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**Contents:**

This course will discuss some of the key nano-scale electronic phenomena and both approaches from classical physics and quantum physics will be used. Relevant topics are e. The student shall, with relatively simple physical models applied to recent experimental results, learn how basic physics can be used to describe and understand the behavior of electrons in nano-scale materials.

The course will hopefully motivate for further theoretical and experimental studies of electron transport in nano-scale materials. The student should know key effects and phenomena within electron transport in nano-scale materials. The student should learn how to analyze effects and phenomena within nanophysics by applying basic classical physics and quantum mechanics, standard mathematical methods, and simple numerical computations.

The student will learn to find, read, and convey the contents of literature near the research front within the field of nanophysics. Lectures and calculation exercises. Compulsory activities to be agreed upon, dependent on the number of students. Exam date will be agreed upon during the course.

This is done in the derivation of the equivalent circuit model for resonant tunneling devices which incorporates the quantum inductance. In this review, emphasis is given to major developments in quantum transport, computational nanoelectronics, new device concepts, and novel transport physical phenomena found in small structures, with potential device and IC applications and deemed most likely to have a significant impact on the future developments of nanoelectronics.

We use cookies to help provide and enhance our service and tailor content and ads. By continuing you agree to the use of cookies. Both materials have important applications as nanoscale building blocks. Another amazing material in this class, invented by Andre Geim's group in Manchester, is graphene the parent structure of normal graphite , made from a sheet of interconnected carbon atoms with a honeycomb structure. It is a single layered material with very peculiar electronic properties due to its zero energy gaps at special points in the Brillouin zone.

It is now a hot topic of research both in theory and experiment because of its very special and novel electronic properties. Scientists actively working on the nanoscale have already created a multitude of nanoscale components and devices. The never-ending list includes molecular transistors, quantum dots, quantum wires, nanodiodes, nanosensors and biomolecular devices. Many more applications can be found in the ubiquitous Wikipedia entry for Nano-technology http: While 'nano' means precisely small, 'meso' is a broader term, being intermediate between the microscopic molecular and macroscopic bulk scales.

In practice, the 'mesoscopic' regime partly overlaps the description of 'nanoscopic'. In mesoscopic physics the concept of 'quantum coherence' is widely used. To practitioners in this field, a mesoscopic system inevitably means one that sustains phase-coherent transport.

Within a single-particle picture of the situation, a one-electron wave function remains coherent across the entire system of interest. It is only in the presence of elastic energy-conserving scattering that coherence of the wave function's phase can be retained. Inelastic scattering is a process arising out of energy nonconserving collisions that involve, not the scattering of electrons off static and passive objects, but rather collisions between it and other active, dynamical players in the transport process.

Let us recall the various length scales that regulate the fate of a charge carrier:.

Additionally, Thouless length is defined as. This is the characteristic path length through which an electron wave propagates diffusively analogous to a classical random walk before losing its phase coherence. More about coherence later. That is how a normal conductive material exhibits resistive dissipation.

In a statistical mechanical sense there are some generic and universal features observed for the properties of mesosystems. We return to these questions below. On the other hand, nanosystems are often non-generic, with the rich variety of their chemical characteristics playing a crucial role. Their properties are highly sample-specific and their interaction with the environment varies in a non-universal way. Typically, their experimentally observed properties inhabit the grey area between two distinct aspects: They must work together to obtain meaningful results when phenomena can occur at all length scales from short to long, over energy scales from meV to tens of eV, and involving properties ranging from the generic to quite specific.

Many specialists are already working in the respective areas and perforce learning to speak one another's language. Below we examine just a few of the ingredients that are needed for a true nanoscience. The localized electronic states become progressively delocalized upon the increasing overlap of wave functions as the system size increases towards the bulk limit.

Some physical properties, notably electrical conductivity, appear only as a consequence of spatial extendedness on the part of the electron wave function, thereby manifesting its quantum mechanical nature. It provides a unified view of the performance of atomic-scale objects, including electrons, photons and other elementary particles and excitations. Energy levels with increase of size.

