nano- and micromaterials, 2008, p.344

Tohoku University, Institute of Materials Research E-Mail: ohno@ynu.ac.jp, mtanaka@ynu.ac.jp, jun@ynu.ac.jp Yokohama National University, Graduate School of Engineering, Department of Ph

advances in materials research 9

way on the latest progress in basic materials sciences It contains both theoretically and

experimentally oriented texts written by leading experts in the f ield Advances in Materials

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2 Advances in Scanning Probe Microscopy

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Preparation, Properties, and Applications

Editors: A Inoue and K Hashimoto

4 Materials Science in Static High Magnetic Fields

Editors: K Watanabe and M Motokawa

5 Structure and Properties of Aperiodic Materials

Editors: Y Kawazoe and Y Waseda

6 Fiber Crystal Growth from the Melt

Editors: T Fukuda, P Rudolph, and S Uda

7 Advanced Materials Characterization for Corrosion Products

Formed on the Steel Surface

Editors: Y Waseda and S Suzuki

8 Shaped Crystals

Growth by Micro-Pulling-Down Technique

Editors: T Fukuda and V.I Chani

9 Nano- and Micromaterials

Editors: K Ohno, M Tanaka, J Takeda, and Y Kawazoe

Series Editor-in-Chief: Y Kawazoe

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Series Editors: M Hasegawa

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Computational Materials Design

advances in materials research

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Jun Takeda Yoshiyuki Kawazoe

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Nano- and MicromaterialsWith 204 Figures

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Katahira, Sendai 980-8577, Japan

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Institute for Materials Research, Tohoku University

Department of Physics, Florida Atlantic University

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In nanotechnology to date, much emphasis is placed on the creation of thenanostructures by means of micro- and atomic manipulations This researchfield has been highly respected and promoted by the society, polytics, andeconomics Rapid progress in this field has been greatly stimulated by morefundamental study on nano- and micromaterials In this respect, the scien-tists and engineers in different fields of physics, chemistry, materials science,and information technology including experimentalists, theorists, and alsoresearchers doing computer simulations have collaborated to form a newinterdisciplinary field.

This book covers the recent advances in this growing research field, inparticular, those developed mainly in the interdisciplinary research projectnamed “Materials science for nano- and microscale control: Creation of newstructures and functions,” which was formed in 2004 in the Graduate School

of Engineering of Yokohama National University in collaboration with theInstitute for Materials Research, Tohoku University and other universities.The topics described in this book are as follows

In computational materials design, first-principles calculations and lations can give reliable guidelines for structural and functional controls ofnanomaterials In this respect, the development of new computational meth-ods, in particular, for the excited states of materials, is highly desirable toinvestigate atomic and electronic dynamics on the nano- and microscales The

simu-state-of-the-art GW and T -matrix calculations, transport calculations, and

lattice dynamics calculations will be explained in detail in this book Fromexperimental point of view, in particular from the viewpoint of structuralcontrols, the use of the self-organization of surface or local nanostructurescontrolled by light or heat is described in detail, in which a variety ofuseful structures appear through grain boundary motions on submicronscales Such novel nanointegration technologies are particularly useful to cre-ate quantum dots or quantum well devices, and such applications are alsodescribed in detail Also a variety of interesting optically controlled chem-ical or catalytic reactions, and phase transitions are described in detail for

particular interesting systems Moreover, the functionalities of quantum dots,the creation of micro-/nanomachines using microstereolithography, and thedevelopment of new techniques of laser spectroscopy to observe dynamicalprocesses related to optic functionalities are described in detail.

We hope that this book would be benefit to not only the scientists orengineers in this field but also the researchers in other fields to see what isgoing on in the researches of nano- and micromaterials

Finally, we would like to thank C.E Ascheron and his coworkers atSpringer-Verlag in Heidelberg for their continuous help in completing thisbook

Jun Takeda Yoshiyuki Kawazoe

1 General Introduction

K Ohno 1

References 15

2 Nanometer-Scale Structure Formation on Solid Surfaces M Tanaka, K Shudo, and S Ohno 19

2.1 Introduction 19

2.2 Atomic Layer Etching Processes on Silicon Surfaces 21

2.2.1 Introduction 21

2.2.2 Real-Time Optical Measurements 24

2.2.3 Adsorption of Halogen Atoms: Sticking Coefficient and Potential Barrier 26

2.2.4 Site-Selective Adsorption 34

2.2.5 Desorption of Silicon Halides and Restoration of the DAS Structure 39

2.2.6 Summary 48

2.3 Nanoscale Fabrication Processes of Silicon Surfaces with Halogens 50 2.3.1 Introduction 50

2.3.2 Scanning Tunneling Microscopy 53

2.3.3 Thermal Desorption Process 56

2.3.4 Cluster Alignment by Passive Fabrication 62

2.3.5 Active Fabrication 68

2.3.6 Summary 76

2.4 Self-Organized Nanopattern Formation on Copper Surfaces 77

2.4.1 Introduction 77

2.4.2 Experiments 78

2.4.3 Novel Phenomena on Cu(001)–c(2×2)N 79

2.4.4 Nanopattern Formation at Vicinal Surfaces 79

2.4.5 Strain-Dependent Nucleation of Metal Islands 82

2.4.6 Strain-Dependent Dissociation of Oxygen Molecules 85

2.4.7 Summary 88

References 89

3 Ultrafast Laser Spectroscopy Applicable

to Nano- and Micromaterials

J Takeda 97

3.1 Introduction 97

3.2 Femtosecond Optical Kerr Gate Luminescence Spectroscopy 97

3.2.1 Time-Resolved Luminescence Spectroscopy: Up-Conversion Technique vs Opical Kerr Gate Method 97

3.2.2 Femtosecond OKG Method: Experimental Setup and Results 99

3.3 Femtosecond Transient Grating Spectroscopy Combined with a Phase Mask 105

3.3.1 Principle of Transient Grating Spectroscopy 105

3.3.2 Transient Grating Spectroscopy Combined with a Phase Mask: Experimental Setup and Results 107

3.4 Femtosecond Real-Time Pump-Probe Imaging Spectroscopy 109

3.4.1 Principle of Real-Time Pump-Probe Imaging Spectroscopy 109 3.4.2 Experimental Demonstrations of Real-Time Pump-Probe Imaging Spectroscopy 112

