Theoretical calculation of turn-on delay time of VCSEL and effect of carriers recombination

It is known that the turn-on delay time, tdtd, for semiconductor lasers depends on the functional form of the recombination rate. Previously, an analytic expression for tdtd had been obtained, following simple approximations. In this paper, on the basis of the rate equations for quantum well vertical cavity surface emitting lasers (VCSEL), an explicit analytical expression for the turn-on delay of the VCSEL has also been deduced for the general case. The time evolution of the carrier density within the turn-on period of VCSEL has been derived for the case, where the Auger effect is considered as a term proportional to the cube of the carrier density.