Electronic Quantum Size Effects

Confined electronic systems are quantum systems in which carriers, either electron or holes, are free to move only in a restricted number of dimensions. In the confined dimension, the sizes of the structural elements are of the order of a few de Broglie wavelengths of the carriers or less. Depending on their dimensionality, these structures can be quantum dots (0-D), quantum wires (1-D), or quantum wells (2-D). Quantum wells are typically produced by the alternate epitaxial growth of two or more different semiconductors. Quantum wires are less commonly encountered, since their fabrication procedures are much more complicated (Sect. 5.3.4). 

One of the most dramatic effects, called the quantum size effect, consists in a redistribution of the energy spectrum of the system, the density of states becoming discrete along the confinement direction. In the most simple particle in a box model of a quantum well, the energies of the corresponding eigenstates are 

The importance of the quantum size effect is mainly determined by the energy differences E +i — En-Quantum size effects become observable when this separation exceeds the thermal energy of the carriers, so that adjacent subbands are differently populated. Since the energy difference En+i — En increases with N, it could be anticipated that quantization effects would 

The existence of discrete electronic states of electrons confined in a small metal cluster has been observed to influence the thermodynamic stability of the system, in particular during the production of sodium clusters in supersonic beams composed of the metal vapor and an inert gas. The statistics of the relative abundances of different particle sizes reveal the existence of magic numbers for the number of atoms in the cluster, A = 8, 20,40,58, 92. [3.9]. This has been interpreted in terms of the existence of degenerate energy levels in a spherical well with infinite-potential walls. Particularly stable structures are obtained when the number of valence electrons is such that it leads to a closed-shell electronic structure, i. e. a structure with a completely filled energy level and an empty up- 

A very general effect of quantum confinement in semiconductors is a widening of their optical band gap. For the model system of an infinite-barrier 2-D quantum well, (3.1) shows that the lowest energy N = 1) of a con- 

---

Rossetti R, Nakahara S and Brus L E 1983 Quantum size effects In the redox potentials, resonance Raman spectra and electronic spectra of CdS crystallites In aqueous solution J. Chem. Phys. 79 1086... 

Quantum efficiencies Quantum efficiency Quantum electronics Quantum fluids Quantum mechanics Quantum size effect Quantumwell... 

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. 

Composites containing nanometer-sized metal particles of a controllable and uniform size in an insulating ceramic matrix are very interesting materials for use as heterogeneous catalysts and for magnetic and electronic applications. They show quantum size effects, particularly the size-induced metal-insulator transition (SIMIT) [1],... 

Model calculations for the Cs suboxides in comparison with elemental Cs have shown that the decrease in the work function that corresponds to an increase in the Fermi level with respect to the vacuum level can be explained semi-quantitatively with the assumption of a void metal [65], The Coulomb repulsion of the conduction electrons by the cluster centers results in an electronic confinement and a raising of the Fermi energy due to a quantum size effect. 

As the radius of a semiconductor crystallite approaches the exciton-Bohr-radius its electronic properties begin to change, whereupon quantum size effects can be expected. The Bohr radius ub of an exciton is given by... 

Kayanuma Y (1988) Quantum size effects of interacting electrons and holes in semiconductor microciystals with spherical shape. Phys Rev B 38 9797-9805... 

---