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In large nanoparticles the energy levels become dense to form quasi-continuum bands. When a system size is at the atomic scale, it is only quantum mechanics that can account for the observed physical properties. In the jargon of the field, 'quantum confinement' means that the de Broglie wavelength of the particles is comparable to the size of the system that contains them. Small size implies strong quantum confinement effects. Bulk extended matter, when sufficiently curtailed in one of its dimensions, for example in the z -direction, will behave as a quasi-two-dimensional system in the complementary x — y -plane.

The price to be one paid for this is to lose the long-range extendedness of the wave function in the z -direction; the energy of motion along that axis becomes quantized as the wave function is confined. Repeating the restriction in a second direction, say the y -direction, will make the system quasi-one-dimensional in the remaining x -direction; now the wave function is deliberately forced to occupy a small region within the y — z -plane. One last restriction along the x -axis of motion would produce a quasi-zero-dimensional system, where all extendedness of the wave function has been lost, in every dimension.

The entire electronic system is localized in a relatively tiny volume of x , y and z. We have made, then, an 'artificial atom' or a quantum dot. Matter in spatial dimensions from 3 to 0 and their corresponding density of states.

NanoScience and Technology The first comprehensive monograph covering the complete spectrum of mesoscopic physics in electronic nanodevices; It will. Mesoscopic Physics and Electronics (NanoScience and Technology) [Tsuneya Ando, Yasuhiko Arakawa, Kazuhito Furuya, Susumu Komiyama, Hisao.

Zero dimension is called a quantum dot, one dimension a quantum wire and two dimensions is known as a 2D electron gas. From this brief discussion we learn that the electronic, optical and mechanical elastic properties of materials are radically changed by both size and shape. Well-established technical achievements, including zero-dimensional quantum dots, have been attained through ingenious size manipulation—and for that the quantum-confinement effect is crucial.

It would be instructive to follow how the theory of quantum confinement tracks the behaviour of an exciton a jointly bound electron and hole pair as it crosses over to an atomic-like orbital as its host space is progressively diminished. A rather good approximation of an exciton's behaviour is the 3D model of a particle in a shrinking box. A systematic solution to this problem provides the mathematical connection between the evolution of energy states and the dimensionality of the space within which the wave function exists. It is obvious in any case that decreasing the volume, or the dimensionality, of the available space increases the energy of the states.

Using the above wave functions and energies one can calculate carrier density and the density of the states the availability of quantum states are those solutions allowed within the system. This qualitatively different part of the quantum picture is crucial to understanding the dynamics of electrons acting under an externally applied field; a problem that governs both the characterization of nanodevices and their eventual practical uses. Here we remark that if an electrically active system's length is reduced to the nanoscale, there will be considerable changes in its properties.

At the bulk phase, the device interfaces are expected to control some of the macroscopically observed properties for instance, they affect access resistance. But at the nanoscale, a system's interfaces with the 'rest of the universe' have more spectacular effects. What is the role of a surface? A surface is said to be the first frontier or line of defence for any interaction with the outside world. In general a system always minimizes its free energy. Unless it is truly isolated thermodynamically, it must do so in the presence of its mechanical and electromagnetic coupling to the world outside its boundaries.

So the question is: The smaller the size of the system, the larger the ratio of its surface area S to volume V is. A high ratio implies a strong thermodynamic 'driving force' that speeds up many of the processes that minimize thermodynamic free energy. Chemically, the smaller the size of a material sample, the faster its reactions at a relatively large S.

A porous material's chemical reactivity e. For the same reason as a high S: V ratio, nano- or mesomaterials have a higher chemical reactivity compared to the bulk. For biological systems, surface-to-volume ratios are more significant still. The surface-to-volume ratio for a 3D cube can be readily obtained. The fraction of boundary atoms is in every way significant. Even this most simple size argument demonstrates the potential importance of surface-mediated effects over bulk effects as the system size is reduced. Thus, the smaller the system, the more its surfaces must dominate its actual properties.

