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This is the complete lecture note for MME505 Nanoscience and Nanotechnology. You can read it online below, open it in the full viewer, or download the PDF for offline study. It pairs with the course's video lectures, so you can read and watch together.
Course code: MME 505 Course title: Nanoscience and Nanotechnology Course credit load: 2 Units Series 1: Fundamental Concepts in Nanoscience and Nanotechnology, Review of Quantum Mechanics and Nanosystems • Part 1.1: Fundamental Concepts in Nanoscience and Nanotechnology o Sub Part 1.1.1: The Nanoscale and Its Definitions o Sub Part 1.1.2: Surface-to-Volume Ratio and Surface Atoms o Sub Part 1.1.3: Dimensionality of Nanostructures • Part 1.2: Review of Quantum Mechanics o Sub Part 1.2.1: Wave-Particle Duality and the de Broglie Wavelength o Sub Part 1.2.2: The Schrödinger Equation and the Wavefunction o Sub Part 1.2.3: The Particle in a Box • Part 1.3: Quantum Confinement in Nanosystems o Sub Part 1.3.1: Quantum Confinement o Sub Part 1.3.2: Quantum Wells, Wires and Dots o Sub Part 1.3.3: Size-Dependent Band Gap of Nanocrystals • Part 1.4: Electron Transport and Charging in Nanosystems o Sub Part 1.4.1: Quantum Tunnelling o Sub Part 1.4.2: Single-Electron Charging and Coulomb Blockade o Sub Part 1.4.3: Ballistic Transport and the Quantum of Conductance
Introduction Gold is yellow, chemically unreactive and melts at 1064 °C, yet a gold particle a few nanometres across can appear red, act as a catalyst and melt far below that temperature. Nothing has been added to the gold; only its size has changed. This is the puzzle at the heart of nanoscience, and the rest of this course rests on solving it. The aim of this Series is to equip you to explain what nanoscience is, why size changes the behaviour of matter, and how the quantum mechanics of confined electrons governs the properties of nanosystems. We shall commence with fundamental concepts in nanoscience and nanotechnology, including scale, surface effects and dimensionality. Next, we will explore a review of quantum mechanics, from wave-particle duality to the particle in a box. Afterwards, we will turn to quantum confinement in nanosystems, covering wells, wires, dots and the size-dependent band gap. We will conclude with electron transport and charging in nanosystems, including tunnelling, Coulomb blockade and ballistic transport. Series Learning Outcomes Upon completing this Series, you should be able to: • SLO 1.1: define nanoscience and nanotechnology and describe the nanometre scale, • SLO 1.2: explain how the surface-to-volume ratio and the dimensionality of nanostructures distinguish them from bulk matter, • SLO 1.3: explain the wave nature of matter using the de Broglie relation and the Schrödinger equation, • SLO 1.4: calculate the energy levels of a particle in a one-dimensional box, • SLO 1.5: explain quantum confinement in quantum wells, wires and dots, • SLO 1.6: explain the size dependence of the band gap of a semiconductor nanocrystal, • SLO 1.7: explain quantum tunnelling and single-electron charging in nanosystems, and • SLO 1.8: describe ballistic transport and the quantum of conductance. 1.1 Fundamental Concepts in Nanoscience and Nanotechnology 1.1.1 The Nanoscale and Its Definitions
The nanometre is one billionth of a metre, or 10⁻⁹ m, and the nanoscale is usually taken to span about 1 to 100 nm. At this scale, matter is built from small groups of atoms, since a typical atom is a few tenths of a nanometre across. A human hair is about 80 000 nm wide, and a red blood cell is about 7000 nm across, so the nanoscale lies far below anything visible to the eye. Most of the objects of interest here are larger than atoms but smaller than cells. Nanoscience is the study of the structure and properties of matter at the nanoscale, where behaviour often differs from that of bulk material. Nanotechnology is the design, production and use of structures, devices and systems by controlling shape and size at the nanoscale. The physicist Richard Feynman anticipated this field in a 1959 lecture on manipulating matter atom by atom, and the term nanotechnology was introduced by Norio Taniguchi in 1974. Worked example: A gold atom is about 0.288 nm across, so a row of atoms across a 10 nm particle contains about 10/0.288 ≈ 35 atoms. A hair of width 80 000 nm is 80 000/10 = 8000 times wider than this particle. Application: Knowing the nanoscale range helps to identify which materials and devices count as nanoscale, and which are simply small. Fill in the blank: One billionth of a metre is called a __________. 