References 117

4 Defects in Anatase Titanium Dioxide T Sekiya and S Kurita 121

4.1 Introduction 121

4.2 Growth of Anatase Single Crystal 122

4.3 Control of Defect States 123

4.3.1 Heat Treatment Under Oxygen Pressure 123

4.3.2 Heat Treatment Under Hydrogen Atmosphere 124

4.4 Properties of Anatase 129

4.4.1 Absorption Edge 129

4.4.2 Photoluminescence 131

4.4.3 EPR Spectra 132

4.4.4 Electric Conduction 134

4.5 Carrier Control by Photoirradiation 137

4.5.1 Photoconductivity 137

4.5.2 EPR 138

References 140

5 Organic Radical 1,3,5-Trithia-2,4,6-Triazapentalenyl (TTTA) as Strongly Correlated Electronic Systems: Experiment and Theory J Takeda, Y Noguchi, S Ishii, and K Ohno 143

5.1 Introduction 143

5.2 Crystalline Structure 144

5.3 Experimental 146

5.3.1 Paramagnetic Susceptibility and Electron Spin Resonance 146

5.3.2 Reflectivity 150

5.3.3 Photoinduced Magnetic Phase Transition 151

5.4 Electronic Structure Calculations 157

5.4.1 Results Within the LDA 157

5.4.2 Breakdown of the LDA 161

5.4.3 T -Matrix Theory 162

5.4.4 Results in the T -Matrix Theory 164

5.4.5 Concluding Remarks 167

References 168

6 Ab Initio GW Calculations Using an All-Electron Approach S Ishii, K Ohno, and Y Kawazoe 171

6.1 Introduction 171

6.2 Many-Body Perturbation Theory and GW Approximation 172

6.3 Choice of Basis-Set Function 175

6.4 Application to Clusters and Molecules 176

6.4.1 Alkali-Metal Clusters 176

6.4.2 Semiconductor Clusters 178

6.4.3 Gallium Arsenide Clusters and Crystal 180

6.4.4 Benzene Molecule 183

6.4.5 Why Are LDA Eigenvalues of HOMO Level Shallower Than Experiments? 184

6.5 Self-Consistent GW vs First Iterative GW (G0W0) 184

6.6 Appendix: Proof of WT Identity 185

6.7 Summary 187

References 187

7 First-Principles Calculations Involving Two-Particle Excited States of Atoms and Molecules Using T -Matrix Theory Y Noguchi, S Ishii, and K Ohno 189

7.1 Background 189

7.2 Methodology: T -Matrix Theory 191

7.3 Double Electron Affinity of Alkali-Metal Clusters 193

7.3.1 Introduction 193

7.3.2 Effect of the Coulomb Interaction in the DEA Spectra 193

7.3.3 Short-Range Repulsive Coulomb Interaction Within the T -Matrix Theory 195

7.3.4 Summary 196

7.4 Double Ionization Energy Spectra 196

7.4.1 Introduction 196

7.4.2 Two-Valence-Electron Systems 198

7.4.3 Inert Gas Atoms 199

7.4.4 CO and C2H2 Molecules 200

7.4.5 Summary 202

7.5 Two-Electron Distribution Functions and Short-Range Electron Correlations 202

7.5.1 Introduction 202

7.5.2 Methodology 204

7.5.3 Ar 204

7.5.4 CO 206

7.5.5 CO2 208

7.5.6 C2H2 210

7.5.7 Summary 211

7.6 Summary 212

7.7 Appendix 213

7.7.1 Fourier Transformation of Green’s Function 213

7.7.2 Fourier Transformation of K-Matrix 214

7.7.3 Fourier Transformation of T -Matrix 215

References 216

8 Green’s Function Formulation of Electronic Transport at Nanoscale A.A Farajian, O.V Pupysheva, B.I Yakobson, and Y Kawazoe 219

8.1 Introduction 219

8.2 Landauer’s Transport Formalism: The Green’s Function Implementation 220

8.2.1 Multichannel Landauer’s Formula 220

8.2.2 Surface Green’s Function Matching Method 221

8.2.3 Scattering Matrix and Transport Properties 223

8.2.4 Alternative Formulation of the Total Conductance 226

8.3 Carbon Nanotube Heterostructures 227

8.3.1 Conductance of Nanotubes with Vacancy or Pentagon–Heptagon Defects 227

8.3.2 Doped Nanotube Junctions: Rectification and Novel Mechanism for Negative Differential Resistance 230

8.3.3 Effects of Random Disorder on Transport of Nanotubes 234

8.4 Functional Molecule Between Two Metallic Contacts 235

8.4.1 Transport Through Xylyl-Dithiol Molecule Attached to Two Gold Electrodes 235

8.4.2 Transport Through Benzene-Dithiol Molecule Attached to Two Gold Electrodes 238

8.5 Summary 239

References 240

9 Self-Assembled Quantum Dot Structure Composed

of III–V Compound Semiconductors

K Mukai 243

9.1 Introduction 243

9.2 Control of QD Structure by Growth Condition 244

9.2.1 Control of Growth Parameters 244

9.2.2 Closely Stacked QDs 246

9.2.3 QD Buried in Strained Layer 248

9.3 Growth Process of QD Structure 252

9.4 Analysis of QD Structure 256

9.4.1 Grazing Incidence X-Ray Scattering 256

9.4.2 Scanning Tunneling Microscopy 258

9.5 Summary and Perspective 259

References 260

10 Potential-Tailored Quantum Wells for High- Performance Optical Modulators/Switches T Arakawa and K Tada 263

10.1 Introduction 263

10.2 Parabolic Potential Quantum Well 264

10.3 Graded-Gap Quantum Well 266

10.4 Asymmetric Coupled Quantum Well 268

10.5 Intermixing Quantum Well 271

10.6 Summary 272

References 272

11 Thermodynamic Properties of Materials Using Lattice-Gas Models with Renormalized Potentials R Sahara, H Mizuseki, K Ohno, and Y Kawazoe 275

11.1 Introduction 275

11.2 Scheme of the Potential Renormalization 276

11.3 Application of the Potential Renormalization 278

11.3.1 Application to Melting Behavior of Si 278

11.3.2 Application to Cu–Au Phase Diagram 282

11.3.3 Application to Transition and Noble Metals 286

11.3.4 Order–Disorder Phase Transition of L10 FePt Alloy Using the Renormalized Potential Combined with First-Principles Calculations 287

