 ) in comparison with the experimental ﬁndings (showing changes of G− frequencies in a range about 80 cm−1 wide). On the other hand, if correctly applied, the simple Kakitani deﬁnition of CC stretching force constants (1) and (9) gives the possibility of adapting the ﬁeld to any desired carbon structure and, in particular, to any SWNT. What we have to do is to obtain the coeﬃcient of the π orbitals (in the form of Bloch functions) for any carbon nanotube with tube indexes (n, m). As in the case of vibrational coordinates, the tube symmetry can be fully introduced for the determination of the electronic structure, thus reducing the H¨ uckel Hamiltonian to the same dimensions (2 × 2) as for graphite. As described above, the important point is to remember that θ1 and θ2 assume now different values for any nanotube considered, as prescribed by (10). In other words, this fact (i.e., “selection” of special θ1 and θ2 values) can be described following the more usual solid state physics language: we have performed a “sampling” (due to the introduction of the new boundary conditions of nanotubes, i.e., due to conﬁnement in one dimension) of the electronic π states of graphite. In this light, it is not surprising to ﬁnd that mutual polarizabilities between bonds at the same distance have diﬀerent values while changing the tube structure (i.e., by changing the n and m parameters appearing in (10)). An explicit expression for Πij can be worked out for any carbon nanotube according to the following equation: Πi(0,0) ,j(n1 ,n2 ) =

π N 1 π 1 n1 ,n2 dξ dξ πij . (2π)2 N 2 −π −π

(11)

µ,µ

n1 ,n2 The function Πij is a known function of µ, µ and ξ, ξ , through θ1 , θ2 , θ1 , θ2 . If we compare (11) with the corresponding one in the case of graphite (8), we immediately realize that two of the four integrals are now replaced by simple sums over the indexes µ, µ . This indeed corresponds to “moving” along discrete lines (one for each µ value allowed) in the ﬁrst BZ of graphite, the path of integration being parametrically described by the variable ξ(ξ ). Values of Πij obtained by numerical integration according to (11) allow us to extend in a fully consistent way the Ohno force ﬁeld already applied to graphite (see Sect. 3.2) to any SWNT. However, despite the relative simplicity of the theory, problems arise from the fact that we have to establish a threshold distance of interaction d: this

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Fig. 6. Raman frequencies of G+ and G− frequencies of nanotubes with decreasing diameters, as predicted according to the valence force ﬁelds described in the text (generalized Ohno ﬁelds). Open circles: armchair (metallic) nanotubes; ﬁlled circles: metallic zig-zag nanotubes; ﬁlled triangles: metallic chiral nanotubes; open squares: semiconducting zig-zag nanotubes; ﬁlled squares: semiconducting chiral nanotubes

implies to arbitrarily put to 0 bond–bond interactions involving CC pairs at distance farther than d. The choice of d is indeed strictly related to the degree of numerical accuracy which we are able to reach in the calculation of integrals. Notice, moreover, that the functions which we have to integrate are oscillating functions, which undergo faster and faster oscillations as the distance of the bonds increases. In light of the above observations, we present the data collected in Fig. 6 as a very preliminary results. On the other hand, the trends of G+ and G− frequencies obtained with our generalised force ﬁelds seem to be a very promising beginning of a more systematic study. A wide dispersion in frequency while decreasing the tube diameters has been obtained; moreover, a diﬀerent behaviour for metallic and semiconducting nanotubes is predicted. An important piece of information which we can extract from these results is the fact that the same electron–phonon coupling parameter (for all the nanotubes considered, f3 has been ﬁxed to the empirical value proposed by Ohno) works in diﬀerent ways in the presence of diﬀerent electronic structures (described by bond–bond polarizabilities calculated on the basis of the suitable π electron states) characteristic of the nanotube considered. The same conclusion about the peculiar role of the speciﬁc electronic structure of any carbon nanotube in determining the vibrational potential was ﬁrst stressed in [44] and illustrated by ﬁrst-principle calculations on armchair carbon nanotubes. In a very simple way, easily generalised to any nanotube structure, our

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treatment clearly states the inadequacy of the usual zone folding procedure often followed in the past to obtain the description of phonons in SWNTs directly from the dispersion curves of graphite.

4 Conclusions A common simple treatment of the harmonic vibrational potential for π conjugated systems consisting of sequences of CC bonds arranged in diﬀerent topologies can be obtained in the frame of H¨ uckel theory for pz electrons. Following this idea, we have extended the original Kakitani [7] equations (ﬁrst derived for molecular systems and then generalized by Piseri et al. to the case of polyacetylene [31]) to the cases of graphite and of carbon nanotubes. Notice that the extension of H¨ uckel theory to inﬁnite systems corresponds to the one electron tight-binding eﬀective Hamiltonian for π electrons, in the language of solid state physics. This formalism allows us to explicitly consider the role of the electron– phonon coupling in determining the Raman response of a wide family of carbon materials. In the theory, the electron–phonon coupling is described by just one parameter, namely ∂β/∂R, and its eﬀect on vibrational potential is modulated by the characteristic electronic properties of the material considered, namely through bond–bond mutual polarizabilities. In this way the model provides a common ground, useful for the comparison of the experimental Raman features observed for many diﬀerent systems. We brieﬂy summarize here the main results obtained for the materials discussed in this work: 1. Electron–phonon coupling in polyenes and polyacetylene gives rise to: – long-range CC stretching interactions and softening of R− modes with conjugation length – bond alternation in the equilibrium structure of PA – selective enhancement of the Raman intensity of the R− modes 2. Electron–phonon coupling in graphite, polycyclic aromatic hydrocarbons and related carbon materials is responsible for: – long-range CC stretching interactions and softening of A modes with π electron delocalisation – bond “alternation” (e.g., appearance of benzeniod-like relaxed structures) in the presence of conﬁnement – selective enhancement of the Raman intensity of the D line in the presence of conﬁnement (A modes) 3. The electron–phonon coupling in single-wall carbon nanotubes gives rise to long-range CC stretching interactions modulated by the diﬀerent electronic structures. As a consequence, diﬀerent dispersion laws for G- bands can be predicted on this basis, in agreement with the experimental observations.

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Preliminary calculations on SWNTs indicate that bond orders are also aﬀected by conﬁnement and symmetry decreases, thus removing the perfectly “equalized” bond structure of graphite. Further investigation on this point, supported by high-level ﬁrst-principle calculations, would give new insight about the mechanism which rules Raman activity and its dependence upon the symmetry of the nanotube and its characteristic electronic structure. Work is in progress along this line. Acknowledgements The authors are indebted to F. Mauri, A. Ferrari and S. Piscanec for the very useful discussions about electronic structure and vibrational potential of carbon nanotubes, and to C. Vergara for his assistance in the setup of the numerical methods for integral calculations. This work was supported by a grant from MURST (Italy) (FIRB project “Carbon-based micro- and nanostructures”, RBNE019NKS).

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[42] M. Tommasini, E. D. Donato, C. Corni, L. Motta, C. Castiglioni, G. Zerbi: in preparation [43] E. B. Wilson, J. C. Decius, P. C. Cross: Molecular Vibrations: The Theory of Infrared and Raman Vibrational Spectra (McGraw-Hill, New York 1955) [44] S. Piscanec, A. C. Ferrari, F. Mauri, M. Lazzeri, J. Robertson: Proceedings of the XIX International WintherSchool “Electronic Properties of Novel Materials” IWEPNM2005 (American Institute of Physics, New York)

Index annealing, 382 conﬁnement, 382–384, 392–395, 397, 399, 400 conjugation length, 383 D band, 384, 391 defects, 383, 395 density functional theory (DFT), 386, 390–393 dimerisation, 386, 390, 393, 394 bonds dimerisation, 395 dimerisation parameter, 387 dispersion, 383, 384, 386, 398, 399 phonon dispersion, 388, 391 eﬀective conjugation coordinate theory (ECCT), 385, 388, 390 electron–phonon coupling, 382, 385, 387–393, 395, 398, 399 electron-phonon coupling, 384 ﬁrst principle calculations, 386, 398, 400 fullerene, 383 G band, 395–398 graphene, 381–384, 390, 392, 393, 396

nanotubes, 381–383, 395–399 armchair nanotubes, 398 chirality, 397 chiral vector, 396 single-walled nanotubes (SWNTs), 395–397, 399, 400 zig-zag nanotubes, 398 oligomers, 382, 390 Peierls distortion, 389 polarizability, 388, 390, 391, 395, 397 bond–bond polarizability, 398 bond-bond polarizability, 386, 388 polyacetylene, 382–384, 386–390, 392, 393 long chains, 385, 388 short chains, 385 polycyclic aromatic hydrocarbons (PAHs), 382, 390, 393 polyenes, 383, 385, 386, 389, 390, 392 polymers, 383, 384 polyconjugated polymers, 383 quantum chemistry, 382

Kohn anomaly, 392

Raman scattering, 399 Raman activity, 385, 386, 388–390, 393, 400 Raman intensity, 386 resonant Raman scattering, 383, 386 selection rules, 384, 393 Raman spectroscopy, 381, 383–386, 390–392, 395

molecular approach, 384, 391 molecular dynamics, 390

valence force ﬁeld, 382, 385–387, 390, 392, 396–398

H¨ uckel theory, 382, 384, 386, 387, 389, 391, 392, 394, 399 highly oriented pyrolytic graphite (HOPG), 383

Raman Spectroscopy and Optical Properties of Amorphous Diamond-Like Carbon Films Leonid Khriachtchev Laboratory of Physical Chemistry, University of Helsinki, P.O. Box 55, FIN-00014 Helsinki, Finland [email protected] Abstract. The Raman spectroscopy and optical characterization of amorphous hydrogen-free diamond-like carbon ﬁlms is described. The samples were prepared by using mass-separated carbon ion beam and pulsed arc discharge deposition methods. For the samples prepared with both deposition methods, the correlation between the sp3 fraction and the shape of the Raman spectra was obtained. The refractive index and absorption of these ﬁlms were also studied and compared with the Raman spectra, and the optical properties were found to correlate with the Raman spectra for the samples prepared with ion beam technique. The eﬀect of interference of light on Raman spectra was found to be important for the carbon ﬁlms with low absorption. The developed characterization methods were applied to study modiﬁcations of carbon ﬁlm structure upon irradiation with energetic ions and thermal annealing.

1 Introduction Studies of diamond-like carbon (DLC) ﬁlms are popular because this material is hard, chemically inert and optically transparent [1]. Hydrogen-free DLC ﬁlms have been taken into the focus of research from the early 1990s, and this material can be prepared by using mass-separated ion beams (MSIB) [2, 3, 4], pulsed or continuous arc discharge [4, 5], laser ablation [6], and other methods. The term tetrahedral amorphous carbon (ta-C) is often used to denote this hydrogen-free material with a high sp3 fraction (η). No microcrystalline inclusions or layered structure have been found for ta-C. The growth of the ta-C network is probably a process of subplantation of the energetic particles into the bulk [7], although the surface growth mechanism was also proposed [8]. Theoretical simulations of ta-C were performed for materials with η ∼ 80-90% [9, 10]. The theoretically obtained vibrational properties are mainly characterized by unlocalized low-frequency modes in the 200 to 1300 cm−1 region, and the additional modes with frequencies above 1300 cm−1 are associated with well-localized geometrical anomalies in the network. A simple structural model contemplates small sp2 -bonded carbon clusters, embedded in a more transparent sp3 -bonded carbon host. Raman spectroscopy has been successfully used to characterize DLC materials. From the beginning, Raman spectra of hydrogenated DLC were mainly studied [11, 12]. Raman spectroscopy of hydrogen-free DLC has also G. Messina, S. Santangelo (Eds.): Carbon, The Future Material for Advanced Technology Applications, Topics Appl. Phys. 100, 403–421 (2006) © Springer-Verlag Berlin Heidelberg 2006

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gained research activity, and Raman spectra of hydrogen-free DLC ﬁlms prepared by laser deposition [13, 14], MSIB [15, 16], and pulsed cathodic arc discharge (PCAD) [17] were reported. It was attractive to search for correlation between the Raman spectra and the characteristic ﬁlm parameters, and this was found for various hydrogen-free DLC samples with excitation at 514.5 nm [15, 16, 17, 18, 19]. The studies with UV excitation further developed the Raman characterization of hydrogen-free DLC ﬁlms, and the band around 1100 cm−1 originating from the sp3 -bonded carbon atoms was demonstrated [20]. Optical properties of hydrogen-free DLC in the visible spectral region have been studied for DLC ﬁlms prepared by laser deposition [21], direct current arc discharge [22, 23], and MSIB methods [24, 25]. For ta-C, the refractive index is typically 2.4–2.5, approaching the value of crystalline diamond, and the absorption coeﬃcient is below 104 cm−1 . Raman characterization of thin ﬁlms is essentially inﬂuenced by their optical properties due to interference of light. First, interference of light can change Raman signals measured from thin solid ﬁlms [26, 27]. Second, interference-induced modiﬁcations of the spectral shape were found for MSIB DLC ﬁlms [28]. These eﬀects are quite strong for transparent hydrogen-free DLC ﬁlms, and they should be taken into account while characterizing DLC with Raman spectroscopy. The interference eﬀect on the Raman spectra was used to estimate absorption of hydrogen-free DLC ﬁlms [29], and the systematic correlation between the Raman spectra and the optical properties was found [25]. In the present contribution, we give an overview of some characterization approaches and results obtained for hydrogen-free DLC by using Raman spectroscopy and optical methods. The consideration is mainly limited to the research performed in the Laboratory of Physical Chemistry at the University of Helsinki [16, 17, 18, 19, 25, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37].

2 Experimental Details The hydrogen-free DLC ﬁlms were prepared by using MSIB and PCAD methods. The best samples possess sp3 fractions as high as 80%. The ﬁlms (typically from 100 to 500 nm thick) were deposited onto either crystalline silicon (Si) substrates or aluminum (Al) layers. In order to enhance Raman scattering from surface structures (surface-enhanced Raman scattering, SERS), some of the DLC ﬁlms were covered with very thin (∼ 3 nm) silver (Ag) layers. The deposition methods are described in more detail elsewhere [16,17,18,19]. The Raman measurements were carried out using two experimental setups. The earlier studies used a 1 m Jarrell Ash spectrometer (8 cm−1 resolution) equipped with a cooled low-noise photomultiplier tube and an Ar+ laser (Spectra-Physics, Model 164, ∼200 mW at 514.5 nm). The spectra were typically recorded in 120–200 points in the region from 100 to 2100 cm−1 . The second setup included a single-stage spectrometer (Acton SpectraPro

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Raman intensity

1,0

S = (I1300 - I1100) / I1100

G band

0,5

D band

I500

I1550

0,0 0

500

1000

1500

2000 -1

Raman shift (cm ) Fig. 1. Raman spectrum of a MSIB ﬁlm (E = 1000 eV) measured with excitation at 514.5 nm. The Raman parameters used in the analysis are shown

500I, resolution 10 cm−1 ) equipped with a charge-coupled device camera (Andor InstaSpec IV) and an Ar+ laser (Omnichrome 543-AP, ∼100 mW at 514.5 nm). The laser radiation (in most experiments at 514.5 nm) was focused to the sample surface, and Raman light was detected in the transverse direction without polarization analysis. Since we did not notice any diﬀerence between the results for various pressure and temperature conditions, most of the spectra were recorded under normal laboratory conditions. No visible degradation of the coatings was produced by laser radiation. For the optical studies, we measured Raman intensity and reﬂection from ﬁlm areas with varying thickness. The studied ﬁlms were wedged, which was due to inhomogeneous carbon-ion deposition ﬂux, so that the thickness dependence could be studied by changing the probed point. The ﬁlm optical thickness nD can be found by using the fact that the thicknesses of (2m + 1)λ/4nA and mλ/2nA correspond to minimal and maximal reﬂection, respectively, where A is the geometrical parameter depending on the irradiation scheme and λ is the laser wavelength. The optical thicknesses between the mλ/4nA values are evaluated by extrapolation.

3 Raman Diagnostics Figure 1 demonstrates the Raman spectrum for a MSIB ﬁlm, deposited with ion energy E = 1000 eV, after Si background subtraction. The spectrum

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mainly consists of two broad bands around 1550 and 500 cm−1 and some additional scattering between them. The asymmetrical peak at about 1550 cm−1 is attributed to well-localized sp2 -bonded clusters residing in the DLC network. The broader band in the 400 to 800 cm−1 range originates from a wider spatial area of the structure characterized by diﬀerent sorts of mixed bonds [9,10,13]. The approach of resonant Raman spectroscopy demonstrated that this spectrum is the result of Raman scattering, while possible contributions of photoluminescence were small. In order to describe the Raman spectra numerically, we use the following Raman parameters (Fig. 1): (i) The R = I500 /I1550 intensity ratio, where I500 and I1550 are the Raman intensities at 500 cm−1 and at the main peak maximum, respectively. Since these Raman intensities correspond to diﬀerently bonded carbon atoms, this parameter is expected to correlate with the sp3 fraction. (ii) The S = (I1300 − I1100 )/I1100 parameter, which describes an average slope in the 1100 to 1300 cm−1 interval. This parameter reﬂects the shape of the main peak in the spectral region of the D band, typically located around 1300–1400 cm−1 . Furthermore, Raman spectra with UV excitation reveal a band around 1100 cm−1 originating from sp3 -bonded carbon [20], and this contribution probably inﬂuences the value of S measured with the visible excitation. (iii) The width and the position of D and G bands and the D/G intensity ratio. These data are conventionally used to characterize carbon materials, providing good results for hydrogenated or poor hydrogen-free DLC [11, 12]. However, these parameters are not fully satisfactory in diagnostics of ta-C when the D band is very weak. Figure 2 presents these Raman parameters measured from central MSIB ﬁlm areas as a function of the deposition ion energy. The minimum of S = 0.02, the maximum of R = 0.65, and the highest frequency of the G bands occurs for deposition energies from 60 to 300 eV. This energy interval corresponds to the optimal deposition conditions when considering ﬁlm parameters such as sp3 fraction, electrical resistance, and roughness [38, 39]. A similar dependence of the Raman parameters on the discharge voltage was found for the PCAD ﬁlms [19, 30]. The best ﬁlms (voltages from 300 to 500 V) are characterized by R = 0.60 and S = 0.10, the G band is located at 1560 cm−1 and has a width (FWHM) of ∼240 cm−1 , and the D/G intensity ratio is ∼0.20. These values only slightly diﬀer from the parameters obtained for the optimal MSIB ﬁlms. The D/G intensity ratio increases for high arc voltages (≥ 1 kV). In addition, new spectral features at ∼715 and 450 cm−1 were found for ﬁlms deposited with the 4.5 kV voltage. This double-peak low-frequency spectrum corresponds to the vibrational density of states of graphite, and it is a signature of ﬂat sp2 -bonded carbon regions and demonstrates an increase of the sp2 -cluster size for higher plasma ion energy. The double-peak structure in the low-frequency region, and hence

Intensity ratio, R

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Slope, S

Raman Spectroscopy and Optical Properties of DLC Films

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(a)

0,4 0,2

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407

(c)

1570 1550 1530

240 210

(d)

180 1

10

2

10

3

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4

10

Ion energy (eV) Fig. 2. Raman parameters as a function of the MSIB energy. The measurements were performed for central ﬁlm areas with excitation at 514.5 nm

ﬂat graphite-like layers, is retained in the case of a substrate parallel to the plasma ﬂow [19]. Raman spectra of the MSIB ﬁlms were studied with excitation by various Ar+ -laser lines [18]. On one hand, the Raman spectra of DCL show clear resonance enhancement. For excitation at 488 nm, the I500 /I1550 intensity ratio exceeds 0.8 for samples prepared with the optimum deposition energy. On the other hand, the basic behavior of spectral features demonstrated in Fig. 2 for 514.5 nm excitation remains qualitatively the same for other laser wavelengths. The observed resonant behavior corresponds to the 2.0–2.5 eV optical gap known for ta-C.

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Ref. 17 Ref. 18 Ref. 19

Intensity ratio, R

0,6

0,4

0,2 0,0

0,2

0,4

0,6

0,8

3

sp fraction Fig. 3. Correlation between the sp3 fraction (η) and the I500 /I1550 intensity ratio (R) for MSIB [18] and PCAD [17, 19] ﬁlms

The sp3 fraction is an important parameter of carbon materials; however, its extraction based on Raman spectroscopy is indirect. Raman spectra with visible excitation probe mainly sp2 -bonded carbon clusters due to a much larger scattering cross section of the graphite network, and the signal essentially depends on the structure and size of the sp2 -bonded clusters. In principle, diﬀerent Raman spectra for the same sp3 fraction can be obtained depending on the method of ﬁlm preparation. Nevertheless, the experiments show that the Raman spectra correlate with the sp3 fraction quite straightforwardly [17,18,19]. We used the available data on the sp3 fraction to obtain the Raman parameters as a function of η. The result for the R parameter is shown in Fig. 3. The presented data allow sp3 fractions to be estimated from the Raman spectra. The dependence of R on η can be modeled assuming three phases in the carbon network that are characterized by bonds between sp2 sites only, mixed bonds between sp2 and sp3 sites, and bonds between sp3 sites only. If the I1550 signal mainly originates from the sp2 -bonded sites, we can write R = a1 + a2 η + a3 η/(η − 1),

(1)

where the coeﬃcients a1 , a2 , and a3 characterize the scattering at 500 cm−1 from the sp2 , sp2 -sp3 mixed, and sp3 networks, respectively, and the corresponding coeﬃcient responsible for Raman intensity at 1550 cm−1 (sp2 carbon atoms) is equal to 1. The ﬁt of the experimental data by (1) yields a1 = 0.19, a2 = 0.21, a3 = 0.07 for the MSIB ﬁlms, and a1 = 0.26, a2 = 0.08, a3

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= 0.08 for the PCAD ﬁlms. Although the employed model is very simple, the obtained result is satisfactory. The ﬁt gives a3 1, which means a smaller scattering cross-section for the sp3 -bonded carbon atoms as compared with graphite. A diﬀerence in coeﬃcient a2 , which describes the mixed bonds, is seen for the two deposition methods, which might originate from suﬃciently diﬀerent short-range order, namely, larger sp2 -bonded carbon clusters for the PCAD material. Indeed, it is the case of large clusters when mixed bonds do not contribute much to the Raman scattering. Diﬀerences between Raman parameters obtained for MSIB ﬁlms with similar sp3 fractions but with diﬀerent deposition energies can be noticed. For E = 1000 eV, we obtained R = 0.50, S = 0.15, whereas for E = 40 eV the results are R = 0.35 and S = 0.55 although the sp3 fractions are similar (η = 0.65). This observation can be interpreted assuming that the mean size of sp2 -bonded clusters is smaller for the higher carbon ion energy. Indeed, the D/G intensity ratio increases with the cluster size [12], and this corresponds to a relative increase of S. For smaller clusters, the proportion of mixed bonds responsible for the low-frequency vibrations increases, leading to a relative increase of R. The spectral data shown in Fig. 2 were obtained for central areas of the MSIB samples. It was found that the Raman parameters change with the probed area. A decrease of R and an increase of S were systematically observed towards the sample edges, which reﬂects a decrease of the sp3 fraction (see Sect. 5) [18, 30]. This behavior was connected with impurities implanted into the network during deposition. The eﬀect of impurities is relatively stronger for lower deposition rates, i.e., for edges of the deposition area.

4 Eﬀects Induced by Interference of Light The measured Raman intensity depends on the ﬁlm thickness due to interference of light reﬂected from the air–ﬁlm and ﬁlm–substrate interfaces. The local laser intensity controlling the total intensity scattered from a given point is a function of the distance from this point to the reﬂecting surfaces. The Raman light leaving the ﬁlm is also modiﬁed by interference of light. In addition to the simple amplitude change, a spectral eﬀect generally takes place because diﬀerent parts of Raman spectra have diﬀerent wavelengths; hence the phase diﬀerence between interfering light beams changes with the Raman shift [28]. In our calculations, the Raman signal from a ﬁlm with thickness D, absorption coeﬃcient α, and refractive index n1 deposited onto a substrate with refractive index n2 was examined. A collimated laser beam is nearly orthogonal to the ﬁlm and backscattering light is collected in a small solid angle. Raman scattering is assumed to be spherically symmetric and proportional to the local laser intensity. The phase diﬀerence between the interfering beams

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Ag-500V-Al

Raman intensity, I1550

100

10 100eV-Al

1 100eV-Si 0

1

2

3

4

5

6

Film thickness (λ/4n) Fig. 4. Raman intensity at 1550 cm−1 as a function of the ﬁlm thickness for a MSIB ﬁlm (E = 100 eV) on silicon, a MSIB ﬁlm (E = 100 eV) on aluminum, and a Ag-coated PCAD ﬁlm (V = 500 V) on aluminum. The lines guide the eye

is considered as a function of Raman shift. The experimental angles between the ﬁlm surface, the laser beam, and the detection axis are computationally taken into account. A computational approach to a more complicated optical system with many layers (superlattice) is described elsewhere [40]. The present calculations give the Raman intensity as a function of the ﬁlm optical properties. The interference eﬀect appears quite strong for thick weakly absorbing ﬁlms with a high refractive index deposited onto highly reﬂecting substrates. Because of the localization of the surface scattering, its intensity undergoes much stronger interference-induced modiﬁcations as compared to the signal from the ﬁlm bulk. For the ﬁlm thickness D = mλ/2n, the Raman signal from the surface structure is strongly suppressed, and the bulk signal is mainly measured. The reasons for this selective discrimination of the surface scattering at this thickness are small laser intensity on the ﬁlm surface and out-of-phase return of the Raman light from the substrate. In particular, it is the case for the half-wave thickness when the middle part of the ﬁlm is essentially probed and the Raman signal from the optical interfaces is suppressed. Figure 4 shows the experimental Raman intensity I1550 as a function of ﬁlm thickness provided by various ﬁlm areas for three diﬀerent samples. The observed oscillating behavior is due to interference of light as described in this section. The interference eﬀect is stronger for the aluminum-substrate ﬁlm than for the sample on silicon. The eﬀect is further enhanced for the sample covered by a thin silver layer when Raman scattering from the surface is

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strong [41]. For the SERS sample, the 1550 cm−1 intensity decreases by a large factor (∼85) when the ﬁlm thickness increases from the quarter-wave to half-wave value. At the half-wave thickness, the contribution of surfaceenhanced Raman scattering is about 30%, while the rest of the signal at 1550 cm−1 originates from the bulk. The ratio of the surface signals at the half-wave and quarter-wave thickness (Q12 ) is ∼1/200 so that the surface signal can be, indeed, eﬃciently suppressed using interference of light. The ﬁlm absorption can be extracted by comparing experimental and computational data on the interference eﬀect if the ﬁlm refractive index is known. The refractive index can be found by measuring the corresponding Brewster angle. Using this method for the central area of the MSIB ﬁlm (E = 100 eV) on a Si substrate, we obtain an amplitude absorption coeﬃcient of (0.60 ± 0.20) · 104 cm−1 at 514.5 nm, which agrees with the data by other authors [24]. For the silver-covered PCAD ﬁlm (V = 500 V, η = 77%) on aluminum, the measured suppression factor Q12 = 1/200 yields α = 3.6 · 104 cm−1 , i.e., the PCAD material is much more absorbing than the MSIB material with a similar sp3 fraction. For another SERS sample on silicon (MSIB, E = 100 eV), the suppression factor Q12 is 0.13, yielding α = 1.2 · 104 cm−1 , which corresponds to an averaged absorption coeﬃcient of the two probed points with D = λ/4n and λ/2n. By employing the intensity ratio between two other points Q23 = ID=λ/2n /ID=3λ/4n , which is 0.091, we obtain for the averaged absorption coeﬃcient of this ﬁlm area α = 0.5 · 104 cm−1 . This latter result shows an increase of the absorption towards the MSIB ﬁlm edges. In addition to the simple amplitude changes, it was experimentally conﬁrmed that light interference can modify the shape of Raman spectra [28,29]. This spectral eﬀect was demonstrated by using an Al-substrate sample (MSIB, E = 100 eV). Figure 5a shows a dramatic diﬀerence between two spectra recorded from adjacent ﬁlm areas with similar structural properties, and the only available explanation of this spectral change is based on interference of light. For a similar Si-substrate sample, the observed spectral modiﬁcations are smaller by a factor of ∼5, which agrees with the calculations. Figure 5b presents the thickness dependence of the I500 /I1550 ratio measured for the central area of the MSIB sample on Al. The data points demonstrate very strong interference-induced changes of the Raman intensity ratio. The change of the intensity ratio is found to be very sensitive to the ﬁlm absorption. Assuming nearly constant optical properties in the central ﬁlm area, we ﬁt the calculated curve to the experimental data with the absorption coeﬃcient as a parameter. With realistic values n1 = 2.50, r2 = 0.90 (amplitude reﬂection), and R = 0.70, the best ﬁt is obtained for α = (0.6 ± 0.2) · 104 cm−1 , in perfect agreement with our earlier estimates. A possible contribution of the surface scattering to the ordinary Raman spectra deserves brief analysis. The interference eﬀect on the signal originating from surface structures is independent of surface enhancement of Raman scattering, and the suppression of the surface signal should be similar for ﬁlms

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D = 3λ/2n D = 7λ/4n

(a)

0,5

0,0 0

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Intensity ratio, R

Raman shift (cm )

1,2

(b)

0,8

0,4

5,5

6,0

6,5

7,0

7,5

8,0

Film thickness (λ/4n) Fig. 5. (a) Raman spectra measured from two close ﬁlm areas with diﬀerent thickness of a MSIB ﬁlm (E = 100 eV) on aluminum. (b) Raman intensity ratio R as a function of the ﬁlm thickness for the same sample. The line is from calculations

with and without silver coatings. At the half-wave thickness, the Raman spectra mainly originate from the ﬁlm bulk and the surface signal is suppressed. We analyzed the experimental Raman spectra of MSIB and PCAD ﬁlms with varying thickness and found no systematic changes in the spectral shape arising from the interference-controlled depth selection of the Raman scattering. All the periodic changes of Raman signals could be explained on the basis of Raman scattering in the ﬁlm bulk. It follows that the reported Raman spectra of DLC ﬁlms on silicon substrates characterize the bulk structure. The Raman signal from a substrate is also inﬂuenced by interference of light in the covering DLC ﬁlm. The laser intensity penetrating into the substrate material and the scattering light leaving the ﬁlm both depend on the

2,4

413

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(a)

0,3 2,1 0,2 1,8

0,1

1,5

Thickness (µm)

Refractive index

Raman Spectroscopy and Optical Properties of DLC Films

0,0

4

4

-1

α (10 cm )

514.5 nm 3 2 1

633 nm

(b)

Raman parameters

0 0,8

R 0,6 0,4 0,2

S

(c) 0,0 -4

-2

0

2

4

Displacement (mm) Fig. 6. Properties of MSIB ﬁlms (E = 100 eV) as a function of the displacement from the deposition center. (a) Refractive index and thickness. (b) Absorption coeﬃcient at 514.5 and 633 nm. The data at 633 nm were obtained with two methods (see text for details). (c) Raman parameters (R and S)

ﬁlm thickness. The light interference eﬀect on Raman signal from a substrate can be also used to extract ﬁlm absorption (see Sect. 5).

