Energy level structure quantum dots

Figure 10.9. (a) Schematic structure of a silicon quantum dot crystal and (b) its calculated electronic structure as a function of interparticle distance H. The size of the nanoparticles is L = 6.5 nm. At small H, a splitting of the quantized energy levels of single dots results in the formation of three-dimensional minibands. Reproduced from Ref. 64, Copyright 2001, with permission from the American Institute of Physics. 

The Energy Level Structure of Low-dimensional Multi-electron Quantum Dots... 

In the present contribution the interpretation of the energy-level structure of quasi-one-dimensional quantum dots of two and three electrons is reviewed in detail by examining the polyad structure of the energy levels and the symmetry of the spatial part of the Cl wave functions due to the Pauli principle. The interpretation based on the polyad quantum number is applied to the four electron case and is shown to be applicable to general multi-electron cases. The qualitative differences in the energy-level structure between quasi-one-dimensional and quasi-ta>o-dimensional quantum dots are briefly discussed by referring to differences in the structure of their internal space. 

The STL technique has by now been extensively applied to generate light emission from individual semiconductor and metal quantum dots. These nanoparticles are generally smaller than 100 nm and larger than a few atoms. In the case of semiconductors, quantum confinement causes the energy level structure... 

The fuzzy frontier between the molecular and the nanometric level can be elucidated from an electronic point of view. Molecules and small clusters can be described as systems in which the metal atoms form well-defined bonding and antibonding orbitals. Large clusters or small nanoparticles (quantum dots) with dimensions of a few nanometers are intermediate between the size of molecules and bulk material, presenting discrete energy levels with a small band gap owing to quantum-mechanical rules. Finally, larger particles tend to lose this trend and display a typical band structure similar to that of the bulk material. 

Nano-scale and molecular-scale systems are naturally described by discrete-level models, for example eigenstates of quantum dots, molecular orbitals, or atomic orbitals. But the leads are very large (infinite) and have a continuous energy spectrum. To include the lead effects systematically, it is reasonable to start from the discrete-level representation for the whole system. It can be made by the tight-binding (TB) model, which was proposed to describe quantum systems in which the localized electronic states play an essential role, it is widely used as an alternative to the plane wave description of electrons in solids, and also as a method to calculate the electronic structure of molecules in quantum chemistry. 

---