Zero-Dimensional Systems Quantum Dots

When charge carriers and excitations are confined in all three dimensions the system is called a QD. The division is somewhat arbitrary since, for instance, clusters composed of very few atoms are not necessarily considered as QDs. Although clusters are smaller than the De Broghe wavelength, their properties depend critically on their exact number of atoms. Large clusters have a well-defined lattice and their properties no longer depend critically on their exact number of atoms. With the term QDs, reference will be made to such systems [49, 50]. 

In a QD, the movement of electrons is confined in all three dimensions, and there are only discrete (fex, fey, fez)-states in the fe-space. Each individual state in the fe-space can be represented by a point, the final consequence being that only discrete energy 

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As far as a zero-dimensional system (quantum dot) is concerned, the density of states can be represented by N5( — ) at each of the quantum states. The coefficient N contains the spin degeneracy factor, any accidental degeneracy of the bound state involved, and the number of quantum dots per unit volume [35]. See Figure 3.3 for a plot of the density of states in 3D, 2D, ID, and OD systems. 

Even though the expressions nanomaterials or nanocomposites are recent (and very successful), these industrial materials have existed for at least a century and apparently always existed in nature (in minerals and vegetables). These small particles range in size from a few to several tens of nanometres and are called quasi zero-dimensional mesoscopic systems, quantum dots, quantized or Q particles, etc According to Jordan et al. nano-sized inclusions are defined as those that have at least one dimension in the range 1 100 mn. In materials research, the development of polymer nanocomposites is rapidly emerging as a multidisciplinary research activity whose results could broaden the applications of polymers to the great benefit of many different industries. 

An interesting type of quantum phase transition are boundary transitions where only the degrees of freedom of a subsystem become critical while the bulk remains imcritical. The simplest case is the so-called impurity quantum phase transitions where the free energy contribution of the impurity (or, in general, a zero-dimensional subsystem) becomes singular at the quantum critical point. Such transitions occur in anisotropic Kondo systems, quantum dots, and in spin systems coupled to dissipative baths as examples. Impurity quantum phase transitions require the thermodynamic limit in the bulk (bath) system but are completely independent from possible phase transitions of the bath. A recent review of impurity quantum phase transitions can be found in Ref. 42. 

The class of nanomaterials that maybe termed zero-dimensional comprise systems that are confined within up to several hundreds of nanometers in aU three dimensions. Although there exists no clear-cut size threshold at which a system switches from a zero-dimensional system to bulk, there is a rather weU-defined class of systems that fit the above definition with unique and intriguing properties. The most commonly studied zero-dimensional systems are quantum dots, nanoparticles (or clusters), and cage-like structures. In this section, we shall begin with an overview of methods used to study such materials. 

Matrix-stabilized (glass, NaCl) CuCl nanocrystals is a typical zero-dimensional material, which constitutes a quantum dot system in which excitons are weakly confined [4]. Small angle X-ray scattering study has established that the resultant... 

Nanoclusters cannot be considered as infinite arrays of atoms and molecules. They represent a new class of materials with hybrid molecular-solid state properties. There is clear evidence that nanoclusters can exhibit structure and properties quite distinct from those of bulk systems. These clusters might be termed quantum dots (QDs) that is, an electron or exciton can be confined in zero-dimensional space. 

Figure 1 presents the typical geometries of the nanodimensional fillers which are commonly used to modify the elastomeric matrix [5], Nanoparticles possess many shapes and sizes (Fig. 1), but primarily they have three simple geometric forms sphere, cylinder and plate type. Three-dimensional nanofillers (3D) are relatively equiaxed particles, smaller than 100 nm (often below 50 nm [6]), e.g. nano SiOa, Ti02. These nanoparticles are described in the Sects. 2.2-2.4. Sometimes in the literature, the term 3D nanofillers (spherical) is described as a zero-dimensional (OD) system, but actually OD nanofillers are represented by POSS molecules, fullerenes, crystals or quantum dots [6]. What s more, very often the term physical form of these nanoparticles is referred to as agglomerates . The dispersion of particles from agglomerates to nanoparticles seems to be a big challenge to all... 

In principle, the low-dimensional semiconductors are divided into the two-dimensional quantum wells and superlattices, the one-dimensional quantum wires, and the zero-dimensional quantum dots. In the following, we list the most common fabrication methods for each of these systems. 

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