Front Matter

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Fundamentals of PICOSCIENCE

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Fundamentals of PICOSCIENCE

Edited by

Klaus D. Sattler

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CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2014 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20130517 International Standard Book Number-13: 978-1-4665-0510-0 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com

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Contents Preface........................................................................................................................................................... ix Editor............................................................................................................................................................. xi Contributors................................................................................................................................................ xiii

Part I  Picoscale Detection

1 Picometer Detection by Adaptive Holographic Interferometry......................................................................3 Umberto Bortolozzo, Stefania Residori, Jean-Pierre Hiugnard, and Alexei A. Kamshilin

2 Single Atom in an Optical Cavity: An Open Quantum System.................................................................... 27 John D. Close, Rachel Poldy, Ben C. Buchler, and Nicholas P. Robins

3 Measurements of Subnanometer Molecular Layers..........................................................................................43 Maciej Kokot

4 Electrostatic Potential Mapping in Electron Holography............................................................................... 55 Lew Rabenberg

Part II  Picoscale Characterization

5 Interferometric Measurements at the Picometer Scale....................................................................................77 Marco Pisani

6 Protein Crystallography at Subatomic Resolution............................................................................................ 95 Tatiana Petrova and Alberto Podjarny

7 X-Ray Optics: Toward Subnanometer Focusing.............................................................................................. 125 Christian G. Schroer

Part III  Picoscale Imaging

8 Imaging Small Molecules by Scanning Probe Microscopy........................................................................... 139 Shirley Chiang

9 Neutron Holographic Imaging with Picometer Accuracy............................................................................ 161 László Cser, Gerhard Krexner, Márton Markó, and Alex Szakál

10

Subnanometer-Scale Electron Microscopy Analysis ...................................................................................... 179 Sergio Lozano-Perez

v

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Contents

11

Atomic-Scale Imaging of Dielectric Point Defects ......................................................................................... 195

12

Picometer-Scale Dynamical Single-Molecule Imaging by High-Energy Probe . . ....................................209

Clayton C. Williams Yuji C. Sasaki

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Part IV  Scanning Probe Microscopy

13

Atomic-Resolution Frequency Modulation ....................................................................................................... 237

14

Theory for Picoscale Scanning Tunneling Microscopy ................................................................................. 253

15

Electrochemical STM: Atomic Structure of Metal/Electrolyte Interfaces ............................................... 269

16

Cold-Atom Scanning Probe Microscopy: An Overview . . .............................................................................. 287

17

Atomic Resolution Ultrafast Scanning Tunneling Microscope.. ................................................................. 303

Takeshi Fukuma Jouko Nieminen

Knud Gentz and Klaus Wandelt

Andreas Günther, Hendrik Hölscher, and József Fortágh Qingyou Lu

Part V  Electron Orbitals

18

Imaging Atomic Orbitals with Scanning Tunneling Microscopy .. ............................................................. 319

19

STM of Quantum Corrals ...................................................................................................................................... 351

20

Attosecond Imaging of Molecular Orbitals ...................................................................................................... 373

21

Picoscale Electron Density Analysis of Organic Crystals.. ........................................................................... 391

Alexander N. Chaika, Sergey I. Bozhko, and Igor V. Shvets Akira Tamura

David M. Villeneuve

Yusuke Wakabayashi

Part VI Atomic-Scale Magnetism

22

Atomic-Scale Magnetism Studied by Spin-Polarized Scanning Tunneling Microscopy . . .................... 413

23

Atomic and Molecular Magnets on Surfaces . . ..................................................................................................447

24

Spin Inelastic Electron Spectroscopy for Single Magnetic Atoms . . ............................................................ 471

Oswald Pietzsch and Roland Wiesendanger Harald Brune and Pietro Gambardella

Aaron Hurley, Nadjib Baadji, and Stefano Sanvito

Part VII  Picowires

25

Ferromagnetism in One-Dimensional Atomic Chains .................................................................................. 495

26

Carbon Atomic Chains ........................................................................................................................................... 505

27

Single-Atom Electromigration in Atomic-Scale Conductors . . ..................................................................... 529

Jisang Hong

Igor M. Mikhailovskij, Evgenij V. Sadanov, and Tatjana I. Mazilova Masaaki Araidai and Masaru Tsukada

Contents

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Part VIII  Picometer Positioning

28

Picometer Positioning Using a Femtosecond Optical Comb .......................................................................543

29

Detection of Subnanometer Ultrasonic Displacements . . ............................................................................... 553

30

Picometer-Scale Optical Noninterferometric Displacement Measurements .................................................... 579

31

Direct Observation of X-Ray-Induced Atomic Motion.. ................................................................................ 585

Mariko Kajima

Tomaž Požar and Janez Možina Ezio Puppin Akira Saito

Part IX  Picoscale Devices

32

Mirrors with a Subnanometer Surface Shape Accuracy ................................................................................ 595

33

Single Molecule Electronics .................................................................................................................................. 617

34

Single-Atom Transistors for Light ....................................................................................................................... 635

35

Carbon-Based Zero-, One-, and Two-Dimensional Materials for Device Application.. ....................... 655

36

Subnanometer Characterization of Nanoelectronic Devices ....................................................................... 677

37

Chromophores for Picoscale Optical Computers ............................................................................................ 705