5 Optical Characterization In this section, optical properties of DLC ﬁlms are considered in correlation with the Raman spectra. The optical thickness proﬁles were obtained by measuring the positions of maxima and minima of normal reﬂection [25]. The data obtained for excitation at 488, 514.5, and 633 nm show that the refractive indexes are similar at these wavelengths. To estimate the refractive index for various ﬁlm areas, the corresponding Brewster angles were mea-

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sured. The refractive index (accuracy ∼ 2%) versus the displacement from the deposition center is presented in Fig. 6a by solid circles. The highest refractive index (n = 2.50) is observed for the central ﬁlm area, and this value agrees with the refractive indexes of the optimal ﬁlms prepared with laser ablation [21] and continuous cathodic arc deposition methods [22, 23]. The ﬁlm edges possess a lower refractive index (n = 1.80), which is more speciﬁc for hydrogenated DLC [11]. The thickness proﬁle can be obtained as the optical thickness divided by the refractive index, and the result is shown in Fig. 6a. The obtained thickness of (380 ± 10) nm at the ﬁlm deposition center agrees with the proﬁlometric measurements. The path length of laser radiation inside the material is known, and the Brewster-angle reﬂection estimates the absorption coeﬃcient with the accuracy of reﬂection from the DCL–substrate interface. Using an amplitude reﬂection coeﬃcient at the DCL–Al interface r2 = 0.90, we obtain the amplitude absorption coeﬃcient presented in Fig. 6b by solid triangles for λ = 633 nm. The absorption coeﬃcient changes from ∼ 0.2 · 104 cm−1 at the deposition center to ∼ 2.0 · 104 cm−1 at the 50 nm thick edges. The ﬁlm absorption coeﬃcient can be extracted in a diﬀerent way. For the three-medium optical system (ambient-ﬁlm-substrate) the maximum and minimum reﬂection coeﬃcients can be expressed analytically in terms of optical properties. The absorption coeﬃcient is provided by ﬁtting the calculated values to the experimental data. The extracted values are presented in Fig. 6b by open symbols for two laser wavelengths (514.5 and 633 nm). The absorption at these wavelengths diﬀers by a factor of ∼2. The data obtained for irradiation at the Brewster angles and at 90◦ (λ = 633 nm) are in good agreement, which conﬁrms the validity of the approaches employed. In Fig. 6c, the Raman parameters R and S are shown as a function of the displacement from the deposition center, the data for seven MSIB (E = 100 eV) samples being averaged. The decrease of R and the increase of S indicate a decrease of the sp3 fraction towards the ﬁlm edge. The R parameter behaves similarly to the refractive index, and the S parameter qualitatively follows the ﬁlm absorption. The correlation between the absorption coeﬃcient and the R parameter obtained in these experiments (method A) is presented in Fig. 7 by open symbols. The optical measurements were further developed [32]. As mentioned earlier, the Raman signal from a Si substrate depends on the optical properties of the deposited DLC ﬁlm. For a MSIB ﬁlm (E = 100 eV), Fig. 8 presents Raman intensity at 520 cm−1 from the Si substrate and the reﬂection coeﬃcient versus the position on the ﬁlm, the curves being normalized by the signals outside the ﬁlm. These data were measured simultaneously using nearly normal irradiation and collection of light. The extreme values of the signals correspond to ﬁlm thickness of λ/n1 , 3λ/4n1 , λ/2n1 , and λ/4n1 . The Raman signals from the Si substrate and the reﬂection coeﬃcients at these points can be written analytically [32]. The expressions for the Raman signal and

Raman Spectroscopy and Optical Properties of DLC Films

415

100 eV / method A 100 eV / method B 30 eV / method B

4

4

-1

α (10 cm )

3

2

1

0 0,2

0,3

0,4

0,5

0,6

0,7

0,8

Raman intensity ratio, R Fig. 7. DLC absorption coeﬃcient at 514.5 nm as a function of the R = I500 /I1550 ratio. The data were obtained using two methods A and B (see text for details)

Raman intensity / Reflection

2,0

Raman intensity 1,5

1,0

0,5

Reflection 0,0 -6

-4

-2

0

2

4

6

Displacement (mm) Fig. 8. Raman intensity of the silicon substrate at 520 cm−1 and normal reﬂection as a function of the displacement from the deposition center. The data are obtained for a MSIB ﬁlm (E = 100 eV) on a silicon substrate with excitation at 514.5 nm

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reﬂection coeﬃcient apply to the same sample point, and they can be solved numerically providing α and n1 with the accuracy of 2% and 10%, respectively. For the example shown in Fig. 8, I520 = 1.65, r = 0.14 at D = 3λ/4n1 , and I520 = 0.70, r = 0.91 at D = λ/n1 , which yields α = 0.50 · 104 cm−1 and n1 = 2.50. For the MSIB samples, the decrease of the deposition energy from 100 to 30 eV leads to an increase of both refractive index and absorption coeﬃcient. A similar trend for refractive index to increase when the deposition energy decreases was observed by Lossy et al. for direct current arc discharge deposition, and the eﬀect was attributed to variations in the arrangement of carbon atoms [22]. The increase of absorption for the lower deposition energy is probably associated with a rise of the sp2 fraction as compared to the optimum deposition conditions and structural modiﬁcation of the sp2 carbon clusters. The extracted absorption coeﬃcient is not proportional to the sp2 fraction, and the change of sp2 fraction from 20% to 30% (E = 100 and 30 eV) increases absorption by a factor of ∼4. The rearrangement of the carbon network should change the optical gap, and some decrease of the optical gap for small ion deposition energies was observed experimentally for ﬁlms prepared by a ﬁltered cathodic arc [22] and MSIB deposition [24]. The correlation between R and α measured for MSIB ﬁlms is shown in Fig. 7 (method B), and it agrees with the data provided by method A. For a PCAD samples (η = 77%), we obtained a relatively strong absorption (α = 4 · 104 cm−1 ). We can speculate that the structure of sp2 clusters is diﬀerent for our MSIB and PCAD samples; namely, the larger cluster size takes place in the latter case. Both absorption coeﬃcient and refractive index of the PCAD samples show extensive variations that are probably resulted from various deposition details.

6 Some Applications The irradiation of carbon materials by energetic ions is of fundamental and practical value, and it has been repeatedly addressed [33, 34, 35, 42, 43, 44, 45, 46, 47]. We studied modiﬁcations of hydrogen-free DLC ﬁlms by 50 kV Ga+ focused ion beam [33]. The best PCAD ﬁlm possessed a sp3 fraction of 80% and mass density of 3.1 g/cm3 . The Raman spectra were found to be very sensitive to the ion iradiation. The data obtained for the Raman parameters R and S suggest radiation-induced graphitization of the material. It was estimated from the Raman spectra that the sp3 fraction decreases to 50% for the 0.01 nC/µm2 dose and to 30% for the 0.02 nC/µm2 dose. Upon ion irradiation, the D/G intensity ratio increases and the G band shifts to lower energies (Fig. 9a). The increase of the D/G intensity ratio features rising sp2 -bonded clusters, however, the material remains amorphous in the whole range of doses used. After ion irradiation, the signal from the Si substrate considerably decreases reﬂecting an increase of ﬁlm absorption due to

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2

(a)

1

-1

G-band position (cm )

1560

1540

0,00

0,05

0,10

0

2

Dose (nC/µm ) 1600

4

(b)

D/G intersity ratio

1580

1580 2

1560

0

250

500

750

1000

0

o

Annealing temperature ( C) Fig. 9. G band position and D/G intensity ratio as a function of (a) dose of 50 kV Ga+ ions and (b) annealing temperature

rising sp2 -bonded imperfections. It was estimated that the absorption coeﬃcient increases for a dose of 0.1 nC/µm2 by a factor of 12 as compared with the as-grown material. The properties of strongly irradiated DLC materials (> 0.1 nC/µm2 ) are quite independent of their original structure. In agreement with the observed irradiation-induced decrease of the G-band energy, similar mode softening was observed for MSIB ﬁlms when very energetic carbon ions (5 keV) were used for deposition, leading to destruction of the carbon network during its formation [16]. A downshift of the G band was observed upon Si implantation into DLC [35]. Thermal stability of DLC is a practically important property [34, 48, 49]. The Raman spectra of DLC ﬁlms (initially η ∼ 45%) display progressive graphitization when the annealing temperature increases, as suggested by an increase of both G band frequency and D/G intensity ratio (Fig. 9b) [34]. The R parameter decreases for higher annealing temperatures indicating an eﬃcient reduction of the sp3 fraction. The thermal mobility of various atoms in the carbon network (for instance, Si [35]) was studied at high anneal-

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ing temperatures (above 1000◦ C). The observed annealing-induced degradation of diamond-like properties means that the obtained diﬀusion coeﬃcients practically apply to a sp2 -bonded carbon structure. The elevated deposition temperature (∼ 400◦C) leads to an essentially graphitic structure [34]. The carbon materials doped with various atoms are more complicated to analyze based on Raman spectroscopy, with the possible exception of hydrogen [11, 12]. Our studies in this area include hydrogenated DLC [37], carbon materials doped with nitrogen [31], argon [30], silicon [34, 35], and B–C–N coatings [36]. For example, it was found that the extensive doping of the carbon network during deposition with Si (33 at. %) makes the structure less sensitive to the annealing and deposition temperature and ion-beam irradiation [34]. Doping with nitrogen leads to a strong photoluminescence [31], which further complicates the Raman analysis. Some additional uncertainty is introduced in the case of high-dose implantation, as discussed elsewhere [33].

7 Conclusions Raman spectroscopy can be successfully used to characterize structure of amorphous hydrogen-free DLC ﬁlms. The correlation of the Raman spectra with the deposition energy, and hence with the sp3 fraction, has been found, demonstrating the quantitative Raman diagnostics of this material. The developed characterization method essentially uses the Raman intensity at ∼ 500 cm−1 . Raman spectra of DLC ﬁlms are modiﬁed due to interference of light. The interference changes numerical parameters of the Raman spectra, which inﬂuences the diagnostics of the microstructure and this eﬀect should be always carefully considered. The use of interference of light allows selective enhancement of Raman scattering from the bulk structure or from the ﬁlm surface. This analysis shows that the reported Raman spectra essentially originate from the ﬁlm bulk structure. By analyzing the thickness dependence of Raman intensity and reﬂection, we estimated the absorption coeﬃcient and refractive indexes of various DLC ﬁlms. The Raman scattering from the substrate can be also employed for this analysis. For the optimal DLC materials, we found a refractive index of ∼ 2.5 and an absorption coeﬃcient of ∼ 0.2 · 104 cm−1 (at 633 nm). For MSIB ﬁlms, the Raman spectra show a straightforward correlation with the absorption coeﬃcient, which indicates the close connection between the optical and structural properties. In particular, the most transparent ﬁlms have the highest sp3 fractions. For PCAD ﬁlms, relation between the Raman spectra and the optical properties is less clear. The developed methods were applied to study structural modiﬁcations of DLC ﬁlms upon thermal annealing and ion irradiation. Some data can be obtained for doped carbon materials, but the interpretation of the results becomes less straightforward.

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Acknowledgments The work was supported by the Academy of Finland and the Center for International Mobility (Finland). I would like to thank all my collaborators in these studies, especially A. Stanishevsky, R. Lappalainen, E. VainonenAhlgren, J. Likonen, T. Ahlgren, M. R¨ as¨anen, and J. Keinonen.

References [1] Y. Lifshitz: Diamond Relat. Mater. 5, 388 (1996) 403 [2] J. Ishikawa, Y. Takeiri, K. Ogawa, et al.: J. Appl. Phys. 61, 2509 (1987) 403 [3] Y. Lifshitz, S. R. Kasi, J. W. Rabalais: Mater. Sci. Forum 237, 52–53 (1989) 403 [4] J. P. Hirvonen, J. Koskinen, R. Lappalainen, et al.: Mater. Sci. Forum 197, 52–53 (1989) 403 [5] I. I. Aksenov, V. I. Strelnitskij: Surf. Coat. Technol. 47, 98 (1991) 403 [6] J. Robertson: Surf. Coat. Technol. 50, 185 (1992) 403 [7] Y. Lifshitz, S. R. Kasi, J. W. Rabalais: Phys. Rev. Lett. 62, 1290 (1989) 403 [8] N. A. Marks, D. R. McKenzie, B. A. Pailthorpe: Phys. Rev. B 53, 4117 (1996) 403 [9] C. Z. Wang, K. M. Ho: Phys. Rev. Lett. 71, 1184 (1993) 403, 406 [10] D. A. Drabold, P. A. Fedders, P. Stumm: Phys. Rev. B 49, 16415 (1994) 403, 406 [11] M. Yoshikawa: Mater. Sci. Forum 365, 52–53 (1989) 403, 406, 414, 418 [12] M. A. Tamor, W. C. Vassell: J. Appl. Phys. 76, 3823 (1994) 403, 406, 409, 418 [13] W. S. Bacsa, J. S. Lannin, D. L. Pappas, et al.: Phys. Rev. B 47, 10931 (1993) 404, 406 [14] F. Xiong, Y. Y. Wang, W. Leppert, et al.: J. Mater. Res. 8, 2265 (1993) 404 [15] S. Prawer, K. W. Nugent, Y. Lifshitz, et al.: Diamond Relat. Mater. 5, 433 (1996) 404 [16] L. Y. Khriachtchev, M. Hakovirta, R. Lappalainen, et al.: Phys. Lett. A 217, 354 (1996) 404, 417 [17] A. V. Stanishevsky, L. Y. Khriachtchev: Diamond Relat. Mater. 5, 1355 (1996) 404, 408 [18] L. Y. Khriachtchev, M. Hakovirta, R. Lappalainen, et al.: Diamond Relat. Mater. 6, 694 (1997) 404, 407, 408, 409 [19] A. V. Stanishevsky, L. Y. Khriachtchev, R. Lappalainen, et al.: Diamond Relat. Mater. 6, 1026 (1997) 404, 406, 407, 408 [20] K. W. R. Gilkes, H. S. Sands, D. N. Batchelder, et al.: Appl. Phys. Lett. 70, 1980 (1997) 404, 406 [21] D. L. Pappas, K. L. Saenger, J. Bruley, et al.: J. Appl. Phys. 71, 5675 (1992) 404, 414 [22] R. Lossy, D. L. Pappas, R. A. Roy, et al.: J. Appl. Phys. 77, 4750 (1995) 404, 414, 416 [23] S. Xu, B. T. Tay, H. S. Tan, et al.: J. Appl. Phys. 79, 7234 (1996) 404, 414

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[24] Y. Lifshitz, G. D. Lempert, E. Grossman, et al.: Diamond Relat. Mater. 6, 687 (1997) 404, 411, 416 [25] L. Y. Khriachtchev, M. R¨ as¨ anen, R. Lappalainen: J. Appl. Phys. 82, 413 (1997) 404, 413 [26] R. J. Nemanich, C. C. Tsai, G. A. N. Connell: Phys. Rev. Lett. 44, 273 (1980) 404 [27] A. H.-L. Goﬀ: Thin Solid Films 142, 193 (1986) 404 [28] L. Y. Khriachtchev, M. R¨ as¨ anen, R. Lappalainen: J. Appl. Phys. 79, 8712 (1996) 404, 409, 411 [29] L. Y. Khriachtchev, R. Lappalainen, M. R¨ as¨ anen: Diamond Relat. Mater. 7, 1451 (1998) 404, 411 [30] L. Y. Khriachtchev, R. Lappalainen, M. Hakovirta, et al.: Diamond Based Composites and Related Materials, vol. 3, NATO ASI Series 38 (1997) pp. 309– 321 404, 406, 409, 418 [31] A. Stanishevsky, L. Khriachtchev, I. Akula: Diamond Relat. Mater. 7, 1190 (1998) 404, 418 [32] L. Y. Khriachtchev, R. Lappalainen, M. R¨ as¨ anen: Thin Solid Films 325, 192 (1998) 404, 414 [33] A. Stanishevsky, L. Khriachtchev: J. Appl. Phys. 86, 7052 (1999) 404, 416, 418 [34] L. Khriachtchev, E. Vainonen-Ahlgren, T. Sajavaara, et al.: J. Appl. Phys. 88, 2118 (2000) 404, 416, 417, 418 [35] E. Vainonen-Ahlgren, T. Ahlgren, L. Khriachtchev, et al.: J. Nuclear Mater. 290, 216 (2001) 404, 416, 417, 418 [36] A. Stanishevsky, H. Li, A. Badzian, et al.: Thin Solid Films 398, 270 (2001) 404, 418 [37] K. Heinola, T. Ahlgren, W. Rydman, et al.: Physica Scripta T 108, 63 (2004) 404, 418 [38] Y. Lifshitz, G. D. Lempert, E. Gossman, et al.: Diamond Rel. Mater. 4, 318 (1995) 406 [39] M. Hakovirta, J. Salo, R. Lappalainen, et al.: Phys. Lett. A 205, 287 (1995) 406 [40] L. Khriachtchev, S. Novikov, O. Kilpel¨ a: J. Appl. Phys. 87, 7805 (2000) 410 [41] T. L´ opez-R´ıoz: Diamond Relat. Mater. 5, 608 (1996) 411 [42] D. G. McCulloch, S. Prawer, A. Hoﬀman: Phys. Rev. B 50, 5905 (1994) 416 [43] D. G. McCulloch, E. G. Gerstner, D. R. McKenzie, et al.: Phys. Rev. B 52, 850 (1995) 416 [44] V. D. Vankar, N. Dilawar: Vacuum 47, 1275 (1996) 416 [45] K. C. Walter, H. H. Kung, C. J. Maggiore: Appl. Phys. Lett. 71, 1320 (1997) 416 [46] J. R. Shi, Z. Sun, X. Shi, S. P. Lau, B. K. Tay, J. Pelzl: Thin Solid Films 377, 269 (2000) 416 [47] W. Y. Luk, O. Kutsay, I. Bello, et al.: Diamond Relat. Mater. 13, 1427 (2004) 416 [48] C. W. Ong, X. A. Zhao, J. T. Cheung, et al.: Thin Solid Films 258, 34 (1995) 417 [49] R. Kalish, Y. Lifshitz, K. Nugent, et al.: Appl. Phys. Lett. 74, 2936 (1999) 417

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Index ta-C, 403 absorption coeﬃcient, 404, 409, 411, 413–418 annealing, 403, 417, 418 D band, 406 D/G band intensity ratio, 406, 409, 416, 417 diamond-like carbon (DLC), 403, 404, 406, 412, 413, 415, 416, 418 G band, 406, 416, 417 interference of light, 409 ion irradiation, 416 mass-separated ion beams (MSIB), 403–405, 407–414, 416–418

optical characterization, 403, 413 optical properties, 404, 410, 411, 413, 414, 418 pulsed cathodic arc discharge (PCAD), 404, 406, 408–412, 416, 418 Raman parameters, 406–409, 414 Raman scattering, 409, 418 Raman intensity, 410, 414, 415 Raman spectroscopy, 403–406, 408, 409, 418 refractive index, 403, 404, 409–411, 413, 414, 416, 418 surface enhanced Raman spectroscopy (SERS), 404, 411 thermal stability, 417

Raman Spectroscopy of CVD Carbon Thin Films Excited by Near-Infrared Light Margit Ko´ os, Mikl´ os Veres, S´ara T´ oth, and Mikl´ os F¨ ule Research Institute for Solid State Physics and Optics of the Hungarian Academy of Sciences, Konkoly Thege M.u. 29-33, H-1121 Budapest, Hungary [email protected] Abstract. The interpretation of the Raman spectra of amorphous carbon thin ﬁlms is still controversial. The concept of their decomposition into D and G peaks does not work in some cases, when presence of additional bands can be deduced from the shape of the spectra. One to investigate these extra component bands is to change the excitation wavelength. This results in the enhancement of the Raman scattering cross-section of the diﬀerent structural units. Our investigations were aimed to detect the component bands become intense by using infrared excitation (785 nm) in the Raman spectra of amorphous carbon thin ﬁlms prepared from benzene and methane in a wide range of deposition parameters. By comparing the visible and infrared excited Raman spectra it will be proven that the well-known G band of the a-C:H layers consists of two components, one of which exhibiting no dispersion. It will be also shown that he infrared excitation makes distinguishable Raman bands assigned to delocalized (π) electronic structure due to resonant enhancement of the scattering.

1 Introduction 1.1 The Raman Eﬀect When monochromatic light of frequency ω L scatters in a medium, scattered light intensities shifted from ω L by certain Ω i values can be observed in the spectrum of the scattered light. The value of these shifts depends on the properties of the scattering media and it does not vary when changing ω L . This phenomenon is the “Raman scattering”. During a Raman experiment the scattered light is measured, and it is represented in relative wavenumbers, taking the laser wavenumber being equal to zero. Raman scattering is an inelastic scattering of light on elementary excitations of the medium. The elementary excitations are usually rotational or vibrational transitions of a molecule or lattice vibrations (phonons) in a solid. The inelastic scattering is a two-phonon process, where the absorption of an incoming photon of energy EL = ω L with energy transfer and the creation of an ωS scattered photon take place simultaneously in the medium. The energy diﬀerence is equal to the Ω energy of the elementary excitation. If the energy transfer is positive (ω L ≥ ωS ) the process is called Stokes scattering, the opposite case (ω L ≤ ωS ) is known as anti-Stokes scattering. G. Messina, S. Santangelo (Eds.): Carbon, The Future Material for Advanced Technology Applications, Topics Appl. Phys. 100, 423–445 (2006) © Springer-Verlag Berlin Heidelberg 2006

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The E = E0 cos (ω L t ) electromagnetic ﬁeld of frequency ω L acting on a medium induces a dipole moment µin determined by the polarizability of the medium: µin = αE = αE 0 cos (ω L t ).

(1)

A molecule or an elementary cell consisting of N atoms has 3N degrees of freedom, 3 of which are transitional, 3 (2 for a linear system) are rotational and 3N − 6 (3N − 5 for a linear system) are vibrational ones. 3N Cartesian coordinates are needed to describe the motion of such a system. It is suitable to use “internal coordinates”, describing the variations of bond lengths and bond angles during vibrations. Combining these coordinates, the orthogonal vibrational “normal modes” of the molecule (cell) can be described. The αij components of the polarizability tensor can be expressed through the normal coordinates of the system: 2 ∂αij ∂ αij 1 Qk + (2) Qk Qk + · · · . αij = (αij )0 + ∂Qk 0 2 ∂Qk ∂Qk k

k,k

Restricting (2) to ﬁrst-order terms, combining (1) with (2) and applying trigonometric identities, we get: µin,ij = (αij )0 E 0 cos (ω L t) 1 ∂αij + Qk E 0 2 ∂Qk 0 k

· {cos [(ω L + Ω)t + φk ] + cos [(ω L − Ω)t − φk ]} . (3) From (3) it can be seen that during a scattering process a medium will emit photons at frequencies ω L , ω L +Ω and ω L −Ω corresponding to Rayleigh, anti-Stokes and Stokes scattering, respectively. While Raleigh scattering does always exist, Raman scattering occurs only if the polarizability of the medium changes during the scattering process. The ﬁrst-order terms of the polarizability tensor represent the components of the “Raman tensor” R. Energy and momentum are conserved in the Raman process: ωS = ω L ± Ω kS = kL + kph ,

(4)

where kL , kS and kph are the momenta of the incoming and scattered photons and of the phonon, respectively. According to (4), the energy loss of the photon equals the energy of the lattice vibration. Considering that, for the visible light the 104 cm−1 magnitude of kL and kS is much less than the size of the ﬁrst Brillouin zone of the crystals (about 1010 cm−1 ), it can be concluded that only zone centre phonons participate in the scattering.

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In the classical picture described above, the mechanism of the scattering does not matter. The quantum mechanical treatment of the process considers the electron–photon and electron–phonon interactions through their Hamiltonians He−R,σ and He−ph,ρ (σ and ρ being the polarizations of the incoming and scattered photons, respectively). The core of the quantum mechanical treatment of the Raman scattering is the transition matrix element K2f,10 : ω ,f ,i|H S e−R,ρ |0 ,f ,b0,f,b|He−ph |0,0,a0,0,a|He−R,σ |ω L ,0,i , (5) K2f,10 = (E L −Eaie −iγ )(E S −Ebie −iγ ) a,b

where |ω L , 0, i is the initial state characterized by the incoming photon of E L = ω L energy, by the phonon in 0 state (no excited phonon) and by the electron in ground state i. The ﬁnal state ω S , f , i| is characterized by the photon of E S =ω S energy, by the phonon in the f state and by the electron in the ground state; a and b are the intermediate states participating in the e e and Ebi are the energy diﬀerences of states a and i as scattering process. Eai well as b and i, respectively; γ is the lifetime of the excited states. According to (5) the Raman scattering is a three-step process consisting of: (a) absorption of the incoming photon with transition of the electron into an excited state (creation of an electron–hole pair) (b) inelastic scattering of the electron on a phonon (c) recombination of the electron and the hole with emission of the scattered photon The three steps take place simultaneously. The electron can be excited from the ground state either into a virtual state or into an existing state. In the latter case, the scattering is “resonant”. The K2f,10 matrix element is related to the Raman tensor (R) through the polarization vectors of the incoming (eL ) and scattered (eS ) light: K2f,10 = eL · R · eS . The scattered intensity is proportional to the square of the transition matrix element: 2

I ∼ |K2f,10 | . It is diﬃcult to calculate the intensity of the process since the transition matrix elements are diﬃcult to determined. The number of lines observed in the Raman spectra is less than the number of phonons existing in the crystal. This is not only due to the degeneracy of the phonons, but it is because of the number of phonons which can participate in the scattering is limited by the “selection rules”. The ﬁrst restriction is that the scattering takes place only on zone-centre phonons. Additionally, during the scattering the polarizability of the medium should change, which

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requires the phonons to have certain symmetries. The simplest way to determine whether a given phonon will cause a nonzero polarizability change is to take into account group theory considerations. When the energy of the incoming or outgoing photon is close to an existing energy transition of the medium, a signiﬁcant increase in the Raman intensity can be observed due to resonant enhancement of the scattering. Depending on whether the resonance is for the incoming or scattered light, one can distinguish between incoming and outgoing resonances. In noncrystalline materials there is no elementary cell and the periodicity is lost. This leads to breakdown of the selection rules. As a result, in these materials any phonon can participate in the scattering. However, the vibrations will not be extended in the whole crystal, instead they will be localized. The Raman spectrum is obtained by summing all of these localized vibrations [1]:

4

I (ω) = (ωL − ω)

b

1 Cb [1 + n (ω, T )] gb (ω) , ω

(6)

where Cb is the coupling coeﬃcient of vibrational transitions, gb is the density of vibrational states, n (ω, T ) is the Bose–Einstein distribution function. From (6) it can be seen that the Raman intensity is determined by the density of vibrational states. 1.2 Raman Spectra of Carbon Materials The basic electronic conﬁguration of a stand-alone carbon atom diﬀers from that during bonding. In the latter case, the electronic orbitals of carbon combine, forming hybridized orbitals: sp3 , sp2 and sp hybridization states are known for carbon atoms, which form three-dimensional, layered and chainlike structures like diamond, graphite and carbyne. In disordered carbons, atoms of diﬀerent hybridization are mixed. Besides, hydrogen can also be present in the structure. Because of the large variety of atomic arrangements in carbon materials, their properties, both crystalline and amorphous, vary in a wide range. Among the several diﬀerent models proposed for the a-C:H [2, 3], nowadays the cluster model [4, 5] has found wide acceptance since that best describes the electronic structure of amorphous carbons. Most of the experimental data obtained for a-C:H ﬁlms were successfully explained with this model. The cluster model is based on considerations of the H¨ uckel approximation, treating the σ and π states separately [4]. It was found that the π bonding of carbon atoms favours a clustering of sp2 sites predominanatly into planar structures formed by sixfold rings. As a result, in the amorphous carbon matrix there are sp2 clusters of diﬀerent sizes surrounded by a matrix of sp3 carbon atoms. It should be noted that the cluster model was reformulated [6]. According to it, in clusters, the sp2 hybridized carbon atoms can be

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arranged, besides into rings, into chains too [7, 8]. The energy of the π states of the cluster strongly depends on the size and on the level of conjugation of the cluster. The higher the cluster size, the lower the gap between the valence π and conduction π ∗ states. The energy of the σ states is much higher than that of π ones. Raman spectroscopy has been proved to be a very suitable method for structural characterization of carbon materials [9, 10, 11, 12, 13, 14, 15]. The method is highly sensitive to changes in the bonding conﬁguration of carbon atoms, especially to that of sp2 hybridized ones, since the π states of the sp2 clusters result in narrow band gaps, which cause the Raman scattering process to be resonantly enhanced. The Raman spectrum of diamond consists of one zone-centre mode at 1332 cm−1 having T2g symmetry. In the spectrum of single crystal graphite, a peak can be observed at 1580 cm−1 corresponding to zone-centred E2g mode, usually labelled as “G” (graphitic) band, assigned to C–C stretching vibrations of the atoms in hexagonal rings of the graphene sheet. Besides, an interplanar E2g stretching vibration mode is also present at 42 cm−1 [16]. In “nonperfect” or microcrystalline graphite, another band of A1g symmetry, called the “D” (disordered) peak [17], corresponding to breathing vibrations of the hexagonal rings at the grain boundaries, appears at 1350 cm−1 . The D band is a result of a double resonant scattering process activated by the defects of the crystal [18]. There are other bands of small intensity observed in the Raman spectra of graphite [19], as well as intensive second- and higher-order peaks above 2000 cm−1 [20], but these are not relevant for the interpretation of the spectra of amorphous carbons. Due to the speciﬁc band structure of graphite, where the conduction and valence bands cross at the K point but a forbidden gap exists in other points of the Brillouin zone, the Raman scattering in graphite is always resonant. On the contrary, the band gap of diamond is around 5 eV, hence for visible excitation the intensity of its 1332 cm−1 mode is about one ﬁftieth that of the G peak of graphite [21]. The Raman spectra of amorphous carbons consist of a broad band in the 1000–1700 cm−1 range. This composite band is usually decomposed into two peaks centred around 1350 and 1580 cm−1 , which are near the position of D and G bands of microcrystalline or nonperfect graphite. This similarity was the origin of the labelling and ﬁrst explanation of the Raman spectra of amorphous carbons [9]. The D band of amorphous carbon materials is assigned to breathing vibrations of rings or ring-like structures; the stretching modes of these species give rise to the scattering in the G band region [14]. However, besides the stretching vibrations of carbon atoms arranged in rings, those forming chains also contribute to the G band [13]. The parameters of the two bands (position, width and their intensity ratio) are used for the characterization of carbon-containing materials [10, 11]. The shape of the Raman spectrum is considered to depend on the sp2 /sp3 ratio, clustering of the sp2 hybridized carbon atoms and arrangement of these

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atoms in the clusters [15]. The position of the G band indicates the type of arrangement of carbon atoms in the clusters: if its value is around 1580 cm−1 , the clusters have graphitic character, while lower positions indicate a diﬀerent arrangement. The peak width is the measure of structural ordering: the narrower the peak, the more ordered the structure. Another parameter used for a-C:H thin layers characterization is the intensity ratio of D and G bands. The I D /I G ratio was found to be related to the size of the sp2 clusters in the amorphous carbon structure. It is assumed that for microcrystalline graphite the I D /I G ratio is inversely proportional to the crystallite size LA [22]: ID c = . IG LA

(7)

Experimental measurements performed on ta-C thin ﬁlms showed that for amorphous carbons having sp2 clusters below ≈ 2 nm size the ratio is proportional to the square of the cluster size LC [14, 23]: ID = c L C 2 . IG

(8)

The constants c and c in (7) and (8) were found to be dependent on the excitation energy. The I D /I G ratio is the measure of ordering of the a-C:H structure. The higher the intensity ratio, the higher the cluster size, thus the higher the ordering of the structure. Raman spectroscopic measurements with diﬀerent excitation wavelengths can furnish additional information on the a-C:H structure [10, 24, 25, 26, 27]. The bonding sites having sp2 carbon atoms are generally arranged into clusters of diﬀerent sizes, which exhibit band gap depending on cluster size. For diﬀerent laser energies, E L , the conditions of resonant Raman scattering will be fulﬁlled for diﬀerent clusters, whose band gaps are equal to that. However, the vibrational frequency depends on the cluster size: the higher the size, the lower the frequency of the vibrations [28]. Additionally, when using lasers in the UV region, the sp3 sites can be resonantly excited, thus their bonding conﬁguration can also be examined. A characteristic feature of the D and G bands in the Raman spectra of amorphous carbon is their “dispersion”, the shift of the peak position when changing the excitation energy. The dispersion was also observed for the D band of graphite [29]. It was found that for diﬀerent amorphous carbons (hydrogenated and nonhydrogenated) the rate of the shift varies in a wide range [15]. For a-C:H thin ﬁlms (polymeric and diamond-like) the position of both D and G bands shifts to higher wavenumbers with the increase of E L [15, 24, 30]. It was found that in graphite the Raman scattering cross-section is strongly enhanced for the phonons having wavevector kph equal to the wavevector k of the electronic transition excited by the incident photon [29]. For diverse E L , this condition is fulﬁlled for phonons at diﬀerent distances from the K point of the zone boundary, hence the energy of the phonon participating in the scattering also varies with E L [18]. In a-C:H the dispersion

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of the bands is diﬀerently explained. Since there is no Brillouin zone, the selection rules have no meaning. As noted earlier, when changing the excitation energy, diﬀerent clusters will participate in resonant scattering. The band gap of the cluster is inversely proportional to its size. Thus, the higher the E L , the lower the mean size of the clusters involved in the resonant scattering. The lower the cluster size, the higher the frequency of its vibrations. Up to now, systematic Raman investigations on amorphous carbon thin ﬁlms of diﬀerent types were performed mainly with excitations in the visible and UV region [11,12,14,15]. The aim of the increase of the probe energy was that the sp3 hybridized carbon sites, having higher band gap, could be excited too. However, the resonant enhancement of Raman scattering from graphitic structure or/and materials containing several sp2 bonded sites arranged in nanoclusters at low-energy excitation can provide additional information on the structure of the a-C:H ﬁlms. In the following, results of Raman spectroscopic studies, performed with visible and infrared excitations, on a series of a-C:H samples prepared by radio-frequency chemical vapour deposition at diﬀerent self-bias voltages, from benzene and methane, will be presented in detail.

