Applied Physics of Carbon Nanotubes (eBook)

Foreword 7
Preface 11
Contents 13
List of Contributors 19
Part I Theory and Modelling 22
1 From Quantum Models to Novel E.ects to New Applications: Theory of Nanotube Devices 23
1.1 Introduction: Classical vs. Quantum Modelling 23
1.2 Classical Terms: Weak Screening in 1D Systems 25
1.3 Quantum Terms. I. Quantum Capacitance 31
1.4 Quantum Terms. II. Spontaneous Symmetry Breaking 38
1.5 Quantum Terms. III. Band Structure Engineering 45
1.6 Novel Device Concepts: Metallic Field – E . ect Transistor (METFET) 49
References 57
2 Symmetry Based Fundamentals of Carbon Nanotubes 60
2.1 Introduction 60
2.2 Con.guration and Symmetry 61
2.3 Symmetry Based Band Calculations 68
2.4 Optical Absorption 79
2.5 Phonons 87
2.6 Symmetry Breaks Friction: Super-Slippery Walls 99
References 104
3 Elastic Continuum Models of Phonons in Carbon Nanotubes 108
3.1 Introduction 108
3.2 Acoustic Modes in Single Wall Nanotubes 109
3.3 Optical Modes in Multi-wall Nanotubes 121
3.4 Quantized Vibrational Modes in Hollow Spheres 127
3.5 Conclusions 128
References 128
Part II Synthesis and Characterization 130
4 Direct Growth of Single Walled Carbon Nanotubes on Flat Substrates for Nanoscale Electronic Applications 131
4.1 Introduction 131
4.2 Diameter Control 132
4.3 Orientation Control 136
4.4 Growth of Superlong and Well-Aligned SWNTs on a Flat Surface by the Fast- Heating Process 137
4.5 Growth Mechanism 140
4.6 Advantages of Long and Oriented Nanotubes for Device Applications 147
4.7 Summary 147
References 148
5 Nano-Peapods Encapsulating Fullerenes 151
5.1 Introduction 151
5.2 High-Yield Synthesis of Nano-Peapods 152
5.3 Packing Alignment of the Fullerenes Inside SWNTs 155
5.4 Electronic Structures of Nano-Peapods 157
5.5 Transport Properties of Nano-Peapods 160
5.6 Nano-Peapod as a Sample Cell at Nanometer Scale 162
5.7 Peapod as a Nano-Reactor 163
5.8 Conclusions 166
References 166
6 The Selective Chemistry of Single Walled Carbon Nanotubes 169
6.1 Introduction: Advances in Carbon Nanotube Characterization 169
6.2 Selective Covalent Chemistry of Single- Walled Carbon Nanotubes 171
6.3 Selective Non-covalent Chemistry: Charge Transfer 182
6.4 Selective Non-covalent Chemistry: Solvatochromism 188
References 195
Part III Optical Spectroscopy 199
7 Fluorescence Spectroscopy of Single- Walled Carbon Nanotubes 200
7.1 Introduction 200
7.2 Observation of Photoluminescence 202
7.3 Deciphering the (n, m) Spectral Assignment 203
7.4 Implications of the Spectral Assignment 204
7.5 Transition Line Shapes and Single- Nanotube Optical Spectroscopy 209
7.6 Influence of Sample Preparation on Optical Spectra 211
7.7 Spectro.uorimetric Sample Analysis 212
7.8 Detection, Imaging, and Electroluminescence 215
7.9 Conclusions 217
References 217
8 The Raman Response of Double Wall Carbon Nanotubes 220
8.1 Introduction 220
8.2 Experimental 222
8.3 Results and Discussion 223
References 239
Part IV Transport and Electromechanical Applications 242
9 Carbon Nanotube Electronics and Optoelectronics 243
9.1 Introduction 243
9.2 Electronic Structure and Electrical Properties of Carbon Nanotubes 244
9.3 Potential and Realized Advantages of Carbon Nanotubes in Electronics Applications 246
9.4 Fabrication and Performance of Carbon Nanotube Field- E . ect Transistors 247
9.5 Carbon Nanotube Transistor Operation in Terms of a Schottky Barrier Model 251
9.6 The Role of Nanotube Diameter and Gate Oxide Thickness 253
9.7 Environmental In.uences on the Performance of CNT- FETs 255
9.8 Scaling of CNT-FETs 257
9.9 Prototype Carbon Nanotube Circuits 258
9.10 Optoelectronic Properties of Carbon Nanotubes 260
9.11 Summary 264
References 265
10 Carbon Nanotube–Biomolecule Interactions: Applications in Carbon Nanotube Separation and Biosensing 268
10.1 Introduction 268
10.2 DNA-Assisted Dispersion and Separation of Carbon Nanotubes 269
10.3 Separation of Carbon Nanotubes Dispersed by Non- ionic Surfactant 273
10.4 Structure and Electrostatics of the DNA/ CNT Hybrid Material 277
10.5 E.ects of Protein Adsorption on the Electronic Properties of Single Walled Carbon Nanotubes 282
References 285
11 Electrical and Mechanical Properties of Nanotubes Determined Using In- situ TEM Probes 287
11.1 Introduction 287
11.2 Studies of Carbon Nanotubes 292
11.3 Studies of Boron Nitride Nanotubes 313
11.4 Electron Field Emission from BN Nanotubes 314
11.5 Electrical Breakdown and Conduction of BN Nanotubes 316
References 317
12 Nanomanipulator Measurements of the Mechanics of Nanostructures and Nanocomposites 321
12.1 Introduction 321
12.2 Nanomanipulators 323
12.3 Nanomanipulator-Based Mechanics Measurements 332
12.4 Summary and Future Directions 347
References 349
Color Plates 352
Index 358