Maria Mikhailovna Barysheva, Nikolay Ivanovich Chkhalo, Aleksei Evgenievich Pestov, Nikolay Nikolaevich Salashchenko, Mikhail Nikolaevich Toropov, and Maria Vladimirovna Zorina Simon J. Higgins and Richard J. Nichols Andrew Scott Parkins Young Kuk

Pierre Eyben, Jay Mody, Aftab Nazir, Andreas Schulze, Trudo Clarysse, Thomas Hantschel, and Wilfried Vandervorst Heinz Langhals

Index. . .......................................................................................................................................................... 729

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Preface Nanoscale science has brought many new effects and inventions and is the basis for a worldwide surge in nanotechnology. Currently, there are more than one million scientists involved in projects with nanoscale structures and materials. From the development of new quantum mechanical methods to farreaching applications in the electronic industry and medical diagnostics, nanoscience has inspired numerous scientists and engineers to new instrumental developments and inventions. Even the general public is now informed about many of the benefits of nanoscience. New terms such as “fullerenes,” “nanotubes,” and “quantum dots” are increasingly often used in public discussions. “Nano” has become the magic word for “extremely small.” Every day there are reports of new effects and materials, and many surprises can be expected in the future for structures at this size. We are entering an era of ever smaller and more efficient devices, which will rely on smaller designs and structures. One

nanometer is a billionth of a meter, and it is about ten times the diameter of a hydrogen atom. Is there a size range beyond nano that is accessible to us? Do we already have instruments to probe this range? How can we develop new instruments to visualize and measure structures at the subnanometer size? Answers to these and other questions are given in this book, Fundamentals of Picoscience. It describes methods and materials at the picometer-size scale, which is the next size range below nanometer, covering three orders of magnitude. One picometer is the length of a trillionth of a meter. Compared to a human cell of typically ten microns, this is about ten million times smaller. To access this extremely small size, instrumentation has been developed only in recent years, and there are efforts at many research and industry laboratories to move further into this very small range. This book corresponds to these developments and covers some of the instrumentation and experiments undertaken at the picometer-size scale.

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Editor Klaus D. Sattler performed his undergraduate and master’s studies at the University of Karlsruhe and at the Nuclear Research Center in Karlsruhe, Germany. He received his PhD under the guidance of Professors G. Busch and H. C. Siegmann at the Swiss Federal Institute of Technology (ETH) in Zurich, where he was among the first to study spin-polarized photoelectron emission. In 1976, he began a group for atomic cluster research at the University of Konstanz in Germany, where he built the first source for atomic clusters and led his team to pioneering discoveries such as “magic numbers” and “Coulomb explosion.” He was at UC Berkeley for three years as a Heisenberg fellow, where he initiated the first studies of atomic clusters on surfaces with a scanning tunneling microscope. Dr. Sattler accepted a position as professor of physics at the University of Hawaii in 1988. There, he initiated a research group for nanophysics, which, using scanning probe microscopy,

obtained the first atomic-scale images of carbon nanotubes, directly confirming the graphene network. In 1994, his group produced the first carbon nanocones. In collaboration with ETH Zurich, he also studied the formation of polycyclic aromatic hydrocarbons and nanoparticles in hydrocarbon flames. Other research has involved nanopatterning of nanoparticle films, charge density waves on rotated graphene sheets, band gap studies of quantum dots, and graphene foldings. His current work focuses on novel nanomaterials, nanodiamonds and graphene quantum dots, and solar photocatalysis with nanoparticles for the purification of water. Among his many accomplishments, Dr. Sattler was awarded the prestigious Walter Schottky Prize by the German Physical Society in 1983. At the University of Hawaii, he teaches courses in general physics, solid-state physics, and quantum mechanics. In his private time, he has worked as musical director at an avant-garde theater in Zurich, composed music for theatrical plays, and conducted several critically acclaimed musicals. He has also studied the philosophy of Vedanta. He loves to play the piano (classical, rock, and jazz) and enjoys spending time at the ocean and with his family.

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Contributors Masaaki Araidai World Premier Institute Advanced Materials Research Tohoku University Sendai, Japan

Harald Brune Institute of Condensed Matter Physics Swiss Federal Institute of Technology Lausanne, Switzerland

and

Ben C. Buchler Department of Quantum Science The Research School of Physics and Engineering The Australian National University Canberra, Australian Capital Territory, Australia

Core Research for Evolutional Science and Technology Japan Science and Technology Agency Kawaguchi, Japan and Center for Computational Sciences University of Tsukuba Tsukuba, Japan Nadjib Baadji School of Physics and Center for Research on Adaptive Nanostructures and Nanodevices Trinity College Dublin Dublin, Ireland Maria Mikhailovna Barysheva Institute for Physics of Microstructures Russian Academy of Sciences Nizhny Novgorod, Russia Umberto Bortolozzo Institut Non Linéaire de Nice Centre National de la Recherche Scientifique University of Nice-Sophia Antipolis Valbonne, France Sergey I. Bozhko Institute of Solid State Physics Russian Academy of Sciences Chernogolovka, Russia