1.1.2 Surface-to-Volume Ratio and Surface Atoms The surface-to-volume ratio is the surface area of an object divided by its volume, and for a sphere of radius r it equals 3/r. It rises sharply as size falls, so a nanoparticle exposes a very large area for its volume. Atoms at the surface have fewer neighbours than atoms inside, so they are less strongly bound and more reactive. In a nanoparticle a large share of the atoms are surface atoms, and this changes its chemical and physical behaviour. The fraction of atoms in a surface layer one atom thick can be estimated as 1 − (1 − 2a/d)³, where a is the atomic diameter and d is the particle diameter. The fraction is negligible in bulk material, but it becomes large as d approaches a few nanometres. Since surface atoms carry extra energy, small particles melt at lower temperatures and react more readily than large ones, and this is the origin of many enhanced properties. Worked example: For gold, a = 0.288 nm. At d = 100 nm, the surface fraction is 1 − (0.99424)³ ≈ 1.7%. At d = 10 nm it is 1 − (0.9424)³ ≈ 16%, and at d = 2 nm it is 1 − (0.712)³ ≈ 64%. Dividing a 1 cm cube into 10 nm cubes raises its surface area from 6 × 10⁻⁴ m² to 600 m², a millionfold increase. Application: The huge surface area of nanoparticles is used in catalysts and sensors, where reactions take place at the surface. Fill in the blank: For a sphere of radius r, the surface-to-volume ratio is given by __________ divided by r.
1.1.3 Dimensionality of Nanostructures Nanostructures are classified by how many of their dimensions lie in the nanoscale range. A zero-dimensional structure, such as a quantum dot, a tiny crystal whose electrons are confined in all directions, has all three dimensions at the nanoscale. A one-dimensional structure, such as a nanowire or nanotube, has two nanoscale dimensions and one long dimension. A two-dimensional structure, such as a thin film, has only one nanoscale dimension. A three-dimensional nanostructured material has no single nanoscale dimension, but it is built from nanoscale units, such as the tiny grains of a nanocrystalline metal. The class matters because it decides how freely electrons and other carriers can move. In a nanowire they move freely along the length only, in a film they move in a plane, and in a dot they cannot move freely at all. The same material can therefore behave very differently in each form. Worked example: A film 5 nm thick and 1 cm × 1 cm in area is two-dimensional, since only its thickness is nanoscale. A nanowire 20 nm in diameter and 10 μm long is one-dimensional, with an aspect ratio of 10 000/20 = 500. Application: Classification by dimensionality tells a designer which quantum effects to expect, and so which material form to use. Fill in the blank: A structure with two dimensions in the nanoscale range and one long dimension, such as a nanowire, is __________-dimensional. Figure 1.1: The nanoscale in relation to familiar objects on a logarithmic scale.
Pilot questions 1.1 1. Define a nanometre and state the usual range of the nanoscale. (Linked to SLO 1.1) 2. Distinguish between nanoscience and nanotechnology. (Linked to SLO 1.1) 3. Why are surface atoms more reactive than atoms in the interior? (Linked to SLO 1.2) 4. Write the surface-to-volume ratio of a sphere of radius r. (Linked to SLO 1.2) 5. What is a quantum dot in terms of dimensionality? (Linked to SLO 1.2) 1.2 Review of Quantum Mechanics 1.2.1 Wave-Particle Duality and the de Broglie Wavelength At small scales, particles such as electrons show wave behaviour, and light shows particle behaviour. Electrons form diffraction patterns when they pass through crystals, which is a wave property, and light knocks electrons out of metals in packets called photons, which is a particle property. This dual behaviour is called wave-particle duality, and it becomes important whenever an object is comparable in size to the wavelength of its particles. The de Broglie wavelength of a particle of momentum p is λ = h/p, where h is Planck's constant, 6.626 × 10⁻³⁴ J s. For a particle of mass m and kinetic energy E, this gives λ = h/(2mE)^(1/2). The heavier or faster the particle, the shorter its wavelength. An electron of low energy has a wavelength of about a nanometre, similar to the size of a nanostructure, whereas a ball has a wavelength far too small to notice. Worked example: For an electron, λ = 1.226/E^(1/2) nm, with E in electronvolts. At E = 1 eV, λ = 1.23 nm, and at E = 10 eV, λ = 1.226/3.162 = 0.388 nm,
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