11.4 Summary 289

References 289

12 Optically Driven Micromachines for Biochip Application S Maruo 291

12.1 Introduction 291

12.1.1 Two-Photon Microstereolithography for Production of 3D Micromachines 292

12.1.2 Assembly-Free, Single-Step Fabrication Process of

Movable Microparts 293

12.2 Optically Driven Micromachines 296

12.2.1 Optical Trapping 296

12.2.2 Optical Driving Method of Multiple Micromachines 298

12.2.3 Optimization of Time-Divided Laser Scanning 300

12.2.4 Cooperative Control of Micromanipulators 302

12.2.5 Optically Driven Micropump 303

12.2.6 Concept of All-Optically Controlled Biochip 307

12.3 Conclusion and Future Prospect 307

References 308

13 Study of Complex Plasmas M Shindo and O Ishihara 311

13.1 Overview of Complex Plasma Research 311

13.2 Charging of a Dust Particle in a Plasma 312

13.3 Measurements of the Charge of Dust Particles Levitating in Electron Beam Plasma [12] 313

13.4 Various Approaches to Plasma-Aided Design of Microparticles System in Ion Flow 315

13.4.1 Analysis of Ion Trajectories Around a Dust Particle in Ion Flow [17] 316

13.4.2 Wake Potential Formation to Bind Dust Particles Aligned Along Ion Flow 318

13.4.3 Attractive Force Between Dust Particles Aligned Perpendicular to Ion Flow [30] 320

13.5 Simulation Study of Cluster Design of Charged Dust Particles 321

13.6 Complex Plasma Experiment in Cryogenic Environment [38] 323

13.7 Summary 325

References 326

Index 329

Taro Arakawa

Department of Electrical

and Computer Engineering

Graduate School of Engineering

Yokohama National University

Graduate School of Engineering

Yokohama National University

Graduate School of Engineering

Yokohama National University

Susumu Kurita

Department of PhysicsGraduate School of EngineeringYokohama National University79-5 Tokiwadai, Hodogaya-kuYokoham 240-8501, Japan

Shoji Maruo

Department of MechanicalEngineering

Graduate School of EngineeringYokohama National University79-5 Tokiwadai, Hodogaya-kuYokohama 240-8501, JapanPRESTO

Japan Science and TechnologyAgency

5 Sanbancho, Chiyoda-kuTokyo 102-0075, Japanmaruo@ynu.ac.jp

Graduate School of Engineering

Yokohama National University

Graduate School of Engineering

Yokohama National University

79-5 Tokiwadai, Hodogaya-ku

Yokohama 240-8501, Japan

Research Fellow (DC2) of Japan

Society for the Promotion of Science

Yokohama National University

Graduate School of Engineering

Yokohama National University

Olga V Pupysheva

Department of MechanicalEngineering and Materials ScienceRice University

Houston, TX 77005, USAovp@rice.edu

Ryoji Sahara

Institute for Materials ResearchTohoku University

Sendai 980-8577, Japansahara@imr.edu

Takao Sekiya

Department of PhysicsGraduate School of EngineeringYokohama National University79-5 Tokiwadai, Hodogaya-kuYokoham 240-8501, Japansekiya@ynu.ac.jp

Masako Shindo

Department of PhysicsGraduate School of EngineeringYokohama National University79-5 Tokiwadai, Hodogaya-kuYokohama 240-8501, Japanshindo@ynu.ac.jp

Ken-ichi Shudo

Department of PhysicsGraduate School of EngineeringYokohama National University79-5 Tokiwadai, Hodogaya-kuYokoham 240-8501, Japanken1@ynu.ac.jp

Kunio Tada

Graduate School of Engineering

Kanazawa Institute of Technology

Graduate School of Engineering

Yokohama National University

Boris I Yakobson

Department of MechanicalEngineering and Materials ScienceRice University

Houston, TX 77005, USAbiy@rice.edu

General Introduction

K Ohno

In a fundamental part of the field of nano- and microscale science, revolutionalprogress has been made since last two decades, in a way highly respected bythe society, politics, and economics In this stream, scientists and engineersfrom different fields of physics, chemistry, materials science, and informa-tion technology, including experimentalists, theorists, and researchers doingcomputer simulations, have collaborated to form a new interdisciplinary fieldcalled nanotechnology

In the field of electronics, for example, since the invent of the transistor byShockley, Brattain, and Bardeen in 1940s, downsizing of the electronic deviceshas been continued According to the so-called Moore’s law, the density or thenumber of transistors per unit area on an integrated circuit is doubled every 2

years; in other words, the size of transistors decreases by a factor of 1/8 every

decade starting from 1 cm in 1950, and it is certainly∼ 50 nm in 2007 as shown

in Fig 1.1 Figure 1.2 shows the atomic structure of the interface between Siand SiO2[1, 2] For example, a titanium deposition on top of silicon surfaces(Fig 1.3) [3] is considered as a way to increase the mobility of the electronicdevices A lot of experimental and theoretical efforts have been devoted tothese and many related but different systems However, it is anticipated thatthe fabrication of electronic devices based on the present-day semiconductortechnology will soon face the technical limit, and the use of nanolithography

or self-organization controlled by light or heat (see Chap 2), or the use ofnew idea such as quantum dots or molecular devices is highly expected As arelated topic, microstereolithography (Chap 12) will be useful to manipulatemicromachines

When the size or the dimension of materials decreases, a variety of newphenomena which have never been expected in bulk materials will appear Itwould be a tremendous idea to use them as the future devices First of all,when the size decreases, the quantum effect becomes, in general, dominant aspointed out by Kubo in 1962 [4], and this is often called as the Kubo effect.Consider for example metals Near the Fermi level, metals have continuumspectra and the splitting between adjacent quantum levels is quite small and

Fig 1.1. Moore’s law of the minimum size of transistor used in the integratedcircuit

Fig 1.2.Si/SiO2interface

Fig 1.3 Ti on Si (001) surface (a) Pedestal site and (b) dimer vacancy site [3]

Fig 1.4. Ionization potential (IP) and electron affinity (EA) and their relation tothe energy levels

negligible However, in clusters made of small number of atoms, the ting between adjacent quantum levels is finite, and in general this splittingincreases when the number of atoms in the cluster decreases or equivalentlywhen the size of the cluster decreases This is true not only for semiconductorclusters but also metal clusters

split-For neutral clusters and molecules, the electron affinity (EA) is defined asthe maximum energy gain to attach an electron from infinitely apart to thelowest unoccupied molecular orbital (LUMO), and the ionization potential(IP) is defined as the minimum energy required to detach an electron from thehighest occupied molecular orbital (HOMO) to infinitely apart The absolutevalues of the LUMO and HOMO energies correspond EA and IP, respectively,and the IP minus EA gives the energy gap; see Fig 1.4 There is a generaltendency that the energy gap increases when the size of the cluster decreasesalthough there are exceptions due to the irregular geometries of the bond

between atoms For the GW approximation, see Chap 6.