Alexander N. Chaika Institute of Solid State Physics Russian Academy of Sciences Chernogolovka, Russia Shirley Chiang Department of Physics University of California, Davis Davis, California Nikolay Ivanovich Chkhalo Institute for Physics of Microstructures Russian Academy of Sciences Nizhny Novgorod, Russia Trudo Clarysse Interuniversity Microelectronics Centre Leuven, Belgium John D. Close Department of Quantum Science The Research School of Physics and Engineering The Australian National University Canberra, Australian Capital Territory, Australia

László Cser Neutron Spectroscopy Department Wigner Research Centre for Physics Hungarian Academy of Sciences Budapest, Hungary Pierre Eyben Interuniversity Microelectronics Centre Leuven, Belgium József Fortágh Department of Physics University of Tübingen Tübingen, Germany Takeshi Fukuma Frontier Science Organization and Division of Electrical Engineering and Computer Science and Bio-AFM Frontier Research Center Kanazawa University Kanazawa, Japan and Japan Science and Technology Agency Precursory Research for Embryonic Science and Technology Kawaguchi, Japan Pietro Gambardella Catalan Institute of Nanotechnology Barcelona, Spain and Department of Materials Eidgenössische Technische Hochschule Zürich, Switzerland

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Contributors

Knud Gentz Institute of Physics and Theoretical Chemistry University of Bonn Bonn, Germany

Maciej Kokot Faculty of Electronics, Telecommunications, and Informatics Gdańsk University of Technology Gdańsk, Poland

Andreas Günther Department of Physics University of Tübingen Tübingen, Germany

Gerhard Krexner Faculty of Physics University of Vienna Vienna, Austria

Thomas Hantschel Interuniversity Microelectronics Centre Leuven, Belgium

Young Kuk Department of Physics and Astronomy Seoul National University Seoul, South Korea

Simon J. Higgins Department of Chemistry School of Physical Sciences University of Liverpool Liverpool, England

Heinz Langhals Department of Chemistry Ludwig Maximilians University of Munich Munich, Germany

Jean-Pierre Hiugnard Jphopto Consultant Palaiseau, France Hendrik Hölscher Institute for Microstructure Technology Karlsruhe Institute of Technology Eggenstein-Leopoldshafen, Germany Jisang Hong Department of Physics Pukyong National University Busan, South Korea Aaron Hurley School of Physics and Center for Research on Adaptive Nanostructures and Nanodevices Trinity College Dublin Dublin, Ireland Mariko Kajima Dimensional Standards Section National Metrology Institute of Japan National Institute of Advanced Industrial Science and Technology Tsukuba, Japan Alexei A. Kamshilin Department of Applied Physics University of Eastern Finland Kuopio, Finland

Sergio Lozano-Perez Department of Materials University of Oxford Oxford, United Kingdom Qingyou Lu High Magnetic Field Laboratory Chinese Academy of Sciences and Hefei National Lab for Physical Sciences at Microscale University of Science and Technology of China Hefei, Anhui, People’s Republic of China Márton Markó Neutron Spectroscopy Department Wigner Research Centre for Physics Hungarian Academy of Sciences Budapest, Hungary Tatjana I. Mazilova National Science Center Kharkov Institute of Physics and Technology Kharkov, Ukraine Igor M. Mikhailovskij National Science Center Kharkov Institute of Physics and Technology Kharkov, Ukraine Jay Mody IBM Systems and Technology Hopewell Junction, New York

Janez Možina Faculty of Mechanical Engineering University of Ljubljana Ljubljana, Slovenia Aftab Nazir Interuniversity Microelectronics Centre and Department of Physics and Astronomy Katholieke Universiteit Leuven Leuven, Belgium Richard J. Nichols Department of Chemistry School of Physical Sciences University of Liverpool Liverpool, United Kingdom Jouko Nieminen Department of Physics Tampere University of Technology Tampere, Finland and Department of Physics Northeastern University Boston, Massachusetts Andrew Scott Parkins Department of Physics University of Auckland Auckland, New Zealand Aleksei Evgenievich Pestov Institute for Physics of Microstructures Russian Academy of Sciences Nizhny Novgorod, Russia Tatiana Petrova Institute of Mathematical Problems of Biology Russian Academy of Sciences Pushchino, Russia Oswald Pietzsch Institute of Applied Physics and Microstructure Advanced Research Center University of Hamburg Hamburg, Germany Marco Pisani Mechanics Division National Institute for Metrological Research Torino, Italy

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Contributors

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Alberto Podjarny Department of Integrative Biology Institut de Génétique et de Biologie Moléculaire et Cellulaire Université de Strasbourg Illkirch, France Rachel Poldy Department of Quantum Science The Research School of Physics and Engineering The Australian National University Canberra, Australian Capital Territory, Australia Tomaž Požar Faculty of Mechanical Engineering University of Ljubljana Ljubljana, Slovenia Ezio Puppin Dipartimento di Fisica Consorzio Nazionale Interuniversitario per le Scienze Fisiche della Materia Politecnico di Milano Milano, Italy Lew Rabenberg Department of Mechanical Engineering Texas Materials Institute The University of Texas at Austin Austin, Texas Stefania Residori Institut Non Linéaire de Nice Centre National de la Recherche Scientifique Institut Nonlinéaire de Nice University of Nice-Sophia Antipolis Valbonne, France Nicholas P. Robins Department of Quantum Science The Research School of Physics and Engineering The Australian National University Canberra, Australian Capital Territory, Australia Evgenij V. Sadanov National Science Center Kharkov Institute of Physics and Technology Kharkov, Ukraine

