In indirect gap semiconductors, such as silicon and germanium, it was found experimentally
that generation/recombination occurs primarily via trap centers. A theory of this effect has
been established by SHOCKLEY and READ  and HALL
2.3.4 Generation/Recombination Processes
Symbolic band diagram showing the four partial processes involved in indirect
Interaction among the partial systems electrons, holes, and traps is described by four partial
processes (Fig. 2.5)
Here , , , are the respective rate constants. This description assumes
acceptor-like traps which can exist in a neutral or a negatively charged state. Donor-like
traps, which have a neutral and a positively charged state, lead however to exactly the same
expression for the net recombination rate.
- Electron capture. An electron from the conduction band is trapped by an
unoccupied defect which becomes occupied.
- Electron emission. An electron from an occupied trap moves to the conduction
band. The trap becomes unoccupied.
- Hole capture. An electron from an occupied trap moves to the valence band and
neutralizes a hole. The trap becomes unoccupied.
- Hole emission. An electron from the valence band is trapped by a defect, thus
leaving a hole in the valence band and an occupied trap.
The generation- and recombination rates of electrons/holes within an energy interval
are described by the law of mass action which states that the rates
are proportional to the concentration of the involved reactants [43, p.54]
The occupation probability of an energy level is given by the FERMI-DIRAC
with , , and being the respective quasi FERMI levels and the
ground-state degeneracy of the trap [44, p.122] which is assumed to be 1 in
M. Gritsch: Numerical Modeling of Silicon-on-Insulator MOSFETs PDF