Experimentally, quantum levels of bulk samples are measured by thephotoemission or inverse photoemission experiment The photoemission deter-mines the quantum levels of the occupied states from the absorbed photonenergy minus the emitted excited electron, while the inverse photoemissiondetermines those of the empty states from the absorbed electron energyminus the emitted photon energy For clusters, the mass of charged clusters

is separated by the time-of-flight (TOF) method, which uses the acceleration

proportional to e/m under an applied electric field Simultaneously, by

photo-irradiation, the electron affinity (EA) is measured as the threshold value of

a photon energy with which the negatively charged clusters is photodetachedand neutralized

Irrespective to bulk or cluster, optical absorption spectra is different fromthe photoemission and inverse photoemission spectra This is because, in theoptical absorption process, the excited electron does not go away from the

cluster but still trapped inside the cluster, forming an electron–hole pair calledexciton Due to the binding energy of the Coulomb attraction between theelectron and hole, the threshold energy of the optical absorption is generallysmaller than the energy gap.

For semiconductor clusters, the phenomenon that the photoluminescenceenergy is smaller than the optical absorption energy, i.e., the photolumines-cence has longer wavelength than the optical absorption, is called the Stokesshift This phenomenon occurs because the relaxation of atomic geometrytakes place in each process Then because the wavelength of the photolu-minescence is different from the incident light, it can be detected distinctlyfrom everywhere the cluster exists Moreover, the color of the photolumines-cence depends on the cluster size The clusters showing strong luminescenceare therefore useful to mark particular biomolecule, for example, since theluminescence with different wavelengths is controlled by the cluster size Inthis respect, CdSe clusters are often used in biomedical experiments Since thezero-dimensional system inside which charged carriers and excitations are con-fined is called the quantum dot, these clusters are often called quantum dots.(More commonly the term “quantum dot” is used in electron transport prob-lems explained later.) Stable structures and optical absorption spectra of smallCdSe clusters (Fig 1.5) have been calculated from first principles [5–7] Forpassivated nonstoichiometric CdSe clusters, the result of the state-of-the-artfirst-principles calculation solving the Bethe–Salpeter equation for the two-particle Green’s function is compared with the result of the time-dependentdensity functional theory in [8] The wavelength of the absorption peaks isstrongly size dependent and monotonically increases as the size of the clus-ter decreases The majority of the clusters have a series of dark transitionsbefore the first bright transition This may explain the long radiative life timesobserved experimentally

For an example of metal clusters, FePt clusters have attracted considerableinterest because it can be used for magnetic thin films with high coercivity.Figure 1.6 shows the structure of FePt cluster with a diameter of 17 nm at3,000 K determined by a fcc-lattice Monte Carlo simulation using the total

Fig 1.5. Most stable structure of (CdSe)13and (CdSe)34 After Noguchi et al [5]and Kasuya et al [6]

Fig 1.6.Structure of FePt cluster with a diameter of 17 nm at 3,000 K

energies determined by a first-principles calculation (see Chap 11) [9, 10] Auclusters are also of much current interest because it was found to exhibitcatalytic behavior [11, 12]

To control the energy gap in p–n junction has been crucially important in

semiconductor technology This idea may be directly used to create the highperformance solar battery The tuning of the optical absorption spectra tothe spectra of sun light is basically possible by combining different sized clus-ters Another example is the photosynthesis in chlorophyll or light-harvestingproperty in dendrimers (see Chap 3)

Figure 1.7 is a π-conjugated dendrimer, star-shaped stilbenoid

phthalo-cyanine (SSS1Pc) with oligo (p-phenylenevinylene) peripheries, which shows a

light-harvesting property [13–16] The calculated wavefunctions [16] are shown

in Fig 1.8, in which the levels are clearly separated to those belonging to theperipheries (P) and those belonging to the core (C) When an electron isselectively excited in the periphery (P), electron and hole transfer from theperiphery to the core throughπ-conjugated network as shown in Fig 1.9 Fromdynamics simulation [16], it has been found that the one-way electron and holetransfer occurs more easily in dendrimers with planar structure than in thosewith steric hindrance becauseπ-conjugation is well maintained in the planarstructure This results well explain the experiments by Akai et al [13, 14] andTakeda et al [15]

Another example of the gap control is a photocatalysis In this respect,metal oxide such as anatase TiO2 (see Fig 1.10) has been widely investigated(see Chap 4) In particular, the doping of transition metal impurity is quiteimportant in controlling the energy gap suitably

Fig 1.7 Structure of (a) SSS1Pc-1 and (b) SSS1Pc-2 In both (a) and (b), upper

figures show the front view and lower figures show the side view The structure of

SSS1Pc-2 (b) is three-dimensional due to steric hindrance between the peripheries

Fig 1.8. (Color online) Amplitude of the wave function at the ground state ofSSS1Pc-2 The cubes are the unit cells For each level, the points at the center and

the upper right side show the core and the periphery, respectively Gray and black

areas denote the positive and negative values of the wave function, respectively

For example, the dissociation of H2O by solar energy would be one ofthe wonderful applications in the photocatalytic reaction Figure 1.11a showsthe absorption of H2O on the surface of anatase crystal Figure 1.11b, cshows the geometry and wavefunction of the most stable, adsorbed groundstate [17]

Periphery (P) Core (C) P-LUMO

Fig 1.9.The energy eigenvalues of SSS1Pc-2 Black and white circles denote

elec-trons and holes, respectively First, an electron is excited from the (almost doublydegenerate) P-HOMO levels to the (doubly degenerate) P-LUMO levels on the

periphery side (solid line with an arrow ) Then, the electron is transferred from the P-LUMO levels to the (doubly degenerate) C-LUMO levels (dashed line with an

arrow ), and the hole is transferred from the P-HOMO levels to the C-HOMO level

(dotted line with an arrow )

Fig 1.10 (a) The unit cell of anatase (TiO2) crystal Large and small circles

cor-respond, respectively, to oxygen and titanium atoms (b) The supercell for treating

the surface of anatase (TiO2) crystal

Figure 1.12 shows a schematic diagram of the dissociation of H2O molecule

by photocatalyst Figure 1.12a is the simplest scheme, in which four holescreated by light absorption induce a reaction 2H2O→ 4H+ + O2+ 4e − and

produce an oxygen molecule, while two electrons induce a reaction 2H++ 2e −

→ H2 and produce a hydrogen molecule Figure 1.12b is a combination oftwo independent reactions using different catalysts can induce oxygen and

hydrogen molecules separately, called the Z scheme [18].