2 Infrared Excited Raman Spectroscopy of Amorphous Carbon Thin Films 2.1 a-C:H Thin Films Prepared from Benzene The a-C:H thin ﬁlm samples were deposited onto Si substrates by radiofrequency (2.54 MHz) chemical vapour deposition (CVD) method [31] from benzene at diﬀerent chamber pressures (8–20 Pa) and self-bias voltages (10– 700 V). The electrode with the substrate had negative self-bias potential, however, for simplicity, in the following only the magnitude of the self-bias voltage is given without the “−” sign. Raman spectroscopic measurements were carried out on the samples using a Renishaw 1000 Raman spectrometer attached to a microscope. A 488 nm (2.54 eV) line of an Ar ion laser and a 785 nm (1.58 eV) diode laser served as excitation sources. The 100× objective focused the excitation beam to a spot having diameter of ≈ 1 µm. Baseline correction on the measured spectra was performed by ﬁtting their baseline to a Gaussian function and subtracting the ﬁtted data from the experimentally measured ones. Raman spectra of a-C:H thin layers measured at 488 nm of probe wavelength are shown in Fig. 1. The data are normalized on their maxima. The change of the shape of the spectra with self-bias well reﬂects the evolution of the amorphous carbon structure. In the spectrum of the sample prepared at 10 V the G peak is located around 1600 cm−1 . With the increase of self-bias up to 300 V, it shifts to lower wavenumbers and, above this voltage, the peak positions move into opposite direction. The intensity of the D band also increases with self-bias. The spectra of the samples prepared at low

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Fig. 1. Raman spectra excited by 488 nm of a-C:H thin ﬁlms prepared from benzene at pressure of 18 Pa and diﬀerent self-bias voltages

deposition voltages have bad signal/noise ratios due to the high intensity of the luminescence background. The weak peak around 1000 cm−1 , observable in some spectra, arises from the Si substrate. In the 1000–1700 cm−1 wavenumber region the spectra were ﬁtted to two Gaussians. The dependence of the position and peak width of the G and D bands on the self-bias voltage is shown in Fig. 2, where data obtained for a series of samples prepared at 8 Pa are also provided. It can be seen that there is a minimum in the position of the G peak around 300 V, where diamond-like layers are formed, while the D band has the lowest location around 100–200 V. Above 500 V, the G peak position increases and approaches the 1580 cm−1 peak of graphite. The peak width decreases, implying that some kind of ordering takes place in the a-C:H structure. In this region, the graphitization of the structure begins, and above 600 V of self-bias, the structure can be considered as graphitic a-C:H. Similar behaviour is observable for the G peak parameters at low voltages, where polymeric a-C:H layers are formed. For the samples prepared below 30 V, it reaches the position of 1600 cm−1 , well above the G peak position

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Fig. 2. Dependence of (a) the peak position and (b) the peak width on self-bias voltage of the D and G bands of a-C:H thin ﬁlms prepared from benzene at pressures of 8 and 18 Pa

of graphite, suggesting that the G peak in the spectra of these samples does not arise from graphitic domains. The band narrowing suggests the ordering of the structure. In Fig. 3, it can be seen that the I D /I G ratio has a minimal value in the diamond-like a-C:H ﬁlms, around 300 V self-bias. As we discussed before, the D band can be attributed to scattering of breathing modes rings or ring-like structure formed by sp2 -hybridized carbon atoms, while stretching modes of both rings and chains formed by sp2 sites contribute to scattering in the G

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Fig. 3. Dependence of intensity ratio of the D and G bands of the Raman spectra of a-C:H ﬁlm prepared from benzene at pressures of 8 and 18 Pa on self-bias voltage

band region. Hence, the I D /I G ratio indicates the ratio of the amount of (sp2 ) ring-like structural units to the total amount of (sp2 ) rings and chains. The increase of the I D /I G ratio is due to the presence of benzene rings or of their substituted forms in the structure, below 300 V self-bias. At the same time, the formation of graphitic structure, at large deposition voltages, explains the increase of the I D /I G ratio in that region. This explanation is in good accordance with the change of the G peak position with self-bias. Above and below that region, the a-C:H structure becomes more ordered. On strength of the analysis of the G band behaviour, one can conclude that this ordering in polymeric and graphitic layers has diﬀerent origin. This is supported by Raman spectroscopic investigations performed with infrared excitation. In several works [13, 32, 33, 34], it is noted that the use of two peaks for the decomposition of the Raman spectra of a-C:H thin ﬁlms is inaccurate, so the ﬁtted curve diﬀers from the experimental one. This suggests that not only structural units, vibrating at frequencies of G and D peaks, contribute to the spectra. However, since it is diﬃcult to determine the parameters of the extra peaks, the attempts made for their assignment have controversial results [13, 15, 33]. One way to obtain additional information on these bands is to change the excitation wavelength, since the dispersion of the peaks can be diﬀerent. Earlier investigations showed that the Raman scattering spectra of the amorphous carbon materials excited in the infrared light region can give additional information on the bonding structure [35]. Raman spectra of the samples measured by 785 nm excitation are shown in Fig. 4. The region

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Fig. 4. Raman spectra excited by 785 nm of a-C:H thin ﬁlms prepared from benzene at pressure of 18 Pa and diﬀerent self-bias voltage U SB

around 1000 cm−1 was cut out since, due to the resonance enhancement, the Raman scattering intensity arising from the Si substrate is several orders of magnitude higher than that of the a-C:H ﬁlms. By comparing Figs. 1 and 4, it can be concluded that there are signiﬁcant diﬀerences in the spectra of the same samples, especially at low self-bias voltages. While broad bands are characteristic of the 488 nm excited spectra, sharp peaks, at 1200, 1300, 1450 and 1600 cm−1 wavenumbers, can be found in the infrared excited ones of these ﬁlms. Besides the 1000–1600 cm−1 region, a broad band can also be seen around 1800 cm−1 . The increase of the self-bias results in broadening of the bands and shifting of their positions. At 120 V self-bias new bands appear in the spectra around 1200 cm−1 . The spectra were decomposed by sets of Gaussian and Lorentzian curves. It is convenient to analyse the narrow bands in the spectra of polymeric ﬁlms separately from broad bands. Figure 5 compares the Raman spectrum of the a-C:H ﬁlm prepared at 10 V self-bias with that of the benzene. Additionally, the spectrum of the part of the ﬁlm detached from the substrate is also provided. It can be seen

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Fig. 5. Comparison of the Raman spectra excited by 785 nm of (a) benzene, (b) detached from the substrate and (c) as-prepared a-C:H thin ﬁlm deposited from benzene at pressure of 18 Pa and 10 V of self-bias

that bands at 1190 and 1607 cm−1 in the spectra of the a-C:H ﬁlm arise from the presence of benzene rings in the structure. Another benzene peak at 1007 cm−1 , masked by the band of Si substrate, is observable only in the spectra of the detached ﬁlm. The diﬀerences in the band positions can be explained considering that there are not separate benzene rings, but substituted ones present in the structure. The substitution changes the symmetry of the molecule, thus forbidden Raman bands appear in the spectra too. Peaks at 1037, 1160, 1288 and 1448 cm−1 are related to substituted benzene, whose presence was supported by infrared transmission measurements [36] (not presented here). It is accepted that the sp3 carbon atoms contribute to the Raman spectra when it is excited in the UV region. Contrarily to this, information on the bonding conﬁguration of sp3 hybridized carbon atoms can also be deduced from the infrared excited spectra of the a-C:H ﬁlms prepared at low selfbias voltages. The small peak around 1382 cm−1 is presumably related to symmetric C–H deformation vibrations of sp3 CH3 groups. This mode usually has low Raman intensity, but not in the case of sp3 CH3 group attached to carbon atoms having double or triple bonds or to a benzene ring. The asymmetric pair of the vibration is around 1450 cm−1 , overlapped by the 1448 cm−1 mode of benzene. The characteristic C–H mode of sp3 CH2 group contributes to the spectra at 1300 cm−1 . The evolution of these bands with self-bias voltage (Fig. 4) evidences the intact benzene rings are present in the spectra of the a-C:H ﬁlms up to 80 V. The decomposition shows that, as a background of these narrow peaks, there are two broad bands, observable in the spectra of the 10 V sample, centred at 1378 and 1599 cm−1 . Their position is similar to that of the D and

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G bands in the spectrum excited by 488 nm (Fig. 2). The G band position (1599 cm−1 ) is higher than that in graphite (1580 cm−1 ). It is close to the 1607 cm−1 peak of the substituted benzene. This suggests that the sp2 carbon atoms in the amorphous carbon matrix have an arrangement close to that they have in a benzene molecule. Presumably, the amorphous phase of the sample contains a high amount of distorted benzene rings. As the self-bias increases, the shape of the spectra changes signiﬁcantly. In the spectra of the 80 and 120 V samples, in the 1000–1700 cm−1 wavenumber range, four broad bands are observable, centred around 1140, 1260, 1430 and 1566 cm−1 . The close position of the 1566 cm−1 peak to the G peak in the 488 nm excited Raman spectrum of the sample (at 1560 cm−1 ) suggests that this band is the G one, too. However, we must take into account that the D and G bands of a-C:H have dispersion. By estimating from the dispersion rates up to 785 nm of excitation, the D band of a-C:H ﬁlms has to be located around 1250 cm−1 and the G one is around 1430 cm−1 . By comparing these values with the data obtained for the 120 V sample, it can be assumed that the 1260 and 1430 cm−1 peaks of that correspond to the D and G peaks. So one gets the conclusion that there are two bands in the infrared excited spectrum that correspond to the G band: one, at lower wavenumbers, around 1430 cm−1 , showing dispersion, and the second, around 1566 cm−1 , having no dispersion. In Fig. 6 the dependence of the positions and widths of the broad bands, found in the 785 nm excited Raman spectra, on the self-bias voltage are shown. In the spectrum of the 10 V sample, the band showing no dispersion (“G(n−d) ” in the following) is located at 1599 cm−1 . The increasing selfbias causes the shift of the band position to lower wavenumbers. It reaches 1570 cm−1 at 120 V and does not vary signiﬁcantly above that voltage value. The band width is almost the same in the whole self-bias range. The position of the G peak that shows dispersion (“G(d) ” in the following) ﬂuctuates around 1430 cm−1 and broadens with the increasing self-bias. The position of the D band located at 1378 cm−1 in the spectrum of the 10 V ﬁlm decreases rapidly with the increase of the self-bias, down to 1230 cm−1 at 200 V, to the position expected with considering the dispersion. Above that voltage the band position does not change remarkably up to 500 V and increases above that value. As it was noted earlier, the dispersion of the bands in amorphous carbons is due to the size distribution of the clusters having diﬀerent band gaps. If one goes into the details of the phenomenon, which was observed also in hydrocarbon polymers built of “conjugated chains” (chains consisting of sp2 carbon atoms connected with alternating single and double bonds), it turns out that it is not the size that determines the band gap of a cluster, but the delocalization of the π electrons in it. The cluster size is only the upper limit for the delocalization length. The level of delocalization is determined by the lengths of conjugated regions, which depend on the bonding conﬁguration of the sp2 carbon atoms. Several fac-

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Fig. 6. Dependence of (a) the position and (b) width on self-bias voltage of the broad bands found in the Raman spectra excited by 785 nm of a-C:H thin ﬁlms prepared from benzene

tors can aﬀect on the delocalization length of a conjugated chain, including kinks, breaks in the periodicity of the alternating bonds and attachment of side-chains. It is known that the benzene molecule has an electronic conﬁguration such that its π electrons are delocalized only within the ring, but not out of it. From the absence of the G(d) band and the downshift of position of the D peak up to 80 V self-bias, it can be concluded that the increasing deposition

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voltage causes the increase of the extent of π electron delocalization in sp2 clusters. The behaviour of the G(n−d) band indicates that the atomic arrangement in the clusters of a-C:H matrix transforms. In the layers prepared at low self-biases, mainly distorted benzene rings form the cluster, while, with the increase of the voltage, the ratio of carbon atoms arranged into chains rises, as well as the delocalization length characteristic for the clusters. The amount of the intact benzene rings also decreases with the increasing self-bias from 10 V, and above 120 V they are completely destroyed. Above 120 V self-bias, the G(d) peak broadens and its intensity increases relative to the G(n−d) band. In the spectra of the 300 V sample, the two bands overlap, so as they can easily be treated as one. When the structure becomes graphitic (700 V), the G(n−d) band rises since there are graphitic rings present in the structure. The decomposition showed the presence of another broad peak located at 1130 cm−1 in the spectra of samples deposited at self-biases in the 80– 200 V range. The band shifts to higher wavenumbers with increasing self-bias. A similar band in the spectra of a-C:H was reported earlier and was related to vibrations of sp2 chains (trans-polyacethylene-like structural units) [37], sp3 carbon phase [38] and nano-crystalline diamond [13, 33]. The peak appears together with the 1430 cm−1 one, which was assigned to C–C stretching vibrations of structural units having large delocalization lengths of their π electrons. A typical representative of hydrocarbon chains, built of sp2 carbon atoms, is trans-polyacethylene. It has characteristic Raman peaks around 1450 cm−1 and 1100 cm−1 , both showing dispersion. Presumably, the 1130 cm−1 band can be assigned to vibrations of sp2 chains. Model calculations showed that, for short polyacethylene chains, the position of the latter band strongly depends on the chain length too, and shifts to lower wavenumbers with increasing chain length, while there is no such eﬀect observable for the other band [39]. The increase of the peak position with selfbias shows that, as the ﬁlms become more diamond-like, the length of the conjugated chains decreases in the clusters. Above 200 V, the band cannot be decomposed due to its overlapping with the D band. In conclusion, it was shown that infrared-excited Raman spectroscopy is an excellent tool for characterization of diﬀerent types of a-C:H thin ﬁlms. It can provide additional information on the bonding conﬁguration of carbon atoms in the structure. The spectra recorded by near-infrared excitation were decomposed into four peaks. It was found that the G peak has two components, one of which shows dispersion, while the position of the other does not change with excitation wavelength. In the lower wavenumber region, besides the D band around 1130 cm−1 , another peak appears in the spectra, related to vibrations of carbon atoms arranged into chains. By using the infrared-excited Raman spectroscopy, the evolution of the structure of a-C:H layers prepared from benzene was investigated. It was shown that, at low self-bias voltages (up to 120 V), intact (substituted) ben-

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zene rings embedded into the amorphous structure. In addition, the amorphous matrix of the ﬁlm prepared at 10 V contains structural units not differing remarkably from benzene. Their content, as well as that of substituted benzene decreases with increasing self-bias. The sp2 carbon atoms arrange into chains. The small delocalization length also increases with deposition voltage. From 120 V to 400 V, the chains dominate the sp2 clusters. The increasing with self-bias graphitic character will dominate the spectra of the samples above 400 V. Visible and infrared excited Raman spectroscopic measurements were also performed on a-C:H samples prepared from methane in a wide self-bias range. In the following, the results of these investigations will be presented. 2.2 a-C:H Thin Layers Prepared From Methane The methane ﬁlms were prepared similarly to benzene ones at chamber pressures of 13 Pa. The Raman spectra of the a-C:H ﬁlms excited at 488 nm are shown in Fig. 7. The shape of the spectra is similar to those presented in Fig. 1. The only diﬀerence is that there was not so high a luminescence background observable in the samples prepared at low voltages. The spectra were analysed similarly to the benzene ones. Figure 8 shows the variation of positions and widths of D and G bands with the self-bias voltage. Contrarily to the layers prepared from benzene (Fig. 2), the positions of both bands increase monotonically with the self-bias. The peak width of the D band increases also monotonically, while that of the G peak, after a small increase, decreases above 60 V. The comparison with the results obtained for the a-C:H ﬁlms deposited from diﬀerent source gases shows that in the low self-bias range the sample series prepared from benzene and methane behave diﬀerently. In case of the benzene layers, the presence of ring-like units (distorted benzene rings) in the amorphous structure causes the G peak to appear around 1600 cm−1 . On the contrary, in the 30 V sample prepared from methane, the G peak is located at 1537 cm−1 , suggesting that chain-like structural units are mainly present in the sp2 clusters. The shift of the G band to higher wavenumbers with increasing self-bias indicates the increase of the amount of ring-like structures in the sp2 clusters of the ﬁlm. This is supported by the change of the I D /I G ratio of the ﬁlms (Fig. 9), which also diﬀers from that of the benzene ones. It rises monotonically with the increasing self-bias, showing the increase of the ratio of the rings in the structure. The huge diﬀerence in the bonding structure of a-C:H ﬁlms prepared from methane and benzene at low self-biases are also evidenced from their Raman spectra excited at 785 nm. While the spectra of the benzene ﬁlms are characterized by narrow peaks (Fig. 4), those of methane layers are composed of broad bands (Fig. 10). The spectrum of the layer prepared from methane at 30 V self-bias is similar to the spectra of the ﬁlms prepared from benzene at 300–500 V potential and evolves with the increase of the self-bias similarly

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Fig. 7. Raman spectra excited by 488 nm of a-C:H thin ﬁlms prepared from methane at diﬀerent self-bias voltage U SB

to the benzene ones above 300 V, where the π sites have large delocalization length. The spectra were decomposed by a set of four Gaussians. The variation of the positions and peak widths of the component bands with self-bias voltage are shown in Fig. 11. The positions of component bands are similar to those found in the benzene samples above 200 V self-bias. This implies that these peaks have the same origin. Hence, the infrared-excited Raman spectra of methane layers also have the D, G(d) and G(n−d) bands (around 1230, 1430 and 1570 cm−1 , respectively), as well as the peak assigned to vibrations of sp2 carbon atoms arranged into chains (around 1150 cm−1 ). The position of the latter band, located in the spectra of the 30 V sample at 1105 cm−1 , shifts to lower wavenumbers with the increase of the self-bias, showing the increase of the sp2 chain lengths of in the clusters [39], and becomes undetectable in the spectrum of the 600 V sample. In the ﬁlms prepared from benzene, the band is positioned at higher wavenumbers, indicating the smaller chain lengths in the clusters of those layers.

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Fig. 8. Dependence of (a) the peak position and (b) the peak width on self-bias voltage of the D and G bands of a-C:H thin ﬁlms prepared from methane

The position and width of the G(d) band do not change signiﬁcantly with the increase of the self-bias, but its intensity decreases as the graphitic character of the structure strengthens. This is accompanied by the shift of the G(n−d) peak from 1560 cm−1 to higher wavenumbers. The comparison of the bonding conﬁguration of the a-C:H thin layers prepared from methane and benzene shows that the structure of the ﬁlms prepared under similar conditions diﬀers signiﬁcantly at low self-biases. In the benzene molecule, the carbon atoms have preferential arrangement. At

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Fig. 9. Dependence of intensity ratio of the D and G bands of the Raman spectra of a-C:H ﬁlm prepared from methane on self-bias voltage

Fig. 10. 785 nm excited Raman spectra of a-C:H thin ﬁlms prepared from methane at diﬀerent self-bias voltage U SB

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Fig. 11. Dependence of (a) the position and (b) width on self-bias voltage of the broad bands found in the Raman spectra excited by 785 nm of a-C:H thin ﬁlms prepared from methane

low ion energies, the amorphous carbon matrix mainly consists of distorted benzene rings, so that besides intact rings, distorted benzene rings are also present in the a-C:H matrix. This arrangement causes the π electrons to be highly localized in the rings of clusters. As the ion energy increases, these rings are destroyed in the plasma, as well as during the bombardment of the surface of the growing ﬁlm, and the atoms rearrange, forming sp2 clusters characterized by large delocalization lengths. Clusters containing large

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amount of sp2 chains develop in the self-bias region, where diamond-like aC:H forms. With further increase of the deposition voltage, the graphitic clusters will dominate in the layer. On the contrary, for the methane molecule consisting of only one carbon atom, there is no preferential arrangement. Therefore, during ﬁlm formation, the topology of the carbon atoms develops without initial constraints, excepting for the bonding angles, set by the hybridization state of the carbon atom. The sp2 clusters, formed at low self-biases, are built of carbon atoms arranged in both rings and chains and have large delocalization lengths, compared to the benzene ones prepared under similar conditions. The increase of the deposition voltage up to the region, where diamond-like carbon deposits, causes the lengthening of the sp2 chains. Above this self-bias, the graphitization of the structure starts, similarly to the benzene layers. In conclusion, it was shown that Raman scattering excited in the nearinfrared region can provide additional information about the bonding conﬁguration of of a-C:H thin ﬁlms in a wide range of deposition conditions. Hence, it can be dependably used for quality control of these materials. The method was proved to be highly sensitive to the arrangement of the carbon atoms in the sp2 clusters. The discrepant dispersion of the component peaks made the composite spectra to be decomposed more obvious, and it could give an experimental basis for the assignment of the bands found in the Raman spectra of a-C:H.

References [1] R. Shuker, R. Gamon: Phys. Rev. Letters 25, 222 (1970) 426 [2] S. Craig, G. L. Harding: Thin Solid Films 96, 345 (1982) 426 [3] D. R. McKenzie, R. C. McPhedran, N. Savvides, L. C. Botten: Philos. Mag. B 48, 341 (1983) 426 [4] J. Robertson: Adv. Phys. 35, 317 (1986) 426 [5] J. Robertson, E. P. O’Reilly: Phys. Rev. B 35, 2946 (1987) 426 [6] J. Robertson: Mat. Sci. Eng. R 37, 129 (2002) 426 [7] T. Frauenheim, P. Blaudeck, U. Stephan, G. Jungnickel: Phys. Rev. B 48, 4823 (1993) 427 [8] G. Jungnickel, T. Frauenheim, D. Proezag, P. Blaudeck, U. Stephan: Phys. Rev. B 50, 6709 (1994) 427 [9] R. Nemanich, J. Glass, G. Lucovsky, , R. Shroder: J. Vac. Sci. Technol. A 6, 1783 (1988) 427 [10] M. A. Tamor, J. A. Haire, C. H. Wu, K. C. Hass: Appl. Phys. Lett. 54, 123 (1989) 427, 428 [11] S. Xu, M. Hundhausen, J. Ristein, B. Yan, L. Ley: J. Non-Cryst. Solids 1127, 164–166 (1993) 427, 429 [12] M. A. Tamor, W. C. Vassel: J. Appl. Phys. 76, 3823 (1994) 427, 429 [13] J. Schwan, S. Ulrich, V. Bathori, H. Erhardt, , S. R. P. Silva: J. Appl. Phys. 80, 440 (1996) 427, 432, 437

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[14] A. C. Ferrari, J. Robertson: Phys. Rev. B 61, 14095 (2000) 427, 428, 429 [15] A. C. Ferrari, J. Robertson: Phys. Rev. B 64, 75414 (2001) 427, 428, 429, 432 [16] M. J. Pelletier (Ed.): Analytical Applications of Raman Spectroscopy (Blackwell Science 1999) 427 [17] R. Nemanich, S. A. Solin: Phys. Rev. B 20, 392 (1979) 427 [18] J. Maultzsch, S. Reich, C. Thomsen: Phys. Rev. B 70, 155403 (2004) 427, 428 [19] Y. Kawashima, G. Katagiri: Phys. Rev. B 52, 10053 (1995) 427 [20] P. H. Tan, C. Y. Hu: Phys. Rev. B 64, 214301 (2001) 427 [21] J. Wagner, M. Ramsteiner, C. Wild, P. Koidl: Phys. Rev. B 40, 1817 (1989) 427 [22] F. Tuinstra, J. L. Koenig: J. Chem. Phys. 53, 1126 (1970) 428 [23] M. Chhowalla, A. C. Ferrari, J. Robertson, G. A. J. Amaratunga: Appl. Phys. Lett. 76, 1419 (2000) 428 [24] M. Ramsteiner, J. Wagner: Appl. Phys. Lett. 51, 1355 (1987) 428 [25] M. Yoshikawa, G. Katagiri, H. Ishida, A. Ishitani, T. Akamatsu: Solid State Commun. 66, 1177 (1988) 428 [26] M. Yoshikawa, N. Nagai, M. Matsuki, H. Fukuda, G. Katagiri, H. Ishida, A. Ishitani, I. Nagai: Phys. Rev. B 46, 7169 (1992) 428 [27] I. P´ ocsik, M. Ko´ os, M. Hundhausen, L. Ley: Amorphous Carbon: State of the Art (World Scientiﬁc, Singapore 1998) p. 224 428 [28] C. Mapelli, C. Castiglioni, G. Zerbi, K. M¨ ullen: Phys. Rev. B 60, 12710 (2000) 428 [29] I. P´ ocsik, M. Hundhausen, M. Ko´ os, L. Ley: J. Non-Cryst. Solids 1083, 227– 230 (1998) 428 [30] M. Ramsteiner, J. Wagner: Appl. Phys. Lett. 51, 1355 (1987) 428 os, I. P´ ocsik, J. Kokavecz, Z. T´ oth, [31] M. Veres, M. F¨ ule, S. T´ oth, M. Ko´ G. Radn´ oczi: J. Non-Cryst. Solids 351, 981 (2005) 429 [32] J. Rao, K. J. Lawson, J. R. Nicholls: Surface Coatings Technol. 197, 154 (2005) 432 [33] S. R. P. Silva, G. Amaratunga, E. Salje, K. Knowles: J. Mater. Res. 29, 4962 (1994) 432, 437 [34] A. I. Kulak, A. V. Kondratyuk, T. I. Kulak, M. P. Samtsov, D. Meissner: Chem. Phys. Lett. 378, 95 (2003) 432 [35] I. P´ ocsik, M. Ko´ os, S. H. Moustafa, J. A. Andor, O. Berkesi, M. Hundhausen: Michrochim. Acta [Suppl.] 14, 755 (1997) 432 [36] M. Veres, M. Ko´ os, I. P´ ocsik: Diamond Relat. Mater. 11, 1115 (2002) 434 [37] A. C. Ferrari, J. Robertson: Phys. Rev. B 63, 121405 (2001) 437 [38] R. E. Shroder, R. J. Nemanich, J. T. Glass: Phys. Rev. B 41, 3738 (1990) 437 [39] F. J. Owens: Physica E 25, 404 (2005) 437, 439

Index π states, 423, 426

a-C:H, 426, 428–443

σ states, 427

sp2 -bonded clusters, 426–429, 435, 437–439, 442, 443

a-C, 428

Raman Spectroscopy of CVD Carbon Thin Films cluster conjugation level, 427 cluster size, 426–429, 435 sp2 -chains, 427, 431, 432, 435–439, 443 chain length, 439, 443 sp2 -rings, 426, 427, 431, 434, 435, 437, 438, 442, 443 distorted rings, 435, 437, 438, 442 six-fold rings, 426 sp3 /sp2 bonding ratio, 427 ta-C, 428

445

dispersive G band, 435–437, 439, 440 non-dispersive G band, 435, 437, 439, 440 graphene, 427 graphite, 426–428, 430, 431, 435 graphitization, 430, 438, 443 H¨ uckel approximation, 426 multi-wavelength Raman spectroscopy (MWRS), 428

amorphous carbon thin ﬁlms, 423 normal modes, 424 chemical vapour deposition (CVD) radio frequency CVD, 429 cluster model, 426 clustering, 426–429, 435, 437, 438 coherence length, 428 crystallite size, 428 D band, 427–432, 434–438, 440 D/G band intensity ratio, 428, 431, 432, 438, 441 diamond, 426, 427 diamond-like carbon (DLC), 428, 430, 431, 437, 443 dispersion, 423, 428, 432, 435–437, 439, 440, 443 electron-phonon coupling, 425 electron-photon coupling, 425 G band, 423, 427–432, 435, 437, 438, 440

phonons, 423, 425 zone centre phonons, 424 polarizability, 424, 425 polarizability tensor, 424 Raleigh scattering, 424 Raman scattering, 423 anti-Stokes scattering, 423 infrared excitation, 423, 429, 432–435, 437–439 Raman intensity, 426 Raman spectrum, 426 Raman tensor, 424, 425 resonant Raman scattering, 425, 428 selection rules, 425 breakdown of the selection rules, 426 Stokes scattering, 423 visible excitation, 423, 424, 427, 429, 438

The Role of Hydrogen in the Electronic Structure of Amorphous Carbon: An Electron Spectroscopy Study Lucia Calliari, Massimiliano Filippi, Nadhira Laidani, Gloria Gottardi, Ruben Bartali, Victor Micheli, and Mariano Anderle ITC-irst I-38050 Povo (Trento), Italy [email protected] Abstract. Two processes are examined by electron spectroscopy techniques, namely hydrogen incorporation into amorphous carbon (a-C) and hydrogen evolution from hydrogenated amorphous carbon (a-C:H). The energy E p of the π + σ plasmon loss (related to the material mass density) turns out to be the most sensitive indicator of the degree of H incorporation. Other spectral features, on the other hand, consistently conﬁrm that H acts as a stabilizer of the sp3 phase in amorphous carbon systems. H evolution is thermally activated from a-C:H once the material stability threshold (≈ 100◦ C for the ﬁlm of the present study) is exceeded. It ﬁrst leads to massive sp3 to sp2 conversion, followed by graphitic order development. No univocal relationship exists between the sp2 fraction and the π band photoemission intensity.

