FIRST-PRINCIPLES STUDIES ON THE INTERACTIONS BETWEEN TRANSITION-METAL ATOMS, Si(001), AND NANOTUBES PENG GUOWEN NATIONAL UNIVERSITY OF SINGAPORE 2007 FIRST-PRINCIPLES STUDIES ON THE INTERACTIONS BETWEEN TRANSITION-METAL ATOMS, Si(001), AND NANOTUBES PENG GUOWEN (M.Sc., Dalian University of Technology) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF PHYSICS NATIONAL UNIVERSITY OF SINGAPORE 2007 Acknowledgements I am indebted to my advisors, Professor Feng Yuan Ping and Professor Alfred Huan Cheng Hon, for their advice, guidance, kindness, and encouragement throughout my thesis work. I would like to thank Professor Tok Eng Soon, Professor David J. Srolovitz (Yeshiva University), and Dr. Chi Dong Zhi (IMRE) for their valuable suggestions and discussions. Special thanks to our group members, Zhao Fangfang, Sun Han, Dr. Sun Yiyang, Dr. Liu Lei, Dr. Pan Hui, Dr. Dong Yufeng, Wu Rongqin, Yang Ming, and Shen Lei, for their valuable discussions and kind help. I acknowledge the National University of Singapore for the research scholarship, which enables me to conduct my research projects and finish this thesis. Finally, I thank my parents for their love and support. i Table of Contents Acknowledgements i Abstract vi Publications ix List of Tables xi List of Figures xii Introduction 1.1 Si-based MOSFETs and CNT-FETs . . . . . . . . . . . . . . . . . . 1.2 Growth of Si-based MOSFETs and CNT-FETs . . . . . . . . . . . 1.3 Interactions between transition-metal atoms, Si(001), and nanotubes 1.3.1 Interactions of transition-metal atoms with Si(001) . . . . . 1.3.2 Interactions of transition-metal atoms with nanotubes . . . . 1.3.3 Interactions of nanotubes with Si(001) . . . . . . . . . . . . 10 Objectives of the thesis work . . . . . . . . . . . . . . . . . . . . . . 12 1.4 First-principles methods 2.1 Many-body quantum mechanics . . . . . . . . . . . . . . . . . . . . 15 16 ii 2.2 Earlier approximations . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2.1 The Born-Oppenheimer approximation . . . . . . . . . . . . 18 2.2.2 The Hartree approximation . . . . . . . . . . . . . . . . . . 21 2.2.3 The Hartree-Fock approximation . . . . . . . . . . . . . . . 22 Density functional theory . . . . . . . . . . . . . . . . . . . . . . . . 24 2.3.1 The Thomas-Fermi model . . . . . . . . . . . . . . . . . . . 24 2.3.2 The Hohenberg-Kohn theorems . . . . . . . . . . . . . . . . 26 2.3.3 The Levy constrained-search formulation . . . . . . . . . . . 29 2.3.4 The Kohn-Sham equations . . . . . . . . . . . . . . . . . . . 32 2.4 The local density approximation . . . . . . . . . . . . . . . . . . . . 36 2.5 Bloch’s theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.6 Brillouin zone sampling . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.7 Plane-wave basis sets . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.8 The pseudopotential approximation . . . . . . . . . . . . . . . . . . 44 2.9 The nudged elastic band method . . . . . . . . . . . . . . . . . . . 47 2.3 Adsorption and diffusion of Co on Si(001) surfaces 52 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.2 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.3.1 Adsorption sites of Co on Si(001) . . . . . . . . . . . . . . . 55 3.3.2 Diffusion of Co on the surface and into the subsurface . . . . 59 3.3.3 Diffusion of Co into deeper layers . . . . . . . . . . . . . . . 66 3.3.4 Formation mechanism of dimer vacancy defects . . . . . . . 69 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 3.4 iii Interaction of Manganese with single-walled B2 O nanotubes 76 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 4.2 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.3.1 Interaction of Mn with the graphitic B2 O sheet . . . . . . . 82 4.3.2 Adsorption of Mn to the outer wall of (3,0) B2 O nanotube . 85 4.3.3 Adsorption of Mn to the inner wall of (3,0) B2 O nanotube . 88 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 4.4 Transition-metal nanowire encapsulated Bx Cy Nz composite nanotubes 95 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 5.2 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . 97 5.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.4 5.3.1 The reduction of the magnetism of nanowires . . . . . . . . 101 5.3.2 The stability of TM/BC3 hybrid structures . . . . . . . . . . 102 5.3.3 High spin polarization of TM/nanotube hybrid structures . . 103 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Carbon in Si(001): the Si(001)-c(4 × 4) reconstruction 107 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 6.2 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . 110 6.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 111 6.3.1 Structural models . . . . . . . . . . . . . . . . . . . . . . . . 111 6.3.2 Kinetics of dimer rotations . . . . . . . . . . . . . . . . . . . 112 6.3.3 A new stable 1RD model . . . . . . . . . . . . . . . . . . . . 