Fig 1.11. Reaction between H2O molecule and the surface of anatase crystal

Transition metal oxides are well-known strongly correlated systems, whoseelectronic structure is hardly treated by the standard band structure cal-culation Similar and related topic is a synthetic metals and organic Mottinsulators For example, the high-temperature phase of an organic radical1,3,5-trithia-2,4,6-triazapentalenyl (TTTA) crystal exhibits a Mott insulator

phase [19] (see Chap 5) The state-of-the-art T -matrix calculation solving the

Bethe–Salpeter equation can handle the multiple scattering and short-rangecorrelations between electrons, and enables us to evaluate the on-site Coulomb

energy U of this material (see Chaps 5 and 7) By this method, it is

demon-strated that the so-called “Coulomb hole” plays a very important role in theproblem of short-range electron correlations

Quantum dots are more commonly considered in the electron transportproblem in confined area (see Chaps 8 and 9) The electron transport through

a quite small structure such as quantum dots is governed by the quantum

effects For example consider a spherical particle with a diameter of d ded in the medium of dielectric constant ε Then the capacitance of this

(If we consider a Cooper pair in a superconductor, e2 should be replaced by

4e2.) When the size d (and therefore the capacitance C) of this cluster becomes

h ν

H

O

H H

O

O O O

H H

O2

H2

H H O

H H O

B

h

H H

O e–

e+

A

PtHH+

O2

H2

O O H

H H O

H H O H

H O

H+

H H O

and produce a hydrogen molecule (b) Two independent reactions using different

catalysts can induce oxygen and hydrogen molecules separately

extremely small, this energy E becomes large and exceed the thermal energy

kBT In this case, the electron transfer (i.e., the conductance) is blocked.

This phenomenon is called “Coulomb blockade.” Then, according to the biasvoltage, the electric current jumps up stepwise This anomalous conductingbehavior can be observed in nanometer-sized metal clusters embedded in theoxide tunnel junction sandwiched by metal conductors at quite low temper-

ature The origin of E in (1.2) is the electron–electron repulsive interaction

inside the quantum dot, and this problem is related to the problem of strongly

correlated electrons Such an problem can be treated by the T -matrix theory

(see Chaps 5 and 7)

When the confined area is two-dimensional, the structure is called tum well” (see Chap 10) The density of states in two-dimensional materials

“quan-is much sharper than in three-dimensional materials, and therefore quantum

Fig 1.13.TTTA crystal in which the electronic charge distribution shaded by blueclouds is restricted inside each molecule in the HT phase or between the dimerizedmolecules in the LT phase

wells are widely used as diode lasers They are used also for the ture field effect transistor (HFET) which is called also as the high electronmobility transistor (HEMT)

heterostruc-Related but completely new idea in the physics of nanotechnology is based

on the wavefunction control instead of the energy gap control One example

is the quantum computing, which uses, for example, the quantum spin states

| ↑  and | ↓  called “qubits.” Although there are still many problems to be

solved, quantum dot may be used as a qubit in the future Qubits may bealso realized by constructing three Josephson junctions in a superconductingcircuit (see Fig 1.14) [20, 22] In the classical von Neumann-type computer,this information is used just as 0 or 1 In contrast, in the quantum computer,the mixture of the two quantum states is also used, and certain problems such

as integer factorization is expected to be solved exponentially faster than theclassical computer Another example is the use of the Aharonov–Bohm (AB)effect A well-known example of the AB effect is as follows: The wavefunction

of a charged particle passing around a long solenoid experiences a phase shift

as a result of the enclosed magnetic field though the magnetic field is zero

in the region through which the particle passes As is seen in this example,the electron wavefunction may become physical quantity and may be used todevelop completely new electric devices in the future

(a) (b)

Fig 1.14 (a) Josephson junction of 800 nm wide and (b) superconducting loop

including three Josephson junctions working as a qubit Both of them are made ofaluminum Courtesy of Shimazu [20]

Fig 1.15 Structure created in dust plasma (a) is the side view, while (b) and (c)

are the cross section view After Ishihara [21]

A completely different but very interesting topic is a complex plasmaknown also as a dust plasma It includes fine particles of size ranging fromnanometers to micrometers in size What is interesting is the creation of hollowstructure of dust particles despite the Coulomb repulsive interaction betweendust particles Figure 1.15 is a computer simulation image of the structure.See Chap 13 for more details

As a new kind of low-dimensional materials, fullerenes and nanotubes made

of only carbon atoms have attracted considerable interests since the ery of C60 by Kroto et al in 1985 [23] By laser ablation or arc dischargeexperiments using a graphite rod, carbon chain molecules are aggregated in

discov-a pldiscov-asmdiscov-a stdiscov-ate Fullerenes discov-are crediscov-ated when the pldiscov-asmdiscov-a is cooled down in discov-ahelium gas atmosphere Fullerenes a hollow, closed cage structure made of

(a) (b) (c)

Fig 1.16.Na insertion into carbon nanotube

spherical network of six- and five-membered rings It is well-known that, due

to mathematical Euler theorem, the number of five-membered rings is always

12 The most abundant fullerene is C60, which has a soccer ball shape Thenext abundant fullerene is C70, which has a rugby (foot) ball shape, and thereare many higher fullerenes such as C74, C76, C78, C82, C84, C90, C94,

On the other hand, carbon nanotubes have a hollow cylindrical tube ture formed from a rolled graphite sheet and therefore made of six-memberedrings only [24] Carbon nanotubes have very high tensile strength and elastic

struc-moduli due to the covalent sp2 bonds between adjacent carbon atoms.The encapsulation of foreign atoms or molecules inside fullerenes and car-bon nanotubes has been also investigated Figure 1.16 represents the snapshots

of the first-principles molecular dynamics simulation of inserting a sodiumatom with 70 eV kinetic energy into a single-walled carbon nanotube [25],although no such experiment has been performed yet If these materials could

be created experimentally, they would be applied to a molecule-based diode orconductor as well as the gold nanowires [26] For the calculation of transportproperties of these materials, see Chap 8