Akira Saito Department of Precision Science and Technology Graduate School of Engineering Osaka University Osaka, Japan and RIKEN/SPring-8 Sayo, Japan Nikolay Nikolaevich Salashchenko Institute for Physics of Microstructures Russian Academy of Sciences Nizhny Novgorod, Russia Stefano Sanvito School of Physics and Center for Research on Adaptive Nanostructures and Nanodevices Trinity College Dublin Dublin, Ireland Yuji C. Sasaki Biomedical Group SPring-8 Japan Synchrotron Radiation Research Institute Mikazuki, Japan and Japan Science and Technology Agency Core Research for Evolutional Science and Technology Sasaki Team Tachikawa, Japan and Department of Advanced Materials Science Graduate School of Frontier Sciences The University of Tokyo Chiba, Japan Christian G. Schroer Institute of Structural Physics Technische Universität Dresden Dresden, Germany Andreas Schulze Interuniversity Microelectronics Centre and Department of Physics and Astronomy Katholieke Universiteit Leuven Leuven, Belgium

Igor V. Shvets School of Physics and Center for Research on Adaptive Nanostructures and Nanodevices Trinity College Dublin Dublin, Ireland Alex Szakál Neutron Spectroscopy Department Wigner Research Centre for Physics Hungarian Academy of Sciences Budapest, Hungary Akira Tamura Graduate School of Engineering Saitama Institute of Technology Fukaya, Japan Mikhail Nikolaevich Toropov Institute for Physics of Microstructures Russian Academy of Sciences Nizhny Novgorod, Russia Masaru Tsukada World Premier Institute Advanced Materials Research Tohoku University Sendai, Japan and Core Research for Evolutional Science and Technology Japan Science and Technology Agency Kawaguchi, Japan Wilfried Vandervorst Interuniversity Microelectronics Centre and Department of Physics and Astronomy Katholieke Universiteit Leuven Leuven, Belgium David M. Villeneuve Joint Attosecond Science Laboratory National Research Council of Canada and University of Ottawa Ottawa, Ontario, Canada Yusuke Wakabayashi Division of Materials Physics Graduate School of Engineering Science Osaka University Osaka, Japan

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Klaus Wandelt Institute of Physical and Theoretical Chemistry University of Bonn Bonn, Germany and

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Institute of Experimental Physics University of Wroclaw Wroclaw, Poland

Contributors

Roland Wiesendanger Institute of Applied Physics and Microstructure Advanced Research Center University of Hamburg Hamburg, Germany

Clayton C. Williams Department of Physics and Astronomy University of Utah Salt Lake City, Utah Maria Vladimirovna Zorina Institute for Physics of Microstructures Russian Academy of Sciences Nizhny Novgorod, Russia

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Picometer Positioning

28 Picometer Positioning Using a Femtosecond Optical Comb  Mariko Kajima...............................................................543



29 Detection of Subnanometer Ultrasonic Displacements  Tomaž Požar and Janez Možina............................................ 553



30 Picometer-Scale Optical Noninterferometric Displacement Measurements  Ezio Puppin......................................... 579



31 Direct Observation of X-Ray-Induced Atomic Motion  Akira Saito.................................................................................585

Introduction  •  Femtosecond Optical Frequency Comb  •  Picometer Positioning Using a Zooming Interferometer  •  Picometer Measurement Using a Fabry–Perot Resonator  •  References

Introduction • Detection Principles and Sensors • Conclusions • Acknowledgment • References References

Introduction • Experimental • Results and Discussion • Conclusion • Acknowledgments • References

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29 Detection of Subnanometer Ultrasonic Displacements 29.1 Introduction..............................................................................................................................553 29.2 Detection Principles and Sensors...........................................................................................555

Tomaž Požar University of Ljubljana

Janez Možina University of Ljubljana

Piezoelectric Detection • Electrostatic Detection • Electromagnetic Detection •  Optical Detection

29.3 Conclusions.............................................................................................................................. 569 Acknowledgment................................................................................................................................. 569 References............................................................................................................................................. 569

29.1 Introduction Ultrasound is understood as mechanical motion with frequency content above 20 kHz, the upper limit of human hearing [1], and below 10 THz, the beginning of hypersound [2]. Although the definition of the lower bound originates from sound, it can also be used for mechanical wave propagation in liquids and solids. Specifically for solids, ultrasound is considered as different types of high-frequency mechanical waves that propagate with various velocities, reflect, refract, interfere, disperse, mode convert, and attenuate within the sample [3]. Ultrasound in solids can be generated by many diverse sources. With respect to location, sources can induce ultrasound on the surface [4–6] or in the interior [7,8] of samples. They can be localized to a very small volume. Such sources are called point sources [9]. On the other hand, they can also generate ultrasound over an extended volume. For this reason, these sources are dubbed extended sources [10]. With respect to the duration of the emission of ultrasound and consecutively to its frequency content, ultrasonic sources can be classified as impulsive (wide bandwidth) or harmonic (narrow bandwidth) or as sources with an arbitrary temporal distribution lying between the two aforementioned extremes. The shortest ultrasonic sources are due to either a mere absorption or ablation of the surface of solid samples with Q-switched laser pulses [11,12]. The frequency content of thus-induced waves can reach up to several 100 MHz [13,14]. Higher surface acoustic wave (SAW) frequencies, up to 1 GHz, can be generated with picosecond laser pulses [2] and even higher, up to 90 GHz, with femtosecond lasers [15]. On the contrary, harmonically vibrating piezoelectric transducers in contact with the solid sample enable generation of very narrow-band ultrasonic waves [16]. Such waves, especially when they are standing waves, are often referred to as vibrations.

