Next: Bibliography
Up: Progetto
Strategico Previous: Wigner function approach to
In the past few years the physics of quantum dots and their mathematical modeling have been receiving a great deal of attention. The semiconductor technology is expected to produce nanometer-scale transistor, based on quantum dots. A quantum dot is 3D potential well whose size (in any direction) is comparable with the De Broglie wavelength of electrons, so that quantum effects are dominant.
New techniques are available which allow to produce regular arrays of InAs quantum dots on a GaAs substrate (see Appl. Phys. Letters, vol. 71, pag. 3254 (1997) and vol. 73, pag. 505 (1998)). The final aim is to build a transistor device where the current flows by a dot-to-dot tunneling of electrons.
Since ``few'' electrons are involved in such process, a similar device represents an intermediate step between the usual ``electron gas'' transistor and the SET (Single Electron Transistor). The number of electrons involved is too small for a (quantum) Boltzmann-like approach but too large for a full Schrödinger treatment. For this reason it is of primary importance to construct a mathematical model which may give a sufficiently accurate description keeping at the same time a certain level of simplicity.
By now, the single quantum dot has been deeply investigated and also systems of two coupled quantum dots have been studied [6]. Our research effort tries, on one hand, to extend these existing results to the case of many coupled dots and, on the other hand, to develop ad-hoc techniques, such as second quantization (Hubbard-like models), cellular automata and Wigner-like approaches.
Next: Bibliography
Up: Progetto
Strategico Previous: Wigner function approach to