1 Introduction Carbon is unique in the variety of crystalline and disordered structures it can give rise to, owing to the variety of possible hybridizations (sp3 , sp2 and sp1 ) of its electron states. Among the disordered structures, amorphous carbons are a class of metastable materials produced under conditions far from thermodynamic equilibrium, so that the lower energy crystalline phase is not formed. They are described as a mixture of mainly threefold and fourfold coordinated atoms. Because a one-to-one correspondence exists between carbon coordination and bonding state for crystalline materials, diamond and graphite, the same was assumed also for amorphous materials, leading to interchangeably characterize them either in terms of the relative amount of threefold and fourfold coordinated atoms or in terms of the fraction of sp2 - and sp3 -bonded atoms. However, this is not strictly true for the amorphous state, where strained conﬁgurations may result in intermediate hybridizations of the electron states [1, 2, 3]. As a consequence, a one-to-one relationship between atomic coordination and electron states hybridization no longer holds in this case [4, 5]. Nevertheless, a great deal of experimental work has been successfully performed under the assumption that atoms in a-C can indeed be classiﬁed according to a well-deﬁned hybridization state (sp2 or sp3 ) [2]. G. Messina, S. Santangelo (Eds.): Carbon, The Future Material for Advanced Technology Applications, Topics Appl. Phys. 100, 447–463 (2006) © Springer-Verlag Berlin Heidelberg 2006

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In spite of its importance, however, just knowing the fraction of atoms in one hybridization state or the other does not univocally determine the electronic structure of a-C [6]. This is due to the π-bonding-driven interaction among sp2 sites [6], which, for a given sp2 fraction, may result in a variety of electronic structures depending on the spatial distribution of the sp2 sites. Basically, the distribution can be spatially inhomogeneous, with nanosized graphitic domains randomly distributed through the system, or spatially homogeneous, with the sp2 sites spread through the sp3 phase like in a “raisin cake” [7]. Systems of the former type, where a conjugated π electron structure exists in graphitic regions, are referred to as “graphitic” [8], and they are described by Robertson’s cluster model [9]. Systems of the latter type, where the graphitic structure is destroyed and a conjugated π electron system does not exist, are referred to as “nongraphitic” [8]. They are described by a revised version of the original Robertson’s cluster model [10]. Needless to say, each of the above two categories includes a variety of materials which diﬀer either in the size of the graphitic domains or in the way sp2 sites interact (isolated sites, pairs, chains, even- and odd-membered rings). Knowledge of the electronic structure of amorphous carbon systems (needed to predict the material properties) thus requires specifying the clustering features of the sp2 sites in addition to the sp2 fraction [6]. Closely related to amorphous carbons are their hydrogenated analogues (a-C:H), whose properties are even more diﬃcult to foresee as compared to a-C systems. In fact, besides the sp2 fraction and the clustering features of the sp2 sites, shared with a-C materials, the H content and the way it is incorporated are in this case further structural features relevant to the material properties [6]. When incorporated into the structure of amorphous carbon materials, H primarily saturates π bonds, thereby converting sp2 C=C into sp3 ≡CH, =CH2 and −CH3 bonds [6, 11]. In this sense, it generally leads to an increased sp3 fraction and a wide energy gap (≈ 3 eV). However, the material mechanical properties get poorer and its mass density decreases, mainly as a result of the reduced cross-linking in the carbon network [11]. A number of techniques were employed to characterize a-C and a-C:H materials. They can be divided into techniques that probe either the C atom environment (diﬀraction techniques), or the electron states about the C atom (electron spectroscopy techniques). In the former case, the atomic coordination, together with bond lengths and bond angle distributions, is measured. In the latter case, the electronic structure is described, from which the sp2 fraction and the possible existence of a conjugated π electron structure can in principle be derived. In the present work, selected examples from the class of a-C:H materials are investigated by electron spectroscopy techniques that probe the occupied electronic structure. These include core level photoemission, X-ray and

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UV excited valence band (VB) photoemission, C KVV Auger emission and electron energy loss spectroscopy (EELS) in the plasmon region. The focus is ﬁrst on the problem of unraveling eﬀects due to changes in the sp2 fraction, on the one hand, and in sp2 clustering, on the other hand. The two are in fact often tangled in the features of electron spectra. Second, we address the issue about how and to which extent H is incorporated into the structure of amorphous carbon. It is well known in this regard that H cannot be directly detected by electron spectroscopy techniques, so that its presence can only be indirectly revealed. The paper is organized as follows. After the introduction, experimental methods are given in Sect. 2. Sections 3 and 4 describe two experiments selected to discuss the electronic structure changes brought about by adding hydrogen to a-C (Sect. 3) and by subtracting hydrogen from a-C:H (Sect. 4). In particular, Sect. 3 deals with the investigation of a series of ﬁlms deposited by graphite sputtering in Ar–H2 plasma, with variable H2 concentration in the plasma feed gas. On the other hand, Sect. 4 refers to a vacuum annealing experiment (from room temperature (RT) up to 700◦C) performed on a hydrogenated amorphous carbon sample in order to cause hydrogen evolution from the ﬁlm. Concluding remarks are given in Sect. 5.

2 Experimental 2.1 Hydrogen Incorporation in the Structure of a-C Amorphous carbon ﬁlms were deposited on silicon wafers by sputtering a graphite target in 5 Pa rf (13.56 MHz) discharges at variable power. A constant dc self-bias on the cathode was maintained at −550 V, corresponding to an eﬀective load power of 40 W. The H2 concentration in the feed gas ranged from 0 to 100 vol. %, but the useful range for ﬁlm growth was limited to 0–84%. The total ﬂux of H2 was 30 sccm. The samples were mounted on a rotating support, at a distance of 8 cm from the cathode and without application of any external bias, so that the ﬁlms grew at the ﬂoating potential given by the plasma. Both the cathode and the sample holder were water cooled. The thickness of the ﬁlms, as measured by a mechanical stylus proﬁlometer, ranged from 100 to 480 nm. X-ray photoemission spectra (XPS) and X-ray excited Auger emission spectra were acquired within a SCIENTA ESCA200 instrument equipped with a monochromatic Al Kα (hν = 1486.6 eV) X-ray source and a hemispherical analyzer. No electrical charge compensation was required to perform the analysis. Electrons were detected along the surface normal. The energy resolution, as measured on the Ag Fermi edge, was 0.4 eV for the C 1s spectrum and 0.6 eV for the C KVV and VB emission spectra.

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2.2 Temperature-Induced Hydrogen Evolution from a-C:H The a-C:H ﬁlm used for the annealing experiment was deposited on (100) Si wafers in a capacitively coupled RF-PECVD system (13.56 MHz) using a mixture of CH4 –CO2 (50% CO2 ) as gas precursor. The sample was mounted on the water-cooled anode and ion assistance during ﬁlm growth was obtained by applying a pulsed bipolar (±50 V) bias voltage, with a 100 kHz frequency and a constant duty cycle of 50% (for the positive part of the pulse) [12]. The annealing experiment took place in a separated ultra high vacuum (UHV) system equipped with a sample preparation chamber and an analysis chamber. The ﬁlm was step annealed from RT to 700◦ C in the former, while electron spectra were measured, after each annealing step, in the latter. The sample, clamped on a Mo sample holder, was heated by radiation and electron bombardment from a tungsten ﬁlament at the back of the sample holder. The temperature was measured by a nickel–chromel thermocouple. For each annealing step, the temperature was increased at a rate of 10◦ C/min up to the maximum temperature, where the sample was kept for 5 min. UV photoemission spectra were excited by the HeII (hν = 40.8 eV) line from a He discharge lamp. C KVV Auger spectra were induced by X-rays from a nonmonochromatic Mg Kα (hν = 1253.6 eV) source, while EEL spectra were associated with a backscattered primary electron beam of 2 keV. All spectra were acquired with a double-pass cylindrical mirror analyzer (CMA) at an energy resolution, as measured on a Pd Fermi edge, of 0.5 eV for VB photoemission and 1 eV for C KVV emission. For the EEL spectrum, the energy resolution is 1.3 eV, as given by the FWHM of the backscattered electron peak.

3 Hydrogen Incorporation in the Structure of a-C The eﬀects of hydrogenation are examined on a series of amorphous carbon ﬁlms deposited by graphite sputtering in Ar–H2 plasma [13, 14]. The H2 content in the gas mixture, hereafter referred to as [H2 ], varies from 0 to 84%. Contrary to a possible expectation, the hydrogen content in the ﬁlms does not increase monotonically with [H2 ]. The integrated FTIR absorbance of the C–Hx bonds in the ﬁlms, related to the bound hydrogen content, exhibits [13] a sharp maximum for low (≈ 10%) [H2 ] and decreases beyond this maximum as [H2 ] increases. The behavior was explained elsewhere [13] in terms of the diﬀerent graphite sputtering regimes occurring at low and high H2 concentrations in the feed gas. Figure 1 shows the low-energy EEL spectrum associated with C 1s photoelectrons for two ﬁlms deposited at [H2 ] = 0% and [H2 ] = 16%, respectively. For carbon systems, this spectrum is dominated by two plasmon loss features: a low-energy peak (≈ 4 − 6.5 eV) assigned to excitations involving π electrons

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Fig. 1. EEL spectrum for a [H2 ] = 0 % (continuous line) and a [H2 ] = 16 % (dotted line) ﬁlm. The zero-loss peaks are normalized to a common height

only and a high-energy peak (≈ 23–34 eV) assigned to excitations involving both π and σ electrons. The energy, E p , of the π + σ plasmon is related to the material electron (and hence atomic) density through the relation: ne 2 , (1) E p = ω = 0 m which is derived within the free electron approximation. Here n is the valence electron density taking part in the plasma oscillation (each C atom is assumed to contribute four electrons), e is the electron charge, 0 is the vacuum dielectric function and m is the free electron mass. The ﬁgure shows that the ﬁlm deposited in a hydrogen-containing plasma is characterized by a lower E p , and hence by a lower mass density, as compared to the ﬁlm deposited in pure Ar plasma. To measure E p , a linear background was subtracted and the π+σ plasmon feature was ﬁtted to a Gaussian peak. Its evolution over the ﬁlm series is given in Fig. 2. The straight line is the best ﬁt through the [H2 ] = 0 points. At [H2 ] = 0 %, E p is ≈ 25 eV, which is typical for unhydrogenated amorphous carbon ﬁlms [15]. As soon as [H2 ] becomes diﬀerent from zero, an abrupt decrease down to ≈ 22 eV is observed for [H2 ] = 3%. From this point on, however, E p increases with [H2 ]. In C–H systems, a decrease in mass density is related to an increased H content in the material, and it is not only due to the low H mass, but also to the reduced average coordination number. For the present ﬁlms, a variation in the H content was indeed demonstrated by FTIR measurements [13]. We therefore conclude from Fig. 2 that the H content in the ﬁlms increases, goes

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Fig. 2. Energy of the π + σ plasmon as a function of the H2 concentration in the palsma feed gas

through a maximum and then decreases as the H2 concentration in the gas mixture increases from 0 to 84%. By enabling us to tell apart ﬁlms diﬀering in the H content, E p turns out to be the most sensitive indicator of the ﬁlm H content. In contrast, other spectral features only single out ﬁlms deposited at [H2 ] = 0% from ﬁlms deposited at [H2 ] = 0, while they are not sensitive enough to discriminate among ﬁlms in the [H2 ] = 0 region [14]. For this reason, the eﬀects of hydrogenation on the ﬁlm electronic structure are considered in Fig. 3 by comparing spectra from ﬁlms deposited at [H2 ] = 0% (continuous line) and [H2 ] = 0 (dotted line), without specifying the [H2 ] value. Figure 3a shows the EEL spectrum associated with C 1s photoelectrons and already considered with regard to the π + σ plasmon energy. Here we focus on the π plasmon, detected at ≈ 4.4 eV from the zero-loss peak on the [H2 ] = 0 spectrum, but missing on the [H2 ] = 0 spectrum. The π plasmon is known to probe graphitic ordering, rather than just the sp2 fraction [6,16,17]. For graphite, it is intense and it occurs at 6.5 eV from the zero-loss peak. It has a FWHM of 2.4 eV, which implies a decay time τ of plasma oscillations on the order of 10−15 s. The peak has similar features for samples where, in spite of a missing long-range graphitic order, the C atoms are nonetheless predominantly bonded in warped graphite-like planes, such as in glassy

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Fig. 3. Comparison between [H2 ] = 0 and [H2 ] = 0 spectra: π plasmon loss associated with C 1s photoelectrons (a), C 1s photoemission (b), VB photoemission (c), C KVV emission (d). Spectra in each panel are normalized to a common height of the most intense C feature. Binding and kinetic energies are referred to the Fermi level. On part (d) the vertical line marked EF represents the Fermi level oﬀset by the C 1s binding energy

carbon [18] or carbon nanotubes [19]. If, however, disorder is introduced into such threefold-coordinated materials and the size of graphitic regions becomes smaller, the π plasmon peak shifts to lower energy, decreases in height and broadens [19]. For “nongraphitic” amorphous carbon, where no graphite-like regions exist, the π plasmon peak vanishes, even though the material is highly sp2 bonded [16].

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Figure 3a shows that π bonding exists in the ﬁlm deposited in pure Ar plasma, though the low energy and low intensity of the π plasmon peak suggest a very limited clustering of the sp2 sites. On the other hand, the disappearance of the feature for ﬁlms grown in a hydrogen-containing atmosphere is most likely indicative of π bonding saturation by hydrogen. Such an eﬀect is observed also on the two VB-related spectra, namely VB photoemission (Fig. 3c) and C KVV Auger emission (Fig. 3d). (Remember that the latter basically represents a self-fold of the VB density of states (DOS) [20,21]). For [H2 ] = 0, both spectra exhibit a decrease in the DOS near the Fermi level E F . While in fact π states reach E F for the ﬁlm deposited in Ar plasma, these states are washed out for ﬁlms grown in Ar–H2 plasma. The related high binding energy shift in the VB top, E V (enlarged in the inset of Fig. 3c is estimated around 1 eV, which represents a lower limit for the energy gap. The total gap width cannot be measured, in fact, by probing only the occupied electron states. In addition to sweeping out π states from the Fermi level region, the presence of H2 in the plasma feed gas also causes a narrowing of the σ band. This is seen on the VB photoemission spectrum (Fig. 3c) for the 2s states (the diﬀerent widths of the C 2s peaks are not an artifact due to the presence of the Ar 3s peak) and on the C KVV spectrum (Fig. 3d) for the 2p states. Remember that the latter spectrum is contributed by σ2p states around the peak maximum and by π2p states at the spectrum leading edge [21]. Both the 2s and the 2p DOS thus decrease in width when hydrogen is added to the amorphous carbon network. By modeling X-Ray excited VB photoemission (s DOS sensitive) and X-Ray emission (p DOS sensitive) spectra, it was demonstrated [22] that a narrowing in the σ2s and in the combined σ2p and πp states distribution occurs on moving from graphite to diamond. Experimentally, a narrowing of spectral features on going from graphite to diamond has been observed for X-Ray VB photoemission spectra [23] and for C KVV Auger spectra [24]. The narrowing of spectral features observed for hydrogen-containing ﬁlms is therefore understood in terms of an increased sp3 fraction. Note that Ar is seen on the [H2 ] = 0 spectra. Due to a favorable photoionization cross section [25], it is particularly evident on the VB photoemission spectrum, though its concentration, as estimated from the Ar 2p and C 1s peaks, is on the order of a few at. %. In contrast, Ar is not observed on the [H2 ] = 0 spectrum, because of a decreased density of Ar+ ions in the plasma when [H2 ] = 0 [13]. Figure 3b shows the C 1s spectrum after subtracting a Shirley background. The spectra are aligned to a common energy of 284.45 eV (characteristic of [H2 ] = 0 spectra). A mild electrostatic charging occurring for [H2 ] = 0 ﬁlms under photon irradiation prevents us from discussing possible changes in the C 1s binding energy, so that we only focus on peak shape. The FWHM of the two spectra is around 1.2 eV. A small high binding en-

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ergy tail is observed on all spectra and it is assigned to C–O bonds, given that a certain amount of oxygen (4–10 %) is present in the ﬁlm near-surface region. However, a statistics of over 15 samples consistently shows that ﬁlms produced in a pure Ar plasma exhibit a high binding energy tail which cannot be accounted for by C–O components unless unrealistic O concentrations are assumed (note that the two spectra in Fig. 3 refer to samples having the same O content). Line asymmetry in core-level photoemission is associated with small energy electron–hole excitations near the Fermi level as a response to the created photo-hole. As such, it is characteristic of metals and semimetals, like graphite [26, 27]. The concept was used to describe the C 1s spectrum from amorphous carbon systems [28, 29, 30], and asymmetry was shown to be related to the existence of a π DOS near the Fermi level. This is also the case here: an asymmetric C 1s lineshape is observed only for ﬁlms (deposited in pure Ar plasma) whose π states reach the Fermi level. All spectra in Fig. 3 thus consistently show that H removes π states from the VB top, thereby opening a gap, and leads to an increased sp3 fraction.

4 Temperature-Induced Hydrogen Evolution from a-C:H Hydrogen evolution from a-C:H materials is easily obtained, for example, by thermal annealing and was experimentally demonstrated by either measuring the gaseous species evolving from the ﬁlms [31, 32] or by characterizing the ﬁlm composition via H sensitive techniques, such as FTIR [31, 33, 34]. Here we present results from an experiment in which a hydrogenated amorphous carbon ﬁlm is step-annealed in vacuum from RT up to 700◦ C. After each annealing step, the near-surface composition and structure are characterized in terms of UV-excited VB photoemission, Auger emission and EELS in the plasmon region. The HeII excited VB photoemission spectrum from a sample annealed at 400◦ C (dotted line) is compared to the spectrum from a RT sample (continuous line) in Fig. 4. A background, consisting of a third-degree polynomial extrapolated from the energy regions at either side of the peak, was subtracted from the spectra, which were then normalized to a common height. The diﬀerence spectrum (400◦ C− RT) is also given. The spectra diﬀer in two energy regions, namely from 0 to 5 eV and from 8 to 12 eV. Thermal annealing clearly removes electron states from the latter region and generates new states in the former. The upper VB (0–5 eV) is where π states are located, while the region around 10 eV is where H-induced states in the σp band occur. This was shown by calculated DOS [9, 35], and it was also demonstrated in experiments in which a diamond surface undergoes repeated cycles of hydrogenation and annealing [36, 37]. Such cycles lead, respectively, to a H-terminated and clean, reconstructed surface. Correspondingly, a transfer of

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Fig. 4. HeII (hν = 40.8 eV) excited VB photoemission spectra: RT (continuous line), 400◦ C (dotted line). The diﬀerence spectrum (400◦ C − RT) is also shown

states from the π region to the C–H states region and vice versa is observed. For diamond, π states are associated with the reconstruction of the clean surface [37], while the H termination inhibits surface reconstruction and freezes the atoms in their tetrahedral bulk conﬁguration. Considering the analogy with diamond on the one hand, and the fact that H is known [6] to stabilize the sp3 phase in a-C:H on the other hand, C–H states between 8 and 12 eV have most likely to be associated with sp3 -hybridized electron states. Annealing at 400◦ C therefore causes the disappearance of H-induced (sp3 hybridized) electron states and the corresponding formation of π states. In other words, dangling bonds generated by temperature-induced H desorption are saturated via π bond formation. The evolution of H-induced states and π states intensity over the considered temperature range is depicted in Fig. 5a, b. To measure the respective intensity, spectra were handled as in Fig. 4. For each temperature T , the diﬀerence between the spectrum at temperature T and the RT spectrum was calculated. On the diﬀerence spectrum, the negative area in the 8–12 eV region is assigned to C–H states, while the positive area in the 0–5 eV region is assigned to π states. The C–H states contribution to the spectrum (Fig. 5a) is stable up to a temperature of 100◦ C. It decreases markedly on going from 100 to 250◦ C

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Fig. 5. Temperature evolution of three spectral features: C–H states area (a), π states area (b), ∆ (c). See text for the intensity measurements (referred to the RT spectrum). The horizontal dashed line in part (c) gives the ∆ value we measured for graphite

and tends to stabilize above this temperature, where only a slight decrease is observed. Also the π states contribution to the spectrum (Fig. 5b) remains constant, at the RT value, up to 100◦ C. From 100 to 250◦ C, it increases sharply. Above 250◦ C, however, no stabilization occurs. On the contrary, the π states’ contribution to the spectrum keeps on increasing, though to a lower rate, over the 250–500◦C range, and it increases at a faster rate over the 500–700◦C range. Thus only up to 250◦ C does their behavior mirror the C–H states’ evolution. It reveals that, from 100◦C to 250◦ C, H evolves from the ﬁlm and π states are formed at the expense of C–H (sp3 -hybridized) states. At higher temperatures, however, the fate of the π states is not linked to the fate of C–H states. Figure 5c gives the temperature evolution of the energetic distance ∆, measured on the derivative C KVV spectrum and deﬁned in the inset. ∆ is stable, around 16 eV, up to 150◦ C. It markedly increases to ≈ 21 eV on going

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Fig. 6. HeII (hν = 40.8 eV) excited VB photoemission spectra: T = 400◦ C (continuous line), T = 700◦ C (dotted line). Also shown is the diﬀerence spectrum (700◦ C−400◦ C)

from 150 to 300◦C, while it is nearly stable above 400◦ C. ∆ is known [38,39] to be a sensitive probe of the electron states’ hybridization about the C atom. It increases from ≈ 13 eV for fully sp3 -hybridized diamond to ≈ 23 eV for fully sp2 -hybridized graphite, and it takes intermediate values for amorphous carbon materials. The marked increase in ∆ over the 150–300◦C range is therefore understood as a change in the electron states’ hybridization from sp3 to sp2 . At higher temperatures, the transformation tends to saturate to a value near that of graphite. A consistent picture is thus derived from the three panels of Fig. 5 for T ≤ 300◦ C. The ﬁlm is stable up to 100–150◦C, at which temperature structural changes are initiated. These consist in H evolution from the ﬁlm between 100◦ C and 300◦C, resulting in sp3 to sp2 conversion. Above 300◦C, ∆ follows the C–H states evolution, thus indicating that, once the H desorption process is exhausted, the same also holds for sp3 to sp2 conversion. It seems therefore that the π band intensity gain revealed by VB photoemission (Fig. 5b) above 300◦ C cannot be assigned to an increase in the sp2 fraction. To clarify this point, Fig. 6 compares the 400◦C (continuous line) to the 700◦ C (dotted line) HeII-excited VB photoemission spectrum. Both spectra are background subtracted and normalized to a common height, as explained before. The diﬀerence spectrum (700◦C–400◦ C) is also shown. At

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variance with respect to Fig. 4, the π band intensity gain observed here is not balanced by a corresponding intensity decrease in the σp band. Note that the apparent widening of the σp band around 5 eV (leading to a peak in the diﬀerence spectrum) has to be nearly entirely ascribed to the intensity gain of the π band, which increases in height and width, on going from 400 to 700◦ C. The observed behavior suggests that the π band intensity gain in VB photoemission (Fig. 5b) has diﬀerent origins in diﬀerent temperature regimes. To gain further insight into the matter, Fig. 7 considers another π-related spectral feature, namely the π plasmon of the EEL spectrum associated with a backscattered primary electron beam of 2 keV. The π plasmon spectrum is given at four selected temperatures: RT, 400, 600 and 700◦ C. At RT, a nearly vanishing π peak is observed. As explained in the previous section, this indicates either a very small sp2 fraction or, in any case, a homogeneous distribution of the sp2 sites within the sp3 phase, without formation of graphite-like clusters. At 400◦ C, a π plasmon peak is observed, which reveals the presence of π states at this stage. As T increases from 400 to 600 and 700◦ C, the π peak increases in height, its energy increases from 5.2 to 5.6 to 5.8 eV, while its FWHM decreases from 4 to 3.5 to 3 eV. The evolution indicates that [19], once the sp2 fraction has grown up, graphite-like ordering develops in the system through the formation of graphite-like clusters with progressively increasing size. This provides us with a key to understand the temperature evolution of the π band intensity in the VB photoemission spectrum (Fig. 5b). Below 300◦ C where electron states are transferred from the σp to the π band, its increase is due to an increase in the sp2 fraction. On the other hand, its further intensity gain above 300◦C must be due to the rearrangement of sp2 sites into clusters of increasing size. Apparently, π states in a graphite-like network have a greater photoemission yield than π states in a nongraphitic environment. In a recent paper [40], the question was raised whether the photoemission π band intensity is aﬀected by the sp2 fraction alone or in addition by the π network structure. From the present annealing experiment, we conclude that it is aﬀected by both structural features. We have, in fact, clear indications (∆ and C–H states evolution) that our ﬁlm is highly sp2 -hybridized once T is around 300–400◦C, so that only below these temperatures can the π band intensity gain be assigned to an increase in the sp2 fraction. At higher temperatures, on the other hand, the observed further increase in the π band intensity can only be brought about by the ﬁlm transformation from nongraphitic to graphitic.

5 Concluding Remarks The eﬀects of amorphous carbon hydrogenation are examined by considering a series of ﬁlms deposited in Ar–H2 plasma with variable H2 concen-

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Fig. 7. π plasmon peak (EEL spectrum) at four selected temperatures. The zeroloss peaks are normalized to a common height

tration. Hydrogen is incorporated into ﬁlms grown in a hydrogen-containing atmosphere. This leads to a reduced mass density, mainly as a result of reduced cross-linking in the hydrogenated network. Hydrogen incorporation markedly changes the electronic structure of otherwise graphite-like amorphous carbon ﬁlms: π states are swept out from the Fermi level region, and the system turns from semimetallic into semiconducting, due to the opening of a gap (greater than 1 eV). The saturation of π bonds leads to an increased sp3 fraction, revealed by a narrowing in the 2s and 2p VB DOS, and to the disappearance of small graphitic domains revealed, for the unhydrogenated ﬁlms, by the π states reaching E F , the asymmetric C 1s line and the measurable π plasmon intensity on the EEL spectrum. The reverse process, dehydrogenation of a-C:H, is examined by thermally inducing hydrogen evolution from the system. Three temperature regimes are basically distinguished. From RT up to ≈ 100◦ C, the investigated ﬁlm is stable. Structural modiﬁcations are initiated above this temperature. From ≈ 100 to ≈ 300◦ C, hydrogen desorbs from the system, causing massive sp3 to sp2 conversion. At even higher temperatures, a reorganization of the sp2 sites into graphite-like regions of progressively increasing size takes place.

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No univocal relationship exists between the sp2 fraction and the intensity of the π band in UV excited VB photoemission. Acknowledgements The work was funded by Provincia Autonoma di Trento (Fondo Progetti per la Ricerca).

References [1] C. Gao, Y. Y. Wang, A. L. Ritter, J. R. Dennison: Phys. Rev. Lett. 62, 945 (1989) 447 [2] D. R. McKenzie: Rep. Prog. Phys. 59, 1611 (1996) 447 [3] P. Ruﬃeux, O. Gr¨ oning, M. Bielmann, P. Mauron, L. Schlapbach, P. Gr¨ oning: Phys. Rev. B 66, 245416 (2002) 447 [4] R. Haerle, E. Riedo, A. Pasquarello, A. Baldereschi: Phys. Rev. B 65, 045101 (2001) 447 [5] J. T. Titantah, D. Lamoen: Phys. Rev. B 70, 075115 (2004) 447 [6] J. Robertson: Mater. Sci. and Engineering: R 37, 129 (2002) 448, 452, 456 [7] M. M. Golzan, D. R. McKenzie, D. J. Miller, S. J. Collocott, G. A. J. Amaratunga: Diamond Relat. Mater. 4, 912 (1995) 448 [8] K. Takai, M. Oga, H. Sato, T. Enoki, Y. Ohki, A. Taomoto, K. Suenaga, S. Iijima: Phys. Rev. B 67, 214202 (2003) 448 [9] J. Robertson, E. P. O’Reilly: Phys. Rev. B 35, 2946 (1987) 448, 455 [10] J. Robertson: Diamond Relat. Mater. 4, 297 (1995) 448 [11] J. K. Walters, R. J. Newport: J. Phys.: Condens. Matter 7, 1755 (1995) 448 [12] G. Gottardi, N. Laidani, R. Bartali, M. Filippi, L. Calliari, R. S. Brusa, S. Mariazzi, C. Macchi, M. Anderle: Diamond Relat. Mater. 14, 1031 (2005) 450 [13] N. Laidani, R. Bartali, P. Tosi, M. Anderle: J. Phys. D: Appl. Phys. 37, 2593 (2004) 450, 451, 454 [14] L. Calliari, M. Filippi, N. Laidani, M. Anderle: J. Electron Spectr. Relat. Phenomena 150, 40 (2006) 450, 452 [15] J. Fink, T. M¨ uller-Heinzerling, J. Pﬂ¨ uger, A. Bubenzer, P. Koidl, G. Crecelius: Solid State Commun. 47, 687 (1983) 451 [16] J. Kulik, Y. Lifshitz, G. D. Lempert, J. W. Rabalais, D. Marton: J. Appl. Phys. 76, 5063 (1994) 452, 453 [17] Y. Lifshitz: Diamond Relat. Mater. 12, 130 (2003) 452 [18] D. G. McCulloch, S. Prawer, A. Hoﬀman: Phys. Rev. B 50, 5905 (1994) 453 [19] M. M. Brzhezinskaya, E. M. Baitinger, V. V. Shnitov: Physica B 348, 95 (2004) 453, 459 [20] J. E. Houston, J. J. W. Rogers, R. R. Rye, F. L. Hutson, D. E. Ramaker: Phys. Rev. B 34, 1215 (1986) 454 [21] L. Calliari, G. Speranza, J. C. Lascovich, A. Santoni: Surf. Sci. 501/3, 253 (2002) 454 [22] K. Endo, S. Koizumi, T. Otsuka, M. Suhara, T. Morohasi, E. Z. Kurmaev, D. P. Chong: J. Computational Chemistry 22, 102 (2001) 454

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[23] F. R. McFeely, S. P. Kowalczyk, L. Ley, R. G. Cavell, R. A. Pollak, D. A. Shirley: Phys. Rev. B 9, 5268 (1974) 454 [24] A. P. Dementjev, M. N. Pethukov: Surf. Interf. Analysis 24, 517 (1996) 454 [25] J. Yeh: Atomic Calculation of Photoionization Cross-Sections and Asymmetry Parameters (Gordon and Breach, Longhorne 1993) 454 [26] P. M. T. M. van Attekum, G. K. Wertheim: Phys. Rev. Lett. 43, 1896 (1979) 455 [27] F. Sette, G. K. Wertheim, Y. Ma, G. Meigs, S. Modesti, C. T. Chen: Phys. Rev. B 41, 9766 (1990) 455 [28] J. Diaz, G. Paolicelli, S. Ferrer, F. Comin: Phys. Rev. B 54, 8064 (1996) 455 [29] J. Diaz, S. Anders, X. Zhou, E. J. Moler, S. A. Kellar, Z. Hussain: Phys. Rev. B 64, 125204 (2001) 455 [30] J. Hong, S. Lee, C. Cardinaud, G. Turban: J. Non-Crystalline Solids 265, 125 (2000) 455 [31] Y. Bounouh, M. L. Thye, A. Dehbi-Alaoui, A. Matthews, J. P. Stoquert: Phys. Rev. B 51, 9597 (1995) 455 [32] N. M. Conway, A. C. Ferrari, A. J. Flewitt, J. Robertson, W. I. Milne, A. Tagliaferro, W. Beyer: Diamond Relat. Mater. 9, 765 (2000) 455 [33] M. Clin, M. Benlahsen, A. Zeinert, K. Zellama, C. Naud: Thin Solid Films 372, 60 (2000) 455 [34] L. Calliari, M. Filippi, N. Laidani: Surf. Interf. Analysis, 36, 1126 (2004) 455 [35] J. Sch¨ afer, J. Ristein, R. Graupner, L. Ley, U. Stephan, T. Frauenheim, V. S. Veerasamy, G. A. J. Amaratunga, M. Weiler, H. Ehrhardt: Phys. Rev. B 53, 7762 (1996) 455 [36] R. Graupner, J. Ristein, L. Ley: Surf. Sci. 320, 201 (1994) 455 [37] B. B. Pate: Surf. Sci. 165, 83 (1986) 455, 456 [38] J. C. Lascovich, R. Giorgi, S. Scaglione: Appl. Surf. Sci. 47, 17 (1991) 458 [39] D. E. Ramaker: Chemical information from Auger lineshapes, in D. Briggs, J. T. Grant (Eds.): Surface Analysis by Auger and X-Ray Photoelectron Spectroscopy (IM Publications and Surface Spectra Ltd, UK 2003) pp. 465–500 458 [40] P. Reinke, M. G. Garnier, P. Oelhafen: J. Electron Spectr. Relat. Phenomena 136, 239 (2004) 459

Index π states, 452, 456 a-C, 447 a-C:H, 447 Auger emission spectroscopy, 449–455, 457 electron energy loss spectroscopy (EELS), 449–452, 458–460 electron energy loss spectroscopy (EELS), 455

hydrogen desorption, 455–458, 460 photoemission spectroscopy, 450, 453–461 plasmon energy, 451–453 UV photoemission spectra (UPS), 450, 461, 462 x-ray photoemission spectroscopy (XPS), 449

UV-Induced Photoconduction in Diamond Emanuele Pace1 , Antonio De Sio1 , and Salvatore Scuderi2 1

2

Dipartimento di Astronomia e Scienza dello Spazio, Universit` a di Firenze, Largo E. Fermi 2, I-50125 Firenze, Italy INAF – Osservatorio Astroﬁsico di Catania, Via S. Soﬁa 78, I-95123 Catania, Italy [email protected]

Abstract. Owing to its physical properties, diamond is a very promising candidate for UV photon detection. The synthesis of very high quality polycrystalline diamond thick ﬁlms and single crystals is presently accomplished routinely using the chemical vapour deposition (CVD) technique. Metal/diamond/metal ohmic junctions are produced by depositing electrical contacts on the front surface (coplanar contacts) or on both front and back (sandwich contacts). The investigation of diamond properties in the wavelength range 100–300 nm is of considerable interest in order to attain ultraviolet (UV) detectors having high quantum eﬃciency against no sensitivity to visible photons, along with radiation hardness and chemical inertness. Improvements in diamond synthesis techniques and processing technology now make available very high quality polycrystalline diamond ﬁlms as well as opticalgrade single crystals with dimensions suﬃciently large for developing detectors. Several problems limiting the performance have been solved, and single-pixel detectors are close to being suitable for exploitation. This paper reviews the status of the art of diamond-based UV detectors, their application in speciﬁc ﬁelds, such as excimer lasers, photolithography and space experiments, and the perspectives.