It has also been revealed that a polyyne molecule (C10H2) can be putinside an open-ended single-walled carbon nanotube [27] There is an energygain of about 1.7 eV when C10H2 The bonding between C10H2and SWNT isdue to the large area of weak overlap of the wave functions in the intermolec-ular region inside the SWNT [28]; see Fig 1.17 A recent related experimentshowing the molecular motion inside SWNT has been reported in [29].The so-called endohedral fullerene, which has at least one foreign atominside the cage of the fullerene, have attracted interested Experimentally, ithas been confirmed that at least one lanthanum, yttrium, or scandium atomcan be encapsulated inside C82 or C84 using arc-discharge vaporization ofcomposite rods made of graphite and the metal oxide [30] The creation ofendohedral C60 is possible, though the creation rate is very low, by using anuclear recoil of isotope nuclear reaction [31] Figure 1.18 represents a snap-shots of a first-principles molecular dynamics simulation of the insertion of

Po atom with 40 eV kinetic energy into C60 It is quite amazing that such aheavy element as Po can be successfully encapsulated inside C60with such lowenergy Experimentally, the existence of Po@C60in the solvent was certainly

polyyne molecule

Fig 1.17.Wave function of the HOMO level of C10H2@SWNT

Fig 1.18. Snapshots of a first-principles molecular dynamics simulation of a Poatom insertion into C60 with 40 eV kinetic energy

confirmed in the synchronized measurements using high-performance liquidchromatography and UV detector [31]

As a related topic, the electron capture (EC) decay rate of 7Be sulated in C60 was measured using a reference method comparing with therate in Be metal crystal, and it was found that the half-life of7Be endohedralC60 (7Be@C60) decreases about 0.83% than inside Be metal crystal [32, 33]

encap-Fig 1.19. Structure of the 3D polymers crosslinked by [2 + 2] cycloadditionalfour-membered rings

Fig 1.20.Optimized 3D structure of peanut-shaped polymers crosslinked by

eight-membered rings in a monoclinic unit cell (a) is a side view and (b) is a view of the

cross section of this structure

The decay rate is further accelerated when the 7Be@C60 sample is cooleddown at liquid helium temperature (its half-life is 1.5% shorter than Bemetal) [34] This phenomenon can be explained theoretically by the calcu-lation of the electron density at the7Be nucleus position inside the C60 cageand in the Be metal crystal The theoretical estimates are in fair agreementwith the experimental observations [34, 35]

Fig 1.21.Structure of polymer

Fullerene polymers made of C60 are also interesting [36] Figure 1.19represents C60 polymer networks crosslinked by [2+2] cycloadditional four-membered rings, and Fig 1.20 represents a peanut-shaped fused C60polymerchains crosslinked by eight-membered rings, which are considered as a modelfor the electron beam irradiated C60samples [37] Owing to the overlap of wave

functions as well as the hybrid networks of sp2-like (threefold coordinated)

and sp3-like (fourfold coordinated) carbon atoms, the electronic structure isconsiderably different from each other The resulting electronic structure iseither semiconductor or semimetal depending on the spatial dimensionality ofmaterials [36]

Another interesting topic in nano- and micromaterials is soft materials likeflexible polymers, although they are not described in detail in this book Forexample, micelle formation of AB block-copolymers can be used as a dragdelivery system (DDS) in biomedical applications Figure 1.21 represents anexample of the mixture of water, oil, and amphiphilic polymers [38]

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Nanometer-Scale Structure Formation

on nanostructures in rather lower dimensions, on solid surfaces Moreover,

“nano-” usually means the range of a few to hundreds of nm; however, weconcentrate on the structures one order smaller than usual, in other words,the structures in “atomic scale” rather than “nanometer scale,” especiallythose formed on well-characterized surfaces under ultrahigh vacuum (UHV)conditions Even in this scale, nanostructures can be formed both by self-organization and by ultrafine machining Before we present our latest studies,some categories of this kind of nanostructures are introduced in this section

We do not attempt to present a detailed review with reference to huge number

of articles, but give a few examples of each category with emphasis on theinitial works or fundamental studies

Self-organization process can potentially produce uniform nanostructures

in wide area It is more attractive in fabricating nanodevices if the trollability is achieved Self-organized nanostructures are classified into somecategories, for instance, those on metal surfaces are different from those onsemiconductor surfaces [1]

con-Surface reconstruction on a (110) surface of face-centered-cubic metals (Ni,

Cu, Pd, Ag, Ie, Pt, Au) is probably oldest known self-organized tures on surfaces [2] Added row and missing row reconstructions are found

nanostruc-on diatomic gas molecule-adsorbed surfaces and nanostruc-on alkali-metal adsorbedsurfaces as well as on clean surfaces [3] The driving force of this kind ofreconstruction is simply thought to be surface energy; however, the recon-struction is as a result of subtle energy balance between electronic energyand surface energy Very low coverage of gas molecule or alkali-metal inducesthe reconstruction, which means that local coordination number and nonlocal

charge distribution of transferred charge play important roles of the struction Prototype of nanopatterned metal surfaces is observed on vicinalAu(111) and nitrogen-covered Cu(001), and the pattern formation is explained

recon-by the elastic continuum model [4] Long-range elasticity is dominant toform not only these prototypes but also all kinds of adlayers, and can be

a tool for self-organization [5] These structures are used as templates forgrowing one-dimensional (1D) and two-dimensional (2D) structures Metalepitaxy on metal surfaces, such as Cu/Ru(0001) and Au/Ni(111), exhibitsalso nanopatterns [6]

