In Chapter 2, the reduction of the extent of a solid in one or more dimensions was shown to lead to a dramatic alteration of the overall behavior of the solids. Generally, the physical properties of any given material can be characterized by some critical length, e.g., thermal diffusion length and attenuation distance. What makes nanoparticles very interesting and endows them with their remarkable properties is that their dimensions are smaller than a relevant critical length. Accordingly, the electron states of nanostructures are quantized, leading to new and usually striking electrical, thermal, magnetic, optical, and mechanical properties at the nanoscale. Accordingly, nanostructures are of both basic and practical interest since their physico-chemical properties can be tailored by controlling their size and shape at the nanoscale, leading to improved and/or novel applications.

The energy spectrum (i.e., the ensemble of discrete eigenenergies) of a quantum well, quantum wire, or quantum dot can be engineered by controlling (i) the size and shape of the confinement region and (ii) the strength of the confinement potential. The resulting control over the physico-chemical properties of the nanostructures is limited only by the accuracy of the experimental techniques used for the fabrication of the low-dimensional structures (Chapter 4). The situation is not unlike that of quantum phenomena, many of which were described at the beginning of the 20th century but could not be demonstrated until the 1960s to 1970s when appropriate nanofabrication techniques were developed.

Not only is fabrication at the nanoscale limited by the available techniques, but other practically unavoidable factors such as imperfections-known to influence the properties of any material-may have very significant impacts on the properties of nanomaterials. As such, size dispersion, shape dispersion, defects, residual stresses, impurities, etc., are of great importance for devices of reduced dimensionality. These factors may, in many instances, create a gap between expectation and realization.

As in Chapter 2, the reader who is not interested in the details on how the electrical, thermal, magnetic, optical, and mechanical properties change at the nanoscale may prefer to skip to Section 3.7, wherein the most significant propertiesare summarized.