Displacement-measuring sensors that detect vibrations are called vibrometers. Ultrasonic sources may be of large scale, such as earthquakes, where a sudden release of energy in the Earth’s crust, due to the motion of tectonic plates, creates seismic waves [17,18]. Their miniature counterpart, acoustic emission [18–22], is a phenomenon that arises from a rapid release of stress energy in the form of ultrasound within or on the surface of a material. Acoustic emission sources may be point defects, slips, or dislocations in crystals, twinning or grain boundary movement of polycrystallines, corrosion, fatigue cracks, plastic deformations, phase transformations, creation and collapsing of voids, crushing of inclusions, initiation and growth of cracks in materials, friction, cavitation, leaks, and realignment or growth of magnetic domains. Often, as is the case of the previous examples, the onset time on ultrasound is unknown. Ultrasound can also be generated by mechanical impacts with solids [23,24] through a linear momentum transfer from the impacting body to the mechanical waves [25]. Ultrasound can be generated deliberately for various applications with ultrasonic actuators [26–29] or other types of ultrasonic sources [28]. In general, ultrasonic actuators are slightly modified versions of the same devices that are also used to sense ultrasonic motion. Their principle of operation will be described in the following section. Examples of artificial wide-bandwidth, impulsive ultrasonic sources are small elastic ball impacts [30–32], electric sparks [33–36], expanding plasmas [37,38], and laserpulse ablation of uncoated [11,39–44] or constrained surfaces [11,45,46]. Artificial ultrasonic sources with wide-bandwidth, step-like temporal dependence include radially loaded glass capillary fractures [30,47–49], pencil lead breaks (Hsu–Nielsen source) [30,31,50–52], fractures of small grains [53], and thermoelastic generation with laser pulses [39–43,54]. Helium gas jet 553

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impact may be employed as a continuous white noise generator of ultrasound [55–57]. Particle impacts, such as electrons from a scanning electron microscope, are used in electron-acoustic microscopy to generate ultrasound in solids [58–60]. Charged particles [61] and even ultrahigh-energy cosmic-ray neutrinos [62] may also generate ultrasound of detectable amplitude. Ultrasound generation may be achieved by electromagnetic radiation at wavelengths other than those emitted by lasers, for example, by pulsed x-ray radiation from synchrotrons [63], microwaves [64,65], and radio frequencies [66]. This chapter deals with the detection of minute displacements whose amplitudes are smaller than 1 nm and are caused by ultrasonic motion. The main attention will be given to present various means of sensing the out-of-plane (normal or vertical, denoted by u) component of the surface displacement vector in solids. These displacements are the result of reflections of ultrasonic waves from the boundaries of a solid body. Even though most detectors are predominantly responsive to a single component, either the in-plane (tangential or horizontal, denoted by w) or out-of-plane component, of the displacement vector, it is often the case that the measured displacement is deteriorated by the other components of displacement. On the other hand, some detectors are capable of measuring both the in- and outof-plane displacement simultaneously [67–71], but the majority of detectors respond only to the out-of-plane component. Ultrasonic time-dependent displacements can also be obtained by integration of time derivatives of displacement, especially velocity and acceleration. Piezoelectric detectors, for instance, are known to respond to a frequency-dependent mixture of displacement, velocity, and acceleration [72]. Such detectors which are not directly linked to a single physical quantity are difficult to calibrate. Detector that measures a linear combination of displacement and its time derivatives is therefore not suitable for absolute measurements, but can still be used for qualitative measurements: to determine the arrival times of ultrasonic waves or to perform frequency count of ultrasound-emitting events. Ideal displacement-measuring detectors should thus be linearly sensitive to a single component of a single physical quantity, preferably to displacement itself. Additionally, its frequency response should be flat in the frequency band of interest. Special design is often required to approach these requirements [72,73]. Ideal linear detectors with flat frequency response are fully characterized by a frequency-independent figure of merit called sensitivity S. The units of sensitivity are V/m, because most commonly one reads the output in volts for a given displacement in meters. Determination of the value of sensitivity is called absolute calibration. Practically, sensitivity does not have a constant value and has to be expressed as a function of frequency. To achieve sufficiently large sensitivity, the measured signal often needs to be amplified. Amplification, however, has its own transfer function and adds additional noise to the system. Ultrasonic displacement-measuring detectors can be characterized by the following features: sensitivity, minimal detectable displacement also called noise-equivalent displacement, resolution, dynamic range, and frequency characteristics (ultrasonic

