For the non degenerated case, that is, for the FERMI level several below , , MAXWELL-BOLTZMANN statistics can be assumed

which further allows to assume

Using the approximations (2.212) and (2.213) and the analog approximations for holes, equations (2.209) and (2.210) can be written as

where and are the lifetimes for electrons and holes, respectively. The characteristic parameters describing the interaction of carriers and trap centers are the capture cross sections and . If they are known the rate constants (and thus also the lifetimes) can be expressed as

(2.216) |

where and are the thermal velocities of electrons and holes, respectively.

Using the following expressions for the electron and hole concentrations

(2.217) |

and the handy abbreviations and for the electron and hole concentrations when the FERMI level is equal to the trap level

(2.218) | ||

(2.219) |

eqns. (2.214) and (2.215) can be written as

(2.220) | ||

(2.221) |

Making use of the steady state condition eqn. (2.211) the following expression for is found

Inserting eqn. (2.222) either in eqn. (2.214) or eqn. (2.215) yields the well known SHOCKLEY-READ-HALL net recombination rate

(2.223) |