1 Introduction Despite their steady improvement over the last decades, the UV imaging detectors currently available exhibit some limitations, inherent to silicon technology or to electron multiplication, that become crucial, for example, in the context of space missions or UV laser lithography where reliability, durability, low cost, sensitivity, radiation hardness and solar blindness are required. In order to produce an innovative solid-state detector that copes with this demand, the proper material must be selected among those having wide band-gap energy, because of their negligible absorption of visible photons and intrinsic very low dark currents. Currently, nitrides (GaN, AlGaN, InGaN), SiC and synthetic diamond are widely investigated for these applications. Diamond has a unique combination of superior physical properties, displacing concurrent materials, which makes it the ideal candidate for photoconductive detectors replacing silicon in UV applications. Recent advances in the deposition techniques allow the synthesis of diamond ﬁlms with such exceptional properties that overwhelm those of natural diamond in many cases. These G. Messina, S. Santangelo (Eds.): Carbon, The Future Material for Advanced Technology Applications, Topics Appl. Phys. 100, 463–504 (2006) © Springer-Verlag Berlin Heidelberg 2006

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properties make synthetic diamond a “frontier” material for advanced electronic applications in harsh environments where conventional devices cannot operate without special precautions. Nowadays, the CDV technique makes available thick, large-area polycrystalline ﬁlms. Many research teams have thoroughly investigated UV detectors using interdigitated electrodes on polycrystalline CVD diamond [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], and diamond-based UV detectors are commercially available [13]. Unfortunately, the results of these eﬀorts invariably suggest that, even if the performance of single-pixel detectors is dramatically improved, polycrystalline material is unsuitable for imaging applications. The response of polycrystalline diamond detectors is, in fact, not uniform over the area of the detector; they show long time-constants and a response which varies with time. The homogeneity of homoepitaxial CVD diamond single crystals and the absence of grain boundaries, with respect to polycrystalline ﬁlms, holds out the promise to overcome all of these diﬃculties. This paper describes the state of the art of diamond-based UV photon detectors. After a general overview of the ﬁeld, the main physical properties of diamond will be discussed in order to explain why diamond is considered a promising material for UV detectors. The synthesis of diamond layers will be brieﬂy described to emphasize the crucial role of the material quality and how it correlates with the detector performance. The following sections will describe the principle of charge photogeneration and of detector types and operation along with the expected performances and perspectives. A concise description of some relevant applications of diamond UV detectors will conclude this review.

2 Overview Synthetic diamonds were available until the late 1980s only as small crystallites with variable properties. The emergence of new and improved techniques, particularly CVD [14], to grow thin ﬁlms of diamond encouraged research into solid-state devices made from this material. Diamond has uncommon physical and mechanical properties: it is very hard, chemically inert, an excellent thermal conductor [15] and has outstanding electrical and optical characteristics [16]. Such appealing properties have attracted academic and industrial interest to use them in practical applications. Synthesis techniques have made important progress and Europe is at present the undisputed leader in the production of CVD diamond. This material has been so far exploited commercially for cutting tools, hard coatings, cold emitters for displays [17], windows [18], thermal conductors, etc. For example, high-power CO2 laser and gyrotron diamond windows have been produced in Europe [19]. In Japan, Surface Acoustic Wave (SAW) devices [20] for GHz frequency telecommunications have been commercialised by Sumitomo. In the USA, CVD diamond is intensively studied for various applications such as ﬁeld emission displays, SAWs, etc. For these applications, however, the quality of the material does

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not have to be as high as that required by electronics, optoelectronics and detectors, where top-level quality of diamond ﬁlms is absolutely necessary [21]. Presently, CVD techniques produce mainly polycrystalline diamond layers over nondiamond substrates (typically silicon) [14]. This method is advantageous, because large sizes and controlled quality can be obtained. Nevertheless, the polycrystalline structure can introduce a large concentration of impurities, defects and grain boundaries that can trap or recombine the photogenerated free charges [22, 23]. These interactions strongly inﬂuence the device response by reducing the photoinduced current and slowing the response time [24]. The distribution of these defects is not homogeneous in the samples, and it can be cause of nonuniform sensitivity on the detector surface. Moreover, they are responsible for the instability of devices due to polarisation eﬀects and long-term drifts caused by accumulation of charge by particular deep-traps [25, 26]. These eﬀects are not yet fully understood, and their control is still one of the essential tasks to develop good functioning devices. In addition, the nature of the surface [27,28] and it diﬃcult to fabricate reliable and reproducible electric contacts with peculiar geometry [29, 30]. To date, the technology to produce high-quality polycrystalline diamond ﬁlms and devices is not ﬁrmly established [31, 32], even though several groups have studied the opportunities oﬀered by diamond as a radiation-sensitive material [33]. So, the use of high-quality single crystals to produce devices is becoming a necessity, especially for those groups that recently have been engaged in producing pixel arrays. Therefore, the interest in single-crystal diamond growth techniques has increased. High-pressure and high-temperature (HPHT) single-crystal diamond synthesis is long well known. HPHT diamonds are more homogeneous but are not completely defect-free, so they still present problems in electronic applications. In fact, it is very diﬃcult to control HPHT parameters, and consequently they are not reproducible, with nitrogen and metal catalyst inclusions. Elimination of these contaminations increases the quality, although the samples are smaller and more expensive. Recently, the synthesis techniques have been improved, and homoepitaxial CVD diamond growth has increased. This technique permits the fabrication of high-quality IIa-type single-crystal diamond samples [34, 35, 36]. The limit of homoepitaxial CVD growth is still the size of the samples, but now singlecrystal diamond of 1 cm2 with exceptional electronic performances are available. For instance, charge mobility has increased up to 4500 and 3800 cm2 /Vs for electrons and holes, respectively, increasing the collection distance up to several millimetres in contrast to the hundred of microns of the best polycrystalline diamond ﬁlms [37, 38, 39, 40, 41]. Even if the homoepitaxial growth is more complex, it allows the realization of very promising devices, as reported in [42, 43, 44, 45, 46]. UV detectors currently available for industrial, scientiﬁc and medical applications are mainly based on well-developed, low-cost and versatile materials. Although well adapted to the detection of low-energy radi-

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ation, they are unsuitable whenever visible-blind, chemically inert and radiation-hard sensors are required. In such circumstances, the detectors currently used often comprised standard diodes or CCDs with shields, ﬁlters and cooling systems. Moreover, cooling and protection from aggressive environments requires sensors sealed within cameras. The use of diamond oﬀers unmatched performance in harsh environments or in the presence of high-doses of ionising radiation. Other semiconductors, such as Si, Ge or new wide-band gap materials, cannot be used in such environments without special precautions. A number of potential applications exist where diamond is the only viable solution; these range from environmental monitoring to oil recovery and from the nuclear industry to optoelectronics. One of the most promising is UV photon sensing, in particular in satellite-borne instruments [47]. In space environment, current UV detectors, such as Si diodes, photomultipliers or CCDs, suffer from problems aﬀecting their performances or causing heavy instrument payloads. Some of these problems are radiation hardness, visible-light sensitivity, cooling systems, high-voltage biasing and thermal stability. Diamond appears to be the most interesting solution, as its wide band gap (5.5 eV) results in a very low leakage current (no cooling systems required) and in a selective absorption of light with wavelengths shorter than 225 nm (visible-blind detectors) [48]. Electronic properties [16, 49] and radiation hardness [50, 51] are other attractive features. These characteristics have stimulated research on diamond UV detectors. Experimental groups in the USA have tested natural diamond [2, 3]. Again, natural diamond is an expensive limited resource and the optimal crystal must be selected among many of them. Nevertheless, the encouraging results have pushed US and European teams to investigate the functional properties of CVD diamond. Research projects involving international collaborations between universities and research centres have been funded and are under way to study the feasibility of diamond UV detectors for scientiﬁc and industrial applications [45, 52, 53, 54, 55, 56, 57, 58, 59, 60]. So far, there was only one industrial product: a photoconductive detector commercialised by Centronic, following an EU–Brite–Euram supported project. This detector had a high sensitivity limited to a narrow UV band [4, 6], and it relied on the surface properties of the material. The response time was improved at the expense of sensitivity [54], and it was comparable to or faster than the response time of well-developed silicon detectors. High-speed UV detectors have been produced to follow short laser pulses [61, 62, 63, 64]. Fast response to pulsed radiation can be properly ascribed to charge excitation from valence to conduction band, typically a very fast process. However, many applications require a fast response also to continuous radiation sources [65] that induce diﬀerent excitation mechanisms [66]. These problems need further study but presently prevent end users from using diamond detectors. A new frontier in the ﬁeld of UV detectors is the attempt to achieve bidimensional pixel arrays. Applications in UV astronomy, photolithography, and laser and synchrotron beam characterisation and proﬁling should beneﬁt

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from the availability of such imagers. However, this research is presently at the forefront of the diamond device technology and the nonuniformity of diamond polycrystalline layers represents one of the main limitations to a full development. Single crystals may be the solution, but their present size prevents the development of large formats.

3 Properties of Diamond Diamond crystal has a cubic structure formed by one carbon atom surrounded by four tetrahedrally arranged nearest neighbours (sp3 σ-type bonds). This crystal structure is found also in silicon and germanium. The bond distance in diamond between two nearest neighbours is 0.154 nm, compared with 0.234 nm for silicon and 0.245 nm for germanium. As a result, the atomic number density in diamond is 1.77 × 1023 cm−3 , the highest of any materials at normal pressure, and its mass density is 3.52 g cm−3 . The cohesive energy of diamond, i.e., the energy required to disassemble a solid into its constituent atoms, is almost twice as large as that of silicon and germanium. This dense structure and strong bonding give diamond extreme hardness and wear resistance. The high propagation velocity of phonons is an eﬀect of such a compact structure. As the diamond elementary cell contains two carbon atoms, the phonon spectrum has both acoustic and optical branches. Diamond is an insulator, with an insigniﬁcant number of electrons in the conduction band. This implies that heat conduction is due to acoustic phonons, providing the extremely high thermal conductivity of diamond (25 W cm−1 s−1 , compared to 4 W cm−1 s−1 for copper at room temperature). Diamond can eﬃciently dissipate its own heat or the heat generated elsewhere and can tolerate high temperature. It is one of the rare materials that naturally conduct heat yet electrically insulate. Its inertness to acids or other chemical agents, deriving from the high binding energy of carbon atoms in the diamond lattice, is another important property of diamond that is essential for applications in harsh environments. The electrical and optical properties of diamond result from its wide band gap energy, i.e., Eg = 5.470 ± 0.005 eV at 295 K. Electrically, diamond is an insulator, but it can behave as a semiconductor by introducing donor or acceptor atoms. Like silicon, diamond has an indirect band gap. The maximum of the valence band lies at the centre of the Brillouin zone in the reciprocal space; the lowest point of the conduction band is near the zone boundary in the K = (111) direction, where the band gap, Eg , is deﬁned. Diamond has a large breakdown electric ﬁeld (about 107 V cm−1 ) and its saturation velocity is approximately 107 cm s−1 . The electron and hole mobility is 1800 cm2 V−1 s−1 and 1200 cm2 V−1 s−1 , respectively. Achieving current saturation at a high electric ﬁeld and high charge mobility are interesting

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properties of diamond-based devices in view of electronic applications. Table 1 lists some typical material and operating parameter values of diamond compared with those of silicon. Table 1. Physical properties of diamond at room temperature Properties

Units

Diamond Silicon

Atomic number Density Binding energy Evaporation temperature Breakdown voltage Band gap energy Resistivity Dielectric constant Electron mobility Hole mobility Saturation velocity

− g cm−3 eV/atom ◦ C V eV Ω cm − cm2 V−1 s−1 cm2 V−1 s−1 µm/ns

6 3.5 7.37 4100 107 5.5 > 1012 5.6 1800 1200 220

14 2.32 4.63 1420 103 * 1.1 105 11.7 1500 480 100

∗ for a p–n junction

Optically, pure diamond exhibits no photon absorption or luminescence in the visible spectral range, at λ > 225 nm. This property is very important for visible-blind UV photodetectors. On the other hand, photons with λ < 225 nm are absorbed when they impinge on diamond. This process gives rise to the electron excitation from the valence band to the conduction band, and diamond exhibits photoinduced electrical conductivity. This will be discussed in a following paragraph. Absorbance and reﬂectance are other important optical properties that contribute to the performance of detectors [3, 16, 67].

4 Synthesis of Diamond The promising characteristics of natural diamond for applications in detectors and in harsh environments have been demonstrated in the USA. In spite of the very limited resource of appropriate quality natural gems and their cost, people have studied the functional properties of this material. The advent of synthetic diamond ﬁlms, in particular those produced by CVD, has radically increased the availability of diamonds for technological and mechanical applications. The production of CVD diamond ﬁlms suitable for detector applications is still a challenge that is being pursued worldwide, and it is one of the current technological frontiers in the production of advanced materials. The heteroepitaxial CVD growth allows the synthesis of large polycrystalline slices (up to 6 in diameter) on a variety of substrates [33, 54, 68, 69,

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70, 71]. This approach is based on creating a hot plasma region (> 1500 ◦ C) near a substrate (typically at 700–800 ◦ C) at a lower pressure than other techniques. In the vapour phase, the thermal decomposition of carbon-containing gases such as methane occurs. The hydrocarbon gas is mixed with a large concentration of molecular hydrogen gas. A power source excites the gas mixture so that the carbon atoms link together onto the substrate, forming the sp3 bonds leading to the diamond lattice and eventually the polycrystalline ﬁlm. In various CVD processes, it is common to start from a reactive gas phase, which is composed of carbon and hydrogen. The most readily apparent role of atomic hydrogen is to etch selectively nondiamond-bonded material, thereby reducing the incorporation of graphite in the completed ﬁlm. Oxygen is frequently added, either directly or as a part of the carbon carriers (CO or CO2 ). The presence of oxygen can have a marked inﬂuence on the deposition processes, as can the temperature of the CVD gas phase and substrate. An increasing CH4 content induces a preferential orientation of diamond crystals [72]. For the highest values of CH4 content, a (100) preferential orientation and then a textured ﬁlm can be obtained. The preferential orientation of diamond crystals can be checked by the X-ray diﬀraction (XRD) technique [73]. Several techniques are employed to produce the plasma, such as hot-ﬁlament CVD, the DC glow discharge or microwave plasma-enhanced CVD [32]. The latter technique is presently the preferred one, because the plasma occurs in a region far from any parts of the reactor, so that the contamination of the ﬁlm is very limited. Natural diamond and CVD diamond have the same crystal lattice. However, the diﬀerent production processes introduce diﬀerent impurity concentrations and diﬀerent structural defect densities. These diﬀerences may likely result in diﬀerent material properties, e.g., mechanical strength, thermal conductivity and electrical conductivity. Although natural diamond is single crystal, it is far from perfect, containing high densities of impurities and structural defects. As CVD diamond growth technology has matured, the quality of the polycrystalline diamonds has improved: some of the material properties of new CVD diamond ﬁlms have already exceeded those of natural diamond. Synthetic single diamonds have been available since the 1950s after the ASEA Laboratories and the General Electric Company developed independently HPHT diamond synthesis. This technique is rather simple in principle: a small volume ﬁlled with hydrocarbons is heated at more than 2000◦C and the volume reduced by increasing the pressure to Gbar values. In order to avoid the formation of graphite – which is energetically preferred – some catalyst metals, such as nickel, cobalt or iron, are included in the gas mixture. HPHT diamonds are usually yellowish because of a high nitrogen concentration (up to 100 p.p.m.). Recently, a few companies have been able to provide some small stones of pure diamond (IIa type). The CVD technique is used also to synthesise homoepitaxial diamond ﬁlms. The parameters of the synthesis are nearly the same as those of heteroepitaxial

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growth, but the substrate is a natural or HPHT diamond gem. This is at the same time the advantage and the disadvantage of such a technique. Homoepitaxial growth produces single crystals, so the overall crystalline quality is better than in polycrystalline ﬁlms, because of the absence of stresses inside crystals, twinning crystals, defects and grain boundaries. Unfortunately, the size of natural or synthetic gems is limited in size and therefore the maximum size of homoepitaxial ﬁlms is currently around 1 cm2 . Single-crystal diamond ﬁlms are grown on (100) HPHT diamond substrates. The crystalline quality of this material is comparable with that of natural diamond, but unless ﬁlms are grown under very carefully controlled deposition conditions [74, 75], structural imperfections can form on the growth side [76, 77] acting as preferential site for impurity and nondiamond phase incorporation. Recently, homoepitaxial diamond has aroused a lot of interest owing to advances in the synthesis of larger samples and improved electrical properties. It was used to fabricate electronic devices [78, 79], and recently the growth of device-grade homoepitaxial diamond ﬁlms has been claimed [77].

5 Experimental Methods Using UV photons to study the photoelectrical properties of diamond ﬁlms is a consolidated technique providing information on both the material properties and the device performance. Material properties can be investigated at sub-band gap photon energies because nondiamond structures forming intragap energy levels absorb such photons. At higher energies, the diamond ﬁlm absorbs photons, and therefore radiation can be used to analyze the photoelectrical characteristics [80, 81, 82, 83]. In addition, it is generally accepted that the photoconductive properties of diamond ﬁlms change going deeper in the material from the surface to the bulk and to the nucleation side. Photoconductivity, time and spectral response are the main electrooptical properties investigated to characterise the performance of diamond UV photoconductors. Researchers routinely make use of diﬀerent experimental equipments to measure the spectral response in the visible and in the UV range. Optical tests in the deep UV range (at wavelengths below 180 nm) require vacuum systems, as well as vacuum-grade materials and sources, whilst measurements at longer wavelengths can be performed in air. In addition, diamond is transparent at wavelengths above 225 nm, except for contributions from impurities and defects in the crystals. As a result, special instrumentation, based on heterodyne detection techniques, is required to observe very low level signals. The apparatus used for the detector characterisation in the vacuum UV range is based on a deuterium lamp (for λ > 120 nm) or a gas discharge source (for λ < 200 nm) placed at the entrance slit of a vacuum monochromator, which is evacuated down to a pressure p ∼ 10−6 Torr. The radiation sources are sealed or must be interfaced directly to the vacuum. Photons entering

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the monochromator impinge on a grating that can rotate around its axis perpendicular to the optical path, so that only the selected wavelength can illuminate the exit slit, where it is possible to arrange the detector. If the spot size on the detector is smaller than the electrode overall dimensions, the response is independent from the sensitive area. Generally, the estimated light power is on the order of tens of nW/nm on the detector. By applying a bias voltage, the response of such detectors to such a monochromatic illumination is a photocurrent that can be measured using an electrometer. The detector characterisation in the visible is performed through a different instrumentation. The monochromator is not evacuated and the photocurrent is measured after chopped illumination. The light source is typically a tungsten lamp irradiating continuously from infrared to visible. Another source is the mercury–xenon lamp, emitting spectral lines superimposed to a continuous spectrum that covers the range from infrared to UV (about 200 nm). A chopper inserted between the source and the entrance slit of the monochromator produces pulsed monochromatic radiation at the exit slit. A lock-in ampliﬁer can detect the alternating current induced by the chopped illumination, while rejecting any DC signal, such as the dark current. This experimental technique allows very high sensitivity, so that signals over 7–8 intensity decades and signal-to-noise ratio (SNR) < 1 can be recorded [5, 80, 84]. Table 2. Attenuation lengths in IIa-type diamond ﬁlms [85] Wavelength Attenuation length, L0 nm µm 140 150 160 170 180 190 200 210 220 222.5 224 225 227 230 250

0.013 0.015 0.02 0.03 0.3 1.3 1.7 3 9 100 400 500 900 2 000 10 000

High-quality diamond layers present a sharp absorption edge at the band gap energy. Correspondingly, the penetration depth, deﬁned as the reciprocal of the absorption coeﬃcient, of photons shortens very rapidly from centime-

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tres down to a few nanometres, as reported in the Table 2 [85]. This feature provides a unique opportunity to use UV photons in a small spectral range in order to probe the photoelectric and the charge transport properties of diamond layers at diﬀerent depths up to the surface proximity. In particular, transients of photocurrent induced by UV photons emitted by a lamp and short pulses from an UV laser represent the optimal probe as rising and falling photocurrent edges and time response provide information on trapping or polarization eﬀects. Pulsed radiation was used from UV laser sources. The system is based on excimer lasers emitting radiation at 125 nm, 157 nm and 193 nm, while one can get pulses at 266 nm and 213 nm using the fourth and ﬁfth harmonic of the fundamental wavelength of a Nd:YAG laser. The pulses from these lasers have duration around 10−9 s (4–10 ns) at a repetition rate of tens of Hz with energy variable from 0.1 µJ to hundreds of µJ. It is possible to measure this energy using pyroelectric probes with uncertainty within 5%. Photocurrent pulses are measured using an oscilloscope directly connected to the device through a bias-T.

6 Electro-Optical Properties The research on diamond UV detectors shows an increasing trend of their electro-optical performance over the last two decades. Scientiﬁc and technological eﬀorts have provided a positive outcome with encouraging results, allowing expectations for an imminent availability of a new generation of high performance UV detectors. The technology required to produce CVD diamond and photoconductor devices has been strongly improved. Finally, the production of high-precision coplanar electric contacts with spacing d, ranging between 10 and 100 microns, is now consolidated, even if their reproducibility and reliability is still a concern. Hundreds of single-pixel photoconductors have been developed and their electro-optical performance investigated thoroughly in the UV and visible range. The results assess the excellent performance of the intrinsic diamond-based detectors. In order to specify the performance of photodetectors, quantum eﬃciency and dark current have to be determined along with time response for a certain applied electric ﬁeld E. The quantum eﬃciency, i.e., the average number of carriers excited in the conduction band by an incident photon, is related to the detector sensitivity, while the dark current is related to its thermal noise and metal–diamond interface. Therefore, these quantities contribute signiﬁcantly to the SNR of the detector, a parameter that actually estimates its detectivity. The dark current of diamond detectors is generally measured at room temperature in air or in vacuum, because, considering the wide band gap and the very high resistivity, one may expect very low levels of leakage current in diamond, even in the case of ohmic contacts. Low-level dark current at

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room temperature is a very important topic, since one of the main targets of researchers is to exploit this diamond electrical property in order to improve the SNR while avoiding cooling systems. The dark current behaviour as a function of the bias voltage also gives information on the characteristics of the metal–diamond junction. The I–V curves of devices tested in air show nonlinear and higher values than those of the same devices measured in an evacuated environment: this is due to air and water vapour conductivity. This is pointed out by comparing I–V curves of coplanar contacts and sandwich geometry. Therefore, reliable measurements must be carried out in vacuum or using guard rings, the latter only in case of transverse contacts. The quantum eﬃciency gives information on the device spectral responsivity, highlights the presence of gain in photoconductors and allows the evaluation of visible blindness. In addition, photoinduced charge yield in the visible and infrared range is used to identify intragap energy levels due to impurity species inside diamond ﬁlms or defects [86]. The spectral response is determined by measuring the photocurrent in a detector under illumination and by comparing it to that in a calibrated photodiode. Therefore, the external quantum eﬃciency η can be estimated as: η = ηp

Id , Ip

(1)

where ηp is the external quantum eﬃciency of the calibrated photodiode at a certain wavelength, Ip and Id are the photocurrents measured respectively by the photodiode and the diamond detector, taking care that the spot light is smaller than the contact size. Due to the presence of traps, the collected charge Qc is diﬀerent from the photogenerated charge Qph : E Qc = Qph µτ , d

(2)

and, correspondingly Qc E = Iph µτ Id = . t d

(3)

Thus, the external quantum eﬃciency can be expressed as η = EQE =

ηp Iph Ip

E µτ = η0 G. d

(4)

The external quantum eﬃciency (EQE) of diamond detectors is the product of two terms: the ﬁrst, η0 = ηp (Iph /Ip ), is the real quantum eﬃciency,

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i.e., the number of photogenerated carriers per incident photon, while the second, G = µτ E/d, is the gain factor, which will be discussed in depth at the end of Sect. 7. Detectors based on high-quality diamond ﬁlms currently have quantum eﬃciency measured values greater than 1, and other speciﬁc measurements are required to separate the contribution of the two terms. A relevant and now well-established topic is that diamond photoconductors exhibit high UV sensitivity and photoconductive gain coupled to very low dark current. For instance, it has been observed that good detectors yield gain G > 200 at 200 nm and very low dark currents (< 10 pA/mm2 at 100 V) along with very strong visible rejection (107 ) [42, 87, 88]. As a clear consequence, the minimum detectable signal is very low. By using these data we can estimate the noise-equivalent-power (NEP), i.e., a signal (measured in watts) giving SNR = 1. NEP may have values around 10−11 W cm−2 . Diamond detectors can be based on diﬀerent substrate materials: natural diamond, CVD polycrystalline diamond wafers, CVD or HPHT single-crystal diamonds. Natural diamond was used in early experiments, when the synthesis of diamond layers was at earlier stages. Nowadays, gems are used just as reference because of the superior quality of synthetic layers, so detectors based on poly- and monocrystalline layers will be discussed. 6.1 Polycrystalline Diamond Detectors A discussion on the performance of a detector starts usually from its sensitivity, even compared with the dark current levels, in order to highlight its detection capability, especially in presence of low-level photon ﬂuxes. The main characteristic of diamond detectors is their high eﬃciency at UV wavelengths against visible light. Diamond technology is not yet mature for mass production of UV detectors, but it has made large steps ahead during the last decade. This means that their capability of detecting UV signals with a photoconductive gain G > 1 while rejecting visible signals has been greatly improved along with response time and removal of some detrimental eﬀects aﬀecting even recent UV detectors. In addition, dark current levels can be smaller than 1 pA/mm2 with an applied ﬁeld of 1 V/µm. Figure 1 shows a typical spectral response of current polycrystalline diamond UV detectors. These detectors exhibit a peak of eﬃciency around 200 nm, with gain ranging between 100 and 300 as reported by several authors. The spectral range has been extended to the visible and infrared regions to show the very high rejection factor, typically 107 [5, 87, 89]. The sharp sensitivity cutoﬀ at 225 nm is one of the main important features, which makes diamond the solid-state detector with the best solar-blindness. After the results of Jackman’s team in 1996 [5] that claims improved UV selectivity and global detector performance using a special gas treatment, it was generally believed that surface treatments were needed in order to enhance the detector response. More recently, several results show that similar or superior performances can be obtained without any surface treatments. Other authors

External quantum efficiency (e/γ)

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2

10 1 10 0 10 -1 10 -2 10 -3 10 -4 10 -5 10 -6 10 -7 10 -8 10

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Wavelength (nm) Fig. 1. Spectral response of a diamond photoconductive detector in a wavelength range extended from the vacuum UV to the near infrared. It is worth noting the exceptional visible rejection ratio that is about 107 at 400 nm and > 108 at 700 nm, while the infrared discrimination factor is > 109

have extended the investigated spectral range to shorter wavelengths down to 120 nm in order to analyse the vacuum UV photoresponse [53, 60, 64, 87]. In principle, a constant eﬃciency should be expected because photons are completely absorbed, even in very thin diamond layers. The curve in Fig. 1 shows that the eﬃciency decreases, and the measurements from other authors, even if stopping at 180 nm, conﬁrm this trend [4, 5, 84]. A possible explanation is a thin layer of contaminants or a high density of surface states at the diamond surface that generates a “dead layer” [90]. This means that taking care of the surface and the material quality this eﬀect should be limited. Another hypothesis moves from the size of diamond crystals: a small ratio between the volume of the crystal and the surface of the grain boundary could aﬀect the photoresponse. An indication comes from the response of diﬀerent substrates: polycrystalline ﬁlms with small grains, as that in Fig. 1, the same with greater crystals, and single crystals. The latter, as reported below, shows much smaller eﬃciency reduction at short wavelengths. We may expect that the material quality and the device processing technology inﬂuence the detector photoresponse, so it is important to identify the critical parameters and their contribution. The relevant facts are: (a) Some researchers have demonstrated that diﬀerent deposition techniques and parameters lead to diﬀerent material quality and morphology and that these correlate with the UV detector performance. The photoluminescence (PL) and Raman peaks provide information on the material quality; so their correlation with the detector eﬃciency can be expected and indeed demonstrated by some groups (Fig. 2) [89, 91, 92, 93, 94]. The