123 iv 6.3.4 6.4 A possible method to search for new stable structures . . . . 125 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Adsorption of ˚ A carbon nanotubes on Si(001) surfaces 127 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 7.2 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . 129 7.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . 131 7.4 7.3.1 Adsorption of a (3,3) CNT on Si(001) surfaces . . . . . . . . 131 7.3.2 Adsorption of a (2,2)@(6,6) CNT on Si(001) surfaces . . . . 141 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 Concluding remarks 143 8.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 8.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 References 148 v Abstract Interactions between transition-metal atoms, Si(001), and nanotubes are very important to the growth processes of Si-based metal-oxide-semiconductor field-effect transistors and nanotube-based field-effect transistors. In this thesis, first-principles methods were employed to investigate these interactions. Firstly, the interaction of transition-metal atoms with Si(001) surfaces was investigated by examining the adsorption and diffusion of Co on Si(001) surfaces at the initial stage of growth. The favorable surface and subsurface binding sites of Co on Si(001) were determined. It was found that Co atoms diffuse quickly to the subsurface from the surface, while the surface diffusion is slower. The calculated diffusion coefficients for Co diffusion from the surface into the subsurface are comparable to experimental results. It was found that the deposited Co will quickly diffuse into the deeper interstitial sites with increasing Co coverage. The formation mechanism of the dimer vacancy defect from the most stable subsurface structure, i.e. the under dimer structure, via Si ejection was also examined. It was found that the energy barrier of Si ejection is higher than those of Co diffusion into the subsurface and Co inward diffusion to the deeper layers. These results are in good agreement with experiment results and helpful for understanding the formation of vi silicides on Si substrates. Secondly, the interactions of transition-metal atoms with nanotubes were investigated through two case studies, i.e. the interaction of Mn with a single-walled (3,0) B2 O nanotube and the transition-metal nanowire encapsulated composite Bx Cy Nz nanotubes, to examine the catalytic roles of transition-metal atoms during the growth of nanotubes and to design the functionalized nanotubes with transitionmetal atoms. The study on the interaction of Mn with a single-walled (3,0) B2 O nanotube provided the structural, electronic, and magnetic properties of Mn-doped graphitic B2 O sheets and B2 O nanotubes. A comparative study on Bx Cy Nz nanotubes filled by transition-metal nanowires was performed to understand the electronic and magnetic properties of these functionalized nanotubes. It was found that the magnetism of the encapsulated nanowires is weakened by the interactions between nanowires and nanotubes. BC3 nanotubes were found energetically more favorable than other Bx Cy Nz nanotubes for covering the encapsulated transition metal nanowires. These functionalized nanotubes show high spin polarization which is useful in spintronics. Finally, the interactions between carbon nanotubes and Si(001) surfaces were investigated through two studies, i.e. the study of the interaction of C impurities with Si(001) surfaces and the study of the adsorption of ultrasmall carbon nanotubes (CNTs) on Si(001) substrates. In the study on the interaction of carbon impurities with Si(001) surfaces, transformations between different structural models of the Si(001)-c(4 × 4) surface via Si dimer rotations were addressed. We showed how dimers rotate in passing the refined missing dimer model to the recently proposed rotated dimer model with small energy barriers. A new low-energy structural vii model with a single rotated dimer for the carbon-induced Si(001)-c(4 × 4) surface was identified along the minimum energy path. A possible method of searching for new stable structures along reaction paths by the nudged elastic band calculations was proposed. In the study on the adsorption of ultrasmall CNTs on Si(001), we showed that ultrasmall CNTs were more active than CNTs with large diameters. The binding energies of ultrasmall CNTs on Si(001) surfaces are significantly larger than those of larger diameter CNTs on Si(001). In addition, the electronic structures of the CNT/Si(001) hybrid structure were found to be sensitive to the adsorption sites. viii Chapter 8. Concluding remarks to the interaction of the nanowire with nanotube, i.e. the hybridization between the 3d electrons of the nanowire and the s and p electrons of the host tube. The BC3 nanotubes were found to be energetically more favorable than other Bx Cy Nz nanobutes as host tubes for encapsulated