Fundamentals of Picoscience

signal bandwidth, compensation bandwidth, and resonant behavior). Ultrasound-measuring detectors demand a special design when they are used in hostile and harsh environments, such as when measuring ultrasound at elevated temperatures [74], in toxic, in acid/basic, or in radioactive environments. Optical detectors are often preferred in such cases. The contact nature of detectors also varies [75]. Some need direct contact with the measuring surface (piezoelectric sensors). Their sensitivity is enhanced with a thin layer of liquid couplant that provides a better acoustic impedance match between the sample and the sensor. Capacitive and electromagnetic detectors operate in close proximity to the sample surface. Capacitive ones have a gap of a few micrometers [76], while electromagnetic ­detectors work up to a liftoff distance of 2 mm [77]. True contactless, standoff detectors are optical devices and can be separated from the measuring surface for up to 2 m. These detectors are also nonperturbing, which means that they have negligible influence on the ultrasound propagation, while others, especially those of contact nature, alter surface motion by their presence. Small fraction of ultrasonic energy is also transmitted to the air above the surface of the sample. If piezoelectric and capacitive sensors are lifted from the surface while they are still capable of detecting ultrasound-induced air pressure changes, they are air coupled. The advantage of air coupling is that the measurement becomes noncontact through the detection of airborne leaky waves leaked from material surfaces. However, the sensitivity is reduced due to a large acoustic impedance mismatch between air and solid. Moreover, the absorption of ultrasound in the air becomes severe for high frequencies and goes as the square of the frequency. Due to this reason, air-­ coupled sensors are used below 1 MHz. To increase the sensitivity and improve impedance mismatch, samples are rather water ­coupled, that is, immersed in water. Ultrasonic surface displacements cannot be measured on all solid samples with all types of detectors. Material properties of the solid determine the possible detection principles. For instance, transparent samples cannot be inspected with optical techniques when insufficient light is returned toward the detector. Samples with rough surfaces cause problem to all detectors. The performance of optical detectors is severely degraded by high surface absorptivity of light (laser beam), highly scattering surfaces, and surface tilts. On the other hand, electromagnetic sensors require the samples to be either conductive or ferromagnetic. Ultrasound in conductive materials can be detected with Lorentz force mechanism. When the material is ferromagnetic, magnetostriction is the underlying detection principle. Generally, capacitive sensors of ultrasound demand conductive samples, but they can also be adapted to measure ultrasound on nonconductive materials. The active area of the detector size is also an important parameter. Its detecting area (aperture) is directly connected with the maximum detectable frequency and thus sets the limit to the detectable signal bandwidth. From geometrical reasoning, a detector with a diameter d cannot discern SAWs propagating tangentially to the sensor with velocity c with frequencies larger than f = c/d. When at high

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Detection of Subnanometer Ultrasonic Displacements

frequencies multiple wavelengths are averaged over the area of contact, the amplitude of the recorded wave decreases. This is called an aperture effect [78,79] and depends on the direction of the incoming ultrasonic wave, being most significant for waves propagating tangentially to the sensor face, and has no effect on plane waves with wave fronts parallel with the measuring surface. Frequency response upper limit of a displacement detector is also determined by the detector and auxiliary electronics. Further, when detectors are used in arrays [80,81], single detector units often need to be miniaturized. If needed, classical sensors are nowadays produced as very small devices called microelectromechanical system (MEMS) sensors either as capacitive micromachined ultrasonic transducers (CMUTs) [82–86] or their piezoelectric counterparts PMUTs [87–91]. Optical devices can be made more compact and robust with optical fibers [92,93]. Both small detector size and delivery of light through optical fibers in optical detectors enable access to remote and difficultly accessible places that other, larger detectors cannot reach. Finally, not all detectors have reached industrial and commercial stages. Some are used mainly in laboratories. Perhaps, the most widely used are piezoelectric detectors since they have the largest sensitivity and are not expensive. There is also a distinction between absolute sensors and calibrated sensors. Interferometers are self-calibrated, absolute sensors, because the displacement history of objects with adequate reflectance can be accurately and precisely measured since the measured relative length is based on counting fractions of the well-defined wavelength of the stabilized laser source. Other sensors need to be precalibrated, say, with interferometers or other calibration methods [79]. Although ultrasonic displacements can be much larger than 1  nm [12], it is possible to measure displacements even below 10 fm using a sensitive lock-in detection scheme for bandwidth reduction [94,95]. For comparison, the diameter of an atomic nucleus is 2.4 fm A1/3, where A is the nucleon number. Thus, the diameter of 56Fe is ∼10 fm. The measured displacement is not the displacement of a single atom making up a solid. It is rather the average value of displacements of a multitude of atoms in contact with the sensor or having remote effect on the measurement. It is worth keeping in mind that the measured ultrasonic displacement can be in the order of some nucleic radii, but this value is averaged over an area consisting of usually several orders of magnitude >109 atoms. For example, in laser-based detection of ultrasound, a laser spot focused to a 10 μm diameter covers about 109 atoms on the surface of body-centered cubic crystal structure of α-iron, where the closest separation between atoms is 0.25 nm. The minimal detectable displacement of any displacementmeasuring sensor is set by the fundamental limit called the thermal rattle, also called the phonon shot noise. The surface atoms experience a thermally induced random motion which is macroscopically manifested as a temperature-dependent mechanical noise. This is a mechanical equivalent of the wellknown Johnson–Nyquist noise used to calculate the voltage and current fluctuations in a resistor. The root-mean-square (RMS)

out-of-plane displacement fluctuation of a surface area on a solid, isotropic, half-space is approximately u min 