1 From Quantum Models to Novel Effects to New Applications: Theory of Nanotube Devices by S.V. Rotkin (p. 3-4)

Classical and quantum effects in the physics of nanotube devices are presented. In particular, weak screening in one–dimensional systems is shown to essentially modify textbook theory of field–effect devices and lead to an interesting dependence of the device characteristics on geometrical factors.

The capacitance of a nanoscale device has two main components: a classical geometric capacitance and a quantum term. The latter is related to a finite density of states of the nanosystem. Derivation of this density of states in the presence of external perturbations is a difficult task. We present some examples of the modification of the nanotube bandstructure by external perturbations.

Electric fields can be used for band gap engineering in nanotubes, which may be translated into the device function. The concept of the Metallic Field–Effect Transistor is proposed. This device shows, at least theoretically, metallic conductance in the ON state and insulating behavior in the OFF state, which may be important for applications.

1.1 Introduction: Classical vs. Quantum Modelling

One of the expectations of nanotechnology, an area foreseen by Dr. Richard P. Feynman in 1959 [1], is that we may be able to access quantum properties of materials, which may ultimately lead to new applications and new device operations, which are not possible at the macroscale. To enable this new technology a theory that can make both qualitative and quantitative predictions is needed, whether it be a classical or quantum theory or a combination of both. In this chapter we give a few examples and present the quantum vs. the classical approach using recent results from our modelling of nanotube based devices.

Carbon nanotubes (NTs), discovered in 1991 [2], nowadays represent a new class of electronic materials. The electronic properties of NTs depend on their symmetry [3]. This is not unusual but for a single–wall nanotube (SWNT) there are just a couple of geometrical parameters: a curvature radius, R, and a helicity angle (the measure of chirality of the SWNT lattice), which solely define transport [4], optical [5] and even, to some extent, chemical [6,7] properties of a SWNT.

Knowledge of these two parameters will allow us to divide all possible NTs into several distinct classes. Two thirds of SWNTs have a forbidden band gap, which makes them semiconductors. The band gaps of the semiconductor SWNTs are in the optical region (near–IR/visible), depending on the value of R. The experimental fact that, over a wide range of R, the energy gap is proportional to the curvature, 1/R [5], is a clear manifestation of a simple quantum effect of a space quantization of an electron. When winding around the tube circumference, the electron acquires a phase. After making a full turn the phase has to be 2π, which results in a so–called quantization condition.

The quantization energy sets the separation between the conduction and valence bands, and therefore the optical gap. In a similar way, as the atomic size (atomic number) of an element in the Periodic Table solely defines the properties of the substance, the curvature radius and the helicity angle of a SWNT define its electronic material properties. One third of SWNTs are either metals or narrow gap semiconductors (often called “quasi–metals” in NT literature). The difference between the gap size in the last two SWNT classes appears in the second order of the curvature, 1/R2. The gap in the quasi–metallic SWNT scales as γ/R2, where γ  2.7 eV is the hopping integral which gives the NT energy scale. In the same second order of the curvature, 1/R2, the first SWNT class (semiconductors) splits into two sub–classes by their chirality. All this constitutes a specific “Periodic Table” of nanotubes.

The other important property of nanotubes relates to their third dimension: we have already considered the radius and chirality of the tube but not the length. Recent success in NT synthesis (see also [8]) allowed experimental study of NTs with R ∼ 1 nm and lengths of about several hundreds to thousands of microns, which implies an aspect ratio of 1:100,000 and greater. Certainly, this object must show physics similar to the physics of a one– dimensional (1D) wire, for example, a weak screening. Below we demonstrate that the weak 1D screening properties of NTs have important consequences for electronic devices.