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ηav (%)

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IPL/Idiam (adim) Fig. 2. Average detection eﬃciency ηav as a function of the IPL /Idiam ratio [91]. The parameter IPL /Idiam is the ratio between the signal of the PL peak and of the diamond Raman peak. The clear correlation between such indicators suggests that the worsening in the detection performance is due to the higher incorporation of defects and impurities occurring at higher CH4 concentrations

eﬃciency is also directly related to the average orientation of the crystals in the polycrystalline ﬁlms, as shown in Fig. 3 [95, 96]. Finally, the spectral response curves in Fig. 4 conﬁrm that the sensitivity and the discrimination factor depend on the material quality that is determined by diﬀerent synthesis techniques [84]. Therefore, techniques producing highquality randomly oriented large crystals provide the best material for UV detectors, maximising the ratio between the volume and the surface, i.e., the grain boundaries of the crystal. (b) Several authors have discussed the time response of UV detectors, showing that this is generally aﬀected by a slow, sometimes very slow, rising time and then by a persistence of the photocurrent (PPC) after having turned oﬀ the radiation source (Fig. 5) [3, 8, 97]. In principle, diamond detectors should be very fast, owing to the very high mobility of the photogenerated carriers. However, a variable but large concentration of impurities and defects, producing energy states inside the large diamond band gap, causes a variation of the time response related to their diﬀerent trapping and release time. The gain–bandwidth product, which is typical of electronic devices, suggests that UV diamond detectors can exhibit improved time response at the expense of gain, and this is conﬁrmed by experimental results [54, 66]. By carefully tailoring the material and the electrode processing, sensitive and fast detectors can be achieved [60, 87, 98]. Long-time response eﬀect is not present when pulsed light is used to excite electrons. Very fast responses have been

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Photocurrent (nA)

transverse co-planar 10

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Fig. 3. Measured photocurrent as a function of the preferential orientation of crystals in the diamond ﬁlms (parameter P (ikl); see [34] for the details). This plot shows the sharp decrease of the photoresponse when the CH4 concentration increases. The correlation has been observed in the case of planar contacts as well as of sandwich contacts, as expected 1,0

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Wavelength (nm)

Fig. 4. Normalized photoresponse of some diamond detectors: a microwave plasma CVD-grown sample (i), a hot-ﬁlament CVD-grown ﬁlm (ii) and a microwave plasma CVD-grown sample with high nitrogen content (iii). The curve (iv) is relative to sample (ii) after a long UV exposure and this shows the eﬀects of the persistence of the photocurrent (data from [32])

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Fig. 5. Transients of photocurrent for CVD polycrystalline diamond. The left panel shows a transient aﬀected by an ever-increasing photocurrent and the PPC after UV irradiation at 225 nm. The right panel demonstrate the eﬀects of the PPC on subsequent pulses

obtained by several authors using diamond photoconductors to detect UV excimer laser pulses [56, 82, 99, 100]. Detectors were also fabricated exhibiting response times of less than 70 ps FWHM at 125 nm [64]. (c) The performance of diﬀerent detectors may vary, even if the material and the electrode processing are the same [101]. Two pairs of electrodes on the same substrate may have diﬀerent characteristics, thus providing irreproducible responses. This is likely due to the diﬃculty of producing identical metal–diamond interfaces and thus identical ohmic contacts. The PPC is an important topic aﬀecting performance and full exploitation of UV detectors based on polycrystalline diamond. Therefore, it is important to evaluate its eﬀects on the photoresponse to nonpulsed radiation. The PPC is an extra current observed after the radiation source has been turned oﬀ. Many hours can be required to return to the dark current level measured before the irradiation. By switching on the radiation source after some seconds or minutes, the photocurrent reaches quickly the values it had before turning oﬀ the radiation and, it begins to grow. The overall eﬀect is an ever-increasing photocurrent, as can be seen in Fig. 5, still observable in many UV detectors. Figure 6 shows another consequence of the PPC. It can aﬀect the spectral response when the wavelength range is scanned, producing an upward-scanned spectral response very diﬀerent from a downward-scanned one [102]. Irradiating the sample for a long time with intense UV ﬂuxes (UV “priming”) and then scanning the spectrum, the highest quantum eﬃciency values have been measured, reproducing the behaviour of the spectral response aﬀected by the PPC. Stabilizing the response by priming techniques is usually adopted for X-ray and particle diamond detectors. Priming is not eﬀective for UV detectors, but UV priming can saturate all the traps and centres that aﬀect UV

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Fig. 6. The inﬂuence of the PPC on the spectral response can be observed using two diﬀerent scanning directions and after UV priming (solid line). The radiation source has a very intense peak at 160 nm and is very stable (1% maximum variation). The wavelength scanning after this peak is aﬀected by the PPC. The photon ﬂuxes at the other wavelengths are so low that apparently they do not modify the spectrum

photoconduction, as indicated by these results. However, this priming is very unstable: it disappears in a few hours and is strongly reduced after a few minutes. Very recently, Brescia et al. have reported on the photoresponse of detectors fabricated on polycrystalline diamond that is comparable to that of single-crystal detectors. The group at IAF, Frieburg, has synthesised 500 µm thick diamond ﬁlms. A layer 400 µm thick at the substrate side has been removed and the growth surface has been polished, so as to obtain a ﬁnal thickness of approximately 50 µm. High-quality cylindrical large crystals, much larger than the interelectrode distance then form the front surface. This and the removal of the contaminated back layer are eventually the explanation for such enhanced photoresponse. Sandwich structures have been also studied in order to pave the way to imaging detectors. Indeed, this electronic structure allows compact and easily addressable bidimensional pixel structures. However, the nonhomogeneous illumination of the substrate, due to the short penetration depth of photons at wavelengths shorter than 225 nm, gives rise to polarisation eﬀects and to a nonlinear quantum eﬃciency that saturates at higher photon ﬂuxes. The quenching of the quantum eﬃciency is apparently enhanced by increasing the beam light intensity. De Sio et al. have also shown that the photoresponse quenching depends on the photon wavelength [102]. All the photocurrent transients show a quasirectangular shape at wavelengths longer than 220–230 nm, while this shape changes signiﬁcantly

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Wavelength (nm) Fig. 7. Absolute spectral response of two sandwich detectors fabricated on CVD polycrystalline ﬁlms having diﬀerent thicknesses (500 µm for CVD1 and 40 µm for CVD2). The lower graph shows the EQE curve obtained for the CVD2 sample in coplanar geometry

at shorter wavelengths, exhibiting a photocurrent quenching after an initial peak. This eﬀect is not present in coplanar contacts. A possible explanation lies on the nonuniform illumination of the material layer that produces polarisation. Photons with λ > 225 nm pass through diamond layers because the absorption length is longer than the ﬁlm thickness (see Table 2). In this case, photons are absorbed in the whole layer. Conversely, photons are absorbed in thinner and thinner material layers when λ < 225 nm. Collins et al. [98]

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argued that, for energies above about 5.15 eV, most of the photons are absorbed before reaching the back contact, while all the carriers are generated virtually within a few µm of the surface for energies above 5.6 eV. When the thickness of the specimen is greater than the charge collection distance, the photocurrent is made up of an induced current, associated with the movement of the carriers in the electric ﬁeld [103], together with the ﬂow of current from those carriers that actually reach the electrodes. For short wavelengths, no carriers reach the back contact on the specimen, and the photocurrent is dominated by the induced current. An impact of this eﬀect on the spectral responsivity may be expected. Figure 7 shows the results for two detectors in sandwich conﬁguration having diﬀerent thicknesses of the diamond layer. The spectral response is rather similar and highlights a quenched eﬃciency at wavelengths shorter than 220 nm or 230 nm. The diﬀerent peak wavelengths can be explained taking into account the diﬀerent thickness: the wavelengths between 220 nm and 230 nm still pass through the thinner sample, thus reducing the collection eﬃciency, but producing a uniform illumination of the layer. The spectral response data suggest a possible dependence on the photon beam intensity. The radiation source emits a line peak at 160 nm that is one order of magnitude more intense than the emission at the other wavelengths. The EQE plots show a minimum exactly at that wavelength with a shape resembling the source emission line; this lets us suppose that higher intensity causes lower eﬃciency. In order to analyze these aspects in more detail, De Sio et al. have illuminated the same samples with UV lasers, emitting nanosecond pulses at 193 nm, 213 nm and 266 nm. They have analyzed the peak voltage against the beam intensity and observed that it saturates for photon ﬂuxes above 1013 photons/s. This saturation, observed also by other authors [82, 104], is accompanied by an increasing width, but the total collected charge, calculated as T 1 V (t) dt , Q= Rosc 0 where Rosc is the oscilloscope input impedance, still shows saturation at higher ﬂuxes. The EQE reported in Fig. 8 conﬁrms this charge saturation: it should be constant if plotted against intensity, whereas it decreases and saturates at higher ﬂuxes. Lansley et al. have developed speciﬁc surface treatments to provide linearity and to eliminate peak and width saturation, but at the expense of sensitivity [104]. 6.2 Single-Crystal Diamond Detectors Brescia et al. [42] have reported on the ﬁrst results of electro-optical characterisation of single-pixel UV detectors based on CVD single-crystal diamond. Photocurrent measurements were carried out illuminating the sample

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Fig. 8. External quantum eﬃciency versus laser beam intensity at two diﬀerent wavelengths

at 160 nm. Devices on homoepitaxial diamond show currents more than one order of magnitude higher than that of a standard polycrystalline diamond. In addition, the ratio between photocurrent and dark current is about 3–4 orders of magnitude in the measured voltage range. To analyse the sensitivity of such a device as a function of wavelength, photocurrent measurements have been carried out under calibrated illumination transients. Figure 9 shows these transients, highlighting the good response time of single-crystal detectors and the stability of the photocurrent. Therefore, no PPC apparently aﬀects the detector response. These data have been used to estimate the EQE of the device in Fig. 10. Maximum EQE is much greater than unity, due to the high photoconductive gain. However, the device exhibits a nonoptimal solar blindness, due to the increasing absorption length (which is 4 µm, namely the CVD layer thickness, at around 215 nm) with decreasing photon energy. In such case, the authors have not removed the Ib-type diamond substrate, and then its nitrogen content absorbs photons at longer wavelengths, aﬀecting the photoconductive process. No evidence of PPC eﬀects has been observed by scanning these spectra from short wavelengths to longer and vice versa. The same authors have investigated if the nitrogen content may inhibit the performance of UV detectors. Two planar interdigitated contacts were deposited on one of the two surfaces of an HPHT Ib-type diamond crystal and the spectral response of such device was measured. The very high quantum eﬃciency obtained with this photoconductor is reported in Fig. 11. The same

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Fig. 9. Response time of a single-crystal diamond UV detector. The device has been irradiated at 160 nm at two diﬀerent applied electric ﬁelds

Fig. 10. External quantum eﬃciency of a UV photoconductor based on a homoepitaxial diamond ﬁlm biased at two diﬀerent electrical ﬁelds. The eﬃciency peak at 210 nm is strongly enhanced, by a factor of 30, by a small increase of the electric ﬁeld (a factor of 5)

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Fig. 11. External quantum eﬃciency for the same diamond detector, based on a HPHT Ib-type diamond ﬁlm, with a couple of electric contacts (upper curve) that were removed before depositing another couple of contacts on the same surface (lower curve)

ﬁgure also shows the much smaller spectral photoresponse obtained from the same diamond ﬁlm after removing the electric contacts, cleaning the surface from any kind of residual and having deposited a new pair of contacts. The perspectives of using single crystals for UV detectors are very promising. High-purity large crystals (side > 7 mm) have been already achieved [41, 105] with unprecedented optical and electronic performance [38, 44], so further enhancements of UV performance can be expected. De Sio et al. tested a photoconductive device based on a 500 µm thick freestanding homoepitaxial single-crystal CVD diamond. Photoconductive measurements in coplanar and transverse conﬁgurations have been performed to characterize the device sensitivity in the 140–250 nm spectral range. Very high sensitivity values were achieved in both conﬁgurations. It has emerged that the sensitivity in the transverse conﬁguration is at least 300 times higher than in the coplanar conﬁguration. They observed high sensitivity in steady-state photoconductive measurements carried out in a relatively thick diamond ultraviolet detector in a transverse conﬁguration [106].

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7 Single-Pixel Detectors 7.1 Photodetectors Typically, a diamond-based photon detector is in the form of a two-terminal metal–insulator–metal (MIM) device. The insulator is undoped diamond. The metal contacts can be ohmic or rectifying. The structure of the electric contacts depends on the application and speciﬁcally on the energy of the photons emitted by the excitation source used to create the excess carriers. An electronic structure consisting of two metal electrodes separated by a high-resistivity diamond layer is called a sandwich structure. It is generally applied to high-energy X-ray or gamma-ray detection, since diamond ﬁlms are quasitransparent at those energies. An external voltage that is applied to the metal contacts produces an electric ﬁeld across the device. The direction of the incident photons is nearly parallel to the electric ﬁeld, and the electron– hole pair generation occurs in the bulk of the material. A coplanar structure, i.e., two electric contacts, usually interdigitated, lying on the same surface, is used when the charge excitation follows the UV photon or low-energy X-ray absorption. In this case, the direction of incident photons is perpendicular to the applied electric ﬁeld. The penetration depth in diamond is small, and the electron–hole pair generation occurs near the exposed surface (generally the growth surface). The sandwich structure provides information on the bulk of the material, while coplanar contacts give information on the electrical properties near the surface. Therefore, using both measurements, the relationship between bulk and surface properties can be investigated, along with the relationship between the transport properties of charges drifting perpendicularly or along the surface. As already stated, UV photons are absorbed in a very thin layer close to the illuminated surface, so coplanar device structures are generally preferred to fabricate UV detectors. However, sandwich structures have been studied recently [60], especially for single-crystal substrates in order to improve their performance under UV illumination because they can be integrated more easily in a pixel array detector. Large-array formats require many electrical connections to bias and read-out each pixel; actually, it appears rather impossible to accomplish them using coplanar contacts. 7.2 Photoconductor A diamond-based photoconductor is operated by connecting it in series to a DC-voltage power supply and to an electrometer. Photons are incident on and absorbed in the very ﬁrst ﬁlm layers, thereby exciting electrons into the conduction band. The result of such an excitation is a decrease of the material resistance and hence an increase of the current ﬂowing through the electrometer. Therefore, current variations are proportional to photon ﬂux

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variations; this current excess is called photocurrent. The amount of photocurrent depends also on the applied bias voltage, on the photon wavelength and on the distance between electrodes, although at high ﬁelds the current saturates. The electric contact on diamond surface must be ohmic. It is diﬃcult to fabricate good ohmic contacts on diamond due to its inert and wide band gap nature [30]. It is necessary to somehow modify the structure of a perfect diamond surface so that the voltage drop across the metal–diamond interface is negligibly small as compared to that across the active portion of the device. By selecting or intentionally creating damaged surfaces, good contacts can be accomplished. However, producing reliable and reproducible ohmic contacts is to date a major concern. Presently, the techniques used to get ohmic contacts are ion implantation of boron atoms in the diamond regions under the metal contacts or the use of carbide-forming metals, such as titanium or chromium. Although the potential barrier height does not change, ion implantation produces a narrower voltage-drop region, and photogenerated charges can move from diamond to the contact by tunnelling through the barrier. On the other hand, the ohmic behaviour of some speciﬁc metals is likely due to the formation of carbide at the metal–diamond interface. These metals are evaporated on diamond and then annealed at high temperature (typically 400◦ C) to enhance carbide formation. A thicker layer of gold coats the metallic contact in order to avoid oxidation; a buﬀer layer, generally platinum, is used sometimes in between to avoid interdiﬀusion of gold into the metal. Some authors use gold contacts on diamond because it can be easily evaporated thermally. Sputtering can be another technique, but priming eﬀects, i.e., the saturation of intragap energy levels and then the enhancement of the diamond photoconductive properties, due to electrons emitted from the electron gun have been observed. Gold forms Schottky barriers and its adhesion on diamond surface, especially on smooth surfaces, is very poor. Annealing at 400◦ C produces gold ohmic contacts, but their properties are not reproducible. The extremely high resistivity of intrinsic diamond eliminates the need for reverse-biased junctions or doped material in order to suppress thermally generated currents. In addition, the large band gap produces negligible dark currents and then very low level photocurrents can be detected. Charge generation and collection in photoconductors can be described by considering a uniform device with mobile charge carriers, electrons and holes, generated by incident radiation [33, 107]. If a ﬂux F0 (t) of photons at a given wavelength irradiates a photoconductive detector, the carrier generation rate is G(t) = η0 F0 (t), with η0 the above-deﬁned quantum eﬃciency. The number of charges, N , is related to the generation rate according to the equation: N dN = G(t) . dt τ

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For a pulsed irradiation, the carrier density at the end of the excitation (t = 0) is N = N0 , and its subsequent time evolution is t N (t) = N0 exp − , τ while being N = Gτ = η0 F0 τ , in the steady state, when the generation rate equals the recombination rate. If an external electric ﬁeld E is applied, the excited carriers move covering an average drift distance, L = vd τ = µEτ ,

(5)

which is determined by their drift velocity vd and lifetime τ . Since electrons and holes have diﬀerent eﬀective masses (m∗e and m∗h ) and exist in diﬀerent energy bands, the values of electron mobility (µe ) and hole mobility (µh ) may be diﬀerent and, in addition, the electron (τe ) and hole lifetimes (τh ) may not be equal, (5) should be written as L = (µe τe + µh τh )E. Owing to the electric ﬁeld, each of these carriers drifts with mean velocity vd = µ(E)E that gives rise to a photocurrent in the external circuit, i.e., i = qvd /d (Ramo–Shockley theorem [103]). The total current is the product of i by the number of carriers N τ L qF0 η0 vd τ = qF0 η0 I = iN = = qF0 η0 , d τd d where τd = d/vd is the drift time for carriers crossing the distance d. The factor (τ /τd ) or (L/d) represents the fraction of the distance that an excited carrier drifts before recombining. If L/d > 1, the photogenerated charge will be entirely collected, and L/d = µτ E/d can be considered as a photocurrent gain factor G. On the other hand, if L/d < 1, only a fraction of the photogenerated charge will be detected. In this last case, an accurate detector design must prevent the eﬀects of space charge buildup: the uncollected charge can accumulate in the device forming a net charge, which distorts the electric ﬁeld locally and leads to reduced detection eﬃciency. 7.3 Photodiode An ideal diode junction allows current to ﬂow easily (with low contact resistance) if forward biased and very little current to ﬂow if reverse biased. P-type material is currently achieved by adding boron atoms to the diamond lattice, while n-type diamond is still an open issue for many research groups. As a result, p–n diamond diodes are not yet fully available and junctions are currently limited to Schottky barriers.

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In most applications, Schottky interfaces are reverse biased, with the voltage value ﬁxing the barrier height and the width of the depletion region. Since CVD diamond layers are available, many authors have published their results on Schottky junctions using natural, polycrystalline or single-crystal borondoped diamond. The target was to produce Schottky diodes with small reverse leakage currents operating also at high temperature (> 400 ◦ C) [28,49]. However, diodes manufactured on p-type CVD diamond suﬀered from relatively large leakage currents. Adding a thin defect-free insulating layer between the metal contact and diamond (MIS diode structure) reduces the leakage current. Intrinsic diamond is an insulator, so MIS structures can easily achieved by depositing an intrinsic layer on top of the p-type substrate. A thin SiO2 layer (∼ 2 nm) has also been used successfully to reduce the leakage current (metal–oxide–semiconductor structure, MOS), but I–V characteristics of MOS devices degrade with increasing temperature [108, 109]. The MIS structure is more advantageous than the Schottky barrier because charge carriers can be driven to an accumulation region. On the other hand, MIS structures have a higher density of interface states, producing a larger current noise. The electrical properties of Schottky contacts on diamond, such as barrier heights, exhibit small dependence on the properties of diﬀerent metals, such as their work functions or electronegativity. Treatments of the diamond surface along with selecting proper metals, metal deposition parameters and subsequent treatments, e.g., annealing, strongly determine the I–V characteristics of the contacts. Typically, Au or Al contacts – but also other metals such as W and Mo – on doped or undoped diamond are used. It is possible to fabricate diamond detectors by using two electric contacts, blocking or ohmic, separated by diamond. For example, a sandwich conﬁguration with a semitransparent blocking front contact and an ohmic back contact gives Schottky-type photodiodes. A diamond layer deposited on a p-type silicon substrate forms an isotype heterojunction with a highly recombinant interface, which is essentially an ohmic contact [8]. Two coplanar blocking contacts are equivalent to two back-to-back Schottky diodes and therefore described by a symmetrical relationship: qV , Id = I0 tanh ξKB T where ξ is the diode quality factor and KB the Boltzmann constant. A similar equation holds when these structures are illuminated, substituting (I0 + Iph ) for I0 , where Iph is the current photogenerated in the junction. So, the device does not exhibit any photoelectric signal at zero bias. Such behaviour is rather diﬀerent from a single Schottky photodiode, which exhibits a small nonzero short circuit current under illumination. Photocurrent in diamond photodiodes depends on the applied external ﬁeld, but also on the device geometry and on the direction of the incident

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light with respect to the applied ﬁeld. For a diamond ﬁlm having thickness T and sandwich contacts, the light propagates along the electric ﬁeld direction, and the minority carrier photocurrent can be written [110]: 1 − eBT , I = qF0 (1 − R) α B where α is the absorption coeﬃcient, R is the front surface reﬂectivity and B =α+

1 , L

while the photocurrent from coplanar contacts, where light and ﬁeld directions are approximately perpendicular, is: L d I = qF0 η 1 − exp − . L d It is noteworthy that no internal gain is expected for photodiodes: the quantum eﬃciency can never exceed unity.

8 Pixel Array Detectors One of the most important targets of developing detectors is eventually to produce arrays of pixels for imaging applications. Some projects presented by European research groups outline the interest in the ﬁeld of diamond pixel detectors. For instance, the RD42 Collaboration at CERN has started in 2001 a program to develop two-dimensional particle detectors based on CVD polycrystalline diamond [111], following research and investigation on microstrip particle trackers (from 2000) [112, 113]. At the end of 2002, a European Consortium, called BOLD, including Universities, Astrophysical Observatories and Research Centers [114], has started a program supported by the European Space Agency (ESA) to develop image sensors for the XUV range. Other groups are developing small two-dimensional detectors (5 × 5 pixels) in order to measure proﬁles of UV laser beams [115] or synchrotron radiation beams [116]. The major concern limiting the development of diamond detector arrays is the highly inhomogeneous spatial response [98]. Small pixel detectors for UV laser beam proﬁling have been developed by fabricating an array of squared large – 4 mm each – coplanar contacts. This device has achieved interesting results, even if cross-calibration is required to take into account spatial nonuniformity. Electrical connections to the oﬀ-chip readout are still an issue, because they are obtained through wires – one for each pixel and one common – passing in front of the sensitive area. Moreover, these wire-bonding connections can be a practical solution for small arrays, but they are not scalable to large array formats. Some research groups [53, 81, 117] are studying diﬀerent

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Fig. 12. Sketch of a CMOS imager (the lower substrate) coupled to a diamond photosensitive layer (the upper layer ) using indium bumps. The very thin layer on top of the sensitive layer is an open electrode

viable solutions for UV imagers. The most promising solution is a hybrid detector, where a layer of sensitive material is used to absorb UV photons and a CMOS device includes the readout electronics, as sketched in Fig. 12. An array of square contacts is deposited on one of the two surfaces of the sensitive material and electrically connected to a similar pixel array of readout circuits by means of indium bumps, a technique named ﬂip chipping. The pixel array and the on-chip readout electronics are implemented with CMOS technology. The reports from the RD42 group on prototypes of CMOS ﬂip-chipped detectors – pixel or microstrip detectors on diamond layers – developed in the ﬁeld of particle detection shows encouraging results. Since the early 1990s, an explosion of activity in the area of CMOS image sensors has taken place. Several important factors have contributed to the emergence of CMOS image sensors at this time rather than 10 to 20 years ago. The primary factor consists of recent demand for low-power, miniaturized digital imaging systems. A second important factor is that CMOS currently oﬀers submicron feature sizes as well as low concentration of defects and contaminants. Moreover, CMOS image sensors have an intrinsically panchromatic response to visible and near-infrared photons [118,119]. One of the main drawbacks of this imaging technology is the extension of such a performance in diﬀerent portions of the spectrum. An opportunity currently investigated is introducing proper solutions and materials compatible with the CMOS process in order to apply this well-known technology in the ﬁeld of UV imagers. Progress in the ﬁeld of diamond synthesis and processing for electronic devices along with the maturity and reliability of CMOS technology leads to the development of a complete system-on-a-chip (SOAC) UV imager. An analog signal electronic chain is often integrated on a simple chip to provide noise reduction and removal of artefacts such as ﬁxed-pattern noise. One of the key steps in realizing a digital imager on a chip is developing an on-chip ADC suitable for integration with the image sensor.

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Fig. 13. The absolute quantum eﬃciency of diamond detectors compared with CCD and MCP detectors

Advantages of integrating CMOS technology with diamond layers using the ﬂip-chipping technique are high visible rejection ratio, high eﬃciency in the UV portion of the wavelength spectrum, very low noise, ultrafast frame rate, low power consumption and high level of radiation hardness, with stable response on a wide temporal range. In particular, radiation hardness can be achieved even if a silicon-based technology is adopted. CMOS devices are in fact intrinsically radiation hard because of the technology of the gate oxide. These devices have been tested in several severe conditions and results highlight their radiation harness to particle doses up to 10 MRad (see, for example, [120]).

9 Applications The comparison between the performance of diamond UV detectors and CCD detectors [121] or MCP detectors [122], generally used to detect photons in this spectral region, is reported in Fig. 13 and highlights the high sensitivity of diamond detectors, especially when they are based on a single-crystal ﬁlm. Therefore, diamond detectors appear to be suitable for UV applications. The measurements show the highest sensitivity along with a very low dark current and the best visible rejection among the commonly used detectors (included GaN and AlN detectors). In addition, they have very low power consumption, owing to the photocurrent values obtained at low bias voltage. Table 3

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Table 3. Possible applications of diamond-based UV detectors

Environment

Pollution, ozone, flame, and gas monitoring Solar UV monitoring Photochemistry Toxic gas detection (ammonia, hydrocarbons) Toxic or flammable-solvent monitoring in air-ducts in industries Toxic chemical storage sites and hazardous waste disposal areas Germicidal water disinfection

Medical

Biotechnology safety systems HPL Chromatography UV curing applications Analytical and chemical instruments (disinfections that kill bacteria viruses and some cysts) Protein crystallography Skin cancer caused by UV radiation Observation of fluorescence Spectroradiometry Dermatological diagnosis Treatment and dental polymerisation

Societal

Quantification of UV exposure to personnel Monitoring UV radiation in workplace activity such as welding

Technological

Flame monitoring in aircraft engine Burners monitoring in gas turbines UV spectroscopy of gas on electric discharges Mass spectroscopy laboratory analysis UV spectroscopy of plasma in reactors Excimer laser applications

Industrial processes Industrial process control systems Detection of gasses in high temperature environments such as furnaces or reactors Flame monitoring in commercial hydrocarbon-fuelled heating systems and in furnaces Semiconductor processing Turbine air intake and exhaust Control of chemical processes involving gaseous compositiary UV analysis of material degradation and ageing Oil industry

Monitoring of flammable liquids or gases during cleaning and maintenance work on empty tanks Oil and gas platform (offshore and onshore installations) monitoring Petrochemical and chemical industries and refineries monitoring Transportation of dangerous materials Fuel and gas storage loading and distribution Aromatic hydrocarbons (Benzene, Toluene, Xylene etc.) Desulphurisation process in refineries, oil platforms, pipelines, refuelling stations

Military

Missile threat warning UV search and track

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summarises the possible applications of diamond UV detectors. Three speciﬁc applications that would beneﬁt from the availability of such detectors are hereafter described in some detail. 9.1 UV Lasers A particularly promising application of diamond UV detectors is monitoring the operation of high-power UV laser systems. Excimer lasers are the most intense sources of highly monochromatic UV radiation, and they are currently employed in a wide range of applications, including laser PCB drilling, high-performance micromachining, next-generation photolithography tools and the preparation of biological materials [99, 100, 123, 124, 125]. Each laser emits intense UV light at a speciﬁc wavelength in the range 157– 248 nm and beam monitoring means controlling beam uniformity, shape and radiation dose. Laser tubes are continuously operated for about one month, i.e., ∼ 108 pulses, at kHz frequencies and ﬂuences of a few mJ/cm2 [126]. A typical requirement is for reliable operation of monitoring detectors during the laser lifetime, so that they can be replaced at the same time. CCD detectors are currently used, providing accurate proﬁling with high resolution. However, they suﬀer from some drawbacks such as low UV sensitivity, higher sensitivity to visible light, and poor radiation hardness and operational lifetime when monitoring 50% degradation after as few as 105 pulses has been reported [126]. The properties of diamond make it the best alternative. CVD diamond UV photoconductors based on coplanar interdigitated electrode structures have been developed and tested by a number of groups in the ﬁeld [56, 64, 127, 128, 129, 130]. In particular, Jackman et al. have shown that they can follow the 15 ns pulses of the 193 nm excimer laser providing sensitivity, speed and stability matching the requirements. The ﬁrst detector structures fabricated on as-grown material showed a dependence of the dark current and photocurrent curves on previous illumination with UV or visible light [97]. Subsequently, Jackman’s group has shown that successive treatments can progressively modify the sensitivity and response times of photoconductors fabricated on polycrystalline diamond. Therefore, a combination of material treatments and careful design can lead to devices overwhelming the previous limits, but with reduced sensitivity [4, 5, 131]. Suitably designed and treated CVD diamond photoconductive structures exhibit excellent either long-term performance or damage levels, with relatively modest degradation of diamond devices exposed to beam ﬂuences of 1−2 mJ/cm2 for ∼ 108 pulses. It is important to stress that currently no other detector can meet all the necessary requirements, apart from CVD diamond devices. Other groups have investigated the use of highly oriented diamond (HOD) for UV detectors [62, 132]. The basic idea is that, in order to limit the detrimental eﬀects of the grain boundaries on the recombination time of the photoexcited carriers [133, 134],