1 πf

k BT∆f . Re(Z ( f ))

(29.1)

This expression [96–98] is valid for kBT >> hf, where f is the frequency, kB is the Boltzmann constant, T is the absolute temperature, ∆f is the frequency bandwidth, h is the Planck constant, and Z = F/v is the complex mechanical impedance defined as the ratio of an applied point force F and the resultant surface velocity v. Using the expression for Z given in [99] and a circular surface area of 1 mm diameter on Al, the value of umin is between 10−16 and 10−17 m/√Hz in the bandwidth between 100 kHz and 1 MHz [96]. As an example, the thermal rattle at 1 MHz and bandwidth of 100 Hz gives a 0.1 fm RMS amplitude of the outof-plane displacement. Applications in science and industry where detection of sub-nanometer ultrasonic displacements plays a major role will not be discussed in this chapter. It is however worth to mention some fields where minute ultrasonic displacements often need to be measured: optodynamics [5,12,25,100–103], monitoring of laser material processing [104–106], laser-based ultrasonics [43,107–111], acoustic emission [18–22], nondestructive testing of materials [20,112,113], microseismology [81], and medicine [114].

29.2 Detection Principles and Sensors Various physical phenomena can be exploited as transduction mechanisms to detect ultrasonic displacements of solid surfaces. They are primarily gathered in four distinct detection groups depending on the underlying physics: piezoelectric, electrostatic, electromagnetic, and optical. Within each detection group, the transduction principles are first concisely introduced, followed by a description of the most common sensor types that make use of the presented detection method. The performance characteristics, advantages, and deficiencies of each sensor of ultrasound are given. Detectors are compared within each group and between groups. In-depth explanation was intentionally omitted to keep the description simple.

29.2.1 Piezoelectric Detection Piezoelectric ultrasonic sensors use the piezoelectric effect or piezoelectricity as a transduction mechanism to measure a frequency-dependent mixture of displacement, velocity, and acceleration of surfaces by converting these physical quantities to an electrical charge. A charge-to-voltage converter called charge amplifier is then used to proportionally convert electrical charge to voltage. Piezoelectric effect, discovered by Jacques and Pierre Curie in 1880, is a phenomenon where electrical charge accumulates on the surface of certain ceramics (e.g., lead– zirconate–titanate) and crystals (e.g., quartz) in response to an

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Fundamentals of Picoscience

Fz

Fz

c

qx c

b

y

Fz

x

Signal out

(29.2)



released in z-direction by a force Fz which is also applied along z-direction is characterized by a piezoelectric coefficient dzz with units of C/N. In the transverse mode (Figure 29.1, right sketch), the charge is generated on lateral faces in respect to the applied force. Here, the amount of charge a q x = −d xz Fz c



(29.3)

depends on the dimensions a and c of the piezoelectric cuboid and is determined by a different piezoelectric coefficient dxz . We assumed that the charge was generated only in x-direction by a force Fz applied perpendicularly in z-direction. In the shear mode, the charge is again highly proportional to the applied forces and is independent of the size and shape of the PZT. In addition to the piezoelectric effect, piezoceramic materials commonly show the ability to generate an electrical signal also when the temperature of the sensing element changes. This effect is called pyroelectricity. Basic construction of a classical piezoelectric ultrasonic sensor [79,115,116] mounted on the surface of a solid is shown in Figure 29.2. Thin slab of PZT, cut in such a way that it operates in a longitudinal mode, is placed in contact with the measuring surface. The contacting surfaces are lubricated by a liquid couplant with acoustic impedance that matches the impedance of the PZT. Piezoelectric slab is backed by a large damping mass and sealed in

w

FIGURE 29.2  Cutaway schematic drawing of a classical piezoelectric sensor.

a suitable housing. Thus, built sensor is mainly sensitive to ultrasonic out-of-plane displacements u. The whole sensor is pressed against the measuring surface so that PZT will be statically preloaded. Normal displacements of the measuring surface will either compress or extend the PZT depending on the polarity of the incoming ultrasonic wave (compression or rarefaction). Timevarying stress in the PZT will cause a proportional time-varying accumulation of electrical charge on opposite sides of the PZT slab. Two electrodes are attached to the charged PZT surfaces. The outside surface of the outer electrode has to be electrically shielded so that both conductive and nonconductive solids can be measured. Often, the signal from these electrodes is preamplified already within the casing to reduce signal noise due to parasitic capacitance. The output voltage is in general not proportional to normal ultrasonic displacement u, because classical ultrasonic sensors have complex transfer functions and do not have a flat frequency response (see Figure 29.3). They can be designed to sense only a portion of the whole frequency range of interest,

Highest sensitivity

High pass

q z = d zz Fz

u

Magnitude (sensitivity)

applied mechanical stress and consequent mechanical deformation. The accumulated charge is usually highly proportional to the applied force. There are three distinguishable modes of operation depending on how a piezoelectric material (PZT) is cut: longitudinal, transverse, and shear. Imagine a rectangular cuboid of PZT with edge lengths a, b, and c in x, y, and z axes, respectively. In the longitudinal mode of operation (Figure 29.1, left sketch), the charge is generated on the same surfaces where the force is applied and is independent of the geometrical dimensions and shape of the PZT. A charge



Casing

a

FIGURE 29.1  Longitudinal (left) and transverse (right) mode of PZT operation.



