Quantum Confinement and Models of the Luminescence Process

This section gives a brief overview of theoretical investigations dealing with the properties of quantum-confined silicon structures. 

Every atom shows specific, discrete energy levels for electrons. These levels are either empty or occupied by one or two (spin-paired) electrons according to the Pauli exclusion principle. The energy of the levels can be found by solving the Schrodinger equation. Exact solutions, however, can only be obtained for single electron atoms (hydrogenic atoms). 

If many atoms are bound together, for example in a crystal, their atomic orbitals overlap and form energy bands with a high density of states. Different bands may be separated by gaps of forbidden energy for electrons. The calculation of electron levels in the periodic potential of a crystal is a many-electron problem and requires several approximations for a successful solution. 

The minute network structure of microporous silicon is between the two extremes of a single atom and a large crystal. A crystallite of a few hundred silicon atoms is large enough to have a rich electronic band structure but is still small enough to show an increase in the energy of an electron-hole pair (exciton) due to 

The effect of an increase in fundamental bandgap due to size quantization is not specific to silicon, but common to all semiconductors [He2, Br3, Wei]. 

---