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Chapter 2:
Low-Dimensional Structures

When one or more of the dimensions of a solid are reduced sufficiently, its physicochemical characteristics notably depart from those of the bulk solid.With reduction in size, novel electrical, mechanical, chemical, magnetic, and optical properties can be introduced. The resulting structure is then called a low-dimensional structure (or system). The confinement of particles, usually electrons or holes, to a lowdimensional structure leads to a dramatic change in their behavior and to the manifestation of size effects that usually fall into the category of quantum-size effects.

Low-dimensional structures show new properties in a way that is different from simply the miniaturization of a particular device. Although the minimum size needed to obtain new properties will vary with many material-dependent factors, the value usually falls in the range of a few nanometers. For this reason, low-dimensional structures are popularly called nanostructures.

Thus, nanostructures have at least one dimension in the range of a few nanometers and exhibit new physico-chemical properties not shown by the corresponding large-scale structures of the same composition (Chapter 3). Nanostructures constitute a bridge between molecules and bulk materials. Suitable control of the properties and responses of nanostructures can lead to new devices and technologies. Accordingly, nanoscience and nanotechnology primarily deal with the synthesis, characterization, exploration, and exploitation of nanostructured materials. Table 2.1 lists common nanostructures and their typical dimensions. In Chapter 6, materials used to fabricate these nanostructures as well as relevant phenomena are presented.

Low-dimensional structures are usually classified according to the number of reduced dimensions they have. More precisely, the dimensionality refers to the number of degrees of freedom in the particle momentum. Accordingly, depending on the dimensionality, the following classification is made:

Three-dimensional (3D) structure or bulk structure: No quantization of the particle motion occurs, i.e., the particle is free.

Two-dimensional (2D) structure or quantum well: Quantization of the particle motion occurs in one direction, while the particle is free to move in the other two directions.

One-dimensional (1D) structure or quantum wire: Quantization occurs in two directions, leading to free movement along only one direction.

Zero-dimensional (0D) structure or quantum dot (sometimes called "quantum box"): Quantization occurs in all three directions.

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