transition metal nanowires. These functionalized nanutubes show high spin polarization, which is useful in spintronics. The interactions between carbon nanotubes and Si(001) surfaces were investigated through two studies, i.e. the preliminary study on the interactions of C impurities with Si(001) surfaces and the study on the adsorption of ultrasmall carbon nanotubes (CNTs) on Si(001) substrates. In the study of the carbon-induced Si(001)c(4 × 4) structure, we found that the rotational barriers for transforming from the refined missing dimer model [89] to the recently proposed rotated dimer model [80] via dimer rotations are small. The small energy barriers between different models can explain the rich features of experimental scanning tunneling microscopy (STM) images [71, 80, 87, 89] of the Si(001)-c(4 × 4) structure. In particular, a new lowenergy atomic structural model with a single rotated dimer for the carbon-induced Si(001)-c(4 × 4) surface was found along the minimum energy path of dimer rotations. The stabilization mechanism of this new stable structural model could be ascribed to the annihilation of one surface dangling bond and the formation of an sp2 -like bonding in the subsurface. The simulated STM image of this novel structure is asymmetric which is consistent with earlier experimental reports [71, 87]. In addition, a possible method of searching for new stable structures along the reaction paths by the nudged elastic band calculations was proposed. This method should be useful to locate new stable/metastable structures for similar systems. In the study on the adsorption of ultrasmall CNTs on Si(001), we found that the 145 Chapter 8. Concluding remarks binding energies of ultrasmall CNTs on Si(001) are significantly larger than those of CNTs with larger diameters on Si(001), resulting from the larger curvature effect of the ultrasmall diameter CNTs. It was found that the adsorption sites at the surface trench for CNTs parallel to the Si dimer rows, and between the Si dimers for CNTs perpendicular to the Si dimer rows are very stable. The adsorbed CNTs at these two sites are perpendicular to each other, which is consistent with experimental results [66]. The electronic structures of the CNT/Si(001) hybrid structure were found to be sensitive to the adsorption sites. These results are very helpful for designing CNT based field-effect transistors (CNT-FETs) on Si substrates. 8.2 Future work The studies on the interactions of transition-metal atoms with the Si(001) surfaces can be extended to similar systems. For example, the study on the interaction of TM atoms with H-terminated Si(001) surfaces is very interesting because the hydrogenation of Si surfaces is expected to significantly affect the silicidation process [17, 18]. Another research direction is to investigate the interaction of Si(001) surfaces with other interesting metal atoms, for example, rare-earth (RE) atoms, since rare-earth silicides, such as ErSi2−x , DySi2−x , and YSi2−x , are very promising and potentially useful in the semiconductor industry [159–162]. First-principles studies on the interaction of RE atoms with Si substrates should be conducted to understand the formation of rare-earth silicide films grown on Si substrates. Furthermore, first-principles studies on the diffusion of Si within RESi2−x /Si substrate will be also very interesting, since the diffusion is one of 146 Chapter 8. Concluding remarks determinants of the stability of rare-earth silicides. Further studies on the functionalized nanutubes with transition-metal atoms or other foreign atoms are also very useful. The functionalized nanutubes will be very promising in the molecular devices. For example, the decoration of CNTs with foreign atoms, the coating of CNTs with metal atoms, and the filling of CNTs with molecules, will be of great interest. A first-principles study of Mn coating CNTs is under way. Further study is highly recommended to examine the atomic structure of the carbon-induced Si(001)-c(4 × 4) surface. With the limitation of the pseudopotential approximation used in our study of the carbon-induced Si(001)-c(4 × 4) surface, we are unable to calculate the X-ray photoemission spectra of different Si(001)-c(4 × 4) models and compare them with experimental data [77] to provide further support on our proposed low-energy model [139]. Further work on calculating the X-ray photoemission spectra of different Si(001)-c(4 × 4) models by using full-potential method would be useful. In addition, low-temperature STM experiments on the Si(001)-c(4 × 4) surface should be carried out, to verify the novel structure model proposed in our study unambiguously [139]. Further studies are also recommended to examine the interactions of nanotubes with Si(001) surfaces, for example, to determine energy barriers for CNTs rotating on Si substrates from one stable adsorption site to another stable site; to investigate the binding trends of multi-walled CNTs adsorbed on Si(001) substrates and so on. 