Assume both electron and hole concentrations in a semiconductor are raised by n above their equilibrium values. Define a net minority carrier lifetime t by

Assume both electron and hole concentrations in a semiconductor are raised by δn above their equilibrium values. Define a net minority carrier lifetime t by R = δn/t. give expressions for t in terms of the carrier concentrations ng and nb: the energy of the recombination level, as expressed by ng * and nh *; and the time constants tg and th, in the limits of very small and very large values of δn. Under what doping condition is t independent of δn?