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HOD ﬁlms could be used as a valid alternative to the single crystals. Indeed, the reduction of the misorientation and the grain boundary angle are expected to reduce grain boundary eﬀects, to increase the free-carrier mobility resulting in an increase of the detection eﬃciency. They fabricated UV detectors using HOD ﬁlms and measured the response of the sensors after pulsed irradiation of an ArF excimer laser or a dye laser. Kobashi et al. have found that detected pulses exhibit two peaks for case of the ArF laser and three peaks after dye laser irradiation. They infer that the peaks following the ﬁrst are due to a carrier emission from trap states at grain boundaries. Achard et al. claim an HOD ﬁlm exhibiting a signiﬁcantly higher photoresponse and a discrimination factor of 103 between above and below band gap photon energies. They compare these results to those obtained using detector fabricated on randomly oriented polycrystalline diamond ﬁlms, and they reports superior in the performance of HOD ﬁlms. This is in accordance with the results in [64], but not with previous results from other groups, showing that detectors based on HOD ﬁlms do not perform as well as those based on ﬁlms with randomly oriented crystals when illuminated with continuous irradiation [93, 94, 95]. 9.2 Photolithography Moore’s Law states that the gate density in silicon integrated circuits quadruples every 3 years. The photolithography technique forms the device structures by projecting the desired circuit image (mask) onto the silicon wafer. The ultimate feature size achievable, and hence the gate density, is limited by the wavelength of the radiation used to illuminate the mask. The target is to achieve ever-smaller feature sizes, so excimer lasers have ruled out mercury UV lamps because they emit intense pulsed beams at shorter wavelengths, from the 248 nm radiation available from KrF ﬁlled excimer lasers to the recently introduced 193 nm radiation from ArF lasers. The next step is to operate at 157 nm to realise device structures of 100 nm and below [135]. A very bright source for this wavelength is the molecular ﬂuorine laser [136]. This development is accompanied by the need for a suitable solid-state photodetector sensitive to this wavelength with a lifetime ﬁtting long continuous operation (107 –108 laser pulses). There is currently no commercial silicon detector available for monitoring at 157 nm, because their sensitivity falls down around 10%, due to the combination of the short penetration depth of photons in silicon and its spontaneously passivated surface. In addition, it is diﬃcult to stabilise the silicon detector photoresponse, because they are cooled to reduce the dark current and layers of condensed contaminants formed on the sensitive area cause a decreasing eﬃciency. This opens opportunities for a completely new electronic material and hence to diamond. Owing to its extreme properties, CVD diamond is an ideal candidate for this application. Photodetectors based on this material should be both radiation-hard and visible-blind whilst being sensitive to the

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UV wavelengths [137]. Gaudin et al. have shown that photoconductors suitable for laser applications can be fabricated from polycrystalline diamond by careful tailoring of device design and surface treatments [131]. Recently, again Jackman’s group assessed for the ﬁrst time coplanar interdigitated gold photoconductor structures on free-standing thin ﬁlm diamond by exposing them to 157 nm pulsed radiation up to the ﬂuence value of 1.4 mJ cm2 . They demonstrated that the detectors were capable of following the 15–20 ns laser pulses. Device gain was found to be linear with applied bias (±30 V) with a sensitivity of 10 V/mJ cm2 over the linear portion. Unfortunately, the longterm lifetime tests were limited to 104 –105 pulses, but no obvious degradation in characteristics was observed. 9.3 Space Astronomy The UV spectral region is of particular interest for astrophysics. UV allows the study of a rich interval of emission and absorption lines due to species and states of ionization of atoms and molecules useful for the diagnostics of plasmas and gases. UV observations are rather recent because atmospheric absorption forces observations from space. This has caused major technological problems for instrumentation developments. Presently, we are living in an exciting transition time for UV astrophysics. Planned missions have been launched and most are even ﬁnished. In the meantime, new missions are still under deﬁnition. These missions are mainly solar missions (Solar Orbiter, Solar B, SDO), but also missions towards galactic and extragalactic regions, like WSO/UV. That situation will allow some years for the development of new technologies. The urgent demand for new technologies, which will push current observation limits, has induced main space agencies (ESA and NASA) to form European and US research groups with the aim to conceive innovative optical and spectroscopic instruments and in particular to develop new-generation detectors. The detector is a crucial component of every astronomical experiment since it plays a critical role in determining the overall performance, even if it represents only a small fraction of the instrument total cost. Therefore, detectors have been and are still very important for a remarkable technological investment. Although UV imaging detectors currently available represent an improvement over the last decades, they exhibit some limitations due to silicon technology. These limitations become crucial in space missions where reliability, durability, low cost, sensitivity, radiation-hardness and solar-blindness are required. Presently, photon-counting detectors represent the only viable option, since they are radiation-hard and, by using proper selection of the photocathode, solar-blind. Initially the quantum eﬃciency in the UV of a typical photon-counting detector is about 30%, although it decreases progressively until values around 10%, due to photocathode degradation. However, a photon-counting detection system requires high voltage and an accurate and stable coupling to the intensiﬁer with the signal readout system (typically CCD or anode array), which increase the satellite payload,

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the complexity and the probability of failure. Another problem is related to the sources to be observed. Many UV astronomical sources are weak and associated with very bright visible emissions. It follows that the use of photon-counting detectors coupled with optical systems able to remove visible signals (monochromators and light traps) is necessary. When the UV ﬂux is more than 102 photons/(s · cm2 ) – as from the Sun – photon-counting detectors may run into signal pile-up problems and integrating detectors may be damaged by the radiations. A strong eﬀort in technological research aimed at the development of UV solid-state image sensors is therefore necessary. Diamond exhibits unparalleled properties with respect to other wide band gap materials. The high crystalline quality achieved with present synthetic techniques and an activation energy of 5.5 eV makes diamond detectors intrinsically solar-blind and possessing a very low dark current. Moreover, high carrier mobility and radiation hardness makes diamond appealing for UV detector development. A few sensors based on single-crystal diamond exhibited photoconductive gains up to G = 700 at 200 nm with rise and fall times shorter than one second and without evidence of persistent photocurrents [42]. The application of diamond detectors in astrophysics will bring: (a) technological advantages over the current detectors, such as lower power consumption, longer detector lifetime, lower electric insulation and more compact detectors without coolers, radiation shields, optical ﬁlters. (b) performance advantages, such as long-time stability, owing to corrosion and radiation resistance, intrinsic solar-blindness, low dark-current levels, and high quantum eﬃciency. The comparison between these results and the performance of a CCD detector [121] and an MCP detector [122], generally used in space UV experiments, is reported in Fig. 13 and it highlights the high sensitivity of diamond detectors, especially when they are based on single crystals. NEP values of 10−11 –10−12 W cm−2 coupled to response times on the order of 1 s, even if not exceptional for silicon detectors, are already suitable for astronomical observations. Diamond can compete with silicon detectors owing to the unmatched visible rejection among the commonly used detectors (included GaN and AlN detectors) and its performance and technological advantages [138]. Diamond UV imagers are, we hope, the next step. Pixel arrays on diamond substrates represent a strong technological eﬀort involving material synthesis and electronic processing. The advent of hybrid CMOS detectors oﬀers the advantages of combining layers that are very sensitive to UV with highly integrated and radiation-hard devices, also allowing strong mass reduction, owing to a very compact SOAC that requires only a 5 V power supply [53, 117].

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10 Conclusions Diamond-based photodetector properties have been reviewed in this article. The electro-optical properties of the material and the electronic structures fabricated on it have been discussed. This material is still a promising candidate for UV photon detection at room temperature, oﬀering superior eﬃciency in the range 100–300 nm and unsurpassed UV/visible discrimination. These features pose diamond as the best UV detector currently available, but some problems limit its full exploitation, and work is in progress to solve them. The quality of the material is the ﬁrst crucial step to maximise the eﬃciency of the detectors; the results of optical characterisation and their correlation with the detector performance clearly demonstrate this statement. Considerable improvements have been achieved. Reproducible high-quality CVD diamond can now be produced even in research laboratories, but still polycrystalline diamond is not competitive, more than ever in view of fabricating pixel array detectors. Single-pixel detectors could be used for space applications because they ﬁt the typical speciﬁcations of astronomical observations. Unfortunately, this is too small a niche for attracting any industrial developments, and singlepixel detectors do not meet the interest of the astronomers, as the imagers do. On the other hand, UV diamond detectors appear to be suitable for fast detection of laser pulses, in particular for VUV lithography, where silicon devices show poor performance. Interest may be renewed by recent progress in the synthesis of opticalgrade single crystals. Sizes of up to 10 mm are currently available with superlative electrical performance. The results of the ﬁrst experiments in the UV region conﬁrm the expectation, so it is possible to assume that in the near future some eﬀorts will be focused on the development of UV detectors based on large single crystals. Some groups have started programs to develop pixel arrays on diamond. The inhomogeneous spatial response observed in the polycrystalline ﬁlms is the actual barrier, and it is probably diﬃcult to ﬁnd solutions to overwhelm it, owing to the intrinsic defective nature of this form of diamond. Singlecrystal diamond can be the solution, even if the dimensions are still rather small. However, the device technology on diamond and the reproducibility of material processing procedures and electronic structures are still an issue and a number of problems remain unsolved. Therefore, replicating electric contacts on the diamond surface does not assure identical metal/diamond interfaces, and hence this contributes to the nonuniformity of the detector response. Notwithstanding present technological limitations to the full development and exploitation of UV detectors, diamond remains the most promising candidate to replace silicon detectors in many applications, in particular those requiring its unique and extreme properties.

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Index blindness solar blindness, 482 visible blindness, 466, 468 charge lifetime, 487 charge mobility, 487 chemical vapour deposition (CVD), 463, 464 coplanar contacts, 480, 489 coplanar structure, 485 CVD diamond, 464, 468, 469, 472 homoepitaxial CVD diamond, 464, 465 single-crystal diamond, 481 dark current, 472 defects grain boundaries, 470 detectors CCD detectors, 491, 493, 496 CMOS detectors, 490, 496 detector gain, 474 diamond-based detectors, 474, 481 imaging detectors, 463 MCP detectors, 491, 496 MOS detectors, 488 pixel-array detectors, 489, 497 single-pixel detectors, 497 time response, 476 UV detectors, 463–465, 472, 474, 476, 481, 484, 485 diamond, 463, 467 diamond detector array, 489

diamond growth, 465, 468, 469 diamond properties, 467, 468, 470, 472 highly-oriented diamond, 493 homoepitaxial diamond, 470 HPHT diamond, 469, 470, 474 IIa type diamond, 469 natural diamond, 463, 466, 468–470, 474, 488 single-crystal diamond, 463–465, 474, 484, 488 diodes MIS diode, 488 external quantum eﬃciency (EQE), 473, 480–482 glow discharge, 469 heteroepitaxial growth, 470 high-pressure high-temperature (HPHT), 465, 469 homoepitaxial growth, 465, 470 hot ﬁlament, 469 image sensors, 489 CMOS image sensors, 490 UV imagers, 490 metal-insulator-metal (MIM), 485 metal-oxide-semiconductor (MOS), 488 metal-semiconductor-metal (MSM), 485

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metal/diamond interfaces, 478 penetration depth, 471, 479 photoconductive gain, 473, 482 photoconductivity, 470 photoconductors, 472, 485 UV photoconductors, 470, 493 photocurrent, 486 photocurrent persistence, 476, 478, 479, 482 photodetectors, 468, 472, 485, 494 diamond-based photodetectors, 497 photodiodes, 487, 488 photon counting, 495 photoresponse, 475, 479 vacuum UV photoresponse, 475 plasma-enhanced chemical vapour deposition (PECVD), 469

polycrystalline diamond, 463–465, 469, 474, 488, 495, 497 priming, 478 UV priming, 478 quantum eﬃciency, 463, 472, 473, 486 response time, 482 sandwich contacts, 479, 489 sandwich structure, 485 Schottky barrier, 486–488 Schottky contacts, 488 Schottky diode, 488 spectral response, 481 surface treatment, 495 x-ray diﬀraction (XRD), 469

Vibrational Spectroscopy in Ion-Irradiated Carbon-Based Thin Films Giuseppe Compagnini1 , Orazio Puglisi1 , Giuseppe A. Baratta2, and Giovanni Strazzulla2 1

2

Dipartimento di Scienze Chimiche, Universit` a di Catania, Viale A. Doria 6, Catania I-95125, Italy [email protected] INAF-Osservatorio Astroﬁsico di Catania, Via S. Soﬁa 78, I-95123 Catania, Italy [email protected]

Abstract. In this work we present and discuss some selected experiments on ionirradiated carbon-based thin ﬁlms. Vibrational spectroscopy is used to investigate the materials structure and to explore the mechanisms of ion beam-induced modiﬁcations in many carbon solids such as crystalline carbon and carbon alloys, hydrocarbon molecules and exotic carbon species.

1 Introduction For many years the vibrational properties of carbon-based amorphous thin ﬁlms have been considered crowded with information for two main reasons. First of all, the position and relative intensities of the bands observed in Raman scattering or infrared absorption measurements are indicative of the bonding state of the carbon atoms and allow the study of the materials in which heteroatomic bonds are included as constituents (carbon alloys, hydrogenated and nitrated systems). Second, the shape and width of the bands are directly connected with structural relaxation phenomena or with the extension of the nanocrystalline domains that are typically found in the amorphous microscopic structure. If we consider additional beneﬁts such as the nondestructive nature of the techniques and their accessibility and low cost for many laboratories, it is easy to understand why they are among the most used for carbon materials. In the case of pure amorphous carbons, the Raman technique has a dominant position [1]. This is because it is more suitable in the detection and characterization of homonuclear C–C bonds, even though the relaxation of the selection rules typical of the amorphous state frequently gives the possibility to observe other kinds of vibrations. On the other hand, infrared absorption is very useful in the detection of heteronuclear bonds. This is the case of the so-called hydrogenated and nitrated carbon materials or of carbon alloys such as a-Si1−x Cx systems. Particularly interesting is the study of carbon materials subjected to ion irradiation or other particle bombardment. General features of the ion bombardment are the formation of metastable phases and the introduction of G. Messina, S. Santangelo (Eds.): Carbon, The Future Material for Advanced Technology Applications, Topics Appl. Phys. 100, 505–520 (2006) © Springer-Verlag Berlin Heidelberg 2006

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foreign species in a controlled thickness range between a few nanometers and few microns, depending on the ion species and their energy. The ﬁrst eﬀect is due to the unusual energy release that is typical of the ion collision cascade, while the second can be used either for semiconductor doping or for the formation of new thin ﬁlms or buried layers. In the case of crystalline carbon, many experiments on ion implantation in diamond have been performed for the last three decades. One objective has been its doping [2, 3, 4]. Others focused on the transformation of diamond (sp3 hybridization) into a graphite-like sp2 -bonded amorphous carbon [5, 6] in which the threshold for the sp3 –sp2 conversion and the resulting amorphous carbon properties were found to strongly depend on the implantation temperature. In any case, depending on the nature, energy and ﬂux of the particles, the properties of the irradiated carbon samples can be changed in diﬀerent ways. It has been found that damage beyond the amorphization threshold in diamond leads, upon thermal annealing, to relaxation of the diamond structure to graphite for sub-MeV ion irradiation, while for MeV alpha particles irradiation annealing restores the original diamond structure [7]. Other important ﬁelds in which keV–MeV irradiation of carbon-based solids ﬁnd applications are: polymer irradiation in ion beam lithography [8,9], high-energy graphite particle irradiation studies for applications into nuclear fusion materials [10], formation of biocompatible materials by ion beam surface modiﬁcations of amorphous carbons [11] and the application of all the irradiated materials’ features to the astrophysical ﬁeld. In this last case the interest is due to the supposed presence of carbon species in the interstellar and circumstellar media as well as in many objects of the solar system [12, 13, 14]. Observed and/or predicted carbon-bearing solids (or large molecules) include species with diﬀerent hybridizations (sp1 , sp2 , sp3 ) such as amorphous carbons, polycyclic aromatic hydrocarbons, fullerenes, nanodiamonds, graphite and linear carbon chains. A complete overview of these ﬁelds is impossible; however, in the following we report a series of selected experiments for large class of carbon-based species from crystalline carbon forms and carbon alloys, to hydrocarbon molecules and unusual carbon species. The aim is to explore the mechanisms of ion irradiation-induced modiﬁcations in many carbon-based solids.

2 Irradiation of Crystalline Carbon and Carbon Alloys One of the best ways to produce amorphous materials in the form of thin ﬁlms is to induce amorphization by using ion bombardment. This procedure has been successfully used for several elemental solids and compounds [15, 16]. For the covalent group IV materials like silicon or germanium, ion beam amorphization produces a so-called continuous random network of tetrahedral sites [17]. In the case of carbon the situation is complicated by the diﬀerent bonding possibilities. Moreover, amorphous carbon (a-C) can be obtained by

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Fig. 1. I D /I G intensity ratio in ion-damaged HOPG as a function of the deposited energy. The inset shows a typical Raman spectrum for a keV ion-produced amorphous carbon

ion irradiation starting from graphite, diamond or other crystalline forms. Raman spectroscopy is able to characterize the irradiation eﬀects starting from early stages to the ﬁnal amorphization. If one consider the irradiation of a highly oriented pyrolitic graphite (HOPG) sample at low ﬂuences, Raman spectra show the formation of a feature at 1360 cm−1 , called the D line, which is accompanied by the formerly present 1580 cm−1 peak (G line) [18, 19]. It is now clear that the G line is due to the bond stretching of all pairs of sp2 atoms in both rings and chains. The D peak is attributable to the breathing mode of some pieces of graphene sheets formed by ballistic collisions during the irradiation [20, 21]. Once the ion ﬂuence is increased to overcome few eV/atom, a collapse to the amorphous phase is observed with a typical Raman spectrum reported in the inset of Fig. 1. Again, D and G bands are present even though the deconvolution of the entire signal is frequently ambiguous. Figure 1 also shows the evolution of the I D /I G intensity ratio for the irradiation of graphite in the early stages of the process. The data have been reported for diﬀerent irradiating ions and ﬂuences (circles refer to 1015 ions/cm2 , squares to 1014 ions/cm2 ) at an ion energy of 100 keV [22]. These data are reported as function of the energy lost by the beam through ballistic collisions, considered the fundamental parameter which determines the vibrational and electronic properties of the ﬁnal amorphous layer. Even

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though ballistic collisions are considered random and are produced in a highdensity collision cascade (typical values for 400 keV He+ irradiation are 4 × 10−14 eV/(atom cm−2 )), rearrangements following these processes produce materials which are not purely sp2 hybridized. Their electronic nature can be studied through electron energy loss spectroscopy experiments. In particular, it has been shown that amorphous carbons obtained by keV ion irradiation of diamond or graphite at room temperature possesses nearly 80% sp2 bonding arrangement so that the vibrational features can be mainly assigned to the trigonal carbon component. The ﬁnal result is also independent of the initial crystalline structure of the irradiated carbon. A careful study of the D and G lines and their signiﬁcance for the amorphous carbon structure has been recently given by Ferrari et al. [21]. These authors pointed out that there is a strict correlation between the intensity ratios and the extension of the graphite domains found in a-C and nanocrystalline graphite. These considerations on the degree of order have been successfully applied in the study of carbonaceous materials that have been identiﬁed in the so-called interplanetary dust particles (IDPs). Indeed, since fast-particle bombardment is one of the most important processes suffered by materials (dust, asteroids, comets, etc.) present in the solar system, the Raman spectra of a number of diﬀerent ion-irradiated carbons have been compared with those obtained for IDPs caught on airbone impacting collectors at an altitude of 18–20 km and believed to be extraterrestrial in origin [12]. The diﬀerent degrees of order observed could be indicative of diﬀerent irradiation doses by solar wind particles suﬀered by IDPs in the interplanetary medium before the collection in the Earth’s atmosphere. Let us now consider what happens when elements other than carbon participate in the structure of the ﬁnal amorphous layer. It has been observed that keV ion irradiation produces variable amounts of trigonal carbons when diﬀerent amounts of hydrogen are introduced in the sample structure. This can be done either starting from a hydrogenated material (as in the case of the amorphization of hydrocarbons, see next section) or by introducing hydrogen by H+ irradiation. In particular, an increase of the hydrogen concentration favors the formation of tetrahedral bonds. This increase of tetrahedral sites is also responsible for an increase of the optical energy gap and of the resistivity, giving materials frequently termed as hydrogenated amorphous carbons. The presence of other group IV elements also deeply inﬂuences the bonding state. One of the most interesting examples related to this topic is the study of binary amorphous carbon-based alloys like a-Si1−x Cx with diﬀerent stoichiometry. Again, vibrational spectroscopy is an excellent tool to monitor the behaviour of the local order in covalently bonded solids through the analysis of the properties of their fundamental units [23]. In particular, Raman spectroscopy provides good detection and characterization of homonuclear C–C and Si–Si vibrations through their intense signals located in the range 1000–2000 cm−1 and 300–500 cm−1 , respectively. Moreover, the relaxation

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Fig. 2. Combined Raman and infrared data for crystalline and ion-irradiated stoichiometric SiC

of the selection rules typical of the amorphous state gives the possibility to also observe vibrations coming from heteronuclear bonds like Si–C (between 700 and 800 cm−1 ). Figure 2 shows a collection of Raman and infrared data in crystalline and amorphous SiC. Amorphization has been induced by Ar+ 300 keV ion irradiation. It is straightforward to observe that the Raman spectrum of the a-SiC shows all the three signals obtainable in a random mixture of silicon and carbon atoms, that is, Si–Si (500 cm−1 ), Si–C (800 cm−1 ) and C– C (1430 cm−1 ) vibrations. Heteronuclear bond vibrations are also observed in the infrared absorption spectrum with a relevant increase in width and decrease in intensity for the case of the amorphized layer. Interestingly, the position and width of the C-C signal in a-Si1−x Cx alloys is quite diﬀerent with respect to those commonly found in all the hydrogenated and unhydrogenated amorphous carbons (see also the inset in Fig. 1), since it is symmetrical and only 170 cm−1 wide [24]. The diﬀerence can be ascribed to the chemical environment of the carbon subsystem, embedded into a silicon matrix that favors the formation of sp3 -arranged carbon atoms, considered predominant in these amorphous silicon carbon alloys. Similar results are obtained in a-GeC samples [25]. Analogous considerations can be done for the Si–Si signal at around 480 cm−1 . In this respect it has been recently reported that [26] the width of this band is almost twice that of ion-

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implanted amorphous silicon. This can be explained with the diﬀerences in bond angle distortion (∆θ). In the case of a-SiC samples this has been evaluated as ∆θ = 22.5◦ . Moreover, upon annealing ∆θ increases up to 27◦ at 700◦ C, while for amorphous silicon it decreases from 12.3◦ to 9.5◦ . Relaxation of the a-SiC matrix provides the energy required to increase the distortion of the silicon clusters. Annealing experiments conducted at 1000◦C have also shown that the disorder-induced 1430 cm−1 signal is reversible. This occurs in all the alloys with x ≤ 0.5. The observation is consistent with the fact that sp2 graphitelike rings (strong stability) are never formed in substoichiometric alloys and, as a consequence of ion irradiation, all the carbon atoms are “used” to obtain silicon carbide crystalline grains eventually embedded in a silicon excess. The experimental observations regarding the behaviour of the C–C Raman signal are reported in Fig. 3. Diﬀerent alloys are obtained by implanting diﬀerent amounts of carbon atoms into a silicon layer, in such a way to have a uniform thin ﬁlm. In all of the as-prepared samples (Fig. 3a) the C–C signal is observable if the carbon concentration is above a bonding percolation threshold (around x = 0.4). This signal disappears after 1000◦ C annealing for all the substoichiometric samples, while for higher carbon concentrations, sp2 clustering is obtained (well-resolved D and G components) with the precipitation of pure carbon phases embedded into a SiC matrix [27]. Combination of Raman scattering and infrared absorption data has also permitted [23] researchers to quantitatively determine the fraction of C–C bonds as a function of the carbon concentration, revealing that there is an onset in the formation of C–C bonds just at x = 0.4, consistent with the qualitative behavior seen in Fig. 3. The increase of the signal intensities with increasing carbon concentration is in agreement with the known theories of random bonding in amorphous alloys.

3 Irradiation of Hydrocarbons (Oligomers, Polymers and Frozen Gases) The eﬀect of ion irradiation on organic molecules is strongly related to the amount of the deposited energy and to the nature of the species involved. A ﬁrst eﬀect of the ionizing radiation is to change the molecular structure through a series of nonconventional chemical reactions. Typical examples are the eﬀects of cross-linking [28] and scission [29] observed in several irradiated polymer chains at moderate or low energy releases (below 0.1 eV/atom). At these stages ion-induced enhanced chemical processes are also observed such as polymer unzipping eﬀects typical of PMMA [30, 31]. These processes, which occur naturally at temperatures of about 360◦ C at which methacrylate monomer is the most abundant product of the PMMA pyrolysis, are observed at lower temperatures (120–200◦C) if the polymer is irradiated. Other reported phenomena are the evolution of simple gaseous molecules like

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Fig. 3. Raman data in the region of C–C signals for a-Si1−x Cx samples as a function of the carbon content. As-deposited and 1000◦ C-annealed samples are shown

H2 , CH4 or more complex species [29]. A useful parameter to characterize ion beam eﬀects on polymers is the so-called chemical yield G (number of events by 100 eV if ion deposited energy). This quantity depends on the type of polymer and on the ion energy. For instance, alkane chains, like those which constitute the polyethylene structure, release a large amount of H2 molecules with a G = 2 H2 /100 eV accompanied with the formation of crosslinks (cl) with a G = 1.2 cl/100 eV. The analysis of these irradiated targets by vibrational spectroscopy can be correlated to the change of some important physico-chemical properties such as the solubility change or the wetting response of the irradiated surface. As an example we cite a series of experiments on the irradiation of assembled aliphatic molecules grafted to a silver metal surface through S–Ag bonds [32, 33]. The monolayers (CH3 (CH2 )11 S–Ag) are irradiated by 100 keV H+ ions at ﬂuences in the range 1012 –1014 ions/cm2 and are studied by surface-enhanced Raman (infrared) spectroscopy [34], which ensures a cross-section magniﬁcation (105 –108) with respect to conventional vibrational techniques.

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Fig. 4. Correlation between wetting response and surface composition in ion-irradiated alkane self-assembled monolayers

The observation of the CH stretching regions both in the Raman spectra and in the infrared ones, before and after the irradiation, is in agreement with above-mentioned hydrogen loss: – There is a decrease in the CH3 /CH2 stretching intensity ratio. – There is the formation of oleﬁnic groups with CH stretching signals above 3000 cm−1 . Figure 4 reports the correlation between the wetting response of the surface as obtained by measuring the water liquid contact angle, and the change in the chemical structure induced by irradiation. Wetting data indicate that ion irradiation changes the ambient interface from a layer of CH3 groups to a more polar one, thus decreasing the contact angle. Then, hydrocarbon molecules have lost a signiﬁcant amount of the original aliphatic character to become a rather carbonaceous material. At higher irradiation ﬂuences (higher deposited energies) the formation of a carbonaceous layer (whose thickness depends on the irradiation parameters) is a dominating feature. This can be observed either by irradiating large molecules, polymers or frozen gases. In the case of the irradiation of ices, most of the studies have been centered on the so-called solid residue, obtained once the irradiated sample has been annealed at room temperature. Indeed, among the eﬀects induced by fast ions, the formation of an organic residue evolving at high doses towards an ion-produced hydrogenated amorphous carbon (IPHAC) is particularly interesting. IPHAC formation has been observed in several kinds of carbon-containing ices (C6 H6 , CH4 , C4 H10 , etc.) for a combination of bombarding ions (H, He, Ar, etc.) and ion energies (ranging between a few keV and MeV). It has been shown, by in situ Raman spectroscopy, that 3 keV He+ irradiation of a frozen benzene ﬁlm leads to the formation of an IPHAC even at

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low temperature (T = 77 K) [35]. In that experiment the penetration depth of ions (about 0.04 µm) was much less than the thickness of the benzene ﬁlm (about 2 µm thick). After warm up to room temperature, no feature due to the benzene ice was present in the spectrum because the underlying unirradiated ice has sublimated, passing through the porous structure of the residue. Only the C=C 1560 cm−1 Raman band was observed. In situ IR spectroscopy has also evidenced the presence of both sp1 (CH stretching in monosubstituted acetylenes) and sp3 carbon hybridizations (CH2 aliphatic stretching) in addition to the sp2 hybridization. Further irradiation of the organic residues at room temperature (Fig. 5) determines an increase of the I D /I G ratio with the dose up to a saturation value, while the H/C ratio measured by elastic recoil detection and the optical gap decreases [35]. Figure 5 is divided into three regions delimited by broken vertical lines. Up to a total dose of 10 eV/atom, the deposited frozen ﬁlm remains a molecular solid (no optical gap can be measured). Here the relative amount of H atoms bound to sp2 carbon sites decreases strongly with respect to sp1 and sp3 sites (see the two bottom lines). No amorphous carbon feature can be clearly seen in the Raman spectrum. In the second region (10–25 eV/C atom), the ratios of diﬀerent hybridization remain constant, a strong H loss is observed and the amorphous carbon Raman feature become observable: the material has changed into a polymer-like compound (an optical gap can be measured). The D line is almost absent in the Raman spectrum. In the third region (≥ 25 eV/C atom) the relative number of H atoms bound to sp2 sites decreases strongly with respect to sp1 and sp3 sites (note, however, that all the C–H bands become weaker and weaker due to the H loss), the ratio of the D to the G line increases: the material has changed in an amorphous carbon ﬁlm with a decreasing optical gap. These results were interpreted in terms of an increasing average sp2 cluster size attributed to the preferential hydrogen loss from sp2 sites with respect to sp3 sites (see [35] for further details). A similar trend has been obtained on an aliphatic (C4 H10 ) ice at 10 K. Recently, it has been shown that ion irradiation can drive the formation of amorphous carbon also in a pure methane ice and in the case of a mixtures containing several ices [36]. In particular, 30 keV He+ irradiation of an H2 O : CH4 : N2 = 1 : 6 : 3 icy mixture at 12 K leads to the formation of a hydrogenated amorphous carbon. Even in this case the Raman results are consistent with an increasing size or number of the sp2 clusters. This supports the idea that the process of IPHAC formation is general. Anyway, there seems to be great diﬀerence in the eﬃciency of the process itself [36].

