Low-dimensional systems: quantum size effects and electronic properties of semiconductor microcrystallites (zero-dimensional systems) and some quasi-two-dimensional systems

Abstract

This review is concerned with quantum confinement effects in low-dimensional semiconductor systems. The emphasis is on the optical properties, including luminescence, of nanometre-sized microcrystallites, also referred to as zerodimensional systems. There is some discussion on certain of the two-dimensional systems, such as thin films and layer structures. The increase in energy of excitation peaks (blue shift) as the radius R of a microcrystallite is reduced is treated theoretically, and experimental data when they are available are used to assess the reliability of the different models that have been used. These experiments normally make use of microcrystallites dispersed in a large-bandgap matrix such as glass, rocksalt, polymers, zeolites or liquids. Exciton binding energies E _b are larger than for bulk semiconductors, and oscillator strengths are higher for the microcrystallites.

The regimes of direct interest are as follows. Firstly there is the so-called weak-confinement regime where R is greater than the bulk exciton Bohr radius a _B. Experimentally, semiconductors such as CuCl with a _B ≈ 7 Å, are suitable for study in this case. Secondly there is the moderate-confinement regime, where R ≈ a _B, and a _h < R < a _h, a _h and a _e being the hole and electron Bohr radii respectively. Finally there is the strong-confinement regime, with R < a _B, and R < a _h, a _e. For this case we are concerned with a ladder of discrete energy levels, as in molecular systems, rather than energy bands. The electrons and holes are treated as independent particles, and for excited states we refer to electron-hole pairs rather than excitons. Suitable materials for investigation in this regime are the II–VI semiconductors, and also GaAs and Ge, for which a _B is relatively large.

Although a number of different theoretical models have been used, none can be described as completely first-principles calculations, and there is room for improvement on this aspect. However, useful expressions have been developed by Brus and by Lippens and Lannoo, giving the energy of excited states as a function of R, in terms of the bulk energy gap, kinetic energy, Coulomb energy and correlation energy.

Other phenomena discussed are firstly biexciton formation by the use of high intensity laser beams and secondly nonlinear optical effects. Strong nonlinearities and short decay times for excited states have been predicted, and the models developed cover both the resonant and the non-resonant cases. The possibility of using microcrystallites embedded at reasonable concentrations in a glass matrix in the field of optical communications and optical switching is also considered.