Researchers in the US recently made a surprisingly novel chemical structure that has the largest internal surface area ever observed in an ordered material. With a decrease in size, the surface area and surface energy increase, and thereby the melting point of a sufficiently small sample decreases. It is a very similar story for nanoelectronic devices: The latter's nature can substantially modify, and indeed often dominate, observed transport behaviour. As we indicated earlier atoms in nanostructures have a higher average energy than atoms in larger structures, because most of them are surface atoms and the uneven bonding generates new tensional forces not otherwise experienced at equilibrium in the deep bulk.

Consequently, the chemical activity of a material can be exponentially improved as the material is reduced in size at the nanoscale. The properties of nanosystems are significantly affected by minor changes in size, shape or surface states of their particular structures. In summary, at the nanoscale, properties become strongly size-dependent. Here are some examples of various properties related to some phenomena sensitive to size: Obviously these new qualitative and quantitative properties herald entirely new applications which, being out of the reach of our earlier science of bulk materials, often lack any obvious technological precedents.

They represent a truly unexplored domain. Already, for a long time, we have been studying the physics, chemistry and biology of atoms, molecules, clusters and other collective entities; what is so special about so-called nano- or mesoscience? Viewed from the right perspective one would find that the objects mentioned above are never encountered in an isolated state— in vacuo , so to speak.

Rather, we find them to be always coupled to some active environment. This embedding in the environment also known as the 'bath' introduces the idea of dissipation friction whereby the system's energy is transferred irreversibly to the bath. As first analysed by Einstein in his third famous paper from , it is the evident stability of an embedded system, together with the ubiquitous presence of energy dissipation, which implies that the system is subject to fluctuating microscopic forces.

The counterbalancing of the twin effects of fluctuation and dissipation induces the system to relax settle down to thermal equilibrium, at a characteristic energy temperature set by the bath. In quantum dynamics there is yet another feature beyond those two dynamical drivers: Coherence, by its nature, introduces a very high level of orderly correlations.

The rate of spatial decay in a particle's quantum-state correlations is characterized by the coherence length.

This phenomenon is known as quantized ballistic conductance. Recommended previous knowledge Basic knowledge of physics, including quantum mechanics and solid state physics. For biological systems, surface-to-volume ratios are more significant still. A porous material's chemical reactivity e. In mesoscopic physics the concept of 'quantum coherence' is widely used. V ratio, nano- or mesomaterials have a higher chemical reactivity compared to the bulk.

As mentioned earlier, in mesosystems, the coherence length is much larger than the inter-particle separation but still smaller than the system size. However, once a system's inevitable coupling to the environment is taken into account, the correlations are degraded; an effect known, logically enough, as 'decoherence' or 'dephasing'. It is precisely this interaction of the system with the enveloping bath that makes nanoscience non-trivial from a fundamental point of view. In other words, it is the essential quantum nature of nanoscopic matter intimately interacting with its much bigger, macroscopic surroundings that defines its 'nanoscopic' aspect in the first place.

We make this point explicit in the following sections.

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Let us first try to conceive of the nano-object as being strictly closed, in contrast with genuine matter, which always dwells in and so must interact with a large open environment. In the former scenario the system can be said, almost trivially, to be in its own thermodynamic equilibrium. We have both phenomenological and microscopic methods to study that idealized state in a self-contained and satisfactory way.

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Generally, for a molecular system, the energy levels are discrete: For a nanosystem, the energy levels are still in principle discrete, but those levels are now numerous and spaced closely together in quasi-continuous energy bands. Gaps remain between such bands, which may either decrease or increase; in any case we can calculate all this using standard electronic structure techniques. In the bulk limit the energy bands become continuous spectra, while finite gaps separate the distinct bands.