Auger recombination plays an important role in lasers operating in the long-wavelength regime (> 1 μm).
Indeed, the Auger recombination time decreases exponentially with the inverse of the band gap energy and with
temperature. A frequently used technique to estimate the Auger coefficient is the turn-on delay experiment, in
which the time delay between the current pulse and the laser light pulse is evaluated. We reviewed the theory
behind this experiment and found a discrepancy of the standard formulae used in the literature. This discrepancy
occurs due to the assumption that the differential recombination time is independent of the carrier density, which
is generally not justified. In particular, for short-wavelength lasers, it is expected that bimolecular recombination
dominates, whereas for long-wavelength lasers, Auger recombination dominates. These two contributions can
lead to additional linear and quadratic dependences of the differential recombination time on the carrier density.
A general formula for the turn-on delay is thus derived, which explicitly includes capture, radiative and Auger
recombination mechanisms. Analytical details for using this formula are given and it is shown how it reduces
when a particular recombination process dominates. Estimations for the different recombination coefficients
are found by fitting experimental data with the formula derived. This procedure is then applied to the case
of long-wavelength vertical-cavity surface-emitting lasers (VCSELs) that incorporate InAlGaAs/InP systems in
their active region.