Zero-dimensional systems

Figure 7. Electronic situation in a zero-dimensional system, (a) Only discrete energy levels are allowed, (b) The density of states is described by discrete energy levels to be occupied by individual electrons. (Reprinted from Ref. [5], 2004, with permission from Wiley-VCH.)...

For zero-dimensional systems, as in the case of Si nanocrystals (Si-NCs) the band-gap increases with decreasing size. Visible luminescence external efficiency in excess of 23% has been obtained in nanostructured Si [1,10,16],... 

In this paper we present a comprehensive first-principles study of the structural, electronic and optical properties of undoped and doped Si nanosystems. The aim is to investigate, in a systematic way, their structural, electronic and stability properties as a function of dimensionality and size, as well as pointing out the main changes induced by the nanostructure excitation. A comparison between the results obtained using different Density Functional Theory based methods will be presented. We will report results concerning two-dimensional, one-dimensional and zero-dimensional systems. In particular the absorption and emission spectra and the effects induced by the creation of an electron-hole pair are calculated and discussed in detail, including many-body effects. 

In a Si zero-dimensional system the strong quantum confinement can increase the optical infrared gap of bulk Si and consequently shift the optical transition energies towards the visible range [65,66]. This is the reason for which silicon nanocrystals (Si-NCs) with a passivated surface are used as the natural trial model for theoretical simulations on Si based light emitting materials, such as porous Si or Si nanocrystals dispersed in a matrix. In this section we present a comprehensive analysis of the structural, electronic and optical properties of Si-NCs as a function of size, symmetry and surface passivation. We will also point out the main changes induced... 

FIG. 4. Excess conductivity vs reduced temperature of KjCw). The slope of this curve has been proposed for a zero-dimensional system. A three-dimensional system exhibits fluctuation conductivity indicated by curve 3D, based on the measured coherence length gl(0)-26 A. Inset The divergence of the conductivity in unrenormalized quantities. The two lines indicate the theoretical prediction for a OD and a 3D system, respectively. The arrow indicates the mean-field transition temperature T,o-... 

Yoffe A. D. (1993), Low-dimensional systems—quantum-size effects and electronic-properties of semiconductor microcrystallites (zero-dimensional systems) and some quasi-2-dimensional systems , Adv. Phys. 42, 173-266. 

The IGTT model and its many elaborations have been widely used in studies of microheterogeneous systems. The model is based on the stochastic distribution of probes and quenchers over the confinements. Before discussing it, however, we approach the problem from the aspect of diffusion-limited reactions and consider how a change from a homogeneous three-dimensional (3-D) solution into effectively 2-D, 1-D, and 0-D systems (with 0-D we refer to a system limited in all three dimensions such as a spherical micelle) will affect the diffusion-controlled deactivation process. The stochastic methods apply only to the zero-dimensional systems we present some of the elaborations of the IGTT model with particular relevance to microemulsion systems and the complications that arise therein. We then review and discuss some of the experimental studies. It appears as if much more could be done with microemulsions, but the standard methods from studies of normal micelles have to be used with utmost care. 

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. 

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. 

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