Self-organized nanostructure formation on semiconductor surfaces, cially IV group semiconductors [7] and III–V group semiconductors [8], hasbeen more extensively studied than that on metal surfaces because of poten-tial applications in industries As for IV group semiconductors, elongated Agislands with aspect ratios greater than 50:1 were formed on Si(001) and theformation of this 1D structure was a result of elastic relaxation of the strainedlayer [9] The 1D structures are found also in other systems Self-assembled

espe-Ge nanowires were grown on Si(113) by molecular beam epitaxy [10] Bi linestructures were formed on Si(001) in the vicinity of its desorption tempera-ture [11] The 2D structures, such as the growth of Ge layers on Si surface, havebeen a subject of greater interest than these 1D structures Ge nanoislandswere formed by taking advantage of the Stranski–Krastanow (SK) growthmode [12, 13] Coherent SK growth was explained in terms of elastic deforma-tion around the islands The island size and spacing grow progressively moreuniform, when Si layers and Si0.25Ge0.75layers are formed alternately on thesenanoislands [14] An approach toward nanointegration through the control ofself-organization processes of surface structures – such as surface reconstruc-tion, atomic steps, and the phase boundaries of reconstructed domains – wasproposed [15] On the other hand, as for III–V group semiconductors, theflat (211), (311), and (111) GaAs surfaces break up into regular facets andmake superlattices with lateral corrugation of the interfaces during multi-layer molecular beam epitaxy [16] Quantum dots have been developed sincedislocation-free strained In0.5Ga0.5As islands were found during the growth on

a GaAs(001) substrate [17] More practical methods to obtain highly uniformdot size and density were proposed [18, 19]

The prototype of the ultrafine machining is the method using Ga+focusedion beam (FIB) with a diameter of only 100 nm [20] Significant progress hasbeen made in FIB technology and it is now a powerful tool in lithography,etching, deposition, doping, and even 3D nanostructures [21] However, thedimension of nanostructures produced with this method is still beyond thescale focused in this section

Best spatial resolution in ultrafine machining is achieved with a ning tunneling microscopy (STM) which can manipulate atoms one by one.Atom manipulation was first demonstrated by sliding Xe atoms on Ni(110) at

scan-4 K to form an “IBM” logo where each letter was written by a collection ofatoms [22] Anther example is excision of S atoms from MoS surface by field

evaporation to form characters at room temperature (RT) [23] scale modification of H-passivated Si(111) surface in air was also reported [24].Under UHV condition, nanoscale patterning of H-passivated Si(100) surfacewas achieved by local desorption of hydrogen due to tunneling current, andonly the patterned area was subsequently oxidized [25] Tunneling electronsnot only manipulate an atom, but also form an effective excitation sourcefor inducing chemical reaction The concept of bond-selective chemistry usingthis mechanism was proposed with the examples of single O2molecule disso-ciation on Pt(111) and displacement of Si adatoms on Si(111) [26] Fe(CO)molecules were formed starting from Fe atoms and CO molecules adsorbed

Nanometer-on a Ag(110) surface [27] The feasibility of inducing all the steps of a face chemical reaction by using the STM tips was shown by the synthesis ofbiphenyl molecules starting from iodobenzene adsorbed on Cu(111) [28, 29].Although spatial resolution of surface modifications using STM is perfect,

sur-it cannot be applied directly to the production of devices As a more practicalway, possibility of nanostructuring the surface by inelastic processes, induced

by electrons or photons, has been widely discussed Modification of materials

by electronic excitation is becoming attractive due to recent advances in laserand synchrotron radiation [30]

In this section, we present our latest studies on nanometer-scale structure formation on solid surfaces since 2002 in the following sections In Sect 2.2,

the fundamental processes of layer-by-layer etching of a Si(111) surface aredescribed Nanostructures in the lateral direction are also found: Halogenatoms are adsorbed at selective sites, and clusters are formed during the des-orption process In Sect 2.3, how to control silicon surface at the atomic scale

is described with regard to the dynamic processes, for example, passive cation due to thermal process to align nanoclusters and active fabrication vianonequilibrium reaction pathways due to electronic excitation In Sect 2.4,

fabri-an example of self-orgfabri-anization on a metal surface is introduced: Nitrogenadsorption on Cu(001) surface induced strain and forms patch patterns whichare used as a template for nanoscale arrangements

2.2 Atomic Layer Etching Processes

desorp-at the desorp-atomic scale is growing Halogen etching is also a promising date method for atomic layer etching, which is one of the basic techniques

candi-to fabricate nanometer-scale structures [34] Reaction between halogens andsemiconductor surfaces has therefore attracted much attention in the recentyears Halogen etching consists of several stages; adsorption of halogen atoms

on the surface, desorption of silicon halides, and reconstruction of the cleansurface Understanding of the atomic-scale mechanisms of these fundamentalprocesses will be useful to optimize etching conditions and necessary for futuredevelopment of atomic-scale etching Although atomic-scale etching itself is akind of ultrafine machining, our studies on the fundamental processes of theetching have revealed that they involve self-organizing processes, for instance,halogen atoms can be adsorbed at selective sites to form adsorbate patternsand nanoclusters can be formed by the thermal treatment of halogen-coveredsurface In this section, the atomic-scale mechanisms of these fundamentalprocesses are elucidated mainly by means of real-time optical measurements.Etching of the Si(001) surface is preferentially studied in connection withindustrial applications, but etching of the Si(111) surface is also of interest,because the dimer-adatom-stacking fault (DAS) structure [35] has a variety

of sites with different chemical reactivity [36] The DAS model is illustrated

in the left half of Fig 2.1 STM has greatly improved our understanding ofchemical processes at the atomic scale, and most studies have focused onthe electronic states or the morphology mainly of the Si adatoms However,another type of dangling bond on the rest-atoms which are not accessed bySTM must have some role in surface reactions

The static properties at each stage in the fundamental processes of halogenetching have been revealed by a variety of methods It is known that chlo-rine atoms first react with adatom sites to form monochlorides and remove

dangling bond states near EF at low coverage [37, 38], while further sure produces SiCl2 and SiCl3 species [39, 40] These polychlorides tend to

expo-be formed on the center adatom sites [41] On the other hand, there is littledirect evidence for the presence of polybromide species, although their pres-ence is generally accepted In the right half of Fig 2.1, the chloride speciesare schematically shown When a dichloride is formed, the back-bond of theadatom is broken and a new dangling bond appears on the rest-atom, as illus-trated in Fig 2.1 With further chlorine, the second back-bond is broken toform a trichloride