4 Irradiation of sp-Rich Amorphous Carbon Phases Even though many papers have been published on the eﬀects of ion irradiation on diamond and diamond-like materials as well as on organic carbon-based

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3 keV He on C6H6 ID

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1 0

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20

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Dose (eV/C-atom) Fig. 5. Overview of experimental results obtained with various techniques (Raman, IR and elastic recoil detection) after ion irradiation of frozen benzene

systems and graphitic-like entities (included fullerenes, nanotubes and carbon onions), there is still a lack in the literature regarding the irradiation of linear carbon species. These materials are essentially constituted by sp-hybridized carbon atoms to form linear carbon chains frequently termed as carbynes [37]. Several authors claim to be able to obtain a relevant percentage of carbynoid species in their produced amorphous carbons, but these species easily react or cross-link once exposed to air [38, 39, 40]. Methods of preparation are based both on physical processes and chemical routes. In the ﬁrst case ultrafast temperature treatments in conﬁned geometries are needed to reach the desired point in the carbon phase diagram where

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Fig. 6. Typical Raman spectrum for an amorphous carbon thin ﬁlm containing carbynoid features. The inset shows the carbon triple-bond signal as observed with Raman and infrared spectroscopies

carbynes seem to be stable [38]. In the second case several approaches are used such as arc discharge between graphite electrodes submerged in various solvents [41], dehydrogenation of polymers [37], electrochemical carbonization or condensation of end-capped chain molecules produced in the gas phase [42]. Consistent amounts of sp species are also found in carbon clusters obtained by adiabatic condensation of carbon plasmas [43, 44]. These species can be deposited onto suitable substrates once seeded into a buﬀer gas which undergoes a supersonic expansion [45]. A characteristic vibrational feature of carbyne systems is to present C– C stretching vibrations located at higher wavenumbers (around 2100 cm−1 ) with respect to those detected for trigonal and tetrahedral carbon bonds. A Raman spectrum in which the signal at 2100 cm−1 is evidenced for cluster beam deposited thin ﬁlms is reported in Fig. 6 as an inset [40]. Frequently this signal is considered as the convolution of those coming from polyynes (alternate single and triple bonds, at 2100 cm−1 ) and polycumulenes (double bonds at 2000 cm−1 ). The irradiation by means of 200 keV Ar+ beams produces eﬀects on both graphite-like and sp signals. The ﬁrst is modiﬁed by changing the D/G intensity ratio as already observed, while the intensity of the sp signal decreases by increasing the ion ﬂuence as reported in Fig. 6. Assuming that resonance enhancements for sp-bonded species are independent of the structural changes associated with ion bombardment, this decrease indicates that ion irradiation destroys the carbyne chains in terms of the disappearance of triple carbon

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Fig. 7. The evolution of the carbyne features as observed using infrared absorption. Left scale refers to the sharp 2110 cm−1 component, while right scale reports the wide component

bond signals. At the same time, the shape of the 2100 cm−1 band shows a mild change. While one should expect similar trends in the analysis of the infrared absorption data, something diﬀerent has been revealed as reported in Fig. 7. As the ion ﬂuence increases, the broad sp C–C stretching carbon band gradually changes in a sharper peak located at 2110 cm−1 (inset of Fig. 7). Then, despite the fact that sp carbon bonds are known to be highly unstable, when irradiation is performed a new sharp component at 2110 cm−1 appears, even though the intensity of the above-mentioned broad band decreases at increasing ﬂuences. The rest of Fig. 7 gives quantitatively the decrease of the wide component and the increase of the sharp one as a function of the ion ﬂuence (φ). These data are obtained by a proper deconvolution of the overall signal into a sharp component (2110 cm−1 ) and two contributions related to the broad band (polycumulene and polyyne). It is interesting to observe that ﬁts of these experimental data with exponential curves such as: – 1− e−σφ (growth of the 2110 cm−1 sharp line) – e−σφ (decrease of the broad triple bond stretching band) give similar cross sections (σ). In particular, these are 3.7 ± 1 × 10−14 cm2 for the wide component and 4.3 ± 1×−14 cm2 for the sharp one, suggesting a correlation between the two phenomena. Similar analysis on the already reported

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Fig. 8. Correlation between the 2110 cm−1 line and the observed 3300 cm−1 CH stretching component, observed after ion irradiation

Raman data gives a cross section ﬁve times greater (see solid line in Fig. 6). This discrepancy can be attributed to diﬀerences in the processes involved in obtaining the vibrational features (that is, diﬀerences in the spectroscopic processes, i.e., between Raman scattering and infrared absorption). Following a wide consensus present in the literature, it is easy to attribute the sharp 2110 cm−1 signal to the formation of monosubstituted acetylenic, diacetylenic or oligoacetylenic structures which our results indicate to be formed upon irradiation [40]. The similarity between the mentioned cross sections conﬁrms that these structures are formed as a consequence of the fragmentation of the long carbyne chains induced by ion irradiation. Moreover, the decrease of the carbyne signal in the Raman spectrum can be due to the formation of polar molecular structures, more easily revealed with IR spectroscopy, than with Raman scattering (mutual exclusion rule). The presence of hydrogen species in the carbon residue-containing sp species also induces the formation of hydrogenated acetylenic molecules, as observed looking at the CH stretching region. The general eﬀect of the ion beam is to decrease the intensity of the aliphatic CH stretching bonds and to induce the appearance of a signal located at 3300 cm−1 , attributed to alkynic CH bonds. Their formation can be related to the known eﬀect of ion irradiation to induce hydrogen loss in hydrogenated carbon structures (see previous section). Such hydrogen molecules are then readily available to

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interact with sp hybridized carbons. Figure 8 shows the behaviour of 2100 cm−1 and 3300 cm−1 bands as a function of ion ﬂuence. It is straightforward to conﬁrm a correlation between them, indicating the formation of short monosubstituted sp structures which are hydrogen-terminated on one side.

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Index a-C, 506 a-Si1−x Cx , 508 sp1 hybridisation, 514

carbyne, 515 clustering, 510 cross-links, 510, 511, 514

amorphization, 509 amorphous carbon thin ﬁlms, 505

diamond, 506 ﬁlm stoichiometry, 508, 510

biocompatibility, 506 carbon-containing ices, 512

highly oriented pyrolytic graphite (HOPG), 507

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ices, 512 infrared absorption, 505, 509–512, 515–517 interplanetary dust particles (IDPs), 508 ion beam, 505 ion implantation, 506 ion irradiation, 510 ion produced hydrogenated amorphous carbon (IPHAC), 512 linear carbon species, 514

organic molecules, 510 polycumulenes, 515 polymers, 510 polymer chains, 510 polyynes, 515 Raman spectroscopy, 507–512, 514–517 surface enhanced Raman spectroscopy (SERS), 511

monosubstituted sp structures, 518

vibrational spectroscopy, 505, 508, 511

oligomers, 510

wetting response, 511

Index

π states, 95–97, 99, 100, 102, 103, 423, 426, 452, 456 σ states, 95–97, 427 a-C, 55, 83, 98, 137, 149, 175, 176, 181, 428, 447, 506 a-C:H, 138, 218–220, 222–224, 227–230, 232–234, 426, 428–443, 447 a-C:H:F, 219–224, 226, 228–234 a-C:H:F:N, 219, 233 a-C:H:N, 1–5, 10, 11, 13, 14, 16, 17, 218, 220–224, 226, 228–230, 233 a-Si1−x Cx , 508 sp2 -bonded clusters, 5, 10, 18, 38, 95, 98–103, 137, 139, 142, 179–181, 183, 217, 426–429, 435, 437–439, 442, 443 cluster conjugation level, 427 cluster size, 5, 8, 10, 11, 18, 103, 139–141, 144, 147, 226, 359, 372, 376, 377, 426–429, 435 distorted clusters, 102, 103, 142 intercluster interaction, 137, 147 intracluster interaction, 137, 142, 150 undistorted clusters, 97, 142 sp2 -chains, 139, 427, 431, 432, 435–439, 443 chain length, 439, 443 sp2 -rings, 139, 141, 145, 426, 427, 431, 434, 435, 437, 438, 442, 443 distorted rings, 435, 437, 438, 442 ﬁve-fold rings, 145 six-fold rings, 145, 426 sp1 hybridisation, 96, 97, 514 sp2 hybridisation, 96, 97 sp3 backbone, 98–103 sp3 hybridisation, 96, 97 sp3 /sp2 bonding ratio, 17, 62, 97–99, 101, 293, 295, 360, 374, 427

ta-C, 98, 138, 149, 162, 163, 360, 362–365, 367, 373, 374, 376, 378, 403, 428 ta-C:H, 98, 149 ta-C:N, 149 absorption coeﬃcient, 404, 409, 411, 413–418 acceptor acceptor states, 304 donor acceptor pair recombination, 304 accommodation length, 100, 101, 103 acoustic phonon, 154 acoustic waves, 153 acoustic wave velocity, 154, 155, 157, 159, 160, 163 surface acoustic waves (SAWs), 154, 155, 157–159, 162, 164, 168 pseudo surface waves (PSAWs), 159 SAW velocity, 154, 155, 159 activation energy, 128–132 alkaline phosphatase (ALP), 58–61, 66, 67, 70, 71 amorphization, 509 amorphous carbon, 95, 98 characteristic lengths, 99, 100 amorphous carbon thin ﬁlms, 137, 163, 423, 505 annealing, 41, 175–180, 184, 228, 382, 403, 417, 418 approximated solutions, 1, 2, 10, 11, 13 arc discharge, 82 atomic force microscopy (AFM), 229, 233, 234, 361, 371–373 atomic structures, 187 Auger emission spectroscopy, 449–455, 457

522

Index

background gas, 371, 372, 376, 377 bioactivity, 55, 58, 60, 65, 73 biocompatibility, 55–58, 64, 71, 506 biomaterials, 57, 64, 73 biomedical implants, 55–57, 64, 73 blindness solar blindness, 482 visible blindness, 466, 468 bond length alternation (BLA), 31 eﬀective BLA (EBLA), 31, 34 bone sialoprotein (BSP), 57, 58, 61, 66, 67, 70–72 Brillouin scattering, 153–159, 161–164, 167–170 surface Brillouin scattering, 157, 163–165 buckminsterfullerene, 78, 79 C168 , 198, 199 C180 , 200, 201 C186 , 198 C20 , 200 C24 , 363 C2610 , 196 C264 , 196 C276 , 198, 199 C276 :C84 , 198, 199 C28 , 196 C36 , 190, 200 C408 , 198, 199 C60 , 78, 79, 187, 191–194, 198, 200, 359 C60 :Li, 207 C60 :N, 192 C60 :Rb, 192 C60 with hydrogen, 207–211 doped C60 , 191 C67 , 203 C70 , 79, 190, 194 C72 , 194 C74 , 192–195, 203 C74 :Ca, 194 C74 :Eu, 194 C74 :Gd, 194 C74 :La, 194 C74 :Si, 192–195 C76 , 194 C82 , 192 C84 , 192, 198, 199 C84 :C24 , 197

C84 D2 , 198, 200 C84 D2d , 200 C84 Td , 198 C84 Td , 200 carbon chemical bonding, 290 carbon clusters, 194 endohedral clusters, 192 carbon coordination, 17, 98–101, 230, 291 threefold and fourfold coordination, 17, 292, 296 carbon-containing ices, 512 carbyne, 515 carrier mobility, 110, 116 catalytic chemical vapour deposition (CVD), 83 cathodoluminescence (CL), 251, 304 charge collection distance (CCD), 110, 117, 118, 130, 244, 245, 247, 249, 256, 263, 306–309, 315 charge collection eﬃciency (CCE), 240, 242, 244–254, 258, 260–263, 280–285 CCE maps, 242, 244 charge collection spectrum, 111–113, 125 charge lifetime, 487 charge mobility, 487 chemical shift, 290 chemical vapour deposition (CVD), 83, 107–112, 269, 329, 463, 464 CVD heteroepitaxial growth (CVDHG), 269 CVD heteroepitaxial growth (pCVD), 269 radio frequency CVD, 429 chiral vector, 79 cluster assembled (CA) ﬁlms, 362, 368–375, 377 cluster model, 426 cluster–cluster interaction, 100 cluster-assembled (CA) ﬁlms, 372, 376, 378 cluster-cluster interaction, 147 cluster-cluster separation, 149 clustering, 97, 137, 145, 146, 360, 426–429, 435, 437, 438, 510

Index graphite-like clusters, 175, 180, 181, 183 CNx thin ﬁlms, 289, 290, 296, 298 coatings, 56–58, 67, 71–73, 360 bioactive coatings, 55 biomedical coatings, 57, 360 protective coatings, 218 coherence length, 372, 377, 428 columnar ﬁlm, 367, 368, 371 node-like ﬁlm, 367, 368, 371 columnar growth, 109, 111–113, 115, 116, 118 conﬁnement, 28, 36, 38, 39, 382–384, 392–395, 397, 399, 400 conjugation length, 30, 383 eﬀective conjugation length (ECL), 30 coplanar contacts, 480, 489 coplanar structure, 485 core level photoelectron peak, 290 cross-links, 510, 511, 514 crystallite size, 428 cumulene, 32 current persistent, 304, 308, 317, 319–324 radiation induced, 304, 306, 308, 311, 313 sensitivity, 311 CVD diamond, 242, 244, 254, 263, 345–348, 464, 468, 469, 472 homoepitaxial CVD diamond, 464, 465 single-crystal diamond, 481 cytotoxicity, 58, 59, 64, 65, 71 D band, 36–38, 63, 145, 149, 177, 179, 180, 224, 225, 364, 384, 391, 406, 427–432, 434–438, 440 D-band dipersion, 37 D-band, 38 D/G band intensity ratio, 177, 179–184, 225, 226, 406, 409, 416, 417, 428, 431, 432, 438, 441 D/G-band intensity ratio, 145, 149 D/G band intensity ratio, 295, 366, 375 D/G band intensity ratio, 295, 298–300, 364, 372 dark current, 472

523

defects, 27, 28, 33–35, 108, 142, 144, 148, 383, 395 defects distribution, 108, 110–113, 115–117, 119, 133, 279, 280 grain boundaries, 108, 109, 112, 113, 115, 116, 118–120, 333, 341, 345, 346, 470 grain boundaries distribution, 112, 113, 116, 118 in diamond, 329, 333, 334, 341, 347, 352–356 band A, 304 band A, 308, 310, 311, 315, 316 band B, 308–311, 313, 321–323 neutron irradiation, 313, 315, 324 in-grain defects, 112, 113, 115, 116, 118, 119 in-grain defects distribution, 112, 113, 115, 118 dendritic ﬁlm, 367, 371 density, 224, 227–229, 293 density functional theory (DFT), 32, 386, 390–393 detector eﬃciency, 110 detectors, 108, 240, 241, 244, 248, 253, 254, 256, 261, 263 CCD detectors, 491, 493, 496 CMOS detectors, 490, 496 detector gain, 474 diamond-based detectors, 346, 474, 481 imaging detectors, 463 MCP detectors, 491, 496 MOS detectors, 488 pixel-array detectors, 489, 497 single-pixel detectors, 497 time response, 476 UV detectors, 463–465, 472, 474, 476, 481, 484, 485 detrapping, 123–129, 131 diamond, 26, 41, 96, 97, 107, 161, 217, 329, 359, 426, 427, 463, 467, 506 defects in diamond, 269, 270 diamond detector array, 489 diamond detectors, 267–273, 277, 278 diamond growth, 465, 468, 469 diamond nucleation, 329, 336, 338, 339

524

Index

diamond properties, 345, 467, 468, 470, 472 high-quality diamond, 347, 348, 351–357 highly-oriented diamond, 493 homoepitaxial diamond, 345–348, 352, 355–357, 470 HPHT diamond, 346, 469, 470, 474 IIa type diamond, 469 IIb type diamond, 348, 352 natural diamond, 348, 352, 463, 466, 468–470, 474, 488 nitrogen contamination, 347, 353–356 silicon contamination, 347 single-crystal diamond, 345, 463–465, 474, 484, 488 transport in diamond, 273–279 Hecht’s model, 275 diamond-like carbon (DLC), 25, 56, 57, 97, 99, 138, 139, 144, 147, 149, 150, 162, 164–166, 175, 218, 224, 228–230, 234, 294, 359, 360, 362, 363, 365, 368, 376, 403, 404, 406, 412, 413, 415, 416, 418, 428, 430, 431, 437, 443 diamondlike carbon (DLC), 217, 293 dimensionless arguments, 4–6, 8 dimerisation, 386, 390, 393, 394 bonds dimerisation, 395 dimerisation parameter, 387 diodes MIS diode, 488 disorder, 100, 101, 137, 139–141, 150 homogeneous disorder, 140 inhomogeneous disorder, 140, 141 dispersion, 166, 383, 384, 386, 398, 399, 423, 428, 432, 435–437, 439, 440, 443 phonon dispersion, 26, 388, 391 distortions, 98–103 donor deep acceptor centers, 308 deep donor level, 305, 308 donor acceptor pair recombination, 304 D band, 293, 294, 296, 298 eﬀective conjugation coordinate theory (ECCT), 38, 385, 388, 390

elastic constants, 155, 156, 158, 160–162, 164, 165, 168 elastic moduli, 155, 159–161, 163, 166 elastic properties, 154, 155, 170 elastic scattering, 153 electrical conductivity, 102, 103 electrical properties, 63, 218, 219 electroluminescence, 304 electron diﬀraction (ED), 176–181, 183, 184 electron energy loss spectroscopy (EELS), 224, 226, 361, 362, 367, 368, 449–452, 458–460 electron energy loss spectroscopy (EELS), 455 electron paramagnetic resonance (EPR), 142 electron spin resonance (ESR), 142–144, 146, 150 ESR signal, 102, 103 electron–phonon coupling, 28, 30, 38, 382, 385, 387–393, 395, 398, 399 electron-phonon coupling, 384, 425 electron-photon coupling, 425 electronic properties, 95 external quantum eﬃciency (EQE), 473, 480–482 fading optical fading, 305 thermal fading, 310, 317, 319 fast component, 123, 128 fast photography, 287–289, 296, 299 ﬁgure of merit for growth process, 17 ﬁlm stoichiometry, 3, 11, 12, 14–17, 508, 510 ﬁrst order kinetics, 310, 316, 319 ﬁrst principle calculations, 24, 28, 30, 32, 34, 386, 398, 400 ﬂoppiness, 98 ﬂuorine incorporation, 217–219, 223, 224, 226–228, 230, 231 free expansion regime, 297 frequency, 316 friction coeﬃcient, 56, 57, 219, 229, 232, 233, 360 fullerene, 25, 41, 187–192, 218, 359, 383 fullerene materials, 188, 189, 207 giant fullerene, 192, 199

Index fullerite, 162 G band, 3, 4, 8, 10, 11, 17, 18, 37, 63, 140, 141, 177–180, 224, 225, 364, 395–398, 406, 416, 417, 423, 427–432, 435, 437, 438, 440 dispersive G band, 435–437, 439, 440 non-dispersive G band, 435, 437, 439, 440 G-band, 150 G-band, 145, 149 glassy carbon, 98 glow discharge, 84, 469 graphene, 78–80, 97, 102, 162, 218, 381–384, 390, 392, 393, 396, 427 graphite, 28, 41, 96, 97, 161, 217, 359, 426–428, 430, 431, 435 graphite-like carbon (GLC), 25, 139, 142, 175, 218, 287 graphitization, 41, 147, 175, 179, 180, 184, 205, 230, 234, 292, 293, 299, 430, 438, 443 G band, 293, 294, 298 H¨ uckel theory, 382, 384, 386, 387, 389, 391, 392, 394, 399 H¨ uckel approximation, 426 haemocompatibility, 56, 57 hardness, 56, 57, 218, 229–231, 233, 234, 360 Hecht theory, 110, 111, 114, 116, 118, 275, 278 heteroepitaxial growth, 329, 346, 470 high-pressure high-temperature (HPHT), 107, 346, 465, 469 high-resolution electron microscopy (HREM), 191, 192 highest occupied molecular orbital (HOMO), 194 highly oriented pyrolytic graphite (HOPG), 383, 507 HOMO–LUMO gap, 29, 30 HOMO-LUMO gap, 194, 203 homoepitaxial growth, 329, 346, 465, 470 hot ﬁlament, 469 hybrid arc-discharge, 187, 189, 190, 192, 203 hydrogen adsorption, 42, 44, 45

525

hydrogen desorption, 14, 16, 42, 455–458, 460 hydrogen incorporation, 218 hydrogen storage, 44, 207–209, 211 hydrogenated amorphous carbon, 162 hydrogenated amorphous carbonnitrides, 1 hydrogenated diamond-like carbon (DLC:H), 99, 138, 142, 149 hydrogenated graphite-like carbon (GLC:H), 99 hydrogenated polymer-like carbon (PLC:H), 99 hydrophobicity, 219, 231, 232, 235 ices, 512 image sensors, 489 CMOS image sensors, 490 UV imagers, 490 inelastic scattering, 153 infrared (IR) spectroscopy, 24, 25, 33–36, 42, 224, 227, 229, 361–364 infrared absorption, 505, 509–512, 515–517 interference of light, 409 internal stress, 217, 218, 229–231, 234 interplanetary dust particles (IDPs), 508 ion beam, 505 ion beam analysis (IBA), 220, 224 ion beam induced charge (IBIC), 241–243, 245–252, 257, 258, 260, 261, 263 frontal IBIC, 242–244, 262, 263 IBIC maps, 244, 245, 252, 259–263 lateral IBIC, 242, 243, 245–250, 253, 259, 262, 263 ion beam induced luminescence (IBIL), 240–242, 251–256, 263 frontal IBIL, 253, 254, 256 IBIL maps, 251–253, 255, 256, 263 lateral IBIL, 252, 253 ion beam-induced charge (IBIC), 240 ion beam-induced luminescence (IBIL), 240 ion bombardment (IB), 176, 181–184 ion implantation, 506 ion irradiation, 416, 510

526

Index

ion produced hydrogenated amorphous carbon (IPHAC), 512 Kohn anomaly, 28, 32, 392 laser vaporisation, 82 lattice dynamics, 24, 27, 29, 33 light scattering, 154 limited hyperbolic function, 321 linear carbon species, 514 linear model, 308, 310 low-frequency Raman, 169 lowest unoccupied molecular orbital (LUMO), 194 magnetron sputtering, 176 mass spectrometry, 84, 85 mass-separated ion beams (MSIB), 403–405, 407–414, 416–418 mechanical properties, 98, 99, 101–103, 153, 217–219, 229 metal-insulator-metal (MIM), 485 metal-oxide-semiconductor (MOS), 488 metal-semiconductor-metal (MSM), 485 metal/diamond interfaces, 478 metallofullerene, 187, 190, 192 microscopic growth variables, 12–15 microstructure, 175, 176, 178–181, 183, 184, 217, 219, 224, 228, 233 graphite-like structure, 179, 183 mineralization, 57, 60, 64–67, 71 Mo substrates, 329–341 molecular approach, 24, 29, 38, 384, 391 molecular dynamics, 24, 27, 33, 35, 207, 390 monosubstituted sp structures, 518 Monte Carlo simulation, 113 MTT test, 65, 67 multi-wavelength Raman spectroscopy (MWRS), 428 multiwavelength Raman spectroscopy (MWRS), 37–40 nano-glassy carbon, 372, 377 nanocages, 187, 189, 207 nanocage materials, 189

nanocapsules, 187, 190, 192, 200, 202–205, 207–211 self-organization, 187, 209 one-dimensional self-organization, 209 nanoﬁbres, 80, 82 herringbone nanoﬁbres, 81 stacked nanoﬁbres, 81 nanohorns, 187, 202, 203 nanoparticles, 210 gold nanoparticles, 210, 211 nanostructured carbon, 162 nanostructures hollow-cage-nanostructures, 187 nanotribology, 229 nanotubes, 25, 28, 41, 77–85, 87–89, 166, 187, 192, 196, 201–203, 208, 210, 211, 218, 359, 381–383, 395–399 armchair nanotubes, 79, 80, 398 chiral nanotubes, 79 chiral vector, 79 chirality, 397 chiral vector, 396 growth mechanism, 85 mininanotube, 200 multi-walled nanotubes (MWNTs), 200 multiwalled nanotubes (MWNTs), 77, 79, 82, 84, 206 single-walled nanotubes (SWNT), 166, 167 single-walled nanotubes (SWNTs), 79, 81, 82, 156, 162, 167–169, 200, 395–397, 399, 400 zig-zag nanotubes, 79, 80, 398 nanowires, 200, 203, 210, 211 nitrogen, 374, 376, 377 nitrogen incorporation, 10, 12–17, 147, 217–219, 221, 224, 226, 228, 230, 232, 234 normal modes, 424 nucleation, 329–341 fast phase, 338, 339 nucleation probability, 339 nucleation rate, 338 slow phase, 338 statistical study, 336–339

Index surface nucleation density, 338 oligomers, 25, 27, 28, 30–32, 382, 390, 510 onions, 187, 196–199 tetrahedral onions, 196–198 optical characterization, 403, 413 optical gap, 102, 103 optical microscopy (OM), 345, 347–349, 355 optical properties, 59, 102, 137, 218, 360, 404, 410, 411, 413, 414, 418 optoelectronic properties, 99, 101–103 organic molecules, 510 P´ ocsik diagram, 37, 39, 40 Peierls distortion, 29, 32, 39, 389 penetration depth, 112, 471, 479 percolation, 98, 101, 102 percolation threshold, 98 phonons, 423, 425 zone centre phonons, 424 photoconductive gain, 473, 482 photoconductivity, 103, 304, 305, 308, 470 photoconductors, 472, 485 UV photoconductors, 470, 493 photocurrent, 486 photocurrent persistence, 476, 478, 479, 482 photodetectors, 468, 472, 485, 494 diamond-based photodetectors, 497 photodiodes, 487, 488 photoemission spectroscopy, 450, 453–461 photoluminescence (PL), 187, 189, 204, 329, 331, 333–335, 345, 347, 352–355 micro-PL analysis, 333–336, 348, 352–356 photon counting, 495 photoresponse, 475, 479 vacuum UV photoresponse, 475 physical approximants, 1, 10, 11, 18 plasma, 83 plasma expansion, 296, 299 plasma plume, 361, 373 plume stopping, 297

527

plasma-enhanced chemical vapour deposition (PECVD), 77, 83, 84, 87, 89, 138, 142, 218, 219, 228, 233, 345, 469 plasmon energy, 451–453 polarizability, 388, 390, 391, 395, 397, 424, 425 bond–bond polarizability, 398 bond-bond polarizability, 386, 388 polarizability tensor, 424 polyacetylene, 382–384, 386–390, 392, 393 long chains, 385, 388 short chains, 385 polyacetylene (PA), 28, 29, 32, 41 polyconjugated systems, 31 polycrystalline diamond, 108, 109, 112, 116, 345–347, 352, 354, 356, 357, 463–465, 469, 474, 488, 495, 497 polycumulenes, 515 polycyclic aromatic hydrocarbons (PAHs), 36–38, 42, 382, 390, 393 polyenes, 383, 385, 386, 389, 390, 392 polymer-like carbon (PLC), 138, 139, 142, 144, 147, 224, 227–229, 234 polymers, 29, 30, 33, 34, 217, 383, 384, 510 polyconjugated polymers, 30, 31, 34, 383 polymer chains, 510 polymethylene, 25 polyyne, 32, 33, 41 polyynes, 515 priming, 478 UV priming, 478 process approximation, 2, 13–15, 18 process modelling, 13–15 proliferation, 57, 59, 64, 65, 71 pulsed cathodic arc discharge (PCAD), 404, 406, 408–412, 416, 418 pulsed laser ablation (PLA), 288, 296, 299 pulsed laser deposition (PLD), 360, 361, 376 pyrolytic carbons, 37, 42 Q-arguments, 1, 6, 8, 9 quantum chemistry, 38, 382 quantum eﬃciency, 463, 472, 473, 486

528

Index

quasi equilibrium (QE) approximation, 321 quasi- elastic scattering, 154 quasi-equilibrium (QE) approximation, 312 Raleigh scattering, 424 Raman dimensionless arguments, 6–8 Raman parameters, 406–409, 414 Raman scattering, 35, 154, 350, 351, 354, 399, 409, 418, 423 anti-Stokes scattering, 423 ﬁrst-order Raman scattering, 350 infrared excitation, 423, 429, 432–435, 437–439 Raman activity, 385, 386, 388–390, 393, 400 Raman cross section, 29, 36 Raman intensity, 34, 386, 410, 414, 415, 426 Raman spectrum, 426 Raman tensor, 424, 425 resonant Raman scattering, 28, 30, 383, 386, 425, 428 second-order Raman scattering, 351, 352 selection rules, 28, 384, 393, 425 breakdown of the selection rules, 426 Stokes scattering, 423 visible excitation, 423, 424, 427, 429, 438 Raman spectroscopy, 1–3, 17, 24–28, 32–36, 42, 63, 137, 140–142, 144, 145, 149, 176, 179–181, 224–226, 229, 288, 289, 293–295, 298–300, 329–333, 335–337, 345, 347, 348, 350–352, 355, 356, 362–365, 371, 373, 381, 383–386, 390–392, 395, 403–406, 408, 409, 418, 507–512, 514–517 micro-Raman analysis, 331–333, 337, 348, 351–356 Ramo’s theorem, 110, 123–125, 245–247, 274 rate equations, 303, 309, 312, 313 Rayleigh wave, 154, 155, 159, 162, 164 modiﬁed Rayleigh wave, 159, 160

modiﬁed Rayleigh wave velocity, 160, 163 Rayleigh wave velocity, 154, 161, 162, 164 reactive sputtering, 2, 13 reﬂection electron energy loss spectroscopy (REELS), 288–292, 295, 300 refractive index, 63, 403, 404, 409–411, 413, 414, 416, 418 residual gas analysis (RGA), 84, 85, 88, 89 resistivity, 175–178, 180, 181, 183 resistivity anisotropy, 175–181, 184 response time, 482 rigidity, 98, 100 sandwich contacts, 479, 489 sandwich structure, 485 scaling laws, 1, 2, 15, 17, 18 derivation method, 1, 4, 7–9, 17 validity range, 9 scanning electron microscopy (SEM), 60, 65, 68, 69, 71, 330, 333, 334, 336, 345, 347–350, 355, 361, 362, 367, 369–371 scanning tunneling microscopy (STM), 147 Schottky barrier, 486–488 Schottky contacts, 488 Schottky diode, 488 Sezawa wave, 155, 159, 160, 162 shock wave, 296, 298–300 SiC, 200, 202–205 silicon incorporation, 218 slow component, 123–125, 127–129 spectral response, 481 spin density, 102, 103 subplantation model, 217, 218, 374 substrate bias, 181 surface enhanced Raman spectroscopy (SERS), 32, 404, 411, 511 surface treatment, 495 T band, 364, 365 T/G band intensity ratio, 366 T/G band intensity ratio, 365 Tauc gap, 137, 139–141, 144, 147, 150 tetrahedral amorphous carbon, 98, 139

Index tetrahedral hydrogenated amorphous carbon, 98 thermal stability, 218, 219, 228, 417 thermal-induced gas eﬀusion, 228 time constant, 123, 126, 128–132 transmission electron microscopy (TEM), 176, 177, 181–183, 361, 373, 377 trap, 108 density per unit energy, 310, 315 depumping, 108, 128, 129, 307, 310 priming, 108, 111–113, 115, 117 pumping, 108, 111, 113, 115, 117, 122, 124, 125, 128–130, 306, 307, 311 trap ﬁlling, 307, 311 trapping, 110, 113, 123–131 tribological properties, 56, 217, 219, 229 ultra-large scale integrated circuits (ULSI), 209, 219, 229 self-assembled ULSI, 212 ultra-thin carbon ﬁlms, 156, 162–166 ultrananocrytalline diamond (UNCD), 148, 149 unipolar conduction, 308–310

529

Urbach energy, 137, 139–141, 150 UV photoemission spectra (UPS), 450, 461, 462, 524 valence force ﬁeld, 25–27, 30, 382, 385–387, 390, 392, 396–398 variable energy method (VEM), 119–122, 130 variable incidence method (VIM), 119–122, 130 viability, 58, 59, 65, 71 vibrational spectroscopy, 505, 508, 511 wear resistance, 56, 57, 229, 233, 234 wettability, 219, 232 wetting response, 511 X-ray beam induced charge (XBIC), 257–263 XBIC maps, 258–263 x-ray diﬀraction (XRD), 469 X-ray photoemission spectroscopy (XPS), 288, 291, 292, 295, 298–300 x-ray photoemission spectroscopy (XPS), 224, 227, 289–291, 449