Backing mass

Low pass

z Fz

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b

Resonance

a

PZT

qz

Couplant

Flat response

Frequency

FIGURE 29.3  Typical frequency response of a classical piezoelectric sensor.

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Detection of Subnanometer Ultrasonic Displacements

Couplant

PZT

usually between 10 kHz and 1 MHz, by choosing the appropriate dimensions (usually thickness) of the piezoelectric element. Piezoelectric ultrasonic sensors can measure ultrasound with sensitivity of about 1 V/nm as displacement sensors and few V/(mm/s) as velocity sensors [72,117]. The noise-equivalent displacement is often below 1 pm. The dynamic amplitude range of piezoelectric ultrasonic sensors is around 120 dB or 106. They can be used in environments with temperatures up to 600°C if aluminum nitride is used as a PZT [118]. They have another useful property when measuring ultrasound, that is, to measure only dynamic events and so automatically compensate for low-frequency motion of measuring objects that are caused by environmental vibrations. This intrinsic low-frequency cutoff is a consequence of the leakage of the accumulated charge. As seen in Figure 29.3, this acts as a high-pass filter which determines the low-frequency cutoff (compensational bandwidth) through a time constant given by the capacitance and resistance of the device. Additionally, piezoelectric ultrasonic sensors are also insensitive to electromagnetic fields and radiation, enabling measurements under harsh conditions. The most common commercially available piezoelectric ultrasonic sensors are of a resonant type, because they provide greater sensitivity near the resonance frequency (see Figure 29.3). Unfortunately, resonant devices lack the bandwidth needed to analyze incoming waveforms. They are not suitable for absolute measurements, but can still be used for qualitative measurements: to give a reasonably accurate estimate of the arrival times of ultrasonic waves or to perform frequency count of ultrasound-emitting events. However, beyond the direction of surface motion caused by the earliest ultrasonic wave, the received signal is more a function of the sensor than of the true displacement history. When the ultrasonic wave excites the measuring surface of the solid it often sets the sensor into vibration, thus masking the desired signal. This effect is called ringing. The frequency content of such signal for the most part reflects merely the normal modes of vibration of the solid and the sensor. To avoid frequency-dependent effects of classical PZT sensors, such as their resonant behavior at high frequencies and reflections of ultrasonic waves within the PZT slab and backing mass [119], specially designed, wideband conical piezoelectric ultrasonic sensors were developed [73,78,81,88,89,99,117, 119–127]. Conical piezoelectric ultrasonic sensors were introduced by the National Institute of Standards and Technology (NIST) for use in the field of wideband quantitative acoustic emission [78]. They are used where the actual displacement is to be measured with precision and accuracy. A generalized cross-sectional scheme of the conical piezoelectric ultrasonic sensors is displayed in Figure 29.4. The conical design of the sensor PZT element, usually made from a lead–zirconate–titanate composition PZT-5a, eliminates the aperture effect by keeping the contact area small. The contacting face of the truncated PZT cone is around 0.5–2 mm in diameter [72,117] in contrast to a few 10 mm diameter of the sensing element of the classical piezoelectric sensors. This sets the upper limit of frequency response for, for example, detection of SAWs at f = (3000 m/s)/(1 mm) = 3 MHz. The wideband frequency response (both phase and magnitude) of conical piezoelectric

Backing mass

Casing

Signal out u w

FIGURE 29.4  Cutaway schematic drawing of a conical piezoelectric sensor.

sensors is practically flat within ±3 dB from 10 kHz to 1 MHz. Moreover, such detectors are sensitive only to the normal component of displacement vector and their output is directly proportional to displacement in the frequency range from 10 kHz to 1 MHz [73,122]. Theoretical analysis of the proportionality between the output voltage and the out-of-plane displacement of the measured surface is beyond the scope of this section, but can be found in [99]. The asymmetric design of the PZT cone also reduces the degeneracies of the normal modes of the usual piezoelectric disk element [99,120]. The signal is amplified already in the vicinity of the PZT so that it is not corrupted by electromagnetic noise and capacitive loading from the cable between the sensor and the A/D converter. The material of the backing mass (brass or lead alloy) needs to be large to reduce resonances at lower frequencies. Its acoustic impedance has to match the PZT material and has to prevent back-reflections of the passing ultrasonic wave to return to the PZT cone. The former is important, because the ultrasonic wave has to pass the PZT element unaffected. The latter is achieved by choosing a backing material with high internal acoustic attenuation and by cutting the backside of the backing mass at an angle to prevent direct reflections. In general, all mechanical parts of the wideband piezoelectric sensor that are affected by the ultrasound call for an asymmetric design to reduce possible mechanical resonances [119]. For instance, the NIST conical reference transducer’s backing block has no parallel faces and no right angles to ensure that only high-order multiple reflected elastic waves can reenter the PZT element [127]. The minimal detectable displacement measured with the optimized conical piezoelectric transducers outmatches other ultrasonic displacement sensors by 10–100 dB and is