  A very long lifetime emission with non-single exponential decay
characteristic has been reported for single InAs/GaAs quantum dot (QD) samples,
in which there exists a long-lived metastable state in the wetting layer (WL)
[ACS Photonics 2020,7,3228-3235]. In this article we have proposed a new
three-level model to simulate the emission decay curve. In this model, assuming
that the excitons in metastable state will diffuse and be trapped by QDs, and
then emit fluorescence in QDs, a stretched-like exponential decay formula is
derived as I(t)=At^({\beta}-1)e^(-(rt)^{\beta}), which can well describe the
long lifetime decay curve with an analytical expression of average lifetime
<{\tau}>=1/r{\Gamma}(1/{\beta}+1), where {\Gamma} is the Gamma function.
Furthermore, based on the proposed three-level model, an expression of the
second-order auto-correlation function g^2 (t) which can well fit the measured
g^2 (t) curve is also obtained.
