Transient lifetime measurements rely on the decay of carriers over time. Carriers are generated by a very short pulse of light and the decay of the carrier density with time is measured.
Illumination at and minority carrier density. The pulse of light is very short and the carrier density typically follows an exponential decay. Move the mouse over the graph to see that the carrier density decay is a straight line on log scale.
The lifetime is then the

which leads to the final relation between lifetime and excess carrier density


Minority-Carrier Lifetime (no Auger correction) vs. Carrier Density
Transient lifetime measurement