An energy state, Et, in the band gap can behave as a recombination/generation center or as a majority or minority carrier trapping center. This is determined primarily by the charge of this gap state. In n-type semiconductor, for example, a gap state with charge -1 is most likely a recombination center because, once a minority carrier (hole) is captured by this state (the -1 charge is attractive to hole), it is easy to capture an electron (because there are so many of them and the state with charge 0 is not repulsive to electron). However, in n-type semiconductor, a gap state with -2 charge is likely to be a hole trap because, once a minority carrier hole is trapped (-2 charge is attractive to hole), the charge is still -1 which is repulsive to the majority carrier electron and makes it hard to capture a subsequent electron. And therefore, the captured hole will be re-emitted thermally before an electron is captured, which makes it a hole trap.
The capture efficiency of carriers by these gap states (associated with chemical impurities or structural defects) depends on the capture cross section, which is a measure of the probability of the capturing event. The cross section of attractive centers is 1E-12 to 1E-15 cm2; the cross section of neutral centers is 1E-15 to 1E-17 cm2; and the cross section of repulsive centers is ~1E-22 cm2 [ref.1].
In the following applet, the four basic processes (en, cn, ep, and cp) in the Shockley-Read-Hall statistics are introduced, and the recombination/generation and the carrier trapping processes are visualized. I showed the processes only in terms of electrons. In a separate applet, I will show the processes using both electron and hole, indicating the charge state of the gap states also.
ref.1: J.W.Mayer and S.S.Lau, "ELECTRONIC MATERIALS SCIENCE: For Integrated Circuits in Si and GaAs", Macmillan Publishing, New York, 1990.