Wires, quantum

Heath J R and LeGoues F K 1993 A liquid solution synthesis of single crystal germanium quantum wires Chem. Phys. Lett. 208 263... 

Eigure 4.30 is an example of X-ray mapping of an (In,Ga)As quantum wire structure using a TEM/STEM Philips GM20 equipped with a thermally-assisted field-emitter and a Ge EDXS detector (Tracor Northern) [4.124]. The cross-section STEM bright-... 

Band gap engineetring confined hetetrostruciutres. When the thickness of a crystalline film is comparable with the de Broglie wavelength, the conduction and valence bands will break into subbands and as the thickness increases, the Fermi energy of the electrons oscillates. This leads to the so-called quantum size effects, which had been precociously predicted in Russia by Lifshitz and Kosevich (1953). A piece of semiconductor which is very small in one, two or three dimensions - a confined structure - is called a quantum well, quantum wire or quantum dot, respectively, and much fundamental physics research has been devoted to these in the last two decades. However, the world of MSE only became involved when several quantum wells were combined into what is now termed a heterostructure. 

The birth of the field of carbon nanotubes is marked by the publication by lijima of the observation of multi-walled nanotubes with outer diameters as small as 55 A, and inner diameters as small as 23 A, and a nanotube consisting of only two coaxial cylinders [2]. This paper was important in making the connection between carbon fullerenes, which are quantum dots, with carbon nanotubes, which are quantum wires. FurtheiTnore this seminal paper [2] has stimulated extensive theoretical and experimental research for the past five years and has led to the creation of a rapidly developing research field. 

In conclusion, wc have shown the interesting information which one can get from electrical resistivity measurements on SWCNT and MWCNT and the exciting applications which can be derived. MWCNTs behave as an ultimate carbon fibre revealing specific 2D quantum transport features at low temperatures weak localisation and universal conductance fluctuations. SWCNTs behave as pure quantum wires which, if limited in length, reduce to quantum dots. Thus, each type of CNT has its own features which are strongly dependent on the dimensionality of the electronic gas. We have also briefly discussed the very recent experimental results obtained on the thermopower of SWCNT bundles and the effect of intercalation on the electrical resistivity of these systems. 

The schematic model is depicted in Fig. 8. As the bias voltage increases, the number of the molecular orbitals available for conduction also increases (Fig. 8) and it results in the step-wise increase in the current. It was also found that the conductance peak plotted vs. the bias voltage decreases and broadens with increasing temperature to ca. 1 K. This fact supports the idea that transport of carriers from one electrode to another can take place through one molecular orbital delocalising over whole length of the CNT, or at least the distance between two electrodes (140 nm). In other words, individual CNTs work as coherent quantum wires. 

More subtle effects of the dielectric constant and the applied bias can be found in the case of semiconductors and low-dimensionality systems, such as quantum wires and dots. For example, band bending due to the applied electric field can give rise to accumulation and depletion layers that change locally the electrostatic force. This force spectroscopy character has been shown by Gekhtman et al. in the case of Bi wires [38]. 

The Ak values in y- and z-direction are quantized, but not in x-direction, resulting in a parabola with Ak O. The density-of-states within the quantum wire results in hyperbolas for each individual ky- and fc -state. 

S.J. Trans, M.H. Devoret, H. Dai, A. Thess, R.E. Smalley, L.J. Geerligs, and C. Dekker, Individual single-wall carbon nanotubes as quantum wires. Nature 386, 474-476 (1997). 

Tans SJ, Devoret MH, Dai H, Thess A, Smalley RE, Geerligs LJ, DekkerC (1997) Individual single-wall carbon nanotubes as quantum wire. Nature 386 474—477... 

Dekker, C. 1999. Carbon nanotubes as molecular quantum wires. Phys. Today 52 22-28. 

Fig. 1 Schematic drawing to show the concept of system dimensionality (a) bulk semiconductors, 3D (b) thin film, layer structure, quantum well, 2D (c) linear chain structure, quantum wire, ID (d) cluster, colloid, nanocrystal, quantum dot, OD. In the bottom, it is shown the corresponding density of states [A( )] versus energy (E) diagram (for ideal cases).

Nano-structures comments on an example of extreme microstructure In a chapter entitled Materials in Extreme States , Cahn (2001) dedicated several comments to the extreme microstructures and summed up principles and technology of nano-structured materials. Historical remarks were cited starting from the early recognition that working at the nano-scale is truly different from traditional material science. The chemical behaviour and electronic structure change when dimensions are comparable to the length scale of electronic wave functions. Quantum effects do become important at this scale, as predicted by Lifshitz and Kosevich (1953). As for their nomenclature, notice that a piece of semiconductor which is very small in one, two- or three-dimensions, that is a confined structure, is called a quantum well, a quantum wire or a quantum dot, respectively. 

SAXS is sensitive to variations in the electronic density in a material, and so provides information about the shape and size of clusters in micro PS. In contrast to the quantum wire structure proposed in early publications [Cal, Lei], the crystallites in micro PS are found to be almost spherical. There has been some evidence that the dimensions in the growth direction are somewhat smaller than those parallel to the surface [Fr2], The latter result, however, is still controversial because investigations by spectroscopic techniques indicate an opposite elongation [Mi4], A combination of grazing incidence diffraction (GID) and SAXS measurements on various freestanding micro PS films showed crystallite diameters from about 1.5 to 4 nm, depending on formation conditions. A good correlation between size reduction and blue shift of the PL peak position has been observed [Bi3],... 

A very crude model to calculate the increase in bandgap energy is the effective-mass particle-in-a-box approximation. Assuming parabolic bands and infinitely high barriers the lowest conduction band (CB) level of a quantum wire with a square cross-section of side length w is shifted by AEC compared to the value Ec of the bulk crystal [Lei, Ho3] ... 

The methodology used to answer these questions can be classified as either semi-empirical or based on first principles. The confined structure is assumed to be two-dimensional (2D = quantum well), one-dimensional (lD = quantum wire) or zero-dimensional (0D = quantum dot). 

Fluctuations in the thickness of quantum wires can be assumed to be present in a porous network and will drastically reduce the carrier mobility. 

Figure 17.1. (a) Quantum wells, (b) quantum wires, (c) ordered arrays of quantum boxes, (d) random quantum dots, and (e) an aggregate of nanometer-size grains. 

P. Petroff, Direct Growth of Nanometer-Size Quantum Wire Superlattices... 

E. Hanamura, Optical Responses of Quantum Wires/Dots and Microcavities... 

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