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Lett. 88, 021908 (2006). 160 [...]... reviewed in Section 1.3 5 Chapter 1 Introduction 1.3 Interactions between transition- metal atoms, Si(001), and nanotubes 1.3.1 Interactions of transition- metal atoms with Si(001) Transition- metal silicides, especially 3d TM silicides, are of great importance as metallic contacts in Si-based MOSFETs [12–18] The small lattice mismatches and the similar structures between TM silicides and Si allow high-quality... determining the favorable binding sites on the surface and in the subsurface, Co diffusion on the surface and into the subsurface is examined in detail Furthermore, the Co inward diffusion into the deeper layers is discussed The formation mechanism of dimer vacancy defects is also examined Secondly, we investigate the interactions between TM atoms and nanotubes through two case studies, i.e the interaction of... structures for similar systems The results on the adsorption of the ultrasmall CNTs on Si(001) may be useful for assembling CNTs on Si(001) substrates properly First- principles calculations based on density functional theory and the pseudopotential approximation are used to investigate the interactions in the above mentioned studies A review on the basic theories of first -principles methods is given in... study the interactions between carbon nanotubes and Si(001) surfaces through two studies, i.e the preliminary study on the interactions of C impurities with Si(001) surfaces and the study on the adsorption of ultrasmall CNTs on Si(001) substrates In the preliminary study, we mainly examine the transformations of different existing models of the carbon-induced Si(001)-c(4 × 4) surface via Si dimer rotations... silicides The results on the interaction of Mn with B2 O can help us understand the potential catalytic role of TM atoms in the synthesis of B2 O nanotubes, and the effect of adsorption of TM atoms on the properties of B2 O nanotubes The study on the interactions of Bx Cy Nz nanotubes with 13 Chapter 1 Introduction TM nanowires could be useful for designing nanotube-based spin-transport devices The results on. .. between TM atoms, Si(001), and nanotubes are very important in the growth processes of Si-based MOSFETs and CNT-FETs Information of these interactions can help us understand the growth mechanism of TM silicides in MOSFETs, the roles played by the TM catalysts during the synthesis of nanotubes, and the knowledge of assembling CNT-FETs properly on Si wafers Due to the importance of these interactions, much... electron-electron interactions If the electron-electron interactions can be approximated by an effective electron-electron potential, one can reduce equation (2.1) to a set of single electron Schr¨dinger o equations This is the original idea of the Hartree approximation [97] as well as the subsequent Hartree-Fock approximation [98, 99] 20 Chapter 2 First- principles methods 2.2.2 The Hartree approximation In the. .. 64] Such integration requires the control of the shape, location and orientations of CNTs on Si surfaces [65–67] Thus, a clear microscopic understanding of the interactions of CNTs with Si(001) is of great importance Before addressing the interactions of CNTs with Si(001), the interaction of C impurity atoms with Si(001) surfaces deserves much work On one hand, carbon incorporation into Si substrate... nanochips based upon CNTs could be fabricated in the near future In modern Si-based microelectronics and future CNT-based nanoelectronics, the growth processes of Si-based MOSFETs and CNT-FETs are the keys During these growth processes, the interactions between transition- metal atoms, Si(001), and nanotubes are very important A brief introduction of the growth processes of MOSFETs and CNT-FETs will... govern the behaviors of electrons and nuclei in a many-body system After introducing earlier approximations, including the Born-Oppenheimer approximation, the Hartree and Hartree-Fock approximations, we present the basic concepts of the density functional theory The local density approximation and generalized gradient approximation for the exchange-correlation functional are discussed The Bloch’s theorem . FIRST-PRINCIPLES STUDIES ON THE INTERACTIONS BETWEEN TRANSITION-METAL ATOMS, Si(001), AND NANOTUBES PENG GUOWEN NATIONAL UNIVERSITY OF SINGAPORE 2007 FIRST-PRINCIPLES STUDIES ON THE INTERACTIONS. atoms, Si(001), and nanotubes 6 1.3.1 Interactions of transition-metal atoms with Si(001) . . . . . 6 1.3.2 Interactions of transition-metal atoms with nanotubes . . . . 8 1.3.3 Interactions of nanotubes. given in Section 1.2, followed by the review of the interactions between transition-metal atoms, Si(001), and nanotubes in Section 1.3. 1.2 Growth of Si-based MOSFETs and CNT-FETs To construct a