Annealing at about 700 K for a Cl-saturated surface and at 500–650 K

for a Br-saturated surface removes Si adatoms, and the rest-surface (the

surface consisting of rest-atoms; see Figs 2.37 and 2.41) covered with gen atoms takes a 1×1 structure as in Fig 2.27 [37–39, 42, 43] Ultraviolet

halo-laser irradiation also produces this kind of rest-surface [41, 44] X-ray toelectron spectroscopy [39, 40] and surface-enhanced X-ray absorption finestructure [45] studies confirmed that only monochloride species remain afterannealing above 673 K In accordance with the above observations, a thermaldesorption spectroscopy (TDS) study revealed that polychlorides species aredesorbed as a peak at 690 K, and a laser-induced thermal desorption (LITD)study showed that the SiCl species almost disappears above 630 K [46] On

pho-Top View

Side View

Clean Cl-adsorbed

D M

M

M M

a

a a

r r r

a a

E E E

Si restatoms

(bonded to the adatom originally)

Fig 2.1. (a) Structural model of clean (left half ) and Cl-adsorbed Si(111)–7 ×7

DAS surfaces (right half ) a and r indicate the dangling bonds on Si adatoms and

Si rest-atoms, respectively Mono-, di-, and trichlorides are marked as M , D, and

T , respectively Hatched Cl atoms terminate the adatom dangling bonds (N ) or

the newly emerging dangling bonds (E) at the rest-atoms (b) Dichloride formation

from a Si monochloride The back-bond of the adatom is broken and a new danglingemerges at the rest-atom

the 1×1 Br-terminated rest-surface, many bilayer islands and clusters are

found [43, 47] When the halogen-covered rest-surface is heated above 900 K,halogen atoms are desorbed mainly as SiCl2[40,46] and SiBr2[48], as shown by

a TDS study As for the desorption mechanism, an STM study indicated thatspontaneous Br etching of Si(111) at 700–900 K results in step retreat [43]

In this way, one Si layer is taken off, and a clean 7×7 DAS structure is

sub-sequently restored In spite of these studies, the dynamic processes of thedesorption of silicon chlorides and the reconstruction to form the 7×7 DAS

structure are still poorly understood, and need to be established before therelative reactivity of halogens on the Si(111) surface can be discussed

2.2.2 Real-Time Optical Measurements

Real-time in situ observation is essential to investigate the kinetics Opticalmethods are superior to others, because they are noninvasive, nondestructive,and capable of very rapid response The optical responses of the surfaces arerelated to the surface electronic states [49–53] Studies on halogen-etching pro-cesses on Si(111) introduced in this section were investigated by means of twooptical methods: surface differential reflectivity (SDR) spectroscopy and sec-ond harmonic generation (SHG) These optical methods were combined withTDS which gives the total halogen coverage These experimental techniquesare not so popular compared with standard techniques for surface analysissuch as electron spectroscopy Accordingly, principles of these techniques arebriefly introduced and their experimental procedures are described

Surface Differential Reflectivity Spectroscopy

SDR spectroscopy was proved to be a powerful tool for the real-time study

of hydrogen adsorption on Si(111) [49] Differential reflectivity is defined as

∆R/R ≡ (Ra− Rc)/Rc, where Ra and Rc are the reflectivities of the covered and clean surfaces, respectively Spectral features of adsorption onadatom dangling bonds and breaking of adatom back-bonds were identified

H-from the calculation of the ∆R/R spectrum for the hydrogenated 7 ×7

sur-face [54, 55] These spectral features arise from the sursur-face states of the cleansurface, so that the SDR spectrum is considered not to depend on the adsor-bate These features develop with time during adsorption processes, whereas

in the desorption processes, they decay with time as the clean surface ture is restored Magnitudes of the SDR spectral features is interpreted to beproportional to the densities of saturated dangling bonds and broken bondbreakage

struc-The schematic diagram of the experimental setup is shown in Fig 2.2 [56].Measurements reported in this section were performed in an UHV chamber

at a base pressure of 2× 10 −8Pa The 7×7 structure of the clean surface

Preamplifier Controller

SHG Monochro - mator

Digital Oscilloscope

AgCl Electrochemical Cell

Q - Switched

N d : YAG Laser

Imaging Assembly

Monochro mator

-Quartz Plate

F3

Fig 2.2.Experimental setup for SDR and SHG See [56] for detail

was confirmed by low-energy electron diffraction Halogen gas was ated in the vacuum with a AgX (X = Cl, Br) electrochemical cell dopedwith CdX2 (5% wt) [57] The electrochemical cell produces more atoms thanmolecules [58] The setup for the SDR measurement is as follows Light from

gener-a hgener-alogen tungsten lgener-amp (LS1) or gener-a deuterium lgener-amp (LS2) wgener-as polgener-arized izontally with a Glan-Taylor prism (P1), and separated into a probe beam

hor-(90%) and a reference beam (10%) The p-polarized probe beam was

intro-duced into the vacuum chamber and incident on the surface at an angle of

70◦from the surface normal The specularly reflected probe beam and the

reference beam were introduced via optical fibers to a grating spectrographwith an imaging assembly correcting astigmatism The spectra of both beamswere detected by a dual photodiode array, and the intensity of the reflectedspectrum was normalized with respect to the reference spectrum Photoin-duced electrons in the diode array were accumulated at each pixel for 10 s toimprove the signal-to-noise ratio

Second Harmonic Generation

SHG has been employed more extensively than SDR to observe the kinetics ofadsorption [51, 59] and desorption [60, 61] on Si(111) When the fundamentalwave of a Nd:YAG laser is used as a pump laser, the two-photon energy of thefundamental wave is resonant to the S3–U1 transition [52], where S3 and U1states are attributed to the adatom back-bond and the adatom dangling bond,

respectively The nonlinear susceptibility χ(2)then decreases linearly with thecoverage at low coverage The adsorption process on adatom dangling bonds

at low coverage is therefore detected more sensitively by SHG, and vice versa

at high coverage However, SDR is superior rather than complementary toSHG as a tool of real-time measurement, because SDR reveals the adsorptionprocess in the full exposure range and provides information about not onlythe adsorption on adatom dangling bonds, but also the breaking of adatomback-bonds

In the SHG measurement, the fundamental wave (1,064 nm, 8 ns) of a switched Nd:YAG laser was used as a pumping laser The duration of the lightpulse of the fundamental wave was 8 ns The laser radiation polarized alongthe [211] direction with a half-wave plate was incident on the surface of thespecimen with an incident angle of about 20◦ The reflected second harmonic

Q-(SH) signal was passed through another polarizer, purified with a bandpassfilter (F3) and a monochromator, and detected by a photomultiplier and gateintegrated with a digitizing oscilloscope Part of the incident light was directed

to a quartz plate which produced strong SH signal used as a reference signal.The SH intensity was numerically obtained from the reflected signal divided

by the reference signal